%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM667^4 : TPTP v9.3.1. Released v7.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n002.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 08:18:28 AM UTC 2026
% Result : Theorem 3.91s 0.93s
% Output : Refutation 3.91s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM667^4 : TPTP v9.3.1. Released v7.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n002.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 12:36:07 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
% 0.20/0.27 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
% 0.53/0.41 % (1212105)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.53/0.41 % (1212132)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=250535746:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.53/0.41 % (1212139)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.53/0.41 % (1212139)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
% 0.53/0.41 % (1212134)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2103629421:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.53/0.41 % (1212136)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=453275877:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.53/0.41 % (1212135)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=3364721782: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)
% 0.53/0.41 % (1212137)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3316874014:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.53/0.41 % (1212139)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=2825279483:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.53/0.41 % (1212133)lrs+10_16_si=on:nwc=1.5:random_seed=1386831840:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.53/0.41 % (1212134)Instruction limit reached!
% 0.53/0.41 % (1212134)------------------------------
% 0.53/0.41 % (1212134)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.53/0.41 % (1212134)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.53/0.41 % (1212134)CaDiCaL version: 2.1.3
% 0.53/0.41 % (1212134)Termination reason: Instruction limit
% 0.53/0.41 % (1212134)Termination phase: shuffling
% 0.53/0.41 % (1212134)Time elapsed: 0.004 s
% 0.53/0.41 % (1212134)Peak memory usage: 10 MB
% 0.53/0.41 % (1212134)Instructions burned: 8 (million)
% 0.53/0.41 % (1212133)Instruction limit reached!
% 0.53/0.41 % (1212133)------------------------------
% 0.53/0.41 % (1212133)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.53/0.41 % (1212133)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.53/0.41 % (1212133)CaDiCaL version: 2.1.3
% 0.53/0.41 % (1212133)Termination reason: Instruction limit
% 0.53/0.41 % (1212133)Termination phase: shuffling
% 0.53/0.41 % (1212133)Time elapsed: 0.009 s
% 0.53/0.41 % (1212133)Peak memory usage: 10 MB
% 0.53/0.41 % (1212133)Instructions burned: 18 (million)
% 0.53/0.41 % (1212136)Instruction limit reached!
% 0.53/0.41 % (1212136)------------------------------
% 0.53/0.41 % (1212136)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.53/0.41 % (1212136)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.53/0.41 % (1212136)CaDiCaL version: 2.1.3
% 0.53/0.41 % (1212136)Termination reason: Instruction limit
% 0.53/0.41 % (1212136)Termination phase: Property scanning
% 0.53/0.41 % (1212136)Time elapsed: 0.012 s
% 0.53/0.41 % (1212136)Peak memory usage: 10 MB
% 0.53/0.41 % (1212136)Instructions burned: 25 (million)
% 0.53/0.41 % (1212132)Instruction limit reached!
% 0.53/0.41 % (1212132)------------------------------
% 0.53/0.41 % (1212132)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.53/0.41 % (1212132)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.53/0.41 % (1212132)CaDiCaL version: 2.1.3
% 0.53/0.41 % (1212132)Termination reason: Instruction limit
% 0.53/0.41 % (1212132)Termination phase: Function definition elimination
% 0.53/0.41 % (1212132)Time elapsed: 0.022 s
% 0.53/0.41 % (1212132)Peak memory usage: 11 MB
% 0.53/0.41 % (1212132)Instructions burned: 92 (million)
% 0.53/0.41 % (1212159)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2037423899:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.53/0.41 % (1212163)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=2277058523:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.53/0.45 % (1212159)Instruction limit reached!
% 0.53/0.45 % (1212159)------------------------------
% 0.53/0.45 % (1212159)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.53/0.45 % (1212159)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.53/0.45 % (1212159)CaDiCaL version: 2.1.3
% 0.53/0.45 % (1212159)Termination reason: Instruction limit
% 0.53/0.45 % (1212159)Termination phase: shuffling
% 0.53/0.45 % (1212159)Time elapsed: 0.002 s
% 0.53/0.45 % (1212159)Peak memory usage: 10 MB
% 0.53/0.45 % (1212159)Instructions burned: 4 (million)
% 0.53/0.45 % (1212162)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.53/0.45 % (1212163)Instruction limit reached!
% 0.53/0.45 % (1212163)------------------------------
% 0.53/0.45 % (1212163)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.53/0.45 % (1212163)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.53/0.45 % (1212163)CaDiCaL version: 2.1.3
% 0.53/0.45 % (1212163)Termination reason: Instruction limit
% 0.53/0.45 % (1212163)Termination phase: shuffling
% 0.53/0.45 % (1212163)Time elapsed: 0.004 s
% 0.53/0.45 % (1212163)Peak memory usage: 10 MB
% 0.53/0.45 % (1212163)Instructions burned: 14 (million)
% 0.53/0.45 % (1212160)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=3353520601:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.53/0.45 % (1212162)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=1214079875:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.53/0.45 % (1212137)Instruction limit reached!
% 0.53/0.45 % (1212137)------------------------------
% 0.53/0.45 % (1212137)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.53/0.45 % (1212137)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.53/0.45 % (1212137)CaDiCaL version: 2.1.3
% 0.53/0.45 % (1212137)Termination reason: Instruction limit
% 0.53/0.45 % (1212137)Termination phase: Function definition elimination
% 0.53/0.45 % (1212137)Time elapsed: 0.034 s
% 0.53/0.45 % (1212137)Peak memory usage: 11 MB
% 0.53/0.45 % (1212137)Instructions burned: 75 (million)
% 0.53/0.45 % (1212160)Instruction limit reached!
% 0.53/0.45 % (1212160)------------------------------
% 0.53/0.45 % (1212160)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.53/0.45 % (1212160)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.53/0.45 % (1212160)CaDiCaL version: 2.1.3
% 0.53/0.45 % (1212160)Termination reason: Instruction limit
% 0.53/0.45 % (1212160)Termination phase: shuffling
% 0.53/0.45 % (1212160)Time elapsed: 0.003 s
% 0.53/0.45 % (1212160)Peak memory usage: 10 MB
% 0.53/0.45 % (1212160)Instructions burned: 6 (million)
% 0.53/0.45 % (1212162)Instruction limit reached!
% 0.53/0.45 % (1212162)------------------------------
% 0.53/0.45 % (1212162)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.53/0.45 % (1212162)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.53/0.45 % (1212162)CaDiCaL version: 2.1.3
% 0.53/0.45 % (1212162)Termination reason: Instruction limit
% 0.53/0.45 % (1212162)Termination phase: shuffling
% 0.53/0.45 % (1212162)Time elapsed: 0.004 s
% 0.53/0.45 % (1212162)Peak memory usage: 10 MB
% 0.53/0.45 % (1212162)Instructions burned: 9 (million)
% 0.53/0.45 % (1212170)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=2172919060:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.53/0.45 % (1212169)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
% 0.53/0.45 % (1212169)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.53/0.45 % (1212169)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=3565058696:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.53/0.45 % (1212174)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 1.21/0.48 % (1212173)lrs+10_1_si=on:cs=on:random_seed=2975818280:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 1.21/0.48 % (1212174)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=3466259237:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 1.21/0.48 % (1212175)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=3068495428:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 1.21/0.48 % (1212174)Instruction limit reached!
% 1.21/0.48 % (1212174)------------------------------
% 1.21/0.48 % (1212174)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.21/0.48 % (1212174)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.21/0.48 % (1212174)CaDiCaL version: 2.1.3
% 1.21/0.48 % (1212174)Termination reason: Instruction limit
% 1.21/0.48 % (1212174)Termination phase: shuffling
% 1.21/0.48 % (1212174)Time elapsed: 0.002 s
% 1.21/0.48 % (1212174)Peak memory usage: 10 MB
% 1.21/0.48 % (1212174)Instructions burned: 3 (million)
% 1.21/0.48 % (1212169)Instruction limit reached!
% 1.21/0.48 % (1212169)------------------------------
% 1.21/0.48 % (1212169)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.21/0.48 % (1212169)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.21/0.48 % (1212169)CaDiCaL version: 2.1.3
% 1.21/0.48 % (1212169)Termination reason: Instruction limit
% 1.21/0.48 % (1212169)Termination phase: Property scanning
% 1.21/0.48 % (1212169)Time elapsed: 0.013 s
% 1.21/0.48 % (1212169)Peak memory usage: 10 MB
% 1.21/0.48 % (1212169)Instructions burned: 28 (million)
% 1.21/0.48 % (1212173)Instruction limit reached!
% 1.21/0.48 % (1212173)------------------------------
% 1.21/0.48 % (1212173)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.21/0.48 % (1212173)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.21/0.48 % (1212173)CaDiCaL version: 2.1.3
% 1.21/0.48 % (1212173)Termination reason: Instruction limit
% 1.21/0.48 % (1212173)Termination phase: shuffling
% 1.21/0.48 % (1212173)Time elapsed: 0.004 s
% 1.21/0.48 % (1212173)Peak memory usage: 10 MB
% 1.21/0.48 % (1212173)Instructions burned: 9 (million)
% 1.21/0.48 % (1212170)Instruction limit reached!
% 1.21/0.48 % (1212170)------------------------------
% 1.21/0.48 % (1212170)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.21/0.48 % (1212170)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.21/0.48 % (1212170)CaDiCaL version: 2.1.3
% 1.21/0.48 % (1212170)Termination reason: Instruction limit
% 1.21/0.48 % (1212170)Termination phase: Function definition elimination
% 1.21/0.48 % (1212170)Time elapsed: 0.020 s
% 1.21/0.48 % (1212170)Peak memory usage: 11 MB
% 1.21/0.48 % (1212170)Instructions burned: 88 (million)
% 1.21/0.48 % (1212184)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=3610366767:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 1.21/0.48 % (1212175)Instruction limit reached!
% 1.21/0.48 % (1212175)------------------------------
% 1.21/0.48 % (1212175)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.21/0.48 % (1212175)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.21/0.48 % (1212175)CaDiCaL version: 2.1.3
% 1.21/0.48 % (1212175)Termination reason: Instruction limit
% 1.21/0.48 % (1212175)Termination phase: Property scanning
% 1.21/0.48 % (1212175)Time elapsed: 0.018 s
% 1.21/0.48 % (1212175)Peak memory usage: 11 MB
% 1.21/0.48 % (1212175)Instructions burned: 39 (million)
% 1.21/0.48 % (1212181)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=2055810255:st=2:i=249:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/249Mi)
% 1.21/0.48 % (1212139)Instruction limit reached!
% 1.21/0.48 % (1212139)------------------------------
% 1.21/0.48 % (1212139)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.21/0.48 % (1212139)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.21/0.48 % (1212139)CaDiCaL version: 2.1.3
% 1.21/0.48 % (1212139)Termination reason: Instruction limit
% 1.21/0.48 % (1212139)Termination phase: Function definition elimination
% 1.21/0.48 % (1212139)Time elapsed: 0.076 s
% 1.21/0.48 % (1212139)Peak memory usage: 11 MB
% 1.21/0.48 % (1212139)Instructions burned: 158 (million)
% 1.21/0.48 % (1212182)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=350464700:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 1.21/0.51 % (1212183)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=3357143995:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 1.21/0.51 % (1212183)Instruction limit reached!
% 1.21/0.51 % (1212183)------------------------------
% 1.21/0.51 % (1212183)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.21/0.51 % (1212183)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.21/0.51 % (1212183)CaDiCaL version: 2.1.3
% 1.21/0.51 % (1212183)Termination reason: Instruction limit
% 1.21/0.51 % (1212183)Termination phase: shuffling
% 1.21/0.51 % (1212183)Time elapsed: 0.006 s
% 1.21/0.51 % (1212183)Peak memory usage: 10 MB
% 1.21/0.51 % (1212183)Instructions burned: 14 (million)
% 1.21/0.51 % (1212182)Instruction limit reached!
% 1.21/0.51 % (1212182)------------------------------
% 1.21/0.51 % (1212182)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.21/0.51 % (1212182)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.21/0.51 % (1212182)CaDiCaL version: 2.1.3
% 1.21/0.51 % (1212182)Termination reason: Instruction limit
% 1.21/0.51 % (1212182)Termination phase: Property scanning
% 1.21/0.51 % (1212182)Time elapsed: 0.012 s
% 1.21/0.51 % (1212182)Peak memory usage: 10 MB
% 1.21/0.51 % (1212182)Instructions burned: 27 (million)
% 1.21/0.51 % (1212186)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=583940961:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 1.21/0.51 % (1212189)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=1023164154: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)
% 1.21/0.51 % (1212189)Instruction limit reached!
% 1.21/0.51 % (1212189)------------------------------
% 1.21/0.51 % (1212189)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.21/0.51 % (1212189)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.21/0.51 % (1212189)CaDiCaL version: 2.1.3
% 1.21/0.51 % (1212189)Termination reason: Instruction limit
% 1.21/0.51 % (1212189)Termination phase: shuffling
% 1.21/0.51 % (1212189)Time elapsed: 0.002 s
% 1.21/0.51 % (1212189)Peak memory usage: 10 MB
% 1.21/0.51 % (1212189)Instructions burned: 4 (million)
% 1.21/0.51 % (1212181)Refutation not found, incomplete strategy
% 1.21/0.51 % (1212181)------------------------------
% 1.21/0.51 % (1212181)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.21/0.51 % (1212181)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.21/0.51 % (1212181)CaDiCaL version: 2.1.3
% 1.21/0.51 % (1212181)Termination reason: Refutation not found, incomplete strategy
% 1.21/0.51 % (1212181)Time elapsed: 0.022 s
% 1.21/0.51 % (1212181)Peak memory usage: 13 MB
% 1.21/0.51 % (1212181)Instructions burned: 48 (million)
% 1.21/0.51 % (1212181)------------------------------
% 1.21/0.51 % (1212181)------------------------------
% 1.21/0.51 % (1212186)Instruction limit reached!
% 1.21/0.51 % (1212186)------------------------------
% 1.21/0.51 % (1212186)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.21/0.51 % (1212186)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.21/0.51 % (1212186)CaDiCaL version: 2.1.3
% 1.21/0.51 % (1212186)Termination reason: Instruction limit
% 1.21/0.51 % (1212186)Termination phase: shuffling
% 1.21/0.51 % (1212186)Time elapsed: 0.008 s
% 1.21/0.51 % (1212186)Peak memory usage: 10 MB
% 1.21/0.51 % (1212186)Instructions burned: 18 (million)
% 1.21/0.51 % (1212191)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=3329485004:i=26:ep=R:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/26Mi)
% 1.21/0.51 % (1212192)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=2584278826:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 1.21/0.51 % (1212191)Instruction limit reached!
% 1.21/0.51 % (1212191)------------------------------
% 1.21/0.51 % (1212191)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.21/0.51 % (1212191)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.21/0.51 % (1212191)CaDiCaL version: 2.1.3
% 1.21/0.51 % (1212191)Termination reason: Instruction limit
% 1.91/0.57 % (1212191)Termination phase: Property scanning
% 1.91/0.57 % (1212191)Time elapsed: 0.011 s
% 1.91/0.57 % (1212191)Peak memory usage: 10 MB
% 1.91/0.57 % (1212191)Instructions burned: 26 (million)
% 1.91/0.57 % (1212197)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
% 1.91/0.57 % (1212197)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs
% 1.91/0.57 % (1212195)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=817254080:cond=on:i=60:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/60Mi)
% 1.91/0.57 % (1212198)WARNING Broken Constraint: if choice_reasoning(on) has been set then choice_ax(on) is equal to off
% 1.91/0.57 % (1212192)Instruction limit reached!
% 1.91/0.57 % (1212192)------------------------------
% 1.91/0.57 % (1212192)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.91/0.57 % (1212192)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.91/0.57 % (1212192)CaDiCaL version: 2.1.3
% 1.91/0.57 % (1212192)Termination reason: Instruction limit
% 1.91/0.57 % (1212192)Termination phase: Property scanning
% 1.91/0.57 % (1212192)Time elapsed: 0.011 s
% 1.91/0.57 % (1212192)Peak memory usage: 10 MB
% 1.91/0.57 % (1212192)Instructions burned: 25 (million)
% 1.91/0.57 % (1212197)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=3036293465:i=14:add=off:nm=40:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 1.91/0.57 % (1212198)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=1963168821:i=8:nm=2:rtra=on:fe=abstraction:inj=on_2998 on theBenchmark for (2998ds/8Mi)
% 1.91/0.57 % (1212198)Instruction limit reached!
% 1.91/0.57 % (1212198)------------------------------
% 1.91/0.57 % (1212198)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.91/0.57 % (1212198)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.91/0.57 % (1212198)CaDiCaL version: 2.1.3
% 1.91/0.57 % (1212198)Termination reason: Instruction limit
% 1.91/0.57 % (1212198)Termination phase: shuffling
% 1.91/0.57 % (1212198)Time elapsed: 0.005 s
% 1.91/0.57 % (1212198)Peak memory usage: 10 MB
% 1.91/0.57 % (1212198)Instructions burned: 10 (million)
% 1.91/0.57 % (1212197)Instruction limit reached!
% 1.91/0.57 % (1212197)------------------------------
% 1.91/0.57 % (1212197)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.91/0.57 % (1212197)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.91/0.57 % (1212197)CaDiCaL version: 2.1.3
% 1.91/0.57 % (1212197)Termination reason: Instruction limit
% 1.91/0.57 % (1212197)Termination phase: shuffling
% 1.91/0.57 % (1212197)Time elapsed: 0.006 s
% 1.91/0.57 % (1212197)Peak memory usage: 10 MB
% 1.91/0.57 % (1212197)Instructions burned: 14 (million)
% 1.91/0.57 % (1212200)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=2449858995:uwa_fpi=on:i=31:doe=on:bd=preordered:rtra=on:fsd=on_2998 on theBenchmark for (2998ds/31Mi)
% 1.91/0.57 % (1212202)dis+10_1024_sil=128000:cnfonf=off:si=on:fd=off:random_seed=2663851595:i=7:hud=5:bd=preordered:rtra=on:bet=on_2998 on theBenchmark for (2998ds/7Mi)
% 1.91/0.57 % (1212202)Instruction limit reached!
% 1.91/0.57 % (1212202)------------------------------
% 1.91/0.57 % (1212202)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.91/0.57 % (1212202)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.91/0.57 % (1212202)CaDiCaL version: 2.1.3
% 1.91/0.57 % (1212202)Termination reason: Instruction limit
% 1.91/0.57 % (1212202)Termination phase: shuffling
% 1.91/0.57 % (1212202)Time elapsed: 0.004 s
% 1.91/0.57 % (1212202)Peak memory usage: 10 MB
% 1.91/0.57 % (1212202)Instructions burned: 9 (million)
% 1.91/0.57 % (1212205)lrs+10_1_plsq=on:drc=ordering:cnfonf=lazy_not_gen_be_off:bsd=on:si=on:plsqr=32,1:cs=on:random_seed=1754079265:i=23:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 1.91/0.57 % (1212195)Instruction limit reached!
% 1.91/0.57 % (1212195)------------------------------
% 1.91/0.57 % (1212195)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.25/0.63 % (1212195)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.25/0.63 % (1212195)CaDiCaL version: 2.1.3
% 2.25/0.63 % (1212195)Termination reason: Instruction limit
% 2.25/0.63 % (1212195)Termination phase: Property scanning
% 2.25/0.63 % (1212195)Time elapsed: 0.028 s
% 2.25/0.63 % (1212195)Peak memory usage: 11 MB
% 2.25/0.63 % (1212195)Instructions burned: 62 (million)
% 2.25/0.63 % (1212206)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=71107767:s2a=on:i=20:kws=inv_frequency:bd=all:rtra=on_2998 on theBenchmark for (2998ds/20Mi)
% 2.25/0.63 % (1212200)Instruction limit reached!
% 2.25/0.63 % (1212200)------------------------------
% 2.25/0.63 % (1212200)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.25/0.63 % (1212200)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.25/0.63 % (1212200)CaDiCaL version: 2.1.3
% 2.25/0.63 % (1212200)Termination reason: Instruction limit
% 2.25/0.63 % (1212200)Termination phase: Property scanning
% 2.25/0.63 % (1212200)Time elapsed: 0.014 s
% 2.25/0.63 % (1212200)Peak memory usage: 10 MB
% 2.25/0.63 % (1212200)Instructions burned: 31 (million)
% 2.25/0.63 % (1212205)Instruction limit reached!
% 2.25/0.63 % (1212205)------------------------------
% 2.25/0.63 % (1212205)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.25/0.63 % (1212205)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.25/0.63 % (1212205)CaDiCaL version: 2.1.3
% 2.25/0.63 % (1212205)Termination reason: Instruction limit
% 2.25/0.63 % (1212205)Termination phase: Property scanning
% 2.25/0.63 % (1212205)Time elapsed: 0.010 s
% 2.25/0.63 % (1212205)Peak memory usage: 10 MB
% 2.25/0.63 % (1212205)Instructions burned: 23 (million)
% 2.25/0.63 % (1212206)Instruction limit reached!
% 2.25/0.63 % (1212206)------------------------------
% 2.25/0.63 % (1212206)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.25/0.63 % (1212206)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.25/0.63 % (1212206)CaDiCaL version: 2.1.3
% 2.25/0.63 % (1212206)Termination reason: Instruction limit
% 2.25/0.63 % (1212206)Termination phase: Property scanning
% 2.25/0.63 % (1212206)Time elapsed: 0.010 s
% 2.25/0.63 % (1212206)Peak memory usage: 10 MB
% 2.25/0.63 % (1212206)Instructions burned: 21 (million)
% 2.25/0.63 % (1212184)Instruction limit reached!
% 2.25/0.63 % (1212184)------------------------------
% 2.25/0.63 % (1212184)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.25/0.63 % (1212184)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.25/0.63 % (1212184)CaDiCaL version: 2.1.3
% 2.25/0.63 % (1212184)Termination reason: Instruction limit
% 2.25/0.63 % (1212184)Termination phase: Saturation
% 2.25/0.63 % (1212184)Time elapsed: 0.090 s
% 2.25/0.63 % (1212184)Peak memory usage: 14 MB
% 2.25/0.63 % (1212184)Instructions burned: 329 (million)
% 2.25/0.63 % (1212209)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=2348468536:i=1240:rtra=on:ixr=off_2998 on theBenchmark for (2998ds/1240Mi)
% 2.25/0.63 % (1212212)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=3094267172:i=143:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/143Mi)
% 2.25/0.63 % (1212213)lrs+1002_1_sil=128000:si=on:acc=on:uwa=off:random_seed=1415267080:st=5:s2a=on:i=193:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/193Mi)
% 2.25/0.63 % (1212217)lrs+10_1_to=lpo:sil=128000:si=on:sp=arity:urr=on:random_seed=3737894242:i=181:sd=2:bd=preordered:rtra=on:ss=axioms_2997 on theBenchmark for (2997ds/181Mi)
% 2.25/0.63 % (1212215)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 2.25/0.63 % (1212214)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2692057550:i=42:hud=10:rtra=on_2997 on theBenchmark for (2997ds/42Mi)
% 2.25/0.63 % (1212215)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=1219183275:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2997 on theBenchmark for (2997ds/7Mi)
% 2.25/0.63 % (1212215)Instruction limit reached!
% 2.25/0.63 % (1212215)------------------------------
% 2.25/0.63 % (1212215)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.25/0.63 % (1212215)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.56/0.70 % (1212215)CaDiCaL version: 2.1.3
% 2.56/0.70 % (1212215)Termination reason: Instruction limit
% 2.56/0.70 % (1212215)Termination phase: shuffling
% 2.56/0.70 % (1212215)Time elapsed: 0.004 s
% 2.56/0.70 % (1212215)Peak memory usage: 10 MB
% 2.56/0.70 % (1212215)Instructions burned: 9 (million)
% 2.56/0.70 % (1212214)Instruction limit reached!
