%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : CAT009-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n009.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 0.21s 1.60s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 14
% Syntax : Number of formulae : 27 ( 19 unt; 0 def)
% Number of atoms : 45 ( 2 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 40 ( 22 ~; 18 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 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 : 35 ( 35 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( product(X0,X1,compose(X0,X1))
| ~ defined(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closure_of_composition) ).
fof(f3,axiom,
! [X2,X3,X0,X1] :
( ~ product(X0,X1,X2)
| ~ defined(X2,X3)
| defined(X1,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associative_property2) ).
fof(f5,axiom,
! [X2,X3,X0,X1,X4,X5] :
( product(X0,X5,X4)
| ~ product(X2,X3,X4)
| ~ product(X1,X3,X5)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',category_theory_axiom2) ).
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/sandbox/benchmark/theBenchmark.p',category_theory_axiom4) ).
fof(f8,axiom,
! [X2,X3,X0,X1,X4,X5] :
( product(X5,X1,X4)
| ~ product(X3,X2,X4)
| ~ product(X3,X0,X5)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',category_theory_axiom5) ).
fof(f10,axiom,
! [X0] : identity_map(domain(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain_is_an_identity_map) ).
fof(f12,axiom,
! [X0] : defined(X0,domain(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mapping_from_x_to_its_domain) ).
fof(f14,axiom,
! [X0] : product(X0,domain(X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_on_domain) ).
fof(f15,axiom,
! [X0] : product(codomain(X0),X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_on_codomain) ).
fof(f16,axiom,
! [X0,X1] :
( product(X0,X1,X1)
| ~ identity_map(X0)
| ~ defined(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity1) ).
fof(f17,axiom,
! [X0,X1] :
( product(X0,X1,X0)
| ~ identity_map(X1)
| ~ defined(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity2) ).
fof(f18,axiom,
! [X2,X3,X0,X1] :
( ~ product(X0,X1,X3)
| ~ product(X0,X1,X2)
| X2 = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',composition_is_well_defined) ).
fof(f19,axiom,
defined(b,a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ba_defined) ).
fof(f20,negated_conjecture,
domain(compose(b,a)) != domain(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_domain_of_ba_equals_domain_of_a) ).
fof(f22,plain,
~ product(codomain(domain(a)),domain(a),domain(compose(b,a))),
inference(unit_resulting_resolution,[],[f18,f15,f20]) ).
fof(f29,plain,
product(b,a,compose(b,a)),
inference(unit_resulting_resolution,[],[f1,f19]) ).
fof(f50,plain,
defined(a,domain(compose(b,a))),
inference(unit_resulting_resolution,[],[f3,f12,f29]) ).
fof(f55,plain,
defined(compose(b,a),domain(a)),
inference(unit_resulting_resolution,[],[f7,f14,f19,f29]) ).
fof(f56,plain,
product(compose(b,a),domain(a),compose(b,a)),
inference(unit_resulting_resolution,[],[f8,f14,f29,f29]) ).
fof(f103,plain,
defined(domain(a),domain(compose(b,a))),
inference(unit_resulting_resolution,[],[f3,f14,f50]) ).
fof(f185,plain,
defined(domain(a),domain(a)),
inference(unit_resulting_resolution,[],[f3,f55,f56]) ).
fof(f210,plain,
product(domain(a),domain(a),domain(a)),
inference(unit_resulting_resolution,[],[f16,f10,f185]) ).
fof(f307,plain,
product(domain(a),domain(compose(b,a)),domain(compose(b,a))),
inference(unit_resulting_resolution,[],[f16,f10,f103]) ).
fof(f308,plain,
product(domain(a),domain(compose(b,a)),domain(a)),
inference(unit_resulting_resolution,[],[f17,f10,f103]) ).
fof(f733,plain,
~ product(domain(a),domain(a),domain(compose(b,a))),
inference(unit_resulting_resolution,[],[f5,f15,f22,f210]) ).
fof(f1503,plain,
~ product(domain(a),domain(compose(b,a)),domain(compose(b,a))),
inference(unit_resulting_resolution,[],[f5,f210,f733,f308]) ).
fof(f1541,plain,
$false,
inference(forward_subsumption_resolution,[],[f1503,f307]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : CAT009-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n009.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 21:13:15 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
% 0.21/1.60 % (3484104)Input is clausal, will run a generic CNF schedule.
% 0.21/1.60 % (3484195)lrs+10_1_sil=8000:sp=occurrence:random_seed=941708249:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 0.21/1.60 % (3484195)Instruction limit reached!
% 0.21/1.60 % (3484195)------------------------------
% 0.21/1.60 % (3484195)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.21/1.60 % (3484195)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/1.60 % (3484195)CaDiCaL version: 2.1.3
% 0.21/1.60 % (3484195)Termination reason: Instruction limit
% 0.21/1.60 % (3484195)Termination phase: Saturation
% 0.21/1.60 % (3484195)Time elapsed: 0.037 s
% 0.21/1.60 % (3484195)Peak memory usage: 88 MB
% 0.21/1.60 % (3484195)Instructions burned: 110 (million)
% 0.21/1.60 % (3484193)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3400161189:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 0.21/1.60 % (3484191)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=1646334247:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 0.21/1.60 % (3484198)dis-21_1_sil=8000:lcm=predicate:random_seed=2406386329: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)
% 0.21/1.60 % (3484194)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=4260442220:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 0.21/1.60 % (3484197)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2144298259:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 0.21/1.60 % (3484196)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=599718726:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 0.21/1.60 % (3484198)Instruction limit reached!
