%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : CAT010-1 : 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 : n004.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 5.07s 1.44s
% Output : Refutation 5.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 11
% Syntax : Number of formulae : 19 ( 12 unt; 0 def)
% Number of atoms : 34 ( 2 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 33 ( 18 ~; 15 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 27 ( 27 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( product(X0,X1,compose(X0,X1))
| ~ defined(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',closure_of_composition) ).
fof(f4,axiom,
! [X2,X3,X0,X1,X4] :
( ~ product(X1,X3,X4)
| ~ product(X0,X1,X2)
| ~ defined(X2,X3)
| defined(X0,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',category_theory_axiom1) ).
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/sandbox2/benchmark/theBenchmark.p',category_theory_axiom2) ).
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(f11,axiom,
! [X0] : identity_map(codomain(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',codomain_is_an_identity_map) ).
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(b,a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ba_defined) ).
fof(f20,negated_conjecture,
codomain(compose(b,a)) != codomain(b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_codomain_of_ba_equals_codomain_of_b) ).
fof(f21,plain,
~ product(codomain(codomain(b)),codomain(b),codomain(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(f51,plain,
defined(codomain(b),compose(b,a)),
inference(unit_resulting_resolution,[],[f4,f15,f19,f29]) ).
fof(f105,plain,
defined(codomain(b),codomain(compose(b,a))),
inference(unit_resulting_resolution,[],[f6,f15,f51]) ).
fof(f307,plain,
product(codomain(b),codomain(compose(b,a)),codomain(compose(b,a))),
inference(unit_resulting_resolution,[],[f16,f11,f105]) ).
fof(f308,plain,
product(codomain(b),codomain(compose(b,a)),codomain(b)),
inference(unit_resulting_resolution,[],[f17,f11,f105]) ).
fof(f1490,plain,
~ product(codomain(b),codomain(compose(b,a)),codomain(compose(b,a))),
inference(unit_resulting_resolution,[],[f5,f15,f21,f308]) ).
fof(f1524,plain,
$false,
inference(forward_subsumption_resolution,[],[f1490,f307]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : CAT010-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 % Computer : n004.cluster.edu
% 0.09/0.22 % Model : x86_64 x86_64
% 0.09/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.22 % Memory : 8046.5625MB
% 0.09/0.22 % OS : Linux 6.8.0-71-generic
% 0.09/0.22 % CPULimit : 300
% 0.09/0.22 % WCLimit : 300
% 0.09/0.22 % DateTime : Mon Sep 28 21:13:07 UTC 2026
% 0.09/0.23 % CPUTime :
% 0.09/0.23 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.27 Running first-order theorem proving
% 0.09/0.27 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
% 5.07/1.44 % (782227)Input is clausal, will run a generic CNF schedule.
% 5.07/1.44 % (782278)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=2307455265:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 5.07/1.44 % (782282)lrs+10_1_sil=8000:sp=occurrence:random_seed=4153343910:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 5.07/1.44 % (782287)dis-21_1_sil=8000:lcm=predicate:random_seed=2054538955: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)
% 5.07/1.44 % (782285)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=155014238:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 5.07/1.44 % (782279)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=349879733:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 5.07/1.44 % (782281)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=919868429:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 5.07/1.44 % (782284)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1714374136:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 5.07/1.44 % (782287)Instruction limit reached!
% 5.07/1.44 % (782287)------------------------------
% 5.07/1.44 % (782287)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.07/1.44 % (782287)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.07/1.44 % (782287)CaDiCaL version: 2.1.3
% 5.07/1.44 % (782287)Termination reason: Instruction limit
% 5.07/1.44 % (782287)Termination phase: Saturation
% 5.07/1.44 % (782287)Time elapsed: 0.065 s
% 5.07/1.44 % (782287)Peak memory usage: 88 MB
% 5.07/1.44 % (782287)Instructions burned: 118 (million)
% 5.07/1.44 % (782282)Instruction limit reached!
% 5.07/1.44 % (782282)------------------------------
% 5.07/1.44 % (782282)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.07/1.44 % (782282)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.07/1.44 % (782282)CaDiCaL version: 2.1.3
% 5.07/1.44 % (782282)Termination reason: Instruction limit
% 5.07/1.44 % (782282)Termination phase: Saturation
% 5.07/1.44 % (782282)Time elapsed: 0.067 s
% 5.07/1.44 % (782282)Peak memory usage: 88 MB
% 5.07/1.44 % (782282)Instructions burned: 107 (million)
% 5.07/1.44 % (782284)Instruction limit reached!
