%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : CAT008-1 : 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 : n001.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 09:36:35 AM UTC 2026
% Result : Unsatisfiable 2.82s 1.19s
% Output : Refutation 2.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 15
% Syntax : Number of formulae : 39 ( 12 unt; 0 def)
% Number of atoms : 93 ( 8 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 110 ( 56 ~; 54 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-1 aty)
% Number of variables : 70 ( 70 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X2,X0,X1] :
( ~ product(X0,X1,X2)
| defined(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associative_property1) ).
fof(f3,axiom,
! [X2,X3,X0,X1] :
( ~ product(X0,X1,X2)
| ~ defined(X2,X3)
| defined(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associative_property2) ).
fof(f6,axiom,
! [X2,X3,X0,X1] :
( ~ product(X0,X1,X2)
| ~ defined(X3,X2)
| defined(X3,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',category_theory_axiom3) ).
fof(f7,axiom,
! [X2,X3,X0,X1,X4] :
( ~ product(X3,X0,X4)
| ~ product(X0,X1,X2)
| ~ defined(X3,X2)
| defined(X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',category_theory_axiom4) ).
fof(f10,axiom,
! [X0] : identity_map(domain(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain_is_an_identity_map) ).
fof(f11,axiom,
! [X0] : identity_map(codomain(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',codomain_is_an_identity_map) ).
fof(f12,axiom,
! [X0] : defined(X0,domain(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mapping_from_x_to_its_domain) ).
fof(f13,axiom,
! [X0] : defined(codomain(X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mapping_from_codomain_of_x_to_x) ).
fof(f14,axiom,
! [X0] : product(X0,domain(X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_on_domain) ).
fof(f15,axiom,
! [X0] : product(codomain(X0),X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_on_codomain) ).
fof(f16,axiom,
! [X0,X1] :
( product(X0,X1,X1)
| ~ identity_map(X0)
| ~ defined(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity1) ).
fof(f17,axiom,
! [X0,X1] :
( product(X0,X1,X0)
| ~ identity_map(X1)
| ~ defined(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity2) ).
fof(f18,axiom,
! [X2,X3,X0,X1] :
( ~ product(X0,X1,X3)
| ~ product(X0,X1,X2)
| X2 = X3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',composition_is_well_defined) ).
fof(f19,axiom,
defined(a,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ab_defined) ).
fof(f20,negated_conjecture,
domain(a) != codomain(b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_domain_of_a_equals_codomain_of_b) ).
fof(f25,plain,
! [X0,X1] :
( defined(domain(X0),X1)
| ~ defined(X0,X1) ),
inference(resolution,[],[f3,f14]) ).
fof(f26,plain,
! [X2,X0,X1] :
( ~ defined(X0,X2)
| defined(X2,X1)
| ~ identity_map(X2)
| ~ defined(X0,X1) ),
inference(resolution,[],[f3,f17]) ).
fof(f31,plain,
! [X0,X1] :
( defined(X0,codomain(X1))
| ~ defined(X0,X1) ),
inference(resolution,[],[f6,f15]) ).
fof(f51,plain,
! [X2,X0,X1] :
( ~ product(X0,X1,X2)
| X1 = X2
| ~ identity_map(X0)
| ~ defined(X0,X1) ),
inference(resolution,[],[f18,f16]) ).
fof(f52,plain,
! [X2,X0,X1] :
( ~ product(X0,X1,X2)
| X1 = X2
| ~ identity_map(X0) ),
inference(forward_subsumption_resolution,[],[f51,f2]) ).
fof(f65,plain,
! [X2,X0,X1] :
( ~ product(domain(X0),X1,X2)
| ~ defined(X0,X2)
| defined(X0,X1) ),
inference(resolution,[],[f7,f14]) ).
fof(f98,plain,
! [X0,X1] :
( ~ defined(X1,X0)
| ~ identity_map(X1)
| ~ identity_map(X0)
| X0 = X1 ),
inference(resolution,[],[f52,f17]) ).
fof(f118,plain,
! [X2,X0,X1] :
( defined(codomain(X0),X1)
| ~ identity_map(codomain(X0))
| ~ defined(X2,X1)
| ~ defined(X2,X0) ),
inference(resolution,[],[f26,f31]) ).
fof(f121,plain,
! [X0,X1] :
( ~ defined(codomain(X0),X1)
| ~ identity_map(X0)
| defined(X0,X1) ),
inference(resolution,[],[f26,f13]) ).
fof(f137,plain,
! [X2,X0,X1] :
( ~ defined(X2,X1)
| defined(codomain(X0),X1)
| ~ defined(X2,X0) ),
inference(forward_subsumption_resolution,[],[f118,f11]) ).
fof(f178,plain,
! [X0,X1] :
( ~ defined(X0,domain(X0))
| defined(X0,X1)
| ~ identity_map(X1)
| ~ defined(domain(X0),X1) ),
inference(resolution,[],[f65,f17]) ).
fof(f182,plain,
! [X0,X1] :
( ~ defined(domain(X0),X1)
| ~ identity_map(X1)
| defined(X0,X1) ),
inference(forward_subsumption_resolution,[],[f178,f12]) ).
