%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : CAT010-4 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n006.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 2.53s 1.09s
% Output : Refutation 2.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 7
% Syntax : Number of formulae : 16 ( 11 unt; 0 def)
% Number of atoms : 21 ( 10 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 11 ( 6 ~; 5 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 14 ( 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0] :
( ~ there_exists(domain(X0))
| there_exists(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain_has_elements) ).
fof(f6,axiom,
! [X0,X1] :
( ~ there_exists(compose(X0,X1))
| there_exists(domain(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',composition_implies_domain) ).
fof(f7,axiom,
! [X0,X1] :
( ~ there_exists(compose(X0,X1))
| domain(X0) = codomain(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain_codomain_composition1) ).
fof(f9,axiom,
! [X2,X0,X1] : compose(X0,compose(X1,X2)) = compose(compose(X0,X1),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_of_compose) ).
fof(f11,axiom,
! [X0] : compose(codomain(X0),X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compose_codomain) ).
fof(f12,axiom,
there_exists(compose(a,b)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ab_exists) ).
fof(f13,negated_conjecture,
codomain(compose(a,b)) != codomain(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_codomain_of_ab_equals_codomain_of_a) ).
fof(f17,plain,
there_exists(domain(a)),
inference(resolution,[],[f6,f12]) ).
fof(f20,plain,
there_exists(a),
inference(resolution,[],[f17,f4]) ).
fof(f23,plain,
! [X0] :
( ~ there_exists(X0)
| codomain(X0) = domain(codomain(X0)) ),
inference(superposition,[],[f7,f11]) ).
fof(f25,plain,
! [X0,X1] : compose(X0,X1) = compose(codomain(X0),compose(X0,X1)),
inference(superposition,[],[f9,f11]) ).
fof(f54,plain,
codomain(a) = domain(codomain(a)),
inference(resolution,[],[f23,f20]) ).
fof(f90,plain,
! [X0,X1] :
( ~ there_exists(compose(X0,X1))
| domain(codomain(X0)) = codomain(compose(X0,X1)) ),
inference(superposition,[],[f7,f25]) ).
fof(f642,plain,
codomain(compose(a,b)) = domain(codomain(a)),
inference(resolution,[],[f90,f12]) ).
fof(f656,plain,
codomain(compose(a,b)) = codomain(a),
inference(forward_demodulation,[],[f642,f54]) ).
fof(f658,plain,
$false,
inference(forward_subsumption_resolution,[],[f656,f13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : CAT010-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.17 % Computer : n006.cluster.edu
% 0.07/0.17 % Model : x86_64 x86_64
% 0.07/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.17 % Memory : 8046.5625MB
% 0.07/0.17 % OS : Linux 6.8.0-71-generic
% 0.07/0.17 % CPULimit : 300
% 0.07/0.17 % WCLimit : 300
% 0.07/0.17 % DateTime : Mon Sep 28 21:12:55 UTC 2026
% 0.07/0.17 % CPUTime :
% 0.07/0.17 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.20 Running first-order theorem proving
% 0.07/0.20 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
% 2.53/1.09 % (208438)Input is clausal, will run a generic CNF schedule.
% 2.53/1.09 % (208446)lrs+10_1_sil=8000:sp=occurrence:random_seed=3057030906:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.53/1.09 % (208446)First to succeed.
% 2.53/1.09 % (208446)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-208438"
% 2.53/1.09 % (208443)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=613735973:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.53/1.09 % (208448)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3968981356:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.53/1.09 % (208444)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=692841127:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.53/1.09 % (208447)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=810535829:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.53/1.09 % (208445)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3924457252:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.53/1.09 % (208449)dis-21_1_sil=8000:lcm=predicate:random_seed=3035348967:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 2.53/1.09 % (208449)Refutation not found, incomplete strategy
% 2.53/1.09 % (208449)------------------------------
% 2.53/1.09 % (208449)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.53/1.09 % (208449)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.53/1.09 % (208449)CaDiCaL version: 2.1.3
% 2.53/1.09 % (208449)Termination reason: Refutation not found, incomplete strategy
% 2.53/1.09 % (208449)Time elapsed: 0.001 s
% 2.53/1.09 % (208449)Peak memory usage: 88 MB
% 2.53/1.09 % (208449)Instructions burned: 1 (million)
% 2.53/1.09 % (208448)Also succeeded, but the first one will report.
% 2.53/1.09 % (208447)Also succeeded, but the first one will report.
% 2.53/1.09 % (208446)Refutation found. Thanks to Tanya!
% 2.53/1.09 % SZS status Unsatisfiable for theBenchmark
% 2.53/1.09 % SZS output start Proof for theBenchmark
% See solution above
% 2.53/1.09 % (208446)------------------------------
% 2.53/1.09 % (208446)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.53/1.09 % (208446)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.53/1.09 % (208446)CaDiCaL version: 2.1.3
% 2.53/1.09 % (208446)Termination reason: Refutation
% 2.53/1.09 % (208446)Time elapsed: 0.008 s
% 2.53/1.09 % (208446)Peak memory usage: 88 MB
% 2.53/1.09 % (208446)Instructions burned: 19 (million)
% 2.53/1.09 % (208446)------------------------------
% 2.53/1.09 % (208446)------------------------------
% 2.53/1.09 % (208438)Success in time 0.274 s
% 2.53/1.09 % Vampire exiting
%------------------------------------------------------------------------------