%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : DAT294^1 : 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 : n016.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 07:48:43 AM UTC 2026
% Result : Theorem 0.21s 0.37s
% Output : Refutation 0.78s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : DAT294^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n016.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Sep 29 18:28:50 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running higher-order theorem proving
% 0.09/0.23 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
% 0.21/0.36 % (726395)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.36 % (726405)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2471225055:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.21/0.36 % (726406)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.21/0.36 % (726406)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
% 0.21/0.36 % (726402)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3289101302:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.21/0.36 % (726400)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2774885547:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.36 % (726401)lrs+10_16_si=on:nwc=1.5:random_seed=1829883860:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.21/0.36 % (726404)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2162331457:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.21/0.36 % (726403)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=2268199148: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)
% 0.21/0.36 % (726406)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=806495699:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.21/0.36 % (726402)Instruction limit reached!
% 0.21/0.36 % (726402)------------------------------
% 0.21/0.36 % (726402)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.36 % (726402)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.36 % (726402)CaDiCaL version: 2.1.3
% 0.21/0.36 % (726402)Termination reason: Instruction limit
% 0.21/0.36 % (726402)Termination phase: Saturation
% 0.21/0.36 % (726402)Time elapsed: 0.003 s
% 0.21/0.36 % (726402)Peak memory usage: 12 MB
% 0.21/0.36 % (726402)Instructions burned: 3 (million)
% 0.21/0.36 % (726401)Instruction limit reached!
% 0.21/0.36 % (726401)------------------------------
% 0.21/0.36 % (726401)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.36 % (726401)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.36 % (726401)CaDiCaL version: 2.1.3
% 0.21/0.36 % (726401)Termination reason: Instruction limit
% 0.21/0.36 % (726401)Termination phase: Saturation
% 0.21/0.36 % (726401)Time elapsed: 0.012 s
% 0.21/0.36 % (726401)Peak memory usage: 12 MB
% 0.21/0.36 % (726401)Instructions burned: 19 (million)
% 0.21/0.36 % (726404)Instruction limit reached!
% 0.21/0.36 % (726404)------------------------------
% 0.21/0.36 % (726404)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.36 % (726404)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.36 % (726404)CaDiCaL version: 2.1.3
% 0.21/0.36 % (726404)Termination reason: Instruction limit
% 0.21/0.36 % (726404)Termination phase: Saturation
% 0.21/0.36 % (726404)Time elapsed: 0.015 s
% 0.21/0.36 % (726404)Peak memory usage: 12 MB
% 0.21/0.36 % (726404)Instructions burned: 25 (million)
% 0.21/0.36 % (726405)Instruction limit reached!
% 0.21/0.36 % (726405)------------------------------
% 0.21/0.36 % (726405)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.36 % (726405)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.36 % (726405)CaDiCaL version: 2.1.3
% 0.21/0.36 % (726405)Termination reason: Instruction limit
% 0.21/0.36 % (726405)Termination phase: Saturation
% 0.21/0.36 % (726405)Time elapsed: 0.023 s
% 0.21/0.36 % (726405)Peak memory usage: 13 MB
% 0.21/0.36 % (726405)Instructions burned: 78 (million)
% 0.21/0.36 % (726414)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=73069702:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.21/0.36 % (726414)Instruction limit reached!
% 0.21/0.36 % (726414)------------------------------
% 0.21/0.36 % (726414)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.36 % (726414)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.37 % (726414)CaDiCaL version: 2.1.3
% 0.21/0.37 % (726414)Termination reason: Instruction limit
% 0.21/0.37 % (726414)Termination phase: Saturation
% 0.21/0.37 % (726414)Time elapsed: 0.002 s
% 0.21/0.37 % (726414)Peak memory usage: 12 MB
% 0.21/0.37 % (726414)Instructions burned: 2 (million)
% 0.21/0.37 % (726417)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=1050029385:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.21/0.37 % (726415)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=21451605:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.21/0.37 % (726416)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.21/0.37 % (726416)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=3737376646:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.21/0.37 % (726415)Instruction limit reached!
