%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : COL006-1 : 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 : 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 : Tue Sep 29 09:37:36 AM UTC 2026
% Result : Unsatisfiable 10.34s 2.50s
% Output : Refutation 10.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 3
% Syntax : Number of formulae : 12 ( 12 unt; 0 def)
% Number of atoms : 12 ( 11 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 10 ( 2 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 : 24 ( 24 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
! [X2,X0,X1] : apply(apply(apply(s,X0),X1),X2) = apply(apply(X0,X2),apply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s_definition) ).
fof(f2,negated_conjecture,
! [X0,X1] : apply(apply(k,X0),X1) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',k_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(f6,plain,
! [X2,X0,X1] : apply(X0,apply(X1,X2)) = apply(apply(apply(s,apply(k,X0)),X1),X2),
inference(superposition,[],[f1,f2]) ).
fof(f13,plain,
! [X0,X1] : apply(apply(apply(s,k),X0),X1) = X1,
inference(superposition,[],[f2,f1]) ).
fof(f18,plain,
! [X2,X0,X1] : apply(X0,apply(X1,apply(X2,X1))) = apply(apply(apply(s,apply(s,apply(k,X0))),X2),X1),
inference(superposition,[],[f1,f6]) ).
fof(f39,plain,
! [X0,X1] : apply(X0,X1) = apply(apply(apply(s,apply(s,k)),X0),X1),
inference(superposition,[],[f1,f13]) ).
fof(f48,plain,
! [X2,X0,X1] : apply(apply(apply(s,apply(s,apply(k,X1))),apply(apply(s,k),X2)),X0) = apply(X1,apply(X0,X0)),
inference(superposition,[],[f18,f13]) ).
fof(f656,plain,
! [X0,X1] : apply(X0,apply(X1,X0)) = apply(apply(apply(s,apply(s,apply(s,k))),X1),X0),
inference(superposition,[],[f1,f39]) ).
fof(f772,plain,
! [X0] : apply(X0,f(X0)) != apply(apply(apply(s,apply(s,apply(s,k))),X0),f(X0)),
inference(superposition,[],[f3,f656]) ).
fof(f847,plain,
! [X0,X1] : apply(apply(X1,X1),f(apply(X1,X1))) != apply(apply(apply(apply(s,apply(s,apply(k,apply(s,apply(s,apply(s,k)))))),apply(apply(s,k),X0)),X1),f(apply(X1,X1))),
inference(superposition,[],[f772,f48]) ).
fof(f884,plain,
$false,
inference(equality_resolution,[],[f847]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL006-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.25 % Computer : n016.cluster.edu
% 0.11/0.25 % Model : x86_64 x86_64
% 0.11/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.25 % Memory : 8046.5625MB
% 0.11/0.25 % OS : Linux 6.8.0-71-generic
% 0.11/0.25 % CPULimit : 300
% 0.11/0.25 % WCLimit : 300
% 0.11/0.25 % DateTime : Mon Sep 28 21:34:19 UTC 2026
% 0.11/0.26 % CPUTime :
% 0.11/0.26 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.25/0.31 Running first-order theorem proving
% 0.25/0.31 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
% 10.22/2.50 % (4045058)Detected a unit-equality problem, will run specialized UEQ schedule.
% 10.22/2.50 % (4045077)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=3871000483:i=1187:sd=4:av=off:ss=axioms:sgt=32_3000 on theBenchmark for (3000ds/1187Mi)
% 10.22/2.50 % (4045073)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=1862820721:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_3000 on theBenchmark for (3000ds/130716Mi)
% 10.22/2.50 % (4045076)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=2370294631:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_3000 on theBenchmark for (3000ds/257Mi)
% 10.22/2.50 % (4045071)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=756388135:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_3000 on theBenchmark for (3000ds/138329Mi)
% 10.22/2.50 % (4045075)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=465453363:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_3000 on theBenchmark for (3000ds/181Mi)
% 10.34/2.50 % (4045072)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=62549146:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_3000 on theBenchmark for (3000ds/130792Mi)
% 10.34/2.50 % (4045074)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=447436869:i=136:bd=preordered:ins=2:av=off_3000 on theBenchmark for (3000ds/136Mi)
% 10.34/2.50 % (4045074)Instruction limit reached!
% 10.34/2.50 % (4045074)------------------------------
% 10.34/2.50 % (4045074)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.34/2.50 % (4045074)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.34/2.50 % (4045074)CaDiCaL version: 2.1.3
% 10.34/2.50 % (4045074)Termination reason: Instruction limit
% 10.34/2.50 % (4045074)Termination phase: Saturation
% 10.34/2.50 % (4045074)Time elapsed: 0.134 s
% 10.34/2.50 % (4045074)Peak memory usage: 89 MB
% 10.34/2.50 % (4045074)Instructions burned: 137 (million)
% 10.34/2.50 % (4045075)Instruction limit reached!
