%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO879^1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n013.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 1.42s 0.49s
% Output : Refutation 1.42s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO879^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 % Computer : n013.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 17:23:06 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running higher-order theorem proving
% 0.19/0.26 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.73/0.39 % (2405801)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.73/0.39 % (2405812)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.73/0.39 % (2405812)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
% 0.73/0.39 % (2405812)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=4129745220:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.73/0.39 % (2405810)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=771030045:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.73/0.39 % (2405807)lrs+10_16_si=on:nwc=1.5:random_seed=2784358063:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.73/0.39 % (2405806)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=562692834:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.73/0.39 % (2405808)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=315982926:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.73/0.39 % (2405809)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=2551980594: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)
% 0.73/0.39 % (2405811)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=36621316:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.73/0.39 % (2405808)Instruction limit reached!
% 0.73/0.39 % (2405808)------------------------------
% 0.73/0.39 % (2405808)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.73/0.39 % (2405808)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.73/0.39 % (2405808)CaDiCaL version: 2.1.3
% 0.73/0.39 % (2405808)Termination reason: Instruction limit
% 0.73/0.39 % (2405808)Termination phase: shuffling
% 0.73/0.39 % (2405808)Time elapsed: 0.002 s
% 0.73/0.39 % (2405808)Peak memory usage: 10 MB
% 0.73/0.39 % (2405808)Instructions burned: 5 (million)
% 0.73/0.39 % (2405807)Instruction limit reached!
% 0.73/0.39 % (2405807)------------------------------
% 0.73/0.39 % (2405807)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.73/0.39 % (2405807)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.73/0.39 % (2405807)CaDiCaL version: 2.1.3
% 0.73/0.39 % (2405807)Termination reason: Instruction limit
% 0.73/0.39 % (2405807)Termination phase: Property scanning
% 0.73/0.39 % (2405807)Time elapsed: 0.009 s
% 0.73/0.39 % (2405807)Peak memory usage: 10 MB
% 0.73/0.39 % (2405807)Instructions burned: 19 (million)
% 0.73/0.39 % (2405810)Instruction limit reached!
% 0.73/0.39 % (2405810)------------------------------
% 0.73/0.39 % (2405810)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.73/0.39 % (2405810)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.73/0.39 % (2405810)CaDiCaL version: 2.1.3
% 0.73/0.39 % (2405810)Termination reason: Instruction limit
% 0.73/0.39 % (2405810)Termination phase: Naming
% 0.73/0.39 % (2405810)Time elapsed: 0.011 s
% 0.73/0.39 % (2405810)Peak memory usage: 10 MB
% 0.73/0.39 % (2405810)Instructions burned: 25 (million)
% 0.73/0.39 % (2405820)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3727209595:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.73/0.39 % (2405820)Instruction limit reached!
% 0.73/0.39 % (2405820)------------------------------
% 0.73/0.39 % (2405820)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.73/0.39 % (2405820)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.73/0.39 % (2405820)CaDiCaL version: 2.1.3
% 0.73/0.39 % (2405820)Termination reason: Instruction limit
% 0.73/0.39 % (2405820)Termination phase: shuffling
% 0.73/0.39 % (2405820)Time elapsed: 0.003 s
% 0.73/0.39 % (2405820)Peak memory usage: 10 MB
% 0.73/0.39 % (2405820)Instructions burned: 6 (million)
% 0.73/0.39 % (2405822)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.73/0.42 % (2405821)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=4255015117:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.73/0.42 % (2405822)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=3419003727:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.73/0.42 % (2405821)Instruction limit reached!
% 0.73/0.42 % (2405821)------------------------------
% 0.73/0.42 % (2405821)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.73/0.42 % (2405821)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.73/0.42 % (2405821)CaDiCaL version: 2.1.3
% 0.73/0.42 % (2405821)Termination reason: Instruction limit
% 0.73/0.42 % (2405821)Termination phase: shuffling
% 0.73/0.42 % (2405821)Time elapsed: 0.003 s
% 0.73/0.42 % (2405821)Peak memory usage: 10 MB
% 0.73/0.42 % (2405821)Instructions burned: 7 (million)
% 0.73/0.42 % (2405822)Instruction limit reached!
% 0.73/0.42 % (2405822)------------------------------
% 0.73/0.42 % (2405822)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.73/0.42 % (2405822)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.73/0.42 % (2405822)CaDiCaL version: 2.1.3
% 0.73/0.42 % (2405822)Termination reason: Instruction limit
% 0.73/0.42 % (2405822)Termination phase: shuffling
% 0.73/0.42 % (2405822)Time elapsed: 0.004 s
% 0.73/0.42 % (2405822)Peak memory usage: 10 MB
% 0.73/0.42 % (2405822)Instructions burned: 9 (million)
% 0.73/0.42 % (2405811)Instruction limit reached!
% 0.73/0.42 % (2405811)------------------------------
% 0.73/0.42 % (2405811)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.73/0.42 % (2405811)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.73/0.42 % (2405811)CaDiCaL version: 2.1.3
% 0.73/0.42 % (2405812)Instruction limit reached!
% 0.73/0.42 % (2405812)------------------------------
% 0.73/0.42 % (2405812)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.73/0.42 % (2405812)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.73/0.42 % (2405811)Termination reason: Instruction limit
% 0.73/0.42 % (2405811)Termination phase: Saturation
% 0.73/0.42 % (2405811)Time elapsed: 0.034 s
% 0.73/0.42 % (2405812)CaDiCaL version: 2.1.3
% 0.73/0.42 % (2405811)Peak memory usage: 12 MB
% 0.73/0.42 % (2405811)Instructions burned: 76 (million)
% 0.73/0.42 % (2405812)Termination reason: Instruction limit
% 0.73/0.42 % (2405812)Termination phase: Saturation
% 0.73/0.42 % (2405812)Time elapsed: 0.043 s
% 0.73/0.42 % (2405812)Peak memory usage: 14 MB
% 0.73/0.42 % (2405812)Instructions burned: 162 (million)
% 0.73/0.42 % (2405830)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.73/0.42 % (2405824)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=1161662325:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.73/0.42 % (2405806)Instruction limit reached!
% 0.73/0.42 % (2405806)------------------------------
% 0.73/0.42 % (2405806)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.73/0.42 % (2405806)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.73/0.42 % (2405806)CaDiCaL version: 2.1.3
% 0.73/0.42 % (2405806)Termination reason: Instruction limit
% 0.73/0.42 % (2405806)Termination phase: Saturation
% 0.73/0.42 % (2405806)Time elapsed: 0.047 s
% 0.73/0.42 % (2405806)Peak memory usage: 12 MB
% 0.73/0.42 % (2405806)Instructions burned: 87 (million)
% 0.73/0.42 % (2405830)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=1160512407:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.73/0.42 % (2405827)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
% 0.73/0.42 % (2405827)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.73/0.42 % (2405830)Instruction limit reached!
% 0.73/0.42 % (2405830)------------------------------
% 0.73/0.42 % (2405830)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.73/0.42 % (2405830)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.73/0.45 % (2405830)CaDiCaL version: 2.1.3
% 0.73/0.45 % (2405830)Termination reason: Instruction limit
% 0.73/0.45 % (2405830)Termination phase: shuffling
% 0.73/0.45 % (2405830)Time elapsed: 0.003 s
% 0.73/0.45 % (2405830)Peak memory usage: 10 MB
% 0.73/0.45 % (2405830)Instructions burned: 14 (million)
% 0.73/0.45 % (2405827)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=2568543291:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.73/0.45 % (2405824)Instruction limit reached!
% 0.73/0.45 % (2405824)------------------------------
% 0.73/0.45 % (2405824)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.73/0.45 % (2405824)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.73/0.45 % (2405824)CaDiCaL version: 2.1.3
% 0.73/0.45 % (2405824)Termination reason: Instruction limit
% 0.73/0.45 % (2405824)Termination phase: shuffling
% 0.73/0.45 % (2405824)Time elapsed: 0.006 s
% 0.73/0.45 % (2405824)Peak memory usage: 10 MB
% 0.73/0.45 % (2405824)Instructions burned: 14 (million)
% 0.73/0.45 % (2405829)lrs+10_1_si=on:cs=on:random_seed=1653012331:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.73/0.45 % (2405828)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=1225048904:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.73/0.45 % (2405829)Instruction limit reached!
% 0.73/0.45 % (2405829)------------------------------
% 0.73/0.45 % (2405829)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.73/0.45 % (2405829)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.73/0.45 % (2405829)CaDiCaL version: 2.1.3
% 0.73/0.45 % (2405829)Termination reason: Instruction limit
% 0.73/0.45 % (2405829)Termination phase: shuffling
% 0.73/0.45 % (2405829)Time elapsed: 0.004 s
% 0.73/0.45 % (2405829)Peak memory usage: 10 MB
% 0.73/0.45 % (2405829)Instructions burned: 9 (million)
% 0.73/0.45 % (2405827)Instruction limit reached!
% 0.73/0.45 % (2405827)------------------------------
% 0.73/0.45 % (2405827)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.73/0.45 % (2405827)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.73/0.45 % (2405827)CaDiCaL version: 2.1.3
% 0.73/0.45 % (2405827)Termination reason: Instruction limit
% 0.73/0.45 % (2405827)Termination phase: Property scanning
% 0.73/0.45 % (2405827)Time elapsed: 0.012 s
% 0.73/0.45 % (2405827)Peak memory usage: 10 MB
% 0.73/0.45 % (2405827)Instructions burned: 29 (million)
% 0.73/0.45 % (2405836)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=2168821512:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/25Mi)
% 0.73/0.45 % (2405833)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=2804697237:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.73/0.45 % (2405834)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=3827728451:st=2:i=249:sd=1:rtra=on:ss=axioms_2999 on theBenchmark for (2999ds/249Mi)
% 0.73/0.45 % (2405836)Instruction limit reached!
% 0.73/0.45 % (2405836)------------------------------
% 0.73/0.45 % (2405836)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.73/0.45 % (2405836)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.73/0.45 % (2405836)CaDiCaL version: 2.1.3
% 0.73/0.45 % (2405836)Termination reason: Instruction limit
% 0.73/0.45 % (2405836)Termination phase: SInE selection
% 0.73/0.45 % (2405836)Time elapsed: 0.007 s
% 0.73/0.45 % (2405836)Peak memory usage: 10 MB
% 0.73/0.45 % (2405836)Instructions burned: 29 (million)
% 0.73/0.45 % (2405839)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=2816113374:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2999 on theBenchmark for (2999ds/14Mi)
% 0.73/0.45 % (2405840)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=2285736326:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2999 on theBenchmark for (2999ds/327Mi)
% 0.73/0.45 % (2405839)Instruction limit reached!
% 0.73/0.45 % (2405839)------------------------------
% 0.73/0.45 % (2405839)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.73/0.45 % (2405839)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.42/0.49 % (2405844)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=2862511070:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 1.42/0.49 % (2405839)CaDiCaL version: 2.1.3
% 1.42/0.49 % (2405839)Termination reason: Instruction limit
% 1.42/0.49 % (2405839)Termination phase: shuffling
% 1.42/0.49 % (2405839)Time elapsed: 0.006 s
% 1.42/0.49 % (2405839)Peak memory usage: 10 MB
% 1.42/0.49 % (2405839)Instructions burned: 14 (million)
% 1.42/0.49 % (2405833)Instruction limit reached!
% 1.42/0.49 % (2405833)------------------------------
% 1.42/0.49 % (2405833)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.42/0.49 % (2405833)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.42/0.49 % (2405833)CaDiCaL version: 2.1.3
% 1.42/0.49 % (2405833)Termination reason: Instruction limit
% 1.42/0.49 % (2405833)Termination phase: Saturation
% 1.42/0.49 % (2405833)Time elapsed: 0.018 s
% 1.42/0.49 % (2405833)Peak memory usage: 12 MB
% 1.42/0.49 % (2405833)Instructions burned: 38 (million)
% 1.42/0.49 % (2405844)Instruction limit reached!
% 1.42/0.49 % (2405844)------------------------------
% 1.42/0.49 % (2405844)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.42/0.49 % (2405844)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.42/0.49 % (2405844)CaDiCaL version: 2.1.3
% 1.42/0.49 % (2405844)Termination reason: Instruction limit
% 1.42/0.49 % (2405844)Termination phase: shuffling
% 1.42/0.49 % (2405844)Time elapsed: 0.003 s
% 1.42/0.49 % (2405844)Peak memory usage: 10 MB
% 1.42/0.49 % (2405844)Instructions burned: 14 (million)
% 1.42/0.49 % (2405828)Instruction limit reached!