% 2.56/0.70 % (1212214)------------------------------
% 2.56/0.70 % (1212214)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.56/0.70 % (1212214)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.56/0.70 % (1212214)CaDiCaL version: 2.1.3
% 2.56/0.70 % (1212214)Termination reason: Instruction limit
% 2.56/0.70 % (1212214)Termination phase: Property scanning
% 2.56/0.70 % (1212214)Time elapsed: 0.019 s
% 2.56/0.70 % (1212214)Peak memory usage: 11 MB
% 2.56/0.70 % (1212214)Instructions burned: 42 (million)
% 2.56/0.70 % (1212223)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=3741160574: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)
% 2.56/0.70 % (1212224)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(5) has been set then sine_level_split_queue(off) is equal to on
% 2.56/0.70 % (1212224)lrs+1002_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=arity:cbe=off:uwa=all:slsqc=5:random_seed=3856707783:st=4:s2a=on:i=6:add=on:doe=on:hud=10:rtra=on:bet=on:ss=axioms_2997 on theBenchmark for (2997ds/6Mi)
% 2.56/0.70 % (1212224)Instruction limit reached!
% 2.56/0.70 % (1212224)------------------------------
% 2.56/0.70 % (1212224)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.56/0.70 % (1212224)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.56/0.70 % (1212224)CaDiCaL version: 2.1.3
% 2.56/0.70 % (1212224)Termination reason: Instruction limit
% 2.56/0.70 % (1212224)Termination phase: shuffling
% 2.56/0.70 % (1212224)Time elapsed: 0.003 s
% 2.56/0.70 % (1212224)Peak memory usage: 10 MB
% 2.56/0.70 % (1212224)Instructions burned: 6 (million)
% 2.56/0.70 % (1212217)Instruction limit reached!
% 2.56/0.70 % (1212217)------------------------------
% 2.56/0.70 % (1212217)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.56/0.70 % (1212217)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.56/0.70 % (1212217)CaDiCaL version: 2.1.3
% 2.56/0.70 % (1212217)Termination reason: Instruction limit
% 2.56/0.70 % (1212217)Termination phase: Saturation
% 2.56/0.70 % (1212217)Time elapsed: 0.048 s
% 2.56/0.70 % (1212217)Peak memory usage: 13 MB
% 2.56/0.70 % (1212217)Instructions burned: 182 (million)
% 2.56/0.70 % (1212212)Instruction limit reached!
% 2.56/0.70 % (1212212)------------------------------
% 2.56/0.70 % (1212212)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.56/0.70 % (1212212)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.56/0.70 % (1212212)CaDiCaL version: 2.1.3
% 2.56/0.70 % (1212212)Termination reason: Instruction limit
% 2.56/0.70 % (1212212)Termination phase: Function definition elimination
% 2.56/0.70 % (1212212)Time elapsed: 0.059 s
% 2.56/0.70 % (1212212)Peak memory usage: 11 MB
% 2.56/0.70 % (1212212)Instructions burned: 145 (million)
% 2.56/0.70 % (1212228)dis+1010_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:sas=cadical:si=on:sos=all:uwa=off:sac=on:random_seed=3907542025:i=19:add=on:rtra=on_2997 on theBenchmark for (2997ds/19Mi)
% 2.56/0.70 % (1212223)Refutation not found, incomplete strategy
% 2.56/0.70 % (1212223)------------------------------
% 2.56/0.70 % (1212223)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.56/0.70 % (1212223)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.56/0.70 % (1212223)CaDiCaL version: 2.1.3
% 2.56/0.70 % (1212223)Termination reason: Refutation not found, incomplete strategy
% 2.56/0.70 % (1212223)Time elapsed: 0.034 s
% 2.56/0.70 % (1212223)Peak memory usage: 13 MB
% 2.56/0.70 % (1212223)Instructions burned: 70 (million)
% 2.56/0.70 % (1212228)Instruction limit reached!
% 2.56/0.70 % (1212228)------------------------------
% 2.56/0.70 % (1212228)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.56/0.70 % (1212228)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.56/0.70 % (1212228)CaDiCaL version: 2.1.3
% 2.56/0.70 % (1212228)Termination reason: Instruction limit
% 2.56/0.70 % (1212228)Termination phase: Property scanning
% 2.56/0.77 % (1212228)Time elapsed: 0.005 s
% 2.56/0.77 % (1212228)Peak memory usage: 10 MB
% 2.56/0.77 % (1212228)Instructions burned: 22 (million)
% 2.56/0.77 % (1212227)ott+2_5:4_anc=none:to=lpo:si=on:lma=off:cbe=off:uwa=ground:nwc=3:random_seed=3155411208:uwa_fpi=on:i=22:add=on:doe=on:ins=1:rtra=on_2997 on theBenchmark for (2997ds/22Mi)
% 2.56/0.77 % (1212223)------------------------------
% 2.56/0.77 % (1212223)------------------------------
% 2.56/0.77 % (1212229)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=2641646551:i=316:bs=unit_only:ins=25:rtra=on:ntd=on_2997 on theBenchmark for (2997ds/316Mi)
% 2.56/0.77 % (1212232)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=2158790907:hsq=on:hsqr=16,1:s2a=on:i=853:add=off:bd=all:nm=64:rtra=on:gtg=position:c=on:ntd=on_2997 on theBenchmark for (2997ds/853Mi)
% 2.56/0.77 % (1212227)Instruction limit reached!
% 2.56/0.77 % (1212227)------------------------------
% 2.56/0.77 % (1212227)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.56/0.77 % (1212227)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.56/0.77 % (1212227)CaDiCaL version: 2.1.3
% 2.56/0.77 % (1212227)Termination reason: Instruction limit
% 2.56/0.77 % (1212227)Termination phase: Property scanning
% 2.56/0.77 % (1212227)Time elapsed: 0.010 s
% 2.56/0.77 % (1212227)Peak memory usage: 10 MB
% 2.56/0.77 % (1212227)Instructions burned: 22 (million)
% 2.56/0.77 % (1212213)Instruction limit reached!
% 2.56/0.77 % (1212213)------------------------------
% 2.56/0.77 % (1212213)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.56/0.77 % (1212213)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.56/0.77 % (1212213)CaDiCaL version: 2.1.3
% 2.56/0.77 % (1212213)Termination reason: Instruction limit
% 2.56/0.77 % (1212213)Termination phase: Saturation
% 2.56/0.77 % (1212213)Time elapsed: 0.086 s
% 2.56/0.77 % (1212213)Peak memory usage: 14 MB
% 2.56/0.77 % (1212213)Instructions burned: 193 (million)
% 2.56/0.77 % (1212233)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=3256155371:hsq=on:hsqr=16,1:s2a=on:i=45:erml=3:slsql=off:rtra=on:gtg=exists_top:er=filter:ntd=on_2997 on theBenchmark for (2997ds/45Mi)
% 2.56/0.77 % (1212236)lrs+1002_1_sil=128000:fde=unused:e2e=on:si=on:sos=on:uwa=interpreted_only:random_seed=1692661446:i=480:rtra=on_2997 on theBenchmark for (2997ds/480Mi)
% 2.56/0.77 % (1212237)dis+1010_40_sil=128000:si=on:uwa=off:nwc=1:sac=on:chr=on:avsqc=3:random_seed=193993322: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)
% 2.56/0.77 % (1212233)Instruction limit reached!
% 2.56/0.77 % (1212233)------------------------------
% 2.56/0.77 % (1212233)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.56/0.77 % (1212233)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.56/0.77 % (1212233)CaDiCaL version: 2.1.3
% 2.56/0.77 % (1212233)Termination reason: Instruction limit
% 2.56/0.77 % (1212233)Termination phase: SInE selection
% 2.56/0.77 % (1212233)Time elapsed: 0.019 s
% 2.56/0.77 % (1212233)Peak memory usage: 11 MB
% 2.56/0.77 % (1212233)Instructions burned: 45 (million)
% 2.56/0.77 % (1212237)Instruction limit reached!
% 2.56/0.77 % (1212237)------------------------------
% 2.56/0.77 % (1212237)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.56/0.77 % (1212237)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.56/0.77 % (1212237)CaDiCaL version: 2.1.3
% 2.56/0.77 % (1212237)Termination reason: Instruction limit
% 2.56/0.77 % (1212237)Termination phase: Property scanning
% 2.56/0.77 % (1212237)Time elapsed: 0.010 s
% 2.56/0.77 % (1212237)Peak memory usage: 10 MB
% 2.56/0.77 % (1212237)Instructions burned: 22 (million)
% 2.56/0.77 % (1212241)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(2) has been set then sine_level_split_queue(off) is equal to on
% 2.56/0.77 % (1212241)ott+1002_3_si=on:sp=weighted_frequency:spb=goal:cbe=off:slsqc=2:random_seed=2915955762:cts=off:uwa_fpi=on:i=200:av=off:fsr=off:rtra=on:ntd=on_2996 on theBenchmark for (2996ds/200Mi)
% 2.56/0.77 % (1212242)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=1629464176:s2a=on:i=13:kws=inv_frequency:bd=all:rtra=on_2996 on theBenchmark for (2996ds/13Mi)
% 3.38/0.85 % (1212236)Refutation not found, incomplete strategy
% 3.38/0.85 % (1212236)------------------------------
% 3.38/0.85 % (1212236)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.38/0.85 % (1212236)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.38/0.85 % (1212236)CaDiCaL version: 2.1.3
% 3.38/0.85 % (1212236)Termination reason: Refutation not found, incomplete strategy
% 3.38/0.85 % (1212236)Time elapsed: 0.039 s
% 3.38/0.85 % (1212236)Peak memory usage: 13 MB
% 3.38/0.85 % (1212236)Instructions burned: 85 (million)
% 3.38/0.85 % (1212236)------------------------------
% 3.38/0.85 % (1212236)------------------------------
% 3.38/0.85 % (1212242)Instruction limit reached!
% 3.38/0.85 % (1212242)------------------------------
% 3.38/0.85 % (1212242)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.38/0.85 % (1212242)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.38/0.85 % (1212242)CaDiCaL version: 2.1.3
% 3.38/0.85 % (1212242)Termination reason: Instruction limit
% 3.38/0.85 % (1212242)Termination phase: shuffling
% 3.38/0.85 % (1212242)Time elapsed: 0.006 s
% 3.38/0.85 % (1212242)Peak memory usage: 10 MB
% 3.38/0.85 % (1212242)Instructions burned: 13 (million)
% 3.38/0.85 % (1212246)lrs+1004_128_si=on:sos=all:uwa=off:random_seed=1564455560:i=51:fsr=off:rtra=on_2996 on theBenchmark for (2996ds/51Mi)
% 3.38/0.85 % (1212245)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=170994216:i=66:s2at=3:nm=2:rtra=on:rawr=on_2996 on theBenchmark for (2996ds/66Mi)
% 3.38/0.85 % (1212135)Instruction limit reached!
% 3.38/0.85 % (1212135)------------------------------
% 3.38/0.85 % (1212135)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.38/0.85 % (1212135)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.38/0.85 % (1212135)CaDiCaL version: 2.1.3
% 3.38/0.85 % (1212135)Termination reason: Instruction limit
% 3.38/0.85 % (1212135)Termination phase: Saturation
% 3.38/0.85 % (1212135)Time elapsed: 0.347 s
% 3.38/0.85 % (1212135)Peak memory usage: 17 MB
% 3.38/0.85 % (1212135)Instructions burned: 635 (million)
% 3.38/0.85 % (1212246)Instruction limit reached!
% 3.38/0.85 % (1212246)------------------------------
% 3.38/0.85 % (1212246)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.38/0.85 % (1212246)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.38/0.85 % (1212246)CaDiCaL version: 2.1.3
% 3.38/0.85 % (1212246)Termination reason: Instruction limit
% 3.38/0.85 % (1212246)Termination phase: Property scanning
% 3.38/0.85 % (1212246)Time elapsed: 0.022 s
% 3.38/0.85 % (1212246)Peak memory usage: 11 MB
% 3.38/0.85 % (1212246)Instructions burned: 51 (million)
% 3.38/0.85 % (1212245)Instruction limit reached!
% 3.38/0.85 % (1212245)------------------------------
% 3.38/0.85 % (1212245)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.38/0.85 % (1212245)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.38/0.85 % (1212245)CaDiCaL version: 2.1.3
% 3.38/0.85 % (1212245)Termination reason: Instruction limit
% 3.38/0.85 % (1212245)Termination phase: Function definition elimination
% 3.38/0.85 % (1212245)Time elapsed: 0.029 s
% 3.38/0.85 % (1212245)Peak memory usage: 11 MB
% 3.38/0.85 % (1212245)Instructions burned: 68 (million)
% 3.38/0.85 % (1212249)dis+1002_64_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:cbe=off:uwa=off:nwc=0.5:random_seed=2920690760:i=31:kws=inv_frequency:bd=all:rtra=on:ntd=on_2996 on theBenchmark for (2996ds/31Mi)
% 3.38/0.85 % (1212250)dis+1010_40_to=kbo:tgt=full:fde=unused:si=on:sp=const_frequency:lma=off:cbe=off:uwa=interpreted_only:random_seed=2861230748:i=137:kws=precedence:bd=all:rtra=on:c=on:ntd=on_2996 on theBenchmark for (2996ds/137Mi)
% 3.38/0.85 % (1212229)Instruction limit reached!
% 3.38/0.85 % (1212229)------------------------------
% 3.38/0.85 % (1212229)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.38/0.85 % (1212229)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.38/0.85 % (1212229)CaDiCaL version: 2.1.3
% 3.38/0.85 % (1212229)Termination reason: Instruction limit
% 3.38/0.85 % (1212229)Termination phase: Function definition elimination
% 3.38/0.85 % (1212229)Time elapsed: 0.124 s
% 3.38/0.85 % (1212229)Peak memory usage: 11 MB
% 3.38/0.85 % (1212229)Instructions burned: 316 (million)
% 3.91/0.93 % (1212241)Instruction limit reached!
% 3.91/0.93 % (1212241)------------------------------
% 3.91/0.93 % (1212241)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.91/0.93 % (1212241)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.91/0.93 % (1212241)CaDiCaL version: 2.1.3
% 3.91/0.93 % (1212241)Termination reason: Instruction limit
% 3.91/0.93 % (1212241)Termination phase: Function definition elimination
% 3.91/0.93 % (1212241)Time elapsed: 0.079 s
% 3.91/0.93 % (1212241)Peak memory usage: 11 MB
% 3.91/0.93 % (1212241)Instructions burned: 201 (million)
% 3.91/0.93 % (1212251)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=3881367429:cond=on:i=34:hud=10:nm=10:rtra=on_2995 on theBenchmark for (2995ds/34Mi)
% 3.91/0.93 % (1212249)Instruction limit reached!
% 3.91/0.93 % (1212249)------------------------------
% 3.91/0.93 % (1212249)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.91/0.93 % (1212249)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.91/0.93 % (1212249)CaDiCaL version: 2.1.3
% 3.91/0.93 % (1212249)Termination reason: Instruction limit
% 3.91/0.93 % (1212249)Termination phase: Property scanning
% 3.91/0.93 % (1212249)Time elapsed: 0.014 s
% 3.91/0.93 % (1212249)Peak memory usage: 10 MB
% 3.91/0.93 % (1212249)Instructions burned: 32 (million)
% 3.91/0.93 % (1212254)lrs+1010_1_sil=128000:hsqc=4:si=on:sos=on:random_seed=2845132228:hsq=on:i=67:hsqaw=5:rtra=on:fe=abstraction:ntd=on_2995 on theBenchmark for (2995ds/67Mi)
% 3.91/0.93 % (1212255)WARNING Broken Constraint: if sine_generality_threshold(60) has been set then sine_selection(off) is not equal to off
% 3.91/0.93 % (1212251)Instruction limit reached!
% 3.91/0.93 % (1212251)------------------------------
% 3.91/0.93 % (1212251)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.91/0.93 % (1212251)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.91/0.93 % (1212251)CaDiCaL version: 2.1.3
% 3.91/0.93 % (1212251)Termination reason: Instruction limit
% 3.91/0.93 % (1212251)Termination phase: Property scanning
% 3.91/0.93 % (1212251)Time elapsed: 0.015 s
% 3.91/0.93 % (1212251)Peak memory usage: 10 MB
% 3.91/0.93 % (1212251)Instructions burned: 35 (million)
% 3.91/0.93 % (1212255)dis+21_1_to=lpo:sil=128000:cnfonf=lazy_not_gen_be_off:si=on:sp=unary_frequency:bsr=on:random_seed=2561888403:i=180:hud=16:bd=all:fsr=off:rtra=on:sgt=60:ntd=on_2995 on theBenchmark for (2995ds/180Mi)
% 3.91/0.93 % (1212257)lrs+1002_1_sil=128000:si=on:uwa=off:random_seed=1601861322:st=2:i=246:sd=3:rtra=on:ss=axioms_2995 on theBenchmark for (2995ds/246Mi)
% 3.91/0.93 % (1212259)lrs+10_7_sil=128000:tgt=full:si=on:lma=off:uwa=off:nwc=1:sac=on:random_seed=3555733953:cond=on:i=96:bd=all:rtra=on_2995 on theBenchmark for (2995ds/96Mi)
% 3.91/0.93 % (1212254)Instruction limit reached!
% 3.91/0.93 % (1212254)------------------------------
% 3.91/0.93 % (1212254)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.91/0.93 % (1212254)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.91/0.93 % (1212254)CaDiCaL version: 2.1.3
% 3.91/0.93 % (1212254)Termination reason: Instruction limit
% 3.91/0.93 % (1212254)Termination phase: Function definition elimination
% 3.91/0.93 % (1212254)Time elapsed: 0.029 s
% 3.91/0.93 % (1212254)Peak memory usage: 11 MB
% 3.91/0.93 % (1212254)Instructions burned: 69 (million)
% 3.91/0.93 % (1212263)lrs+10_1_sil=128000:si=on:sos=on:urr=on:random_seed=655882535:i=427:sd=1:rtra=on:ss=axioms_2995 on theBenchmark for (2995ds/427Mi)
% 3.91/0.93 % (1212250)Instruction limit reached!
% 3.91/0.93 % (1212250)------------------------------
% 3.91/0.93 % (1212250)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.91/0.93 % (1212250)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.91/0.93 % (1212250)CaDiCaL version: 2.1.3
% 3.91/0.93 % (1212250)Termination reason: Instruction limit
% 3.91/0.93 % (1212250)Termination phase: Saturation
% 3.91/0.93 % (1212250)Time elapsed: 0.070 s
% 3.91/0.93 % (1212250)Peak memory usage: 13 MB
% 3.91/0.93 % (1212250)Instructions burned: 138 (million)
% 3.91/0.93 % (1212257)Refutation not found, incomplete strategy
% 3.91/0.93 % (1212257)------------------------------
% 3.91/0.93 % (1212257)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.91/0.93 % (1212257)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.91/0.93 % (1212257)CaDiCaL version: 2.1.3
% 3.91/0.93 % (1212257)Termination reason: Refutation not found, incomplete strategy
% 3.91/0.93 % (1212257)Time elapsed: 0.041 s
% 3.91/0.93 % (1212257)Peak memory usage: 13 MB
% 3.91/0.93 % (1212257)Instructions burned: 87 (million)
% 3.91/0.93 % (1212257)------------------------------
% 3.91/0.93 % (1212257)------------------------------
% 3.91/0.93 % (1212259)Instruction limit reached!
% 3.91/0.93 % (1212259)------------------------------
% 3.91/0.93 % (1212259)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.91/0.93 % (1212259)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.91/0.93 % (1212259)CaDiCaL version: 2.1.3
% 3.91/0.93 % (1212259)Termination reason: Instruction limit
% 3.91/0.93 % (1212259)Termination phase: Function definition elimination
% 3.91/0.93 % (1212259)Time elapsed: 0.041 s
% 3.91/0.93 % (1212259)Peak memory usage: 11 MB
% 3.91/0.93 % (1212259)Instructions burned: 99 (million)
% 3.91/0.93 % (1212263)Refutation not found, incomplete strategy
% 3.91/0.93 % (1212263)------------------------------
% 3.91/0.93 % (1212263)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.91/0.93 % (1212263)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.91/0.93 % (1212263)CaDiCaL version: 2.1.3
% 3.91/0.93 % (1212263)Termination reason: Refutation not found, incomplete strategy
% 3.91/0.93 % (1212263)Time elapsed: 0.021 s
% 3.91/0.93 % (1212263)Peak memory usage: 13 MB
% 3.91/0.93 % (1212263)Instructions burned: 45 (million)
% 3.91/0.93 % (1212265)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=1958837147:st=3:s2a=on:i=874:sd=3:rtra=on:ss=axioms_2995 on theBenchmark for (2995ds/874Mi)
% 3.91/0.93 % (1212263)------------------------------
% 3.91/0.93 % (1212263)------------------------------
% 3.91/0.93 % (1212266)dis+1010_4_sas=cadical:si=on:cbe=off:nwc=20:random_seed=3700066434:st=6:s2a=on:i=515:sd=2:nm=2:rtra=on:ss=axioms_2995 on theBenchmark for (2995ds/515Mi)
% 3.91/0.93 % (1212255)Instruction limit reached!
% 3.91/0.93 % (1212255)------------------------------
% 3.91/0.93 % (1212255)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.91/0.93 % (1212255)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.91/0.93 % (1212255)CaDiCaL version: 2.1.3
% 3.91/0.93 % (1212255)Termination reason: Instruction limit
% 3.91/0.93 % (1212255)Termination phase: Function definition elimination
% 3.91/0.93 % (1212255)Time elapsed: 0.072 s
% 3.91/0.93 % (1212255)Peak memory usage: 11 MB
% 3.91/0.93 % (1212255)Instructions burned: 180 (million)
% 3.91/0.93 % (1212267)lrs+1002_1_cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:random_seed=3641910488:st=1.5:i=130:rtra=on:ss=axioms_2994 on theBenchmark for (2994ds/130Mi)
% 3.91/0.93 % (1212269)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=2558307259:i=44:ep=R:rtra=on:ntd=on_2994 on theBenchmark for (2994ds/44Mi)
% 3.91/0.93 % (1212271)lrs+1010_8:1_sil=128000:fde=unused:e2e=on:si=on:sos=on:urr=on:uwa=one_side_constant:fd=off:random_seed=2248821156:s2a=on:i=571:nm=16:rtra=on_2994 on theBenchmark for (2994ds/571Mi)
% 3.91/0.93 % (1212232)Instruction limit reached!
% 3.91/0.93 % (1212232)------------------------------
% 3.91/0.93 % (1212232)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.91/0.93 % (1212232)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.91/0.93 % (1212232)CaDiCaL version: 2.1.3
% 3.91/0.93 % (1212232)Termination reason: Instruction limit
% 3.91/0.93 % (1212232)Termination phase: Saturation
% 3.91/0.93 % (1212232)Time elapsed: 0.249 s
% 3.91/0.93 % (1212232)Peak memory usage: 17 MB
% 3.91/0.93 % (1212232)Instructions burned: 853 (million)
% 3.91/0.93 % (1212269)Instruction limit reached!
% 3.91/0.93 % (1212269)------------------------------
% 3.91/0.93 % (1212269)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.91/0.93 % (1212269)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.91/0.93 % (1212269)CaDiCaL version: 2.1.3
% 3.91/0.93 % (1212269)Termination reason: Instruction limit
% 3.91/0.93 % (1212269)Termination phase: Property scanning
% 3.91/0.93 % (1212269)Time elapsed: 0.020 s
% 3.91/0.93 % (1212269)Peak memory usage: 11 MB
% 3.91/0.93 % (1212269)Instructions burned: 46 (million)
% 3.91/0.93 % (1212276)lrs+10_5:1_to=lpo:sil=128000:si=on:uwa=one_side_interpreted:random_seed=955516961:cts=off:i=95:piset=pi_sigma:bd=all:rtra=on:ntd=on_2994 on theBenchmark for (2994ds/95Mi)
% 3.91/0.93 % (1212275)dis+1010_8_to=lpo:sil=128000:tgt=ground:si=on:sp=reverse_frequency:cbe=off:uwa=off:random_seed=2723814140:i=450:rtra=on:ixr=off:ntd=on_2994 on theBenchmark for (2994ds/450Mi)
% 3.91/0.93 % (1212276)Instruction limit reached!
