%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : DAT122^1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n008.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 07:48:22 AM UTC 2026
% Result : Theorem 0.49s 0.45s
% Output : Refutation 0.49s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : DAT122^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.18 % Computer : n008.cluster.edu
% 0.11/0.18 % Model : x86_64 x86_64
% 0.11/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.18 % Memory : 8046.5625MB
% 0.11/0.18 % OS : Linux 6.8.0-71-generic
% 0.11/0.18 % CPULimit : 300
% 0.11/0.18 % WCLimit : 300
% 0.11/0.18 % DateTime : Tue Sep 29 17:59:09 UTC 2026
% 0.11/0.18 % CPUTime :
% 0.11/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.22 Running higher-order theorem proving
% 0.11/0.28 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.49/0.42 % (3512469)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.49/0.42 % (3512493)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1577240930:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.49/0.42 % (3512494)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.49/0.42 % (3512494)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
% 0.49/0.42 % (3512488)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=520312305:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.49/0.42 % (3512489)lrs+10_16_si=on:nwc=1.5:random_seed=2874114904:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.49/0.42 % (3512492)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=536068064:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.49/0.42 % (3512491)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=2510472182: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)
% 0.49/0.42 % (3512494)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=3594182941:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.49/0.42 % (3512490)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1195356704:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.49/0.42 % (3512489)Instruction limit reached!
% 0.49/0.42 % (3512489)------------------------------
% 0.49/0.42 % (3512489)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.49/0.42 % (3512489)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.49/0.42 % (3512489)CaDiCaL version: 2.1.3
% 0.49/0.42 % (3512489)Termination reason: Instruction limit
% 0.49/0.42 % (3512489)Termination phase: shuffling
% 0.49/0.42 % (3512489)Time elapsed: 0.010 s
% 0.49/0.42 % (3512489)Peak memory usage: 10 MB
% 0.49/0.42 % (3512489)Instructions burned: 18 (million)
% 0.49/0.42 % (3512490)Instruction limit reached!
% 0.49/0.42 % (3512490)------------------------------
% 0.49/0.42 % (3512490)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.49/0.42 % (3512490)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.49/0.42 % (3512490)CaDiCaL version: 2.1.3
% 0.49/0.42 % (3512490)Termination reason: Instruction limit
% 0.49/0.42 % (3512490)Termination phase: shuffling
% 0.49/0.42 % (3512490)Time elapsed: 0.002 s
% 0.49/0.42 % (3512490)Peak memory usage: 10 MB
% 0.49/0.42 % (3512490)Instructions burned: 3 (million)
% 0.49/0.42 % (3512493)Instruction limit reached!
% 0.49/0.42 % (3512493)------------------------------
% 0.49/0.42 % (3512493)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.49/0.42 % (3512493)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.49/0.42 % (3512493)CaDiCaL version: 2.1.3
% 0.49/0.42 % (3512493)Termination reason: Instruction limit
% 0.49/0.42 % (3512493)Termination phase: Equality resolution with deletion
% 0.49/0.42 % (3512492)Instruction limit reached!
% 0.49/0.42 % (3512492)------------------------------
% 0.49/0.42 % (3512492)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.49/0.42 % (3512493)Time elapsed: 0.021 s
% 0.49/0.42 % (3512492)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.49/0.42 % (3512493)Peak memory usage: 12 MB
% 0.49/0.42 % (3512492)CaDiCaL version: 2.1.3
% 0.49/0.42 % (3512492)Termination reason: Instruction limit
% 0.49/0.42 % (3512492)Termination phase: Property scanning
% 0.49/0.42 % (3512492)Time elapsed: 0.013 s
% 0.49/0.42 % (3512492)Peak memory usage: 11 MB
% 0.49/0.42 % (3512492)Instructions burned: 25 (million)
% 0.49/0.42 % (3512493)Instructions burned: 79 (million)
% 0.49/0.42 % (3512517)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=3111160600:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.49/0.42 % (3512511)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3264649009:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.49/0.45 % (3512517)Instruction limit reached!
% 0.49/0.45 % (3512517)------------------------------
% 0.49/0.45 % (3512517)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.49/0.45 % (3512516)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.49/0.45 % (3512517)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.49/0.45 % (3512517)CaDiCaL version: 2.1.3
% 0.49/0.45 % (3512517)Termination reason: Instruction limit
% 0.49/0.45 % (3512517)Termination phase: shuffling
% 0.49/0.45 % (3512517)Time elapsed: 0.004 s
% 0.49/0.45 % (3512517)Peak memory usage: 11 MB
% 0.49/0.45 % (3512517)Instructions burned: 16 (million)
% 0.49/0.45 % (3512513)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=771010102:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.49/0.45 % (3512511)Instruction limit reached!
% 0.49/0.45 % (3512511)------------------------------
% 0.49/0.45 % (3512511)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.49/0.45 % (3512511)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.49/0.45 % (3512511)CaDiCaL version: 2.1.3
% 0.49/0.45 % (3512511)Termination reason: Instruction limit
% 0.49/0.45 % (3512511)Termination phase: shuffling
% 0.49/0.45 % (3512511)Time elapsed: 0.002 s
% 0.49/0.45 % (3512511)Peak memory usage: 10 MB
% 0.49/0.45 % (3512511)Instructions burned: 3 (million)
% 0.49/0.45 % (3512516)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=929212949:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.49/0.45 % (3512513)Instruction limit reached!
% 0.49/0.45 % (3512513)------------------------------
% 0.49/0.45 % (3512513)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.49/0.45 % (3512513)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.49/0.45 % (3512513)CaDiCaL version: 2.1.3
% 0.49/0.45 % (3512513)Termination reason: Instruction limit
% 0.49/0.45 % (3512513)Termination phase: shuffling
% 0.49/0.45 % (3512513)Time elapsed: 0.003 s
% 0.49/0.45 % (3512513)Peak memory usage: 10 MB
% 0.49/0.45 % (3512513)Instructions burned: 5 (million)
% 0.49/0.45 % (3512516)Instruction limit reached!
% 0.49/0.45 % (3512516)------------------------------
% 0.49/0.45 % (3512516)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.49/0.45 % (3512516)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.49/0.45 % (3512516)CaDiCaL version: 2.1.3
% 0.49/0.45 % (3512516)Termination reason: Instruction limit
% 0.49/0.45 % (3512516)Termination phase: shuffling
% 0.49/0.45 % (3512516)Time elapsed: 0.004 s
% 0.49/0.45 % (3512516)Peak memory usage: 10 MB
% 0.49/0.45 % (3512516)Instructions burned: 7 (million)
% 0.49/0.45 % (3512526)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
% 0.49/0.45 % (3512526)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.49/0.45 % (3512526)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=555885028:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.49/0.45 % (3512488)Instruction limit reached!
% 0.49/0.45 % (3512488)------------------------------
% 0.49/0.45 % (3512488)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.49/0.45 % (3512488)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.49/0.45 % (3512488)CaDiCaL version: 2.1.3
% 0.49/0.45 % (3512488)Termination reason: Instruction limit
% 0.49/0.45 % (3512488)Termination phase: Property scanning
% 0.49/0.45 % (3512488)Time elapsed: 0.044 s
% 0.49/0.45 % (3512488)Peak memory usage: 12 MB
% 0.49/0.45 % (3512488)Instructions burned: 88 (million)
% 0.49/0.45 % (3512526)Instruction limit reached!
