%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : COL065-1 : 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 : n014.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 09:37:50 AM UTC 2026
% Result : Unsatisfiable 11.49s 2.41s
% Output : Refutation 11.49s
% 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 ( 3 avg)
% Maximal term depth : 13 ( 3 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 23 ( 23 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
! [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,negated_conjecture,
! [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(apply(X0,f(X0)),g(X0)),h(X0)),i(X0)) != apply(apply(f(X0),i(X0)),apply(g(X0),h(X0))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_g_combinator) ).
fof(f8,plain,
! [X0,X1] : apply(apply(f(apply(apply(b,X0),X1)),i(apply(apply(b,X0),X1))),apply(g(apply(apply(b,X0),X1)),h(apply(apply(b,X0),X1)))) != apply(apply(apply(apply(X0,apply(X1,f(apply(apply(b,X0),X1)))),g(apply(apply(b,X0),X1))),h(apply(apply(b,X0),X1))),i(apply(apply(b,X0),X1))),
inference(superposition,[],[f3,f1]) ).
fof(f15,plain,
! [X0] : apply(apply(f(apply(apply(b,b),X0)),i(apply(apply(b,b),X0))),apply(g(apply(apply(b,b),X0)),h(apply(apply(b,b),X0)))) != apply(apply(apply(X0,f(apply(apply(b,b),X0))),apply(g(apply(apply(b,b),X0)),h(apply(apply(b,b),X0)))),i(apply(apply(b,b),X0))),
inference(superposition,[],[f8,f1]) ).
fof(f17,plain,
! [X0,X1] : apply(apply(f(apply(apply(b,b),apply(apply(b,X0),X1))),i(apply(apply(b,b),apply(apply(b,X0),X1)))),apply(g(apply(apply(b,b),apply(apply(b,X0),X1))),h(apply(apply(b,b),apply(apply(b,X0),X1))))) != apply(apply(apply(X0,apply(X1,f(apply(apply(b,b),apply(apply(b,X0),X1))))),apply(g(apply(apply(b,b),apply(apply(b,X0),X1))),h(apply(apply(b,b),apply(apply(b,X0),X1))))),i(apply(apply(b,b),apply(apply(b,X0),X1)))),
inference(superposition,[],[f15,f1]) ).
fof(f133,plain,
! [X2,X0,X1] : apply(apply(f(apply(apply(b,b),apply(apply(b,X2),apply(apply(b,X0),X1)))),i(apply(apply(b,b),apply(apply(b,X2),apply(apply(b,X0),X1))))),apply(g(apply(apply(b,b),apply(apply(b,X2),apply(apply(b,X0),X1)))),h(apply(apply(b,b),apply(apply(b,X2),apply(apply(b,X0),X1)))))) != apply(apply(apply(X2,apply(X0,apply(X1,f(apply(apply(b,b),apply(apply(b,X2),apply(apply(b,X0),X1))))))),apply(g(apply(apply(b,b),apply(apply(b,X2),apply(apply(b,X0),X1)))),h(apply(apply(b,b),apply(apply(b,X2),apply(apply(b,X0),X1)))))),i(apply(apply(b,b),apply(apply(b,X2),apply(apply(b,X0),X1))))),
inference(superposition,[],[f17,f1]) ).
fof(f143,plain,
! [X2,X0,X1] : apply(apply(f(apply(apply(b,b),apply(apply(b,apply(t,X2)),apply(apply(b,X0),X1)))),i(apply(apply(b,b),apply(apply(b,apply(t,X2)),apply(apply(b,X0),X1))))),apply(g(apply(apply(b,b),apply(apply(b,apply(t,X2)),apply(apply(b,X0),X1)))),h(apply(apply(b,b),apply(apply(b,apply(t,X2)),apply(apply(b,X0),X1)))))) != apply(apply(apply(apply(X0,apply(X1,f(apply(apply(b,b),apply(apply(b,apply(t,X2)),apply(apply(b,X0),X1)))))),X2),apply(g(apply(apply(b,b),apply(apply(b,apply(t,X2)),apply(apply(b,X0),X1)))),h(apply(apply(b,b),apply(apply(b,apply(t,X2)),apply(apply(b,X0),X1)))))),i(apply(apply(b,b),apply(apply(b,apply(t,X2)),apply(apply(b,X0),X1))))),
inference(superposition,[],[f133,f2]) ).