% 3.91/0.93 % (1212276)------------------------------
% 3.91/0.93 % (1212276)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.91/0.93 % (1212276)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.91/0.93 % (1212276)CaDiCaL version: 2.1.3
% 3.91/0.93 % (1212276)Termination reason: Instruction limit
% 3.91/0.93 % (1212276)Termination phase: Function definition elimination
% 3.91/0.93 % (1212276)Time elapsed: 0.021 s
% 3.91/0.93 % (1212276)Peak memory usage: 11 MB
% 3.91/0.93 % (1212276)Instructions burned: 95 (million)
% 3.91/0.93 % (1212267)Instruction limit reached!
% 3.91/0.93 % (1212267)------------------------------
% 3.91/0.93 % (1212267)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.91/0.93 % (1212267)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.91/0.93 % (1212267)CaDiCaL version: 2.1.3
% 3.91/0.93 % (1212267)Termination reason: Instruction limit
% 3.91/0.93 % (1212267)Termination phase: Saturation
% 3.91/0.93 % (1212267)Time elapsed: 0.059 s
% 3.91/0.93 % (1212267)Peak memory usage: 13 MB
% 3.91/0.93 % (1212267)Instructions burned: 130 (million)
% 3.91/0.93 % (1212279)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=176253540:s2a=on:i=65:add=on:bd=preordered:ins=10:rtra=on_2994 on theBenchmark for (2994ds/65Mi)
% 3.91/0.93 % (1212280)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=719092791: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_2994 on theBenchmark for (2994ds/105Mi)
% 3.91/0.93 % (1212279)Instruction limit reached!
% 3.91/0.93 % (1212279)------------------------------
% 3.91/0.93 % (1212279)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.91/0.93 % (1212279)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.91/0.93 % (1212279)CaDiCaL version: 2.1.3
% 3.91/0.93 % (1212279)Termination reason: Instruction limit
% 3.91/0.93 % (1212279)Termination phase: Function definition elimination
% 3.91/0.93 % (1212279)Time elapsed: 0.015 s
% 3.91/0.93 % (1212279)Peak memory usage: 11 MB
% 3.91/0.93 % (1212279)Instructions burned: 65 (million)
% 3.91/0.93 % (1212283)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=2661565426: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)
% 3.91/0.93 % (1212266) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1212105-1212266"...
% 3.91/0.93 % (1212280)Instruction limit reached!
% 3.91/0.93 % (1212280)------------------------------
% 3.91/0.93 % (1212280)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.91/0.93 % (1212266)...printing done.
% 3.91/0.93 % (1212280)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.91/0.93 % (1212280)CaDiCaL version: 2.1.3
% 3.91/0.93 % (1212280)Termination reason: Instruction limit
% 3.91/0.93 % (1212280)Termination phase: Function definition elimination
% 3.91/0.93 % (1212280)Time elapsed: 0.045 s
% 3.91/0.93 % (1212280)Peak memory usage: 11 MB
% 3.91/0.93 % (1212280)Instructions burned: 108 (million)
% 3.91/0.93 % (1212266)Refutation found. Thanks to Tanya!
% 3.91/0.93 % SZS status Theorem for theBenchmark
% 3.91/0.93 % SZS output start Proof for theBenchmark
% 3.91/0.93 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 3.91/0.93 thf(func_def_0, type, is_of: ($i > ($i > $o) > $o)).
% 3.91/0.93 thf(func_def_2, type, all_of: (($i > $o) > ($i > $o) > $o)).
% 3.91/0.93 thf(func_def_3, type, eps: (($i > $o) > $i)).
% 3.91/0.93 thf(func_def_4, type, in: ($i > $i > $o)).
% 3.91/0.93 thf(func_def_5, type, d_Subq: ($i > $i > $o)).
% 3.91/0.93 thf(func_def_7, type, union: ($i > $i)).
% 3.91/0.93 thf(func_def_8, type, power: ($i > $i)).
% 3.91/0.93 thf(func_def_9, type, repl: ($i > ($i > $i) > $i)).
% 3.91/0.93 thf(func_def_10, type, d_Union_closed: ($i > $o)).
% 3.91/0.93 thf(func_def_11, type, d_Power_closed: ($i > $o)).
% 3.91/0.93 thf(func_def_12, type, d_Repl_closed: ($i > $o)).
% 3.91/0.93 thf(func_def_13, type, d_ZF_closed: ($i > $o)).
% 3.91/0.93 thf(func_def_14, type, univof: ($i > $i)).
% 3.91/0.93 thf(func_def_15, type, if: ($o > $i > $i > $i)).
% 3.91/0.93 thf(func_def_16, type, nIn: ($i > $i > $o)).
% 3.91/0.93 thf(func_def_17, type, d_UPair: ($i > $i > $i)).
% 3.91/0.93 thf(func_def_18, type, d_Sing: ($i > $i)).
% 3.91/0.93 thf(func_def_19, type, binunion: ($i > $i > $i)).
% 3.91/0.93 thf(func_def_20, type, famunion: ($i > ($i > $i) > $i)).
% 3.91/0.93 thf(func_def_21, type, d_Sep: ($i > ($i > $o) > $i)).
% 3.91/0.93 thf(func_def_22, type, d_ReplSep: ($i > ($i > $o) > ($i > $i) > $i)).
% 3.91/0.93 thf(func_def_23, type, setminus: ($i > $i > $i)).
% 3.91/0.93 thf(func_def_24, type, d_In_rec_G: (($i > ($i > $i) > $i) > $i > $i > $o)).
% 3.91/0.93 thf(func_def_25, type, d_In_rec: (($i > ($i > $i) > $i) > $i > $i)).
% 3.91/0.93 thf(func_def_26, type, ordsucc: ($i > $i)).
% 3.91/0.93 thf(func_def_27, type, nat_p: ($i > $o)).
% 3.91/0.93 thf(func_def_29, type, d_Inj1: ($i > $i)).
% 3.91/0.93 thf(func_def_30, type, d_Inj0: ($i > $i)).
% 3.91/0.93 thf(func_def_31, type, d_Unj: ($i > $i)).
% 3.91/0.93 thf(func_def_32, type, pair: ($i > $i > $i)).
% 3.91/0.93 thf(func_def_33, type, proj0: ($i > $i)).
% 3.91/0.93 thf(func_def_34, type, proj1: ($i > $i)).
% 3.91/0.93 thf(func_def_35, type, d_Sigma: ($i > ($i > $i) > $i)).
% 3.91/0.93 thf(func_def_36, type, setprod: ($i > $i > $i)).
% 3.91/0.93 thf(func_def_37, type, ap: ($i > $i > $i)).
% 3.91/0.93 thf(func_def_38, type, pair_p: ($i > $o)).
% 3.91/0.93 thf(func_def_39, type, d_Pi: ($i > ($i > $i) > $i)).
% 3.91/0.93 thf(func_def_40, type, imp: ($o > $o > $o)).
% 3.91/0.93 thf(func_def_41, type, d_not: ($o > $o)).
% 3.91/0.93 thf(func_def_42, type, wel: ($o > $o)).
% 3.91/0.93 thf(func_def_43, type, obvious: $o).
% 3.91/0.93 thf(func_def_44, type, l_ec: ($o > $o > $o)).
% 3.91/0.93 thf(func_def_45, type, d_and: ($o > $o > $o)).
% 3.91/0.93 thf(func_def_46, type, l_or: ($o > $o > $o)).
% 3.91/0.93 thf(func_def_47, type, orec: ($o > $o > $o)).
% 3.91/0.93 thf(func_def_48, type, l_iff: ($o > $o > $o)).
% 3.91/0.93 thf(func_def_49, type, all: ($i > ($i > $o) > $o)).
% 3.91/0.93 thf(func_def_50, type, non: ($i > ($i > $o) > $i > $o)).
% 3.91/0.93 thf(func_def_51, type, l_some: ($i > ($i > $o) > $o)).
% 3.91/0.93 thf(func_def_52, type, or3: ($o > $o > $o > $o)).
% 3.91/0.93 thf(func_def_53, type, and3: ($o > $o > $o > $o)).
% 3.91/0.93 thf(func_def_54, type, ec3: ($o > $o > $o > $o)).
% 3.91/0.93 thf(func_def_55, type, orec3: ($o > $o > $o > $o)).
% 3.91/0.93 thf(func_def_56, type, e_is: ($i > $i > $i > $o)).
% 3.91/0.93 thf(func_def_57, type, amone: ($i > ($i > $o) > $o)).
% 3.91/0.93 thf(func_def_58, type, one: ($i > ($i > $o) > $o)).
% 3.91/0.93 thf(func_def_59, type, ind: ($i > ($i > $o) > $i)).
% 3.91/0.93 thf(func_def_60, type, injective: ($i > $i > $i > $o)).
% 3.91/0.93 thf(func_def_61, type, image: ($i > $i > $i > $i > $o)).
% 3.91/0.93 thf(func_def_62, type, tofs: ($i > $i > $i > $i > $i)).
% 3.91/0.93 thf(func_def_63, type, soft: ($i > $i > $i > $i > $i)).
% 3.91/0.93 thf(func_def_64, type, inverse: ($i > $i > $i > $i)).
% 3.91/0.93 thf(func_def_65, type, surjective: ($i > $i > $i > $o)).
% 3.91/0.93 thf(func_def_66, type, bijective: ($i > $i > $i > $o)).
% 3.91/0.93 thf(func_def_67, type, invf: ($i > $i > $i > $i)).
% 3.91/0.93 thf(func_def_68, type, inj_h: ($i > $i > $i > $i > $i > $i)).
% 3.91/0.93 thf(func_def_69, type, e_in: ($i > ($i > $o) > $i > $i)).
% 3.91/0.93 thf(func_def_70, type, out: ($i > ($i > $o) > $i > $i)).
% 3.91/0.93 thf(func_def_71, type, d_pair: ($i > $i > $i > $i > $i)).
% 3.91/0.93 thf(func_def_72, type, first: ($i > $i > $i > $i)).
% 3.91/0.93 thf(func_def_73, type, second: ($i > $i > $i > $i)).
% 3.91/0.93 thf(func_def_74, type, prop1: ($o > $i > $i > $i > $i > $o)).
% 3.91/0.93 thf(func_def_75, type, ite: ($o > $i > $i > $i > $i)).
% 3.91/0.93 thf(func_def_76, type, wissel_wa: ($i > $i > $i > $i > $i)).
% 3.91/0.93 thf(func_def_77, type, wissel_wb: ($i > $i > $i > $i > $i)).
% 3.91/0.93 thf(func_def_78, type, wissel: ($i > $i > $i > $i)).
% 3.91/0.93 thf(func_def_79, type, changef: ($i > $i > $i > $i > $i > $i)).
% 3.91/0.93 thf(func_def_80, type, r_ec: ($o > $o > $o)).
% 3.91/0.93 thf(func_def_81, type, esti: ($i > $i > $i > $o)).
% 3.91/0.93 thf(func_def_82, type, empty: ($i > $i > $o)).
% 3.91/0.93 thf(func_def_83, type, nonempty: ($i > $i > $o)).
% 3.91/0.93 thf(func_def_84, type, incl: ($i > $i > $i > $o)).
% 3.91/0.93 thf(func_def_85, type, st_disj: ($i > $i > $i > $o)).
% 3.91/0.93 thf(func_def_86, type, nissetprop: ($i > $i > $i > $i > $o)).
% 3.91/0.93 thf(func_def_87, type, unmore: ($i > $i > $i > $i)).
% 3.91/0.93 thf(func_def_88, type, ecelt: ($i > ($i > $i > $o) > $i > $i)).
% 3.91/0.93 thf(func_def_89, type, ecp: ($i > ($i > $i > $o) > $i > $i > $o)).
% 3.91/0.93 thf(func_def_90, type, anec: ($i > ($i > $i > $o) > $i > $o)).
% 3.91/0.93 thf(func_def_91, type, ect: ($i > ($i > $i > $o) > $i)).
% 3.91/0.93 thf(func_def_92, type, ectset: ($i > ($i > $i > $o) > $i > $i)).
% 3.91/0.93 thf(func_def_93, type, ectelt: ($i > ($i > $i > $o) > $i > $i)).
% 3.91/0.93 thf(func_def_94, type, ecect: ($i > ($i > $i > $o) > $i > $i)).
% 3.91/0.93 thf(func_def_95, type, fixfu: ($i > ($i > $i > $o) > $i > $i > $o)).
% 3.91/0.93 thf(func_def_96, type, d_10_prop1: ($i > ($i > $i > $o) > $i > $i > $i > $i > $i > $o)).
% 3.91/0.93 thf(func_def_97, type, prop2: ($i > ($i > $i > $o) > $i > $i > $i > $i > $o)).
% 3.91/0.93 thf(func_def_98, type, indeq: ($i > ($i > $i > $o) > $i > $i > $i > $i)).
% 3.91/0.93 thf(func_def_99, type, fixfu2: ($i > ($i > $i > $o) > $i > $i > $o)).
% 3.91/0.93 thf(func_def_100, type, d_11_i: ($i > ($i > $i > $o) > $i > $i > $i > $i)).
% 3.91/0.93 thf(func_def_101, type, indeq2: ($i > ($i > $i > $o) > $i > $i > $i > $i > $i)).
% 3.91/0.93 thf(func_def_103, type, n_is: ($i > $i > $o)).
% 3.91/0.93 thf(func_def_104, type, nis: ($i > $i > $o)).
% 3.91/0.93 thf(func_def_105, type, n_in: ($i > $i > $o)).
% 3.91/0.93 thf(func_def_106, type, n_some: (($i > $o) > $o)).
% 3.91/0.93 thf(func_def_107, type, n_all: (($i > $o) > $o)).
% 3.91/0.93 thf(func_def_108, type, n_one: (($i > $o) > $o)).
% 3.91/0.93 thf(func_def_110, type, cond1: ($i > $o)).
% 3.91/0.93 thf(func_def_111, type, cond2: ($i > $o)).
% 3.91/0.93 thf(func_def_112, type, i1_s: (($i > $o) > $i)).
% 3.91/0.93 thf(func_def_113, type, d_22_prop1: ($i > $o)).
% 3.91/0.93 thf(func_def_114, type, d_23_prop1: ($i > $o)).
% 3.91/0.93 thf(func_def_115, type, d_24_prop1: ($i > $o)).
% 3.91/0.93 thf(func_def_116, type, d_24_prop2: ($i > $i > $o)).
% 3.91/0.93 thf(func_def_117, type, prop3: ($i > $i > $i > $o)).
% 3.91/0.93 thf(func_def_118, type, prop4: ($i > $o)).
% 3.91/0.93 thf(func_def_119, type, d_24_g: ($i > $i)).
% 3.91/0.93 thf(func_def_120, type, plus: ($i > $i)).
% 3.91/0.93 thf(func_def_121, type, n_pl: ($i > $i > $i)).
% 3.91/0.93 thf(func_def_122, type, d_25_prop1: ($i > $i > $i > $o)).
% 3.91/0.93 thf(func_def_123, type, d_26_prop1: ($i > $i > $o)).
% 3.91/0.93 thf(func_def_124, type, d_27_prop1: ($i > $i > $o)).
% 3.91/0.93 thf(func_def_125, type, d_28_prop1: ($i > $i > $i > $o)).
% 3.91/0.93 thf(func_def_126, type, diffprop: ($i > $i > $i > $o)).
% 3.91/0.93 thf(func_def_127, type, d_29_ii: ($i > $i > $o)).
% 3.91/0.93 thf(func_def_128, type, iii: ($i > $i > $o)).
% 3.91/0.93 thf(func_def_129, type, d_29_prop1: ($i > $i > $o)).
% 3.91/0.93 thf(func_def_130, type, moreis: ($i > $i > $o)).
% 3.91/0.93 thf(func_def_131, type, lessis: ($i > $i > $o)).
% 3.91/0.93 thf(func_def_132, type, vIMP: ($o > $o > $o)).
% 3.91/0.93 thf(func_def_133, type, db1: !>[X0: $tType]:(X0)).
% 3.91/0.93 thf(func_def_134, type, db0: !>[X0: $tType]:(X0)).
% 3.91/0.93 thf(func_def_135, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 3.91/0.93 thf(func_def_138, type, db4: !>[X0: $tType]:(X0)).
% 3.91/0.93 thf(func_def_139, type, db3: !>[X0: $tType]:(X0)).
% 3.91/0.93 thf(func_def_140, type, db2: !>[X0: $tType]:(X0)).
% 3.91/0.93 thf(func_def_141, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 3.91/0.93 thf(func_def_142, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 3.91/0.93 thf(func_def_143, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 3.91/0.93 thf(func_def_144, type, vAND: ($o > $o > $o)).
% 3.91/0.93 thf(func_def_145, type, db5: !>[X0: $tType]:(X0)).
% 3.91/0.93 thf(func_def_146, type, db6: !>[X0: $tType]:(X0)).
% 3.91/0.93 thf(func_def_147, type, db7: !>[X0: $tType]:(X0)).
% 3.91/0.93 thf(func_def_148, type, vNOT: ($o > $o)).
% 3.91/0.93 thf(func_def_149, type, vOR: ($o > $o > $o)).
% 3.91/0.93 thf(func_def_150, type, sP0: ($i > ($i > $i) > $i > $o)).
% 3.91/0.93 thf(func_def_151, type, sP1: (($i > $o) > $o)).
% 3.91/0.93 thf(func_def_152, type, sK2: ($i > ($i > $i) > ($i > $i) > $i)).
% 3.91/0.93 thf(func_def_153, type, sK3: ($i > $i > $i > $i)).
% 3.91/0.93 thf(func_def_154, type, sK4: (($i > $i) > $i > ($i > $i) > $i)).
% 3.91/0.93 thf(func_def_155, type, sK5: ($i > $i)).
% 3.91/0.93 thf(func_def_156, type, sK6: (($i > $o) > $i)).
% 3.91/0.93 thf(func_def_157, type, sK7: (($i > $o) > $i)).
% 3.91/0.93 thf(func_def_158, type, sK8: ($i > $i > $o)).
% 3.91/0.93 thf(func_def_159, type, sK9: (($i > $o) > $i)).
% 3.91/0.93 thf(func_def_160, type, sK10: (($i > $o) > $i)).
% 3.91/0.93 thf(func_def_161, type, sK11: (($i > $o) > $i)).
% 3.91/0.93 thf(func_def_162, type, sK12: ($i > $i > $o)).
% 3.91/0.93 thf(func_def_163, type, sK13: (($i > $o) > $i)).
% 3.91/0.93 thf(func_def_164, type, sK14: ($i > $i > $i > $i)).
% 3.91/0.93 thf(func_def_165, type, sK15: (($i > $o) > $i)).
% 3.91/0.93 thf(func_def_166, type, sK16: ($i > $i > $o)).
% 3.91/0.93 thf(func_def_167, type, sK17: (($i > $o) > $i)).
% 3.91/0.93 thf(func_def_168, type, sK18: (($i > $o) > $i)).
% 3.91/0.93 thf(func_def_169, type, sK19: (($i > $o) > $i)).
% 3.91/0.93 thf(func_def_170, type, sK20: (($i > $o) > $i)).
% 3.91/0.93 thf(func_def_171, type, sK21: ($i > $i > $o)).
% 3.91/0.93 thf(func_def_172, type, sK22: ($i > $i > $o)).
% 3.91/0.93 thf(func_def_177, type, sK27: (($i > $i > $i) > ($i > $i) > ($i > $i > $i) > $i)).
% 3.91/0.93 thf(func_def_178, type, sK28: (($i > $i > $i) > ($i > $i) > ($i > $i > $i) > $i)).
% 3.91/0.93 thf(func_def_179, type, sK29: (($i > $i) > ($i > $i > $i) > ($i > $i > $i) > $i)).
% 3.91/0.93 thf(func_def_180, type, sK30: (($i > $i) > ($i > $i > $i) > $i)).
% 3.91/0.93 thf(func_def_181, type, sK31: ($i > $i)).
% 3.91/0.93 thf(func_def_182, type, sK32: ($i > $i > $i)).
% 3.91/0.93 thf(f1,axiom,(
% 3.91/0.93 ((^[X0 : $i, X1 : ($i > $o)] : ((X1 @ X0))) = is_of)),
% 3.91/0.93 file('/export/starexec/sandbox2/benchmark/Axioms/NUM007^0.ax',def_is_of)).
% 3.91/0.93 thf(f2,axiom,(
% 3.91/0.93 (all_of = (^[X0 : ($i > $o), X1 : ($i > $o)] : (! [X2 : $i] : ((is_of @ X2 @ X0) => (X1 @ X2)))))),
% 3.91/0.93 file('/export/starexec/sandbox2/benchmark/Axioms/NUM007^0.ax',def_all_of)).
% 3.91/0.93 thf(f5,axiom,(
% 3.91/0.93 ! [X0 : ($i > $o)] : (! [X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X1) => (X0 @ X2)) => (X0 @ X1)) => ! [X1 : $i] : (X0 @ X1))),
% 3.91/0.93 file('/export/starexec/sandbox2/benchmark/Axioms/NUM007^0.ax',k_In_ind)).
% 3.91/0.93 thf(f74,axiom,(
% 3.91/0.93 (imp = (^[X0 : $o, X1 : $o] : (X0 => X1)))),
% 3.91/0.93 file('/export/starexec/sandbox2/benchmark/Axioms/NUM007^0.ax',def_imp)).
% 3.91/0.93 thf(f75,axiom,(
% 3.91/0.93 (d_not = (^[X0 : $o] : ((imp @ X0 @ $false))))),
% 3.91/0.93 file('/export/starexec/sandbox2/benchmark/Axioms/NUM007^0.ax',def_d_not)).
% 3.91/0.93 thf(f81,axiom,(
% 3.91/0.93 (l_or = (^[X0 : $o] : ((imp @ (d_not @ X0)))))),
% 3.91/0.93 file('/export/starexec/sandbox2/benchmark/Axioms/NUM007^0.ax',def_l_or)).
% 3.91/0.93 thf(f91,axiom,(
% 3.91/0.93 ((^[X0 : $i, X1 : $i, X2 : $i] : ((X1 = X2))) = e_is)),
% 3.91/0.93 file('/export/starexec/sandbox2/benchmark/Axioms/NUM007^0.ax',def_e_is)).
% 3.91/0.93 thf(f157,axiom,(
% 3.91/0.93 (n_is = ((e_is @ nat)))),
% 3.91/0.93 file('/export/starexec/sandbox2/benchmark/Axioms/NUM007^0.ax',def_n_is)).
% 3.91/0.93 thf(f160,axiom,(
% 3.91/0.93 (n_some = ((l_some @ nat)))),
% 3.91/0.93 file('/export/starexec/sandbox2/benchmark/Axioms/NUM007^0.ax',def_n_some)).
% 3.91/0.93 thf(f203,axiom,(
% 3.91/0.93 ((^[X0 : $i, X1 : $i, X2 : $i] : ((n_is @ X0 @ (n_pl @ X1 @ X2)))) = diffprop)),
% 3.91/0.93 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',def_diffprop)).
% 3.91/0.93 thf(f205,axiom,(
% 3.91/0.93 (d_29_ii = (^[X0 : $i, X1 : $i] : ((n_some @ (diffprop @ X0 @ X1)))))),
% 3.91/0.93 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',def_d_29_ii)).
% 3.91/0.93 thf(f206,axiom,(
% 3.91/0.93 ((^[X0 : $i, X1 : $i] : ((n_some @ (diffprop @ X1 @ X0)))) = iii)),
% 3.91/0.93 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',def_iii)).
% 3.91/0.93 thf(f217,axiom,(
% 3.91/0.93 ((^[X0 : $i, X1 : $i] : ((l_or @ (iii @ X0 @ X1) @ (n_is @ X0 @ X1)))) = lessis)),
% 3.91/0.93 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',def_lessis)).
% 3.91/0.93 thf(f221,axiom,(
% 3.91/0.93 (all_of @ (^[X0 : $i] : ((in @ X0 @ nat))) @ (^[X0 : $i] : ((all_of @ (^[X1 : $i] : ((in @ X1 @ nat))) @ (^[X1 : $i] : ((lessis @ X0 @ X1) => (d_not @ (d_29_ii @ X0 @ X1))))))))),
% 3.91/0.93 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz10d)).
