%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO873^1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:48:31 AM UTC 2026
% Result : Theorem 9.27s 1.88s
% Output : Refutation 9.27s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO873^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n019.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 17:22:48 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.21 Running higher-order theorem proving
% 0.08/0.24 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.72/0.37 % (1104950)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.72/0.37 % (1104960)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1339353277:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.72/0.37 % (1104961)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.72/0.37 % (1104961)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.72/0.37 % (1104955)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=77387990:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.72/0.37 % (1104956)lrs+10_16_si=on:nwc=1.5:random_seed=3314458216:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.72/0.37 % (1104957)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1060491384:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.72/0.37 % (1104959)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2348888813:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.72/0.37 % (1104958)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=2612723439:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.72/0.37 % (1104961)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=1977922159:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.72/0.37 % (1104957)Instruction limit reached!
% 0.72/0.37 % (1104957)------------------------------
% 0.72/0.37 % (1104957)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.72/0.37 % (1104957)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.72/0.37 % (1104957)CaDiCaL version: 2.1.3
% 0.72/0.37 % (1104957)Termination reason: Instruction limit
% 0.72/0.37 % (1104957)Termination phase: shuffling
% 0.72/0.37 % (1104957)Time elapsed: 0.002 s
% 0.72/0.37 % (1104957)Peak memory usage: 10 MB
% 0.72/0.37 % (1104957)Instructions burned: 4 (million)
% 0.72/0.37 % (1104956)Instruction limit reached!
% 0.72/0.37 % (1104956)------------------------------
% 0.72/0.37 % (1104956)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.72/0.37 % (1104956)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.72/0.37 % (1104956)CaDiCaL version: 2.1.3
% 0.72/0.37 % (1104956)Termination reason: Instruction limit
% 0.72/0.37 % (1104956)Termination phase: Property scanning
% 0.72/0.37 % (1104956)Time elapsed: 0.008 s
% 0.72/0.37 % (1104956)Peak memory usage: 10 MB
% 0.72/0.37 % (1104956)Instructions burned: 19 (million)
% 0.72/0.37 % (1104960)Instruction limit reached!
% 0.72/0.37 % (1104960)------------------------------
% 0.72/0.37 % (1104960)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.72/0.37 % (1104960)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.72/0.37 % (1104960)CaDiCaL version: 2.1.3
% 0.72/0.37 % (1104960)Termination reason: Instruction limit
% 0.72/0.37 % (1104960)Termination phase: Function definition elimination
% 0.72/0.37 % (1104960)Time elapsed: 0.017 s
% 0.72/0.37 % (1104960)Peak memory usage: 11 MB
% 0.72/0.37 % (1104960)Instructions burned: 77 (million)
% 0.72/0.37 % (1104959)Instruction limit reached!
% 0.72/0.37 % (1104959)------------------------------
% 0.72/0.37 % (1104959)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.72/0.37 % (1104959)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.72/0.37 % (1104959)CaDiCaL version: 2.1.3
% 0.72/0.37 % (1104959)Termination reason: Instruction limit
% 0.72/0.37 % (1104959)Termination phase: Property scanning
% 0.72/0.37 % (1104959)Time elapsed: 0.010 s
% 0.72/0.37 % (1104959)Peak memory usage: 10 MB
% 0.72/0.37 % (1104959)Instructions burned: 24 (million)
% 0.72/0.37 % (1104971)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.72/0.37 % (1104971)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=332876277:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.72/0.39 % (1104969)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3104313411:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.72/0.39 % (1104971)Instruction limit reached!
% 0.72/0.39 % (1104971)------------------------------
% 0.72/0.39 % (1104971)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.72/0.39 % (1104971)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.72/0.39 % (1104971)CaDiCaL version: 2.1.3
% 0.72/0.39 % (1104971)Termination reason: Instruction limit
% 0.72/0.39 % (1104971)Termination phase: shuffling
% 0.72/0.39 % (1104971)Time elapsed: 0.002 s
% 0.72/0.39 % (1104971)Peak memory usage: 10 MB
% 0.72/0.39 % (1104971)Instructions burned: 8 (million)
% 0.72/0.39 % (1104969)Instruction limit reached!
% 0.72/0.39 % (1104969)------------------------------
% 0.72/0.39 % (1104969)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.72/0.39 % (1104969)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.72/0.39 % (1104969)CaDiCaL version: 2.1.3
% 0.72/0.39 % (1104969)Termination reason: Instruction limit
% 0.72/0.39 % (1104969)Termination phase: shuffling
% 0.72/0.39 % (1104969)Time elapsed: 0.002 s
% 0.72/0.39 % (1104969)Peak memory usage: 10 MB
% 0.72/0.39 % (1104969)Instructions burned: 4 (million)
% 0.72/0.39 % (1104970)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=1225051064:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.72/0.39 % (1104972)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=1627064530:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.72/0.39 % (1104970)Instruction limit reached!
% 0.72/0.39 % (1104970)------------------------------
% 0.72/0.39 % (1104970)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.72/0.39 % (1104970)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.72/0.39 % (1104970)CaDiCaL version: 2.1.3
% 0.72/0.39 % (1104970)Termination reason: Instruction limit
% 0.72/0.39 % (1104970)Termination phase: shuffling
% 0.72/0.39 % (1104970)Time elapsed: 0.003 s
% 0.72/0.39 % (1104970)Peak memory usage: 10 MB
% 0.72/0.39 % (1104970)Instructions burned: 6 (million)
% 0.72/0.39 % (1104975)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.72/0.39 % (1104975)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.72/0.39 % (1104975)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=901153989:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.72/0.39 % (1104955)Instruction limit reached!
% 0.72/0.39 % (1104955)------------------------------
% 0.72/0.39 % (1104955)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.72/0.39 % (1104955)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.72/0.39 % (1104955)CaDiCaL version: 2.1.3
% 0.72/0.39 % (1104955)Termination reason: Instruction limit
% 0.72/0.39 % (1104955)Termination phase: Property scanning
% 0.72/0.39 % (1104955)Time elapsed: 0.036 s
% 0.72/0.39 % (1104955)Peak memory usage: 11 MB
% 0.72/0.39 % (1104955)Instructions burned: 89 (million)
% 0.72/0.39 % (1104972)Instruction limit reached!
% 0.72/0.39 % (1104972)------------------------------
% 0.72/0.39 % (1104972)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.72/0.39 % (1104972)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.72/0.39 % (1104972)CaDiCaL version: 2.1.3
% 0.72/0.39 % (1104972)Termination reason: Instruction limit
% 0.72/0.39 % (1104972)Termination phase: shuffling
% 0.72/0.39 % (1104972)Time elapsed: 0.006 s
% 0.72/0.39 % (1104972)Peak memory usage: 10 MB
% 0.72/0.39 % (1104972)Instructions burned: 14 (million)
% 0.72/0.39 % (1104976)lrs+1002_64_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:sp=occurrence:lma=off:plsqr=32,1:uwa=interpreted_only:random_seed=138647404:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.72/0.39 % (1104975)Instruction limit reached!
% 0.72/0.39 % (1104975)------------------------------
% 0.72/0.39 % (1104975)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.72/0.42 % (1104975)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.72/0.42 % (1104975)CaDiCaL version: 2.1.3
% 0.72/0.42 % (1104975)Termination reason: Instruction limit
% 0.72/0.42 % (1104975)Termination phase: Function definition elimination
% 0.72/0.42 % (1104975)Time elapsed: 0.009 s
% 0.72/0.42 % (1104975)Peak memory usage: 10 MB
% 0.72/0.42 % (1104975)Instructions burned: 43 (million)
% 0.72/0.42 % (1104979)lrs+10_1_si=on:cs=on:random_seed=711507813:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.72/0.42 % (1104984)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=327362333:st=2:i=249:sd=1:rtra=on:ss=axioms_2999 on theBenchmark for (2999ds/249Mi)
% 0.72/0.42 % (1104981)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.72/0.42 % (1104979)Instruction limit reached!
% 0.72/0.42 % (1104979)------------------------------
% 0.72/0.42 % (1104979)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.72/0.43 % (1104979)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.72/0.43 % (1104979)CaDiCaL version: 2.1.3
% 0.72/0.43 % (1104979)Termination reason: Instruction limit
% 0.72/0.43 % (1104979)Termination phase: shuffling
% 0.72/0.43 % (1104979)Time elapsed: 0.005 s
% 0.72/0.43 % (1104979)Peak memory usage: 10 MB
% 0.72/0.43 % (1104979)Instructions burned: 9 (million)
% 0.72/0.43 % (1104982)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=2899564555:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.72/0.43 % (1104981)ott+1002_20_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:sp=unary_frequency:plsqr=1,32:bce=on:uwa=interpreted_only:foolp=on:random_seed=635540610:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.72/0.43 % (1104981)Instruction limit reached!
% 0.72/0.43 % (1104981)------------------------------
% 0.72/0.43 % (1104981)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.72/0.43 % (1104981)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.72/0.43 % (1104981)CaDiCaL version: 2.1.3
% 0.72/0.43 % (1104981)Termination reason: Instruction limit
% 0.72/0.43 % (1104981)Termination phase: shuffling
% 0.72/0.43 % (1104981)Time elapsed: 0.002 s
% 0.72/0.43 % (1104981)Peak memory usage: 10 MB
% 0.72/0.43 % (1104981)Instructions burned: 3 (million)
% 0.72/0.43 % (1104961)Instruction limit reached!
% 0.72/0.43 % (1104961)------------------------------
% 0.72/0.43 % (1104961)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.72/0.43 % (1104961)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.72/0.43 % (1104961)CaDiCaL version: 2.1.3
% 0.72/0.43 % (1104961)Termination reason: Instruction limit
% 0.72/0.43 % (1104961)Termination phase: Saturation
% 0.72/0.43 % (1104961)Time elapsed: 0.073 s
% 0.72/0.43 % (1104961)Peak memory usage: 13 MB
% 0.72/0.43 % (1104961)Instructions burned: 160 (million)
% 0.72/0.43 % (1104982)Instruction limit reached!
% 0.72/0.43 % (1104982)------------------------------
% 0.72/0.43 % (1104982)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.72/0.43 % (1104982)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.72/0.43 % (1104982)CaDiCaL version: 2.1.3
% 0.72/0.43 % (1104982)Termination reason: Instruction limit
% 0.72/0.43 % (1104982)Termination phase: Saturation
% 0.72/0.43 % (1104982)Time elapsed: 0.018 s
% 0.72/0.43 % (1104982)Peak memory usage: 12 MB
% 0.72/0.43 % (1104982)Instructions burned: 39 (million)
% 0.72/0.43 % (1104976)Instruction limit reached!
% 0.72/0.43 % (1104976)------------------------------
% 0.72/0.43 % (1104976)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.72/0.43 % (1104976)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.72/0.43 % (1104976)CaDiCaL version: 2.1.3
% 0.72/0.43 % (1104976)Termination reason: Instruction limit
% 0.72/0.43 % (1104976)Termination phase: Property scanning
% 0.72/0.43 % (1104976)Time elapsed: 0.035 s
% 0.72/0.43 % (1104976)Peak memory usage: 11 MB
% 0.72/0.43 % (1104976)Instructions burned: 88 (million)
% 0.72/0.43 % (1104990)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=3929744462:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2999 on theBenchmark for (2999ds/14Mi)
% 0.72/0.43 % (1104984)Refutation not found, incomplete strategy
% 1.43/0.48 % (1104984)------------------------------
% 1.43/0.48 % (1104984)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.43/0.48 % (1104984)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.43/0.48 % (1104984)CaDiCaL version: 2.1.3
% 1.43/0.48 % (1104984)Termination reason: Refutation not found, incomplete strategy
% 1.43/0.48 % (1104984)Time elapsed: 0.028 s
% 1.43/0.48 % (1104984)Peak memory usage: 13 MB
% 1.43/0.48 % (1104984)Instructions burned: 118 (million)
% 1.43/0.48 % (1104984)------------------------------
% 1.43/0.48 % (1104984)------------------------------
% 1.43/0.48 % (1104987)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=4289656493:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/25Mi)
% 1.43/0.48 % (1104990)Instruction limit reached!
% 1.43/0.48 % (1104990)------------------------------
% 1.43/0.48 % (1104990)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.43/0.48 % (1104990)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.43/0.48 % (1104990)CaDiCaL version: 2.1.3
% 1.43/0.48 % (1104990)Termination reason: Instruction limit
% 1.43/0.48 % (1104990)Termination phase: Property scanning
% 1.43/0.48 % (1104990)Time elapsed: 0.007 s
% 1.43/0.48 % (1104990)Peak memory usage: 10 MB
% 1.43/0.48 % (1104990)Instructions burned: 16 (million)
% 1.43/0.48 % (1104995)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=1312536773:i=26:ep=R:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/26Mi)
% 1.43/0.48 % (1104991)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=506472707:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 1.43/0.48 % (1104987)Instruction limit reached!
% 1.43/0.48 % (1104987)------------------------------
% 1.43/0.48 % (1104987)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.43/0.48 % (1104987)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.43/0.48 % (1104987)CaDiCaL version: 2.1.3
% 1.43/0.48 % (1104987)Termination reason: Instruction limit
% 1.43/0.48 % (1104987)Termination phase: SInE selection
% 1.43/0.48 % (1104987)Time elapsed: 0.011 s
% 1.43/0.48 % (1104987)Peak memory usage: 10 MB
% 1.43/0.48 % (1104987)Instructions burned: 26 (million)
% 1.43/0.48 % (1104992)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=2787347278:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 1.43/0.48 % (1104994)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=3116122800:st=4:i=2:add=off:sd=3:nm=16:fsr=off:rtra=on:ss=axioms:sgt=8:ntd=on_2998 on theBenchmark for (2998ds/2Mi)
% 1.43/0.48 % (1104995)Instruction limit reached!
% 1.43/0.48 % (1104995)------------------------------
% 1.43/0.48 % (1104995)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.43/0.48 % (1104995)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.43/0.48 % (1104995)CaDiCaL version: 2.1.3
% 1.43/0.48 % (1104995)Termination reason: Instruction limit
% 1.43/0.48 % (1104995)Termination phase: Property scanning
% 1.43/0.48 % (1104995)Time elapsed: 0.006 s
% 1.43/0.48 % (1104995)Peak memory usage: 10 MB
% 1.43/0.48 % (1104995)Instructions burned: 28 (million)
% 1.43/0.48 % (1104994)Instruction limit reached!
% 1.43/0.48 % (1104994)------------------------------
% 1.43/0.48 % (1104994)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.43/0.48 % (1104994)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.43/0.48 % (1104994)CaDiCaL version: 2.1.3
% 1.43/0.48 % (1104994)Termination reason: Instruction limit
% 1.43/0.48 % (1104994)Termination phase: shuffling
% 1.43/0.48 % (1104994)Time elapsed: 0.002 s
% 1.43/0.48 % (1104994)Peak memory usage: 10 MB
% 1.43/0.48 % (1104994)Instructions burned: 4 (million)
% 1.43/0.48 % (1104992)Instruction limit reached!
% 1.43/0.48 % (1104992)------------------------------
% 1.43/0.48 % (1104992)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.43/0.48 % (1104992)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.43/0.48 % (1104992)CaDiCaL version: 2.1.3
% 1.43/0.48 % (1104992)Termination reason: Instruction limit
% 1.43/0.48 % (1104992)Termination phase: shuffling
% 1.43/0.48 % (1104992)Time elapsed: 0.006 s
% 1.43/0.48 % (1104992)Peak memory usage: 10 MB
% 1.43/0.48 % (1104992)Instructions burned: 14 (million)
% 1.43/0.56 % (1104997)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=3896264126:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 1.43/0.56 % (1105003)WARNING Broken Constraint: if sine_to_age_generality_threshold(10) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 1.43/0.56 % (1105003)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs
% 1.43/0.56 % (1105003)ott+21_1_to=kbo:sil=128000:cnfonf=lazy_gen:bsd=on:si=on:sp=const_frequency:lma=off:uwa=off:foolp=on:s2agt=10:lwlo=on:random_seed=4019178866:i=14:add=off:nm=40:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 1.43/0.56 % (1105003)Instruction limit reached!
% 1.43/0.56 % (1105003)------------------------------
% 1.43/0.56 % (1105003)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.43/0.56 % (1105003)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.43/0.56 % (1105001)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=2166699313:cond=on:i=60:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/60Mi)
% 1.43/0.56 % (1105003)CaDiCaL version: 2.1.3
% 1.43/0.56 % (1105003)Termination reason: Instruction limit
% 1.43/0.56 % (1105003)Termination phase: Property scanning
% 1.43/0.56 % (1105003)Time elapsed: 0.004 s
% 1.43/0.56 % (1105003)Peak memory usage: 10 MB
% 1.43/0.56 % (1105003)Instructions burned: 18 (million)
% 1.43/0.56 % (1105004)WARNING Broken Constraint: if choice_reasoning(on) has been set then choice_ax(on) is equal to off
% 1.43/0.56 % (1104997)Instruction limit reached!
% 1.43/0.56 % (1104997)------------------------------
% 1.43/0.56 % (1104997)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.43/0.56 % (1104997)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.43/0.56 % (1104997)CaDiCaL version: 2.1.3
% 1.43/0.56 % (1104997)Termination reason: Instruction limit
% 1.43/0.56 % (1104997)Termination phase: Property scanning
% 1.43/0.56 % (1104997)Time elapsed: 0.010 s
% 1.43/0.56 % (1104997)Peak memory usage: 10 MB
% 1.43/0.56 % (1104997)Instructions burned: 24 (million)
% 1.43/0.56 % (1105004)lrs+1010_4:1_slsqr=8,1:to=kbo:cha=on:drc=off:si=on:sp=arity:lcm=predicate:uwa=off:fd=preordered:gs=on:nwc=5:s2agt=32:slsqc=1:kmz=on:updr=off:chr=on:pe=on:slsq=on:random_seed=3945386450:i=8:nm=2:rtra=on:fe=abstraction:inj=on_2998 on theBenchmark for (2998ds/8Mi)
% 1.43/0.56 % (1105005)dis+1004_50_to=lpo:drc=off:fde=unused:cnfonf=lazy_not_gen_be_off:si=on:sp=reverse_arity:spb=units:cbe=off:foolp=on:random_seed=1797207884:uwa_fpi=on:i=31:doe=on:bd=preordered:rtra=on:fsd=on_2998 on theBenchmark for (2998ds/31Mi)
% 1.43/0.56 % (1105004)Instruction limit reached!
% 1.43/0.56 % (1105004)------------------------------
% 1.43/0.56 % (1105004)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.43/0.56 % (1105004)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.43/0.56 % (1105004)CaDiCaL version: 2.1.3
% 1.43/0.56 % (1105004)Termination reason: Instruction limit
% 1.43/0.56 % (1105004)Termination phase: shuffling
% 1.43/0.56 % (1105004)Time elapsed: 0.004 s
% 1.43/0.56 % (1105004)Peak memory usage: 10 MB
% 1.43/0.56 % (1105004)Instructions burned: 9 (million)
% 1.43/0.56 % (1105009)dis+10_1024_sil=128000:cnfonf=off:si=on:fd=off:random_seed=3511935255:i=7:hud=5:bd=preordered:rtra=on:bet=on_2998 on theBenchmark for (2998ds/7Mi)
% 1.43/0.56 % (1105009)Instruction limit reached!
% 1.43/0.56 % (1105009)------------------------------
% 1.43/0.56 % (1105009)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.43/0.56 % (1105009)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.43/0.56 % (1105009)CaDiCaL version: 2.1.3
% 1.43/0.56 % (1105009)Termination reason: Instruction limit
% 1.43/0.56 % (1105009)Termination phase: shuffling
% 1.43/0.56 % (1105009)Time elapsed: 0.002 s
% 1.43/0.56 % (1105009)Peak memory usage: 10 MB
% 1.43/0.56 % (1105009)Instructions burned: 8 (million)
% 1.43/0.56 % (1105005)Instruction limit reached!
% 1.43/0.56 % (1105005)------------------------------
% 1.43/0.56 % (1105005)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.43/0.56 % (1105005)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.43/0.56 % (1105005)CaDiCaL version: 2.1.3
% 2.18/0.61 % (1105005)Termination reason: Instruction limit
% 2.18/0.61 % (1105005)Termination phase: Property scanning
% 2.18/0.61 % (1105005)Time elapsed: 0.014 s
% 2.18/0.61 % (1105005)Peak memory usage: 10 MB
% 2.18/0.61 % (1105005)Instructions burned: 32 (million)
% 2.18/0.61 % (1105010)lrs+10_1_plsq=on:drc=ordering:cnfonf=lazy_not_gen_be_off:bsd=on:si=on:plsqr=32,1:cs=on:random_seed=2849297404:i=23:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 2.18/0.61 % (1105015)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=2605817145:i=1240:rtra=on:ixr=off_2998 on theBenchmark for (2998ds/1240Mi)
% 2.18/0.61 % (1105001)Instruction limit reached!
% 2.18/0.61 % (1105001)------------------------------
% 2.18/0.61 % (1105001)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.18/0.61 % (1105001)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.18/0.61 % (1105001)CaDiCaL version: 2.1.3
% 2.18/0.61 % (1105001)Termination reason: Instruction limit
% 2.18/0.61 % (1105001)Termination phase: Saturation
% 2.18/0.61 % (1105001)Time elapsed: 0.027 s
% 2.18/0.61 % (1105001)Peak memory usage: 12 MB
% 2.18/0.61 % (1105001)Instructions burned: 61 (million)
% 2.18/0.61 % (1105014)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=357049980:s2a=on:i=20:kws=inv_frequency:bd=all:rtra=on_2998 on theBenchmark for (2998ds/20Mi)
% 2.18/0.61 % (1105010)Instruction limit reached!
% 2.18/0.61 % (1105010)------------------------------
% 2.18/0.61 % (1105010)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.18/0.61 % (1105010)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.18/0.61 % (1105010)CaDiCaL version: 2.1.3
% 2.18/0.61 % (1105010)Termination reason: Instruction limit
% 2.18/0.61 % (1105010)Termination phase: Property scanning
% 2.18/0.61 % (1105010)Time elapsed: 0.010 s
% 2.18/0.61 % (1105010)Peak memory usage: 10 MB
% 2.18/0.61 % (1105010)Instructions burned: 24 (million)
% 2.18/0.61 % (1105014)Instruction limit reached!
% 2.18/0.61 % (1105014)------------------------------
% 2.18/0.61 % (1105014)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.18/0.61 % (1105014)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.18/0.61 % (1105014)CaDiCaL version: 2.1.3
% 2.18/0.61 % (1105014)Termination reason: Instruction limit
% 2.18/0.61 % (1105014)Termination phase: Property scanning
% 2.18/0.61 % (1105014)Time elapsed: 0.010 s
% 2.18/0.61 % (1105014)Peak memory usage: 10 MB
% 2.18/0.61 % (1105014)Instructions burned: 22 (million)
% 2.18/0.61 % (1105017)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=2728917047:i=143:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/143Mi)
% 2.18/0.61 % (1105020)lrs+1002_1_sil=128000:si=on:acc=on:uwa=off:random_seed=2647767647:st=5:s2a=on:i=193:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/193Mi)
% 2.18/0.61 % (1105022)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 2.18/0.61 % (1105021)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3125613346:i=42:hud=10:rtra=on_2998 on theBenchmark for (2998ds/42Mi)
% 2.18/0.61 % (1105022)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=3166268998:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2998 on theBenchmark for (2998ds/7Mi)
% 2.18/0.61 % (1105022)Instruction limit reached!
% 2.18/0.61 % (1105022)------------------------------
% 2.18/0.61 % (1105022)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.18/0.61 % (1105022)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.18/0.61 % (1105022)CaDiCaL version: 2.1.3
% 2.18/0.61 % (1105022)Termination reason: Instruction limit
% 2.18/0.61 % (1105022)Termination phase: shuffling
% 2.18/0.61 % (1105022)Time elapsed: 0.004 s
% 2.18/0.61 % (1105022)Peak memory usage: 10 MB
% 2.18/0.61 % (1105022)Instructions burned: 8 (million)
% 2.18/0.61 % (1105021)Instruction limit reached!
% 2.18/0.61 % (1105021)------------------------------
% 2.18/0.61 % (1105021)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.18/0.61 % (1105021)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.18/0.61 % (1105021)CaDiCaL version: 2.1.3
% 2.18/0.61 % (1105021)Termination reason: Instruction limit
% 2.18/0.61 % (1105021)Termination phase: Function definition elimination
% 2.18/0.61 % (1105021)Time elapsed: 0.019 s
% 2.51/0.69 % (1105021)Peak memory usage: 11 MB
% 2.51/0.69 % (1105021)Instructions burned: 43 (million)
% 2.51/0.69 % (1105027)lrs+10_1_to=lpo:sil=128000:si=on:sp=arity:urr=on:random_seed=3647556348:i=181:sd=2:bd=preordered:rtra=on:ss=axioms_2997 on theBenchmark for (2997ds/181Mi)
% 2.51/0.69 % (1105028)dis+10_8_sil=128000:plsq=on:plsqc=1:si=on:sp=unary_first:sos=on:lma=off:plsqr=64,1:uwa=interpreted_only:foolp=on:random_seed=3744110564:st=3:avsq=on:i=169:avsqr=8,1:sd=2:kws=precedence:bd=preordered:rtra=on:ss=axioms:ntd=on_2997 on theBenchmark for (2997ds/169Mi)
% 2.51/0.69 % (1105017)Instruction limit reached!
% 2.51/0.69 % (1105017)------------------------------
% 2.51/0.69 % (1105017)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.51/0.69 % (1105017)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.51/0.69 % (1105017)CaDiCaL version: 2.1.3
% 2.51/0.69 % (1105017)Termination reason: Instruction limit
% 2.51/0.69 % (1105017)Termination phase: Saturation
% 2.51/0.69 % (1105017)Time elapsed: 0.060 s
% 2.51/0.69 % (1105017)Peak memory usage: 12 MB
% 2.51/0.69 % (1105017)Instructions burned: 144 (million)
% 2.51/0.69 % (1105031)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(5) has been set then sine_level_split_queue(off) is equal to on
% 2.51/0.69 % (1104991)Instruction limit reached!
% 2.51/0.69 % (1104991)------------------------------
% 2.51/0.69 % (1104991)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.51/0.69 % (1104991)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.51/0.69 % (1104991)CaDiCaL version: 2.1.3
% 2.51/0.69 % (1104991)Termination reason: Instruction limit
% 2.51/0.69 % (1104991)Termination phase: Saturation
% 2.51/0.69 % (1104991)Time elapsed: 0.139 s
% 2.51/0.69 % (1104991)Peak memory usage: 15 MB
% 2.51/0.69 % (1104991)Instructions burned: 329 (million)
% 2.51/0.69 % (1105031)lrs+1002_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=arity:cbe=off:uwa=all:slsqc=5:random_seed=4257183446:st=4:s2a=on:i=6:add=on:doe=on:hud=10:rtra=on:bet=on:ss=axioms_2997 on theBenchmark for (2997ds/6Mi)
% 2.51/0.69 % (1105031)Instruction limit reached!
% 2.51/0.69 % (1105031)------------------------------
% 2.51/0.69 % (1105031)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.51/0.69 % (1105031)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.51/0.69 % (1105031)CaDiCaL version: 2.1.3
% 2.51/0.69 % (1105031)Termination reason: Instruction limit
% 2.51/0.69 % (1105031)Termination phase: shuffling
% 2.51/0.69 % (1105031)Time elapsed: 0.003 s
% 2.51/0.69 % (1105031)Peak memory usage: 10 MB
% 2.51/0.69 % (1105031)Instructions burned: 7 (million)
% 2.51/0.69 % (1105020)Instruction limit reached!
% 2.51/0.69 % (1105020)------------------------------
% 2.51/0.69 % (1105020)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.51/0.69 % (1105020)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.51/0.69 % (1105020)CaDiCaL version: 2.1.3
% 2.51/0.69 % (1105020)Termination reason: Instruction limit
% 2.51/0.69 % (1105020)Termination phase: Saturation
% 2.51/0.69 % (1105020)Time elapsed: 0.086 s
% 2.51/0.69 % (1105020)Peak memory usage: 14 MB
% 2.51/0.69 % (1105020)Instructions burned: 195 (million)
% 2.51/0.69 % (1105032)ott+2_5:4_anc=none:to=lpo:si=on:lma=off:cbe=off:uwa=ground:nwc=3:random_seed=3884930987:uwa_fpi=on:i=22:add=on:doe=on:ins=1:rtra=on_2997 on theBenchmark for (2997ds/22Mi)
% 2.51/0.69 % (1105034)dis+1010_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:sas=cadical:si=on:sos=all:uwa=off:sac=on:random_seed=3186047591:i=19:add=on:rtra=on_2997 on theBenchmark for (2997ds/19Mi)
% 2.51/0.69 % (1105032)Instruction limit reached!
% 2.51/0.69 % (1105032)------------------------------
% 2.51/0.69 % (1105032)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.51/0.69 % (1105032)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.51/0.69 % (1105032)CaDiCaL version: 2.1.3
% 2.51/0.69 % (1105032)Termination reason: Instruction limit
% 2.51/0.69 % (1105032)Termination phase: Property scanning
% 2.51/0.69 % (1105032)Time elapsed: 0.010 s
% 2.51/0.69 % (1105032)Peak memory usage: 10 MB
% 2.51/0.69 % (1105032)Instructions burned: 23 (million)
% 2.51/0.69 % (1105034)Instruction limit reached!
% 2.51/0.69 % (1105034)------------------------------
% 2.51/0.69 % (1105034)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.51/0.69 % (1105034)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.59/0.75 % (1105034)CaDiCaL version: 2.1.3
% 2.59/0.75 % (1105034)Termination reason: Instruction limit
% 2.59/0.75 % (1105034)Termination phase: Property scanning
% 2.59/0.75 % (1105034)Time elapsed: 0.011 s
% 2.59/0.75 % (1105034)Peak memory usage: 10 MB
% 2.59/0.75 % (1105034)Instructions burned: 24 (million)
% 2.59/0.75 % (1105035)ott+10_1_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:lma=off:plsqr=128,1:urr=ec_only:uwa=off:rp=on:nwc=20:br=off:random_seed=2395896293:i=316:bs=unit_only:ins=25:rtra=on:ntd=on_2997 on theBenchmark for (2997ds/316Mi)
% 2.59/0.75 % (1105028)Instruction limit reached!
% 2.59/0.75 % (1105028)------------------------------
% 2.59/0.75 % (1105028)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.59/0.75 % (1105028)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.59/0.75 % (1105028)CaDiCaL version: 2.1.3
% 2.59/0.75 % (1105028)Termination reason: Instruction limit
% 2.59/0.75 % (1105028)Termination phase: Saturation
% 2.59/0.75 % (1105028)Time elapsed: 0.070 s
% 2.59/0.75 % (1105028)Peak memory usage: 13 MB
% 2.59/0.75 % (1105028)Instructions burned: 169 (million)
% 2.59/0.75 % (1105027)Instruction limit reached!
% 2.59/0.75 % (1105027)------------------------------
% 2.59/0.75 % (1105027)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.59/0.75 % (1105027)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.59/0.75 % (1105027)CaDiCaL version: 2.1.3
% 2.59/0.75 % (1105027)Termination reason: Instruction limit
% 2.59/0.75 % (1105027)Termination phase: Saturation
% 2.59/0.75 % (1105027)Time elapsed: 0.086 s
% 2.59/0.75 % (1105027)Peak memory usage: 13 MB
% 2.59/0.75 % (1105027)Instructions burned: 182 (million)
% 2.59/0.75 % (1105038)dis+1004_4:1_slsqr=1,2:to=lpo:plsq=on:fde=unused:e2e=on:si=on:spb=goal_then_units:acc=on:urr=on:uwa=off:fd=preordered:s2agt=16:slsqc=1:slsq=on:random_seed=3657996583:hsq=on:hsqr=16,1:s2a=on:i=853:add=off:bd=all:nm=64:rtra=on:gtg=position:c=on:ntd=on_2996 on theBenchmark for (2996ds/853Mi)
% 2.59/0.75 % (1105040)dis+1003_3:4_to=kbo:plsq=on:prc=on:sims=off:e2e=on:si=on:spb=intro:acc=on:urr=on:uwa=off:foolp=on:s2agt=32:slsqc=3:slsq=on:random_seed=3629773938:hsq=on:hsqr=16,1:s2a=on:i=45:erml=3:slsql=off:rtra=on:gtg=exists_top:er=filter:ntd=on_2996 on theBenchmark for (2996ds/45Mi)
% 2.59/0.75 % (1105041)lrs+1002_1_sil=128000:fde=unused:e2e=on:si=on:sos=on:uwa=interpreted_only:random_seed=4026498448:i=480:rtra=on_2996 on theBenchmark for (2996ds/480Mi)
% 2.59/0.75 % (1105042)dis+1010_40_sil=128000:si=on:uwa=off:nwc=1:sac=on:chr=on:avsqc=3:random_seed=328500286:avsq=on:i=21:avsqr=8,1:kws=frequency:fgj=on:bd=all:rtra=on:fe=axiom:ntd=on_2996 on theBenchmark for (2996ds/21Mi)
% 2.59/0.75 % (1105042)Instruction limit reached!
% 2.59/0.75 % (1105042)------------------------------
% 2.59/0.75 % (1105042)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.59/0.75 % (1105042)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.59/0.75 % (1105042)CaDiCaL version: 2.1.3
% 2.59/0.75 % (1105042)Termination reason: Instruction limit
% 2.59/0.75 % (1105042)Termination phase: Property scanning
% 2.59/0.75 % (1105042)Time elapsed: 0.009 s
% 2.59/0.75 % (1105042)Peak memory usage: 10 MB
% 2.59/0.75 % (1105042)Instructions burned: 22 (million)
% 2.59/0.75 % (1105040)Instruction limit reached!
% 2.59/0.75 % (1105040)------------------------------
% 2.59/0.75 % (1105040)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.59/0.75 % (1105040)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.59/0.75 % (1105040)CaDiCaL version: 2.1.3
% 2.59/0.75 % (1105040)Termination reason: Instruction limit
% 2.59/0.75 % (1105040)Termination phase: Property scanning
% 2.59/0.75 % (1105040)Time elapsed: 0.020 s
% 2.59/0.75 % (1105040)Peak memory usage: 11 MB
% 2.59/0.75 % (1105040)Instructions burned: 46 (million)
% 2.59/0.75 % (1105041)Refutation not found, incomplete strategy
% 2.59/0.75 % (1105041)------------------------------
% 2.59/0.75 % (1105041)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.59/0.75 % (1105041)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.59/0.75 % (1105041)CaDiCaL version: 2.1.3
% 2.59/0.75 % (1105041)Termination reason: Refutation not found, incomplete strategy
% 2.59/0.75 % (1105041)Time elapsed: 0.025 s
% 2.59/0.75 % (1105041)Peak memory usage: 13 MB
% 2.59/0.75 % (1105041)Instructions burned: 53 (million)
% 2.59/0.75 % (1105041)------------------------------
% 3.50/0.81 % (1105041)------------------------------
% 3.50/0.81 % (1105047)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(2) has been set then sine_level_split_queue(off) is equal to on
% 3.50/0.81 % (1105047)ott+1002_3_si=on:sp=weighted_frequency:spb=goal:cbe=off:slsqc=2:random_seed=2843352377:cts=off:uwa_fpi=on:i=200:av=off:fsr=off:rtra=on:ntd=on_2996 on theBenchmark for (2996ds/200Mi)
% 3.50/0.81 % (1105048)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=563799810:s2a=on:i=13:kws=inv_frequency:bd=all:rtra=on_2996 on theBenchmark for (2996ds/13Mi)
% 3.50/0.81 % (1105048)Instruction limit reached!
% 3.50/0.81 % (1105048)------------------------------
% 3.50/0.81 % (1105048)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.50/0.81 % (1105048)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.50/0.81 % (1105048)CaDiCaL version: 2.1.3
% 3.50/0.81 % (1105048)Termination reason: Instruction limit
% 3.50/0.81 % (1105048)Termination phase: shuffling
% 3.50/0.81 % (1105048)Time elapsed: 0.006 s
% 3.50/0.81 % (1105048)Peak memory usage: 10 MB
% 3.50/0.81 % (1105048)Instructions burned: 14 (million)
% 3.50/0.81 % (1105049)lrs+1010_1_anc=none:slsqr=1,2:sil=128000:cnfonf=conj_eager:sas=cadical:si=on:hi=on:uwa=one_side_interpreted:rp=on:nwc=2:slsqc=3:slsq=on:random_seed=3533179774:i=66:s2at=3:nm=2:rtra=on:rawr=on_2996 on theBenchmark for (2996ds/66Mi)
% 3.50/0.81 % (1105052)lrs+1004_128_si=on:sos=all:uwa=off:random_seed=3591675550:i=51:fsr=off:rtra=on_2996 on theBenchmark for (2996ds/51Mi)
% 3.50/0.81 % (1104958)Instruction limit reached!
% 3.50/0.81 % (1104958)------------------------------
% 3.50/0.81 % (1104958)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.50/0.81 % (1104958)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.50/0.81 % (1104958)CaDiCaL version: 2.1.3
% 3.50/0.81 % (1104958)Termination reason: Instruction limit
% 3.50/0.81 % (1104958)Termination phase: Saturation
% 3.50/0.81 % (1104958)Time elapsed: 0.358 s
% 3.50/0.81 % (1104958)Peak memory usage: 17 MB
% 3.50/0.81 % (1104958)Instructions burned: 636 (million)
% 3.50/0.81 % (1105049)Instruction limit reached!
% 3.50/0.81 % (1105049)------------------------------
% 3.50/0.81 % (1105049)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.50/0.81 % (1105049)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.50/0.81 % (1105049)CaDiCaL version: 2.1.3
% 3.50/0.81 % (1105049)Termination reason: Instruction limit
% 3.50/0.81 % (1105049)Termination phase: Function definition elimination
% 3.50/0.81 % (1105049)Time elapsed: 0.027 s
% 3.50/0.81 % (1105049)Peak memory usage: 11 MB
% 3.50/0.81 % (1105049)Instructions burned: 66 (million)
% 3.50/0.81 % (1105055)dis+1002_64_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:cbe=off:uwa=off:nwc=0.5:random_seed=2453986236:i=31:kws=inv_frequency:bd=all:rtra=on:ntd=on_2996 on theBenchmark for (2996ds/31Mi)
% 3.50/0.81 % (1105052)Instruction limit reached!
% 3.50/0.81 % (1105052)------------------------------
% 3.50/0.81 % (1105052)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.50/0.81 % (1105052)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.50/0.81 % (1105052)CaDiCaL version: 2.1.3
% 3.50/0.81 % (1105052)Termination reason: Instruction limit
% 3.50/0.81 % (1105052)Termination phase: Function definition elimination
% 3.50/0.81 % (1105052)Time elapsed: 0.021 s
% 3.50/0.81 % (1105052)Peak memory usage: 11 MB
% 3.50/0.81 % (1105052)Instructions burned: 51 (million)
% 3.50/0.81 % (1105056)dis+1010_40_to=kbo:tgt=full:fde=unused:si=on:sp=const_frequency:lma=off:cbe=off:uwa=interpreted_only:random_seed=2698106138:i=137:kws=precedence:bd=all:rtra=on:c=on:ntd=on_2995 on theBenchmark for (2995ds/137Mi)
% 3.50/0.81 % (1105055)Instruction limit reached!
% 3.50/0.81 % (1105055)------------------------------
% 3.50/0.81 % (1105055)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.50/0.81 % (1105055)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.50/0.81 % (1105055)CaDiCaL version: 2.1.3
% 3.50/0.81 % (1105055)Termination reason: Instruction limit
% 3.50/0.81 % (1105055)Termination phase: Property scanning
% 3.50/0.81 % (1105055)Time elapsed: 0.014 s
% 3.50/0.81 % (1105055)Peak memory usage: 10 MB
% 3.50/0.81 % (1105055)Instructions burned: 32 (million)
% 3.50/0.81 % (1105058)dis+10_2_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_pi_sigma_gen:si=on:sp=occurrence:plsqr=5,1:bsr=on:plsql=on:random_seed=1858710034:cond=on:i=34:hud=10:nm=10:rtra=on_2995 on theBenchmark for (2995ds/34Mi)
% 3.80/0.95 % (1105035)Refutation not found, incomplete strategy
% 3.80/0.95 % (1105035)------------------------------
% 3.80/0.95 % (1105035)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.80/0.95 % (1105035)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.80/0.95 % (1105035)CaDiCaL version: 2.1.3
% 3.80/0.95 % (1105035)Termination reason: Refutation not found, incomplete strategy
% 3.80/0.95 % (1105035)Time elapsed: 0.134 s
% 3.80/0.95 % (1105035)Peak memory usage: 16 MB
% 3.80/0.95 % (1105035)Instructions burned: 316 (million)
% 3.80/0.95 % (1105035)------------------------------
% 3.80/0.95 % (1105035)------------------------------
% 3.80/0.95 % (1105015)Instruction limit reached!
% 3.80/0.95 % (1105015)------------------------------
% 3.80/0.95 % (1105015)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.80/0.95 % (1105015)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.80/0.95 % (1105015)CaDiCaL version: 2.1.3
% 3.80/0.95 % (1105015)Termination reason: Instruction limit
% 3.80/0.95 % (1105015)Termination phase: Saturation
% 3.80/0.95 % (1105015)Time elapsed: 0.271 s
% 3.80/0.95 % (1105015)Peak memory usage: 19 MB
% 3.80/0.95 % (1105015)Instructions burned: 1242 (million)
% 3.80/0.95 % (1105047)Instruction limit reached!
% 3.80/0.95 % (1105047)------------------------------
% 3.80/0.95 % (1105047)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.80/0.95 % (1105047)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.80/0.95 % (1105047)CaDiCaL version: 2.1.3
% 3.80/0.95 % (1105047)Termination reason: Instruction limit
% 3.80/0.95 % (1105047)Termination phase: Saturation
% 3.80/0.95 % (1105047)Time elapsed: 0.082 s
% 3.80/0.95 % (1105047)Peak memory usage: 12 MB
% 3.80/0.95 % (1105047)Instructions burned: 201 (million)
% 3.80/0.95 % (1105060)lrs+1010_1_sil=128000:hsqc=4:si=on:sos=on:random_seed=145042461:hsq=on:i=67:hsqaw=5:rtra=on:fe=abstraction:ntd=on_2995 on theBenchmark for (2995ds/67Mi)
% 3.80/0.95 % (1105058)Instruction limit reached!
% 3.80/0.95 % (1105058)------------------------------
% 3.80/0.95 % (1105058)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.80/0.95 % (1105058)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.80/0.95 % (1105058)CaDiCaL version: 2.1.3
% 3.80/0.95 % (1105058)Termination reason: Instruction limit
% 3.80/0.95 % (1105058)Termination phase: Function definition elimination
% 3.80/0.95 % (1105058)Time elapsed: 0.015 s
% 3.80/0.95 % (1105058)Peak memory usage: 10 MB
% 3.80/0.95 % (1105058)Instructions burned: 36 (million)
% 3.80/0.95 % (1105063)lrs+1002_1_sil=128000:si=on:uwa=off:random_seed=2656118270:st=2:i=246:sd=3:rtra=on:ss=axioms_2995 on theBenchmark for (2995ds/246Mi)
% 3.80/0.95 % (1105062)WARNING Broken Constraint: if sine_generality_threshold(60) has been set then sine_selection(off) is not equal to off
% 3.80/0.95 % (1105062)dis+21_1_to=lpo:sil=128000:cnfonf=lazy_not_gen_be_off:si=on:sp=unary_frequency:bsr=on:random_seed=2017959138:i=180:hud=16:bd=all:fsr=off:rtra=on:sgt=60:ntd=on_2995 on theBenchmark for (2995ds/180Mi)
% 3.80/0.95 % (1105065)lrs+10_7_sil=128000:tgt=full:si=on:lma=off:uwa=off:nwc=1:sac=on:random_seed=4202953622:cond=on:i=96:bd=all:rtra=on_2995 on theBenchmark for (2995ds/96Mi)
% 3.80/0.95 % (1105066)lrs+10_1_sil=128000:si=on:sos=on:urr=on:random_seed=4287077250:i=427:sd=1:rtra=on:ss=axioms_2995 on theBenchmark for (2995ds/427Mi)
% 3.80/0.95 % (1105060)Instruction limit reached!
% 3.80/0.95 % (1105060)------------------------------
% 3.80/0.95 % (1105060)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.80/0.95 % (1105060)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.80/0.95 % (1105060)CaDiCaL version: 2.1.3
% 3.80/0.95 % (1105060)Termination reason: Instruction limit
% 3.80/0.95 % (1105060)Termination phase: Function definition elimination
% 3.80/0.95 % (1105060)Time elapsed: 0.028 s
% 3.80/0.95 % (1105060)Peak memory usage: 11 MB
% 3.80/0.95 % (1105060)Instructions burned: 68 (million)
% 3.80/0.95 % (1105071)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=2626566409:st=3:s2a=on:i=874:sd=3:rtra=on:ss=axioms_2995 on theBenchmark for (2995ds/874Mi)
% 3.80/0.95 % (1105056)Instruction limit reached!
% 3.80/0.95 % (1105056)------------------------------
% 3.80/0.95 % (1105056)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.47/1.04 % (1105056)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.47/1.04 % (1105056)CaDiCaL version: 2.1.3
% 5.47/1.04 % (1105056)Termination reason: Instruction limit
% 5.47/1.04 % (1105056)Termination phase: Saturation
% 5.47/1.04 % (1105056)Time elapsed: 0.074 s
% 5.47/1.04 % (1105056)Peak memory usage: 13 MB
% 5.47/1.04 % (1105056)Instructions burned: 138 (million)
% 5.47/1.04 % (1105065)Instruction limit reached!
% 5.47/1.04 % (1105065)------------------------------
% 5.47/1.04 % (1105065)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.47/1.04 % (1105065)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.47/1.04 % (1105065)CaDiCaL version: 2.1.3
% 5.47/1.04 % (1105065)Termination reason: Instruction limit
% 5.47/1.04 % (1105065)Termination phase: Property scanning
% 5.47/1.04 % (1105065)Time elapsed: 0.039 s
% 5.47/1.04 % (1105065)Peak memory usage: 11 MB
% 5.47/1.04 % (1105065)Instructions burned: 99 (million)
% 5.47/1.04 % (1105063)Instruction limit reached!
% 5.47/1.04 % (1105063)------------------------------
% 5.47/1.04 % (1105063)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.47/1.04 % (1105063)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.47/1.04 % (1105063)CaDiCaL version: 2.1.3
% 5.47/1.04 % (1105063)Termination reason: Instruction limit
% 5.47/1.04 % (1105063)Termination phase: Saturation
% 5.47/1.04 % (1105063)Time elapsed: 0.056 s
% 5.47/1.04 % (1105063)Peak memory usage: 15 MB
% 5.47/1.04 % (1105063)Instructions burned: 246 (million)
% 5.47/1.04 % (1105073)dis+1010_4_sas=cadical:si=on:cbe=off:nwc=20:random_seed=1762399084:st=6:s2a=on:i=515:sd=2:nm=2:rtra=on:ss=axioms_2994 on theBenchmark for (2994ds/515Mi)
% 5.47/1.04 % (1105075)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=4085492641:i=44:ep=R:rtra=on:ntd=on_2994 on theBenchmark for (2994ds/44Mi)
% 5.47/1.04 % (1105074)lrs+1002_1_cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:random_seed=3868014421:st=1.5:i=130:rtra=on:ss=axioms_2994 on theBenchmark for (2994ds/130Mi)
% 5.47/1.04 % (1105062)Instruction limit reached!
% 5.47/1.04 % (1105062)------------------------------
% 5.47/1.04 % (1105062)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.47/1.04 % (1105062)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.47/1.04 % (1105062)CaDiCaL version: 2.1.3
% 5.47/1.04 % (1105062)Termination reason: Instruction limit
% 5.47/1.04 % (1105062)Termination phase: Saturation
% 5.47/1.04 % (1105062)Time elapsed: 0.073 s
% 5.47/1.04 % (1105062)Peak memory usage: 12 MB
% 5.47/1.04 % (1105062)Instructions burned: 180 (million)
% 5.47/1.04 % (1105075)Instruction limit reached!
% 5.47/1.04 % (1105075)------------------------------
% 5.47/1.04 % (1105075)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.47/1.04 % (1105075)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.47/1.04 % (1105075)CaDiCaL version: 2.1.3
% 5.47/1.04 % (1105075)Termination reason: Instruction limit
% 5.47/1.04 % (1105075)Termination phase: Function definition elimination
% 5.47/1.04 % (1105075)Time elapsed: 0.010 s
% 5.47/1.04 % (1105075)Peak memory usage: 10 MB
% 5.47/1.04 % (1105075)Instructions burned: 49 (million)
% 5.47/1.04 % (1105066)Refutation not found, incomplete strategy
% 5.47/1.04 % (1105066)------------------------------
% 5.47/1.04 % (1105066)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.47/1.04 % (1105066)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.47/1.04 % (1105066)CaDiCaL version: 2.1.3
% 5.47/1.04 % (1105066)Termination reason: Refutation not found, incomplete strategy
% 5.47/1.04 % (1105066)Time elapsed: 0.071 s
% 5.47/1.04 % (1105066)Peak memory usage: 14 MB
% 5.47/1.04 % (1105066)Instructions burned: 162 (million)
% 5.47/1.04 % (1105066)------------------------------
% 5.47/1.04 % (1105066)------------------------------
% 5.47/1.04 % (1105080)dis+1010_8_to=lpo:sil=128000:tgt=ground:si=on:sp=reverse_frequency:cbe=off:uwa=off:random_seed=4286208989:i=450:rtra=on:ixr=off:ntd=on_2994 on theBenchmark for (2994ds/450Mi)
% 5.47/1.04 % (1105079)lrs+1010_8:1_sil=128000:fde=unused:e2e=on:si=on:sos=on:urr=on:uwa=one_side_constant:fd=off:random_seed=1203620126:s2a=on:i=571:nm=16:rtra=on_2994 on theBenchmark for (2994ds/571Mi)
% 5.47/1.04 % (1105081)lrs+10_5:1_to=lpo:sil=128000:si=on:uwa=one_side_interpreted:random_seed=3920971598:cts=off:i=95:piset=pi_sigma:bd=all:rtra=on:ntd=on_2994 on theBenchmark for (2994ds/95Mi)
% 5.47/1.12 % (1105074)Instruction limit reached!
% 5.47/1.12 % (1105074)------------------------------
% 5.47/1.12 % (1105074)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.47/1.12 % (1105074)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.47/1.12 % (1105074)CaDiCaL version: 2.1.3
% 5.47/1.12 % (1105074)Termination reason: Instruction limit
% 5.47/1.12 % (1105074)Termination phase: Saturation
% 5.47/1.12 % (1105074)Time elapsed: 0.063 s
% 5.47/1.12 % (1105074)Peak memory usage: 14 MB
% 5.47/1.12 % (1105074)Instructions burned: 131 (million)
% 5.47/1.12 % (1105081)Instruction limit reached!
% 5.47/1.12 % (1105081)------------------------------
% 5.47/1.12 % (1105081)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.47/1.12 % (1105081)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.47/1.12 % (1105081)CaDiCaL version: 2.1.3
% 5.47/1.12 % (1105081)Termination reason: Instruction limit
% 5.47/1.12 % (1105081)Termination phase: Saturation
% 5.47/1.12 % (1105081)Time elapsed: 0.038 s
% 5.47/1.12 % (1105081)Peak memory usage: 12 MB
% 5.47/1.12 % (1105081)Instructions burned: 95 (million)
% 5.47/1.12 % (1105085)lrs+1003_1_sil=128000:drc=off:cnfonf=lazy_pi_sigma_gen:si=on:uwa=one_side_interpreted:fd=off:rp=on:sac=on:random_seed=547188073:s2a=on:i=65:add=on:bd=preordered:ins=10:rtra=on_2994 on theBenchmark for (2994ds/65Mi)
% 5.47/1.12 % (1105086)dis+1010_2:1_slsqr=2,1:to=lpo:plsq=on:cnfonf=lazy_pi_sigma_gen:si=on:sp=reverse_arity:acc=on:uwa=hol:fd=preordered:s2agt=16:flr=on:pe=on:slsq=on:random_seed=1304007969:uwa_fpi=on:avsq=on:s2a=on:cond=fast:i=105:s2at=1.5:aac=none:fgj=on:piset=and:hud=3:fsr=off:rtra=on:er=filter:rawr=on_2993 on theBenchmark for (2993ds/105Mi)
% 5.47/1.12 % (1105085)Instruction limit reached!
% 5.47/1.12 % (1105085)------------------------------
% 5.47/1.12 % (1105085)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.47/1.12 % (1105085)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.47/1.12 % (1105085)CaDiCaL version: 2.1.3
% 5.47/1.12 % (1105085)Termination reason: Instruction limit
% 5.47/1.12 % (1105085)Termination phase: Function definition elimination
% 5.47/1.12 % (1105085)Time elapsed: 0.027 s
% 5.47/1.12 % (1105085)Peak memory usage: 11 MB
% 5.47/1.12 % (1105085)Instructions burned: 66 (million)
% 5.47/1.12 % (1105080)Instruction limit reached!
% 5.47/1.12 % (1105080)------------------------------
% 5.47/1.12 % (1105080)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.47/1.12 % (1105080)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.47/1.12 % (1105080)CaDiCaL version: 2.1.3
% 5.47/1.12 % (1105080)Termination reason: Instruction limit
% 5.47/1.12 % (1105080)Termination phase: Saturation
% 5.47/1.12 % (1105080)Time elapsed: 0.097 s
% 5.47/1.12 % (1105080)Peak memory usage: 13 MB
% 5.47/1.12 % (1105080)Instructions burned: 453 (million)
% 5.47/1.12 % (1105090)lrs+10_1_sil=128000:drc=off:si=on:fs=off:urr=on:uwa=one_side_constant:random_seed=2777969715:st=10:i=375:sd=1:bd=all:fsr=off:rtra=on:ss=axioms_2993 on theBenchmark for (2993ds/375Mi)
% 5.47/1.12 % (1105089)dis+10_4:1_sfv=off:to=kbo:fde=unused:cnfonf=off:sas=cadical:e2e=on:si=on:sp=occurrence:acc=on:uwa=off:fd=preordered:foolp=on:random_seed=83575784:hsq=on:hsqr=16,1:s2a=on:i=5755:piset=or:nm=32:rtra=on:ss=axioms:c=on:sgt=8:rawr=on_2993 on theBenchmark for (2993ds/5755Mi)
% 5.47/1.12 % (1105086)Instruction limit reached!
% 5.47/1.12 % (1105086)------------------------------
% 5.47/1.12 % (1105086)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.47/1.12 % (1105086)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.47/1.12 % (1105086)CaDiCaL version: 2.1.3
% 5.47/1.12 % (1105086)Termination reason: Instruction limit
% 5.47/1.12 % (1105086)Termination phase: Saturation
% 5.47/1.12 % (1105086)Time elapsed: 0.043 s
% 5.47/1.12 % (1105086)Peak memory usage: 12 MB
% 5.47/1.12 % (1105086)Instructions burned: 108 (million)
% 5.47/1.12 % (1105093)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3419040430:s2a=on:i=495:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2993 on theBenchmark for (2993ds/495Mi)
% 5.47/1.12 % (1105038)Instruction limit reached!
% 5.47/1.12 % (1105038)------------------------------
% 5.47/1.12 % (1105038)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.47/1.12 % (1105038)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.24/1.21 % (1105038)CaDiCaL version: 2.1.3
% 6.24/1.21 % (1105038)Termination reason: Instruction limit
% 6.24/1.21 % (1105038)Termination phase: Saturation
% 6.24/1.21 % (1105038)Time elapsed: 0.377 s
% 6.24/1.21 % (1105038)Peak memory usage: 14 MB
% 6.24/1.21 % (1105038)Instructions burned: 854 (million)
% 6.24/1.21 % (1105095)dis+10_2_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_pi_sigma_gen:si=on:sp=occurrence:plsqr=5,1:bsr=on:plsql=on:random_seed=3927113653:cond=on:i=34:hud=10:nm=10:rtra=on_2993 on theBenchmark for (2993ds/34Mi)
% 6.24/1.21 % (1105073)Instruction limit reached!
% 6.24/1.21 % (1105073)------------------------------
% 6.24/1.21 % (1105073)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.24/1.21 % (1105073)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.24/1.21 % (1105073)CaDiCaL version: 2.1.3
% 6.24/1.21 % (1105073)Termination reason: Instruction limit
% 6.24/1.21 % (1105073)Termination phase: Saturation
% 6.24/1.21 % (1105073)Time elapsed: 0.214 s
% 6.24/1.21 % (1105073)Peak memory usage: 16 MB
% 6.24/1.21 % (1105073)Instructions burned: 516 (million)
% 6.24/1.21 % (1105095)Instruction limit reached!
% 6.24/1.21 % (1105095)------------------------------
% 6.24/1.21 % (1105095)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.24/1.21 % (1105095)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.24/1.21 % (1105095)CaDiCaL version: 2.1.3
% 6.24/1.21 % (1105095)Termination reason: Instruction limit
% 6.24/1.21 % (1105095)Termination phase: Function definition elimination
% 6.24/1.21 % (1105095)Time elapsed: 0.015 s
% 6.24/1.21 % (1105095)Peak memory usage: 10 MB
% 6.24/1.21 % (1105095)Instructions burned: 36 (million)
% 6.24/1.21 % (1105090)Instruction limit reached!
% 6.24/1.21 % (1105090)------------------------------
% 6.24/1.21 % (1105090)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.24/1.21 % (1105090)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.24/1.21 % (1105090)CaDiCaL version: 2.1.3
% 6.24/1.21 % (1105090)Termination reason: Instruction limit
% 6.24/1.21 % (1105090)Termination phase: Saturation
% 6.24/1.21 % (1105090)Time elapsed: 0.096 s
% 6.24/1.21 % (1105090)Peak memory usage: 14 MB
% 6.24/1.21 % (1105090)Instructions burned: 385 (million)
% 6.24/1.21 % (1105097)ott+1002_4_tgt=ground:si=on:tsa=off:nwc=1:random_seed=2855717706:s2a=on:i=91:piset=or:hud=5:rtra=on:fe=abstraction_2992 on theBenchmark for (2992ds/91Mi)
% 6.24/1.21 % (1105098)dis+2_1_sil=128000:tgt=ground:e2e=on:si=on:sos=on:urr=on:uwa=off:nwc=2:random_seed=2765605047:i=66:sd=50:kws=inv_arity:bd=preordered:nm=64:rtra=on:ss=axioms:c=on:ntd=on_2992 on theBenchmark for (2992ds/66Mi)
% 6.24/1.21 % (1105099)ott+2_5:4_anc=none:to=lpo:si=on:lma=off:cbe=off:uwa=ground:nwc=3:random_seed=1288471764:uwa_fpi=on:i=22:add=on:doe=on:ins=1:rtra=on_2992 on theBenchmark for (2992ds/22Mi)
% 6.24/1.21 % (1105099)Instruction limit reached!
% 6.24/1.21 % (1105099)------------------------------
% 6.24/1.21 % (1105099)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.24/1.21 % (1105099)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.24/1.21 % (1105099)CaDiCaL version: 2.1.3
% 6.24/1.21 % (1105099)Termination reason: Instruction limit
% 6.24/1.21 % (1105099)Termination phase: Property scanning
% 6.24/1.21 % (1105099)Time elapsed: 0.005 s
% 6.24/1.21 % (1105099)Peak memory usage: 10 MB
% 6.24/1.21 % (1105099)Instructions burned: 24 (million)
% 6.24/1.21 % (1105103)lrs+21_16_anc=none:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:sas=cadical:si=on:plsqr=32,1:uwa=interpreted_only:foolp=on:nwc=3:random_seed=164729072:i=338:bd=all:ins=4:rtra=on_2992 on theBenchmark for (2992ds/338Mi)
% 6.24/1.21 % (1105098)Instruction limit reached!
% 6.24/1.21 % (1105098)------------------------------
% 6.24/1.21 % (1105098)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.24/1.21 % (1105098)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.24/1.21 % (1105098)CaDiCaL version: 2.1.3
% 6.24/1.21 % (1105098)Termination reason: Instruction limit
% 6.24/1.21 % (1105098)Termination phase: Saturation
% 6.24/1.21 % (1105098)Time elapsed: 0.031 s
% 6.24/1.21 % (1105098)Peak memory usage: 12 MB
% 6.24/1.21 % (1105098)Instructions burned: 67 (million)
% 6.24/1.21 % (1105079)Instruction limit reached!
% 6.24/1.21 % (1105079)------------------------------
% 6.24/1.21 % (1105079)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.24/1.21 % (1105079)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.84/1.35 % (1105079)CaDiCaL version: 2.1.3
% 6.84/1.35 % (1105079)Termination reason: Instruction limit
% 6.84/1.35 % (1105079)Termination phase: Saturation
% 6.84/1.35 % (1105079)Time elapsed: 0.234 s
% 6.84/1.35 % (1105079)Peak memory usage: 14 MB
% 6.84/1.35 % (1105079)Instructions burned: 572 (million)
% 6.84/1.35 % (1105097)Instruction limit reached!
% 6.84/1.35 % (1105097)------------------------------
% 6.84/1.35 % (1105097)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.84/1.35 % (1105097)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.84/1.35 % (1105097)CaDiCaL version: 2.1.3
% 6.84/1.35 % (1105097)Termination reason: Instruction limit
% 6.84/1.35 % (1105097)Termination phase: Saturation
% 6.84/1.35 % (1105097)Time elapsed: 0.038 s
% 6.84/1.35 % (1105097)Peak memory usage: 13 MB
% 6.84/1.35 % (1105097)Instructions burned: 92 (million)
% 6.84/1.35 % (1105105)lrs+10_1_sil=128000:si=on:urr=on:random_seed=74017189:i=28:sd=1:rtra=on:ss=axioms:sgt=64_2992 on theBenchmark for (2992ds/28Mi)
% 6.84/1.35 % (1105106)WARNING Broken Constraint: if avatar_split_queue_ratios(1,16) has been set then avatar_split_queue(off) is equal to on
% 6.84/1.35 % (1105106)lrs+1010_2:13_to=kbo:sil=128000:cnfonf=lazy_not_gen:si=on:sp=const_min:uwa=interpreted_only:random_seed=1899277557:i=137:add=off:avsqr=1,16:kws=inv_arity:bd=preordered:nm=0:rtra=on:ntd=on:rawr=on_2992 on theBenchmark for (2992ds/137Mi)
% 6.84/1.35 % (1105107)dis+10_32_sil=128000:tgt=ground:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=32,1:uwa=one_side_interpreted:nwc=1:random_seed=3553498614:hsq=on:hsqr=1,8:i=340:hsql=off:bd=preordered:av=off:rtra=on_2992 on theBenchmark for (2992ds/340Mi)
% 6.84/1.35 % (1105105)Instruction limit reached!
% 6.84/1.35 % (1105105)------------------------------
% 6.84/1.35 % (1105105)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.84/1.35 % (1105105)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.84/1.35 % (1105105)CaDiCaL version: 2.1.3
% 6.84/1.35 % (1105105)Termination reason: Instruction limit
% 6.84/1.35 % (1105105)Termination phase: Preprocessing 2
% 6.84/1.35 % (1105105)Time elapsed: 0.013 s
% 6.84/1.35 % (1105105)Peak memory usage: 10 MB
% 6.84/1.35 % (1105105)Instructions burned: 29 (million)
% 6.84/1.35 % (1105111)dis+1004_1_sil=128000:si=on:sos=on:uwa=one_side_interpreted:random_seed=675940877:i=227:sd=1:bd=all:rtra=on:ss=axioms_2991 on theBenchmark for (2991ds/227Mi)
% 6.84/1.35 % (1105071)Instruction limit reached!
% 6.84/1.35 % (1105071)------------------------------
% 6.84/1.35 % (1105071)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.84/1.35 % (1105071)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.84/1.35 % (1105071)CaDiCaL version: 2.1.3
% 6.84/1.35 % (1105071)Termination reason: Instruction limit
% 6.84/1.35 % (1105071)Termination phase: Saturation
% 6.84/1.35 % (1105071)Time elapsed: 0.353 s
% 6.84/1.35 % (1105071)Peak memory usage: 16 MB
% 6.84/1.35 % (1105071)Instructions burned: 874 (million)
% 6.84/1.35 % (1105103)Instruction limit reached!
% 6.84/1.35 % (1105103)------------------------------
% 6.84/1.35 % (1105103)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.84/1.35 % (1105103)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.84/1.35 % (1105103)CaDiCaL version: 2.1.3
% 6.84/1.35 % (1105103)Termination reason: Instruction limit
% 6.84/1.35 % (1105103)Termination phase: Saturation
% 6.84/1.35 % (1105103)Time elapsed: 0.076 s
% 6.84/1.35 % (1105103)Peak memory usage: 17 MB
% 6.84/1.35 % (1105103)Instructions burned: 343 (million)
% 6.84/1.35 % (1105113)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(1) has been set then sine_level_split_queue(off) is equal to on
% 6.84/1.35 % (1105113)dis+1010_1_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:nwc=2:slsqc=1:random_seed=940818892:i=373:hud=10:nm=16:av=off:rtra=on:ntd=on_2991 on theBenchmark for (2991ds/373Mi)
% 6.84/1.35 % (1105106)Instruction limit reached!
% 6.84/1.35 % (1105106)------------------------------
% 6.84/1.35 % (1105106)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.84/1.35 % (1105106)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.84/1.35 % (1105106)CaDiCaL version: 2.1.3
% 6.84/1.35 % (1105106)Termination reason: Instruction limit
% 6.84/1.35 % (1105106)Termination phase: Saturation
% 6.84/1.35 % (1105106)Time elapsed: 0.055 s
% 6.84/1.35 % (1105106)Peak memory usage: 12 MB
% 7.58/1.47 % (1105106)Instructions burned: 138 (million)
% 7.58/1.47 % (1105114)lrs+10_64_anc=all_dependent:sil=128000:e2e=on:si=on:cbe=off:uwa=off:random_seed=2558751692:i=116:ep=RSTC:rtra=on:ntd=on_2991 on theBenchmark for (2991ds/116Mi)
% 7.58/1.47 % (1105111)Refutation not found, incomplete strategy
% 7.58/1.47 % (1105111)------------------------------
% 7.58/1.47 % (1105111)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.58/1.47 % (1105111)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.58/1.47 % (1105111)CaDiCaL version: 2.1.3
% 7.58/1.47 % (1105111)Termination reason: Refutation not found, incomplete strategy
% 7.58/1.47 % (1105111)Time elapsed: 0.046 s
% 7.58/1.47 % (1105111)Peak memory usage: 13 MB
% 7.58/1.47 % (1105111)Instructions burned: 101 (million)
% 7.58/1.47 % (1105093)Instruction limit reached!
% 7.58/1.47 % (1105093)------------------------------
% 7.58/1.47 % (1105093)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.58/1.47 % (1105093)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.58/1.47 % (1105093)CaDiCaL version: 2.1.3
% 7.58/1.47 % (1105093)Termination reason: Instruction limit
% 7.58/1.47 % (1105093)Termination phase: Saturation
% 7.58/1.47 % (1105093)Time elapsed: 0.198 s
% 7.58/1.47 % (1105093)Peak memory usage: 13 MB
% 7.58/1.47 % (1105093)Instructions burned: 497 (million)
% 7.58/1.47 % (1105111)------------------------------
% 7.58/1.47 % (1105111)------------------------------
% 7.58/1.47 % (1105116)lrs+10_1_sil=128000:drc=off:si=on:sos=on:erd=off:urr=on:uwa=interpreted_only:random_seed=4245901980:i=575:rtra=on_2991 on theBenchmark for (2991ds/575Mi)
% 7.58/1.47 % (1105118)dis+2_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:fdtod=off:sp=const_max:lma=off:random_seed=2100654547:cts=off:i=270:doe=on:hud=5:bs=unit_only:bd=preordered:nm=30:ins=25:rtra=on_2991 on theBenchmark for (2991ds/270Mi)
% 7.58/1.47 % (1105120)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=115155791:hsq=on:hsqr=16,1:s2a=on:i=9840:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2991 on theBenchmark for (2991ds/9840Mi)
% 7.58/1.47 % (1105114)Instruction limit reached!
% 7.58/1.47 % (1105114)------------------------------
% 7.58/1.47 % (1105114)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.58/1.47 % (1105114)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.58/1.47 % (1105114)CaDiCaL version: 2.1.3
% 7.58/1.47 % (1105114)Termination reason: Instruction limit
% 7.58/1.47 % (1105114)Termination phase: Saturation
% 7.58/1.47 % (1105114)Time elapsed: 0.047 s
% 7.58/1.47 % (1105114)Peak memory usage: 12 MB
% 7.58/1.47 % (1105114)Instructions burned: 116 (million)
% 7.58/1.47 % (1105123)lrs+1010_1_sil=128000:si=on:sos=all:uwa=off:nwc=1:random_seed=3809365139:i=421:rtra=on:ss=axioms_2990 on theBenchmark for (2990ds/421Mi)
% 7.58/1.47 % (1105113)Instruction limit reached!
% 7.58/1.47 % (1105113)------------------------------
% 7.58/1.47 % (1105113)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.58/1.47 % (1105113)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.58/1.47 % (1105113)CaDiCaL version: 2.1.3
% 7.58/1.47 % (1105113)Termination reason: Instruction limit
% 7.58/1.47 % (1105113)Termination phase: Saturation
% 7.58/1.47 % (1105113)Time elapsed: 0.082 s
% 7.58/1.47 % (1105113)Peak memory usage: 13 MB
% 7.58/1.47 % (1105113)Instructions burned: 376 (million)
% 7.58/1.47 % (1105125)WARNING Broken Constraint: if sine_to_age_tolerance(3) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 7.58/1.47 % (1105107)Instruction limit reached!
% 7.58/1.47 % (1105107)------------------------------
% 7.58/1.47 % (1105107)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.58/1.47 % (1105107)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.58/1.47 % (1105107)CaDiCaL version: 2.1.3
% 7.58/1.47 % (1105107)Termination reason: Instruction limit
% 7.58/1.47 % (1105107)Termination phase: Saturation
% 7.58/1.47 % (1105107)Time elapsed: 0.145 s
% 7.58/1.47 % (1105107)Peak memory usage: 14 MB
% 7.58/1.47 % (1105107)Instructions burned: 341 (million)
% 7.58/1.47 % (1105125)lrs+10_40_sil=128000:tgt=full:cnfonf=off:si=on:sp=reverse_frequency:spb=goal_then_units:uwa=off:fd=preordered:nwc=1:random_seed=4159425245:avsq=on:i=270:s2at=3:avsqr=1,16:rtra=on:ntd=on_2990 on theBenchmark for (2990ds/270Mi)
% 8.23/1.70 % (1105127)dis+1002_64_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:cbe=off:uwa=off:nwc=0.5:random_seed=1278974205:i=31:kws=inv_frequency:bd=all:rtra=on:ntd=on_2990 on theBenchmark for (2990ds/31Mi)
% 8.23/1.70 % (1105127)Instruction limit reached!
% 8.23/1.70 % (1105127)------------------------------
% 8.23/1.70 % (1105127)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.23/1.70 % (1105127)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.23/1.70 % (1105127)CaDiCaL version: 2.1.3
% 8.23/1.70 % (1105127)Termination reason: Instruction limit
% 8.23/1.70 % (1105127)Termination phase: Property scanning
% 8.23/1.70 % (1105127)Time elapsed: 0.014 s
% 8.23/1.70 % (1105127)Peak memory usage: 10 MB
% 8.23/1.70 % (1105127)Instructions burned: 33 (million)
% 8.23/1.70 % (1105125)Refutation not found, incomplete strategy
% 8.23/1.70 % (1105125)------------------------------
% 8.23/1.70 % (1105125)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.23/1.70 % (1105125)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.23/1.70 % (1105125)CaDiCaL version: 2.1.3
% 8.23/1.70 % (1105125)Termination reason: Refutation not found, incomplete strategy
% 8.23/1.70 % (1105125)Time elapsed: 0.045 s
% 8.23/1.70 % (1105125)Peak memory usage: 14 MB
% 8.23/1.70 % (1105125)Instructions burned: 197 (million)
% 8.23/1.70 % (1105125)------------------------------
% 8.23/1.70 % (1105125)------------------------------
% 8.23/1.70 % (1105129)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 8.23/1.70 % (1105129)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 8.23/1.70 % (1105129)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=1578715874:hsqr=1,8:i=1440:s2at=5:add=on:nm=2:rtra=on_2990 on theBenchmark for (2990ds/1440Mi)
% 8.23/1.70 % (1105118)Instruction limit reached!
% 8.23/1.70 % (1105118)------------------------------
% 8.23/1.70 % (1105118)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.23/1.70 % (1105118)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.23/1.70 % (1105118)CaDiCaL version: 2.1.3
% 8.23/1.70 % (1105118)Termination reason: Instruction limit
% 8.23/1.70 % (1105118)Termination phase: Saturation
% 8.23/1.70 % (1105118)Time elapsed: 0.108 s
% 8.23/1.70 % (1105118)Peak memory usage: 12 MB
% 8.23/1.70 % (1105118)Instructions burned: 271 (million)
% 8.23/1.70 % (1105130)dis+10_2_sil=128000:si=on:random_seed=1194554619:s2a=on:i=339:av=off:rtra=on:fe=abstraction:ss=axioms:fsd=on:ntd=on_2989 on theBenchmark for (2989ds/339Mi)
% 8.23/1.70 % (1105132)lrs+2_16:1_si=on:cbe=off:uwa=interpreted_only:random_seed=1857786869:i=111:add=on:fgj=on:rtra=on:fdi=1024_2989 on theBenchmark for (2989ds/111Mi)
% 8.23/1.70 % (1105132)Instruction limit reached!
% 8.23/1.70 % (1105132)------------------------------
% 8.23/1.70 % (1105132)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.23/1.70 % (1105132)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.23/1.70 % (1105132)CaDiCaL version: 2.1.3
% 8.23/1.70 % (1105132)Termination reason: Instruction limit
% 8.23/1.70 % (1105132)Termination phase: Saturation
% 8.23/1.70 % (1105132)Time elapsed: 0.045 s
% 8.23/1.70 % (1105132)Peak memory usage: 12 MB
% 8.23/1.70 % (1105132)Instructions burned: 112 (million)
% 8.23/1.70 % (1105135)dis+10_8_sil=128000:plsq=on:plsqc=1:si=on:sp=unary_first:sos=on:lma=off:plsqr=64,1:uwa=interpreted_only:foolp=on:random_seed=58100976:st=3:avsq=on:i=122:avsqr=8,1:sd=2:kws=precedence:bd=preordered:rtra=on:ss=axioms:ntd=on_2989 on theBenchmark for (2989ds/122Mi)
% 8.23/1.70 % (1105130)Instruction limit reached!
% 8.23/1.70 % (1105130)------------------------------
% 8.23/1.70 % (1105130)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.23/1.70 % (1105130)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.23/1.70 % (1105130)CaDiCaL version: 2.1.3
% 8.23/1.70 % (1105130)Termination reason: Instruction limit
% 8.23/1.70 % (1105130)Termination phase: Saturation
% 8.23/1.70 % (1105130)Time elapsed: 0.083 s
% 9.27/1.84 % (1105130)Peak memory usage: 13 MB
% 9.27/1.84 % (1105130)Instructions burned: 340 (million)
% 9.27/1.84 % (1105137)dis+1010_3:2_anc=all_dependent:sil=128000:si=on:sos=on:lma=off:spb=goal_then_units:bce=on:fd=off:random_seed=1275798439:uwa_fpi=on:avsq=on:i=136:avsqr=1,32:hud=15:nm=0:rtra=on:ntd=on_2989 on theBenchmark for (2989ds/136Mi)
% 9.27/1.84 % (1105116)Instruction limit reached!
% 9.27/1.84 % (1105116)------------------------------
% 9.27/1.84 % (1105116)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 9.27/1.84 % (1105116)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.27/1.84 % (1105116)CaDiCaL version: 2.1.3
% 9.27/1.84 % (1105116)Termination reason: Instruction limit
% 9.27/1.84 % (1105116)Termination phase: Saturation
% 9.27/1.84 % (1105116)Time elapsed: 0.228 s
% 9.27/1.84 % (1105116)Peak memory usage: 13 MB
% 9.27/1.84 % (1105116)Instructions burned: 575 (million)
% 9.27/1.84 % (1105123)Instruction limit reached!
% 9.27/1.84 % (1105123)------------------------------
% 9.27/1.84 % (1105123)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 9.27/1.84 % (1105123)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.27/1.84 % (1105123)CaDiCaL version: 2.1.3
% 9.27/1.84 % (1105123)Termination reason: Instruction limit
% 9.27/1.84 % (1105123)Termination phase: Saturation
% 9.27/1.84 % (1105123)Time elapsed: 0.180 s
% 9.27/1.84 % (1105123)Peak memory usage: 14 MB
% 9.27/1.84 % (1105123)Instructions burned: 422 (million)
% 9.27/1.84 % (1105139)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=3205931047:hsq=on:st=2:i=232:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2988 on theBenchmark for (2988ds/232Mi)
% 9.27/1.84 % (1105137)Instruction limit reached!
% 9.27/1.84 % (1105137)------------------------------
% 9.27/1.84 % (1105137)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 9.27/1.84 % (1105137)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.27/1.84 % (1105137)CaDiCaL version: 2.1.3
% 9.27/1.84 % (1105137)Termination reason: Instruction limit
% 9.27/1.84 % (1105137)Termination phase: Saturation
% 9.27/1.84 % (1105137)Time elapsed: 0.029 s
% 9.27/1.84 % (1105137)Peak memory usage: 12 MB
% 9.27/1.84 % (1105137)Instructions burned: 138 (million)
% 9.27/1.84 % (1105140)lrs+1010_8:1_sil=128000:tgt=ground:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:sos=on:plsqr=256,1:uwa=off:random_seed=2020029799:i=1254:kws=precedence:bd=preordered:av=off:rtra=on_2988 on theBenchmark for (2988ds/1254Mi)
% 9.27/1.84 % (1105143)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(discount) is equal to lrs
% 9.27/1.84 % (1105143)dis+1002_5:4_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_simp:si=on:plsqr=878,253:plsql=on:uwa=interpreted_only:lwlo=on:random_seed=1911893062:s2a=on:i=281:add=on:rtra=on:fe=axiom:fdi=1024_2988 on theBenchmark for (2988ds/281Mi)
% 9.27/1.84 % (1105135)Instruction limit reached!
% 9.27/1.84 % (1105135)------------------------------
% 9.27/1.84 % (1105135)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 9.27/1.84 % (1105135)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.27/1.84 % (1105135)CaDiCaL version: 2.1.3
% 9.27/1.84 % (1105135)Termination reason: Instruction limit
% 9.27/1.84 % (1105135)Termination phase: Saturation
% 9.27/1.84 % (1105135)Time elapsed: 0.053 s
% 9.27/1.84 % (1105135)Peak memory usage: 12 MB
% 9.27/1.84 % (1105135)Instructions burned: 127 (million)
% 9.27/1.84 % (1105145)dis+1010_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:sas=cadical:si=on:sos=all:uwa=off:sac=on:random_seed=2850851652:i=619:add=on:rtra=on_2988 on theBenchmark for (2988ds/619Mi)
% 9.27/1.84 % (1105143)Instruction limit reached!
% 9.27/1.84 % (1105143)------------------------------
% 9.27/1.84 % (1105143)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 9.27/1.84 % (1105143)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.27/1.84 % (1105143)CaDiCaL version: 2.1.3
% 9.27/1.84 % (1105143)Termination reason: Instruction limit
% 9.27/1.84 % (1105143)Termination phase: Saturation
% 9.27/1.84 % (1105143)Time elapsed: 0.060 s
% 9.27/1.84 % (1105143)Peak memory usage: 12 MB
% 9.27/1.84 % (1105143)Instructions burned: 285 (million)
% 9.27/1.84 % (1105147)ott+10_1_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:lma=off:plsqr=128,1:urr=ec_only:uwa=off:rp=on:nwc=20:br=off:random_seed=2634046539:i=865:bs=unit_only:ins=25:rtra=on:ntd=on_2987 on theBenchmark for (2987ds/865Mi)
% 9.27/1.88 % (1105139)Instruction limit reached!
% 9.27/1.88 % (1105139)------------------------------
% 9.27/1.88 % (1105139)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 9.27/1.88 % (1105139)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.27/1.88 % (1105139)CaDiCaL version: 2.1.3
% 9.27/1.88 % (1105139)Termination reason: Instruction limit
% 9.27/1.88 % (1105139)Termination phase: Saturation
% 9.27/1.88 % (1105139)Time elapsed: 0.124 s
% 9.27/1.88 % (1105139)Peak memory usage: 14 MB
% 9.27/1.88 % (1105139)Instructions burned: 232 (million)
% 9.27/1.88 % (1105149)lrs+10_1_sil=128000:si=on:urr=on:random_seed=3307287696:i=212:sd=1:rtra=on:ss=axioms:sgt=64_2987 on theBenchmark for (2987ds/212Mi)
% 9.27/1.88 % (1105147)Refutation not found, incomplete strategy
% 9.27/1.88 % (1105147)------------------------------
% 9.27/1.88 % (1105147)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 9.27/1.88 % (1105147)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.27/1.88 % (1105147)CaDiCaL version: 2.1.3
% 9.27/1.88 % (1105147)Termination reason: Refutation not found, incomplete strategy
% 9.27/1.88 % (1105147)Time elapsed: 0.071 s
% 9.27/1.88 % (1105147)Peak memory usage: 16 MB
% 9.27/1.88 % (1105147)Instructions burned: 316 (million)
% 9.27/1.88 % (1105147)------------------------------
% 9.27/1.88 % (1105147)------------------------------
% 9.27/1.88 % (1105151)lrs+1010_64_sil=128000:si=on:avsql=on:uwa=off:random_seed=1617515888:hsq=on:st=3:avsq=on:i=130:avsqr=1,16:sd=1:rtra=on:ss=axioms_2987 on theBenchmark for (2987ds/130Mi)
% 9.27/1.88 % (1105151)Instruction limit reached!