% 0.21/0.37 % (726415)------------------------------
% 0.21/0.37 % (726415)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.37 % (726417)Instruction limit reached!
% 0.21/0.37 % (726417)------------------------------
% 0.21/0.37 % (726417)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.37 % (726417)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.37 % (726415)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.37 % (726417)CaDiCaL version: 2.1.3
% 0.21/0.37 % (726417)Termination reason: Instruction limit
% 0.21/0.37 % (726417)Termination phase: Saturation
% 0.21/0.37 % (726415)CaDiCaL version: 2.1.3
% 0.21/0.37 % (726417)Time elapsed: 0.005 s
% 0.21/0.37 % (726415)Termination reason: Instruction limit
% 0.21/0.37 % (726415)Termination phase: Saturation
% 0.21/0.37 % (726417)Peak memory usage: 12 MB
% 0.21/0.37 % (726415)Time elapsed: 0.004 s
% 0.21/0.37 % (726417)Instructions burned: 14 (million)
% 0.21/0.37 % (726415)Peak memory usage: 12 MB
% 0.21/0.37 % (726415)Instructions burned: 6 (million)
% 0.21/0.37 % (726416)Instruction limit reached!
% 0.21/0.37 % (726416)------------------------------
% 0.21/0.37 % (726416)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.37 % (726416)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.37 % (726416)CaDiCaL version: 2.1.3
% 0.21/0.37 % (726416)Termination reason: Instruction limit
% 0.21/0.37 % (726416)Termination phase: Saturation
% 0.21/0.37 % (726416)Time elapsed: 0.005 s
% 0.21/0.37 % (726416)Peak memory usage: 12 MB
% 0.21/0.37 % (726416)Instructions burned: 8 (million)
% 0.21/0.37 % (726419)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
% 0.21/0.37 % (726419)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.21/0.37 % (726419)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=1285185024:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.21/0.37 % (726423)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=2774887004:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.21/0.37 % (726400)Instruction limit reached!
% 0.21/0.37 % (726400)------------------------------
% 0.21/0.37 % (726400)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.37 % (726400)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.37 % (726400)CaDiCaL version: 2.1.3
% 0.21/0.37 % (726400)Termination reason: Instruction limit
% 0.21/0.37 % (726400)Termination phase: Saturation
% 0.21/0.37 % (726400)Time elapsed: 0.050 s
% 0.21/0.37 % (726400)Peak memory usage: 12 MB
% 0.21/0.37 % (726400)Instructions burned: 87 (million)
% 0.21/0.37 % (726424)lrs+10_1_si=on:cs=on:random_seed=3634735277:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.21/0.37 % (726425)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.21/0.37 % (726425)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=2509743680:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.21/0.37 % (726424)Instruction limit reached!
% 0.21/0.37 % (726424)------------------------------
% 0.21/0.37 % (726424)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.37 % (726424)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.37 % (726424)CaDiCaL version: 2.1.3
% 0.21/0.37 % (726424)Termination reason: Instruction limit
% 0.21/0.37 % (726424)Termination phase: Saturation
% 0.21/0.37 % (726424)Time elapsed: 0.005 s
% 0.21/0.37 % (726424)Peak memory usage: 12 MB
% 0.21/0.37 % (726424)Instructions burned: 9 (million)
% 0.21/0.37 % (726419)Instruction limit reached!
% 0.21/0.37 % (726419)------------------------------
% 0.21/0.37 % (726419)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.37 % (726419)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.37 % (726419)CaDiCaL version: 2.1.3
% 0.21/0.37 % (726419)Termination reason: Instruction limit
% 0.21/0.37 % (726419)Termination phase: Saturation
% 0.21/0.37 % (726419)Time elapsed: 0.017 s
% 0.21/0.37 % (726419)Peak memory usage: 12 MB
% 0.21/0.37 % (726419)Instructions burned: 28 (million)
% 0.21/0.37 % (726425)Instruction limit reached!
