%------------------------------------------------------------------------------
% File : Vampire-SAT---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 SAT
% Computer : n017.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 09:36:54 AM UTC 2026
% Result : Unsatisfiable 0.25s 0.39s
% Output : Refutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of formulae : 26 ( 26 unt; 0 def)
% Number of atoms : 26 ( 25 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 1 ( 1 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-4 aty)
% Number of variables : 25 ( 25 !; 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(f36,plain,
! [X0,X1] : compose(X0,X1) = compose(codomain(X0),compose(X0,X1)),
inference(superposition,[],[f19,f21]) ).
fof(f57,plain,
true = ifeq(true,true,there_exists(domain(a)),true),
inference(superposition,[],[f14,f23]) ).
fof(f58,plain,
true = there_exists(domain(a)),
inference(forward_demodulation,[],[f57,f3]) ).
fof(f60,plain,
true = ifeq(true,true,there_exists(a),true),
inference(superposition,[],[f10,f58]) ).
fof(f66,plain,
true = there_exists(a),
inference(forward_demodulation,[],[f60,f3]) ).
fof(f69,plain,
! [X0] : codomain(X0) = ifeq2(there_exists(X0),true,domain(codomain(X0)),codomain(X0)),
inference(superposition,[],[f16,f21]) ).
fof(f109,plain,
! [X0,X1] : codomain(compose(X0,X1)) = ifeq2(there_exists(compose(X0,X1)),true,domain(codomain(X0)),codomain(compose(X0,X1))),
inference(superposition,[],[f16,f36]) ).
fof(f262,plain,
codomain(a) = ifeq2(true,true,domain(codomain(a)),codomain(a)),
inference(superposition,[],[f69,f66]) ).
fof(f267,plain,
codomain(a) = domain(codomain(a)),
inference(forward_demodulation,[],[f262,f2]) ).
fof(f2011,plain,
codomain(compose(a,b)) = ifeq2(true,true,domain(codomain(a)),codomain(compose(a,b))),
inference(superposition,[],[f109,f23]) ).
fof(f2047,plain,
codomain(compose(a,b)) = domain(codomain(a)),
inference(forward_demodulation,[],[f2011,f2]) ).
fof(f2051,plain,
codomain(compose(a,b)) = codomain(a),
inference(forward_demodulation,[],[f2047,f267]) ).
fof(f2053,plain,
$false,
inference(forward_subsumption_resolution,[],[f2051,f24]) ).
%------------------------------------------------------------------------------
%----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 SAT
% 0.10/0.22 % Computer : n017.cluster.edu
% 0.10/0.22 % Model : x86_64 x86_64
% 0.10/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.22 % Memory : 8046.5625MB
% 0.10/0.22 % OS : Linux 6.8.0-71-generic
% 0.10/0.22 % CPULimit : 300
% 0.10/0.22 % WCLimit : 300
% 0.10/0.22 % DateTime : Mon Sep 28 21:08:36 UTC 2026
% 0.10/0.23 % CPUTime :
% 0.10/0.23 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.25/0.28 Running first-order model finding
% 0.25/0.28 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.25/0.39 % (4033604)Will run a generic schedule for satisfiability detection.
% 0.25/0.39 % (4033610)% WARNING: option uhcvi not known.
% 0.25/0.39 % (4033610)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1313290347:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.25/0.39 % (4033613)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3348195108:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.25/0.39 % (4033609)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1826809988_2999 on theBenchmark for (2999ds/0Mi)
% 0.25/0.39 % (4033615)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=660258397:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.25/0.39 % (4033611)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2990681255:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.25/0.39 % (4033612)dis+10_1_sil=32000:sp=arity:random_seed=2484647610:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.25/0.39 % (4033614)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3111031754:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.25/0.39 % TRYING [1]
% 0.25/0.39 % TRYING [2]
% 0.25/0.39 % TRYING [3]
% 0.25/0.39 % TRYING [4]
% 0.25/0.39 % (4033612) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-4033604-4033612"...
% 0.25/0.39 % (4033612)...printing done.
% 0.25/0.39 % (4033613) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-4033604-4033613"...
% 0.25/0.39 % (4033612)Refutation found. Thanks to Tanya!
% 0.25/0.39 % SZS status Unsatisfiable for theBenchmark
% 0.25/0.39 % SZS output start Proof for theBenchmark
% See solution above
% 0.25/0.39 % (4033612)------------------------------
% 0.25/0.39 % (4033612)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.25/0.39 % (4033612)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.25/0.39 % (4033612)CaDiCaL version: 2.1.3
% 0.25/0.39 % (4033612)Termination reason: Refutation
% 0.25/0.39 % (4033612)Time elapsed: 0.046 s
% 0.25/0.39 % (4033612)Peak memory usage: 12 MB
% 0.25/0.39 % (4033612)Instructions burned: 80 (million)
% 0.25/0.39 % (4033604)Success in time 0.096 s
% 0.25/0.39 % Vampire exiting
%------------------------------------------------------------------------------