% 1.42/0.49 % (2405828)------------------------------
% 1.42/0.49 % (2405828)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.42/0.49 % (2405828)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.42/0.49 % (2405828)CaDiCaL version: 2.1.3
% 1.42/0.49 % (2405828)Termination reason: Instruction limit
% 1.42/0.49 % (2405828)Termination phase: Saturation
% 1.42/0.49 % (2405828)Time elapsed: 0.037 s
% 1.42/0.49 % (2405828)Peak memory usage: 12 MB
% 1.42/0.49 % (2405828)Instructions burned: 87 (million)
% 1.42/0.49 % (2405850)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=2591495150:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 1.42/0.49 % (2405848)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=1665875269: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)
% 1.42/0.49 % (2405850)Instruction limit reached!
% 1.42/0.49 % (2405850)------------------------------
% 1.42/0.49 % (2405850)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.42/0.49 % (2405850)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.42/0.49 % (2405850)CaDiCaL version: 2.1.3
% 1.42/0.49 % (2405850)Termination reason: Instruction limit
% 1.42/0.49 % (2405850)Termination phase: Property scanning
% 1.42/0.49 % (2405850)Time elapsed: 0.005 s
% 1.42/0.49 % (2405850)Peak memory usage: 10 MB
% 1.42/0.49 % (2405850)Instructions burned: 23 (million)
% 1.42/0.49 % (2405849)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=3204488031:i=26:ep=R:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/26Mi)
% 1.42/0.49 % (2405848)Instruction limit reached!
% 1.42/0.49 % (2405848)------------------------------
% 1.42/0.49 % (2405848)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.42/0.49 % (2405848)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.42/0.49 % (2405848)CaDiCaL version: 2.1.3
% 1.42/0.49 % (2405848)Termination reason: Instruction limit
% 1.42/0.49 % (2405848)Termination phase: shuffling
% 1.42/0.49 % (2405848)Time elapsed: 0.002 s
% 1.42/0.49 % (2405848)Peak memory usage: 10 MB
% 1.42/0.49 % (2405848)Instructions burned: 4 (million)
% 1.42/0.49 % (2405851)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=83491401:cond=on:i=60:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/60Mi)
% 1.42/0.49 % (2405849)Instruction limit reached!
% 1.42/0.49 % (2405849)------------------------------
% 1.42/0.49 % (2405849)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.42/0.49 % (2405849)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.42/0.49 % (2405849)CaDiCaL version: 2.1.3
% 1.42/0.49 % (2405849)Termination reason: Instruction limit
% 1.42/0.49 % (2405849)Termination phase: Property scanning
% 1.42/0.49 % (2405849)Time elapsed: 0.012 s
% 1.42/0.49 % (2405849)Peak memory usage: 10 MB
% 1.42/0.49 % (2405849)Instructions burned: 27 (million)
% 1.42/0.49 % (2405854)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
% 1.42/0.49 % (2405854)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs
% 1.42/0.49 % (2405856)WARNING Broken Constraint: if choice_reasoning(on) has been set then choice_ax(on) is equal to off
% 1.42/0.49 % (2405834)Refutation not found, incomplete strategy
% 1.42/0.49 % (2405834)------------------------------
% 1.42/0.49 % (2405834)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.42/0.49 % (2405834)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.42/0.49 % (2405834)CaDiCaL version: 2.1.3
% 1.42/0.49 % (2405834)Termination reason: Refutation not found, incomplete strategy
% 1.42/0.49 % (2405834)Time elapsed: 0.053 s
% 1.42/0.49 % (2405834)Peak memory usage: 12 MB
% 1.42/0.49 % (2405834)Instructions burned: 62 (million)
% 1.42/0.49 % (2405854)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=571292844:i=14:add=off:nm=40:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 1.42/0.49 % (2405834)------------------------------
% 1.42/0.49 % (2405834)------------------------------
% 1.42/0.49 % (2405856)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=4235477451:i=8:nm=2:rtra=on:fe=abstraction:inj=on_2998 on theBenchmark for (2998ds/8Mi)
% 1.42/0.49 % (2405854)Instruction limit reached!
% 1.42/0.49 % (2405854)------------------------------
% 1.42/0.49 % (2405854)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.42/0.49 % (2405854)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.42/0.49 % (2405854)CaDiCaL version: 2.1.3
% 1.42/0.49 % (2405854)Termination reason: Instruction limit
% 1.42/0.49 % (2405854)Termination phase: shuffling
% 1.42/0.49 % (2405854)Time elapsed: 0.006 s
% 1.42/0.49 % (2405854)Peak memory usage: 10 MB
% 1.42/0.49 % (2405854)Instructions burned: 14 (million)
% 1.42/0.49 % (2405856)Instruction limit reached!
% 1.42/0.49 % (2405856)------------------------------
% 1.42/0.49 % (2405856)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.42/0.49 % (2405856)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.42/0.49 % (2405856)CaDiCaL version: 2.1.3
% 1.42/0.49 % (2405856)Termination reason: Instruction limit
% 1.42/0.49 % (2405856)Termination phase: shuffling
% 1.42/0.49 % (2405856)Time elapsed: 0.004 s
% 1.42/0.49 % (2405856)Peak memory usage: 10 MB
% 1.42/0.49 % (2405856)Instructions burned: 9 (million)
% 1.42/0.49 % (2405858)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=2507599799:uwa_fpi=on:i=31:doe=on:bd=preordered:rtra=on:fsd=on_2998 on theBenchmark for (2998ds/31Mi)
% 1.42/0.49 % (2405860)dis+10_1024_sil=128000:cnfonf=off:si=on:fd=off:random_seed=1797609808:i=7:hud=5:bd=preordered:rtra=on:bet=on_2998 on theBenchmark for (2998ds/7Mi)
% 1.42/0.49 % (2405860)Instruction limit reached!
% 1.42/0.49 % (2405860)------------------------------
% 1.42/0.49 % (2405860)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.42/0.49 % (2405860)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.42/0.49 % (2405860)CaDiCaL version: 2.1.3
% 1.42/0.49 % (2405860)Termination reason: Instruction limit
% 1.42/0.49 % (2405860)Termination phase: shuffling
% 1.42/0.49 % (2405860)Time elapsed: 0.002 s
% 1.42/0.49 % (2405860)Peak memory usage: 10 MB
% 1.42/0.49 % (2405860)Instructions burned: 9 (million)
% 1.42/0.49 % (2405851)Instruction limit reached!
% 1.42/0.49 % (2405851)------------------------------
% 1.42/0.49 % (2405851)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.42/0.49 % (2405851)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.42/0.49 % (2405851)CaDiCaL version: 2.1.3
% 1.42/0.49 % (2405851)Termination reason: Instruction limit
% 1.42/0.49 % (2405851)Termination phase: Saturation
% 1.42/0.49 % (2405851)Time elapsed: 0.029 s
% 1.42/0.49 % (2405851)Peak memory usage: 13 MB
% 1.42/0.49 % (2405851)Instructions burned: 61 (million)
% 1.42/0.49 % (2405862)lrs+10_1_plsq=on:drc=ordering:cnfonf=lazy_not_gen_be_off:bsd=on:si=on:plsqr=32,1:cs=on:random_seed=2282766595:i=23:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 1.42/0.49 % (2405858)Instruction limit reached!
% 1.42/0.49 % (2405858)------------------------------
% 1.42/0.49 % (2405858)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.42/0.49 % (2405858)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.42/0.49 % (2405858)CaDiCaL version: 2.1.3
% 1.42/0.49 % (2405858)Termination reason: Instruction limit
% 1.42/0.49 % (2405858)Termination phase: Property scanning
% 1.42/0.49 % (2405858)Time elapsed: 0.014 s
% 1.42/0.49 % (2405858)Peak memory usage: 10 MB
% 1.42/0.49 % (2405858)Instructions burned: 32 (million)
% 1.42/0.49 % (2405866)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=1969408312:i=1240:rtra=on:ixr=off_2998 on theBenchmark for (2998ds/1240Mi)
% 1.42/0.49 % (2405862)Instruction limit reached!
% 1.42/0.49 % (2405862)------------------------------
% 1.42/0.49 % (2405862)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.42/0.49 % (2405862)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.42/0.49 % (2405863)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=1072484302:s2a=on:i=20:kws=inv_frequency:bd=all:rtra=on_2998 on theBenchmark for (2998ds/20Mi)
% 1.42/0.49 % (2405862)CaDiCaL version: 2.1.3
% 1.42/0.49 % (2405862)Termination reason: Instruction limit
% 1.42/0.49 % (2405862)Termination phase: Property scanning
% 1.42/0.49 % (2405862)Time elapsed: 0.010 s
% 1.42/0.49 % (2405862)Peak memory usage: 10 MB
% 1.42/0.49 % (2405862)Instructions burned: 24 (million)
% 1.42/0.49 % (2405867)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=1490012575:i=143:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/143Mi)
% 1.42/0.49 % (2405869)lrs+1002_1_sil=128000:si=on:acc=on:uwa=off:random_seed=2459945776:st=5:s2a=on:i=193:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/193Mi)
% 1.42/0.49 % (2405863)Instruction limit reached!
% 1.42/0.49 % (2405863)------------------------------
% 1.42/0.49 % (2405863)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.42/0.49 % (2405863)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.42/0.49 % (2405863)CaDiCaL version: 2.1.3
% 1.42/0.49 % (2405863)Termination reason: Instruction limit
% 1.42/0.49 % (2405863)Termination phase: Property scanning
% 1.42/0.49 % (2405863)Time elapsed: 0.017 s
% 1.42/0.49 % (2405863)Peak memory usage: 10 MB
% 1.42/0.49 % (2405863)Instructions burned: 20 (million)
% 1.42/0.49 % (2405872)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3320940340:i=42:hud=10:rtra=on_2998 on theBenchmark for (2998ds/42Mi)
% 1.42/0.49 % (2405866) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2405801-2405866"...
% 1.42/0.49 % (2405866)...printing done.
% 1.42/0.49 % (2405866)Refutation found. Thanks to Tanya!
% 1.42/0.49 % SZS status Theorem for theBenchmark
% 1.42/0.49 % SZS output start Proof for theBenchmark
% 1.42/0.49 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 1.42/0.49 thf(func_def_0, type, c_Eps_i: (($i > $o) > $i)).
% 1.42/0.49 thf(func_def_1, type, c_False: $o).
% 1.42/0.49 thf(func_def_2, type, c_True: $o).
% 1.42/0.49 thf(func_def_3, type, c_not: ($o > $o)).
% 1.42/0.49 thf(func_def_4, type, c_and: ($o > $o > $o)).
% 1.42/0.49 thf(func_def_5, type, c_or: ($o > $o > $o)).
% 1.42/0.49 thf(func_def_6, type, c_iff: ($o > $o > $o)).
% 1.42/0.49 thf(func_def_7, type, c_In: ($i > $i > $o)).
% 1.42/0.49 thf(func_def_8, type, c_Subq: ($i > $i > $o)).
% 1.42/0.49 thf(func_def_10, type, c_Union: ($i > $i)).
% 1.42/0.49 thf(func_def_11, type, c_Power: ($i > $i)).
% 1.42/0.49 thf(func_def_12, type, c_Repl: ($i > ($i > $i) > $i)).
% 1.42/0.49 thf(func_def_13, type, c_TransSet: ($i > $o)).
% 1.42/0.49 thf(func_def_14, type, c_atleast2: ($i > $o)).
% 1.42/0.49 thf(func_def_15, type, c_atleast3: ($i > $o)).
% 1.42/0.49 thf(func_def_16, type, c_atleast4: ($i > $o)).
% 1.42/0.49 thf(func_def_17, type, c_atleast5: ($i > $o)).
% 1.42/0.49 thf(func_def_18, type, c_atleast6: ($i > $o)).
% 1.42/0.49 thf(func_def_19, type, c_exactly2: ($i > $o)).
% 1.42/0.49 thf(func_def_20, type, c_exactly3: ($i > $o)).
% 1.42/0.49 thf(func_def_21, type, c_exactly4: ($i > $o)).
% 1.42/0.49 thf(func_def_22, type, c_exactly5: ($i > $o)).
% 1.42/0.49 thf(func_def_23, type, c_exu_i: (($i > $o) > $o)).
% 1.42/0.49 thf(func_def_24, type, c_reflexive_i: (($i > $i > $o) > $o)).
% 1.42/0.49 thf(func_def_25, type, c_irreflexive_i: (($i > $i > $o) > $o)).
% 1.42/0.49 thf(func_def_26, type, c_symmetric_i: (($i > $i > $o) > $o)).
% 1.42/0.49 thf(func_def_27, type, c_antisymmetric_i: (($i > $i > $o) > $o)).
% 1.42/0.49 thf(func_def_28, type, c_transitive_i: (($i > $i > $o) > $o)).
% 1.42/0.49 thf(func_def_29, type, c_eqreln_i: (($i > $i > $o) > $o)).