% 9.27/1.88 % (1105151)------------------------------
% 9.27/1.88 % (1105151)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 9.27/1.88 % (1105151)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.27/1.88 % (1105151)CaDiCaL version: 2.1.3
% 9.27/1.88 % (1105151)Termination reason: Instruction limit
% 9.27/1.88 % (1105151)Termination phase: Saturation
% 9.27/1.88 % (1105151)Time elapsed: 0.036 s
% 9.27/1.88 % (1105151)Peak memory usage: 13 MB
% 9.27/1.88 % (1105151)Instructions burned: 130 (million)
% 9.27/1.88 % (1105153)lrs+1002_1_cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:random_seed=3171476546:st=1.5:i=346:rtra=on:ss=axioms_2986 on theBenchmark for (2986ds/346Mi)
% 9.27/1.88 % (1105149)Instruction limit reached!
% 9.27/1.88 % (1105149)------------------------------
% 9.27/1.88 % (1105149)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 9.27/1.88 % (1105149)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.27/1.88 % (1105149)CaDiCaL version: 2.1.3
% 9.27/1.88 % (1105149)Termination reason: Instruction limit
% 9.27/1.88 % (1105149)Termination phase: Saturation
% 9.27/1.88 % (1105149)Time elapsed: 0.085 s
% 9.27/1.88 % (1105149)Peak memory usage: 12 MB
% 9.27/1.88 % (1105149)Instructions burned: 213 (million)
% 9.27/1.88 % (1105155)lrs+1010_3_sil=128000:si=on:slsq=on:random_seed=2546260051:avsq=on:i=152:avsqr=8,1:hud=5:ins=1:fsr=off:rtra=on_2986 on theBenchmark for (2986ds/152Mi)
% 9.27/1.88 % (1105145)Instruction limit reached!
% 9.27/1.88 % (1105145)------------------------------
% 9.27/1.88 % (1105145)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 9.27/1.88 % (1105145)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.27/1.88 % (1105145)CaDiCaL version: 2.1.3
% 9.27/1.88 % (1105145)Termination reason: Instruction limit
% 9.27/1.88 % (1105145)Termination phase: Saturation
% 9.27/1.88 % (1105145)Time elapsed: 0.275 s
% 9.27/1.88 % (1105145)Peak memory usage: 19 MB
% 9.27/1.88 % (1105145)Instructions burned: 621 (million)
% 9.27/1.88 % (1105155)Instruction limit reached!
% 9.27/1.88 % (1105155)------------------------------
% 9.27/1.88 % (1105155)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 9.27/1.88 % (1105155)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.27/1.88 % (1105155)CaDiCaL version: 2.1.3
% 9.27/1.88 % (1105155)Termination reason: Instruction limit
% 9.27/1.88 % (1105155)Termination phase: Saturation
% 9.27/1.88 % (1105155)Time elapsed: 0.062 s
% 9.27/1.88 % (1105155)Peak memory usage: 12 MB
% 9.27/1.88 % (1105155)Instructions burned: 152 (million)
% 9.27/1.88 % (1105153)Instruction limit reached!
% 9.27/1.88 % (1105153)------------------------------
% 9.27/1.88 % (1105153)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 9.27/1.88 % (1105153)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.27/1.88 % (1105153)CaDiCaL version: 2.1.3
% 9.27/1.88 % (1105153)Termination reason: Instruction limit
% 9.27/1.88 % (1105153)Termination phase: Saturation
% 9.27/1.88 % (1105153)Time elapsed: 0.094 s
% 9.27/1.88 % (1105153)Peak memory usage: 15 MB
% 9.27/1.88 % (1105153)Instructions burned: 349 (million)
% 9.27/1.88 % (1105158)dis+10_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=one_side_interpreted:nwc=5:random_seed=981594947:st=2.5:i=387:sd=2:rtra=on:ss=axioms_2985 on theBenchmark for (2985ds/387Mi)
% 9.27/1.88 % (1105157)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=2670225321:i=75:ep=R:rtra=on:ntd=on_2985 on theBenchmark for (2985ds/75Mi)
% 9.27/1.88 % (1105159)dis+1004_50_to=lpo:drc=off:fde=unused:cnfonf=lazy_not_gen_be_off:si=on:sp=reverse_arity:spb=units:cbe=off:foolp=on:random_seed=1800065578:uwa_fpi=on:i=148:doe=on:bd=preordered:rtra=on:fsd=on_2985 on theBenchmark for (2985ds/148Mi)
% 9.27/1.88 % (1105157)Instruction limit reached!
% 9.27/1.88 % (1105157)------------------------------
% 9.27/1.88 % (1105157)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 9.27/1.88 % (1105157)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.27/1.88 % (1105157)CaDiCaL version: 2.1.3
% 9.27/1.88 % (1105157)Termination reason: Instruction limit
% 9.27/1.88 % (1105157)Termination phase: Property scanning
% 9.27/1.88 % (1105157)Time elapsed: 0.031 s
% 9.27/1.88 % (1105157)Peak memory usage: 11 MB
% 9.27/1.88 % (1105157)Instructions burned: 76 (million)
% 9.27/1.88 % (1105163)dis+1010_3_si=on:uwa=one_side_interpreted:random_seed=785480828:i=161:piset=and:rtra=on:ntd=on_2985 on theBenchmark for (2985ds/161Mi)
% 9.27/1.88 % (1105140) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1104950-1105140"...
% 9.27/1.88 % (1105159)Instruction limit reached!
% 9.27/1.88 % (1105159)------------------------------
% 9.27/1.88 % (1105159)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 9.27/1.88 % (1105159)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.27/1.88 % (1105159)CaDiCaL version: 2.1.3
% 9.27/1.88 % (1105159)Termination reason: Instruction limit
% 9.27/1.88 % (1105159)Termination phase: Saturation
% 9.27/1.88 % (1105159)Time elapsed: 0.073 s
% 9.27/1.88 % (1105159)Peak memory usage: 13 MB
% 9.27/1.88 % (1105159)Instructions burned: 150 (million)
% 9.27/1.88 % (1105158)Instruction limit reached!
% 9.27/1.88 % (1105158)------------------------------
% 9.27/1.88 % (1105158)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 9.27/1.88 % (1105158)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.27/1.88 % (1105158)CaDiCaL version: 2.1.3
% 9.27/1.88 % (1105158)Termination reason: Instruction limit
% 9.27/1.88 % (1105158)Termination phase: Saturation
% 9.27/1.88 % (1105158)Time elapsed: 0.090 s
% 9.27/1.88 % (1105158)Peak memory usage: 16 MB
% 9.27/1.88 % (1105158)Instructions burned: 392 (million)
% 9.27/1.88 % (1105166)ott-1003_1_sil=128000:plsq=on:plsqc=1:si=on:sp=weighted_frequency:lma=off:plsqr=1,32:urr=on:cbe=off:random_seed=3147824973:i=136:add=on:ins=4:rtra=on:sup=off_2984 on theBenchmark for (2984ds/136Mi)
% 9.27/1.88 % (1105165)lrs+10_1_sil=128000:si=on:random_seed=1228793675:st=5:i=888:sd=3:bd=preordered:rtra=on:ss=axioms_2984 on theBenchmark for (2984ds/888Mi)
% 9.27/1.88 % (1105163)Instruction limit reached!
% 9.27/1.88 % (1105163)------------------------------
% 9.27/1.88 % (1105163)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 9.27/1.88 % (1105163)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.27/1.88 % (1105163)CaDiCaL version: 2.1.3
% 9.27/1.88 % (1105163)Termination reason: Instruction limit
% 9.27/1.88 % (1105163)Termination phase: Saturation
% 9.27/1.88 % (1105163)Time elapsed: 0.067 s
% 9.27/1.88 % (1105163)Peak memory usage: 13 MB
% 9.27/1.88 % (1105163)Instructions burned: 163 (million)
% 9.27/1.88 % (1105129)Instruction limit reached!
% 9.27/1.88 % (1105129)------------------------------
% 9.27/1.88 % (1105129)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 9.27/1.88 % (1105129)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.27/1.88 % (1105129)CaDiCaL version: 2.1.3
% 9.27/1.88 % (1105129)Termination reason: Instruction limit
% 9.27/1.88 % (1105129)Termination phase: Saturation
% 9.27/1.88 % (1105129)Time elapsed: 0.575 s
% 9.27/1.88 % (1105129)Peak memory usage: 14 MB
% 9.27/1.88 % (1105129)Instructions burned: 1442 (million)
% 9.27/1.88 % (1105166)Instruction limit reached!
% 9.27/1.88 % (1105166)------------------------------
% 9.27/1.88 % (1105166)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 9.27/1.88 % (1105166)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.27/1.88 % (1105166)CaDiCaL version: 2.1.3
% 9.27/1.88 % (1105166)Termination reason: Instruction limit
% 9.27/1.88 % (1105166)Termination phase: Saturation
% 9.27/1.88 % (1105166)Time elapsed: 0.029 s
% 9.27/1.88 % (1105166)Peak memory usage: 12 MB
% 9.27/1.88 % (1105166)Instructions burned: 137 (million)
% 9.27/1.88 % (1105171)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=3530121004:i=2186:rtra=on:ixr=off_2984 on theBenchmark for (2984ds/2186Mi)
% 9.27/1.88 % (1105169)lrs+1010_1_anc=none:slsqr=1,2:sil=128000:cnfonf=conj_eager:sas=cadical:si=on:hi=on:uwa=one_side_interpreted:rp=on:nwc=2:slsqc=3:slsq=on:random_seed=3642760665:i=88:s2at=3:nm=2:rtra=on:rawr=on_2984 on theBenchmark for (2984ds/88Mi)
% 9.27/1.88 % (1105170)dis+1002_5:4_to=kbo:sil=128000:cnfonf=conj_eager:si=on:sp=reverse_arity:lma=off:hi=on:nwc=20:random_seed=2357662238:s2a=on:cond=on:i=93:add=on:bd=preordered:rtra=on:er=filter_2984 on theBenchmark for (2984ds/93Mi)
% 9.27/1.88 % (1105140)...printing done.
% 9.27/1.88 % (1105140)Refutation found. Thanks to Tanya!
% 9.27/1.88 % SZS status Theorem for theBenchmark
% 9.27/1.88 % SZS output start Proof for theBenchmark
% 9.27/1.88 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 9.27/1.88 thf(func_def_0, type, c_Eps_i: (($i > $o) > $i)).
% 9.27/1.88 thf(func_def_1, type, c_False: $o).
% 9.27/1.88 thf(func_def_2, type, c_True: $o).
% 9.27/1.88 thf(func_def_3, type, c_not: ($o > $o)).
% 9.27/1.88 thf(func_def_4, type, c_and: ($o > $o > $o)).
% 9.27/1.88 thf(func_def_5, type, c_or: ($o > $o > $o)).
% 9.27/1.88 thf(func_def_6, type, c_iff: ($o > $o > $o)).
% 9.27/1.88 thf(func_def_7, type, c_In: ($i > $i > $o)).
% 9.27/1.88 thf(func_def_8, type, c_Subq: ($i > $i > $o)).
% 9.27/1.88 thf(func_def_10, type, c_Union: ($i > $i)).
% 9.27/1.88 thf(func_def_11, type, c_Power: ($i > $i)).
% 9.27/1.88 thf(func_def_12, type, c_Repl: ($i > ($i > $i) > $i)).
% 9.27/1.88 thf(func_def_13, type, c_TransSet: ($i > $o)).
% 9.27/1.88 thf(func_def_14, type, c_atleast2: ($i > $o)).
% 9.27/1.88 thf(func_def_15, type, c_atleast3: ($i > $o)).
% 9.27/1.88 thf(func_def_16, type, c_atleast4: ($i > $o)).
% 9.27/1.88 thf(func_def_17, type, c_atleast5: ($i > $o)).
% 9.27/1.88 thf(func_def_18, type, c_atleast6: ($i > $o)).
% 9.27/1.88 thf(func_def_19, type, c_exactly2: ($i > $o)).
% 9.27/1.88 thf(func_def_20, type, c_exactly3: ($i > $o)).
% 9.27/1.88 thf(func_def_21, type, c_exactly4: ($i > $o)).
% 9.27/1.88 thf(func_def_22, type, c_exactly5: ($i > $o)).
% 9.27/1.88 thf(func_def_23, type, c_exu_i: (($i > $o) > $o)).
% 9.27/1.88 thf(func_def_24, type, c_reflexive_i: (($i > $i > $o) > $o)).
% 9.27/1.88 thf(func_def_25, type, c_irreflexive_i: (($i > $i > $o) > $o)).
% 9.27/1.88 thf(func_def_26, type, c_symmetric_i: (($i > $i > $o) > $o)).
% 9.27/1.88 thf(func_def_27, type, c_antisymmetric_i: (($i > $i > $o) > $o)).
% 9.27/1.88 thf(func_def_28, type, c_transitive_i: (($i > $i > $o) > $o)).
% 9.27/1.88 thf(func_def_29, type, c_eqreln_i: (($i > $i > $o) > $o)).
% 9.27/1.88 thf(func_def_30, type, c_per_i: (($i > $i > $o) > $o)).
% 9.27/1.88 thf(func_def_31, type, c_linear_i: (($i > $i > $o) > $o)).
% 9.27/1.88 thf(func_def_32, type, c_trichotomous_or_i: (($i > $i > $o) > $o)).
% 9.27/1.88 thf(func_def_33, type, c_partialorder_i: (($i > $i > $o) > $o)).
% 9.27/1.88 thf(func_def_34, type, c_totalorder_i: (($i > $i > $o) > $o)).
% 9.27/1.88 thf(func_def_35, type, c_strictpartialorder_i: (($i > $i > $o) > $o)).
% 9.27/1.88 thf(func_def_36, type, c_stricttotalorder_i: (($i > $i > $o) > $o)).
% 9.27/1.88 thf(func_def_37, type, c_If_i: ($o > $i > $i > $i)).
% 9.27/1.88 thf(func_def_38, type, c_exactly1of2: ($o > $o > $o)).
% 9.27/1.88 thf(func_def_39, type, c_exactly1of3: ($o > $o > $o > $o)).
% 9.27/1.88 thf(func_def_40, type, c_nIn: ($i > $i > $o)).
% 9.27/1.88 thf(func_def_41, type, c_nSubq: ($i > $i > $o)).
% 9.27/1.88 thf(func_def_42, type, c_UPair: ($i > $i > $i)).
% 9.27/1.88 thf(func_def_43, type, c_Sing: ($i > $i)).
% 9.27/1.88 thf(func_def_44, type, c_binunion: ($i > $i > $i)).
% 9.27/1.88 thf(func_def_45, type, c_SetAdjoin: ($i > $i > $i)).
% 9.27/1.88 thf(func_def_46, type, c_famunion: ($i > ($i > $i) > $i)).
% 9.27/1.88 thf(func_def_47, type, c_Sep: ($i > ($i > $o) > $i)).
% 9.27/1.88 thf(func_def_48, type, c_ReplSep: ($i > ($i > $o) > ($i > $i) > $i)).
% 9.27/1.88 thf(func_def_49, type, c_binintersect: ($i > $i > $i)).
% 9.27/1.88 thf(func_def_50, type, c_setminus: ($i > $i > $i)).
% 9.27/1.88 thf(func_def_51, type, c_inj: ($i > $i > ($i > $i) > $o)).
% 9.27/1.88 thf(func_def_52, type, c_bij: ($i > $i > ($i > $i) > $o)).
% 9.27/1.88 thf(func_def_53, type, c_atleastp: ($i > $i > $o)).
% 9.27/1.88 thf(func_def_54, type, c_equip: ($i > $i > $o)).
% 9.27/1.88 thf(func_def_55, type, c_In_rec_poly_G_i: (($i > ($i > $i) > $i) > $i > $i > $o)).
% 9.27/1.88 thf(func_def_56, type, c_In_rec_poly_i: (($i > ($i > $i) > $i) > $i > $i)).
% 9.27/1.88 thf(func_def_57, type, c_ordsucc: ($i > $i)).
% 9.27/1.88 thf(func_def_58, type, c_nat_p: ($i > $o)).
% 9.27/1.88 thf(func_def_59, type, c_nat_primrec: ($i > ($i > $i > $i) > $i > $i)).
% 9.27/1.88 thf(func_def_60, type, c_add_nat: ($i > $i > $i)).
% 9.27/1.88 thf(func_def_61, type, c_mul_nat: ($i > $i > $i)).
% 9.27/1.88 thf(func_def_62, type, c_ordinal: ($i > $o)).
% 9.27/1.88 thf(func_def_63, type, c_V_: ($i > $i)).
% 9.27/1.88 thf(func_def_64, type, c_Inj1: ($i > $i)).
% 9.27/1.88 thf(func_def_65, type, c_Inj0: ($i > $i)).
% 9.27/1.88 thf(func_def_66, type, c_Unj: ($i > $i)).
% 9.27/1.88 thf(func_def_67, type, c_combine_funcs: ($i > $i > ($i > $i) > ($i > $i) > $i > $i)).
% 9.27/1.88 thf(func_def_68, type, c_setsum: ($i > $i > $i)).
% 9.27/1.88 thf(func_def_69, type, c_proj0: ($i > $i)).
% 9.27/1.88 thf(func_def_70, type, c_proj1: ($i > $i)).
% 9.27/1.88 thf(func_def_71, type, c_binrep: ($i > $i > $i)).
% 9.27/1.88 thf(func_def_72, type, c_lam: ($i > ($i > $i) > $i)).
% 9.27/1.88 thf(func_def_73, type, c_setprod: ($i > $i > $i)).
% 9.27/1.88 thf(func_def_74, type, c_ap: ($i > $i > $i)).
% 9.27/1.88 thf(func_def_75, type, c_setsum_p: ($i > $o)).
% 9.27/1.88 thf(func_def_76, type, c_tuple_p: ($i > $i > $o)).
% 9.27/1.88 thf(func_def_77, type, c_Pi: ($i > ($i > $i) > $i)).
% 9.27/1.88 thf(func_def_78, type, c_setexp: ($i > $i > $i)).
% 9.27/1.88 thf(func_def_79, type, c_Sep2: ($i > ($i > $i) > ($i > $i > $o) > $i)).
% 9.27/1.88 thf(func_def_80, type, c_set_of_pairs: ($i > $o)).
% 9.27/1.88 thf(func_def_81, type, c_lam2: ($i > ($i > $i) > ($i > $i > $i) > $i)).
% 9.27/1.88 thf(func_def_82, type, c_PNoEq_: ($i > ($i > $o) > ($i > $o) > $o)).
% 9.27/1.88 thf(func_def_83, type, c_PNoLt_: ($i > ($i > $o) > ($i > $o) > $o)).
% 9.27/1.88 thf(func_def_84, type, c_PNoLt: ($i > ($i > $o) > $i > ($i > $o) > $o)).
% 9.27/1.88 thf(func_def_85, type, c_PNoLe: ($i > ($i > $o) > $i > ($i > $o) > $o)).
% 9.27/1.88 thf(func_def_86, type, c_PNo_downc: (($i > ($i > $o) > $o) > $i > ($i > $o) > $o)).
% 9.27/1.88 thf(func_def_87, type, c_PNo_upc: (($i > ($i > $o) > $o) > $i > ($i > $o) > $o)).
% 9.27/1.88 thf(func_def_88, type, c_SNoElts_: ($i > $i)).
% 9.27/1.88 thf(func_def_89, type, c_SNo_: ($i > $i > $o)).
% 9.27/1.88 thf(func_def_90, type, c_PSNo: ($i > ($i > $o) > $i)).
% 9.27/1.88 thf(func_def_91, type, c_SNo: ($i > $o)).
% 9.27/1.88 thf(func_def_92, type, c_SNoLev: ($i > $i)).
% 9.27/1.88 thf(func_def_93, type, c_SNoEq_: ($i > $i > $i > $o)).
% 9.27/1.88 thf(func_def_94, type, c_SNoLt: ($i > $i > $o)).
% 9.27/1.88 thf(func_def_95, type, c_SNoLe: ($i > $i > $o)).
% 9.27/1.88 thf(func_def_96, type, c_binop_on: ($i > ($i > $i > $i) > $o)).
% 9.27/1.88 thf(func_def_97, type, c_Loop: ($i > ($i > $i > $i) > ($i > $i > $i) > ($i > $i > $i) > $i > $o)).
% 9.27/1.88 thf(func_def_98, type, c_Loop_with_defs: ($i > ($i > $i > $i) > ($i > $i > $i) > ($i > $i > $i) > $i > ($i > $i > $i) > ($i > $i > $i > $i) > ($i > $i > $i) > ($i > $i > $i > $i) > ($i > $i > $i > $i) > ($i > $i > $i) > ($i > $i > $i) > ($i > $i > $i) > ($i > $i > $i) > $o)).
% 9.27/1.88 thf(func_def_99, type, c_Loop_with_defs_cex1: ($i > ($i > $i > $i) > ($i > $i > $i) > ($i > $i > $i) > $i > ($i > $i > $i) > ($i > $i > $i > $i) > ($i > $i > $i) > ($i > $i > $i > $i) > ($i > $i > $i > $i) > ($i > $i > $i) > ($i > $i > $i) > ($i > $i > $i) > ($i > $i > $i) > $o)).
% 9.27/1.88 thf(func_def_100, type, c_Loop_with_defs_cex2: ($i > ($i > $i > $i) > ($i > $i > $i) > ($i > $i > $i) > $i > ($i > $i > $i) > ($i > $i > $i > $i) > ($i > $i > $i) > ($i > $i > $i > $i) > ($i > $i > $i > $i) > ($i > $i > $i) > ($i > $i > $i) > ($i > $i > $i) > ($i > $i > $i) > $o)).
% 9.27/1.88 thf(func_def_101, type, c_combinator: ($i > $o)).
% 9.27/1.88 thf(func_def_102, type, c_combinator_equiv: ($i > $i > $o)).
% 9.27/1.88 thf(func_def_103, type, c_equip_mod: ($i > $i > $i > $o)).
% 9.27/1.88 thf(func_def_105, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 9.27/1.88 thf(func_def_106, type, db2: !>[X0: $tType]:(X0)).
% 9.27/1.88 thf(func_def_107, type, db1: !>[X0: $tType]:(X0)).
% 9.27/1.88 thf(func_def_108, type, db0: !>[X0: $tType]:(X0)).
% 9.27/1.88 thf(func_def_109, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 9.27/1.88 thf(func_def_110, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 9.27/1.88 thf(func_def_111, type, vIMP: ($o > $o > $o)).
% 9.27/1.88 thf(func_def_112, type, db3: !>[X0: $tType]:(X0)).
% 9.27/1.88 thf(func_def_113, type, db4: !>[X0: $tType]:(X0)).
% 9.27/1.88 thf(func_def_114, type, db7: !>[X0: $tType]:(X0)).
% 9.27/1.88 thf(func_def_115, type, db5: !>[X0: $tType]:(X0)).
% 9.27/1.88 thf(func_def_116, type, db6: !>[X0: $tType]:(X0)).
% 9.27/1.88 thf(func_def_117, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 9.27/1.88 thf(func_def_120, type, db13: !>[X0: $tType]:(X0)).
% 9.27/1.88 thf(func_def_121, type, db12: !>[X0: $tType]:(X0)).
% 9.27/1.88 thf(func_def_122, type, db11: !>[X0: $tType]:(X0)).
% 9.27/1.88 thf(func_def_123, type, db10: !>[X0: $tType]:(X0)).
% 9.27/1.88 thf(func_def_124, type, db9: !>[X0: $tType]:(X0)).
% 9.27/1.88 thf(func_def_125, type, db14: !>[X0: $tType]:(X0)).
% 9.27/1.88 thf(func_def_126, type, db15: !>[X0: $tType]:(X0)).
% 9.27/1.88 thf(func_def_127, type, db16: !>[X0: $tType]:(X0)).
% 9.27/1.88 thf(func_def_128, type, db8: !>[X0: $tType]:(X0)).
% 9.27/1.88 thf(func_def_129, type, db17: !>[X0: $tType]:(X0)).
% 9.27/1.88 thf(func_def_130, type, db18: !>[X0: $tType]:(X0)).
% 9.27/1.88 thf(func_def_131, type, vNOT: ($o > $o)).
% 9.27/1.88 thf(func_def_144, type, sF12: $o).
% 9.27/1.88 thf(func_def_145, type, sF13: $o).
% 9.27/1.88 thf(func_def_146, type, sF14: $o).
% 9.27/1.88 thf(func_def_147, type, sK15: $o).
% 9.27/1.88 thf(f5,axiom,(
% 9.27/1.88 (c_not @ ? [X0 : $i] : (c_In @ X0 @ c_Empty))),
% 9.27/1.88 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax5)).
% 9.27/1.88 thf(f13,axiom,(
% 9.27/1.88 ((^[X0 : $o] : (X0 => c_False)) = c_not)),
% 9.27/1.88 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax13)).
% 9.27/1.88 thf(f14,axiom,(
% 9.27/1.88 ((^[X0 : $o, X1 : $o] : (! [X2 : $o] : ((X0 => (X1 => X2)) => X2))) = c_and)),
% 9.27/1.88 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax14)).
% 9.27/1.88 thf(f15,axiom,(
% 9.27/1.88 (c_or = (^[X0 : $o, X1 : $o] : (! [X2 : $o] : ((X0 => X2) => ((X1 => X2) => X2)))))),
% 9.27/1.88 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax15)).
% 9.27/1.88 thf(f17,axiom,(
% 9.27/1.88 ((^[X0 : $i, X1 : $i] : (! [X2 : $i] : ((c_In @ X2 @ X0) => (c_In @ X2 @ X1)))) = c_Subq)),
% 9.27/1.88 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax17)).
% 9.27/1.88 thf(f18,axiom,(
% 9.27/1.88 (c_TransSet = (^[X0 : $i] : (! [X1 : $i] : ((c_In @ X1 @ X0) => (c_Subq @ X1 @ X0)))))),
% 9.27/1.88 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax18)).
% 9.27/1.88 thf(f19,axiom,(
% 9.27/1.88 ((^[X0 : $i] : (? [X1 : $i] : (c_and @ (c_In @ X1 @ X0) @ (c_not @ (c_Subq @ X0 @ (c_Power @ X1)))))) = c_atleast2)),
% 9.27/1.88 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax19)).
% 9.27/1.88 thf(f20,axiom,(
% 9.27/1.88 (c_atleast3 = (^[X0 : $i] : (? [X1 : $i] : (c_and @ (c_Subq @ X1 @ X0) @ (c_and @ (c_not @ (c_Subq @ X0 @ X1)) @ (c_atleast2 @ X1))))))),
% 9.27/1.88 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax20)).
% 9.27/1.88 thf(f24,axiom,(
% 9.27/1.88 (c_exactly2 = (^[X0 : $i] : ((c_and @ (c_atleast2 @ X0) @ (c_not @ (c_atleast3 @ X0))))))),
% 9.27/1.88 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax24)).
% 9.27/1.88 thf(f42,axiom,(
% 9.27/1.88 (c_If_i = (^[X0 : $o, X1 : $i, X2 : $i] : ((c_Eps_i @ (^[X3 : $i] : ((c_or @ (c_and @ X0 @ (X3 = X1)) @ (c_and @ (c_not @ X0) @ (X3 = X2)))))))))),
% 9.27/1.88 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax42)).
% 9.27/1.88 thf(f43,axiom,(
% 9.27/1.88 ((^[X0 : $o, X1 : $o] : ((c_or @ (c_and @ X0 @ (c_not @ X1)) @ (c_and @ (c_not @ X0) @ X1)))) = c_exactly1of2)),
% 9.27/1.88 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax43)).
% 9.27/1.88 thf(f47,axiom,(
% 9.27/1.88 (c_UPair = (^[X0 : $i, X1 : $i] : ((c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[X2 : $i] : ((c_If_i @ (c_In @ c_Empty @ X2) @ X0 @ X1)))))))),
% 9.27/1.88 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax47)).
% 9.27/1.88 thf(f48,axiom,(
% 9.27/1.88 ((^[X0 : $i] : ((c_UPair @ X0 @ X0))) = c_Sing)),
% 9.27/1.88 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax48)).
% 9.27/1.88 thf(f49,axiom,(
% 9.27/1.88 ((^[X0 : $i, X1 : $i] : ((c_Union @ (c_UPair @ X0 @ X1)))) = c_binunion)),
% 9.27/1.88 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax49)).
% 9.27/1.88 thf(f50,axiom,(
% 9.27/1.88 ((^[X0 : $i, X1 : $i] : ((c_binunion @ X0 @ (c_Sing @ X1)))) = c_SetAdjoin)),
% 9.27/1.88 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax50)).
% 9.27/1.88 thf(f51,axiom,(
% 9.27/1.88 ((^[X0 : $i, X1 : ($i > $i)] : ((c_Union @ (c_Repl @ X0 @ (^[X2 : $i] : ((X1 @ X2))))))) = c_famunion)),
% 9.27/1.88 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax51)).
% 9.27/1.88 thf(f52,axiom,(
% 9.27/1.88 ((^[X0 : $i, X1 : ($i > $o)] : ((c_If_i @ ? [X2 : $i] : (c_and @ (c_In @ X2 @ X0) @ (X1 @ X2)) @ (c_Repl @ X0 @ (^[X2 : $i] : (((^[X3 : $i] : ((c_If_i @ (X1 @ X3) @ X3 @ (c_Eps_i @ (^[X4 : $i] : ((c_and @ (c_In @ X4 @ X0) @ (X1 @ X4)))))))) @ X2)))) @ c_Empty))) = c_Sep)),
% 9.27/1.88 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax52)).
% 9.27/1.88 thf(f54,axiom,(
% 9.27/1.88 ((^[X0 : $i, X1 : $i] : ((c_Sep @ X0 @ (^[X2 : $i] : ((c_In @ X2 @ X1)))))) = c_binintersect)),
% 9.27/1.88 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax54)).
% 9.27/1.88 thf(f60,axiom,(
% 9.27/1.88 (c_In_rec_poly_G_i = (^[X0 : ($i > ($i > $i) > $i), X1 : $i, X2 : $i] : (! [X3 : ($i > $i > $o)] : (! [X4 : $i,X5 : ($i > $i)] : (! [X6 : $i] : ((c_In @ X6 @ X4) => (X3 @ X6 @ (X5 @ X6))) => (X3 @ X4 @ (X0 @ X4 @ X5))) => (X3 @ X1 @ X2)))))),
% 9.27/1.88 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax60)).
% 9.27/1.88 thf(f61,axiom,(
% 9.27/1.88 ((^[X0 : ($i > ($i > $i) > $i), X1 : $i] : ((c_Eps_i @ (^[X2 : $i] : ((c_In_rec_poly_G_i @ X0 @ X1 @ X2)))))) = c_In_rec_poly_i)),
% 9.27/1.88 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax61)).
% 9.27/1.88 thf(f62,axiom,(
% 9.27/1.88 (c_ordsucc = (^[X0 : $i] : ((c_binunion @ X0 @ (c_Sing @ X0)))))),
% 9.27/1.88 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax62)).
% 9.27/1.88 thf(f67,axiom,(
% 9.27/1.88 (c_ordinal = (^[X0 : $i] : ((c_and @ (c_TransSet @ X0) @ ! [X1 : $i] : ((c_In @ X1 @ X0) => (c_TransSet @ X1))))))),
% 9.27/1.88 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax67)).
% 9.27/1.88 thf(f69,axiom,(
% 9.27/1.88 (((c_In_rec_poly_i @ (^[X0 : $i, X1 : ($i > $i)] : ((c_binunion @ (c_Sing @ c_Empty) @ (c_Repl @ X0 @ (^[X2 : $i] : ((X1 @ X2))))))))) = c_Inj1)),
% 9.27/1.88 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax69)).
% 9.27/1.88 thf(f70,axiom,(
% 9.27/1.88 ((^[X0 : $i] : ((c_Repl @ X0 @ (^[X1 : $i] : ((c_Inj1 @ X1)))))) = c_Inj0)),
% 9.27/1.88 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax70)).
% 9.27/1.88 thf(f73,axiom,(
% 9.27/1.88 (c_setsum = (^[X0 : $i, X1 : $i] : ((c_binunion @ (c_Repl @ X0 @ (^[X2 : $i] : ((c_Inj0 @ X2)))) @ (c_Repl @ X1 @ (^[X2 : $i] : ((c_Inj1 @ X2))))))))),
% 9.27/1.88 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax73)).
% 9.27/1.88 thf(f76,axiom,(
% 9.27/1.88 ((^[X0 : $i, X1 : $i] : ((c_setsum @ X0 @ (c_Power @ X1)))) = c_binrep)),
% 9.27/1.88 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax76)).
% 9.27/1.88 thf(f77,axiom,(
% 9.27/1.88 ((^[X0 : $i, X1 : ($i > $i)] : ((c_famunion @ X0 @ (^[X2 : $i] : ((c_Repl @ (X1 @ X2) @ (^[X3 : $i] : ((c_setsum @ X2 @ X3))))))))) = c_lam)),
% 9.27/1.88 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax77)).
% 9.27/1.88 thf(f78,axiom,(
% 9.27/1.88 ((^[X0 : $i, X1 : $i] : ((c_lam @ X0 @ (^[X2 : $i] : (X1))))) = c_setprod)),
% 9.27/1.88 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax78)).
% 9.27/1.88 thf(f93,axiom,(
% 9.27/1.88 (c_SNoElts_ = (^[X0 : $i] : ((c_binunion @ X0 @ (c_Repl @ X0 @ (^[X1 : $i] : (((^[X2 : $i] : ((c_SetAdjoin @ X2 @ (c_Sing @ (c_ordsucc @ c_Empty))))) @ X1))))))))),
% 9.27/1.88 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax93)).
% 9.27/1.88 thf(f94,axiom,(
% 9.27/1.88 (c_SNo_ = (^[X0 : $i, X1 : $i] : ((c_and @ (c_Subq @ X1 @ (c_SNoElts_ @ X0)) @ ! [X2 : $i] : ((c_In @ X2 @ X0) => (c_exactly1of2 @ (c_In @ ((^[X3 : $i] : ((c_SetAdjoin @ X3 @ (c_Sing @ (c_ordsucc @ c_Empty))))) @ X2) @ X1) @ (c_In @ X2 @ X1)))))))),
% 9.27/1.88 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax94)).
% 9.27/1.88 thf(f96,axiom,(
% 9.27/1.88 (c_SNo = (^[X0 : $i] : (? [X1 : $i] : (c_and @ (c_ordinal @ X1) @ (c_SNo_ @ X1 @ X0)))))),
% 9.27/1.88 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax96)).
% 9.27/1.88 thf(f109,conjecture,(
% 9.27/1.88 (c_not @ ! [X0 : ($i > $o),X1 : ($i > $i)] : (c_and @ ((X0 @ (X1 @ (c_binintersect @ (X1 @ (c_Power @ c_Empty)) @ (X1 @ (c_binrep @ (c_Power @ (c_Power @ (c_Power @ c_Empty))) @ c_Empty))))) => ((c_TransSet @ (X1 @ c_Empty)) => ! [X2 : $i] : ((c_In @ X2 @ c_Empty) => ? [X3 : $i] : (c_and @ (c_Subq @ X3 @ X2) @ (c_exactly2 @ (c_ordsucc @ (X1 @ X3))))))) => ? [X2 : $i] : (c_and @ ? [X3 : $i] : (c_and @ (c_Subq @ X3 @ X2) @ (X2 = ((X1 @ X2))) => ? [X4 : $i] : (c_and @ (c_Subq @ X4 @ X2) @ (c_not @ (X0 @ (c_setprod @ X3 @ (c_binrep @ (c_Power @ (c_binrep @ (c_Power @ (c_Power @ c_Empty)) @ c_Empty)) @ (c_Power @ (c_Power @ c_Empty)))))))) @ (c_not @ (c_SNo @ X2))) @ (c_not @ (X0 @ (X1 @ (X1 @ (X1 @ (c_binrep @ (c_binrep @ (c_Power @ (c_binrep @ (c_Power @ (c_Power @ c_Empty)) @ c_Empty)) @ (c_Power @ c_Empty)) @ c_Empty))))))))),
% 9.27/1.88 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj)).
% 9.27/1.88 thf(f110,negated_conjecture,(
% 9.27/1.88 ~(c_not @ ! [X0 : ($i > $o),X1 : ($i > $i)] : (c_and @ ((X0 @ (X1 @ (c_binintersect @ (X1 @ (c_Power @ c_Empty)) @ (X1 @ (c_binrep @ (c_Power @ (c_Power @ (c_Power @ c_Empty))) @ c_Empty))))) => ((c_TransSet @ (X1 @ c_Empty)) => ! [X2 : $i] : ((c_In @ X2 @ c_Empty) => ? [X3 : $i] : (c_and @ (c_Subq @ X3 @ X2) @ (c_exactly2 @ (c_ordsucc @ (X1 @ X3))))))) => ? [X2 : $i] : (c_and @ ? [X3 : $i] : (c_and @ (c_Subq @ X3 @ X2) @ (X2 = ((X1 @ X2))) => ? [X4 : $i] : (c_and @ (c_Subq @ X4 @ X2) @ (c_not @ (X0 @ (c_setprod @ X3 @ (c_binrep @ (c_Power @ (c_binrep @ (c_Power @ (c_Power @ c_Empty)) @ c_Empty)) @ (c_Power @ (c_Power @ c_Empty)))))))) @ (c_not @ (c_SNo @ X2))) @ (c_not @ (X0 @ (X1 @ (X1 @ (X1 @ (c_binrep @ (c_binrep @ (c_Power @ (c_binrep @ (c_Power @ (c_Power @ c_Empty)) @ c_Empty)) @ (c_Power @ c_Empty)) @ c_Empty))))))))),
% 9.27/1.88 inference(negated_conjecture,[status(cth)],[f109])).
% 9.27/1.88 thf(f113,plain,(
% 9.27/1.88 (c_or = (^[X0 : $o, X1 : $o] : (! [X2 : $o] : ((X0 => X2) => ((X1 => X2) => X2)))))),
% 9.27/1.88 inference(rectify,[],[f15])).
% 9.27/1.88 thf(f114,plain,(
% 9.27/1.88 (c_or = (^[Y0 : $o]: ((^[Y1 : $o]: (!! @ $o @ (^[Y2 : $o]: ((Y0 => Y2) => ((Y1 => Y2) => Y2))))))))),
% 9.27/1.88 inference(fool_elimination,[],[f113])).
% 9.27/1.88 thf(f132,plain,(
% 9.27/1.88 (c_UPair = (^[X0 : $i, X1 : $i] : ((c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[X2 : $i] : ((c_If_i @ (c_In @ c_Empty @ X2) @ X0 @ X1)))))))),
% 9.27/1.88 inference(rectify,[],[f47])).
% 9.27/1.88 thf(f133,plain,(
% 9.27/1.88 (c_UPair = (^[Y0 : $i]: ((^[Y1 : $i]: (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y2 : $i]: (c_If_i @ (c_In @ c_Empty @ Y2) @ Y0 @ Y1)))))))),
% 9.27/1.88 inference(fool_elimination,[],[f132])).
% 9.27/1.88 thf(f148,plain,(
% 9.27/1.88 ((^[X0 : $i] : (? [X1 : $i] : (c_and @ (c_In @ X1 @ X0) @ (c_not @ (c_Subq @ X0 @ (c_Power @ X1)))))) = c_atleast2)),
% 9.27/1.88 inference(rectify,[],[f19])).
% 9.27/1.88 thf(f149,plain,(
% 9.27/1.88 (c_atleast2 = (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (c_and @ (c_In @ Y1 @ Y0) @ (c_not @ (c_Subq @ Y0 @ (c_Power @ Y1))))))))),
% 9.27/1.88 inference(fool_elimination,[],[f148])).
% 9.27/1.88 thf(f155,plain,(
% 9.27/1.88 (c_ordsucc = (^[Y0 : $i]: (c_binunion @ Y0 @ (c_Sing @ Y0))))),
% 9.27/1.88 inference(fool_elimination,[],[f62])).
% 9.27/1.88 thf(f162,plain,(
% 9.27/1.88 ((^[X0 : $i, X1 : $i] : ((c_lam @ X0 @ (^[X2 : $i] : (X1))))) = c_setprod)),
% 9.27/1.88 inference(rectify,[],[f78])).
% 9.27/1.88 thf(f163,plain,(
% 9.27/1.88 (c_setprod = (^[Y0 : $i]: ((^[Y1 : $i]: (c_lam @ Y0 @ (^[Y2 : $i]: (Y1)))))))),
% 9.27/1.88 inference(fool_elimination,[],[f162])).
% 9.27/1.88 thf(f176,plain,(
% 9.27/1.88 (c_SNo = (^[X0 : $i] : (? [X1 : $i] : (c_and @ (c_ordinal @ X1) @ (c_SNo_ @ X1 @ X0)))))),
% 9.27/1.88 inference(rectify,[],[f96])).
% 9.27/1.88 thf(f177,plain,(
% 9.27/1.88 (c_SNo = (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (c_and @ (c_ordinal @ Y1) @ (c_SNo_ @ Y1 @ Y0))))))),
% 9.27/1.88 inference(fool_elimination,[],[f176])).
% 9.27/1.88 thf(f180,plain,(
% 9.27/1.88 (c_binrep = (^[Y0 : $i]: ((^[Y1 : $i]: (c_setsum @ Y0 @ (c_Power @ Y1))))))),
% 9.27/1.88 inference(fool_elimination,[],[f76])).
% 9.27/1.88 thf(f183,plain,(
% 9.27/1.88 ((^[X0 : $i, X1 : ($i > $o)] : ((c_If_i @ ? [X2 : $i] : (c_and @ (c_In @ X2 @ X0) @ (X1 @ X2)) @ (c_Repl @ X0 @ (^[X3 : $i] : (((^[X4 : $i] : ((c_If_i @ (X1 @ X4) @ X4 @ (c_Eps_i @ (^[X5 : $i] : ((c_and @ (c_In @ X5 @ X0) @ (X1 @ X5)))))))) @ X3)))) @ c_Empty))) = c_Sep)),
% 9.27/1.88 inference(rectify,[],[f52])).
% 9.27/1.88 thf(f184,plain,(
% 9.27/1.88 (c_Sep = (^[Y0 : $i]: ((^[Y1 : $i > $o]: (c_If_i @ (?? @ $i @ (^[Y2 : $i]: (c_and @ (c_In @ Y2 @ Y0) @ (Y1 @ Y2)))) @ (c_Repl @ Y0 @ (^[Y2 : $i]: ((^[Y3 : $i]: (c_If_i @ (Y1 @ Y3) @ Y3 @ (c_Eps_i @ (^[Y4 : $i]: (c_and @ (c_In @ Y4 @ Y0) @ (Y1 @ Y4)))))) @ Y2))) @ c_Empty)))))),
% 9.27/1.88 inference(fool_elimination,[],[f183])).
% 9.27/1.88 thf(f190,plain,(
% 9.27/1.88 (c_ordinal = (^[X0 : $i] : ((c_and @ (c_TransSet @ X0) @ ! [X1 : $i] : ((c_In @ X1 @ X0) => (c_TransSet @ X1))))))),
% 9.27/1.88 inference(rectify,[],[f67])).
% 9.27/1.88 thf(f191,plain,(
% 9.27/1.88 (c_ordinal = (^[Y0 : $i]: (c_and @ (c_TransSet @ Y0) @ (!! @ $i @ (^[Y1 : $i]: ((c_In @ Y1 @ Y0) => (c_TransSet @ Y1)))))))),
% 9.27/1.88 inference(fool_elimination,[],[f190])).
% 9.27/1.88 thf(f194,plain,(
% 9.27/1.88 (c_TransSet = (^[X0 : $i] : (! [X1 : $i] : ((c_In @ X1 @ X0) => (c_Subq @ X1 @ X0)))))),
% 9.27/1.88 inference(rectify,[],[f18])).
% 9.27/1.88 thf(f195,plain,(
% 9.27/1.88 (c_TransSet = (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((c_In @ Y1 @ Y0) => (c_Subq @ Y1 @ Y0))))))),
% 9.27/1.88 inference(fool_elimination,[],[f194])).
% 9.27/1.88 thf(f196,plain,(
% 9.27/1.88 (((c_In_rec_poly_i @ (^[X0 : $i, X1 : ($i > $i)] : ((c_binunion @ (c_Sing @ c_Empty) @ (c_Repl @ X0 @ (^[X2 : $i] : ((X1 @ X2))))))))) = c_Inj1)),
% 9.27/1.88 inference(rectify,[],[f69])).
% 9.27/1.88 thf(f197,plain,(
% 9.27/1.88 (c_Inj1 = ((c_In_rec_poly_i @ (^[Y0 : $i]: ((^[Y1 : $i > $i]: (c_binunion @ (c_Sing @ c_Empty) @ (c_Repl @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))))))))))),
% 9.27/1.88 inference(fool_elimination,[],[f196])).
% 9.27/1.88 thf(f204,plain,(
% 9.27/1.88 (c_setsum = (^[X0 : $i, X1 : $i] : ((c_binunion @ (c_Repl @ X0 @ (^[X2 : $i] : ((c_Inj0 @ X2)))) @ (c_Repl @ X1 @ (^[X3 : $i] : ((c_Inj1 @ X3))))))))),
% 9.27/1.88 inference(rectify,[],[f73])).
% 9.27/1.88 thf(f205,plain,(
% 9.27/1.88 (c_setsum = (^[Y0 : $i]: ((^[Y1 : $i]: (c_binunion @ (c_Repl @ Y0 @ (^[Y2 : $i]: (c_Inj0 @ Y2))) @ (c_Repl @ Y1 @ (^[Y2 : $i]: (c_Inj1 @ Y2))))))))),
% 9.27/1.88 inference(fool_elimination,[],[f204])).
% 9.27/1.88 thf(f206,plain,(
% 9.27/1.88 (c_SetAdjoin = (^[Y0 : $i]: ((^[Y1 : $i]: (c_binunion @ Y0 @ (c_Sing @ Y1))))))),
% 9.27/1.88 inference(fool_elimination,[],[f50])).
% 9.27/1.88 thf(f211,plain,(
% 9.27/1.88 (c_Sing = (^[Y0 : $i]: (c_UPair @ Y0 @ Y0)))),
% 9.27/1.88 inference(fool_elimination,[],[f48])).
% 9.27/1.88 thf(f214,plain,(
% 9.27/1.88 ((^[X0 : ($i > ($i > $i) > $i), X1 : $i] : ((c_Eps_i @ (^[X2 : $i] : ((c_In_rec_poly_G_i @ X0 @ X1 @ X2)))))) = c_In_rec_poly_i)),
% 9.27/1.88 inference(rectify,[],[f61])).
% 9.27/1.88 thf(f215,plain,(
% 9.27/1.88 (c_In_rec_poly_i = (^[Y0 : $i > ($i > $i) > $i]: ((^[Y1 : $i]: (c_Eps_i @ (^[Y2 : $i]: (c_In_rec_poly_G_i @ Y0 @ Y1 @ Y2)))))))),
% 9.27/1.88 inference(fool_elimination,[],[f214])).
% 9.27/1.88 thf(f216,plain,(
% 9.27/1.88 ((^[X0 : $i] : ((c_Repl @ X0 @ (^[X1 : $i] : ((c_Inj1 @ X1)))))) = c_Inj0)),
% 9.27/1.88 inference(rectify,[],[f70])).
% 9.27/1.88 thf(f217,plain,(
% 9.27/1.88 (c_Inj0 = (^[Y0 : $i]: (c_Repl @ Y0 @ (^[Y1 : $i]: (c_Inj1 @ Y1)))))),
% 9.27/1.88 inference(fool_elimination,[],[f216])).
% 9.27/1.88 thf(f227,plain,(
% 9.27/1.88 (c_binunion = (^[Y0 : $i]: ((^[Y1 : $i]: (c_Union @ (c_UPair @ Y0 @ Y1))))))),
% 9.27/1.88 inference(fool_elimination,[],[f49])).
% 9.27/1.88 thf(f238,plain,(
% 9.27/1.88 ((^[X0 : $o, X1 : $o] : (! [X2 : $o] : ((X0 => (X1 => X2)) => X2))) = c_and)),
% 9.27/1.88 inference(rectify,[],[f14])).
% 9.27/1.88 thf(f239,plain,(
% 9.27/1.88 (c_and = (^[Y0 : $o]: ((^[Y1 : $o]: (!! @ $o @ (^[Y2 : $o]: ((Y0 => (Y1 => Y2)) => Y2)))))))),
% 9.27/1.88 inference(fool_elimination,[],[f238])).
% 9.27/1.88 thf(f240,plain,(
% 9.27/1.88 (c_In_rec_poly_G_i = (^[X0 : ($i > ($i > $i) > $i), X1 : $i, X2 : $i] : (! [X3 : ($i > $i > $o)] : (! [X4 : $i,X5 : ($i > $i)] : (! [X6 : $i] : ((c_In @ X6 @ X4) => (X3 @ X6 @ (X5 @ X6))) => (X3 @ X4 @ (X0 @ X4 @ X5))) => (X3 @ X1 @ X2)))))),
% 9.27/1.88 inference(rectify,[],[f60])).
% 9.27/1.88 thf(f241,plain,(
% 9.27/1.88 (c_In_rec_poly_G_i = (^[Y0 : $i > ($i > $i) > $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: ((!! @ ($i > $i) @ (^[Y4 : $i > $i]: (!! @ $i @ (^[Y5 : $i]: ((!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ Y5) => (Y3 @ Y6 @ (Y4 @ Y6))))) => (Y3 @ Y5 @ (Y0 @ Y5 @ Y4))))))) => (Y3 @ Y1 @ Y2))))))))))),
% 9.27/1.88 inference(fool_elimination,[],[f240])).
% 9.27/1.88 thf(f243,plain,(
% 9.27/1.88 (c_exactly2 = (^[Y0 : $i]: (c_and @ (c_atleast2 @ Y0) @ (c_not @ (c_atleast3 @ Y0)))))),
% 9.27/1.88 inference(fool_elimination,[],[f24])).
% 9.27/1.88 thf(f249,plain,(
% 9.27/1.88 ((^[X0 : $i, X1 : ($i > $i)] : ((c_Union @ (c_Repl @ X0 @ (^[X2 : $i] : ((X1 @ X2))))))) = c_famunion)),
% 9.27/1.88 inference(rectify,[],[f51])).
% 9.27/1.88 thf(f250,plain,(
% 9.27/1.88 (c_famunion = (^[Y0 : $i]: ((^[Y1 : $i > $i]: (c_Union @ (c_Repl @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))))))))),
% 9.27/1.88 inference(fool_elimination,[],[f249])).
% 9.27/1.88 thf(f251,plain,(
% 9.27/1.88 (c_atleast3 = (^[X0 : $i] : (? [X1 : $i] : (c_and @ (c_Subq @ X1 @ X0) @ (c_and @ (c_not @ (c_Subq @ X0 @ X1)) @ (c_atleast2 @ X1))))))),
% 9.27/1.88 inference(rectify,[],[f20])).
% 9.27/1.88 thf(f252,plain,(
% 9.27/1.88 (c_atleast3 = (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (c_and @ (c_Subq @ Y1 @ Y0) @ (c_and @ (c_not @ (c_Subq @ Y0 @ Y1)) @ (c_atleast2 @ Y1)))))))),
% 9.27/1.88 inference(fool_elimination,[],[f251])).
% 9.27/1.88 thf(f255,plain,(
% 9.27/1.88 (c_not @ ? [X0 : $i] : (c_In @ X0 @ c_Empty))),
% 9.27/1.88 inference(rectify,[],[f5])).
% 9.27/1.88 thf(f256,plain,(
% 9.27/1.88 ($true = ((c_not @ (?? @ $i @ (^[Y0 : $i]: (c_In @ Y0 @ c_Empty))))))),
% 9.27/1.88 inference(fool_elimination,[],[f255])).
% 9.27/1.88 thf(f265,plain,(
% 9.27/1.88 ~(c_not @ ! [X0 : ($i > $o),X1 : ($i > $i)] : (c_and @ ((X0 @ (X1 @ (c_binintersect @ (X1 @ (c_Power @ c_Empty)) @ (X1 @ (c_binrep @ (c_Power @ (c_Power @ (c_Power @ c_Empty))) @ c_Empty))))) => ((c_TransSet @ (X1 @ c_Empty)) => ! [X2 : $i] : ((c_In @ X2 @ c_Empty) => ? [X3 : $i] : (c_and @ (c_Subq @ X3 @ X2) @ (c_exactly2 @ (c_ordsucc @ (X1 @ X3))))))) => ? [X4 : $i] : (c_and @ ? [X5 : $i] : (c_and @ (c_Subq @ X5 @ X4) @ (((X1 @ X4)) = X4) => ? [X6 : $i] : (c_and @ (c_Subq @ X6 @ X4) @ (c_not @ (X0 @ (c_setprod @ X5 @ (c_binrep @ (c_Power @ (c_binrep @ (c_Power @ (c_Power @ c_Empty)) @ c_Empty)) @ (c_Power @ (c_Power @ c_Empty)))))))) @ (c_not @ (c_SNo @ X4))) @ (c_not @ (X0 @ (X1 @ (X1 @ (X1 @ (c_binrep @ (c_binrep @ (c_Power @ (c_binrep @ (c_Power @ (c_Power @ c_Empty)) @ c_Empty)) @ (c_Power @ c_Empty)) @ c_Empty))))))))),
% 9.27/1.88 inference(rectify,[],[f110])).
% 9.27/1.88 thf(f266,plain,(
% 9.27/1.88 ($true = ((~ (c_not @ (!! @ ($i > $i) @ (^[Y0 : $i > $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (c_and @ (((Y1 @ (Y0 @ (c_binintersect @ (Y0 @ (c_Power @ c_Empty)) @ (Y0 @ (c_binrep @ (c_Power @ (c_Power @ (c_Power @ c_Empty))) @ c_Empty))))) => ((c_TransSet @ (Y0 @ c_Empty)) => (!! @ $i @ (^[Y2 : $i]: ((c_In @ Y2 @ c_Empty) => (?? @ $i @ (^[Y3 : $i]: (c_and @ (c_Subq @ Y3 @ Y2) @ (c_exactly2 @ (c_ordsucc @ (Y0 @ Y3))))))))))) => (?? @ $i @ (^[Y2 : $i]: (c_and @ (?? @ $i @ (^[Y3 : $i]: (c_and @ (c_Subq @ Y3 @ Y2) @ (((Y0 @ Y2) = Y2) => (?? @ $i @ (^[Y4 : $i]: (c_and @ (c_Subq @ Y4 @ Y2) @ (c_not @ (Y1 @ (c_setprod @ Y3 @ (c_binrep @ (c_Power @ (c_binrep @ (c_Power @ (c_Power @ c_Empty)) @ c_Empty)) @ (c_Power @ (c_Power @ c_Empty))))))))))))) @ (c_not @ (c_SNo @ Y2)))))) @ (c_not @ (Y1 @ (Y0 @ (Y0 @ (Y0 @ (c_binrep @ (c_binrep @ (c_Power @ (c_binrep @ (c_Power @ (c_Power @ c_Empty)) @ c_Empty)) @ (c_Power @ c_Empty)) @ c_Empty)))))))))))))))),
% 9.27/1.88 inference(fool_elimination,[],[f265])).
% 9.27/1.88 thf(f277,plain,(
% 9.27/1.88 ((^[X0 : $i, X1 : $i] : ((c_Sep @ X0 @ (^[X2 : $i] : ((c_In @ X2 @ X1)))))) = c_binintersect)),
% 9.27/1.88 inference(rectify,[],[f54])).
% 9.27/1.88 thf(f278,plain,(
% 9.27/1.88 (c_binintersect = (^[Y0 : $i]: ((^[Y1 : $i]: (c_Sep @ Y0 @ (^[Y2 : $i]: (c_In @ Y2 @ Y1)))))))),
% 9.27/1.88 inference(fool_elimination,[],[f277])).
% 9.27/1.88 thf(f281,plain,(
% 9.27/1.88 (c_If_i = (^[X0 : $o, X1 : $i, X2 : $i] : ((c_Eps_i @ (^[X3 : $i] : ((c_or @ (c_and @ X0 @ (X3 = X1)) @ (c_and @ (c_not @ X0) @ (X3 = X2)))))))))),
% 9.27/1.88 inference(rectify,[],[f42])).
% 9.27/1.88 thf(f282,plain,(
% 9.27/1.88 (c_If_i = (^[Y0 : $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (c_Eps_i @ (^[Y3 : $i]: (c_or @ (c_and @ Y0 @ (Y1 = Y3)) @ (c_and @ (c_not @ Y0) @ (Y2 = Y3)))))))))))),
% 9.27/1.88 inference(fool_elimination,[],[f281])).
% 9.27/1.88 thf(f287,plain,(
% 9.27/1.88 ((^[X0 : $i, X1 : ($i > $i)] : ((c_famunion @ X0 @ (^[X2 : $i] : ((c_Repl @ (X1 @ X2) @ (^[X3 : $i] : ((c_setsum @ X2 @ X3))))))))) = c_lam)),
% 9.27/1.88 inference(rectify,[],[f77])).
% 9.27/1.88 thf(f288,plain,(
% 9.27/1.88 (c_lam = (^[Y0 : $i]: ((^[Y1 : $i > $i]: (c_famunion @ Y0 @ (^[Y2 : $i]: (c_Repl @ (Y1 @ Y2) @ (^[Y3 : $i]: (c_setsum @ Y2 @ Y3)))))))))),
% 9.27/1.88 inference(fool_elimination,[],[f287])).
% 9.27/1.88 thf(f289,plain,(
% 9.27/1.88 (c_exactly1of2 = (^[Y0 : $o]: ((^[Y1 : $o]: (c_or @ (c_and @ Y0 @ (c_not @ Y1)) @ (c_and @ (c_not @ Y0) @ Y1))))))),
% 9.27/1.88 inference(fool_elimination,[],[f43])).
% 9.27/1.88 thf(f294,plain,(
% 9.27/1.88 ((^[X0 : $o] : (X0 => c_False)) = c_not)),
% 9.27/1.88 inference(rectify,[],[f13])).
% 9.27/1.88 thf(f295,plain,(
% 9.27/1.88 (c_not = (^[Y0 : $o]: (Y0 => c_False)))),
% 9.27/1.88 inference(fool_elimination,[],[f294])).
% 9.27/1.88 thf(f296,plain,(
% 9.27/1.88 (c_SNoElts_ = (^[X0 : $i] : ((c_binunion @ X0 @ (c_Repl @ X0 @ (^[X1 : $i] : (((^[X2 : $i] : ((c_SetAdjoin @ X2 @ (c_Sing @ (c_ordsucc @ c_Empty))))) @ X1))))))))),
% 9.27/1.88 inference(rectify,[],[f93])).
% 9.27/1.88 thf(f297,plain,(
% 9.27/1.88 (c_SNoElts_ = (^[Y0 : $i]: (c_binunion @ Y0 @ (c_Repl @ Y0 @ (^[Y1 : $i]: ((^[Y2 : $i]: (c_SetAdjoin @ Y2 @ (c_Sing @ (c_ordsucc @ c_Empty)))) @ Y1))))))),
% 9.27/1.88 inference(fool_elimination,[],[f296])).
% 9.27/1.88 thf(f300,plain,(
% 9.27/1.88 ((^[X0 : $i, X1 : $i] : (! [X2 : $i] : ((c_In @ X2 @ X0) => (c_In @ X2 @ X1)))) = c_Subq)),
% 9.27/1.88 inference(rectify,[],[f17])).
% 9.27/1.88 thf(f301,plain,(
% 9.27/1.88 (c_Subq = (^[Y0 : $i]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((c_In @ Y2 @ Y0) => (c_In @ Y2 @ Y1))))))))),
% 9.27/1.88 inference(fool_elimination,[],[f300])).
% 9.27/1.88 thf(f302,plain,(
% 9.27/1.88 (c_SNo_ = (^[X0 : $i, X1 : $i] : ((c_and @ (c_Subq @ X1 @ (c_SNoElts_ @ X0)) @ ! [X2 : $i] : ((c_In @ X2 @ X0) => (c_exactly1of2 @ (c_In @ ((^[X3 : $i] : ((c_SetAdjoin @ X3 @ (c_Sing @ (c_ordsucc @ c_Empty))))) @ X2) @ X1) @ (c_In @ X2 @ X1)))))))),
% 9.27/1.88 inference(rectify,[],[f94])).
% 9.27/1.88 thf(f303,plain,(
% 9.27/1.88 (c_SNo_ = (^[Y0 : $i]: ((^[Y1 : $i]: (c_and @ (c_Subq @ Y1 @ (c_SNoElts_ @ Y0)) @ (!! @ $i @ (^[Y2 : $i]: ((c_In @ Y2 @ Y0) => (c_exactly1of2 @ (c_In @ ((^[Y3 : $i]: (c_SetAdjoin @ Y3 @ (c_Sing @ (c_ordsucc @ c_Empty)))) @ Y2) @ Y1) @ (c_In @ Y2 @ Y1))))))))))),
% 9.27/1.88 inference(fool_elimination,[],[f302])).
% 9.27/1.88 thf(f309,plain,(
% 9.27/1.88 (c_TransSet = (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((c_In @ Y1 @ Y0) => (c_Subq @ Y1 @ Y0))))))),
% 9.27/1.88 inference(cnf_transformation,[],[f195])).
% 9.27/1.88 thf(f310,plain,(
% 9.27/1.88 ($true = ((~ (c_not @ (!! @ ($i > $i) @ (^[Y0 : $i > $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (c_and @ (((Y1 @ (Y0 @ (c_binintersect @ (Y0 @ (c_Power @ c_Empty)) @ (Y0 @ (c_binrep @ (c_Power @ (c_Power @ (c_Power @ c_Empty))) @ c_Empty))))) => ((c_TransSet @ (Y0 @ c_Empty)) => (!! @ $i @ (^[Y2 : $i]: ((c_In @ Y2 @ c_Empty) => (?? @ $i @ (^[Y3 : $i]: (c_and @ (c_Subq @ Y3 @ Y2) @ (c_exactly2 @ (c_ordsucc @ (Y0 @ Y3))))))))))) => (?? @ $i @ (^[Y2 : $i]: (c_and @ (?? @ $i @ (^[Y3 : $i]: (c_and @ (c_Subq @ Y3 @ Y2) @ (((Y0 @ Y2) = Y2) => (?? @ $i @ (^[Y4 : $i]: (c_and @ (c_Subq @ Y4 @ Y2) @ (c_not @ (Y1 @ (c_setprod @ Y3 @ (c_binrep @ (c_Power @ (c_binrep @ (c_Power @ (c_Power @ c_Empty)) @ c_Empty)) @ (c_Power @ (c_Power @ c_Empty))))))))))))) @ (c_not @ (c_SNo @ Y2)))))) @ (c_not @ (Y1 @ (Y0 @ (Y0 @ (Y0 @ (c_binrep @ (c_binrep @ (c_Power @ (c_binrep @ (c_Power @ (c_Power @ c_Empty)) @ c_Empty)) @ (c_Power @ c_Empty)) @ c_Empty)))))))))))))))),
% 9.27/1.88 inference(cnf_transformation,[],[f266])).
% 9.27/1.88 thf(f311,plain,(
% 9.27/1.88 (c_binintersect = (^[Y0 : $i]: ((^[Y1 : $i]: (c_Sep @ Y0 @ (^[Y2 : $i]: (c_In @ Y2 @ Y1)))))))),
% 9.27/1.88 inference(cnf_transformation,[],[f278])).
% 9.27/1.88 thf(f314,plain,(
% 9.27/1.88 (c_Sing = (^[Y0 : $i]: (c_UPair @ Y0 @ Y0)))),
% 9.27/1.88 inference(cnf_transformation,[],[f211])).
% 9.27/1.88 thf(f315,plain,(
% 9.27/1.88 ($true = ((c_not @ (?? @ $i @ (^[Y0 : $i]: (c_In @ Y0 @ c_Empty))))))),
% 9.27/1.88 inference(cnf_transformation,[],[f256])).
% 9.27/1.88 thf(f320,plain,(
% 9.27/1.88 (c_SetAdjoin = (^[Y0 : $i]: ((^[Y1 : $i]: (c_binunion @ Y0 @ (c_Sing @ Y1))))))),
% 9.27/1.88 inference(cnf_transformation,[],[f206])).
% 9.27/1.88 thf(f324,plain,(
% 9.27/1.88 (c_Sep = (^[Y0 : $i]: ((^[Y1 : $i > $o]: (c_If_i @ (?? @ $i @ (^[Y2 : $i]: (c_and @ (c_In @ Y2 @ Y0) @ (Y1 @ Y2)))) @ (c_Repl @ Y0 @ (^[Y2 : $i]: ((^[Y3 : $i]: (c_If_i @ (Y1 @ Y3) @ Y3 @ (c_Eps_i @ (^[Y4 : $i]: (c_and @ (c_In @ Y4 @ Y0) @ (Y1 @ Y4)))))) @ Y2))) @ c_Empty)))))),
% 9.27/1.88 inference(cnf_transformation,[],[f184])).
% 9.27/1.88 thf(f327,plain,(
% 9.27/1.88 (c_SNoElts_ = (^[Y0 : $i]: (c_binunion @ Y0 @ (c_Repl @ Y0 @ (^[Y1 : $i]: ((^[Y2 : $i]: (c_SetAdjoin @ Y2 @ (c_Sing @ (c_ordsucc @ c_Empty)))) @ Y1))))))),
% 9.27/1.88 inference(cnf_transformation,[],[f297])).
% 9.27/1.88 thf(f328,plain,(
% 9.27/1.88 (c_In_rec_poly_G_i = (^[Y0 : $i > ($i > $i) > $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: ((!! @ ($i > $i) @ (^[Y4 : $i > $i]: (!! @ $i @ (^[Y5 : $i]: ((!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ Y5) => (Y3 @ Y6 @ (Y4 @ Y6))))) => (Y3 @ Y5 @ (Y0 @ Y5 @ Y4))))))) => (Y3 @ Y1 @ Y2))))))))))),
% 9.27/1.88 inference(cnf_transformation,[],[f241])).
% 9.27/1.88 thf(f330,plain,(
% 9.27/1.88 (c_setprod = (^[Y0 : $i]: ((^[Y1 : $i]: (c_lam @ Y0 @ (^[Y2 : $i]: (Y1)))))))),
% 9.27/1.88 inference(cnf_transformation,[],[f163])).
% 9.27/1.88 thf(f331,plain,(
% 9.27/1.88 (c_famunion = (^[Y0 : $i]: ((^[Y1 : $i > $i]: (c_Union @ (c_Repl @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))))))))),
% 9.27/1.88 inference(cnf_transformation,[],[f250])).
% 9.27/1.88 thf(f339,plain,(
% 9.27/1.88 (c_Inj0 = (^[Y0 : $i]: (c_Repl @ Y0 @ (^[Y1 : $i]: (c_Inj1 @ Y1)))))),
% 9.27/1.88 inference(cnf_transformation,[],[f217])).
% 9.27/1.88 thf(f340,plain,(
% 9.27/1.88 (c_UPair = (^[Y0 : $i]: ((^[Y1 : $i]: (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y2 : $i]: (c_If_i @ (c_In @ c_Empty @ Y2) @ Y0 @ Y1)))))))),
% 9.27/1.88 inference(cnf_transformation,[],[f133])).
% 9.27/1.88 thf(f341,plain,(
% 9.27/1.88 (c_setsum = (^[Y0 : $i]: ((^[Y1 : $i]: (c_binunion @ (c_Repl @ Y0 @ (^[Y2 : $i]: (c_Inj0 @ Y2))) @ (c_Repl @ Y1 @ (^[Y2 : $i]: (c_Inj1 @ Y2))))))))),
% 9.27/1.88 inference(cnf_transformation,[],[f205])).
% 9.27/1.88 thf(f345,plain,(
% 9.27/1.88 (c_lam = (^[Y0 : $i]: ((^[Y1 : $i > $i]: (c_famunion @ Y0 @ (^[Y2 : $i]: (c_Repl @ (Y1 @ Y2) @ (^[Y3 : $i]: (c_setsum @ Y2 @ Y3)))))))))),
% 9.27/1.88 inference(cnf_transformation,[],[f288])).
% 9.27/1.88 thf(f346,plain,(
% 9.27/1.88 (c_atleast2 = (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (c_and @ (c_In @ Y1 @ Y0) @ (c_not @ (c_Subq @ Y0 @ (c_Power @ Y1))))))))),
% 9.27/1.88 inference(cnf_transformation,[],[f149])).
% 9.27/1.88 thf(f352,plain,(
% 9.27/1.88 (c_ordinal = (^[Y0 : $i]: (c_and @ (c_TransSet @ Y0) @ (!! @ $i @ (^[Y1 : $i]: ((c_In @ Y1 @ Y0) => (c_TransSet @ Y1)))))))),
% 9.27/1.88 inference(cnf_transformation,[],[f191])).
% 9.27/1.88 thf(f353,plain,(
% 9.27/1.88 (c_In_rec_poly_i = (^[Y0 : $i > ($i > $i) > $i]: ((^[Y1 : $i]: (c_Eps_i @ (^[Y2 : $i]: (c_In_rec_poly_G_i @ Y0 @ Y1 @ Y2)))))))),
% 9.27/1.88 inference(cnf_transformation,[],[f215])).
% 9.27/1.88 thf(f357,plain,(
% 9.27/1.88 (c_binunion = (^[Y0 : $i]: ((^[Y1 : $i]: (c_Union @ (c_UPair @ Y0 @ Y1))))))),
% 9.27/1.88 inference(cnf_transformation,[],[f227])).
% 9.27/1.88 thf(f359,plain,(
% 9.27/1.88 (c_atleast3 = (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (c_and @ (c_Subq @ Y1 @ Y0) @ (c_and @ (c_not @ (c_Subq @ Y0 @ Y1)) @ (c_atleast2 @ Y1)))))))),
% 9.27/1.88 inference(cnf_transformation,[],[f252])).
% 9.27/1.88 thf(f368,plain,(
% 9.27/1.88 (c_SNo_ = (^[Y0 : $i]: ((^[Y1 : $i]: (c_and @ (c_Subq @ Y1 @ (c_SNoElts_ @ Y0)) @ (!! @ $i @ (^[Y2 : $i]: ((c_In @ Y2 @ Y0) => (c_exactly1of2 @ (c_In @ ((^[Y3 : $i]: (c_SetAdjoin @ Y3 @ (c_Sing @ (c_ordsucc @ c_Empty)))) @ Y2) @ Y1) @ (c_In @ Y2 @ Y1))))))))))),
% 9.27/1.88 inference(cnf_transformation,[],[f303])).
% 9.27/1.88 thf(f371,plain,(
% 9.27/1.88 (c_binrep = (^[Y0 : $i]: ((^[Y1 : $i]: (c_setsum @ Y0 @ (c_Power @ Y1))))))),
% 9.27/1.88 inference(cnf_transformation,[],[f180])).
% 9.27/1.88 thf(f375,plain,(
% 9.27/1.88 (c_Subq = (^[Y0 : $i]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((c_In @ Y2 @ Y0) => (c_In @ Y2 @ Y1))))))))),
% 9.27/1.88 inference(cnf_transformation,[],[f301])).
% 9.27/1.88 thf(f387,plain,(
% 9.27/1.88 (c_not = (^[Y0 : $o]: (Y0 => c_False)))),
% 9.27/1.88 inference(cnf_transformation,[],[f295])).
% 9.27/1.88 thf(f391,plain,(
% 9.27/1.88 (c_If_i = (^[Y0 : $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (c_Eps_i @ (^[Y3 : $i]: (c_or @ (c_and @ Y0 @ (Y1 = Y3)) @ (c_and @ (c_not @ Y0) @ (Y2 = Y3)))))))))))),
% 9.27/1.88 inference(cnf_transformation,[],[f282])).
% 9.27/1.88 thf(f393,plain,(
% 9.27/1.88 (c_exactly2 = (^[Y0 : $i]: (c_and @ (c_atleast2 @ Y0) @ (c_not @ (c_atleast3 @ Y0)))))),
% 9.27/1.88 inference(cnf_transformation,[],[f243])).
% 9.27/1.88 thf(f401,plain,(
% 9.27/1.88 (c_or = (^[Y0 : $o]: ((^[Y1 : $o]: (!! @ $o @ (^[Y2 : $o]: ((Y0 => Y2) => ((Y1 => Y2) => Y2))))))))),
% 9.27/1.88 inference(cnf_transformation,[],[f114])).
% 9.27/1.88 thf(f402,plain,(
% 9.27/1.88 (c_and = (^[Y0 : $o]: ((^[Y1 : $o]: (!! @ $o @ (^[Y2 : $o]: ((Y0 => (Y1 => Y2)) => Y2)))))))),
% 9.27/1.88 inference(cnf_transformation,[],[f239])).
% 9.27/1.88 thf(f406,plain,(
% 9.27/1.88 (c_Inj1 = ((c_In_rec_poly_i @ (^[Y0 : $i]: ((^[Y1 : $i > $i]: (c_binunion @ (c_Sing @ c_Empty) @ (c_Repl @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))))))))))),
% 9.27/1.88 inference(cnf_transformation,[],[f197])).
% 9.27/1.88 thf(f408,plain,(
% 9.27/1.88 (c_SNo = (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (c_and @ (c_ordinal @ Y1) @ (c_SNo_ @ Y1 @ Y0))))))),
% 9.27/1.88 inference(cnf_transformation,[],[f177])).
% 9.27/1.88 thf(f411,plain,(
% 9.27/1.88 (c_exactly1of2 = (^[Y0 : $o]: ((^[Y1 : $o]: (c_or @ (c_and @ Y0 @ (c_not @ Y1)) @ (c_and @ (c_not @ Y0) @ Y1))))))),
% 9.27/1.88 inference(cnf_transformation,[],[f289])).
% 9.27/1.88 thf(f413,plain,(
% 9.27/1.88 (c_ordsucc = (^[Y0 : $i]: (c_binunion @ Y0 @ (c_Sing @ Y0))))),
% 9.27/1.88 inference(cnf_transformation,[],[f155])).
% 9.27/1.88 thf(f418,definition,(
% 9.27/1.88 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 9.27/1.88 introduced(theory,[fool_exhaustiveness_axiom])).
% 9.27/1.88 thf(f420,plain,(
% 9.27/1.88 (c_TransSet = (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((c_In @ Y1 @ Y0) => ((^[Y2 : $i]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((c_In @ Y4 @ Y2) => (c_In @ Y4 @ Y3))))))) @ Y1 @ Y0))))))),
% 9.27/1.88 inference(definition_unfolding,[],[f309,f375])).
% 9.27/1.88 thf(f421,plain,(
% 9.27/1.88 (c_atleast2 = (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((^[Y2 : $o]: ((^[Y3 : $o]: (!! @ $o @ (^[Y4 : $o]: ((Y2 => (Y3 => Y4)) => Y4)))))) @ (c_In @ Y1 @ Y0) @ ((^[Y2 : $o]: (Y2 => c_False)) @ ((^[Y2 : $i]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((c_In @ Y4 @ Y2) => (c_In @ Y4 @ Y3))))))) @ Y0 @ (c_Power @ Y1))))))))),
% 9.27/1.88 inference(definition_unfolding,[],[f346,f402,f387,f375])).
% 9.27/1.88 thf(f422,plain,(
% 9.27/1.88 (c_atleast3 = (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((^[Y2 : $o]: ((^[Y3 : $o]: (!! @ $o @ (^[Y4 : $o]: ((Y2 => (Y3 => Y4)) => Y4)))))) @ ((^[Y2 : $i]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((c_In @ Y4 @ Y2) => (c_In @ Y4 @ Y3))))))) @ Y1 @ Y0) @ ((^[Y2 : $o]: ((^[Y3 : $o]: (!! @ $o @ (^[Y4 : $o]: ((Y2 => (Y3 => Y4)) => Y4)))))) @ ((^[Y2 : $o]: (Y2 => c_False)) @ ((^[Y2 : $i]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((c_In @ Y4 @ Y2) => (c_In @ Y4 @ Y3))))))) @ Y0 @ Y1)) @ ((^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: ((^[Y4 : $o]: ((^[Y5 : $o]: (!! @ $o @ (^[Y6 : $o]: ((Y4 => (Y5 => Y6)) => Y6)))))) @ (c_In @ Y3 @ Y2) @ ((^[Y4 : $o]: (Y4 => c_False)) @ ((^[Y4 : $i]: ((^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ Y4) => (c_In @ Y6 @ Y5))))))) @ Y2 @ (c_Power @ Y3))))))) @ Y1)))))))),
% 9.27/1.88 inference(definition_unfolding,[],[f359,f402,f375,f402,f387,f375,f421])).
% 9.27/1.88 thf(f426,plain,(
% 9.27/1.88 (c_exactly2 = (^[Y0 : $i]: ((^[Y1 : $o]: ((^[Y2 : $o]: (!! @ $o @ (^[Y3 : $o]: ((Y1 => (Y2 => Y3)) => Y3)))))) @ ((^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: ((^[Y3 : $o]: ((^[Y4 : $o]: (!! @ $o @ (^[Y5 : $o]: ((Y3 => (Y4 => Y5)) => Y5)))))) @ (c_In @ Y2 @ Y1) @ ((^[Y3 : $o]: (Y3 => c_False)) @ ((^[Y3 : $i]: ((^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((c_In @ Y5 @ Y3) => (c_In @ Y5 @ Y4))))))) @ Y1 @ (c_Power @ Y2))))))) @ Y0) @ ((^[Y1 : $o]: (Y1 => c_False)) @ ((^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: ((^[Y3 : $o]: ((^[Y4 : $o]: (!! @ $o @ (^[Y5 : $o]: ((Y3 => (Y4 => Y5)) => Y5)))))) @ ((^[Y3 : $i]: ((^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((c_In @ Y5 @ Y3) => (c_In @ Y5 @ Y4))))))) @ Y2 @ Y1) @ ((^[Y3 : $o]: ((^[Y4 : $o]: (!! @ $o @ (^[Y5 : $o]: ((Y3 => (Y4 => Y5)) => Y5)))))) @ ((^[Y3 : $o]: (Y3 => c_False)) @ ((^[Y3 : $i]: ((^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((c_In @ Y5 @ Y3) => (c_In @ Y5 @ Y4))))))) @ Y1 @ Y2)) @ ((^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((^[Y5 : $o]: ((^[Y6 : $o]: (!! @ $o @ (^[Y7 : $o]: ((Y5 => (Y6 => Y7)) => Y7)))))) @ (c_In @ Y4 @ Y3) @ ((^[Y5 : $o]: (Y5 => c_False)) @ ((^[Y5 : $i]: ((^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((c_In @ Y7 @ Y5) => (c_In @ Y7 @ Y6))))))) @ Y3 @ (c_Power @ Y4))))))) @ Y2)))))) @ Y0)))))),
% 9.27/1.88 inference(definition_unfolding,[],[f393,f402,f421,f387,f422])).
% 9.27/1.88 thf(f440,plain,(
% 9.27/1.88 (c_If_i = (^[Y0 : $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (c_Eps_i @ (^[Y3 : $i]: ((^[Y4 : $o]: ((^[Y5 : $o]: (!! @ $o @ (^[Y6 : $o]: ((Y4 => Y6) => ((Y5 => Y6) => Y6))))))) @ ((^[Y4 : $o]: ((^[Y5 : $o]: (!! @ $o @ (^[Y6 : $o]: ((Y4 => (Y5 => Y6)) => Y6)))))) @ Y0 @ (Y1 = Y3)) @ ((^[Y4 : $o]: ((^[Y5 : $o]: (!! @ $o @ (^[Y6 : $o]: ((Y4 => (Y5 => Y6)) => Y6)))))) @ ((^[Y4 : $o]: (Y4 => c_False)) @ Y0) @ (Y2 = Y3)))))))))))),
% 9.27/1.88 inference(definition_unfolding,[],[f391,f401,f402,f402,f387])).
% 9.27/1.88 thf(f441,plain,(
% 9.27/1.88 (c_exactly1of2 = (^[Y0 : $o]: ((^[Y1 : $o]: ((^[Y2 : $o]: ((^[Y3 : $o]: (!! @ $o @ (^[Y4 : $o]: ((Y2 => Y4) => ((Y3 => Y4) => Y4))))))) @ ((^[Y2 : $o]: ((^[Y3 : $o]: (!! @ $o @ (^[Y4 : $o]: ((Y2 => (Y3 => Y4)) => Y4)))))) @ Y0 @ ((^[Y2 : $o]: (Y2 => c_False)) @ Y1)) @ ((^[Y2 : $o]: ((^[Y3 : $o]: (!! @ $o @ (^[Y4 : $o]: ((Y2 => (Y3 => Y4)) => Y4)))))) @ ((^[Y2 : $o]: (Y2 => c_False)) @ Y0) @ Y1))))))),
% 9.27/1.88 inference(definition_unfolding,[],[f411,f401,f402,f387,f402,f387])).
% 9.27/1.88 thf(f445,plain,(
% 9.27/1.88 (c_UPair = (^[Y0 : $i]: ((^[Y1 : $i]: (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y2 : $i]: ((^[Y3 : $o]: ((^[Y4 : $i]: ((^[Y5 : $i]: (c_Eps_i @ (^[Y6 : $i]: ((^[Y7 : $o]: ((^[Y8 : $o]: (!! @ $o @ (^[Y9 : $o]: ((Y7 => Y9) => ((Y8 => Y9) => Y9))))))) @ ((^[Y7 : $o]: ((^[Y8 : $o]: (!! @ $o @ (^[Y9 : $o]: ((Y7 => (Y8 => Y9)) => Y9)))))) @ Y3 @ (Y4 = Y6)) @ ((^[Y7 : $o]: ((^[Y8 : $o]: (!! @ $o @ (^[Y9 : $o]: ((Y7 => (Y8 => Y9)) => Y9)))))) @ ((^[Y7 : $o]: (Y7 => c_False)) @ Y3) @ (Y5 = Y6)))))))))) @ (c_In @ c_Empty @ Y2) @ Y0 @ Y1)))))))),
% 9.27/1.88 inference(definition_unfolding,[],[f340,f440])).
