%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : COL064-10 : 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 : 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 09:37:49 AM UTC 2026
% Result : Unsatisfiable 3.41s 1.26s
% Output : Refutation 3.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 16 ( 16 unt; 1 def)
% Number of atoms : 16 ( 4 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 11 ( 11 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 8 ( 8 !; 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,apply(apply(b,b),t))),apply(apply(b,b),t))),t),x),y),z) != apply(apply(z,x),y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_v_combinator) ).
fof(f4,definition,
~ sP0(apply(apply(apply(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t))),t),x),y),z)),
introduced(definition,[new_symbols(definition,[sP0])],[inequality_splitting_name_introduction]) ).
fof(f5,plain,
sP0(apply(apply(z,x),y)),
inference(inequality_splitting,[],[f3,f4]) ).
fof(f6,plain,
~ sP0(apply(apply(apply(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)),apply(t,x)),y),z)),
inference(backward_demodulation,[],[f4,f1]) ).
fof(f7,plain,
~ sP0(apply(apply(apply(apply(t,apply(apply(b,b),t)),apply(apply(apply(b,b),t),apply(t,x))),y),z)),
inference(forward_demodulation,[],[f6,f1]) ).
fof(f8,plain,
~ sP0(apply(apply(apply(apply(t,apply(apply(b,b),t)),apply(b,apply(t,apply(t,x)))),y),z)),
inference(forward_demodulation,[],[f7,f1]) ).
fof(f11,plain,
~ sP0(apply(apply(apply(apply(b,apply(t,apply(t,x))),apply(apply(b,b),t)),y),z)),
inference(superposition,[],[f8,f2]) ).
fof(f16,plain,
~ sP0(apply(apply(apply(t,apply(t,x)),apply(apply(apply(b,b),t),y)),z)),
inference(forward_demodulation,[],[f11,f1]) ).
fof(f18,plain,
~ sP0(apply(apply(apply(t,apply(t,x)),apply(b,apply(t,y))),z)),
inference(forward_demodulation,[],[f16,f1]) ).
fof(f21,plain,
! [X2,X0,X1] : apply(X1,apply(X0,X2)) = apply(apply(apply(t,X0),apply(b,X1)),X2),
inference(superposition,[],[f1,f2]) ).
fof(f27,plain,
~ sP0(apply(apply(t,y),apply(apply(t,x),z))),
inference(backward_demodulation,[],[f18,f21]) ).
fof(f33,plain,
~ sP0(apply(apply(t,y),apply(z,x))),
inference(superposition,[],[f27,f2]) ).
fof(f34,plain,
~ sP0(apply(apply(z,x),y)),
inference(superposition,[],[f33,f2]) ).
fof(f35,plain,
$false,
inference(forward_subsumption_resolution,[],[f34,f5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL064-10 : TPTP v9.3.1. Bugfixed v1.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.20 % Computer : n014.cluster.edu
% 0.08/0.20 % Model : x86_64 x86_64
% 0.08/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.20 % Memory : 8046.5625MB
% 0.08/0.20 % OS : Linux 6.8.0-71-generic
% 0.08/0.20 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.20 % DateTime : Mon Sep 28 21:32:16 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.24 Running first-order theorem proving
% 0.08/0.24 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
% 3.41/1.26 % (2211442)Detected a unit-equality problem, will run specialized UEQ schedule.
% 3.41/1.26 % (2211449)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=2211319640:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 3.41/1.26 % (2211448)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=1682265266:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 3.41/1.26 % (2211450)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=48410028:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 3.41/1.26 % (2211451)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=1260285195:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 3.41/1.26 % (2211450)First to succeed.
% 3.41/1.26 % (2211450)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2211442"
% 3.41/1.26 % (2211447)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=3056304654:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 3.41/1.26 % (2211453)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=1200973079:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 3.41/1.26 % (2211452)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=4150098816:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 3.41/1.26 % (2211453)Also succeeded, but the first one will report.
% 3.41/1.26 % (2211452)Also succeeded, but the first one will report.
% 3.41/1.26 % (2211451)Instruction limit reached!
% 3.41/1.26 % (2211451)------------------------------
% 3.41/1.26 % (2211451)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.41/1.26 % (2211451)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.41/1.26 % (2211451)CaDiCaL version: 2.1.3
% 3.41/1.26 % (2211451)Termination reason: Instruction limit
% 3.41/1.26 % (2211451)Termination phase: Saturation
% 3.41/1.26 % (2211451)Time elapsed: 0.094 s
% 3.41/1.26 % (2211451)Peak memory usage: 88 MB
% 3.41/1.26 % (2211451)Instructions burned: 181 (million)
% 3.41/1.26 % (2211461)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=1331088554:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2997 on theBenchmark for (2997ds/2051Mi)
% 3.41/1.26 % (2211450)Refutation found. Thanks to Tanya!
% 3.41/1.26 % SZS status Unsatisfiable for theBenchmark
% 3.41/1.26 % SZS output start Proof for theBenchmark
% See solution above
% 3.41/1.26 % (2211450)------------------------------
% 3.41/1.26 % (2211450)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.41/1.26 % (2211450)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.41/1.26 % (2211450)CaDiCaL version: 2.1.3
% 3.41/1.26 % (2211450)Termination reason: Refutation
% 3.41/1.26 % (2211450)Time elapsed: 0.003 s
% 3.41/1.26 % (2211450)Peak memory usage: 88 MB
% 3.41/1.26 % (2211450)Instructions burned: 3 (million)
% 3.41/1.26 % (2211450)------------------------------
% 3.41/1.26 % (2211450)------------------------------
% 3.41/1.26 % (2211442)Success in time 0.397 s
% 3.41/1.26 % Vampire exiting
%------------------------------------------------------------------------------