% 0.49/0.45 % (3512526)------------------------------
% 0.49/0.45 % (3512526)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.49/0.45 % (3512526)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.49/0.45 % (3512526)CaDiCaL version: 2.1.3
% 0.49/0.45 % (3512526)Termination reason: Instruction limit
% 0.49/0.45 % (3512526)Termination phase: shuffling
% 0.49/0.45 % (3512526)Time elapsed: 0.007 s
% 0.49/0.45 % (3512526)Peak memory usage: 10 MB
% 0.49/0.45 % (3512526)Instructions burned: 29 (million)
% 0.49/0.45 % (3512528)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=3728272615:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.49/0.45 % (3512531)lrs+10_1_si=on:cs=on:random_seed=930679682:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.49/0.45 % (3512534)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.49/0.45 % (3512534)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=3943171141:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.49/0.45 % (3512531)Instruction limit reached!
% 0.49/0.45 % (3512531)------------------------------
% 0.49/0.45 % (3512531)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.49/0.45 % (3512540)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=1141043770:st=2:i=249:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/249Mi)
% 0.49/0.45 % (3512531)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.49/0.45 % (3512531)CaDiCaL version: 2.1.3
% 0.49/0.45 % (3512531)Termination reason: Instruction limit
% 0.49/0.45 % (3512531)Termination phase: shuffling
% 0.49/0.45 % (3512531)Time elapsed: 0.005 s
% 0.49/0.45 % (3512531)Peak memory usage: 10 MB
% 0.49/0.45 % (3512531)Instructions burned: 10 (million)
% 0.49/0.45 % (3512534)Instruction limit reached!
% 0.49/0.45 % (3512534)------------------------------
% 0.49/0.45 % (3512534)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.49/0.45 % (3512534)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.49/0.45 % (3512534)CaDiCaL version: 2.1.3
% 0.49/0.45 % (3512534)Termination reason: Instruction limit
% 0.49/0.45 % (3512534)Termination phase: shuffling
% 0.49/0.45 % (3512534)Time elapsed: 0.002 s
% 0.49/0.45 % (3512534)Peak memory usage: 10 MB
% 0.49/0.45 % (3512534)Instructions burned: 3 (million)
% 0.49/0.45 % (3512539)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=1243840763:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.49/0.45 % (3512540)Refutation not found, incomplete strategy
% 0.49/0.45 % (3512540)------------------------------
% 0.49/0.45 % (3512540)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.49/0.45 % (3512540)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.49/0.45 % (3512540)CaDiCaL version: 2.1.3
% 0.49/0.45 % (3512540)Termination reason: Refutation not found, incomplete strategy
% 0.49/0.45 % (3512540)Time elapsed: 0.012 s
% 0.49/0.45 % (3512540)Peak memory usage: 13 MB
% 0.49/0.45 % (3512540)Instructions burned: 45 (million)
% 0.49/0.45 % (3512540)------------------------------
% 0.49/0.45 % (3512540)------------------------------
% 0.49/0.45 % (3512548)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=1637279566:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 0.49/0.45 % (3512549)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=762832800:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 0.49/0.45 % (3512494)Instruction limit reached!
% 0.49/0.45 % (3512494)------------------------------
% 0.49/0.45 % (3512494)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.49/0.45 % (3512494)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.49/0.45 % (3512494)CaDiCaL version: 2.1.3
% 0.49/0.45 % (3512494)Termination reason: Instruction limit
% 0.49/0.45 % (3512494)Termination phase: Saturation
% 0.49/0.45 % (3512494)Time elapsed: 0.080 s
% 0.49/0.45 % (3512494)Peak memory usage: 14 MB
% 0.49/0.45 % (3512494)Instructions burned: 158 (million)
% 0.49/0.45 % (3512554)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=1633533798:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 0.49/0.45 % (3512539)Instruction limit reached!
% 0.49/0.45 % (3512539)------------------------------
% 0.49/0.45 % (3512539)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.49/0.45 % (3512539)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.49/0.45 % (3512539)CaDiCaL version: 2.1.3
% 0.49/0.45 % (3512539)Termination reason: Instruction limit
% 0.49/0.45 % (3512539)Termination phase: Saturation
% 0.49/0.45 % (3512539)Time elapsed: 0.020 s
% 0.49/0.45 % (3512539)Peak memory usage: 13 MB
% 0.49/0.45 % (3512539)Instructions burned: 39 (million)
% 0.49/0.45 % (3512549)Instruction limit reached!
% 0.49/0.45 % (3512549)------------------------------
% 0.49/0.45 % (3512549)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.49/0.45 % (3512549)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.49/0.45 % (3512549)CaDiCaL version: 2.1.3
% 0.49/0.45 % (3512549)Termination reason: Instruction limit
% 0.49/0.45 % (3512549)Termination phase: shuffling
% 0.49/0.45 % (3512549)Time elapsed: 0.007 s
% 0.49/0.45 % (3512549)Peak memory usage: 10 MB
% 0.49/0.45 % (3512549)Instructions burned: 15 (million)
% 0.49/0.45 % (3512528)Instruction limit reached!
% 0.49/0.45 % (3512528)------------------------------
% 0.49/0.45 % (3512528)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.49/0.45 % (3512528)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.49/0.45 % (3512528)CaDiCaL version: 2.1.3
% 0.49/0.45 % (3512528)Termination reason: Instruction limit
% 0.49/0.45 % (3512528)Termination phase: Preprocessing 3
% 0.49/0.45 % (3512528)Time elapsed: 0.039 s
% 0.49/0.45 % (3512528)Peak memory usage: 11 MB
% 0.49/0.45 % (3512528)Instructions burned: 86 (million)
% 0.49/0.45 % (3512548)Instruction limit reached!
% 0.49/0.45 % (3512548)------------------------------
% 0.49/0.45 % (3512548)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.49/0.45 % (3512548)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.49/0.45 % (3512548)CaDiCaL version: 2.1.3
% 0.49/0.45 % (3512548)Termination reason: Instruction limit
% 0.49/0.45 % (3512548)Termination phase: Property scanning
% 0.49/0.45 % (3512548)Time elapsed: 0.013 s
% 0.49/0.45 % (3512548)Peak memory usage: 11 MB
% 0.49/0.45 % (3512548)Instructions burned: 27 (million)
% 0.49/0.45 % (3512491) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3512469-3512491"...
% 0.49/0.45 % (3512558)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=3665776756:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 0.49/0.45 % (3512562)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=1753670728: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)
% 0.49/0.45 % (3512491)...printing done.
% 0.49/0.45 % (3512491)Refutation found. Thanks to Tanya!
% 0.49/0.45 % SZS status Theorem for theBenchmark
% 0.49/0.45 % SZS output start Proof for theBenchmark
% 0.49/0.45 thf(type_def_5, type, coindu1593790203_llist: $tType > $tType).
% 0.49/0.45 thf(type_def_6, type, tuple_isomorphism: ($tType * $tType * $tType) > $tType).
% 0.49/0.45 thf(type_def_7, type, code_natural: $tType).
% 0.49/0.45 thf(type_def_8, type, code_term: $tType).
% 0.49/0.45 thf(type_def_9, type, product_unit: $tType).
% 0.49/0.45 thf(type_def_10, type, product_prod: ($tType * $tType) > $tType).
% 0.49/0.45 thf(type_def_11, type, extended_enat: $tType).