% 9.27/1.88 thf(f446,plain,(
% 9.27/1.88 (c_Sing = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y3 : $i]: ((^[Y4 : $o]: ((^[Y5 : $i]: ((^[Y6 : $i]: (c_Eps_i @ (^[Y7 : $i]: ((^[Y8 : $o]: ((^[Y9 : $o]: (!! @ $o @ (^[Y10 : $o]: ((Y8 => Y10) => ((Y9 => Y10) => Y10))))))) @ ((^[Y8 : $o]: ((^[Y9 : $o]: (!! @ $o @ (^[Y10 : $o]: ((Y8 => (Y9 => Y10)) => Y10)))))) @ Y4 @ (Y5 = Y7)) @ ((^[Y8 : $o]: ((^[Y9 : $o]: (!! @ $o @ (^[Y10 : $o]: ((Y8 => (Y9 => Y10)) => Y10)))))) @ ((^[Y8 : $o]: (Y8 => c_False)) @ Y4) @ (Y6 = Y7)))))))))) @ (c_In @ c_Empty @ Y3) @ Y1 @ Y2)))))) @ Y0 @ Y0)))),
% 9.27/1.88 inference(definition_unfolding,[],[f314,f445])).
% 9.27/1.88 thf(f447,plain,(
% 9.27/1.88 (c_binunion = (^[Y0 : $i]: ((^[Y1 : $i]: (c_Union @ ((^[Y2 : $i]: ((^[Y3 : $i]: (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y4 : $i]: ((^[Y5 : $o]: ((^[Y6 : $i]: ((^[Y7 : $i]: (c_Eps_i @ (^[Y8 : $i]: ((^[Y9 : $o]: ((^[Y10 : $o]: (!! @ $o @ (^[Y11 : $o]: ((Y9 => Y11) => ((Y10 => Y11) => Y11))))))) @ ((^[Y9 : $o]: ((^[Y10 : $o]: (!! @ $o @ (^[Y11 : $o]: ((Y9 => (Y10 => Y11)) => Y11)))))) @ Y5 @ (Y6 = Y8)) @ ((^[Y9 : $o]: ((^[Y10 : $o]: (!! @ $o @ (^[Y11 : $o]: ((Y9 => (Y10 => Y11)) => Y11)))))) @ ((^[Y9 : $o]: (Y9 => c_False)) @ Y5) @ (Y7 = Y8)))))))))) @ (c_In @ c_Empty @ Y4) @ Y2 @ Y3)))))) @ Y0 @ Y1))))))),
% 9.27/1.88 inference(definition_unfolding,[],[f357,f445])).
% 9.27/1.88 thf(f448,plain,(
% 9.27/1.88 (c_SetAdjoin = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: (c_Union @ ((^[Y4 : $i]: ((^[Y5 : $i]: (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y6 : $i]: ((^[Y7 : $o]: ((^[Y8 : $i]: ((^[Y9 : $i]: (c_Eps_i @ (^[Y10 : $i]: ((^[Y11 : $o]: ((^[Y12 : $o]: (!! @ $o @ (^[Y13 : $o]: ((Y11 => Y13) => ((Y12 => Y13) => Y13))))))) @ ((^[Y11 : $o]: ((^[Y12 : $o]: (!! @ $o @ (^[Y13 : $o]: ((Y11 => (Y12 => Y13)) => Y13)))))) @ Y7 @ (Y8 = Y10)) @ ((^[Y11 : $o]: ((^[Y12 : $o]: (!! @ $o @ (^[Y13 : $o]: ((Y11 => (Y12 => Y13)) => Y13)))))) @ ((^[Y11 : $o]: (Y11 => c_False)) @ Y7) @ (Y9 = Y10)))))))))) @ (c_In @ c_Empty @ Y6) @ Y4 @ Y5)))))) @ Y2 @ Y3))))) @ Y0 @ ((^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y5 : $i]: ((^[Y6 : $o]: ((^[Y7 : $i]: ((^[Y8 : $i]: (c_Eps_i @ (^[Y9 : $i]: ((^[Y10 : $o]: ((^[Y11 : $o]: (!! @ $o @ (^[Y12 : $o]: ((Y10 => Y12) => ((Y11 => Y12) => Y12))))))) @ ((^[Y10 : $o]: ((^[Y11 : $o]: (!! @ $o @ (^[Y12 : $o]: ((Y10 => (Y11 => Y12)) => Y12)))))) @ Y6 @ (Y7 = Y9)) @ ((^[Y10 : $o]: ((^[Y11 : $o]: (!! @ $o @ (^[Y12 : $o]: ((Y10 => (Y11 => Y12)) => Y12)))))) @ ((^[Y10 : $o]: (Y10 => c_False)) @ Y6) @ (Y8 = Y9)))))))))) @ (c_In @ c_Empty @ Y5) @ Y3 @ Y4)))))) @ Y2 @ Y2)) @ Y1))))))),
% 9.27/1.88 inference(definition_unfolding,[],[f320,f447,f446])).
% 9.27/1.88 thf(f449,plain,(
% 9.27/1.88 (c_Sep = (^[Y0 : $i]: ((^[Y1 : $i > $o]: ((^[Y2 : $o]: ((^[Y3 : $i]: ((^[Y4 : $i]: (c_Eps_i @ (^[Y5 : $i]: ((^[Y6 : $o]: ((^[Y7 : $o]: (!! @ $o @ (^[Y8 : $o]: ((Y6 => Y8) => ((Y7 => Y8) => Y8))))))) @ ((^[Y6 : $o]: ((^[Y7 : $o]: (!! @ $o @ (^[Y8 : $o]: ((Y6 => (Y7 => Y8)) => Y8)))))) @ Y2 @ (Y3 = Y5)) @ ((^[Y6 : $o]: ((^[Y7 : $o]: (!! @ $o @ (^[Y8 : $o]: ((Y6 => (Y7 => Y8)) => Y8)))))) @ ((^[Y6 : $o]: (Y6 => c_False)) @ Y2) @ (Y4 = Y5)))))))))) @ (?? @ $i @ (^[Y2 : $i]: ((^[Y3 : $o]: ((^[Y4 : $o]: (!! @ $o @ (^[Y5 : $o]: ((Y3 => (Y4 => Y5)) => Y5)))))) @ (c_In @ Y2 @ Y0) @ (Y1 @ Y2)))) @ (c_Repl @ Y0 @ (^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $o]: ((^[Y5 : $i]: ((^[Y6 : $i]: (c_Eps_i @ (^[Y7 : $i]: ((^[Y8 : $o]: ((^[Y9 : $o]: (!! @ $o @ (^[Y10 : $o]: ((Y8 => Y10) => ((Y9 => Y10) => Y10))))))) @ ((^[Y8 : $o]: ((^[Y9 : $o]: (!! @ $o @ (^[Y10 : $o]: ((Y8 => (Y9 => Y10)) => Y10)))))) @ Y4 @ (Y5 = Y7)) @ ((^[Y8 : $o]: ((^[Y9 : $o]: (!! @ $o @ (^[Y10 : $o]: ((Y8 => (Y9 => Y10)) => Y10)))))) @ ((^[Y8 : $o]: (Y8 => c_False)) @ Y4) @ (Y6 = Y7)))))))))) @ (Y1 @ Y3) @ Y3 @ (c_Eps_i @ (^[Y4 : $i]: ((^[Y5 : $o]: ((^[Y6 : $o]: (!! @ $o @ (^[Y7 : $o]: ((Y5 => (Y6 => Y7)) => Y7)))))) @ (c_In @ Y4 @ Y0) @ (Y1 @ Y4)))))) @ Y2))) @ c_Empty)))))),
% 9.27/1.88 inference(definition_unfolding,[],[f324,f440,f402,f440,f402])).
% 9.27/1.88 thf(f451,plain,(
% 9.27/1.88 (c_binintersect = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i > $o]: ((^[Y4 : $o]: ((^[Y5 : $i]: ((^[Y6 : $i]: (c_Eps_i @ (^[Y7 : $i]: ((^[Y8 : $o]: ((^[Y9 : $o]: (!! @ $o @ (^[Y10 : $o]: ((Y8 => Y10) => ((Y9 => Y10) => Y10))))))) @ ((^[Y8 : $o]: ((^[Y9 : $o]: (!! @ $o @ (^[Y10 : $o]: ((Y8 => (Y9 => Y10)) => Y10)))))) @ Y4 @ (Y5 = Y7)) @ ((^[Y8 : $o]: ((^[Y9 : $o]: (!! @ $o @ (^[Y10 : $o]: ((Y8 => (Y9 => Y10)) => Y10)))))) @ ((^[Y8 : $o]: (Y8 => c_False)) @ Y4) @ (Y6 = Y7)))))))))) @ (?? @ $i @ (^[Y4 : $i]: ((^[Y5 : $o]: ((^[Y6 : $o]: (!! @ $o @ (^[Y7 : $o]: ((Y5 => (Y6 => Y7)) => Y7)))))) @ (c_In @ Y4 @ Y2) @ (Y3 @ Y4)))) @ (c_Repl @ Y2 @ (^[Y4 : $i]: ((^[Y5 : $i]: ((^[Y6 : $o]: ((^[Y7 : $i]: ((^[Y8 : $i]: (c_Eps_i @ (^[Y9 : $i]: ((^[Y10 : $o]: ((^[Y11 : $o]: (!! @ $o @ (^[Y12 : $o]: ((Y10 => Y12) => ((Y11 => Y12) => Y12))))))) @ ((^[Y10 : $o]: ((^[Y11 : $o]: (!! @ $o @ (^[Y12 : $o]: ((Y10 => (Y11 => Y12)) => Y12)))))) @ Y6 @ (Y7 = Y9)) @ ((^[Y10 : $o]: ((^[Y11 : $o]: (!! @ $o @ (^[Y12 : $o]: ((Y10 => (Y11 => Y12)) => Y12)))))) @ ((^[Y10 : $o]: (Y10 => c_False)) @ Y6) @ (Y8 = Y9)))))))))) @ (Y3 @ Y5) @ Y5 @ (c_Eps_i @ (^[Y6 : $i]: ((^[Y7 : $o]: ((^[Y8 : $o]: (!! @ $o @ (^[Y9 : $o]: ((Y7 => (Y8 => Y9)) => Y9)))))) @ (c_In @ Y6 @ Y2) @ (Y3 @ Y6)))))) @ Y4))) @ c_Empty)))) @ Y0 @ (^[Y2 : $i]: (c_In @ Y2 @ Y1)))))))),
% 9.27/1.88 inference(definition_unfolding,[],[f311,f449])).
% 9.27/1.88 thf(f457,plain,(
% 9.27/1.88 (c_In_rec_poly_i = (^[Y0 : $i > ($i > $i) > $i]: ((^[Y1 : $i]: (c_Eps_i @ (^[Y2 : $i]: ((^[Y3 : $i > ($i > $i) > $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: ((!! @ ($i > $i) @ (^[Y7 : $i > $i]: (!! @ $i @ (^[Y8 : $i]: ((!! @ $i @ (^[Y9 : $i]: ((c_In @ Y9 @ Y8) => (Y6 @ Y9 @ (Y7 @ Y9))))) => (Y6 @ Y8 @ (Y3 @ Y8 @ Y7))))))) => (Y6 @ Y4 @ Y5))))))))) @ Y0 @ Y1 @ Y2)))))))),
% 9.27/1.88 inference(definition_unfolding,[],[f353,f328])).
% 9.27/1.88 thf(f458,plain,(
% 9.27/1.88 (c_ordsucc = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (c_Union @ ((^[Y3 : $i]: ((^[Y4 : $i]: (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y5 : $i]: ((^[Y6 : $o]: ((^[Y7 : $i]: ((^[Y8 : $i]: (c_Eps_i @ (^[Y9 : $i]: ((^[Y10 : $o]: ((^[Y11 : $o]: (!! @ $o @ (^[Y12 : $o]: ((Y10 => Y12) => ((Y11 => Y12) => Y12))))))) @ ((^[Y10 : $o]: ((^[Y11 : $o]: (!! @ $o @ (^[Y12 : $o]: ((Y10 => (Y11 => Y12)) => Y12)))))) @ Y6 @ (Y7 = Y9)) @ ((^[Y10 : $o]: ((^[Y11 : $o]: (!! @ $o @ (^[Y12 : $o]: ((Y10 => (Y11 => Y12)) => Y12)))))) @ ((^[Y10 : $o]: (Y10 => c_False)) @ Y6) @ (Y8 = Y9)))))))))) @ (c_In @ c_Empty @ Y5) @ Y3 @ Y4)))))) @ Y1 @ Y2))))) @ Y0 @ ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y4 : $i]: ((^[Y5 : $o]: ((^[Y6 : $i]: ((^[Y7 : $i]: (c_Eps_i @ (^[Y8 : $i]: ((^[Y9 : $o]: ((^[Y10 : $o]: (!! @ $o @ (^[Y11 : $o]: ((Y9 => Y11) => ((Y10 => Y11) => Y11))))))) @ ((^[Y9 : $o]: ((^[Y10 : $o]: (!! @ $o @ (^[Y11 : $o]: ((Y9 => (Y10 => Y11)) => Y11)))))) @ Y5 @ (Y6 = Y8)) @ ((^[Y9 : $o]: ((^[Y10 : $o]: (!! @ $o @ (^[Y11 : $o]: ((Y9 => (Y10 => Y11)) => Y11)))))) @ ((^[Y9 : $o]: (Y9 => c_False)) @ Y5) @ (Y7 = Y8)))))))))) @ (c_In @ c_Empty @ Y4) @ Y2 @ Y3)))))) @ Y1 @ Y1)) @ Y0))))),
% 9.27/1.88 inference(definition_unfolding,[],[f413,f447,f446])).
% 9.27/1.88 thf(f463,plain,(
% 9.27/1.88 (c_ordinal = (^[Y0 : $i]: ((^[Y1 : $o]: ((^[Y2 : $o]: (!! @ $o @ (^[Y3 : $o]: ((Y1 => (Y2 => Y3)) => Y3)))))) @ ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((c_In @ Y2 @ Y1) => ((^[Y3 : $i]: ((^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((c_In @ Y5 @ Y3) => (c_In @ Y5 @ Y4))))))) @ Y2 @ Y1))))) @ Y0) @ (!! @ $i @ (^[Y1 : $i]: ((c_In @ Y1 @ Y0) => ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((c_In @ Y3 @ Y2) => ((^[Y4 : $i]: ((^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ Y4) => (c_In @ Y6 @ Y5))))))) @ Y3 @ Y2))))) @ Y1)))))))),
% 9.27/1.88 inference(definition_unfolding,[],[f352,f402,f420,f420])).
% 9.27/1.88 thf(f465,plain,(
% 9.27/1.88 (c_Inj1 = (((^[Y0 : $i > ($i > $i) > $i]: ((^[Y1 : $i]: (c_Eps_i @ (^[Y2 : $i]: ((^[Y3 : $i > ($i > $i) > $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: ((!! @ ($i > $i) @ (^[Y7 : $i > $i]: (!! @ $i @ (^[Y8 : $i]: ((!! @ $i @ (^[Y9 : $i]: ((c_In @ Y9 @ Y8) => (Y6 @ Y9 @ (Y7 @ Y9))))) => (Y6 @ Y8 @ (Y3 @ Y8 @ Y7))))))) => (Y6 @ Y4 @ Y5))))))))) @ Y0 @ Y1 @ Y2)))))) @ (^[Y0 : $i]: ((^[Y1 : $i > $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: (c_Union @ ((^[Y4 : $i]: ((^[Y5 : $i]: (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y6 : $i]: ((^[Y7 : $o]: ((^[Y8 : $i]: ((^[Y9 : $i]: (c_Eps_i @ (^[Y10 : $i]: ((^[Y11 : $o]: ((^[Y12 : $o]: (!! @ $o @ (^[Y13 : $o]: ((Y11 => Y13) => ((Y12 => Y13) => Y13))))))) @ ((^[Y11 : $o]: ((^[Y12 : $o]: (!! @ $o @ (^[Y13 : $o]: ((Y11 => (Y12 => Y13)) => Y13)))))) @ Y7 @ (Y8 = Y10)) @ ((^[Y11 : $o]: ((^[Y12 : $o]: (!! @ $o @ (^[Y13 : $o]: ((Y11 => (Y12 => Y13)) => Y13)))))) @ ((^[Y11 : $o]: (Y11 => c_False)) @ Y7) @ (Y9 = Y10)))))))))) @ (c_In @ c_Empty @ Y6) @ Y4 @ Y5)))))) @ Y2 @ Y3))))) @ ((^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y5 : $i]: ((^[Y6 : $o]: ((^[Y7 : $i]: ((^[Y8 : $i]: (c_Eps_i @ (^[Y9 : $i]: ((^[Y10 : $o]: ((^[Y11 : $o]: (!! @ $o @ (^[Y12 : $o]: ((Y10 => Y12) => ((Y11 => Y12) => Y12))))))) @ ((^[Y10 : $o]: ((^[Y11 : $o]: (!! @ $o @ (^[Y12 : $o]: ((Y10 => (Y11 => Y12)) => Y12)))))) @ Y6 @ (Y7 = Y9)) @ ((^[Y10 : $o]: ((^[Y11 : $o]: (!! @ $o @ (^[Y12 : $o]: ((Y10 => (Y11 => Y12)) => Y12)))))) @ ((^[Y10 : $o]: (Y10 => c_False)) @ Y6) @ (Y8 = Y9)))))))))) @ (c_In @ c_Empty @ Y5) @ Y3 @ Y4)))))) @ Y2 @ Y2)) @ c_Empty) @ (c_Repl @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))))))))))),
% 9.27/1.88 inference(definition_unfolding,[],[f406,f457,f447,f446])).
% 9.27/1.88 thf(f466,plain,(
% 9.27/1.88 (c_Inj0 = (^[Y0 : $i]: (c_Repl @ Y0 @ (^[Y1 : $i]: ((^[Y2 : $i > ($i > $i) > $i]: ((^[Y3 : $i]: (c_Eps_i @ (^[Y4 : $i]: ((^[Y5 : $i > ($i > $i) > $i]: ((^[Y6 : $i]: ((^[Y7 : $i]: (!! @ ($i > $i > $o) @ (^[Y8 : $i > $i > $o]: ((!! @ ($i > $i) @ (^[Y9 : $i > $i]: (!! @ $i @ (^[Y10 : $i]: ((!! @ $i @ (^[Y11 : $i]: ((c_In @ Y11 @ Y10) => (Y8 @ Y11 @ (Y9 @ Y11))))) => (Y8 @ Y10 @ (Y5 @ Y10 @ Y9))))))) => (Y8 @ Y6 @ Y7))))))))) @ Y2 @ Y3 @ Y4)))))) @ (^[Y2 : $i]: ((^[Y3 : $i > $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: (c_Union @ ((^[Y6 : $i]: ((^[Y7 : $i]: (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y8 : $i]: ((^[Y9 : $o]: ((^[Y10 : $i]: ((^[Y11 : $i]: (c_Eps_i @ (^[Y12 : $i]: ((^[Y13 : $o]: ((^[Y14 : $o]: (!! @ $o @ (^[Y15 : $o]: ((Y13 => Y15) => ((Y14 => Y15) => Y15))))))) @ ((^[Y13 : $o]: ((^[Y14 : $o]: (!! @ $o @ (^[Y15 : $o]: ((Y13 => (Y14 => Y15)) => Y15)))))) @ Y9 @ (Y10 = Y12)) @ ((^[Y13 : $o]: ((^[Y14 : $o]: (!! @ $o @ (^[Y15 : $o]: ((Y13 => (Y14 => Y15)) => Y15)))))) @ ((^[Y13 : $o]: (Y13 => c_False)) @ Y9) @ (Y11 = Y12)))))))))) @ (c_In @ c_Empty @ Y8) @ Y6 @ Y7)))))) @ Y4 @ Y5))))) @ ((^[Y4 : $i]: ((^[Y5 : $i]: ((^[Y6 : $i]: (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y7 : $i]: ((^[Y8 : $o]: ((^[Y9 : $i]: ((^[Y10 : $i]: (c_Eps_i @ (^[Y11 : $i]: ((^[Y12 : $o]: ((^[Y13 : $o]: (!! @ $o @ (^[Y14 : $o]: ((Y12 => Y14) => ((Y13 => Y14) => Y14))))))) @ ((^[Y12 : $o]: ((^[Y13 : $o]: (!! @ $o @ (^[Y14 : $o]: ((Y12 => (Y13 => Y14)) => Y14)))))) @ Y8 @ (Y9 = Y11)) @ ((^[Y12 : $o]: ((^[Y13 : $o]: (!! @ $o @ (^[Y14 : $o]: ((Y12 => (Y13 => Y14)) => Y14)))))) @ ((^[Y12 : $o]: (Y12 => c_False)) @ Y8) @ (Y10 = Y11)))))))))) @ (c_In @ c_Empty @ Y7) @ Y5 @ Y6)))))) @ Y4 @ Y4)) @ c_Empty) @ (c_Repl @ Y2 @ (^[Y4 : $i]: (Y3 @ Y4))))))) @ Y1)))))),
% 9.27/1.88 inference(definition_unfolding,[],[f339,f465])).
% 9.27/1.88 thf(f469,plain,(
% 9.27/1.88 (c_setsum = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: (c_Union @ ((^[Y4 : $i]: ((^[Y5 : $i]: (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y6 : $i]: ((^[Y7 : $o]: ((^[Y8 : $i]: ((^[Y9 : $i]: (c_Eps_i @ (^[Y10 : $i]: ((^[Y11 : $o]: ((^[Y12 : $o]: (!! @ $o @ (^[Y13 : $o]: ((Y11 => Y13) => ((Y12 => Y13) => Y13))))))) @ ((^[Y11 : $o]: ((^[Y12 : $o]: (!! @ $o @ (^[Y13 : $o]: ((Y11 => (Y12 => Y13)) => Y13)))))) @ Y7 @ (Y8 = Y10)) @ ((^[Y11 : $o]: ((^[Y12 : $o]: (!! @ $o @ (^[Y13 : $o]: ((Y11 => (Y12 => Y13)) => Y13)))))) @ ((^[Y11 : $o]: (Y11 => c_False)) @ Y7) @ (Y9 = Y10)))))))))) @ (c_In @ c_Empty @ Y6) @ Y4 @ Y5)))))) @ Y2 @ Y3))))) @ (c_Repl @ Y0 @ (^[Y2 : $i]: ((^[Y3 : $i]: (c_Repl @ Y3 @ (^[Y4 : $i]: ((^[Y5 : $i > ($i > $i) > $i]: ((^[Y6 : $i]: (c_Eps_i @ (^[Y7 : $i]: ((^[Y8 : $i > ($i > $i) > $i]: ((^[Y9 : $i]: ((^[Y10 : $i]: (!! @ ($i > $i > $o) @ (^[Y11 : $i > $i > $o]: ((!! @ ($i > $i) @ (^[Y12 : $i > $i]: (!! @ $i @ (^[Y13 : $i]: ((!! @ $i @ (^[Y14 : $i]: ((c_In @ Y14 @ Y13) => (Y11 @ Y14 @ (Y12 @ Y14))))) => (Y11 @ Y13 @ (Y8 @ Y13 @ Y12))))))) => (Y11 @ Y9 @ Y10))))))))) @ Y5 @ Y6 @ Y7)))))) @ (^[Y5 : $i]: ((^[Y6 : $i > $i]: ((^[Y7 : $i]: ((^[Y8 : $i]: (c_Union @ ((^[Y9 : $i]: ((^[Y10 : $i]: (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y11 : $i]: ((^[Y12 : $o]: ((^[Y13 : $i]: ((^[Y14 : $i]: (c_Eps_i @ (^[Y15 : $i]: ((^[Y16 : $o]: ((^[Y17 : $o]: (!! @ $o @ (^[Y18 : $o]: ((Y16 => Y18) => ((Y17 => Y18) => Y18))))))) @ ((^[Y16 : $o]: ((^[Y17 : $o]: (!! @ $o @ (^[Y18 : $o]: ((Y16 => (Y17 => Y18)) => Y18)))))) @ Y12 @ (Y13 = Y15)) @ ((^[Y16 : $o]: ((^[Y17 : $o]: (!! @ $o @ (^[Y18 : $o]: ((Y16 => (Y17 => Y18)) => Y18)))))) @ ((^[Y16 : $o]: (Y16 => c_False)) @ Y12) @ (Y14 = Y15)))))))))) @ (c_In @ c_Empty @ Y11) @ Y9 @ Y10)))))) @ Y7 @ Y8))))) @ ((^[Y7 : $i]: ((^[Y8 : $i]: ((^[Y9 : $i]: (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y10 : $i]: ((^[Y11 : $o]: ((^[Y12 : $i]: ((^[Y13 : $i]: (c_Eps_i @ (^[Y14 : $i]: ((^[Y15 : $o]: ((^[Y16 : $o]: (!! @ $o @ (^[Y17 : $o]: ((Y15 => Y17) => ((Y16 => Y17) => Y17))))))) @ ((^[Y15 : $o]: ((^[Y16 : $o]: (!! @ $o @ (^[Y17 : $o]: ((Y15 => (Y16 => Y17)) => Y17)))))) @ Y11 @ (Y12 = Y14)) @ ((^[Y15 : $o]: ((^[Y16 : $o]: (!! @ $o @ (^[Y17 : $o]: ((Y15 => (Y16 => Y17)) => Y17)))))) @ ((^[Y15 : $o]: (Y15 => c_False)) @ Y11) @ (Y13 = Y14)))))))))) @ (c_In @ c_Empty @ Y10) @ Y8 @ Y9)))))) @ Y7 @ Y7)) @ c_Empty) @ (c_Repl @ Y5 @ (^[Y7 : $i]: (Y6 @ Y7))))))) @ Y4)))) @ Y2))) @ (c_Repl @ Y1 @ (^[Y2 : $i]: ((^[Y3 : $i > ($i > $i) > $i]: ((^[Y4 : $i]: (c_Eps_i @ (^[Y5 : $i]: ((^[Y6 : $i > ($i > $i) > $i]: ((^[Y7 : $i]: ((^[Y8 : $i]: (!! @ ($i > $i > $o) @ (^[Y9 : $i > $i > $o]: ((!! @ ($i > $i) @ (^[Y10 : $i > $i]: (!! @ $i @ (^[Y11 : $i]: ((!! @ $i @ (^[Y12 : $i]: ((c_In @ Y12 @ Y11) => (Y9 @ Y12 @ (Y10 @ Y12))))) => (Y9 @ Y11 @ (Y6 @ Y11 @ Y10))))))) => (Y9 @ Y7 @ Y8))))))))) @ Y3 @ Y4 @ Y5)))))) @ (^[Y3 : $i]: ((^[Y4 : $i > $i]: ((^[Y5 : $i]: ((^[Y6 : $i]: (c_Union @ ((^[Y7 : $i]: ((^[Y8 : $i]: (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y9 : $i]: ((^[Y10 : $o]: ((^[Y11 : $i]: ((^[Y12 : $i]: (c_Eps_i @ (^[Y13 : $i]: ((^[Y14 : $o]: ((^[Y15 : $o]: (!! @ $o @ (^[Y16 : $o]: ((Y14 => Y16) => ((Y15 => Y16) => Y16))))))) @ ((^[Y14 : $o]: ((^[Y15 : $o]: (!! @ $o @ (^[Y16 : $o]: ((Y14 => (Y15 => Y16)) => Y16)))))) @ Y10 @ (Y11 = Y13)) @ ((^[Y14 : $o]: ((^[Y15 : $o]: (!! @ $o @ (^[Y16 : $o]: ((Y14 => (Y15 => Y16)) => Y16)))))) @ ((^[Y14 : $o]: (Y14 => c_False)) @ Y10) @ (Y12 = Y13)))))))))) @ (c_In @ c_Empty @ Y9) @ Y7 @ Y8)))))) @ Y5 @ Y6))))) @ ((^[Y5 : $i]: ((^[Y6 : $i]: ((^[Y7 : $i]: (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y8 : $i]: ((^[Y9 : $o]: ((^[Y10 : $i]: ((^[Y11 : $i]: (c_Eps_i @ (^[Y12 : $i]: ((^[Y13 : $o]: ((^[Y14 : $o]: (!! @ $o @ (^[Y15 : $o]: ((Y13 => Y15) => ((Y14 => Y15) => Y15))))))) @ ((^[Y13 : $o]: ((^[Y14 : $o]: (!! @ $o @ (^[Y15 : $o]: ((Y13 => (Y14 => Y15)) => Y15)))))) @ Y9 @ (Y10 = Y12)) @ ((^[Y13 : $o]: ((^[Y14 : $o]: (!! @ $o @ (^[Y15 : $o]: ((Y13 => (Y14 => Y15)) => Y15)))))) @ ((^[Y13 : $o]: (Y13 => c_False)) @ Y9) @ (Y11 = Y12)))))))))) @ (c_In @ c_Empty @ Y8) @ Y6 @ Y7)))))) @ Y5 @ Y5)) @ c_Empty) @ (c_Repl @ Y3 @ (^[Y5 : $i]: (Y4 @ Y5))))))) @ Y2))))))))),
% 9.27/1.88 inference(definition_unfolding,[],[f341,f447,f466,f465])).
% 9.27/1.88 thf(f472,plain,(
% 9.27/1.88 (c_binrep = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: (c_Union @ ((^[Y6 : $i]: ((^[Y7 : $i]: (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y8 : $i]: ((^[Y9 : $o]: ((^[Y10 : $i]: ((^[Y11 : $i]: (c_Eps_i @ (^[Y12 : $i]: ((^[Y13 : $o]: ((^[Y14 : $o]: (!! @ $o @ (^[Y15 : $o]: ((Y13 => Y15) => ((Y14 => Y15) => Y15))))))) @ ((^[Y13 : $o]: ((^[Y14 : $o]: (!! @ $o @ (^[Y15 : $o]: ((Y13 => (Y14 => Y15)) => Y15)))))) @ Y9 @ (Y10 = Y12)) @ ((^[Y13 : $o]: ((^[Y14 : $o]: (!! @ $o @ (^[Y15 : $o]: ((Y13 => (Y14 => Y15)) => Y15)))))) @ ((^[Y13 : $o]: (Y13 => c_False)) @ Y9) @ (Y11 = Y12)))))))))) @ (c_In @ c_Empty @ Y8) @ Y6 @ Y7)))))) @ Y4 @ Y5))))) @ (c_Repl @ Y2 @ (^[Y4 : $i]: ((^[Y5 : $i]: (c_Repl @ Y5 @ (^[Y6 : $i]: ((^[Y7 : $i > ($i > $i) > $i]: ((^[Y8 : $i]: (c_Eps_i @ (^[Y9 : $i]: ((^[Y10 : $i > ($i > $i) > $i]: ((^[Y11 : $i]: ((^[Y12 : $i]: (!! @ ($i > $i > $o) @ (^[Y13 : $i > $i > $o]: ((!! @ ($i > $i) @ (^[Y14 : $i > $i]: (!! @ $i @ (^[Y15 : $i]: ((!! @ $i @ (^[Y16 : $i]: ((c_In @ Y16 @ Y15) => (Y13 @ Y16 @ (Y14 @ Y16))))) => (Y13 @ Y15 @ (Y10 @ Y15 @ Y14))))))) => (Y13 @ Y11 @ Y12))))))))) @ Y7 @ Y8 @ Y9)))))) @ (^[Y7 : $i]: ((^[Y8 : $i > $i]: ((^[Y9 : $i]: ((^[Y10 : $i]: (c_Union @ ((^[Y11 : $i]: ((^[Y12 : $i]: (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y13 : $i]: ((^[Y14 : $o]: ((^[Y15 : $i]: ((^[Y16 : $i]: (c_Eps_i @ (^[Y17 : $i]: ((^[Y18 : $o]: ((^[Y19 : $o]: (!! @ $o @ (^[Y20 : $o]: ((Y18 => Y20) => ((Y19 => Y20) => Y20))))))) @ ((^[Y18 : $o]: ((^[Y19 : $o]: (!! @ $o @ (^[Y20 : $o]: ((Y18 => (Y19 => Y20)) => Y20)))))) @ Y14 @ (Y15 = Y17)) @ ((^[Y18 : $o]: ((^[Y19 : $o]: (!! @ $o @ (^[Y20 : $o]: ((Y18 => (Y19 => Y20)) => Y20)))))) @ ((^[Y18 : $o]: (Y18 => c_False)) @ Y14) @ (Y16 = Y17)))))))))) @ (c_In @ c_Empty @ Y13) @ Y11 @ Y12)))))) @ Y9 @ Y10))))) @ ((^[Y9 : $i]: ((^[Y10 : $i]: ((^[Y11 : $i]: (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y12 : $i]: ((^[Y13 : $o]: ((^[Y14 : $i]: ((^[Y15 : $i]: (c_Eps_i @ (^[Y16 : $i]: ((^[Y17 : $o]: ((^[Y18 : $o]: (!! @ $o @ (^[Y19 : $o]: ((Y17 => Y19) => ((Y18 => Y19) => Y19))))))) @ ((^[Y17 : $o]: ((^[Y18 : $o]: (!! @ $o @ (^[Y19 : $o]: ((Y17 => (Y18 => Y19)) => Y19)))))) @ Y13 @ (Y14 = Y16)) @ ((^[Y17 : $o]: ((^[Y18 : $o]: (!! @ $o @ (^[Y19 : $o]: ((Y17 => (Y18 => Y19)) => Y19)))))) @ ((^[Y17 : $o]: (Y17 => c_False)) @ Y13) @ (Y15 = Y16)))))))))) @ (c_In @ c_Empty @ Y12) @ Y10 @ Y11)))))) @ Y9 @ Y9)) @ c_Empty) @ (c_Repl @ Y7 @ (^[Y9 : $i]: (Y8 @ Y9))))))) @ Y6)))) @ Y4))) @ (c_Repl @ Y3 @ (^[Y4 : $i]: ((^[Y5 : $i > ($i > $i) > $i]: ((^[Y6 : $i]: (c_Eps_i @ (^[Y7 : $i]: ((^[Y8 : $i > ($i > $i) > $i]: ((^[Y9 : $i]: ((^[Y10 : $i]: (!! @ ($i > $i > $o) @ (^[Y11 : $i > $i > $o]: ((!! @ ($i > $i) @ (^[Y12 : $i > $i]: (!! @ $i @ (^[Y13 : $i]: ((!! @ $i @ (^[Y14 : $i]: ((c_In @ Y14 @ Y13) => (Y11 @ Y14 @ (Y12 @ Y14))))) => (Y11 @ Y13 @ (Y8 @ Y13 @ Y12))))))) => (Y11 @ Y9 @ Y10))))))))) @ Y5 @ Y6 @ Y7)))))) @ (^[Y5 : $i]: ((^[Y6 : $i > $i]: ((^[Y7 : $i]: ((^[Y8 : $i]: (c_Union @ ((^[Y9 : $i]: ((^[Y10 : $i]: (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y11 : $i]: ((^[Y12 : $o]: ((^[Y13 : $i]: ((^[Y14 : $i]: (c_Eps_i @ (^[Y15 : $i]: ((^[Y16 : $o]: ((^[Y17 : $o]: (!! @ $o @ (^[Y18 : $o]: ((Y16 => Y18) => ((Y17 => Y18) => Y18))))))) @ ((^[Y16 : $o]: ((^[Y17 : $o]: (!! @ $o @ (^[Y18 : $o]: ((Y16 => (Y17 => Y18)) => Y18)))))) @ Y12 @ (Y13 = Y15)) @ ((^[Y16 : $o]: ((^[Y17 : $o]: (!! @ $o @ (^[Y18 : $o]: ((Y16 => (Y17 => Y18)) => Y18)))))) @ ((^[Y16 : $o]: (Y16 => c_False)) @ Y12) @ (Y14 = Y15)))))))))) @ (c_In @ c_Empty @ Y11) @ Y9 @ Y10)))))) @ Y7 @ Y8))))) @ ((^[Y7 : $i]: ((^[Y8 : $i]: ((^[Y9 : $i]: (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y10 : $i]: ((^[Y11 : $o]: ((^[Y12 : $i]: ((^[Y13 : $i]: (c_Eps_i @ (^[Y14 : $i]: ((^[Y15 : $o]: ((^[Y16 : $o]: (!! @ $o @ (^[Y17 : $o]: ((Y15 => Y17) => ((Y16 => Y17) => Y17))))))) @ ((^[Y15 : $o]: ((^[Y16 : $o]: (!! @ $o @ (^[Y17 : $o]: ((Y15 => (Y16 => Y17)) => Y17)))))) @ Y11 @ (Y12 = Y14)) @ ((^[Y15 : $o]: ((^[Y16 : $o]: (!! @ $o @ (^[Y17 : $o]: ((Y15 => (Y16 => Y17)) => Y17)))))) @ ((^[Y15 : $o]: (Y15 => c_False)) @ Y11) @ (Y13 = Y14)))))))))) @ (c_In @ c_Empty @ Y10) @ Y8 @ Y9)))))) @ Y7 @ Y7)) @ c_Empty) @ (c_Repl @ Y5 @ (^[Y7 : $i]: (Y6 @ Y7))))))) @ Y4))))))) @ Y0 @ (c_Power @ Y1))))))),
% 9.27/1.88 inference(definition_unfolding,[],[f371,f469])).
% 9.27/1.88 thf(f473,plain,(
% 9.27/1.88 (c_lam = (^[Y0 : $i]: ((^[Y1 : $i > $i]: ((^[Y2 : $i]: ((^[Y3 : $i > $i]: (c_Union @ (c_Repl @ Y2 @ (^[Y4 : $i]: (Y3 @ Y4))))))) @ Y0 @ (^[Y2 : $i]: (c_Repl @ (Y1 @ Y2) @ (^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: ((^[Y6 : $i]: ((^[Y7 : $i]: (c_Union @ ((^[Y8 : $i]: ((^[Y9 : $i]: (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y10 : $i]: ((^[Y11 : $o]: ((^[Y12 : $i]: ((^[Y13 : $i]: (c_Eps_i @ (^[Y14 : $i]: ((^[Y15 : $o]: ((^[Y16 : $o]: (!! @ $o @ (^[Y17 : $o]: ((Y15 => Y17) => ((Y16 => Y17) => Y17))))))) @ ((^[Y15 : $o]: ((^[Y16 : $o]: (!! @ $o @ (^[Y17 : $o]: ((Y15 => (Y16 => Y17)) => Y17)))))) @ Y11 @ (Y12 = Y14)) @ ((^[Y15 : $o]: ((^[Y16 : $o]: (!! @ $o @ (^[Y17 : $o]: ((Y15 => (Y16 => Y17)) => Y17)))))) @ ((^[Y15 : $o]: (Y15 => c_False)) @ Y11) @ (Y13 = Y14)))))))))) @ (c_In @ c_Empty @ Y10) @ Y8 @ Y9)))))) @ Y6 @ Y7))))) @ (c_Repl @ Y4 @ (^[Y6 : $i]: ((^[Y7 : $i]: (c_Repl @ Y7 @ (^[Y8 : $i]: ((^[Y9 : $i > ($i > $i) > $i]: ((^[Y10 : $i]: (c_Eps_i @ (^[Y11 : $i]: ((^[Y12 : $i > ($i > $i) > $i]: ((^[Y13 : $i]: ((^[Y14 : $i]: (!! @ ($i > $i > $o) @ (^[Y15 : $i > $i > $o]: ((!! @ ($i > $i) @ (^[Y16 : $i > $i]: (!! @ $i @ (^[Y17 : $i]: ((!! @ $i @ (^[Y18 : $i]: ((c_In @ Y18 @ Y17) => (Y15 @ Y18 @ (Y16 @ Y18))))) => (Y15 @ Y17 @ (Y12 @ Y17 @ Y16))))))) => (Y15 @ Y13 @ Y14))))))))) @ Y9 @ Y10 @ Y11)))))) @ (^[Y9 : $i]: ((^[Y10 : $i > $i]: ((^[Y11 : $i]: ((^[Y12 : $i]: (c_Union @ ((^[Y13 : $i]: ((^[Y14 : $i]: (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y15 : $i]: ((^[Y16 : $o]: ((^[Y17 : $i]: ((^[Y18 : $i]: (c_Eps_i @ (^[Y19 : $i]: ((^[Y20 : $o]: ((^[Y21 : $o]: (!! @ $o @ (^[Y22 : $o]: ((Y20 => Y22) => ((Y21 => Y22) => Y22))))))) @ ((^[Y20 : $o]: ((^[Y21 : $o]: (!! @ $o @ (^[Y22 : $o]: ((Y20 => (Y21 => Y22)) => Y22)))))) @ Y16 @ (Y17 = Y19)) @ ((^[Y20 : $o]: ((^[Y21 : $o]: (!! @ $o @ (^[Y22 : $o]: ((Y20 => (Y21 => Y22)) => Y22)))))) @ ((^[Y20 : $o]: (Y20 => c_False)) @ Y16) @ (Y18 = Y19)))))))))) @ (c_In @ c_Empty @ Y15) @ Y13 @ Y14)))))) @ Y11 @ Y12))))) @ ((^[Y11 : $i]: ((^[Y12 : $i]: ((^[Y13 : $i]: (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y14 : $i]: ((^[Y15 : $o]: ((^[Y16 : $i]: ((^[Y17 : $i]: (c_Eps_i @ (^[Y18 : $i]: ((^[Y19 : $o]: ((^[Y20 : $o]: (!! @ $o @ (^[Y21 : $o]: ((Y19 => Y21) => ((Y20 => Y21) => Y21))))))) @ ((^[Y19 : $o]: ((^[Y20 : $o]: (!! @ $o @ (^[Y21 : $o]: ((Y19 => (Y20 => Y21)) => Y21)))))) @ Y15 @ (Y16 = Y18)) @ ((^[Y19 : $o]: ((^[Y20 : $o]: (!! @ $o @ (^[Y21 : $o]: ((Y19 => (Y20 => Y21)) => Y21)))))) @ ((^[Y19 : $o]: (Y19 => c_False)) @ Y15) @ (Y17 = Y18)))))))))) @ (c_In @ c_Empty @ Y14) @ Y12 @ Y13)))))) @ Y11 @ Y11)) @ c_Empty) @ (c_Repl @ Y9 @ (^[Y11 : $i]: (Y10 @ Y11))))))) @ Y8)))) @ Y6))) @ (c_Repl @ Y5 @ (^[Y6 : $i]: ((^[Y7 : $i > ($i > $i) > $i]: ((^[Y8 : $i]: (c_Eps_i @ (^[Y9 : $i]: ((^[Y10 : $i > ($i > $i) > $i]: ((^[Y11 : $i]: ((^[Y12 : $i]: (!! @ ($i > $i > $o) @ (^[Y13 : $i > $i > $o]: ((!! @ ($i > $i) @ (^[Y14 : $i > $i]: (!! @ $i @ (^[Y15 : $i]: ((!! @ $i @ (^[Y16 : $i]: ((c_In @ Y16 @ Y15) => (Y13 @ Y16 @ (Y14 @ Y16))))) => (Y13 @ Y15 @ (Y10 @ Y15 @ Y14))))))) => (Y13 @ Y11 @ Y12))))))))) @ Y7 @ Y8 @ Y9)))))) @ (^[Y7 : $i]: ((^[Y8 : $i > $i]: ((^[Y9 : $i]: ((^[Y10 : $i]: (c_Union @ ((^[Y11 : $i]: ((^[Y12 : $i]: (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y13 : $i]: ((^[Y14 : $o]: ((^[Y15 : $i]: ((^[Y16 : $i]: (c_Eps_i @ (^[Y17 : $i]: ((^[Y18 : $o]: ((^[Y19 : $o]: (!! @ $o @ (^[Y20 : $o]: ((Y18 => Y20) => ((Y19 => Y20) => Y20))))))) @ ((^[Y18 : $o]: ((^[Y19 : $o]: (!! @ $o @ (^[Y20 : $o]: ((Y18 => (Y19 => Y20)) => Y20)))))) @ Y14 @ (Y15 = Y17)) @ ((^[Y18 : $o]: ((^[Y19 : $o]: (!! @ $o @ (^[Y20 : $o]: ((Y18 => (Y19 => Y20)) => Y20)))))) @ ((^[Y18 : $o]: (Y18 => c_False)) @ Y14) @ (Y16 = Y17)))))))))) @ (c_In @ c_Empty @ Y13) @ Y11 @ Y12)))))) @ Y9 @ Y10))))) @ ((^[Y9 : $i]: ((^[Y10 : $i]: ((^[Y11 : $i]: (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y12 : $i]: ((^[Y13 : $o]: ((^[Y14 : $i]: ((^[Y15 : $i]: (c_Eps_i @ (^[Y16 : $i]: ((^[Y17 : $o]: ((^[Y18 : $o]: (!! @ $o @ (^[Y19 : $o]: ((Y17 => Y19) => ((Y18 => Y19) => Y19))))))) @ ((^[Y17 : $o]: ((^[Y18 : $o]: (!! @ $o @ (^[Y19 : $o]: ((Y17 => (Y18 => Y19)) => Y19)))))) @ Y13 @ (Y14 = Y16)) @ ((^[Y17 : $o]: ((^[Y18 : $o]: (!! @ $o @ (^[Y19 : $o]: ((Y17 => (Y18 => Y19)) => Y19)))))) @ ((^[Y17 : $o]: (Y17 => c_False)) @ Y13) @ (Y15 = Y16)))))))))) @ (c_In @ c_Empty @ Y12) @ Y10 @ Y11)))))) @ Y9 @ Y9)) @ c_Empty) @ (c_Repl @ Y7 @ (^[Y9 : $i]: (Y8 @ Y9))))))) @ Y6))))))) @ Y2 @ Y3)))))))))),
% 9.27/1.88 inference(definition_unfolding,[],[f345,f331,f469])).
% 9.27/1.88 thf(f474,plain,(
% 9.27/1.88 (c_setprod = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i > $i]: ((^[Y4 : $i]: ((^[Y5 : $i > $i]: (c_Union @ (c_Repl @ Y4 @ (^[Y6 : $i]: (Y5 @ Y6))))))) @ Y2 @ (^[Y4 : $i]: (c_Repl @ (Y3 @ Y4) @ (^[Y5 : $i]: ((^[Y6 : $i]: ((^[Y7 : $i]: ((^[Y8 : $i]: ((^[Y9 : $i]: (c_Union @ ((^[Y10 : $i]: ((^[Y11 : $i]: (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y12 : $i]: ((^[Y13 : $o]: ((^[Y14 : $i]: ((^[Y15 : $i]: (c_Eps_i @ (^[Y16 : $i]: ((^[Y17 : $o]: ((^[Y18 : $o]: (!! @ $o @ (^[Y19 : $o]: ((Y17 => Y19) => ((Y18 => Y19) => Y19))))))) @ ((^[Y17 : $o]: ((^[Y18 : $o]: (!! @ $o @ (^[Y19 : $o]: ((Y17 => (Y18 => Y19)) => Y19)))))) @ Y13 @ (Y14 = Y16)) @ ((^[Y17 : $o]: ((^[Y18 : $o]: (!! @ $o @ (^[Y19 : $o]: ((Y17 => (Y18 => Y19)) => Y19)))))) @ ((^[Y17 : $o]: (Y17 => c_False)) @ Y13) @ (Y15 = Y16)))))))))) @ (c_In @ c_Empty @ Y12) @ Y10 @ Y11)))))) @ Y8 @ Y9))))) @ (c_Repl @ Y6 @ (^[Y8 : $i]: ((^[Y9 : $i]: (c_Repl @ Y9 @ (^[Y10 : $i]: ((^[Y11 : $i > ($i > $i) > $i]: ((^[Y12 : $i]: (c_Eps_i @ (^[Y13 : $i]: ((^[Y14 : $i > ($i > $i) > $i]: ((^[Y15 : $i]: ((^[Y16 : $i]: (!! @ ($i > $i > $o) @ (^[Y17 : $i > $i > $o]: ((!! @ ($i > $i) @ (^[Y18 : $i > $i]: (!! @ $i @ (^[Y19 : $i]: ((!! @ $i @ (^[Y20 : $i]: ((c_In @ Y20 @ Y19) => (Y17 @ Y20 @ (Y18 @ Y20))))) => (Y17 @ Y19 @ (Y14 @ Y19 @ Y18))))))) => (Y17 @ Y15 @ Y16))))))))) @ Y11 @ Y12 @ Y13)))))) @ (^[Y11 : $i]: ((^[Y12 : $i > $i]: ((^[Y13 : $i]: ((^[Y14 : $i]: (c_Union @ ((^[Y15 : $i]: ((^[Y16 : $i]: (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y17 : $i]: ((^[Y18 : $o]: ((^[Y19 : $i]: ((^[Y20 : $i]: (c_Eps_i @ (^[Y21 : $i]: ((^[Y22 : $o]: ((^[Y23 : $o]: (!! @ $o @ (^[Y24 : $o]: ((Y22 => Y24) => ((Y23 => Y24) => Y24))))))) @ ((^[Y22 : $o]: ((^[Y23 : $o]: (!! @ $o @ (^[Y24 : $o]: ((Y22 => (Y23 => Y24)) => Y24)))))) @ Y18 @ (Y19 = Y21)) @ ((^[Y22 : $o]: ((^[Y23 : $o]: (!! @ $o @ (^[Y24 : $o]: ((Y22 => (Y23 => Y24)) => Y24)))))) @ ((^[Y22 : $o]: (Y22 => c_False)) @ Y18) @ (Y20 = Y21)))))))))) @ (c_In @ c_Empty @ Y17) @ Y15 @ Y16)))))) @ Y13 @ Y14))))) @ ((^[Y13 : $i]: ((^[Y14 : $i]: ((^[Y15 : $i]: (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y16 : $i]: ((^[Y17 : $o]: ((^[Y18 : $i]: ((^[Y19 : $i]: (c_Eps_i @ (^[Y20 : $i]: ((^[Y21 : $o]: ((^[Y22 : $o]: (!! @ $o @ (^[Y23 : $o]: ((Y21 => Y23) => ((Y22 => Y23) => Y23))))))) @ ((^[Y21 : $o]: ((^[Y22 : $o]: (!! @ $o @ (^[Y23 : $o]: ((Y21 => (Y22 => Y23)) => Y23)))))) @ Y17 @ (Y18 = Y20)) @ ((^[Y21 : $o]: ((^[Y22 : $o]: (!! @ $o @ (^[Y23 : $o]: ((Y21 => (Y22 => Y23)) => Y23)))))) @ ((^[Y21 : $o]: (Y21 => c_False)) @ Y17) @ (Y19 = Y20)))))))))) @ (c_In @ c_Empty @ Y16) @ Y14 @ Y15)))))) @ Y13 @ Y13)) @ c_Empty) @ (c_Repl @ Y11 @ (^[Y13 : $i]: (Y12 @ Y13))))))) @ Y10)))) @ Y8))) @ (c_Repl @ Y7 @ (^[Y8 : $i]: ((^[Y9 : $i > ($i > $i) > $i]: ((^[Y10 : $i]: (c_Eps_i @ (^[Y11 : $i]: ((^[Y12 : $i > ($i > $i) > $i]: ((^[Y13 : $i]: ((^[Y14 : $i]: (!! @ ($i > $i > $o) @ (^[Y15 : $i > $i > $o]: ((!! @ ($i > $i) @ (^[Y16 : $i > $i]: (!! @ $i @ (^[Y17 : $i]: ((!! @ $i @ (^[Y18 : $i]: ((c_In @ Y18 @ Y17) => (Y15 @ Y18 @ (Y16 @ Y18))))) => (Y15 @ Y17 @ (Y12 @ Y17 @ Y16))))))) => (Y15 @ Y13 @ Y14))))))))) @ Y9 @ Y10 @ Y11)))))) @ (^[Y9 : $i]: ((^[Y10 : $i > $i]: ((^[Y11 : $i]: ((^[Y12 : $i]: (c_Union @ ((^[Y13 : $i]: ((^[Y14 : $i]: (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y15 : $i]: ((^[Y16 : $o]: ((^[Y17 : $i]: ((^[Y18 : $i]: (c_Eps_i @ (^[Y19 : $i]: ((^[Y20 : $o]: ((^[Y21 : $o]: (!! @ $o @ (^[Y22 : $o]: ((Y20 => Y22) => ((Y21 => Y22) => Y22))))))) @ ((^[Y20 : $o]: ((^[Y21 : $o]: (!! @ $o @ (^[Y22 : $o]: ((Y20 => (Y21 => Y22)) => Y22)))))) @ Y16 @ (Y17 = Y19)) @ ((^[Y20 : $o]: ((^[Y21 : $o]: (!! @ $o @ (^[Y22 : $o]: ((Y20 => (Y21 => Y22)) => Y22)))))) @ ((^[Y20 : $o]: (Y20 => c_False)) @ Y16) @ (Y18 = Y19)))))))))) @ (c_In @ c_Empty @ Y15) @ Y13 @ Y14)))))) @ Y11 @ Y12))))) @ ((^[Y11 : $i]: ((^[Y12 : $i]: ((^[Y13 : $i]: (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y14 : $i]: ((^[Y15 : $o]: ((^[Y16 : $i]: ((^[Y17 : $i]: (c_Eps_i @ (^[Y18 : $i]: ((^[Y19 : $o]: ((^[Y20 : $o]: (!! @ $o @ (^[Y21 : $o]: ((Y19 => Y21) => ((Y20 => Y21) => Y21))))))) @ ((^[Y19 : $o]: ((^[Y20 : $o]: (!! @ $o @ (^[Y21 : $o]: ((Y19 => (Y20 => Y21)) => Y21)))))) @ Y15 @ (Y16 = Y18)) @ ((^[Y19 : $o]: ((^[Y20 : $o]: (!! @ $o @ (^[Y21 : $o]: ((Y19 => (Y20 => Y21)) => Y21)))))) @ ((^[Y19 : $o]: (Y19 => c_False)) @ Y15) @ (Y17 = Y18)))))))))) @ (c_In @ c_Empty @ Y14) @ Y12 @ Y13)))))) @ Y11 @ Y11)) @ c_Empty) @ (c_Repl @ Y9 @ (^[Y11 : $i]: (Y10 @ Y11))))))) @ Y8))))))) @ Y4 @ Y5)))))))) @ Y0 @ (^[Y2 : $i]: (Y1)))))))),
% 9.27/1.88 inference(definition_unfolding,[],[f330,f473])).
% 9.27/1.88 thf(f489,plain,(
% 9.27/1.88 (c_SNoElts_ = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (c_Union @ ((^[Y3 : $i]: ((^[Y4 : $i]: (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y5 : $i]: ((^[Y6 : $o]: ((^[Y7 : $i]: ((^[Y8 : $i]: (c_Eps_i @ (^[Y9 : $i]: ((^[Y10 : $o]: ((^[Y11 : $o]: (!! @ $o @ (^[Y12 : $o]: ((Y10 => Y12) => ((Y11 => Y12) => Y12))))))) @ ((^[Y10 : $o]: ((^[Y11 : $o]: (!! @ $o @ (^[Y12 : $o]: ((Y10 => (Y11 => Y12)) => Y12)))))) @ Y6 @ (Y7 = Y9)) @ ((^[Y10 : $o]: ((^[Y11 : $o]: (!! @ $o @ (^[Y12 : $o]: ((Y10 => (Y11 => Y12)) => Y12)))))) @ ((^[Y10 : $o]: (Y10 => c_False)) @ Y6) @ (Y8 = Y9)))))))))) @ (c_In @ c_Empty @ Y5) @ Y3 @ Y4)))))) @ Y1 @ Y2))))) @ Y0 @ (c_Repl @ Y0 @ (^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: ((^[Y6 : $i]: (c_Union @ ((^[Y7 : $i]: ((^[Y8 : $i]: (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y9 : $i]: ((^[Y10 : $o]: ((^[Y11 : $i]: ((^[Y12 : $i]: (c_Eps_i @ (^[Y13 : $i]: ((^[Y14 : $o]: ((^[Y15 : $o]: (!! @ $o @ (^[Y16 : $o]: ((Y14 => Y16) => ((Y15 => Y16) => Y16))))))) @ ((^[Y14 : $o]: ((^[Y15 : $o]: (!! @ $o @ (^[Y16 : $o]: ((Y14 => (Y15 => Y16)) => Y16)))))) @ Y10 @ (Y11 = Y13)) @ ((^[Y14 : $o]: ((^[Y15 : $o]: (!! @ $o @ (^[Y16 : $o]: ((Y14 => (Y15 => Y16)) => Y16)))))) @ ((^[Y14 : $o]: (Y14 => c_False)) @ Y10) @ (Y12 = Y13)))))))))) @ (c_In @ c_Empty @ Y9) @ Y7 @ Y8)))))) @ Y5 @ Y6))))) @ Y3 @ ((^[Y5 : $i]: ((^[Y6 : $i]: ((^[Y7 : $i]: (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y8 : $i]: ((^[Y9 : $o]: ((^[Y10 : $i]: ((^[Y11 : $i]: (c_Eps_i @ (^[Y12 : $i]: ((^[Y13 : $o]: ((^[Y14 : $o]: (!! @ $o @ (^[Y15 : $o]: ((Y13 => Y15) => ((Y14 => Y15) => Y15))))))) @ ((^[Y13 : $o]: ((^[Y14 : $o]: (!! @ $o @ (^[Y15 : $o]: ((Y13 => (Y14 => Y15)) => Y15)))))) @ Y9 @ (Y10 = Y12)) @ ((^[Y13 : $o]: ((^[Y14 : $o]: (!! @ $o @ (^[Y15 : $o]: ((Y13 => (Y14 => Y15)) => Y15)))))) @ ((^[Y13 : $o]: (Y13 => c_False)) @ Y9) @ (Y11 = Y12)))))))))) @ (c_In @ c_Empty @ Y8) @ Y6 @ Y7)))))) @ Y5 @ Y5)) @ Y4))))) @ Y2 @ ((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y6 : $i]: ((^[Y7 : $o]: ((^[Y8 : $i]: ((^[Y9 : $i]: (c_Eps_i @ (^[Y10 : $i]: ((^[Y11 : $o]: ((^[Y12 : $o]: (!! @ $o @ (^[Y13 : $o]: ((Y11 => Y13) => ((Y12 => Y13) => Y13))))))) @ ((^[Y11 : $o]: ((^[Y12 : $o]: (!! @ $o @ (^[Y13 : $o]: ((Y11 => (Y12 => Y13)) => Y13)))))) @ Y7 @ (Y8 = Y10)) @ ((^[Y11 : $o]: ((^[Y12 : $o]: (!! @ $o @ (^[Y13 : $o]: ((Y11 => (Y12 => Y13)) => Y13)))))) @ ((^[Y11 : $o]: (Y11 => c_False)) @ Y7) @ (Y9 = Y10)))))))))) @ (c_In @ c_Empty @ Y6) @ Y4 @ Y5)))))) @ Y3 @ Y3)) @ ((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: (c_Union @ ((^[Y6 : $i]: ((^[Y7 : $i]: (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y8 : $i]: ((^[Y9 : $o]: ((^[Y10 : $i]: ((^[Y11 : $i]: (c_Eps_i @ (^[Y12 : $i]: ((^[Y13 : $o]: ((^[Y14 : $o]: (!! @ $o @ (^[Y15 : $o]: ((Y13 => Y15) => ((Y14 => Y15) => Y15))))))) @ ((^[Y13 : $o]: ((^[Y14 : $o]: (!! @ $o @ (^[Y15 : $o]: ((Y13 => (Y14 => Y15)) => Y15)))))) @ Y9 @ (Y10 = Y12)) @ ((^[Y13 : $o]: ((^[Y14 : $o]: (!! @ $o @ (^[Y15 : $o]: ((Y13 => (Y14 => Y15)) => Y15)))))) @ ((^[Y13 : $o]: (Y13 => c_False)) @ Y9) @ (Y11 = Y12)))))))))) @ (c_In @ c_Empty @ Y8) @ Y6 @ Y7)))))) @ Y4 @ Y5))))) @ Y3 @ ((^[Y4 : $i]: ((^[Y5 : $i]: ((^[Y6 : $i]: (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y7 : $i]: ((^[Y8 : $o]: ((^[Y9 : $i]: ((^[Y10 : $i]: (c_Eps_i @ (^[Y11 : $i]: ((^[Y12 : $o]: ((^[Y13 : $o]: (!! @ $o @ (^[Y14 : $o]: ((Y12 => Y14) => ((Y13 => Y14) => Y14))))))) @ ((^[Y12 : $o]: ((^[Y13 : $o]: (!! @ $o @ (^[Y14 : $o]: ((Y12 => (Y13 => Y14)) => Y14)))))) @ Y8 @ (Y9 = Y11)) @ ((^[Y12 : $o]: ((^[Y13 : $o]: (!! @ $o @ (^[Y14 : $o]: ((Y12 => (Y13 => Y14)) => Y14)))))) @ ((^[Y12 : $o]: (Y12 => c_False)) @ Y8) @ (Y10 = Y11)))))))))) @ (c_In @ c_Empty @ Y7) @ Y5 @ Y6)))))) @ Y4 @ Y4)) @ Y3))) @ c_Empty)))) @ Y1))))))),
% 9.27/1.88 inference(definition_unfolding,[],[f327,f447,f448,f446,f458])).
% 9.27/1.88 thf(f490,plain,(
% 9.27/1.88 (c_SNo_ = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $o]: ((^[Y3 : $o]: (!! @ $o @ (^[Y4 : $o]: ((Y2 => (Y3 => Y4)) => Y4)))))) @ ((^[Y2 : $i]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((c_In @ Y4 @ Y2) => (c_In @ Y4 @ Y3))))))) @ Y1 @ ((^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: (c_Union @ ((^[Y5 : $i]: ((^[Y6 : $i]: (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y7 : $i]: ((^[Y8 : $o]: ((^[Y9 : $i]: ((^[Y10 : $i]: (c_Eps_i @ (^[Y11 : $i]: ((^[Y12 : $o]: ((^[Y13 : $o]: (!! @ $o @ (^[Y14 : $o]: ((Y12 => Y14) => ((Y13 => Y14) => Y14))))))) @ ((^[Y12 : $o]: ((^[Y13 : $o]: (!! @ $o @ (^[Y14 : $o]: ((Y12 => (Y13 => Y14)) => Y14)))))) @ Y8 @ (Y9 = Y11)) @ ((^[Y12 : $o]: ((^[Y13 : $o]: (!! @ $o @ (^[Y14 : $o]: ((Y12 => (Y13 => Y14)) => Y14)))))) @ ((^[Y12 : $o]: (Y12 => c_False)) @ Y8) @ (Y10 = Y11)))))))))) @ (c_In @ c_Empty @ Y7) @ Y5 @ Y6)))))) @ Y3 @ Y4))))) @ Y2 @ (c_Repl @ Y2 @ (^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: ((^[Y6 : $i]: ((^[Y7 : $i]: ((^[Y8 : $i]: (c_Union @ ((^[Y9 : $i]: ((^[Y10 : $i]: (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y11 : $i]: ((^[Y12 : $o]: ((^[Y13 : $i]: ((^[Y14 : $i]: (c_Eps_i @ (^[Y15 : $i]: ((^[Y16 : $o]: ((^[Y17 : $o]: (!! 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@ $o @ (^[Y15 : $o]: ((Y13 => Y15) => ((Y14 => Y15) => Y15))))))) @ ((^[Y13 : $o]: ((^[Y14 : $o]: (!! @ $o @ (^[Y15 : $o]: ((Y13 => (Y14 => Y15)) => Y15)))))) @ Y9 @ (Y10 = Y12)) @ ((^[Y13 : $o]: ((^[Y14 : $o]: (!! @ $o @ (^[Y15 : $o]: ((Y13 => (Y14 => Y15)) => Y15)))))) @ ((^[Y13 : $o]: (Y13 => c_False)) @ Y9) @ (Y11 = Y12)))))))))) @ (c_In @ c_Empty @ Y8) @ Y6 @ Y7)))))) @ Y5 @ Y5)) @ Y4))) @ c_Empty)))) @ Y2) @ Y1) @ (c_In @ Y2 @ Y1))))))))))),
% 9.27/1.88 inference(definition_unfolding,[],[f368,f402,f375,f489,f441,f448,f446,f458])).
% 9.27/1.88 thf(f492,plain,(
% 9.27/1.88 (c_SNo = (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((^[Y2 : $o]: ((^[Y3 : $o]: (!! @ $o @ (^[Y4 : $o]: ((Y2 => (Y3 => Y4)) => Y4)))))) @ ((^[Y2 : $i]: ((^[Y3 : $o]: ((^[Y4 : $o]: (!! @ $o @ (^[Y5 : $o]: ((Y3 => (Y4 => Y5)) => Y5)))))) @ ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((c_In @ Y4 @ Y3) => ((^[Y5 : $i]: ((^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((c_In @ Y7 @ Y5) => (c_In @ Y7 @ Y6))))))) @ Y4 @ Y3))))) @ Y2) @ (!! @ $i @ (^[Y3 : $i]: ((c_In @ Y3 @ Y2) => ((^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((c_In @ Y5 @ Y4) => ((^[Y6 : $i]: ((^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((c_In @ Y8 @ Y6) => (c_In @ Y8 @ Y7))))))) @ Y5 @ Y4))))) @ Y3)))))) @ Y1) @ ((^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $o]: ((^[Y5 : $o]: (!! @ $o @ (^[Y6 : $o]: ((Y4 => (Y5 => Y6)) => Y6)))))) @ ((^[Y4 : $i]: ((^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ Y4) => (c_In @ Y6 @ Y5))))))) @ Y3 @ ((^[Y4 : $i]: ((^[Y5 : $i]: ((^[Y6 : $i]: (c_Union @ ((^[Y7 : $i]: ((^[Y8 : $i]: (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y9 : $i]: ((^[Y10 : $o]: ((^[Y11 : $i]: ((^[Y12 : $i]: (c_Eps_i @ (^[Y13 : $i]: ((^[Y14 : $o]: ((^[Y15 : $o]: (!! 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% 9.27/1.88 inference(definition_unfolding,[],[f408,f402,f463,f490])).
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% 9.27/1.88 inference(definition_unfolding,[],[f310,f387,f402,f451,f472,f420,f402,f375,f426,f458,f402,f402,f375,f402,f375,f387,f474,f472,f472,f387,f492,f387,f472,f472,f472])).
% 9.27/1.88 thf(f505,plain,(
% 9.27/1.88 ($true = (((^[Y0 : $o]: (Y0 => c_False)) @ (?? @ $i @ (^[Y0 : $i]: (c_In @ Y0 @ c_Empty))))))),
% 9.27/1.88 inference(definition_unfolding,[],[f315,f387])).
% 9.27/1.88 thf(f512,definition,(
% 9.27/1.88 (sF0 = ((c_Power @ c_Empty)))),
% 9.27/1.88 introduced(definition,[new_symbols(definition,[sF0])],[function_definition])).
% 9.27/1.88 thf(f513,plain,(
% 9.27/1.88 (((c_Power @ c_Empty)) = sF0)),
% 9.27/1.88 inference(reorient_equations,[],[f512])).
% 9.27/1.88 thf(f514,definition,(
% 9.27/1.88 (sF1 = ((c_Power @ sF0)))),
% 9.27/1.88 introduced(definition,[new_symbols(definition,[sF1])],[function_definition])).
% 9.27/1.88 thf(f515,plain,(
% 9.27/1.88 (((c_Power @ sF0)) = sF1)),
% 9.27/1.88 inference(reorient_equations,[],[f514])).
% 9.27/1.88 thf(f516,definition,(
% 9.27/1.88 (sF2 = (((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (c_Repl @ sF1 @ (^[Y3 : $i]: ((^[Y4 : $o]: ((^[Y5 : $i]: ((^[Y6 : $i]: (c_Eps_i @ (^[Y7 : $i]: ((^[Y8 : $o]: ((^[Y9 : $o]: (!! @ $o @ (^[Y10 : $o]: ((Y8 => Y10) => ((Y9 => Y10) => Y10))))))) @ ((^[Y8 : $o]: ((^[Y9 : $o]: (!! @ $o @ (^[Y10 : $o]: ((Y8 => (Y9 => Y10)) => Y10)))))) @ Y4 @ (Y5 = Y7)) @ ((^[Y8 : $o]: ((^[Y9 : $o]: (!! @ $o @ (^[Y10 : $o]: ((Y8 => (Y9 => Y10)) => Y10)))))) @ ((^[Y8 : $o]: (Y8 => c_False)) @ Y4) @ (Y6 = Y7)))))))))) @ (c_In @ c_Empty @ Y3) @ Y1 @ Y2)))))) @ Y0 @ Y0)) @ c_Empty)))),
% 9.27/1.88 introduced(definition,[new_symbols(definition,[sF2])],[function_definition])).
% 9.27/1.88 thf(f517,plain,(
% 9.27/1.88 ((((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (c_Repl @ sF1 @ (^[Y3 : $i]: ((^[Y4 : $o]: ((^[Y5 : $i]: ((^[Y6 : $i]: (c_Eps_i @ (^[Y7 : $i]: ((^[Y8 : $o]: ((^[Y9 : $o]: (!! @ $o @ (^[Y10 : $o]: ((Y8 => Y10) => ((Y9 => Y10) => Y10))))))) @ ((^[Y8 : $o]: ((^[Y9 : $o]: (!! @ $o @ (^[Y10 : $o]: ((Y8 => (Y9 => Y10)) => Y10)))))) @ Y4 @ (Y5 = Y7)) @ ((^[Y8 : $o]: ((^[Y9 : $o]: (!! @ $o @ (^[Y10 : $o]: ((Y8 => (Y9 => Y10)) => Y10)))))) @ ((^[Y8 : $o]: (Y8 => c_False)) @ Y4) @ (Y6 = Y7)))))))))) @ (c_In @ c_Empty @ Y3) @ Y1 @ Y2)))))) @ Y0 @ Y0)) @ c_Empty)) = sF2)),
% 9.27/1.88 inference(reorient_equations,[],[f516])).
% 9.27/1.88 thf(f518,definition,(
% 9.27/1.88 (sF3 = ((c_Power @ sF1)))),
% 9.27/1.88 introduced(definition,[new_symbols(definition,[sF3])],[function_definition])).
% 9.27/1.88 thf(f519,plain,(
% 9.27/1.88 (((c_Power @ sF1)) = sF3)),
% 9.27/1.88 inference(reorient_equations,[],[f518])).
% 9.27/1.88 thf(f520,definition,(
% 9.27/1.88 (sF4 = (((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: (c_Union @ ((^[Y6 : $i]: ((^[Y7 : $i]: (c_Repl @ sF1 @ (^[Y8 : $i]: ((^[Y9 : $o]: ((^[Y10 : $i]: ((^[Y11 : $i]: (c_Eps_i @ (^[Y12 : $i]: ((^[Y13 : $o]: ((^[Y14 : $o]: (!! @ $o @ (^[Y15 : $o]: ((Y13 => Y15) => ((Y14 => Y15) => Y15))))))) @ ((^[Y13 : $o]: ((^[Y14 : $o]: (!! @ $o @ (^[Y15 : $o]: ((Y13 => (Y14 => Y15)) => Y15)))))) @ Y9 @ (Y10 = Y12)) @ ((^[Y13 : $o]: ((^[Y14 : $o]: (!! @ $o @ (^[Y15 : $o]: ((Y13 => (Y14 => Y15)) => Y15)))))) @ ((^[Y13 : $o]: (Y13 => c_False)) @ Y9) @ (Y11 = Y12)))))))))) @ (c_In @ c_Empty @ Y8) @ Y6 @ Y7)))))) @ Y4 @ Y5))))) @ (c_Repl @ Y2 @ (^[Y4 : $i]: ((^[Y5 : $i]: (c_Repl @ Y5 @ (^[Y6 : $i]: ((^[Y7 : $i > ($i > $i) > $i]: ((^[Y8 : $i]: (c_Eps_i @ (^[Y9 : $i]: ((^[Y10 : $i > ($i > $i) > $i]: ((^[Y11 : $i]: ((^[Y12 : $i]: (!! @ ($i > $i > $o) @ (^[Y13 : $i > $i > $o]: ((!! @ ($i > $i) @ (^[Y14 : $i > $i]: (!! @ $i @ (^[Y15 : $i]: ((!! @ $i @ (^[Y16 : $i]: ((c_In @ Y16 @ Y15) => (Y13 @ Y16 @ (Y14 @ Y16))))) => (Y13 @ Y15 @ (Y10 @ Y15 @ Y14))))))) => (Y13 @ Y11 @ Y12))))))))) @ Y7 @ Y8 @ Y9)))))) @ (^[Y7 : $i]: ((^[Y8 : $i > $i]: ((^[Y9 : $i]: ((^[Y10 : $i]: (c_Union @ ((^[Y11 : $i]: ((^[Y12 : $i]: (c_Repl @ sF1 @ (^[Y13 : $i]: ((^[Y14 : $o]: ((^[Y15 : $i]: ((^[Y16 : $i]: (c_Eps_i @ (^[Y17 : $i]: ((^[Y18 : $o]: ((^[Y19 : $o]: (!! @ $o @ (^[Y20 : $o]: ((Y18 => Y20) => ((Y19 => Y20) => Y20))))))) @ ((^[Y18 : $o]: ((^[Y19 : $o]: (!! @ $o @ (^[Y20 : $o]: ((Y18 => (Y19 => Y20)) => Y20)))))) @ Y14 @ (Y15 = Y17)) @ ((^[Y18 : $o]: ((^[Y19 : $o]: (!! @ $o @ (^[Y20 : $o]: ((Y18 => (Y19 => Y20)) => Y20)))))) @ ((^[Y18 : $o]: (Y18 => c_False)) @ Y14) @ (Y16 = Y17)))))))))) @ (c_In @ c_Empty @ Y13) @ Y11 @ Y12)))))) @ Y9 @ Y10))))) @ sF2 @ (c_Repl @ Y7 @ (^[Y9 : $i]: (Y8 @ Y9))))))) @ Y6)))) @ Y4))) @ (c_Repl @ Y3 @ (^[Y4 : $i]: ((^[Y5 : $i > ($i > $i) > $i]: ((^[Y6 : $i]: (c_Eps_i @ (^[Y7 : $i]: ((^[Y8 : $i > ($i > $i) > $i]: ((^[Y9 : $i]: ((^[Y10 : $i]: (!! @ ($i > $i > $o) @ (^[Y11 : $i > $i > $o]: ((!! @ ($i > $i) @ (^[Y12 : $i > $i]: (!! @ $i @ (^[Y13 : $i]: ((!! @ $i @ (^[Y14 : $i]: ((c_In @ Y14 @ Y13) => (Y11 @ Y14 @ (Y12 @ Y14))))) => (Y11 @ Y13 @ (Y8 @ Y13 @ Y12))))))) => (Y11 @ Y9 @ Y10))))))))) @ Y5 @ Y6 @ Y7)))))) @ (^[Y5 : $i]: ((^[Y6 : $i > $i]: ((^[Y7 : $i]: ((^[Y8 : $i]: (c_Union @ ((^[Y9 : $i]: ((^[Y10 : $i]: (c_Repl @ sF1 @ (^[Y11 : $i]: ((^[Y12 : $o]: ((^[Y13 : $i]: ((^[Y14 : $i]: (c_Eps_i @ (^[Y15 : $i]: ((^[Y16 : $o]: ((^[Y17 : $o]: (!! @ $o @ (^[Y18 : $o]: ((Y16 => Y18) => ((Y17 => Y18) => Y18))))))) @ ((^[Y16 : $o]: ((^[Y17 : $o]: (!! @ $o @ (^[Y18 : $o]: ((Y16 => (Y17 => Y18)) => Y18)))))) @ Y12 @ (Y13 = Y15)) @ ((^[Y16 : $o]: ((^[Y17 : $o]: (!! @ $o @ (^[Y18 : $o]: ((Y16 => (Y17 => Y18)) => Y18)))))) @ ((^[Y16 : $o]: (Y16 => c_False)) @ Y12) @ (Y14 = Y15)))))))))) @ (c_In @ c_Empty @ Y11) @ Y9 @ Y10)))))) @ Y7 @ Y8))))) @ sF2 @ (c_Repl @ Y5 @ (^[Y7 : $i]: (Y6 @ Y7))))))) @ Y4))))))) @ Y0 @ (c_Power @ Y1))))) @ sF3 @ c_Empty)))),
% 9.27/1.88 introduced(definition,[new_symbols(definition,[sF4])],[function_definition])).
% 9.27/1.88 thf(f521,plain,(
% 9.27/1.88 ((((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: (c_Union @ ((^[Y6 : $i]: ((^[Y7 : $i]: (c_Repl @ sF1 @ (^[Y8 : $i]: ((^[Y9 : $o]: ((^[Y10 : $i]: ((^[Y11 : $i]: (c_Eps_i @ (^[Y12 : $i]: ((^[Y13 : $o]: ((^[Y14 : $o]: (!! @ $o @ (^[Y15 : $o]: ((Y13 => Y15) => ((Y14 => Y15) => Y15))))))) @ ((^[Y13 : $o]: ((^[Y14 : $o]: (!! @ $o @ (^[Y15 : $o]: ((Y13 => (Y14 => Y15)) => Y15)))))) @ Y9 @ (Y10 = Y12)) @ ((^[Y13 : $o]: ((^[Y14 : $o]: (!! @ $o @ (^[Y15 : $o]: ((Y13 => (Y14 => Y15)) => Y15)))))) @ ((^[Y13 : $o]: (Y13 => c_False)) @ Y9) @ (Y11 = Y12)))))))))) @ (c_In @ c_Empty @ Y8) @ Y6 @ Y7)))))) @ Y4 @ Y5))))) @ (c_Repl @ Y2 @ (^[Y4 : $i]: ((^[Y5 : $i]: (c_Repl @ Y5 @ (^[Y6 : $i]: ((^[Y7 : $i > ($i > $i) > $i]: ((^[Y8 : $i]: (c_Eps_i @ (^[Y9 : $i]: ((^[Y10 : $i > ($i > $i) > $i]: ((^[Y11 : $i]: ((^[Y12 : $i]: (!! @ ($i > $i > $o) @ (^[Y13 : $i > $i > $o]: ((!! @ ($i > $i) @ (^[Y14 : $i > $i]: (!! @ $i @ (^[Y15 : $i]: ((!! @ $i @ (^[Y16 : $i]: ((c_In @ Y16 @ Y15) => (Y13 @ Y16 @ (Y14 @ Y16))))) => (Y13 @ Y15 @ (Y10 @ Y15 @ Y14))))))) => (Y13 @ Y11 @ Y12))))))))) @ Y7 @ Y8 @ Y9)))))) @ (^[Y7 : $i]: ((^[Y8 : $i > $i]: ((^[Y9 : $i]: ((^[Y10 : $i]: (c_Union @ ((^[Y11 : $i]: ((^[Y12 : $i]: (c_Repl @ sF1 @ (^[Y13 : $i]: ((^[Y14 : $o]: ((^[Y15 : $i]: ((^[Y16 : $i]: (c_Eps_i @ (^[Y17 : $i]: ((^[Y18 : $o]: ((^[Y19 : $o]: (!! @ $o @ (^[Y20 : $o]: ((Y18 => Y20) => ((Y19 => Y20) => Y20))))))) @ ((^[Y18 : $o]: ((^[Y19 : $o]: (!! @ $o @ (^[Y20 : $o]: ((Y18 => (Y19 => Y20)) => Y20)))))) @ Y14 @ (Y15 = Y17)) @ ((^[Y18 : $o]: ((^[Y19 : $o]: (!! @ $o @ (^[Y20 : $o]: ((Y18 => (Y19 => Y20)) => Y20)))))) @ ((^[Y18 : $o]: (Y18 => c_False)) @ Y14) @ (Y16 = Y17)))))))))) @ (c_In @ c_Empty @ Y13) @ Y11 @ Y12)))))) @ Y9 @ Y10))))) @ sF2 @ (c_Repl @ Y7 @ (^[Y9 : $i]: (Y8 @ Y9))))))) @ Y6)))) @ Y4))) @ (c_Repl @ Y3 @ (^[Y4 : $i]: ((^[Y5 : $i > ($i > $i) > $i]: ((^[Y6 : $i]: (c_Eps_i @ (^[Y7 : $i]: ((^[Y8 : $i > ($i > $i) > $i]: ((^[Y9 : $i]: ((^[Y10 : $i]: (!! @ ($i > $i > $o) @ (^[Y11 : $i > $i > $o]: ((!! @ ($i > $i) @ (^[Y12 : $i > $i]: (!! @ $i @ (^[Y13 : $i]: ((!! @ $i @ (^[Y14 : $i]: ((c_In @ Y14 @ Y13) => (Y11 @ Y14 @ (Y12 @ Y14))))) => (Y11 @ Y13 @ (Y8 @ Y13 @ Y12))))))) => (Y11 @ Y9 @ Y10))))))))) @ Y5 @ Y6 @ Y7)))))) @ (^[Y5 : $i]: ((^[Y6 : $i > $i]: ((^[Y7 : $i]: ((^[Y8 : $i]: (c_Union @ ((^[Y9 : $i]: ((^[Y10 : $i]: (c_Repl @ sF1 @ (^[Y11 : $i]: ((^[Y12 : $o]: ((^[Y13 : $i]: ((^[Y14 : $i]: (c_Eps_i @ (^[Y15 : $i]: ((^[Y16 : $o]: ((^[Y17 : $o]: (!! @ $o @ (^[Y18 : $o]: ((Y16 => Y18) => ((Y17 => Y18) => Y18))))))) @ ((^[Y16 : $o]: ((^[Y17 : $o]: (!! @ $o @ (^[Y18 : $o]: ((Y16 => (Y17 => Y18)) => Y18)))))) @ Y12 @ (Y13 = Y15)) @ ((^[Y16 : $o]: ((^[Y17 : $o]: (!! @ $o @ (^[Y18 : $o]: ((Y16 => (Y17 => Y18)) => Y18)))))) @ ((^[Y16 : $o]: (Y16 => c_False)) @ Y12) @ (Y14 = Y15)))))))))) @ (c_In @ c_Empty @ Y11) @ Y9 @ Y10)))))) @ Y7 @ Y8))))) @ sF2 @ (c_Repl @ Y5 @ (^[Y7 : $i]: (Y6 @ Y7))))))) @ Y4))))))) @ Y0 @ (c_Power @ Y1))))) @ sF3 @ c_Empty)) = sF4)),
% 9.27/1.88 inference(reorient_equations,[],[f520])).
