%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : COL062-1 : 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 : 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 09:37:47 AM UTC 2026
% Result : Unsatisfiable 5.12s 1.46s
% Output : Refutation 5.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% 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 : 9 ( 9 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 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 : 19 ( 19 !; 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,
! [X0,X1] : apply(apply(t,X0),X1) = apply(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t_definition) ).
fof(f3,negated_conjecture,
! [X0] : apply(apply(apply(X0,f(X0)),g(X0)),h(X0)) != apply(apply(f(X0),h(X0)),g(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_c_combinator) ).
fof(f8,plain,
! [X0,X1] : apply(apply(f(apply(apply(b,X0),X1)),h(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(f15,plain,
! [X0,X1] : apply(apply(f(apply(apply(b,apply(t,X1)),X0)),h(apply(apply(b,apply(t,X1)),X0))),g(apply(apply(b,apply(t,X1)),X0))) != apply(apply(apply(apply(X0,f(apply(apply(b,apply(t,X1)),X0))),X1),g(apply(apply(b,apply(t,X1)),X0))),h(apply(apply(b,apply(t,X1)),X0))),
inference(superposition,[],[f8,f2]) ).
fof(f44,plain,
! [X2,X0,X1] : apply(apply(f(apply(apply(b,apply(t,X2)),apply(apply(b,X0),X1))),h(apply(apply(b,apply(t,X2)),apply(apply(b,X0),X1)))),g(apply(apply(b,apply(t,X2)),apply(apply(b,X0),X1)))) != apply(apply(apply(apply(X0,apply(X1,f(apply(apply(b,apply(t,X2)),apply(apply(b,X0),X1))))),X2),g(apply(apply(b,apply(t,X2)),apply(apply(b,X0),X1)))),h(apply(apply(b,apply(t,X2)),apply(apply(b,X0),X1)))),
inference(superposition,[],[f15,f1]) ).
fof(f257,plain,
! [X0,X1] : apply(apply(f(apply(apply(b,apply(t,X1)),apply(apply(b,b),X0))),h(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,[],[f44,f1]) ).
fof(f428,plain,
! [X0] : apply(apply(f(apply(apply(b,apply(t,X0)),apply(apply(b,b),t))),h(apply(apply(b,apply(t,X0)),apply(apply(b,b),t)))),g(apply(apply(b,apply(t,X0)),apply(apply(b,b),t)))) != apply(apply(apply(X0,g(apply(apply(b,apply(t,X0)),apply(apply(b,b),t)))),f(apply(apply(b,apply(t,X0)),apply(apply(b,b),t)))),h(apply(apply(b,apply(t,X0)),apply(apply(b,b),t)))),
inference(superposition,[],[f257,f2]) ).
fof(f441,plain,
! [X0,X1] : apply(apply(f(apply(apply(b,apply(t,apply(apply(b,X0),X1))),apply(apply(b,b),t))),h(apply(apply(b,apply(t,apply(apply(b,X0),X1))),apply(apply(b,b),t)))),g(apply(apply(b,apply(t,apply(apply(b,X0),X1))),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),t))))),f(apply(apply(b,apply(t,apply(apply(b,X0),X1))),apply(apply(b,b),t)))),h(apply(apply(b,apply(t,apply(apply(b,X0),X1))),apply(apply(b,b),t)))),
inference(superposition,[],[f428,f1]) ).
fof(f1917,plain,
! [X0] : apply(apply(X0,g(apply(apply(b,apply(t,apply(apply(b,b),X0))),apply(apply(b,b),t)))),apply(f(apply(apply(b,apply(t,apply(apply(b,b),X0))),apply(apply(b,b),t))),h(apply(apply(b,apply(t,apply(apply(b,b),X0))),apply(apply(b,b),t))))) != apply(apply(f(apply(apply(b,apply(t,apply(apply(b,b),X0))),apply(apply(b,b),t))),h(apply(apply(b,apply(t,apply(apply(b,b),X0))),apply(apply(b,b),t)))),g(apply(apply(b,apply(t,apply(apply(b,b),X0))),apply(apply(b,b),t)))),
inference(superposition,[],[f441,f1]) ).
fof(f1922,plain,
apply(apply(f(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t))),h(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),g(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))) != apply(apply(f(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t))),h(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),g(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),
inference(superposition,[],[f1917,f2]) ).
fof(f1924,plain,
$false,
inference(trivial_inequality_removal,[],[f1922]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COL062-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.17 % Computer : n013.cluster.edu
% 0.08/0.17 % Model : x86_64 x86_64
% 0.08/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.17 % Memory : 8046.5625MB
% 0.08/0.17 % OS : Linux 6.8.0-71-generic
% 0.08/0.17 % CPULimit : 300
% 0.08/0.17 % WCLimit : 300
% 0.08/0.17 % DateTime : Mon Sep 28 21:31:48 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.20 Running first-order theorem proving
% 0.08/0.20 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
% 5.12/1.46 % (1604521)Detected a unit-equality problem, will run specialized UEQ schedule.
