%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : COL043-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n015.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 : Tue Sep 29 09:37:42 AM UTC 2026
% Result : Unsatisfiable 0.36s 2.70s
% Output : Refutation 0.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 14 ( 14 unt; 0 def)
% Number of atoms : 14 ( 13 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 12 ( 3 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 30 ( 30 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : apply(apply(apply(b,X0),X1),X2) = apply(X0,apply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_definition) ).
fof(f2,axiom,
! [X2,X0,X1] : apply(apply(apply(h,X0),X1),X2) = apply(apply(apply(X0,X1),X2),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',h_definition) ).
fof(f3,negated_conjecture,
! [X0] : apply(X0,f(X0)) != apply(f(X0),apply(X0,f(X0))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_fixed_point) ).
fof(f8,plain,
! [X2,X0,X1] : apply(apply(apply(h,apply(b,X0)),X1),X2) = apply(apply(X0,apply(X1,X2)),X1),
inference(superposition,[],[f2,f1]) ).
fof(f12,plain,
! [X0,X1] : apply(apply(apply(h,h),X0),X1) = apply(apply(apply(X0,X1),X0),X1),
inference(superposition,[],[f2,f2]) ).
fof(f14,plain,
! [X0,X1] : apply(X0,apply(X1,f(apply(apply(b,X0),X1)))) != apply(f(apply(apply(b,X0),X1)),apply(X0,apply(X1,f(apply(apply(b,X0),X1))))),
inference(superposition,[],[f3,f1]) ).
fof(f15,plain,
! [X2,X0,X1] : apply(X2,apply(X0,apply(X1,f(apply(apply(b,X2),apply(apply(b,X0),X1)))))) != apply(f(apply(apply(b,X2),apply(apply(b,X0),X1))),apply(X2,apply(X0,apply(X1,f(apply(apply(b,X2),apply(apply(b,X0),X1))))))),
inference(superposition,[],[f14,f1]) ).
fof(f40,plain,
! [X2,X0,X1] : apply(X0,apply(apply(X1,X2),X1)) = apply(apply(apply(h,apply(b,apply(b,X0))),X1),X2),
inference(superposition,[],[f1,f8]) ).
fof(f79,plain,
! [X0,X1] : apply(apply(apply(h,h),apply(b,apply(b,X0))),X1) = apply(X0,apply(apply(X1,apply(b,apply(b,X0))),X1)),
inference(superposition,[],[f2,f40]) ).
fof(f112,plain,
! [X2,X3,X0,X1] : apply(X0,apply(X1,apply(X2,apply(X3,f(apply(apply(b,apply(apply(b,X0),X1)),apply(apply(b,X2),X3))))))) != apply(f(apply(apply(b,apply(apply(b,X0),X1)),apply(apply(b,X2),X3))),apply(X0,apply(X1,apply(X2,apply(X3,f(apply(apply(b,apply(apply(b,X0),X1)),apply(apply(b,X2),X3)))))))),
inference(superposition,[],[f15,f1]) ).
fof(f151,plain,
! [X2,X0,X1] : apply(X0,apply(apply(apply(X1,apply(b,apply(b,apply(b,X0)))),X1),X2)) = apply(apply(apply(apply(h,h),apply(b,apply(b,apply(b,X0)))),X1),X2),
inference(superposition,[],[f1,f79]) ).
fof(f531,plain,
! [X0] : apply(apply(apply(h,h),apply(h,h)),apply(b,apply(b,apply(b,X0)))) = apply(X0,apply(apply(apply(h,h),apply(h,h)),apply(b,apply(b,apply(b,X0))))),
inference(superposition,[],[f151,f12]) ).
fof(f615,plain,
apply(apply(apply(h,h),apply(h,h)),apply(b,apply(b,apply(b,f(apply(apply(b,apply(apply(b,apply(apply(h,h),apply(h,h))),b)),apply(apply(b,b),b))))))) != apply(apply(apply(h,h),apply(h,h)),apply(b,apply(b,apply(b,f(apply(apply(b,apply(apply(b,apply(apply(h,h),apply(h,h))),b)),apply(apply(b,b),b))))))),
inference(superposition,[],[f112,f531]) ).
fof(f616,plain,
$false,
inference(trivial_inequality_removal,[],[f615]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : COL043-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.10 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.24/0.32 % Computer : n015.cluster.edu
% 0.24/0.32 % Model : x86_64 x86_64
% 0.24/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.24/0.32 % Memory : 8046.5625MB
% 0.24/0.32 % OS : Linux 6.8.0-71-generic
% 0.24/0.32 % CPULimit : 300
% 0.24/0.32 % WCLimit : 300
% 0.24/0.32 % DateTime : Mon Sep 28 21:33:47 UTC 2026
% 0.24/0.32 % CPUTime :
% 0.24/0.32 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.24/0.38 Running first-order theorem proving
% 0.24/0.38 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.36/2.70 % (3056254)Detected a unit-equality problem, will run specialized UEQ schedule.
