%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : CAT010-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n019.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 1.46s 0.48s
% Output : Refutation 1.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 16
% Syntax : Number of formulae : 45 ( 12 unt; 0 def)
% Number of atoms : 103 ( 14 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 117 ( 59 ~; 58 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 91 ( 91 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( product(X0,X1,compose(X0,X1))
| ~ defined(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax',closure_of_composition) ).
fof(f2,axiom,
! [X2,X0,X1] :
( ~ product(X0,X1,X2)
| defined(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax',associative_property1) ).
fof(f6,axiom,
! [X2,X3,X0,X1] :
( ~ product(X0,X1,X2)
| ~ defined(X3,X2)
| defined(X3,X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax',category_theory_axiom3) ).
fof(f8,axiom,
! [X2,X3,X0,X1,X4,X5] :
( ~ product(X3,X0,X5)
| ~ product(X3,X2,X4)
| ~ product(X0,X1,X2)
| product(X5,X1,X4) ),
file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax',category_theory_axiom5) ).
fof(f9,axiom,
! [X2,X0,X1] :
( ~ defined(X1,X2)
| ~ defined(X0,X1)
| ~ identity_map(X1)
| defined(X0,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax',category_theory_axiom6) ).
fof(f10,axiom,
! [X0] : identity_map(domain(X0)),
file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax',domain_is_an_identity_map) ).
fof(f11,axiom,
! [X0] : identity_map(codomain(X0)),
file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax',codomain_is_an_identity_map) ).
fof(f12,axiom,
! [X0] : defined(X0,domain(X0)),
file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax',mapping_from_x_to_its_domain) ).
fof(f13,axiom,
! [X0] : defined(codomain(X0),X0),
file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax',mapping_from_codomain_of_x_to_x) ).
fof(f14,axiom,
! [X0] : product(X0,domain(X0),X0),
file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax',product_on_domain) ).
fof(f15,axiom,
! [X0] : product(codomain(X0),X0,X0),
file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax',product_on_codomain) ).
fof(f16,axiom,
! [X0,X1] :
( product(X0,X1,X1)
| ~ identity_map(X0)
| ~ defined(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax',identity1) ).
fof(f17,axiom,
! [X0,X1] :
( product(X0,X1,X0)
| ~ identity_map(X1)
| ~ defined(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax',identity2) ).
fof(f18,axiom,
! [X2,X3,X0,X1] :
( ~ product(X0,X1,X3)
| ~ product(X0,X1,X2)
| X2 = X3 ),
file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax',composition_is_well_defined) ).
fof(f19,axiom,
defined(b,a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ba_defined) ).
fof(f20,negated_conjecture,
codomain(compose(b,a)) != codomain(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_codomain_of_ba_equals_codomain_of_b) ).
fof(f21,plain,
! [X0,X1] :
( defined(X0,domain(X1))
| ~ identity_map(X1)
| ~ defined(X0,X1) ),
inference(resolution,[],[f9,f12]) ).
fof(f31,plain,
! [X2,X0,X1] :
( ~ defined(X2,X1)
| ~ defined(X1,X0)
| ~ identity_map(X0)
| ~ identity_map(X1)
| defined(X2,domain(X0)) ),
inference(resolution,[],[f21,f9]) ).
fof(f32,plain,
! [X0,X1] :
( ~ defined(domain(X0),X1)
| ~ identity_map(X1)
| ~ identity_map(domain(X0))
| defined(X0,domain(X1)) ),
inference(resolution,[],[f31,f12]) ).
fof(f44,plain,
! [X0,X1] :
( ~ defined(domain(X0),X1)
| ~ identity_map(X1)
| defined(X0,domain(X1)) ),
inference(forward_subsumption_resolution,[],[f32,f10]) ).
fof(f449,plain,
! [X2,X0,X1] :
( ~ defined(X0,compose(X1,X2))
| defined(X0,X1)
| ~ defined(X1,X2) ),
inference(resolution,[],[f6,f1]) ).