% 0.49/0.45 thf(type_def_12, type, typerep: $tType).
% 0.49/0.45 thf(type_def_13, type, literal: $tType).
% 0.49/0.45 thf(type_def_14, type, sum_sum: ($tType * $tType) > $tType).
% 0.49/0.45 thf(type_def_15, type, option: $tType > $tType).
% 0.49/0.45 thf(type_def_16, type, set: $tType > $tType).
% 0.49/0.45 thf(type_def_17, type, nat: $tType).
% 0.49/0.45 thf(type_def_18, type, itself: $tType > $tType).
% 0.49/0.45 thf(type_def_19, type, a: $tType).
% 0.49/0.45 thf(type_def_20, type, sTfun: ($tType * $tType) > $tType).
% 0.49/0.45 thf(func_def_0, type, enum: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.49/0.45 thf(func_def_1, type, typerep2: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.49/0.45 thf(func_def_2, type, type: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.49/0.45 thf(func_def_3, type, cl_HOL_Oequal: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.49/0.45 thf(func_def_4, type, code_term_of: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.49/0.45 thf(func_def_5, type, size: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.49/0.45 thf(func_def_6, type, zero: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.49/0.45 thf(func_def_7, type, semiring_1: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.49/0.45 thf(func_def_8, type, quickcheck_random: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.49/0.45 thf(func_def_9, type, semiring_numeral_div: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.49/0.45 thf(func_def_10, type, code_Suc: (code_natural > code_natural)).
% 0.49/0.45 thf(func_def_11, type, code_case_natural: !>[X0: $tType]:((X0 > (code_natural > X0) > code_natural > X0))).
% 0.49/0.45 thf(func_def_12, type, code_rec_natural: !>[X0: $tType]:((X0 > (code_natural > X0 > X0) > code_natural > X0))).
% 0.49/0.45 thf(func_def_13, type, code_size_natural: (code_natural > nat)).
% 0.49/0.45 thf(func_def_14, type, coindu1529956631erates: !>[X0: $tType]:(((X0 > X0) > X0 > coindu1593790203_llist @ X0))).
% 0.49/0.45 thf(func_def_15, type, coindu268472904append: !>[X0: $tType]:((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0))).
% 0.49/0.45 thf(func_def_16, type, coindu300403952lexord: !>[X0: $tType]:(((X0 > X0 > $o) > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > $o))).
% 0.49/0.45 thf(func_def_17, type, coindu1121789889_LCons: !>[X0: $tType]:((X0 > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0))).
% 0.49/0.45 thf(func_def_18, type, coindu1598213697e_LNil: !>[X0: $tType]:(coindu1593790203_llist @ X0)).
% 0.49/0.45 thf(func_def_19, type, coindu882539134_llist: !>[X0: $tType, X1: $tType]:((X0 > (X1 > coindu1593790203_llist @ X1 > X0) > coindu1593790203_llist @ X1 > X0))).
% 0.49/0.45 thf(func_def_20, type, coindu1046438764le_lhd: !>[X0: $tType]:((coindu1593790203_llist @ X0 > X0))).
% 0.49/0.45 thf(func_def_21, type, coindu987187967t_all2: !>[X0: $tType, X1: $tType]:(((X0 > X1 > $o) > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X1 > $o))).
% 0.49/0.45 thf(func_def_22, type, coindu1062782156e_lmap: !>[X0: $tType, X1: $tType]:(((X0 > X1) > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X1))).
% 0.49/0.45 thf(func_def_23, type, coindu335574135_lnull: !>[X0: $tType]:((coindu1593790203_llist @ X0 > $o))).
% 0.49/0.45 thf(func_def_24, type, coindu1047225960le_ltl: !>[X0: $tType]:((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0))).
% 0.49/0.45 thf(func_def_25, type, coindu567634248member: !>[X0: $tType]:((X0 > coindu1593790203_llist @ X0 > $o))).
% 0.49/0.45 thf(func_def_26, type, coindu749330388e_lnth: !>[X0: $tType]:((coindu1593790203_llist @ X0 > nat > X0))).
% 0.49/0.45 thf(func_def_27, type, coindu1696667936prefix: !>[X0: $tType]:((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > $o))).
% 0.49/0.45 thf(func_def_28, type, coindu574146665prefix: !>[X0: $tType]:((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > $o))).
% 0.49/0.45 thf(func_def_29, type, coindu1802687541_ltake: !>[X0: $tType]:((extended_enat > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0))).
% 0.49/0.45 thf(func_def_30, type, coindu721411036eWhile: !>[X0: $tType]:(((X0 > $o) > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0))).
% 0.49/0.45 thf(func_def_31, type, coindu847746867e_lzip: !>[X0: $tType, X1: $tType]:((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X1 > coindu1593790203_llist @ product_prod @ X0 @ X1))).
% 0.49/0.45 thf(func_def_32, type, coindu1599971794_llist: !>[X0: $tType, X1: $tType]:(((X0 > $o) > (X0 > X1) > (X0 > X0) > X0 > coindu1593790203_llist @ X1))).
% 0.49/0.45 thf(func_def_33, type, coindu440805660e_enat: !>[X0: $tType]:((X0 > (extended_enat > X0) > extended_enat > X0))).
% 0.49/0.45 thf(func_def_34, type, coinductive_epred: (extended_enat > extended_enat)).
% 0.49/0.45 thf(func_def_35, type, coindu1491768222unfold: !>[X0: $tType]:(((X0 > $o) > (X0 > X0) > X0 > extended_enat))).
% 0.49/0.45 thf(func_def_36, type, semiri577515795es_aux: !>[X0: $tType]:((product_prod @ X0 @ X0 > $o))).
% 0.49/0.45 thf(func_def_37, type, extended_case_enat: !>[X0: $tType]:(((nat > X0) > X0 > extended_enat > X0))).
% 0.49/0.45 thf(func_def_38, type, extended_the_enat: (extended_enat > nat)).
% 0.49/0.45 thf(func_def_39, type, zero_zero: !>[X0: $tType]:(X0)).
% 0.49/0.45 thf(func_def_40, type, size_bool: ($o > nat)).
% 0.49/0.45 thf(func_def_41, type, default_default: !>[X0: $tType]:(X0)).
% 0.49/0.45 thf(func_def_42, type, if: !>[X0: $tType]:(($o > X0 > X0 > X0))).
% 0.49/0.45 thf(func_def_43, type, rec_nat: !>[X0: $tType]:((X0 > (nat > X0 > X0) > nat > X0))).
% 0.49/0.45 thf(func_def_44, type, semiri532925092at_aux: !>[X0: $tType]:(((X0 > X0) > nat > X0 > X0))).
% 0.49/0.45 thf(func_def_45, type, size_size: !>[X0: $tType]:((X0 > nat))).
% 0.49/0.45 thf(func_def_46, type, product_Pair: !>[X0: $tType, X1: $tType]:((X0 > X1 > product_prod @ X0 @ X1))).
% 0.49/0.45 thf(func_def_47, type, product_Unity: product_unit).
% 0.49/0.45 thf(func_def_48, type, produc2004651681e_prod: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2))).
% 0.49/0.45 thf(func_def_49, type, product_rec_bool: !>[X0: $tType]:((X0 > X0 > $o > X0))).
% 0.49/0.45 thf(func_def_50, type, product_rec_prod: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2))).