fof(f469,plain,
! [X0,X1] :
( ~ identity_map(codomain(X0))
| defined(X1,codomain(X0))
| ~ defined(domain(X1),X0) ),
inference(resolution,[],[f182,f31]) ).
fof(f477,plain,
! [X0,X1] :
( ~ defined(domain(X1),X0)
| defined(X1,codomain(X0)) ),
inference(forward_subsumption_resolution,[],[f469,f11]) ).
fof(f582,plain,
! [X0,X1] :
( ~ identity_map(domain(X0))
| ~ identity_map(X1)
| domain(X0) = X1
| ~ defined(X0,X1) ),
inference(resolution,[],[f98,f25]) ).
fof(f603,plain,
! [X0,X1] :
( ~ defined(X0,X1)
| domain(X0) = X1
| ~ identity_map(X1) ),
inference(forward_subsumption_resolution,[],[f582,f10]) ).
fof(f670,plain,
! [X0] :
( defined(codomain(X0),b)
| ~ defined(a,X0) ),
inference(resolution,[],[f137,f19]) ).
fof(f681,plain,
! [X0] :
( ~ defined(a,X0)
| ~ identity_map(X0)
| defined(X0,b) ),
inference(resolution,[],[f670,f121]) ).
fof(f970,plain,
( ~ identity_map(domain(a))
| defined(domain(a),b) ),
inference(resolution,[],[f681,f12]) ).
fof(f977,plain,
defined(domain(a),b),
inference(forward_subsumption_resolution,[],[f970,f10]) ).
fof(f1014,plain,
defined(a,codomain(b)),
inference(resolution,[],[f977,f477]) ).
fof(f1051,plain,
( domain(a) = codomain(b)
| ~ identity_map(codomain(b)) ),
inference(resolution,[],[f1014,f603]) ).
fof(f1052,plain,
~ identity_map(codomain(b)),
inference(forward_subsumption_resolution,[],[f1051,f20]) ).
fof(f1054,plain,
$false,
inference(forward_subsumption_resolution,[],[f1052,f11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : CAT008-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n001.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 21:19:04 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running first-order theorem proving
% 0.09/0.23 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
% 2.82/1.19 % (759546)Input is clausal, will run a generic CNF schedule.
% 2.82/1.19 % (759565)lrs+10_1_sil=8000:sp=occurrence:random_seed=3637902080:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.82/1.19 % (759565)First to succeed.
% 2.82/1.19 % (759565)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-759546"
% 2.82/1.19 % (759562)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=180043188:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.82/1.19 % (759568)dis-21_1_sil=8000:lcm=predicate:random_seed=2881196916: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)
% 2.82/1.19 % (759566)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2676585930:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.82/1.19 % (759567)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2089890636:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.82/1.19 % (759564)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=144432963:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.82/1.19 % (759563)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1421442786:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.82/1.19 % (759566)Also succeeded, but the first one will report.
% 2.82/1.19 % (759568)Instruction limit reached!
% 2.82/1.19 % (759568)------------------------------
% 2.82/1.19 % (759568)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.82/1.19 % (759568)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.82/1.19 % (759568)CaDiCaL version: 2.1.3
% 2.82/1.19 % (759568)Termination reason: Instruction limit
% 2.82/1.19 % (759568)Termination phase: Saturation
% 2.82/1.19 % (759568)Time elapsed: 0.063 s
% 2.82/1.19 % (759568)Peak memory usage: 88 MB
% 2.82/1.19 % (759568)Instructions burned: 118 (million)
% 2.82/1.19 % (759567)Instruction limit reached!
% 2.82/1.19 % (759567)------------------------------
% 2.82/1.19 % (759567)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.82/1.19 % (759567)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.82/1.19 % (759567)CaDiCaL version: 2.1.3
% 2.82/1.19 % (759567)Termination reason: Instruction limit
% 2.82/1.19 % (759567)Termination phase: Saturation
% 2.82/1.19 % (759567)Time elapsed: 0.118 s
% 2.82/1.19 % (759567)Peak memory usage: 88 MB
% 2.82/1.19 % (759567)Instructions burned: 181 (million)
% 2.82/1.19 % (759565)Refutation found. Thanks to Tanya!
% 2.82/1.19 % SZS status Unsatisfiable for theBenchmark
% 2.82/1.19 % SZS output start Proof for theBenchmark
% See solution above
% 2.82/1.19 % (759565)------------------------------
% 2.82/1.19 % (759565)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.82/1.19 % (759565)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.82/1.19 % (759565)CaDiCaL version: 2.1.3
% 2.82/1.19 % (759565)Termination reason: Refutation
% 2.82/1.19 % (759565)Time elapsed: 0.011 s
% 2.82/1.19 % (759565)Peak memory usage: 88 MB
% 2.82/1.19 % (759565)Instructions burned: 30 (million)
% 2.82/1.19 % (759565)------------------------------
% 2.82/1.19 % (759565)------------------------------
% 2.82/1.19 % (759546)Success in time 0.306 s
% 2.82/1.19 % Vampire exiting
%------------------------------------------------------------------------------