% 0.21/0.37 % (726425)------------------------------
% 0.21/0.37 % (726425)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.37 % (726425)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.37 % (726425)CaDiCaL version: 2.1.3
% 0.21/0.37 % (726425)Termination reason: Instruction limit
% 0.21/0.37 % (726425)Termination phase: Saturation
% 0.21/0.37 % (726425)Time elapsed: 0.003 s
% 0.21/0.37 % (726425)Peak memory usage: 12 MB
% 0.21/0.37 % (726425)Instructions burned: 4 (million)
% 0.21/0.37 % (726428)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=2959270605:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.21/0.37 % (726428)Refutation not found, incomplete strategy
% 0.21/0.37 % (726428)------------------------------
% 0.21/0.37 % (726428)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.37 % (726428)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.37 % (726428)CaDiCaL version: 2.1.3
% 0.21/0.37 % (726428)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.37 % (726428)Time elapsed: 0.001 s
% 0.21/0.37 % (726428)Peak memory usage: 12 MB
% 0.21/0.37 % (726423)Instruction limit reached!
% 0.21/0.37 % (726423)------------------------------
% 0.21/0.37 % (726423)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.37 % (726423)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.37 % (726423)CaDiCaL version: 2.1.3
% 0.21/0.37 % (726423)Termination reason: Instruction limit
% 0.21/0.37 % (726423)Termination phase: Saturation
% 0.21/0.37 % (726423)Time elapsed: 0.025 s
% 0.21/0.37 % (726423)Peak memory usage: 13 MB
% 0.21/0.37 % (726423)Instructions burned: 88 (million)
% 0.21/0.37 % (726428)------------------------------
% 0.21/0.37 % (726428)------------------------------
% 0.21/0.37 % (726431)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=3792561916:st=2:i=249:sd=1:rtra=on:ss=axioms_2999 on theBenchmark for (2999ds/249Mi)
% 0.21/0.37 % (726431)Refutation not found, incomplete strategy
% 0.21/0.37 % (726431)------------------------------
% 0.21/0.37 % (726431)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.37 % (726431)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.37 % (726431)CaDiCaL version: 2.1.3
% 0.21/0.37 % (726431)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.37 % (726431)Time elapsed: 0.002 s
% 0.21/0.37 % (726431)Peak memory usage: 12 MB
% 0.21/0.37 % (726431)Instructions burned: 1 (million)
% 0.21/0.37 % (726433)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=4197028449:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2999 on theBenchmark for (2999ds/14Mi)
% 0.21/0.37 % (726431)------------------------------
% 0.21/0.37 % (726431)------------------------------
% 0.21/0.37 % (726432)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=171123146:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/25Mi)
% 0.21/0.37 % (726435)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=3543895968:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 0.21/0.37 % (726406)Instruction limit reached!
% 0.21/0.37 % (726406)------------------------------
% 0.21/0.37 % (726406)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.37 % (726406)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.37 % (726406)CaDiCaL version: 2.1.3
% 0.21/0.37 % (726406)Termination reason: Instruction limit
% 0.21/0.37 % (726406)Termination phase: Saturation
% 0.21/0.37 % (726406)Time elapsed: 0.088 s
% 0.21/0.37 % (726406)Peak memory usage: 12 MB
% 0.21/0.37 % (726406)Instructions burned: 157 (million)
% 0.21/0.37 % (726433) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-726395-726433"...
% 0.21/0.37 % (726433)...printing done.
% 0.21/0.37 % (726433)Refutation found. Thanks to Tanya!
% 0.21/0.37 % SZS status Theorem for theBenchmark
% 0.21/0.37 % SZS output start Proof for theBenchmark
% 0.21/0.37 thf(type_def_5, type, 'type/ind_types/list': $tType > $tType).