% 0.49/0.45 thf(func_def_51, type, product_rec_unit: !>[X0: $tType]:((X0 > product_unit > X0))).
% 0.49/0.45 thf(func_def_52, type, product_case_unit: !>[X0: $tType]:((X0 > product_unit > X0))).
% 0.49/0.45 thf(func_def_53, type, product_size_unit: (product_unit > nat)).
% 0.49/0.45 thf(func_def_54, type, type2: !>[X0: $tType]:(itself @ X0)).
% 0.49/0.45 thf(func_def_55, type, collect: !>[X0: $tType]:(((X0 > $o) > set @ X0))).
% 0.49/0.45 thf(func_def_56, type, member: !>[X0: $tType]:((X0 > set @ X0 > $o))).
% 0.49/0.45 thf(func_def_57, type, xs: coindu1593790203_llist @ a).
% 0.49/0.45 thf(func_def_61, type, vAND: ($o > $o > $o)).
% 0.49/0.45 thf(func_def_62, type, db1: !>[X0: $tType]:(X0)).
% 0.49/0.45 thf(func_def_63, type, db0: !>[X0: $tType]:(X0)).
% 0.49/0.45 thf(func_def_64, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.49/0.45 thf(func_def_65, type, vIMP: ($o > $o > $o)).
% 0.49/0.45 thf(func_def_66, type, vNOT: ($o > $o)).
% 0.49/0.45 thf(func_def_67, type, db2: !>[X0: $tType]:(X0)).
% 0.49/0.45 thf(func_def_68, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.49/0.45 thf(func_def_69, type, db3: !>[X0: $tType]:(X0)).
% 0.49/0.45 thf(func_def_70, type, vOR: ($o > $o > $o)).
% 0.49/0.45 thf(func_def_71, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.49/0.45 thf(func_def_72, type, db4: !>[X0: $tType]:(X0)).
% 0.49/0.45 thf(func_def_73, type, db6: !>[X0: $tType]:(X0)).
% 0.49/0.45 thf(func_def_74, type, db5: !>[X0: $tType]:(X0)).
% 0.49/0.45 thf(func_def_75, type, sP0: !>[X0: $tType]:((coindu1593790203_llist @ X0 > (X0 > X0 > $o) > coindu1593790203_llist @ X0 > $o))).
% 0.49/0.45 thf(func_def_76, type, sK1: (code_natural > code_natural)).
% 0.49/0.45 thf(func_def_77, type, sK2: !>[X0: $tType]:(((code_natural > X0) > (code_natural > X0) > code_natural))).
% 0.49/0.45 thf(func_def_78, type, sK3: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X3 @ product_prod @ X4 @ product_prod @ X0 @ product_prod @ X5 @ product_prod @ X2 @ X1 > X5))).
% 0.49/0.45 thf(func_def_79, type, sK4: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X3 @ product_prod @ X4 @ product_prod @ X0 @ product_prod @ X5 @ product_prod @ X2 @ X1 > X0))).
% 0.49/0.45 thf(func_def_80, type, sK5: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X3 @ product_prod @ X4 @ product_prod @ X0 @ product_prod @ X5 @ product_prod @ X2 @ X1 > X1))).
% 0.49/0.45 thf(func_def_81, type, sK6: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X3 @ product_prod @ X4 @ product_prod @ X0 @ product_prod @ X5 @ product_prod @ X2 @ X1 > X2))).
% 0.49/0.45 thf(func_def_82, type, sK7: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X3 @ product_prod @ X4 @ product_prod @ X0 @ product_prod @ X5 @ product_prod @ X2 @ X1 > X4))).
% 0.49/0.45 thf(func_def_83, type, sK8: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X3 @ product_prod @ X4 @ product_prod @ X0 @ product_prod @ X5 @ product_prod @ X2 @ X1 > X3))).
% 0.49/0.45 thf(func_def_84, type, sK9: !>[X0: $tType]:(((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > $o) > coindu1593790203_llist @ X0))).
% 0.49/0.45 thf(func_def_85, type, sK10: !>[X0: $tType]:(((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > $o) > coindu1593790203_llist @ X0))).
% 0.49/0.45 thf(func_def_86, type, sK11: !>[X0: $tType]:((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0))).
% 0.49/0.45 thf(func_def_87, type, sK12: !>[X0: $tType]:((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0))).
% 0.49/0.45 thf(func_def_88, type, sK13: !>[X0: $tType]:((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > X0))).
% 0.49/0.45 thf(func_def_89, type, sK14: !>[X0: $tType]:((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0))).
% 0.49/0.45 thf(func_def_90, type, sK15: ((code_natural > $o) > code_natural)).
% 0.49/0.45 thf(func_def_91, type, sK16: ((extended_enat > extended_enat > $o) > extended_enat)).
% 0.49/0.45 thf(func_def_92, type, sK17: ((extended_enat > extended_enat > $o) > extended_enat)).
% 0.49/0.45 thf(func_def_93, type, sK18: ((extended_enat > extended_enat > $o) > extended_enat)).
% 0.49/0.45 thf(func_def_94, type, sK19: ((extended_enat > extended_enat > $o) > extended_enat)).
% 0.49/0.45 thf(func_def_95, type, sK20: !>[X0: $tType, X1: $tType]:(((product_prod @ X0 @ X1 > $o) > X1))).
% 0.49/0.45 thf(func_def_96, type, sK21: !>[X0: $tType, X1: $tType]:(((product_prod @ X0 @ X1 > $o) > X0))).
% 0.49/0.45 thf(func_def_97, type, sK22: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X3 @ product_prod @ X5 @ product_prod @ X0 @ product_prod @ X4 @ product_prod @ X2 @ X1 > $o) > X0))).
% 0.49/0.45 thf(func_def_98, type, sK23: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X3 @ product_prod @ X5 @ product_prod @ X0 @ product_prod @ X4 @ product_prod @ X2 @ X1 > $o) > X1))).
% 0.49/0.45 thf(func_def_99, type, sK24: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X3 @ product_prod @ X5 @ product_prod @ X0 @ product_prod @ X4 @ product_prod @ X2 @ X1 > $o) > X3))).
% 0.49/0.45 thf(func_def_100, type, sK25: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X3 @ product_prod @ X5 @ product_prod @ X0 @ product_prod @ X4 @ product_prod @ X2 @ X1 > $o) > X4))).
% 0.49/0.45 thf(func_def_101, type, sK26: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X3 @ product_prod @ X5 @ product_prod @ X0 @ product_prod @ X4 @ product_prod @ X2 @ X1 > $o) > X2))).
% 0.49/0.45 thf(func_def_102, type, sK27: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X3 @ product_prod @ X5 @ product_prod @ X0 @ product_prod @ X4 @ product_prod @ X2 @ X1 > $o) > X5))).
% 0.49/0.45 thf(func_def_103, type, sK28: !>[X0: $tType]:(((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > $o) > coindu1593790203_llist @ X0))).
% 0.49/0.45 thf(func_def_104, type, sK29: !>[X0: $tType]:(((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > $o) > coindu1593790203_llist @ X0))).
% 0.49/0.45 thf(func_def_105, type, sK30: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X0 @ product_prod @ X5 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X6 @ product_prod @ X2 @ X1 > $o) > X0))).
% 0.49/0.45 thf(func_def_106, type, sK31: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X0 @ product_prod @ X5 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X6 @ product_prod @ X2 @ X1 > $o) > X6))).