% 9.27/1.88 thf(f522,definition,(
% 9.27/1.88 (sF5 = (((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: (c_Union @ ((^[Y6 : $i]: ((^[Y7 : $i]: (c_Repl @ sF1 @ (^[Y8 : $i]: ((^[Y9 : $o]: ((^[Y10 : $i]: ((^[Y11 : $i]: (c_Eps_i @ (^[Y12 : $i]: ((^[Y13 : $o]: ((^[Y14 : $o]: (!! @ $o @ (^[Y15 : $o]: ((Y13 => Y15) => ((Y14 => Y15) => Y15))))))) @ ((^[Y13 : $o]: ((^[Y14 : $o]: (!! @ $o @ (^[Y15 : $o]: ((Y13 => (Y14 => Y15)) => Y15)))))) @ Y9 @ (Y10 = Y12)) @ ((^[Y13 : $o]: ((^[Y14 : $o]: (!! @ $o @ (^[Y15 : $o]: ((Y13 => (Y14 => Y15)) => Y15)))))) @ ((^[Y13 : $o]: (Y13 => c_False)) @ Y9) @ (Y11 = Y12)))))))))) @ (c_In @ c_Empty @ Y8) @ Y6 @ Y7)))))) @ Y4 @ Y5))))) @ (c_Repl @ Y2 @ (^[Y4 : $i]: ((^[Y5 : $i]: (c_Repl @ Y5 @ (^[Y6 : $i]: ((^[Y7 : $i > ($i > $i) > $i]: ((^[Y8 : $i]: (c_Eps_i @ (^[Y9 : $i]: ((^[Y10 : $i > ($i > $i) > $i]: ((^[Y11 : $i]: ((^[Y12 : $i]: (!! @ ($i > $i > $o) @ (^[Y13 : $i > $i > $o]: ((!! @ ($i > $i) @ (^[Y14 : $i > $i]: (!! @ $i @ (^[Y15 : $i]: ((!! @ $i @ (^[Y16 : $i]: ((c_In @ Y16 @ Y15) => (Y13 @ Y16 @ (Y14 @ Y16))))) => (Y13 @ Y15 @ (Y10 @ Y15 @ Y14))))))) => (Y13 @ Y11 @ Y12))))))))) @ Y7 @ Y8 @ Y9)))))) @ (^[Y7 : $i]: ((^[Y8 : $i > $i]: ((^[Y9 : $i]: ((^[Y10 : $i]: (c_Union @ ((^[Y11 : $i]: ((^[Y12 : $i]: (c_Repl @ sF1 @ (^[Y13 : $i]: ((^[Y14 : $o]: ((^[Y15 : $i]: ((^[Y16 : $i]: (c_Eps_i @ (^[Y17 : $i]: ((^[Y18 : $o]: ((^[Y19 : $o]: (!! @ $o @ (^[Y20 : $o]: ((Y18 => Y20) => ((Y19 => Y20) => Y20))))))) @ ((^[Y18 : $o]: ((^[Y19 : $o]: (!! @ $o @ (^[Y20 : $o]: ((Y18 => (Y19 => Y20)) => Y20)))))) @ Y14 @ (Y15 = Y17)) @ ((^[Y18 : $o]: ((^[Y19 : $o]: (!! @ $o @ (^[Y20 : $o]: ((Y18 => (Y19 => Y20)) => Y20)))))) @ ((^[Y18 : $o]: (Y18 => c_False)) @ Y14) @ (Y16 = Y17)))))))))) @ (c_In @ c_Empty @ Y13) @ Y11 @ Y12)))))) @ Y9 @ Y10))))) @ sF2 @ (c_Repl @ Y7 @ (^[Y9 : $i]: (Y8 @ Y9))))))) @ Y6)))) @ Y4))) @ (c_Repl @ Y3 @ (^[Y4 : $i]: ((^[Y5 : $i > ($i > $i) > $i]: ((^[Y6 : $i]: (c_Eps_i @ (^[Y7 : $i]: ((^[Y8 : $i > ($i > $i) > $i]: ((^[Y9 : $i]: ((^[Y10 : $i]: (!! @ ($i > $i > $o) @ (^[Y11 : $i > $i > $o]: ((!! @ ($i > $i) @ (^[Y12 : $i > $i]: (!! @ $i @ (^[Y13 : $i]: ((!! @ $i @ (^[Y14 : $i]: ((c_In @ Y14 @ Y13) => (Y11 @ Y14 @ (Y12 @ Y14))))) => (Y11 @ Y13 @ (Y8 @ Y13 @ Y12))))))) => (Y11 @ Y9 @ Y10))))))))) @ Y5 @ Y6 @ Y7)))))) @ (^[Y5 : $i]: ((^[Y6 : $i > $i]: ((^[Y7 : $i]: ((^[Y8 : $i]: (c_Union @ ((^[Y9 : $i]: ((^[Y10 : $i]: (c_Repl @ sF1 @ (^[Y11 : $i]: ((^[Y12 : $o]: ((^[Y13 : $i]: ((^[Y14 : $i]: (c_Eps_i @ (^[Y15 : $i]: ((^[Y16 : $o]: ((^[Y17 : $o]: (!! @ $o @ (^[Y18 : $o]: ((Y16 => Y18) => ((Y17 => Y18) => Y18))))))) @ ((^[Y16 : $o]: ((^[Y17 : $o]: (!! @ $o @ (^[Y18 : $o]: ((Y16 => (Y17 => Y18)) => Y18)))))) @ Y12 @ (Y13 = Y15)) @ ((^[Y16 : $o]: ((^[Y17 : $o]: (!! @ $o @ (^[Y18 : $o]: ((Y16 => (Y17 => Y18)) => Y18)))))) @ ((^[Y16 : $o]: (Y16 => c_False)) @ Y12) @ (Y14 = Y15)))))))))) @ (c_In @ c_Empty @ Y11) @ Y9 @ Y10)))))) @ Y7 @ Y8))))) @ sF2 @ (c_Repl @ Y5 @ (^[Y7 : $i]: (Y6 @ Y7))))))) @ Y4))))))) @ Y0 @ (c_Power @ Y1))))) @ sF1 @ c_Empty)))),
% 9.27/1.88 introduced(definition,[new_symbols(definition,[sF5])],[function_definition])).
% 9.27/1.88 thf(f523,plain,(
% 9.27/1.88 ((((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: (c_Union @ ((^[Y6 : $i]: ((^[Y7 : $i]: (c_Repl @ sF1 @ (^[Y8 : $i]: ((^[Y9 : $o]: ((^[Y10 : $i]: ((^[Y11 : $i]: (c_Eps_i @ (^[Y12 : $i]: ((^[Y13 : $o]: ((^[Y14 : $o]: (!! @ $o @ (^[Y15 : $o]: ((Y13 => Y15) => ((Y14 => Y15) => Y15))))))) @ ((^[Y13 : $o]: ((^[Y14 : $o]: (!! @ $o @ (^[Y15 : $o]: ((Y13 => (Y14 => Y15)) => Y15)))))) @ Y9 @ (Y10 = Y12)) @ ((^[Y13 : $o]: ((^[Y14 : $o]: (!! @ $o @ (^[Y15 : $o]: ((Y13 => (Y14 => Y15)) => Y15)))))) @ ((^[Y13 : $o]: (Y13 => c_False)) @ Y9) @ (Y11 = Y12)))))))))) @ (c_In @ c_Empty @ Y8) @ Y6 @ Y7)))))) @ Y4 @ Y5))))) @ (c_Repl @ Y2 @ (^[Y4 : $i]: ((^[Y5 : $i]: (c_Repl @ Y5 @ (^[Y6 : $i]: ((^[Y7 : $i > ($i > $i) > $i]: ((^[Y8 : $i]: (c_Eps_i @ (^[Y9 : $i]: ((^[Y10 : $i > ($i > $i) > $i]: ((^[Y11 : $i]: ((^[Y12 : $i]: (!! @ ($i > $i > $o) @ (^[Y13 : $i > $i > $o]: ((!! @ ($i > $i) @ (^[Y14 : $i > $i]: (!! @ $i @ (^[Y15 : $i]: ((!! @ $i @ (^[Y16 : $i]: ((c_In @ Y16 @ Y15) => (Y13 @ Y16 @ (Y14 @ Y16))))) => (Y13 @ Y15 @ (Y10 @ Y15 @ Y14))))))) => (Y13 @ Y11 @ Y12))))))))) @ Y7 @ Y8 @ Y9)))))) @ (^[Y7 : $i]: ((^[Y8 : $i > $i]: ((^[Y9 : $i]: ((^[Y10 : $i]: (c_Union @ ((^[Y11 : $i]: ((^[Y12 : $i]: (c_Repl @ sF1 @ (^[Y13 : $i]: ((^[Y14 : $o]: ((^[Y15 : $i]: ((^[Y16 : $i]: (c_Eps_i @ (^[Y17 : $i]: ((^[Y18 : $o]: ((^[Y19 : $o]: (!! @ $o @ (^[Y20 : $o]: ((Y18 => Y20) => ((Y19 => Y20) => Y20))))))) @ ((^[Y18 : $o]: ((^[Y19 : $o]: (!! @ $o @ (^[Y20 : $o]: ((Y18 => (Y19 => Y20)) => Y20)))))) @ Y14 @ (Y15 = Y17)) @ ((^[Y18 : $o]: ((^[Y19 : $o]: (!! @ $o @ (^[Y20 : $o]: ((Y18 => (Y19 => Y20)) => Y20)))))) @ ((^[Y18 : $o]: (Y18 => c_False)) @ Y14) @ (Y16 = Y17)))))))))) @ (c_In @ c_Empty @ Y13) @ Y11 @ Y12)))))) @ Y9 @ Y10))))) @ sF2 @ (c_Repl @ Y7 @ (^[Y9 : $i]: (Y8 @ Y9))))))) @ Y6)))) @ Y4))) @ (c_Repl @ Y3 @ (^[Y4 : $i]: ((^[Y5 : $i > ($i > $i) > $i]: ((^[Y6 : $i]: (c_Eps_i @ (^[Y7 : $i]: ((^[Y8 : $i > ($i > $i) > $i]: ((^[Y9 : $i]: ((^[Y10 : $i]: (!! @ ($i > $i > $o) @ (^[Y11 : $i > $i > $o]: ((!! @ ($i > $i) @ (^[Y12 : $i > $i]: (!! @ $i @ (^[Y13 : $i]: ((!! @ $i @ (^[Y14 : $i]: ((c_In @ Y14 @ Y13) => (Y11 @ Y14 @ (Y12 @ Y14))))) => (Y11 @ Y13 @ (Y8 @ Y13 @ Y12))))))) => (Y11 @ Y9 @ Y10))))))))) @ Y5 @ Y6 @ Y7)))))) @ (^[Y5 : $i]: ((^[Y6 : $i > $i]: ((^[Y7 : $i]: ((^[Y8 : $i]: (c_Union @ ((^[Y9 : $i]: ((^[Y10 : $i]: (c_Repl @ sF1 @ (^[Y11 : $i]: ((^[Y12 : $o]: ((^[Y13 : $i]: ((^[Y14 : $i]: (c_Eps_i @ (^[Y15 : $i]: ((^[Y16 : $o]: ((^[Y17 : $o]: (!! @ $o @ (^[Y18 : $o]: ((Y16 => Y18) => ((Y17 => Y18) => Y18))))))) @ ((^[Y16 : $o]: ((^[Y17 : $o]: (!! @ $o @ (^[Y18 : $o]: ((Y16 => (Y17 => Y18)) => Y18)))))) @ Y12 @ (Y13 = Y15)) @ ((^[Y16 : $o]: ((^[Y17 : $o]: (!! @ $o @ (^[Y18 : $o]: ((Y16 => (Y17 => Y18)) => Y18)))))) @ ((^[Y16 : $o]: (Y16 => c_False)) @ Y12) @ (Y14 = Y15)))))))))) @ (c_In @ c_Empty @ Y11) @ Y9 @ Y10)))))) @ Y7 @ Y8))))) @ sF2 @ (c_Repl @ Y5 @ (^[Y7 : $i]: (Y6 @ Y7))))))) @ Y4))))))) @ Y0 @ (c_Power @ Y1))))) @ sF1 @ c_Empty)) = sF5)),
% 9.27/1.88 inference(reorient_equations,[],[f522])).
% 9.27/1.88 thf(f524,definition,(
% 9.27/1.88 (sF6 = ((c_Power @ sF5)))),
% 9.27/1.88 introduced(definition,[new_symbols(definition,[sF6])],[function_definition])).
% 9.27/1.88 thf(f525,definition,(
% 9.27/1.88 (sF7 = (((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: (c_Union @ ((^[Y6 : $i]: ((^[Y7 : $i]: (c_Repl @ sF1 @ (^[Y8 : $i]: ((^[Y9 : $o]: ((^[Y10 : $i]: ((^[Y11 : $i]: (c_Eps_i @ (^[Y12 : $i]: ((^[Y13 : $o]: ((^[Y14 : $o]: (!! @ $o @ (^[Y15 : $o]: ((Y13 => Y15) => ((Y14 => Y15) => Y15))))))) @ ((^[Y13 : $o]: ((^[Y14 : $o]: (!! @ $o @ (^[Y15 : $o]: ((Y13 => (Y14 => Y15)) => Y15)))))) @ Y9 @ (Y10 = Y12)) @ ((^[Y13 : $o]: ((^[Y14 : $o]: (!! @ $o @ (^[Y15 : $o]: ((Y13 => (Y14 => Y15)) => Y15)))))) @ ((^[Y13 : $o]: (Y13 => c_False)) @ Y9) @ (Y11 = Y12)))))))))) @ (c_In @ c_Empty @ Y8) @ Y6 @ Y7)))))) @ Y4 @ Y5))))) @ (c_Repl @ Y2 @ (^[Y4 : $i]: ((^[Y5 : $i]: (c_Repl @ Y5 @ (^[Y6 : $i]: ((^[Y7 : $i > ($i > $i) > $i]: ((^[Y8 : $i]: (c_Eps_i @ (^[Y9 : $i]: ((^[Y10 : $i > ($i > $i) > $i]: ((^[Y11 : $i]: ((^[Y12 : $i]: (!! @ ($i > $i > $o) @ (^[Y13 : $i > $i > $o]: ((!! @ ($i > $i) @ (^[Y14 : $i > $i]: (!! @ $i @ (^[Y15 : $i]: ((!! @ $i @ (^[Y16 : $i]: ((c_In @ Y16 @ Y15) => (Y13 @ Y16 @ (Y14 @ Y16))))) => (Y13 @ Y15 @ (Y10 @ Y15 @ Y14))))))) => (Y13 @ Y11 @ Y12))))))))) @ Y7 @ Y8 @ Y9)))))) @ (^[Y7 : $i]: ((^[Y8 : $i > $i]: ((^[Y9 : $i]: ((^[Y10 : $i]: (c_Union @ ((^[Y11 : $i]: ((^[Y12 : $i]: (c_Repl @ sF1 @ (^[Y13 : $i]: ((^[Y14 : $o]: ((^[Y15 : $i]: ((^[Y16 : $i]: (c_Eps_i @ (^[Y17 : $i]: ((^[Y18 : $o]: ((^[Y19 : $o]: (!! @ $o @ (^[Y20 : $o]: ((Y18 => Y20) => ((Y19 => Y20) => Y20))))))) @ ((^[Y18 : $o]: ((^[Y19 : $o]: (!! @ $o @ (^[Y20 : $o]: ((Y18 => (Y19 => Y20)) => Y20)))))) @ Y14 @ (Y15 = Y17)) @ ((^[Y18 : $o]: ((^[Y19 : $o]: (!! @ $o @ (^[Y20 : $o]: ((Y18 => (Y19 => Y20)) => Y20)))))) @ ((^[Y18 : $o]: (Y18 => c_False)) @ Y14) @ (Y16 = Y17)))))))))) @ (c_In @ c_Empty @ Y13) @ Y11 @ Y12)))))) @ Y9 @ Y10))))) @ sF2 @ (c_Repl @ Y7 @ (^[Y9 : $i]: (Y8 @ Y9))))))) @ Y6)))) @ Y4))) @ (c_Repl @ Y3 @ (^[Y4 : $i]: ((^[Y5 : $i > ($i > $i) > $i]: ((^[Y6 : $i]: (c_Eps_i @ (^[Y7 : $i]: ((^[Y8 : $i > ($i > $i) > $i]: ((^[Y9 : $i]: ((^[Y10 : $i]: (!! @ ($i > $i > $o) @ (^[Y11 : $i > $i > $o]: ((!! @ ($i > $i) @ (^[Y12 : $i > $i]: (!! @ $i @ (^[Y13 : $i]: ((!! @ $i @ (^[Y14 : $i]: ((c_In @ Y14 @ Y13) => (Y11 @ Y14 @ (Y12 @ Y14))))) => (Y11 @ Y13 @ (Y8 @ Y13 @ Y12))))))) => (Y11 @ Y9 @ Y10))))))))) @ Y5 @ Y6 @ Y7)))))) @ (^[Y5 : $i]: ((^[Y6 : $i > $i]: ((^[Y7 : $i]: ((^[Y8 : $i]: (c_Union @ ((^[Y9 : $i]: ((^[Y10 : $i]: (c_Repl @ sF1 @ (^[Y11 : $i]: ((^[Y12 : $o]: ((^[Y13 : $i]: ((^[Y14 : $i]: (c_Eps_i @ (^[Y15 : $i]: ((^[Y16 : $o]: ((^[Y17 : $o]: (!! @ $o @ (^[Y18 : $o]: ((Y16 => Y18) => ((Y17 => Y18) => Y18))))))) @ ((^[Y16 : $o]: ((^[Y17 : $o]: (!! @ $o @ (^[Y18 : $o]: ((Y16 => (Y17 => Y18)) => Y18)))))) @ Y12 @ (Y13 = Y15)) @ ((^[Y16 : $o]: ((^[Y17 : $o]: (!! @ $o @ (^[Y18 : $o]: ((Y16 => (Y17 => Y18)) => Y18)))))) @ ((^[Y16 : $o]: (Y16 => c_False)) @ Y12) @ (Y14 = Y15)))))))))) @ (c_In @ c_Empty @ Y11) @ Y9 @ Y10)))))) @ Y7 @ Y8))))) @ sF2 @ (c_Repl @ Y5 @ (^[Y7 : $i]: (Y6 @ Y7))))))) @ Y4))))))) @ Y0 @ (c_Power @ Y1))))) @ sF6 @ sF1)))),
% 9.27/1.88 introduced(definition,[new_symbols(definition,[sF7])],[function_definition])).
% 9.27/1.88 thf(f526,definition,(
% 9.27/1.88 (sF8 = (((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (c_Union @ ((^[Y3 : $i]: ((^[Y4 : $i]: (c_Repl @ sF1 @ (^[Y5 : $i]: ((^[Y6 : $o]: ((^[Y7 : $i]: ((^[Y8 : $i]: (c_Eps_i @ (^[Y9 : $i]: ((^[Y10 : $o]: ((^[Y11 : $o]: (!! @ $o @ (^[Y12 : $o]: ((Y10 => Y12) => ((Y11 => Y12) => Y12))))))) @ ((^[Y10 : $o]: ((^[Y11 : $o]: (!! @ $o @ (^[Y12 : $o]: ((Y10 => (Y11 => Y12)) => Y12)))))) @ Y6 @ (Y7 = Y9)) @ ((^[Y10 : $o]: ((^[Y11 : $o]: (!! @ $o @ (^[Y12 : $o]: ((Y10 => (Y11 => Y12)) => Y12)))))) @ ((^[Y10 : $o]: (Y10 => c_False)) @ Y6) @ (Y8 = Y9)))))))))) @ (c_In @ c_Empty @ Y5) @ Y3 @ Y4)))))) @ Y1 @ Y2))))) @ Y0 @ ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: (c_Repl @ sF1 @ (^[Y4 : $i]: ((^[Y5 : $o]: ((^[Y6 : $i]: ((^[Y7 : $i]: (c_Eps_i @ (^[Y8 : $i]: ((^[Y9 : $o]: ((^[Y10 : $o]: (!! @ $o @ (^[Y11 : $o]: ((Y9 => Y11) => ((Y10 => Y11) => Y11))))))) @ ((^[Y9 : $o]: ((^[Y10 : $o]: (!! @ $o @ (^[Y11 : $o]: ((Y9 => (Y10 => Y11)) => Y11)))))) @ Y5 @ (Y6 = Y8)) @ ((^[Y9 : $o]: ((^[Y10 : $o]: (!! @ $o @ (^[Y11 : $o]: ((Y9 => (Y10 => Y11)) => Y11)))))) @ ((^[Y9 : $o]: (Y9 => c_False)) @ Y5) @ (Y7 = Y8)))))))))) @ (c_In @ c_Empty @ Y4) @ Y2 @ Y3)))))) @ Y1 @ Y1)) @ Y0))) @ c_Empty)))),
% 9.27/1.88 introduced(definition,[new_symbols(definition,[sF8])],[function_definition])).
% 9.27/1.88 thf(f527,definition,(
% 9.27/1.88 (sF9 = (((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (c_Repl @ sF1 @ (^[Y3 : $i]: ((^[Y4 : $o]: ((^[Y5 : $i]: ((^[Y6 : $i]: (c_Eps_i @ (^[Y7 : $i]: ((^[Y8 : $o]: ((^[Y9 : $o]: (!! @ $o @ (^[Y10 : $o]: ((Y8 => Y10) => ((Y9 => Y10) => Y10))))))) @ ((^[Y8 : $o]: ((^[Y9 : $o]: (!! @ $o @ (^[Y10 : $o]: ((Y8 => (Y9 => Y10)) => Y10)))))) @ Y4 @ (Y5 = Y7)) @ ((^[Y8 : $o]: ((^[Y9 : $o]: (!! @ $o @ (^[Y10 : $o]: ((Y8 => (Y9 => Y10)) => Y10)))))) @ ((^[Y8 : $o]: (Y8 => c_False)) @ Y4) @ (Y6 = Y7)))))))))) @ (c_In @ c_Empty @ Y3) @ Y1 @ Y2)))))) @ Y0 @ Y0)) @ sF8)))),
% 9.27/1.88 introduced(definition,[new_symbols(definition,[sF9])],[function_definition])).
% 9.27/1.88 thf(f528,definition,(
% 9.27/1.88 (sF10 = (((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: (c_Union @ ((^[Y6 : $i]: ((^[Y7 : $i]: (c_Repl @ sF1 @ (^[Y8 : $i]: ((^[Y9 : $o]: ((^[Y10 : $i]: ((^[Y11 : $i]: (c_Eps_i @ (^[Y12 : $i]: ((^[Y13 : $o]: ((^[Y14 : $o]: (!! @ $o @ (^[Y15 : $o]: ((Y13 => Y15) => ((Y14 => Y15) => Y15))))))) @ ((^[Y13 : $o]: ((^[Y14 : $o]: (!! @ $o @ (^[Y15 : $o]: ((Y13 => (Y14 => Y15)) => Y15)))))) @ Y9 @ (Y10 = Y12)) @ ((^[Y13 : $o]: ((^[Y14 : $o]: (!! @ $o @ (^[Y15 : $o]: ((Y13 => (Y14 => Y15)) => Y15)))))) @ ((^[Y13 : $o]: (Y13 => c_False)) @ Y9) @ (Y11 = Y12)))))))))) @ (c_In @ c_Empty @ Y8) @ Y6 @ Y7)))))) @ Y4 @ Y5))))) @ (c_Repl @ Y2 @ (^[Y4 : $i]: ((^[Y5 : $i]: (c_Repl @ Y5 @ (^[Y6 : $i]: ((^[Y7 : $i > ($i > $i) > $i]: ((^[Y8 : $i]: (c_Eps_i @ (^[Y9 : $i]: ((^[Y10 : $i > ($i > $i) > $i]: ((^[Y11 : $i]: ((^[Y12 : $i]: (!! @ ($i > $i > $o) @ (^[Y13 : $i > $i > $o]: ((!! @ ($i > $i) @ (^[Y14 : $i > $i]: (!! @ $i @ (^[Y15 : $i]: ((!! @ $i @ (^[Y16 : $i]: ((c_In @ Y16 @ Y15) => (Y13 @ Y16 @ (Y14 @ Y16))))) => (Y13 @ Y15 @ (Y10 @ Y15 @ Y14))))))) => (Y13 @ Y11 @ Y12))))))))) @ Y7 @ Y8 @ Y9)))))) @ (^[Y7 : $i]: ((^[Y8 : $i > $i]: ((^[Y9 : $i]: ((^[Y10 : $i]: (c_Union @ ((^[Y11 : $i]: ((^[Y12 : $i]: (c_Repl @ sF1 @ (^[Y13 : $i]: ((^[Y14 : $o]: ((^[Y15 : $i]: ((^[Y16 : $i]: (c_Eps_i @ (^[Y17 : $i]: ((^[Y18 : $o]: ((^[Y19 : $o]: (!! @ $o @ (^[Y20 : $o]: ((Y18 => Y20) => ((Y19 => Y20) => Y20))))))) @ ((^[Y18 : $o]: ((^[Y19 : $o]: (!! @ $o @ (^[Y20 : $o]: ((Y18 => (Y19 => Y20)) => Y20)))))) @ Y14 @ (Y15 = Y17)) @ ((^[Y18 : $o]: ((^[Y19 : $o]: (!! @ $o @ (^[Y20 : $o]: ((Y18 => (Y19 => Y20)) => Y20)))))) @ ((^[Y18 : $o]: (Y18 => c_False)) @ Y14) @ (Y16 = Y17)))))))))) @ (c_In @ c_Empty @ Y13) @ Y11 @ Y12)))))) @ Y9 @ Y10))))) @ sF2 @ (c_Repl @ Y7 @ (^[Y9 : $i]: (Y8 @ Y9))))))) @ Y6)))) @ Y4))) @ (c_Repl @ Y3 @ (^[Y4 : $i]: ((^[Y5 : $i > ($i > $i) > $i]: ((^[Y6 : $i]: (c_Eps_i @ (^[Y7 : $i]: ((^[Y8 : $i > ($i > $i) > $i]: ((^[Y9 : $i]: ((^[Y10 : $i]: (!! @ ($i > $i > $o) @ (^[Y11 : $i > $i > $o]: ((!! @ ($i > $i) @ (^[Y12 : $i > $i]: (!! @ $i @ (^[Y13 : $i]: ((!! @ $i @ (^[Y14 : $i]: ((c_In @ Y14 @ Y13) => (Y11 @ Y14 @ (Y12 @ Y14))))) => (Y11 @ Y13 @ (Y8 @ Y13 @ Y12))))))) => (Y11 @ Y9 @ Y10))))))))) @ Y5 @ Y6 @ Y7)))))) @ (^[Y5 : $i]: ((^[Y6 : $i > $i]: ((^[Y7 : $i]: ((^[Y8 : $i]: (c_Union @ ((^[Y9 : $i]: ((^[Y10 : $i]: (c_Repl @ sF1 @ (^[Y11 : $i]: ((^[Y12 : $o]: ((^[Y13 : $i]: ((^[Y14 : $i]: (c_Eps_i @ (^[Y15 : $i]: ((^[Y16 : $o]: ((^[Y17 : $o]: (!! @ $o @ (^[Y18 : $o]: ((Y16 => Y18) => ((Y17 => Y18) => Y18))))))) @ ((^[Y16 : $o]: ((^[Y17 : $o]: (!! @ $o @ (^[Y18 : $o]: ((Y16 => (Y17 => Y18)) => Y18)))))) @ Y12 @ (Y13 = Y15)) @ ((^[Y16 : $o]: ((^[Y17 : $o]: (!! @ $o @ (^[Y18 : $o]: ((Y16 => (Y17 => Y18)) => Y18)))))) @ ((^[Y16 : $o]: (Y16 => c_False)) @ Y12) @ (Y14 = Y15)))))))))) @ (c_In @ c_Empty @ Y11) @ Y9 @ Y10)))))) @ Y7 @ Y8))))) @ sF2 @ (c_Repl @ Y5 @ (^[Y7 : $i]: (Y6 @ Y7))))))) @ Y4))))))) @ Y0 @ (c_Power @ Y1))))) @ sF6 @ sF0)))),
% 9.27/1.88 introduced(definition,[new_symbols(definition,[sF10])],[function_definition])).
% 9.27/1.88 thf(f529,definition,(
% 9.27/1.88 (sF11 = (((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: (c_Union @ ((^[Y6 : $i]: ((^[Y7 : $i]: (c_Repl @ sF1 @ (^[Y8 : $i]: ((^[Y9 : $o]: ((^[Y10 : $i]: ((^[Y11 : $i]: (c_Eps_i @ (^[Y12 : $i]: ((^[Y13 : $o]: ((^[Y14 : $o]: (!! @ $o @ (^[Y15 : $o]: ((Y13 => Y15) => ((Y14 => Y15) => Y15))))))) @ ((^[Y13 : $o]: ((^[Y14 : $o]: (!! @ $o @ (^[Y15 : $o]: ((Y13 => (Y14 => Y15)) => Y15)))))) @ Y9 @ (Y10 = Y12)) @ ((^[Y13 : $o]: ((^[Y14 : $o]: (!! @ $o @ (^[Y15 : $o]: ((Y13 => (Y14 => Y15)) => Y15)))))) @ ((^[Y13 : $o]: (Y13 => c_False)) @ Y9) @ (Y11 = Y12)))))))))) @ (c_In @ c_Empty @ Y8) @ Y6 @ Y7)))))) @ Y4 @ Y5))))) @ (c_Repl @ Y2 @ (^[Y4 : $i]: ((^[Y5 : $i]: (c_Repl @ Y5 @ (^[Y6 : $i]: ((^[Y7 : $i > ($i > $i) > $i]: ((^[Y8 : $i]: (c_Eps_i @ (^[Y9 : $i]: ((^[Y10 : $i > ($i > $i) > $i]: ((^[Y11 : $i]: ((^[Y12 : $i]: (!! @ ($i > $i > $o) @ (^[Y13 : $i > $i > $o]: ((!! @ ($i > $i) @ (^[Y14 : $i > $i]: (!! @ $i @ (^[Y15 : $i]: ((!! @ $i @ (^[Y16 : $i]: ((c_In @ Y16 @ Y15) => (Y13 @ Y16 @ (Y14 @ Y16))))) => (Y13 @ Y15 @ (Y10 @ Y15 @ Y14))))))) => (Y13 @ Y11 @ Y12))))))))) @ Y7 @ Y8 @ Y9)))))) @ (^[Y7 : $i]: ((^[Y8 : $i > $i]: ((^[Y9 : $i]: ((^[Y10 : $i]: (c_Union @ ((^[Y11 : $i]: ((^[Y12 : $i]: (c_Repl @ sF1 @ (^[Y13 : $i]: ((^[Y14 : $o]: ((^[Y15 : $i]: ((^[Y16 : $i]: (c_Eps_i @ (^[Y17 : $i]: ((^[Y18 : $o]: ((^[Y19 : $o]: (!! @ $o @ (^[Y20 : $o]: ((Y18 => Y20) => ((Y19 => Y20) => Y20))))))) @ ((^[Y18 : $o]: ((^[Y19 : $o]: (!! @ $o @ (^[Y20 : $o]: ((Y18 => (Y19 => Y20)) => Y20)))))) @ Y14 @ (Y15 = Y17)) @ ((^[Y18 : $o]: ((^[Y19 : $o]: (!! @ $o @ (^[Y20 : $o]: ((Y18 => (Y19 => Y20)) => Y20)))))) @ ((^[Y18 : $o]: (Y18 => c_False)) @ Y14) @ (Y16 = Y17)))))))))) @ (c_In @ c_Empty @ Y13) @ Y11 @ Y12)))))) @ Y9 @ Y10))))) @ sF2 @ (c_Repl @ Y7 @ (^[Y9 : $i]: (Y8 @ Y9))))))) @ Y6)))) @ Y4))) @ (c_Repl @ Y3 @ (^[Y4 : $i]: ((^[Y5 : $i > ($i > $i) > $i]: ((^[Y6 : $i]: (c_Eps_i @ (^[Y7 : $i]: ((^[Y8 : $i > ($i > $i) > $i]: ((^[Y9 : $i]: ((^[Y10 : $i]: (!! @ ($i > $i > $o) @ (^[Y11 : $i > $i > $o]: ((!! @ ($i > $i) @ (^[Y12 : $i > $i]: (!! @ $i @ (^[Y13 : $i]: ((!! @ $i @ (^[Y14 : $i]: ((c_In @ Y14 @ Y13) => (Y11 @ Y14 @ (Y12 @ Y14))))) => (Y11 @ Y13 @ (Y8 @ Y13 @ Y12))))))) => (Y11 @ Y9 @ Y10))))))))) @ Y5 @ Y6 @ Y7)))))) @ (^[Y5 : $i]: ((^[Y6 : $i > $i]: ((^[Y7 : $i]: ((^[Y8 : $i]: (c_Union @ ((^[Y9 : $i]: ((^[Y10 : $i]: (c_Repl @ sF1 @ (^[Y11 : $i]: ((^[Y12 : $o]: ((^[Y13 : $i]: ((^[Y14 : $i]: (c_Eps_i @ (^[Y15 : $i]: ((^[Y16 : $o]: ((^[Y17 : $o]: (!! @ $o @ (^[Y18 : $o]: ((Y16 => Y18) => ((Y17 => Y18) => Y18))))))) @ ((^[Y16 : $o]: ((^[Y17 : $o]: (!! @ $o @ (^[Y18 : $o]: ((Y16 => (Y17 => Y18)) => Y18)))))) @ Y12 @ (Y13 = Y15)) @ ((^[Y16 : $o]: ((^[Y17 : $o]: (!! @ $o @ (^[Y18 : $o]: ((Y16 => (Y17 => Y18)) => Y18)))))) @ ((^[Y16 : $o]: (Y16 => c_False)) @ Y12) @ (Y14 = Y15)))))))))) @ (c_In @ c_Empty @ Y11) @ Y9 @ Y10)))))) @ Y7 @ Y8))))) @ sF2 @ (c_Repl @ Y5 @ (^[Y7 : $i]: (Y6 @ Y7))))))) @ Y4))))))) @ Y0 @ (c_Power @ Y1))))) @ sF10 @ c_Empty)))),
% 9.27/1.88 introduced(definition,[new_symbols(definition,[sF11])],[function_definition])).
% 9.27/1.88 thf(f530,plain,(
% 9.27/1.88 ((((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: (c_Union @ ((^[Y6 : $i]: ((^[Y7 : $i]: (c_Repl @ sF1 @ (^[Y8 : $i]: ((^[Y9 : $o]: ((^[Y10 : $i]: ((^[Y11 : $i]: (c_Eps_i @ (^[Y12 : $i]: ((^[Y13 : $o]: ((^[Y14 : $o]: (!! @ $o @ (^[Y15 : $o]: ((Y13 => Y15) => ((Y14 => Y15) => Y15))))))) @ ((^[Y13 : $o]: ((^[Y14 : $o]: (!! @ $o @ (^[Y15 : $o]: ((Y13 => (Y14 => Y15)) => Y15)))))) @ Y9 @ (Y10 = Y12)) @ ((^[Y13 : $o]: ((^[Y14 : $o]: (!! @ $o @ (^[Y15 : $o]: ((Y13 => (Y14 => Y15)) => Y15)))))) @ ((^[Y13 : $o]: (Y13 => c_False)) @ Y9) @ (Y11 = Y12)))))))))) @ (c_In @ c_Empty @ Y8) @ Y6 @ Y7)))))) @ Y4 @ Y5))))) @ (c_Repl @ Y2 @ (^[Y4 : $i]: ((^[Y5 : $i]: (c_Repl @ Y5 @ (^[Y6 : $i]: ((^[Y7 : $i > ($i > $i) > $i]: ((^[Y8 : $i]: (c_Eps_i @ (^[Y9 : $i]: ((^[Y10 : $i > ($i > $i) > $i]: ((^[Y11 : $i]: ((^[Y12 : $i]: (!! @ ($i > $i > $o) @ (^[Y13 : $i > $i > $o]: ((!! @ ($i > $i) @ (^[Y14 : $i > $i]: (!! @ $i @ (^[Y15 : $i]: ((!! @ $i @ (^[Y16 : $i]: ((c_In @ Y16 @ Y15) => (Y13 @ Y16 @ (Y14 @ Y16))))) => (Y13 @ Y15 @ (Y10 @ Y15 @ Y14))))))) => (Y13 @ Y11 @ Y12))))))))) @ Y7 @ Y8 @ Y9)))))) @ (^[Y7 : $i]: ((^[Y8 : $i > $i]: ((^[Y9 : $i]: ((^[Y10 : $i]: (c_Union @ ((^[Y11 : $i]: ((^[Y12 : $i]: (c_Repl @ sF1 @ (^[Y13 : $i]: ((^[Y14 : $o]: ((^[Y15 : $i]: ((^[Y16 : $i]: (c_Eps_i @ (^[Y17 : $i]: ((^[Y18 : $o]: ((^[Y19 : $o]: (!! @ $o @ (^[Y20 : $o]: ((Y18 => Y20) => ((Y19 => Y20) => Y20))))))) @ ((^[Y18 : $o]: ((^[Y19 : $o]: (!! @ $o @ (^[Y20 : $o]: ((Y18 => (Y19 => Y20)) => Y20)))))) @ Y14 @ (Y15 = Y17)) @ ((^[Y18 : $o]: ((^[Y19 : $o]: (!! @ $o @ (^[Y20 : $o]: ((Y18 => (Y19 => Y20)) => Y20)))))) @ ((^[Y18 : $o]: (Y18 => c_False)) @ Y14) @ (Y16 = Y17)))))))))) @ (c_In @ c_Empty @ Y13) @ Y11 @ Y12)))))) @ Y9 @ Y10))))) @ sF2 @ (c_Repl @ Y7 @ (^[Y9 : $i]: (Y8 @ Y9))))))) @ Y6)))) @ Y4))) @ (c_Repl @ Y3 @ (^[Y4 : $i]: ((^[Y5 : $i > ($i > $i) > $i]: ((^[Y6 : $i]: (c_Eps_i @ (^[Y7 : $i]: ((^[Y8 : $i > ($i > $i) > $i]: ((^[Y9 : $i]: ((^[Y10 : $i]: (!! @ ($i > $i > $o) @ (^[Y11 : $i > $i > $o]: ((!! @ ($i > $i) @ (^[Y12 : $i > $i]: (!! @ $i @ (^[Y13 : $i]: ((!! @ $i @ (^[Y14 : $i]: ((c_In @ Y14 @ Y13) => (Y11 @ Y14 @ (Y12 @ Y14))))) => (Y11 @ Y13 @ (Y8 @ Y13 @ Y12))))))) => (Y11 @ Y9 @ Y10))))))))) @ Y5 @ Y6 @ Y7)))))) @ (^[Y5 : $i]: ((^[Y6 : $i > $i]: ((^[Y7 : $i]: ((^[Y8 : $i]: (c_Union @ ((^[Y9 : $i]: ((^[Y10 : $i]: (c_Repl @ sF1 @ (^[Y11 : $i]: ((^[Y12 : $o]: ((^[Y13 : $i]: ((^[Y14 : $i]: (c_Eps_i @ (^[Y15 : $i]: ((^[Y16 : $o]: ((^[Y17 : $o]: (!! @ $o @ (^[Y18 : $o]: ((Y16 => Y18) => ((Y17 => Y18) => Y18))))))) @ ((^[Y16 : $o]: ((^[Y17 : $o]: (!! @ $o @ (^[Y18 : $o]: ((Y16 => (Y17 => Y18)) => Y18)))))) @ Y12 @ (Y13 = Y15)) @ ((^[Y16 : $o]: ((^[Y17 : $o]: (!! @ $o @ (^[Y18 : $o]: ((Y16 => (Y17 => Y18)) => Y18)))))) @ ((^[Y16 : $o]: (Y16 => c_False)) @ Y12) @ (Y14 = Y15)))))))))) @ (c_In @ c_Empty @ Y11) @ Y9 @ Y10)))))) @ Y7 @ Y8))))) @ sF2 @ (c_Repl @ Y5 @ (^[Y7 : $i]: (Y6 @ Y7))))))) @ Y4))))))) @ Y0 @ (c_Power @ Y1))))) @ sF10 @ c_Empty)) = sF11)),
% 9.27/1.88 inference(reorient_equations,[],[f529])).
% 9.27/1.88 thf(f531,definition,(
% 9.27/1.88 (sF12 = ((!! @ ($i > $i) @ (^[Y0 : $i > $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((^[Y2 : $o]: ((^[Y3 : $o]: (!! @ $o @ (^[Y4 : $o]: ((Y2 => (Y3 => Y4)) => Y4)))))) @ (((Y1 @ (Y0 @ ((^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i > $o]: ((^[Y6 : $o]: ((^[Y7 : $i]: ((^[Y8 : $i]: (c_Eps_i @ (^[Y9 : $i]: ((^[Y10 : $o]: ((^[Y11 : $o]: (!! @ $o @ (^[Y12 : $o]: ((Y10 => Y12) => ((Y11 => Y12) => Y12))))))) @ ((^[Y10 : $o]: ((^[Y11 : $o]: (!! @ $o @ (^[Y12 : $o]: ((Y10 => (Y11 => Y12)) => Y12)))))) @ Y6 @ (Y7 = Y9)) @ ((^[Y10 : $o]: ((^[Y11 : $o]: (!! @ $o @ (^[Y12 : $o]: ((Y10 => (Y11 => Y12)) => Y12)))))) @ ((^[Y10 : $o]: (Y10 => c_False)) @ Y6) @ (Y8 = Y9)))))))))) @ (?? @ $i @ (^[Y6 : $i]: ((^[Y7 : $o]: ((^[Y8 : $o]: (!! @ $o @ (^[Y9 : $o]: ((Y7 => (Y8 => Y9)) => Y9)))))) @ (c_In @ Y6 @ Y4) @ (Y5 @ Y6)))) @ (c_Repl @ Y4 @ (^[Y6 : $i]: ((^[Y7 : $i]: ((^[Y8 : $o]: ((^[Y9 : $i]: ((^[Y10 : $i]: (c_Eps_i @ (^[Y11 : $i]: ((^[Y12 : $o]: ((^[Y13 : $o]: (!! @ $o @ (^[Y14 : $o]: ((Y12 => Y14) => ((Y13 => Y14) => Y14))))))) @ ((^[Y12 : $o]: ((^[Y13 : $o]: (!! @ $o @ (^[Y14 : $o]: ((Y12 => (Y13 => Y14)) => Y14)))))) @ Y8 @ (Y9 = Y11)) @ ((^[Y12 : $o]: ((^[Y13 : $o]: (!! @ $o @ (^[Y14 : $o]: ((Y12 => (Y13 => Y14)) => Y14)))))) @ ((^[Y12 : $o]: (Y12 => c_False)) @ Y8) @ (Y10 = Y11)))))))))) @ (Y5 @ Y7) @ Y7 @ (c_Eps_i @ (^[Y8 : $i]: ((^[Y9 : $o]: ((^[Y10 : $o]: (!! @ $o @ (^[Y11 : $o]: ((Y9 => (Y10 => Y11)) => Y11)))))) @ (c_In @ Y8 @ Y4) @ (Y5 @ Y8)))))) @ Y6))) @ c_Empty)))) @ Y2 @ (^[Y4 : $i]: (c_In @ Y4 @ Y3)))))) @ (Y0 @ sF0) @ (Y0 @ sF4)))) => (((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((c_In @ Y3 @ Y2) => ((^[Y4 : $i]: ((^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ Y4) => (c_In @ Y6 @ Y5))))))) @ Y3 @ Y2))))) @ (Y0 @ c_Empty)) => (!! @ $i @ (^[Y2 : $i]: ((c_In @ Y2 @ c_Empty) => (?? @ $i @ (^[Y3 : $i]: ((^[Y4 : $o]: ((^[Y5 : $o]: (!! @ $o @ (^[Y6 : $o]: ((Y4 => (Y5 => Y6)) => Y6)))))) @ ((^[Y4 : $i]: ((^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ Y4) => (c_In @ Y6 @ Y5))))))) @ Y3 @ Y2) @ ((^[Y4 : $i]: ((^[Y5 : $o]: ((^[Y6 : $o]: (!! @ $o @ (^[Y7 : $o]: ((Y5 => (Y6 => Y7)) => Y7)))))) @ ((^[Y5 : $i]: (?? @ $i @ (^[Y6 : $i]: ((^[Y7 : $o]: ((^[Y8 : $o]: (!! @ $o @ (^[Y9 : $o]: ((Y7 => (Y8 => Y9)) => Y9)))))) @ (c_In @ Y6 @ Y5) @ ((^[Y7 : $o]: (Y7 => c_False)) @ ((^[Y7 : $i]: ((^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((c_In @ Y9 @ Y7) => (c_In @ Y9 @ Y8))))))) @ Y5 @ (c_Power @ Y6))))))) @ Y4) @ ((^[Y5 : $o]: (Y5 => c_False)) @ ((^[Y5 : $i]: (?? @ $i @ (^[Y6 : $i]: ((^[Y7 : $o]: ((^[Y8 : $o]: (!! @ $o @ (^[Y9 : $o]: ((Y7 => (Y8 => Y9)) => Y9)))))) @ ((^[Y7 : $i]: ((^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((c_In @ Y9 @ Y7) => (c_In @ Y9 @ Y8))))))) @ Y6 @ Y5) @ ((^[Y7 : $o]: ((^[Y8 : $o]: (!! @ $o @ (^[Y9 : $o]: ((Y7 => (Y8 => Y9)) => Y9)))))) @ ((^[Y7 : $o]: (Y7 => c_False)) @ ((^[Y7 : $i]: ((^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((c_In @ Y9 @ Y7) => (c_In @ Y9 @ Y8))))))) @ Y5 @ Y6)) @ ((^[Y7 : $i]: (?? @ $i @ (^[Y8 : $i]: ((^[Y9 : $o]: ((^[Y10 : $o]: (!! @ $o @ (^[Y11 : $o]: ((Y9 => (Y10 => Y11)) => Y11)))))) @ (c_In @ Y8 @ Y7) @ ((^[Y9 : $o]: (Y9 => c_False)) @ ((^[Y9 : $i]: ((^[Y10 : $i]: (!! @ $i @ (^[Y11 : $i]: ((c_In @ Y11 @ Y9) => (c_In @ Y11 @ Y10))))))) @ Y7 @ (c_Power @ Y8))))))) @ Y6)))))) @ Y4)))) @ ((^[Y4 : $i]: ((^[Y5 : $i]: ((^[Y6 : $i]: (c_Union @ ((^[Y7 : $i]: ((^[Y8 : $i]: (c_Repl @ sF1 @ (^[Y9 : $i]: ((^[Y10 : $o]: ((^[Y11 : $i]: ((^[Y12 : $i]: (c_Eps_i @ (^[Y13 : $i]: ((^[Y14 : $o]: ((^[Y15 : $o]: (!! @ $o @ (^[Y16 : $o]: ((Y14 => Y16) => ((Y15 => Y16) => Y16))))))) @ ((^[Y14 : $o]: ((^[Y15 : $o]: (!! @ $o @ (^[Y16 : $o]: ((Y14 => (Y15 => Y16)) => Y16)))))) @ Y10 @ (Y11 = Y13)) @ ((^[Y14 : $o]: ((^[Y15 : $o]: (!! @ $o @ (^[Y16 : $o]: ((Y14 => (Y15 => Y16)) => Y16)))))) @ ((^[Y14 : $o]: (Y14 => c_False)) @ Y10) @ (Y12 = Y13)))))))))) @ (c_In @ c_Empty @ Y9) @ Y7 @ Y8)))))) @ Y5 @ Y6))))) @ Y4 @ ((^[Y5 : $i]: ((^[Y6 : $i]: ((^[Y7 : $i]: (c_Repl @ sF1 @ (^[Y8 : $i]: ((^[Y9 : $o]: ((^[Y10 : $i]: ((^[Y11 : $i]: (c_Eps_i @ (^[Y12 : $i]: ((^[Y13 : $o]: ((^[Y14 : $o]: (!! @ $o @ (^[Y15 : $o]: ((Y13 => Y15) => ((Y14 => Y15) => Y15))))))) @ ((^[Y13 : $o]: ((^[Y14 : $o]: (!! @ $o @ (^[Y15 : $o]: ((Y13 => (Y14 => Y15)) => Y15)))))) @ Y9 @ (Y10 = Y12)) @ ((^[Y13 : $o]: ((^[Y14 : $o]: (!! @ $o @ (^[Y15 : $o]: ((Y13 => (Y14 => Y15)) => Y15)))))) @ ((^[Y13 : $o]: (Y13 => c_False)) @ Y9) @ (Y11 = Y12)))))))))) @ (c_In @ c_Empty @ Y8) @ Y6 @ Y7)))))) @ Y5 @ Y5)) @ Y4))) @ (Y0 @ Y3))))))))))) => (?? @ $i @ (^[Y2 : $i]: ((^[Y3 : $o]: ((^[Y4 : $o]: (!! @ $o @ (^[Y5 : $o]: ((Y3 => (Y4 => Y5)) => Y5)))))) @ (?? @ $i @ (^[Y3 : $i]: ((^[Y4 : $o]: ((^[Y5 : $o]: (!! @ $o @ (^[Y6 : $o]: ((Y4 => (Y5 => Y6)) => Y6)))))) @ ((^[Y4 : $i]: ((^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ Y4) => (c_In @ Y6 @ Y5))))))) @ Y3 @ Y2) @ (((Y0 @ Y2) = Y2) => (?? @ $i @ (^[Y4 : $i]: ((^[Y5 : $o]: ((^[Y6 : $o]: (!! @ $o @ (^[Y7 : $o]: ((Y5 => (Y6 => Y7)) => Y7)))))) @ ((^[Y5 : $i]: ((^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((c_In @ Y7 @ Y5) => (c_In @ Y7 @ Y6))))))) @ Y4 @ Y2) @ ((^[Y5 : $o]: (Y5 => c_False)) @ (Y1 @ ((^[Y5 : $i]: ((^[Y6 : $i]: ((^[Y7 : $i]: ((^[Y8 : $i > $i]: ((^[Y9 : $i]: ((^[Y10 : $i > $i]: (c_Union @ (c_Repl @ Y9 @ (^[Y11 : $i]: (Y10 @ Y11))))))) @ Y7 @ (^[Y9 : $i]: (c_Repl @ (Y8 @ Y9) @ (^[Y10 : $i]: ((^[Y11 : $i]: ((^[Y12 : $i]: ((^[Y13 : $i]: ((^[Y14 : $i]: (c_Union @ ((^[Y15 : $i]: ((^[Y16 : $i]: (c_Repl @ sF1 @ (^[Y17 : $i]: ((^[Y18 : $o]: ((^[Y19 : $i]: ((^[Y20 : $i]: (c_Eps_i @ (^[Y21 : $i]: ((^[Y22 : $o]: ((^[Y23 : $o]: (!! @ $o @ (^[Y24 : $o]: ((Y22 => Y24) => ((Y23 => Y24) => Y24))))))) @ ((^[Y22 : $o]: ((^[Y23 : $o]: (!! @ $o @ (^[Y24 : $o]: ((Y22 => (Y23 => Y24)) => Y24)))))) @ Y18 @ (Y19 = Y21)) @ ((^[Y22 : $o]: ((^[Y23 : $o]: (!! @ $o @ (^[Y24 : $o]: ((Y22 => (Y23 => Y24)) => Y24)))))) @ ((^[Y22 : $o]: (Y22 => c_False)) @ Y18) @ (Y20 = Y21)))))))))) @ (c_In @ c_Empty @ Y17) @ Y15 @ Y16)))))) @ Y13 @ Y14))))) @ (c_Repl @ Y11 @ (^[Y13 : $i]: ((^[Y14 : $i]: (c_Repl @ Y14 @ (^[Y15 : $i]: ((^[Y16 : $i > ($i > $i) > $i]: ((^[Y17 : $i]: (c_Eps_i @ (^[Y18 : $i]: ((^[Y19 : $i > ($i > $i) > $i]: ((^[Y20 : $i]: ((^[Y21 : $i]: (!! @ ($i > $i > $o) @ (^[Y22 : $i > $i > $o]: ((!! @ ($i > $i) @ (^[Y23 : $i > $i]: (!! @ $i @ (^[Y24 : $i]: ((!! @ $i @ (^[Y25 : $i]: ((c_In @ Y25 @ Y24) => (Y22 @ Y25 @ (Y23 @ Y25))))) => (Y22 @ Y24 @ (Y19 @ Y24 @ Y23))))))) => (Y22 @ Y20 @ Y21))))))))) @ Y16 @ Y17 @ Y18)))))) @ (^[Y16 : $i]: ((^[Y17 : $i > $i]: ((^[Y18 : $i]: ((^[Y19 : $i]: (c_Union @ ((^[Y20 : $i]: ((^[Y21 : $i]: (c_Repl @ sF1 @ (^[Y22 : $i]: ((^[Y23 : $o]: ((^[Y24 : $i]: ((^[Y25 : $i]: (c_Eps_i @ (^[Y26 : $i]: ((^[Y27 : $o]: ((^[Y28 : $o]: (!! @ $o @ (^[Y29 : $o]: ((Y27 => Y29) => ((Y28 => Y29) => Y29))))))) @ ((^[Y27 : $o]: ((^[Y28 : $o]: (!! @ $o @ (^[Y29 : $o]: ((Y27 => (Y28 => Y29)) => Y29)))))) @ Y23 @ (Y24 = Y26)) @ ((^[Y27 : $o]: ((^[Y28 : $o]: (!! @ $o @ (^[Y29 : $o]: ((Y27 => (Y28 => Y29)) => Y29)))))) @ ((^[Y27 : $o]: (Y27 => c_False)) @ Y23) @ (Y25 = Y26)))))))))) @ (c_In @ c_Empty @ Y22) @ Y20 @ Y21)))))) @ Y18 @ Y19))))) @ sF2 @ (c_Repl @ Y16 @ (^[Y18 : $i]: (Y17 @ Y18))))))) @ Y15)))) @ Y13))) @ (c_Repl @ Y12 @ (^[Y13 : $i]: ((^[Y14 : $i > ($i > $i) > $i]: ((^[Y15 : $i]: (c_Eps_i @ (^[Y16 : $i]: ((^[Y17 : $i > ($i > $i) > $i]: ((^[Y18 : $i]: ((^[Y19 : $i]: (!! @ ($i > $i > $o) @ (^[Y20 : $i > $i > $o]: ((!! @ ($i > $i) @ (^[Y21 : $i > $i]: (!! @ $i @ (^[Y22 : $i]: ((!! @ $i @ (^[Y23 : $i]: ((c_In @ Y23 @ Y22) => (Y20 @ Y23 @ (Y21 @ Y23))))) => (Y20 @ Y22 @ (Y17 @ Y22 @ Y21))))))) => (Y20 @ Y18 @ Y19))))))))) @ Y14 @ Y15 @ Y16)))))) @ (^[Y14 : $i]: ((^[Y15 : $i > $i]: ((^[Y16 : $i]: ((^[Y17 : $i]: (c_Union @ ((^[Y18 : $i]: ((^[Y19 : $i]: (c_Repl @ sF1 @ (^[Y20 : $i]: ((^[Y21 : $o]: ((^[Y22 : $i]: ((^[Y23 : $i]: (c_Eps_i @ (^[Y24 : $i]: ((^[Y25 : $o]: ((^[Y26 : $o]: (!! @ $o @ (^[Y27 : $o]: ((Y25 => Y27) => ((Y26 => Y27) => Y27))))))) @ ((^[Y25 : $o]: ((^[Y26 : $o]: (!! @ $o @ (^[Y27 : $o]: ((Y25 => (Y26 => Y27)) => Y27)))))) @ Y21 @ (Y22 = Y24)) @ ((^[Y25 : $o]: ((^[Y26 : $o]: (!! @ $o @ (^[Y27 : $o]: ((Y25 => (Y26 => Y27)) => Y27)))))) @ ((^[Y25 : $o]: (Y25 => c_False)) @ Y21) @ (Y23 = Y24)))))))))) @ (c_In @ c_Empty @ Y20) @ Y18 @ Y19)))))) @ Y16 @ Y17))))) @ sF2 @ (c_Repl @ Y14 @ (^[Y16 : $i]: (Y15 @ Y16))))))) @ Y13))))))) @ Y9 @ Y10)))))))) @ Y5 @ (^[Y7 : $i]: (Y6)))))) @ Y3 @ sF7)))))))))) @ ((^[Y3 : $o]: (Y3 => c_False)) @ ((^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((^[Y5 : $o]: ((^[Y6 : $o]: (!! @ $o @ (^[Y7 : $o]: ((Y5 => (Y6 => Y7)) => Y7)))))) @ ((^[Y5 : $i]: ((^[Y6 : $o]: ((^[Y7 : $o]: (!! @ $o @ (^[Y8 : $o]: ((Y6 => (Y7 => Y8)) => Y8)))))) @ ((^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((c_In @ Y7 @ Y6) => ((^[Y8 : $i]: ((^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: ((c_In @ Y10 @ Y8) => (c_In @ Y10 @ Y9))))))) @ Y7 @ Y6))))) @ Y5) @ (!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ Y5) => ((^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((c_In @ Y8 @ Y7) => ((^[Y9 : $i]: ((^[Y10 : $i]: (!! @ $i @ (^[Y11 : $i]: ((c_In @ Y11 @ Y9) => (c_In @ Y11 @ Y10))))))) @ Y8 @ Y7))))) @ Y6)))))) @ Y4) @ ((^[Y5 : $i]: ((^[Y6 : $i]: ((^[Y7 : $o]: ((^[Y8 : $o]: (!! @ $o @ (^[Y9 : $o]: ((Y7 => (Y8 => Y9)) => Y9)))))) @ ((^[Y7 : $i]: ((^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((c_In @ Y9 @ Y7) => (c_In @ Y9 @ Y8))))))) @ Y6 @ ((^[Y7 : $i]: ((^[Y8 : $i]: ((^[Y9 : $i]: (c_Union @ ((^[Y10 : $i]: ((^[Y11 : $i]: (c_Repl @ sF1 @ (^[Y12 : $i]: ((^[Y13 : $o]: ((^[Y14 : $i]: ((^[Y15 : $i]: (c_Eps_i @ (^[Y16 : $i]: ((^[Y17 : $o]: ((^[Y18 : $o]: (!! @ $o @ (^[Y19 : $o]: ((Y17 => Y19) => ((Y18 => Y19) => Y19))))))) @ ((^[Y17 : $o]: ((^[Y18 : $o]: (!! @ $o @ (^[Y19 : $o]: ((Y17 => (Y18 => Y19)) => Y19)))))) @ Y13 @ (Y14 = Y16)) @ ((^[Y17 : $o]: ((^[Y18 : $o]: (!! @ $o @ (^[Y19 : $o]: ((Y17 => (Y18 => Y19)) => Y19)))))) @ ((^[Y17 : $o]: (Y17 => c_False)) @ Y13) @ (Y15 = Y16)))))))))) @ (c_In @ c_Empty @ Y12) @ Y10 @ Y11)))))) @ Y8 @ Y9))))) @ Y7 @ (c_Repl @ Y7 @ (^[Y8 : $i]: ((^[Y9 : $i]: ((^[Y10 : $i]: ((^[Y11 : $i]: ((^[Y12 : $i]: ((^[Y13 : $i]: (c_Union @ ((^[Y14 : $i]: ((^[Y15 : $i]: (c_Repl @ sF1 @ (^[Y16 : $i]: ((^[Y17 : $o]: ((^[Y18 : $i]: ((^[Y19 : $i]: (c_Eps_i @ (^[Y20 : $i]: ((^[Y21 : $o]: ((^[Y22 : $o]: (!! @ $o @ (^[Y23 : $o]: ((Y21 => Y23) => ((Y22 => Y23) => Y23))))))) @ ((^[Y21 : $o]: ((^[Y22 : $o]: (!! @ $o @ (^[Y23 : $o]: ((Y21 => (Y22 => Y23)) => Y23)))))) @ Y17 @ (Y18 = Y20)) @ ((^[Y21 : $o]: ((^[Y22 : $o]: (!! @ $o @ (^[Y23 : $o]: ((Y21 => (Y22 => Y23)) => Y23)))))) @ ((^[Y21 : $o]: (Y21 => c_False)) @ Y17) @ (Y19 = Y20)))))))))) @ (c_In @ c_Empty @ Y16) @ Y14 @ Y15)))))) @ Y12 @ Y13))))) @ Y10 @ ((^[Y12 : $i]: ((^[Y13 : $i]: ((^[Y14 : $i]: (c_Repl @ sF1 @ (^[Y15 : $i]: ((^[Y16 : $o]: ((^[Y17 : $i]: ((^[Y18 : $i]: (c_Eps_i @ (^[Y19 : $i]: ((^[Y20 : $o]: ((^[Y21 : $o]: (!! @ $o @ (^[Y22 : $o]: ((Y20 => Y22) => ((Y21 => Y22) => Y22))))))) @ ((^[Y20 : $o]: ((^[Y21 : $o]: (!! @ $o @ (^[Y22 : $o]: ((Y20 => (Y21 => Y22)) => Y22)))))) @ Y16 @ (Y17 = Y19)) @ ((^[Y20 : $o]: ((^[Y21 : $o]: (!! @ $o @ (^[Y22 : $o]: ((Y20 => (Y21 => Y22)) => Y22)))))) @ ((^[Y20 : $o]: (Y20 => c_False)) @ Y16) @ (Y18 = Y19)))))))))) @ (c_In @ c_Empty @ Y15) @ Y13 @ Y14)))))) @ Y12 @ Y12)) @ Y11))))) @ Y9 @ sF9)) @ Y8))))) @ Y5)) @ (!! @ $i @ (^[Y7 : $i]: ((c_In @ Y7 @ Y5) => ((^[Y8 : $o]: ((^[Y9 : $o]: ((^[Y10 : $o]: ((^[Y11 : $o]: (!! @ $o @ (^[Y12 : $o]: ((Y10 => Y12) => ((Y11 => Y12) => Y12))))))) @ ((^[Y10 : $o]: ((^[Y11 : $o]: (!! @ $o @ (^[Y12 : $o]: ((Y10 => (Y11 => Y12)) => Y12)))))) @ Y8 @ ((^[Y10 : $o]: (Y10 => c_False)) @ Y9)) @ ((^[Y10 : $o]: ((^[Y11 : $o]: (!! @ $o @ (^[Y12 : $o]: ((Y10 => (Y11 => Y12)) => Y12)))))) @ ((^[Y10 : $o]: (Y10 => c_False)) @ Y8) @ Y9))))) @ (c_In @ ((^[Y8 : $i]: ((^[Y9 : $i]: ((^[Y10 : $i]: ((^[Y11 : $i]: ((^[Y12 : $i]: (c_Union @ ((^[Y13 : $i]: ((^[Y14 : $i]: (c_Repl @ sF1 @ (^[Y15 : $i]: ((^[Y16 : $o]: ((^[Y17 : $i]: ((^[Y18 : $i]: (c_Eps_i @ (^[Y19 : $i]: ((^[Y20 : $o]: ((^[Y21 : $o]: (!! @ $o @ (^[Y22 : $o]: ((Y20 => Y22) => ((Y21 => Y22) => Y22))))))) @ ((^[Y20 : $o]: ((^[Y21 : $o]: (!! @ $o @ (^[Y22 : $o]: ((Y20 => (Y21 => Y22)) => Y22)))))) @ Y16 @ (Y17 = Y19)) @ ((^[Y20 : $o]: ((^[Y21 : $o]: (!! @ $o @ (^[Y22 : $o]: ((Y20 => (Y21 => Y22)) => Y22)))))) @ ((^[Y20 : $o]: (Y20 => c_False)) @ Y16) @ (Y18 = Y19)))))))))) @ (c_In @ c_Empty @ Y15) @ Y13 @ Y14)))))) @ Y11 @ Y12))))) @ Y9 @ ((^[Y11 : $i]: ((^[Y12 : $i]: ((^[Y13 : $i]: (c_Repl @ sF1 @ (^[Y14 : $i]: ((^[Y15 : $o]: ((^[Y16 : $i]: ((^[Y17 : $i]: (c_Eps_i @ (^[Y18 : $i]: ((^[Y19 : $o]: ((^[Y20 : $o]: (!! @ $o @ (^[Y21 : $o]: ((Y19 => Y21) => ((Y20 => Y21) => Y21))))))) @ ((^[Y19 : $o]: ((^[Y20 : $o]: (!! @ $o @ (^[Y21 : $o]: ((Y19 => (Y20 => Y21)) => Y21)))))) @ Y15 @ (Y16 = Y18)) @ ((^[Y19 : $o]: ((^[Y20 : $o]: (!! @ $o @ (^[Y21 : $o]: ((Y19 => (Y20 => Y21)) => Y21)))))) @ ((^[Y19 : $o]: (Y19 => c_False)) @ Y15) @ (Y17 = Y18)))))))))) @ (c_In @ c_Empty @ Y14) @ Y12 @ Y13)))))) @ Y11 @ Y11)) @ Y10))))) @ Y8 @ sF9)) @ Y7) @ Y6) @ (c_In @ Y7 @ Y6))))))))) @ Y4 @ Y3))))) @ Y2)))))) @ ((^[Y2 : $o]: (Y2 => c_False)) @ (Y1 @ (Y0 @ (Y0 @ (Y0 @ sF11))))))))))))),
% 9.27/1.88 introduced(definition,[new_symbols(definition,[sF12])],[function_definition])).
% 9.27/1.88 thf(f532,plain,(
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% 9.27/1.88 inference(reorient_equations,[],[f531])).
% 9.27/1.88 thf(f533,definition,(
% 9.27/1.88 (sF13 = (((^[Y0 : $o]: (Y0 => c_False)) @ sF12)))),
% 9.27/1.88 introduced(definition,[new_symbols(definition,[sF13])],[function_definition])).
% 9.27/1.88 thf(f534,plain,(
% 9.27/1.88 ((((^[Y0 : $o]: (Y0 => c_False)) @ sF12)) = sF13)),
% 9.27/1.88 inference(reorient_equations,[],[f533])).
% 9.27/1.88 thf(f535,definition,(
% 9.27/1.88 (sF14 = ((~ sF13)))),
% 9.27/1.88 introduced(definition,[new_symbols(definition,[sF14])],[function_definition])).
% 9.27/1.88 thf(f536,plain,(
% 9.27/1.88 ($true = sF14)),
% 9.27/1.88 inference(definition_folding,[],[f504,f535,f534,f532,f530,f528,f513,f524,f523,f515,f513,f517,f515,f513,f515,f513,f517,f515,f513,f515,f513,f515,f513,f517,f515,f513,f515,f513,f517,f515,f513,f515,f513,f515,f513,f517,f515,f513,f515,f513,f517,f515,f513,f515,f513,f515,f513,f527,f526,f515,f513,f515,f513,f515,f513,f515,f513,f515,f513,f527,f526,f515,f513,f515,f513,f515,f513,f515,f513,f515,f513,f515,f513,f525,f515,f513,f524,f523,f515,f513,f517,f515,f513,f515,f513,f517,f515,f513,f515,f513,f515,f513,f517,f515,f513,f515,f513,f517,f515,f513,f515,f513,f515,f513,f517,f515,f513,f515,f513,f517,f515,f513,f515,f513,f515,f513,f515,f513,f515,f513,f521,f519,f515,f513,f517,f515,f513,f515,f513,f517,f515,f513,f515,f513,f515,f513,f513])).
% 9.27/1.88 thf(f537,plain,(
% 9.27/1.88 (((!! @ ($i > $i) @ (^[Y0 : $i > $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $o @ (^[Y2 : $o]: (((((Y1 @ (Y0 @ (c_Eps_i @ (^[Y3 : $i]: (!! @ $o @ (^[Y4 : $o]: (((!! @ $o @ (^[Y5 : $o]: (((?? @ $i @ (^[Y6 : $i]: (!! @ $o @ (^[Y7 : $o]: (((c_In @ Y6 @ (Y0 @ sF0)) => ((c_In @ Y6 @ (Y0 @ sF4)) => Y7)) => Y7))))) => (((c_Repl @ (Y0 @ sF0) @ (^[Y6 : $i]: (c_Eps_i @ (^[Y7 : $i]: (!! @ $o @ (^[Y8 : $o]: (((!! @ $o @ (^[Y9 : $o]: (((c_In @ Y6 @ (Y0 @ sF4)) => ((Y6 = Y7) => Y9)) => Y9))) => Y8) => (((!! @ $o @ (^[Y9 : $o]: ((((c_In @ Y6 @ (Y0 @ sF4)) => c_False) => (((c_Eps_i @ (^[Y10 : $i]: (!! @ $o @ (^[Y11 : $o]: (((c_In @ Y10 @ (Y0 @ sF0)) => ((c_In @ Y10 @ (Y0 @ sF4)) => Y11)) => Y11))))) = Y7) => Y9)) => Y9))) => Y8) => Y8)))))))) = Y3) => Y5)) => Y5))) => Y4) => (((!! @ $o @ (^[Y5 : $o]: ((((?? @ $i @ (^[Y6 : $i]: (!! @ $o @ (^[Y7 : $o]: (((c_In @ Y6 @ (Y0 @ sF0)) => ((c_In @ Y6 @ (Y0 @ sF4)) => Y7)) => Y7))))) => c_False) => ((c_Empty = Y3) => Y5)) => Y5))) => Y4) => Y4)))))))) => ((!! @ $i @ (^[Y3 : $i]: ((c_In @ Y3 @ (Y0 @ c_Empty)) => (!! @ $i @ (^[Y4 : $i]: ((c_In @ Y4 @ Y3) => (c_In @ Y4 @ (Y0 @ c_Empty)))))))) => (!! @ $i @ (^[Y3 : $i]: ((c_In @ Y3 @ c_Empty) => (?? @ $i @ (^[Y4 : $i]: (!! @ $o @ (^[Y5 : $o]: (((!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ Y4) => (c_In @ Y6 @ Y3)))) => ((!! @ $o @ (^[Y6 : $o]: (((?? @ $i @ (^[Y7 : $i]: (!! @ $o @ (^[Y8 : $o]: (((c_In @ Y7 @ (c_Union @ (c_Repl @ sF1 @ (^[Y9 : $i]: (c_Eps_i @ (^[Y10 : $i]: (!! @ $o @ (^[Y11 : $o]: (((!! @ $o @ (^[Y12 : $o]: (((c_In @ c_Empty @ Y9) => (((Y0 @ Y4) = Y10) => Y12)) => Y12))) => Y11) => (((!! @ $o @ (^[Y12 : $o]: ((((c_In @ c_Empty @ Y9) => c_False) => (((c_Repl @ sF1 @ (^[Y13 : $i]: (c_Eps_i @ (^[Y14 : $i]: (!! @ $o @ (^[Y15 : $o]: (((!! @ $o @ (^[Y16 : $o]: (((c_In @ c_Empty @ Y13) => (((Y0 @ Y4) = Y14) => Y16)) => Y16))) => Y15) => (((!! @ $o @ (^[Y16 : $o]: ((((c_In @ c_Empty @ Y13) => c_False) => (((Y0 @ Y4) = Y14) => Y16)) => Y16))) => Y15) => Y15)))))))) = Y10) => Y12)) => Y12))) => Y11) => Y11)))))))))) => (((!! @ $i @ (^[Y9 : $i]: ((c_In @ Y9 @ (c_Union @ (c_Repl @ sF1 @ (^[Y10 : $i]: (c_Eps_i @ (^[Y11 : $i]: (!! @ $o @ (^[Y12 : $o]: (((!! @ $o @ (^[Y13 : $o]: (((c_In @ c_Empty @ Y10) => (((Y0 @ Y4) = Y11) => Y13)) => Y13))) => Y12) => (((!! @ $o @ (^[Y13 : $o]: ((((c_In @ c_Empty @ Y10) => c_False) => (((c_Repl @ sF1 @ (^[Y14 : $i]: (c_Eps_i @ (^[Y15 : $i]: (!! @ $o @ (^[Y16 : $o]: (((!! @ $o @ (^[Y17 : $o]: (((c_In @ c_Empty @ Y14) => (((Y0 @ Y4) = Y15) => Y17)) => Y17))) => Y16) => (((!! @ $o @ (^[Y17 : $o]: ((((c_In @ c_Empty @ Y14) => c_False) => (((Y0 @ Y4) = Y15) => Y17)) => Y17))) => Y16) => Y16)))))))) = Y11) => Y13)) => Y13))) => Y12) => Y12)))))))))) => (c_In @ Y9 @ (c_Power @ Y7))))) => c_False) => Y8)) => Y8))))) => (((?? @ $i @ (^[Y7 : $i]: (!! @ $o @ (^[Y8 : $o]: (((!! @ $i @ (^[Y9 : $i]: ((c_In @ Y9 @ Y7) => (c_In @ Y9 @ (c_Union @ (c_Repl @ sF1 @ (^[Y10 : $i]: (c_Eps_i @ (^[Y11 : $i]: (!! @ $o @ (^[Y12 : $o]: (((!! @ $o @ (^[Y13 : $o]: (((c_In @ c_Empty @ Y10) => (((Y0 @ Y4) = Y11) => Y13)) => Y13))) => Y12) => (((!! @ $o @ (^[Y13 : $o]: ((((c_In @ c_Empty @ Y10) => c_False) => (((c_Repl @ sF1 @ (^[Y14 : $i]: (c_Eps_i @ (^[Y15 : $i]: (!! @ $o @ (^[Y16 : $o]: (((!! @ $o @ (^[Y17 : $o]: (((c_In @ c_Empty @ Y14) => (((Y0 @ Y4) = Y15) => Y17)) => Y17))) => Y16) => (((!! @ $o @ (^[Y17 : $o]: ((((c_In @ c_Empty @ Y14) => c_False) => (((Y0 @ Y4) = Y15) => Y17)) => Y17))) => Y16) => Y16)))))))) = Y11) => Y13)) => Y13))) => Y12) => Y12))))))))))))) => ((!! @ $o @ (^[Y9 : $o]: ((((!! @ $i @ (^[Y10 : $i]: ((c_In @ Y10 @ (c_Union @ (c_Repl @ sF1 @ (^[Y11 : $i]: (c_Eps_i @ (^[Y12 : $i]: (!! @ $o @ (^[Y13 : $o]: (((!! @ $o @ (^[Y14 : $o]: (((c_In @ c_Empty @ Y11) => (((Y0 @ Y4) = Y12) => Y14)) => Y14))) => Y13) => (((!! @ $o @ (^[Y14 : $o]: ((((c_In @ c_Empty @ Y11) => c_False) => (((c_Repl @ sF1 @ (^[Y15 : $i]: (c_Eps_i @ (^[Y16 : $i]: (!! @ $o @ (^[Y17 : $o]: (((!! @ $o @ (^[Y18 : $o]: (((c_In @ c_Empty @ Y15) => (((Y0 @ Y4) = Y16) => Y18)) => Y18))) => Y17) => (((!! @ $o @ (^[Y18 : $o]: ((((c_In @ c_Empty @ Y15) => c_False) => (((Y0 @ Y4) = Y16) => Y18)) => Y18))) => Y17) => Y17)))))))) = Y12) => Y14)) => Y14))) => Y13) => Y13)))))))))) => (c_In @ Y10 @ Y7)))) => c_False) => ((?? @ $i @ (^[Y10 : $i]: (!! @ $o @ (^[Y11 : $o]: (((c_In @ Y10 @ Y7) => (((!! @ $i @ (^[Y12 : $i]: ((c_In @ Y12 @ Y7) => (c_In @ Y12 @ (c_Power @ Y10))))) => c_False) => Y11)) => Y11))))) => Y9)) => Y9))) => Y8)) => Y8))))) => c_False) => Y6)) => Y6))) => Y5)) => Y5)))))))))) => (?? @ $i @ (^[Y3 : $i]: (!! @ $o @ (^[Y4 : $o]: (((?? @ $i @ (^[Y5 : $i]: (!! @ $o @ (^[Y6 : $o]: (((!! @ $i @ (^[Y7 : $i]: ((c_In @ Y7 @ Y5) => (c_In @ Y7 @ Y3)))) => ((((Y0 @ Y3) = Y3) => (?? @ $i @ (^[Y7 : $i]: (!! @ $o @ (^[Y8 : $o]: (((!! @ $i @ (^[Y9 : $i]: ((c_In @ Y9 @ Y7) => (c_In @ Y9 @ Y3)))) => (((Y1 @ (c_Union @ (c_Repl @ Y5 @ (^[Y9 : $i]: (c_Repl @ sF7 @ (^[Y10 : $i]: (c_Union @ (c_Repl @ sF1 @ (^[Y11 : $i]: (c_Eps_i @ (^[Y12 : $i]: (!! @ $o @ (^[Y13 : $o]: (((!! @ $o @ (^[Y14 : $o]: (((c_In @ c_Empty @ Y11) => (((c_Repl @ Y9 @ (^[Y15 : $i]: (c_Repl @ Y15 @ (^[Y16 : $i]: (c_Eps_i @ (^[Y17 : $i]: (!! @ ($i > $i > $o) @ (^[Y18 : $i > $i > $o]: ((!! @ ($i > $i) @ (^[Y19 : $i > $i]: (!! @ $i @ (^[Y20 : $i]: ((!! @ $i @ (^[Y21 : $i]: ((c_In @ Y21 @ Y20) => (Y18 @ Y21 @ (Y19 @ Y21))))) => (Y18 @ Y20 @ (c_Union @ (c_Repl @ sF1 @ (^[Y21 : $i]: (c_Eps_i @ (^[Y22 : $i]: (!! @ $o @ (^[Y23 : $o]: (((!! @ $o @ (^[Y24 : $o]: (((c_In @ c_Empty @ Y21) => ((sF2 = Y22) => Y24)) => Y24))) => Y23) => (((!! @ $o @ (^[Y24 : $o]: ((((c_In @ c_Empty @ Y21) => c_False) => (((c_Repl @ Y20 @ Y19) = Y22) => Y24)) => Y24))) => Y23) => Y23))))))))))))))) => (Y18 @ Y16 @ Y17)))))))))) = Y12) => Y14)) => Y14))) => Y13) => (((!! @ $o @ (^[Y14 : $o]: ((((c_In @ c_Empty @ Y11) => c_False) => (((c_Repl @ Y10 @ (^[Y15 : $i]: (c_Eps_i @ (^[Y16 : $i]: (!! @ ($i > $i > $o) @ (^[Y17 : $i > $i > $o]: ((!! @ ($i > $i) @ (^[Y18 : $i > $i]: (!! @ $i @ (^[Y19 : $i]: ((!! @ $i @ (^[Y20 : $i]: ((c_In @ Y20 @ Y19) => (Y17 @ Y20 @ (Y18 @ Y20))))) => (Y17 @ Y19 @ (c_Union @ (c_Repl @ sF1 @ (^[Y20 : $i]: (c_Eps_i @ (^[Y21 : $i]: (!! @ $o @ (^[Y22 : $o]: (((!! @ $o @ (^[Y23 : $o]: (((c_In @ c_Empty @ Y20) => ((sF2 = Y21) => Y23)) => Y23))) => Y22) => (((!! @ $o @ (^[Y23 : $o]: ((((c_In @ c_Empty @ Y20) => c_False) => (((c_Repl @ Y19 @ Y18) = Y21) => Y23)) => Y23))) => Y22) => Y22))))))))))))))) => (Y17 @ Y15 @ Y16)))))))) = Y12) => Y14)) => Y14))) => Y13) => Y13))))))))))))))) => c_False) => Y8)) => Y8)))))) => Y6)) => Y6))))) => (((?? @ $i @ (^[Y5 : $i]: (!! @ $o @ (^[Y6 : $o]: (((!! @ $o @ (^[Y7 : $o]: (((!! @ $i @ (^[Y8 : $i]: ((c_In @ Y8 @ Y5) => (!! @ $i @ (^[Y9 : $i]: ((c_In @ Y9 @ Y8) => (c_In @ Y9 @ Y5))))))) => ((!! @ $i @ (^[Y8 : $i]: ((c_In @ Y8 @ Y5) => (!! @ $i @ (^[Y9 : $i]: ((c_In @ Y9 @ Y8) => (!! @ $i @ (^[Y10 : $i]: ((c_In @ Y10 @ Y9) => (c_In @ Y10 @ Y8)))))))))) => Y7)) => Y7))) => ((!! @ $o @ (^[Y7 : $o]: (((!! @ $i @ (^[Y8 : $i]: ((c_In @ Y8 @ Y3) => (c_In @ Y8 @ (c_Union @ (c_Repl @ sF1 @ (^[Y9 : $i]: (c_Eps_i @ (^[Y10 : $i]: (!! @ $o @ (^[Y11 : $o]: (((!! @ $o @ (^[Y12 : $o]: (((c_In @ c_Empty @ Y9) => ((Y5 = Y10) => Y12)) => Y12))) => Y11) => (((!! @ $o @ (^[Y12 : $o]: ((((c_In @ c_Empty @ Y9) => c_False) => (((c_Repl @ Y5 @ (^[Y13 : $i]: (c_Union @ (c_Repl @ sF1 @ (^[Y14 : $i]: (c_Eps_i @ (^[Y15 : $i]: (!! @ $o @ (^[Y16 : $o]: (((!! @ $o @ (^[Y17 : $o]: (((c_In @ c_Empty @ Y14) => ((Y13 = Y15) => Y17)) => Y17))) => Y16) => (((!! @ $o @ (^[Y17 : $o]: ((((c_In @ c_Empty @ Y14) => c_False) => (((c_Repl @ sF1 @ (^[Y18 : $i]: (c_Eps_i @ (^[Y19 : $i]: (!! @ $o @ (^[Y20 : $o]: (((!! @ $o @ (^[Y21 : $o]: (((c_In @ c_Empty @ Y18) => ((sF9 = Y19) => Y21)) => Y21))) => Y20) => (((!! @ $o @ (^[Y21 : $o]: ((((c_In @ c_Empty @ Y18) => c_False) => ((sF9 = Y19) => Y21)) => Y21))) => Y20) => Y20)))))))) = Y15) => Y17)) => Y17))) => Y16) => Y16))))))))))) = Y10) => Y12)) => Y12))) => Y11) => Y11))))))))))))) => ((!! @ $i @ (^[Y8 : $i]: ((c_In @ Y8 @ Y5) => (!! @ $o @ (^[Y9 : $o]: (((!! @ $o @ (^[Y10 : $o]: (((c_In @ (c_Union @ (c_Repl @ sF1 @ (^[Y11 : $i]: (c_Eps_i @ (^[Y12 : $i]: (!! @ $o @ (^[Y13 : $o]: (((!! @ $o @ (^[Y14 : $o]: (((c_In @ c_Empty @ Y11) => ((Y8 = Y12) => Y14)) => Y14))) => Y13) => (((!! @ $o @ (^[Y14 : $o]: ((((c_In @ c_Empty @ Y11) => c_False) => (((c_Repl @ sF1 @ (^[Y15 : $i]: (c_Eps_i @ (^[Y16 : $i]: (!! @ $o @ (^[Y17 : $o]: (((!! @ $o @ (^[Y18 : $o]: (((c_In @ c_Empty @ Y15) => ((sF9 = Y16) => Y18)) => Y18))) => Y17) => (((!! @ $o @ (^[Y18 : $o]: ((((c_In @ c_Empty @ Y15) => c_False) => ((sF9 = Y16) => Y18)) => Y18))) => Y17) => Y17)))))))) = Y12) => Y14)) => Y14))) => Y13) => Y13))))))))) @ Y3) => (((c_In @ Y8 @ Y3) => c_False) => Y10)) => Y10))) => Y9) => (((!! @ $o @ (^[Y10 : $o]: ((((c_In @ (c_Union @ (c_Repl @ sF1 @ (^[Y11 : $i]: (c_Eps_i @ (^[Y12 : $i]: (!! @ $o @ (^[Y13 : $o]: (((!! @ $o @ (^[Y14 : $o]: (((c_In @ c_Empty @ Y11) => ((Y8 = Y12) => Y14)) => Y14))) => Y13) => (((!! @ $o @ (^[Y14 : $o]: ((((c_In @ c_Empty @ Y11) => c_False) => (((c_Repl @ sF1 @ (^[Y15 : $i]: (c_Eps_i @ (^[Y16 : $i]: (!! @ $o @ (^[Y17 : $o]: (((!! @ $o @ (^[Y18 : $o]: (((c_In @ c_Empty @ Y15) => ((sF9 = Y16) => Y18)) => Y18))) => Y17) => (((!! @ $o @ (^[Y18 : $o]: ((((c_In @ c_Empty @ Y15) => c_False) => ((sF9 = Y16) => Y18)) => Y18))) => Y17) => Y17)))))))) = Y12) => Y14)) => Y14))) => Y13) => Y13))))))))) @ Y3) => c_False) => ((c_In @ Y8 @ Y3) => Y10)) => Y10))) => Y9) => Y9))))))) => Y7)) => Y7))) => Y6)) => Y6))))) => c_False) => Y4)) => Y4)))))) => (((Y1 @ (Y0 @ (Y0 @ (Y0 @ sF11)))) => c_False) => Y2)) => Y2)))))))) = sF12)),
% 9.27/1.88 inference(beta-eta_normalization,[],[f532])).