% 3.91/0.93 thf(f227,axiom,(
% 3.91/0.93 (all_of @ (^[X0 : $i] : ((in @ X0 @ nat))) @ (^[X0 : $i] : ((all_of @ (^[X1 : $i] : ((in @ X1 @ nat))) @ (^[X1 : $i] : ((d_not @ (lessis @ X0 @ X1)) => (d_29_ii @ X0 @ X1)))))))),
% 3.91/0.93 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz10k)).
% 3.91/0.93 thf(f229,axiom,(
% 3.91/0.93 (all_of @ (^[X0 : $i] : ((in @ X0 @ nat))) @ (^[X0 : $i] : ((all_of @ (^[X1 : $i] : ((in @ X1 @ nat))) @ (^[X1 : $i] : ((all_of @ (^[X2 : $i] : ((in @ X2 @ nat))) @ (^[X2 : $i] : ((lessis @ X0 @ X1) => ((iii @ X1 @ X2) => (iii @ X0 @ X2)))))))))))),
% 3.91/0.93 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz16a)).
% 3.91/0.93 thf(f230,axiom,(
% 3.91/0.93 (all_of @ (^[X0 : $i] : ((in @ X0 @ nat))) @ (^[X0 : $i] : ((all_of @ (^[X1 : $i] : ((in @ X1 @ nat))) @ (^[X1 : $i] : ((all_of @ (^[X2 : $i] : ((in @ X2 @ nat))) @ (^[X2 : $i] : ((iii @ X0 @ X1) => ((lessis @ X1 @ X2) => (iii @ X0 @ X2)))))))))))),
% 3.91/0.93 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz16b)).
% 3.91/0.93 thf(f233,conjecture,(
% 3.91/0.93 (all_of @ (^[X0 : $i] : ((in @ X0 @ nat))) @ (^[X0 : $i] : ((all_of @ (^[X1 : $i] : ((in @ X1 @ nat))) @ (^[X1 : $i] : ((all_of @ (^[X2 : $i] : ((in @ X2 @ nat))) @ (^[X2 : $i] : ((lessis @ X0 @ X1) => ((lessis @ X1 @ X2) => (lessis @ X0 @ X2)))))))))))),
% 3.91/0.93 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz17)).
% 3.91/0.93 thf(f234,negated_conjecture,(
% 3.91/0.93 ~(all_of @ (^[X0 : $i] : ((in @ X0 @ nat))) @ (^[X0 : $i] : ((all_of @ (^[X1 : $i] : ((in @ X1 @ nat))) @ (^[X1 : $i] : ((all_of @ (^[X2 : $i] : ((in @ X2 @ nat))) @ (^[X2 : $i] : ((lessis @ X0 @ X1) => ((lessis @ X1 @ X2) => (lessis @ X0 @ X2)))))))))))),
% 3.91/0.93 inference(negated_conjecture,[status(cth)],[f233])).
% 3.91/0.93 thf(f247,plain,(
% 3.91/0.93 (lessis = (^[Y0 : $i]: ((^[Y1 : $i]: (l_or @ (iii @ Y0 @ Y1) @ (n_is @ Y0 @ Y1))))))),
% 3.91/0.93 inference(fool_elimination,[],[f217])).
% 3.91/0.93 thf(f258,plain,(
% 3.91/0.93 ! [X0 : ($i > $o)] : (! [X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X1) => (X0 @ X2)) => (X0 @ X1)) => ! [X3 : $i] : (X0 @ X3))),
% 3.91/0.93 inference(rectify,[],[f5])).
% 3.91/0.93 thf(f259,plain,(
% 3.91/0.93 ! [X0 : ($i > $o)] : (! [X1 : $i] : (! [X2 : $i] : ((((in @ X2 @ X1)) = $true) => (((X0 @ X2)) = $true)) => (((X0 @ X1)) = $true)) => ! [X3 : $i] : (((X0 @ X3)) = $true))),
% 3.91/0.93 inference(fool_elimination,[],[f258])).
% 3.91/0.93 thf(f292,plain,(
% 3.91/0.93 (all_of @ (^[X0 : $i] : ((in @ X0 @ nat))) @ (^[X1 : $i] : ((all_of @ (^[X2 : $i] : ((in @ X2 @ nat))) @ (^[X3 : $i] : ((all_of @ (^[X4 : $i] : ((in @ X4 @ nat))) @ (^[X5 : $i] : ((lessis @ X1 @ X3) => ((iii @ X3 @ X5) => (iii @ X1 @ X5)))))))))))),
% 3.91/0.93 inference(rectify,[],[f229])).
% 3.91/0.93 thf(f293,plain,(
% 3.91/0.93 ($true = ((all_of @ (^[Y0 : $i]: (in @ Y0 @ nat)) @ (^[Y0 : $i]: (all_of @ (^[Y1 : $i]: (in @ Y1 @ nat)) @ (^[Y1 : $i]: (all_of @ (^[Y2 : $i]: (in @ Y2 @ nat)) @ (^[Y2 : $i]: ((lessis @ Y0 @ Y1) => ((iii @ Y1 @ Y2) => (iii @ Y0 @ Y2)))))))))))),
% 3.91/0.93 inference(fool_elimination,[],[f292])).
% 3.91/0.93 thf(f304,plain,(
% 3.91/0.93 (all_of = (^[X0 : ($i > $o), X1 : ($i > $o)] : (! [X2 : $i] : ((is_of @ X2 @ X0) => (X1 @ X2)))))),
% 3.91/0.93 inference(rectify,[],[f2])).
% 3.91/0.93 thf(f305,plain,(
% 3.91/0.93 (all_of = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((is_of @ Y2 @ Y0) => (Y1 @ Y2))))))))),
% 3.91/0.93 inference(fool_elimination,[],[f304])).
% 3.91/0.93 thf(f308,plain,(
% 3.91/0.93 (diffprop = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (n_is @ Y0 @ (n_pl @ Y1 @ Y2))))))))),
% 3.91/0.93 inference(fool_elimination,[],[f203])).
% 3.91/0.93 thf(f370,plain,(
% 3.91/0.93 (is_of = (^[Y0 : $i]: ((^[Y1 : $i > $o]: (Y1 @ Y0)))))),
% 3.91/0.93 inference(fool_elimination,[],[f1])).
% 3.91/0.93 thf(f389,plain,(
% 3.91/0.93 (imp = (^[X0 : $o, X1 : $o] : (X0 => X1)))),
% 3.91/0.93 inference(rectify,[],[f74])).
% 3.91/0.93 thf(f390,plain,(
% 3.91/0.93 (imp = (^[Y0 : $o]: ((^[Y1 : $o]: (Y0 => Y1)))))),
% 3.91/0.93 inference(fool_elimination,[],[f389])).
% 3.91/0.93 thf(f395,plain,(
% 3.91/0.93 (d_not = (^[X0 : $o] : ((imp @ X0 @ $false))))),
% 3.91/0.93 inference(rectify,[],[f75])).
% 3.91/0.93 thf(f396,plain,(
% 3.91/0.93 (d_not = (^[Y0 : $o]: (imp @ Y0 @ $false)))),
% 3.91/0.93 inference(fool_elimination,[],[f395])).
% 3.91/0.93 thf(f421,plain,(
% 3.91/0.93 (e_is = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (Y1 = Y2)))))))),
% 3.91/0.93 inference(fool_elimination,[],[f91])).
% 3.91/0.93 thf(f431,plain,(
% 3.91/0.93 (l_or = (^[Y0 : $o]: (imp @ (d_not @ Y0))))),
% 3.91/0.93 inference(fool_elimination,[],[f81])).
% 3.91/0.93 thf(f438,plain,(
% 3.91/0.93 ~(all_of @ (^[X0 : $i] : ((in @ X0 @ nat))) @ (^[X1 : $i] : ((all_of @ (^[X2 : $i] : ((in @ X2 @ nat))) @ (^[X3 : $i] : ((all_of @ (^[X4 : $i] : ((in @ X4 @ nat))) @ (^[X5 : $i] : ((lessis @ X1 @ X3) => ((lessis @ X3 @ X5) => (lessis @ X1 @ X5)))))))))))),
% 3.91/0.93 inference(rectify,[],[f234])).
% 3.91/0.93 thf(f439,plain,(
% 3.91/0.93 ~ (((all_of @ (^[Y0 : $i]: (in @ Y0 @ nat)) @ (^[Y0 : $i]: (all_of @ (^[Y1 : $i]: (in @ Y1 @ nat)) @ (^[Y1 : $i]: (all_of @ (^[Y2 : $i]: (in @ Y2 @ nat)) @ (^[Y2 : $i]: ((lessis @ Y0 @ Y1) => ((lessis @ Y1 @ Y2) => (lessis @ Y0 @ Y2)))))))))) = $true)),
% 3.91/0.93 inference(fool_elimination,[],[f438])).
% 3.91/0.93 thf(f461,plain,(
% 3.91/0.93 (all_of @ (^[X0 : $i] : ((in @ X0 @ nat))) @ (^[X1 : $i] : ((all_of @ (^[X2 : $i] : ((in @ X2 @ nat))) @ (^[X3 : $i] : ((d_not @ (lessis @ X1 @ X3)) => (d_29_ii @ X1 @ X3)))))))),
% 3.91/0.93 inference(rectify,[],[f227])).
% 3.91/0.93 thf(f462,plain,(
% 3.91/0.93 (((all_of @ (^[Y0 : $i]: (in @ Y0 @ nat)) @ (^[Y0 : $i]: (all_of @ (^[Y1 : $i]: (in @ Y1 @ nat)) @ (^[Y1 : $i]: ((d_not @ (lessis @ Y0 @ Y1)) => (d_29_ii @ Y0 @ Y1))))))) = $true)),
% 3.91/0.93 inference(fool_elimination,[],[f461])).
% 3.91/0.93 thf(f494,plain,(
% 3.91/0.93 (all_of @ (^[X0 : $i] : ((in @ X0 @ nat))) @ (^[X1 : $i] : ((all_of @ (^[X2 : $i] : ((in @ X2 @ nat))) @ (^[X3 : $i] : ((lessis @ X1 @ X3) => (d_not @ (d_29_ii @ X1 @ X3))))))))),
% 3.91/0.93 inference(rectify,[],[f221])).
% 3.91/0.93 thf(f495,plain,(
% 3.91/0.93 (((all_of @ (^[Y0 : $i]: (in @ Y0 @ nat)) @ (^[Y0 : $i]: (all_of @ (^[Y1 : $i]: (in @ Y1 @ nat)) @ (^[Y1 : $i]: ((lessis @ Y0 @ Y1) => (d_not @ (d_29_ii @ Y0 @ Y1)))))))) = $true)),
% 3.91/0.93 inference(fool_elimination,[],[f494])).
% 3.91/0.93 thf(f498,plain,(
% 3.91/0.93 (all_of @ (^[X0 : $i] : ((in @ X0 @ nat))) @ (^[X1 : $i] : ((all_of @ (^[X2 : $i] : ((in @ X2 @ nat))) @ (^[X3 : $i] : ((all_of @ (^[X4 : $i] : ((in @ X4 @ nat))) @ (^[X5 : $i] : ((iii @ X1 @ X3) => ((lessis @ X3 @ X5) => (iii @ X1 @ X5)))))))))))),
% 3.91/0.93 inference(rectify,[],[f230])).
% 3.91/0.93 thf(f499,plain,(
% 3.91/0.93 (((all_of @ (^[Y0 : $i]: (in @ Y0 @ nat)) @ (^[Y0 : $i]: (all_of @ (^[Y1 : $i]: (in @ Y1 @ nat)) @ (^[Y1 : $i]: (all_of @ (^[Y2 : $i]: (in @ Y2 @ nat)) @ (^[Y2 : $i]: ((iii @ Y0 @ Y1) => ((lessis @ Y1 @ Y2) => (iii @ Y0 @ Y2)))))))))) = $true)),
% 3.91/0.93 inference(fool_elimination,[],[f498])).
% 3.91/0.93 thf(f510,plain,(
% 3.91/0.93 (iii = (^[Y0 : $i]: ((^[Y1 : $i]: (n_some @ (diffprop @ Y1 @ Y0))))))),
% 3.91/0.93 inference(fool_elimination,[],[f206])).
% 3.91/0.93 thf(f559,plain,(
% 3.91/0.93 (d_29_ii = (^[Y0 : $i]: ((^[Y1 : $i]: (n_some @ (diffprop @ Y0 @ Y1))))))),
% 3.91/0.93 inference(fool_elimination,[],[f205])).
% 3.91/0.93 thf(f608,plain,(
% 3.91/0.93 (((all_of @ (^[Y0 : $i]: (in @ Y0 @ nat)) @ (^[Y0 : $i]: (all_of @ (^[Y1 : $i]: (in @ Y1 @ nat)) @ (^[Y1 : $i]: (all_of @ (^[Y2 : $i]: (in @ Y2 @ nat)) @ (^[Y2 : $i]: ((lessis @ Y0 @ Y1) => ((lessis @ Y1 @ Y2) => (lessis @ Y0 @ Y2)))))))))) != $true)),
% 3.91/0.93 inference(flattening,[],[f439])).
% 3.91/0.93 thf(f614,plain,(
% 3.91/0.93 ! [X0 : ($i > $o)] : (? [X1 : $i] : ((((X0 @ X1)) != $true) & ! [X2 : $i] : ((((X0 @ X2)) = $true) | (((in @ X2 @ X1)) != $true))) | ! [X3 : $i] : (((X0 @ X3)) = $true))),
% 3.91/0.93 inference(ennf_transformation,[],[f259])).
% 3.91/0.93 thf(f664,plain,(
% 3.91/0.93 ! [X0 : ($i > $o)] : (((((X0 @ (sK6 @ X0))) != $true) & ! [X2 : $i] : ((((X0 @ X2)) = $true) | ($true != ((in @ X2 @ (sK6 @ X0)))))) | ! [X3 : $i] : (((X0 @ X3)) = $true))),
% 3.91/0.93 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X3,sK2 @ X2 @ X1 @ X0)],[f614])).
% 3.91/0.93 thf(f685,plain,(
% 3.91/0.93 (n_some = ((l_some @ nat)))),
% 3.91/0.93 inference(cnf_transformation,[],[f160])).
% 3.91/0.93 thf(f691,plain,(
% 3.91/0.93 (all_of = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((is_of @ Y2 @ Y0) => (Y1 @ Y2))))))))),
% 3.91/0.93 inference(cnf_transformation,[],[f305])).
% 3.91/0.93 thf(f692,plain,(
% 3.91/0.93 (n_is = ((e_is @ nat)))),
% 3.91/0.93 inference(cnf_transformation,[],[f157])).
% 3.91/0.93 thf(f702,plain,(
% 3.91/0.93 (is_of = (^[Y0 : $i]: ((^[Y1 : $i > $o]: (Y1 @ Y0)))))),
% 3.91/0.93 inference(cnf_transformation,[],[f370])).
% 3.91/0.93 thf(f718,plain,(
% 3.91/0.93 (l_or = (^[Y0 : $o]: (imp @ (d_not @ Y0))))),
% 3.91/0.93 inference(cnf_transformation,[],[f431])).
% 3.91/0.93 thf(f721,plain,(
% 3.91/0.93 (((all_of @ (^[Y0 : $i]: (in @ Y0 @ nat)) @ (^[Y0 : $i]: (all_of @ (^[Y1 : $i]: (in @ Y1 @ nat)) @ (^[Y1 : $i]: (all_of @ (^[Y2 : $i]: (in @ Y2 @ nat)) @ (^[Y2 : $i]: ((iii @ Y0 @ Y1) => ((lessis @ Y1 @ Y2) => (iii @ Y0 @ Y2)))))))))) = $true)),
% 3.91/0.93 inference(cnf_transformation,[],[f499])).
% 3.91/0.93 thf(f731,plain,(
% 3.91/0.93 (lessis = (^[Y0 : $i]: ((^[Y1 : $i]: (l_or @ (iii @ Y0 @ Y1) @ (n_is @ Y0 @ Y1))))))),
% 3.91/0.93 inference(cnf_transformation,[],[f247])).
% 3.91/0.93 thf(f738,plain,(
% 3.91/0.93 (((all_of @ (^[Y0 : $i]: (in @ Y0 @ nat)) @ (^[Y0 : $i]: (all_of @ (^[Y1 : $i]: (in @ Y1 @ nat)) @ (^[Y1 : $i]: (all_of @ (^[Y2 : $i]: (in @ Y2 @ nat)) @ (^[Y2 : $i]: ((lessis @ Y0 @ Y1) => ((lessis @ Y1 @ Y2) => (lessis @ Y0 @ Y2)))))))))) != $true)),
% 3.91/0.93 inference(cnf_transformation,[],[f608])).
% 3.91/0.93 thf(f746,plain,(
% 3.91/0.93 (diffprop = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (n_is @ Y0 @ (n_pl @ Y1 @ Y2))))))))),
% 3.91/0.93 inference(cnf_transformation,[],[f308])).
% 3.91/0.93 thf(f768,plain,(
% 3.91/0.93 (e_is = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (Y1 = Y2)))))))),
% 3.91/0.93 inference(cnf_transformation,[],[f421])).
% 3.91/0.93 thf(f769,plain,(
% 3.91/0.93 ($true = ((all_of @ (^[Y0 : $i]: (in @ Y0 @ nat)) @ (^[Y0 : $i]: (all_of @ (^[Y1 : $i]: (in @ Y1 @ nat)) @ (^[Y1 : $i]: (all_of @ (^[Y2 : $i]: (in @ Y2 @ nat)) @ (^[Y2 : $i]: ((lessis @ Y0 @ Y1) => ((iii @ Y1 @ Y2) => (iii @ Y0 @ Y2)))))))))))),
% 3.91/0.93 inference(cnf_transformation,[],[f293])).
% 3.91/0.93 thf(f771,plain,(
% 3.91/0.93 ( ! [X3 : $i,X0 : ($i > $o)] : ((((X0 @ (sK6 @ X0))) != $true) | (((X0 @ X3)) = $true)) )),
% 3.91/0.93 inference(cnf_transformation,[],[f664])).
% 3.91/0.93 thf(f787,plain,(
% 3.91/0.93 (iii = (^[Y0 : $i]: ((^[Y1 : $i]: (n_some @ (diffprop @ Y1 @ Y0))))))),
% 3.91/0.93 inference(cnf_transformation,[],[f510])).
% 3.91/0.93 thf(f795,plain,(
% 3.91/0.93 (((all_of @ (^[Y0 : $i]: (in @ Y0 @ nat)) @ (^[Y0 : $i]: (all_of @ (^[Y1 : $i]: (in @ Y1 @ nat)) @ (^[Y1 : $i]: ((d_not @ (lessis @ Y0 @ Y1)) => (d_29_ii @ Y0 @ Y1))))))) = $true)),
% 3.91/0.93 inference(cnf_transformation,[],[f462])).
% 3.91/0.93 thf(f803,plain,(
% 3.91/0.93 (((all_of @ (^[Y0 : $i]: (in @ Y0 @ nat)) @ (^[Y0 : $i]: (all_of @ (^[Y1 : $i]: (in @ Y1 @ nat)) @ (^[Y1 : $i]: ((lessis @ Y0 @ Y1) => (d_not @ (d_29_ii @ Y0 @ Y1)))))))) = $true)),
% 3.91/0.93 inference(cnf_transformation,[],[f495])).
% 3.91/0.93 thf(f804,plain,(
% 3.91/0.93 (imp = (^[Y0 : $o]: ((^[Y1 : $o]: (Y0 => Y1)))))),
% 3.91/0.93 inference(cnf_transformation,[],[f390])).
% 3.91/0.93 thf(f815,plain,(
% 3.91/0.93 (d_29_ii = (^[Y0 : $i]: ((^[Y1 : $i]: (n_some @ (diffprop @ Y0 @ Y1))))))),
% 3.91/0.93 inference(cnf_transformation,[],[f559])).
% 3.91/0.93 thf(f818,plain,(
% 3.91/0.93 (d_not = (^[Y0 : $o]: (imp @ Y0 @ $false)))),
% 3.91/0.93 inference(cnf_transformation,[],[f396])).
% 3.91/0.93 thf(f821,plain,(
% 3.91/0.93 (n_is = (((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (Y1 = Y2)))))) @ nat)))),
% 3.91/0.93 inference(definition_unfolding,[],[f692,f768])).
% 3.91/0.93 thf(f822,plain,(
% 3.91/0.93 (diffprop = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: (Y4 = Y5)))))) @ nat @ Y0 @ (n_pl @ Y1 @ Y2))))))))),
% 3.91/0.93 inference(definition_unfolding,[],[f746,f821])).
% 3.91/0.93 thf(f823,plain,(
% 3.91/0.93 (iii = (^[Y0 : $i]: ((^[Y1 : $i]: (l_some @ nat @ ((^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: ((^[Y6 : $i]: ((^[Y7 : $i]: (Y6 = Y7)))))) @ nat @ Y2 @ (n_pl @ Y3 @ Y4))))))) @ Y1 @ Y0))))))),
% 3.91/0.93 inference(definition_unfolding,[],[f787,f685,f822])).
% 3.91/0.93 thf(f824,plain,(
% 3.91/0.93 (all_of = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: (((^[Y3 : $i]: ((^[Y4 : $i > $o]: (Y4 @ Y3)))) @ Y2 @ Y0) => (Y1 @ Y2))))))))),
% 3.91/0.93 inference(definition_unfolding,[],[f691,f702])).
% 3.91/0.93 thf(f825,plain,(
% 3.91/0.93 (d_not = (^[Y0 : $o]: ((^[Y1 : $o]: ((^[Y2 : $o]: (Y1 => Y2)))) @ Y0 @ $false)))),
% 3.91/0.93 inference(definition_unfolding,[],[f818,f804])).
% 3.91/0.93 thf(f826,plain,(
% 3.91/0.93 (l_or = (^[Y0 : $o]: ((^[Y1 : $o]: ((^[Y2 : $o]: (Y1 => Y2)))) @ ((^[Y1 : $o]: ((^[Y2 : $o]: ((^[Y3 : $o]: (Y2 => Y3)))) @ Y1 @ $false)) @ Y0))))),
% 3.91/0.93 inference(definition_unfolding,[],[f718,f804,f825])).
% 3.91/0.93 thf(f827,plain,(
% 3.91/0.93 (d_29_ii = (^[Y0 : $i]: ((^[Y1 : $i]: (l_some @ nat @ ((^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: ((^[Y6 : $i]: ((^[Y7 : $i]: (Y6 = Y7)))))) @ nat @ Y2 @ (n_pl @ Y3 @ Y4))))))) @ Y0 @ Y1))))))),
% 3.91/0.93 inference(definition_unfolding,[],[f815,f685,f822])).
% 3.91/0.93 thf(f829,plain,(
% 3.91/0.93 (lessis = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $o]: ((^[Y3 : $o]: ((^[Y4 : $o]: (Y3 => Y4)))) @ ((^[Y3 : $o]: ((^[Y4 : $o]: ((^[Y5 : $o]: (Y4 => Y5)))) @ Y3 @ $false)) @ Y2))) @ ((^[Y2 : $i]: ((^[Y3 : $i]: (l_some @ nat @ ((^[Y4 : $i]: ((^[Y5 : $i]: ((^[Y6 : $i]: ((^[Y7 : $i]: ((^[Y8 : $i]: ((^[Y9 : $i]: (Y8 = Y9)))))) @ nat @ Y4 @ (n_pl @ Y5 @ Y6))))))) @ Y3 @ Y2))))) @ Y0 @ Y1) @ ((^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: (Y3 = Y4)))))) @ nat @ Y0 @ Y1))))))),
% 3.91/0.93 inference(definition_unfolding,[],[f731,f826,f823,f821])).