% 0.49/0.45 thf(func_def_107, type, sK32: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X0 @ product_prod @ X5 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X6 @ product_prod @ X2 @ X1 > $o) > X4))).
% 0.49/0.45 thf(func_def_108, type, sK33: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X0 @ product_prod @ X5 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X6 @ product_prod @ X2 @ X1 > $o) > X1))).
% 0.49/0.45 thf(func_def_109, type, sK34: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X0 @ product_prod @ X5 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X6 @ product_prod @ X2 @ X1 > $o) > X5))).
% 0.49/0.45 thf(func_def_110, type, sK35: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X0 @ product_prod @ X5 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X6 @ product_prod @ X2 @ X1 > $o) > X2))).
% 0.49/0.45 thf(func_def_111, type, sK36: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X0 @ product_prod @ X5 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X6 @ product_prod @ X2 @ X1 > $o) > X3))).
% 0.49/0.45 thf(func_def_112, type, sK37: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X0 @ product_prod @ X1 @ X2 > $o) > X1))).
% 0.49/0.45 thf(func_def_113, type, sK38: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X0 @ product_prod @ X1 @ X2 > $o) > X2))).
% 0.49/0.45 thf(func_def_114, type, sK39: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X0 @ product_prod @ X1 @ X2 > $o) > X0))).
% 0.49/0.45 thf(func_def_115, type, sK40: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X0 @ product_prod @ X2 @ product_prod @ X3 @ X1 > X1))).
% 0.49/0.45 thf(func_def_116, type, sK41: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X0 @ product_prod @ X2 @ product_prod @ X3 @ X1 > X3))).
% 0.49/0.45 thf(func_def_117, type, sK42: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X0 @ product_prod @ X2 @ product_prod @ X3 @ X1 > X2))).
% 0.49/0.45 thf(func_def_118, type, sK43: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X0 @ product_prod @ X2 @ product_prod @ X3 @ X1 > X0))).
% 0.49/0.45 thf(func_def_119, type, sK44: !>[X0: $tType]:(((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > $o) > coindu1593790203_llist @ X0))).
% 0.49/0.45 thf(func_def_120, type, sK45: !>[X0: $tType]:(((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > $o) > coindu1593790203_llist @ X0))).
% 0.49/0.45 thf(func_def_121, type, sK46: !>[X0: $tType]:((coindu1593790203_llist @ X0 > X0))).
% 0.49/0.45 thf(func_def_122, type, sK47: !>[X0: $tType]:((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0))).
% 0.49/0.45 thf(func_def_123, type, sK48: !>[X0: $tType]:((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > X0 > coindu1593790203_llist @ X0))).
% 0.49/0.45 thf(func_def_124, type, sK49: !>[X0: $tType]:(((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > $o) > coindu1593790203_llist @ X0))).
% 0.49/0.45 thf(func_def_125, type, sK50: !>[X0: $tType]:(((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > $o) > coindu1593790203_llist @ X0))).
% 0.49/0.45 thf(func_def_126, type, sK51: !>[X0: $tType, X1: $tType]:(((product_prod @ X0 @ X1 > $o) > X1))).
% 0.49/0.45 thf(func_def_127, type, sK52: !>[X0: $tType, X1: $tType]:(((product_prod @ X0 @ X1 > $o) > X0))).
% 0.49/0.45 thf(func_def_128, type, sK53: !>[X0: $tType, X1: $tType]:((product_prod @ X1 @ X0 > X1))).
% 0.49/0.45 thf(func_def_129, type, sK54: !>[X0: $tType, X1: $tType]:((product_prod @ X1 @ X0 > X0))).
% 0.49/0.45 thf(func_def_130, type, sK55: !>[X0: $tType, X1: $tType]:(((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X1 > $o) > (X0 > X1 > $o) > coindu1593790203_llist @ X1))).
% 0.49/0.45 thf(func_def_131, type, sK56: !>[X0: $tType, X1: $tType]:(((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X1 > $o) > (X0 > X1 > $o) > coindu1593790203_llist @ X0))).
% 0.49/0.45 thf(func_def_132, type, sK57: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.49/0.45 thf(func_def_133, type, sK58: (product_prod @ code_natural @ code_natural > code_natural)).
% 0.49/0.45 thf(func_def_134, type, sK59: (product_prod @ code_natural @ code_natural > code_natural)).
% 0.49/0.45 thf(func_def_135, type, sK60: (product_prod @ code_natural @ code_natural > code_natural)).
% 0.49/0.45 thf(func_def_136, type, sK61: !>[X0: $tType]:((coindu1593790203_llist @ X0 > (X0 > X0 > $o) > coindu1593790203_llist @ X0 > X0))).
% 0.49/0.45 thf(func_def_137, type, sK62: !>[X0: $tType]:((coindu1593790203_llist @ X0 > (X0 > X0 > $o) > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0))).
% 0.49/0.45 thf(func_def_138, type, sK63: !>[X0: $tType]:((coindu1593790203_llist @ X0 > (X0 > X0 > $o) > coindu1593790203_llist @ X0 > X0))).
% 0.49/0.45 thf(func_def_139, type, sK64: !>[X0: $tType]:((coindu1593790203_llist @ X0 > (X0 > X0 > $o) > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0))).
% 0.49/0.45 thf(func_def_140, type, sK65: !>[X0: $tType]:((coindu1593790203_llist @ X0 > (X0 > X0 > $o) > coindu1593790203_llist @ X0 > X0))).
% 0.49/0.45 thf(func_def_141, type, sK66: !>[X0: $tType]:((coindu1593790203_llist @ X0 > (X0 > X0 > $o) > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0))).
% 0.49/0.45 thf(func_def_142, type, sK67: !>[X0: $tType]:((coindu1593790203_llist @ X0 > (X0 > X0 > $o) > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0))).
% 0.49/0.45 thf(func_def_143, type, sK68: !>[X0: $tType]:((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0))).
% 0.49/0.45 thf(func_def_144, type, sK69: ((code_natural > code_natural > $o) > code_natural)).
% 0.49/0.45 thf(func_def_145, type, sK70: ((code_natural > code_natural > $o) > code_natural)).
% 0.49/0.45 thf(func_def_146, type, sK71: ((code_natural > code_natural > $o) > code_natural)).
% 0.49/0.45 thf(func_def_147, type, sK72: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X1))).
% 0.49/0.45 thf(func_def_148, type, sK73: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X0))).
% 0.49/0.45 thf(func_def_149, type, sK74: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.49/0.45 thf(func_def_150, type, sK75: !>[X0: $tType, X1: $tType]:((coindu1593790203_llist @ X1 > coindu1593790203_llist @ X0 > (X0 > X1 > $o) > X0))).
% 0.49/0.45 thf(func_def_151, type, sK76: !>[X0: $tType, X1: $tType]:((coindu1593790203_llist @ X1 > coindu1593790203_llist @ X0 > (X0 > X1 > $o) > coindu1593790203_llist @ X0))).
% 0.49/0.45 thf(func_def_152, type, sK77: !>[X0: $tType, X1: $tType]:((coindu1593790203_llist @ X1 > coindu1593790203_llist @ X0 > (X0 > X1 > $o) > coindu1593790203_llist @ X1))).
% 0.49/0.45 thf(func_def_153, type, sK78: !>[X0: $tType, X1: $tType]:((coindu1593790203_llist @ X1 > coindu1593790203_llist @ X0 > (X0 > X1 > $o) > X1))).
