%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : COL063-5 : TPTP v9.3.1. Bugfixed v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n007.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 2.63s 0.98s
% Output : Refutation 2.63s
% 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 : 4 ( 2 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 5 ( 5 !; 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,
apply(apply(apply(apply(apply(b,apply(apply(b,apply(t,t)),apply(apply(b,b),b))),t),x),y),z) != apply(apply(z,y),x),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_f_combinator) ).
fof(f4,plain,
apply(apply(z,y),x) != apply(apply(apply(apply(apply(b,apply(t,t)),apply(apply(b,b),b)),apply(t,x)),y),z),
inference(superposition,[],[f3,f1]) ).
fof(f5,plain,
apply(apply(z,y),x) != apply(apply(apply(apply(t,t),apply(apply(apply(b,b),b),apply(t,x))),y),z),
inference(forward_demodulation,[],[f4,f1]) ).
fof(f6,plain,
apply(apply(z,y),x) != apply(apply(apply(apply(apply(apply(b,b),b),apply(t,x)),t),y),z),
inference(forward_demodulation,[],[f5,f2]) ).
fof(f7,plain,
apply(apply(z,y),x) != apply(apply(apply(apply(b,apply(b,apply(t,x))),t),y),z),
inference(forward_demodulation,[],[f6,f1]) ).
fof(f8,plain,
apply(apply(z,y),x) != apply(apply(apply(b,apply(t,x)),apply(t,y)),z),
inference(forward_demodulation,[],[f7,f1]) ).
fof(f9,plain,
apply(apply(z,y),x) != apply(apply(t,x),apply(apply(t,y),z)),
inference(forward_demodulation,[],[f8,f1]) ).
fof(f10,plain,
apply(apply(z,y),x) != apply(apply(apply(t,y),z),x),
inference(forward_demodulation,[],[f9,f2]) ).
fof(f11,plain,
apply(apply(z,y),x) != apply(apply(z,y),x),
inference(forward_demodulation,[],[f10,f2]) ).
fof(f12,plain,
$false,
inference(trivial_inequality_removal,[],[f11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL063-5 : TPTP v9.3.1. Bugfixed v1.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 % Computer : n007.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 21:30:21 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.24 Running first-order theorem proving
% 0.09/0.24 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
% 2.63/0.98 % (2872016)Detected a unit-equality problem, will run specialized UEQ schedule.
% 2.63/0.98 % (2872087)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=1334731026:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 2.63/0.98 % (2872087)First to succeed.
% 2.63/0.98 % (2872087)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2872016"
% 2.63/0.98 % (2872082)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=2814660187:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 2.63/0.98 % (2872085)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=1865846484:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 2.63/0.98 % (2872083)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=3479862661:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 2.63/0.98 % (2872081)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=259275991:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 2.63/0.98 % (2872084)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=3088043807:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 2.63/0.98 % (2872086)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=646356008:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 2.63/0.98 % (2872084)Also succeeded, but the first one will report.
% 2.63/0.98 % (2872086)Also succeeded, but the first one will report.
% 2.63/0.98 % (2872085)Instruction limit reached!
% 2.63/0.98 % (2872085)------------------------------
% 2.63/0.98 % (2872085)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.63/0.98 % (2872085)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.63/0.98 % (2872085)CaDiCaL version: 2.1.3
% 2.63/0.98 % (2872085)Termination reason: Instruction limit
% 2.63/0.98 % (2872085)Termination phase: Saturation
% 2.63/0.98 % (2872085)Time elapsed: 0.103 s
% 2.63/0.98 % (2872085)Peak memory usage: 88 MB
% 2.63/0.98 % (2872085)Instructions burned: 182 (million)
% 2.63/0.98 % (2872087)Refutation found. Thanks to Tanya!
% 2.63/0.98 % SZS status Unsatisfiable for theBenchmark
% 2.63/0.98 % SZS output start Proof for theBenchmark
% See solution above
% 2.63/0.98 % (2872087)------------------------------
% 2.63/0.98 % (2872087)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.63/0.98 % (2872087)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.63/0.98 % (2872087)CaDiCaL version: 2.1.3
% 2.63/0.98 % (2872087)Termination reason: Refutation
% 2.63/0.98 % (2872087)Time elapsed: 0.001 s
% 2.63/0.98 % (2872087)Peak memory usage: 87 MB
% 2.63/0.98 % (2872087)Instructions burned: 1 (million)
% 2.63/0.98 % (2872087)------------------------------
% 2.63/0.98 % (2872087)------------------------------
% 2.63/0.98 % (2872016)Success in time 0.318 s
% 2.63/0.98 % Vampire exiting
%------------------------------------------------------------------------------