% 0.36/2.70 % (3056260)lrs+11_1_ncem=casc2026/models/loop6.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=1535102134:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 0.36/2.70 % (3056259)lrs+1002_1_ncem=casc2026/models/loop7.pt:sil=128000:tgt=ground:npcc=on:drc=off:sp=reverse_frequency:spb=goal:acc=on:s2agt=16:kmz=on:sac=on:random_seed=2998561278:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 0.36/2.70 % (3056262)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=1240972183:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 0.36/2.70 % (3056261)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=3427632107:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 0.36/2.70 % (3056263)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=3913251587:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 0.36/2.70 % (3056264)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=683778832:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 0.36/2.70 % (3056265)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=3518699380:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 0.36/2.70 % (3056262)Instruction limit reached!
% 0.36/2.70 % (3056262)------------------------------
% 0.36/2.70 % (3056262)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.36/2.70 % (3056262)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.36/2.70 % (3056262)CaDiCaL version: 2.1.3
% 0.36/2.70 % (3056262)Termination reason: Instruction limit
% 0.36/2.70 % (3056262)Termination phase: Saturation
% 0.36/2.70 % (3056262)Time elapsed: 0.138 s
% 0.36/2.70 % (3056262)Peak memory usage: 89 MB
% 0.36/2.70 % (3056262)Instructions burned: 136 (million)
% 0.36/2.70 % (3056263)Instruction limit reached!
% 0.36/2.70 % (3056263)------------------------------
% 0.36/2.70 % (3056263)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.36/2.70 % (3056263)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.36/2.70 % (3056263)CaDiCaL version: 2.1.3
% 0.36/2.70 % (3056263)Termination reason: Instruction limit
% 0.36/2.70 % (3056263)Termination phase: Saturation
% 0.36/2.70 % (3056263)Time elapsed: 0.166 s
% 0.36/2.70 % (3056263)Peak memory usage: 89 MB
% 0.36/2.70 % (3056263)Instructions burned: 181 (million)
% 0.36/2.70 % (3056264)Instruction limit reached!
% 0.36/2.70 % (3056264)------------------------------
% 0.36/2.70 % (3056264)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.36/2.70 % (3056264)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.36/2.70 % (3056264)CaDiCaL version: 2.1.3
% 0.36/2.70 % (3056264)Termination reason: Instruction limit
% 0.36/2.70 % (3056264)Termination phase: Saturation
% 0.36/2.70 % (3056264)Time elapsed: 0.270 s
% 0.36/2.70 % (3056264)Peak memory usage: 91 MB
% 0.36/2.70 % (3056264)Instructions burned: 257 (million)
% 0.36/2.70 % (3056273)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=2264424506:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2995 on theBenchmark for (2995ds/2051Mi)
% 0.36/2.70 % (3056274)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=2592723711:i=4948:ss=axioms:sgt=16_2995 on theBenchmark for (2995ds/4948Mi)
% 0.36/2.70 % (3056275)lrs+10_5:1_sil=8000:sos=all:urr=on:br=off:flr=on:random_seed=1279480236:i=215:ep=RSTC_2994 on theBenchmark for (2994ds/215Mi)
% 0.36/2.70 % (3056260)First to succeed.
% 0.36/2.70 % (3056260)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3056254"
% 0.36/2.70 % (3056275)Instruction limit reached!
% 0.36/2.70 % (3056275)------------------------------
% 0.36/2.70 % (3056275)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.36/2.70 % (3056275)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.36/2.70 % (3056275)CaDiCaL version: 2.1.3
% 0.36/2.70 % (3056275)Termination reason: Instruction limit
% 0.36/2.70 % (3056275)Termination phase: Saturation
% 0.36/2.70 % (3056275)Time elapsed: 0.221 s
% 0.36/2.70 % (3056275)Peak memory usage: 89 MB
% 0.36/2.70 % (3056275)Instructions burned: 215 (million)
% 0.36/2.70 % (3056260)Refutation found. Thanks to Tanya!
% 0.36/2.70 % SZS status Unsatisfiable for theBenchmark
% 0.36/2.70 % SZS output start Proof for theBenchmark
% See solution above
% 0.36/2.70 % (3056260)------------------------------
% 0.36/2.70 % (3056260)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.36/2.70 % (3056260)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.36/2.70 % (3056260)CaDiCaL version: 2.1.3
% 0.36/2.70 % (3056260)Termination reason: Refutation
% 0.36/2.70 % (3056260)Time elapsed: 0.713 s
% 0.36/2.70 % (3056260)Peak memory usage: 132 MB
% 0.36/2.70 % (3056260)Instructions burned: 1240 (million)
% 0.36/2.70 % (3056260)------------------------------
% 0.36/2.70 % (3056260)------------------------------
% 0.36/2.70 % (3056254)Success in time 1.172 s
% 0.36/2.70 % Vampire exiting
%------------------------------------------------------------------------------