% 0.21/0.37 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.21/0.37 thf(type_def_7, type, sK2: $tType).
% 0.21/0.37 thf(func_def_0, type, 'const/lists/ALL': !>[X0: $tType]:(((X0 > $o) > 'type/ind_types/list' @ X0 > $o))).
% 0.21/0.37 thf(func_def_1, type, 'const/ind_types/NIL': !>[X0: $tType]:('type/ind_types/list' @ X0)).
% 0.21/0.37 thf(func_def_2, type, 'const/ind_types/CONS': !>[X0: $tType]:((X0 > 'type/ind_types/list' @ X0 > 'type/ind_types/list' @ X0))).
% 0.21/0.37 thf(func_def_6, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.21/0.37 thf(func_def_7, type, vAND: ($o > $o > $o)).
% 0.21/0.37 thf(func_def_8, type, sK0: !>[X0: $tType]:((('type/ind_types/list' @ X0 > $o) > 'type/ind_types/list' @ X0))).
% 0.21/0.37 thf(func_def_9, type, sK1: !>[X0: $tType]:((('type/ind_types/list' @ X0 > $o) > X0))).
% 0.21/0.37 thf(func_def_10, type, sK3: 'type/ind_types/list' @ sK2).
% 0.21/0.37 thf(func_def_11, type, vNOT: ($o > $o)).
% 0.21/0.37 thf(func_def_12, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.21/0.37 thf(func_def_13, type, db0: !>[X0: $tType]:(X0)).
% 0.21/0.37 thf(f1,axiom,(
% 0.21/0.37 ! [X0 : $tType,X1 : ('type/ind_types/list' @ X0 > $o)] : (((X1 @ 'const/ind_types/NIL' @ X0) & ! [X3 : 'type/ind_types/list' @ X0,X2 : X0] : ((X1 @ X3) => (X1 @ ('const/ind_types/CONS' @ X0 @ X2 @ X3)))) => ! [X2 : 'type/ind_types/list' @ X0] : (X1 @ X2))),
% 0.21/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/ind_types/list_INDUCT_')).
% 0.21/0.37 thf(f2,axiom,(
% 0.21/0.37 ! [X0 : $tType,X2 : (X0 > $o),X3 : 'type/ind_types/list' @ X0,X1 : X0] : ((X2 @ X1) & ('const/lists/ALL' @ X0 @ X2 @ X3) = (('const/lists/ALL' @ X0 @ X2 @ ('const/ind_types/CONS' @ X0 @ X1 @ X3))))),
% 0.21/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/lists/ALL_1')).
% 0.21/0.37 thf(f3,axiom,(
% 0.21/0.37 ! [X0 : $tType,X1 : (X0 > $o)] : ((('const/lists/ALL' @ X0 @ X1 @ 'const/ind_types/NIL' @ X0)) = $true)),
% 0.21/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/lists/ALL_0')).
% 0.21/0.37 thf(f4,conjecture,(
% 0.21/0.37 ! [X0 : $tType,X1 : 'type/ind_types/list' @ X0] : ('const/lists/ALL' @ X0 @ (^[X2 : X0] : ($true)) @ X1)),
% 0.21/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/lists/ALL_T_')).
% 0.21/0.37 thf(f5,negated_conjecture,(
% 0.21/0.37 ~ ! [X0 : $tType,X1 : 'type/ind_types/list' @ X0] : ('const/lists/ALL' @ X0 @ (^[X2 : X0] : ($true)) @ X1)),
% 0.21/0.37 inference(negated_conjecture,[status(cth)],[f4])).
% 0.21/0.37 thf(f6,plain,(
% 0.21/0.37 ~ ! [X0 : $tType,X1 : 'type/ind_types/list' @ X0] : ('const/lists/ALL' @ X0 @ (^[X2 : X0] : ($true)) @ X1)),
% 0.21/0.37 inference(rectify,[],[f5])).
