%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : COL064-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n013.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 09:37:49 AM UTC 2026
% Result : Unsatisfiable 0.20s 1.70s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% 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 : 11 ( 11 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 4 avg)
% Maximal term depth : 11 ( 3 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 25 ( 25 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : apply(apply(apply(b,X0),X1),X2) = apply(X0,apply(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_definition) ).
fof(f2,axiom,
! [X0,X1] : apply(apply(t,X0),X1) = apply(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t_definition) ).
fof(f3,negated_conjecture,
! [X0] : apply(apply(apply(X0,f(X0)),g(X0)),h(X0)) != apply(apply(h(X0),f(X0)),g(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_v_combinator) ).
fof(f6,plain,
! [X0,X1] : apply(apply(h(apply(apply(b,X0),X1)),f(apply(apply(b,X0),X1))),g(apply(apply(b,X0),X1))) != apply(apply(apply(X0,apply(X1,f(apply(apply(b,X0),X1)))),g(apply(apply(b,X0),X1))),h(apply(apply(b,X0),X1))),
inference(superposition,[],[f3,f1]) ).
fof(f7,plain,
! [X2,X0,X1] : apply(apply(h(apply(apply(b,X2),apply(apply(b,X0),X1))),f(apply(apply(b,X2),apply(apply(b,X0),X1)))),g(apply(apply(b,X2),apply(apply(b,X0),X1)))) != apply(apply(apply(X2,apply(X0,apply(X1,f(apply(apply(b,X2),apply(apply(b,X0),X1)))))),g(apply(apply(b,X2),apply(apply(b,X0),X1)))),h(apply(apply(b,X2),apply(apply(b,X0),X1)))),
inference(superposition,[],[f6,f1]) ).
fof(f21,plain,
! [X2,X0,X1] : apply(apply(h(apply(apply(b,apply(t,X0)),apply(apply(b,X1),X2))),f(apply(apply(b,apply(t,X0)),apply(apply(b,X1),X2)))),g(apply(apply(b,apply(t,X0)),apply(apply(b,X1),X2)))) != apply(apply(apply(apply(X1,apply(X2,f(apply(apply(b,apply(t,X0)),apply(apply(b,X1),X2))))),X0),g(apply(apply(b,apply(t,X0)),apply(apply(b,X1),X2)))),h(apply(apply(b,apply(t,X0)),apply(apply(b,X1),X2)))),
inference(superposition,[],[f7,f2]) ).
fof(f31,plain,
! [X0,X1] : apply(apply(h(apply(apply(b,apply(t,X1)),apply(apply(b,b),X0))),f(apply(apply(b,apply(t,X1)),apply(apply(b,b),X0)))),g(apply(apply(b,apply(t,X1)),apply(apply(b,b),X0)))) != apply(apply(apply(X0,f(apply(apply(b,apply(t,X1)),apply(apply(b,b),X0)))),apply(X1,g(apply(apply(b,apply(t,X1)),apply(apply(b,b),X0))))),h(apply(apply(b,apply(t,X1)),apply(apply(b,b),X0)))),
inference(superposition,[],[f21,f1]) ).
fof(f32,plain,
! [X2,X0,X1] : apply(apply(h(apply(apply(b,apply(t,X2)),apply(apply(b,b),apply(apply(b,X0),X1)))),f(apply(apply(b,apply(t,X2)),apply(apply(b,b),apply(apply(b,X0),X1))))),g(apply(apply(b,apply(t,X2)),apply(apply(b,b),apply(apply(b,X0),X1))))) != apply(apply(apply(X0,apply(X1,f(apply(apply(b,apply(t,X2)),apply(apply(b,b),apply(apply(b,X0),X1)))))),apply(X2,g(apply(apply(b,apply(t,X2)),apply(apply(b,b),apply(apply(b,X0),X1)))))),h(apply(apply(b,apply(t,X2)),apply(apply(b,b),apply(apply(b,X0),X1))))),
inference(superposition,[],[f31,f1]) ).
fof(f63,plain,
! [X0,X1] : apply(apply(X1,f(apply(apply(b,apply(t,X0)),apply(apply(b,b),apply(apply(b,b),X1))))),apply(apply(X0,g(apply(apply(b,apply(t,X0)),apply(apply(b,b),apply(apply(b,b),X1))))),h(apply(apply(b,apply(t,X0)),apply(apply(b,b),apply(apply(b,b),X1)))))) != apply(apply(h(apply(apply(b,apply(t,X0)),apply(apply(b,b),apply(apply(b,b),X1)))),f(apply(apply(b,apply(t,X0)),apply(apply(b,b),apply(apply(b,b),X1))))),g(apply(apply(b,apply(t,X0)),apply(apply(b,b),apply(apply(b,b),X1))))),
inference(superposition,[],[f32,f1]) ).