% 0.21/1.60 % (3484198)------------------------------
% 0.21/1.60 % (3484198)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.21/1.60 % (3484198)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/1.60 % (3484198)CaDiCaL version: 2.1.3
% 0.21/1.60 % (3484198)Termination reason: Instruction limit
% 0.21/1.60 % (3484198)Termination phase: Saturation
% 0.21/1.60 % (3484198)Time elapsed: 0.073 s
% 0.21/1.60 % (3484198)Peak memory usage: 88 MB
% 0.21/1.60 % (3484198)Instructions burned: 117 (million)
% 0.21/1.60 % (3484196)Instruction limit reached!
% 0.21/1.60 % (3484196)------------------------------
% 0.21/1.60 % (3484196)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.21/1.60 % (3484196)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/1.60 % (3484196)CaDiCaL version: 2.1.3
% 0.21/1.60 % (3484196)Termination reason: Instruction limit
% 0.21/1.60 % (3484196)Termination phase: Saturation
% 0.21/1.60 % (3484196)Time elapsed: 0.077 s
% 0.21/1.60 % (3484196)Peak memory usage: 88 MB
% 0.21/1.60 % (3484196)Instructions burned: 114 (million)
% 0.21/1.60 % (3484197)Instruction limit reached!
% 0.21/1.60 % (3484197)------------------------------
% 0.21/1.60 % (3484197)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.21/1.60 % (3484197)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/1.60 % (3484197)CaDiCaL version: 2.1.3
% 0.21/1.60 % (3484197)Termination reason: Instruction limit
% 0.21/1.60 % (3484197)Termination phase: Saturation
% 0.21/1.60 % (3484197)Time elapsed: 0.141 s
% 0.21/1.60 % (3484197)Peak memory usage: 88 MB
% 0.21/1.60 % (3484197)Instructions burned: 181 (million)
% 0.21/1.60 % (3484232)dis+1010_3_sil=8000:plsq=on:drc=off:fde=none:plsqc=1:bsd=on:plsqr=7,2:sos=on:spb=goal_then_units:random_seed=1359943056:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 0.21/1.60 % (3484232)Refutation not found, incomplete strategy
% 0.21/1.60 % (3484232)------------------------------
% 0.21/1.60 % (3484232)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.21/1.60 % (3484232)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/1.60 % (3484232)CaDiCaL version: 2.1.3
% 0.21/1.60 % (3484232)Termination reason: Refutation not found, incomplete strategy
% 0.21/1.60 % (3484232)Time elapsed: 0.001 s
% 0.21/1.60 % (3484232)Peak memory usage: 88 MB
% 0.21/1.60 % (3484232)Instructions burned: 1 (million)
% 0.21/1.60 % (3484261)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=1999914521:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2997 on theBenchmark for (2997ds/189Mi)
% 0.21/1.60 % (3484262)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=2091519320:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 0.21/1.60 % (3484262)Refutation not found, incomplete strategy
% 0.21/1.60 % (3484262)------------------------------
% 0.21/1.60 % (3484262)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.21/1.60 % (3484262)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/1.60 % (3484262)CaDiCaL version: 2.1.3
% 0.21/1.60 % (3484262)Termination reason: Refutation not found, incomplete strategy
% 0.21/1.60 % (3484262)Time elapsed: 0.001 s
% 0.21/1.60 % (3484262)Peak memory usage: 87 MB
% 0.21/1.60 % (3484261)First to succeed.
% 0.21/1.60 % (3484261)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3484104"
% 0.21/1.60 % (3484232)------------------------------
% 0.21/1.60 % (3484232)------------------------------
% 0.21/1.60 % (3484272)lrs+10_64_to=lpo:sil=8000:random_seed=3489264618:i=126:bd=preordered_2996 on theBenchmark for (2996ds/126Mi)
% 0.21/1.60 % (3484272)Instruction limit reached!
% 0.21/1.60 % (3484272)------------------------------
% 0.21/1.60 % (3484272)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.21/1.60 % (3484272)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/1.60 % (3484272)CaDiCaL version: 2.1.3
% 0.21/1.60 % (3484272)Termination reason: Instruction limit
% 0.21/1.60 % (3484272)Termination phase: Saturation
% 0.21/1.60 % (3484272)Time elapsed: 0.079 s
% 0.21/1.60 % (3484272)Peak memory usage: 88 MB
% 0.21/1.60 % (3484272)Instructions burned: 127 (million)
% 0.21/1.60 % (3484314)lrs+1011_16_to=lpo:sil=8000:drc=off:sp=reverse_frequency:spb=goal_then_units:random_seed=4209963371:avsq=on:i=194:fgj=on:bd=preordered_2995 on theBenchmark for (2995ds/194Mi)
% 0.21/1.60 % (3484314)Also succeeded, but the first one will report.
% 0.21/1.60 % (3484262)------------------------------
% 0.21/1.60 % (3484262)------------------------------
% 0.21/1.60 % (3484261)Refutation found. Thanks to Tanya!
% 0.21/1.60 % SZS status Unsatisfiable for theBenchmark
% 0.21/1.60 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/1.60 % (3484261)------------------------------
% 0.21/1.60 % (3484261)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.21/1.60 % (3484261)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/1.60 % (3484261)CaDiCaL version: 2.1.3
% 0.21/1.60 % (3484261)Termination reason: Refutation
% 0.21/1.60 % (3484261)Time elapsed: 0.042 s
% 0.21/1.60 % (3484261)Peak memory usage: 88 MB
% 0.21/1.60 % (3484261)Instructions burned: 74 (million)
% 0.21/1.60 % (3484261)------------------------------
% 0.21/1.60 % (3484261)------------------------------
% 0.21/1.60 % (3484104)Success in time 0.715 s
% 0.21/1.60 % Vampire exiting
%------------------------------------------------------------------------------