% 0.21/0.37 thf(f7,plain,(
% 0.21/0.37 ~ ! [X0 : $tType,X1 : 'type/ind_types/list' @ X0] : ((('const/lists/ALL' @ X0 @ (^[Y0 : X0]: ($true)) @ X1)) = $true)),
% 0.21/0.37 inference(fool_elimination,[],[f6])).
% 0.21/0.37 thf(f8,plain,(
% 0.21/0.37 ! [X0 : $tType,X1 : (X0 > $o)] : ((('const/lists/ALL' @ X0 @ X1 @ 'const/ind_types/NIL' @ X0)) = $true)),
% 0.21/0.37 inference(fool_elimination,[],[f3])).
% 0.21/0.37 thf(f9,plain,(
% 0.21/0.37 ! [X0 : $tType,X1 : (X0 > $o),X2 : 'type/ind_types/list' @ X0,X3 : X0] : ((X1 @ X3) & ('const/lists/ALL' @ X0 @ X1 @ X2) = (('const/lists/ALL' @ X0 @ X1 @ ('const/ind_types/CONS' @ X0 @ X3 @ X2))))),
% 0.21/0.37 inference(rectify,[],[f2])).
% 0.21/0.37 thf(f10,plain,(
% 0.21/0.37 ! [X0 : $tType,X3 : X0,X2 : 'type/ind_types/list' @ X0,X1 : (X0 > $o)] : (((('const/lists/ALL' @ X0 @ X1 @ X2) & (X1 @ X3))) = (('const/lists/ALL' @ X0 @ X1 @ ('const/ind_types/CONS' @ X0 @ X3 @ X2))))),
% 0.21/0.37 inference(fool_elimination,[],[f9])).
% 0.21/0.37 thf(f11,plain,(
% 0.21/0.37 ! [X0 : $tType,X1 : ('type/ind_types/list' @ X0 > $o)] : (((X1 @ 'const/ind_types/NIL' @ X0) & ! [X2 : 'type/ind_types/list' @ X0,X3 : X0] : ((X1 @ X2) => (X1 @ ('const/ind_types/CONS' @ X0 @ X3 @ X2)))) => ! [X4 : 'type/ind_types/list' @ X0] : (X1 @ X4))),
% 0.21/0.37 inference(rectify,[],[f1])).
% 0.21/0.37 thf(f12,plain,(
% 0.21/0.37 ! [X0 : $tType,X1 : ('type/ind_types/list' @ X0 > $o)] : ((! [X3 : X0,X2 : 'type/ind_types/list' @ X0] : ((((X1 @ X2)) = $true) => ($true = ((X1 @ ('const/ind_types/CONS' @ X0 @ X3 @ X2))))) & (((X1 @ 'const/ind_types/NIL' @ X0)) = $true)) => ! [X4 : 'type/ind_types/list' @ X0] : (((X1 @ X4)) = $true))),
% 0.21/0.37 inference(fool_elimination,[],[f11])).
% 0.21/0.37 thf(f13,plain,(
% 0.21/0.37 ? [X0 : $tType,X1 : 'type/ind_types/list' @ X0] : ((('const/lists/ALL' @ X0 @ (^[Y0 : X0]: ($true)) @ X1)) != $true)),
% 0.21/0.37 inference(ennf_transformation,[],[f7])).
% 0.21/0.37 thf(f14,plain,(
% 0.21/0.37 ! [X0 : $tType,X1 : ('type/ind_types/list' @ X0 > $o)] : (! [X4 : 'type/ind_types/list' @ X0] : (((X1 @ X4)) = $true) | (? [X2 : 'type/ind_types/list' @ X0,X3 : X0] : (($true != ((X1 @ ('const/ind_types/CONS' @ X0 @ X3 @ X2)))) & (((X1 @ X2)) = $true)) | (((X1 @ 'const/ind_types/NIL' @ X0)) != $true)))),
% 0.21/0.37 inference(ennf_transformation,[],[f12])).