% 5.12/1.46 % (1604608)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=1191421225:i=136:bd=preordered:ins=2:av=off_3000 on theBenchmark for (3000ds/136Mi)
% 5.12/1.46 % (1604609)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=3963267492:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_3000 on theBenchmark for (3000ds/181Mi)
% 5.12/1.46 % (1604605)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=1684401696:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_3000 on theBenchmark for (3000ds/138329Mi)
% 5.12/1.46 % (1604607)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=9556958:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_3000 on theBenchmark for (3000ds/130716Mi)
% 5.12/1.46 % (1604606)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=1817334239:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_3000 on theBenchmark for (3000ds/130792Mi)
% 5.12/1.46 % (1604608)Instruction limit reached!
% 5.12/1.46 % (1604608)------------------------------
% 5.12/1.46 % (1604608)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.12/1.46 % (1604608)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.12/1.46 % (1604608)CaDiCaL version: 2.1.3
% 5.12/1.46 % (1604608)Termination reason: Instruction limit
% 5.12/1.46 % (1604608)Termination phase: Saturation
% 5.12/1.46 % (1604608)Time elapsed: 0.046 s
% 5.12/1.46 % (1604608)Peak memory usage: 89 MB
% 5.12/1.46 % (1604608)Instructions burned: 139 (million)
% 5.12/1.46 % (1604610)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=2075670865:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_3000 on theBenchmark for (3000ds/257Mi)
% 5.12/1.46 % (1604611)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=3659348808:i=1187:sd=4:av=off:ss=axioms:sgt=32_3000 on theBenchmark for (3000ds/1187Mi)
% 5.12/1.46 % (1604609)Instruction limit reached!
% 5.12/1.46 % (1604609)------------------------------
% 5.12/1.46 % (1604609)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.12/1.46 % (1604609)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.12/1.46 % (1604609)CaDiCaL version: 2.1.3
% 5.12/1.46 % (1604609)Termination reason: Instruction limit
% 5.12/1.46 % (1604609)Termination phase: Saturation
% 5.12/1.46 % (1604609)Time elapsed: 0.095 s
% 5.12/1.46 % (1604609)Peak memory usage: 88 MB
% 5.12/1.46 % (1604609)Instructions burned: 181 (million)
% 5.12/1.46 % (1604617)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=1385974551:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2998 on theBenchmark for (2998ds/2051Mi)
% 5.12/1.46 % (1604610)Instruction limit reached!
% 5.12/1.46 % (1604610)------------------------------
% 5.12/1.46 % (1604610)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.12/1.46 % (1604610)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.12/1.46 % (1604610)CaDiCaL version: 2.1.3
% 5.12/1.46 % (1604610)Termination reason: Instruction limit
% 5.12/1.46 % (1604610)Termination phase: Saturation
% 5.12/1.46 % (1604610)Time elapsed: 0.151 s
% 5.12/1.46 % (1604610)Peak memory usage: 90 MB
% 5.12/1.46 % (1604610)Instructions burned: 257 (million)
% 5.12/1.46 % (1604621)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=4103236168:i=4948:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/4948Mi)
% 5.12/1.46 % (1604611)First to succeed.
% 5.12/1.46 % (1604611)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1604521"
% 5.12/1.46 % (1604622)lrs+10_5:1_sil=8000:sos=all:urr=on:br=off:flr=on:random_seed=2591038678:i=215:ep=RSTC_2996 on theBenchmark for (2996ds/215Mi)
% 5.12/1.46 % (1604622)Instruction limit reached!
% 5.12/1.46 % (1604622)------------------------------
% 5.12/1.46 % (1604622)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.12/1.46 % (1604622)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.12/1.46 % (1604622)CaDiCaL version: 2.1.3
% 5.12/1.46 % (1604622)Termination reason: Instruction limit
% 5.12/1.46 % (1604622)Termination phase: Saturation
% 5.12/1.46 % (1604622)Time elapsed: 0.117 s
% 5.12/1.46 % (1604622)Peak memory usage: 89 MB
% 5.12/1.46 % (1604622)Instructions burned: 215 (million)
% 5.12/1.46 % (1604617)Also succeeded, but the first one will report.
% 5.12/1.46 % (1604611)Refutation found. Thanks to Tanya!
% 5.12/1.46 % SZS status Unsatisfiable for theBenchmark
% 5.12/1.46 % SZS output start Proof for theBenchmark
% See solution above
% 5.12/1.46 % (1604611)------------------------------
% 5.12/1.46 % (1604611)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.12/1.46 % (1604611)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.12/1.46 % (1604611)CaDiCaL version: 2.1.3
% 5.12/1.46 % (1604611)Termination reason: Refutation
% 5.12/1.46 % (1604611)Time elapsed: 0.226 s
% 5.12/1.46 % (1604611)Peak memory usage: 93 MB
% 5.12/1.46 % (1604611)Instructions burned: 401 (million)
% 5.12/1.46 % (1604611)------------------------------
% 5.12/1.46 % (1604611)------------------------------
% 5.12/1.46 % (1604521)Success in time 0.635 s
% 5.12/1.46 % Vampire exiting
%------------------------------------------------------------------------------