% 3.91/0.93 thf(f875,plain,(
% 3.91/0.93 ((((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: (((^[Y3 : $i]: ((^[Y4 : $i > $o]: (Y4 @ Y3)))) @ Y2 @ Y0) => (Y1 @ Y2))))))) @ (^[Y0 : $i]: (in @ Y0 @ nat)) @ (^[Y0 : $i]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: (!! @ $i @ (^[Y3 : $i]: (((^[Y4 : $i]: ((^[Y5 : $i > $o]: (Y5 @ Y4)))) @ Y3 @ Y1) => (Y2 @ Y3))))))) @ (^[Y1 : $i]: (in @ Y1 @ nat)) @ (^[Y1 : $i]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: (!! @ $i @ (^[Y4 : $i]: (((^[Y5 : $i]: ((^[Y6 : $i > $o]: (Y6 @ Y5)))) @ Y4 @ Y2) => (Y3 @ Y4))))))) @ (^[Y2 : $i]: (in @ Y2 @ nat)) @ (^[Y2 : $i]: (((^[Y3 : $i]: ((^[Y4 : $i]: (l_some @ nat @ ((^[Y5 : $i]: ((^[Y6 : $i]: ((^[Y7 : $i]: ((^[Y8 : $i]: ((^[Y9 : $i]: ((^[Y10 : $i]: (Y9 = Y10)))))) @ nat @ Y5 @ (n_pl @ Y6 @ Y7))))))) @ Y4 @ Y3))))) @ Y0 @ Y1) => (((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $o]: ((^[Y6 : $o]: ((^[Y7 : $o]: (Y6 => Y7)))) @ ((^[Y6 : $o]: ((^[Y7 : $o]: ((^[Y8 : $o]: (Y7 => Y8)))) @ Y6 @ $false)) @ Y5))) @ ((^[Y5 : $i]: ((^[Y6 : $i]: (l_some @ nat @ ((^[Y7 : $i]: ((^[Y8 : $i]: ((^[Y9 : $i]: ((^[Y10 : $i]: ((^[Y11 : $i]: ((^[Y12 : $i]: (Y11 = Y12)))))) @ nat @ Y7 @ (n_pl @ Y8 @ Y9))))))) @ Y6 @ Y5))))) @ Y3 @ Y4) @ ((^[Y5 : $i]: ((^[Y6 : $i]: ((^[Y7 : $i]: (Y6 = Y7)))))) @ nat @ Y3 @ Y4))))) @ Y1 @ Y2) => ((^[Y3 : $i]: ((^[Y4 : $i]: (l_some @ nat @ ((^[Y5 : $i]: ((^[Y6 : $i]: ((^[Y7 : $i]: ((^[Y8 : $i]: ((^[Y9 : $i]: ((^[Y10 : $i]: (Y9 = Y10)))))) @ nat @ Y5 @ (n_pl @ Y6 @ Y7))))))) @ Y4 @ Y3))))) @ Y0 @ Y2)))))))))) = $true)),
% 3.91/0.93 inference(definition_unfolding,[],[f721,f824,f824,f824,f823,f829,f823])).
% 3.91/0.93 thf(f887,plain,(
% 3.91/0.93 ($true != (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: (((^[Y3 : $i]: ((^[Y4 : $i > $o]: (Y4 @ Y3)))) @ Y2 @ Y0) => (Y1 @ Y2))))))) @ (^[Y0 : $i]: (in @ Y0 @ nat)) @ (^[Y0 : $i]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: (!! @ $i @ (^[Y3 : $i]: (((^[Y4 : $i]: ((^[Y5 : $i > $o]: (Y5 @ Y4)))) @ Y3 @ Y1) => (Y2 @ Y3))))))) @ (^[Y1 : $i]: (in @ Y1 @ nat)) @ (^[Y1 : $i]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: (!! @ $i @ (^[Y4 : $i]: (((^[Y5 : $i]: ((^[Y6 : $i > $o]: (Y6 @ Y5)))) @ Y4 @ Y2) => (Y3 @ Y4))))))) @ (^[Y2 : $i]: (in @ Y2 @ nat)) @ (^[Y2 : $i]: (((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $o]: ((^[Y6 : $o]: ((^[Y7 : $o]: (Y6 => Y7)))) @ ((^[Y6 : $o]: ((^[Y7 : $o]: ((^[Y8 : $o]: (Y7 => Y8)))) @ Y6 @ $false)) @ Y5))) @ ((^[Y5 : $i]: ((^[Y6 : $i]: (l_some @ nat @ ((^[Y7 : $i]: ((^[Y8 : $i]: ((^[Y9 : $i]: ((^[Y10 : $i]: ((^[Y11 : $i]: ((^[Y12 : $i]: (Y11 = Y12)))))) @ nat @ Y7 @ (n_pl @ Y8 @ Y9))))))) @ Y6 @ Y5))))) @ Y3 @ Y4) @ ((^[Y5 : $i]: ((^[Y6 : $i]: ((^[Y7 : $i]: (Y6 = Y7)))))) @ nat @ Y3 @ Y4))))) @ Y0 @ Y1) => (((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $o]: ((^[Y6 : $o]: ((^[Y7 : $o]: (Y6 => Y7)))) @ ((^[Y6 : $o]: ((^[Y7 : $o]: ((^[Y8 : $o]: (Y7 => Y8)))) @ Y6 @ $false)) @ Y5))) @ ((^[Y5 : $i]: ((^[Y6 : $i]: (l_some @ nat @ ((^[Y7 : $i]: ((^[Y8 : $i]: ((^[Y9 : $i]: ((^[Y10 : $i]: ((^[Y11 : $i]: ((^[Y12 : $i]: (Y11 = Y12)))))) @ nat @ Y7 @ (n_pl @ Y8 @ Y9))))))) @ Y6 @ Y5))))) @ Y3 @ Y4) @ ((^[Y5 : $i]: ((^[Y6 : $i]: ((^[Y7 : $i]: (Y6 = Y7)))))) @ nat @ Y3 @ Y4))))) @ Y1 @ Y2) => ((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $o]: ((^[Y6 : $o]: ((^[Y7 : $o]: (Y6 => Y7)))) @ ((^[Y6 : $o]: ((^[Y7 : $o]: ((^[Y8 : $o]: (Y7 => Y8)))) @ Y6 @ $false)) @ Y5))) @ ((^[Y5 : $i]: ((^[Y6 : $i]: (l_some @ nat @ ((^[Y7 : $i]: ((^[Y8 : $i]: ((^[Y9 : $i]: ((^[Y10 : $i]: ((^[Y11 : $i]: ((^[Y12 : $i]: (Y11 = Y12)))))) @ nat @ Y7 @ (n_pl @ Y8 @ Y9))))))) @ Y6 @ Y5))))) @ Y3 @ Y4) @ ((^[Y5 : $i]: ((^[Y6 : $i]: ((^[Y7 : $i]: (Y6 = Y7)))))) @ nat @ Y3 @ Y4))))) @ Y0 @ Y2)))))))))))),
% 3.91/0.93 inference(definition_unfolding,[],[f738,f824,f824,f824,f829,f829,f829])).
% 3.91/0.93 thf(f906,plain,(
% 3.91/0.93 ((((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: (((^[Y3 : $i]: ((^[Y4 : $i > $o]: (Y4 @ Y3)))) @ Y2 @ Y0) => (Y1 @ Y2))))))) @ (^[Y0 : $i]: (in @ Y0 @ nat)) @ (^[Y0 : $i]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: (!! @ $i @ (^[Y3 : $i]: (((^[Y4 : $i]: ((^[Y5 : $i > $o]: (Y5 @ Y4)))) @ Y3 @ Y1) => (Y2 @ Y3))))))) @ (^[Y1 : $i]: (in @ Y1 @ nat)) @ (^[Y1 : $i]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: (!! @ $i @ (^[Y4 : $i]: (((^[Y5 : $i]: ((^[Y6 : $i > $o]: (Y6 @ Y5)))) @ Y4 @ Y2) => (Y3 @ Y4))))))) @ (^[Y2 : $i]: (in @ Y2 @ nat)) @ (^[Y2 : $i]: (((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $o]: ((^[Y6 : $o]: ((^[Y7 : $o]: (Y6 => Y7)))) @ ((^[Y6 : $o]: ((^[Y7 : $o]: ((^[Y8 : $o]: (Y7 => Y8)))) @ Y6 @ $false)) @ Y5))) @ ((^[Y5 : $i]: ((^[Y6 : $i]: (l_some @ nat @ ((^[Y7 : $i]: ((^[Y8 : $i]: ((^[Y9 : $i]: ((^[Y10 : $i]: ((^[Y11 : $i]: ((^[Y12 : $i]: (Y11 = Y12)))))) @ nat @ Y7 @ (n_pl @ Y8 @ Y9))))))) @ Y6 @ Y5))))) @ Y3 @ Y4) @ ((^[Y5 : $i]: ((^[Y6 : $i]: ((^[Y7 : $i]: (Y6 = Y7)))))) @ nat @ Y3 @ Y4))))) @ Y0 @ Y1) => (((^[Y3 : $i]: ((^[Y4 : $i]: (l_some @ nat @ ((^[Y5 : $i]: ((^[Y6 : $i]: ((^[Y7 : $i]: ((^[Y8 : $i]: ((^[Y9 : $i]: ((^[Y10 : $i]: (Y9 = Y10)))))) @ nat @ Y5 @ (n_pl @ Y6 @ Y7))))))) @ Y4 @ Y3))))) @ Y1 @ Y2) => ((^[Y3 : $i]: ((^[Y4 : $i]: (l_some @ nat @ ((^[Y5 : $i]: ((^[Y6 : $i]: ((^[Y7 : $i]: ((^[Y8 : $i]: ((^[Y9 : $i]: ((^[Y10 : $i]: (Y9 = Y10)))))) @ nat @ Y5 @ (n_pl @ Y6 @ Y7))))))) @ Y4 @ Y3))))) @ Y0 @ Y2)))))))))) = $true)),
% 3.91/0.93 inference(definition_unfolding,[],[f769,f824,f824,f824,f829,f823,f823])).
% 3.91/0.93 thf(f922,plain,(
% 3.91/0.93 ($true = (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: (((^[Y3 : $i]: ((^[Y4 : $i > $o]: (Y4 @ Y3)))) @ Y2 @ Y0) => (Y1 @ Y2))))))) @ (^[Y0 : $i]: (in @ Y0 @ nat)) @ (^[Y0 : $i]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: (!! @ $i @ (^[Y3 : $i]: (((^[Y4 : $i]: ((^[Y5 : $i > $o]: (Y5 @ Y4)))) @ Y3 @ Y1) => (Y2 @ Y3))))))) @ (^[Y1 : $i]: (in @ Y1 @ nat)) @ (^[Y1 : $i]: (((^[Y2 : $o]: ((^[Y3 : $o]: ((^[Y4 : $o]: (Y3 => Y4)))) @ Y2 @ $false)) @ ((^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $o]: ((^[Y5 : $o]: ((^[Y6 : $o]: (Y5 => Y6)))) @ ((^[Y5 : $o]: ((^[Y6 : $o]: ((^[Y7 : $o]: (Y6 => Y7)))) @ Y5 @ $false)) @ Y4))) @ ((^[Y4 : $i]: ((^[Y5 : $i]: (l_some @ nat @ ((^[Y6 : $i]: ((^[Y7 : $i]: ((^[Y8 : $i]: ((^[Y9 : $i]: ((^[Y10 : $i]: ((^[Y11 : $i]: (Y10 = Y11)))))) @ nat @ Y6 @ (n_pl @ Y7 @ Y8))))))) @ Y5 @ Y4))))) @ Y2 @ Y3) @ ((^[Y4 : $i]: ((^[Y5 : $i]: ((^[Y6 : $i]: (Y5 = Y6)))))) @ nat @ Y2 @ Y3))))) @ Y0 @ Y1)) => ((^[Y2 : $i]: ((^[Y3 : $i]: (l_some @ nat @ ((^[Y4 : $i]: ((^[Y5 : $i]: ((^[Y6 : $i]: ((^[Y7 : $i]: ((^[Y8 : $i]: ((^[Y9 : $i]: (Y8 = Y9)))))) @ nat @ Y4 @ (n_pl @ Y5 @ Y6))))))) @ Y2 @ Y3))))) @ Y0 @ Y1))))))))),
% 3.91/0.93 inference(definition_unfolding,[],[f795,f824,f824,f825,f829,f827])).
% 3.91/0.93 thf(f925,plain,(
% 3.91/0.93 ((((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: (((^[Y3 : $i]: ((^[Y4 : $i > $o]: (Y4 @ Y3)))) @ Y2 @ Y0) => (Y1 @ Y2))))))) @ (^[Y0 : $i]: (in @ Y0 @ nat)) @ (^[Y0 : $i]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: (!! @ $i @ (^[Y3 : $i]: (((^[Y4 : $i]: ((^[Y5 : $i > $o]: (Y5 @ Y4)))) @ Y3 @ Y1) => (Y2 @ Y3))))))) @ (^[Y1 : $i]: (in @ Y1 @ nat)) @ (^[Y1 : $i]: (((^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $o]: ((^[Y5 : $o]: ((^[Y6 : $o]: (Y5 => Y6)))) @ ((^[Y5 : $o]: ((^[Y6 : $o]: ((^[Y7 : $o]: (Y6 => Y7)))) @ Y5 @ $false)) @ Y4))) @ ((^[Y4 : $i]: ((^[Y5 : $i]: (l_some @ nat @ ((^[Y6 : $i]: ((^[Y7 : $i]: ((^[Y8 : $i]: ((^[Y9 : $i]: ((^[Y10 : $i]: ((^[Y11 : $i]: (Y10 = Y11)))))) @ nat @ Y6 @ (n_pl @ Y7 @ Y8))))))) @ Y5 @ Y4))))) @ Y2 @ Y3) @ ((^[Y4 : $i]: ((^[Y5 : $i]: ((^[Y6 : $i]: (Y5 = Y6)))))) @ nat @ Y2 @ Y3))))) @ Y0 @ Y1) => ((^[Y2 : $o]: ((^[Y3 : $o]: ((^[Y4 : $o]: (Y3 => Y4)))) @ Y2 @ $false)) @ ((^[Y2 : $i]: ((^[Y3 : $i]: (l_some @ nat @ ((^[Y4 : $i]: ((^[Y5 : $i]: ((^[Y6 : $i]: ((^[Y7 : $i]: ((^[Y8 : $i]: ((^[Y9 : $i]: (Y8 = Y9)))))) @ nat @ Y4 @ (n_pl @ Y5 @ Y6))))))) @ Y2 @ Y3))))) @ Y0 @ Y1)))))))) = $true)),
% 3.91/0.93 inference(definition_unfolding,[],[f803,f824,f824,f829,f825,f827])).
% 3.91/0.93 thf(f974,plain,(
% 3.91/0.93 ($true = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ nat) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ nat) => ((((l_some @ nat @ (^[Y2 : $i]: (Y1 = (n_pl @ Y0 @ Y2)))) => $false) => (Y0 = Y1)) => ((l_some @ nat @ (^[Y2 : $i]: (Y0 = (n_pl @ Y1 @ Y2)))) => $false))))))))))),
% 3.91/0.93 inference(beta-eta_normalization,[],[f925])).
% 3.91/0.93 thf(f975,plain,(
% 3.91/0.93 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: ((in @ Y0 @ nat) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ nat) => ((((l_some @ nat @ (^[Y2 : $i]: (Y1 = (n_pl @ Y0 @ Y2)))) => $false) => (Y0 = Y1)) => ((l_some @ nat @ (^[Y2 : $i]: (Y0 = (n_pl @ Y1 @ Y2)))) => $false))))))) @ X1)))) )),
% 3.91/0.93 inference(pi_proxy_clausification,[],[f974])).
% 3.91/0.93 thf(f976,plain,(
% 3.91/0.93 ( ! [X1 : $i] : (($true = (((in @ X1 @ nat) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ nat) => ((((l_some @ nat @ (^[Y1 : $i]: (Y0 = (n_pl @ X1 @ Y1)))) => $false) => (X1 = Y0)) => ((l_some @ nat @ (^[Y1 : $i]: (X1 = (n_pl @ Y0 @ Y1)))) => $false))))))))) )),
% 3.91/0.93 inference(beta-eta_normalization,[],[f975])).
% 3.91/0.93 thf(f977,plain,(
% 3.91/0.93 ( ! [X1 : $i] : ((((in @ X1 @ nat)) = $false) | (((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ nat) => ((((l_some @ nat @ (^[Y1 : $i]: (Y0 = (n_pl @ X1 @ Y1)))) => $false) => (X1 = Y0)) => ((l_some @ nat @ (^[Y1 : $i]: (X1 = (n_pl @ Y0 @ Y1)))) => $false)))))) = $true)) )),
% 3.91/0.93 inference(imp_proxy_clausification,[],[f976])).
% 3.91/0.93 thf(f978,plain,(
% 3.91/0.93 ( ! [X2 : $i,X1 : $i] : ((((in @ X1 @ nat)) = $false) | ($true = (((^[Y0 : $i]: ((in @ Y0 @ nat) => ((((l_some @ nat @ (^[Y1 : $i]: (Y0 = (n_pl @ X1 @ Y1)))) => $false) => (X1 = Y0)) => ((l_some @ nat @ (^[Y1 : $i]: (X1 = (n_pl @ Y0 @ Y1)))) => $false)))) @ X2)))) )),
% 3.91/0.93 inference(pi_proxy_clausification,[],[f977])).
% 3.91/0.93 thf(f979,plain,(
% 3.91/0.93 ( ! [X2 : $i,X1 : $i] : ((((in @ X1 @ nat)) = $false) | ($true = (((in @ X2 @ nat) => ((((l_some @ nat @ (^[Y0 : $i]: (X2 = (n_pl @ X1 @ Y0)))) => $false) => (X1 = X2)) => ((l_some @ nat @ (^[Y0 : $i]: (X1 = (n_pl @ X2 @ Y0)))) => $false)))))) )),
% 3.91/0.93 inference(beta-eta_normalization,[],[f978])).
% 3.91/0.93 thf(f980,plain,(
% 3.91/0.93 ( ! [X2 : $i,X1 : $i] : (((((((l_some @ nat @ (^[Y0 : $i]: (X2 = (n_pl @ X1 @ Y0)))) => $false) => (X1 = X2)) => ((l_some @ nat @ (^[Y0 : $i]: (X1 = (n_pl @ X2 @ Y0)))) => $false))) = $true) | (((in @ X1 @ nat)) = $false) | (((in @ X2 @ nat)) = $false)) )),
% 3.91/0.93 inference(imp_proxy_clausification,[],[f979])).
% 3.91/0.93 thf(f981,plain,(
% 3.91/0.93 ( ! [X2 : $i,X1 : $i] : (($false = ((((l_some @ nat @ (^[Y0 : $i]: (X2 = (n_pl @ X1 @ Y0)))) => $false) => (X1 = X2)))) | ((((l_some @ nat @ (^[Y0 : $i]: (X1 = (n_pl @ X2 @ Y0)))) => $false)) = $true) | (((in @ X2 @ nat)) = $false) | (((in @ X1 @ nat)) = $false)) )),
% 3.91/0.93 inference(imp_proxy_clausification,[],[f980])).
% 3.91/0.93 thf(f983,plain,(
% 3.91/0.93 ( ! [X2 : $i,X1 : $i] : ((((in @ X1 @ nat)) = $false) | ((((l_some @ nat @ (^[Y0 : $i]: (X2 = (n_pl @ X1 @ Y0)))) => $false)) = $true) | (((in @ X2 @ nat)) = $false) | ((((l_some @ nat @ (^[Y0 : $i]: (X1 = (n_pl @ X2 @ Y0)))) => $false)) = $true)) )),
% 3.91/0.93 inference(imp_proxy_clausification,[],[f981])).
% 3.91/0.93 thf(f984,plain,(
% 3.91/0.93 ( ! [X2 : $i,X1 : $i] : (((((l_some @ nat @ (^[Y0 : $i]: (X1 = (n_pl @ X2 @ Y0)))) => $false)) = $true) | (((in @ X2 @ nat)) = $false) | ($false = $true) | (((in @ X1 @ nat)) = $false) | ($false = ((l_some @ nat @ (^[Y0 : $i]: (X2 = (n_pl @ X1 @ Y0))))))) )),
% 3.91/0.93 inference(imp_proxy_clausification,[],[f983])).
% 3.91/0.93 thf(f985,plain,(
% 3.91/0.93 ( ! [X2 : $i,X1 : $i] : ((((in @ X1 @ nat)) = $false) | (((l_some @ nat @ (^[Y0 : $i]: (X1 = (n_pl @ X2 @ Y0))))) = $false) | ($false = $true) | ($false = ((l_some @ nat @ (^[Y0 : $i]: (X2 = (n_pl @ X1 @ Y0)))))) | ($false = $true) | (((in @ X2 @ nat)) = $false)) )),
% 3.91/0.93 inference(imp_proxy_clausification,[],[f984])).
% 3.91/0.93 thf(f986,plain,(
% 3.91/0.93 ( ! [X2 : $i,X1 : $i] : (($false = ((l_some @ nat @ (^[Y0 : $i]: (X2 = (n_pl @ X1 @ Y0)))))) | (((in @ X1 @ nat)) = $false) | ($false = $true) | (((l_some @ nat @ (^[Y0 : $i]: (X1 = (n_pl @ X2 @ Y0))))) = $false) | (((in @ X2 @ nat)) = $false)) )),
% 3.91/0.93 inference(duplicate_literal_removal,[],[f985])).
% 3.91/0.93 thf(f987,plain,(
% 3.91/0.93 ( ! [X2 : $i,X1 : $i] : (($false = ((l_some @ nat @ (^[Y0 : $i]: (X2 = (n_pl @ X1 @ Y0)))))) | (((l_some @ nat @ (^[Y0 : $i]: (X1 = (n_pl @ X2 @ Y0))))) = $false) | (((in @ X1 @ nat)) = $false) | (((in @ X2 @ nat)) = $false)) )),
% 3.91/0.93 inference(trivial_inequality_removal,[],[f986])).
% 3.91/0.93 thf(f1018,plain,(
% 3.91/0.93 (((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ nat) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ nat) => (((((l_some @ nat @ (^[Y2 : $i]: (Y1 = (n_pl @ Y0 @ Y2)))) => $false) => (Y0 = Y1)) => $false) => (l_some @ nat @ (^[Y2 : $i]: (Y0 = (n_pl @ Y1 @ Y2)))))))))))) = $true)),
% 3.91/0.93 inference(beta-eta_normalization,[],[f922])).
% 3.91/0.93 thf(f1019,plain,(
% 3.91/0.93 ( ! [X1 : $i] : (((((^[Y0 : $i]: ((in @ Y0 @ nat) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ nat) => (((((l_some @ nat @ (^[Y2 : $i]: (Y1 = (n_pl @ Y0 @ Y2)))) => $false) => (Y0 = Y1)) => $false) => (l_some @ nat @ (^[Y2 : $i]: (Y0 = (n_pl @ Y1 @ Y2)))))))))) @ X1)) = $true)) )),
% 3.91/0.93 inference(pi_proxy_clausification,[],[f1018])).
% 3.91/0.93 thf(f1020,plain,(
% 3.91/0.93 ( ! [X1 : $i] : (($true = (((in @ X1 @ nat) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ nat) => (((((l_some @ nat @ (^[Y1 : $i]: (Y0 = (n_pl @ X1 @ Y1)))) => $false) => (X1 = Y0)) => $false) => (l_some @ nat @ (^[Y1 : $i]: (X1 = (n_pl @ Y0 @ Y1)))))))))))) )),
% 3.91/0.93 inference(beta-eta_normalization,[],[f1019])).
% 3.91/0.93 thf(f1021,plain,(
% 3.91/0.93 ( ! [X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ nat) => (((((l_some @ nat @ (^[Y1 : $i]: (Y0 = (n_pl @ X1 @ Y1)))) => $false) => (X1 = Y0)) => $false) => (l_some @ nat @ (^[Y1 : $i]: (X1 = (n_pl @ Y0 @ Y1)))))))))) | (((in @ X1 @ nat)) = $false)) )),
% 3.91/0.93 inference(imp_proxy_clausification,[],[f1020])).
% 3.91/0.93 thf(f1022,plain,(
% 3.91/0.93 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((in @ Y0 @ nat) => (((((l_some @ nat @ (^[Y1 : $i]: (Y0 = (n_pl @ X1 @ Y1)))) => $false) => (X1 = Y0)) => $false) => (l_some @ nat @ (^[Y1 : $i]: (X1 = (n_pl @ Y0 @ Y1))))))) @ X2))) | (((in @ X1 @ nat)) = $false)) )),
% 3.91/0.93 inference(pi_proxy_clausification,[],[f1021])).