% 5.07/1.44 % (782284)------------------------------
% 5.07/1.44 % (782284)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.07/1.44 % (782284)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.07/1.44 % (782284)CaDiCaL version: 2.1.3
% 5.07/1.44 % (782284)Termination reason: Instruction limit
% 5.07/1.44 % (782284)Termination phase: Saturation
% 5.07/1.44 % (782284)Time elapsed: 0.074 s
% 5.07/1.44 % (782284)Peak memory usage: 88 MB
% 5.07/1.44 % (782284)Instructions burned: 115 (million)
% 5.07/1.44 % (782285)Instruction limit reached!
% 5.07/1.44 % (782285)------------------------------
% 5.07/1.44 % (782285)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.07/1.44 % (782285)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.07/1.44 % (782285)CaDiCaL version: 2.1.3
% 5.07/1.44 % (782285)Termination reason: Instruction limit
% 5.07/1.44 % (782285)Termination phase: Saturation
% 5.07/1.44 % (782285)Time elapsed: 0.114 s
% 5.07/1.44 % (782285)Peak memory usage: 88 MB
% 5.07/1.44 % (782285)Instructions burned: 181 (million)
% 5.07/1.44 % (782353)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=3296847346:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 5.07/1.44 % (782353)Refutation not found, incomplete strategy
% 5.07/1.44 % (782353)------------------------------
% 5.07/1.44 % (782353)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.07/1.44 % (782353)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.07/1.44 % (782353)CaDiCaL version: 2.1.3
% 5.07/1.44 % (782353)Termination reason: Refutation not found, incomplete strategy
% 5.07/1.44 % (782353)Time elapsed: 0.001 s
% 5.07/1.44 % (782353)Peak memory usage: 88 MB
% 5.07/1.44 % (782354)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=73804820:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2998 on theBenchmark for (2998ds/189Mi)
% 5.07/1.44 % (782355)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=3283646546:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 5.07/1.44 % (782355)Refutation not found, incomplete strategy
% 5.07/1.44 % (782355)------------------------------
% 5.07/1.44 % (782355)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.07/1.44 % (782355)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.07/1.44 % (782355)CaDiCaL version: 2.1.3
% 5.07/1.44 % (782355)Termination reason: Refutation not found, incomplete strategy
% 5.07/1.44 % (782355)Time elapsed: 0.001 s
% 5.07/1.44 % (782355)Peak memory usage: 87 MB
% 5.07/1.44 % (782354)First to succeed.
% 5.07/1.44 % (782354)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-782227"
% 5.07/1.44 % (782356)lrs+10_64_to=lpo:sil=8000:random_seed=2811282745:i=126:bd=preordered_2997 on theBenchmark for (2997ds/126Mi)
% 5.07/1.44 % (782278)Also succeeded, but the first one will report.
% 5.07/1.44 % (782356)Instruction limit reached!
% 5.07/1.44 % (782356)------------------------------
% 5.07/1.44 % (782356)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.07/1.44 % (782356)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.07/1.44 % (782356)CaDiCaL version: 2.1.3
% 5.07/1.44 % (782356)Termination reason: Instruction limit
% 5.07/1.44 % (782356)Termination phase: Saturation
% 5.07/1.44 % (782356)Time elapsed: 0.077 s
% 5.07/1.44 % (782356)Peak memory usage: 88 MB
% 5.07/1.44 % (782356)Instructions burned: 126 (million)
% 5.07/1.44 % (782353)------------------------------
% 5.07/1.44 % (782353)------------------------------
% 5.07/1.44 % (782355)------------------------------
% 5.07/1.44 % (782355)------------------------------
% 5.07/1.44 % (782408)lrs+1011_16_to=lpo:sil=8000:drc=off:sp=reverse_frequency:spb=goal_then_units:random_seed=535869433:avsq=on:i=194:fgj=on:bd=preordered_2995 on theBenchmark for (2995ds/194Mi)
% 5.07/1.44 % (782354)Refutation found. Thanks to Tanya!
% 5.07/1.44 % SZS status Unsatisfiable for theBenchmark
% 5.07/1.44 % SZS output start Proof for theBenchmark
% See solution above
% 5.07/1.44 % (782354)------------------------------
% 5.07/1.44 % (782354)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.07/1.44 % (782354)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.07/1.44 % (782354)CaDiCaL version: 2.1.3
% 5.07/1.44 % (782354)Termination reason: Refutation
% 5.07/1.44 % (782354)Time elapsed: 0.042 s
% 5.07/1.44 % (782354)Peak memory usage: 88 MB
% 5.07/1.44 % (782354)Instructions burned: 74 (million)
% 5.07/1.44 % (782354)------------------------------
% 5.07/1.44 % (782354)------------------------------
% 5.07/1.44 % (782227)Success in time 0.621 s
% 5.07/1.44 % Vampire exiting
%------------------------------------------------------------------------------