% 1.42/0.49 thf(func_def_30, type, c_per_i: (($i > $i > $o) > $o)).
% 1.42/0.49 thf(func_def_31, type, c_linear_i: (($i > $i > $o) > $o)).
% 1.42/0.49 thf(func_def_32, type, c_trichotomous_or_i: (($i > $i > $o) > $o)).
% 1.42/0.49 thf(func_def_33, type, c_partialorder_i: (($i > $i > $o) > $o)).
% 1.42/0.49 thf(func_def_34, type, c_totalorder_i: (($i > $i > $o) > $o)).
% 1.42/0.49 thf(func_def_35, type, c_strictpartialorder_i: (($i > $i > $o) > $o)).
% 1.42/0.49 thf(func_def_36, type, c_stricttotalorder_i: (($i > $i > $o) > $o)).
% 1.42/0.49 thf(func_def_37, type, c_If_i: ($o > $i > $i > $i)).
% 1.42/0.49 thf(func_def_38, type, c_exactly1of2: ($o > $o > $o)).
% 1.42/0.49 thf(func_def_39, type, c_exactly1of3: ($o > $o > $o > $o)).
% 1.42/0.49 thf(func_def_40, type, c_nIn: ($i > $i > $o)).
% 1.42/0.49 thf(func_def_41, type, c_nSubq: ($i > $i > $o)).
% 1.42/0.50 thf(func_def_42, type, c_UPair: ($i > $i > $i)).
% 1.42/0.50 thf(func_def_43, type, c_Sing: ($i > $i)).
% 1.42/0.50 thf(func_def_44, type, c_binunion: ($i > $i > $i)).
% 1.42/0.50 thf(func_def_45, type, c_SetAdjoin: ($i > $i > $i)).
% 1.42/0.50 thf(func_def_46, type, c_famunion: ($i > ($i > $i) > $i)).
% 1.42/0.50 thf(func_def_47, type, c_Sep: ($i > ($i > $o) > $i)).
% 1.42/0.50 thf(func_def_48, type, c_ReplSep: ($i > ($i > $o) > ($i > $i) > $i)).
% 1.42/0.50 thf(func_def_49, type, c_binintersect: ($i > $i > $i)).
% 1.42/0.50 thf(func_def_50, type, c_setminus: ($i > $i > $i)).
% 1.42/0.50 thf(func_def_51, type, c_inj: ($i > $i > ($i > $i) > $o)).
% 1.42/0.50 thf(func_def_52, type, c_bij: ($i > $i > ($i > $i) > $o)).
% 1.42/0.50 thf(func_def_53, type, c_atleastp: ($i > $i > $o)).
% 1.42/0.50 thf(func_def_54, type, c_equip: ($i > $i > $o)).
% 1.42/0.50 thf(func_def_55, type, c_In_rec_poly_G_i: (($i > ($i > $i) > $i) > $i > $i > $o)).
% 1.42/0.50 thf(func_def_56, type, c_In_rec_poly_i: (($i > ($i > $i) > $i) > $i > $i)).
% 1.42/0.50 thf(func_def_57, type, c_ordsucc: ($i > $i)).
% 1.42/0.50 thf(func_def_58, type, c_nat_p: ($i > $o)).
% 1.42/0.50 thf(func_def_59, type, c_nat_primrec: ($i > ($i > $i > $i) > $i > $i)).
% 1.42/0.50 thf(func_def_60, type, c_add_nat: ($i > $i > $i)).
% 1.42/0.50 thf(func_def_61, type, c_mul_nat: ($i > $i > $i)).
% 1.42/0.50 thf(func_def_62, type, c_ordinal: ($i > $o)).
% 1.42/0.50 thf(func_def_63, type, c_V_: ($i > $i)).
% 1.42/0.50 thf(func_def_64, type, c_Inj1: ($i > $i)).
% 1.42/0.50 thf(func_def_65, type, c_Inj0: ($i > $i)).
% 1.42/0.50 thf(func_def_66, type, c_Unj: ($i > $i)).
% 1.42/0.50 thf(func_def_67, type, c_combine_funcs: ($i > $i > ($i > $i) > ($i > $i) > $i > $i)).
% 1.42/0.50 thf(func_def_68, type, c_setsum: ($i > $i > $i)).
% 1.42/0.50 thf(func_def_69, type, c_proj0: ($i > $i)).
% 1.42/0.50 thf(func_def_70, type, c_proj1: ($i > $i)).
% 1.42/0.50 thf(func_def_71, type, c_binrep: ($i > $i > $i)).
% 1.42/0.50 thf(func_def_72, type, c_lam: ($i > ($i > $i) > $i)).
% 1.42/0.50 thf(func_def_73, type, c_setprod: ($i > $i > $i)).
% 1.42/0.50 thf(func_def_74, type, c_ap: ($i > $i > $i)).
% 1.42/0.50 thf(func_def_75, type, c_setsum_p: ($i > $o)).
% 1.42/0.50 thf(func_def_76, type, c_tuple_p: ($i > $i > $o)).
% 1.42/0.50 thf(func_def_77, type, c_Pi: ($i > ($i > $i) > $i)).
% 1.42/0.50 thf(func_def_78, type, c_setexp: ($i > $i > $i)).
% 1.42/0.50 thf(func_def_79, type, c_Sep2: ($i > ($i > $i) > ($i > $i > $o) > $i)).
% 1.42/0.50 thf(func_def_80, type, c_set_of_pairs: ($i > $o)).
% 1.42/0.50 thf(func_def_81, type, c_lam2: ($i > ($i > $i) > ($i > $i > $i) > $i)).
% 1.42/0.50 thf(func_def_82, type, c_PNoEq_: ($i > ($i > $o) > ($i > $o) > $o)).
% 1.42/0.50 thf(func_def_83, type, c_PNoLt_: ($i > ($i > $o) > ($i > $o) > $o)).
% 1.42/0.50 thf(func_def_84, type, c_PNoLt: ($i > ($i > $o) > $i > ($i > $o) > $o)).
% 1.42/0.50 thf(func_def_85, type, c_PNoLe: ($i > ($i > $o) > $i > ($i > $o) > $o)).
% 1.42/0.50 thf(func_def_86, type, c_PNo_downc: (($i > ($i > $o) > $o) > $i > ($i > $o) > $o)).
% 1.42/0.50 thf(func_def_87, type, c_PNo_upc: (($i > ($i > $o) > $o) > $i > ($i > $o) > $o)).
% 1.42/0.50 thf(func_def_88, type, c_SNoElts_: ($i > $i)).
% 1.42/0.50 thf(func_def_89, type, c_SNo_: ($i > $i > $o)).
% 1.42/0.50 thf(func_def_90, type, c_PSNo: ($i > ($i > $o) > $i)).
% 1.42/0.50 thf(func_def_91, type, c_SNo: ($i > $o)).
% 1.42/0.50 thf(func_def_92, type, c_SNoLev: ($i > $i)).
% 1.42/0.50 thf(func_def_93, type, c_SNoEq_: ($i > $i > $i > $o)).
% 1.42/0.50 thf(func_def_94, type, c_SNoLt: ($i > $i > $o)).
% 1.42/0.50 thf(func_def_95, type, c_SNoLe: ($i > $i > $o)).
% 1.42/0.50 thf(func_def_96, type, c_binop_on: ($i > ($i > $i > $i) > $o)).
% 1.42/0.50 thf(func_def_97, type, c_Loop: ($i > ($i > $i > $i) > ($i > $i > $i) > ($i > $i > $i) > $i > $o)).
% 1.42/0.50 thf(func_def_98, type, c_Loop_with_defs: ($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) > $o)).
% 1.42/0.50 thf(func_def_99, type, c_Loop_with_defs_cex1: ($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) > $o)).
% 1.42/0.50 thf(func_def_100, type, c_Loop_with_defs_cex2: ($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) > $o)).
% 1.42/0.50 thf(func_def_101, type, c_combinator: ($i > $o)).
% 1.42/0.50 thf(func_def_102, type, c_combinator_equiv: ($i > $i > $o)).
% 1.42/0.50 thf(func_def_103, type, c_equip_mod: ($i > $i > $i > $o)).
% 1.42/0.50 thf(func_def_105, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 1.42/0.50 thf(func_def_106, type, vIMP: ($o > $o > $o)).
% 1.42/0.50 thf(func_def_107, type, db2: !>[X0: $tType]:(X0)).
% 1.42/0.50 thf(func_def_108, type, db0: !>[X0: $tType]:(X0)).
% 1.42/0.50 thf(func_def_109, type, db1: !>[X0: $tType]:(X0)).
% 1.42/0.50 thf(func_def_110, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 1.42/0.50 thf(func_def_111, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 1.42/0.50 thf(func_def_112, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 1.42/0.50 thf(func_def_115, type, db3: !>[X0: $tType]:(X0)).
% 1.42/0.50 thf(func_def_116, type, db13: !>[X0: $tType]:(X0)).
% 1.42/0.50 thf(func_def_117, type, db12: !>[X0: $tType]:(X0)).
% 1.42/0.50 thf(func_def_118, type, db11: !>[X0: $tType]:(X0)).
% 1.42/0.50 thf(func_def_119, type, db10: !>[X0: $tType]:(X0)).
% 1.42/0.50 thf(func_def_120, type, db9: !>[X0: $tType]:(X0)).
% 1.42/0.50 thf(func_def_121, type, db8: !>[X0: $tType]:(X0)).
% 1.42/0.50 thf(func_def_122, type, db7: !>[X0: $tType]:(X0)).
% 1.42/0.50 thf(func_def_123, type, db6: !>[X0: $tType]:(X0)).
% 1.42/0.50 thf(func_def_124, type, db5: !>[X0: $tType]:(X0)).
% 1.42/0.50 thf(func_def_125, type, db4: !>[X0: $tType]:(X0)).
% 1.42/0.50 thf(func_def_126, type, db14: !>[X0: $tType]:(X0)).
% 1.42/0.50 thf(func_def_127, type, db15: !>[X0: $tType]:(X0)).
% 1.42/0.50 thf(func_def_128, type, db16: !>[X0: $tType]:(X0)).
% 1.42/0.50 thf(func_def_129, type, db17: !>[X0: $tType]:(X0)).
% 1.42/0.50 thf(func_def_130, type, db18: !>[X0: $tType]:(X0)).
% 1.42/0.50 thf(func_def_131, type, vNOT: ($o > $o)).
% 1.42/0.50 thf(func_def_133, type, sK1: (($i > $i) > ($i > $o) > $i > ($i > $i > $i) > $i > $o)).
% 1.42/0.50 thf(func_def_134, type, sK2: (($i > $o) > $i)).
% 1.42/0.50 thf(func_def_135, type, sK3: $o).
% 1.42/0.50 thf(func_def_136, type, sK4: ($i > $i > $i)).
% 1.42/0.50 thf(func_def_138, type, sK6: ($i > ($i > $i) > $i > $i > $o)).
% 1.42/0.50 thf(func_def_139, type, sK7: (($i > $o) > $i)).
% 1.42/0.50 thf(func_def_140, type, sK8: $o).
% 1.42/0.50 thf(f2,axiom,(
% 1.42/0.50 ! [X0 : $o] : ((c_not @ (c_not @ X0)) => X0)),
% 1.42/0.50 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax2)).
% 1.42/0.50 thf(f5,axiom,(
% 1.42/0.50 (c_not @ ? [X0 : $i] : (c_In @ X0 @ c_Empty))),
% 1.42/0.50 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax5)).
% 1.42/0.50 thf(f7,axiom,(
% 1.42/0.50 ! [X1 : $i,X0 : $i] : (c_iff @ (c_In @ X1 @ (c_Power @ X0)) @ (c_Subq @ X1 @ X0))),
% 1.42/0.50 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax7)).
% 1.42/0.50 thf(f13,axiom,(
% 1.42/0.50 ((^[X0 : $o] : (X0 => c_False)) = c_not)),
% 1.42/0.50 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax13)).
% 1.42/0.50 thf(f14,axiom,(
% 1.42/0.50 (c_and = (^[X0 : $o, X1 : $o] : (! [X2 : $o] : ((X0 => (X1 => X2)) => X2))))),
% 1.42/0.50 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax14)).
% 1.42/0.50 thf(f16,axiom,(
% 1.42/0.50 ((^[X0 : $o, X1 : $o] : ((c_and @ X0 => X1 @ X1 => X0))) = c_iff)),
% 1.42/0.50 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax16)).
% 1.42/0.50 thf(f17,axiom,(
% 1.42/0.50 (c_Subq = (^[X0 : $i, X1 : $i] : (! [X2 : $i] : ((c_In @ X2 @ X0) => (c_In @ X2 @ X1)))))),
% 1.42/0.50 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax17)).