fof(f71,plain,
! [X0] : apply(apply(apply(X0,g(apply(apply(b,apply(t,X0)),apply(apply(b,b),apply(apply(b,b),t))))),h(apply(apply(b,apply(t,X0)),apply(apply(b,b),apply(apply(b,b),t))))),f(apply(apply(b,apply(t,X0)),apply(apply(b,b),apply(apply(b,b),t))))) != apply(apply(h(apply(apply(b,apply(t,X0)),apply(apply(b,b),apply(apply(b,b),t)))),f(apply(apply(b,apply(t,X0)),apply(apply(b,b),apply(apply(b,b),t))))),g(apply(apply(b,apply(t,X0)),apply(apply(b,b),apply(apply(b,b),t))))),
inference(superposition,[],[f63,f2]) ).
fof(f72,plain,
! [X0,X1] : apply(apply(h(apply(apply(b,apply(t,apply(apply(b,X0),X1))),apply(apply(b,b),apply(apply(b,b),t)))),f(apply(apply(b,apply(t,apply(apply(b,X0),X1))),apply(apply(b,b),apply(apply(b,b),t))))),g(apply(apply(b,apply(t,apply(apply(b,X0),X1))),apply(apply(b,b),apply(apply(b,b),t))))) != apply(apply(apply(X0,apply(X1,g(apply(apply(b,apply(t,apply(apply(b,X0),X1))),apply(apply(b,b),apply(apply(b,b),t)))))),h(apply(apply(b,apply(t,apply(apply(b,X0),X1))),apply(apply(b,b),apply(apply(b,b),t))))),f(apply(apply(b,apply(t,apply(apply(b,X0),X1))),apply(apply(b,b),apply(apply(b,b),t))))),
inference(superposition,[],[f71,f1]) ).
fof(f83,plain,
! [X0] : apply(apply(X0,g(apply(apply(b,apply(t,apply(apply(b,b),X0))),apply(apply(b,b),apply(apply(b,b),t))))),apply(h(apply(apply(b,apply(t,apply(apply(b,b),X0))),apply(apply(b,b),apply(apply(b,b),t)))),f(apply(apply(b,apply(t,apply(apply(b,b),X0))),apply(apply(b,b),apply(apply(b,b),t)))))) != apply(apply(h(apply(apply(b,apply(t,apply(apply(b,b),X0))),apply(apply(b,b),apply(apply(b,b),t)))),f(apply(apply(b,apply(t,apply(apply(b,b),X0))),apply(apply(b,b),apply(apply(b,b),t))))),g(apply(apply(b,apply(t,apply(apply(b,b),X0))),apply(apply(b,b),apply(apply(b,b),t))))),
inference(superposition,[],[f72,f1]) ).
fof(f87,plain,
apply(apply(h(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),apply(apply(b,b),t)))),f(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),apply(apply(b,b),t))))),g(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),apply(apply(b,b),t))))) != apply(apply(h(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),apply(apply(b,b),t)))),f(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),apply(apply(b,b),t))))),g(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),apply(apply(b,b),t))))),
inference(superposition,[],[f83,f2]) ).
fof(f88,plain,
$false,
inference(trivial_inequality_removal,[],[f87]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL064-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n013.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Mon Sep 28 21:31:52 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 first-order theorem proving
% 0.09/0.22 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/1.70 % (1605022)Detected a unit-equality problem, will run specialized UEQ schedule.
% 0.20/1.70 % (1605031)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=1460189525:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 0.20/1.70 % (1605033)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=3065649321:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 0.20/1.70 % (1605027)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=662553528:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 0.20/1.70 % (1605028)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=1193644120:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 0.20/1.70 % (1605030)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=2130112940:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 0.20/1.70 % (1605029)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=161175044:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 0.20/1.70 % (1605032)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=2287351641:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 0.20/1.70 % (1605031)Instruction limit reached!
% 0.20/1.70 % (1605031)------------------------------
% 0.20/1.70 % (1605031)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.20/1.70 % (1605031)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/1.70 % (1605031)CaDiCaL version: 2.1.3
% 0.20/1.70 % (1605031)Termination reason: Instruction limit
% 0.20/1.70 % (1605031)Termination phase: Saturation
% 0.20/1.70 % (1605031)Time elapsed: 0.052 s
% 0.20/1.70 % (1605031)Peak memory usage: 88 MB
% 0.20/1.70 % (1605031)Instructions burned: 184 (million)
% 0.20/1.70 % (1605030)Instruction limit reached!
