%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : COL063-1 : 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 : n011.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 09:37:48 AM UTC 2026
% Result : Unsatisfiable 4.01s 1.05s
% Output : Refutation 4.01s
% 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 ( 4 avg)
% Maximal term depth : 10 ( 2 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 : 21 ( 21 !; 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),g(X0)),f(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_f_combinator) ).
fof(f8,plain,
! [X0,X1] : apply(apply(h(apply(apply(b,X0),X1)),g(apply(apply(b,X0),X1))),f(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(h(apply(apply(b,apply(t,X1)),X0)),g(apply(apply(b,apply(t,X1)),X0))),f(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(h(apply(apply(b,apply(t,X2)),apply(apply(b,X0),X1))),g(apply(apply(b,apply(t,X2)),apply(apply(b,X0),X1)))),f(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(h(apply(apply(b,apply(t,X1)),apply(apply(b,b),X0))),g(apply(apply(b,apply(t,X1)),apply(apply(b,b),X0)))),f(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(f425,plain,
! [X2,X0,X1] : apply(apply(h(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))))),f(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,[],[f257,f1]) ).
fof(f3513,plain,
! [X0,X1] : apply(apply(X0,f(apply(apply(b,apply(t,X1)),apply(apply(b,b),apply(apply(b,b),X0))))),apply(apply(X1,g(apply(apply(b,apply(t,X1)),apply(apply(b,b),apply(apply(b,b),X0))))),h(apply(apply(b,apply(t,X1)),apply(apply(b,b),apply(apply(b,b),X0)))))) != apply(apply(h(apply(apply(b,apply(t,X1)),apply(apply(b,b),apply(apply(b,b),X0)))),g(apply(apply(b,apply(t,X1)),apply(apply(b,b),apply(apply(b,b),X0))))),f(apply(apply(b,apply(t,X1)),apply(apply(b,b),apply(apply(b,b),X0))))),
inference(superposition,[],[f425,f1]) ).
fof(f3543,plain,
! [X0] : apply(apply(h(apply(apply(b,apply(t,t)),apply(apply(b,b),apply(apply(b,b),X0)))),g(apply(apply(b,apply(t,t)),apply(apply(b,b),apply(apply(b,b),X0))))),f(apply(apply(b,apply(t,t)),apply(apply(b,b),apply(apply(b,b),X0))))) != apply(apply(X0,f(apply(apply(b,apply(t,t)),apply(apply(b,b),apply(apply(b,b),X0))))),apply(h(apply(apply(b,apply(t,t)),apply(apply(b,b),apply(apply(b,b),X0)))),g(apply(apply(b,apply(t,t)),apply(apply(b,b),apply(apply(b,b),X0)))))),
inference(superposition,[],[f3513,f2]) ).
fof(f3549,plain,
apply(apply(h(apply(apply(b,apply(t,t)),apply(apply(b,b),apply(apply(b,b),t)))),g(apply(apply(b,apply(t,t)),apply(apply(b,b),apply(apply(b,b),t))))),f(apply(apply(b,apply(t,t)),apply(apply(b,b),apply(apply(b,b),t))))) != apply(apply(h(apply(apply(b,apply(t,t)),apply(apply(b,b),apply(apply(b,b),t)))),g(apply(apply(b,apply(t,t)),apply(apply(b,b),apply(apply(b,b),t))))),f(apply(apply(b,apply(t,t)),apply(apply(b,b),apply(apply(b,b),t))))),
inference(superposition,[],[f3543,f2]) ).
fof(f3551,plain,
$false,
inference(trivial_inequality_removal,[],[f3549]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COL063-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 % Computer : n011.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Mon Sep 28 21:32:27 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running first-order theorem proving
% 0.09/0.23 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
% 4.01/1.05 % (3805845)Detected a unit-equality problem, will run specialized UEQ schedule.
% 4.01/1.05 % (3805856)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=3796734963:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 4.01/1.05 % (3805852)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=529011417:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 4.01/1.05 % (3805851)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=3110615846:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 4.01/1.05 % (3805855)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=3488071921:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 4.01/1.05 % (3805850)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=3619992485:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 4.01/1.05 % (3805853)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=3123520304:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 4.01/1.05 % (3805854)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=2579760170:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 4.01/1.05 % (3805853)Instruction limit reached!
% 4.01/1.05 % (3805853)------------------------------
% 4.01/1.05 % (3805853)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.01/1.05 % (3805853)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.01/1.05 % (3805853)CaDiCaL version: 2.1.3
% 4.01/1.05 % (3805853)Termination reason: Instruction limit
% 4.01/1.05 % (3805853)Termination phase: Saturation
% 4.01/1.05 % (3805853)Time elapsed: 0.080 s
% 4.01/1.05 % (3805853)Peak memory usage: 89 MB
% 4.01/1.05 % (3805853)Instructions burned: 137 (million)
% 4.01/1.05 % (3805854)Instruction limit reached!
% 4.01/1.05 % (3805854)------------------------------
% 4.01/1.05 % (3805854)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.01/1.05 % (3805854)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.01/1.05 % (3805854)CaDiCaL version: 2.1.3
% 4.01/1.05 % (3805854)Termination reason: Instruction limit
% 4.01/1.05 % (3805854)Termination phase: Saturation
% 4.01/1.05 % (3805854)Time elapsed: 0.094 s
% 4.01/1.05 % (3805854)Peak memory usage: 88 MB
% 4.01/1.05 % (3805854)Instructions burned: 182 (million)
% 4.01/1.05 % (3805855)Instruction limit reached!
% 4.01/1.05 % (3805855)------------------------------
% 4.01/1.05 % (3805855)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.01/1.05 % (3805855)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.01/1.05 % (3805855)CaDiCaL version: 2.1.3
% 4.01/1.05 % (3805855)Termination reason: Instruction limit
% 4.01/1.05 % (3805855)Termination phase: Saturation
% 4.01/1.05 % (3805855)Time elapsed: 0.147 s
% 4.01/1.05 % (3805855)Peak memory usage: 90 MB
% 4.01/1.05 % (3805855)Instructions burned: 258 (million)
% 4.01/1.05 % (3805856)First to succeed.
% 4.01/1.05 % (3805856)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3805845"
% 4.01/1.05 % (3805864)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=3841095508:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2997 on theBenchmark for (2997ds/2051Mi)
% 4.01/1.05 % (3805865)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=2932614977:i=4948:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/4948Mi)
% 4.01/1.05 % (3805866)lrs+10_5:1_sil=8000:sos=all:urr=on:br=off:flr=on:random_seed=2675374988:i=215:ep=RSTC_2996 on theBenchmark for (2996ds/215Mi)
% 4.01/1.05 % (3805856)Refutation found. Thanks to Tanya!
% 4.01/1.05 % SZS status Unsatisfiable for theBenchmark
% 4.01/1.05 % SZS output start Proof for theBenchmark
% See solution above
% 4.01/1.05 % (3805856)------------------------------
% 4.01/1.05 % (3805856)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.01/1.05 % (3805856)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.01/1.05 % (3805856)CaDiCaL version: 2.1.3
% 4.01/1.05 % (3805856)Termination reason: Refutation
% 4.01/1.05 % (3805856)Time elapsed: 0.231 s
% 4.01/1.05 % (3805856)Peak memory usage: 97 MB
% 4.01/1.05 % (3805856)Instructions burned: 766 (million)
% 4.01/1.05 % (3805856)------------------------------
% 4.01/1.05 % (3805856)------------------------------
% 4.01/1.05 % (3805845)Success in time 0.521 s
% 4.01/1.06 % Vampire exiting
%------------------------------------------------------------------------------