% 9.27/1.88 thf(f544,plain,(
% 9.27/1.88 (sF13 = ((sF12 => c_False)))),
% 9.27/1.88 inference(beta-eta_normalization,[],[f534])).
% 9.27/1.88 thf(f551,plain,(
% 9.27/1.88 ($true = (((?? @ $i @ (^[Y0 : $i]: (c_In @ Y0 @ c_Empty))) => c_False)))),
% 9.27/1.88 inference(beta-eta_normalization,[],[f505])).
% 9.27/1.88 thf(f557,plain,(
% 9.27/1.88 ($true = ((~ sF13)))),
% 9.27/1.88 inference(backward_demodulation,[],[f535,f536])).
% 9.27/1.88 thf(f558,plain,(
% 9.27/1.88 (sF13 = $false)),
% 9.27/1.88 inference(not_proxy_clausification,[],[f557])).
% 9.27/1.88 thf(f563,plain,(
% 9.27/1.88 ($false = ((sF12 => c_False)))),
% 9.27/1.88 inference(backward_demodulation,[],[f544,f558])).
% 9.27/1.88 thf(f567,plain,(
% 9.27/1.88 (c_False = $false)),
% 9.27/1.88 inference(imp_proxy_clausification,[],[f563])).
% 9.27/1.88 thf(f568,plain,(
% 9.27/1.88 ($true = sF12)),
% 9.27/1.88 inference(imp_proxy_clausification,[],[f563])).
% 9.27/1.88 thf(f577,plain,(
% 9.27/1.88 ($true = ((!! @ ($i > $i) @ (^[Y0 : $i > $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $o @ (^[Y2 : $o]: (((((Y1 @ (Y0 @ (c_Eps_i @ (^[Y3 : $i]: (!! @ $o @ (^[Y4 : $o]: (((!! @ $o @ (^[Y5 : $o]: (((?? @ $i @ (^[Y6 : $i]: (!! @ $o @ (^[Y7 : $o]: (((c_In @ Y6 @ (Y0 @ sF0)) => ((c_In @ Y6 @ (Y0 @ sF4)) => Y7)) => Y7))))) => (((c_Repl @ (Y0 @ sF0) @ (^[Y6 : $i]: (c_Eps_i @ (^[Y7 : $i]: (!! @ $o @ (^[Y8 : $o]: (((!! @ $o @ (^[Y9 : $o]: (((c_In @ Y6 @ (Y0 @ sF4)) => ((Y6 = Y7) => Y9)) => Y9))) => Y8) => (((!! @ $o @ (^[Y9 : $o]: ((((c_In @ Y6 @ (Y0 @ sF4)) => c_False) => (((c_Eps_i @ (^[Y10 : $i]: (!! @ $o @ (^[Y11 : $o]: (((c_In @ Y10 @ (Y0 @ sF0)) => ((c_In @ Y10 @ (Y0 @ sF4)) => Y11)) => Y11))))) = Y7) => Y9)) => Y9))) => Y8) => Y8)))))))) = Y3) => Y5)) => Y5))) => Y4) => (((!! @ $o @ (^[Y5 : $o]: ((((?? @ $i @ (^[Y6 : $i]: (!! @ $o @ (^[Y7 : $o]: (((c_In @ Y6 @ (Y0 @ sF0)) => ((c_In @ Y6 @ (Y0 @ sF4)) => Y7)) => Y7))))) => c_False) => ((c_Empty = Y3) => Y5)) => Y5))) => Y4) => Y4)))))))) => ((!! @ $i @ (^[Y3 : $i]: ((c_In @ Y3 @ (Y0 @ c_Empty)) => (!! @ $i @ (^[Y4 : $i]: ((c_In @ Y4 @ Y3) => (c_In @ Y4 @ (Y0 @ c_Empty)))))))) => (!! @ $i @ (^[Y3 : $i]: ((c_In @ Y3 @ c_Empty) => (?? @ $i @ (^[Y4 : $i]: (!! @ $o @ (^[Y5 : $o]: (((!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ Y4) => (c_In @ Y6 @ Y3)))) => ((!! @ $o @ (^[Y6 : $o]: (((?? @ $i @ (^[Y7 : $i]: (!! @ $o @ (^[Y8 : $o]: (((c_In @ Y7 @ (c_Union @ (c_Repl @ sF1 @ (^[Y9 : $i]: (c_Eps_i @ (^[Y10 : $i]: (!! @ $o @ (^[Y11 : $o]: (((!! @ $o @ (^[Y12 : $o]: (((c_In @ c_Empty @ Y9) => (((Y0 @ Y4) = Y10) => Y12)) => Y12))) => Y11) => (((!! @ $o @ (^[Y12 : $o]: ((((c_In @ c_Empty @ Y9) => c_False) => (((c_Repl @ sF1 @ (^[Y13 : $i]: (c_Eps_i @ (^[Y14 : $i]: (!! @ $o @ (^[Y15 : $o]: (((!! @ $o @ (^[Y16 : $o]: (((c_In @ c_Empty @ Y13) => (((Y0 @ Y4) = Y14) => Y16)) => Y16))) => Y15) => (((!! @ $o @ (^[Y16 : $o]: ((((c_In @ c_Empty @ Y13) => c_False) => (((Y0 @ Y4) = Y14) => Y16)) => Y16))) => Y15) => Y15)))))))) = Y10) => Y12)) => Y12))) => Y11) => Y11)))))))))) => (((!! @ $i @ (^[Y9 : $i]: ((c_In @ Y9 @ (c_Union @ (c_Repl @ sF1 @ (^[Y10 : $i]: (c_Eps_i @ (^[Y11 : $i]: (!! @ $o @ (^[Y12 : $o]: (((!! @ $o @ (^[Y13 : $o]: (((c_In @ c_Empty @ Y10) => (((Y0 @ Y4) = Y11) => Y13)) => Y13))) => Y12) => (((!! @ $o @ (^[Y13 : $o]: ((((c_In @ c_Empty @ Y10) => c_False) => (((c_Repl @ sF1 @ (^[Y14 : $i]: (c_Eps_i @ (^[Y15 : $i]: (!! @ $o @ (^[Y16 : $o]: (((!! @ $o @ (^[Y17 : $o]: (((c_In @ c_Empty @ Y14) => (((Y0 @ Y4) = Y15) => Y17)) => Y17))) => Y16) => (((!! @ $o @ (^[Y17 : $o]: ((((c_In @ c_Empty @ Y14) => c_False) => (((Y0 @ Y4) = Y15) => Y17)) => Y17))) => Y16) => Y16)))))))) = Y11) => Y13)) => Y13))) => Y12) => Y12)))))))))) => (c_In @ Y9 @ (c_Power @ Y7))))) => c_False) => Y8)) => Y8))))) => (((?? @ $i @ (^[Y7 : $i]: (!! @ $o @ (^[Y8 : $o]: (((!! @ $i @ (^[Y9 : $i]: ((c_In @ Y9 @ Y7) => (c_In @ Y9 @ (c_Union @ (c_Repl @ sF1 @ (^[Y10 : $i]: (c_Eps_i @ (^[Y11 : $i]: (!! @ $o @ (^[Y12 : $o]: (((!! @ $o @ (^[Y13 : $o]: (((c_In @ c_Empty @ Y10) => (((Y0 @ Y4) = Y11) => Y13)) => Y13))) => Y12) => (((!! @ $o @ (^[Y13 : $o]: ((((c_In @ c_Empty @ Y10) => c_False) => (((c_Repl @ sF1 @ (^[Y14 : $i]: (c_Eps_i @ (^[Y15 : $i]: (!! @ $o @ (^[Y16 : $o]: (((!! @ $o @ (^[Y17 : $o]: (((c_In @ c_Empty @ Y14) => (((Y0 @ Y4) = Y15) => Y17)) => Y17))) => Y16) => (((!! @ $o @ (^[Y17 : $o]: ((((c_In @ c_Empty @ Y14) => c_False) => (((Y0 @ Y4) = Y15) => Y17)) => Y17))) => Y16) => Y16)))))))) = Y11) => Y13)) => Y13))) => Y12) => Y12))))))))))))) => ((!! @ $o @ (^[Y9 : $o]: ((((!! @ $i @ (^[Y10 : $i]: ((c_In @ Y10 @ (c_Union @ (c_Repl @ sF1 @ (^[Y11 : $i]: (c_Eps_i @ (^[Y12 : $i]: (!! @ $o @ (^[Y13 : $o]: (((!! @ $o @ (^[Y14 : $o]: (((c_In @ c_Empty @ Y11) => (((Y0 @ Y4) = Y12) => Y14)) => Y14))) => Y13) => (((!! @ $o @ (^[Y14 : $o]: ((((c_In @ c_Empty @ Y11) => c_False) => (((c_Repl @ sF1 @ (^[Y15 : $i]: (c_Eps_i @ (^[Y16 : $i]: (!! @ $o @ (^[Y17 : $o]: (((!! @ $o @ (^[Y18 : $o]: (((c_In @ c_Empty @ Y15) => (((Y0 @ Y4) = Y16) => Y18)) => Y18))) => Y17) => (((!! @ $o @ (^[Y18 : $o]: ((((c_In @ c_Empty @ Y15) => c_False) => (((Y0 @ Y4) = Y16) => Y18)) => Y18))) => Y17) => Y17)))))))) = Y12) => Y14)) => Y14))) => Y13) => Y13)))))))))) => (c_In @ Y10 @ Y7)))) => c_False) => ((?? @ $i @ (^[Y10 : $i]: (!! @ $o @ (^[Y11 : $o]: (((c_In @ Y10 @ Y7) => (((!! @ $i @ (^[Y12 : $i]: ((c_In @ Y12 @ Y7) => (c_In @ Y12 @ (c_Power @ Y10))))) => c_False) => Y11)) => Y11))))) => Y9)) => Y9))) => Y8)) => Y8))))) => c_False) => Y6)) => Y6))) => Y5)) => Y5)))))))))) => (?? @ $i @ (^[Y3 : $i]: (!! @ $o @ (^[Y4 : $o]: (((?? @ $i @ (^[Y5 : $i]: (!! @ $o @ (^[Y6 : $o]: (((!! @ $i @ (^[Y7 : $i]: ((c_In @ Y7 @ Y5) => (c_In @ Y7 @ Y3)))) => ((((Y0 @ Y3) = Y3) => (?? @ $i @ (^[Y7 : $i]: (!! @ $o @ (^[Y8 : $o]: (((!! @ $i @ (^[Y9 : $i]: ((c_In @ Y9 @ Y7) => (c_In @ Y9 @ Y3)))) => (((Y1 @ (c_Union @ (c_Repl @ Y5 @ (^[Y9 : $i]: (c_Repl @ sF7 @ (^[Y10 : $i]: (c_Union @ (c_Repl @ sF1 @ (^[Y11 : $i]: (c_Eps_i @ (^[Y12 : $i]: (!! @ $o @ (^[Y13 : $o]: (((!! @ $o @ (^[Y14 : $o]: (((c_In @ c_Empty @ Y11) => (((c_Repl @ Y9 @ (^[Y15 : $i]: (c_Repl @ Y15 @ (^[Y16 : $i]: (c_Eps_i @ (^[Y17 : $i]: (!! @ ($i > $i > $o) @ (^[Y18 : $i > $i > $o]: ((!! @ ($i > $i) @ (^[Y19 : $i > $i]: (!! @ $i @ (^[Y20 : $i]: ((!! @ $i @ (^[Y21 : $i]: ((c_In @ Y21 @ Y20) => (Y18 @ Y21 @ (Y19 @ Y21))))) => (Y18 @ Y20 @ (c_Union @ (c_Repl @ sF1 @ (^[Y21 : $i]: (c_Eps_i @ (^[Y22 : $i]: (!! @ $o @ (^[Y23 : $o]: (((!! @ $o @ (^[Y24 : $o]: (((c_In @ c_Empty @ Y21) => ((sF2 = Y22) => Y24)) => Y24))) => Y23) => (((!! @ $o @ (^[Y24 : $o]: ((((c_In @ c_Empty @ Y21) => c_False) => (((c_Repl @ Y20 @ Y19) = Y22) => Y24)) => Y24))) => Y23) => Y23))))))))))))))) => (Y18 @ Y16 @ Y17)))))))))) = Y12) => Y14)) => Y14))) => Y13) => (((!! @ $o @ (^[Y14 : $o]: ((((c_In @ c_Empty @ Y11) => c_False) => (((c_Repl @ Y10 @ (^[Y15 : $i]: (c_Eps_i @ (^[Y16 : $i]: (!! @ ($i > $i > $o) @ (^[Y17 : $i > $i > $o]: ((!! @ ($i > $i) @ (^[Y18 : $i > $i]: (!! @ $i @ (^[Y19 : $i]: ((!! @ $i @ (^[Y20 : $i]: ((c_In @ Y20 @ Y19) => (Y17 @ Y20 @ (Y18 @ Y20))))) => (Y17 @ Y19 @ (c_Union @ (c_Repl @ sF1 @ (^[Y20 : $i]: (c_Eps_i @ (^[Y21 : $i]: (!! @ $o @ (^[Y22 : $o]: (((!! @ $o @ (^[Y23 : $o]: (((c_In @ c_Empty @ Y20) => ((sF2 = Y21) => Y23)) => Y23))) => Y22) => (((!! @ $o @ (^[Y23 : $o]: ((((c_In @ c_Empty @ Y20) => c_False) => (((c_Repl @ Y19 @ Y18) = Y21) => Y23)) => Y23))) => Y22) => Y22))))))))))))))) => (Y17 @ Y15 @ Y16)))))))) = Y12) => Y14)) => Y14))) => Y13) => Y13))))))))))))))) => c_False) => Y8)) => Y8)))))) => Y6)) => Y6))))) => (((?? @ $i @ (^[Y5 : $i]: (!! @ $o @ (^[Y6 : $o]: (((!! @ $o @ (^[Y7 : $o]: (((!! @ $i @ (^[Y8 : $i]: ((c_In @ Y8 @ Y5) => (!! @ $i @ (^[Y9 : $i]: ((c_In @ Y9 @ Y8) => (c_In @ Y9 @ Y5))))))) => ((!! @ $i @ (^[Y8 : $i]: ((c_In @ Y8 @ Y5) => (!! @ $i @ (^[Y9 : $i]: ((c_In @ Y9 @ Y8) => (!! @ $i @ (^[Y10 : $i]: ((c_In @ Y10 @ Y9) => (c_In @ Y10 @ Y8)))))))))) => Y7)) => Y7))) => ((!! @ $o @ (^[Y7 : $o]: (((!! @ $i @ (^[Y8 : $i]: ((c_In @ Y8 @ Y3) => (c_In @ Y8 @ (c_Union @ (c_Repl @ sF1 @ (^[Y9 : $i]: (c_Eps_i @ (^[Y10 : $i]: (!! @ $o @ (^[Y11 : $o]: (((!! @ $o @ (^[Y12 : $o]: (((c_In @ c_Empty @ Y9) => ((Y5 = Y10) => Y12)) => Y12))) => Y11) => (((!! @ $o @ (^[Y12 : $o]: ((((c_In @ c_Empty @ Y9) => c_False) => (((c_Repl @ Y5 @ (^[Y13 : $i]: (c_Union @ (c_Repl @ sF1 @ (^[Y14 : $i]: (c_Eps_i @ (^[Y15 : $i]: (!! @ $o @ (^[Y16 : $o]: (((!! @ $o @ (^[Y17 : $o]: (((c_In @ c_Empty @ Y14) => ((Y13 = Y15) => Y17)) => Y17))) => Y16) => (((!! @ $o @ (^[Y17 : $o]: ((((c_In @ c_Empty @ Y14) => c_False) => (((c_Repl @ sF1 @ (^[Y18 : $i]: (c_Eps_i @ (^[Y19 : $i]: (!! @ $o @ (^[Y20 : $o]: (((!! @ $o @ (^[Y21 : $o]: (((c_In @ c_Empty @ Y18) => ((sF9 = Y19) => Y21)) => Y21))) => Y20) => (((!! @ $o @ (^[Y21 : $o]: ((((c_In @ c_Empty @ Y18) => c_False) => ((sF9 = Y19) => Y21)) => Y21))) => Y20) => Y20)))))))) = Y15) => Y17)) => Y17))) => Y16) => Y16))))))))))) = Y10) => Y12)) => Y12))) => Y11) => Y11))))))))))))) => ((!! @ $i @ (^[Y8 : $i]: ((c_In @ Y8 @ Y5) => (!! @ $o @ (^[Y9 : $o]: (((!! @ $o @ (^[Y10 : $o]: (((c_In @ (c_Union @ (c_Repl @ sF1 @ (^[Y11 : $i]: (c_Eps_i @ (^[Y12 : $i]: (!! @ $o @ (^[Y13 : $o]: (((!! @ $o @ (^[Y14 : $o]: (((c_In @ c_Empty @ Y11) => ((Y8 = Y12) => Y14)) => Y14))) => Y13) => (((!! @ $o @ (^[Y14 : $o]: ((((c_In @ c_Empty @ Y11) => c_False) => (((c_Repl @ sF1 @ (^[Y15 : $i]: (c_Eps_i @ (^[Y16 : $i]: (!! @ $o @ (^[Y17 : $o]: (((!! @ $o @ (^[Y18 : $o]: (((c_In @ c_Empty @ Y15) => ((sF9 = Y16) => Y18)) => Y18))) => Y17) => (((!! @ $o @ (^[Y18 : $o]: ((((c_In @ c_Empty @ Y15) => c_False) => ((sF9 = Y16) => Y18)) => Y18))) => Y17) => Y17)))))))) = Y12) => Y14)) => Y14))) => Y13) => Y13))))))))) @ Y3) => (((c_In @ Y8 @ Y3) => c_False) => Y10)) => Y10))) => Y9) => (((!! @ $o @ (^[Y10 : $o]: ((((c_In @ (c_Union @ (c_Repl @ sF1 @ (^[Y11 : $i]: (c_Eps_i @ (^[Y12 : $i]: (!! @ $o @ (^[Y13 : $o]: (((!! @ $o @ (^[Y14 : $o]: (((c_In @ c_Empty @ Y11) => ((Y8 = Y12) => Y14)) => Y14))) => Y13) => (((!! @ $o @ (^[Y14 : $o]: ((((c_In @ c_Empty @ Y11) => c_False) => (((c_Repl @ sF1 @ (^[Y15 : $i]: (c_Eps_i @ (^[Y16 : $i]: (!! @ $o @ (^[Y17 : $o]: (((!! @ $o @ (^[Y18 : $o]: (((c_In @ c_Empty @ Y15) => ((sF9 = Y16) => Y18)) => Y18))) => Y17) => (((!! @ $o @ (^[Y18 : $o]: ((((c_In @ c_Empty @ Y15) => c_False) => ((sF9 = Y16) => Y18)) => Y18))) => Y17) => Y17)))))))) = Y12) => Y14)) => Y14))) => Y13) => Y13))))))))) @ Y3) => c_False) => ((c_In @ Y8 @ Y3) => Y10)) => Y10))) => Y9) => Y9))))))) => Y7)) => Y7))) => Y6)) => Y6))))) => c_False) => Y4)) => Y4)))))) => (((Y1 @ (Y0 @ (Y0 @ (Y0 @ sF11)))) => c_False) => Y2)) => Y2)))))))))),
% 9.27/1.88 inference(backward_demodulation,[],[f537,f568])).
% 9.27/1.88 thf(f579,plain,(
% 9.27/1.88 ($true = (((?? @ $i @ (^[Y0 : $i]: (c_In @ Y0 @ c_Empty))) => $false)))),
% 9.27/1.88 inference(backward_demodulation,[],[f551,f567])).
% 9.27/1.88 thf(f581,plain,(
% 9.27/1.88 ($true = ((~ (?? @ $i @ (^[Y0 : $i]: (c_In @ Y0 @ c_Empty))))))),
% 9.27/1.88 inference(boolean_simplification,[],[f579])).
% 9.27/1.88 thf(f588,plain,(
% 9.27/1.88 (((?? @ $i @ (^[Y0 : $i]: (c_In @ Y0 @ c_Empty)))) = $false)),
% 9.27/1.88 inference(not_proxy_clausification,[],[f581])).
% 9.27/1.88 thf(f594,plain,(
% 9.27/1.88 ( ! [X1 : $i] : (((((^[Y0 : $i]: (c_In @ Y0 @ c_Empty)) @ X1)) = $false)) )),
% 9.27/1.88 inference(pi_proxy_clausification,[],[f588])).
% 9.27/1.88 thf(f596,plain,(
% 9.27/1.88 ( ! [X1 : $i] : ((((c_In @ X1 @ c_Empty)) = $false)) )),
% 9.27/1.88 inference(beta-eta_normalization,[],[f594])).
% 9.27/1.88 thf(f600,plain,(
% 9.27/1.88 ( ! [X1 : ($i > $i)] : (($true = (((^[Y0 : $i > $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $o @ (^[Y2 : $o]: (((((Y1 @ (Y0 @ (c_Eps_i @ (^[Y3 : $i]: (!! @ $o @ (^[Y4 : $o]: (((!! @ $o @ (^[Y5 : $o]: (((?? @ $i @ (^[Y6 : $i]: (!! @ $o @ (^[Y7 : $o]: (((c_In @ Y6 @ (Y0 @ sF0)) => ((c_In @ Y6 @ (Y0 @ sF4)) => Y7)) => Y7))))) => (((c_Repl @ (Y0 @ sF0) @ (^[Y6 : $i]: (c_Eps_i @ (^[Y7 : $i]: (!! @ $o @ (^[Y8 : $o]: (((!! @ $o @ (^[Y9 : $o]: (((c_In @ Y6 @ (Y0 @ sF4)) => ((Y6 = Y7) => Y9)) => Y9))) => Y8) => (((!! @ $o @ (^[Y9 : $o]: ((((c_In @ Y6 @ (Y0 @ sF4)) => c_False) => (((c_Eps_i @ (^[Y10 : $i]: (!! @ $o @ (^[Y11 : $o]: (((c_In @ Y10 @ (Y0 @ sF0)) => ((c_In @ Y10 @ (Y0 @ sF4)) => Y11)) => Y11))))) = Y7) => Y9)) => Y9))) => Y8) => Y8)))))))) = Y3) => Y5)) => Y5))) => Y4) => (((!! @ $o @ (^[Y5 : $o]: ((((?? @ $i @ (^[Y6 : $i]: (!! @ $o @ (^[Y7 : $o]: (((c_In @ Y6 @ (Y0 @ sF0)) => ((c_In @ Y6 @ (Y0 @ sF4)) => Y7)) => Y7))))) => c_False) => ((c_Empty = Y3) => Y5)) => Y5))) => Y4) => Y4)))))))) => ((!! @ $i @ (^[Y3 : $i]: ((c_In @ Y3 @ (Y0 @ c_Empty)) => (!! @ $i @ (^[Y4 : $i]: ((c_In @ Y4 @ Y3) => (c_In @ Y4 @ (Y0 @ c_Empty)))))))) => (!! @ $i @ (^[Y3 : $i]: ((c_In @ Y3 @ c_Empty) => (?? @ $i @ (^[Y4 : $i]: (!! @ $o @ (^[Y5 : $o]: (((!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ Y4) => (c_In @ Y6 @ Y3)))) => ((!! @ $o @ (^[Y6 : $o]: (((?? @ $i @ (^[Y7 : $i]: (!! @ $o @ (^[Y8 : $o]: (((c_In @ Y7 @ (c_Union @ (c_Repl @ sF1 @ (^[Y9 : $i]: (c_Eps_i @ (^[Y10 : $i]: (!! @ $o @ (^[Y11 : $o]: (((!! @ $o @ (^[Y12 : $o]: (((c_In @ c_Empty @ Y9) => (((Y0 @ Y4) = Y10) => Y12)) => Y12))) => Y11) => (((!! @ $o @ (^[Y12 : $o]: ((((c_In @ c_Empty @ Y9) => c_False) => (((c_Repl @ sF1 @ (^[Y13 : $i]: (c_Eps_i @ (^[Y14 : $i]: (!! @ $o @ (^[Y15 : $o]: (((!! @ $o @ (^[Y16 : $o]: (((c_In @ c_Empty @ Y13) => (((Y0 @ Y4) = Y14) => Y16)) => Y16))) => Y15) => (((!! @ $o @ (^[Y16 : $o]: ((((c_In @ c_Empty @ Y13) => c_False) => (((Y0 @ Y4) = Y14) => Y16)) => Y16))) => Y15) => Y15)))))))) = Y10) => Y12)) => Y12))) => Y11) => Y11)))))))))) => (((!! @ $i @ (^[Y9 : $i]: ((c_In @ Y9 @ (c_Union @ (c_Repl @ sF1 @ (^[Y10 : $i]: (c_Eps_i @ (^[Y11 : $i]: (!! @ $o @ (^[Y12 : $o]: (((!! @ $o @ (^[Y13 : $o]: (((c_In @ c_Empty @ Y10) => (((Y0 @ Y4) = Y11) => Y13)) => Y13))) => Y12) => (((!! @ $o @ (^[Y13 : $o]: ((((c_In @ c_Empty @ Y10) => c_False) => (((c_Repl @ sF1 @ (^[Y14 : $i]: (c_Eps_i @ (^[Y15 : $i]: (!! @ $o @ (^[Y16 : $o]: (((!! @ $o @ (^[Y17 : $o]: (((c_In @ c_Empty @ Y14) => (((Y0 @ Y4) = Y15) => Y17)) => Y17))) => Y16) => (((!! @ $o @ (^[Y17 : $o]: ((((c_In @ c_Empty @ Y14) => c_False) => (((Y0 @ Y4) = Y15) => Y17)) => Y17))) => Y16) => Y16)))))))) = Y11) => Y13)) => Y13))) => Y12) => Y12)))))))))) => (c_In @ Y9 @ (c_Power @ Y7))))) => c_False) => Y8)) => Y8))))) => (((?? @ $i @ (^[Y7 : $i]: (!! @ $o @ (^[Y8 : $o]: (((!! @ $i @ (^[Y9 : $i]: ((c_In @ Y9 @ Y7) => (c_In @ Y9 @ (c_Union @ (c_Repl @ sF1 @ (^[Y10 : $i]: (c_Eps_i @ (^[Y11 : $i]: (!! @ $o @ (^[Y12 : $o]: (((!! @ $o @ (^[Y13 : $o]: (((c_In @ c_Empty @ Y10) => (((Y0 @ Y4) = Y11) => Y13)) => Y13))) => Y12) => (((!! @ $o @ (^[Y13 : $o]: ((((c_In @ c_Empty @ Y10) => c_False) => (((c_Repl @ sF1 @ (^[Y14 : $i]: (c_Eps_i @ (^[Y15 : $i]: (!! @ $o @ (^[Y16 : $o]: (((!! @ $o @ (^[Y17 : $o]: (((c_In @ c_Empty @ Y14) => (((Y0 @ Y4) = Y15) => Y17)) => Y17))) => Y16) => (((!! @ $o @ (^[Y17 : $o]: ((((c_In @ c_Empty @ Y14) => c_False) => (((Y0 @ Y4) = Y15) => Y17)) => Y17))) => Y16) => Y16)))))))) = Y11) => Y13)) => Y13))) => Y12) => Y12))))))))))))) => ((!! @ $o @ (^[Y9 : $o]: ((((!! @ $i @ (^[Y10 : $i]: ((c_In @ Y10 @ (c_Union @ (c_Repl @ sF1 @ (^[Y11 : $i]: (c_Eps_i @ (^[Y12 : $i]: (!! @ $o @ (^[Y13 : $o]: (((!! @ $o @ (^[Y14 : $o]: (((c_In @ c_Empty @ Y11) => (((Y0 @ Y4) = Y12) => Y14)) => Y14))) => Y13) => (((!! @ $o @ (^[Y14 : $o]: ((((c_In @ c_Empty @ Y11) => c_False) => (((c_Repl @ sF1 @ (^[Y15 : $i]: (c_Eps_i @ (^[Y16 : $i]: (!! @ $o @ (^[Y17 : $o]: (((!! @ $o @ (^[Y18 : $o]: (((c_In @ c_Empty @ Y15) => (((Y0 @ Y4) = Y16) => Y18)) => Y18))) => Y17) => (((!! @ $o @ (^[Y18 : $o]: ((((c_In @ c_Empty @ Y15) => c_False) => (((Y0 @ Y4) = Y16) => Y18)) => Y18))) => Y17) => Y17)))))))) = Y12) => Y14)) => Y14))) => Y13) => Y13)))))))))) => (c_In @ Y10 @ Y7)))) => c_False) => ((?? 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% 9.27/1.88 inference(pi_proxy_clausification,[],[f577])).
% 9.27/1.88 thf(f601,plain,(
% 9.27/1.88 ( ! 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@ $i @ (^[Y6 : $i]: (!! @ $o @ (^[Y7 : $o]: (((!! @ $i @ (^[Y8 : $i]: ((c_In @ Y8 @ Y6) => (c_In @ Y8 @ (c_Union @ (c_Repl @ sF1 @ (^[Y9 : $i]: (c_Eps_i @ (^[Y10 : $i]: (!! @ $o @ (^[Y11 : $o]: (((!! @ $o @ (^[Y12 : $o]: (((c_In @ c_Empty @ Y9) => (((X1 @ Y3) = Y10) => Y12)) => Y12))) => Y11) => (((!! @ $o @ (^[Y12 : $o]: ((((c_In @ c_Empty @ Y9) => c_False) => (((c_Repl @ sF1 @ (^[Y13 : $i]: (c_Eps_i @ (^[Y14 : $i]: (!! @ $o @ (^[Y15 : $o]: (((!! @ $o @ (^[Y16 : $o]: (((c_In @ c_Empty @ Y13) => (((X1 @ Y3) = Y14) => Y16)) => Y16))) => Y15) => (((!! @ $o @ (^[Y16 : $o]: ((((c_In @ c_Empty @ Y13) => c_False) => (((X1 @ Y3) = Y14) => Y16)) => Y16))) => Y15) => Y15)))))))) = Y10) => Y12)) => Y12))) => Y11) => Y11))))))))))))) => ((!! @ $o @ (^[Y8 : $o]: ((((!! @ $i @ (^[Y9 : $i]: ((c_In @ Y9 @ (c_Union @ (c_Repl @ sF1 @ (^[Y10 : $i]: (c_Eps_i @ (^[Y11 : $i]: (!! @ $o @ (^[Y12 : $o]: (((!! @ $o @ (^[Y13 : $o]: (((c_In @ c_Empty @ Y10) => (((X1 @ Y3) = Y11) => Y13)) => Y13))) => Y12) => (((!! @ $o @ (^[Y13 : $o]: ((((c_In @ c_Empty @ Y10) => c_False) => (((c_Repl @ sF1 @ (^[Y14 : $i]: (c_Eps_i @ (^[Y15 : $i]: (!! @ $o @ (^[Y16 : $o]: (((!! @ $o @ (^[Y17 : $o]: (((c_In @ c_Empty @ Y14) => (((X1 @ Y3) = Y15) => Y17)) => Y17))) => Y16) => (((!! @ $o @ (^[Y17 : $o]: ((((c_In @ c_Empty @ Y14) => c_False) => (((X1 @ Y3) = Y15) => Y17)) => Y17))) => Y16) => Y16)))))))) = Y11) => Y13)) => Y13))) => Y12) => Y12)))))))))) => (c_In @ Y9 @ Y6)))) => c_False) => ((?? @ $i @ (^[Y9 : $i]: (!! @ $o @ (^[Y10 : $o]: (((c_In @ Y9 @ Y6) => (((!! @ $i @ (^[Y11 : $i]: ((c_In @ Y11 @ Y6) => (c_In @ Y11 @ (c_Power @ Y9))))) => c_False) => Y10)) => Y10))))) => Y8)) => Y8))) => Y7)) => Y7))))) => c_False) => Y5)) => Y5))) => Y4)) => Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $o @ (^[Y3 : $o]: (((?? @ $i @ (^[Y4 : $i]: (!! @ $o @ (^[Y5 : $o]: (((!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ Y4) => (c_In @ Y6 @ Y2)))) => ((((X1 @ Y2) = Y2) => (?? @ $i @ (^[Y6 : $i]: (!! @ $o @ (^[Y7 : $o]: (((!! @ $i @ (^[Y8 : $i]: ((c_In @ Y8 @ Y6) => (c_In @ Y8 @ Y2)))) => (((Y0 @ (c_Union @ (c_Repl @ Y4 @ (^[Y8 : $i]: (c_Repl @ sF7 @ (^[Y9 : $i]: (c_Union @ (c_Repl @ sF1 @ (^[Y10 : $i]: (c_Eps_i @ (^[Y11 : $i]: (!! @ $o @ (^[Y12 : $o]: (((!! @ $o @ (^[Y13 : $o]: (((c_In @ c_Empty @ Y10) => (((c_Repl @ Y8 @ (^[Y14 : $i]: (c_Repl @ Y14 @ (^[Y15 : $i]: (c_Eps_i @ (^[Y16 : $i]: (!! @ ($i > $i > $o) @ (^[Y17 : $i > $i > $o]: ((!! @ ($i > $i) @ (^[Y18 : $i > $i]: (!! @ $i @ (^[Y19 : $i]: ((!! @ $i @ (^[Y20 : $i]: ((c_In @ Y20 @ Y19) => (Y17 @ Y20 @ (Y18 @ Y20))))) => (Y17 @ Y19 @ (c_Union @ (c_Repl @ sF1 @ (^[Y20 : $i]: (c_Eps_i @ (^[Y21 : $i]: (!! @ $o @ (^[Y22 : $o]: (((!! @ $o @ (^[Y23 : $o]: (((c_In @ c_Empty @ Y20) => ((sF2 = Y21) => Y23)) => Y23))) => Y22) => (((!! @ $o @ (^[Y23 : $o]: ((((c_In @ c_Empty @ Y20) => c_False) => (((c_Repl @ Y19 @ Y18) = Y21) => Y23)) => Y23))) => Y22) => Y22))))))))))))))) => (Y17 @ Y15 @ Y16)))))))))) = Y11) => Y13)) => Y13))) => Y12) => (((!! @ $o @ (^[Y13 : $o]: ((((c_In @ c_Empty @ Y10) => c_False) => (((c_Repl @ Y9 @ (^[Y14 : $i]: (c_Eps_i @ (^[Y15 : $i]: (!! @ ($i > $i > $o) @ (^[Y16 : $i > $i > $o]: ((!! @ ($i > $i) @ (^[Y17 : $i > $i]: (!! @ $i @ (^[Y18 : $i]: ((!! @ $i @ (^[Y19 : $i]: ((c_In @ Y19 @ Y18) => (Y16 @ Y19 @ (Y17 @ Y19))))) => (Y16 @ Y18 @ (c_Union @ (c_Repl @ sF1 @ (^[Y19 : $i]: (c_Eps_i @ (^[Y20 : $i]: (!! @ $o @ (^[Y21 : $o]: (((!! @ $o @ (^[Y22 : $o]: (((c_In @ c_Empty @ Y19) => ((sF2 = Y20) => Y22)) => Y22))) => Y21) => (((!! @ $o @ (^[Y22 : $o]: ((((c_In @ c_Empty @ Y19) => c_False) => (((c_Repl @ Y18 @ Y17) = Y20) => Y22)) => Y22))) => Y21) => Y21))))))))))))))) => (Y16 @ Y14 @ Y15)))))))) = Y11) => Y13)) => Y13))) => Y12) => Y12))))))))))))))) => c_False) => Y7)) => Y7)))))) => Y5)) => Y5))))) => (((?? @ $i @ (^[Y4 : $i]: (!! @ $o @ (^[Y5 : $o]: (((!! @ $o @ (^[Y6 : $o]: (((!! @ $i @ (^[Y7 : $i]: ((c_In @ Y7 @ Y4) => (!! @ $i @ (^[Y8 : $i]: ((c_In @ Y8 @ Y7) => (c_In @ Y8 @ Y4))))))) => ((!! @ $i @ (^[Y7 : $i]: ((c_In @ Y7 @ Y4) => (!! @ $i @ (^[Y8 : $i]: ((c_In @ Y8 @ Y7) => (!! @ $i @ (^[Y9 : $i]: ((c_In @ Y9 @ Y8) => (c_In @ Y9 @ Y7)))))))))) => Y6)) => Y6))) => ((!! @ $o @ (^[Y6 : $o]: (((!! @ $i @ (^[Y7 : $i]: ((c_In @ Y7 @ Y2) => (c_In @ Y7 @ (c_Union @ (c_Repl @ sF1 @ (^[Y8 : $i]: (c_Eps_i @ (^[Y9 : $i]: (!! @ $o @ (^[Y10 : $o]: (((!! @ $o @ (^[Y11 : $o]: (((c_In @ c_Empty @ Y8) => ((Y4 = Y9) => Y11)) => Y11))) => Y10) => (((!! @ $o @ (^[Y11 : $o]: ((((c_In @ c_Empty @ Y8) => c_False) => (((c_Repl @ Y4 @ (^[Y12 : $i]: (c_Union @ (c_Repl @ sF1 @ (^[Y13 : $i]: (c_Eps_i @ (^[Y14 : $i]: (!! @ $o @ (^[Y15 : $o]: (((!! @ $o @ (^[Y16 : $o]: (((c_In @ c_Empty @ Y13) => ((Y12 = Y14) => Y16)) => Y16))) => Y15) => (((!! @ $o @ (^[Y16 : $o]: ((((c_In @ c_Empty @ Y13) => c_False) => (((c_Repl @ sF1 @ (^[Y17 : $i]: (c_Eps_i @ (^[Y18 : $i]: (!! @ $o @ (^[Y19 : $o]: (((!! @ $o @ (^[Y20 : $o]: (((c_In @ c_Empty @ Y17) => ((sF9 = Y18) => Y20)) => Y20))) => Y19) => (((!! @ $o @ (^[Y20 : $o]: ((((c_In @ c_Empty @ Y17) => c_False) => ((sF9 = Y18) => Y20)) => Y20))) => Y19) => Y19)))))))) = Y14) => Y16)) => Y16))) => Y15) => Y15))))))))))) = Y9) => Y11)) => Y11))) => Y10) => Y10))))))))))))) => ((!! @ $i @ (^[Y7 : $i]: ((c_In @ Y7 @ Y4) => (!! @ $o @ (^[Y8 : $o]: (((!! @ $o @ (^[Y9 : $o]: (((c_In @ (c_Union @ (c_Repl @ sF1 @ (^[Y10 : $i]: (c_Eps_i @ (^[Y11 : $i]: (!! @ $o @ (^[Y12 : $o]: (((!! @ $o @ (^[Y13 : $o]: (((c_In @ c_Empty @ Y10) => ((Y7 = Y11) => Y13)) => Y13))) => Y12) => (((!! @ $o @ (^[Y13 : $o]: ((((c_In @ c_Empty @ Y10) => c_False) => (((c_Repl @ sF1 @ (^[Y14 : $i]: (c_Eps_i @ (^[Y15 : $i]: (!! @ $o @ (^[Y16 : $o]: (((!! @ $o @ (^[Y17 : $o]: (((c_In @ c_Empty @ Y14) => ((sF9 = Y15) => Y17)) => Y17))) => Y16) => (((!! @ $o @ (^[Y17 : $o]: ((((c_In @ c_Empty @ Y14) => c_False) => ((sF9 = Y15) => Y17)) => Y17))) => Y16) => Y16)))))))) = Y11) => Y13)) => Y13))) => Y12) => Y12))))))))) @ Y2) => (((c_In @ Y7 @ Y2) => c_False) => Y9)) => Y9))) => Y8) => (((!! @ $o @ (^[Y9 : $o]: ((((c_In @ (c_Union @ (c_Repl @ sF1 @ (^[Y10 : $i]: (c_Eps_i @ (^[Y11 : $i]: (!! @ $o @ (^[Y12 : $o]: (((!! @ $o @ (^[Y13 : $o]: (((c_In @ c_Empty @ Y10) => ((Y7 = Y11) => Y13)) => Y13))) => Y12) => (((!! @ $o @ (^[Y13 : $o]: ((((c_In @ c_Empty @ Y10) => c_False) => (((c_Repl @ sF1 @ (^[Y14 : $i]: (c_Eps_i @ (^[Y15 : $i]: (!! @ $o @ (^[Y16 : $o]: (((!! @ $o @ (^[Y17 : $o]: (((c_In @ c_Empty @ Y14) => ((sF9 = Y15) => Y17)) => Y17))) => Y16) => (((!! @ $o @ (^[Y17 : $o]: ((((c_In @ c_Empty @ Y14) => c_False) => ((sF9 = Y15) => Y17)) => Y17))) => Y16) => Y16)))))))) = Y11) => Y13)) => Y13))) => Y12) => Y12))))))))) @ Y2) => c_False) => ((c_In @ Y7 @ Y2) => Y9)) => Y9))) => Y8) => Y8))))))) => Y6)) => Y6))) => Y5)) => Y5))))) => c_False) => Y3)) => Y3)))))) => (((Y0 @ (X1 @ (X1 @ (X1 @ sF11)))) => c_False) => Y1)) => Y1)))))))) )),
% 9.27/1.88 inference(beta-eta_normalization,[],[f600])).
% 9.27/1.88 thf(f604,plain,(
% 9.27/1.88 ( ! [X2 : ($i > $o),X1 : ($i > $i)] : (($true = (((^[Y0 : $i > $o]: (!! @ $o @ (^[Y1 : $o]: (((((Y0 @ (X1 @ (c_Eps_i @ (^[Y2 : $i]: (!! @ $o @ (^[Y3 : $o]: (((!! @ $o @ (^[Y4 : $o]: (((?? @ $i @ (^[Y5 : $i]: (!! @ $o @ (^[Y6 : $o]: (((c_In @ Y5 @ (X1 @ sF0)) => ((c_In @ Y5 @ (X1 @ sF4)) => Y6)) => Y6))))) => (((c_Repl @ (X1 @ sF0) @ (^[Y5 : $i]: (c_Eps_i @ (^[Y6 : $i]: (!! @ $o @ (^[Y7 : $o]: (((!! @ $o @ (^[Y8 : $o]: (((c_In @ Y5 @ (X1 @ sF4)) => ((Y5 = Y6) => Y8)) => Y8))) => Y7) => (((!! @ $o @ (^[Y8 : $o]: ((((c_In @ Y5 @ (X1 @ sF4)) => c_False) => (((c_Eps_i @ (^[Y9 : $i]: (!! @ $o @ (^[Y10 : $o]: (((c_In @ Y9 @ (X1 @ sF0)) => ((c_In @ Y9 @ (X1 @ sF4)) => Y10)) => Y10))))) = Y6) => Y8)) => Y8))) => Y7) => Y7)))))))) = Y2) => Y4)) => Y4))) => Y3) => (((!! @ $o @ (^[Y4 : $o]: ((((?? @ $i @ (^[Y5 : $i]: (!! @ $o @ (^[Y6 : $o]: (((c_In @ Y5 @ (X1 @ sF0)) => ((c_In @ Y5 @ (X1 @ sF4)) => Y6)) => Y6))))) => c_False) => ((c_Empty = Y2) => Y4)) => Y4))) => Y3) => Y3)))))))) => ((!! @ $i @ (^[Y2 : $i]: ((c_In @ Y2 @ (X1 @ c_Empty)) => (!! @ $i @ (^[Y3 : $i]: ((c_In @ Y3 @ Y2) => (c_In @ Y3 @ (X1 @ c_Empty)))))))) => (!! @ $i @ (^[Y2 : $i]: ((c_In @ Y2 @ c_Empty) => (?? @ $i @ (^[Y3 : $i]: (!! @ $o @ (^[Y4 : $o]: (((!! @ $i @ (^[Y5 : $i]: ((c_In @ Y5 @ Y3) => (c_In @ Y5 @ Y2)))) => ((!! @ $o @ (^[Y5 : $o]: (((?? @ $i @ (^[Y6 : $i]: (!! @ $o @ (^[Y7 : $o]: (((c_In @ Y6 @ (c_Union @ (c_Repl @ sF1 @ (^[Y8 : $i]: (c_Eps_i @ (^[Y9 : $i]: (!! @ $o @ (^[Y10 : $o]: (((!! @ $o @ (^[Y11 : $o]: (((c_In @ c_Empty @ Y8) => (((X1 @ Y3) = Y9) => Y11)) => Y11))) => Y10) => (((!! @ $o @ (^[Y11 : $o]: ((((c_In @ c_Empty @ Y8) => c_False) => (((c_Repl @ sF1 @ (^[Y12 : $i]: (c_Eps_i @ (^[Y13 : $i]: (!! @ $o @ (^[Y14 : $o]: (((!! @ $o @ (^[Y15 : $o]: (((c_In @ c_Empty @ Y12) => (((X1 @ Y3) = Y13) => Y15)) => Y15))) => Y14) => (((!! @ $o @ (^[Y15 : $o]: ((((c_In @ c_Empty @ Y12) => c_False) => (((X1 @ Y3) = Y13) => Y15)) => Y15))) => Y14) => Y14)))))))) = Y9) => Y11)) => Y11))) => Y10) => Y10)))))))))) => (((!! @ $i @ (^[Y8 : $i]: ((c_In @ Y8 @ (c_Union @ (c_Repl @ sF1 @ (^[Y9 : $i]: (c_Eps_i @ (^[Y10 : $i]: (!! @ $o @ (^[Y11 : $o]: (((!! @ $o @ (^[Y12 : $o]: (((c_In @ c_Empty @ Y9) => (((X1 @ Y3) = Y10) => Y12)) => Y12))) => Y11) => (((!! @ $o @ (^[Y12 : $o]: ((((c_In @ c_Empty @ Y9) => c_False) => (((c_Repl @ sF1 @ (^[Y13 : $i]: (c_Eps_i @ (^[Y14 : $i]: (!! @ $o @ (^[Y15 : $o]: (((!! @ $o @ (^[Y16 : $o]: (((c_In @ c_Empty @ Y13) => (((X1 @ Y3) = Y14) => Y16)) => Y16))) => Y15) => (((!! @ $o @ (^[Y16 : $o]: ((((c_In @ c_Empty @ Y13) => c_False) => (((X1 @ Y3) = Y14) => Y16)) => Y16))) => Y15) => Y15)))))))) = Y10) => Y12)) => Y12))) => Y11) => Y11)))))))))) => (c_In @ Y8 @ (c_Power @ Y6))))) => c_False) => Y7)) => Y7))))) => (((?? @ $i @ (^[Y6 : $i]: (!! @ $o @ (^[Y7 : $o]: (((!! @ $i @ (^[Y8 : $i]: ((c_In @ Y8 @ Y6) => (c_In @ Y8 @ (c_Union @ (c_Repl @ sF1 @ (^[Y9 : $i]: (c_Eps_i @ (^[Y10 : $i]: (!! @ $o @ (^[Y11 : $o]: (((!! @ $o @ (^[Y12 : $o]: (((c_In @ c_Empty @ Y9) => (((X1 @ Y3) = Y10) => Y12)) => Y12))) => Y11) => (((!! @ $o @ (^[Y12 : $o]: ((((c_In @ c_Empty @ Y9) => c_False) => (((c_Repl @ sF1 @ (^[Y13 : $i]: (c_Eps_i @ (^[Y14 : $i]: (!! @ $o @ (^[Y15 : $o]: (((!! @ $o @ (^[Y16 : $o]: (((c_In @ c_Empty @ Y13) => (((X1 @ Y3) = Y14) => Y16)) => Y16))) => Y15) => (((!! @ $o @ (^[Y16 : $o]: ((((c_In @ c_Empty @ Y13) => c_False) => (((X1 @ Y3) = Y14) => Y16)) => Y16))) => Y15) => Y15)))))))) = Y10) => Y12)) => Y12))) => Y11) => Y11))))))))))))) => ((!! @ $o @ (^[Y8 : $o]: ((((!! @ $i @ (^[Y9 : $i]: ((c_In @ Y9 @ (c_Union @ (c_Repl @ sF1 @ (^[Y10 : $i]: (c_Eps_i @ (^[Y11 : $i]: (!! @ $o @ (^[Y12 : $o]: (((!! @ $o @ (^[Y13 : $o]: (((c_In @ c_Empty @ Y10) => (((X1 @ Y3) = Y11) => Y13)) => Y13))) => Y12) => (((!! @ $o @ (^[Y13 : $o]: ((((c_In @ c_Empty @ Y10) => c_False) => (((c_Repl @ sF1 @ (^[Y14 : $i]: (c_Eps_i @ (^[Y15 : $i]: (!! @ $o @ (^[Y16 : $o]: (((!! @ $o @ (^[Y17 : $o]: (((c_In @ c_Empty @ Y14) => (((X1 @ Y3) = Y15) => Y17)) => Y17))) => Y16) => (((!! @ $o @ (^[Y17 : $o]: ((((c_In @ c_Empty @ Y14) => c_False) => (((X1 @ Y3) = Y15) => Y17)) => Y17))) => Y16) => Y16)))))))) = Y11) => Y13)) => Y13))) => Y12) => Y12)))))))))) => (c_In @ Y9 @ Y6)))) => c_False) => ((?? 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% 9.27/1.88 inference(pi_proxy_clausification,[],[f601])).
% 9.27/1.88 thf(f605,plain,(
% 9.27/1.88 ( ! 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@ $i @ (^[Y3 : $i]: (!! @ $o @ (^[Y4 : $o]: (((!! @ $o @ (^[Y5 : $o]: (((!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ Y3) => (!! @ $i @ (^[Y7 : $i]: ((c_In @ Y7 @ Y6) => (c_In @ Y7 @ Y3))))))) => ((!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ Y3) => (!! @ $i @ (^[Y7 : $i]: ((c_In @ Y7 @ Y6) => (!! @ $i @ (^[Y8 : $i]: ((c_In @ Y8 @ Y7) => (c_In @ Y8 @ Y6)))))))))) => Y5)) => Y5))) => ((!! @ $o @ (^[Y5 : $o]: (((!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ Y1) => (c_In @ Y6 @ (c_Union @ (c_Repl @ sF1 @ (^[Y7 : $i]: (c_Eps_i @ (^[Y8 : $i]: (!! @ $o @ (^[Y9 : $o]: (((!! @ $o @ (^[Y10 : $o]: (((c_In @ c_Empty @ Y7) => ((Y3 = Y8) => Y10)) => Y10))) => Y9) => (((!! @ $o @ (^[Y10 : $o]: ((((c_In @ c_Empty @ Y7) => c_False) => (((c_Repl @ Y3 @ (^[Y11 : $i]: (c_Union @ (c_Repl @ sF1 @ (^[Y12 : $i]: (c_Eps_i @ (^[Y13 : $i]: (!! @ $o @ (^[Y14 : $o]: (((!! @ $o @ (^[Y15 : $o]: (((c_In @ c_Empty @ Y12) => ((Y11 = Y13) => Y15)) => Y15))) => Y14) => (((!! @ $o @ (^[Y15 : $o]: ((((c_In @ c_Empty @ Y12) => c_False) => (((c_Repl @ sF1 @ (^[Y16 : $i]: (c_Eps_i @ (^[Y17 : $i]: (!! @ $o @ (^[Y18 : $o]: (((!! @ $o @ (^[Y19 : $o]: (((c_In @ c_Empty @ Y16) => ((sF9 = Y17) => Y19)) => Y19))) => Y18) => (((!! @ $o @ (^[Y19 : $o]: ((((c_In @ c_Empty @ Y16) => c_False) => ((sF9 = Y17) => Y19)) => Y19))) => Y18) => Y18)))))))) = Y13) => Y15)) => Y15))) => Y14) => Y14))))))))))) = Y8) => Y10)) => Y10))) => Y9) => Y9))))))))))))) => ((!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ Y3) => (!! @ $o @ (^[Y7 : $o]: (((!! @ $o @ (^[Y8 : $o]: (((c_In @ (c_Union @ (c_Repl @ sF1 @ (^[Y9 : $i]: (c_Eps_i @ (^[Y10 : $i]: (!! @ $o @ (^[Y11 : $o]: (((!! @ $o @ (^[Y12 : $o]: (((c_In @ c_Empty @ Y9) => ((Y6 = Y10) => Y12)) => Y12))) => Y11) => (((!! @ $o @ (^[Y12 : $o]: ((((c_In @ c_Empty @ Y9) => c_False) => (((c_Repl @ sF1 @ (^[Y13 : $i]: (c_Eps_i @ (^[Y14 : $i]: (!! @ $o @ (^[Y15 : $o]: (((!! @ $o @ (^[Y16 : $o]: (((c_In @ c_Empty @ Y13) => ((sF9 = Y14) => Y16)) => Y16))) => Y15) => (((!! @ $o @ (^[Y16 : $o]: ((((c_In @ c_Empty @ Y13) => c_False) => ((sF9 = Y14) => Y16)) => Y16))) => Y15) => Y15)))))))) = Y10) => Y12)) => Y12))) => Y11) => Y11))))))))) @ Y1) => (((c_In @ Y6 @ Y1) => c_False) => Y8)) => Y8))) => Y7) => (((!! @ $o @ (^[Y8 : $o]: ((((c_In @ (c_Union @ (c_Repl @ sF1 @ (^[Y9 : $i]: (c_Eps_i @ (^[Y10 : $i]: (!! @ $o @ (^[Y11 : $o]: (((!! @ $o @ (^[Y12 : $o]: (((c_In @ c_Empty @ Y9) => ((Y6 = Y10) => Y12)) => Y12))) => Y11) => (((!! @ $o @ (^[Y12 : $o]: ((((c_In @ c_Empty @ Y9) => c_False) => (((c_Repl @ sF1 @ (^[Y13 : $i]: (c_Eps_i @ (^[Y14 : $i]: (!! @ $o @ (^[Y15 : $o]: (((!! @ $o @ (^[Y16 : $o]: (((c_In @ c_Empty @ Y13) => ((sF9 = Y14) => Y16)) => Y16))) => Y15) => (((!! @ $o @ (^[Y16 : $o]: ((((c_In @ c_Empty @ Y13) => c_False) => ((sF9 = Y14) => Y16)) => Y16))) => Y15) => Y15)))))))) = Y10) => Y12)) => Y12))) => Y11) => Y11))))))))) @ Y1) => c_False) => ((c_In @ Y6 @ Y1) => Y8)) => Y8))) => Y7) => Y7))))))) => Y5)) => Y5))) => Y4)) => Y4))))) => c_False) => Y2)) => Y2)))))) => (((X2 @ (X1 @ (X1 @ (X1 @ sF11)))) => c_False) => Y0)) => Y0)))))) )),
% 9.27/1.88 inference(beta-eta_normalization,[],[f604])).
% 9.27/1.88 thf(f606,plain,(
% 9.27/1.88 ( ! 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% 9.27/1.88 inference(pi_proxy_clausification,[],[f605])).
% 9.27/1.88 thf(f607,plain,(
% 9.27/1.88 ( ! 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@ $i @ (^[Y2 : $i]: (!! @ $o @ (^[Y3 : $o]: (((!! @ $o @ (^[Y4 : $o]: (((!! @ $i @ (^[Y5 : $i]: ((c_In @ Y5 @ Y2) => (!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ Y5) => (c_In @ Y6 @ Y2))))))) => ((!! @ $i @ (^[Y5 : $i]: ((c_In @ Y5 @ Y2) => (!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ Y5) => (!! @ $i @ (^[Y7 : $i]: ((c_In @ Y7 @ Y6) => (c_In @ Y7 @ Y5)))))))))) => Y4)) => Y4))) => ((!! @ $o @ (^[Y4 : $o]: (((!! @ $i @ (^[Y5 : $i]: ((c_In @ Y5 @ Y0) => (c_In @ Y5 @ (c_Union @ (c_Repl @ sF1 @ (^[Y6 : $i]: (c_Eps_i @ (^[Y7 : $i]: (!! @ $o @ (^[Y8 : $o]: (((!! @ $o @ (^[Y9 : $o]: (((c_In @ c_Empty @ Y6) => ((Y2 = Y7) => Y9)) => Y9))) => Y8) => (((!! @ $o @ (^[Y9 : $o]: ((((c_In @ c_Empty @ Y6) => c_False) => (((c_Repl @ Y2 @ (^[Y10 : $i]: (c_Union @ (c_Repl @ sF1 @ (^[Y11 : $i]: (c_Eps_i @ (^[Y12 : $i]: (!! @ $o @ (^[Y13 : $o]: (((!! @ $o @ (^[Y14 : $o]: (((c_In @ c_Empty @ Y11) => ((Y10 = Y12) => Y14)) => Y14))) => Y13) => (((!! @ $o @ (^[Y14 : $o]: ((((c_In @ c_Empty @ Y11) => c_False) => (((c_Repl @ sF1 @ (^[Y15 : $i]: (c_Eps_i @ (^[Y16 : $i]: (!! @ $o @ (^[Y17 : $o]: (((!! @ $o @ (^[Y18 : $o]: (((c_In @ c_Empty @ Y15) => ((sF9 = Y16) => Y18)) => Y18))) => Y17) => (((!! @ $o @ (^[Y18 : $o]: ((((c_In @ c_Empty @ Y15) => c_False) => ((sF9 = Y16) => Y18)) => Y18))) => Y17) => Y17)))))))) = Y12) => Y14)) => Y14))) => Y13) => Y13))))))))))) = Y7) => Y9)) => Y9))) => Y8) => Y8))))))))))))) => ((!! @ $i @ (^[Y5 : $i]: ((c_In @ Y5 @ Y2) => (!! @ $o @ (^[Y6 : $o]: (((!! @ $o @ (^[Y7 : $o]: (((c_In @ (c_Union @ (c_Repl @ sF1 @ (^[Y8 : $i]: (c_Eps_i @ (^[Y9 : $i]: (!! @ $o @ (^[Y10 : $o]: (((!! @ $o @ (^[Y11 : $o]: (((c_In @ c_Empty @ Y8) => ((Y5 = Y9) => Y11)) => Y11))) => Y10) => (((!! @ $o @ (^[Y11 : $o]: ((((c_In @ c_Empty @ Y8) => c_False) => (((c_Repl @ sF1 @ (^[Y12 : $i]: (c_Eps_i @ (^[Y13 : $i]: (!! @ $o @ (^[Y14 : $o]: (((!! @ $o @ (^[Y15 : $o]: (((c_In @ c_Empty @ Y12) => ((sF9 = Y13) => Y15)) => Y15))) => Y14) => (((!! @ $o @ (^[Y15 : $o]: ((((c_In @ c_Empty @ Y12) => c_False) => ((sF9 = Y13) => Y15)) => Y15))) => Y14) => Y14)))))))) = Y9) => Y11)) => Y11))) => Y10) => Y10))))))))) @ Y0) => (((c_In @ Y5 @ Y0) => c_False) => Y7)) => Y7))) => Y6) => (((!! @ $o @ (^[Y7 : $o]: ((((c_In @ (c_Union @ (c_Repl @ sF1 @ (^[Y8 : $i]: (c_Eps_i @ (^[Y9 : $i]: (!! @ $o @ (^[Y10 : $o]: (((!! @ $o @ (^[Y11 : $o]: (((c_In @ c_Empty @ Y8) => ((Y5 = Y9) => Y11)) => Y11))) => Y10) => (((!! @ $o @ (^[Y11 : $o]: ((((c_In @ c_Empty @ Y8) => c_False) => (((c_Repl @ sF1 @ (^[Y12 : $i]: (c_Eps_i @ (^[Y13 : $i]: (!! @ $o @ (^[Y14 : $o]: (((!! @ $o @ (^[Y15 : $o]: (((c_In @ c_Empty @ Y12) => ((sF9 = Y13) => Y15)) => Y15))) => Y14) => (((!! @ $o @ (^[Y15 : $o]: ((((c_In @ c_Empty @ Y12) => c_False) => ((sF9 = Y13) => Y15)) => Y15))) => Y14) => Y14)))))))) = Y9) => Y11)) => Y11))) => Y10) => Y10))))))))) @ Y0) => c_False) => ((c_In @ Y5 @ Y0) => Y7)) => Y7))) => Y6) => Y6))))))) => Y4)) => Y4))) => Y3)) => Y3))))) => c_False) => Y1)) => Y1)))))) => (((X2 @ (X1 @ (X1 @ (X1 @ sF11)))) => c_False) => X3)) => X3)))) )),
% 9.27/1.88 inference(beta-eta_normalization,[],[f606])).
% 9.27/1.88 thf(f608,plain,(
% 9.27/1.88 ( ! [X2 : ($i > $o),X3 : $o,X1 : ($i > $i)] : (($true = ((((((X2 @ (X1 @ (c_Eps_i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: (((!! @ $o @ (^[Y2 : $o]: (((?? @ $i @ (^[Y3 : $i]: (!! @ $o @ (^[Y4 : $o]: (((c_In @ Y3 @ (X1 @ sF0)) => ((c_In @ Y3 @ (X1 @ sF4)) => Y4)) => Y4))))) => (((c_Repl @ (X1 @ sF0) @ (^[Y3 : $i]: (c_Eps_i @ (^[Y4 : $i]: (!! @ $o @ (^[Y5 : $o]: (((!! @ $o @ (^[Y6 : $o]: (((c_In @ Y3 @ (X1 @ sF4)) => ((Y3 = Y4) => Y6)) => Y6))) => Y5) => (((!! @ $o @ (^[Y6 : $o]: ((((c_In @ Y3 @ (X1 @ sF4)) => $false) => (((c_Eps_i @ (^[Y7 : $i]: (!! @ $o @ (^[Y8 : $o]: (((c_In @ Y7 @ (X1 @ sF0)) => ((c_In @ Y7 @ (X1 @ sF4)) => Y8)) => Y8))))) = Y4) => Y6)) => Y6))) => Y5) => Y5)))))))) = Y0) => Y2)) => Y2))) => Y1) => (((!! @ $o @ (^[Y2 : $o]: ((((?? @ $i @ (^[Y3 : $i]: (!! @ $o @ (^[Y4 : $o]: (((c_In @ Y3 @ (X1 @ sF0)) => ((c_In @ Y3 @ (X1 @ sF4)) => Y4)) => Y4))))) => $false) => ((c_Empty = Y0) => Y2)) => Y2))) => Y1) => Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: ((c_In @ Y0 @ (X1 @ c_Empty)) => (!! @ $i @ (^[Y1 : $i]: ((c_In @ Y1 @ Y0) => (c_In @ Y1 @ (X1 @ c_Empty)))))))) => (!! @ $i @ (^[Y0 : $i]: ((c_In @ Y0 @ c_Empty) => (?? @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: (((!! @ $i @ (^[Y3 : $i]: ((c_In @ Y3 @ Y1) => (c_In @ Y3 @ Y0)))) => ((!! @ $o @ (^[Y3 : $o]: (((?? @ $i @ (^[Y4 : $i]: (!! @ $o @ (^[Y5 : $o]: (((c_In @ Y4 @ (c_Union @ (c_Repl @ sF1 @ (^[Y6 : $i]: (c_Eps_i @ (^[Y7 : $i]: (!! @ $o @ (^[Y8 : $o]: (((!! @ $o @ (^[Y9 : $o]: (((c_In @ c_Empty @ Y6) => (((X1 @ Y1) = Y7) => Y9)) => Y9))) => Y8) => (((!! @ $o @ (^[Y9 : $o]: ((((c_In @ c_Empty @ Y6) => $false) => (((c_Repl @ sF1 @ (^[Y10 : $i]: (c_Eps_i @ (^[Y11 : $i]: (!! @ $o @ (^[Y12 : $o]: (((!! @ $o @ (^[Y13 : $o]: (((c_In @ c_Empty @ Y10) => (((X1 @ Y1) = Y11) => Y13)) => Y13))) => Y12) => (((!! @ $o @ (^[Y13 : $o]: ((((c_In @ c_Empty @ Y10) => $false) => (((X1 @ Y1) = Y11) => Y13)) => Y13))) => Y12) => Y12)))))))) = Y7) => Y9)) => Y9))) => Y8) => Y8)))))))))) => (((!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ (c_Union @ (c_Repl @ sF1 @ (^[Y7 : $i]: (c_Eps_i @ (^[Y8 : $i]: (!! @ $o @ (^[Y9 : $o]: (((!! @ $o @ (^[Y10 : $o]: (((c_In @ c_Empty @ Y7) => (((X1 @ Y1) = Y8) => Y10)) => Y10))) => Y9) => (((!! @ $o @ (^[Y10 : $o]: ((((c_In @ c_Empty @ Y7) => $false) => (((c_Repl @ sF1 @ (^[Y11 : $i]: (c_Eps_i @ (^[Y12 : $i]: (!! @ $o @ (^[Y13 : $o]: (((!! @ $o @ (^[Y14 : $o]: (((c_In @ c_Empty @ Y11) => (((X1 @ Y1) = Y12) => Y14)) => Y14))) => Y13) => (((!! @ $o @ (^[Y14 : $o]: ((((c_In @ c_Empty @ Y11) => $false) => (((X1 @ Y1) = Y12) => Y14)) => Y14))) => Y13) => Y13)))))))) = Y8) => Y10)) => Y10))) => Y9) => Y9)))))))))) => (c_In @ Y6 @ (c_Power @ Y4))))) => $false) => Y5)) => Y5))))) => (((?? @ $i @ (^[Y4 : $i]: (!! @ $o @ (^[Y5 : $o]: (((!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ Y4) => (c_In @ Y6 @ (c_Union @ (c_Repl @ sF1 @ (^[Y7 : $i]: (c_Eps_i @ (^[Y8 : $i]: (!! @ $o @ (^[Y9 : $o]: (((!! @ $o @ (^[Y10 : $o]: (((c_In @ c_Empty @ Y7) => (((X1 @ Y1) = Y8) => Y10)) => Y10))) => Y9) => (((!! @ $o @ (^[Y10 : $o]: ((((c_In @ c_Empty @ Y7) => $false) => (((c_Repl @ sF1 @ (^[Y11 : $i]: (c_Eps_i @ (^[Y12 : $i]: (!! @ $o @ (^[Y13 : $o]: (((!! @ $o @ (^[Y14 : $o]: (((c_In @ c_Empty @ Y11) => (((X1 @ Y1) = Y12) => Y14)) => Y14))) => Y13) => (((!! @ $o @ (^[Y14 : $o]: ((((c_In @ c_Empty @ Y11) => $false) => (((X1 @ Y1) = Y12) => Y14)) => Y14))) => Y13) => Y13)))))))) = Y8) => Y10)) => Y10))) => Y9) => Y9))))))))))))) => ((!! @ $o @ (^[Y6 : $o]: ((((!! @ $i @ (^[Y7 : $i]: ((c_In @ Y7 @ (c_Union @ (c_Repl @ sF1 @ (^[Y8 : $i]: (c_Eps_i @ (^[Y9 : $i]: (!! @ $o @ (^[Y10 : $o]: (((!! @ $o @ (^[Y11 : $o]: (((c_In @ c_Empty @ Y8) => (((X1 @ Y1) = Y9) => Y11)) => Y11))) => Y10) => (((!! @ $o @ (^[Y11 : $o]: ((((c_In @ c_Empty @ Y8) => $false) => (((c_Repl @ sF1 @ (^[Y12 : $i]: (c_Eps_i @ (^[Y13 : $i]: (!! @ $o @ (^[Y14 : $o]: (((!! @ $o @ (^[Y15 : $o]: (((c_In @ c_Empty @ Y12) => (((X1 @ Y1) = Y13) => Y15)) => Y15))) => Y14) => (((!! @ $o @ (^[Y15 : $o]: ((((c_In @ c_Empty @ Y12) => $false) => (((X1 @ Y1) = Y13) => Y15)) => Y15))) => Y14) => Y14)))))))) = Y9) => Y11)) => Y11))) => Y10) => Y10)))))))))) => (c_In @ Y7 @ Y4)))) => $false) => ((?? @ $i @ (^[Y7 : $i]: (!! @ $o @ (^[Y8 : $o]: (((c_In @ Y7 @ Y4) => (((!! @ $i @ (^[Y9 : $i]: ((c_In @ Y9 @ Y4) => (c_In @ Y9 @ (c_Power @ Y7))))) => $false) => Y8)) => Y8))))) => Y6)) => Y6))) => Y5)) => Y5))))) => $false) => Y3)) => Y3))) => Y2)) => Y2)))))))))) => (?? @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: (((?? @ $i @ (^[Y2 : $i]: (!! @ $o @ (^[Y3 : $o]: (((!! @ $i @ (^[Y4 : $i]: ((c_In @ Y4 @ Y2) => (c_In @ Y4 @ Y0)))) => ((((X1 @ Y0) = Y0) => (?? @ $i @ (^[Y4 : $i]: (!! @ $o @ (^[Y5 : $o]: (((!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ Y4) => (c_In @ Y6 @ Y0)))) => (((X2 @ (c_Union @ (c_Repl @ Y2 @ (^[Y6 : $i]: (c_Repl @ sF7 @ (^[Y7 : $i]: (c_Union @ (c_Repl @ sF1 @ (^[Y8 : $i]: (c_Eps_i @ (^[Y9 : $i]: (!! @ $o @ (^[Y10 : $o]: (((!! @ $o @ (^[Y11 : $o]: (((c_In @ c_Empty @ Y8) => (((c_Repl @ Y6 @ (^[Y12 : $i]: (c_Repl @ Y12 @ (^[Y13 : $i]: (c_Eps_i @ (^[Y14 : $i]: (!! @ ($i > $i > $o) @ (^[Y15 : $i > $i > $o]: ((!! @ ($i > $i) @ (^[Y16 : $i > $i]: (!! @ $i @ (^[Y17 : $i]: ((!! @ $i @ (^[Y18 : $i]: ((c_In @ Y18 @ Y17) => (Y15 @ Y18 @ (Y16 @ Y18))))) => (Y15 @ Y17 @ (c_Union @ (c_Repl @ sF1 @ (^[Y18 : $i]: (c_Eps_i @ (^[Y19 : $i]: (!! @ $o @ (^[Y20 : $o]: (((!! @ $o @ (^[Y21 : $o]: (((c_In @ c_Empty @ Y18) => ((sF2 = Y19) => Y21)) => Y21))) => Y20) => (((!! @ $o @ (^[Y21 : $o]: ((((c_In @ c_Empty @ Y18) => $false) => (((c_Repl @ Y17 @ Y16) = Y19) => Y21)) => Y21))) => Y20) => Y20))))))))))))))) => (Y15 @ Y13 @ Y14)))))))))) = Y9) => Y11)) => Y11))) => Y10) => (((!! @ $o @ (^[Y11 : $o]: ((((c_In @ c_Empty @ Y8) => $false) => (((c_Repl @ Y7 @ (^[Y12 : $i]: (c_Eps_i @ (^[Y13 : $i]: (!! @ ($i > $i > $o) @ (^[Y14 : $i > $i > $o]: ((!! @ ($i > $i) @ (^[Y15 : $i > $i]: (!! @ $i @ (^[Y16 : $i]: ((!! @ $i @ (^[Y17 : $i]: ((c_In @ Y17 @ Y16) => (Y14 @ Y17 @ (Y15 @ Y17))))) => (Y14 @ Y16 @ (c_Union @ (c_Repl @ sF1 @ (^[Y17 : $i]: (c_Eps_i @ (^[Y18 : $i]: (!! @ $o @ (^[Y19 : $o]: (((!! @ $o @ (^[Y20 : $o]: (((c_In @ c_Empty @ Y17) => ((sF2 = Y18) => Y20)) => Y20))) => Y19) => (((!! @ $o @ (^[Y20 : $o]: ((((c_In @ c_Empty @ Y17) => $false) => (((c_Repl @ Y16 @ Y15) = Y18) => Y20)) => Y20))) => Y19) => Y19))))))))))))))) => (Y14 @ Y12 @ Y13)))))))) = Y9) => Y11)) => Y11))) => Y10) => Y10))))))))))))))) => $false) => Y5)) => Y5)))))) => Y3)) => Y3))))) => (((?? @ $i @ (^[Y2 : $i]: (!! @ $o @ (^[Y3 : $o]: (((!! @ $o @ (^[Y4 : $o]: (((!! @ $i @ (^[Y5 : $i]: ((c_In @ Y5 @ Y2) => (!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ Y5) => (c_In @ Y6 @ Y2))))))) => ((!! @ $i @ (^[Y5 : $i]: ((c_In @ Y5 @ Y2) => (!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ Y5) => (!! @ $i @ (^[Y7 : $i]: ((c_In @ Y7 @ Y6) => (c_In @ Y7 @ Y5)))))))))) => Y4)) => Y4))) => ((!! @ $o @ (^[Y4 : $o]: (((!! @ $i @ (^[Y5 : $i]: ((c_In @ Y5 @ Y0) => (c_In @ Y5 @ (c_Union @ (c_Repl @ sF1 @ (^[Y6 : $i]: (c_Eps_i @ (^[Y7 : $i]: (!! @ $o @ (^[Y8 : $o]: (((!! @ $o @ (^[Y9 : $o]: (((c_In @ c_Empty @ Y6) => ((Y2 = Y7) => Y9)) => Y9))) => Y8) => (((!! @ $o @ (^[Y9 : $o]: ((((c_In @ c_Empty @ Y6) => $false) => (((c_Repl @ Y2 @ (^[Y10 : $i]: (c_Union @ (c_Repl @ sF1 @ (^[Y11 : $i]: (c_Eps_i @ (^[Y12 : $i]: (!! @ $o @ (^[Y13 : $o]: (((!! @ $o @ (^[Y14 : $o]: (((c_In @ c_Empty @ Y11) => ((Y10 = Y12) => Y14)) => Y14))) => Y13) => (((!! @ $o @ (^[Y14 : $o]: ((((c_In @ c_Empty @ Y11) => $false) => (((c_Repl @ sF1 @ (^[Y15 : $i]: (c_Eps_i @ (^[Y16 : $i]: (!! @ $o @ (^[Y17 : $o]: (((!! @ $o @ (^[Y18 : $o]: (((c_In @ c_Empty @ Y15) => ((sF9 = Y16) => Y18)) => Y18))) => Y17) => (((!! @ $o @ (^[Y18 : $o]: ((((c_In @ c_Empty @ Y15) => $false) => ((sF9 = Y16) => Y18)) => Y18))) => Y17) => Y17)))))))) = Y12) => Y14)) => Y14))) => Y13) => Y13))))))))))) = Y7) => Y9)) => Y9))) => Y8) => Y8))))))))))))) => ((!! @ $i @ (^[Y5 : $i]: ((c_In @ Y5 @ Y2) => (!! @ $o @ (^[Y6 : $o]: (((!! @ $o @ (^[Y7 : $o]: (((c_In @ (c_Union @ (c_Repl @ sF1 @ (^[Y8 : $i]: (c_Eps_i @ (^[Y9 : $i]: (!! @ $o @ (^[Y10 : $o]: (((!! @ $o @ (^[Y11 : $o]: (((c_In @ c_Empty @ Y8) => ((Y5 = Y9) => Y11)) => Y11))) => Y10) => (((!! @ $o @ (^[Y11 : $o]: ((((c_In @ c_Empty @ Y8) => $false) => (((c_Repl @ sF1 @ (^[Y12 : $i]: (c_Eps_i @ (^[Y13 : $i]: (!! @ $o @ (^[Y14 : $o]: (((!! @ $o @ (^[Y15 : $o]: (((c_In @ c_Empty @ Y12) => ((sF9 = Y13) => Y15)) => Y15))) => Y14) => (((!! @ $o @ (^[Y15 : $o]: ((((c_In @ c_Empty @ Y12) => $false) => ((sF9 = Y13) => Y15)) => Y15))) => Y14) => Y14)))))))) = Y9) => Y11)) => Y11))) => Y10) => Y10))))))))) @ Y0) => (((c_In @ Y5 @ Y0) => $false) => Y7)) => Y7))) => Y6) => (((!! @ $o @ (^[Y7 : $o]: ((((c_In @ (c_Union @ (c_Repl @ sF1 @ (^[Y8 : $i]: (c_Eps_i @ (^[Y9 : $i]: (!! @ $o @ (^[Y10 : $o]: (((!! @ $o @ (^[Y11 : $o]: (((c_In @ c_Empty @ Y8) => ((Y5 = Y9) => Y11)) => Y11))) => Y10) => (((!! @ $o @ (^[Y11 : $o]: ((((c_In @ c_Empty @ Y8) => $false) => (((c_Repl @ sF1 @ (^[Y12 : $i]: (c_Eps_i @ (^[Y13 : $i]: (!! @ $o @ (^[Y14 : $o]: (((!! @ $o @ (^[Y15 : $o]: (((c_In @ c_Empty @ Y12) => ((sF9 = Y13) => Y15)) => Y15))) => Y14) => (((!! @ $o @ (^[Y15 : $o]: ((((c_In @ c_Empty @ Y12) => $false) => ((sF9 = Y13) => Y15)) => Y15))) => Y14) => Y14)))))))) = Y9) => Y11)) => Y11))) => Y10) => Y10))))))))) @ Y0) => $false) => ((c_In @ Y5 @ Y0) => Y7)) => Y7))) => Y6) => Y6))))))) => Y4)) => Y4))) => Y3)) => Y3))))) => $false) => Y1)) => Y1)))))) => (((X2 @ (X1 @ (X1 @ (X1 @ sF11)))) => $false) => X3)) => X3)))) )),
% 9.27/1.88 inference(forward_demodulation,[],[f607,f567])).