% 1.42/0.50 thf(f109,conjecture,(
% 1.42/0.50 (c_not @ ! [X1 : ($i > $i > $i),X6 : $i,X9 : $i,X2 : ($i > $o),X7 : $i,X5 : $i,X8 : $i,X0 : ($i > $i > $o),X3 : ($i > $o),X4 : ($i > $i)] : ((c_and @ ! [X10 : $i] : ((((X4 @ X9)) = X10) => ((c_and @ (X2 @ X10) @ (X7 = X5) => (c_and @ ! [X11 : $i] : (X9 = X8) @ ? [X11 : $i] : (X3 @ X10))) => ? [X11 : $i] : (X7 = X7))) @ (c_not @ (X3 @ (X4 @ (X4 @ (X1 @ X7 @ X5)))))) => (X6 = X9)))),
% 1.42/0.50 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj)).
% 1.42/0.50 thf(f110,negated_conjecture,(
% 1.42/0.50 ~(c_not @ ! [X1 : ($i > $i > $i),X6 : $i,X9 : $i,X2 : ($i > $o),X7 : $i,X5 : $i,X8 : $i,X0 : ($i > $i > $o),X3 : ($i > $o),X4 : ($i > $i)] : ((c_and @ ! [X10 : $i] : ((((X4 @ X9)) = X10) => ((c_and @ (X2 @ X10) @ (X7 = X5) => (c_and @ ! [X11 : $i] : (X9 = X8) @ ? [X11 : $i] : (X3 @ X10))) => ? [X11 : $i] : (X7 = X7))) @ (c_not @ (X3 @ (X4 @ (X4 @ (X1 @ X7 @ X5)))))) => (X6 = X9)))),
% 1.42/0.50 inference(negated_conjecture,[status(cth)],[f109])).
% 1.42/0.50 thf(f113,plain,(
% 1.42/0.50 ((^[X0 : $o] : (X0 => c_False)) = c_not)),
% 1.42/0.50 inference(rectify,[],[f13])).
% 1.42/0.50 thf(f114,plain,(
% 1.42/0.50 (c_not = (^[Y0 : $o]: (Y0 => c_False)))),
% 1.42/0.50 inference(fool_elimination,[],[f113])).
% 1.42/0.50 thf(f121,plain,(
% 1.42/0.50 (c_not @ ? [X0 : $i] : (c_In @ X0 @ c_Empty))),
% 1.42/0.50 inference(rectify,[],[f5])).
% 1.42/0.50 thf(f122,plain,(
% 1.42/0.50 (((c_not @ (?? @ $i @ (^[Y0 : $i]: (c_In @ Y0 @ c_Empty))))) = $true)),
% 1.42/0.50 inference(fool_elimination,[],[f121])).
% 1.42/0.50 thf(f147,plain,(
% 1.42/0.50 ((^[X0 : $o, X1 : $o] : ((c_and @ X0 => X1 @ X1 => X0))) = c_iff)),
% 1.42/0.50 inference(rectify,[],[f16])).
% 1.42/0.50 thf(f148,plain,(
% 1.42/0.50 (c_iff = (^[Y0 : $o]: ((^[Y1 : $o]: (c_and @ (Y0 => Y1) @ (Y1 => Y0))))))),
% 1.42/0.50 inference(fool_elimination,[],[f147])).
% 1.42/0.50 thf(f168,plain,(
% 1.42/0.50 ! [X0 : $i,X1 : $i] : (c_iff @ (c_In @ X0 @ (c_Power @ X1)) @ (c_Subq @ X0 @ X1))),
% 1.42/0.50 inference(rectify,[],[f7])).
% 1.42/0.50 thf(f169,plain,(
% 1.42/0.50 ($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (c_iff @ (c_In @ Y1 @ (c_Power @ Y0)) @ (c_Subq @ Y1 @ Y0))))))))),
% 1.42/0.50 inference(fool_elimination,[],[f168])).
% 1.42/0.50 thf(f215,plain,(
% 1.42/0.50 ! [X0 : $o] : ((c_not @ (c_not @ X0)) => X0)),
% 1.42/0.50 inference(rectify,[],[f2])).
% 1.42/0.50 thf(f216,plain,(
% 1.42/0.50 ($true = ((!! @ $o @ (^[Y0 : $o]: ((c_not @ (c_not @ Y0)) => Y0)))))),
% 1.42/0.50 inference(fool_elimination,[],[f215])).
% 1.42/0.50 thf(f272,plain,(
% 1.42/0.50 ~(c_not @ ! [X0 : ($i > $i > $i),X1 : $i,X2 : $i,X3 : ($i > $o),X4 : $i,X5 : $i,X6 : $i,X8 : ($i > $o),X9 : ($i > $i)] : ((c_and @ ! [X10 : $i] : ((((X9 @ X2)) = X10) => ((c_and @ (X3 @ X10) @ (X4 = X5) => (c_and @ (X2 = X6) @ (X8 @ X10))) => (X4 = X4))) @ (c_not @ (X8 @ (X9 @ (X9 @ (X0 @ X4 @ X5)))))) => (X1 = X2)))),
% 1.42/0.50 inference(rectify,[],[f110])).
% 1.42/0.50 thf(f273,plain,(
% 1.42/0.50 (((~ (c_not @ (!! @ ($i > $i) @ (^[Y0 : $i > $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ ($i > $o) @ (^[Y5 : $i > $o]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ ($i > $i > $i) @ (^[Y8 : $i > $i > $i]: ((c_and @ (!! @ $i @ (^[Y9 : $i]: (((Y0 @ Y6) = Y9) => ((c_and @ (Y5 @ Y9) @ ((Y4 = Y3) => (c_and @ (Y6 = Y2) @ (Y1 @ Y9)))) => (Y4 = Y4))))) @ (c_not @ (Y1 @ (Y0 @ (Y0 @ (Y8 @ Y4 @ Y3)))))) => (Y7 = Y6))))))))))))))))))))))) = $true)),
% 1.42/0.50 inference(fool_elimination,[],[f272])).
% 1.42/0.50 thf(f283,plain,(
% 1.42/0.50 (c_and = (^[X0 : $o, X1 : $o] : (! [X2 : $o] : ((X0 => (X1 => X2)) => X2))))),
% 1.42/0.50 inference(rectify,[],[f14])).
% 1.42/0.50 thf(f284,plain,(
% 1.42/0.50 (c_and = (^[Y0 : $o]: ((^[Y1 : $o]: (!! @ $o @ (^[Y2 : $o]: ((Y0 => (Y1 => Y2)) => Y2)))))))),
% 1.42/0.50 inference(fool_elimination,[],[f283])).
% 1.42/0.50 thf(f287,plain,(
% 1.42/0.50 (c_Subq = (^[X0 : $i, X1 : $i] : (! [X2 : $i] : ((c_In @ X2 @ X0) => (c_In @ X2 @ X1)))))),
% 1.42/0.50 inference(rectify,[],[f17])).
% 1.42/0.50 thf(f288,plain,(
% 1.42/0.50 (c_Subq = (^[Y0 : $i]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((c_In @ Y2 @ Y0) => (c_In @ Y2 @ Y1))))))))),
% 1.42/0.50 inference(fool_elimination,[],[f287])).
% 1.42/0.50 thf(f309,plain,(
% 1.42/0.50 (c_and = (^[Y0 : $o]: ((^[Y1 : $o]: (!! @ $o @ (^[Y2 : $o]: ((Y0 => (Y1 => Y2)) => Y2)))))))),
% 1.42/0.50 inference(cnf_transformation,[],[f284])).
% 1.42/0.50 thf(f316,plain,(
% 1.42/0.50 ($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (c_iff @ (c_In @ Y1 @ (c_Power @ Y0)) @ (c_Subq @ Y1 @ Y0))))))))),
% 1.42/0.50 inference(cnf_transformation,[],[f169])).
% 1.42/0.50 thf(f320,plain,(
% 1.42/0.50 (c_Subq = (^[Y0 : $i]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((c_In @ Y2 @ Y0) => (c_In @ Y2 @ Y1))))))))),
% 1.42/0.50 inference(cnf_transformation,[],[f288])).
% 1.42/0.50 thf(f327,plain,(
% 1.42/0.50 (((c_not @ (?? @ $i @ (^[Y0 : $i]: (c_In @ Y0 @ c_Empty))))) = $true)),
% 1.42/0.50 inference(cnf_transformation,[],[f122])).
% 1.42/0.50 thf(f360,plain,(
% 1.42/0.50 (((~ (c_not @ (!! @ ($i > $i) @ (^[Y0 : $i > $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ ($i > $o) @ (^[Y5 : $i > $o]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ ($i > $i > $i) @ (^[Y8 : $i > $i > $i]: ((c_and @ (!! @ $i @ (^[Y9 : $i]: (((Y0 @ Y6) = Y9) => ((c_and @ (Y5 @ Y9) @ ((Y4 = Y3) => (c_and @ (Y6 = Y2) @ (Y1 @ Y9)))) => (Y4 = Y4))))) @ (c_not @ (Y1 @ (Y0 @ (Y0 @ (Y8 @ Y4 @ Y3)))))) => (Y7 = Y6))))))))))))))))))))))) = $true)),
% 1.42/0.50 inference(cnf_transformation,[],[f273])).
% 1.42/0.50 thf(f369,plain,(
% 1.42/0.50 ($true = ((!! @ $o @ (^[Y0 : $o]: ((c_not @ (c_not @ Y0)) => Y0)))))),
% 1.42/0.50 inference(cnf_transformation,[],[f216])).
% 1.42/0.50 thf(f411,plain,(
% 1.42/0.50 (c_not = (^[Y0 : $o]: (Y0 => c_False)))),
% 1.42/0.50 inference(cnf_transformation,[],[f114])).
% 1.42/0.50 thf(f415,plain,(
% 1.42/0.50 (c_iff = (^[Y0 : $o]: ((^[Y1 : $o]: (c_and @ (Y0 => Y1) @ (Y1 => Y0))))))),
% 1.42/0.50 inference(cnf_transformation,[],[f148])).
% 1.42/0.50 thf(f419,plain,(
% 1.42/0.50 (c_iff = (^[Y0 : $o]: ((^[Y1 : $o]: ((^[Y2 : $o]: ((^[Y3 : $o]: (!! @ $o @ (^[Y4 : $o]: ((Y2 => (Y3 => Y4)) => Y4)))))) @ (Y0 => Y1) @ (Y1 => Y0))))))),
% 1.42/0.50 inference(definition_unfolding,[],[f415,f309])).
% 1.42/0.50 thf(f504,plain,(
% 1.42/0.50 ($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((^[Y2 : $o]: ((^[Y3 : $o]: ((^[Y4 : $o]: ((^[Y5 : $o]: (!! @ $o @ (^[Y6 : $o]: ((Y4 => (Y5 => Y6)) => Y6)))))) @ (Y2 => Y3) @ (Y3 => Y2))))) @ (c_In @ Y1 @ (c_Power @ Y0)) @ ((^[Y2 : $i]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((c_In @ Y4 @ Y2) => (c_In @ Y4 @ Y3))))))) @ Y1 @ Y0))))))))),
% 1.42/0.50 inference(definition_unfolding,[],[f316,f419,f320])).
% 1.42/0.50 thf(f506,plain,(
% 1.42/0.50 ((((^[Y0 : $o]: (Y0 => c_False)) @ (?? @ $i @ (^[Y0 : $i]: (c_In @ Y0 @ c_Empty))))) = $true)),
% 1.42/0.50 inference(definition_unfolding,[],[f327,f411])).
% 1.42/0.50 thf(f509,plain,(
% 1.42/0.50 ($true = ((~ ((^[Y0 : $o]: (Y0 => c_False)) @ (!! @ ($i > $i) @ (^[Y0 : $i > $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ ($i > $o) @ (^[Y5 : $i > $o]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ ($i > $i > $i) @ (^[Y8 : $i > $i > $i]: (((^[Y9 : $o]: ((^[Y10 : $o]: (!! @ $o @ (^[Y11 : $o]: ((Y9 => (Y10 => Y11)) => Y11)))))) @ (!! @ $i @ (^[Y9 : $i]: (((Y0 @ Y6) = Y9) => (((^[Y10 : $o]: ((^[Y11 : $o]: (!! @ $o @ (^[Y12 : $o]: ((Y10 => (Y11 => Y12)) => Y12)))))) @ (Y5 @ Y9) @ ((Y4 = Y3) => ((^[Y10 : $o]: ((^[Y11 : $o]: (!! @ $o @ (^[Y12 : $o]: ((Y10 => (Y11 => Y12)) => Y12)))))) @ (Y6 = Y2) @ (Y1 @ Y9)))) => (Y4 = Y4))))) @ ((^[Y9 : $o]: (Y9 => c_False)) @ (Y1 @ (Y0 @ (Y0 @ (Y8 @ Y4 @ Y3)))))) => (Y7 = Y6))))))))))))))))))))))))),
% 1.42/0.50 inference(definition_unfolding,[],[f360,f411,f309,f309,f309,f411])).