% 0.49/0.45 thf(func_def_154, type, sK79: !>[X0: $tType, X1: $tType]:((coindu1593790203_llist @ X1 > coindu1593790203_llist @ X0 > X0 > (X1 > X0) > coindu1593790203_llist @ X1))).
% 0.49/0.45 thf(func_def_155, type, sK80: !>[X0: $tType, X1: $tType]:((coindu1593790203_llist @ X1 > coindu1593790203_llist @ X0 > X0 > (X1 > X0) > X1))).
% 0.49/0.45 thf(func_def_156, type, sK81: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > $o) > X2))).
% 0.49/0.45 thf(func_def_157, type, sK82: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > $o) > X3))).
% 0.49/0.45 thf(func_def_158, type, sK83: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > $o) > X0))).
% 0.49/0.45 thf(func_def_159, type, sK84: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > $o) > X1))).
% 0.49/0.45 thf(func_def_160, type, sK85: !>[X0: $tType]:((set @ product_prod @ coindu1593790203_llist @ X0 @ coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0))).
% 0.49/0.45 thf(func_def_161, type, sK86: !>[X0: $tType]:((set @ product_prod @ coindu1593790203_llist @ X0 @ coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0))).
% 0.49/0.45 thf(func_def_162, type, sK87: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X0 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X4 @ X1 > $o) > X4))).
% 0.49/0.45 thf(func_def_163, type, sK88: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X0 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X4 @ X1 > $o) > X1))).
% 0.49/0.45 thf(func_def_164, type, sK89: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X0 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X4 @ X1 > $o) > X3))).
% 0.49/0.45 thf(func_def_165, type, sK90: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X0 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X4 @ X1 > $o) > X2))).
% 0.49/0.45 thf(func_def_166, type, sK91: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X0 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X4 @ X1 > $o) > X0))).
% 0.49/0.45 thf(func_def_167, type, sK92: !>[X0: $tType]:(((X0 > X0 > $o) > (coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > $o) > coindu1593790203_llist @ X0))).
% 0.49/0.45 thf(func_def_168, type, sK93: !>[X0: $tType]:(((X0 > X0 > $o) > (coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > $o) > coindu1593790203_llist @ X0))).
% 0.49/0.45 thf(func_def_169, type, sK94: !>[X0: $tType]:((coindu1593790203_llist @ X0 > X0))).
% 0.49/0.45 thf(func_def_170, type, sK95: !>[X0: $tType]:((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0))).
% 0.49/0.45 thf(func_def_171, type, sK96: !>[X0: $tType]:((coindu1593790203_llist @ X0 > X0 > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0))).
% 0.49/0.45 thf(func_def_172, type, sK97: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X1 @ product_prod @ X0 @ product_prod @ X4 @ product_prod @ X3 @ X2 > X2))).
% 0.49/0.45 thf(func_def_173, type, sK98: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X1 @ product_prod @ X0 @ product_prod @ X4 @ product_prod @ X3 @ X2 > X1))).
% 0.49/0.45 thf(func_def_174, type, sK99: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X1 @ product_prod @ X0 @ product_prod @ X4 @ product_prod @ X3 @ X2 > X3))).
% 0.49/0.45 thf(func_def_175, type, sK100: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X1 @ product_prod @ X0 @ product_prod @ X4 @ product_prod @ X3 @ X2 > X0))).
% 0.49/0.45 thf(func_def_176, type, sK101: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X1 @ product_prod @ X0 @ product_prod @ X4 @ product_prod @ X3 @ X2 > X4))).
% 0.49/0.45 thf(func_def_177, type, sK102: !>[X0: $tType]:((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0))).
% 0.49/0.45 thf(func_def_178, type, sK103: !>[X0: $tType]:((coindu1593790203_llist @ X0 > X0))).
% 0.49/0.45 thf(func_def_179, type, sK104: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X0 @ product_prod @ X6 @ product_prod @ X3 @ product_prod @ X1 @ X2 > X5))).
% 0.49/0.45 thf(func_def_180, type, sK105: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X0 @ product_prod @ X6 @ product_prod @ X3 @ product_prod @ X1 @ X2 > X3))).
% 0.49/0.45 thf(func_def_181, type, sK106: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X0 @ product_prod @ X6 @ product_prod @ X3 @ product_prod @ X1 @ X2 > X1))).
% 0.49/0.45 thf(func_def_182, type, sK107: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X0 @ product_prod @ X6 @ product_prod @ X3 @ product_prod @ X1 @ X2 > X2))).
% 0.49/0.45 thf(func_def_183, type, sK108: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X0 @ product_prod @ X6 @ product_prod @ X3 @ product_prod @ X1 @ X2 > X6))).
% 0.49/0.45 thf(func_def_184, type, sK109: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X0 @ product_prod @ X6 @ product_prod @ X3 @ product_prod @ X1 @ X2 > X4))).
% 0.49/0.45 thf(func_def_185, type, sK110: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X0 @ product_prod @ X6 @ product_prod @ X3 @ product_prod @ X1 @ X2 > X0))).
% 0.49/0.45 thf(func_def_186, type, sK111: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X0 > X1) > X0))).
% 0.49/0.45 thf(func_def_187, type, sK112: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X1 @ product_prod @ X0 @ X2 > X0))).
% 0.49/0.45 thf(func_def_188, type, sK113: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X1 @ product_prod @ X0 @ X2 > X1))).
% 0.49/0.45 thf(func_def_189, type, sK114: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X1 @ product_prod @ X0 @ X2 > X2))).
% 0.49/0.45 thf(func_def_190, type, sK115: ((extended_enat > extended_enat > $o) > extended_enat)).
% 0.49/0.45 thf(func_def_191, type, sK116: ((extended_enat > extended_enat > $o) > extended_enat)).
% 0.49/0.45 thf(f24,axiom,(
% 0.49/0.45 ! [X0 : $tType,X2 : coindu1593790203_llist @ X0,X1 : X0] : (((coindu749330388e_lnth @ X0 @ (coindu1121789889_LCons @ X0 @ X1 @ X2) @ zero_zero @ nat)) = X1)),
% 0.49/0.45 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_lnth__0)).
% 0.49/0.45 thf(f52,axiom,(
% 0.49/0.45 ! [X0 : $tType,X1 : coindu1593790203_llist @ X0] : ((X1 != coindu1598213697e_LNil @ X0) = ? [X2 : X0,X3 : coindu1593790203_llist @ X0] : (X1 = ((coindu1121789889_LCons @ X0 @ X2 @ X3))))),
% 0.49/0.45 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_neq__LNil__conv)).
% 0.49/0.45 thf(f75,axiom,(
% 0.49/0.45 ! [X0 : $tType,X2 : coindu1593790203_llist @ X0,X1 : X0] : (((coindu1046438764le_lhd @ X0 @ (coindu1121789889_LCons @ X0 @ X1 @ X2))) = X1)),
% 0.49/0.45 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_lhd__LCons)).
% 0.49/0.45 thf(f76,axiom,(
% 0.49/0.45 ! [X0 : $tType] : (coindu335574135_lnull @ X0 @ coindu1598213697e_LNil @ X0)),
% 0.49/0.45 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_llist_Odisc_I1_J)).
% 0.49/0.45 thf(f328,axiom,(
% 0.49/0.45 ~(coindu335574135_lnull @ a @ xs)),
% 0.49/0.45 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0)).