% 0.20/1.70 % (1605030)------------------------------
% 0.20/1.70 % (1605030)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.20/1.70 % (1605030)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/1.70 % (1605030)CaDiCaL version: 2.1.3
% 0.20/1.70 % (1605030)Termination reason: Instruction limit
% 0.20/1.70 % (1605030)Termination phase: Saturation
% 0.20/1.70 % (1605030)Time elapsed: 0.080 s
% 0.20/1.70 % (1605030)Peak memory usage: 89 MB
% 0.20/1.70 % (1605030)Instructions burned: 137 (million)
% 0.20/1.70 % (1605041)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=1499921129:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2998 on theBenchmark for (2998ds/2051Mi)
% 0.20/1.70 % (1605032)Instruction limit reached!
% 0.20/1.70 % (1605032)------------------------------
% 0.20/1.70 % (1605032)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.20/1.70 % (1605032)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/1.70 % (1605032)CaDiCaL version: 2.1.3
% 0.20/1.70 % (1605032)Termination reason: Instruction limit
% 0.20/1.70 % (1605032)Termination phase: Saturation
% 0.20/1.70 % (1605032)Time elapsed: 0.149 s
% 0.20/1.70 % (1605032)Peak memory usage: 90 MB
% 0.20/1.70 % (1605032)Instructions burned: 258 (million)
% 0.20/1.70 % (1605042)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=3388261141:i=4948:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/4948Mi)
% 0.20/1.70 % (1605044)lrs+10_5:1_sil=8000:sos=all:urr=on:br=off:flr=on:random_seed=4239778802:i=215:ep=RSTC_2996 on theBenchmark for (2996ds/215Mi)
% 0.20/1.70 % (1605044)Instruction limit reached!
% 0.20/1.70 % (1605044)------------------------------
% 0.20/1.70 % (1605044)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.20/1.70 % (1605044)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/1.70 % (1605044)CaDiCaL version: 2.1.3
% 0.20/1.70 % (1605044)Termination reason: Instruction limit
% 0.20/1.70 % (1605044)Termination phase: Saturation
% 0.20/1.70 % (1605044)Time elapsed: 0.119 s
% 0.20/1.70 % (1605044)Peak memory usage: 89 MB
% 0.20/1.70 % (1605044)Instructions burned: 217 (million)
% 0.20/1.70 % (1605041)First to succeed.
% 0.20/1.70 % (1605041)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1605022"
% 0.20/1.70 % (1605047)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=292252860:avsq=on:i=317:avsqr=1,16:kws=arity_squared:add=off:fgj=on:ins=10:fsr=off:gtg=exists_sym_2994 on theBenchmark for (2994ds/317Mi)
% 0.20/1.70 % (1605028)Also succeeded, but the first one will report.
% 0.20/1.70 % (1605033)Instruction limit reached!
% 0.20/1.70 % (1605033)------------------------------
% 0.20/1.70 % (1605033)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.20/1.70 % (1605033)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/1.70 % (1605033)CaDiCaL version: 2.1.3
% 0.20/1.70 % (1605033)Termination reason: Instruction limit
% 0.20/1.70 % (1605033)Termination phase: Saturation
% 0.20/1.70 % (1605033)Time elapsed: 0.660 s
% 0.20/1.70 % (1605033)Peak memory usage: 102 MB
% 0.20/1.70 % (1605033)Instructions burned: 1188 (million)
% 0.20/1.70 % (1605027)Also succeeded, but the first one will report.
% 0.20/1.70 % (1605029)Also succeeded, but the first one will report.
% 0.20/1.70 % (1605041)Refutation found. Thanks to Tanya!
% 0.20/1.70 % SZS status Unsatisfiable for theBenchmark
% 0.20/1.70 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/1.70 % (1605041)------------------------------
% 0.20/1.70 % (1605041)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.20/1.70 % (1605041)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/1.70 % (1605041)CaDiCaL version: 2.1.3
% 0.20/1.70 % (1605041)Termination reason: Refutation
% 0.20/1.70 % (1605041)Time elapsed: 0.414 s
% 0.20/1.70 % (1605041)Peak memory usage: 129 MB
% 0.20/1.70 % (1605041)Instructions burned: 1039 (million)
% 0.20/1.70 % (1605041)------------------------------
% 0.20/1.70 % (1605041)------------------------------
% 0.20/1.70 % (1605022)Success in time 0.842 s
% 0.20/1.70 % Vampire exiting
%------------------------------------------------------------------------------