% 1.42/0.50 thf(f510,plain,(
% 1.42/0.50 (((!! @ $o @ (^[Y0 : $o]: (((^[Y1 : $o]: (Y1 => c_False)) @ ((^[Y1 : $o]: (Y1 => c_False)) @ Y0)) => Y0)))) = $true)),
% 1.42/0.50 inference(definition_unfolding,[],[f369,f411,f411])).
% 1.42/0.50 thf(f512,plain,(
% 1.42/0.50 ($true = ((!! @ $o @ (^[Y0 : $o]: (((Y0 => c_False) => c_False) => Y0)))))),
% 1.42/0.50 inference(beta-eta_normalization,[],[f510])).
% 1.42/0.50 thf(f513,plain,(
% 1.42/0.50 (((~ ((!! @ ($i > $i) @ (^[Y0 : $i > $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ ($i > $o) @ (^[Y5 : $i > $o]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ ($i > $i > $i) @ (^[Y8 : $i > $i > $i]: ((!! @ $o @ (^[Y9 : $o]: (((!! @ $i @ (^[Y10 : $i]: (((Y0 @ Y6) = Y10) => ((!! @ $o @ (^[Y11 : $o]: (((Y5 @ Y10) => (((Y4 = Y3) => (!! @ $o @ (^[Y12 : $o]: (((Y6 = Y2) => ((Y1 @ Y10) => Y12)) => Y12)))) => Y11)) => Y11))) => (Y4 = Y4))))) => (((Y1 @ (Y0 @ (Y0 @ (Y8 @ Y4 @ Y3)))) => c_False) => Y9)) => Y9))) => (Y7 = Y6)))))))))))))))))))) => c_False))) = $true)),
% 1.42/0.50 inference(beta-eta_normalization,[],[f509])).
% 1.42/0.50 thf(f514,plain,(
% 1.42/0.50 ($true = ((~ ((!! @ ($i > $i) @ (^[Y0 : $i > $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ ($i > $o) @ (^[Y5 : $i > $o]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ ($i > $i > $i) @ (^[Y8 : $i > $i > $i]: ((!! @ $o @ (^[Y9 : $o]: (((!! @ $i @ (^[Y10 : $i]: (((Y0 @ Y6) = Y10) => ((!! @ $o @ (^[Y11 : $o]: (((Y5 @ Y10) => (((Y4 = Y3) => (!! @ $o @ (^[Y12 : $o]: (((Y6 = Y2) => ((Y1 @ Y10) => Y12)) => Y12)))) => Y11)) => Y11))) => $true)))) => (((Y1 @ (Y0 @ (Y0 @ (Y8 @ Y4 @ Y3)))) => c_False) => Y9)) => Y9))) => (Y7 = Y6)))))))))))))))))))) => c_False))))),
% 1.42/0.50 inference(boolean_simplification,[],[f513])).
% 1.42/0.50 thf(f515,plain,(
% 1.42/0.50 ($true = ((~ ((!! @ ($i > $i) @ (^[Y0 : $i > $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ ($i > $o) @ (^[Y5 : $i > $o]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ ($i > $i > $i) @ (^[Y8 : $i > $i > $i]: ((!! @ $o @ (^[Y9 : $o]: (((!! @ $i @ (^[Y10 : $i]: (((Y0 @ Y6) = Y10) => $true))) => (((Y1 @ (Y0 @ (Y0 @ (Y8 @ Y4 @ Y3)))) => c_False) => Y9)) => Y9))) => (Y7 = Y6)))))))))))))))))))) => c_False))))),
% 1.42/0.50 inference(boolean_simplification,[],[f514])).
% 1.42/0.50 thf(f516,plain,(
% 1.42/0.50 (((~ ((!! @ ($i > $i) @ (^[Y0 : $i > $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ ($i > $o) @ (^[Y5 : $i > $o]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ ($i > $i > $i) @ (^[Y8 : $i > $i > $i]: ((!! @ $o @ (^[Y9 : $o]: (((!! @ $i @ (^[Y10 : $i]: ($true))) => (((Y1 @ (Y0 @ (Y0 @ (Y8 @ Y4 @ Y3)))) => c_False) => Y9)) => Y9))) => (Y7 = Y6)))))))))))))))))))) => c_False))) = $true)),
% 1.42/0.50 inference(boolean_simplification,[],[f515])).
% 1.42/0.50 thf(f524,plain,(
% 1.42/0.50 ($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: ((((c_In @ Y1 @ (c_Power @ Y0)) => (!! @ $i @ (^[Y3 : $i]: ((c_In @ Y3 @ Y1) => (c_In @ Y3 @ Y0))))) => (((!! @ $i @ (^[Y3 : $i]: ((c_In @ Y3 @ Y1) => (c_In @ Y3 @ Y0)))) => (c_In @ Y1 @ (c_Power @ Y0))) => Y2)) => Y2)))))))))),
% 1.42/0.50 inference(beta-eta_normalization,[],[f504])).
% 1.42/0.50 thf(f525,plain,(
% 1.42/0.50 ((((?? @ $i @ (^[Y0 : $i]: (c_In @ Y0 @ c_Empty))) => c_False)) = $true)),
% 1.42/0.50 inference(beta-eta_normalization,[],[f506])).
% 1.42/0.50 thf(f528,plain,(
% 1.42/0.50 ((((!! @ ($i > $i) @ (^[Y0 : $i > $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ ($i > $o) @ (^[Y5 : $i > $o]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ ($i > $i > $i) @ (^[Y8 : $i > $i > $i]: ((!! @ $o @ (^[Y9 : $o]: (((!! @ $i @ (^[Y10 : $i]: ($true))) => (((Y1 @ (Y0 @ (Y0 @ (Y8 @ Y4 @ Y3)))) => c_False) => Y9)) => Y9))) => (Y7 = Y6)))))))))))))))))))) => c_False)) = $false)),
% 1.42/0.50 inference(not_proxy_clausification,[],[f516])).
% 1.42/0.50 thf(f531,plain,(
% 1.42/0.50 (c_False = $true) | ($false = ((?? @ $i @ (^[Y0 : $i]: (c_In @ Y0 @ c_Empty)))))),
% 1.42/0.50 inference(imp_proxy_clausification,[],[f525])).
% 1.42/0.50 thf(f537,definition,(
% 1.42/0.50 spl0_2 <=> (c_False = $true)),
% 1.42/0.50 introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition])).
% 1.42/0.50 thf(f539,plain,(
% 1.42/0.50 (c_False = $true) | ~spl0_2),
% 1.42/0.50 inference(avatar_component_clause,[],[f537])).
% 1.42/0.50 thf(f546,definition,(
% 1.42/0.50 spl0_4 <=> (c_False = $false)),
% 1.42/0.50 introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition])).
% 1.42/0.50 thf(f548,plain,(
% 1.42/0.50 (c_False = $false) | ~spl0_4),
% 1.42/0.50 inference(avatar_component_clause,[],[f546])).
% 1.42/0.50 thf(f550,plain,(
% 1.42/0.50 (c_False = $false)),
% 1.42/0.50 inference(imp_proxy_clausification,[],[f528])).
% 1.42/0.50 thf(f551,plain,(
% 1.42/0.50 ($true = ((!! @ ($i > $i) @ (^[Y0 : $i > $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ ($i > $o) @ (^[Y5 : $i > $o]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ ($i > $i > $i) @ (^[Y8 : $i > $i > $i]: ((!! @ $o @ (^[Y9 : $o]: (((!! @ $i @ (^[Y10 : $i]: ($true))) => (((Y1 @ (Y0 @ (Y0 @ (Y8 @ Y4 @ Y3)))) => c_False) => Y9)) => Y9))) => (Y7 = Y6))))))))))))))))))))))),
% 1.42/0.50 inference(imp_proxy_clausification,[],[f528])).
% 1.42/0.50 thf(f571,definition,(
% 1.42/0.50 spl0_9 <=> ($false = ((?? @ $i @ (^[Y0 : $i]: (c_In @ Y0 @ c_Empty)))))),
% 1.42/0.50 introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition])).
% 1.42/0.50 thf(f573,plain,(
% 1.42/0.50 ($false = ((?? @ $i @ (^[Y0 : $i]: (c_In @ Y0 @ c_Empty))))) | ~spl0_9),
% 1.42/0.50 inference(avatar_component_clause,[],[f571])).
% 1.42/0.50 thf(f574,plain,(
% 1.42/0.50 spl0_2 | spl0_9),
% 1.42/0.50 inference(avatar_split_clause,[],[f531,f571,f537])).
% 1.42/0.50 thf(f575,plain,(
% 1.42/0.50 spl0_4),
% 1.42/0.50 inference(avatar_split_clause,[],[f550,f546])).
% 1.42/0.50 thf(f576,plain,(
% 1.42/0.50 ( ! [X1 : ($i > $i)] : (($true = (((^[Y0 : $i > $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ ($i > $o) @ (^[Y5 : $i > $o]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ ($i > $i > $i) @ (^[Y8 : $i > $i > $i]: ((!! @ $o @ (^[Y9 : $o]: (((!! @ $i @ (^[Y10 : $i]: ($true))) => (((Y1 @ (Y0 @ (Y0 @ (Y8 @ Y4 @ Y3)))) => c_False) => Y9)) => Y9))) => (Y7 = Y6))))))))))))))))))) @ X1)))) )),
% 1.42/0.50 inference(pi_proxy_clausification,[],[f551])).
% 1.42/0.50 thf(f577,plain,(
% 1.42/0.50 ( ! [X1 : ($i > $i)] : ((((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ ($i > $o) @ (^[Y4 : $i > $o]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ ($i > $i > $i) @ (^[Y7 : $i > $i > $i]: ((!! @ $o @ (^[Y8 : $o]: (((!! @ $i @ (^[Y9 : $i]: ($true))) => (((Y0 @ (X1 @ (X1 @ (Y7 @ Y3 @ Y2)))) => c_False) => Y8)) => Y8))) => (Y6 = Y5))))))))))))))))))) = $true)) )),
% 1.42/0.50 inference(beta-eta_normalization,[],[f576])).
% 1.42/0.50 thf(f578,plain,(
% 1.42/0.50 ( ! [X2 : ($i > $o),X1 : ($i > $i)] : (((((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ ($i > $o) @ (^[Y4 : $i > $o]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ ($i > $i > $i) @ (^[Y7 : $i > $i > $i]: ((!! @ $o @ (^[Y8 : $o]: (((!! @ $i @ (^[Y9 : $i]: ($true))) => (((Y0 @ (X1 @ (X1 @ (Y7 @ Y3 @ Y2)))) => c_False) => Y8)) => Y8))) => (Y6 = Y5))))))))))))))))) @ X2)) = $true)) )),
% 1.42/0.50 inference(pi_proxy_clausification,[],[f577])).
% 1.42/0.50 thf(f579,plain,(
% 1.42/0.50 ( ! [X2 : ($i > $o),X1 : ($i > $i)] : (($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ ($i > $i > $i) @ (^[Y6 : $i > $i > $i]: ((!! @ $o @ (^[Y7 : $o]: (((!! @ $i @ (^[Y8 : $i]: ($true))) => (((X2 @ (X1 @ (X1 @ (Y6 @ Y2 @ Y1)))) => c_False) => Y7)) => Y7))) => (Y5 = Y4))))))))))))))))))) )),
% 1.42/0.50 inference(beta-eta_normalization,[],[f578])).
% 1.42/0.50 thf(f580,plain,(
% 1.42/0.50 ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $i)] : (((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ ($i > $i > $i) @ (^[Y6 : $i > $i > $i]: ((!! @ $o @ (^[Y7 : $o]: (((!! @ $i @ (^[Y8 : $i]: ($true))) => (((X2 @ (X1 @ (X1 @ (Y6 @ Y2 @ Y1)))) => c_False) => Y7)) => Y7))) => (Y5 = Y4))))))))))))))) @ X3)) = $true)) )),
% 1.42/0.50 inference(pi_proxy_clausification,[],[f579])).
% 1.42/0.50 thf(f581,plain,(
% 1.42/0.50 ( ! [X2 : ($i > $o),X1 : ($i > $i)] : ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ ($i > $i > $i) @ (^[Y5 : $i > $i > $i]: ((!! @ $o @ (^[Y6 : $o]: (((!! @ $i @ (^[Y7 : $i]: ($true))) => (((X2 @ (X1 @ (X1 @ (Y5 @ Y1 @ Y0)))) => c_False) => Y6)) => Y6))) => (Y4 = Y3))))))))))))))) = $true)) )),
% 1.42/0.50 inference(beta-eta_normalization,[],[f580])).