% 0.49/0.45 thf(f329,conjecture,(
% 0.49/0.45 (((coindu1046438764le_lhd @ a @ xs)) = ((coindu749330388e_lnth @ a @ xs @ zero_zero @ nat)))),
% 0.49/0.45 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1)).
% 0.49/0.45 thf(f330,negated_conjecture,(
% 0.49/0.45 ~ (((coindu1046438764le_lhd @ a @ xs)) = ((coindu749330388e_lnth @ a @ xs @ zero_zero @ nat)))),
% 0.49/0.45 inference(negated_conjecture,[status(cth)],[f329])).
% 0.49/0.45 thf(f357,plain,(
% 0.49/0.45 ! [X0 : $tType] : (coindu335574135_lnull @ X0 @ coindu1598213697e_LNil @ X0)),
% 0.49/0.45 inference(rectify,[],[f76])).
% 0.49/0.45 thf(f358,plain,(
% 0.49/0.45 ! [X0 : $tType] : (((coindu335574135_lnull @ X0 @ coindu1598213697e_LNil @ X0)) = $true)),
% 0.49/0.45 inference(fool_elimination,[],[f357])).
% 0.49/0.45 thf(f366,plain,(
% 0.49/0.45 ~(coindu335574135_lnull @ a @ xs)),
% 0.49/0.45 inference(rectify,[],[f328])).
% 0.49/0.45 thf(f367,plain,(
% 0.49/0.45 ~ (((coindu335574135_lnull @ a @ xs)) = $true)),
% 0.49/0.45 inference(fool_elimination,[],[f366])).
% 0.49/0.45 thf(f663,plain,(
% 0.49/0.45 ! [X0 : $tType,X1 : coindu1593790203_llist @ X0] : (? [X2 : X0,X3 : coindu1593790203_llist @ X0] : (((coindu1121789889_LCons @ X0 @ X2 @ X3)) = X1) <=> (coindu1598213697e_LNil @ X0 != X1))),
% 0.49/0.45 inference(fool_elimination,[],[f52])).
% 0.49/0.45 thf(f819,plain,(
% 0.49/0.45 (((coindu335574135_lnull @ a @ xs)) != $true)),
% 0.49/0.45 inference(flattening,[],[f367])).
% 0.49/0.45 thf(f889,plain,(
% 0.49/0.45 (((coindu1046438764le_lhd @ a @ xs)) != ((coindu749330388e_lnth @ a @ xs @ zero_zero @ nat)))),
% 0.49/0.45 inference(flattening,[],[f330])).
% 0.49/0.45 thf(f915,plain,(
% 0.49/0.45 ! [X0 : $tType,X1 : coindu1593790203_llist @ X0,X2 : X0] : (((coindu749330388e_lnth @ X0 @ (coindu1121789889_LCons @ X0 @ X2 @ X1) @ zero_zero @ nat)) = X2)),
% 0.49/0.45 inference(rectify,[],[f24])).
% 0.49/0.45 thf(f1212,plain,(
% 0.49/0.45 ! [X0 : $tType,X1 : coindu1593790203_llist @ X0] : ((? [X2 : X0,X3 : coindu1593790203_llist @ X0] : (((coindu1121789889_LCons @ X0 @ X2 @ X3)) = X1) | (coindu1598213697e_LNil @ X0 = X1)) & ((coindu1598213697e_LNil @ X0 != X1) | ! [X2 : X0,X3 : coindu1593790203_llist @ X0] : (((coindu1121789889_LCons @ X0 @ X2 @ X3)) != X1)))),
% 0.49/0.45 inference(nnf_transformation,[],[f663])).
% 0.49/0.45 thf(f1213,plain,(
% 0.49/0.45 ! [X0 : $tType,X1 : coindu1593790203_llist @ X0] : ((? [X2 : X0,X3 : coindu1593790203_llist @ X0] : (((coindu1121789889_LCons @ X0 @ X2 @ X3)) = X1) | (coindu1598213697e_LNil @ X0 = X1)) & ((coindu1598213697e_LNil @ X0 != X1) | ! [X4 : X0,X5 : coindu1593790203_llist @ X0] : (((coindu1121789889_LCons @ X0 @ X4 @ X5)) != X1)))),
% 0.49/0.45 inference(rectify,[],[f1212])).
% 0.49/0.45 thf(f1214,plain,(
% 0.49/0.45 ! [X0 : $tType,X1 : coindu1593790203_llist @ X0] : (((((coindu1121789889_LCons @ X0 @ (sK46 @ X0 @ X1) @ (sK47 @ X0 @ X1))) = X1) | (coindu1598213697e_LNil @ X0 = X1)) & ((coindu1598213697e_LNil @ X0 != X1) | ! [X4 : X0,X5 : coindu1593790203_llist @ X0] : (((coindu1121789889_LCons @ X0 @ X4 @ X5)) != X1)))),
% 0.49/0.45 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP]),skolemize(X1,sK1 @ X0),skolemize(X1,sK1 @ X0)],[f1213])).
% 0.49/0.45 thf(f1293,plain,(
% 0.49/0.45 ! [X0 : $tType,X1 : coindu1593790203_llist @ X0,X2 : X0] : (((coindu1046438764le_lhd @ X0 @ (coindu1121789889_LCons @ X0 @ X2 @ X1))) = X2)),
% 0.49/0.45 inference(rectify,[],[f75])).
% 0.49/0.45 thf(f1457,plain,(
% 0.49/0.45 (((coindu335574135_lnull @ a @ xs)) != $true)),
% 0.49/0.45 inference(cnf_transformation,[],[f819])).
% 0.49/0.45 thf(f1554,plain,(
% 0.49/0.45 ( ! [X0 : $tType,X2 : X0,X1 : coindu1593790203_llist @ X0] : ((((coindu749330388e_lnth @ X0 @ (coindu1121789889_LCons @ X0 @ X2 @ X1) @ zero_zero @ nat)) = X2)) )),
% 0.49/0.45 inference(cnf_transformation,[],[f915])).
% 0.49/0.45 thf(f1569,plain,(
% 0.49/0.45 ( ! [X0 : $tType,X1 : coindu1593790203_llist @ X0] : ((((coindu1121789889_LCons @ X0 @ (sK46 @ X0 @ X1) @ (sK47 @ X0 @ X1))) = X1) | (coindu1598213697e_LNil @ X0 = X1)) )),
% 0.49/0.45 inference(cnf_transformation,[],[f1214])).
% 0.49/0.45 thf(f1691,plain,(
% 0.49/0.45 ( ! [X0 : $tType] : ((((coindu335574135_lnull @ X0 @ coindu1598213697e_LNil @ X0)) = $true)) )),
% 0.49/0.45 inference(cnf_transformation,[],[f358])).
% 0.49/0.45 thf(f1726,plain,(
% 0.49/0.45 ( ! [X0 : $tType,X2 : X0,X1 : coindu1593790203_llist @ X0] : ((((coindu1046438764le_lhd @ X0 @ (coindu1121789889_LCons @ X0 @ X2 @ X1))) = X2)) )),
% 0.49/0.45 inference(cnf_transformation,[],[f1293])).
% 0.49/0.45 thf(f1827,plain,(
% 0.49/0.45 (((coindu1046438764le_lhd @ a @ xs)) != ((coindu749330388e_lnth @ a @ xs @ zero_zero @ nat)))),
% 0.49/0.45 inference(cnf_transformation,[],[f889])).