% 9.27/1.88 thf(f609,plain,(
% 9.27/1.88 ( ! [X2 : ($i > $o),X3 : $o,X1 : ($i > $i)] : (($true = ((((((X2 @ (X1 @ (c_Eps_i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: (((!! @ $o @ (^[Y2 : $o]: (((?? @ $i @ (^[Y3 : $i]: (!! @ $o @ (^[Y4 : $o]: (((c_In @ Y3 @ (X1 @ sF0)) => ((c_In @ Y3 @ (X1 @ sF4)) => Y4)) => Y4))))) => (((c_Repl @ (X1 @ sF0) @ (^[Y3 : $i]: (c_Eps_i @ (^[Y4 : $i]: (!! @ $o @ (^[Y5 : $o]: (((!! @ $o @ (^[Y6 : $o]: (((c_In @ Y3 @ (X1 @ sF4)) => ((Y3 = Y4) => Y6)) => Y6))) => Y5) => (((!! @ $o @ (^[Y6 : $o]: ((((c_In @ Y3 @ (X1 @ sF4)) => $false) => (((c_Eps_i @ (^[Y7 : $i]: (!! @ $o @ (^[Y8 : $o]: (((c_In @ Y7 @ (X1 @ sF0)) => ((c_In @ Y7 @ (X1 @ sF4)) => Y8)) => Y8))))) = Y4) => Y6)) => Y6))) => Y5) => Y5)))))))) = Y0) => Y2)) => Y2))) => Y1) => (((!! @ $o @ (^[Y2 : $o]: ((((?? @ $i @ (^[Y3 : $i]: (!! @ $o @ (^[Y4 : $o]: (((c_In @ Y3 @ (X1 @ sF0)) => ((c_In @ Y3 @ (X1 @ sF4)) => Y4)) => Y4))))) => $false) => ((c_Empty = Y0) => Y2)) => Y2))) => Y1) => Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: ((c_In @ Y0 @ (X1 @ c_Empty)) => (!! @ $i @ (^[Y1 : $i]: ((c_In @ Y1 @ Y0) => (c_In @ Y1 @ (X1 @ c_Empty)))))))) => (!! @ $i @ (^[Y0 : $i]: ((c_In @ Y0 @ c_Empty) => (?? @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: (((!! @ $i @ (^[Y3 : $i]: ((c_In @ Y3 @ Y1) => (c_In @ Y3 @ Y0)))) => ((!! @ $o @ (^[Y3 : $o]: (((?? @ $i @ (^[Y4 : $i]: (!! @ $o @ (^[Y5 : $o]: (((c_In @ Y4 @ (c_Union @ (c_Repl @ sF1 @ (^[Y6 : $i]: (c_Eps_i @ (^[Y7 : $i]: (!! @ $o @ (^[Y8 : $o]: (((!! @ $o @ (^[Y9 : $o]: (((c_In @ c_Empty @ Y6) => (((X1 @ Y1) = Y7) => Y9)) => Y9))) => Y8) => (((!! @ $o @ (^[Y9 : $o]: ((((c_In @ c_Empty @ Y6) => $false) => (((c_Repl @ sF1 @ (^[Y10 : $i]: (c_Eps_i @ (^[Y11 : $i]: (!! @ $o @ (^[Y12 : $o]: (((!! @ $o @ (^[Y13 : $o]: (((c_In @ c_Empty @ Y10) => (((X1 @ Y1) = Y11) => Y13)) => Y13))) => Y12) => (((!! @ $o @ (^[Y13 : $o]: ((((c_In @ c_Empty @ Y10) => $false) => (((X1 @ Y1) = Y11) => Y13)) => Y13))) => Y12) => Y12)))))))) = Y7) => Y9)) => Y9))) => Y8) => Y8)))))))))) => (((!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ (c_Union @ (c_Repl @ sF1 @ (^[Y7 : $i]: (c_Eps_i @ (^[Y8 : $i]: (!! @ $o @ (^[Y9 : $o]: (((!! @ $o @ (^[Y10 : $o]: (((c_In @ c_Empty @ Y7) => (((X1 @ Y1) = Y8) => Y10)) => Y10))) => Y9) => (((!! @ $o @ (^[Y10 : $o]: ((((c_In @ c_Empty @ Y7) => $false) => (((c_Repl @ sF1 @ (^[Y11 : $i]: (c_Eps_i @ (^[Y12 : $i]: (!! @ $o @ (^[Y13 : $o]: (((!! @ $o @ (^[Y14 : $o]: (((c_In @ c_Empty @ Y11) => (((X1 @ Y1) = Y12) => Y14)) => Y14))) => Y13) => (((!! @ $o @ (^[Y14 : $o]: ((((c_In @ c_Empty @ Y11) => $false) => (((X1 @ Y1) = Y12) => Y14)) => Y14))) => Y13) => Y13)))))))) = Y8) => Y10)) => Y10))) => Y9) => Y9)))))))))) => (c_In @ Y6 @ (c_Power @ Y4))))) => $false) => Y5)) => Y5))))) => (((?? @ $i @ (^[Y4 : $i]: (!! @ $o @ (^[Y5 : $o]: (((!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ Y4) => (c_In @ Y6 @ (c_Union @ (c_Repl @ sF1 @ (^[Y7 : $i]: (c_Eps_i @ (^[Y8 : $i]: (!! @ $o @ (^[Y9 : $o]: (((!! @ $o @ (^[Y10 : $o]: (((c_In @ c_Empty @ Y7) => (((X1 @ Y1) = Y8) => Y10)) => Y10))) => Y9) => (((!! @ $o @ (^[Y10 : $o]: ((((c_In @ c_Empty @ Y7) => $false) => (((c_Repl @ sF1 @ (^[Y11 : $i]: (c_Eps_i @ (^[Y12 : $i]: (!! @ $o @ (^[Y13 : $o]: (((!! @ $o @ (^[Y14 : $o]: (((c_In @ c_Empty @ Y11) => (((X1 @ Y1) = Y12) => Y14)) => Y14))) => Y13) => (((!! @ $o @ (^[Y14 : $o]: ((((c_In @ c_Empty @ Y11) => $false) => (((X1 @ Y1) = Y12) => Y14)) => Y14))) => Y13) => Y13)))))))) = Y8) => Y10)) => Y10))) => Y9) => Y9))))))))))))) => ((!! @ $o @ (^[Y6 : $o]: ((((!! @ $i @ (^[Y7 : $i]: ((c_In @ Y7 @ (c_Union @ (c_Repl @ sF1 @ (^[Y8 : $i]: (c_Eps_i @ (^[Y9 : $i]: (!! @ $o @ (^[Y10 : $o]: (((!! @ $o @ (^[Y11 : $o]: (((c_In @ c_Empty @ Y8) => (((X1 @ Y1) = Y9) => Y11)) => Y11))) => Y10) => (((!! @ $o @ (^[Y11 : $o]: ((((c_In @ c_Empty @ Y8) => $false) => (((c_Repl @ sF1 @ (^[Y12 : $i]: (c_Eps_i @ (^[Y13 : $i]: (!! @ $o @ (^[Y14 : $o]: (((!! @ $o @ (^[Y15 : $o]: (((c_In @ c_Empty @ Y12) => (((X1 @ Y1) = Y13) => Y15)) => Y15))) => Y14) => (((!! @ $o @ (^[Y15 : $o]: ((((c_In @ c_Empty @ Y12) => $false) => (((X1 @ Y1) = Y13) => Y15)) => Y15))) => Y14) => Y14)))))))) = Y9) => Y11)) => Y11))) => Y10) => Y10)))))))))) => (c_In @ Y7 @ Y4)))) => $false) => ((?? @ $i @ (^[Y7 : $i]: (!! @ $o @ (^[Y8 : $o]: (((c_In @ Y7 @ Y4) => (((!! @ $i @ (^[Y9 : $i]: ((c_In @ Y9 @ Y4) => (c_In @ Y9 @ (c_Power @ Y7))))) => $false) => Y8)) => Y8))))) => Y6)) => Y6))) => Y5)) => Y5))))) => $false) => Y3)) => Y3))) => Y2)) => Y2)))))))))) => (?? @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: (((?? @ $i @ (^[Y2 : $i]: (!! @ $o @ (^[Y3 : $o]: (((!! @ $i @ (^[Y4 : $i]: ((c_In @ Y4 @ Y2) => (c_In @ Y4 @ Y0)))) => ((((X1 @ Y0) = Y0) => (?? @ $i @ (^[Y4 : $i]: (!! @ $o @ (^[Y5 : $o]: (((!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ Y4) => (c_In @ Y6 @ Y0)))) => (((X2 @ (c_Union @ (c_Repl @ Y2 @ (^[Y6 : $i]: (c_Repl @ sF7 @ (^[Y7 : $i]: (c_Union @ (c_Repl @ sF1 @ (^[Y8 : $i]: (c_Eps_i @ (^[Y9 : $i]: (!! @ $o @ (^[Y10 : $o]: (((!! @ $o @ (^[Y11 : $o]: (((c_In @ c_Empty @ Y8) => (((c_Repl @ Y6 @ (^[Y12 : $i]: (c_Repl @ Y12 @ (^[Y13 : $i]: (c_Eps_i @ (^[Y14 : $i]: (!! @ ($i > $i > $o) @ (^[Y15 : $i > $i > $o]: ((!! @ ($i > $i) @ (^[Y16 : $i > $i]: (!! @ $i @ (^[Y17 : $i]: ((!! @ $i @ (^[Y18 : $i]: ((c_In @ Y18 @ Y17) => (Y15 @ Y18 @ (Y16 @ Y18))))) => (Y15 @ Y17 @ (c_Union @ (c_Repl @ sF1 @ (^[Y18 : $i]: (c_Eps_i @ (^[Y19 : $i]: (!! @ $o @ (^[Y20 : $o]: (((!! @ $o @ (^[Y21 : $o]: (((c_In @ c_Empty @ Y18) => ((sF2 = Y19) => Y21)) => Y21))) => Y20) => (((!! @ $o @ (^[Y21 : $o]: ((((c_In @ c_Empty @ Y18) => $false) => (((c_Repl @ Y17 @ Y16) = Y19) => Y21)) => Y21))) => Y20) => Y20))))))))))))))) => (Y15 @ Y13 @ Y14)))))))))) = Y9) => Y11)) => Y11))) => Y10) => (((!! @ $o @ (^[Y11 : $o]: ((((c_In @ c_Empty @ Y8) => $false) => (((c_Repl @ Y7 @ (^[Y12 : $i]: (c_Eps_i @ (^[Y13 : $i]: (!! @ ($i > $i > $o) @ (^[Y14 : $i > $i > $o]: ((!! @ ($i > $i) @ (^[Y15 : $i > $i]: (!! @ $i @ (^[Y16 : $i]: ((!! @ $i @ (^[Y17 : $i]: ((c_In @ Y17 @ Y16) => (Y14 @ Y17 @ (Y15 @ Y17))))) => (Y14 @ Y16 @ (c_Union @ (c_Repl @ sF1 @ (^[Y17 : $i]: (c_Eps_i @ (^[Y18 : $i]: (!! @ $o @ (^[Y19 : $o]: (((!! @ $o @ (^[Y20 : $o]: (((c_In @ c_Empty @ Y17) => ((sF2 = Y18) => Y20)) => Y20))) => Y19) => (((!! @ $o @ (^[Y20 : $o]: ((((c_In @ c_Empty @ Y17) => $false) => (((c_Repl @ Y16 @ Y15) = Y18) => Y20)) => Y20))) => Y19) => Y19))))))))))))))) => (Y14 @ Y12 @ Y13)))))))) = Y9) => Y11)) => Y11))) => Y10) => Y10))))))))))))))) => $false) => Y5)) => Y5)))))) => Y3)) => Y3))))) => (((?? @ $i @ (^[Y2 : $i]: (!! @ $o @ (^[Y3 : $o]: (((!! @ $o @ (^[Y4 : $o]: (((!! @ $i @ (^[Y5 : $i]: ((c_In @ Y5 @ Y2) => (!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ Y5) => (c_In @ Y6 @ Y2))))))) => ((!! @ $i @ (^[Y5 : $i]: ((c_In @ Y5 @ Y2) => (!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ Y5) => (!! @ $i @ (^[Y7 : $i]: ((c_In @ Y7 @ Y6) => (c_In @ Y7 @ Y5)))))))))) => Y4)) => Y4))) => ((!! @ $o @ (^[Y4 : $o]: (((!! @ $i @ (^[Y5 : $i]: ((c_In @ Y5 @ Y0) => (c_In @ Y5 @ (c_Union @ (c_Repl @ sF1 @ (^[Y6 : $i]: (c_Eps_i @ (^[Y7 : $i]: (!! @ $o @ (^[Y8 : $o]: (((!! @ $o @ (^[Y9 : $o]: (((c_In @ c_Empty @ Y6) => ((Y2 = Y7) => Y9)) => Y9))) => Y8) => (((!! @ $o @ (^[Y9 : $o]: ((((c_In @ c_Empty @ Y6) => $false) => (((c_Repl @ Y2 @ (^[Y10 : $i]: (c_Union @ (c_Repl @ sF1 @ (^[Y11 : $i]: (c_Eps_i @ (^[Y12 : $i]: (!! @ $o @ (^[Y13 : $o]: (((!! @ $o @ (^[Y14 : $o]: (((c_In @ c_Empty @ Y11) => ((Y10 = Y12) => Y14)) => Y14))) => Y13) => (((!! @ $o @ (^[Y14 : $o]: ((((c_In @ c_Empty @ Y11) => $false) => (((c_Repl @ sF1 @ (^[Y15 : $i]: (c_Eps_i @ (^[Y16 : $i]: (!! @ $o @ (^[Y17 : $o]: (((!! @ $o @ (^[Y18 : $o]: (((c_In @ c_Empty @ Y15) => ((sF9 = Y16) => Y18)) => Y18))) => Y17) => (((!! @ $o @ (^[Y18 : $o]: ((((c_In @ c_Empty @ Y15) => $false) => ((sF9 = Y16) => Y18)) => Y18))) => Y17) => Y17)))))))) = Y12) => Y14)) => Y14))) => Y13) => Y13))))))))))) = Y7) => Y9)) => Y9))) => Y8) => Y8))))))))))))) => ((!! @ $i @ (^[Y5 : $i]: ((c_In @ Y5 @ Y2) => (!! @ $o @ (^[Y6 : $o]: (((!! @ $o @ (^[Y7 : $o]: (((c_In @ (c_Union @ (c_Repl @ sF1 @ (^[Y8 : $i]: (c_Eps_i @ (^[Y9 : $i]: (!! @ $o @ (^[Y10 : $o]: (((!! @ $o @ (^[Y11 : $o]: (((c_In @ c_Empty @ Y8) => ((Y5 = Y9) => Y11)) => Y11))) => Y10) => (((!! @ $o @ (^[Y11 : $o]: ((((c_In @ c_Empty @ Y8) => $false) => (((c_Repl @ sF1 @ (^[Y12 : $i]: (c_Eps_i @ (^[Y13 : $i]: (!! @ $o @ (^[Y14 : $o]: (((!! @ $o @ (^[Y15 : $o]: (((c_In @ c_Empty @ Y12) => ((sF9 = Y13) => Y15)) => Y15))) => Y14) => (((!! @ $o @ (^[Y15 : $o]: ((((c_In @ c_Empty @ Y12) => $false) => ((sF9 = Y13) => Y15)) => Y15))) => Y14) => Y14)))))))) = Y9) => Y11)) => Y11))) => Y10) => Y10))))))))) @ Y0) => (((c_In @ Y5 @ Y0) => $false) => Y7)) => Y7))) => Y6) => (((!! @ $o @ (^[Y7 : $o]: ((((c_In @ (c_Union @ (c_Repl @ sF1 @ (^[Y8 : $i]: (c_Eps_i @ (^[Y9 : $i]: (!! @ $o @ (^[Y10 : $o]: (((!! @ $o @ (^[Y11 : $o]: (((c_In @ c_Empty @ Y8) => ((Y5 = Y9) => Y11)) => Y11))) => Y10) => (((!! @ $o @ (^[Y11 : $o]: ((((c_In @ c_Empty @ Y8) => $false) => (((c_Repl @ sF1 @ (^[Y12 : $i]: (c_Eps_i @ (^[Y13 : $i]: (!! @ $o @ (^[Y14 : $o]: (((!! @ $o @ (^[Y15 : $o]: (((c_In @ c_Empty @ Y12) => ((sF9 = Y13) => Y15)) => Y15))) => Y14) => (((!! @ $o @ (^[Y15 : $o]: ((((c_In @ c_Empty @ Y12) => $false) => ((sF9 = Y13) => Y15)) => Y15))) => Y14) => Y14)))))))) = Y9) => Y11)) => Y11))) => Y10) => Y10))))))))) @ Y0) => $false) => ((c_In @ Y5 @ Y0) => Y7)) => Y7))) => Y6) => Y6))))))) => Y4)) => Y4))) => Y3)) => Y3))))) => $false) => Y1)) => Y1)))))) => ((~ (X2 @ (X1 @ (X1 @ (X1 @ sF11))))) => X3)) => X3)))) )),
% 9.27/1.88 inference(boolean_simplification,[],[f608])).
% 9.27/1.88 thf(f610,plain,(
% 9.27/1.88 ( ! [X2 : ($i > $o),X3 : $o,X1 : ($i > $i)] : (($true = ((((((X2 @ (X1 @ (c_Eps_i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: (((!! @ $o @ (^[Y2 : $o]: (((?? @ $i @ (^[Y3 : $i]: (!! @ $o @ (^[Y4 : $o]: (((c_In @ Y3 @ (X1 @ sF0)) => ((c_In @ Y3 @ (X1 @ sF4)) => Y4)) => Y4))))) => (((c_Repl @ (X1 @ sF0) @ (^[Y3 : $i]: (c_Eps_i @ (^[Y4 : $i]: (!! @ $o @ (^[Y5 : $o]: (((!! @ $o @ (^[Y6 : $o]: (((c_In @ Y3 @ (X1 @ sF4)) => ((Y3 = Y4) => Y6)) => Y6))) => Y5) => (((!! @ $o @ (^[Y6 : $o]: ((((c_In @ Y3 @ (X1 @ sF4)) => $false) => (((c_Eps_i @ (^[Y7 : $i]: (!! @ $o @ (^[Y8 : $o]: (((c_In @ Y7 @ (X1 @ sF0)) => ((c_In @ Y7 @ (X1 @ sF4)) => Y8)) => Y8))))) = Y4) => Y6)) => Y6))) => Y5) => Y5)))))))) = Y0) => Y2)) => Y2))) => Y1) => (((!! @ $o @ (^[Y2 : $o]: ((((?? @ $i @ (^[Y3 : $i]: (!! @ $o @ (^[Y4 : $o]: (((c_In @ Y3 @ (X1 @ sF0)) => ((c_In @ Y3 @ (X1 @ sF4)) => Y4)) => Y4))))) => $false) => ((c_Empty = Y0) => Y2)) => Y2))) => Y1) => Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: ((c_In @ Y0 @ (X1 @ c_Empty)) => (!! @ $i @ (^[Y1 : $i]: ((c_In @ Y1 @ Y0) => (c_In @ Y1 @ (X1 @ c_Empty)))))))) => (!! @ $i @ (^[Y0 : $i]: ((c_In @ Y0 @ c_Empty) => (?? @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: (((!! @ $i @ (^[Y3 : $i]: ((c_In @ Y3 @ Y1) => (c_In @ Y3 @ Y0)))) => ((!! @ $o @ (^[Y3 : $o]: (((?? @ $i @ (^[Y4 : $i]: (!! @ $o @ (^[Y5 : $o]: (((c_In @ Y4 @ (c_Union @ (c_Repl @ sF1 @ (^[Y6 : $i]: (c_Eps_i @ (^[Y7 : $i]: (!! @ $o @ (^[Y8 : $o]: (((!! @ $o @ (^[Y9 : $o]: (((c_In @ c_Empty @ Y6) => (((X1 @ Y1) = Y7) => Y9)) => Y9))) => Y8) => (((!! @ $o @ (^[Y9 : $o]: ((((c_In @ c_Empty @ Y6) => $false) => (((c_Repl @ sF1 @ (^[Y10 : $i]: (c_Eps_i @ (^[Y11 : $i]: (!! @ $o @ (^[Y12 : $o]: (((!! @ $o @ (^[Y13 : $o]: (((c_In @ c_Empty @ Y10) => (((X1 @ Y1) = Y11) => Y13)) => Y13))) => Y12) => (((!! @ $o @ (^[Y13 : $o]: ((((c_In @ c_Empty @ Y10) => $false) => (((X1 @ Y1) = Y11) => Y13)) => Y13))) => Y12) => Y12)))))))) = Y7) => Y9)) => Y9))) => Y8) => Y8)))))))))) => (((!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ (c_Union @ (c_Repl @ sF1 @ (^[Y7 : $i]: (c_Eps_i @ (^[Y8 : $i]: (!! @ $o @ (^[Y9 : $o]: (((!! @ $o @ (^[Y10 : $o]: (((c_In @ c_Empty @ Y7) => (((X1 @ Y1) = Y8) => Y10)) => Y10))) => Y9) => (((!! @ $o @ (^[Y10 : $o]: ((((c_In @ c_Empty @ Y7) => $false) => (((c_Repl @ sF1 @ (^[Y11 : $i]: (c_Eps_i @ (^[Y12 : $i]: (!! @ $o @ (^[Y13 : $o]: (((!! @ $o @ (^[Y14 : $o]: (((c_In @ c_Empty @ Y11) => (((X1 @ Y1) = Y12) => Y14)) => Y14))) => Y13) => (((!! @ $o @ (^[Y14 : $o]: ((((c_In @ c_Empty @ Y11) => $false) => (((X1 @ Y1) = Y12) => Y14)) => Y14))) => Y13) => Y13)))))))) = Y8) => Y10)) => Y10))) => Y9) => Y9)))))))))) => (c_In @ Y6 @ (c_Power @ Y4))))) => $false) => Y5)) => Y5))))) => (((?? @ $i @ (^[Y4 : $i]: (!! @ $o @ (^[Y5 : $o]: (((!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ Y4) => (c_In @ Y6 @ (c_Union @ (c_Repl @ sF1 @ (^[Y7 : $i]: (c_Eps_i @ (^[Y8 : $i]: (!! @ $o @ (^[Y9 : $o]: (((!! @ $o @ (^[Y10 : $o]: (((c_In @ c_Empty @ Y7) => (((X1 @ Y1) = Y8) => Y10)) => Y10))) => Y9) => (((!! @ $o @ (^[Y10 : $o]: ((((c_In @ c_Empty @ Y7) => $false) => (((c_Repl @ sF1 @ (^[Y11 : $i]: (c_Eps_i @ (^[Y12 : $i]: (!! @ $o @ (^[Y13 : $o]: (((!! @ $o @ (^[Y14 : $o]: (((c_In @ c_Empty @ Y11) => (((X1 @ Y1) = Y12) => Y14)) => Y14))) => Y13) => (((!! @ $o @ (^[Y14 : $o]: ((((c_In @ c_Empty @ Y11) => $false) => (((X1 @ Y1) = Y12) => Y14)) => Y14))) => Y13) => Y13)))))))) = Y8) => Y10)) => Y10))) => Y9) => Y9))))))))))))) => ((!! @ $o @ (^[Y6 : $o]: ((((!! @ $i @ (^[Y7 : $i]: ((c_In @ Y7 @ (c_Union @ (c_Repl @ sF1 @ (^[Y8 : $i]: (c_Eps_i @ (^[Y9 : $i]: (!! @ $o @ (^[Y10 : $o]: (((!! @ $o @ (^[Y11 : $o]: (((c_In @ c_Empty @ Y8) => (((X1 @ Y1) = Y9) => Y11)) => Y11))) => Y10) => (((!! @ $o @ (^[Y11 : $o]: ((((c_In @ c_Empty @ Y8) => $false) => (((c_Repl @ sF1 @ (^[Y12 : $i]: (c_Eps_i @ (^[Y13 : $i]: (!! @ $o @ (^[Y14 : $o]: (((!! @ $o @ (^[Y15 : $o]: (((c_In @ c_Empty @ Y12) => (((X1 @ Y1) = Y13) => Y15)) => Y15))) => Y14) => (((!! @ $o @ (^[Y15 : $o]: ((((c_In @ c_Empty @ Y12) => $false) => (((X1 @ Y1) = Y13) => Y15)) => Y15))) => Y14) => Y14)))))))) = Y9) => Y11)) => Y11))) => Y10) => Y10)))))))))) => (c_In @ Y7 @ Y4)))) => $false) => ((?? @ $i @ (^[Y7 : $i]: (!! @ $o @ (^[Y8 : $o]: (((c_In @ Y7 @ Y4) => (((!! @ $i @ (^[Y9 : $i]: ((c_In @ Y9 @ Y4) => (c_In @ Y9 @ (c_Power @ Y7))))) => $false) => Y8)) => Y8))))) => Y6)) => Y6))) => Y5)) => Y5))))) => $false) => Y3)) => Y3))) => Y2)) => Y2)))))))))) => (?? @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: (((?? @ $i @ (^[Y2 : $i]: (!! @ $o @ (^[Y3 : $o]: (((!! @ $i @ (^[Y4 : $i]: ((c_In @ Y4 @ Y2) => (c_In @ Y4 @ Y0)))) => ((((X1 @ Y0) = Y0) => (?? @ $i @ (^[Y4 : $i]: (!! @ $o @ (^[Y5 : $o]: (((!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ Y4) => (c_In @ Y6 @ Y0)))) => (((X2 @ (c_Union @ (c_Repl @ Y2 @ (^[Y6 : $i]: (c_Repl @ sF7 @ (^[Y7 : $i]: (c_Union @ (c_Repl @ sF1 @ (^[Y8 : $i]: (c_Eps_i @ (^[Y9 : $i]: (!! @ $o @ (^[Y10 : $o]: (((!! @ $o @ (^[Y11 : $o]: (((c_In @ c_Empty @ Y8) => (((c_Repl @ Y6 @ (^[Y12 : $i]: (c_Repl @ Y12 @ (^[Y13 : $i]: (c_Eps_i @ (^[Y14 : $i]: (!! @ ($i > $i > $o) @ (^[Y15 : $i > $i > $o]: ((!! @ ($i > $i) @ (^[Y16 : $i > $i]: (!! @ $i @ (^[Y17 : $i]: ((!! @ $i @ (^[Y18 : $i]: ((c_In @ Y18 @ Y17) => (Y15 @ Y18 @ (Y16 @ Y18))))) => (Y15 @ Y17 @ (c_Union @ (c_Repl @ sF1 @ (^[Y18 : $i]: (c_Eps_i @ (^[Y19 : $i]: (!! @ $o @ (^[Y20 : $o]: (((!! @ $o @ (^[Y21 : $o]: (((c_In @ c_Empty @ Y18) => ((sF2 = Y19) => Y21)) => Y21))) => Y20) => (((!! @ $o @ (^[Y21 : $o]: ((((c_In @ c_Empty @ Y18) => $false) => (((c_Repl @ Y17 @ Y16) = Y19) => Y21)) => Y21))) => Y20) => Y20))))))))))))))) => (Y15 @ Y13 @ Y14)))))))))) = Y9) => Y11)) => Y11))) => Y10) => (((!! @ $o @ (^[Y11 : $o]: ((((c_In @ c_Empty @ Y8) => $false) => (((c_Repl @ Y7 @ (^[Y12 : $i]: (c_Eps_i @ (^[Y13 : $i]: (!! @ ($i > $i > $o) @ (^[Y14 : $i > $i > $o]: ((!! @ ($i > $i) @ (^[Y15 : $i > $i]: (!! @ $i @ (^[Y16 : $i]: ((!! @ $i @ (^[Y17 : $i]: ((c_In @ Y17 @ Y16) => (Y14 @ Y17 @ (Y15 @ Y17))))) => (Y14 @ Y16 @ (c_Union @ (c_Repl @ sF1 @ (^[Y17 : $i]: (c_Eps_i @ (^[Y18 : $i]: (!! @ $o @ (^[Y19 : $o]: (((!! @ $o @ (^[Y20 : $o]: (((c_In @ c_Empty @ Y17) => ((sF2 = Y18) => Y20)) => Y20))) => Y19) => (((!! @ $o @ (^[Y20 : $o]: ((((c_In @ c_Empty @ Y17) => $false) => (((c_Repl @ Y16 @ Y15) = Y18) => Y20)) => Y20))) => Y19) => Y19))))))))))))))) => (Y14 @ Y12 @ Y13)))))))) = Y9) => Y11)) => Y11))) => Y10) => Y10))))))))))))))) => $false) => Y5)) => Y5)))))) => Y3)) => Y3))))) => ((~ (?? @ $i @ (^[Y2 : $i]: (!! @ $o @ (^[Y3 : $o]: (((!! @ $o @ (^[Y4 : $o]: (((!! @ $i @ (^[Y5 : $i]: ((c_In @ Y5 @ Y2) => (!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ Y5) => (c_In @ Y6 @ Y2))))))) => ((!! @ $i @ (^[Y5 : $i]: ((c_In @ Y5 @ Y2) => (!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ Y5) => (!! @ $i @ (^[Y7 : $i]: ((c_In @ Y7 @ Y6) => (c_In @ Y7 @ Y5)))))))))) => Y4)) => Y4))) => ((!! @ $o @ (^[Y4 : $o]: (((!! @ $i @ (^[Y5 : $i]: ((c_In @ Y5 @ Y0) => (c_In @ Y5 @ (c_Union @ (c_Repl @ sF1 @ (^[Y6 : $i]: (c_Eps_i @ (^[Y7 : $i]: (!! @ $o @ (^[Y8 : $o]: (((!! @ $o @ (^[Y9 : $o]: (((c_In @ c_Empty @ Y6) => ((Y2 = Y7) => Y9)) => Y9))) => Y8) => (((!! @ $o @ (^[Y9 : $o]: ((((c_In @ c_Empty @ Y6) => $false) => (((c_Repl @ Y2 @ (^[Y10 : $i]: (c_Union @ (c_Repl @ sF1 @ (^[Y11 : $i]: (c_Eps_i @ (^[Y12 : $i]: (!! @ $o @ (^[Y13 : $o]: (((!! @ $o @ (^[Y14 : $o]: (((c_In @ c_Empty @ Y11) => ((Y10 = Y12) => Y14)) => Y14))) => Y13) => (((!! @ $o @ (^[Y14 : $o]: ((((c_In @ c_Empty @ Y11) => $false) => (((c_Repl @ sF1 @ (^[Y15 : $i]: (c_Eps_i @ (^[Y16 : $i]: (!! @ $o @ (^[Y17 : $o]: (((!! @ $o @ (^[Y18 : $o]: (((c_In @ c_Empty @ Y15) => ((sF9 = Y16) => Y18)) => Y18))) => Y17) => (((!! @ $o @ (^[Y18 : $o]: ((((c_In @ c_Empty @ Y15) => $false) => ((sF9 = Y16) => Y18)) => Y18))) => Y17) => Y17)))))))) = Y12) => Y14)) => Y14))) => Y13) => Y13))))))))))) = Y7) => Y9)) => Y9))) => Y8) => Y8))))))))))))) => ((!! @ $i @ (^[Y5 : $i]: ((c_In @ Y5 @ Y2) => (!! @ $o @ (^[Y6 : $o]: (((!! @ $o @ (^[Y7 : $o]: (((c_In @ (c_Union @ (c_Repl @ sF1 @ (^[Y8 : $i]: (c_Eps_i @ (^[Y9 : $i]: (!! @ $o @ (^[Y10 : $o]: (((!! @ $o @ (^[Y11 : $o]: (((c_In @ c_Empty @ Y8) => ((Y5 = Y9) => Y11)) => Y11))) => Y10) => (((!! @ $o @ (^[Y11 : $o]: ((((c_In @ c_Empty @ Y8) => $false) => (((c_Repl @ sF1 @ (^[Y12 : $i]: (c_Eps_i @ (^[Y13 : $i]: (!! @ $o @ (^[Y14 : $o]: (((!! @ $o @ (^[Y15 : $o]: (((c_In @ c_Empty @ Y12) => ((sF9 = Y13) => Y15)) => Y15))) => Y14) => (((!! @ $o @ (^[Y15 : $o]: ((((c_In @ c_Empty @ Y12) => $false) => ((sF9 = Y13) => Y15)) => Y15))) => Y14) => Y14)))))))) = Y9) => Y11)) => Y11))) => Y10) => Y10))))))))) @ Y0) => (((c_In @ Y5 @ Y0) => $false) => Y7)) => Y7))) => Y6) => (((!! @ $o @ (^[Y7 : $o]: ((((c_In @ (c_Union @ (c_Repl @ sF1 @ (^[Y8 : $i]: (c_Eps_i @ (^[Y9 : $i]: (!! @ $o @ (^[Y10 : $o]: (((!! @ $o @ (^[Y11 : $o]: (((c_In @ c_Empty @ Y8) => ((Y5 = Y9) => Y11)) => Y11))) => Y10) => (((!! @ $o @ (^[Y11 : $o]: ((((c_In @ c_Empty @ Y8) => $false) => (((c_Repl @ sF1 @ (^[Y12 : $i]: (c_Eps_i @ (^[Y13 : $i]: (!! @ $o @ (^[Y14 : $o]: (((!! @ $o @ (^[Y15 : $o]: (((c_In @ c_Empty @ Y12) => ((sF9 = Y13) => Y15)) => Y15))) => Y14) => (((!! @ $o @ (^[Y15 : $o]: ((((c_In @ c_Empty @ Y12) => $false) => ((sF9 = Y13) => Y15)) => Y15))) => Y14) => Y14)))))))) = Y9) => Y11)) => Y11))) => Y10) => Y10))))))))) @ Y0) => $false) => ((c_In @ Y5 @ Y0) => Y7)) => Y7))) => Y6) => Y6))))))) => Y4)) => Y4))) => Y3)) => Y3)))))) => Y1)) => Y1)))))) => ((~ (X2 @ (X1 @ (X1 @ (X1 @ sF11))))) => X3)) => X3)))) )),
% 9.27/1.88 inference(boolean_simplification,[],[f609])).
% 9.27/1.88 thf(f611,plain,(
% 9.27/1.88 ( ! [X2 : ($i > $o),X3 : $o,X1 : ($i > $i)] : (($true = ((((((X2 @ (X1 @ (c_Eps_i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: (((!! @ $o @ (^[Y2 : $o]: (((?? @ $i @ (^[Y3 : $i]: (!! @ $o @ (^[Y4 : $o]: (((c_In @ Y3 @ (X1 @ sF0)) => ((c_In @ Y3 @ (X1 @ sF4)) => Y4)) => Y4))))) => (((c_Repl @ (X1 @ sF0) @ (^[Y3 : $i]: (c_Eps_i @ (^[Y4 : $i]: (!! @ $o @ (^[Y5 : $o]: (((!! @ $o @ (^[Y6 : $o]: (((c_In @ Y3 @ (X1 @ sF4)) => ((Y3 = Y4) => Y6)) => Y6))) => Y5) => (((!! @ $o @ (^[Y6 : $o]: ((((c_In @ Y3 @ (X1 @ sF4)) => $false) => (((c_Eps_i @ (^[Y7 : $i]: (!! @ $o @ (^[Y8 : $o]: (((c_In @ Y7 @ (X1 @ sF0)) => ((c_In @ Y7 @ (X1 @ sF4)) => Y8)) => Y8))))) = Y4) => Y6)) => Y6))) => Y5) => Y5)))))))) = Y0) => Y2)) => Y2))) => Y1) => (((!! @ $o @ (^[Y2 : $o]: ((((?? @ $i @ (^[Y3 : $i]: (!! @ $o @ (^[Y4 : $o]: (((c_In @ Y3 @ (X1 @ sF0)) => ((c_In @ Y3 @ (X1 @ sF4)) => Y4)) => Y4))))) => $false) => ((c_Empty = Y0) => Y2)) => Y2))) => Y1) => Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: ((c_In @ Y0 @ (X1 @ c_Empty)) => (!! @ $i @ (^[Y1 : $i]: ((c_In @ Y1 @ Y0) => (c_In @ Y1 @ (X1 @ c_Empty)))))))) => (!! @ $i @ (^[Y0 : $i]: ((c_In @ Y0 @ c_Empty) => (?? @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: (((!! @ $i @ (^[Y3 : $i]: ((c_In @ Y3 @ Y1) => (c_In @ Y3 @ Y0)))) => ((!! @ $o @ (^[Y3 : $o]: (((?? @ $i @ (^[Y4 : $i]: (!! @ $o @ (^[Y5 : $o]: (((c_In @ Y4 @ (c_Union @ (c_Repl @ sF1 @ (^[Y6 : $i]: (c_Eps_i @ (^[Y7 : $i]: (!! @ $o @ (^[Y8 : $o]: (((!! @ $o @ (^[Y9 : $o]: (((c_In @ c_Empty @ Y6) => (((X1 @ Y1) = Y7) => Y9)) => Y9))) => Y8) => (((!! @ $o @ (^[Y9 : $o]: ((((c_In @ c_Empty @ Y6) => $false) => (((c_Repl @ sF1 @ (^[Y10 : $i]: (c_Eps_i @ (^[Y11 : $i]: (!! @ $o @ (^[Y12 : $o]: (((!! @ $o @ (^[Y13 : $o]: (((c_In @ c_Empty @ Y10) => (((X1 @ Y1) = Y11) => Y13)) => Y13))) => Y12) => (((!! @ $o @ (^[Y13 : $o]: ((((c_In @ c_Empty @ Y10) => $false) => (((X1 @ Y1) = Y11) => Y13)) => Y13))) => Y12) => Y12)))))))) = Y7) => Y9)) => Y9))) => Y8) => Y8)))))))))) => (((!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ (c_Union @ (c_Repl @ sF1 @ (^[Y7 : $i]: (c_Eps_i @ (^[Y8 : $i]: (!! @ $o @ (^[Y9 : $o]: (((!! @ $o @ (^[Y10 : $o]: (((c_In @ c_Empty @ Y7) => (((X1 @ Y1) = Y8) => Y10)) => Y10))) => Y9) => (((!! @ $o @ (^[Y10 : $o]: ((((c_In @ c_Empty @ Y7) => $false) => (((c_Repl @ sF1 @ (^[Y11 : $i]: (c_Eps_i @ (^[Y12 : $i]: (!! @ $o @ (^[Y13 : $o]: (((!! @ $o @ (^[Y14 : $o]: (((c_In @ c_Empty @ Y11) => (((X1 @ Y1) = Y12) => Y14)) => Y14))) => Y13) => (((!! @ $o @ (^[Y14 : $o]: ((((c_In @ c_Empty @ Y11) => $false) => (((X1 @ Y1) = Y12) => Y14)) => Y14))) => Y13) => Y13)))))))) = Y8) => Y10)) => Y10))) => Y9) => Y9)))))))))) => (c_In @ Y6 @ (c_Power @ Y4))))) => $false) => Y5)) => Y5))))) => (((?? @ $i @ (^[Y4 : $i]: (!! @ $o @ (^[Y5 : $o]: (((!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ Y4) => (c_In @ Y6 @ (c_Union @ (c_Repl @ sF1 @ (^[Y7 : $i]: (c_Eps_i @ (^[Y8 : $i]: (!! @ $o @ (^[Y9 : $o]: (((!! @ $o @ (^[Y10 : $o]: (((c_In @ c_Empty @ Y7) => (((X1 @ Y1) = Y8) => Y10)) => Y10))) => Y9) => (((!! @ $o @ (^[Y10 : $o]: ((((c_In @ c_Empty @ Y7) => $false) => (((c_Repl @ sF1 @ (^[Y11 : $i]: (c_Eps_i @ (^[Y12 : $i]: (!! @ $o @ (^[Y13 : $o]: (((!! @ $o @ (^[Y14 : $o]: (((c_In @ c_Empty @ Y11) => (((X1 @ Y1) = Y12) => Y14)) => Y14))) => Y13) => (((!! @ $o @ (^[Y14 : $o]: ((((c_In @ c_Empty @ Y11) => $false) => (((X1 @ Y1) = Y12) => Y14)) => Y14))) => Y13) => Y13)))))))) = Y8) => Y10)) => Y10))) => Y9) => Y9))))))))))))) => ((!! @ $o @ (^[Y6 : $o]: ((((!! @ $i @ (^[Y7 : $i]: ((c_In @ Y7 @ (c_Union @ (c_Repl @ sF1 @ (^[Y8 : $i]: (c_Eps_i @ (^[Y9 : $i]: (!! @ $o @ (^[Y10 : $o]: (((!! @ $o @ (^[Y11 : $o]: (((c_In @ c_Empty @ Y8) => (((X1 @ Y1) = Y9) => Y11)) => Y11))) => Y10) => (((!! @ $o @ (^[Y11 : $o]: ((((c_In @ c_Empty @ Y8) => $false) => (((c_Repl @ sF1 @ (^[Y12 : $i]: (c_Eps_i @ (^[Y13 : $i]: (!! @ $o @ (^[Y14 : $o]: (((!! @ $o @ (^[Y15 : $o]: (((c_In @ c_Empty @ Y12) => (((X1 @ Y1) = Y13) => Y15)) => Y15))) => Y14) => (((!! @ $o @ (^[Y15 : $o]: ((((c_In @ c_Empty @ Y12) => $false) => (((X1 @ Y1) = Y13) => Y15)) => Y15))) => Y14) => Y14)))))))) = Y9) => Y11)) => Y11))) => Y10) => Y10)))))))))) => (c_In @ Y7 @ Y4)))) => $false) => ((?? @ $i @ (^[Y7 : $i]: (!! @ $o @ (^[Y8 : $o]: (((c_In @ Y7 @ Y4) => (((!! @ $i @ (^[Y9 : $i]: ((c_In @ Y9 @ Y4) => (c_In @ Y9 @ (c_Power @ Y7))))) => $false) => Y8)) => Y8))))) => Y6)) => Y6))) => Y5)) => Y5))))) => $false) => Y3)) => Y3))) => Y2)) => Y2)))))))))) => (?? @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: (((?? @ $i @ (^[Y2 : $i]: (!! @ $o @ (^[Y3 : $o]: (((!! @ $i @ (^[Y4 : $i]: ((c_In @ Y4 @ Y2) => (c_In @ Y4 @ Y0)))) => ((((X1 @ Y0) = Y0) => (?? @ $i @ (^[Y4 : $i]: (!! @ $o @ (^[Y5 : $o]: (((!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ Y4) => (c_In @ Y6 @ Y0)))) => (((X2 @ (c_Union @ (c_Repl @ Y2 @ (^[Y6 : $i]: (c_Repl @ sF7 @ (^[Y7 : $i]: (c_Union @ (c_Repl @ sF1 @ (^[Y8 : $i]: (c_Eps_i @ (^[Y9 : $i]: (!! @ $o @ (^[Y10 : $o]: (((!! @ $o @ (^[Y11 : $o]: (((c_In @ c_Empty @ Y8) => (((c_Repl @ Y6 @ (^[Y12 : $i]: (c_Repl @ Y12 @ (^[Y13 : $i]: (c_Eps_i @ (^[Y14 : $i]: (!! @ ($i > $i > $o) @ (^[Y15 : $i > $i > $o]: ((!! @ ($i > $i) @ (^[Y16 : $i > $i]: (!! @ $i @ (^[Y17 : $i]: ((!! @ $i @ (^[Y18 : $i]: ((c_In @ Y18 @ Y17) => (Y15 @ Y18 @ (Y16 @ Y18))))) => (Y15 @ Y17 @ (c_Union @ (c_Repl @ sF1 @ (^[Y18 : $i]: (c_Eps_i @ (^[Y19 : $i]: (!! @ $o @ (^[Y20 : $o]: (((!! @ $o @ (^[Y21 : $o]: (((c_In @ c_Empty @ Y18) => ((sF2 = Y19) => Y21)) => Y21))) => Y20) => (((!! @ $o @ (^[Y21 : $o]: ((((c_In @ c_Empty @ Y18) => $false) => (((c_Repl @ Y17 @ Y16) = Y19) => Y21)) => Y21))) => Y20) => Y20))))))))))))))) => (Y15 @ Y13 @ Y14)))))))))) = Y9) => Y11)) => Y11))) => Y10) => (((!! @ $o @ (^[Y11 : $o]: ((((c_In @ c_Empty @ Y8) => $false) => (((c_Repl @ Y7 @ (^[Y12 : $i]: (c_Eps_i @ (^[Y13 : $i]: (!! @ ($i > $i > $o) @ (^[Y14 : $i > $i > $o]: ((!! @ ($i > $i) @ (^[Y15 : $i > $i]: (!! @ $i @ (^[Y16 : $i]: ((!! @ $i @ (^[Y17 : $i]: ((c_In @ Y17 @ Y16) => (Y14 @ Y17 @ (Y15 @ Y17))))) => (Y14 @ Y16 @ (c_Union @ (c_Repl @ sF1 @ (^[Y17 : $i]: (c_Eps_i @ (^[Y18 : $i]: (!! @ $o @ (^[Y19 : $o]: (((!! @ $o @ (^[Y20 : $o]: (((c_In @ c_Empty @ Y17) => ((sF2 = Y18) => Y20)) => Y20))) => Y19) => (((!! @ $o @ (^[Y20 : $o]: ((((c_In @ c_Empty @ Y17) => $false) => (((c_Repl @ Y16 @ Y15) = Y18) => Y20)) => Y20))) => Y19) => Y19))))))))))))))) => (Y14 @ Y12 @ Y13)))))))) = Y9) => Y11)) => Y11))) => Y10) => Y10))))))))))))))) => $false) => Y5)) => Y5)))))) => Y3)) => Y3))))) => ((~ (?? @ $i @ (^[Y2 : $i]: (!! @ $o @ (^[Y3 : $o]: (((!! @ $o @ (^[Y4 : $o]: (((!! @ $i @ (^[Y5 : $i]: ((c_In @ Y5 @ Y2) => (!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ Y5) => (c_In @ Y6 @ Y2))))))) => ((!! @ $i @ (^[Y5 : $i]: ((c_In @ Y5 @ Y2) => (!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ Y5) => (!! @ $i @ (^[Y7 : $i]: ((c_In @ Y7 @ Y6) => (c_In @ Y7 @ Y5)))))))))) => Y4)) => Y4))) => ((!! @ $o @ (^[Y4 : $o]: (((!! @ $i @ (^[Y5 : $i]: ((c_In @ Y5 @ Y0) => (c_In @ Y5 @ (c_Union @ (c_Repl @ sF1 @ (^[Y6 : $i]: (c_Eps_i @ (^[Y7 : $i]: (!! @ $o @ (^[Y8 : $o]: (((!! @ $o @ (^[Y9 : $o]: (((c_In @ c_Empty @ Y6) => ((Y2 = Y7) => Y9)) => Y9))) => Y8) => (((!! @ $o @ (^[Y9 : $o]: ((((c_In @ c_Empty @ Y6) => $false) => (((c_Repl @ Y2 @ (^[Y10 : $i]: (c_Union @ (c_Repl @ sF1 @ (^[Y11 : $i]: (c_Eps_i @ (^[Y12 : $i]: (!! @ $o @ (^[Y13 : $o]: (((!! @ $o @ (^[Y14 : $o]: (((c_In @ c_Empty @ Y11) => ((Y10 = Y12) => Y14)) => Y14))) => Y13) => (((!! @ $o @ (^[Y14 : $o]: ((((c_In @ c_Empty @ Y11) => $false) => (((c_Repl @ sF1 @ (^[Y15 : $i]: (c_Eps_i @ (^[Y16 : $i]: (!! @ $o @ (^[Y17 : $o]: (((!! @ $o @ (^[Y18 : $o]: (((c_In @ c_Empty @ Y15) => ((sF9 = Y16) => Y18)) => Y18))) => Y17) => (((!! @ $o @ (^[Y18 : $o]: ((((c_In @ c_Empty @ Y15) => $false) => ((sF9 = Y16) => Y18)) => Y18))) => Y17) => Y17)))))))) = Y12) => Y14)) => Y14))) => Y13) => Y13))))))))))) = Y7) => Y9)) => Y9))) => Y8) => Y8))))))))))))) => ((!! @ $i @ (^[Y5 : $i]: ((c_In @ Y5 @ Y2) => (!! @ $o @ (^[Y6 : $o]: (((!! @ $o @ (^[Y7 : $o]: (((c_In @ (c_Union @ (c_Repl @ sF1 @ (^[Y8 : $i]: (c_Eps_i @ (^[Y9 : $i]: (!! @ $o @ (^[Y10 : $o]: (((!! @ $o @ (^[Y11 : $o]: (((c_In @ c_Empty @ Y8) => ((Y5 = Y9) => Y11)) => Y11))) => Y10) => (((!! @ $o @ (^[Y11 : $o]: ((((c_In @ c_Empty @ Y8) => $false) => (((c_Repl @ sF1 @ (^[Y12 : $i]: (c_Eps_i @ (^[Y13 : $i]: (!! @ $o @ (^[Y14 : $o]: (((!! @ $o @ (^[Y15 : $o]: (((c_In @ c_Empty @ Y12) => ((sF9 = Y13) => Y15)) => Y15))) => Y14) => (((!! @ $o @ (^[Y15 : $o]: ((((c_In @ c_Empty @ Y12) => $false) => ((sF9 = Y13) => Y15)) => Y15))) => Y14) => Y14)))))))) = Y9) => Y11)) => Y11))) => Y10) => Y10))))))))) @ Y0) => (((c_In @ Y5 @ Y0) => $false) => Y7)) => Y7))) => Y6) => (((!! @ $o @ (^[Y7 : $o]: (((~ (c_In @ (c_Union @ (c_Repl @ sF1 @ (^[Y8 : $i]: (c_Eps_i @ (^[Y9 : $i]: (!! @ $o @ (^[Y10 : $o]: (((!! @ $o @ (^[Y11 : $o]: (((c_In @ c_Empty @ Y8) => ((Y5 = Y9) => Y11)) => Y11))) => Y10) => (((!! @ $o @ (^[Y11 : $o]: ((((c_In @ c_Empty @ Y8) => $false) => (((c_Repl @ sF1 @ (^[Y12 : $i]: (c_Eps_i @ (^[Y13 : $i]: (!! @ $o @ (^[Y14 : $o]: (((!! @ $o @ (^[Y15 : $o]: (((c_In @ c_Empty @ Y12) => ((sF9 = Y13) => Y15)) => Y15))) => Y14) => (((!! @ $o @ (^[Y15 : $o]: ((((c_In @ c_Empty @ Y12) => $false) => ((sF9 = Y13) => Y15)) => Y15))) => Y14) => Y14)))))))) = Y9) => Y11)) => Y11))) => Y10) => Y10))))))))) @ Y0)) => ((c_In @ Y5 @ Y0) => Y7)) => Y7))) => Y6) => Y6))))))) => Y4)) => Y4))) => Y3)) => Y3)))))) => Y1)) => Y1)))))) => ((~ (X2 @ (X1 @ (X1 @ (X1 @ sF11))))) => X3)) => X3)))) )),
% 9.27/1.88 inference(boolean_simplification,[],[f610])).
% 9.27/1.88 thf(f612,plain,(
% 9.27/1.88 ( ! [X2 : ($i > $o),X3 : $o,X1 : ($i > $i)] : (($true = ((((((X2 @ (X1 @ (c_Eps_i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: (((!! @ $o @ (^[Y2 : $o]: (((?? @ $i @ (^[Y3 : $i]: (!! @ $o @ (^[Y4 : $o]: (((c_In @ Y3 @ (X1 @ sF0)) => ((c_In @ Y3 @ (X1 @ sF4)) => Y4)) => Y4))))) => (((c_Repl @ (X1 @ sF0) @ (^[Y3 : $i]: (c_Eps_i @ (^[Y4 : $i]: (!! @ $o @ (^[Y5 : $o]: (((!! @ $o @ (^[Y6 : $o]: (((c_In @ Y3 @ (X1 @ sF4)) => ((Y3 = Y4) => Y6)) => Y6))) => Y5) => (((!! @ $o @ (^[Y6 : $o]: ((((c_In @ Y3 @ (X1 @ sF4)) => $false) => (((c_Eps_i @ (^[Y7 : $i]: (!! @ $o @ (^[Y8 : $o]: (((c_In @ Y7 @ (X1 @ sF0)) => ((c_In @ Y7 @ (X1 @ sF4)) => Y8)) => Y8))))) = Y4) => Y6)) => Y6))) => Y5) => Y5)))))))) = Y0) => Y2)) => Y2))) => Y1) => (((!! @ $o @ (^[Y2 : $o]: ((((?? @ $i @ (^[Y3 : $i]: (!! @ $o @ (^[Y4 : $o]: (((c_In @ Y3 @ (X1 @ sF0)) => ((c_In @ Y3 @ (X1 @ sF4)) => Y4)) => Y4))))) => $false) => ((c_Empty = Y0) => Y2)) => Y2))) => Y1) => Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: ((c_In @ Y0 @ (X1 @ c_Empty)) => (!! @ $i @ (^[Y1 : $i]: ((c_In @ Y1 @ Y0) => (c_In @ Y1 @ (X1 @ c_Empty)))))))) => (!! @ $i @ (^[Y0 : $i]: ((c_In @ Y0 @ c_Empty) => (?? @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: (((!! @ $i @ (^[Y3 : $i]: ((c_In @ Y3 @ Y1) => (c_In @ Y3 @ Y0)))) => ((!! @ $o @ (^[Y3 : $o]: (((?? @ $i @ (^[Y4 : $i]: (!! @ $o @ (^[Y5 : $o]: (((c_In @ Y4 @ (c_Union @ (c_Repl @ sF1 @ (^[Y6 : $i]: (c_Eps_i @ (^[Y7 : $i]: (!! @ $o @ (^[Y8 : $o]: (((!! @ $o @ (^[Y9 : $o]: (((c_In @ c_Empty @ Y6) => (((X1 @ Y1) = Y7) => Y9)) => Y9))) => Y8) => (((!! @ $o @ (^[Y9 : $o]: (((~ (c_In @ c_Empty @ Y6)) => (((c_Repl @ sF1 @ (^[Y10 : $i]: (c_Eps_i @ (^[Y11 : $i]: (!! @ $o @ (^[Y12 : $o]: (((!! @ $o @ (^[Y13 : $o]: (((c_In @ c_Empty @ Y10) => (((X1 @ Y1) = Y11) => Y13)) => Y13))) => Y12) => (((!! @ $o @ (^[Y13 : $o]: (((~ (c_In @ c_Empty @ Y10)) => (((X1 @ Y1) = Y11) => Y13)) => Y13))) => Y12) => Y12)))))))) = Y7) => Y9)) => Y9))) => Y8) => Y8)))))))))) => (((!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ (c_Union @ (c_Repl @ sF1 @ (^[Y7 : $i]: (c_Eps_i @ (^[Y8 : $i]: (!! @ $o @ (^[Y9 : $o]: (((!! @ $o @ (^[Y10 : $o]: (((c_In @ c_Empty @ Y7) => (((X1 @ Y1) = Y8) => Y10)) => Y10))) => Y9) => (((!! @ $o @ (^[Y10 : $o]: (((~ (c_In @ c_Empty @ Y7)) => (((c_Repl @ sF1 @ (^[Y11 : $i]: (c_Eps_i @ (^[Y12 : $i]: (!! @ $o @ (^[Y13 : $o]: (((!! @ $o @ (^[Y14 : $o]: (((c_In @ c_Empty @ Y11) => (((X1 @ Y1) = Y12) => Y14)) => Y14))) => Y13) => (((!! @ $o @ (^[Y14 : $o]: (((~ (c_In @ c_Empty @ Y11)) => (((X1 @ Y1) = Y12) => Y14)) => Y14))) => Y13) => Y13)))))))) = Y8) => Y10)) => Y10))) => Y9) => Y9)))))))))) => (c_In @ Y6 @ (c_Power @ Y4))))) => $false) => Y5)) => Y5))))) => (((?? @ $i @ (^[Y4 : $i]: (!! @ $o @ (^[Y5 : $o]: (((!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ Y4) => (c_In @ Y6 @ (c_Union @ (c_Repl @ sF1 @ (^[Y7 : $i]: (c_Eps_i @ (^[Y8 : $i]: (!! @ $o @ (^[Y9 : $o]: (((!! @ $o @ (^[Y10 : $o]: (((c_In @ c_Empty @ Y7) => (((X1 @ Y1) = Y8) => Y10)) => Y10))) => Y9) => (((!! @ $o @ (^[Y10 : $o]: (((~ (c_In @ c_Empty @ Y7)) => (((c_Repl @ sF1 @ (^[Y11 : $i]: (c_Eps_i @ (^[Y12 : $i]: (!! @ $o @ (^[Y13 : $o]: (((!! @ $o @ (^[Y14 : $o]: (((c_In @ c_Empty @ Y11) => (((X1 @ Y1) = Y12) => Y14)) => Y14))) => Y13) => (((!! @ $o @ (^[Y14 : $o]: (((~ (c_In @ c_Empty @ Y11)) => (((X1 @ Y1) = Y12) => Y14)) => Y14))) => Y13) => Y13)))))))) = Y8) => Y10)) => Y10))) => Y9) => Y9))))))))))))) => ((!! @ $o @ (^[Y6 : $o]: ((((!! @ $i @ (^[Y7 : $i]: ((c_In @ Y7 @ (c_Union @ (c_Repl @ sF1 @ (^[Y8 : $i]: (c_Eps_i @ (^[Y9 : $i]: (!! @ $o @ (^[Y10 : $o]: (((!! @ $o @ (^[Y11 : $o]: (((c_In @ c_Empty @ Y8) => (((X1 @ Y1) = Y9) => Y11)) => Y11))) => Y10) => (((!! @ $o @ (^[Y11 : $o]: (((~ (c_In @ c_Empty @ Y8)) => (((c_Repl @ sF1 @ (^[Y12 : $i]: (c_Eps_i @ (^[Y13 : $i]: (!! @ $o @ (^[Y14 : $o]: (((!! @ $o @ (^[Y15 : $o]: (((c_In @ c_Empty @ Y12) => (((X1 @ Y1) = Y13) => Y15)) => Y15))) => Y14) => (((!! @ $o @ (^[Y15 : $o]: (((~ (c_In @ c_Empty @ Y12)) => (((X1 @ Y1) = Y13) => Y15)) => Y15))) => Y14) => Y14)))))))) = Y9) => Y11)) => Y11))) => Y10) => Y10)))))))))) => (c_In @ Y7 @ Y4)))) => $false) => ((?? @ $i @ (^[Y7 : $i]: (!! @ $o @ (^[Y8 : $o]: (((c_In @ Y7 @ Y4) => (((!! @ $i @ (^[Y9 : $i]: ((c_In @ Y9 @ Y4) => (c_In @ Y9 @ (c_Power @ Y7))))) => $false) => Y8)) => Y8))))) => Y6)) => Y6))) => Y5)) => Y5))))) => $false) => Y3)) => Y3))) => Y2)) => Y2)))))))))) => (?? @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: (((?? @ $i @ (^[Y2 : $i]: (!! @ $o @ (^[Y3 : $o]: (((!! @ $i @ (^[Y4 : $i]: ((c_In @ Y4 @ Y2) => (c_In @ Y4 @ Y0)))) => ((((X1 @ Y0) = Y0) => (?? @ $i @ (^[Y4 : $i]: (!! @ $o @ (^[Y5 : $o]: (((!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ Y4) => (c_In @ Y6 @ Y0)))) => (((X2 @ (c_Union @ (c_Repl @ Y2 @ (^[Y6 : $i]: (c_Repl @ sF7 @ (^[Y7 : $i]: (c_Union @ (c_Repl @ sF1 @ (^[Y8 : $i]: (c_Eps_i @ (^[Y9 : $i]: (!! @ $o @ (^[Y10 : $o]: (((!! @ $o @ (^[Y11 : $o]: (((c_In @ c_Empty @ Y8) => (((c_Repl @ Y6 @ (^[Y12 : $i]: (c_Repl @ Y12 @ (^[Y13 : $i]: (c_Eps_i @ (^[Y14 : $i]: (!! @ ($i > $i > $o) @ (^[Y15 : $i > $i > $o]: ((!! @ ($i > $i) @ (^[Y16 : $i > $i]: (!! @ $i @ (^[Y17 : $i]: ((!! @ $i @ (^[Y18 : $i]: ((c_In @ Y18 @ Y17) => (Y15 @ Y18 @ (Y16 @ Y18))))) => (Y15 @ Y17 @ (c_Union @ (c_Repl @ sF1 @ (^[Y18 : $i]: (c_Eps_i @ (^[Y19 : $i]: (!! @ $o @ (^[Y20 : $o]: (((!! @ $o @ (^[Y21 : $o]: (((c_In @ c_Empty @ Y18) => ((sF2 = Y19) => Y21)) => Y21))) => Y20) => (((!! @ $o @ (^[Y21 : $o]: (((~ (c_In @ c_Empty @ Y18)) => (((c_Repl @ Y17 @ Y16) = Y19) => Y21)) => Y21))) => Y20) => Y20))))))))))))))) => (Y15 @ Y13 @ Y14)))))))))) = Y9) => Y11)) => Y11))) => Y10) => (((!! @ $o @ (^[Y11 : $o]: (((~ (c_In @ c_Empty @ Y8)) => (((c_Repl @ Y7 @ (^[Y12 : $i]: (c_Eps_i @ (^[Y13 : $i]: (!! @ ($i > $i > $o) @ (^[Y14 : $i > $i > $o]: ((!! @ ($i > $i) @ (^[Y15 : $i > $i]: (!! @ $i @ (^[Y16 : $i]: ((!! @ $i @ (^[Y17 : $i]: ((c_In @ Y17 @ Y16) => (Y14 @ Y17 @ (Y15 @ Y17))))) => (Y14 @ Y16 @ (c_Union @ (c_Repl @ sF1 @ (^[Y17 : $i]: (c_Eps_i @ (^[Y18 : $i]: (!! @ $o @ (^[Y19 : $o]: (((!! @ $o @ (^[Y20 : $o]: (((c_In @ c_Empty @ Y17) => ((sF2 = Y18) => Y20)) => Y20))) => Y19) => (((!! @ $o @ (^[Y20 : $o]: (((~ (c_In @ c_Empty @ Y17)) => (((c_Repl @ Y16 @ Y15) = Y18) => Y20)) => Y20))) => Y19) => Y19))))))))))))))) => (Y14 @ Y12 @ Y13)))))))) = Y9) => Y11)) => Y11))) => Y10) => Y10))))))))))))))) => $false) => Y5)) => Y5)))))) => Y3)) => Y3))))) => ((~ (?? @ $i @ (^[Y2 : $i]: (!! @ $o @ (^[Y3 : $o]: (((!! @ $o @ (^[Y4 : $o]: (((!! @ $i @ (^[Y5 : $i]: ((c_In @ Y5 @ Y2) => (!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ Y5) => (c_In @ Y6 @ Y2))))))) => ((!! @ $i @ (^[Y5 : $i]: ((c_In @ Y5 @ Y2) => (!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ Y5) => (!! @ $i @ (^[Y7 : $i]: ((c_In @ Y7 @ Y6) => (c_In @ Y7 @ Y5)))))))))) => Y4)) => Y4))) => ((!! @ $o @ (^[Y4 : $o]: (((!! @ $i @ (^[Y5 : $i]: ((c_In @ Y5 @ Y0) => (c_In @ Y5 @ (c_Union @ (c_Repl @ sF1 @ (^[Y6 : $i]: (c_Eps_i @ (^[Y7 : $i]: (!! @ $o @ (^[Y8 : $o]: (((!! @ $o @ (^[Y9 : $o]: (((c_In @ c_Empty @ Y6) => ((Y2 = Y7) => Y9)) => Y9))) => Y8) => (((!! @ $o @ (^[Y9 : $o]: (((~ (c_In @ c_Empty @ Y6)) => (((c_Repl @ Y2 @ (^[Y10 : $i]: (c_Union @ (c_Repl @ sF1 @ (^[Y11 : $i]: (c_Eps_i @ (^[Y12 : $i]: (!! @ $o @ (^[Y13 : $o]: (((!! @ $o @ (^[Y14 : $o]: (((c_In @ c_Empty @ Y11) => ((Y10 = Y12) => Y14)) => Y14))) => Y13) => (((!! @ $o @ (^[Y14 : $o]: (((~ (c_In @ c_Empty @ Y11)) => (((c_Repl @ sF1 @ (^[Y15 : $i]: (c_Eps_i @ (^[Y16 : $i]: (!! @ $o @ (^[Y17 : $o]: (((!! @ $o @ (^[Y18 : $o]: (((c_In @ c_Empty @ Y15) => ((sF9 = Y16) => Y18)) => Y18))) => Y17) => (((!! @ $o @ (^[Y18 : $o]: (((~ (c_In @ c_Empty @ Y15)) => ((sF9 = Y16) => Y18)) => Y18))) => Y17) => Y17)))))))) = Y12) => Y14)) => Y14))) => Y13) => Y13))))))))))) = Y7) => Y9)) => Y9))) => Y8) => Y8))))))))))))) => ((!! @ $i @ (^[Y5 : $i]: ((c_In @ Y5 @ Y2) => (!! @ $o @ (^[Y6 : $o]: (((!! @ $o @ (^[Y7 : $o]: (((c_In @ (c_Union @ (c_Repl @ sF1 @ (^[Y8 : $i]: (c_Eps_i @ (^[Y9 : $i]: (!! @ $o @ (^[Y10 : $o]: (((!! @ $o @ (^[Y11 : $o]: (((c_In @ c_Empty @ Y8) => ((Y5 = Y9) => Y11)) => Y11))) => Y10) => (((!! @ $o @ (^[Y11 : $o]: (((~ (c_In @ c_Empty @ Y8)) => (((c_Repl @ sF1 @ (^[Y12 : $i]: (c_Eps_i @ (^[Y13 : $i]: (!! @ $o @ (^[Y14 : $o]: (((!! @ $o @ (^[Y15 : $o]: (((c_In @ c_Empty @ Y12) => ((sF9 = Y13) => Y15)) => Y15))) => Y14) => (((!! @ $o @ (^[Y15 : $o]: (((~ (c_In @ c_Empty @ Y12)) => ((sF9 = Y13) => Y15)) => Y15))) => Y14) => Y14)))))))) = Y9) => Y11)) => Y11))) => Y10) => Y10))))))))) @ Y0) => (((c_In @ Y5 @ Y0) => $false) => Y7)) => Y7))) => Y6) => (((!! @ $o @ (^[Y7 : $o]: (((~ (c_In @ (c_Union @ (c_Repl @ sF1 @ (^[Y8 : $i]: (c_Eps_i @ (^[Y9 : $i]: (!! @ $o @ (^[Y10 : $o]: (((!! @ $o @ (^[Y11 : $o]: (((c_In @ c_Empty @ Y8) => ((Y5 = Y9) => Y11)) => Y11))) => Y10) => (((!! @ $o @ (^[Y11 : $o]: (((~ (c_In @ c_Empty @ Y8)) => (((c_Repl @ sF1 @ (^[Y12 : $i]: (c_Eps_i @ (^[Y13 : $i]: (!! @ $o @ (^[Y14 : $o]: (((!! @ $o @ (^[Y15 : $o]: (((c_In @ c_Empty @ Y12) => ((sF9 = Y13) => Y15)) => Y15))) => Y14) => (((!! @ $o @ (^[Y15 : $o]: (((~ (c_In @ c_Empty @ Y12)) => ((sF9 = Y13) => Y15)) => Y15))) => Y14) => Y14)))))))) = Y9) => Y11)) => Y11))) => Y10) => Y10))))))))) @ Y0)) => ((c_In @ Y5 @ Y0) => Y7)) => Y7))) => Y6) => Y6))))))) => Y4)) => Y4))) => Y3)) => Y3)))))) => Y1)) => Y1)))))) => ((~ (X2 @ (X1 @ (X1 @ (X1 @ sF11))))) => X3)) => X3)))) )),
% 9.27/1.88 inference(boolean_simplification,[],[f611])).
% 9.27/1.88 thf(f613,plain,(
% 9.27/1.88 ( ! [X2 : ($i > $o),X3 : $o,X1 : ($i > $i)] : (($true = ((((((X2 @ (X1 @ (c_Eps_i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: (((!! @ $o @ (^[Y2 : $o]: (((?? @ $i @ (^[Y3 : $i]: (!! @ $o @ (^[Y4 : $o]: (((c_In @ Y3 @ (X1 @ sF0)) => ((c_In @ Y3 @ (X1 @ sF4)) => Y4)) => Y4))))) => (((c_Repl @ (X1 @ sF0) @ (^[Y3 : $i]: (c_Eps_i @ (^[Y4 : $i]: (!! @ $o @ (^[Y5 : $o]: (((!! @ $o @ (^[Y6 : $o]: (((c_In @ Y3 @ (X1 @ sF4)) => ((Y3 = Y4) => Y6)) => Y6))) => Y5) => (((!! @ $o @ (^[Y6 : $o]: ((((c_In @ Y3 @ (X1 @ sF4)) => $false) => (((c_Eps_i @ (^[Y7 : $i]: (!! @ $o @ (^[Y8 : $o]: (((c_In @ Y7 @ (X1 @ sF0)) => ((c_In @ Y7 @ (X1 @ sF4)) => Y8)) => Y8))))) = Y4) => Y6)) => Y6))) => Y5) => Y5)))))))) = Y0) => Y2)) => Y2))) => Y1) => (((!! @ $o @ (^[Y2 : $o]: ((((?? @ $i @ (^[Y3 : $i]: (!! @ $o @ (^[Y4 : $o]: (((c_In @ Y3 @ (X1 @ sF0)) => ((c_In @ Y3 @ (X1 @ sF4)) => Y4)) => Y4))))) => $false) => ((c_Empty = Y0) => Y2)) => Y2))) => Y1) => Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: ((c_In @ Y0 @ (X1 @ c_Empty)) => (!! @ $i @ (^[Y1 : $i]: ((c_In @ Y1 @ Y0) => (c_In @ Y1 @ (X1 @ c_Empty)))))))) => (!! @ $i @ (^[Y0 : $i]: ((c_In @ Y0 @ c_Empty) => (?? @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: (((!! @ $i @ (^[Y3 : $i]: ((c_In @ Y3 @ Y1) => (c_In @ Y3 @ Y0)))) => ((!! @ $o @ (^[Y3 : $o]: (((?? @ $i @ (^[Y4 : $i]: (!! @ $o @ (^[Y5 : $o]: (((c_In @ Y4 @ (c_Union @ (c_Repl @ sF1 @ (^[Y6 : $i]: (c_Eps_i @ (^[Y7 : $i]: (!! @ $o @ (^[Y8 : $o]: (((!! @ $o @ (^[Y9 : $o]: (((c_In @ c_Empty @ Y6) => (((X1 @ Y1) = Y7) => Y9)) => Y9))) => Y8) => (((!! @ $o @ (^[Y9 : $o]: (((~ (c_In @ c_Empty @ Y6)) => (((c_Repl @ sF1 @ (^[Y10 : $i]: (c_Eps_i @ (^[Y11 : $i]: (!! @ $o @ (^[Y12 : $o]: (((!! @ $o @ (^[Y13 : $o]: (((c_In @ c_Empty @ Y10) => (((X1 @ Y1) = Y11) => Y13)) => Y13))) => Y12) => (((!! @ $o @ (^[Y13 : $o]: (((~ (c_In @ c_Empty @ Y10)) => (((X1 @ Y1) = Y11) => Y13)) => Y13))) => Y12) => Y12)))))))) = Y7) => Y9)) => Y9))) => Y8) => Y8)))))))))) => (((!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ (c_Union @ (c_Repl @ sF1 @ (^[Y7 : $i]: (c_Eps_i @ (^[Y8 : $i]: (!! @ $o @ (^[Y9 : $o]: (((!! @ $o @ (^[Y10 : $o]: (((c_In @ c_Empty @ Y7) => (((X1 @ Y1) = Y8) => Y10)) => Y10))) => Y9) => (((!! @ $o @ (^[Y10 : $o]: (((~ (c_In @ c_Empty @ Y7)) => (((c_Repl @ sF1 @ (^[Y11 : $i]: (c_Eps_i @ (^[Y12 : $i]: (!! @ $o @ (^[Y13 : $o]: (((!! @ $o @ (^[Y14 : $o]: (((c_In @ c_Empty @ Y11) => (((X1 @ Y1) = Y12) => Y14)) => Y14))) => Y13) => (((!! @ $o @ (^[Y14 : $o]: (((~ (c_In @ c_Empty @ Y11)) => (((X1 @ Y1) = Y12) => Y14)) => Y14))) => Y13) => Y13)))))))) = Y8) => Y10)) => Y10))) => Y9) => Y9)))))))))) => (c_In @ Y6 @ (c_Power @ Y4))))) => $false) => Y5)) => Y5))))) => (((?? @ $i @ (^[Y4 : $i]: (!! @ $o @ (^[Y5 : $o]: (((!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ Y4) => (c_In @ Y6 @ (c_Union @ (c_Repl @ sF1 @ (^[Y7 : $i]: (c_Eps_i @ (^[Y8 : $i]: (!! @ $o @ (^[Y9 : $o]: (((!! @ $o @ (^[Y10 : $o]: (((c_In @ c_Empty @ Y7) => (((X1 @ Y1) = Y8) => Y10)) => Y10))) => Y9) => (((!! @ $o @ (^[Y10 : $o]: (((~ (c_In @ c_Empty @ Y7)) => (((c_Repl @ sF1 @ (^[Y11 : $i]: (c_Eps_i @ (^[Y12 : $i]: (!! @ $o @ (^[Y13 : $o]: (((!! @ $o @ (^[Y14 : $o]: (((c_In @ c_Empty @ Y11) => (((X1 @ Y1) = Y12) => Y14)) => Y14))) => Y13) => (((!! @ $o @ (^[Y14 : $o]: (((~ (c_In @ c_Empty @ Y11)) => (((X1 @ Y1) = Y12) => Y14)) => Y14))) => Y13) => Y13)))))))) = Y8) => Y10)) => Y10))) => Y9) => Y9))))))))))))) => ((!! @ $o @ (^[Y6 : $o]: ((((!! @ $i @ (^[Y7 : $i]: ((c_In @ Y7 @ (c_Union @ (c_Repl @ sF1 @ (^[Y8 : $i]: (c_Eps_i @ (^[Y9 : $i]: (!! @ $o @ (^[Y10 : $o]: (((!! @ $o @ (^[Y11 : $o]: (((c_In @ c_Empty @ Y8) => (((X1 @ Y1) = Y9) => Y11)) => Y11))) => Y10) => (((!! @ $o @ (^[Y11 : $o]: (((~ (c_In @ c_Empty @ Y8)) => (((c_Repl @ sF1 @ (^[Y12 : $i]: (c_Eps_i @ (^[Y13 : $i]: (!! @ $o @ (^[Y14 : $o]: (((!! @ $o @ (^[Y15 : $o]: (((c_In @ c_Empty @ Y12) => (((X1 @ Y1) = Y13) => Y15)) => Y15))) => Y14) => (((!! @ $o @ (^[Y15 : $o]: (((~ (c_In @ c_Empty @ Y12)) => (((X1 @ Y1) = Y13) => Y15)) => Y15))) => Y14) => Y14)))))))) = Y9) => Y11)) => Y11))) => Y10) => Y10)))))))))) => (c_In @ Y7 @ Y4)))) => $false) => ((?? @ $i @ (^[Y7 : $i]: (!! @ $o @ (^[Y8 : $o]: (((c_In @ Y7 @ Y4) => (((!! @ $i @ (^[Y9 : $i]: ((c_In @ Y9 @ Y4) => (c_In @ Y9 @ (c_Power @ Y7))))) => $false) => Y8)) => Y8))))) => Y6)) => Y6))) => Y5)) => Y5))))) => $false) => Y3)) => Y3))) => Y2)) => Y2)))))))))) => (?? @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: (((?? @ $i @ (^[Y2 : $i]: (!! @ $o @ (^[Y3 : $o]: (((!! @ $i @ (^[Y4 : $i]: ((c_In @ Y4 @ Y2) => (c_In @ Y4 @ Y0)))) => ((((X1 @ Y0) = Y0) => (?? @ $i @ (^[Y4 : $i]: (!! @ $o @ (^[Y5 : $o]: (((!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ Y4) => (c_In @ Y6 @ Y0)))) => (((X2 @ (c_Union @ (c_Repl @ Y2 @ (^[Y6 : $i]: (c_Repl @ sF7 @ (^[Y7 : $i]: (c_Union @ (c_Repl @ sF1 @ (^[Y8 : $i]: (c_Eps_i @ (^[Y9 : $i]: (!! @ $o @ (^[Y10 : $o]: (((!! @ $o @ (^[Y11 : $o]: (((c_In @ c_Empty @ Y8) => (((c_Repl @ Y6 @ (^[Y12 : $i]: (c_Repl @ Y12 @ (^[Y13 : $i]: (c_Eps_i @ (^[Y14 : $i]: (!! @ ($i > $i > $o) @ (^[Y15 : $i > $i > $o]: ((!! @ ($i > $i) @ (^[Y16 : $i > $i]: (!! @ $i @ (^[Y17 : $i]: ((!! @ $i @ (^[Y18 : $i]: ((c_In @ Y18 @ Y17) => (Y15 @ Y18 @ (Y16 @ Y18))))) => (Y15 @ Y17 @ (c_Union @ (c_Repl @ sF1 @ (^[Y18 : $i]: (c_Eps_i @ (^[Y19 : $i]: (!! @ $o @ (^[Y20 : $o]: (((!! @ $o @ (^[Y21 : $o]: (((c_In @ c_Empty @ Y18) => ((sF2 = Y19) => Y21)) => Y21))) => Y20) => (((!! @ $o @ (^[Y21 : $o]: (((~ (c_In @ c_Empty @ Y18)) => (((c_Repl @ Y17 @ Y16) = Y19) => Y21)) => Y21))) => Y20) => Y20))))))))))))))) => (Y15 @ Y13 @ Y14)))))))))) = Y9) => Y11)) => Y11))) => Y10) => (((!! @ $o @ (^[Y11 : $o]: (((~ (c_In @ c_Empty @ Y8)) => (((c_Repl @ Y7 @ (^[Y12 : $i]: (c_Eps_i @ (^[Y13 : $i]: (!! @ ($i > $i > $o) @ (^[Y14 : $i > $i > $o]: ((!! @ ($i > $i) @ (^[Y15 : $i > $i]: (!! @ $i @ (^[Y16 : $i]: ((!! @ $i @ (^[Y17 : $i]: ((c_In @ Y17 @ Y16) => (Y14 @ Y17 @ (Y15 @ Y17))))) => (Y14 @ Y16 @ (c_Union @ (c_Repl @ sF1 @ (^[Y17 : $i]: (c_Eps_i @ (^[Y18 : $i]: (!! @ $o @ (^[Y19 : $o]: (((!! @ $o @ (^[Y20 : $o]: (((c_In @ c_Empty @ Y17) => ((sF2 = Y18) => Y20)) => Y20))) => Y19) => (((!! @ $o @ (^[Y20 : $o]: (((~ (c_In @ c_Empty @ Y17)) => (((c_Repl @ Y16 @ Y15) = Y18) => Y20)) => Y20))) => Y19) => Y19))))))))))))))) => (Y14 @ Y12 @ Y13)))))))) = Y9) => Y11)) => Y11))) => Y10) => Y10))))))))))))))) => $false) => Y5)) => Y5)))))) => Y3)) => Y3))))) => ((~ (?? @ $i @ (^[Y2 : $i]: (!! @ $o @ (^[Y3 : $o]: (((!! @ $o @ (^[Y4 : $o]: (((!! @ $i @ (^[Y5 : $i]: ((c_In @ Y5 @ Y2) => (!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ Y5) => (c_In @ Y6 @ Y2))))))) => ((!! @ $i @ (^[Y5 : $i]: ((c_In @ Y5 @ Y2) => (!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ Y5) => (!! @ $i @ (^[Y7 : $i]: ((c_In @ Y7 @ Y6) => (c_In @ Y7 @ Y5)))))))))) => Y4)) => Y4))) => ((!! @ $o @ (^[Y4 : $o]: (((!! @ $i @ (^[Y5 : $i]: ((c_In @ Y5 @ Y0) => (c_In @ Y5 @ (c_Union @ (c_Repl @ sF1 @ (^[Y6 : $i]: (c_Eps_i @ (^[Y7 : $i]: (!! @ $o @ (^[Y8 : $o]: (((!! @ $o @ (^[Y9 : $o]: (((c_In @ c_Empty @ Y6) => ((Y2 = Y7) => Y9)) => Y9))) => Y8) => (((!! @ $o @ (^[Y9 : $o]: (((~ (c_In @ c_Empty @ Y6)) => (((c_Repl @ Y2 @ (^[Y10 : $i]: (c_Union @ (c_Repl @ sF1 @ (^[Y11 : $i]: (c_Eps_i @ (^[Y12 : $i]: (!! @ $o @ (^[Y13 : $o]: (((!! @ $o @ (^[Y14 : $o]: (((c_In @ c_Empty @ Y11) => ((Y10 = Y12) => Y14)) => Y14))) => Y13) => (((!! @ $o @ (^[Y14 : $o]: (((~ (c_In @ c_Empty @ Y11)) => (((c_Repl @ sF1 @ (^[Y15 : $i]: (c_Eps_i @ (^[Y16 : $i]: (!! @ $o @ (^[Y17 : $o]: (((!! @ $o @ (^[Y18 : $o]: (((c_In @ c_Empty @ Y15) => ((sF9 = Y16) => Y18)) => Y18))) => Y17) => (((!! @ $o @ (^[Y18 : $o]: (((~ (c_In @ c_Empty @ Y15)) => ((sF9 = Y16) => Y18)) => Y18))) => Y17) => Y17)))))))) = Y12) => Y14)) => Y14))) => Y13) => Y13))))))))))) = Y7) => Y9)) => Y9))) => Y8) => Y8))))))))))))) => ((!! @ $i @ (^[Y5 : $i]: ((c_In @ Y5 @ Y2) => (!! @ $o @ (^[Y6 : $o]: (((!! @ $o @ (^[Y7 : $o]: (((c_In @ (c_Union @ (c_Repl @ sF1 @ (^[Y8 : $i]: (c_Eps_i @ (^[Y9 : $i]: (!! @ $o @ (^[Y10 : $o]: (((!! @ $o @ (^[Y11 : $o]: (((c_In @ c_Empty @ Y8) => ((Y5 = Y9) => Y11)) => Y11))) => Y10) => (((!! @ $o @ (^[Y11 : $o]: (((~ (c_In @ c_Empty @ Y8)) => (((c_Repl @ sF1 @ (^[Y12 : $i]: (c_Eps_i @ (^[Y13 : $i]: (!! @ $o @ (^[Y14 : $o]: (((!! @ $o @ (^[Y15 : $o]: (((c_In @ c_Empty @ Y12) => ((sF9 = Y13) => Y15)) => Y15))) => Y14) => (((!! @ $o @ (^[Y15 : $o]: (((~ (c_In @ c_Empty @ Y12)) => ((sF9 = Y13) => Y15)) => Y15))) => Y14) => Y14)))))))) = Y9) => Y11)) => Y11))) => Y10) => Y10))))))))) @ Y0) => ((~ (c_In @ Y5 @ Y0)) => Y7)) => Y7))) => Y6) => (((!! @ $o @ (^[Y7 : $o]: (((~ (c_In @ (c_Union @ (c_Repl @ sF1 @ (^[Y8 : $i]: (c_Eps_i @ (^[Y9 : $i]: (!! @ $o @ (^[Y10 : $o]: (((!! @ $o @ (^[Y11 : $o]: (((c_In @ c_Empty @ Y8) => ((Y5 = Y9) => Y11)) => Y11))) => Y10) => (((!! @ $o @ (^[Y11 : $o]: (((~ (c_In @ c_Empty @ Y8)) => (((c_Repl @ sF1 @ (^[Y12 : $i]: (c_Eps_i @ (^[Y13 : $i]: (!! @ $o @ (^[Y14 : $o]: (((!! @ $o @ (^[Y15 : $o]: (((c_In @ c_Empty @ Y12) => ((sF9 = Y13) => Y15)) => Y15))) => Y14) => (((!! @ $o @ (^[Y15 : $o]: (((~ (c_In @ c_Empty @ Y12)) => ((sF9 = Y13) => Y15)) => Y15))) => Y14) => Y14)))))))) = Y9) => Y11)) => Y11))) => Y10) => Y10))))))))) @ Y0)) => ((c_In @ Y5 @ Y0) => Y7)) => Y7))) => Y6) => Y6))))))) => Y4)) => Y4))) => Y3)) => Y3)))))) => Y1)) => Y1)))))) => ((~ (X2 @ (X1 @ (X1 @ (X1 @ sF11))))) => X3)) => X3)))) )),
% 9.27/1.88 inference(boolean_simplification,[],[f612])).