% 1.42/0.50 thf(f589,plain,(
% 1.42/0.50 ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $i)] : (($true = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ ($i > $i > $i) @ (^[Y5 : $i > $i > $i]: ((!! @ $o @ (^[Y6 : $o]: (((!! @ $i @ (^[Y7 : $i]: ($true))) => (((X2 @ (X1 @ (X1 @ (Y5 @ Y1 @ Y0)))) => c_False) => Y6)) => Y6))) => (Y4 = Y3))))))))))))) @ X3)))) )),
% 1.42/0.50 inference(pi_proxy_clausification,[],[f581])).
% 1.42/0.50 thf(f590,plain,(
% 1.42/0.50 ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $i)] : ((((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ ($i > $i > $i) @ (^[Y4 : $i > $i > $i]: ((!! @ $o @ (^[Y5 : $o]: (((!! @ $i @ (^[Y6 : $i]: ($true))) => (((X2 @ (X1 @ (X1 @ (Y4 @ Y0 @ X3)))) => c_False) => Y5)) => Y5))) => (Y3 = Y2))))))))))))) = $true)) )),
% 1.42/0.50 inference(beta-eta_normalization,[],[f589])).
% 1.42/0.50 thf(f591,plain,(
% 1.42/0.50 ( ! [X1 : $o] : (($true = (((^[Y0 : $o]: (((Y0 => c_False) => c_False) => Y0)) @ X1)))) )),
% 1.42/0.50 inference(pi_proxy_clausification,[],[f512])).
% 1.42/0.50 thf(f592,plain,(
% 1.42/0.50 ( ! [X1 : $o] : ((((((X1 => c_False) => c_False) => X1)) = $true)) )),
% 1.42/0.50 inference(beta-eta_normalization,[],[f591])).
% 1.42/0.50 thf(f593,plain,(
% 1.42/0.50 ( ! [X1 : $o] : ((((((X1 => $true) => $true) => X1)) = $true)) ) | ~spl0_2),
% 1.42/0.50 inference(forward_demodulation,[],[f592,f539])).
% 1.42/0.50 thf(f594,plain,(
% 1.42/0.50 ( ! [X1 : $o] : (((($true => X1)) = $true)) ) | ~spl0_2),
% 1.42/0.50 inference(boolean_simplification,[],[f593])).
% 1.42/0.50 thf(f595,plain,(
% 1.42/0.50 ( ! [X1 : $o] : (($true = X1)) ) | ~spl0_2),
% 1.42/0.50 inference(boolean_simplification,[],[f594])).
% 1.42/0.50 thf(f596,plain,(
% 1.42/0.50 ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $i),X4 : $i] : (($true = (((^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ ($i > $i > $i) @ (^[Y4 : $i > $i > $i]: ((!! @ $o @ (^[Y5 : $o]: (((!! @ $i @ (^[Y6 : $i]: ($true))) => (((X2 @ (X1 @ (X1 @ (Y4 @ Y0 @ X3)))) => c_False) => Y5)) => Y5))) => (Y3 = Y2))))))))))) @ X4)))) )),
% 1.42/0.50 inference(pi_proxy_clausification,[],[f590])).
% 1.42/0.50 thf(f597,plain,(
% 1.42/0.50 ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $i),X4 : $i] : (($true = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $i) @ (^[Y3 : $i > $i > $i]: ((!! @ $o @ (^[Y4 : $o]: (((!! @ $i @ (^[Y5 : $i]: ($true))) => (((X2 @ (X1 @ (X1 @ (Y3 @ X4 @ X3)))) => c_False) => Y4)) => Y4))) => (Y2 = Y1))))))))))))) )),
% 1.42/0.50 inference(beta-eta_normalization,[],[f596])).
% 1.42/0.50 thf(f610,plain,(
% 1.42/0.50 ($false = $true) | (~spl0_2 | ~spl0_4)),
% 1.42/0.50 inference(forward_demodulation,[],[f548,f595])).
% 1.42/0.50 thf(f611,plain,(
% 1.42/0.50 $false | (~spl0_2 | ~spl0_4)),
% 1.42/0.50 inference(trivial_inequality_removal,[],[f610])).
% 1.42/0.50 thf(f612,plain,(
% 1.42/0.50 ~spl0_2 | ~spl0_4),
% 1.42/0.50 inference(avatar_contradiction_clause,[],[f611])).
% 1.42/0.50 thf(f617,definition,(
% 1.42/0.50 spl0_10 <=> ! [X1 : $o] : ($true = X1)),
% 1.42/0.50 introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition])).
% 1.42/0.50 thf(f618,plain,(
% 1.42/0.50 ( ! [X1 : $o] : (($true = X1)) ) | ~spl0_10),
% 1.42/0.50 inference(avatar_component_clause,[],[f617])).
% 1.42/0.50 thf(f621,plain,(
% 1.42/0.50 ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $i),X4 : $i,X5 : ($i > $o)] : (((((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $i) @ (^[Y3 : $i > $i > $i]: ((!! @ $o @ (^[Y4 : $o]: (((!! @ $i @ (^[Y5 : $i]: ($true))) => (((X2 @ (X1 @ (X1 @ (Y3 @ X4 @ X3)))) => c_False) => Y4)) => Y4))) => (Y2 = Y1))))))))) @ X5)) = $true)) )),
% 1.42/0.50 inference(pi_proxy_clausification,[],[f597])).
% 1.42/0.50 thf(f622,plain,(
% 1.42/0.50 ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $i),X4 : $i] : ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $i) @ (^[Y2 : $i > $i > $i]: ((!! @ $o @ (^[Y3 : $o]: (((!! @ $i @ (^[Y4 : $i]: ($true))) => (((X2 @ (X1 @ (X1 @ (Y2 @ X4 @ X3)))) => c_False) => Y3)) => Y3))) => (Y1 = Y0))))))))) = $true)) )),
% 1.42/0.50 inference(beta-eta_normalization,[],[f621])).
% 1.42/0.50 thf(f623,plain,(
% 1.42/0.50 ( ! [X1 : $i] : (($false = (((^[Y0 : $i]: (c_In @ Y0 @ c_Empty)) @ X1)))) ) | ~spl0_9),
% 1.42/0.50 inference(pi_proxy_clausification,[],[f573])).
% 1.42/0.50 thf(f625,plain,(
% 1.42/0.50 ( ! [X1 : $i] : ((((c_In @ X1 @ c_Empty)) = $false)) ) | ~spl0_9),
% 1.42/0.50 inference(beta-eta_normalization,[],[f623])).
% 1.42/0.50 thf(f627,plain,(
% 1.42/0.50 ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $i),X4 : $i,X5 : $i] : (((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $i) @ (^[Y2 : $i > $i > $i]: ((!! @ $o @ (^[Y3 : $o]: (((!! @ $i @ (^[Y4 : $i]: ($true))) => (((X2 @ (X1 @ (X1 @ (Y2 @ X4 @ X3)))) => c_False) => Y3)) => Y3))) => (Y1 = Y0))))))) @ X5)) = $true)) )),
% 1.42/0.50 inference(pi_proxy_clausification,[],[f622])).
% 1.42/0.50 thf(f628,plain,(
% 1.42/0.50 ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $i),X4 : $i,X5 : $i] : ((((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $i) @ (^[Y1 : $i > $i > $i]: ((!! @ $o @ (^[Y2 : $o]: (((!! @ $i @ (^[Y3 : $i]: ($true))) => (((X2 @ (X1 @ (X1 @ (Y1 @ X4 @ X3)))) => c_False) => Y2)) => Y2))) => (Y0 = X5))))))) = $true)) )),
% 1.42/0.50 inference(beta-eta_normalization,[],[f627])).
% 1.42/0.50 thf(f631,plain,(
% 1.42/0.50 ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $i),X6 : $i,X4 : $i,X5 : $i] : (($true = (((^[Y0 : $i]: (!! @ ($i > $i > $i) @ (^[Y1 : $i > $i > $i]: ((!! @ $o @ (^[Y2 : $o]: (((!! @ $i @ (^[Y3 : $i]: ($true))) => (((X2 @ (X1 @ (X1 @ (Y1 @ X4 @ X3)))) => c_False) => Y2)) => Y2))) => (Y0 = X5))))) @ X6)))) )),
% 1.42/0.50 inference(pi_proxy_clausification,[],[f628])).
% 1.42/0.50 thf(f632,plain,(
% 1.42/0.50 ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $i),X6 : $i,X4 : $i,X5 : $i] : ((((!! @ ($i > $i > $i) @ (^[Y0 : $i > $i > $i]: ((!! @ $o @ (^[Y1 : $o]: (((!! @ $i @ (^[Y2 : $i]: ($true))) => (((X2 @ (X1 @ (X1 @ (Y0 @ X4 @ X3)))) => c_False) => Y1)) => Y1))) => (X6 = X5))))) = $true)) )),
% 1.42/0.50 inference(beta-eta_normalization,[],[f631])).
% 1.42/0.50 thf(f636,plain,(
% 1.42/0.50 ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $i),X6 : $i,X7 : ($i > $i > $i),X4 : $i,X5 : $i] : (($true = (((^[Y0 : $i > $i > $i]: ((!! @ $o @ (^[Y1 : $o]: (((!! @ $i @ (^[Y2 : $i]: ($true))) => (((X2 @ (X1 @ (X1 @ (Y0 @ X4 @ X3)))) => c_False) => Y1)) => Y1))) => (X6 = X5))) @ X7)))) )),
% 1.42/0.50 inference(pi_proxy_clausification,[],[f632])).
% 1.42/0.50 thf(f637,plain,(
% 1.42/0.50 ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $i),X6 : $i,X7 : ($i > $i > $i),X4 : $i,X5 : $i] : (((((!! @ $o @ (^[Y0 : $o]: (((!! @ $i @ (^[Y1 : $i]: ($true))) => (((X2 @ (X1 @ (X1 @ (X7 @ X4 @ X3)))) => c_False) => Y0)) => Y0))) => (X6 = X5))) = $true)) )),
% 1.42/0.50 inference(beta-eta_normalization,[],[f636])).
% 1.42/0.50 thf(f638,plain,(
% 1.42/0.50 ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $i),X6 : $i,X7 : ($i > $i > $i),X4 : $i,X5 : $i] : (($true = ((X6 = X5))) | (((!! @ $o @ (^[Y0 : $o]: (((!! @ $i @ (^[Y1 : $i]: ($true))) => (((X2 @ (X1 @ (X1 @ (X7 @ X4 @ X3)))) => c_False) => Y0)) => Y0)))) = $false)) )),
% 1.42/0.50 inference(imp_proxy_clausification,[],[f637])).
% 1.42/0.50 thf(f639,plain,(
% 1.42/0.50 ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $i),X6 : $i,X7 : ($i > $i > $i),X4 : $i,X5 : $i] : ((X5 = X6) | (((!! @ $o @ (^[Y0 : $o]: (((!! @ $i @ (^[Y1 : $i]: ($true))) => (((X2 @ (X1 @ (X1 @ (X7 @ X4 @ X3)))) => c_False) => Y0)) => Y0)))) = $false)) )),
% 1.42/0.50 inference(equality_proxy_clausification,[],[f638])).
% 1.42/0.50 thf(f641,definition,(
% 1.42/0.50 spl0_11 <=> ! [X2 : ($i > $o),X4 : $i,X7 : ($i > $i > $i),X3 : $i,X1 : ($i > $i)] : (((!! @ $o @ (^[Y0 : $o]: (((!! @ $i @ (^[Y1 : $i]: ($true))) => (((X2 @ (X1 @ (X1 @ (X7 @ X4 @ X3)))) => c_False) => Y0)) => Y0)))) = $false)),
% 1.42/0.50 introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition])).
% 1.42/0.50 thf(f642,plain,(
% 1.42/0.50 ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $i),X7 : ($i > $i > $i),X4 : $i] : ((((!! @ $o @ (^[Y0 : $o]: (((!! @ $i @ (^[Y1 : $i]: ($true))) => (((X2 @ (X1 @ (X1 @ (X7 @ X4 @ X3)))) => c_False) => Y0)) => Y0)))) = $false)) ) | ~spl0_11),
% 1.42/0.50 inference(avatar_component_clause,[],[f641])).
% 1.42/0.50 thf(f644,definition,(
% 1.42/0.50 spl0_12 <=> ! [X6 : $i,X5 : $i] : (X5 = X6)),
% 1.42/0.50 introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition])).
% 1.42/0.50 thf(f645,plain,(
% 1.42/0.50 ( ! [X6 : $i,X5 : $i] : ((X5 = X6)) ) | ~spl0_12),
% 1.42/0.50 inference(avatar_component_clause,[],[f644])).