% 10.34/2.50 % (4045075)------------------------------
% 10.34/2.50 % (4045075)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.34/2.50 % (4045075)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.34/2.50 % (4045075)CaDiCaL version: 2.1.3
% 10.34/2.50 % (4045075)Termination reason: Instruction limit
% 10.34/2.50 % (4045075)Termination phase: Saturation
% 10.34/2.50 % (4045075)Time elapsed: 0.164 s
% 10.34/2.50 % (4045075)Peak memory usage: 89 MB
% 10.34/2.50 % (4045075)Instructions burned: 181 (million)
% 10.34/2.50 % (4045076)Instruction limit reached!
% 10.34/2.50 % (4045076)------------------------------
% 10.34/2.50 % (4045076)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.34/2.50 % (4045076)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.34/2.50 % (4045076)CaDiCaL version: 2.1.3
% 10.34/2.50 % (4045076)Termination reason: Instruction limit
% 10.34/2.50 % (4045076)Termination phase: Saturation
% 10.34/2.50 % (4045076)Time elapsed: 0.250 s
% 10.34/2.50 % (4045076)Peak memory usage: 91 MB
% 10.34/2.50 % (4045076)Instructions burned: 258 (million)
% 10.34/2.50 % (4045085)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=3504048539:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2996 on theBenchmark for (2996ds/2051Mi)
% 10.34/2.50 % (4045086)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=1457401540:i=4948:ss=axioms:sgt=16_2996 on theBenchmark for (2996ds/4948Mi)
% 10.34/2.50 % (4045087)lrs+10_5:1_sil=8000:sos=all:urr=on:br=off:flr=on:random_seed=828469904:i=215:ep=RSTC_2995 on theBenchmark for (2995ds/215Mi)
% 10.34/2.50 % (4045087)Instruction limit reached!
% 10.34/2.50 % (4045087)------------------------------
% 10.34/2.50 % (4045087)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.34/2.50 % (4045087)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.34/2.50 % (4045087)CaDiCaL version: 2.1.3
% 10.34/2.50 % (4045087)Termination reason: Instruction limit
% 10.34/2.50 % (4045087)Termination phase: Saturation
% 10.34/2.50 % (4045087)Time elapsed: 0.199 s
% 10.34/2.50 % (4045087)Peak memory usage: 90 MB
% 10.34/2.50 % (4045087)Instructions burned: 215 (million)
% 10.34/2.50 % (4045073)First to succeed.
% 10.34/2.50 % (4045073)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-4045058"
% 10.34/2.50 % (4045093)lrs+11_1_sil=16000:tgt=full:fde=none:sp=reverse_frequency:lma=off:fs=off:acc=on:bsr=unit_only:rp=on:random_seed=3577056708:avsq=on:i=317:avsqr=1,16:kws=arity_squared:add=off:fgj=on:ins=10:fsr=off:gtg=exists_sym_2991 on theBenchmark for (2991ds/317Mi)
% 10.34/2.50 % (4045077)Instruction limit reached!
% 10.34/2.50 % (4045077)------------------------------
% 10.34/2.50 % (4045077)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.34/2.50 % (4045077)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.34/2.50 % (4045077)CaDiCaL version: 2.1.3
% 10.34/2.50 % (4045077)Termination reason: Instruction limit
% 10.34/2.50 % (4045077)Termination phase: Saturation
% 10.34/2.50 % (4045077)Time elapsed: 0.986 s
% 10.34/2.50 % (4045077)Peak memory usage: 99 MB
% 10.34/2.50 % (4045077)Instructions burned: 1188 (million)
% 10.34/2.50 % (4045071)Also succeeded, but the first one will report.
% 10.34/2.50 % (4045073)Refutation found. Thanks to Tanya!
% 10.34/2.50 % SZS status Unsatisfiable for theBenchmark
% 10.34/2.50 % SZS output start Proof for theBenchmark
% See solution above
% 10.34/2.50 % (4045073)------------------------------
% 10.34/2.50 % (4045073)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.34/2.50 % (4045073)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.34/2.50 % (4045073)CaDiCaL version: 2.1.3
% 10.34/2.50 % (4045073)Termination reason: Refutation
% 10.34/2.50 % (4045073)Time elapsed: 0.868 s
% 10.34/2.50 % (4045073)Peak memory usage: 133 MB
% 10.34/2.50 % (4045073)Instructions burned: 1386 (million)
% 10.34/2.50 % (4045073)------------------------------
% 10.34/2.50 % (4045073)------------------------------
% 10.34/2.50 % (4045058)Success in time 1.315 s
% 10.34/2.50 % Vampire exiting
%------------------------------------------------------------------------------