fof(f450,plain,
! [X0,X1] :
( defined(X0,codomain(X1))
| ~ defined(X0,X1) ),
inference(resolution,[],[f6,f15]) ).
fof(f458,plain,
! [X0,X1] :
( ~ defined(domain(X0),X1)
| ~ identity_map(codomain(X1))
| defined(X0,domain(codomain(X1))) ),
inference(resolution,[],[f450,f44]) ).
fof(f465,plain,
! [X0,X1] :
( defined(X0,domain(codomain(X1)))
| ~ defined(domain(X0),X1) ),
inference(forward_subsumption_resolution,[],[f458,f11]) ).
fof(f1056,plain,
! [X0,X1] :
( ~ product(X0,domain(X0),X1)
| X0 = X1 ),
inference(resolution,[],[f18,f14]) ).
fof(f1058,plain,
! [X2,X0,X1] :
( ~ product(X0,X1,X2)
| X1 = X2
| ~ identity_map(X0)
| ~ defined(X0,X1) ),
inference(resolution,[],[f18,f16]) ).
fof(f1065,plain,
! [X2,X0,X1] :
( ~ identity_map(X0)
| X1 = X2
| ~ product(X0,X1,X2) ),
inference(forward_subsumption_resolution,[],[f1058,f2]) ).
fof(f1099,plain,
! [X0] :
( domain(X0) = X0
| ~ identity_map(X0)
| ~ defined(X0,domain(X0)) ),
inference(resolution,[],[f1056,f16]) ).
fof(f1104,plain,
! [X0] :
( ~ identity_map(X0)
| domain(X0) = X0 ),
inference(forward_subsumption_resolution,[],[f1099,f12]) ).
fof(f1110,plain,
! [X0] : domain(X0) = domain(domain(X0)),
inference(resolution,[],[f1104,f10]) ).
fof(f1111,plain,
! [X0] : codomain(X0) = domain(codomain(X0)),
inference(resolution,[],[f1104,f11]) ).
fof(f1772,plain,
! [X2,X3,X0,X1] :
( ~ product(domain(X0),X3,X1)
| ~ product(X0,X1,X2)
| product(X0,X3,X2) ),
inference(resolution,[],[f8,f14]) ).
fof(f1785,plain,
! [X2,X0,X1] :
( ~ identity_map(X2)
| product(X0,X2,X1)
| ~ product(X0,domain(X0),X1)
| ~ defined(domain(X0),X2) ),
inference(resolution,[],[f1772,f17]) ).
fof(f1792,plain,
! [X2,X0,X1] :
( ~ product(X0,domain(X0),X2)
| product(X0,domain(X1),X2)
| ~ defined(domain(X0),domain(X1)) ),
inference(resolution,[],[f1785,f10]) ).
fof(f1796,plain,
! [X0,X1] :
( ~ defined(domain(X0),domain(X1))
| product(X0,domain(X1),X0) ),
inference(resolution,[],[f1792,f14]) ).
fof(f1930,plain,
! [X0,X1] :
( product(X0,domain(codomain(X1)),X0)
| ~ defined(domain(domain(X0)),X1) ),
inference(resolution,[],[f1796,f465]) ).
fof(f1939,plain,
! [X0,X1] :
( product(X0,codomain(X1),X0)
| ~ defined(domain(domain(X0)),X1) ),
inference(forward_demodulation,[],[f1930,f1111]) ).
fof(f1968,plain,
! [X0,X1] :
( product(X0,codomain(X1),X0)
| ~ defined(domain(X0),X1) ),
inference(forward_demodulation,[],[f1939,f1110]) ).
fof(f2289,plain,
! [X2,X0,X1] :
( ~ product(codomain(X2),X0,X1)
| X0 = X1 ),
inference(resolution,[],[f1065,f11]) ).