% 1.42/0.50 thf(f646,plain,(
% 1.42/0.50 spl0_11 | spl0_12),
% 1.42/0.50 inference(avatar_split_clause,[],[f639,f644,f641])).
% 1.42/0.50 thf(f649,plain,(
% 1.42/0.50 ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $i),X7 : ($i > $i > $i),X4 : $i] : (($false = (((^[Y0 : $o]: (((!! @ $i @ (^[Y1 : $i]: ($true))) => (((X2 @ (X1 @ (X1 @ (X7 @ X4 @ X3)))) => c_False) => Y0)) => Y0)) @ (sK1 @ X1 @ X2 @ X3 @ X7 @ X4))))) ) | ~spl0_11),
% 1.42/0.50 inference(sigma_proxy_clausification,[],[f642])).
% 1.42/0.50 thf(f652,plain,(
% 1.42/0.50 ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $i),X7 : ($i > $i > $i),X4 : $i] : (($false = ((((!! @ $i @ (^[Y0 : $i]: ($true))) => (((X2 @ (X1 @ (X1 @ (X7 @ X4 @ X3)))) => c_False) => (sK1 @ X1 @ X2 @ X3 @ X7 @ X4))) => (sK1 @ X1 @ X2 @ X3 @ X7 @ X4))))) ) | ~spl0_11),
% 1.42/0.50 inference(beta-eta_normalization,[],[f649])).
% 1.42/0.50 thf(f653,plain,(
% 1.42/0.50 ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $i),X7 : ($i > $i > $i),X4 : $i] : (($false = ((sK1 @ X1 @ X2 @ X3 @ X7 @ X4)))) ) | ~spl0_11),
% 1.42/0.50 inference(imp_proxy_clausification,[],[f652])).
% 1.42/0.50 thf(f663,definition,(
% 1.42/0.50 spl0_14 <=> ($false = ((!! @ $i @ (^[Y0 : $i]: ($true)))))),
% 1.42/0.50 introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition])).
% 1.42/0.50 thf(f665,plain,(
% 1.42/0.50 ($false = ((!! @ $i @ (^[Y0 : $i]: ($true))))) | ~spl0_14),
% 1.42/0.50 inference(avatar_component_clause,[],[f663])).
% 1.42/0.50 thf(f668,definition,(
% 1.42/0.50 spl0_15 <=> ! [X2 : ($i > $o),X4 : $i,X7 : ($i > $i > $i),X3 : $i,X1 : ($i > $i)] : ((((X2 @ (X1 @ (X1 @ (X7 @ X4 @ X3))))) = $true) | ($true = ((sK1 @ X1 @ X2 @ X3 @ X7 @ X4))))),
% 1.42/0.50 introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition])).
% 1.42/0.50 thf(f669,plain,(
% 1.42/0.50 ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $i),X7 : ($i > $i > $i),X4 : $i] : ((((X2 @ (X1 @ (X1 @ (X7 @ X4 @ X3))))) = $true) | ($true = ((sK1 @ X1 @ X2 @ X3 @ X7 @ X4)))) ) | ~spl0_15),
% 1.42/0.50 inference(avatar_component_clause,[],[f668])).
% 1.42/0.50 thf(f674,plain,(
% 1.42/0.50 ( ! [X0 : $i,X1 : $i] : ((((c_In @ X1 @ X0)) = $false)) ) | (~spl0_9 | ~spl0_12)),
% 1.42/0.50 inference(superposition,[],[f625,f645])).
% 1.42/0.50 thf(f747,plain,(
% 1.42/0.50 ( ! [X1 : $i] : (((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: ((((c_In @ Y1 @ (c_Power @ Y0)) => (!! @ $i @ (^[Y3 : $i]: ((c_In @ Y3 @ Y1) => (c_In @ Y3 @ Y0))))) => (((!! @ $i @ (^[Y3 : $i]: ((c_In @ Y3 @ Y1) => (c_In @ Y3 @ Y0)))) => (c_In @ Y1 @ (c_Power @ Y0))) => Y2)) => Y2)))))) @ X1)) = $true)) )),
% 1.42/0.50 inference(pi_proxy_clausification,[],[f524])).
% 1.42/0.50 thf(f748,plain,(
% 1.42/0.50 ( ! [X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((((c_In @ Y0 @ (c_Power @ X1)) => (!! @ $i @ (^[Y2 : $i]: ((c_In @ Y2 @ Y0) => (c_In @ Y2 @ X1))))) => (((!! @ $i @ (^[Y2 : $i]: ((c_In @ Y2 @ Y0) => (c_In @ Y2 @ X1)))) => (c_In @ Y0 @ (c_Power @ X1))) => Y1)) => Y1)))))))) )),
% 1.42/0.50 inference(beta-eta_normalization,[],[f747])).
% 1.42/0.50 thf(f749,plain,(
% 1.42/0.50 ( ! [X2 : $i,X1 : $i] : (((((^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((((c_In @ Y0 @ (c_Power @ X1)) => (!! @ $i @ (^[Y2 : $i]: ((c_In @ Y2 @ Y0) => (c_In @ Y2 @ X1))))) => (((!! @ $i @ (^[Y2 : $i]: ((c_In @ Y2 @ Y0) => (c_In @ Y2 @ X1)))) => (c_In @ Y0 @ (c_Power @ X1))) => Y1)) => Y1)))) @ X2)) = $true)) )),
% 1.42/0.50 inference(pi_proxy_clausification,[],[f748])).
% 1.42/0.50 thf(f750,plain,(
% 1.42/0.50 ( ! [X2 : $i,X1 : $i] : ((((!! @ $o @ (^[Y0 : $o]: ((((c_In @ X2 @ (c_Power @ X1)) => (!! @ $i @ (^[Y1 : $i]: ((c_In @ Y1 @ X2) => (c_In @ Y1 @ X1))))) => (((!! @ $i @ (^[Y1 : $i]: ((c_In @ Y1 @ X2) => (c_In @ Y1 @ X1)))) => (c_In @ X2 @ (c_Power @ X1))) => Y0)) => Y0)))) = $true)) )),
% 1.42/0.50 inference(beta-eta_normalization,[],[f749])).
% 1.42/0.50 thf(f751,plain,(
% 1.42/0.50 ( ! [X2 : $i,X3 : $o,X1 : $i] : (((((^[Y0 : $o]: ((((c_In @ X2 @ (c_Power @ X1)) => (!! @ $i @ (^[Y1 : $i]: ((c_In @ Y1 @ X2) => (c_In @ Y1 @ X1))))) => (((!! @ $i @ (^[Y1 : $i]: ((c_In @ Y1 @ X2) => (c_In @ Y1 @ X1)))) => (c_In @ X2 @ (c_Power @ X1))) => Y0)) => Y0)) @ X3)) = $true)) )),
% 1.42/0.50 inference(pi_proxy_clausification,[],[f750])).
% 1.42/0.50 thf(f752,plain,(
% 1.42/0.50 ( ! [X2 : $i,X3 : $o,X1 : $i] : (($true = (((((c_In @ X2 @ (c_Power @ X1)) => (!! @ $i @ (^[Y0 : $i]: ((c_In @ Y0 @ X2) => (c_In @ Y0 @ X1))))) => (((!! @ $i @ (^[Y0 : $i]: ((c_In @ Y0 @ X2) => (c_In @ Y0 @ X1)))) => (c_In @ X2 @ (c_Power @ X1))) => X3)) => X3)))) )),
% 1.42/0.50 inference(beta-eta_normalization,[],[f751])).
% 1.42/0.50 thf(f753,plain,(
% 1.42/0.50 ( ! [X2 : $i,X3 : $o,X1 : $i] : (((((($false => (!! @ $i @ (^[Y0 : $i]: ((c_In @ Y0 @ X2) => (c_In @ Y0 @ X1))))) => (((!! @ $i @ (^[Y0 : $i]: ((c_In @ Y0 @ X2) => (c_In @ Y0 @ X1)))) => $false) => X3)) => X3)) = $true)) ) | (~spl0_9 | ~spl0_12)),
% 1.42/0.50 inference(forward_demodulation,[],[f752,f674])).
% 1.42/0.50 thf(f754,plain,(
% 1.42/0.50 ( ! [X2 : $i,X3 : $o,X1 : $i] : (((((($false => (!! @ $i @ (^[Y0 : $i]: ((c_In @ Y0 @ X2) => (c_In @ Y0 @ X1))))) => ((~ (!! @ $i @ (^[Y0 : $i]: ((c_In @ Y0 @ X2) => (c_In @ Y0 @ X1))))) => X3)) => X3)) = $true)) ) | (~spl0_9 | ~spl0_12)),
% 1.42/0.50 inference(boolean_simplification,[],[f753])).
% 1.42/0.50 thf(f755,plain,(
% 1.42/0.50 ( ! [X2 : $i,X3 : $o,X1 : $i] : (($true = ((($true => ((~ (!! @ $i @ (^[Y0 : $i]: ((c_In @ Y0 @ X2) => (c_In @ Y0 @ X1))))) => X3)) => X3)))) ) | (~spl0_9 | ~spl0_12)),
% 1.42/0.50 inference(boolean_simplification,[],[f754])).
% 1.42/0.50 thf(f756,plain,(
% 1.42/0.50 ( ! [X2 : $i,X3 : $o,X1 : $i] : ((((((~ (!! @ $i @ (^[Y0 : $i]: ((c_In @ Y0 @ X2) => (c_In @ Y0 @ X1))))) => X3) => X3)) = $true)) ) | (~spl0_9 | ~spl0_12)),
% 1.42/0.50 inference(boolean_simplification,[],[f755])).
% 1.42/0.50 thf(f757,plain,(
% 1.42/0.50 ( ! [X2 : $i,X3 : $o,X1 : $i] : (($true = X3) | ((((~ (!! @ $i @ (^[Y0 : $i]: ((c_In @ Y0 @ X2) => (c_In @ Y0 @ X1))))) => X3)) = $false)) ) | (~spl0_9 | ~spl0_12)),
% 1.42/0.50 inference(imp_proxy_clausification,[],[f756])).
% 1.42/0.50 thf(f759,plain,(
% 1.42/0.50 ( ! [X2 : $i,X3 : $o,X1 : $i] : (($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((c_In @ Y0 @ X2) => (c_In @ Y0 @ X1))))))) | ($true = X3)) ) | (~spl0_9 | ~spl0_12)),
% 1.42/0.50 inference(imp_proxy_clausification,[],[f757])).
% 1.42/0.50 thf(f760,plain,(
% 1.42/0.50 ( ! [X2 : $i,X3 : $o,X1 : $i] : (($false = ((!! @ $i @ (^[Y0 : $i]: ((c_In @ Y0 @ X2) => (c_In @ Y0 @ X1)))))) | ($true = X3)) ) | (~spl0_9 | ~spl0_12)),
% 1.42/0.50 inference(not_proxy_clausification,[],[f759])).
% 1.42/0.50 thf(f762,definition,(
% 1.42/0.50 spl0_16 <=> ! [X2 : $i,X1 : $i] : ($false = ((!! @ $i @ (^[Y0 : $i]: ((c_In @ Y0 @ X2) => (c_In @ Y0 @ X1))))))),
% 1.42/0.50 introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition])).
% 1.42/0.50 thf(f763,plain,(
% 1.42/0.50 ( ! [X2 : $i,X1 : $i] : (($false = ((!! @ $i @ (^[Y0 : $i]: ((c_In @ Y0 @ X2) => (c_In @ Y0 @ X1))))))) ) | ~spl0_16),
% 1.42/0.50 inference(avatar_component_clause,[],[f762])).
% 1.42/0.50 thf(f764,plain,(
% 1.42/0.50 spl0_10 | spl0_16 | ~spl0_9 | ~spl0_12),
% 1.42/0.50 inference(avatar_split_clause,[],[f760,f644,f571,f762,f617])).
% 1.42/0.50 thf(f769,plain,(
% 1.42/0.50 ($false = $true) | (~spl0_4 | ~spl0_10)),
% 1.42/0.50 inference(superposition,[],[f548,f618])).
% 1.42/0.50 thf(f782,plain,(
% 1.42/0.50 $false | (~spl0_4 | ~spl0_10)),
% 1.42/0.50 inference(trivial_inequality_removal,[],[f769])).
% 1.42/0.50 thf(f783,plain,(
% 1.42/0.50 ~spl0_4 | ~spl0_10),
% 1.42/0.50 inference(avatar_contradiction_clause,[],[f782])).