% 3.91/0.93 thf(f1023,plain,(
% 3.91/0.93 ( ! [X2 : $i,X1 : $i] : ((((in @ X1 @ nat)) = $false) | ($true = (((in @ X2 @ nat) => (((((l_some @ nat @ (^[Y0 : $i]: (X2 = (n_pl @ X1 @ Y0)))) => $false) => (X1 = X2)) => $false) => (l_some @ nat @ (^[Y0 : $i]: (X1 = (n_pl @ X2 @ Y0))))))))) )),
% 3.91/0.93 inference(beta-eta_normalization,[],[f1022])).
% 3.91/0.93 thf(f1024,plain,(
% 3.91/0.93 ( ! [X2 : $i,X1 : $i] : ((((in @ X1 @ nat)) = $false) | (((((((l_some @ nat @ (^[Y0 : $i]: (X2 = (n_pl @ X1 @ Y0)))) => $false) => (X1 = X2)) => $false) => (l_some @ nat @ (^[Y0 : $i]: (X1 = (n_pl @ X2 @ Y0)))))) = $true) | (((in @ X2 @ nat)) = $false)) )),
% 3.91/0.93 inference(imp_proxy_clausification,[],[f1023])).
% 3.91/0.93 thf(f1025,plain,(
% 3.91/0.93 ( ! [X2 : $i,X1 : $i] : ((((in @ X2 @ nat)) = $false) | (((in @ X1 @ nat)) = $false) | ($false = (((((l_some @ nat @ (^[Y0 : $i]: (X2 = (n_pl @ X1 @ Y0)))) => $false) => (X1 = X2)) => $false))) | (((l_some @ nat @ (^[Y0 : $i]: (X1 = (n_pl @ X2 @ Y0))))) = $true)) )),
% 3.91/0.93 inference(imp_proxy_clausification,[],[f1024])).
% 3.91/0.93 thf(f1027,plain,(
% 3.91/0.93 ( ! [X2 : $i,X1 : $i] : (($true = ((((l_some @ nat @ (^[Y0 : $i]: (X2 = (n_pl @ X1 @ Y0)))) => $false) => (X1 = X2)))) | (((l_some @ nat @ (^[Y0 : $i]: (X1 = (n_pl @ X2 @ Y0))))) = $true) | (((in @ X2 @ nat)) = $false) | (((in @ X1 @ nat)) = $false)) )),
% 3.91/0.93 inference(imp_proxy_clausification,[],[f1025])).
% 3.91/0.93 thf(f1028,plain,(
% 3.91/0.93 ( ! [X2 : $i,X1 : $i] : ((((in @ X2 @ nat)) = $false) | (((X1 = X2)) = $true) | (((l_some @ nat @ (^[Y0 : $i]: (X1 = (n_pl @ X2 @ Y0))))) = $true) | ($false = (((l_some @ nat @ (^[Y0 : $i]: (X2 = (n_pl @ X1 @ Y0)))) => $false))) | (((in @ X1 @ nat)) = $false)) )),
% 3.91/0.93 inference(imp_proxy_clausification,[],[f1027])).
% 3.91/0.93 thf(f1029,plain,(
% 3.91/0.93 ( ! [X2 : $i,X1 : $i] : ((((in @ X2 @ nat)) = $false) | (((l_some @ nat @ (^[Y0 : $i]: (X1 = (n_pl @ X2 @ Y0))))) = $true) | (((in @ X1 @ nat)) = $false) | ($false = (((l_some @ nat @ (^[Y0 : $i]: (X2 = (n_pl @ X1 @ Y0)))) => $false))) | (X1 = X2)) )),
% 3.91/0.93 inference(equality_proxy_clausification,[],[f1028])).
% 3.91/0.93 thf(f1031,plain,(
% 3.91/0.93 ( ! [X2 : $i,X1 : $i] : ((((l_some @ nat @ (^[Y0 : $i]: (X2 = (n_pl @ X1 @ Y0))))) = $true) | (((l_some @ nat @ (^[Y0 : $i]: (X1 = (n_pl @ X2 @ Y0))))) = $true) | (X1 = X2) | (((in @ X1 @ nat)) = $false) | (((in @ X2 @ nat)) = $false)) )),
% 3.91/0.93 inference(imp_proxy_clausification,[],[f1029])).
% 3.91/0.93 thf(f1228,plain,(
% 3.91/0.93 (((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ nat) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ nat) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ nat) => ((l_some @ nat @ (^[Y3 : $i]: (Y1 = (n_pl @ Y0 @ Y3)))) => ((((l_some @ nat @ (^[Y3 : $i]: (Y2 = (n_pl @ Y1 @ Y3)))) => $false) => (Y1 = Y2)) => (l_some @ nat @ (^[Y3 : $i]: (Y2 = (n_pl @ Y0 @ Y3)))))))))))))))) = $true)),
% 3.91/0.93 inference(beta-eta_normalization,[],[f875])).
% 3.91/0.93 thf(f1229,plain,(
% 3.91/0.93 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: ((in @ Y0 @ nat) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ nat) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ nat) => ((l_some @ nat @ (^[Y3 : $i]: (Y1 = (n_pl @ Y0 @ Y3)))) => ((((l_some @ nat @ (^[Y3 : $i]: (Y2 = (n_pl @ Y1 @ Y3)))) => $false) => (Y1 = Y2)) => (l_some @ nat @ (^[Y3 : $i]: (Y2 = (n_pl @ Y0 @ Y3)))))))))))))) @ X1)))) )),
% 3.91/0.93 inference(pi_proxy_clausification,[],[f1228])).
% 3.91/0.93 thf(f1230,plain,(
% 3.91/0.93 ( ! [X1 : $i] : (((((in @ X1 @ nat) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ nat) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ nat) => ((l_some @ nat @ (^[Y2 : $i]: (Y0 = (n_pl @ X1 @ Y2)))) => ((((l_some @ nat @ (^[Y2 : $i]: (Y1 = (n_pl @ Y0 @ Y2)))) => $false) => (Y0 = Y1)) => (l_some @ nat @ (^[Y2 : $i]: (Y1 = (n_pl @ X1 @ Y2)))))))))))))) = $true)) )),
% 3.91/0.93 inference(beta-eta_normalization,[],[f1229])).
% 3.91/0.93 thf(f1231,plain,(
% 3.91/0.93 ( ! [X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ nat) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ nat) => ((l_some @ nat @ (^[Y2 : $i]: (Y0 = (n_pl @ X1 @ Y2)))) => ((((l_some @ nat @ (^[Y2 : $i]: (Y1 = (n_pl @ Y0 @ Y2)))) => $false) => (Y0 = Y1)) => (l_some @ nat @ (^[Y2 : $i]: (Y1 = (n_pl @ X1 @ Y2)))))))))))))) | (((in @ X1 @ nat)) = $false)) )),
% 3.91/0.93 inference(imp_proxy_clausification,[],[f1230])).
% 3.91/0.93 thf(f1232,plain,(
% 3.91/0.93 ( ! [X2 : $i,X1 : $i] : ((((in @ X1 @ nat)) = $false) | ((((^[Y0 : $i]: ((in @ Y0 @ nat) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ nat) => ((l_some @ nat @ (^[Y2 : $i]: (Y0 = (n_pl @ X1 @ Y2)))) => ((((l_some @ nat @ (^[Y2 : $i]: (Y1 = (n_pl @ Y0 @ Y2)))) => $false) => (Y0 = Y1)) => (l_some @ nat @ (^[Y2 : $i]: (Y1 = (n_pl @ X1 @ Y2))))))))))) @ X2)) = $true)) )),
% 3.91/0.93 inference(pi_proxy_clausification,[],[f1231])).
% 3.91/0.93 thf(f1233,plain,(
% 3.91/0.93 ( ! [X2 : $i,X1 : $i] : (((((in @ X2 @ nat) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ nat) => ((l_some @ nat @ (^[Y1 : $i]: (X2 = (n_pl @ X1 @ Y1)))) => ((((l_some @ nat @ (^[Y1 : $i]: (Y0 = (n_pl @ X2 @ Y1)))) => $false) => (X2 = Y0)) => (l_some @ nat @ (^[Y1 : $i]: (Y0 = (n_pl @ X1 @ Y1))))))))))) = $true) | (((in @ X1 @ nat)) = $false)) )),
% 3.91/0.93 inference(beta-eta_normalization,[],[f1232])).
% 3.91/0.93 thf(f1234,plain,(
% 3.91/0.93 ( ! [X2 : $i,X1 : $i] : ((((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ nat) => ((l_some @ nat @ (^[Y1 : $i]: (X2 = (n_pl @ X1 @ Y1)))) => ((((l_some @ nat @ (^[Y1 : $i]: (Y0 = (n_pl @ X2 @ Y1)))) => $false) => (X2 = Y0)) => (l_some @ nat @ (^[Y1 : $i]: (Y0 = (n_pl @ X1 @ Y1)))))))))) = $true) | (((in @ X2 @ nat)) = $false) | (((in @ X1 @ nat)) = $false)) )),
% 3.91/0.93 inference(imp_proxy_clausification,[],[f1233])).
% 3.91/0.93 thf(f1235,plain,(
% 3.91/0.93 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((in @ X1 @ nat)) = $false) | ($true = (((^[Y0 : $i]: ((in @ Y0 @ nat) => ((l_some @ nat @ (^[Y1 : $i]: (X2 = (n_pl @ X1 @ Y1)))) => ((((l_some @ nat @ (^[Y1 : $i]: (Y0 = (n_pl @ X2 @ Y1)))) => $false) => (X2 = Y0)) => (l_some @ nat @ (^[Y1 : $i]: (Y0 = (n_pl @ X1 @ Y1)))))))) @ X3))) | (((in @ X2 @ nat)) = $false)) )),
% 3.91/0.93 inference(pi_proxy_clausification,[],[f1234])).
% 3.91/0.93 thf(f1236,plain,(
% 3.91/0.93 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((in @ X3 @ nat) => ((l_some @ nat @ (^[Y0 : $i]: (X2 = (n_pl @ X1 @ Y0)))) => ((((l_some @ nat @ (^[Y0 : $i]: (X3 = (n_pl @ X2 @ Y0)))) => $false) => (X2 = X3)) => (l_some @ nat @ (^[Y0 : $i]: (X3 = (n_pl @ X1 @ Y0))))))))) | (((in @ X1 @ nat)) = $false) | (((in @ X2 @ nat)) = $false)) )),
% 3.91/0.93 inference(beta-eta_normalization,[],[f1235])).
% 3.91/0.93 thf(f1237,plain,(
% 3.91/0.93 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((l_some @ nat @ (^[Y0 : $i]: (X2 = (n_pl @ X1 @ Y0)))) => ((((l_some @ nat @ (^[Y0 : $i]: (X3 = (n_pl @ X2 @ Y0)))) => $false) => (X2 = X3)) => (l_some @ nat @ (^[Y0 : $i]: (X3 = (n_pl @ X1 @ Y0)))))))) | ($false = ((in @ X3 @ nat))) | (((in @ X1 @ nat)) = $false) | (((in @ X2 @ nat)) = $false)) )),
% 3.91/0.93 inference(imp_proxy_clausification,[],[f1236])).
% 3.91/0.93 thf(f1238,plain,(
% 3.91/0.93 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = ((in @ X3 @ nat))) | ($false = ((l_some @ nat @ (^[Y0 : $i]: (X2 = (n_pl @ X1 @ Y0)))))) | (((in @ X2 @ nat)) = $false) | ($true = (((((l_some @ nat @ (^[Y0 : $i]: (X3 = (n_pl @ X2 @ Y0)))) => $false) => (X2 = X3)) => (l_some @ nat @ (^[Y0 : $i]: (X3 = (n_pl @ X1 @ Y0))))))) | (((in @ X1 @ nat)) = $false)) )),
% 3.91/0.93 inference(imp_proxy_clausification,[],[f1237])).
% 3.91/0.93 thf(f1239,plain,(
% 3.91/0.93 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((in @ X2 @ nat)) = $false) | ($false = ((in @ X3 @ nat))) | (((in @ X1 @ nat)) = $false) | (((((l_some @ nat @ (^[Y0 : $i]: (X3 = (n_pl @ X2 @ Y0)))) => $false) => (X2 = X3))) = $false) | ($false = ((l_some @ nat @ (^[Y0 : $i]: (X2 = (n_pl @ X1 @ Y0)))))) | (((l_some @ nat @ (^[Y0 : $i]: (X3 = (n_pl @ X1 @ Y0))))) = $true)) )),
% 3.91/0.93 inference(imp_proxy_clausification,[],[f1238])).
% 3.91/0.93 thf(f1241,plain,(
% 3.91/0.93 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = ((in @ X3 @ nat))) | (((l_some @ nat @ (^[Y0 : $i]: (X3 = (n_pl @ X1 @ Y0))))) = $true) | (((in @ X2 @ nat)) = $false) | (((in @ X1 @ nat)) = $false) | ((((l_some @ nat @ (^[Y0 : $i]: (X3 = (n_pl @ X2 @ Y0)))) => $false)) = $true) | ($false = ((l_some @ nat @ (^[Y0 : $i]: (X2 = (n_pl @ X1 @ Y0))))))) )),
% 3.91/0.93 inference(imp_proxy_clausification,[],[f1239])).
% 3.91/0.93 thf(f1242,plain,(
% 3.91/0.93 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = $true) | ($false = ((l_some @ nat @ (^[Y0 : $i]: (X3 = (n_pl @ X2 @ Y0)))))) | (((in @ X1 @ nat)) = $false) | (((l_some @ nat @ (^[Y0 : $i]: (X3 = (n_pl @ X1 @ Y0))))) = $true) | (((in @ X2 @ nat)) = $false) | ($false = ((in @ X3 @ nat))) | ($false = ((l_some @ nat @ (^[Y0 : $i]: (X2 = (n_pl @ X1 @ Y0))))))) )),
% 3.91/0.93 inference(imp_proxy_clausification,[],[f1241])).
% 3.91/0.93 thf(f1243,plain,(
% 3.91/0.93 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = ((l_some @ nat @ (^[Y0 : $i]: (X3 = (n_pl @ X2 @ Y0)))))) | ($false = ((l_some @ nat @ (^[Y0 : $i]: (X2 = (n_pl @ X1 @ Y0)))))) | (((in @ X2 @ nat)) = $false) | ($false = ((in @ X3 @ nat))) | (((in @ X1 @ nat)) = $false) | (((l_some @ nat @ (^[Y0 : $i]: (X3 = (n_pl @ X1 @ Y0))))) = $true)) )),
% 3.91/0.93 inference(trivial_inequality_removal,[],[f1242])).
% 3.91/0.93 thf(f1639,plain,(
% 3.91/0.93 ($true = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ nat) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ nat) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ nat) => ((((l_some @ nat @ (^[Y3 : $i]: (Y1 = (n_pl @ Y0 @ Y3)))) => $false) => (Y0 = Y1)) => ((l_some @ nat @ (^[Y3 : $i]: (Y2 = (n_pl @ Y1 @ Y3)))) => (l_some @ nat @ (^[Y3 : $i]: (Y2 = (n_pl @ Y0 @ Y3)))))))))))))))))),
% 3.91/0.93 inference(beta-eta_normalization,[],[f906])).
% 3.91/0.93 thf(f1640,plain,(
% 3.91/0.93 ( ! [X1 : $i] : (((((^[Y0 : $i]: ((in @ Y0 @ nat) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ nat) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ nat) => ((((l_some @ nat @ (^[Y3 : $i]: (Y1 = (n_pl @ Y0 @ Y3)))) => $false) => (Y0 = Y1)) => ((l_some @ nat @ (^[Y3 : $i]: (Y2 = (n_pl @ Y1 @ Y3)))) => (l_some @ nat @ (^[Y3 : $i]: (Y2 = (n_pl @ Y0 @ Y3)))))))))))))) @ X1)) = $true)) )),
% 3.91/0.93 inference(pi_proxy_clausification,[],[f1639])).
% 3.91/0.93 thf(f1641,plain,(
% 3.91/0.93 ( ! [X1 : $i] : (($true = (((in @ X1 @ nat) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ nat) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ nat) => ((((l_some @ nat @ (^[Y2 : $i]: (Y0 = (n_pl @ X1 @ Y2)))) => $false) => (X1 = Y0)) => ((l_some @ nat @ (^[Y2 : $i]: (Y1 = (n_pl @ Y0 @ Y2)))) => (l_some @ nat @ (^[Y2 : $i]: (Y1 = (n_pl @ X1 @ Y2)))))))))))))))) )),
% 3.91/0.93 inference(beta-eta_normalization,[],[f1640])).
% 3.91/0.93 thf(f1642,plain,(
% 3.91/0.93 ( ! [X1 : $i] : ((((in @ X1 @ nat)) = $false) | (((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ nat) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ nat) => ((((l_some @ nat @ (^[Y2 : $i]: (Y0 = (n_pl @ X1 @ Y2)))) => $false) => (X1 = Y0)) => ((l_some @ nat @ (^[Y2 : $i]: (Y1 = (n_pl @ Y0 @ Y2)))) => (l_some @ nat @ (^[Y2 : $i]: (Y1 = (n_pl @ X1 @ Y2))))))))))))) = $true)) )),
% 3.91/0.93 inference(imp_proxy_clausification,[],[f1641])).
% 3.91/0.93 thf(f1643,plain,(
% 3.91/0.93 ( ! [X2 : $i,X1 : $i] : ((((in @ X1 @ nat)) = $false) | ((((^[Y0 : $i]: ((in @ Y0 @ nat) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ nat) => ((((l_some @ nat @ (^[Y2 : $i]: (Y0 = (n_pl @ X1 @ Y2)))) => $false) => (X1 = Y0)) => ((l_some @ nat @ (^[Y2 : $i]: (Y1 = (n_pl @ Y0 @ Y2)))) => (l_some @ nat @ (^[Y2 : $i]: (Y1 = (n_pl @ X1 @ Y2))))))))))) @ X2)) = $true)) )),
% 3.91/0.93 inference(pi_proxy_clausification,[],[f1642])).
% 3.91/0.93 thf(f1644,plain,(
% 3.91/0.93 ( ! [X2 : $i,X1 : $i] : (((((in @ X2 @ nat) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ nat) => ((((l_some @ nat @ (^[Y1 : $i]: (X2 = (n_pl @ X1 @ Y1)))) => $false) => (X1 = X2)) => ((l_some @ nat @ (^[Y1 : $i]: (Y0 = (n_pl @ X2 @ Y1)))) => (l_some @ nat @ (^[Y1 : $i]: (Y0 = (n_pl @ X1 @ Y1))))))))))) = $true) | (((in @ X1 @ nat)) = $false)) )),
% 3.91/0.93 inference(beta-eta_normalization,[],[f1643])).
% 3.91/0.93 thf(f1645,plain,(
% 3.91/0.93 ( ! [X2 : $i,X1 : $i] : ((((in @ X2 @ nat)) = $false) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ nat) => ((((l_some @ nat @ (^[Y1 : $i]: (X2 = (n_pl @ X1 @ Y1)))) => $false) => (X1 = X2)) => ((l_some @ nat @ (^[Y1 : $i]: (Y0 = (n_pl @ X2 @ Y1)))) => (l_some @ nat @ (^[Y1 : $i]: (Y0 = (n_pl @ X1 @ Y1))))))))))) | (((in @ X1 @ nat)) = $false)) )),
% 3.91/0.93 inference(imp_proxy_clausification,[],[f1644])).
% 3.91/0.93 thf(f1646,plain,(
% 3.91/0.93 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((in @ X1 @ nat)) = $false) | (((in @ X2 @ nat)) = $false) | ($true = (((^[Y0 : $i]: ((in @ Y0 @ nat) => ((((l_some @ nat @ (^[Y1 : $i]: (X2 = (n_pl @ X1 @ Y1)))) => $false) => (X1 = X2)) => ((l_some @ nat @ (^[Y1 : $i]: (Y0 = (n_pl @ X2 @ Y1)))) => (l_some @ nat @ (^[Y1 : $i]: (Y0 = (n_pl @ X1 @ Y1)))))))) @ X3)))) )),
% 3.91/0.93 inference(pi_proxy_clausification,[],[f1645])).
% 3.91/0.93 thf(f1647,plain,(
% 3.91/0.93 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((in @ X1 @ nat)) = $false) | ($true = (((in @ X3 @ nat) => ((((l_some @ nat @ (^[Y0 : $i]: (X2 = (n_pl @ X1 @ Y0)))) => $false) => (X1 = X2)) => ((l_some @ nat @ (^[Y0 : $i]: (X3 = (n_pl @ X2 @ Y0)))) => (l_some @ nat @ (^[Y0 : $i]: (X3 = (n_pl @ X1 @ Y0))))))))) | (((in @ X2 @ nat)) = $false)) )),
% 3.91/0.93 inference(beta-eta_normalization,[],[f1646])).
% 3.91/0.93 thf(f1648,plain,(
% 3.91/0.93 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((((l_some @ nat @ (^[Y0 : $i]: (X2 = (n_pl @ X1 @ Y0)))) => $false) => (X1 = X2)) => ((l_some @ nat @ (^[Y0 : $i]: (X3 = (n_pl @ X2 @ Y0)))) => (l_some @ nat @ (^[Y0 : $i]: (X3 = (n_pl @ X1 @ Y0)))))))) | (((in @ X2 @ nat)) = $false) | ($false = ((in @ X3 @ nat))) | (((in @ X1 @ nat)) = $false)) )),
% 3.91/0.93 inference(imp_proxy_clausification,[],[f1647])).
% 3.91/0.93 thf(f1649,plain,(
% 3.91/0.93 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((in @ X1 @ nat)) = $false) | ($false = ((in @ X3 @ nat))) | ($false = ((((l_some @ nat @ (^[Y0 : $i]: (X2 = (n_pl @ X1 @ Y0)))) => $false) => (X1 = X2)))) | ((((l_some @ nat @ (^[Y0 : $i]: (X3 = (n_pl @ X2 @ Y0)))) => (l_some @ nat @ (^[Y0 : $i]: (X3 = (n_pl @ X1 @ Y0)))))) = $true) | (((in @ X2 @ nat)) = $false)) )),
% 3.91/0.93 inference(imp_proxy_clausification,[],[f1648])).
% 3.91/0.93 thf(f1650,plain,(
% 3.91/0.93 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = ((in @ X3 @ nat))) | (((X1 = X2)) = $false) | ((((l_some @ nat @ (^[Y0 : $i]: (X3 = (n_pl @ X2 @ Y0)))) => (l_some @ nat @ (^[Y0 : $i]: (X3 = (n_pl @ X1 @ Y0)))))) = $true) | (((in @ X2 @ nat)) = $false) | (((in @ X1 @ nat)) = $false)) )),
% 3.91/0.93 inference(imp_proxy_clausification,[],[f1649])).
% 3.91/0.93 thf(f1655,plain,(
% 3.91/0.93 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = ((in @ X3 @ nat))) | (((in @ X2 @ nat)) = $false) | ((((l_some @ nat @ (^[Y0 : $i]: (X3 = (n_pl @ X2 @ Y0)))) => (l_some @ nat @ (^[Y0 : $i]: (X3 = (n_pl @ X1 @ Y0)))))) = $true) | (X1 != X2) | (((in @ X1 @ nat)) = $false)) )),
% 3.91/0.93 inference(equality_proxy_clausification,[],[f1650])).
% 3.91/0.93 thf(f1656,plain,(
% 3.91/0.93 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = ((l_some @ nat @ (^[Y0 : $i]: (X3 = (n_pl @ X2 @ Y0)))))) | (((in @ X2 @ nat)) = $false) | (((l_some @ nat @ (^[Y0 : $i]: (X3 = (n_pl @ X1 @ Y0))))) = $true) | ($false = ((in @ X3 @ nat))) | (((in @ X1 @ nat)) = $false) | (X1 != X2)) )),
% 3.91/0.93 inference(imp_proxy_clausification,[],[f1655])).
% 3.91/0.93 thf(f1657,plain,(
% 3.91/0.93 ($true != ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ nat) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ nat) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ nat) => ((((l_some @ nat @ (^[Y3 : $i]: (Y1 = (n_pl @ Y0 @ Y3)))) => $false) => (Y0 = Y1)) => ((((l_some @ nat @ (^[Y3 : $i]: (Y2 = (n_pl @ Y1 @ Y3)))) => $false) => (Y1 = Y2)) => (((l_some @ nat @ (^[Y3 : $i]: (Y2 = (n_pl @ Y0 @ Y3)))) => $false) => (Y0 = Y2)))))))))))))))),
% 3.91/0.93 inference(beta-eta_normalization,[],[f887])).