% 9.27/1.88 thf(f614,plain,(
% 9.27/1.88 ( ! 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@ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: (((!! @ $i @ (^[Y3 : $i]: ((c_In @ Y3 @ Y1) => (c_In @ Y3 @ Y0)))) => ((!! @ $o @ (^[Y3 : $o]: (((?? @ $i @ (^[Y4 : $i]: (!! @ $o @ (^[Y5 : $o]: (((c_In @ Y4 @ (c_Union @ (c_Repl @ sF1 @ (^[Y6 : $i]: (c_Eps_i @ (^[Y7 : $i]: (!! @ $o @ (^[Y8 : $o]: (((!! @ $o @ (^[Y9 : $o]: (((c_In @ c_Empty @ Y6) => (((X1 @ Y1) = Y7) => Y9)) => Y9))) => Y8) => (((!! @ $o @ (^[Y9 : $o]: (((~ (c_In @ c_Empty @ Y6)) => (((c_Repl @ sF1 @ (^[Y10 : $i]: (c_Eps_i @ (^[Y11 : $i]: (!! @ $o @ (^[Y12 : $o]: (((!! @ $o @ (^[Y13 : $o]: (((c_In @ c_Empty @ Y10) => (((X1 @ Y1) = Y11) => Y13)) => Y13))) => Y12) => (((!! @ $o @ (^[Y13 : $o]: (((~ (c_In @ c_Empty @ Y10)) => (((X1 @ Y1) = Y11) => Y13)) => Y13))) => Y12) => Y12)))))))) = Y7) => Y9)) => Y9))) => Y8) => Y8)))))))))) => (((!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ (c_Union @ (c_Repl @ sF1 @ (^[Y7 : $i]: (c_Eps_i @ (^[Y8 : $i]: (!! @ $o @ (^[Y9 : $o]: (((!! @ $o @ (^[Y10 : $o]: (((c_In @ c_Empty @ Y7) => (((X1 @ Y1) = Y8) => Y10)) => Y10))) => Y9) => (((!! @ $o @ (^[Y10 : $o]: (((~ (c_In @ c_Empty @ Y7)) => (((c_Repl @ sF1 @ (^[Y11 : $i]: (c_Eps_i @ (^[Y12 : $i]: (!! @ $o @ (^[Y13 : $o]: (((!! @ $o @ (^[Y14 : $o]: (((c_In @ c_Empty @ Y11) => (((X1 @ Y1) = Y12) => Y14)) => Y14))) => Y13) => (((!! @ $o @ (^[Y14 : $o]: (((~ (c_In @ c_Empty @ Y11)) => (((X1 @ Y1) = Y12) => Y14)) => Y14))) => Y13) => Y13)))))))) = Y8) => Y10)) => Y10))) => Y9) => Y9)))))))))) => (c_In @ Y6 @ (c_Power @ Y4))))) => $false) => Y5)) => Y5))))) => (((?? @ $i @ (^[Y4 : $i]: (!! @ $o @ (^[Y5 : $o]: (((!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ Y4) => (c_In @ Y6 @ (c_Union @ (c_Repl @ sF1 @ (^[Y7 : $i]: (c_Eps_i @ (^[Y8 : $i]: (!! @ $o @ (^[Y9 : $o]: (((!! @ $o @ (^[Y10 : $o]: (((c_In @ c_Empty @ Y7) => (((X1 @ Y1) = Y8) => Y10)) => Y10))) => Y9) => (((!! @ $o @ (^[Y10 : $o]: (((~ (c_In @ c_Empty @ Y7)) => (((c_Repl @ sF1 @ (^[Y11 : $i]: (c_Eps_i @ (^[Y12 : $i]: (!! @ $o @ (^[Y13 : $o]: (((!! @ $o @ (^[Y14 : $o]: (((c_In @ c_Empty @ Y11) => (((X1 @ Y1) = Y12) => Y14)) => Y14))) => Y13) => (((!! @ $o @ (^[Y14 : $o]: (((~ (c_In @ c_Empty @ Y11)) => (((X1 @ Y1) = Y12) => Y14)) => Y14))) => Y13) => Y13)))))))) = Y8) => Y10)) => Y10))) => Y9) => Y9))))))))))))) => ((!! @ $o @ (^[Y6 : $o]: ((((!! @ $i @ (^[Y7 : $i]: ((c_In @ Y7 @ (c_Union @ (c_Repl @ sF1 @ (^[Y8 : $i]: (c_Eps_i @ (^[Y9 : $i]: (!! @ $o @ (^[Y10 : $o]: (((!! @ $o @ (^[Y11 : $o]: (((c_In @ c_Empty @ Y8) => (((X1 @ Y1) = Y9) => Y11)) => Y11))) => Y10) => (((!! @ $o @ (^[Y11 : $o]: (((~ (c_In @ c_Empty @ Y8)) => (((c_Repl @ sF1 @ (^[Y12 : $i]: (c_Eps_i @ (^[Y13 : $i]: (!! @ $o @ (^[Y14 : $o]: (((!! @ $o @ (^[Y15 : $o]: (((c_In @ c_Empty @ Y12) => (((X1 @ Y1) = Y13) => Y15)) => Y15))) => Y14) => (((!! @ $o @ (^[Y15 : $o]: (((~ (c_In @ c_Empty @ Y12)) => (((X1 @ Y1) = Y13) => Y15)) => Y15))) => Y14) => Y14)))))))) = Y9) => Y11)) => Y11))) => Y10) => Y10)))))))))) => (c_In @ Y7 @ Y4)))) => $false) => ((?? @ $i @ (^[Y7 : $i]: (!! @ $o @ (^[Y8 : $o]: (((c_In @ Y7 @ Y4) => (((!! @ $i @ (^[Y9 : $i]: ((c_In @ Y9 @ Y4) => (c_In @ Y9 @ (c_Power @ Y7))))) => $false) => Y8)) => Y8))))) => Y6)) => Y6))) => Y5)) => Y5))))) => $false) => Y3)) => Y3))) => Y2)) => Y2)))))))))) => (?? @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: (((?? @ $i @ (^[Y2 : $i]: (!! @ $o @ (^[Y3 : $o]: (((!! @ $i @ (^[Y4 : $i]: ((c_In @ Y4 @ Y2) => (c_In @ Y4 @ Y0)))) => ((((X1 @ Y0) = Y0) => (?? @ $i @ (^[Y4 : $i]: (!! @ $o @ (^[Y5 : $o]: (((!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ Y4) => (c_In @ Y6 @ Y0)))) => ((~ (X2 @ (c_Union @ (c_Repl @ Y2 @ (^[Y6 : $i]: (c_Repl @ sF7 @ (^[Y7 : $i]: (c_Union @ (c_Repl @ sF1 @ (^[Y8 : $i]: (c_Eps_i @ (^[Y9 : $i]: (!! @ $o @ (^[Y10 : $o]: (((!! @ $o @ (^[Y11 : $o]: (((c_In @ c_Empty @ Y8) => (((c_Repl @ Y6 @ (^[Y12 : $i]: (c_Repl @ Y12 @ (^[Y13 : $i]: (c_Eps_i @ (^[Y14 : $i]: (!! @ ($i > $i > $o) @ (^[Y15 : $i > $i > $o]: ((!! @ ($i > $i) @ (^[Y16 : $i > $i]: (!! @ $i @ (^[Y17 : $i]: ((!! @ $i @ (^[Y18 : $i]: ((c_In @ Y18 @ Y17) => (Y15 @ Y18 @ (Y16 @ Y18))))) => (Y15 @ Y17 @ (c_Union @ (c_Repl @ sF1 @ (^[Y18 : $i]: (c_Eps_i @ (^[Y19 : $i]: (!! @ $o @ (^[Y20 : $o]: (((!! @ $o @ (^[Y21 : $o]: (((c_In @ c_Empty @ Y18) => ((sF2 = Y19) => Y21)) => Y21))) => Y20) => (((!! @ $o @ (^[Y21 : $o]: (((~ (c_In @ c_Empty @ Y18)) => (((c_Repl @ Y17 @ Y16) = Y19) => Y21)) => Y21))) => Y20) => Y20))))))))))))))) => (Y15 @ Y13 @ Y14)))))))))) = Y9) => Y11)) => Y11))) => Y10) => (((!! @ $o @ (^[Y11 : $o]: (((~ (c_In @ c_Empty @ Y8)) => (((c_Repl @ Y7 @ (^[Y12 : $i]: (c_Eps_i @ (^[Y13 : $i]: (!! @ ($i > $i > $o) @ (^[Y14 : $i > $i > $o]: ((!! @ ($i > $i) @ (^[Y15 : $i > $i]: (!! @ $i @ (^[Y16 : $i]: ((!! @ $i @ (^[Y17 : $i]: ((c_In @ Y17 @ Y16) => (Y14 @ Y17 @ (Y15 @ Y17))))) => (Y14 @ Y16 @ (c_Union @ (c_Repl @ sF1 @ (^[Y17 : $i]: (c_Eps_i @ (^[Y18 : $i]: (!! @ $o @ (^[Y19 : $o]: (((!! @ $o @ (^[Y20 : $o]: (((c_In @ c_Empty @ Y17) => ((sF2 = Y18) => Y20)) => Y20))) => Y19) => (((!! @ $o @ (^[Y20 : $o]: (((~ (c_In @ c_Empty @ Y17)) => (((c_Repl @ Y16 @ Y15) = Y18) => Y20)) => Y20))) => Y19) => Y19))))))))))))))) => (Y14 @ Y12 @ Y13)))))))) = Y9) => Y11)) => Y11))) => Y10) => Y10)))))))))))))))) => Y5)) => Y5)))))) => Y3)) => Y3))))) => ((~ (?? @ $i @ (^[Y2 : $i]: (!! @ $o @ (^[Y3 : $o]: (((!! @ $o @ (^[Y4 : $o]: (((!! @ $i @ (^[Y5 : $i]: ((c_In @ Y5 @ Y2) => (!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ Y5) => (c_In @ Y6 @ Y2))))))) => ((!! @ $i @ (^[Y5 : $i]: ((c_In @ Y5 @ Y2) => (!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ Y5) => (!! @ $i @ (^[Y7 : $i]: ((c_In @ Y7 @ Y6) => (c_In @ Y7 @ Y5)))))))))) => Y4)) => Y4))) => ((!! @ $o @ (^[Y4 : $o]: (((!! @ $i @ (^[Y5 : $i]: ((c_In @ Y5 @ Y0) => (c_In @ Y5 @ (c_Union @ (c_Repl @ sF1 @ (^[Y6 : $i]: (c_Eps_i @ (^[Y7 : $i]: (!! @ $o @ (^[Y8 : $o]: (((!! @ $o @ (^[Y9 : $o]: (((c_In @ c_Empty @ Y6) => ((Y2 = Y7) => Y9)) => Y9))) => Y8) => (((!! @ $o @ (^[Y9 : $o]: (((~ (c_In @ c_Empty @ Y6)) => (((c_Repl @ Y2 @ (^[Y10 : $i]: (c_Union @ (c_Repl @ sF1 @ (^[Y11 : $i]: (c_Eps_i @ (^[Y12 : $i]: (!! @ $o @ (^[Y13 : $o]: (((!! @ $o @ (^[Y14 : $o]: (((c_In @ c_Empty @ Y11) => ((Y10 = Y12) => Y14)) => Y14))) => Y13) => (((!! @ $o @ (^[Y14 : $o]: (((~ (c_In @ c_Empty @ Y11)) => (((c_Repl @ sF1 @ (^[Y15 : $i]: (c_Eps_i @ (^[Y16 : $i]: (!! @ $o @ (^[Y17 : $o]: (((!! @ $o @ (^[Y18 : $o]: (((c_In @ c_Empty @ Y15) => ((sF9 = Y16) => Y18)) => Y18))) => Y17) => (((!! @ $o @ (^[Y18 : $o]: (((~ (c_In @ c_Empty @ Y15)) => ((sF9 = Y16) => Y18)) => Y18))) => Y17) => Y17)))))))) = Y12) => Y14)) => Y14))) => Y13) => Y13))))))))))) = Y7) => Y9)) => Y9))) => Y8) => Y8))))))))))))) => ((!! @ $i @ (^[Y5 : $i]: ((c_In @ Y5 @ Y2) => (!! @ $o @ (^[Y6 : $o]: (((!! @ $o @ (^[Y7 : $o]: (((c_In @ (c_Union @ (c_Repl @ sF1 @ (^[Y8 : $i]: (c_Eps_i @ (^[Y9 : $i]: (!! @ $o @ (^[Y10 : $o]: (((!! @ $o @ (^[Y11 : $o]: (((c_In @ c_Empty @ Y8) => ((Y5 = Y9) => Y11)) => Y11))) => Y10) => (((!! @ $o @ (^[Y11 : $o]: (((~ (c_In @ c_Empty @ Y8)) => (((c_Repl @ sF1 @ (^[Y12 : $i]: (c_Eps_i @ (^[Y13 : $i]: (!! @ $o @ (^[Y14 : $o]: (((!! @ $o @ (^[Y15 : $o]: (((c_In @ c_Empty @ Y12) => ((sF9 = Y13) => Y15)) => Y15))) => Y14) => (((!! @ $o @ (^[Y15 : $o]: (((~ (c_In @ c_Empty @ Y12)) => ((sF9 = Y13) => Y15)) => Y15))) => Y14) => Y14)))))))) = Y9) => Y11)) => Y11))) => Y10) => Y10))))))))) @ Y0) => ((~ (c_In @ Y5 @ Y0)) => Y7)) => Y7))) => Y6) => (((!! @ $o @ (^[Y7 : $o]: (((~ (c_In @ (c_Union @ (c_Repl @ sF1 @ (^[Y8 : $i]: (c_Eps_i @ (^[Y9 : $i]: (!! @ $o @ (^[Y10 : $o]: (((!! @ $o @ (^[Y11 : $o]: (((c_In @ c_Empty @ Y8) => ((Y5 = Y9) => Y11)) => Y11))) => Y10) => (((!! @ $o @ (^[Y11 : $o]: (((~ (c_In @ c_Empty @ Y8)) => (((c_Repl @ sF1 @ (^[Y12 : $i]: (c_Eps_i @ (^[Y13 : $i]: (!! @ $o @ (^[Y14 : $o]: (((!! @ $o @ (^[Y15 : $o]: (((c_In @ c_Empty @ Y12) => ((sF9 = Y13) => Y15)) => Y15))) => Y14) => (((!! @ $o @ (^[Y15 : $o]: (((~ (c_In @ c_Empty @ Y12)) => ((sF9 = Y13) => Y15)) => Y15))) => Y14) => Y14)))))))) = Y9) => Y11)) => Y11))) => Y10) => Y10))))))))) @ Y0)) => ((c_In @ Y5 @ Y0) => Y7)) => Y7))) => Y6) => Y6))))))) => Y4)) => Y4))) => Y3)) => Y3)))))) => Y1)) => Y1)))))) => ((~ (X2 @ (X1 @ (X1 @ (X1 @ sF11))))) => X3)) => X3)))) )),
% 9.27/1.88 inference(boolean_simplification,[],[f613])).
% 9.27/1.88 thf(f615,plain,(
% 9.27/1.88 ( ! [X2 : ($i > $o),X3 : $o,X1 : ($i > $i)] : (($true = ((((((X2 @ (X1 @ (c_Eps_i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: (((!! @ $o @ (^[Y2 : $o]: (((?? @ $i @ (^[Y3 : $i]: (!! @ $o @ (^[Y4 : $o]: (((c_In @ Y3 @ (X1 @ sF0)) => ((c_In @ Y3 @ (X1 @ sF4)) => Y4)) => Y4))))) => (((c_Repl @ (X1 @ sF0) @ (^[Y3 : $i]: (c_Eps_i @ (^[Y4 : $i]: (!! @ $o @ (^[Y5 : $o]: (((!! @ $o @ (^[Y6 : $o]: (((c_In @ Y3 @ (X1 @ sF4)) => ((Y3 = Y4) => Y6)) => Y6))) => Y5) => (((!! @ $o @ (^[Y6 : $o]: ((((c_In @ Y3 @ (X1 @ sF4)) => $false) => (((c_Eps_i @ (^[Y7 : $i]: (!! @ $o @ (^[Y8 : $o]: (((c_In @ Y7 @ (X1 @ sF0)) => ((c_In @ Y7 @ (X1 @ sF4)) => Y8)) => Y8))))) = Y4) => Y6)) => Y6))) => Y5) => Y5)))))))) = Y0) => Y2)) => Y2))) => Y1) => (((!! @ $o @ (^[Y2 : $o]: ((((?? @ $i @ (^[Y3 : $i]: (!! @ $o @ (^[Y4 : $o]: (((c_In @ Y3 @ (X1 @ sF0)) => ((c_In @ Y3 @ (X1 @ sF4)) => Y4)) => Y4))))) => $false) => ((c_Empty = Y0) => Y2)) => Y2))) => Y1) => Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: ((c_In @ Y0 @ (X1 @ c_Empty)) => (!! @ $i @ (^[Y1 : $i]: ((c_In @ Y1 @ Y0) => (c_In @ Y1 @ (X1 @ c_Empty)))))))) => (!! @ $i @ (^[Y0 : $i]: ((c_In @ Y0 @ c_Empty) => (?? @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: (((!! @ $i @ (^[Y3 : $i]: ((c_In @ Y3 @ Y1) => (c_In @ Y3 @ Y0)))) => ((!! @ $o @ (^[Y3 : $o]: (((?? @ $i @ (^[Y4 : $i]: (!! @ $o @ (^[Y5 : $o]: (((c_In @ Y4 @ (c_Union @ (c_Repl @ sF1 @ (^[Y6 : $i]: (c_Eps_i @ (^[Y7 : $i]: (!! @ $o @ (^[Y8 : $o]: (((!! @ $o @ (^[Y9 : $o]: (((c_In @ c_Empty @ Y6) => (((X1 @ Y1) = Y7) => Y9)) => Y9))) => Y8) => (((!! @ $o @ (^[Y9 : $o]: (((~ (c_In @ c_Empty @ Y6)) => (((c_Repl @ sF1 @ (^[Y10 : $i]: (c_Eps_i @ (^[Y11 : $i]: (!! @ $o @ (^[Y12 : $o]: (((!! @ $o @ (^[Y13 : $o]: (((c_In @ c_Empty @ Y10) => (((X1 @ Y1) = Y11) => Y13)) => Y13))) => Y12) => (((!! @ $o @ (^[Y13 : $o]: (((~ (c_In @ c_Empty @ Y10)) => (((X1 @ Y1) = Y11) => Y13)) => Y13))) => Y12) => Y12)))))))) = Y7) => Y9)) => Y9))) => Y8) => Y8)))))))))) => (((!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ (c_Union @ (c_Repl @ sF1 @ (^[Y7 : $i]: (c_Eps_i @ (^[Y8 : $i]: (!! @ $o @ (^[Y9 : $o]: (((!! @ $o @ (^[Y10 : $o]: (((c_In @ c_Empty @ Y7) => (((X1 @ Y1) = Y8) => Y10)) => Y10))) => Y9) => (((!! @ $o @ (^[Y10 : $o]: (((~ (c_In @ c_Empty @ Y7)) => (((c_Repl @ sF1 @ (^[Y11 : $i]: (c_Eps_i @ (^[Y12 : $i]: (!! @ $o @ (^[Y13 : $o]: (((!! @ $o @ (^[Y14 : $o]: (((c_In @ c_Empty @ Y11) => (((X1 @ Y1) = Y12) => Y14)) => Y14))) => Y13) => (((!! @ $o @ (^[Y14 : $o]: (((~ (c_In @ c_Empty @ Y11)) => (((X1 @ Y1) = Y12) => Y14)) => Y14))) => Y13) => Y13)))))))) = Y8) => Y10)) => Y10))) => Y9) => Y9)))))))))) => (c_In @ Y6 @ (c_Power @ Y4))))) => $false) => Y5)) => Y5))))) => ((~ (?? @ $i @ (^[Y4 : $i]: (!! @ $o @ (^[Y5 : $o]: (((!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ Y4) => (c_In @ Y6 @ (c_Union @ (c_Repl @ sF1 @ (^[Y7 : $i]: (c_Eps_i @ (^[Y8 : $i]: (!! @ $o @ (^[Y9 : $o]: (((!! @ $o @ (^[Y10 : $o]: (((c_In @ c_Empty @ Y7) => (((X1 @ Y1) = Y8) => Y10)) => Y10))) => Y9) => (((!! @ $o @ (^[Y10 : $o]: (((~ (c_In @ c_Empty @ Y7)) => (((c_Repl @ sF1 @ (^[Y11 : $i]: (c_Eps_i @ (^[Y12 : $i]: (!! @ $o @ (^[Y13 : $o]: (((!! @ $o @ (^[Y14 : $o]: (((c_In @ c_Empty @ Y11) => (((X1 @ Y1) = Y12) => Y14)) => Y14))) => Y13) => (((!! @ $o @ (^[Y14 : $o]: (((~ (c_In @ c_Empty @ Y11)) => (((X1 @ Y1) = Y12) => Y14)) => Y14))) => Y13) => Y13)))))))) = Y8) => Y10)) => Y10))) => Y9) => Y9))))))))))))) => ((!! @ $o @ (^[Y6 : $o]: ((((!! @ $i @ (^[Y7 : $i]: ((c_In @ Y7 @ (c_Union @ (c_Repl @ sF1 @ (^[Y8 : $i]: (c_Eps_i @ (^[Y9 : $i]: (!! @ $o @ (^[Y10 : $o]: (((!! @ $o @ (^[Y11 : $o]: (((c_In @ c_Empty @ Y8) => (((X1 @ Y1) = Y9) => Y11)) => Y11))) => Y10) => (((!! @ $o @ (^[Y11 : $o]: (((~ (c_In @ c_Empty @ Y8)) => (((c_Repl @ sF1 @ (^[Y12 : $i]: (c_Eps_i @ (^[Y13 : $i]: (!! @ $o @ (^[Y14 : $o]: (((!! @ $o @ (^[Y15 : $o]: (((c_In @ c_Empty @ Y12) => (((X1 @ Y1) = Y13) => Y15)) => Y15))) => Y14) => (((!! @ $o @ (^[Y15 : $o]: (((~ (c_In @ c_Empty @ Y12)) => (((X1 @ Y1) = Y13) => Y15)) => Y15))) => Y14) => Y14)))))))) = Y9) => Y11)) => Y11))) => Y10) => Y10)))))))))) => (c_In @ Y7 @ Y4)))) => $false) => ((?? @ $i @ (^[Y7 : $i]: (!! @ $o @ (^[Y8 : $o]: (((c_In @ Y7 @ Y4) => (((!! @ $i @ (^[Y9 : $i]: ((c_In @ Y9 @ Y4) => (c_In @ Y9 @ (c_Power @ Y7))))) => $false) => Y8)) => Y8))))) => Y6)) => Y6))) => Y5)) => Y5)))))) => Y3)) => Y3))) => Y2)) => Y2)))))))))) => (?? @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: (((?? @ $i @ (^[Y2 : $i]: (!! @ $o @ (^[Y3 : $o]: (((!! @ $i @ (^[Y4 : $i]: ((c_In @ Y4 @ Y2) => (c_In @ Y4 @ Y0)))) => ((((X1 @ Y0) = Y0) => (?? @ $i @ (^[Y4 : $i]: (!! @ $o @ (^[Y5 : $o]: (((!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ Y4) => (c_In @ Y6 @ Y0)))) => ((~ (X2 @ (c_Union @ (c_Repl @ Y2 @ (^[Y6 : $i]: (c_Repl @ sF7 @ (^[Y7 : $i]: (c_Union @ (c_Repl @ sF1 @ (^[Y8 : $i]: (c_Eps_i @ (^[Y9 : $i]: (!! @ $o @ (^[Y10 : $o]: (((!! @ $o @ (^[Y11 : $o]: (((c_In @ c_Empty @ Y8) => (((c_Repl @ Y6 @ (^[Y12 : $i]: (c_Repl @ Y12 @ (^[Y13 : $i]: (c_Eps_i @ (^[Y14 : $i]: (!! @ ($i > $i > $o) @ (^[Y15 : $i > $i > $o]: ((!! @ ($i > $i) @ (^[Y16 : $i > $i]: (!! @ $i @ (^[Y17 : $i]: ((!! @ $i @ (^[Y18 : $i]: ((c_In @ Y18 @ Y17) => (Y15 @ Y18 @ (Y16 @ Y18))))) => (Y15 @ Y17 @ (c_Union @ (c_Repl @ sF1 @ (^[Y18 : $i]: (c_Eps_i @ (^[Y19 : $i]: (!! @ $o @ (^[Y20 : $o]: (((!! @ $o @ (^[Y21 : $o]: (((c_In @ c_Empty @ Y18) => ((sF2 = Y19) => Y21)) => Y21))) => Y20) => (((!! @ $o @ (^[Y21 : $o]: (((~ (c_In @ c_Empty @ Y18)) => (((c_Repl @ Y17 @ Y16) = Y19) => Y21)) => Y21))) => Y20) => Y20))))))))))))))) => (Y15 @ Y13 @ Y14)))))))))) = Y9) => Y11)) => Y11))) => Y10) => (((!! @ $o @ (^[Y11 : $o]: (((~ (c_In @ c_Empty @ Y8)) => (((c_Repl @ Y7 @ (^[Y12 : $i]: (c_Eps_i @ (^[Y13 : $i]: (!! @ ($i > $i > $o) @ (^[Y14 : $i > $i > $o]: ((!! @ ($i > $i) @ (^[Y15 : $i > $i]: (!! @ $i @ (^[Y16 : $i]: ((!! @ $i @ (^[Y17 : $i]: ((c_In @ Y17 @ Y16) => (Y14 @ Y17 @ (Y15 @ Y17))))) => (Y14 @ Y16 @ (c_Union @ (c_Repl @ sF1 @ (^[Y17 : $i]: (c_Eps_i @ (^[Y18 : $i]: (!! @ $o @ (^[Y19 : $o]: (((!! @ $o @ (^[Y20 : $o]: (((c_In @ c_Empty @ Y17) => ((sF2 = Y18) => Y20)) => Y20))) => Y19) => (((!! @ $o @ (^[Y20 : $o]: (((~ (c_In @ c_Empty @ Y17)) => (((c_Repl @ Y16 @ Y15) = Y18) => Y20)) => Y20))) => Y19) => Y19))))))))))))))) => (Y14 @ Y12 @ Y13)))))))) = Y9) => Y11)) => Y11))) => Y10) => Y10)))))))))))))))) => Y5)) => Y5)))))) => Y3)) => Y3))))) => ((~ (?? @ $i @ (^[Y2 : $i]: (!! @ $o @ (^[Y3 : $o]: (((!! @ $o @ (^[Y4 : $o]: (((!! @ $i @ (^[Y5 : $i]: ((c_In @ Y5 @ Y2) => (!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ Y5) => (c_In @ Y6 @ Y2))))))) => ((!! @ $i @ (^[Y5 : $i]: ((c_In @ Y5 @ Y2) => (!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ Y5) => (!! @ $i @ (^[Y7 : $i]: ((c_In @ Y7 @ Y6) => (c_In @ Y7 @ Y5)))))))))) => Y4)) => Y4))) => ((!! @ $o @ (^[Y4 : $o]: (((!! @ $i @ (^[Y5 : $i]: ((c_In @ Y5 @ Y0) => (c_In @ Y5 @ (c_Union @ (c_Repl @ sF1 @ (^[Y6 : $i]: (c_Eps_i @ (^[Y7 : $i]: (!! @ $o @ (^[Y8 : $o]: (((!! @ $o @ (^[Y9 : $o]: (((c_In @ c_Empty @ Y6) => ((Y2 = Y7) => Y9)) => Y9))) => Y8) => (((!! @ $o @ (^[Y9 : $o]: (((~ (c_In @ c_Empty @ Y6)) => (((c_Repl @ Y2 @ (^[Y10 : $i]: (c_Union @ (c_Repl @ sF1 @ (^[Y11 : $i]: (c_Eps_i @ (^[Y12 : $i]: (!! @ $o @ (^[Y13 : $o]: (((!! @ $o @ (^[Y14 : $o]: (((c_In @ c_Empty @ Y11) => ((Y10 = Y12) => Y14)) => Y14))) => Y13) => (((!! @ $o @ (^[Y14 : $o]: (((~ (c_In @ c_Empty @ Y11)) => (((c_Repl @ sF1 @ (^[Y15 : $i]: (c_Eps_i @ (^[Y16 : $i]: (!! @ $o @ (^[Y17 : $o]: (((!! @ $o @ (^[Y18 : $o]: (((c_In @ c_Empty @ Y15) => ((sF9 = Y16) => Y18)) => Y18))) => Y17) => (((!! @ $o @ (^[Y18 : $o]: (((~ (c_In @ c_Empty @ Y15)) => ((sF9 = Y16) => Y18)) => Y18))) => Y17) => Y17)))))))) = Y12) => Y14)) => Y14))) => Y13) => Y13))))))))))) = Y7) => Y9)) => Y9))) => Y8) => Y8))))))))))))) => ((!! @ $i @ (^[Y5 : $i]: ((c_In @ Y5 @ Y2) => (!! @ $o @ (^[Y6 : $o]: (((!! @ $o @ (^[Y7 : $o]: (((c_In @ (c_Union @ (c_Repl @ sF1 @ (^[Y8 : $i]: (c_Eps_i @ (^[Y9 : $i]: (!! @ $o @ (^[Y10 : $o]: (((!! @ $o @ (^[Y11 : $o]: (((c_In @ c_Empty @ Y8) => ((Y5 = Y9) => Y11)) => Y11))) => Y10) => (((!! @ $o @ (^[Y11 : $o]: (((~ (c_In @ c_Empty @ Y8)) => (((c_Repl @ sF1 @ (^[Y12 : $i]: (c_Eps_i @ (^[Y13 : $i]: (!! @ $o @ (^[Y14 : $o]: (((!! @ $o @ (^[Y15 : $o]: (((c_In @ c_Empty @ Y12) => ((sF9 = Y13) => Y15)) => Y15))) => Y14) => (((!! @ $o @ (^[Y15 : $o]: (((~ (c_In @ c_Empty @ Y12)) => ((sF9 = Y13) => Y15)) => Y15))) => Y14) => Y14)))))))) = Y9) => Y11)) => Y11))) => Y10) => Y10))))))))) @ Y0) => ((~ (c_In @ Y5 @ Y0)) => Y7)) => Y7))) => Y6) => (((!! @ $o @ (^[Y7 : $o]: (((~ (c_In @ (c_Union @ (c_Repl @ sF1 @ (^[Y8 : $i]: (c_Eps_i @ (^[Y9 : $i]: (!! @ $o @ (^[Y10 : $o]: (((!! @ $o @ (^[Y11 : $o]: (((c_In @ c_Empty @ Y8) => ((Y5 = Y9) => Y11)) => Y11))) => Y10) => (((!! @ $o @ (^[Y11 : $o]: (((~ (c_In @ c_Empty @ Y8)) => (((c_Repl @ sF1 @ (^[Y12 : $i]: (c_Eps_i @ (^[Y13 : $i]: (!! @ $o @ (^[Y14 : $o]: (((!! @ $o @ (^[Y15 : $o]: (((c_In @ c_Empty @ Y12) => ((sF9 = Y13) => Y15)) => Y15))) => Y14) => (((!! @ $o @ (^[Y15 : $o]: (((~ (c_In @ c_Empty @ Y12)) => ((sF9 = Y13) => Y15)) => Y15))) => Y14) => Y14)))))))) = Y9) => Y11)) => Y11))) => Y10) => Y10))))))))) @ Y0)) => ((c_In @ Y5 @ Y0) => Y7)) => Y7))) => Y6) => Y6))))))) => Y4)) => Y4))) => Y3)) => Y3)))))) => Y1)) => Y1)))))) => ((~ (X2 @ (X1 @ (X1 @ (X1 @ sF11))))) => X3)) => X3)))) )),
% 9.27/1.88 inference(boolean_simplification,[],[f614])).
% 9.27/1.88 thf(f616,plain,(
% 9.27/1.88 ( ! [X2 : ($i > $o),X3 : $o,X1 : ($i > $i)] : (($true = ((((((X2 @ (X1 @ (c_Eps_i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: (((!! @ $o @ (^[Y2 : $o]: (((?? @ $i @ (^[Y3 : $i]: (!! @ $o @ (^[Y4 : $o]: (((c_In @ Y3 @ (X1 @ sF0)) => ((c_In @ Y3 @ (X1 @ sF4)) => Y4)) => Y4))))) => (((c_Repl @ (X1 @ sF0) @ (^[Y3 : $i]: (c_Eps_i @ (^[Y4 : $i]: (!! @ $o @ (^[Y5 : $o]: (((!! @ $o @ (^[Y6 : $o]: (((c_In @ Y3 @ (X1 @ sF4)) => ((Y3 = Y4) => Y6)) => Y6))) => Y5) => (((!! @ $o @ (^[Y6 : $o]: ((((c_In @ Y3 @ (X1 @ sF4)) => $false) => (((c_Eps_i @ (^[Y7 : $i]: (!! @ $o @ (^[Y8 : $o]: (((c_In @ Y7 @ (X1 @ sF0)) => ((c_In @ Y7 @ (X1 @ sF4)) => Y8)) => Y8))))) = Y4) => Y6)) => Y6))) => Y5) => Y5)))))))) = Y0) => Y2)) => Y2))) => Y1) => (((!! @ $o @ (^[Y2 : $o]: ((((?? @ $i @ (^[Y3 : $i]: (!! @ $o @ (^[Y4 : $o]: (((c_In @ Y3 @ (X1 @ sF0)) => ((c_In @ Y3 @ (X1 @ sF4)) => Y4)) => Y4))))) => $false) => ((c_Empty = Y0) => Y2)) => Y2))) => Y1) => Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: ((c_In @ Y0 @ (X1 @ c_Empty)) => (!! @ $i @ (^[Y1 : $i]: ((c_In @ Y1 @ Y0) => (c_In @ Y1 @ (X1 @ c_Empty)))))))) => (!! @ $i @ (^[Y0 : $i]: ((c_In @ Y0 @ c_Empty) => (?? @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: (((!! @ $i @ (^[Y3 : $i]: ((c_In @ Y3 @ Y1) => (c_In @ Y3 @ Y0)))) => ((!! @ $o @ (^[Y3 : $o]: (((?? @ $i @ (^[Y4 : $i]: (!! @ $o @ (^[Y5 : $o]: (((c_In @ Y4 @ (c_Union @ (c_Repl @ sF1 @ (^[Y6 : $i]: (c_Eps_i @ (^[Y7 : $i]: (!! @ $o @ (^[Y8 : $o]: (((!! @ $o @ (^[Y9 : $o]: (((c_In @ c_Empty @ Y6) => (((X1 @ Y1) = Y7) => Y9)) => Y9))) => Y8) => (((!! @ $o @ (^[Y9 : $o]: (((~ (c_In @ c_Empty @ Y6)) => (((c_Repl @ sF1 @ (^[Y10 : $i]: (c_Eps_i @ (^[Y11 : $i]: (!! @ $o @ (^[Y12 : $o]: (((!! @ $o @ (^[Y13 : $o]: (((c_In @ c_Empty @ Y10) => (((X1 @ Y1) = Y11) => Y13)) => Y13))) => Y12) => (((!! @ $o @ (^[Y13 : $o]: (((~ (c_In @ c_Empty @ Y10)) => (((X1 @ Y1) = Y11) => Y13)) => Y13))) => Y12) => Y12)))))))) = Y7) => Y9)) => Y9))) => Y8) => Y8)))))))))) => (((!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ (c_Union @ (c_Repl @ sF1 @ (^[Y7 : $i]: (c_Eps_i @ (^[Y8 : $i]: (!! @ $o @ (^[Y9 : $o]: (((!! @ $o @ (^[Y10 : $o]: (((c_In @ c_Empty @ Y7) => (((X1 @ Y1) = Y8) => Y10)) => Y10))) => Y9) => (((!! @ $o @ (^[Y10 : $o]: (((~ (c_In @ c_Empty @ Y7)) => (((c_Repl @ sF1 @ (^[Y11 : $i]: (c_Eps_i @ (^[Y12 : $i]: (!! @ $o @ (^[Y13 : $o]: (((!! @ $o @ (^[Y14 : $o]: (((c_In @ c_Empty @ Y11) => (((X1 @ Y1) = Y12) => Y14)) => Y14))) => Y13) => (((!! @ $o @ (^[Y14 : $o]: (((~ (c_In @ c_Empty @ Y11)) => (((X1 @ Y1) = Y12) => Y14)) => Y14))) => Y13) => Y13)))))))) = Y8) => Y10)) => Y10))) => Y9) => Y9)))))))))) => (c_In @ Y6 @ (c_Power @ Y4))))) => $false) => Y5)) => Y5))))) => ((~ (?? @ $i @ (^[Y4 : $i]: (!! @ $o @ (^[Y5 : $o]: (((!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ Y4) => (c_In @ Y6 @ (c_Union @ (c_Repl @ sF1 @ (^[Y7 : $i]: (c_Eps_i @ (^[Y8 : $i]: (!! @ $o @ (^[Y9 : $o]: (((!! @ $o @ (^[Y10 : $o]: (((c_In @ c_Empty @ Y7) => (((X1 @ Y1) = Y8) => Y10)) => Y10))) => Y9) => (((!! @ $o @ (^[Y10 : $o]: (((~ (c_In @ c_Empty @ Y7)) => (((c_Repl @ sF1 @ (^[Y11 : $i]: (c_Eps_i @ (^[Y12 : $i]: (!! @ $o @ (^[Y13 : $o]: (((!! @ $o @ (^[Y14 : $o]: (((c_In @ c_Empty @ Y11) => (((X1 @ Y1) = Y12) => Y14)) => Y14))) => Y13) => (((!! @ $o @ (^[Y14 : $o]: (((~ (c_In @ c_Empty @ Y11)) => (((X1 @ Y1) = Y12) => Y14)) => Y14))) => Y13) => Y13)))))))) = Y8) => Y10)) => Y10))) => Y9) => Y9))))))))))))) => ((!! @ $o @ (^[Y6 : $o]: ((((!! @ $i @ (^[Y7 : $i]: ((c_In @ Y7 @ (c_Union @ (c_Repl @ sF1 @ (^[Y8 : $i]: (c_Eps_i @ (^[Y9 : $i]: (!! @ $o @ (^[Y10 : $o]: (((!! @ $o @ (^[Y11 : $o]: (((c_In @ c_Empty @ Y8) => (((X1 @ Y1) = Y9) => Y11)) => Y11))) => Y10) => (((!! @ $o @ (^[Y11 : $o]: (((~ (c_In @ c_Empty @ Y8)) => (((c_Repl @ sF1 @ (^[Y12 : $i]: (c_Eps_i @ (^[Y13 : $i]: (!! @ $o @ (^[Y14 : $o]: (((!! @ $o @ (^[Y15 : $o]: (((c_In @ c_Empty @ Y12) => (((X1 @ Y1) = Y13) => Y15)) => Y15))) => Y14) => (((!! @ $o @ (^[Y15 : $o]: (((~ (c_In @ c_Empty @ Y12)) => (((X1 @ Y1) = Y13) => Y15)) => Y15))) => Y14) => Y14)))))))) = Y9) => Y11)) => Y11))) => Y10) => Y10)))))))))) => (c_In @ Y7 @ Y4)))) => $false) => ((?? @ $i @ (^[Y7 : $i]: (!! @ $o @ (^[Y8 : $o]: (((c_In @ Y7 @ Y4) => ((~ (!! @ $i @ (^[Y9 : $i]: ((c_In @ Y9 @ Y4) => (c_In @ Y9 @ (c_Power @ Y7)))))) => Y8)) => Y8))))) => Y6)) => Y6))) => Y5)) => Y5)))))) => Y3)) => Y3))) => Y2)) => Y2)))))))))) => (?? @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: (((?? @ $i @ (^[Y2 : $i]: (!! @ $o @ (^[Y3 : $o]: (((!! @ $i @ (^[Y4 : $i]: ((c_In @ Y4 @ Y2) => (c_In @ Y4 @ Y0)))) => ((((X1 @ Y0) = Y0) => (?? @ $i @ (^[Y4 : $i]: (!! @ $o @ (^[Y5 : $o]: (((!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ Y4) => (c_In @ Y6 @ Y0)))) => ((~ (X2 @ (c_Union @ (c_Repl @ Y2 @ (^[Y6 : $i]: (c_Repl @ sF7 @ (^[Y7 : $i]: (c_Union @ (c_Repl @ sF1 @ (^[Y8 : $i]: (c_Eps_i @ (^[Y9 : $i]: (!! @ $o @ (^[Y10 : $o]: (((!! @ $o @ (^[Y11 : $o]: (((c_In @ c_Empty @ Y8) => (((c_Repl @ Y6 @ (^[Y12 : $i]: (c_Repl @ Y12 @ (^[Y13 : $i]: (c_Eps_i @ (^[Y14 : $i]: (!! @ ($i > $i > $o) @ (^[Y15 : $i > $i > $o]: ((!! @ ($i > $i) @ (^[Y16 : $i > $i]: (!! @ $i @ (^[Y17 : $i]: ((!! @ $i @ (^[Y18 : $i]: ((c_In @ Y18 @ Y17) => (Y15 @ Y18 @ (Y16 @ Y18))))) => (Y15 @ Y17 @ (c_Union @ (c_Repl @ sF1 @ (^[Y18 : $i]: (c_Eps_i @ (^[Y19 : $i]: (!! @ $o @ (^[Y20 : $o]: (((!! @ $o @ (^[Y21 : $o]: (((c_In @ c_Empty @ Y18) => ((sF2 = Y19) => Y21)) => Y21))) => Y20) => (((!! @ $o @ (^[Y21 : $o]: (((~ (c_In @ c_Empty @ Y18)) => (((c_Repl @ Y17 @ Y16) = Y19) => Y21)) => Y21))) => Y20) => Y20))))))))))))))) => (Y15 @ Y13 @ Y14)))))))))) = Y9) => Y11)) => Y11))) => Y10) => (((!! @ $o @ (^[Y11 : $o]: (((~ (c_In @ c_Empty @ Y8)) => (((c_Repl @ Y7 @ (^[Y12 : $i]: (c_Eps_i @ (^[Y13 : $i]: (!! @ ($i > $i > $o) @ (^[Y14 : $i > $i > $o]: ((!! @ ($i > $i) @ (^[Y15 : $i > $i]: (!! @ $i @ (^[Y16 : $i]: ((!! @ $i @ (^[Y17 : $i]: ((c_In @ Y17 @ Y16) => (Y14 @ Y17 @ (Y15 @ Y17))))) => (Y14 @ Y16 @ (c_Union @ (c_Repl @ sF1 @ (^[Y17 : $i]: (c_Eps_i @ (^[Y18 : $i]: (!! @ $o @ (^[Y19 : $o]: (((!! @ $o @ (^[Y20 : $o]: (((c_In @ c_Empty @ Y17) => ((sF2 = Y18) => Y20)) => Y20))) => Y19) => (((!! @ $o @ (^[Y20 : $o]: (((~ (c_In @ c_Empty @ Y17)) => (((c_Repl @ Y16 @ Y15) = Y18) => Y20)) => Y20))) => Y19) => Y19))))))))))))))) => (Y14 @ Y12 @ Y13)))))))) = Y9) => Y11)) => Y11))) => Y10) => Y10)))))))))))))))) => Y5)) => Y5)))))) => Y3)) => Y3))))) => ((~ (?? @ $i @ (^[Y2 : $i]: (!! @ $o @ (^[Y3 : $o]: (((!! @ $o @ (^[Y4 : $o]: (((!! @ $i @ (^[Y5 : $i]: ((c_In @ Y5 @ Y2) => (!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ Y5) => (c_In @ Y6 @ Y2))))))) => ((!! @ $i @ (^[Y5 : $i]: ((c_In @ Y5 @ Y2) => (!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ Y5) => (!! @ $i @ (^[Y7 : $i]: ((c_In @ Y7 @ Y6) => (c_In @ Y7 @ Y5)))))))))) => Y4)) => Y4))) => ((!! @ $o @ (^[Y4 : $o]: (((!! @ $i @ (^[Y5 : $i]: ((c_In @ Y5 @ Y0) => (c_In @ Y5 @ (c_Union @ (c_Repl @ sF1 @ (^[Y6 : $i]: (c_Eps_i @ (^[Y7 : $i]: (!! @ $o @ (^[Y8 : $o]: (((!! @ $o @ (^[Y9 : $o]: (((c_In @ c_Empty @ Y6) => ((Y2 = Y7) => Y9)) => Y9))) => Y8) => (((!! @ $o @ (^[Y9 : $o]: (((~ (c_In @ c_Empty @ Y6)) => (((c_Repl @ Y2 @ (^[Y10 : $i]: (c_Union @ (c_Repl @ sF1 @ (^[Y11 : $i]: (c_Eps_i @ (^[Y12 : $i]: (!! @ $o @ (^[Y13 : $o]: (((!! @ $o @ (^[Y14 : $o]: (((c_In @ c_Empty @ Y11) => ((Y10 = Y12) => Y14)) => Y14))) => Y13) => (((!! @ $o @ (^[Y14 : $o]: (((~ (c_In @ c_Empty @ Y11)) => (((c_Repl @ sF1 @ (^[Y15 : $i]: (c_Eps_i @ (^[Y16 : $i]: (!! @ $o @ (^[Y17 : $o]: (((!! @ $o @ (^[Y18 : $o]: (((c_In @ c_Empty @ Y15) => ((sF9 = Y16) => Y18)) => Y18))) => Y17) => (((!! @ $o @ (^[Y18 : $o]: (((~ (c_In @ c_Empty @ Y15)) => ((sF9 = Y16) => Y18)) => Y18))) => Y17) => Y17)))))))) = Y12) => Y14)) => Y14))) => Y13) => Y13))))))))))) = Y7) => Y9)) => Y9))) => Y8) => Y8))))))))))))) => ((!! @ $i @ (^[Y5 : $i]: ((c_In @ Y5 @ Y2) => (!! @ $o @ (^[Y6 : $o]: (((!! @ $o @ (^[Y7 : $o]: (((c_In @ (c_Union @ (c_Repl @ sF1 @ (^[Y8 : $i]: (c_Eps_i @ (^[Y9 : $i]: (!! @ $o @ (^[Y10 : $o]: (((!! @ $o @ (^[Y11 : $o]: (((c_In @ c_Empty @ Y8) => ((Y5 = Y9) => Y11)) => Y11))) => Y10) => (((!! @ $o @ (^[Y11 : $o]: (((~ (c_In @ c_Empty @ Y8)) => (((c_Repl @ sF1 @ (^[Y12 : $i]: (c_Eps_i @ (^[Y13 : $i]: (!! @ $o @ (^[Y14 : $o]: (((!! @ $o @ (^[Y15 : $o]: (((c_In @ c_Empty @ Y12) => ((sF9 = Y13) => Y15)) => Y15))) => Y14) => (((!! @ $o @ (^[Y15 : $o]: (((~ (c_In @ c_Empty @ Y12)) => ((sF9 = Y13) => Y15)) => Y15))) => Y14) => Y14)))))))) = Y9) => Y11)) => Y11))) => Y10) => Y10))))))))) @ Y0) => ((~ (c_In @ Y5 @ Y0)) => Y7)) => Y7))) => Y6) => (((!! @ $o @ (^[Y7 : $o]: (((~ (c_In @ (c_Union @ (c_Repl @ sF1 @ (^[Y8 : $i]: (c_Eps_i @ (^[Y9 : $i]: (!! @ $o @ (^[Y10 : $o]: (((!! @ $o @ (^[Y11 : $o]: (((c_In @ c_Empty @ Y8) => ((Y5 = Y9) => Y11)) => Y11))) => Y10) => (((!! @ $o @ (^[Y11 : $o]: (((~ (c_In @ c_Empty @ Y8)) => (((c_Repl @ sF1 @ (^[Y12 : $i]: (c_Eps_i @ (^[Y13 : $i]: (!! @ $o @ (^[Y14 : $o]: (((!! @ $o @ (^[Y15 : $o]: (((c_In @ c_Empty @ Y12) => ((sF9 = Y13) => Y15)) => Y15))) => Y14) => (((!! @ $o @ (^[Y15 : $o]: (((~ (c_In @ c_Empty @ Y12)) => ((sF9 = Y13) => Y15)) => Y15))) => Y14) => Y14)))))))) = Y9) => Y11)) => Y11))) => Y10) => Y10))))))))) @ Y0)) => ((c_In @ Y5 @ Y0) => Y7)) => Y7))) => Y6) => Y6))))))) => Y4)) => Y4))) => Y3)) => Y3)))))) => Y1)) => Y1)))))) => ((~ (X2 @ (X1 @ (X1 @ (X1 @ sF11))))) => X3)) => X3)))) )),
% 9.27/1.88 inference(boolean_simplification,[],[f615])).
% 9.27/1.88 thf(f617,plain,(
% 9.27/1.88 ( ! [X2 : ($i > $o),X3 : $o,X1 : ($i > $i)] : (($true = ((((((X2 @ (X1 @ (c_Eps_i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: (((!! @ $o @ (^[Y2 : $o]: (((?? @ $i @ (^[Y3 : $i]: (!! @ $o @ (^[Y4 : $o]: (((c_In @ Y3 @ (X1 @ sF0)) => ((c_In @ Y3 @ (X1 @ sF4)) => Y4)) => Y4))))) => (((c_Repl @ (X1 @ sF0) @ (^[Y3 : $i]: (c_Eps_i @ (^[Y4 : $i]: (!! @ $o @ (^[Y5 : $o]: (((!! @ $o @ (^[Y6 : $o]: (((c_In @ Y3 @ (X1 @ sF4)) => ((Y3 = Y4) => Y6)) => Y6))) => Y5) => (((!! @ $o @ (^[Y6 : $o]: ((((c_In @ Y3 @ (X1 @ sF4)) => $false) => (((c_Eps_i @ (^[Y7 : $i]: (!! @ $o @ (^[Y8 : $o]: (((c_In @ Y7 @ (X1 @ sF0)) => ((c_In @ Y7 @ (X1 @ sF4)) => Y8)) => Y8))))) = Y4) => Y6)) => Y6))) => Y5) => Y5)))))))) = Y0) => Y2)) => Y2))) => Y1) => (((!! @ $o @ (^[Y2 : $o]: ((((?? @ $i @ (^[Y3 : $i]: (!! @ $o @ (^[Y4 : $o]: (((c_In @ Y3 @ (X1 @ sF0)) => ((c_In @ Y3 @ (X1 @ sF4)) => Y4)) => Y4))))) => $false) => ((c_Empty = Y0) => Y2)) => Y2))) => Y1) => Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: ((c_In @ Y0 @ (X1 @ c_Empty)) => (!! @ $i @ (^[Y1 : $i]: ((c_In @ Y1 @ Y0) => (c_In @ Y1 @ (X1 @ c_Empty)))))))) => (!! @ $i @ (^[Y0 : $i]: ((c_In @ Y0 @ c_Empty) => (?? @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: (((!! @ $i @ (^[Y3 : $i]: ((c_In @ Y3 @ Y1) => (c_In @ Y3 @ Y0)))) => ((!! @ $o @ (^[Y3 : $o]: (((?? @ $i @ (^[Y4 : $i]: (!! @ $o @ (^[Y5 : $o]: (((c_In @ Y4 @ (c_Union @ (c_Repl @ sF1 @ (^[Y6 : $i]: (c_Eps_i @ (^[Y7 : $i]: (!! @ $o @ (^[Y8 : $o]: (((!! @ $o @ (^[Y9 : $o]: (((c_In @ c_Empty @ Y6) => (((X1 @ Y1) = Y7) => Y9)) => Y9))) => Y8) => (((!! @ $o @ (^[Y9 : $o]: (((~ (c_In @ c_Empty @ Y6)) => (((c_Repl @ sF1 @ (^[Y10 : $i]: (c_Eps_i @ (^[Y11 : $i]: (!! @ $o @ (^[Y12 : $o]: (((!! @ $o @ (^[Y13 : $o]: (((c_In @ c_Empty @ Y10) => (((X1 @ Y1) = Y11) => Y13)) => Y13))) => Y12) => (((!! @ $o @ (^[Y13 : $o]: (((~ (c_In @ c_Empty @ Y10)) => (((X1 @ Y1) = Y11) => Y13)) => Y13))) => Y12) => Y12)))))))) = Y7) => Y9)) => Y9))) => Y8) => Y8)))))))))) => (((!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ (c_Union @ (c_Repl @ sF1 @ (^[Y7 : $i]: (c_Eps_i @ (^[Y8 : $i]: (!! @ $o @ (^[Y9 : $o]: (((!! @ $o @ (^[Y10 : $o]: (((c_In @ c_Empty @ Y7) => (((X1 @ Y1) = Y8) => Y10)) => Y10))) => Y9) => (((!! @ $o @ (^[Y10 : $o]: (((~ (c_In @ c_Empty @ Y7)) => (((c_Repl @ sF1 @ (^[Y11 : $i]: (c_Eps_i @ (^[Y12 : $i]: (!! @ $o @ (^[Y13 : $o]: (((!! @ $o @ (^[Y14 : $o]: (((c_In @ c_Empty @ Y11) => (((X1 @ Y1) = Y12) => Y14)) => Y14))) => Y13) => (((!! @ $o @ (^[Y14 : $o]: (((~ (c_In @ c_Empty @ Y11)) => (((X1 @ Y1) = Y12) => Y14)) => Y14))) => Y13) => Y13)))))))) = Y8) => Y10)) => Y10))) => Y9) => Y9)))))))))) => (c_In @ Y6 @ (c_Power @ Y4))))) => $false) => Y5)) => Y5))))) => ((~ (?? @ $i @ (^[Y4 : $i]: (!! @ $o @ (^[Y5 : $o]: (((!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ Y4) => (c_In @ Y6 @ (c_Union @ (c_Repl @ sF1 @ (^[Y7 : $i]: (c_Eps_i @ (^[Y8 : $i]: (!! @ $o @ (^[Y9 : $o]: (((!! @ $o @ (^[Y10 : $o]: (((c_In @ c_Empty @ Y7) => (((X1 @ Y1) = Y8) => Y10)) => Y10))) => Y9) => (((!! @ $o @ (^[Y10 : $o]: (((~ (c_In @ c_Empty @ Y7)) => (((c_Repl @ sF1 @ (^[Y11 : $i]: (c_Eps_i @ (^[Y12 : $i]: (!! @ $o @ (^[Y13 : $o]: (((!! @ $o @ (^[Y14 : $o]: (((c_In @ c_Empty @ Y11) => (((X1 @ Y1) = Y12) => Y14)) => Y14))) => Y13) => (((!! @ $o @ (^[Y14 : $o]: (((~ (c_In @ c_Empty @ Y11)) => (((X1 @ Y1) = Y12) => Y14)) => Y14))) => Y13) => Y13)))))))) = Y8) => Y10)) => Y10))) => Y9) => Y9))))))))))))) => ((!! @ $o @ (^[Y6 : $o]: (((~ (!! @ $i @ (^[Y7 : $i]: ((c_In @ Y7 @ (c_Union @ (c_Repl @ sF1 @ (^[Y8 : $i]: (c_Eps_i @ (^[Y9 : $i]: (!! @ $o @ (^[Y10 : $o]: (((!! @ $o @ (^[Y11 : $o]: (((c_In @ c_Empty @ Y8) => (((X1 @ Y1) = Y9) => Y11)) => Y11))) => Y10) => (((!! @ $o @ (^[Y11 : $o]: (((~ (c_In @ c_Empty @ Y8)) => (((c_Repl @ sF1 @ (^[Y12 : $i]: (c_Eps_i @ (^[Y13 : $i]: (!! @ $o @ (^[Y14 : $o]: (((!! @ $o @ (^[Y15 : $o]: (((c_In @ c_Empty @ Y12) => (((X1 @ Y1) = Y13) => Y15)) => Y15))) => Y14) => (((!! @ $o @ (^[Y15 : $o]: (((~ (c_In @ c_Empty @ Y12)) => (((X1 @ Y1) = Y13) => Y15)) => Y15))) => Y14) => Y14)))))))) = Y9) => Y11)) => Y11))) => Y10) => Y10)))))))))) => (c_In @ Y7 @ Y4))))) => ((?? @ $i @ (^[Y7 : $i]: (!! @ $o @ (^[Y8 : $o]: (((c_In @ Y7 @ Y4) => ((~ (!! @ $i @ (^[Y9 : $i]: ((c_In @ Y9 @ Y4) => (c_In @ Y9 @ (c_Power @ Y7)))))) => Y8)) => Y8))))) => Y6)) => Y6))) => Y5)) => Y5)))))) => Y3)) => Y3))) => Y2)) => Y2)))))))))) => (?? @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: (((?? @ $i @ (^[Y2 : $i]: (!! @ $o @ (^[Y3 : $o]: (((!! @ $i @ (^[Y4 : $i]: ((c_In @ Y4 @ Y2) => (c_In @ Y4 @ Y0)))) => ((((X1 @ Y0) = Y0) => (?? @ $i @ (^[Y4 : $i]: (!! @ $o @ (^[Y5 : $o]: (((!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ Y4) => (c_In @ Y6 @ Y0)))) => ((~ (X2 @ (c_Union @ (c_Repl @ Y2 @ (^[Y6 : $i]: (c_Repl @ sF7 @ (^[Y7 : $i]: (c_Union @ (c_Repl @ sF1 @ (^[Y8 : $i]: (c_Eps_i @ (^[Y9 : $i]: (!! @ $o @ (^[Y10 : $o]: (((!! @ $o @ (^[Y11 : $o]: (((c_In @ c_Empty @ Y8) => (((c_Repl @ Y6 @ (^[Y12 : $i]: (c_Repl @ Y12 @ (^[Y13 : $i]: (c_Eps_i @ (^[Y14 : $i]: (!! @ ($i > $i > $o) @ (^[Y15 : $i > $i > $o]: ((!! @ ($i > $i) @ (^[Y16 : $i > $i]: (!! @ $i @ (^[Y17 : $i]: ((!! @ $i @ (^[Y18 : $i]: ((c_In @ Y18 @ Y17) => (Y15 @ Y18 @ (Y16 @ Y18))))) => (Y15 @ Y17 @ (c_Union @ (c_Repl @ sF1 @ (^[Y18 : $i]: (c_Eps_i @ (^[Y19 : $i]: (!! @ $o @ (^[Y20 : $o]: (((!! @ $o @ (^[Y21 : $o]: (((c_In @ c_Empty @ Y18) => ((sF2 = Y19) => Y21)) => Y21))) => Y20) => (((!! @ $o @ (^[Y21 : $o]: (((~ (c_In @ c_Empty @ Y18)) => (((c_Repl @ Y17 @ Y16) = Y19) => Y21)) => Y21))) => Y20) => Y20))))))))))))))) => (Y15 @ Y13 @ Y14)))))))))) = Y9) => Y11)) => Y11))) => Y10) => (((!! @ $o @ (^[Y11 : $o]: (((~ (c_In @ c_Empty @ Y8)) => (((c_Repl @ Y7 @ (^[Y12 : $i]: (c_Eps_i @ (^[Y13 : $i]: (!! @ ($i > $i > $o) @ (^[Y14 : $i > $i > $o]: ((!! @ ($i > $i) @ (^[Y15 : $i > $i]: (!! @ $i @ (^[Y16 : $i]: ((!! @ $i @ (^[Y17 : $i]: ((c_In @ Y17 @ Y16) => (Y14 @ Y17 @ (Y15 @ Y17))))) => (Y14 @ Y16 @ (c_Union @ (c_Repl @ sF1 @ (^[Y17 : $i]: (c_Eps_i @ (^[Y18 : $i]: (!! @ $o @ (^[Y19 : $o]: (((!! @ $o @ (^[Y20 : $o]: (((c_In @ c_Empty @ Y17) => ((sF2 = Y18) => Y20)) => Y20))) => Y19) => (((!! @ $o @ (^[Y20 : $o]: (((~ (c_In @ c_Empty @ Y17)) => (((c_Repl @ Y16 @ Y15) = Y18) => Y20)) => Y20))) => Y19) => Y19))))))))))))))) => (Y14 @ Y12 @ Y13)))))))) = Y9) => Y11)) => Y11))) => Y10) => Y10)))))))))))))))) => Y5)) => Y5)))))) => Y3)) => Y3))))) => ((~ (?? @ $i @ (^[Y2 : $i]: (!! @ $o @ (^[Y3 : $o]: (((!! @ $o @ (^[Y4 : $o]: (((!! @ $i @ (^[Y5 : $i]: ((c_In @ Y5 @ Y2) => (!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ Y5) => (c_In @ Y6 @ Y2))))))) => ((!! @ $i @ (^[Y5 : $i]: ((c_In @ Y5 @ Y2) => (!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ Y5) => (!! @ $i @ (^[Y7 : $i]: ((c_In @ Y7 @ Y6) => (c_In @ Y7 @ Y5)))))))))) => Y4)) => Y4))) => ((!! @ $o @ (^[Y4 : $o]: (((!! @ $i @ (^[Y5 : $i]: ((c_In @ Y5 @ Y0) => (c_In @ Y5 @ (c_Union @ (c_Repl @ sF1 @ (^[Y6 : $i]: (c_Eps_i @ (^[Y7 : $i]: (!! @ $o @ (^[Y8 : $o]: (((!! @ $o @ (^[Y9 : $o]: (((c_In @ c_Empty @ Y6) => ((Y2 = Y7) => Y9)) => Y9))) => Y8) => (((!! @ $o @ (^[Y9 : $o]: (((~ (c_In @ c_Empty @ Y6)) => (((c_Repl @ Y2 @ (^[Y10 : $i]: (c_Union @ (c_Repl @ sF1 @ (^[Y11 : $i]: (c_Eps_i @ (^[Y12 : $i]: (!! @ $o @ (^[Y13 : $o]: (((!! @ $o @ (^[Y14 : $o]: (((c_In @ c_Empty @ Y11) => ((Y10 = Y12) => Y14)) => Y14))) => Y13) => (((!! @ $o @ (^[Y14 : $o]: (((~ (c_In @ c_Empty @ Y11)) => (((c_Repl @ sF1 @ (^[Y15 : $i]: (c_Eps_i @ (^[Y16 : $i]: (!! @ $o @ (^[Y17 : $o]: (((!! @ $o @ (^[Y18 : $o]: (((c_In @ c_Empty @ Y15) => ((sF9 = Y16) => Y18)) => Y18))) => Y17) => (((!! @ $o @ (^[Y18 : $o]: (((~ (c_In @ c_Empty @ Y15)) => ((sF9 = Y16) => Y18)) => Y18))) => Y17) => Y17)))))))) = Y12) => Y14)) => Y14))) => Y13) => Y13))))))))))) = Y7) => Y9)) => Y9))) => Y8) => Y8))))))))))))) => ((!! @ $i @ (^[Y5 : $i]: ((c_In @ Y5 @ Y2) => (!! @ $o @ (^[Y6 : $o]: (((!! @ $o @ (^[Y7 : $o]: (((c_In @ (c_Union @ (c_Repl @ sF1 @ (^[Y8 : $i]: (c_Eps_i @ (^[Y9 : $i]: (!! @ $o @ (^[Y10 : $o]: (((!! @ $o @ (^[Y11 : $o]: (((c_In @ c_Empty @ Y8) => ((Y5 = Y9) => Y11)) => Y11))) => Y10) => (((!! @ $o @ (^[Y11 : $o]: (((~ (c_In @ c_Empty @ Y8)) => (((c_Repl @ sF1 @ (^[Y12 : $i]: (c_Eps_i @ (^[Y13 : $i]: (!! @ $o @ (^[Y14 : $o]: (((!! @ $o @ (^[Y15 : $o]: (((c_In @ c_Empty @ Y12) => ((sF9 = Y13) => Y15)) => Y15))) => Y14) => (((!! @ $o @ (^[Y15 : $o]: (((~ (c_In @ c_Empty @ Y12)) => ((sF9 = Y13) => Y15)) => Y15))) => Y14) => Y14)))))))) = Y9) => Y11)) => Y11))) => Y10) => Y10))))))))) @ Y0) => ((~ (c_In @ Y5 @ Y0)) => Y7)) => Y7))) => Y6) => (((!! @ $o @ (^[Y7 : $o]: (((~ (c_In @ (c_Union @ (c_Repl @ sF1 @ (^[Y8 : $i]: (c_Eps_i @ (^[Y9 : $i]: (!! @ $o @ (^[Y10 : $o]: (((!! @ $o @ (^[Y11 : $o]: (((c_In @ c_Empty @ Y8) => ((Y5 = Y9) => Y11)) => Y11))) => Y10) => (((!! @ $o @ (^[Y11 : $o]: (((~ (c_In @ c_Empty @ Y8)) => (((c_Repl @ sF1 @ (^[Y12 : $i]: (c_Eps_i @ (^[Y13 : $i]: (!! @ $o @ (^[Y14 : $o]: (((!! @ $o @ (^[Y15 : $o]: (((c_In @ c_Empty @ Y12) => ((sF9 = Y13) => Y15)) => Y15))) => Y14) => (((!! @ $o @ (^[Y15 : $o]: (((~ (c_In @ c_Empty @ Y12)) => ((sF9 = Y13) => Y15)) => Y15))) => Y14) => Y14)))))))) = Y9) => Y11)) => Y11))) => Y10) => Y10))))))))) @ Y0)) => ((c_In @ Y5 @ Y0) => Y7)) => Y7))) => Y6) => Y6))))))) => Y4)) => Y4))) => Y3)) => Y3)))))) => Y1)) => Y1)))))) => ((~ (X2 @ (X1 @ (X1 @ (X1 @ sF11))))) => X3)) => X3)))) )),
% 9.27/1.88 inference(boolean_simplification,[],[f616])).
% 9.27/1.88 thf(f618,plain,(
% 9.27/1.88 ( ! [X2 : ($i > $o),X3 : $o,X1 : ($i > $i)] : ((((((((X2 @ (X1 @ (c_Eps_i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: (((!! @ $o @ (^[Y2 : $o]: (((?? @ $i @ (^[Y3 : $i]: (!! @ $o @ (^[Y4 : $o]: (((c_In @ Y3 @ (X1 @ sF0)) => ((c_In @ Y3 @ (X1 @ sF4)) => Y4)) => Y4))))) => (((c_Repl @ (X1 @ sF0) @ (^[Y3 : $i]: (c_Eps_i @ (^[Y4 : $i]: (!! @ $o @ (^[Y5 : $o]: (((!! @ $o @ (^[Y6 : $o]: (((c_In @ Y3 @ (X1 @ sF4)) => ((Y3 = Y4) => Y6)) => Y6))) => Y5) => (((!! @ $o @ (^[Y6 : $o]: ((((c_In @ Y3 @ (X1 @ sF4)) => $false) => (((c_Eps_i @ (^[Y7 : $i]: (!! @ $o @ (^[Y8 : $o]: (((c_In @ Y7 @ (X1 @ sF0)) => ((c_In @ Y7 @ (X1 @ sF4)) => Y8)) => Y8))))) = Y4) => Y6)) => Y6))) => Y5) => Y5)))))))) = Y0) => Y2)) => Y2))) => Y1) => (((!! @ $o @ (^[Y2 : $o]: ((((?? @ $i @ (^[Y3 : $i]: (!! @ $o @ (^[Y4 : $o]: (((c_In @ Y3 @ (X1 @ sF0)) => ((c_In @ Y3 @ (X1 @ sF4)) => Y4)) => Y4))))) => $false) => ((c_Empty = Y0) => Y2)) => Y2))) => Y1) => Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: ((c_In @ Y0 @ (X1 @ c_Empty)) => (!! @ $i @ (^[Y1 : $i]: ((c_In @ Y1 @ Y0) => (c_In @ Y1 @ (X1 @ c_Empty)))))))) => (!! @ $i @ (^[Y0 : $i]: ((c_In @ Y0 @ c_Empty) => (?? @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: (((!! @ $i @ (^[Y3 : $i]: ((c_In @ Y3 @ Y1) => (c_In @ Y3 @ Y0)))) => ((!! @ $o @ (^[Y3 : $o]: (((?? @ $i @ (^[Y4 : $i]: (!! @ $o @ (^[Y5 : $o]: (((c_In @ Y4 @ (c_Union @ (c_Repl @ sF1 @ (^[Y6 : $i]: (c_Eps_i @ (^[Y7 : $i]: (!! @ $o @ (^[Y8 : $o]: (((!! @ $o @ (^[Y9 : $o]: (((c_In @ c_Empty @ Y6) => (((X1 @ Y1) = Y7) => Y9)) => Y9))) => Y8) => (((!! @ $o @ (^[Y9 : $o]: (((~ (c_In @ c_Empty @ Y6)) => (((c_Repl @ sF1 @ (^[Y10 : $i]: (c_Eps_i @ (^[Y11 : $i]: (!! @ $o @ (^[Y12 : $o]: (((!! @ $o @ (^[Y13 : $o]: (((c_In @ c_Empty @ Y10) => (((X1 @ Y1) = Y11) => Y13)) => Y13))) => Y12) => (((!! @ $o @ (^[Y13 : $o]: (((~ (c_In @ c_Empty @ Y10)) => (((X1 @ Y1) = Y11) => Y13)) => Y13))) => Y12) => Y12)))))))) = Y7) => Y9)) => Y9))) => Y8) => Y8)))))))))) => ((~ (!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ (c_Union @ (c_Repl @ sF1 @ (^[Y7 : $i]: (c_Eps_i @ (^[Y8 : $i]: (!! @ $o @ (^[Y9 : $o]: (((!! @ $o @ (^[Y10 : $o]: (((c_In @ c_Empty @ Y7) => (((X1 @ Y1) = Y8) => Y10)) => Y10))) => Y9) => (((!! @ $o @ (^[Y10 : $o]: (((~ (c_In @ c_Empty @ Y7)) => (((c_Repl @ sF1 @ (^[Y11 : $i]: (c_Eps_i @ (^[Y12 : $i]: (!! @ $o @ (^[Y13 : $o]: (((!! @ $o @ (^[Y14 : $o]: (((c_In @ c_Empty @ Y11) => (((X1 @ Y1) = Y12) => Y14)) => Y14))) => Y13) => (((!! @ $o @ (^[Y14 : $o]: (((~ (c_In @ c_Empty @ Y11)) => (((X1 @ Y1) = Y12) => Y14)) => Y14))) => Y13) => Y13)))))))) = Y8) => Y10)) => Y10))) => Y9) => Y9)))))))))) => (c_In @ Y6 @ (c_Power @ Y4)))))) => Y5)) => Y5))))) => ((~ (?? @ $i @ (^[Y4 : $i]: (!! @ $o @ (^[Y5 : $o]: (((!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ Y4) => (c_In @ Y6 @ (c_Union @ (c_Repl @ sF1 @ (^[Y7 : $i]: (c_Eps_i @ (^[Y8 : $i]: (!! @ $o @ (^[Y9 : $o]: (((!! @ $o @ (^[Y10 : $o]: (((c_In @ c_Empty @ Y7) => (((X1 @ Y1) = Y8) => Y10)) => Y10))) => Y9) => (((!! @ $o @ (^[Y10 : $o]: (((~ (c_In @ c_Empty @ Y7)) => (((c_Repl @ sF1 @ (^[Y11 : $i]: (c_Eps_i @ (^[Y12 : $i]: (!! @ $o @ (^[Y13 : $o]: (((!! @ $o @ (^[Y14 : $o]: (((c_In @ c_Empty @ Y11) => (((X1 @ Y1) = Y12) => Y14)) => Y14))) => Y13) => (((!! @ $o @ (^[Y14 : $o]: (((~ (c_In @ c_Empty @ Y11)) => (((X1 @ Y1) = Y12) => Y14)) => Y14))) => Y13) => Y13)))))))) = Y8) => Y10)) => Y10))) => Y9) => Y9))))))))))))) => ((!! @ $o @ (^[Y6 : $o]: (((~ (!! @ $i @ (^[Y7 : $i]: ((c_In @ Y7 @ (c_Union @ (c_Repl @ sF1 @ (^[Y8 : $i]: (c_Eps_i @ (^[Y9 : $i]: (!! @ $o @ (^[Y10 : $o]: (((!! @ $o @ (^[Y11 : $o]: (((c_In @ c_Empty @ Y8) => (((X1 @ Y1) = Y9) => Y11)) => Y11))) => Y10) => (((!! @ $o @ (^[Y11 : $o]: (((~ (c_In @ c_Empty @ Y8)) => (((c_Repl @ sF1 @ (^[Y12 : $i]: (c_Eps_i @ (^[Y13 : $i]: (!! @ $o @ (^[Y14 : $o]: (((!! @ $o @ (^[Y15 : $o]: (((c_In @ c_Empty @ Y12) => (((X1 @ Y1) = Y13) => Y15)) => Y15))) => Y14) => (((!! @ $o @ (^[Y15 : $o]: (((~ (c_In @ c_Empty @ Y12)) => (((X1 @ Y1) = Y13) => Y15)) => Y15))) => Y14) => Y14)))))))) = Y9) => Y11)) => Y11))) => Y10) => Y10)))))))))) => (c_In @ Y7 @ Y4))))) => ((?? @ $i @ (^[Y7 : $i]: (!! @ $o @ (^[Y8 : $o]: (((c_In @ Y7 @ Y4) => ((~ (!! @ $i @ (^[Y9 : $i]: ((c_In @ Y9 @ Y4) => (c_In @ Y9 @ (c_Power @ Y7)))))) => Y8)) => Y8))))) => Y6)) => Y6))) => Y5)) => Y5)))))) => Y3)) => Y3))) => Y2)) => Y2)))))))))) => (?? @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: (((?? @ $i @ (^[Y2 : $i]: (!! @ $o @ (^[Y3 : $o]: (((!! @ $i @ (^[Y4 : $i]: ((c_In @ Y4 @ Y2) => (c_In @ Y4 @ Y0)))) => ((((X1 @ Y0) = Y0) => (?? @ $i @ (^[Y4 : $i]: (!! @ $o @ (^[Y5 : $o]: (((!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ Y4) => (c_In @ Y6 @ Y0)))) => ((~ (X2 @ (c_Union @ (c_Repl @ Y2 @ (^[Y6 : $i]: (c_Repl @ sF7 @ (^[Y7 : $i]: (c_Union @ (c_Repl @ sF1 @ (^[Y8 : $i]: (c_Eps_i @ (^[Y9 : $i]: (!! @ $o @ (^[Y10 : $o]: (((!! @ $o @ (^[Y11 : $o]: (((c_In @ c_Empty @ Y8) => (((c_Repl @ Y6 @ (^[Y12 : $i]: (c_Repl @ Y12 @ (^[Y13 : $i]: (c_Eps_i @ (^[Y14 : $i]: (!! @ ($i > $i > $o) @ (^[Y15 : $i > $i > $o]: ((!! @ ($i > $i) @ (^[Y16 : $i > $i]: (!! @ $i @ (^[Y17 : $i]: ((!! @ $i @ (^[Y18 : $i]: ((c_In @ Y18 @ Y17) => (Y15 @ Y18 @ (Y16 @ Y18))))) => (Y15 @ Y17 @ (c_Union @ (c_Repl @ sF1 @ (^[Y18 : $i]: (c_Eps_i @ (^[Y19 : $i]: (!! @ $o @ (^[Y20 : $o]: (((!! @ $o @ (^[Y21 : $o]: (((c_In @ c_Empty @ Y18) => ((sF2 = Y19) => Y21)) => Y21))) => Y20) => (((!! @ $o @ (^[Y21 : $o]: (((~ (c_In @ c_Empty @ Y18)) => (((c_Repl @ Y17 @ Y16) = Y19) => Y21)) => Y21))) => Y20) => Y20))))))))))))))) => (Y15 @ Y13 @ Y14)))))))))) = Y9) => Y11)) => Y11))) => Y10) => (((!! @ $o @ (^[Y11 : $o]: (((~ (c_In @ c_Empty @ Y8)) => (((c_Repl @ Y7 @ (^[Y12 : $i]: (c_Eps_i @ (^[Y13 : $i]: (!! @ ($i > $i > $o) @ (^[Y14 : $i > $i > $o]: ((!! @ ($i > $i) @ (^[Y15 : $i > $i]: (!! @ $i @ (^[Y16 : $i]: ((!! @ $i @ (^[Y17 : $i]: ((c_In @ Y17 @ Y16) => (Y14 @ Y17 @ (Y15 @ Y17))))) => (Y14 @ Y16 @ (c_Union @ (c_Repl @ sF1 @ (^[Y17 : $i]: (c_Eps_i @ (^[Y18 : $i]: (!! @ $o @ (^[Y19 : $o]: (((!! @ $o @ (^[Y20 : $o]: (((c_In @ c_Empty @ Y17) => ((sF2 = Y18) => Y20)) => Y20))) => Y19) => (((!! @ $o @ (^[Y20 : $o]: (((~ (c_In @ c_Empty @ Y17)) => (((c_Repl @ Y16 @ Y15) = Y18) => Y20)) => Y20))) => Y19) => Y19))))))))))))))) => (Y14 @ Y12 @ Y13)))))))) = Y9) => Y11)) => Y11))) => Y10) => Y10)))))))))))))))) => Y5)) => Y5)))))) => Y3)) => Y3))))) => ((~ (?? @ $i @ (^[Y2 : $i]: (!! @ $o @ (^[Y3 : $o]: (((!! @ $o @ (^[Y4 : $o]: (((!! @ $i @ (^[Y5 : $i]: ((c_In @ Y5 @ Y2) => (!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ Y5) => (c_In @ Y6 @ Y2))))))) => ((!! @ $i @ (^[Y5 : $i]: ((c_In @ Y5 @ Y2) => (!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ Y5) => (!! @ $i @ (^[Y7 : $i]: ((c_In @ Y7 @ Y6) => (c_In @ Y7 @ Y5)))))))))) => Y4)) => Y4))) => ((!! @ $o @ (^[Y4 : $o]: (((!! @ $i @ (^[Y5 : $i]: ((c_In @ Y5 @ Y0) => (c_In @ Y5 @ (c_Union @ (c_Repl @ sF1 @ (^[Y6 : $i]: (c_Eps_i @ (^[Y7 : $i]: (!! @ $o @ (^[Y8 : $o]: (((!! @ $o @ (^[Y9 : $o]: (((c_In @ c_Empty @ Y6) => ((Y2 = Y7) => Y9)) => Y9))) => Y8) => (((!! @ $o @ (^[Y9 : $o]: (((~ (c_In @ c_Empty @ Y6)) => (((c_Repl @ Y2 @ (^[Y10 : $i]: (c_Union @ (c_Repl @ sF1 @ (^[Y11 : $i]: (c_Eps_i @ (^[Y12 : $i]: (!! @ $o @ (^[Y13 : $o]: (((!! @ $o @ (^[Y14 : $o]: (((c_In @ c_Empty @ Y11) => ((Y10 = Y12) => Y14)) => Y14))) => Y13) => (((!! @ $o @ (^[Y14 : $o]: (((~ (c_In @ c_Empty @ Y11)) => (((c_Repl @ sF1 @ (^[Y15 : $i]: (c_Eps_i @ (^[Y16 : $i]: (!! @ $o @ (^[Y17 : $o]: (((!! @ $o @ (^[Y18 : $o]: (((c_In @ c_Empty @ Y15) => ((sF9 = Y16) => Y18)) => Y18))) => Y17) => (((!! @ $o @ (^[Y18 : $o]: (((~ (c_In @ c_Empty @ Y15)) => ((sF9 = Y16) => Y18)) => Y18))) => Y17) => Y17)))))))) = Y12) => Y14)) => Y14))) => Y13) => Y13))))))))))) = Y7) => Y9)) => Y9))) => Y8) => Y8))))))))))))) => ((!! @ $i @ (^[Y5 : $i]: ((c_In @ Y5 @ Y2) => (!! @ $o @ (^[Y6 : $o]: (((!! @ $o @ (^[Y7 : $o]: (((c_In @ (c_Union @ (c_Repl @ sF1 @ (^[Y8 : $i]: (c_Eps_i @ (^[Y9 : $i]: (!! @ $o @ (^[Y10 : $o]: (((!! @ $o @ (^[Y11 : $o]: (((c_In @ c_Empty @ Y8) => ((Y5 = Y9) => Y11)) => Y11))) => Y10) => (((!! @ $o @ (^[Y11 : $o]: (((~ (c_In @ c_Empty @ Y8)) => (((c_Repl @ sF1 @ (^[Y12 : $i]: (c_Eps_i @ (^[Y13 : $i]: (!! @ $o @ (^[Y14 : $o]: (((!! @ $o @ (^[Y15 : $o]: (((c_In @ c_Empty @ Y12) => ((sF9 = Y13) => Y15)) => Y15))) => Y14) => (((!! @ $o @ (^[Y15 : $o]: (((~ (c_In @ c_Empty @ Y12)) => ((sF9 = Y13) => Y15)) => Y15))) => Y14) => Y14)))))))) = Y9) => Y11)) => Y11))) => Y10) => Y10))))))))) @ Y0) => ((~ (c_In @ Y5 @ Y0)) => Y7)) => Y7))) => Y6) => (((!! @ $o @ (^[Y7 : $o]: (((~ (c_In @ (c_Union @ (c_Repl @ sF1 @ (^[Y8 : $i]: (c_Eps_i @ (^[Y9 : $i]: (!! @ $o @ (^[Y10 : $o]: (((!! @ $o @ (^[Y11 : $o]: (((c_In @ c_Empty @ Y8) => ((Y5 = Y9) => Y11)) => Y11))) => Y10) => (((!! @ $o @ (^[Y11 : $o]: (((~ (c_In @ c_Empty @ Y8)) => (((c_Repl @ sF1 @ (^[Y12 : $i]: (c_Eps_i @ (^[Y13 : $i]: (!! @ $o @ (^[Y14 : $o]: (((!! @ $o @ (^[Y15 : $o]: (((c_In @ c_Empty @ Y12) => ((sF9 = Y13) => Y15)) => Y15))) => Y14) => (((!! @ $o @ (^[Y15 : $o]: (((~ (c_In @ c_Empty @ Y12)) => ((sF9 = Y13) => Y15)) => Y15))) => Y14) => Y14)))))))) = Y9) => Y11)) => Y11))) => Y10) => Y10))))))))) @ Y0)) => ((c_In @ Y5 @ Y0) => Y7)) => Y7))) => Y6) => Y6))))))) => Y4)) => Y4))) => Y3)) => Y3)))))) => Y1)) => Y1)))))) => ((~ (X2 @ (X1 @ (X1 @ (X1 @ sF11))))) => X3)) => X3)) = $true)) )),
% 9.27/1.88 inference(boolean_simplification,[],[f617])).