% 1.42/0.50 thf(f811,plain,(
% 1.42/0.50 ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $i),X7 : ($i > $i > $i),X4 : $i] : (($false = (((^[Y0 : $o]: (((!! @ $i @ (^[Y1 : $i]: ($true))) => (((X2 @ (X1 @ (X1 @ (X7 @ X4 @ X3)))) => c_False) => Y0)) => Y0)) @ (sK1 @ X1 @ X2 @ X3 @ X7 @ X4))))) ) | ~spl0_11),
% 1.42/0.50 inference(sigma_proxy_clausification,[],[f642])).
% 1.42/0.50 thf(f813,plain,(
% 1.42/0.50 ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $i),X7 : ($i > $i > $i),X4 : $i] : (($false = ((((!! @ $i @ (^[Y0 : $i]: ($true))) => (((X2 @ (X1 @ (X1 @ (X7 @ X4 @ X3)))) => c_False) => (sK1 @ X1 @ X2 @ X3 @ X7 @ X4))) => (sK1 @ X1 @ X2 @ X3 @ X7 @ X4))))) ) | ~spl0_11),
% 1.42/0.50 inference(beta-eta_normalization,[],[f811])).
% 1.42/0.50 thf(f815,plain,(
% 1.42/0.50 ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $i),X7 : ($i > $i > $i),X4 : $i] : ((((((!! @ $i @ (^[Y0 : $i]: ($true))) => (((X2 @ (X1 @ (X1 @ (X7 @ X4 @ X3)))) => $false) => (sK1 @ X1 @ X2 @ X3 @ X7 @ X4))) => (sK1 @ X1 @ X2 @ X3 @ X7 @ X4))) = $false)) ) | (~spl0_4 | ~spl0_11)),
% 1.42/0.50 inference(forward_demodulation,[],[f813,f548])).
% 1.42/0.50 thf(f816,plain,(
% 1.42/0.50 ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $i),X7 : ($i > $i > $i),X4 : $i] : ((((((!! @ $i @ (^[Y0 : $i]: ($true))) => ((~ (X2 @ (X1 @ (X1 @ (X7 @ X4 @ X3))))) => (sK1 @ X1 @ X2 @ X3 @ X7 @ X4))) => (sK1 @ X1 @ X2 @ X3 @ X7 @ X4))) = $false)) ) | (~spl0_4 | ~spl0_11)),
% 1.42/0.50 inference(boolean_simplification,[],[f815])).
% 1.42/0.50 thf(f818,plain,(
% 1.42/0.50 ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $i),X7 : ($i > $i > $i),X4 : $i] : (((((!! @ $i @ (^[Y0 : $i]: ($true))) => ((~ (X2 @ (X1 @ (X1 @ (X7 @ X4 @ X3))))) => (sK1 @ X1 @ X2 @ X3 @ X7 @ X4)))) = $true)) ) | (~spl0_4 | ~spl0_11)),
% 1.42/0.50 inference(imp_proxy_clausification,[],[f816])).
% 1.42/0.50 thf(f819,plain,(
% 1.42/0.50 ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $i),X7 : ($i > $i > $i),X4 : $i] : (((((~ (X2 @ (X1 @ (X1 @ (X7 @ X4 @ X3))))) => (sK1 @ X1 @ X2 @ X3 @ X7 @ X4))) = $true) | ($false = ((!! @ $i @ (^[Y0 : $i]: ($true)))))) ) | (~spl0_4 | ~spl0_11)),
% 1.42/0.50 inference(imp_proxy_clausification,[],[f818])).
% 1.42/0.50 thf(f820,plain,(
% 1.42/0.50 ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $i),X7 : ($i > $i > $i),X4 : $i] : (($false = ((~ (X2 @ (X1 @ (X1 @ (X7 @ X4 @ X3))))))) | ($true = ((sK1 @ X1 @ X2 @ X3 @ X7 @ X4))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ($true)))))) ) | (~spl0_4 | ~spl0_11)),
% 1.42/0.50 inference(imp_proxy_clausification,[],[f819])).
% 1.42/0.50 thf(f821,plain,(
% 1.42/0.50 ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $i),X7 : ($i > $i > $i),X4 : $i] : ((((X2 @ (X1 @ (X1 @ (X7 @ X4 @ X3))))) = $true) | ($true = ((sK1 @ X1 @ X2 @ X3 @ X7 @ X4))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ($true)))))) ) | (~spl0_4 | ~spl0_11)),
% 1.42/0.50 inference(not_proxy_clausification,[],[f820])).
% 1.42/0.50 thf(f822,plain,(
% 1.42/0.50 spl0_14 | spl0_15 | ~spl0_4 | ~spl0_11),
% 1.42/0.50 inference(avatar_split_clause,[],[f821,f641,f546,f668,f663])).
% 1.42/0.50 thf(f829,plain,(
% 1.42/0.50 ($false = (((^[Y0 : $i]: ($true)) @ sK5))) | ~spl0_14),
% 1.42/0.50 inference(sigma_proxy_clausification,[],[f665])).
% 1.42/0.50 thf(f831,plain,(
% 1.42/0.50 ($false = $true) | ~spl0_14),
% 1.42/0.50 inference(beta-eta_normalization,[],[f829])).
% 1.42/0.50 thf(f832,plain,(
% 1.42/0.50 $false | ~spl0_14),
% 1.42/0.50 inference(trivial_inequality_removal,[],[f831])).
% 1.42/0.50 thf(f833,plain,(
% 1.42/0.50 ~spl0_14),
% 1.42/0.50 inference(avatar_contradiction_clause,[],[f832])).
% 1.42/0.50 thf(f848,plain,(
% 1.42/0.50 ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $i),X7 : ($i > $i > $i),X4 : $i] : ((((X2 @ (X1 @ (X1 @ (X7 @ X4 @ X3))))) = $true) | ($false = $true)) ) | (~spl0_11 | ~spl0_15)),
% 1.42/0.50 inference(forward_demodulation,[],[f669,f653])).
% 1.42/0.50 thf(f849,plain,(
% 1.42/0.50 ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $i),X7 : ($i > $i > $i),X4 : $i] : ((((X2 @ (X1 @ (X1 @ (X7 @ X4 @ X3))))) = $true)) ) | (~spl0_11 | ~spl0_15)),
% 1.42/0.50 inference(trivial_inequality_removal,[],[f848])).
% 1.42/0.50 thf(f869,plain,(
% 1.42/0.50 ( ! [X3 : $i,X1 : ($i > $i),X8 : ($i > $o),X7 : ($i > $i > $i),X4 : $i] : (($true = (((^[Y0 : $i]: (~ (X8 @ Y0))) @ (X1 @ (X1 @ (X7 @ X4 @ X3))))))) ) | (~spl0_11 | ~spl0_15)),
% 1.42/0.50 inference(primitive_instantiation,[],[f849])).
% 1.42/0.50 thf(f879,plain,(
% 1.42/0.50 ( ! [X3 : $i,X1 : ($i > $i),X8 : ($i > $o),X7 : ($i > $i > $i),X4 : $i] : (($true = ((~ (X8 @ (X1 @ (X1 @ (X7 @ X4 @ X3)))))))) ) | (~spl0_11 | ~spl0_15)),
% 1.42/0.50 inference(beta-eta_normalization,[],[f869])).
% 1.42/0.50 thf(f881,plain,(
% 1.42/0.50 ($true = ((~ $true))) | (~spl0_11 | ~spl0_15)),
% 1.42/0.50 inference(forward_demodulation,[],[f879,f849])).
% 1.42/0.50 thf(f882,plain,(
% 1.42/0.50 ($false = $true) | (~spl0_11 | ~spl0_15)),
% 1.42/0.50 inference(boolean_simplification,[],[f881])).
% 1.42/0.50 thf(f883,plain,(
% 1.42/0.50 $false | (~spl0_11 | ~spl0_15)),
% 1.42/0.50 inference(trivial_inequality_removal,[],[f882])).
% 1.42/0.50 thf(f884,plain,(
% 1.42/0.50 ~spl0_11 | ~spl0_15),
% 1.42/0.50 inference(avatar_contradiction_clause,[],[f883])).
% 1.42/0.50 thf(f892,plain,(
% 1.42/0.50 ( ! [X2 : $i,X1 : $i] : (($false = (((^[Y0 : $i]: ((c_In @ Y0 @ X2) => (c_In @ Y0 @ X1))) @ (sK4 @ X1 @ X2))))) ) | ~spl0_16),
% 1.42/0.50 inference(sigma_proxy_clausification,[],[f763])).
% 1.42/0.50 thf(f895,plain,(
% 1.42/0.50 ( ! [X2 : $i,X1 : $i] : (($false = (((c_In @ (sK4 @ X1 @ X2) @ X2) => (c_In @ (sK4 @ X1 @ X2) @ X1))))) ) | ~spl0_16),
% 1.42/0.50 inference(beta-eta_normalization,[],[f892])).
% 1.42/0.50 thf(f897,plain,(
% 1.42/0.50 ( ! [X2 : $i,X1 : $i] : (($true = ((c_In @ (sK4 @ X1 @ X2) @ X2)))) ) | ~spl0_16),
% 1.42/0.50 inference(imp_proxy_clausification,[],[f895])).
% 1.42/0.50 thf(f975,plain,(
% 1.42/0.50 ($false = $true) | (~spl0_9 | ~spl0_12 | ~spl0_16)),
% 1.42/0.50 inference(forward_demodulation,[],[f897,f674])).
% 1.42/0.50 thf(f976,plain,(
% 1.42/0.50 $false | (~spl0_9 | ~spl0_12 | ~spl0_16)),
% 1.42/0.50 inference(trivial_inequality_removal,[],[f975])).
% 1.42/0.50 thf(f977,plain,(
% 1.42/0.50 ~spl0_9 | ~spl0_12 | ~spl0_16),
% 1.42/0.50 inference(avatar_contradiction_clause,[],[f976])).
% 1.42/0.50 cnf(s5, plain, spl0_2 | spl0_9, inference(sat_conversion,[],[f574])).
% 1.42/0.50 cnf(s6, plain, spl0_4, inference(sat_conversion,[],[f575])).
% 1.42/0.50 cnf(s7, plain, ~spl0_2 | ~spl0_4, inference(sat_conversion,[],[f612])).
% 1.42/0.50 cnf(s10, plain, spl0_11 | spl0_12, inference(sat_conversion,[],[f646])).
% 1.42/0.50 cnf(s14, plain, ~spl0_9 | spl0_10 | ~spl0_12 | spl0_16, inference(sat_conversion,[],[f764])).
% 1.42/0.50 cnf(s18, plain, ~spl0_4 | ~spl0_10, inference(sat_conversion,[],[f783])).
% 1.42/0.50 cnf(s22, plain, ~spl0_4 | ~spl0_11 | spl0_14 | spl0_15, inference(sat_conversion,[],[f822])).
% 1.42/0.50 cnf(s23, plain, ~spl0_14, inference(sat_conversion,[],[f833])).
% 1.42/0.50 cnf(s29, plain, ~spl0_11 | ~spl0_15, inference(sat_conversion,[],[f884])).
% 1.42/0.50 cnf(s31, plain, ~spl0_9 | ~spl0_12 | ~spl0_16, inference(sat_conversion,[],[f977])).
% 1.42/0.50 cnf(s32, plain, ~spl0_4 | ~spl0_11 | spl0_15, inference(rat,[],[s22,s23])).
% 1.42/0.50 cnf(s35, plain, ~spl0_10, inference(rat,[],[s18,s6])).
% 1.42/0.50 cnf(s36, plain, ~spl0_2, inference(rat,[],[s7,s6])).
% 1.42/0.50 cnf(s41, plain, spl0_9, inference(rat,[],[s5,s36])).
% 1.42/0.50 cnf(s44, plain, ~spl0_12, inference(rat,[],[s14,s31,s35,s41])).
% 1.42/0.50 cnf(s45, plain, spl0_11, inference(rat,[],[s10,s44])).
% 1.42/0.50 cnf(s46, plain, ~spl0_15, inference(rat,[],[s29,s45])).
% 1.42/0.50 cnf(s47, plain, $false, inference(rat,[],[s32,s6,s46,s45])).
% 1.42/0.50 thf(f978,plain,(
% 1.42/0.50 $false),
% 1.42/0.50 inference(avatar_sat_refutation,[],[s47])).
% 1.42/0.50 % SZS output end Proof for theBenchmark
% 1.42/0.50 % (2405866)------------------------------
% 1.42/0.50 % (2405866)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.42/0.50 % (2405866)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.42/0.50 % (2405866)CaDiCaL version: 2.1.3
% 1.42/0.50 % (2405866)Termination reason: Refutation
% 1.42/0.50 % (2405866)Time elapsed: 0.035 s
% 1.42/0.50 % (2405866)Peak memory usage: 14 MB
% 1.42/0.50 % (2405866)Instructions burned: 134 (million)
% 1.42/0.50 % (2405801)Success in time 0.223 s
% 1.42/0.50 % Vampire exiting
%------------------------------------------------------------------------------