fof(f154,plain,
! [X0,X1] : apply(apply(f(apply(apply(b,b),apply(apply(b,apply(t,X1)),apply(apply(b,b),X0)))),i(apply(apply(b,b),apply(apply(b,apply(t,X1)),apply(apply(b,b),X0))))),apply(g(apply(apply(b,b),apply(apply(b,apply(t,X1)),apply(apply(b,b),X0)))),h(apply(apply(b,b),apply(apply(b,apply(t,X1)),apply(apply(b,b),X0)))))) != apply(apply(apply(X0,f(apply(apply(b,b),apply(apply(b,apply(t,X1)),apply(apply(b,b),X0))))),apply(X1,apply(g(apply(apply(b,b),apply(apply(b,apply(t,X1)),apply(apply(b,b),X0)))),h(apply(apply(b,b),apply(apply(b,apply(t,X1)),apply(apply(b,b),X0))))))),i(apply(apply(b,b),apply(apply(b,apply(t,X1)),apply(apply(b,b),X0))))),
inference(superposition,[],[f143,f1]) ).
fof(f159,plain,
! [X0] : apply(apply(f(apply(apply(b,b),apply(apply(b,apply(t,X0)),apply(apply(b,b),t)))),i(apply(apply(b,b),apply(apply(b,apply(t,X0)),apply(apply(b,b),t))))),apply(g(apply(apply(b,b),apply(apply(b,apply(t,X0)),apply(apply(b,b),t)))),h(apply(apply(b,b),apply(apply(b,apply(t,X0)),apply(apply(b,b),t)))))) != apply(apply(apply(X0,apply(g(apply(apply(b,b),apply(apply(b,apply(t,X0)),apply(apply(b,b),t)))),h(apply(apply(b,b),apply(apply(b,apply(t,X0)),apply(apply(b,b),t)))))),f(apply(apply(b,b),apply(apply(b,apply(t,X0)),apply(apply(b,b),t))))),i(apply(apply(b,b),apply(apply(b,apply(t,X0)),apply(apply(b,b),t))))),
inference(superposition,[],[f154,f2]) ).
fof(f163,plain,
! [X0,X1] : apply(apply(f(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,X0),X1))),apply(apply(b,b),t)))),i(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,X0),X1))),apply(apply(b,b),t))))),apply(g(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,X0),X1))),apply(apply(b,b),t)))),h(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,X0),X1))),apply(apply(b,b),t)))))) != apply(apply(apply(X0,apply(X1,apply(g(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,X0),X1))),apply(apply(b,b),t)))),h(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,X0),X1))),apply(apply(b,b),t))))))),f(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,X0),X1))),apply(apply(b,b),t))))),i(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,X0),X1))),apply(apply(b,b),t))))),
inference(superposition,[],[f159,f1]) ).
fof(f173,plain,
! [X0] : apply(apply(X0,apply(g(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),X0))),apply(apply(b,b),t)))),h(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),X0))),apply(apply(b,b),t)))))),apply(f(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),X0))),apply(apply(b,b),t)))),i(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),X0))),apply(apply(b,b),t)))))) != apply(apply(f(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),X0))),apply(apply(b,b),t)))),i(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),X0))),apply(apply(b,b),t))))),apply(g(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),X0))),apply(apply(b,b),t)))),h(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),X0))),apply(apply(b,b),t)))))),
inference(superposition,[],[f163,f1]) ).
fof(f177,plain,
apply(apply(f(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),i(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t))))),apply(g(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),h(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))))) != apply(apply(f(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),i(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t))))),apply(g(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),h(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))))),
inference(superposition,[],[f173,f2]) ).