% 0.21/0.37 thf(f15,plain,(
% 0.21/0.37 ! [X0 : $tType,X1 : ('type/ind_types/list' @ X0 > $o)] : (! [X4 : 'type/ind_types/list' @ X0] : (((X1 @ X4)) = $true) | (((X1 @ 'const/ind_types/NIL' @ X0)) != $true) | ? [X2 : 'type/ind_types/list' @ X0,X3 : X0] : (($true != ((X1 @ ('const/ind_types/CONS' @ X0 @ X3 @ X2)))) & (((X1 @ X2)) = $true)))),
% 0.21/0.37 inference(flattening,[],[f14])).
% 0.21/0.37 thf(f16,plain,(
% 0.21/0.37 ! [X0 : $tType,X1 : X0,X2 : 'type/ind_types/list' @ X0,X3 : (X0 > $o)] : ((('const/lists/ALL' @ X0 @ X3 @ ('const/ind_types/CONS' @ X0 @ X1 @ X2))) = ((('const/lists/ALL' @ X0 @ X3 @ X2) & (X3 @ X1))))),
% 0.21/0.37 inference(rectify,[],[f10])).
% 0.21/0.37 thf(f17,plain,(
% 0.21/0.37 ! [X0 : $tType,X1 : ('type/ind_types/list' @ X0 > $o)] : (! [X2 : 'type/ind_types/list' @ X0] : (((X1 @ X2)) = $true) | (((X1 @ 'const/ind_types/NIL' @ X0)) != $true) | ? [X3 : 'type/ind_types/list' @ X0,X4 : X0] : ((((X1 @ ('const/ind_types/CONS' @ X0 @ X4 @ X3))) != $true) & (((X1 @ X3)) = $true)))),
% 0.21/0.37 inference(rectify,[],[f15])).
% 0.21/0.37 thf(f18,plain,(
% 0.21/0.37 ! [X0 : $tType,X1 : ('type/ind_types/list' @ X0 > $o)] : (! [X2 : 'type/ind_types/list' @ X0] : (((X1 @ X2)) = $true) | (((X1 @ 'const/ind_types/NIL' @ X0)) != $true) | ((((X1 @ ('const/ind_types/CONS' @ X0 @ (sK1 @ X0 @ X1) @ (sK0 @ X0 @ X1)))) != $true) & (((X1 @ (sK0 @ X0 @ X1))) = $true)))),
% 0.21/0.37 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP]),skolemize(X4,sK1 @ X0 @ X1),skolemize(X4,sK1 @ X0 @ X1)],[f17])).
% 0.21/0.37 thf(f19,plain,(
% 0.21/0.37 ((('const/lists/ALL' @ sK2 @ (^[Y0 : sK2]: ($true)) @ sK3)) != $true)),
% 0.21/0.37 inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(X0,sK2),skolemize(X1,sK3)],[f13])).
% 0.21/0.37 thf(f20,plain,(
% 0.21/0.37 ( ! [X0 : $tType,X2 : 'type/ind_types/list' @ X0,X3 : (X0 > $o),X1 : X0] : (((('const/lists/ALL' @ X0 @ X3 @ ('const/ind_types/CONS' @ X0 @ X1 @ X2))) = ((('const/lists/ALL' @ X0 @ X3 @ X2) & (X3 @ X1))))) )),
% 0.21/0.37 inference(cnf_transformation,[],[f16])).
% 0.21/0.37 thf(f21,plain,(
% 0.21/0.37 ( ! [X0 : $tType,X2 : 'type/ind_types/list' @ X0,X1 : ('type/ind_types/list' @ X0 > $o)] : ((((X1 @ 'const/ind_types/NIL' @ X0)) != $true) | (((X1 @ (sK0 @ X0 @ X1))) = $true) | (((X1 @ X2)) = $true)) )),
% 0.21/0.37 inference(cnf_transformation,[],[f18])).