fof(f2349,plain,
! [X0,X1] :
( ~ defined(domain(codomain(X0)),X1)
| codomain(X0) = codomain(X1) ),
inference(resolution,[],[f1968,f2289]) ).
fof(f2356,plain,
! [X0,X1] :
( ~ defined(codomain(X0),X1)
| codomain(X0) = codomain(X1) ),
inference(forward_demodulation,[],[f2349,f1111]) ).
fof(f7568,plain,
! [X0,X1] :
( defined(codomain(compose(X0,X1)),X0)
| ~ defined(X0,X1) ),
inference(resolution,[],[f449,f13]) ).
fof(f7663,plain,
! [X0,X1] :
( ~ defined(X0,X1)
| codomain(X0) = codomain(compose(X0,X1)) ),
inference(resolution,[],[f7568,f2356]) ).
fof(f8552,plain,
codomain(compose(b,a)) = codomain(b),
inference(resolution,[],[f7663,f19]) ).
fof(f8554,plain,
$false,
inference(forward_subsumption_resolution,[],[f8552,f20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : CAT010-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.19 % Computer : n019.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Mon Sep 28 21:13:18 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.22 Running first-order model finding
% 0.08/0.22 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
% 0.87/0.47 % (288906)Will run a generic schedule for satisfiability detection.
% 0.87/0.47 % (288915)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2308677802:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.87/0.47 % (288912)% WARNING: option uhcvi not known.
% 0.87/0.47 % (288911)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=254552262_2999 on theBenchmark for (2999ds/0Mi)
% 0.87/0.47 % (288912)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3695376329:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.87/0.47 % (288913)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2061297909:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.87/0.47 % (288914)dis+10_1_sil=32000:sp=arity:random_seed=657341441:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.87/0.47 % (288916)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=769746009:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.87/0.47 % (288917)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=99646464:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.87/0.47 % TRYING [1]
% 0.87/0.47 % TRYING [2]
% 0.87/0.47 % TRYING [3]
% 0.87/0.47 % TRYING [4]
% 0.87/0.47 % TRYING [5]
% 0.87/0.47 % (288915)Instruction limit reached!
% 0.87/0.47 % (288915)------------------------------
% 0.87/0.47 % (288915)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.87/0.47 % (288915)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.87/0.47 % (288915)CaDiCaL version: 2.1.3
% 0.87/0.47 % (288915)Termination reason: Instruction limit
% 0.87/0.47 % (288915)Termination phase: Saturation
% 0.87/0.47 % (288915)Time elapsed: 0.036 s
% 0.87/0.47 % (288915)Peak memory usage: 12 MB
% 0.87/0.47 % (288915)Instructions burned: 119 (million)
% 0.87/0.47 % (288925)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=2764980402:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.87/0.47 % TRYING [6]
% 0.87/0.47 % TRYING [1]
% 0.87/0.47 % TRYING [2]
% 0.87/0.47 % TRYING [3]
% 0.87/0.47 % TRYING [4]
% 0.87/0.47 % TRYING [5]
% 0.87/0.47 % (288914)Instruction limit reached!
% 0.87/0.47 % (288914)------------------------------
% 0.87/0.47 % (288914)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.87/0.47 % (288914)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.87/0.47 % (288914)CaDiCaL version: 2.1.3
% 0.87/0.47 % (288914)Termination reason: Instruction limit
% 0.87/0.47 % (288914)Termination phase: Saturation
% 0.87/0.47 % (288914)Time elapsed: 0.063 s
% 0.87/0.47 % (288914)Peak memory usage: 12 MB
% 0.87/0.47 % (288914)Instructions burned: 103 (million)
% 0.87/0.47 % TRYING [6]
% 0.87/0.47 % (288916)Instruction limit reached!