fof(f179,plain,
$false,
inference(trivial_inequality_removal,[],[f177]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL065-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.24 % Computer : n014.cluster.edu
% 0.12/0.24 % Model : x86_64 x86_64
% 0.12/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.24 % Memory : 8046.5625MB
% 0.12/0.24 % OS : Linux 6.8.0-71-generic
% 0.12/0.24 % CPULimit : 300
% 0.12/0.24 % WCLimit : 300
% 0.12/0.24 % DateTime : Mon Sep 28 21:33:42 UTC 2026
% 0.12/0.24 % CPUTime :
% 0.12/0.24 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.29 Running first-order theorem proving
% 0.12/0.29 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
% 10.89/2.19 % (2212152)Detected a unit-equality problem, will run specialized UEQ schedule.
% 10.89/2.19 % (2212167)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=2675869004:i=136:bd=preordered:ins=2:av=off_3000 on theBenchmark for (3000ds/136Mi)
% 10.89/2.19 % (2212169)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=544661122:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_3000 on theBenchmark for (3000ds/257Mi)
% 10.89/2.19 % (2212164)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=2927608965:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_3000 on theBenchmark for (3000ds/138329Mi)
% 10.89/2.19 % (2212165)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=3502149297:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_3000 on theBenchmark for (3000ds/130792Mi)
% 10.89/2.19 % (2212166)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=2448404334:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_3000 on theBenchmark for (3000ds/130716Mi)
% 10.89/2.19 % (2212168)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=2360009439:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_3000 on theBenchmark for (3000ds/181Mi)
% 10.89/2.19 % (2212170)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=730723277:i=1187:sd=4:av=off:ss=axioms:sgt=32_3000 on theBenchmark for (3000ds/1187Mi)
% 10.89/2.19 % (2212167)Instruction limit reached!
% 10.89/2.19 % (2212167)------------------------------
% 10.89/2.19 % (2212167)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.89/2.19 % (2212167)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.89/2.19 % (2212167)CaDiCaL version: 2.1.3
% 10.89/2.19 % (2212167)Termination reason: Instruction limit
% 10.89/2.19 % (2212167)Termination phase: Saturation
% 10.89/2.19 % (2212167)Time elapsed: 0.097 s
% 10.89/2.19 % (2212167)Peak memory usage: 89 MB
% 10.89/2.19 % (2212167)Instructions burned: 136 (million)
% 10.89/2.19 % (2212169)Instruction limit reached!
% 10.89/2.19 % (2212169)------------------------------
% 10.89/2.19 % (2212169)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.89/2.19 % (2212169)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.89/2.19 % (2212169)CaDiCaL version: 2.1.3
% 10.89/2.19 % (2212169)Termination reason: Instruction limit
% 10.89/2.19 % (2212169)Termination phase: Saturation
% 10.89/2.19 % (2212169)Time elapsed: 0.160 s
% 10.89/2.19 % (2212169)Peak memory usage: 90 MB
% 10.89/2.19 % (2212169)Instructions burned: 257 (million)
% 10.89/2.19 % (2212168)Instruction limit reached!
% 10.89/2.19 % (2212168)------------------------------
% 10.89/2.19 % (2212168)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.89/2.19 % (2212168)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.89/2.19 % (2212168)CaDiCaL version: 2.1.3
% 10.89/2.19 % (2212168)Termination reason: Instruction limit
% 10.89/2.19 % (2212168)Termination phase: Saturation
% 10.89/2.19 % (2212168)Time elapsed: 0.161 s
% 10.89/2.19 % (2212168)Peak memory usage: 88 MB
% 10.89/2.19 % (2212168)Instructions burned: 182 (million)
% 10.89/2.19 % (2212180)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=1325053824:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2997 on theBenchmark for (2997ds/2051Mi)
% 10.89/2.19 % (2212181)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=441338579:i=4948:ss=axioms:sgt=16_2996 on theBenchmark for (2996ds/4948Mi)
% 10.89/2.19 % (2212182)lrs+10_5:1_sil=8000:sos=all:urr=on:br=off:flr=on:random_seed=2129141821:i=215:ep=RSTC_2996 on theBenchmark for (2996ds/215Mi)
% 10.89/2.19 % (2212182)Instruction limit reached!