% 3.91/0.93 thf(f1658,plain,(
% 3.91/0.93 ((((^[Y0 : $i]: ((in @ Y0 @ nat) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ nat) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ nat) => ((((l_some @ nat @ (^[Y3 : $i]: (Y1 = (n_pl @ Y0 @ Y3)))) => $false) => (Y0 = Y1)) => ((((l_some @ nat @ (^[Y3 : $i]: (Y2 = (n_pl @ Y1 @ Y3)))) => $false) => (Y1 = Y2)) => (((l_some @ nat @ (^[Y3 : $i]: (Y2 = (n_pl @ Y0 @ Y3)))) => $false) => (Y0 = Y2)))))))))))) @ sK23)) = $false)),
% 3.91/0.93 inference(sigma_proxy_clausification,[],[f1657])).
% 3.91/0.94 thf(f1659,plain,(
% 3.91/0.94 ((((in @ sK23 @ nat) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ nat) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ nat) => ((((l_some @ nat @ (^[Y2 : $i]: (Y0 = (n_pl @ sK23 @ Y2)))) => $false) => (sK23 = Y0)) => ((((l_some @ nat @ (^[Y2 : $i]: (Y1 = (n_pl @ Y0 @ Y2)))) => $false) => (Y0 = Y1)) => (((l_some @ nat @ (^[Y2 : $i]: (Y1 = (n_pl @ sK23 @ Y2)))) => $false) => (sK23 = Y1)))))))))))) = $false)),
% 3.91/0.94 inference(beta-eta_normalization,[],[f1658])).
% 3.91/0.94 thf(f1660,plain,(
% 3.91/0.94 (((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ nat) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ nat) => ((((l_some @ nat @ (^[Y2 : $i]: (Y0 = (n_pl @ sK23 @ Y2)))) => $false) => (sK23 = Y0)) => ((((l_some @ nat @ (^[Y2 : $i]: (Y1 = (n_pl @ Y0 @ Y2)))) => $false) => (Y0 = Y1)) => (((l_some @ nat @ (^[Y2 : $i]: (Y1 = (n_pl @ sK23 @ Y2)))) => $false) => (sK23 = Y1))))))))))) = $false)),
% 3.91/0.94 inference(imp_proxy_clausification,[],[f1659])).
% 3.91/0.94 thf(f1661,plain,(
% 3.91/0.94 (((in @ sK23 @ nat)) = $true)),
% 3.91/0.94 inference(imp_proxy_clausification,[],[f1659])).
% 3.91/0.94 thf(f1662,plain,(
% 3.91/0.94 ($false = (((^[Y0 : $i]: ((in @ Y0 @ nat) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ nat) => ((((l_some @ nat @ (^[Y2 : $i]: (Y0 = (n_pl @ sK23 @ Y2)))) => $false) => (sK23 = Y0)) => ((((l_some @ nat @ (^[Y2 : $i]: (Y1 = (n_pl @ Y0 @ Y2)))) => $false) => (Y0 = Y1)) => (((l_some @ nat @ (^[Y2 : $i]: (Y1 = (n_pl @ sK23 @ Y2)))) => $false) => (sK23 = Y1))))))))) @ sK24)))),
% 3.91/0.94 inference(sigma_proxy_clausification,[],[f1660])).
% 3.91/0.94 thf(f1663,plain,(
% 3.91/0.94 ($false = (((in @ sK24 @ nat) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ nat) => ((((l_some @ nat @ (^[Y1 : $i]: (sK24 = (n_pl @ sK23 @ Y1)))) => $false) => (sK23 = sK24)) => ((((l_some @ nat @ (^[Y1 : $i]: (Y0 = (n_pl @ sK24 @ Y1)))) => $false) => (sK24 = Y0)) => (((l_some @ nat @ (^[Y1 : $i]: (Y0 = (n_pl @ sK23 @ Y1)))) => $false) => (sK23 = Y0))))))))))),
% 3.91/0.94 inference(beta-eta_normalization,[],[f1662])).
% 3.91/0.94 thf(f1664,plain,(
% 3.91/0.94 ($false = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ nat) => ((((l_some @ nat @ (^[Y1 : $i]: (sK24 = (n_pl @ sK23 @ Y1)))) => $false) => (sK23 = sK24)) => ((((l_some @ nat @ (^[Y1 : $i]: (Y0 = (n_pl @ sK24 @ Y1)))) => $false) => (sK24 = Y0)) => (((l_some @ nat @ (^[Y1 : $i]: (Y0 = (n_pl @ sK23 @ Y1)))) => $false) => (sK23 = Y0)))))))))),
% 3.91/0.94 inference(imp_proxy_clausification,[],[f1663])).
% 3.91/0.94 thf(f1665,plain,(
% 3.91/0.94 (((in @ sK24 @ nat)) = $true)),
% 3.91/0.94 inference(imp_proxy_clausification,[],[f1663])).
% 3.91/0.94 thf(f1666,plain,(
% 3.91/0.94 ((((^[Y0 : $i]: ((in @ Y0 @ nat) => ((((l_some @ nat @ (^[Y1 : $i]: (sK24 = (n_pl @ sK23 @ Y1)))) => $false) => (sK23 = sK24)) => ((((l_some @ nat @ (^[Y1 : $i]: (Y0 = (n_pl @ sK24 @ Y1)))) => $false) => (sK24 = Y0)) => (((l_some @ nat @ (^[Y1 : $i]: (Y0 = (n_pl @ sK23 @ Y1)))) => $false) => (sK23 = Y0)))))) @ sK25)) = $false)),
% 3.91/0.94 inference(sigma_proxy_clausification,[],[f1664])).
% 3.91/0.94 thf(f1667,plain,(
% 3.91/0.94 ($false = (((in @ sK25 @ nat) => ((((l_some @ nat @ (^[Y0 : $i]: (sK24 = (n_pl @ sK23 @ Y0)))) => $false) => (sK23 = sK24)) => ((((l_some @ nat @ (^[Y0 : $i]: (sK25 = (n_pl @ sK24 @ Y0)))) => $false) => (sK24 = sK25)) => (((l_some @ nat @ (^[Y0 : $i]: (sK25 = (n_pl @ sK23 @ Y0)))) => $false) => (sK23 = sK25)))))))),
% 3.91/0.94 inference(beta-eta_normalization,[],[f1666])).
% 3.91/0.94 thf(f1668,plain,(
% 3.91/0.94 ((((((l_some @ nat @ (^[Y0 : $i]: (sK24 = (n_pl @ sK23 @ Y0)))) => $false) => (sK23 = sK24)) => ((((l_some @ nat @ (^[Y0 : $i]: (sK25 = (n_pl @ sK24 @ Y0)))) => $false) => (sK24 = sK25)) => (((l_some @ nat @ (^[Y0 : $i]: (sK25 = (n_pl @ sK23 @ Y0)))) => $false) => (sK23 = sK25))))) = $false)),
% 3.91/0.94 inference(imp_proxy_clausification,[],[f1667])).
% 3.91/0.94 thf(f1669,plain,(
% 3.91/0.94 (((in @ sK25 @ nat)) = $true)),
% 3.91/0.94 inference(imp_proxy_clausification,[],[f1667])).
% 3.91/0.94 thf(f1670,plain,(
% 3.91/0.94 ((((((l_some @ nat @ (^[Y0 : $i]: (sK25 = (n_pl @ sK24 @ Y0)))) => $false) => (sK24 = sK25)) => (((l_some @ nat @ (^[Y0 : $i]: (sK25 = (n_pl @ sK23 @ Y0)))) => $false) => (sK23 = sK25)))) = $false)),
% 3.91/0.94 inference(imp_proxy_clausification,[],[f1668])).
% 3.91/0.94 thf(f1671,plain,(
% 3.91/0.94 ($true = ((((l_some @ nat @ (^[Y0 : $i]: (sK24 = (n_pl @ sK23 @ Y0)))) => $false) => (sK23 = sK24))))),
% 3.91/0.94 inference(imp_proxy_clausification,[],[f1668])).
% 3.91/0.94 thf(f1672,plain,(
% 3.91/0.94 ($false = (((l_some @ nat @ (^[Y0 : $i]: (sK24 = (n_pl @ sK23 @ Y0)))) => $false))) | ($true = ((sK23 = sK24)))),
% 3.91/0.94 inference(imp_proxy_clausification,[],[f1671])).
% 3.91/0.94 thf(f1674,plain,(
% 3.91/0.94 ($true = ((sK23 = sK24))) | ($true = ((l_some @ nat @ (^[Y0 : $i]: (sK24 = (n_pl @ sK23 @ Y0))))))),
% 3.91/0.94 inference(imp_proxy_clausification,[],[f1672])).
% 3.91/0.94 thf(f1675,plain,(
% 3.91/0.94 (sK23 = sK24) | ($true = ((l_some @ nat @ (^[Y0 : $i]: (sK24 = (n_pl @ sK23 @ Y0))))))),
% 3.91/0.94 inference(equality_proxy_clausification,[],[f1674])).
% 3.91/0.94 thf(f1677,plain,(
% 3.91/0.94 (((((l_some @ nat @ (^[Y0 : $i]: (sK25 = (n_pl @ sK23 @ Y0)))) => $false) => (sK23 = sK25))) = $false)),
% 3.91/0.94 inference(imp_proxy_clausification,[],[f1670])).
% 3.91/0.94 thf(f1678,plain,(
% 3.91/0.94 (((((l_some @ nat @ (^[Y0 : $i]: (sK25 = (n_pl @ sK24 @ Y0)))) => $false) => (sK24 = sK25))) = $true)),
% 3.91/0.94 inference(imp_proxy_clausification,[],[f1670])).
% 3.91/0.94 thf(f1679,plain,(
% 3.91/0.94 ($true = ((sK24 = sK25))) | ($false = (((l_some @ nat @ (^[Y0 : $i]: (sK25 = (n_pl @ sK24 @ Y0)))) => $false)))),
% 3.91/0.94 inference(imp_proxy_clausification,[],[f1678])).
% 3.91/0.94 thf(f1680,plain,(
% 3.91/0.94 ($false = (((l_some @ nat @ (^[Y0 : $i]: (sK25 = (n_pl @ sK24 @ Y0)))) => $false))) | (sK25 = sK24)),
% 3.91/0.94 inference(equality_proxy_clausification,[],[f1679])).
% 3.91/0.94 thf(f1682,plain,(
% 3.91/0.94 (sK25 = sK24) | (((l_some @ nat @ (^[Y0 : $i]: (sK25 = (n_pl @ sK24 @ Y0))))) = $true)),
% 3.91/0.94 inference(imp_proxy_clausification,[],[f1680])).
% 3.91/0.94 thf(f1683,plain,(
% 3.91/0.94 (((sK23 = sK25)) = $false)),
% 3.91/0.94 inference(imp_proxy_clausification,[],[f1677])).
% 3.91/0.94 thf(f1684,plain,(
% 3.91/0.94 ((((l_some @ nat @ (^[Y0 : $i]: (sK25 = (n_pl @ sK23 @ Y0)))) => $false)) = $true)),
% 3.91/0.94 inference(imp_proxy_clausification,[],[f1677])).
% 3.91/0.94 thf(f1685,plain,(
% 3.91/0.94 ($false = $true) | ($false = ((l_some @ nat @ (^[Y0 : $i]: (sK25 = (n_pl @ sK23 @ Y0))))))),
% 3.91/0.94 inference(imp_proxy_clausification,[],[f1684])).
% 3.91/0.94 thf(f1686,plain,(
% 3.91/0.94 ($false = ((l_some @ nat @ (^[Y0 : $i]: (sK25 = (n_pl @ sK23 @ Y0))))))),
% 3.91/0.94 inference(trivial_inequality_removal,[],[f1685])).
% 3.91/0.94 thf(f1687,plain,(
% 3.91/0.94 (sK25 != sK23)),
% 3.91/0.94 inference(equality_proxy_clausification,[],[f1683])).
% 3.91/0.94 thf(f1694,definition,(
% 3.91/0.94 spl26_1 <=> ($true = ((l_some @ nat @ (^[Y0 : $i]: (sK24 = (n_pl @ sK23 @ Y0))))))),
% 3.91/0.94 introduced(definition,[new_symbols(definition,[spl26_1])],[avatar_definition])).
% 3.91/0.94 thf(f1696,plain,(
% 3.91/0.94 ($true = ((l_some @ nat @ (^[Y0 : $i]: (sK24 = (n_pl @ sK23 @ Y0)))))) | ~spl26_1),
% 3.91/0.94 inference(avatar_component_clause,[],[f1694])).
% 3.91/0.94 thf(f1698,definition,(
% 3.91/0.94 spl26_2 <=> (sK23 = sK24)),
% 3.91/0.94 introduced(definition,[new_symbols(definition,[spl26_2])],[avatar_definition])).
% 3.91/0.94 thf(f1700,plain,(
% 3.91/0.94 (sK23 = sK24) | ~spl26_2),
% 3.91/0.94 inference(avatar_component_clause,[],[f1698])).
% 3.91/0.94 thf(f1701,plain,(
% 3.91/0.94 spl26_1 | spl26_2),
% 3.91/0.94 inference(avatar_split_clause,[],[f1675,f1698,f1694])).
% 3.91/0.94 thf(f1703,definition,(
% 3.91/0.94 spl26_3 <=> (sK25 = sK24)),
% 3.91/0.94 introduced(definition,[new_symbols(definition,[spl26_3])],[avatar_definition])).
% 3.91/0.94 thf(f1705,plain,(
% 3.91/0.94 (sK25 = sK24) | ~spl26_3),
% 3.91/0.94 inference(avatar_component_clause,[],[f1703])).
% 3.91/0.94 thf(f1707,definition,(
% 3.91/0.94 spl26_4 <=> (((l_some @ nat @ (^[Y0 : $i]: (sK25 = (n_pl @ sK24 @ Y0))))) = $true)),
% 3.91/0.94 introduced(definition,[new_symbols(definition,[spl26_4])],[avatar_definition])).
% 3.91/0.94 thf(f1709,plain,(
% 3.91/0.94 (((l_some @ nat @ (^[Y0 : $i]: (sK25 = (n_pl @ sK24 @ Y0))))) = $true) | ~spl26_4),
% 3.91/0.94 inference(avatar_component_clause,[],[f1707])).
% 3.91/0.94 thf(f1710,plain,(
% 3.91/0.94 spl26_3 | spl26_4),
% 3.91/0.94 inference(avatar_split_clause,[],[f1682,f1707,f1703])).
% 3.91/0.94 thf(f1714,plain,(
% 3.91/0.94 ( ! [X2 : ($i > $i > $i),X3 : $i,X0 : ($i > $i),X1 : ($i > $i > $i)] : ((nat != ((X0 @ (sK6 @ (^[Y0 : $i]: (l_some @ (X0 @ Y0) @ (^[Y1 : $i]: ((X1 @ Y0 @ Y1) = (X2 @ Y0 @ Y1))))))))) | ($true != $true) | ($true = (((^[Y0 : $i]: (l_some @ (X0 @ Y0) @ ((^[Y1 : $i]: ((^[Y2 : $i]: ((X1 @ Y1 @ Y2) = (X2 @ Y1 @ Y2))))) @ Y0))) @ X3))) | (((X1 @ (sK6 @ (^[Y0 : $i]: (l_some @ (X0 @ Y0) @ (^[Y1 : $i]: ((X1 @ Y0 @ Y1) = (X2 @ Y0 @ Y1)))))))) != (^[Y0 : $i]: (sK24))) | (((n_pl @ sK23)) != ((X2 @ (sK6 @ (^[Y0 : $i]: (l_some @ (X0 @ Y0) @ (^[Y1 : $i]: ((X1 @ Y0 @ Y1) = (X2 @ Y0 @ Y1)))))))))) ) | ~spl26_1),
% 3.91/0.94 inference(constrained_superposition,[],[f771,f1696])).
% 3.91/0.94 thf(f1718,plain,(
% 3.91/0.94 ( ! [X2 : ($i > $i > $i),X3 : $i,X0 : ($i > $i),X1 : ($i > $i > $i)] : ((nat != ((X0 @ (sK6 @ (^[Y0 : $i]: (l_some @ (X0 @ Y0) @ (^[Y1 : $i]: ((X1 @ Y0 @ Y1) = (X2 @ Y0 @ Y1))))))))) | (((n_pl @ sK23)) != ((X2 @ (sK6 @ (^[Y0 : $i]: (l_some @ (X0 @ Y0) @ (^[Y1 : $i]: ((X1 @ Y0 @ Y1) = (X2 @ Y0 @ Y1))))))))) | (((X1 @ (sK6 @ (^[Y0 : $i]: (l_some @ (X0 @ Y0) @ (^[Y1 : $i]: ((X1 @ Y0 @ Y1) = (X2 @ Y0 @ Y1)))))))) != (^[Y0 : $i]: (sK24))) | ($true = (((^[Y0 : $i]: (l_some @ (X0 @ Y0) @ ((^[Y1 : $i]: ((^[Y2 : $i]: ((X1 @ Y1 @ Y2) = (X2 @ Y1 @ Y2))))) @ Y0))) @ X3)))) ) | ~spl26_1),
% 3.91/0.94 inference(trivial_inequality_removal,[],[f1714])).
% 3.91/0.94 thf(f1719,plain,(
% 3.91/0.94 ( ! [X2 : ($i > $i > $i),X3 : $i,X0 : ($i > $i),X1 : ($i > $i > $i)] : ((((n_pl @ sK23)) != ((X2 @ (sK6 @ (^[Y0 : $i]: (l_some @ (X0 @ Y0) @ (^[Y1 : $i]: ((X1 @ Y0 @ Y1) = (X2 @ Y0 @ Y1))))))))) | (((X1 @ (sK6 @ (^[Y0 : $i]: (l_some @ (X0 @ Y0) @ (^[Y1 : $i]: ((X1 @ Y0 @ Y1) = (X2 @ Y0 @ Y1)))))))) != (^[Y0 : $i]: (sK24))) | ($true = ((l_some @ (X0 @ X3) @ (^[Y0 : $i]: ((X1 @ X3 @ Y0) = (X2 @ X3 @ Y0)))))) | (nat != ((X0 @ (sK6 @ (^[Y0 : $i]: (l_some @ (X0 @ Y0) @ (^[Y1 : $i]: ((X1 @ Y0 @ Y1) = (X2 @ Y0 @ Y1)))))))))) ) | ~spl26_1),
% 3.91/0.94 inference(beta-eta_normalization,[],[f1718])).
% 3.91/0.94 thf(f1878,plain,(
% 3.91/0.94 ( ! [X2 : ($i > $i > $i),X3 : $i,X0 : ($i > $i > $i),X1 : ($i > $i)] : ((((X0 @ (sK6 @ (^[Y0 : $i]: (l_some @ (X1 @ Y0) @ (^[Y1 : $i]: ((X0 @ Y0 @ Y1) = ((^[Y2 : $i]: ((^[Y3 : $i]: (n_pl @ (X2 @ Y2 @ Y3) @ ((^[Y4 : $i]: ((^[Y5 : $i]: (Y5)))) @ Y2 @ Y3))))) @ Y0 @ Y1)))))))) != (^[Y0 : $i]: (sK24))) | (((X2 @ (sK6 @ (^[Y0 : $i]: (l_some @ (X1 @ Y0) @ (^[Y1 : $i]: ((X0 @ Y0 @ Y1) = (n_pl @ (X2 @ Y0 @ Y1) @ Y1)))))))) != (^[Y0 : $i]: (sK23))) | (nat != ((X1 @ (sK6 @ (^[Y0 : $i]: (l_some @ (X1 @ Y0) @ (^[Y1 : $i]: ((X0 @ Y0 @ Y1) = ((^[Y2 : $i]: ((^[Y3 : $i]: (n_pl @ (X2 @ Y2 @ Y3) @ ((^[Y4 : $i]: ((^[Y5 : $i]: (Y5)))) @ Y2 @ Y3))))) @ Y0 @ Y1))))))))) | (((l_some @ (X1 @ X3) @ (^[Y0 : $i]: ((X0 @ X3 @ Y0) = ((^[Y1 : $i]: ((^[Y2 : $i]: (n_pl @ (X2 @ Y1 @ Y2) @ ((^[Y3 : $i]: ((^[Y4 : $i]: (Y4)))) @ Y1 @ Y2))))) @ X3 @ Y0))))) = $true)) ) | ~spl26_1),
% 3.91/0.94 inference(equality_resolution,[],[f1719])).
% 3.91/0.94 thf(f1879,plain,(
% 3.91/0.94 ( ! [X2 : ($i > $i > $i),X3 : $i,X0 : ($i > $i > $i),X1 : ($i > $i)] : ((((X2 @ (sK6 @ (^[Y0 : $i]: (l_some @ (X1 @ Y0) @ (^[Y1 : $i]: ((X0 @ Y0 @ Y1) = (n_pl @ (X2 @ Y0 @ Y1) @ Y1)))))))) != (^[Y0 : $i]: (sK23))) | (((l_some @ (X1 @ X3) @ (^[Y0 : $i]: ((X0 @ X3 @ Y0) = (n_pl @ (X2 @ X3 @ Y0) @ Y0))))) = $true) | (((X0 @ (sK6 @ (^[Y0 : $i]: (l_some @ (X1 @ Y0) @ (^[Y1 : $i]: ((X0 @ Y0 @ Y1) = (n_pl @ (X2 @ Y0 @ Y1) @ Y1)))))))) != (^[Y0 : $i]: (sK24))) | (nat != ((X1 @ (sK6 @ (^[Y0 : $i]: (l_some @ (X1 @ Y0) @ (^[Y1 : $i]: ((X0 @ Y0 @ Y1) = (n_pl @ (X2 @ Y0 @ Y1) @ Y1)))))))))) ) | ~spl26_1),
% 3.91/0.94 inference(beta-eta_normalization,[],[f1878])).
% 3.91/0.94 thf(f1884,plain,(
% 3.91/0.94 ( ! [X2 : ($i > $i > $i),X0 : ($i > $i),X1 : $i] : ((nat != ((X0 @ (sK6 @ (^[Y0 : $i]: (l_some @ (X0 @ Y0) @ (^[Y1 : $i]: ((X2 @ Y0 @ Y1) = (n_pl @ ((^[Y2 : $i]: ((^[Y3 : $i]: (sK23)))) @ Y0 @ Y1) @ Y1))))))))) | (((l_some @ (X0 @ X1) @ (^[Y0 : $i]: ((X2 @ X1 @ Y0) = (n_pl @ ((^[Y1 : $i]: ((^[Y2 : $i]: (sK23)))) @ X1 @ Y0) @ Y0))))) = $true) | ((^[Y0 : $i]: (sK24)) != ((X2 @ (sK6 @ (^[Y0 : $i]: (l_some @ (X0 @ Y0) @ (^[Y1 : $i]: ((X2 @ Y0 @ Y1) = (n_pl @ ((^[Y2 : $i]: ((^[Y3 : $i]: (sK23)))) @ Y0 @ Y1) @ Y1)))))))))) ) | ~spl26_1),
% 3.91/0.94 inference(equality_resolution,[],[f1879])).
% 3.91/0.94 thf(f1885,plain,(
% 3.91/0.94 ( ! [X2 : ($i > $i > $i),X0 : ($i > $i),X1 : $i] : (((^[Y0 : $i]: (sK24)) != ((X2 @ (sK6 @ (^[Y0 : $i]: (l_some @ (X0 @ Y0) @ (^[Y1 : $i]: ((X2 @ Y0 @ Y1) = (n_pl @ sK23 @ Y1))))))))) | (nat != ((X0 @ (sK6 @ (^[Y0 : $i]: (l_some @ (X0 @ Y0) @ (^[Y1 : $i]: ((X2 @ Y0 @ Y1) = (n_pl @ sK23 @ Y1))))))))) | (((l_some @ (X0 @ X1) @ (^[Y0 : $i]: ((X2 @ X1 @ Y0) = (n_pl @ sK23 @ Y0))))) = $true)) ) | ~spl26_1),
% 3.91/0.94 inference(beta-eta_normalization,[],[f1884])).