% 0.49/0.45 thf(f2004,definition,(
% 0.49/0.45 spl117_6 <=> (((coindu1046438764le_lhd @ a @ xs)) = ((coindu749330388e_lnth @ a @ xs @ zero_zero @ nat)))),
% 0.49/0.45 introduced(definition,[new_symbols(definition,[spl117_6])],[avatar_definition])).
% 0.49/0.45 thf(f2006,plain,(
% 0.49/0.45 (((coindu1046438764le_lhd @ a @ xs)) != ((coindu749330388e_lnth @ a @ xs @ zero_zero @ nat))) | spl117_6),
% 0.49/0.45 inference(avatar_component_clause,[],[f2004])).
% 0.49/0.45 thf(f2007,plain,(
% 0.49/0.45 ~spl117_6),
% 0.49/0.45 inference(avatar_split_clause,[],[f1827,f2004])).
% 0.49/0.45 thf(f2229,definition,(
% 0.49/0.45 spl117_51 <=> (((coindu335574135_lnull @ a @ xs)) = $true)),
% 0.49/0.45 introduced(definition,[new_symbols(definition,[spl117_51])],[avatar_definition])).
% 0.49/0.45 thf(f2231,plain,(
% 0.49/0.45 (((coindu335574135_lnull @ a @ xs)) != $true) | spl117_51),
% 0.49/0.45 inference(avatar_component_clause,[],[f2229])).
% 0.49/0.45 thf(f2232,plain,(
% 0.49/0.45 ~spl117_51),
% 0.49/0.45 inference(avatar_split_clause,[],[f1457,f2229])).
% 0.49/0.45 thf(f2432,plain,(
% 0.49/0.45 ( ! [X1 : $tType,X0 : coindu1593790203_llist @ X1] : ((((sK46 @ X1 @ X0)) = ((coindu749330388e_lnth @ X1 @ X0 @ zero_zero @ nat))) | (coindu1598213697e_LNil @ X1 = X0)) )),
% 0.49/0.45 inference(superposition,[],[f1554,f1569])).
% 0.49/0.45 thf(f2433,plain,(
% 0.49/0.45 ( ! [X1 : $tType,X0 : coindu1593790203_llist @ X1] : ((((sK46 @ X1 @ X0)) = ((coindu1046438764le_lhd @ X1 @ X0))) | (coindu1598213697e_LNil @ X1 = X0)) )),
% 0.49/0.45 inference(superposition,[],[f1726,f1569])).
% 0.49/0.45 thf(f2456,plain,(
% 0.49/0.45 (xs = coindu1598213697e_LNil @ a) | (((coindu1046438764le_lhd @ a @ xs)) != ((sK46 @ a @ xs))) | spl117_6),
% 0.49/0.45 inference(superposition,[],[f2006,f2432])).
% 0.49/0.45 thf(f2460,plain,(
% 0.49/0.45 (xs = coindu1598213697e_LNil @ a) | spl117_6),
% 0.49/0.45 inference(forward_subsumption_resolution,[],[f2456,f2433])).
% 0.49/0.45 thf(f2463,definition,(
% 0.49/0.45 spl117_69 <=> (xs = coindu1598213697e_LNil @ a)),
% 0.49/0.45 introduced(definition,[new_symbols(definition,[spl117_69])],[avatar_definition])).
% 0.49/0.45 thf(f2465,plain,(
% 0.49/0.45 (xs = coindu1598213697e_LNil @ a) | ~spl117_69),
% 0.49/0.45 inference(avatar_component_clause,[],[f2463])).
% 0.49/0.45 thf(f2466,plain,(
% 0.49/0.45 spl117_69 | spl117_6),
% 0.49/0.45 inference(avatar_split_clause,[],[f2460,f2004,f2463])).
% 0.49/0.45 thf(f2497,plain,(
% 0.49/0.45 ($true != ((coindu335574135_lnull @ a @ coindu1598213697e_LNil @ a))) | (spl117_51 | ~spl117_69)),
% 0.49/0.45 inference(superposition,[],[f2231,f2465])).
% 0.49/0.45 thf(f2505,definition,(
% 0.49/0.45 spl117_71 <=> ($true = ((coindu335574135_lnull @ a @ coindu1598213697e_LNil @ a)))),
% 0.49/0.45 introduced(definition,[new_symbols(definition,[spl117_71])],[avatar_definition])).
% 0.49/0.45 thf(f2507,plain,(
% 0.49/0.45 ($true != ((coindu335574135_lnull @ a @ coindu1598213697e_LNil @ a))) | spl117_71),
% 0.49/0.45 inference(avatar_component_clause,[],[f2505])).
% 0.49/0.45 thf(f2508,plain,(
% 0.49/0.45 ~spl117_71 | spl117_51 | ~spl117_69),
% 0.49/0.45 inference(avatar_split_clause,[],[f2497,f2463,f2229,f2505])).
% 0.49/0.45 thf(f2682,plain,(
% 0.49/0.45 ($true != $true) | spl117_71),
% 0.49/0.45 inference(superposition,[],[f2507,f1691])).
% 0.49/0.45 thf(f2685,plain,(
% 0.49/0.45 $false | spl117_71),
% 0.49/0.45 inference(trivial_inequality_removal,[],[f2682])).
% 0.49/0.45 thf(f2686,plain,(
% 0.49/0.45 spl117_71),
% 0.49/0.45 inference(avatar_contradiction_clause,[],[f2685])).
% 0.49/0.45 cnf(s5, plain, ~spl117_6, inference(sat_conversion,[],[f2007])).
% 0.49/0.45 cnf(s50, plain, ~spl117_51, inference(sat_conversion,[],[f2232])).
% 0.49/0.45 cnf(s68, plain, spl117_6 | spl117_69, inference(sat_conversion,[],[f2466])).
% 0.49/0.45 cnf(s70, plain, spl117_51 | ~spl117_69 | ~spl117_71, inference(sat_conversion,[],[f2508])).
% 0.49/0.45 cnf(s71, plain, spl117_71, inference(sat_conversion,[],[f2686])).
% 0.49/0.45 cnf(s72, plain, spl117_51 | ~spl117_69, inference(rat,[],[s70,s71])).
% 0.49/0.45 cnf(s73, plain, ~spl117_69, inference(rat,[],[s72,s50])).
% 0.49/0.45 cnf(s74, plain, spl117_6, inference(rat,[],[s68,s73])).
% 0.49/0.45 cnf(s75, plain, $false, inference(rat,[],[s5,s74])).
% 0.49/0.45 thf(f2695,plain,(
% 0.49/0.45 $false),
% 0.49/0.45 inference(avatar_sat_refutation,[],[s75])).
% 0.49/0.45 % SZS output end Proof for theBenchmark
% 0.49/0.45 % (3512491)------------------------------
% 0.49/0.45 % (3512491)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.49/0.45 % (3512491)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.49/0.45 % (3512491)CaDiCaL version: 2.1.3
% 0.49/0.45 % (3512491)Termination reason: Refutation
% 0.49/0.45 % (3512491)Time elapsed: 0.101 s
% 0.49/0.45 % (3512491)Peak memory usage: 15 MB
% 0.49/0.45 % (3512491)Instructions burned: 189 (million)
% 0.49/0.45 % (3512469)Success in time 0.159 s
% 0.49/0.45 % Vampire exiting
%------------------------------------------------------------------------------