% 0.21/0.37 thf(f22,plain,(
% 0.21/0.37 ( ! [X0 : $tType,X2 : 'type/ind_types/list' @ X0,X1 : ('type/ind_types/list' @ X0 > $o)] : ((((X1 @ ('const/ind_types/CONS' @ X0 @ (sK1 @ X0 @ X1) @ (sK0 @ X0 @ X1)))) != $true) | (((X1 @ X2)) = $true) | (((X1 @ 'const/ind_types/NIL' @ X0)) != $true)) )),
% 0.21/0.37 inference(cnf_transformation,[],[f18])).
% 0.21/0.37 thf(f23,plain,(
% 0.21/0.37 ((('const/lists/ALL' @ sK2 @ (^[Y0 : sK2]: ($true)) @ sK3)) != $true)),
% 0.21/0.37 inference(cnf_transformation,[],[f19])).
% 0.21/0.37 thf(f24,plain,(
% 0.21/0.37 ( ! [X0 : $tType,X1 : (X0 > $o)] : (((('const/lists/ALL' @ X0 @ X1 @ 'const/ind_types/NIL' @ X0)) = $true)) )),
% 0.21/0.37 inference(cnf_transformation,[],[f8])).
% 0.78/0.37 thf(f27,plain,(
% 0.78/0.37 ( ! [X0 : $tType,X2 : 'type/ind_types/list' @ X0,X3 : (X0 > $o),X1 : X0] : ((((('const/lists/ALL' @ X0 @ X3 @ X2) & (X3 @ X1))) = $false) | ((('const/lists/ALL' @ X0 @ X3 @ ('const/ind_types/CONS' @ X0 @ X1 @ X2))) = $true)) )),
% 0.78/0.37 inference(iff_proxy_clausification,[],[f20])).
% 0.78/0.37 thf(f31,plain,(
% 0.78/0.37 ( ! [X0 : $tType,X2 : 'type/ind_types/list' @ X0,X3 : (X0 > $o),X1 : X0] : (((('const/lists/ALL' @ X0 @ X3 @ ('const/ind_types/CONS' @ X0 @ X1 @ X2))) = $true) | ($false = ((X3 @ X1))) | ($false = (('const/lists/ALL' @ X0 @ X3 @ X2)))) )),
% 0.78/0.37 inference(and_proxy_clausification,[],[f27])).
% 0.78/0.37 thf(f38,plain,(
% 0.78/0.37 ( ! [X0 : $tType,X2 : 'type/ind_types/list' @ X0,X1 : (X0 > $o)] : (($true = (('const/lists/ALL' @ X0 @ X1 @ X2))) | ($true != $true) | ((('const/lists/ALL' @ X0 @ X1 @ (sK0 @ X0 @ ('const/lists/ALL' @ X0 @ X1)))) = $true)) )),
% 0.78/0.37 inference(constrained_superposition,[],[f21,f24])).
% 0.78/0.37 thf(f47,plain,(
% 0.78/0.37 ( ! [X0 : $tType,X2 : 'type/ind_types/list' @ X0,X1 : (X0 > $o)] : (($true = (('const/lists/ALL' @ X0 @ X1 @ X2))) | ((('const/lists/ALL' @ X0 @ X1 @ (sK0 @ X0 @ ('const/lists/ALL' @ X0 @ X1)))) = $true)) )),
% 0.78/0.37 inference(trivial_inequality_removal,[],[f38])).
% 0.78/0.37 thf(f55,plain,(
% 0.78/0.37 ((('const/lists/ALL' @ sK2 @ (^[Y0 : sK2]: ($true)) @ ('const/ind_types/CONS' @ sK2 @ (sK1 @ sK2 @ ('const/lists/ALL' @ sK2 @ (^[Y0 : sK2]: ($true)))) @ (sK0 @ sK2 @ ('const/lists/ALL' @ sK2 @ (^[Y0 : sK2]: ($true))))))) != $true)),
% 0.78/0.37 inference(unit_resulting_resolution,[],[f22,f23,f24])).