% 9.27/1.88 thf(f619,plain,(
% 9.27/1.88 ( ! [X2 : ($i > $o),X3 : $o,X1 : ($i > $i)] : (($true = ((((((X2 @ (X1 @ (c_Eps_i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: (((!! @ $o @ (^[Y2 : $o]: (((?? @ $i @ (^[Y3 : $i]: (!! @ $o @ (^[Y4 : $o]: (((c_In @ Y3 @ (X1 @ sF0)) => ((c_In @ Y3 @ (X1 @ sF4)) => Y4)) => Y4))))) => (((c_Repl @ (X1 @ sF0) @ (^[Y3 : $i]: (c_Eps_i @ (^[Y4 : $i]: (!! @ $o @ (^[Y5 : $o]: (((!! @ $o @ (^[Y6 : $o]: (((c_In @ Y3 @ (X1 @ sF4)) => ((Y3 = Y4) => Y6)) => Y6))) => Y5) => (((!! @ $o @ (^[Y6 : $o]: ((((c_In @ Y3 @ (X1 @ sF4)) => $false) => (((c_Eps_i @ (^[Y7 : $i]: (!! @ $o @ (^[Y8 : $o]: (((c_In @ Y7 @ (X1 @ sF0)) => ((c_In @ Y7 @ (X1 @ sF4)) => Y8)) => Y8))))) = Y4) => Y6)) => Y6))) => Y5) => Y5)))))))) = Y0) => Y2)) => Y2))) => Y1) => (((!! @ $o @ (^[Y2 : $o]: (((~ (?? @ $i @ (^[Y3 : $i]: (!! @ $o @ (^[Y4 : $o]: (((c_In @ Y3 @ (X1 @ sF0)) => ((c_In @ Y3 @ (X1 @ sF4)) => Y4)) => Y4)))))) => ((c_Empty = Y0) => Y2)) => Y2))) => Y1) => Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: ((c_In @ Y0 @ (X1 @ c_Empty)) => (!! @ $i @ (^[Y1 : $i]: ((c_In @ Y1 @ Y0) => (c_In @ Y1 @ (X1 @ c_Empty)))))))) => (!! @ $i @ (^[Y0 : $i]: ((c_In @ Y0 @ c_Empty) => (?? @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: (((!! @ $i @ (^[Y3 : $i]: ((c_In @ Y3 @ Y1) => (c_In @ Y3 @ Y0)))) => ((!! @ $o @ (^[Y3 : $o]: (((?? @ $i @ (^[Y4 : $i]: (!! @ $o @ (^[Y5 : $o]: (((c_In @ Y4 @ (c_Union @ (c_Repl @ sF1 @ (^[Y6 : $i]: (c_Eps_i @ (^[Y7 : $i]: (!! @ $o @ (^[Y8 : $o]: (((!! @ $o @ (^[Y9 : $o]: (((c_In @ c_Empty @ Y6) => (((X1 @ Y1) = Y7) => Y9)) => Y9))) => Y8) => (((!! @ $o @ (^[Y9 : $o]: (((~ (c_In @ c_Empty @ Y6)) => (((c_Repl @ sF1 @ (^[Y10 : $i]: (c_Eps_i @ (^[Y11 : $i]: (!! @ $o @ (^[Y12 : $o]: (((!! @ $o @ (^[Y13 : $o]: (((c_In @ c_Empty @ Y10) => (((X1 @ Y1) = Y11) => Y13)) => Y13))) => Y12) => (((!! @ $o @ (^[Y13 : $o]: (((~ (c_In @ c_Empty @ Y10)) => (((X1 @ Y1) = Y11) => Y13)) => Y13))) => Y12) => Y12)))))))) = Y7) => Y9)) => Y9))) => Y8) => Y8)))))))))) => ((~ (!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ (c_Union @ (c_Repl @ sF1 @ (^[Y7 : $i]: (c_Eps_i @ (^[Y8 : $i]: (!! @ $o @ (^[Y9 : $o]: (((!! @ $o @ (^[Y10 : $o]: (((c_In @ c_Empty @ Y7) => (((X1 @ Y1) = Y8) => Y10)) => Y10))) => Y9) => (((!! @ $o @ (^[Y10 : $o]: (((~ (c_In @ c_Empty @ Y7)) => (((c_Repl @ sF1 @ (^[Y11 : $i]: (c_Eps_i @ (^[Y12 : $i]: (!! @ $o @ (^[Y13 : $o]: (((!! @ $o @ (^[Y14 : $o]: (((c_In @ c_Empty @ Y11) => (((X1 @ Y1) = Y12) => Y14)) => Y14))) => Y13) => (((!! @ $o @ (^[Y14 : $o]: (((~ (c_In @ c_Empty @ Y11)) => (((X1 @ Y1) = Y12) => Y14)) => Y14))) => Y13) => Y13)))))))) = Y8) => Y10)) => Y10))) => Y9) => Y9)))))))))) => (c_In @ Y6 @ (c_Power @ Y4)))))) => Y5)) => Y5))))) => ((~ (?? @ $i @ (^[Y4 : $i]: (!! @ $o @ (^[Y5 : $o]: (((!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ Y4) => (c_In @ Y6 @ (c_Union @ (c_Repl @ sF1 @ (^[Y7 : $i]: (c_Eps_i @ (^[Y8 : $i]: (!! @ $o @ (^[Y9 : $o]: (((!! @ $o @ (^[Y10 : $o]: (((c_In @ c_Empty @ Y7) => (((X1 @ Y1) = Y8) => Y10)) => Y10))) => Y9) => (((!! @ $o @ (^[Y10 : $o]: (((~ (c_In @ c_Empty @ Y7)) => (((c_Repl @ sF1 @ (^[Y11 : $i]: (c_Eps_i @ (^[Y12 : $i]: (!! @ $o @ (^[Y13 : $o]: (((!! @ $o @ (^[Y14 : $o]: (((c_In @ c_Empty @ Y11) => (((X1 @ Y1) = Y12) => Y14)) => Y14))) => Y13) => (((!! @ $o @ (^[Y14 : $o]: (((~ (c_In @ c_Empty @ Y11)) => (((X1 @ Y1) = Y12) => Y14)) => Y14))) => Y13) => Y13)))))))) = Y8) => Y10)) => Y10))) => Y9) => Y9))))))))))))) => ((!! @ $o @ (^[Y6 : $o]: (((~ (!! @ $i @ (^[Y7 : $i]: ((c_In @ Y7 @ (c_Union @ (c_Repl @ sF1 @ (^[Y8 : $i]: (c_Eps_i @ (^[Y9 : $i]: (!! @ $o @ (^[Y10 : $o]: (((!! @ $o @ (^[Y11 : $o]: (((c_In @ c_Empty @ Y8) => (((X1 @ Y1) = Y9) => Y11)) => Y11))) => Y10) => (((!! @ $o @ (^[Y11 : $o]: (((~ (c_In @ c_Empty @ Y8)) => (((c_Repl @ sF1 @ (^[Y12 : $i]: (c_Eps_i @ (^[Y13 : $i]: (!! @ $o @ (^[Y14 : $o]: (((!! @ $o @ (^[Y15 : $o]: (((c_In @ c_Empty @ Y12) => (((X1 @ Y1) = Y13) => Y15)) => Y15))) => Y14) => (((!! @ $o @ (^[Y15 : $o]: (((~ (c_In @ c_Empty @ Y12)) => (((X1 @ Y1) = Y13) => Y15)) => Y15))) => Y14) => Y14)))))))) = Y9) => Y11)) => Y11))) => Y10) => Y10)))))))))) => (c_In @ Y7 @ Y4))))) => ((?? @ $i @ (^[Y7 : $i]: (!! @ $o @ (^[Y8 : $o]: (((c_In @ Y7 @ Y4) => ((~ (!! @ $i @ (^[Y9 : $i]: ((c_In @ Y9 @ Y4) => (c_In @ Y9 @ (c_Power @ Y7)))))) => Y8)) => Y8))))) => Y6)) => Y6))) => Y5)) => Y5)))))) => Y3)) => Y3))) => Y2)) => Y2)))))))))) => (?? @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: (((?? @ $i @ (^[Y2 : $i]: (!! @ $o @ (^[Y3 : $o]: (((!! @ $i @ (^[Y4 : $i]: ((c_In @ Y4 @ Y2) => (c_In @ Y4 @ Y0)))) => ((((X1 @ Y0) = Y0) => (?? @ $i @ (^[Y4 : $i]: (!! @ $o @ (^[Y5 : $o]: (((!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ Y4) => (c_In @ Y6 @ Y0)))) => ((~ (X2 @ (c_Union @ (c_Repl @ Y2 @ (^[Y6 : $i]: (c_Repl @ sF7 @ (^[Y7 : $i]: (c_Union @ (c_Repl @ sF1 @ (^[Y8 : $i]: (c_Eps_i @ (^[Y9 : $i]: (!! @ $o @ (^[Y10 : $o]: (((!! @ $o @ (^[Y11 : $o]: (((c_In @ c_Empty @ Y8) => (((c_Repl @ Y6 @ (^[Y12 : $i]: (c_Repl @ Y12 @ (^[Y13 : $i]: (c_Eps_i @ (^[Y14 : $i]: (!! @ ($i > $i > $o) @ (^[Y15 : $i > $i > $o]: ((!! @ ($i > $i) @ (^[Y16 : $i > $i]: (!! @ $i @ (^[Y17 : $i]: ((!! @ $i @ (^[Y18 : $i]: ((c_In @ Y18 @ Y17) => (Y15 @ Y18 @ (Y16 @ Y18))))) => (Y15 @ Y17 @ (c_Union @ (c_Repl @ sF1 @ (^[Y18 : $i]: (c_Eps_i @ (^[Y19 : $i]: (!! @ $o @ (^[Y20 : $o]: (((!! @ $o @ (^[Y21 : $o]: (((c_In @ c_Empty @ Y18) => ((sF2 = Y19) => Y21)) => Y21))) => Y20) => (((!! @ $o @ (^[Y21 : $o]: (((~ (c_In @ c_Empty @ Y18)) => (((c_Repl @ Y17 @ Y16) = Y19) => Y21)) => Y21))) => Y20) => Y20))))))))))))))) => (Y15 @ Y13 @ Y14)))))))))) = Y9) => Y11)) => Y11))) => Y10) => (((!! @ $o @ (^[Y11 : $o]: (((~ (c_In @ c_Empty @ Y8)) => (((c_Repl @ Y7 @ (^[Y12 : $i]: (c_Eps_i @ (^[Y13 : $i]: (!! @ ($i > $i > $o) @ (^[Y14 : $i > $i > $o]: ((!! @ ($i > $i) @ (^[Y15 : $i > $i]: (!! @ $i @ (^[Y16 : $i]: ((!! @ $i @ (^[Y17 : $i]: ((c_In @ Y17 @ Y16) => (Y14 @ Y17 @ (Y15 @ Y17))))) => (Y14 @ Y16 @ (c_Union @ (c_Repl @ sF1 @ (^[Y17 : $i]: (c_Eps_i @ (^[Y18 : $i]: (!! @ $o @ (^[Y19 : $o]: (((!! @ $o @ (^[Y20 : $o]: (((c_In @ c_Empty @ Y17) => ((sF2 = Y18) => Y20)) => Y20))) => Y19) => (((!! @ $o @ (^[Y20 : $o]: (((~ (c_In @ c_Empty @ Y17)) => (((c_Repl @ Y16 @ Y15) = Y18) => Y20)) => Y20))) => Y19) => Y19))))))))))))))) => (Y14 @ Y12 @ Y13)))))))) = Y9) => Y11)) => Y11))) => Y10) => Y10)))))))))))))))) => Y5)) => Y5)))))) => Y3)) => Y3))))) => ((~ (?? @ $i @ (^[Y2 : $i]: (!! @ $o @ (^[Y3 : $o]: (((!! @ $o @ (^[Y4 : $o]: (((!! @ $i @ (^[Y5 : $i]: ((c_In @ Y5 @ Y2) => (!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ Y5) => (c_In @ Y6 @ Y2))))))) => ((!! @ $i @ (^[Y5 : $i]: ((c_In @ Y5 @ Y2) => (!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ Y5) => (!! @ $i @ (^[Y7 : $i]: ((c_In @ Y7 @ Y6) => (c_In @ Y7 @ Y5)))))))))) => Y4)) => Y4))) => ((!! @ $o @ (^[Y4 : $o]: (((!! @ $i @ (^[Y5 : $i]: ((c_In @ Y5 @ Y0) => (c_In @ Y5 @ (c_Union @ (c_Repl @ sF1 @ (^[Y6 : $i]: (c_Eps_i @ (^[Y7 : $i]: (!! @ $o @ (^[Y8 : $o]: (((!! @ $o @ (^[Y9 : $o]: (((c_In @ c_Empty @ Y6) => ((Y2 = Y7) => Y9)) => Y9))) => Y8) => (((!! @ $o @ (^[Y9 : $o]: (((~ (c_In @ c_Empty @ Y6)) => (((c_Repl @ Y2 @ (^[Y10 : $i]: (c_Union @ (c_Repl @ sF1 @ (^[Y11 : $i]: (c_Eps_i @ (^[Y12 : $i]: (!! @ $o @ (^[Y13 : $o]: (((!! @ $o @ (^[Y14 : $o]: (((c_In @ c_Empty @ Y11) => ((Y10 = Y12) => Y14)) => Y14))) => Y13) => (((!! @ $o @ (^[Y14 : $o]: (((~ (c_In @ c_Empty @ Y11)) => (((c_Repl @ sF1 @ (^[Y15 : $i]: (c_Eps_i @ (^[Y16 : $i]: (!! @ $o @ (^[Y17 : $o]: (((!! @ $o @ (^[Y18 : $o]: (((c_In @ c_Empty @ Y15) => ((sF9 = Y16) => Y18)) => Y18))) => Y17) => (((!! @ $o @ (^[Y18 : $o]: (((~ (c_In @ c_Empty @ Y15)) => ((sF9 = Y16) => Y18)) => Y18))) => Y17) => Y17)))))))) = Y12) => Y14)) => Y14))) => Y13) => Y13))))))))))) = Y7) => Y9)) => Y9))) => Y8) => Y8))))))))))))) => ((!! @ $i @ (^[Y5 : $i]: ((c_In @ Y5 @ Y2) => (!! @ $o @ (^[Y6 : $o]: (((!! @ $o @ (^[Y7 : $o]: (((c_In @ (c_Union @ (c_Repl @ sF1 @ (^[Y8 : $i]: (c_Eps_i @ (^[Y9 : $i]: (!! @ $o @ (^[Y10 : $o]: (((!! @ $o @ (^[Y11 : $o]: (((c_In @ c_Empty @ Y8) => ((Y5 = Y9) => Y11)) => Y11))) => Y10) => (((!! @ $o @ (^[Y11 : $o]: (((~ (c_In @ c_Empty @ Y8)) => (((c_Repl @ sF1 @ (^[Y12 : $i]: (c_Eps_i @ (^[Y13 : $i]: (!! @ $o @ (^[Y14 : $o]: (((!! @ $o @ (^[Y15 : $o]: (((c_In @ c_Empty @ Y12) => ((sF9 = Y13) => Y15)) => Y15))) => Y14) => (((!! @ $o @ (^[Y15 : $o]: (((~ (c_In @ c_Empty @ Y12)) => ((sF9 = Y13) => Y15)) => Y15))) => Y14) => Y14)))))))) = Y9) => Y11)) => Y11))) => Y10) => Y10))))))))) @ Y0) => ((~ (c_In @ Y5 @ Y0)) => Y7)) => Y7))) => Y6) => (((!! @ $o @ (^[Y7 : $o]: (((~ (c_In @ (c_Union @ (c_Repl @ sF1 @ (^[Y8 : $i]: (c_Eps_i @ (^[Y9 : $i]: (!! @ $o @ (^[Y10 : $o]: (((!! @ $o @ (^[Y11 : $o]: (((c_In @ c_Empty @ Y8) => ((Y5 = Y9) => Y11)) => Y11))) => Y10) => (((!! @ $o @ (^[Y11 : $o]: (((~ (c_In @ c_Empty @ Y8)) => (((c_Repl @ sF1 @ (^[Y12 : $i]: (c_Eps_i @ (^[Y13 : $i]: (!! @ $o @ (^[Y14 : $o]: (((!! @ $o @ (^[Y15 : $o]: (((c_In @ c_Empty @ Y12) => ((sF9 = Y13) => Y15)) => Y15))) => Y14) => (((!! @ $o @ (^[Y15 : $o]: (((~ (c_In @ c_Empty @ Y12)) => ((sF9 = Y13) => Y15)) => Y15))) => Y14) => Y14)))))))) = Y9) => Y11)) => Y11))) => Y10) => Y10))))))))) @ Y0)) => ((c_In @ Y5 @ Y0) => Y7)) => Y7))) => Y6) => Y6))))))) => Y4)) => Y4))) => Y3)) => Y3)))))) => Y1)) => Y1)))))) => ((~ (X2 @ (X1 @ (X1 @ (X1 @ sF11))))) => X3)) => X3)))) )),
% 9.27/1.88 inference(boolean_simplification,[],[f618])).
% 9.27/1.88 thf(f620,plain,(
% 9.27/1.88 ( ! [X2 : ($i > $o),X3 : $o,X1 : ($i > $i)] : (($true = ((((((X2 @ (X1 @ (c_Eps_i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: (((!! @ $o @ (^[Y2 : $o]: (((?? @ $i @ (^[Y3 : $i]: (!! @ $o @ (^[Y4 : $o]: (((c_In @ Y3 @ (X1 @ sF0)) => ((c_In @ Y3 @ (X1 @ sF4)) => Y4)) => Y4))))) => (((c_Repl @ (X1 @ sF0) @ (^[Y3 : $i]: (c_Eps_i @ (^[Y4 : $i]: (!! @ $o @ (^[Y5 : $o]: (((!! @ $o @ (^[Y6 : $o]: (((c_In @ Y3 @ (X1 @ sF4)) => ((Y3 = Y4) => Y6)) => Y6))) => Y5) => (((!! @ $o @ (^[Y6 : $o]: (((~ (c_In @ Y3 @ (X1 @ sF4))) => (((c_Eps_i @ (^[Y7 : $i]: (!! @ $o @ (^[Y8 : $o]: (((c_In @ Y7 @ (X1 @ sF0)) => ((c_In @ Y7 @ (X1 @ sF4)) => Y8)) => Y8))))) = Y4) => Y6)) => Y6))) => Y5) => Y5)))))))) = Y0) => Y2)) => Y2))) => Y1) => (((!! @ $o @ (^[Y2 : $o]: (((~ (?? @ $i @ (^[Y3 : $i]: (!! @ $o @ (^[Y4 : $o]: (((c_In @ Y3 @ (X1 @ sF0)) => ((c_In @ Y3 @ (X1 @ sF4)) => Y4)) => Y4)))))) => ((c_Empty = Y0) => Y2)) => Y2))) => Y1) => Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: ((c_In @ Y0 @ (X1 @ c_Empty)) => (!! @ $i @ (^[Y1 : $i]: ((c_In @ Y1 @ Y0) => (c_In @ Y1 @ (X1 @ c_Empty)))))))) => (!! @ $i @ (^[Y0 : $i]: ((c_In @ Y0 @ c_Empty) => (?? @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: (((!! @ $i @ (^[Y3 : $i]: ((c_In @ Y3 @ Y1) => (c_In @ Y3 @ Y0)))) => ((!! @ $o @ (^[Y3 : $o]: (((?? @ $i @ (^[Y4 : $i]: (!! @ $o @ (^[Y5 : $o]: (((c_In @ Y4 @ (c_Union @ (c_Repl @ sF1 @ (^[Y6 : $i]: (c_Eps_i @ (^[Y7 : $i]: (!! @ $o @ (^[Y8 : $o]: (((!! @ $o @ (^[Y9 : $o]: (((c_In @ c_Empty @ Y6) => (((X1 @ Y1) = Y7) => Y9)) => Y9))) => Y8) => (((!! @ $o @ (^[Y9 : $o]: (((~ (c_In @ c_Empty @ Y6)) => (((c_Repl @ sF1 @ (^[Y10 : $i]: (c_Eps_i @ (^[Y11 : $i]: (!! @ $o @ (^[Y12 : $o]: (((!! @ $o @ (^[Y13 : $o]: (((c_In @ c_Empty @ Y10) => (((X1 @ Y1) = Y11) => Y13)) => Y13))) => Y12) => (((!! @ $o @ (^[Y13 : $o]: (((~ (c_In @ c_Empty @ Y10)) => (((X1 @ Y1) = Y11) => Y13)) => Y13))) => Y12) => Y12)))))))) = Y7) => Y9)) => Y9))) => Y8) => Y8)))))))))) => ((~ (!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ (c_Union @ (c_Repl @ sF1 @ (^[Y7 : $i]: (c_Eps_i @ (^[Y8 : $i]: (!! @ $o @ (^[Y9 : $o]: (((!! @ $o @ (^[Y10 : $o]: (((c_In @ c_Empty @ Y7) => (((X1 @ Y1) = Y8) => Y10)) => Y10))) => Y9) => (((!! @ $o @ (^[Y10 : $o]: (((~ (c_In @ c_Empty @ Y7)) => (((c_Repl @ sF1 @ (^[Y11 : $i]: (c_Eps_i @ (^[Y12 : $i]: (!! @ $o @ (^[Y13 : $o]: (((!! @ $o @ (^[Y14 : $o]: (((c_In @ c_Empty @ Y11) => (((X1 @ Y1) = Y12) => Y14)) => Y14))) => Y13) => (((!! @ $o @ (^[Y14 : $o]: (((~ (c_In @ c_Empty @ Y11)) => (((X1 @ Y1) = Y12) => Y14)) => Y14))) => Y13) => Y13)))))))) = Y8) => Y10)) => Y10))) => Y9) => Y9)))))))))) => (c_In @ Y6 @ (c_Power @ Y4)))))) => Y5)) => Y5))))) => ((~ (?? @ $i @ (^[Y4 : $i]: (!! @ $o @ (^[Y5 : $o]: (((!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ Y4) => (c_In @ Y6 @ (c_Union @ (c_Repl @ sF1 @ (^[Y7 : $i]: (c_Eps_i @ (^[Y8 : $i]: (!! @ $o @ (^[Y9 : $o]: (((!! @ $o @ (^[Y10 : $o]: (((c_In @ c_Empty @ Y7) => (((X1 @ Y1) = Y8) => Y10)) => Y10))) => Y9) => (((!! @ $o @ (^[Y10 : $o]: (((~ (c_In @ c_Empty @ Y7)) => (((c_Repl @ sF1 @ (^[Y11 : $i]: (c_Eps_i @ (^[Y12 : $i]: (!! @ $o @ (^[Y13 : $o]: (((!! @ $o @ (^[Y14 : $o]: (((c_In @ c_Empty @ Y11) => (((X1 @ Y1) = Y12) => Y14)) => Y14))) => Y13) => (((!! @ $o @ (^[Y14 : $o]: (((~ (c_In @ c_Empty @ Y11)) => (((X1 @ Y1) = Y12) => Y14)) => Y14))) => Y13) => Y13)))))))) = Y8) => Y10)) => Y10))) => Y9) => Y9))))))))))))) => ((!! @ $o @ (^[Y6 : $o]: (((~ (!! @ $i @ (^[Y7 : $i]: ((c_In @ Y7 @ (c_Union @ (c_Repl @ sF1 @ (^[Y8 : $i]: (c_Eps_i @ (^[Y9 : $i]: (!! @ $o @ (^[Y10 : $o]: (((!! @ $o @ (^[Y11 : $o]: (((c_In @ c_Empty @ Y8) => (((X1 @ Y1) = Y9) => Y11)) => Y11))) => Y10) => (((!! @ $o @ (^[Y11 : $o]: (((~ (c_In @ c_Empty @ Y8)) => (((c_Repl @ sF1 @ (^[Y12 : $i]: (c_Eps_i @ (^[Y13 : $i]: (!! @ $o @ (^[Y14 : $o]: (((!! @ $o @ (^[Y15 : $o]: (((c_In @ c_Empty @ Y12) => (((X1 @ Y1) = Y13) => Y15)) => Y15))) => Y14) => (((!! @ $o @ (^[Y15 : $o]: (((~ (c_In @ c_Empty @ Y12)) => (((X1 @ Y1) = Y13) => Y15)) => Y15))) => Y14) => Y14)))))))) = Y9) => Y11)) => Y11))) => Y10) => Y10)))))))))) => (c_In @ Y7 @ Y4))))) => ((?? @ $i @ (^[Y7 : $i]: (!! @ $o @ (^[Y8 : $o]: (((c_In @ Y7 @ Y4) => ((~ (!! @ $i @ (^[Y9 : $i]: ((c_In @ Y9 @ Y4) => (c_In @ Y9 @ (c_Power @ Y7)))))) => Y8)) => Y8))))) => Y6)) => Y6))) => Y5)) => Y5)))))) => Y3)) => Y3))) => Y2)) => Y2)))))))))) => (?? @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: (((?? @ $i @ (^[Y2 : $i]: (!! @ $o @ (^[Y3 : $o]: (((!! @ $i @ (^[Y4 : $i]: ((c_In @ Y4 @ Y2) => (c_In @ Y4 @ Y0)))) => ((((X1 @ Y0) = Y0) => (?? @ $i @ (^[Y4 : $i]: (!! @ $o @ (^[Y5 : $o]: (((!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ Y4) => (c_In @ Y6 @ Y0)))) => ((~ (X2 @ (c_Union @ (c_Repl @ Y2 @ (^[Y6 : $i]: (c_Repl @ sF7 @ (^[Y7 : $i]: (c_Union @ (c_Repl @ sF1 @ (^[Y8 : $i]: (c_Eps_i @ (^[Y9 : $i]: (!! @ $o @ (^[Y10 : $o]: (((!! @ $o @ (^[Y11 : $o]: (((c_In @ c_Empty @ Y8) => (((c_Repl @ Y6 @ (^[Y12 : $i]: (c_Repl @ Y12 @ (^[Y13 : $i]: (c_Eps_i @ (^[Y14 : $i]: (!! @ ($i > $i > $o) @ (^[Y15 : $i > $i > $o]: ((!! @ ($i > $i) @ (^[Y16 : $i > $i]: (!! @ $i @ (^[Y17 : $i]: ((!! @ $i @ (^[Y18 : $i]: ((c_In @ Y18 @ Y17) => (Y15 @ Y18 @ (Y16 @ Y18))))) => (Y15 @ Y17 @ (c_Union @ (c_Repl @ sF1 @ (^[Y18 : $i]: (c_Eps_i @ (^[Y19 : $i]: (!! @ $o @ (^[Y20 : $o]: (((!! @ $o @ (^[Y21 : $o]: (((c_In @ c_Empty @ Y18) => ((sF2 = Y19) => Y21)) => Y21))) => Y20) => (((!! @ $o @ (^[Y21 : $o]: (((~ (c_In @ c_Empty @ Y18)) => (((c_Repl @ Y17 @ Y16) = Y19) => Y21)) => Y21))) => Y20) => Y20))))))))))))))) => (Y15 @ Y13 @ Y14)))))))))) = Y9) => Y11)) => Y11))) => Y10) => (((!! @ $o @ (^[Y11 : $o]: (((~ (c_In @ c_Empty @ Y8)) => (((c_Repl @ Y7 @ (^[Y12 : $i]: (c_Eps_i @ (^[Y13 : $i]: (!! @ ($i > $i > $o) @ (^[Y14 : $i > $i > $o]: ((!! @ ($i > $i) @ (^[Y15 : $i > $i]: (!! @ $i @ (^[Y16 : $i]: ((!! @ $i @ (^[Y17 : $i]: ((c_In @ Y17 @ Y16) => (Y14 @ Y17 @ (Y15 @ Y17))))) => (Y14 @ Y16 @ (c_Union @ (c_Repl @ sF1 @ (^[Y17 : $i]: (c_Eps_i @ (^[Y18 : $i]: (!! @ $o @ (^[Y19 : $o]: (((!! @ $o @ (^[Y20 : $o]: (((c_In @ c_Empty @ Y17) => ((sF2 = Y18) => Y20)) => Y20))) => Y19) => (((!! @ $o @ (^[Y20 : $o]: (((~ (c_In @ c_Empty @ Y17)) => (((c_Repl @ Y16 @ Y15) = Y18) => Y20)) => Y20))) => Y19) => Y19))))))))))))))) => (Y14 @ Y12 @ Y13)))))))) = Y9) => Y11)) => Y11))) => Y10) => Y10)))))))))))))))) => Y5)) => Y5)))))) => Y3)) => Y3))))) => ((~ (?? @ $i @ (^[Y2 : $i]: (!! @ $o @ (^[Y3 : $o]: (((!! @ $o @ (^[Y4 : $o]: (((!! @ $i @ (^[Y5 : $i]: ((c_In @ Y5 @ Y2) => (!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ Y5) => (c_In @ Y6 @ Y2))))))) => ((!! @ $i @ (^[Y5 : $i]: ((c_In @ Y5 @ Y2) => (!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ Y5) => (!! @ $i @ (^[Y7 : $i]: ((c_In @ Y7 @ Y6) => (c_In @ Y7 @ Y5)))))))))) => Y4)) => Y4))) => ((!! @ $o @ (^[Y4 : $o]: (((!! @ $i @ (^[Y5 : $i]: ((c_In @ Y5 @ Y0) => (c_In @ Y5 @ (c_Union @ (c_Repl @ sF1 @ (^[Y6 : $i]: (c_Eps_i @ (^[Y7 : $i]: (!! @ $o @ (^[Y8 : $o]: (((!! @ $o @ (^[Y9 : $o]: (((c_In @ c_Empty @ Y6) => ((Y2 = Y7) => Y9)) => Y9))) => Y8) => (((!! @ $o @ (^[Y9 : $o]: (((~ (c_In @ c_Empty @ Y6)) => (((c_Repl @ Y2 @ (^[Y10 : $i]: (c_Union @ (c_Repl @ sF1 @ (^[Y11 : $i]: (c_Eps_i @ (^[Y12 : $i]: (!! @ $o @ (^[Y13 : $o]: (((!! @ $o @ (^[Y14 : $o]: (((c_In @ c_Empty @ Y11) => ((Y10 = Y12) => Y14)) => Y14))) => Y13) => (((!! @ $o @ (^[Y14 : $o]: (((~ (c_In @ c_Empty @ Y11)) => (((c_Repl @ sF1 @ (^[Y15 : $i]: (c_Eps_i @ (^[Y16 : $i]: (!! @ $o @ (^[Y17 : $o]: (((!! @ $o @ (^[Y18 : $o]: (((c_In @ c_Empty @ Y15) => ((sF9 = Y16) => Y18)) => Y18))) => Y17) => (((!! @ $o @ (^[Y18 : $o]: (((~ (c_In @ c_Empty @ Y15)) => ((sF9 = Y16) => Y18)) => Y18))) => Y17) => Y17)))))))) = Y12) => Y14)) => Y14))) => Y13) => Y13))))))))))) = Y7) => Y9)) => Y9))) => Y8) => Y8))))))))))))) => ((!! @ $i @ (^[Y5 : $i]: ((c_In @ Y5 @ Y2) => (!! @ $o @ (^[Y6 : $o]: (((!! @ $o @ (^[Y7 : $o]: (((c_In @ (c_Union @ (c_Repl @ sF1 @ (^[Y8 : $i]: (c_Eps_i @ (^[Y9 : $i]: (!! @ $o @ (^[Y10 : $o]: (((!! @ $o @ (^[Y11 : $o]: (((c_In @ c_Empty @ Y8) => ((Y5 = Y9) => Y11)) => Y11))) => Y10) => (((!! @ $o @ (^[Y11 : $o]: (((~ (c_In @ c_Empty @ Y8)) => (((c_Repl @ sF1 @ (^[Y12 : $i]: (c_Eps_i @ (^[Y13 : $i]: (!! @ $o @ (^[Y14 : $o]: (((!! @ $o @ (^[Y15 : $o]: (((c_In @ c_Empty @ Y12) => ((sF9 = Y13) => Y15)) => Y15))) => Y14) => (((!! @ $o @ (^[Y15 : $o]: (((~ (c_In @ c_Empty @ Y12)) => ((sF9 = Y13) => Y15)) => Y15))) => Y14) => Y14)))))))) = Y9) => Y11)) => Y11))) => Y10) => Y10))))))))) @ Y0) => ((~ (c_In @ Y5 @ Y0)) => Y7)) => Y7))) => Y6) => (((!! @ $o @ (^[Y7 : $o]: (((~ (c_In @ (c_Union @ (c_Repl @ sF1 @ (^[Y8 : $i]: (c_Eps_i @ (^[Y9 : $i]: (!! @ $o @ (^[Y10 : $o]: (((!! @ $o @ (^[Y11 : $o]: (((c_In @ c_Empty @ Y8) => ((Y5 = Y9) => Y11)) => Y11))) => Y10) => (((!! @ $o @ (^[Y11 : $o]: (((~ (c_In @ c_Empty @ Y8)) => (((c_Repl @ sF1 @ (^[Y12 : $i]: (c_Eps_i @ (^[Y13 : $i]: (!! @ $o @ (^[Y14 : $o]: (((!! @ $o @ (^[Y15 : $o]: (((c_In @ c_Empty @ Y12) => ((sF9 = Y13) => Y15)) => Y15))) => Y14) => (((!! @ $o @ (^[Y15 : $o]: (((~ (c_In @ c_Empty @ Y12)) => ((sF9 = Y13) => Y15)) => Y15))) => Y14) => Y14)))))))) = Y9) => Y11)) => Y11))) => Y10) => Y10))))))))) @ Y0)) => ((c_In @ Y5 @ Y0) => Y7)) => Y7))) => Y6) => Y6))))))) => Y4)) => Y4))) => Y3)) => Y3)))))) => Y1)) => Y1)))))) => ((~ (X2 @ (X1 @ (X1 @ (X1 @ sF11))))) => X3)) => X3)))) )),
% 9.27/1.88 inference(boolean_simplification,[],[f619])).
% 9.27/1.88 thf(f622,plain,(
% 9.27/1.88 ( ! [X2 : $o,X0 : ($i > $o),X1 : ($i > $i)] : ((((X0 @ (X1 @ (X1 @ (X1 @ sF11))))) = $false) | ($true = ((((((X0 @ (X1 @ (c_Eps_i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: (((!! @ $o @ (^[Y2 : $o]: (((?? @ $i @ (^[Y3 : $i]: (!! @ $o @ (^[Y4 : $o]: (((c_In @ Y3 @ (X1 @ sF0)) => ((c_In @ Y3 @ (X1 @ sF4)) => Y4)) => Y4))))) => (((c_Repl @ (X1 @ sF0) @ (^[Y3 : $i]: (c_Eps_i @ (^[Y4 : $i]: (!! @ $o @ (^[Y5 : $o]: (((!! @ $o @ (^[Y6 : $o]: (((c_In @ Y3 @ (X1 @ sF4)) => ((Y3 = Y4) => Y6)) => Y6))) => Y5) => (((!! @ $o @ (^[Y6 : $o]: (((~ (c_In @ Y3 @ (X1 @ sF4))) => (((c_Eps_i @ (^[Y7 : $i]: (!! @ $o @ (^[Y8 : $o]: (((c_In @ Y7 @ (X1 @ sF0)) => ((c_In @ Y7 @ (X1 @ sF4)) => Y8)) => Y8))))) = Y4) => Y6)) => Y6))) => Y5) => Y5)))))))) = Y0) => Y2)) => Y2))) => Y1) => (((!! @ $o @ (^[Y2 : $o]: (((~ (?? @ $i @ (^[Y3 : $i]: (!! @ $o @ (^[Y4 : $o]: (((c_In @ Y3 @ (X1 @ sF0)) => ((c_In @ Y3 @ (X1 @ sF4)) => Y4)) => Y4)))))) => ((c_Empty = Y0) => Y2)) => Y2))) => Y1) => Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: ((c_In @ Y0 @ (X1 @ c_Empty)) => (!! @ $i @ (^[Y1 : $i]: ((c_In @ Y1 @ Y0) => (c_In @ Y1 @ (X1 @ c_Empty)))))))) => (!! @ $i @ (^[Y0 : $i]: ((c_In @ Y0 @ c_Empty) => (?? @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: (((!! @ $i @ (^[Y3 : $i]: ((c_In @ Y3 @ Y1) => (c_In @ Y3 @ Y0)))) => ((!! @ $o @ (^[Y3 : $o]: (((?? @ $i @ (^[Y4 : $i]: (!! @ $o @ (^[Y5 : $o]: (((c_In @ Y4 @ (c_Union @ (c_Repl @ sF1 @ (^[Y6 : $i]: (c_Eps_i @ (^[Y7 : $i]: (!! @ $o @ (^[Y8 : $o]: (((!! @ $o @ (^[Y9 : $o]: (((c_In @ c_Empty @ Y6) => (((X1 @ Y1) = Y7) => Y9)) => Y9))) => Y8) => (((!! @ $o @ (^[Y9 : $o]: (((~ (c_In @ c_Empty @ Y6)) => (((c_Repl @ sF1 @ (^[Y10 : $i]: (c_Eps_i @ (^[Y11 : $i]: (!! @ $o @ (^[Y12 : $o]: (((!! @ $o @ (^[Y13 : $o]: (((c_In @ c_Empty @ Y10) => (((X1 @ Y1) = Y11) => Y13)) => Y13))) => Y12) => (((!! @ $o @ (^[Y13 : $o]: (((~ (c_In @ c_Empty @ Y10)) => (((X1 @ Y1) = Y11) => Y13)) => Y13))) => Y12) => Y12)))))))) = Y7) => Y9)) => Y9))) => Y8) => Y8)))))))))) => ((~ (!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ (c_Union @ (c_Repl @ sF1 @ (^[Y7 : $i]: (c_Eps_i @ (^[Y8 : $i]: (!! @ $o @ (^[Y9 : $o]: (((!! @ $o @ (^[Y10 : $o]: (((c_In @ c_Empty @ Y7) => (((X1 @ Y1) = Y8) => Y10)) => Y10))) => Y9) => (((!! @ $o @ (^[Y10 : $o]: (((~ (c_In @ c_Empty @ Y7)) => (((c_Repl @ sF1 @ (^[Y11 : $i]: (c_Eps_i @ (^[Y12 : $i]: (!! @ $o @ (^[Y13 : $o]: (((!! @ $o @ (^[Y14 : $o]: (((c_In @ c_Empty @ Y11) => (((X1 @ Y1) = Y12) => Y14)) => Y14))) => Y13) => (((!! @ $o @ (^[Y14 : $o]: (((~ (c_In @ c_Empty @ Y11)) => (((X1 @ Y1) = Y12) => Y14)) => Y14))) => Y13) => Y13)))))))) = Y8) => Y10)) => Y10))) => Y9) => Y9)))))))))) => (c_In @ Y6 @ (c_Power @ Y4)))))) => Y5)) => Y5))))) => ((~ (?? @ $i @ (^[Y4 : $i]: (!! @ $o @ (^[Y5 : $o]: (((!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ Y4) => (c_In @ Y6 @ (c_Union @ (c_Repl @ sF1 @ (^[Y7 : $i]: (c_Eps_i @ (^[Y8 : $i]: (!! @ $o @ (^[Y9 : $o]: (((!! @ $o @ (^[Y10 : $o]: (((c_In @ c_Empty @ Y7) => (((X1 @ Y1) = Y8) => Y10)) => Y10))) => Y9) => (((!! @ $o @ (^[Y10 : $o]: (((~ (c_In @ c_Empty @ Y7)) => (((c_Repl @ sF1 @ (^[Y11 : $i]: (c_Eps_i @ (^[Y12 : $i]: (!! @ $o @ (^[Y13 : $o]: (((!! @ $o @ (^[Y14 : $o]: (((c_In @ c_Empty @ Y11) => (((X1 @ Y1) = Y12) => Y14)) => Y14))) => Y13) => (((!! @ $o @ (^[Y14 : $o]: (((~ (c_In @ c_Empty @ Y11)) => (((X1 @ Y1) = Y12) => Y14)) => Y14))) => Y13) => Y13)))))))) = Y8) => Y10)) => Y10))) => Y9) => Y9))))))))))))) => ((!! @ $o @ (^[Y6 : $o]: (((~ (!! @ $i @ (^[Y7 : $i]: ((c_In @ Y7 @ (c_Union @ (c_Repl @ sF1 @ (^[Y8 : $i]: (c_Eps_i @ (^[Y9 : $i]: (!! @ $o @ (^[Y10 : $o]: (((!! @ $o @ (^[Y11 : $o]: (((c_In @ c_Empty @ Y8) => (((X1 @ Y1) = Y9) => Y11)) => Y11))) => Y10) => (((!! @ $o @ (^[Y11 : $o]: (((~ (c_In @ c_Empty @ Y8)) => (((c_Repl @ sF1 @ (^[Y12 : $i]: (c_Eps_i @ (^[Y13 : $i]: (!! @ $o @ (^[Y14 : $o]: (((!! @ $o @ (^[Y15 : $o]: (((c_In @ c_Empty @ Y12) => (((X1 @ Y1) = Y13) => Y15)) => Y15))) => Y14) => (((!! @ $o @ (^[Y15 : $o]: (((~ (c_In @ c_Empty @ Y12)) => (((X1 @ Y1) = Y13) => Y15)) => Y15))) => Y14) => Y14)))))))) = Y9) => Y11)) => Y11))) => Y10) => Y10)))))))))) => (c_In @ Y7 @ Y4))))) => ((?? @ $i @ (^[Y7 : $i]: (!! @ $o @ (^[Y8 : $o]: (((c_In @ Y7 @ Y4) => ((~ (!! @ $i @ (^[Y9 : $i]: ((c_In @ Y9 @ Y4) => (c_In @ Y9 @ (c_Power @ Y7)))))) => Y8)) => Y8))))) => Y6)) => Y6))) => Y5)) => Y5)))))) => Y3)) => Y3))) => Y2)) => Y2)))))))))) => (?? @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: (((?? @ $i @ (^[Y2 : $i]: (!! @ $o @ (^[Y3 : $o]: (((!! @ $i @ (^[Y4 : $i]: ((c_In @ Y4 @ Y2) => (c_In @ Y4 @ Y0)))) => ((((X1 @ Y0) = Y0) => (?? @ $i @ (^[Y4 : $i]: (!! @ $o @ (^[Y5 : $o]: (((!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ Y4) => (c_In @ Y6 @ Y0)))) => ((~ (X0 @ (c_Union @ (c_Repl @ Y2 @ (^[Y6 : $i]: (c_Repl @ sF7 @ (^[Y7 : $i]: (c_Union @ (c_Repl @ sF1 @ (^[Y8 : $i]: (c_Eps_i @ (^[Y9 : $i]: (!! @ $o @ (^[Y10 : $o]: (((!! @ $o @ (^[Y11 : $o]: (((c_In @ c_Empty @ Y8) => (((c_Repl @ Y6 @ (^[Y12 : $i]: (c_Repl @ Y12 @ (^[Y13 : $i]: (c_Eps_i @ (^[Y14 : $i]: (!! @ ($i > $i > $o) @ (^[Y15 : $i > $i > $o]: ((!! @ ($i > $i) @ (^[Y16 : $i > $i]: (!! @ $i @ (^[Y17 : $i]: ((!! @ $i @ (^[Y18 : $i]: ((c_In @ Y18 @ Y17) => (Y15 @ Y18 @ (Y16 @ Y18))))) => (Y15 @ Y17 @ (c_Union @ (c_Repl @ sF1 @ (^[Y18 : $i]: (c_Eps_i @ (^[Y19 : $i]: (!! @ $o @ (^[Y20 : $o]: (((!! @ $o @ (^[Y21 : $o]: (((c_In @ c_Empty @ Y18) => ((sF2 = Y19) => Y21)) => Y21))) => Y20) => (((!! @ $o @ (^[Y21 : $o]: (((~ (c_In @ c_Empty @ Y18)) => (((c_Repl @ Y17 @ Y16) = Y19) => Y21)) => Y21))) => Y20) => Y20))))))))))))))) => (Y15 @ Y13 @ Y14)))))))))) = Y9) => Y11)) => Y11))) => Y10) => (((!! @ $o @ (^[Y11 : $o]: (((~ (c_In @ c_Empty @ Y8)) => (((c_Repl @ Y7 @ (^[Y12 : $i]: (c_Eps_i @ (^[Y13 : $i]: (!! @ ($i > $i > $o) @ (^[Y14 : $i > $i > $o]: ((!! @ ($i > $i) @ (^[Y15 : $i > $i]: (!! @ $i @ (^[Y16 : $i]: ((!! @ $i @ (^[Y17 : $i]: ((c_In @ Y17 @ Y16) => (Y14 @ Y17 @ (Y15 @ Y17))))) => (Y14 @ Y16 @ (c_Union @ (c_Repl @ sF1 @ (^[Y17 : $i]: (c_Eps_i @ (^[Y18 : $i]: (!! @ $o @ (^[Y19 : $o]: (((!! @ $o @ (^[Y20 : $o]: (((c_In @ c_Empty @ Y17) => ((sF2 = Y18) => Y20)) => Y20))) => Y19) => (((!! @ $o @ (^[Y20 : $o]: (((~ (c_In @ c_Empty @ Y17)) => (((c_Repl @ Y16 @ Y15) = Y18) => Y20)) => Y20))) => Y19) => Y19))))))))))))))) => (Y14 @ Y12 @ Y13)))))))) = Y9) => Y11)) => Y11))) => Y10) => Y10)))))))))))))))) => Y5)) => Y5)))))) => Y3)) => Y3))))) => ((~ (?? @ $i @ (^[Y2 : $i]: (!! @ $o @ (^[Y3 : $o]: (((!! @ $o @ (^[Y4 : $o]: (((!! @ $i @ (^[Y5 : $i]: ((c_In @ Y5 @ Y2) => (!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ Y5) => (c_In @ Y6 @ Y2))))))) => ((!! @ $i @ (^[Y5 : $i]: ((c_In @ Y5 @ Y2) => (!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ Y5) => (!! @ $i @ (^[Y7 : $i]: ((c_In @ Y7 @ Y6) => (c_In @ Y7 @ Y5)))))))))) => Y4)) => Y4))) => ((!! @ $o @ (^[Y4 : $o]: (((!! @ $i @ (^[Y5 : $i]: ((c_In @ Y5 @ Y0) => (c_In @ Y5 @ (c_Union @ (c_Repl @ sF1 @ (^[Y6 : $i]: (c_Eps_i @ (^[Y7 : $i]: (!! @ $o @ (^[Y8 : $o]: (((!! @ $o @ (^[Y9 : $o]: (((c_In @ c_Empty @ Y6) => ((Y2 = Y7) => Y9)) => Y9))) => Y8) => (((!! @ $o @ (^[Y9 : $o]: (((~ (c_In @ c_Empty @ Y6)) => (((c_Repl @ Y2 @ (^[Y10 : $i]: (c_Union @ (c_Repl @ sF1 @ (^[Y11 : $i]: (c_Eps_i @ (^[Y12 : $i]: (!! @ $o @ (^[Y13 : $o]: (((!! @ $o @ (^[Y14 : $o]: (((c_In @ c_Empty @ Y11) => ((Y10 = Y12) => Y14)) => Y14))) => Y13) => (((!! @ $o @ (^[Y14 : $o]: (((~ (c_In @ c_Empty @ Y11)) => (((c_Repl @ sF1 @ (^[Y15 : $i]: (c_Eps_i @ (^[Y16 : $i]: (!! @ $o @ (^[Y17 : $o]: (((!! @ $o @ (^[Y18 : $o]: (((c_In @ c_Empty @ Y15) => ((sF9 = Y16) => Y18)) => Y18))) => Y17) => (((!! @ $o @ (^[Y18 : $o]: (((~ (c_In @ c_Empty @ Y15)) => ((sF9 = Y16) => Y18)) => Y18))) => Y17) => Y17)))))))) = Y12) => Y14)) => Y14))) => Y13) => Y13))))))))))) = Y7) => Y9)) => Y9))) => Y8) => Y8))))))))))))) => ((!! @ $i @ (^[Y5 : $i]: ((c_In @ Y5 @ Y2) => (!! @ $o @ (^[Y6 : $o]: (((!! @ $o @ (^[Y7 : $o]: (((c_In @ (c_Union @ (c_Repl @ sF1 @ (^[Y8 : $i]: (c_Eps_i @ (^[Y9 : $i]: (!! @ $o @ (^[Y10 : $o]: (((!! @ $o @ (^[Y11 : $o]: (((c_In @ c_Empty @ Y8) => ((Y5 = Y9) => Y11)) => Y11))) => Y10) => (((!! @ $o @ (^[Y11 : $o]: (((~ (c_In @ c_Empty @ Y8)) => (((c_Repl @ sF1 @ (^[Y12 : $i]: (c_Eps_i @ (^[Y13 : $i]: (!! @ $o @ (^[Y14 : $o]: (((!! @ $o @ (^[Y15 : $o]: (((c_In @ c_Empty @ Y12) => ((sF9 = Y13) => Y15)) => Y15))) => Y14) => (((!! @ $o @ (^[Y15 : $o]: (((~ (c_In @ c_Empty @ Y12)) => ((sF9 = Y13) => Y15)) => Y15))) => Y14) => Y14)))))))) = Y9) => Y11)) => Y11))) => Y10) => Y10))))))))) @ Y0) => ((~ (c_In @ Y5 @ Y0)) => Y7)) => Y7))) => Y6) => (((!! @ $o @ (^[Y7 : $o]: (((~ (c_In @ (c_Union @ (c_Repl @ sF1 @ (^[Y8 : $i]: (c_Eps_i @ (^[Y9 : $i]: (!! @ $o @ (^[Y10 : $o]: (((!! @ $o @ (^[Y11 : $o]: (((c_In @ c_Empty @ Y8) => ((Y5 = Y9) => Y11)) => Y11))) => Y10) => (((!! @ $o @ (^[Y11 : $o]: (((~ (c_In @ c_Empty @ Y8)) => (((c_Repl @ sF1 @ (^[Y12 : $i]: (c_Eps_i @ (^[Y13 : $i]: (!! @ $o @ (^[Y14 : $o]: (((!! @ $o @ (^[Y15 : $o]: (((c_In @ c_Empty @ Y12) => ((sF9 = Y13) => Y15)) => Y15))) => Y14) => (((!! @ $o @ (^[Y15 : $o]: (((~ (c_In @ c_Empty @ Y12)) => ((sF9 = Y13) => Y15)) => Y15))) => Y14) => Y14)))))))) = Y9) => Y11)) => Y11))) => Y10) => Y10))))))))) @ Y0)) => ((c_In @ Y5 @ Y0) => Y7)) => Y7))) => Y6) => Y6))))))) => Y4)) => Y4))) => Y3)) => Y3)))))) => Y1)) => Y1)))))) => ((~ $true) => X2)) => X2)))) )),
% 9.27/1.88 inference(superposition,[],[f620,f418])).
% 9.27/1.88 thf(f638,plain,(
% 9.27/1.88 ( ! 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@ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: (((!! @ $i @ (^[Y3 : $i]: ((c_In @ Y3 @ Y1) => (c_In @ Y3 @ Y0)))) => ((!! @ $o @ (^[Y3 : $o]: (((?? @ $i @ (^[Y4 : $i]: (!! @ $o @ (^[Y5 : $o]: (((c_In @ Y4 @ (c_Union @ (c_Repl @ sF1 @ (^[Y6 : $i]: (c_Eps_i @ (^[Y7 : $i]: (!! @ $o @ (^[Y8 : $o]: (((!! @ $o @ (^[Y9 : $o]: (((c_In @ c_Empty @ Y6) => (((X1 @ Y1) = Y7) => Y9)) => Y9))) => Y8) => (((!! @ $o @ (^[Y9 : $o]: (((~ (c_In @ c_Empty @ Y6)) => (((c_Repl @ sF1 @ (^[Y10 : $i]: (c_Eps_i @ (^[Y11 : $i]: (!! @ $o @ (^[Y12 : $o]: (((!! @ $o @ (^[Y13 : $o]: (((c_In @ c_Empty @ Y10) => (((X1 @ Y1) = Y11) => Y13)) => Y13))) => Y12) => (((!! @ $o @ (^[Y13 : $o]: (((~ (c_In @ c_Empty @ Y10)) => (((X1 @ Y1) = Y11) => Y13)) => Y13))) => Y12) => Y12)))))))) = Y7) => Y9)) => Y9))) => Y8) => Y8)))))))))) => ((~ (!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ (c_Union @ (c_Repl @ sF1 @ (^[Y7 : $i]: (c_Eps_i @ (^[Y8 : $i]: (!! @ $o @ (^[Y9 : $o]: (((!! @ $o @ (^[Y10 : $o]: (((c_In @ c_Empty @ Y7) => (((X1 @ Y1) = Y8) => Y10)) => Y10))) => Y9) => (((!! @ $o @ (^[Y10 : $o]: (((~ (c_In @ c_Empty @ Y7)) => (((c_Repl @ sF1 @ (^[Y11 : $i]: (c_Eps_i @ (^[Y12 : $i]: (!! @ $o @ (^[Y13 : $o]: (((!! @ $o @ (^[Y14 : $o]: (((c_In @ c_Empty @ Y11) => (((X1 @ Y1) = Y12) => Y14)) => Y14))) => Y13) => (((!! @ $o @ (^[Y14 : $o]: (((~ (c_In @ c_Empty @ Y11)) => (((X1 @ Y1) = Y12) => Y14)) => Y14))) => Y13) => Y13)))))))) = Y8) => Y10)) => Y10))) => Y9) => Y9)))))))))) => (c_In @ Y6 @ (c_Power @ Y4)))))) => Y5)) => Y5))))) => ((~ (?? @ $i @ (^[Y4 : $i]: (!! @ $o @ (^[Y5 : $o]: (((!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ Y4) => (c_In @ Y6 @ (c_Union @ (c_Repl @ sF1 @ (^[Y7 : $i]: (c_Eps_i @ (^[Y8 : $i]: (!! @ $o @ (^[Y9 : $o]: (((!! @ $o @ (^[Y10 : $o]: (((c_In @ c_Empty @ Y7) => (((X1 @ Y1) = Y8) => Y10)) => Y10))) => Y9) => (((!! @ $o @ (^[Y10 : $o]: (((~ (c_In @ c_Empty @ Y7)) => (((c_Repl @ sF1 @ (^[Y11 : $i]: (c_Eps_i @ (^[Y12 : $i]: (!! @ $o @ (^[Y13 : $o]: (((!! @ $o @ (^[Y14 : $o]: (((c_In @ c_Empty @ Y11) => (((X1 @ Y1) = Y12) => Y14)) => Y14))) => Y13) => (((!! @ $o @ (^[Y14 : $o]: (((~ (c_In @ c_Empty @ Y11)) => (((X1 @ Y1) = Y12) => Y14)) => Y14))) => Y13) => Y13)))))))) = Y8) => Y10)) => Y10))) => Y9) => Y9))))))))))))) => ((!! @ $o @ (^[Y6 : $o]: (((~ (!! @ $i @ (^[Y7 : $i]: ((c_In @ Y7 @ (c_Union @ (c_Repl @ sF1 @ (^[Y8 : $i]: (c_Eps_i @ (^[Y9 : $i]: (!! @ $o @ (^[Y10 : $o]: (((!! @ $o @ (^[Y11 : $o]: (((c_In @ c_Empty @ Y8) => (((X1 @ Y1) = Y9) => Y11)) => Y11))) => Y10) => (((!! @ $o @ (^[Y11 : $o]: (((~ (c_In @ c_Empty @ Y8)) => (((c_Repl @ sF1 @ (^[Y12 : $i]: (c_Eps_i @ (^[Y13 : $i]: (!! @ $o @ (^[Y14 : $o]: (((!! @ $o @ (^[Y15 : $o]: (((c_In @ c_Empty @ Y12) => (((X1 @ Y1) = Y13) => Y15)) => Y15))) => Y14) => (((!! @ $o @ (^[Y15 : $o]: (((~ (c_In @ c_Empty @ Y12)) => (((X1 @ Y1) = Y13) => Y15)) => Y15))) => Y14) => Y14)))))))) = Y9) => Y11)) => Y11))) => Y10) => Y10)))))))))) => (c_In @ Y7 @ Y4))))) => ((?? @ $i @ (^[Y7 : $i]: (!! @ $o @ (^[Y8 : $o]: (((c_In @ Y7 @ Y4) => ((~ (!! @ $i @ (^[Y9 : $i]: ((c_In @ Y9 @ Y4) => (c_In @ Y9 @ (c_Power @ Y7)))))) => Y8)) => Y8))))) => Y6)) => Y6))) => Y5)) => Y5)))))) => Y3)) => Y3))) => Y2)) => Y2)))))))))) => (?? @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: (((?? @ $i @ (^[Y2 : $i]: (!! @ $o @ (^[Y3 : $o]: (((!! @ $i @ (^[Y4 : $i]: ((c_In @ Y4 @ Y2) => (c_In @ Y4 @ Y0)))) => ((((X1 @ Y0) = Y0) => (?? @ $i @ (^[Y4 : $i]: (!! @ $o @ (^[Y5 : $o]: (((!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ Y4) => (c_In @ Y6 @ Y0)))) => ((~ (X0 @ (c_Union @ (c_Repl @ Y2 @ (^[Y6 : $i]: (c_Repl @ sF7 @ (^[Y7 : $i]: (c_Union @ (c_Repl @ sF1 @ (^[Y8 : $i]: (c_Eps_i @ (^[Y9 : $i]: (!! @ $o @ (^[Y10 : $o]: (((!! @ $o @ (^[Y11 : $o]: (((c_In @ c_Empty @ Y8) => (((c_Repl @ Y6 @ (^[Y12 : $i]: (c_Repl @ Y12 @ (^[Y13 : $i]: (c_Eps_i @ (^[Y14 : $i]: (!! @ ($i > $i > $o) @ (^[Y15 : $i > $i > $o]: ((!! @ ($i > $i) @ (^[Y16 : $i > $i]: (!! @ $i @ (^[Y17 : $i]: ((!! @ $i @ (^[Y18 : $i]: ((c_In @ Y18 @ Y17) => (Y15 @ Y18 @ (Y16 @ Y18))))) => (Y15 @ Y17 @ (c_Union @ (c_Repl @ sF1 @ (^[Y18 : $i]: (c_Eps_i @ (^[Y19 : $i]: (!! @ $o @ (^[Y20 : $o]: (((!! @ $o @ (^[Y21 : $o]: (((c_In @ c_Empty @ Y18) => ((sF2 = Y19) => Y21)) => Y21))) => Y20) => (((!! @ $o @ (^[Y21 : $o]: (((~ (c_In @ c_Empty @ Y18)) => (((c_Repl @ Y17 @ Y16) = Y19) => Y21)) => Y21))) => Y20) => Y20))))))))))))))) => (Y15 @ Y13 @ Y14)))))))))) = Y9) => Y11)) => Y11))) => Y10) => (((!! @ $o @ (^[Y11 : $o]: (((~ (c_In @ c_Empty @ Y8)) => (((c_Repl @ Y7 @ (^[Y12 : $i]: (c_Eps_i @ (^[Y13 : $i]: (!! @ ($i > $i > $o) @ (^[Y14 : $i > $i > $o]: ((!! @ ($i > $i) @ (^[Y15 : $i > $i]: (!! @ $i @ (^[Y16 : $i]: ((!! @ $i @ (^[Y17 : $i]: ((c_In @ Y17 @ Y16) => (Y14 @ Y17 @ (Y15 @ Y17))))) => (Y14 @ Y16 @ (c_Union @ (c_Repl @ sF1 @ (^[Y17 : $i]: (c_Eps_i @ (^[Y18 : $i]: (!! @ $o @ (^[Y19 : $o]: (((!! @ $o @ (^[Y20 : $o]: (((c_In @ c_Empty @ Y17) => ((sF2 = Y18) => Y20)) => Y20))) => Y19) => (((!! @ $o @ (^[Y20 : $o]: (((~ (c_In @ c_Empty @ Y17)) => (((c_Repl @ Y16 @ Y15) = Y18) => Y20)) => Y20))) => Y19) => Y19))))))))))))))) => (Y14 @ Y12 @ Y13)))))))) = Y9) => Y11)) => Y11))) => Y10) => Y10)))))))))))))))) => Y5)) => Y5)))))) => Y3)) => Y3))))) => ((~ (?? @ $i @ (^[Y2 : $i]: (!! @ $o @ (^[Y3 : $o]: (((!! @ $o @ (^[Y4 : $o]: (((!! @ $i @ (^[Y5 : $i]: ((c_In @ Y5 @ Y2) => (!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ Y5) => (c_In @ Y6 @ Y2))))))) => ((!! @ $i @ (^[Y5 : $i]: ((c_In @ Y5 @ Y2) => (!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ Y5) => (!! @ $i @ (^[Y7 : $i]: ((c_In @ Y7 @ Y6) => (c_In @ Y7 @ Y5)))))))))) => Y4)) => Y4))) => ((!! @ $o @ (^[Y4 : $o]: (((!! @ $i @ (^[Y5 : $i]: ((c_In @ Y5 @ Y0) => (c_In @ Y5 @ (c_Union @ (c_Repl @ sF1 @ (^[Y6 : $i]: (c_Eps_i @ (^[Y7 : $i]: (!! @ $o @ (^[Y8 : $o]: (((!! @ $o @ (^[Y9 : $o]: (((c_In @ c_Empty @ Y6) => ((Y2 = Y7) => Y9)) => Y9))) => Y8) => (((!! @ $o @ (^[Y9 : $o]: (((~ (c_In @ c_Empty @ Y6)) => (((c_Repl @ Y2 @ (^[Y10 : $i]: (c_Union @ (c_Repl @ sF1 @ (^[Y11 : $i]: (c_Eps_i @ (^[Y12 : $i]: (!! @ $o @ (^[Y13 : $o]: (((!! @ $o @ (^[Y14 : $o]: (((c_In @ c_Empty @ Y11) => ((Y10 = Y12) => Y14)) => Y14))) => Y13) => (((!! @ $o @ (^[Y14 : $o]: (((~ (c_In @ c_Empty @ Y11)) => (((c_Repl @ sF1 @ (^[Y15 : $i]: (c_Eps_i @ (^[Y16 : $i]: (!! @ $o @ (^[Y17 : $o]: (((!! @ $o @ (^[Y18 : $o]: (((c_In @ c_Empty @ Y15) => ((sF9 = Y16) => Y18)) => Y18))) => Y17) => (((!! @ $o @ (^[Y18 : $o]: (((~ (c_In @ c_Empty @ Y15)) => ((sF9 = Y16) => Y18)) => Y18))) => Y17) => Y17)))))))) = Y12) => Y14)) => Y14))) => Y13) => Y13))))))))))) = Y7) => Y9)) => Y9))) => Y8) => Y8))))))))))))) => ((!! @ $i @ (^[Y5 : $i]: ((c_In @ Y5 @ Y2) => (!! @ $o @ (^[Y6 : $o]: (((!! @ $o @ (^[Y7 : $o]: (((c_In @ (c_Union @ (c_Repl @ sF1 @ (^[Y8 : $i]: (c_Eps_i @ (^[Y9 : $i]: (!! @ $o @ (^[Y10 : $o]: (((!! @ $o @ (^[Y11 : $o]: (((c_In @ c_Empty @ Y8) => ((Y5 = Y9) => Y11)) => Y11))) => Y10) => (((!! @ $o @ (^[Y11 : $o]: (((~ (c_In @ c_Empty @ Y8)) => (((c_Repl @ sF1 @ (^[Y12 : $i]: (c_Eps_i @ (^[Y13 : $i]: (!! @ $o @ (^[Y14 : $o]: (((!! @ $o @ (^[Y15 : $o]: (((c_In @ c_Empty @ Y12) => ((sF9 = Y13) => Y15)) => Y15))) => Y14) => (((!! @ $o @ (^[Y15 : $o]: (((~ (c_In @ c_Empty @ Y12)) => ((sF9 = Y13) => Y15)) => Y15))) => Y14) => Y14)))))))) = Y9) => Y11)) => Y11))) => Y10) => Y10))))))))) @ Y0) => ((~ (c_In @ Y5 @ Y0)) => Y7)) => Y7))) => Y6) => (((!! @ $o @ (^[Y7 : $o]: (((~ (c_In @ (c_Union @ (c_Repl @ sF1 @ (^[Y8 : $i]: (c_Eps_i @ (^[Y9 : $i]: (!! @ $o @ (^[Y10 : $o]: (((!! @ $o @ (^[Y11 : $o]: (((c_In @ c_Empty @ Y8) => ((Y5 = Y9) => Y11)) => Y11))) => Y10) => (((!! @ $o @ (^[Y11 : $o]: (((~ (c_In @ c_Empty @ Y8)) => (((c_Repl @ sF1 @ (^[Y12 : $i]: (c_Eps_i @ (^[Y13 : $i]: (!! @ $o @ (^[Y14 : $o]: (((!! @ $o @ (^[Y15 : $o]: (((c_In @ c_Empty @ Y12) => ((sF9 = Y13) => Y15)) => Y15))) => Y14) => (((!! @ $o @ (^[Y15 : $o]: (((~ (c_In @ c_Empty @ Y12)) => ((sF9 = Y13) => Y15)) => Y15))) => Y14) => Y14)))))))) = Y9) => Y11)) => Y11))) => Y10) => Y10))))))))) @ Y0)) => ((c_In @ Y5 @ Y0) => Y7)) => Y7))) => Y6) => Y6))))))) => Y4)) => Y4))) => Y3)) => Y3)))))) => Y1)) => Y1)))))) => ($false => X2)) => X2))) | (((X0 @ (X1 @ (X1 @ (X1 @ sF11))))) = $false)) )),
% 9.27/1.88 inference(boolean_simplification,[],[f622])).
% 9.27/1.88 thf(f639,plain,(
% 9.27/1.88 ( ! 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@ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: (((!! @ $i @ (^[Y3 : $i]: ((c_In @ Y3 @ Y1) => (c_In @ Y3 @ Y0)))) => ((!! @ $o @ (^[Y3 : $o]: (((?? @ $i @ (^[Y4 : $i]: (!! @ $o @ (^[Y5 : $o]: (((c_In @ Y4 @ (c_Union @ (c_Repl @ sF1 @ (^[Y6 : $i]: (c_Eps_i @ (^[Y7 : $i]: (!! @ $o @ (^[Y8 : $o]: (((!! @ $o @ (^[Y9 : $o]: (((c_In @ c_Empty @ Y6) => (((X1 @ Y1) = Y7) => Y9)) => Y9))) => Y8) => (((!! @ $o @ (^[Y9 : $o]: (((~ (c_In @ c_Empty @ Y6)) => (((c_Repl @ sF1 @ (^[Y10 : $i]: (c_Eps_i @ (^[Y11 : $i]: (!! @ $o @ (^[Y12 : $o]: (((!! @ $o @ (^[Y13 : $o]: (((c_In @ c_Empty @ Y10) => (((X1 @ Y1) = Y11) => Y13)) => Y13))) => Y12) => (((!! @ $o @ (^[Y13 : $o]: (((~ (c_In @ c_Empty @ Y10)) => (((X1 @ Y1) = Y11) => Y13)) => Y13))) => Y12) => Y12)))))))) = Y7) => Y9)) => Y9))) => Y8) => Y8)))))))))) => ((~ (!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ (c_Union @ (c_Repl @ sF1 @ (^[Y7 : $i]: (c_Eps_i @ (^[Y8 : $i]: (!! @ $o @ (^[Y9 : $o]: (((!! @ $o @ (^[Y10 : $o]: (((c_In @ c_Empty @ Y7) => (((X1 @ Y1) = Y8) => Y10)) => Y10))) => Y9) => (((!! @ $o @ (^[Y10 : $o]: (((~ (c_In @ c_Empty @ Y7)) => (((c_Repl @ sF1 @ (^[Y11 : $i]: (c_Eps_i @ (^[Y12 : $i]: (!! @ $o @ (^[Y13 : $o]: (((!! @ $o @ (^[Y14 : $o]: (((c_In @ c_Empty @ Y11) => (((X1 @ Y1) = Y12) => Y14)) => Y14))) => Y13) => (((!! @ $o @ (^[Y14 : $o]: (((~ (c_In @ c_Empty @ Y11)) => (((X1 @ Y1) = Y12) => Y14)) => Y14))) => Y13) => Y13)))))))) = Y8) => Y10)) => Y10))) => Y9) => Y9)))))))))) => (c_In @ Y6 @ (c_Power @ Y4)))))) => Y5)) => Y5))))) => ((~ (?? @ $i @ (^[Y4 : $i]: (!! @ $o @ (^[Y5 : $o]: (((!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ Y4) => (c_In @ Y6 @ (c_Union @ (c_Repl @ sF1 @ (^[Y7 : $i]: (c_Eps_i @ (^[Y8 : $i]: (!! @ $o @ (^[Y9 : $o]: (((!! @ $o @ (^[Y10 : $o]: (((c_In @ c_Empty @ Y7) => (((X1 @ Y1) = Y8) => Y10)) => Y10))) => Y9) => (((!! @ $o @ (^[Y10 : $o]: (((~ (c_In @ c_Empty @ Y7)) => (((c_Repl @ sF1 @ (^[Y11 : $i]: (c_Eps_i @ (^[Y12 : $i]: (!! @ $o @ (^[Y13 : $o]: (((!! @ $o @ (^[Y14 : $o]: (((c_In @ c_Empty @ Y11) => (((X1 @ Y1) = Y12) => Y14)) => Y14))) => Y13) => (((!! @ $o @ (^[Y14 : $o]: (((~ (c_In @ c_Empty @ Y11)) => (((X1 @ Y1) = Y12) => Y14)) => Y14))) => Y13) => Y13)))))))) = Y8) => Y10)) => Y10))) => Y9) => Y9))))))))))))) => ((!! @ $o @ (^[Y6 : $o]: (((~ (!! @ $i @ (^[Y7 : $i]: ((c_In @ Y7 @ (c_Union @ (c_Repl @ sF1 @ (^[Y8 : $i]: (c_Eps_i @ (^[Y9 : $i]: (!! @ $o @ (^[Y10 : $o]: (((!! @ $o @ (^[Y11 : $o]: (((c_In @ c_Empty @ Y8) => (((X1 @ Y1) = Y9) => Y11)) => Y11))) => Y10) => (((!! @ $o @ (^[Y11 : $o]: (((~ (c_In @ c_Empty @ Y8)) => (((c_Repl @ sF1 @ (^[Y12 : $i]: (c_Eps_i @ (^[Y13 : $i]: (!! @ $o @ (^[Y14 : $o]: (((!! @ $o @ (^[Y15 : $o]: (((c_In @ c_Empty @ Y12) => (((X1 @ Y1) = Y13) => Y15)) => Y15))) => Y14) => (((!! @ $o @ (^[Y15 : $o]: (((~ (c_In @ c_Empty @ Y12)) => (((X1 @ Y1) = Y13) => Y15)) => Y15))) => Y14) => Y14)))))))) = Y9) => Y11)) => Y11))) => Y10) => Y10)))))))))) => (c_In @ Y7 @ Y4))))) => ((?? @ $i @ (^[Y7 : $i]: (!! @ $o @ (^[Y8 : $o]: (((c_In @ Y7 @ Y4) => ((~ (!! @ $i @ (^[Y9 : $i]: ((c_In @ Y9 @ Y4) => (c_In @ Y9 @ (c_Power @ Y7)))))) => Y8)) => Y8))))) => Y6)) => Y6))) => Y5)) => Y5)))))) => Y3)) => Y3))) => Y2)) => Y2)))))))))) => (?? @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: (((?? @ $i @ (^[Y2 : $i]: (!! @ $o @ (^[Y3 : $o]: (((!! @ $i @ (^[Y4 : $i]: ((c_In @ Y4 @ Y2) => (c_In @ Y4 @ Y0)))) => ((((X1 @ Y0) = Y0) => (?? @ $i @ (^[Y4 : $i]: (!! @ $o @ (^[Y5 : $o]: (((!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ Y4) => (c_In @ Y6 @ Y0)))) => ((~ (X0 @ (c_Union @ (c_Repl @ Y2 @ (^[Y6 : $i]: (c_Repl @ sF7 @ (^[Y7 : $i]: (c_Union @ (c_Repl @ sF1 @ (^[Y8 : $i]: (c_Eps_i @ (^[Y9 : $i]: (!! @ $o @ (^[Y10 : $o]: (((!! @ $o @ (^[Y11 : $o]: (((c_In @ c_Empty @ Y8) => (((c_Repl @ Y6 @ (^[Y12 : $i]: (c_Repl @ Y12 @ (^[Y13 : $i]: (c_Eps_i @ (^[Y14 : $i]: (!! @ ($i > $i > $o) @ (^[Y15 : $i > $i > $o]: ((!! @ ($i > $i) @ (^[Y16 : $i > $i]: (!! @ $i @ (^[Y17 : $i]: ((!! @ $i @ (^[Y18 : $i]: ((c_In @ Y18 @ Y17) => (Y15 @ Y18 @ (Y16 @ Y18))))) => (Y15 @ Y17 @ (c_Union @ (c_Repl @ sF1 @ (^[Y18 : $i]: (c_Eps_i @ (^[Y19 : $i]: (!! @ $o @ (^[Y20 : $o]: (((!! @ $o @ (^[Y21 : $o]: (((c_In @ c_Empty @ Y18) => ((sF2 = Y19) => Y21)) => Y21))) => Y20) => (((!! @ $o @ (^[Y21 : $o]: (((~ (c_In @ c_Empty @ Y18)) => (((c_Repl @ Y17 @ Y16) = Y19) => Y21)) => Y21))) => Y20) => Y20))))))))))))))) => (Y15 @ Y13 @ Y14)))))))))) = Y9) => Y11)) => Y11))) => Y10) => (((!! @ $o @ (^[Y11 : $o]: (((~ (c_In @ c_Empty @ Y8)) => (((c_Repl @ Y7 @ (^[Y12 : $i]: (c_Eps_i @ (^[Y13 : $i]: (!! @ ($i > $i > $o) @ (^[Y14 : $i > $i > $o]: ((!! @ ($i > $i) @ (^[Y15 : $i > $i]: (!! @ $i @ (^[Y16 : $i]: ((!! @ $i @ (^[Y17 : $i]: ((c_In @ Y17 @ Y16) => (Y14 @ Y17 @ (Y15 @ Y17))))) => (Y14 @ Y16 @ (c_Union @ (c_Repl @ sF1 @ (^[Y17 : $i]: (c_Eps_i @ (^[Y18 : $i]: (!! @ $o @ (^[Y19 : $o]: (((!! @ $o @ (^[Y20 : $o]: (((c_In @ c_Empty @ Y17) => ((sF2 = Y18) => Y20)) => Y20))) => Y19) => (((!! @ $o @ (^[Y20 : $o]: (((~ (c_In @ c_Empty @ Y17)) => (((c_Repl @ Y16 @ Y15) = Y18) => Y20)) => Y20))) => Y19) => Y19))))))))))))))) => (Y14 @ Y12 @ Y13)))))))) = Y9) => Y11)) => Y11))) => Y10) => Y10)))))))))))))))) => Y5)) => Y5)))))) => Y3)) => Y3))))) => ((~ (?? @ $i @ (^[Y2 : $i]: (!! @ $o @ (^[Y3 : $o]: (((!! @ $o @ (^[Y4 : $o]: (((!! @ $i @ (^[Y5 : $i]: ((c_In @ Y5 @ Y2) => (!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ Y5) => (c_In @ Y6 @ Y2))))))) => ((!! @ $i @ (^[Y5 : $i]: ((c_In @ Y5 @ Y2) => (!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ Y5) => (!! @ $i @ (^[Y7 : $i]: ((c_In @ Y7 @ Y6) => (c_In @ Y7 @ Y5)))))))))) => Y4)) => Y4))) => ((!! @ $o @ (^[Y4 : $o]: (((!! @ $i @ (^[Y5 : $i]: ((c_In @ Y5 @ Y0) => (c_In @ Y5 @ (c_Union @ (c_Repl @ sF1 @ (^[Y6 : $i]: (c_Eps_i @ (^[Y7 : $i]: (!! @ $o @ (^[Y8 : $o]: (((!! @ $o @ (^[Y9 : $o]: (((c_In @ c_Empty @ Y6) => ((Y2 = Y7) => Y9)) => Y9))) => Y8) => (((!! @ $o @ (^[Y9 : $o]: (((~ (c_In @ c_Empty @ Y6)) => (((c_Repl @ Y2 @ (^[Y10 : $i]: (c_Union @ (c_Repl @ sF1 @ (^[Y11 : $i]: (c_Eps_i @ (^[Y12 : $i]: (!! @ $o @ (^[Y13 : $o]: (((!! @ $o @ (^[Y14 : $o]: (((c_In @ c_Empty @ Y11) => ((Y10 = Y12) => Y14)) => Y14))) => Y13) => (((!! @ $o @ (^[Y14 : $o]: (((~ (c_In @ c_Empty @ Y11)) => (((c_Repl @ sF1 @ (^[Y15 : $i]: (c_Eps_i @ (^[Y16 : $i]: (!! @ $o @ (^[Y17 : $o]: (((!! @ $o @ (^[Y18 : $o]: (((c_In @ c_Empty @ Y15) => ((sF9 = Y16) => Y18)) => Y18))) => Y17) => (((!! @ $o @ (^[Y18 : $o]: (((~ (c_In @ c_Empty @ Y15)) => ((sF9 = Y16) => Y18)) => Y18))) => Y17) => Y17)))))))) = Y12) => Y14)) => Y14))) => Y13) => Y13))))))))))) = Y7) => Y9)) => Y9))) => Y8) => Y8))))))))))))) => ((!! @ $i @ (^[Y5 : $i]: ((c_In @ Y5 @ Y2) => (!! @ $o @ (^[Y6 : $o]: (((!! @ $o @ (^[Y7 : $o]: (((c_In @ (c_Union @ (c_Repl @ sF1 @ (^[Y8 : $i]: (c_Eps_i @ (^[Y9 : $i]: (!! @ $o @ (^[Y10 : $o]: (((!! @ $o @ (^[Y11 : $o]: (((c_In @ c_Empty @ Y8) => ((Y5 = Y9) => Y11)) => Y11))) => Y10) => (((!! @ $o @ (^[Y11 : $o]: (((~ (c_In @ c_Empty @ Y8)) => (((c_Repl @ sF1 @ (^[Y12 : $i]: (c_Eps_i @ (^[Y13 : $i]: (!! @ $o @ (^[Y14 : $o]: (((!! @ $o @ (^[Y15 : $o]: (((c_In @ c_Empty @ Y12) => ((sF9 = Y13) => Y15)) => Y15))) => Y14) => (((!! @ $o @ (^[Y15 : $o]: (((~ (c_In @ c_Empty @ Y12)) => ((sF9 = Y13) => Y15)) => Y15))) => Y14) => Y14)))))))) = Y9) => Y11)) => Y11))) => Y10) => Y10))))))))) @ Y0) => ((~ (c_In @ Y5 @ Y0)) => Y7)) => Y7))) => Y6) => (((!! @ $o @ (^[Y7 : $o]: (((~ (c_In @ (c_Union @ (c_Repl @ sF1 @ (^[Y8 : $i]: (c_Eps_i @ (^[Y9 : $i]: (!! @ $o @ (^[Y10 : $o]: (((!! @ $o @ (^[Y11 : $o]: (((c_In @ c_Empty @ Y8) => ((Y5 = Y9) => Y11)) => Y11))) => Y10) => (((!! @ $o @ (^[Y11 : $o]: (((~ (c_In @ c_Empty @ Y8)) => (((c_Repl @ sF1 @ (^[Y12 : $i]: (c_Eps_i @ (^[Y13 : $i]: (!! @ $o @ (^[Y14 : $o]: (((!! @ $o @ (^[Y15 : $o]: (((c_In @ c_Empty @ Y12) => ((sF9 = Y13) => Y15)) => Y15))) => Y14) => (((!! @ $o @ (^[Y15 : $o]: (((~ (c_In @ c_Empty @ Y12)) => ((sF9 = Y13) => Y15)) => Y15))) => Y14) => Y14)))))))) = Y9) => Y11)) => Y11))) => Y10) => Y10))))))))) @ Y0)) => ((c_In @ Y5 @ Y0) => Y7)) => Y7))) => Y6) => Y6))))))) => Y4)) => Y4))) => Y3)) => Y3)))))) => Y1)) => Y1)))))) => $true) => X2)))) )),
% 9.27/1.88 inference(boolean_simplification,[],[f638])).
% 9.27/1.88 thf(f640,plain,(
% 9.27/1.88 ( ! [X2 : $o,X0 : ($i > $o),X1 : ($i > $i)] : (($true = (($true => X2))) | (((X0 @ (X1 @ (X1 @ (X1 @ sF11))))) = $false)) )),
% 9.27/1.88 inference(boolean_simplification,[],[f639])).
% 9.27/1.88 thf(f641,plain,(
% 9.27/1.88 ( ! [X2 : $o,X0 : ($i > $o),X1 : ($i > $i)] : ((((X0 @ (X1 @ (X1 @ (X1 @ sF11))))) = $false) | ($true = X2)) )),
% 9.27/1.88 inference(boolean_simplification,[],[f640])).
% 9.27/1.88 thf(f684,plain,(
% 9.27/1.88 ( ! [X2 : $o,X1 : ($i > $i)] : (($false = (((^[Y0 : $i]: ($true)) @ (X1 @ (X1 @ (X1 @ sF11)))))) | ($true = X2)) )),
% 9.27/1.88 inference(primitive_instantiation,[],[f641])).
% 9.27/1.88 thf(f696,plain,(
% 9.27/1.88 ( ! [X2 : $o] : (($true = $false) | ($true = X2)) )),
% 9.27/1.88 inference(beta-eta_normalization,[],[f684])).
% 9.27/1.88 thf(f697,plain,(
% 9.27/1.88 ( ! [X2 : $o] : (($true = X2)) )),
% 9.27/1.88 inference(trivial_inequality_removal,[],[f696])).
% 9.27/1.88 thf(f714,plain,(
% 9.27/1.88 ($true = $false)),
% 9.27/1.88 inference(superposition,[],[f596,f697])).
% 9.27/1.88 thf(f754,plain,(
% 9.27/1.88 $false),
% 9.27/1.88 inference(trivial_inequality_removal,[],[f714])).
% 9.27/1.88 % SZS output end Proof for theBenchmark
% 9.27/1.88 % (1105140)------------------------------
% 9.27/1.88 % (1105140)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 9.27/1.88 % (1105140)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.27/1.88 % (1105140)CaDiCaL version: 2.1.3
% 9.27/1.88 % (1105140)Termination reason: Refutation
% 9.27/1.88 % (1105140)Time elapsed: 0.481 s
% 9.27/1.88 % (1105140)Peak memory usage: 17 MB
% 9.27/1.88 % (1105140)Instructions burned: 1154 (million)
% 9.27/1.88 % (1104950)Success in time 1.627 s
% 9.27/1.88 % Vampire exiting
%------------------------------------------------------------------------------