% 3.91/0.94 thf(f1887,plain,(
% 3.91/0.94 ( ! [X2 : ($i > $i > $i),X0 : ($i > $i),X1 : $i] : ((((X2 @ (sK6 @ (^[Y0 : $i]: (l_some @ (X0 @ Y0) @ (^[Y1 : $i]: ((X2 @ Y0 @ Y1) = (n_pl @ sK23 @ Y1)))))) @ (sK30 @ X0 @ X2))) != (((^[Y0 : $i]: (sK24)) @ (sK30 @ X0 @ X2)))) | (((l_some @ (X0 @ X1) @ (^[Y0 : $i]: ((X2 @ X1 @ Y0) = (n_pl @ sK23 @ Y0))))) = $true) | (nat != ((X0 @ (sK6 @ (^[Y0 : $i]: (l_some @ (X0 @ Y0) @ (^[Y1 : $i]: ((X2 @ Y0 @ Y1) = (n_pl @ sK23 @ Y1)))))))))) ) | ~spl26_1),
% 3.91/0.94 inference(negative_extensionality,[],[f1885])).
% 3.91/0.94 thf(f1889,plain,(
% 3.91/0.94 ( ! [X2 : ($i > $i > $i),X0 : ($i > $i),X1 : $i] : ((((X2 @ (sK6 @ (^[Y0 : $i]: (l_some @ (X0 @ Y0) @ (^[Y1 : $i]: ((X2 @ Y0 @ Y1) = (n_pl @ sK23 @ Y1)))))) @ (sK30 @ X0 @ X2))) != sK24) | (nat != ((X0 @ (sK6 @ (^[Y0 : $i]: (l_some @ (X0 @ Y0) @ (^[Y1 : $i]: ((X2 @ Y0 @ Y1) = (n_pl @ sK23 @ Y1))))))))) | (((l_some @ (X0 @ X1) @ (^[Y0 : $i]: ((X2 @ X1 @ Y0) = (n_pl @ sK23 @ Y0))))) = $true)) ) | ~spl26_1),
% 3.91/0.94 inference(beta-eta_normalization,[],[f1887])).
% 3.91/0.94 thf(f1923,plain,(
% 3.91/0.94 ( ! [X0 : ($i > $i),X1 : $i] : ((sK24 != sK24) | (nat != ((X0 @ (sK6 @ (^[Y0 : $i]: (l_some @ (X0 @ Y0) @ (^[Y1 : $i]: (((^[Y2 : $i]: ((^[Y3 : $i]: (sK25)))) @ Y0 @ Y1) = (n_pl @ sK23 @ Y1))))))))) | (((l_some @ (X0 @ X1) @ (^[Y0 : $i]: (((^[Y1 : $i]: ((^[Y2 : $i]: (sK25)))) @ X1 @ Y0) = (n_pl @ sK23 @ Y0))))) = $true)) ) | (~spl26_1 | ~spl26_3)),
% 3.91/0.94 inference(constrained_superposition,[],[f1889,f1705])).
% 3.91/0.94 thf(f1926,plain,(
% 3.91/0.94 ( ! [X0 : ($i > $i),X1 : $i] : ((((l_some @ (X0 @ X1) @ (^[Y0 : $i]: (((^[Y1 : $i]: ((^[Y2 : $i]: (sK25)))) @ X1 @ Y0) = (n_pl @ sK23 @ Y0))))) = $true) | (nat != ((X0 @ (sK6 @ (^[Y0 : $i]: (l_some @ (X0 @ Y0) @ (^[Y1 : $i]: (((^[Y2 : $i]: ((^[Y3 : $i]: (sK25)))) @ Y0 @ Y1) = (n_pl @ sK23 @ Y1)))))))))) ) | (~spl26_1 | ~spl26_3)),
% 3.91/0.94 inference(trivial_inequality_removal,[],[f1923])).
% 3.91/0.94 thf(f1927,plain,(
% 3.91/0.94 ( ! [X0 : ($i > $i),X1 : $i] : ((nat != ((X0 @ (sK6 @ (^[Y0 : $i]: (l_some @ (X0 @ Y0) @ (^[Y1 : $i]: (sK25 = (n_pl @ sK23 @ Y1))))))))) | (((l_some @ (X0 @ X1) @ (^[Y0 : $i]: (sK25 = (n_pl @ sK23 @ Y0))))) = $true)) ) | (~spl26_1 | ~spl26_3)),
% 3.91/0.94 inference(beta-eta_normalization,[],[f1926])).
% 3.91/0.94 thf(f1955,plain,(
% 3.91/0.94 ( ! [X0 : $i] : (($true = ((l_some @ ((^[Y0 : $i]: (nat)) @ X0) @ (^[Y0 : $i]: (sK25 = (n_pl @ sK23 @ Y0))))))) ) | (~spl26_1 | ~spl26_3)),
% 3.91/0.94 inference(equality_resolution,[],[f1927])).
% 3.91/0.94 thf(f1956,plain,(
% 3.91/0.94 ($true = ((l_some @ nat @ (^[Y0 : $i]: (sK25 = (n_pl @ sK23 @ Y0)))))) | (~spl26_1 | ~spl26_3)),
% 3.91/0.94 inference(beta-eta_normalization,[],[f1955])).
% 3.91/0.94 thf(f1959,plain,(
% 3.91/0.94 ($false = $true) | (~spl26_1 | ~spl26_3)),
% 3.91/0.94 inference(forward_demodulation,[],[f1956,f1686])).
% 3.91/0.94 thf(f1960,plain,(
% 3.91/0.94 $false | (~spl26_1 | ~spl26_3)),
% 3.91/0.94 inference(trivial_inequality_removal,[],[f1959])).
% 3.91/0.94 thf(f1961,plain,(
% 3.91/0.94 ~spl26_1 | ~spl26_3),
% 3.91/0.94 inference(avatar_contradiction_clause,[],[f1960])).
% 3.91/0.94 thf(f2005,plain,(
% 3.91/0.94 ( ! [X0 : $i] : ((sK24 != X0) | ($false = $true) | (((in @ sK24 @ nat)) = $false) | (((l_some @ nat @ (^[Y0 : $i]: (sK25 = (n_pl @ X0 @ Y0))))) = $true) | (((in @ sK25 @ nat)) = $false) | (((in @ X0 @ nat)) = $false)) ) | ~spl26_4),
% 3.91/0.94 inference(constrained_superposition,[],[f1709,f1656])).
% 3.91/0.94 thf(f2011,plain,(
% 3.91/0.94 (((in @ sK25 @ nat)) = $false) | ($false = $true) | (((in @ sK24 @ nat)) = $false) | (((l_some @ nat @ (^[Y0 : $i]: (sK24 = (n_pl @ sK25 @ Y0))))) = $false) | ~spl26_4),
% 3.91/0.94 inference(constrained_superposition,[],[f987,f1709])).
% 3.91/0.94 thf(f2015,plain,(
% 3.91/0.94 (((l_some @ nat @ (^[Y0 : $i]: (sK24 = (n_pl @ sK25 @ Y0))))) = $false) | (((in @ sK25 @ nat)) = $false) | (((in @ sK24 @ nat)) = $false) | ~spl26_4),
% 3.91/0.94 inference(trivial_inequality_removal,[],[f2011])).
% 3.91/0.94 thf(f2018,plain,(
% 3.91/0.94 ( ! [X0 : $i] : ((sK24 != X0) | (((in @ sK24 @ nat)) = $false) | (((in @ sK25 @ nat)) = $false) | (((l_some @ nat @ (^[Y0 : $i]: (sK25 = (n_pl @ X0 @ Y0))))) = $true) | (((in @ X0 @ nat)) = $false)) ) | ~spl26_4),
% 3.91/0.94 inference(trivial_inequality_removal,[],[f2005])).
% 3.91/0.94 thf(f2026,plain,(
% 3.91/0.94 (((in @ sK24 @ nat)) = $false) | ($false = $true) | (((l_some @ nat @ (^[Y0 : $i]: (sK24 = (n_pl @ sK25 @ Y0))))) = $false) | ~spl26_4),
% 3.91/0.94 inference(forward_demodulation,[],[f2015,f1669])).
% 3.91/0.94 thf(f2027,plain,(
% 3.91/0.94 (((in @ sK24 @ nat)) = $false) | (((l_some @ nat @ (^[Y0 : $i]: (sK24 = (n_pl @ sK25 @ Y0))))) = $false) | ~spl26_4),
% 3.91/0.94 inference(trivial_inequality_removal,[],[f2026])).
% 3.91/0.94 thf(f2028,plain,(
% 3.91/0.94 ( ! [X0 : $i] : ((((l_some @ nat @ (^[Y0 : $i]: (sK25 = (n_pl @ X0 @ Y0))))) = $true) | (((in @ sK25 @ nat)) = $false) | ($false = $true) | (sK24 != X0) | (((in @ X0 @ nat)) = $false)) ) | ~spl26_4),
% 3.91/0.94 inference(forward_demodulation,[],[f2018,f1665])).
% 3.91/0.94 thf(f2029,plain,(
% 3.91/0.94 ( ! [X0 : $i] : ((((l_some @ nat @ (^[Y0 : $i]: (sK25 = (n_pl @ X0 @ Y0))))) = $true) | (sK24 != X0) | (((in @ X0 @ nat)) = $false) | (((in @ sK25 @ nat)) = $false)) ) | ~spl26_4),
% 3.91/0.94 inference(trivial_inequality_removal,[],[f2028])).
% 3.91/0.94 thf(f2038,plain,(
% 3.91/0.94 (((l_some @ nat @ (^[Y0 : $i]: (sK24 = (n_pl @ sK25 @ Y0))))) = $false) | ($false = $true) | ~spl26_4),
% 3.91/0.94 inference(forward_demodulation,[],[f2027,f1665])).
% 3.91/0.94 thf(f2039,plain,(
% 3.91/0.94 (((l_some @ nat @ (^[Y0 : $i]: (sK24 = (n_pl @ sK25 @ Y0))))) = $false) | ~spl26_4),
% 3.91/0.94 inference(trivial_inequality_removal,[],[f2038])).
% 3.91/0.94 thf(f2040,plain,(
% 3.91/0.94 ( ! [X0 : $i] : ((((l_some @ nat @ (^[Y0 : $i]: (sK25 = (n_pl @ X0 @ Y0))))) = $true) | (((in @ X0 @ nat)) = $false) | ($false = $true) | (sK24 != X0)) ) | ~spl26_4),
% 3.91/0.94 inference(forward_demodulation,[],[f2029,f1669])).
% 3.91/0.94 thf(f2041,plain,(
% 3.91/0.94 ( ! [X0 : $i] : ((sK24 != X0) | (((in @ X0 @ nat)) = $false) | (((l_some @ nat @ (^[Y0 : $i]: (sK25 = (n_pl @ X0 @ Y0))))) = $true)) ) | ~spl26_4),
% 3.91/0.94 inference(trivial_inequality_removal,[],[f2040])).
% 3.91/0.94 thf(f2053,plain,(
% 3.91/0.94 ( ! [X0 : $i] : ((((l_some @ nat @ (^[Y0 : $i]: (sK23 = (n_pl @ X0 @ Y0))))) = $false) | (((l_some @ nat @ (^[Y0 : $i]: (sK24 = (n_pl @ X0 @ Y0))))) = $true) | (((in @ sK23 @ nat)) = $false) | ($false = $true) | (((in @ X0 @ nat)) = $false) | (((in @ sK24 @ nat)) = $false)) ) | ~spl26_1),
% 3.91/0.94 inference(constrained_superposition,[],[f1243,f1696])).
% 3.91/0.94 thf(f2062,plain,(
% 3.91/0.94 ( ! [X0 : $i] : ((((in @ X0 @ nat)) = $false) | (((l_some @ nat @ (^[Y0 : $i]: (sK23 = (n_pl @ X0 @ Y0))))) = $false) | (((in @ sK23 @ nat)) = $false) | (((l_some @ nat @ (^[Y0 : $i]: (sK24 = (n_pl @ X0 @ Y0))))) = $true) | (((in @ sK24 @ nat)) = $false)) ) | ~spl26_1),
% 3.91/0.94 inference(trivial_inequality_removal,[],[f2053])).
% 3.91/0.94 thf(f2068,plain,(
% 3.91/0.94 ( ! [X0 : $i] : ((((in @ X0 @ nat)) = $false) | (((l_some @ nat @ (^[Y0 : $i]: (sK23 = (n_pl @ X0 @ Y0))))) = $false) | (((l_some @ nat @ (^[Y0 : $i]: (sK24 = (n_pl @ X0 @ Y0))))) = $true) | (((in @ sK24 @ nat)) = $false) | ($false = $true)) ) | ~spl26_1),
% 3.91/0.94 inference(forward_demodulation,[],[f2062,f1661])).
% 3.91/0.94 thf(f2069,plain,(
% 3.91/0.94 ( ! [X0 : $i] : ((((in @ X0 @ nat)) = $false) | (((l_some @ nat @ (^[Y0 : $i]: (sK23 = (n_pl @ X0 @ Y0))))) = $false) | (((l_some @ nat @ (^[Y0 : $i]: (sK24 = (n_pl @ X0 @ Y0))))) = $true) | (((in @ sK24 @ nat)) = $false)) ) | ~spl26_1),
% 3.91/0.94 inference(trivial_inequality_removal,[],[f2068])).
% 3.91/0.94 thf(f2076,plain,(
% 3.91/0.94 ( ! [X0 : $i] : ((((in @ X0 @ nat)) = $false) | (((l_some @ nat @ (^[Y0 : $i]: (sK24 = (n_pl @ X0 @ Y0))))) = $true) | ($false = $true) | (((l_some @ nat @ (^[Y0 : $i]: (sK23 = (n_pl @ X0 @ Y0))))) = $false)) ) | ~spl26_1),
% 3.91/0.94 inference(forward_demodulation,[],[f2069,f1665])).
% 3.91/0.94 thf(f2077,plain,(
% 3.91/0.94 ( ! [X0 : $i] : ((((l_some @ nat @ (^[Y0 : $i]: (sK24 = (n_pl @ X0 @ Y0))))) = $true) | (((l_some @ nat @ (^[Y0 : $i]: (sK23 = (n_pl @ X0 @ Y0))))) = $false) | (((in @ X0 @ nat)) = $false)) ) | ~spl26_1),
% 3.91/0.94 inference(trivial_inequality_removal,[],[f2076])).
% 3.91/0.94 thf(f2097,plain,(
% 3.91/0.94 ($false = ((l_some @ nat @ (^[Y0 : $i]: (sK23 = (n_pl @ sK25 @ Y0)))))) | (((in @ sK25 @ nat)) = $false) | ($false = $true) | (~spl26_1 | ~spl26_4)),
% 3.91/0.94 inference(constrained_superposition,[],[f2039,f2077])).
% 3.91/0.94 thf(f2106,plain,(
% 3.91/0.94 (((in @ sK25 @ nat)) = $false) | ($false = ((l_some @ nat @ (^[Y0 : $i]: (sK23 = (n_pl @ sK25 @ Y0)))))) | (~spl26_1 | ~spl26_4)),
% 3.91/0.94 inference(trivial_inequality_removal,[],[f2097])).
% 3.91/0.94 thf(f2122,plain,(
% 3.91/0.94 ($false = ((l_some @ nat @ (^[Y0 : $i]: (sK23 = (n_pl @ sK25 @ Y0)))))) | ($false = $true) | (~spl26_1 | ~spl26_4)),
% 3.91/0.94 inference(forward_demodulation,[],[f2106,f1669])).
% 3.91/0.94 thf(f2123,plain,(
% 3.91/0.94 ($false = ((l_some @ nat @ (^[Y0 : $i]: (sK23 = (n_pl @ sK25 @ Y0)))))) | (~spl26_1 | ~spl26_4)),
% 3.91/0.94 inference(trivial_inequality_removal,[],[f2122])).
% 3.91/0.94 thf(f2154,plain,(
% 3.91/0.94 (((in @ sK23 @ nat)) = $false) | (((in @ sK25 @ nat)) = $false) | (sK25 = sK23) | ($true = ((l_some @ nat @ (^[Y0 : $i]: (sK23 = (n_pl @ sK25 @ Y0)))))) | ($false = $true)),
% 3.91/0.94 inference(constrained_superposition,[],[f1031,f1686])).
% 3.91/0.94 thf(f2181,plain,(
% 3.91/0.94 (((in @ sK23 @ nat)) = $false) | (((in @ sK25 @ nat)) = $false) | (sK25 = sK23) | ($true = ((l_some @ nat @ (^[Y0 : $i]: (sK23 = (n_pl @ sK25 @ Y0))))))),
% 3.91/0.94 inference(trivial_inequality_removal,[],[f2154])).
% 3.91/0.94 thf(f2193,plain,(
% 3.91/0.94 (((in @ sK23 @ nat)) = $false) | (((in @ sK25 @ nat)) = $false) | ($true = ((l_some @ nat @ (^[Y0 : $i]: (sK23 = (n_pl @ sK25 @ Y0))))))),
% 3.91/0.94 inference(forward_subsumption_resolution,[],[f2181,f1687])).
% 3.91/0.94 thf(f2200,plain,(
% 3.91/0.94 ($true = ((l_some @ nat @ (^[Y0 : $i]: (sK23 = (n_pl @ sK25 @ Y0)))))) | (((in @ sK25 @ nat)) = $false) | ($false = $true)),
% 3.91/0.94 inference(forward_demodulation,[],[f2193,f1661])).
% 3.91/0.94 thf(f2201,plain,(
% 3.91/0.94 (((in @ sK25 @ nat)) = $false) | ($true = ((l_some @ nat @ (^[Y0 : $i]: (sK23 = (n_pl @ sK25 @ Y0))))))),
% 3.91/0.94 inference(trivial_inequality_removal,[],[f2200])).
% 3.91/0.94 thf(f2208,plain,(
% 3.91/0.94 ($true = ((l_some @ nat @ (^[Y0 : $i]: (sK23 = (n_pl @ sK25 @ Y0)))))) | ($false = $true)),
% 3.91/0.94 inference(forward_demodulation,[],[f2201,f1669])).
% 3.91/0.94 thf(f2209,plain,(
% 3.91/0.94 ($true = ((l_some @ nat @ (^[Y0 : $i]: (sK23 = (n_pl @ sK25 @ Y0))))))),
% 3.91/0.94 inference(trivial_inequality_removal,[],[f2208])).
% 3.91/0.94 thf(f2213,plain,(
% 3.91/0.94 ($false = $true) | (~spl26_1 | ~spl26_4)),
% 3.91/0.94 inference(forward_demodulation,[],[f2209,f2123])).
% 3.91/0.94 thf(f2214,plain,(
% 3.91/0.94 $false | (~spl26_1 | ~spl26_4)),
% 3.91/0.94 inference(trivial_inequality_removal,[],[f2213])).
% 3.91/0.94 thf(f2215,plain,(
% 3.91/0.94 ~spl26_1 | ~spl26_4),
% 3.91/0.94 inference(avatar_contradiction_clause,[],[f2214])).
% 3.91/0.94 thf(f2226,plain,(
% 3.91/0.94 ( ! [X0 : $i] : ((sK23 != X0) | (((in @ X0 @ nat)) = $false) | (((l_some @ nat @ (^[Y0 : $i]: (sK25 = (n_pl @ X0 @ Y0))))) = $true)) ) | (~spl26_2 | ~spl26_4)),
% 3.91/0.94 inference(constrained_superposition,[],[f2041,f1700])).
% 3.91/0.94 thf(f2319,plain,(
% 3.91/0.94 (((in @ sK23 @ nat)) = $false) | ($true = ((l_some @ nat @ (^[Y0 : $i]: (sK25 = (n_pl @ sK23 @ Y0)))))) | (~spl26_2 | ~spl26_4)),
% 3.91/0.94 inference(equality_resolution,[],[f2226])).
% 3.91/0.94 thf(f2320,plain,(
% 3.91/0.94 ($true = ((l_some @ nat @ (^[Y0 : $i]: (sK25 = (n_pl @ sK23 @ Y0)))))) | ($false = $true) | (~spl26_2 | ~spl26_4)),
% 3.91/0.94 inference(forward_demodulation,[],[f2319,f1661])).
% 3.91/0.94 thf(f2321,plain,(
% 3.91/0.94 ($true = ((l_some @ nat @ (^[Y0 : $i]: (sK25 = (n_pl @ sK23 @ Y0)))))) | (~spl26_2 | ~spl26_4)),
% 3.91/0.94 inference(trivial_inequality_removal,[],[f2320])).
% 3.91/0.94 thf(f2322,plain,(
% 3.91/0.94 ($false = $true) | (~spl26_2 | ~spl26_4)),
% 3.91/0.94 inference(forward_demodulation,[],[f2321,f1686])).
% 3.91/0.94 thf(f2323,plain,(
% 3.91/0.94 $false | (~spl26_2 | ~spl26_4)),
% 3.91/0.94 inference(trivial_inequality_removal,[],[f2322])).
% 3.91/0.94 thf(f2324,plain,(
% 3.91/0.94 ~spl26_2 | ~spl26_4),
% 3.91/0.94 inference(avatar_contradiction_clause,[],[f2323])).
% 3.91/0.94 thf(f2327,plain,(
% 3.91/0.94 (sK25 = sK23) | (~spl26_2 | ~spl26_3)),
% 3.91/0.94 inference(forward_demodulation,[],[f1705,f1700])).
% 3.91/0.94 thf(f2328,plain,(
% 3.91/0.94 $false | (~spl26_2 | ~spl26_3)),
% 3.91/0.94 inference(forward_subsumption_resolution,[],[f2327,f1687])).
% 3.91/0.94 thf(f2329,plain,(
% 3.91/0.94 ~spl26_2 | ~spl26_3),
% 3.91/0.94 inference(avatar_contradiction_clause,[],[f2328])).
% 3.91/0.94 cnf(s1, plain, spl26_1 | spl26_2, inference(sat_conversion,[],[f1701])).
% 3.91/0.94 cnf(s2, plain, spl26_3 | spl26_4, inference(sat_conversion,[],[f1710])).
% 3.91/0.94 cnf(s15, plain, ~spl26_1 | ~spl26_3, inference(sat_conversion,[],[f1961])).
% 3.91/0.94 cnf(s26, plain, ~spl26_1 | ~spl26_4, inference(sat_conversion,[],[f2215])).
% 3.91/0.94 cnf(s29, plain, ~spl26_2 | ~spl26_4, inference(sat_conversion,[],[f2324])).
% 3.91/0.94 cnf(s31, plain, ~spl26_2 | ~spl26_3, inference(sat_conversion,[],[f2329])).
% 3.91/0.94 cnf(s32, plain, ~spl26_2, inference(rat,[],[s2,s29,s31])).
% 3.91/0.94 cnf(s33, plain, spl26_1, inference(rat,[],[s1,s32])).
% 3.91/0.94 cnf(s34, plain, ~spl26_4, inference(rat,[],[s26,s33])).
% 3.91/0.94 cnf(s35, plain, ~spl26_3, inference(rat,[],[s15,s33])).
% 3.91/0.94 cnf(s36, plain, $false, inference(rat,[],[s2,s34,s35])).
% 3.91/0.94 thf(f2330,plain,(
% 3.91/0.94 $false),
% 3.91/0.94 inference(avatar_sat_refutation,[],[s36])).
% 3.91/0.94 % SZS output end Proof for theBenchmark
% 3.91/0.94 % (1212266)------------------------------
% 3.91/0.94 % (1212266)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.91/0.94 % (1212266)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.91/0.94 % (1212266)CaDiCaL version: 2.1.3
% 3.91/0.94 % (1212266)Termination reason: Refutation
% 3.91/0.94 % (1212266)Time elapsed: 0.132 s
% 3.91/0.94 % (1212266)Peak memory usage: 15 MB
% 3.91/0.94 % (1212266)Instructions burned: 286 (million)
% 3.91/0.94 % (1212105)Success in time 0.648 s
% 3.91/0.94 % Vampire exiting
%------------------------------------------------------------------------------