%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : CAT010-10 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n003.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 09:36:36 AM UTC 2026
% Result : Unsatisfiable 2.84s 1.12s
% Output : Refutation 2.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 10
% Syntax : Number of formulae : 29 ( 29 unt; 1 def)
% Number of atoms : 29 ( 25 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-4 aty)
% Number of variables : 26 ( 26 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X2,X0,X1] : ifeq2(X0,X0,X1,X2) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom_001) ).
fof(f3,axiom,
! [X2,X0,X1] : ifeq(X0,X0,X1,X2) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom_002) ).
fof(f9,axiom,
! [X0] : ifeq(there_exists(domain(X0)),true,there_exists(X0),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain_has_elements) ).
fof(f10,plain,
! [X0] : true = ifeq(there_exists(domain(X0)),true,there_exists(X0),true),
inference(reorient_equations,[],[f9]) ).
fof(f13,axiom,
! [X0,X1] : ifeq(there_exists(compose(X0,X1)),true,there_exists(domain(X0)),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',composition_implies_domain) ).
fof(f14,plain,
! [X0,X1] : true = ifeq(there_exists(compose(X0,X1)),true,there_exists(domain(X0)),true),
inference(reorient_equations,[],[f13]) ).
fof(f15,axiom,
! [X0,X1] : ifeq2(there_exists(compose(X0,X1)),true,domain(X0),codomain(X1)) = codomain(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain_codomain_composition1) ).
fof(f16,plain,
! [X0,X1] : codomain(X1) = ifeq2(there_exists(compose(X0,X1)),true,domain(X0),codomain(X1)),
inference(reorient_equations,[],[f15]) ).
fof(f19,axiom,
! [X2,X0,X1] : compose(X0,compose(X1,X2)) = compose(compose(X0,X1),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_compose) ).
fof(f21,axiom,
! [X0] : compose(codomain(X0),X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compose_codomain) ).
fof(f22,axiom,
there_exists(compose(a,b)) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ab_exists) ).
fof(f23,plain,
true = there_exists(compose(a,b)),
inference(reorient_equations,[],[f22]) ).
fof(f24,negated_conjecture,
codomain(compose(a,b)) != codomain(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_codomain_of_ab_equals_codomain_of_a) ).
fof(f25,definition,
~ sP0(codomain(compose(a,b))),
introduced(definition,[new_symbols(definition,[sP0])],[inequality_splitting_name_introduction]) ).
fof(f26,plain,
sP0(codomain(a)),
inference(inequality_splitting,[],[f24,f25]) ).
fof(f46,plain,
! [X2,X0,X1] : true = ifeq(there_exists(compose(X0,compose(X1,X2))),true,there_exists(domain(compose(X0,X1))),true),
inference(superposition,[],[f14,f19]) ).
fof(f58,plain,
! [X0] : codomain(X0) = ifeq2(there_exists(X0),true,domain(codomain(X0)),codomain(X0)),
inference(superposition,[],[f16,f21]) ).
fof(f258,plain,
codomain(compose(a,b)) = ifeq2(true,true,domain(codomain(compose(a,b))),codomain(compose(a,b))),
inference(superposition,[],[f58,f23]) ).
fof(f265,plain,
codomain(compose(a,b)) = domain(codomain(compose(a,b))),
inference(forward_demodulation,[],[f258,f2]) ).
fof(f362,plain,
! [X0,X1] : true = ifeq(there_exists(compose(X0,X1)),true,there_exists(domain(compose(codomain(compose(X0,X1)),X0))),true),
inference(superposition,[],[f46,f21]) ).
fof(f2118,plain,
true = ifeq(true,true,there_exists(domain(compose(codomain(compose(a,b)),a))),true),
inference(superposition,[],[f362,f23]) ).
fof(f2153,plain,
true = there_exists(domain(compose(codomain(compose(a,b)),a))),
inference(forward_demodulation,[],[f2118,f3]) ).
fof(f2165,plain,
true = ifeq(true,true,there_exists(compose(codomain(compose(a,b)),a)),true),
inference(superposition,[],[f10,f2153]) ).
fof(f2181,plain,
true = there_exists(compose(codomain(compose(a,b)),a)),
inference(forward_demodulation,[],[f2165,f3]) ).
fof(f2383,plain,
codomain(a) = ifeq2(true,true,domain(codomain(compose(a,b))),codomain(a)),
inference(superposition,[],[f16,f2181]) ).
fof(f2413,plain,
codomain(a) = domain(codomain(compose(a,b))),
inference(forward_demodulation,[],[f2383,f2]) ).
fof(f2425,plain,
codomain(compose(a,b)) = codomain(a),
inference(backward_demodulation,[],[f265,f2413]) ).
fof(f2440,plain,
~ sP0(codomain(a)),
inference(backward_demodulation,[],[f25,f2425]) ).
fof(f2479,plain,
$false,
inference(forward_subsumption_resolution,[],[f2440,f26]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : CAT010-10 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n003.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Mon Sep 28 21:14:57 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
% 2.84/1.12 % (2027825)Detected a unit-equality problem, will run specialized UEQ schedule.
% 2.84/1.12 % (2027860)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=1980803888:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 2.84/1.12 % (2027860)First to succeed.
% 2.84/1.12 % (2027860)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2027825"
% 2.84/1.12 % (2027863)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=3800704046:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 2.84/1.12 % (2027859)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=2840056284:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 2.84/1.12 % (2027857)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=2506592869:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 2.84/1.12 % (2027858)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=3715316383:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 2.84/1.12 % (2027862)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=3738991983:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 2.84/1.12 % (2027861)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=959228895:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 2.84/1.12 % (2027861)Also succeeded, but the first one will report.
% 2.84/1.12 % (2027863)Also succeeded, but the first one will report.
% 2.84/1.12 % (2027860)Refutation found. Thanks to Tanya!
% 2.84/1.12 % SZS status Unsatisfiable for theBenchmark
% 2.84/1.12 % SZS output start Proof for theBenchmark
% See solution above
% 2.84/1.12 % (2027860)------------------------------
% 2.84/1.12 % (2027860)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.84/1.12 % (2027860)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.84/1.12 % (2027860)CaDiCaL version: 2.1.3
% 2.84/1.12 % (2027860)Termination reason: Refutation
% 2.84/1.12 % (2027860)Time elapsed: 0.039 s
% 2.84/1.12 % (2027860)Peak memory usage: 89 MB
% 2.84/1.12 % (2027860)Instructions burned: 116 (million)
% 2.84/1.12 % (2027860)------------------------------
% 2.84/1.12 % (2027860)------------------------------
% 2.84/1.12 % (2027825)Success in time 0.326 s
% 2.84/1.12 % Vampire exiting
%------------------------------------------------------------------------------