% 10.89/2.19 % (2212182)------------------------------
% 10.89/2.19 % (2212182)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.89/2.19 % (2212182)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.89/2.19 % (2212182)CaDiCaL version: 2.1.3
% 10.89/2.19 % (2212182)Termination reason: Instruction limit
% 10.89/2.19 % (2212182)Termination phase: Saturation
% 10.89/2.19 % (2212182)Time elapsed: 0.193 s
% 11.49/2.41 % (2212182)Peak memory usage: 88 MB
% 11.49/2.41 % (2212182)Instructions burned: 215 (million)
% 11.49/2.41 % (2212187)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=2708387774:avsq=on:i=317:avsqr=1,16:kws=arity_squared:add=off:fgj=on:ins=10:fsr=off:gtg=exists_sym_2992 on theBenchmark for (2992ds/317Mi)
% 11.49/2.41 % (2212187)Instruction limit reached!
% 11.49/2.41 % (2212187)------------------------------
% 11.49/2.41 % (2212187)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.49/2.41 % (2212187)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.49/2.41 % (2212187)CaDiCaL version: 2.1.3
% 11.49/2.41 % (2212187)Termination reason: Instruction limit
% 11.49/2.41 % (2212187)Termination phase: Saturation
% 11.49/2.41 % (2212187)Time elapsed: 0.261 s
% 11.49/2.41 % (2212187)Peak memory usage: 89 MB
% 11.49/2.41 % (2212187)Instructions burned: 318 (million)
% 11.49/2.41 % (2212166)First to succeed.
% 11.49/2.41 % (2212166)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2212152"
% 11.49/2.41 % (2212165)Also succeeded, but the first one will report.
% 11.49/2.41 % (2212164)Also succeeded, but the first one will report.
% 11.49/2.41 % (2212170)Instruction limit reached!
% 11.49/2.41 % (2212170)------------------------------
% 11.49/2.41 % (2212170)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.49/2.41 % (2212170)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.49/2.41 % (2212170)CaDiCaL version: 2.1.3
% 11.49/2.41 % (2212170)Termination reason: Instruction limit
% 11.49/2.41 % (2212170)Termination phase: Saturation
% 11.49/2.41 % (2212170)Time elapsed: 1.077 s
% 11.49/2.41 % (2212170)Peak memory usage: 102 MB
% 11.49/2.41 % (2212170)Instructions burned: 1188 (million)
% 11.49/2.41 % (2212189)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=64000:tgt=full:npcc=on:sp=arity:lcm=predicate:urr=on:s2agt=16:br=off:random_seed=3214709812:i=12125:sd=2:fgj=on:ss=axioms:sgt=64_2987 on theBenchmark for (2987ds/12125Mi)
% 11.49/2.41 % (2212166)Refutation found. Thanks to Tanya!
% 11.49/2.41 % SZS status Unsatisfiable for theBenchmark
% 11.49/2.41 % SZS output start Proof for theBenchmark
% See solution above
% 11.49/2.41 % (2212166)------------------------------
% 11.49/2.41 % (2212166)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.49/2.41 % (2212166)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.49/2.41 % (2212166)CaDiCaL version: 2.1.3
% 11.49/2.41 % (2212166)Termination reason: Refutation
% 11.49/2.41 % (2212166)Time elapsed: 1.046 s
% 11.49/2.41 % (2212166)Peak memory usage: 132 MB
% 11.49/2.41 % (2212166)Instructions burned: 1244 (million)
% 11.49/2.41 % (2212166)------------------------------
% 11.49/2.41 % (2212166)------------------------------
% 11.49/2.41 % (2212152)Success in time 1.519 s
% 11.49/2.41 % Vampire exiting
%------------------------------------------------------------------------------