% 0.87/0.47 % (288916)------------------------------
% 0.87/0.47 % (288916)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.87/0.47 % (288916)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.87/0.47 % (288916)CaDiCaL version: 2.1.3
% 0.87/0.47 % (288916)Termination reason: Instruction limit
% 0.87/0.47 % (288916)Termination phase: Saturation
% 0.87/0.47 % (288916)Time elapsed: 0.078 s
% 0.87/0.47 % (288916)Peak memory usage: 12 MB
% 0.87/0.47 % (288916)Instructions burned: 132 (million)
% 0.87/0.47 % (288927)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=2628929591:i=131:bd=preordered:fsd=on_2998 on theBenchmark for (2998ds/131Mi)
% 0.87/0.47 % TRYING [7]
% 0.87/0.47 % (288928)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=1577210258:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 0.87/0.47 % TRYING [7]
% 0.87/0.47 % (288917)Instruction limit reached!
% 0.87/0.47 % (288917)------------------------------
% 0.87/0.47 % (288917)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.87/0.47 % (288917)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.87/0.47 % (288917)CaDiCaL version: 2.1.3
% 0.87/0.47 % (288917)Termination reason: Instruction limit
% 0.87/0.47 % (288917)Termination phase: Saturation
% 0.87/0.47 % (288917)Time elapsed: 0.113 s
% 0.87/0.47 % (288917)Peak memory usage: 13 MB
% 0.87/0.47 % (288917)Instructions burned: 159 (million)
% 0.87/0.47 % (288931)ott-21_1_sil=16000:fs=off:random_seed=1390681484:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 0.87/0.47 % (288927)Instruction limit reached!
% 0.87/0.47 % (288927)------------------------------
% 0.87/0.47 % (288927)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.46/0.48 % (288927)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.46/0.48 % (288927)CaDiCaL version: 2.1.3
% 1.46/0.48 % (288927)Termination reason: Instruction limit
% 1.46/0.48 % (288927)Termination phase: Saturation
% 1.46/0.48 % (288927)Time elapsed: 0.086 s
% 1.46/0.48 % (288927)Peak memory usage: 12 MB
% 1.46/0.48 % (288927)Instructions burned: 132 (million)
% 1.46/0.48 % TRYING [8]
% 1.46/0.48 % (288933)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=4127435588:i=477:bd=all_2997 on theBenchmark for (2997ds/477Mi)
% 1.46/0.48 % TRYING [8]
% 1.46/0.48 % (288928) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-288906-288928"...
% 1.46/0.48 % (288925)Instruction limit reached!
% 1.46/0.48 % (288925)------------------------------
% 1.46/0.48 % (288925)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.46/0.48 % (288925)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.46/0.48 % (288925)CaDiCaL version: 2.1.3
% 1.46/0.48 % (288925)Termination reason: Instruction limit
% 1.46/0.48 % (288925)Termination phase: Finite model building constraint generation
% 1.46/0.48 % (288925)Time elapsed: 0.157 s
% 1.46/0.48 % (288925)Peak memory usage: 28 MB
% 1.46/0.48 % (288925)Instructions burned: 722 (million)
% 1.46/0.48 % (288928)...printing done.
% 1.46/0.48 % (288928)Refutation found. Thanks to Tanya!
% 1.46/0.48 % SZS status Unsatisfiable for theBenchmark
% 1.46/0.48 % SZS output start Proof for theBenchmark
% See solution above
% 1.46/0.48 % (288928)------------------------------
% 1.46/0.48 % (288928)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.46/0.48 % (288928)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.46/0.48 % (288928)CaDiCaL version: 2.1.3
% 1.46/0.48 % (288928)Termination reason: Refutation
% 1.46/0.48 % (288928)Time elapsed: 0.097 s
% 1.46/0.48 % (288928)Peak memory usage: 13 MB
% 1.46/0.48 % (288928)Instructions burned: 188 (million)
% 1.46/0.48 % (288906)Success in time 0.242 s
% 1.46/0.48 % Vampire exiting
%------------------------------------------------------------------------------