% 0.78/0.37 thf(f153,plain,(
% 0.78/0.37 ( ! [X0 : $tType,X1 : (X0 > $o)] : (((('const/lists/ALL' @ X0 @ X1 @ (sK0 @ X0 @ ('const/lists/ALL' @ X0 @ X1)))) = $true) | ($true != $true)) )),
% 0.78/0.37 inference(equality_factoring,[],[f47])).
% 0.78/0.37 thf(f164,plain,(
% 0.78/0.37 ( ! [X0 : $tType,X1 : (X0 > $o)] : (((('const/lists/ALL' @ X0 @ X1 @ (sK0 @ X0 @ ('const/lists/ALL' @ X0 @ X1)))) = $true)) )),
% 0.78/0.37 inference(trivial_inequality_removal,[],[f153])).
% 0.78/0.37 thf(f171,plain,(
% 0.78/0.37 ($true != $true) | ((('const/lists/ALL' @ sK2 @ (^[Y0 : sK2]: ($true)) @ (sK0 @ sK2 @ ('const/lists/ALL' @ sK2 @ (^[Y0 : sK2]: ($true)))))) = $false) | ($false = (((^[Y0 : sK2]: ($true)) @ (sK1 @ sK2 @ ('const/lists/ALL' @ sK2 @ (^[Y0 : sK2]: ($true)))))))),
% 0.78/0.37 inference(constrained_superposition,[],[f55,f31])).
% 0.78/0.37 thf(f175,plain,(
% 0.78/0.37 ((('const/lists/ALL' @ sK2 @ (^[Y0 : sK2]: ($true)) @ (sK0 @ sK2 @ ('const/lists/ALL' @ sK2 @ (^[Y0 : sK2]: ($true)))))) = $false) | ($false = (((^[Y0 : sK2]: ($true)) @ (sK1 @ sK2 @ ('const/lists/ALL' @ sK2 @ (^[Y0 : sK2]: ($true)))))))),
% 0.78/0.37 inference(trivial_inequality_removal,[],[f171])).
% 0.78/0.37 thf(f176,plain,(
% 0.78/0.37 ((('const/lists/ALL' @ sK2 @ (^[Y0 : sK2]: ($true)) @ (sK0 @ sK2 @ ('const/lists/ALL' @ sK2 @ (^[Y0 : sK2]: ($true)))))) = $false) | ($false = $true)),
% 0.78/0.37 inference(beta-eta_normalization,[],[f175])).
% 0.78/0.37 thf(f177,plain,(
% 0.78/0.37 ((('const/lists/ALL' @ sK2 @ (^[Y0 : sK2]: ($true)) @ (sK0 @ sK2 @ ('const/lists/ALL' @ sK2 @ (^[Y0 : sK2]: ($true)))))) = $false)),
% 0.78/0.37 inference(trivial_inequality_removal,[],[f176])).
% 0.78/0.37 thf(f181,plain,(
% 0.78/0.37 ($false = $true)),
% 0.78/0.37 inference(forward_demodulation,[],[f177,f164])).
% 0.78/0.37 thf(f182,plain,(
% 0.78/0.37 $false),
% 0.78/0.37 inference(trivial_inequality_removal,[],[f181])).
% 0.78/0.37 % SZS output end Proof for theBenchmark
% 0.78/0.37 % (726433)------------------------------
% 0.78/0.37 % (726433)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.78/0.37 % (726433)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.78/0.37 % (726433)CaDiCaL version: 2.1.3
% 0.78/0.37 % (726433)Termination reason: Refutation
% 0.78/0.37 % (726433)Time elapsed: 0.009 s
% 0.78/0.37 % (726433)Peak memory usage: 13 MB
% 0.78/0.37 % (726433)Instructions burned: 13 (million)
% 0.78/0.37 % (726395)Success in time 0.132 s
% 0.78/0.37 % Vampire exiting
%------------------------------------------------------------------------------