%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : CAT006-1 : 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 : n002.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 3.67s 1.26s
% Output : Refutation 3.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 10
% Syntax : Number of formulae : 21 ( 8 unt; 0 def)
% Number of atoms : 47 ( 10 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 57 ( 31 ~; 26 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-1 aty)
% Number of variables : 32 ( 32 !; 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(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(h,a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ha_defined) ).
fof(f20,axiom,
identity_map(h),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',h_is_the_identity_map) ).
fof(f21,negated_conjecture,
codomain(a) != h,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_codomain_of_a_is_h) ).
fof(f22,plain,
h != codomain(a),
inference(reorient_equations,[],[f21]) ).
fof(f29,plain,
! [X0,X1] :
( defined(X0,codomain(X1))
| ~ defined(X0,X1) ),
inference(resolution,[],[f6,f15]) ).
fof(f34,plain,
! [X2,X0,X1] :
( ~ product(X0,X1,X2)
| X0 = X2
| ~ identity_map(X1)
| ~ defined(X0,X1) ),
inference(resolution,[],[f18,f17]) ).
fof(f36,plain,
! [X2,X0,X1] :
( ~ product(X0,X1,X2)
| X0 = X2
| ~ identity_map(X1) ),
inference(forward_subsumption_resolution,[],[f34,f2]) ).
fof(f86,plain,
! [X0,X1] :
( ~ defined(X0,X1)
| ~ identity_map(X1)
| ~ identity_map(X0)
| X0 = X1 ),
inference(resolution,[],[f36,f16]) ).
fof(f119,plain,
! [X0,X1] :
( ~ identity_map(codomain(X0))
| ~ identity_map(X1)
| codomain(X0) = X1
| ~ defined(X1,X0) ),
inference(resolution,[],[f86,f29]) ).
fof(f123,plain,
! [X0,X1] :
( codomain(X0) = X1
| ~ identity_map(X1)
| ~ defined(X1,X0) ),
inference(forward_subsumption_resolution,[],[f119,f11]) ).
fof(f128,plain,
! [X0] :
( ~ defined(X0,a)
| ~ identity_map(X0)
| h != X0 ),
inference(superposition,[],[f22,f123]) ).
fof(f146,plain,
( ~ identity_map(h)
| h != h ),
inference(resolution,[],[f128,f19]) ).
fof(f154,plain,
~ identity_map(h),
inference(trivial_inequality_removal,[],[f146]) ).
fof(f155,plain,
$false,
inference(forward_subsumption_resolution,[],[f154,f20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : CAT006-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.09 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.25 % Computer : n002.cluster.edu
% 0.11/0.25 % Model : x86_64 x86_64
% 0.11/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.25 % Memory : 8046.5625MB
% 0.11/0.25 % OS : Linux 6.8.0-71-generic
% 0.11/0.25 % CPULimit : 300
% 0.11/0.25 % WCLimit : 300
% 0.11/0.25 % DateTime : Mon Sep 28 21:15:37 UTC 2026
% 0.11/0.25 % CPUTime :
% 0.11/0.25 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.25/0.29 Running first-order theorem proving
% 0.25/0.29 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
% 3.67/1.26 % (771676)Input is clausal, will run a generic CNF schedule.
% 3.67/1.26 % (771808)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2569419334:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.67/1.26 % (771813)dis-21_1_sil=8000:lcm=predicate:random_seed=73508951: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)
% 3.67/1.26 % (771809)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2231986656:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.67/1.26 % (771807)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=3796148631:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.67/1.26 % (771811)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1951907495:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.67/1.26 % (771810)lrs+10_1_sil=8000:sp=occurrence:random_seed=619444783:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.67/1.26 % (771812)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1809853684:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.67/1.26 % (771811)First to succeed.
% 3.67/1.26 % (771811)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-771676"
% 3.67/1.26 % (771810)Also succeeded, but the first one will report.
% 3.67/1.26 % (771813)Instruction limit reached!
% 3.67/1.26 % (771813)------------------------------
% 3.67/1.26 % (771813)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.67/1.26 % (771813)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.67/1.26 % (771813)CaDiCaL version: 2.1.3
% 3.67/1.26 % (771813)Termination reason: Instruction limit
% 3.67/1.26 % (771813)Termination phase: Saturation
% 3.67/1.26 % (771813)Time elapsed: 0.065 s
% 3.67/1.26 % (771813)Peak memory usage: 88 MB
% 3.67/1.26 % (771813)Instructions burned: 117 (million)
% 3.67/1.26 % (771812)Also succeeded, but the first one will report.
% 3.67/1.26 % (771821)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=25606732:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 3.67/1.26 % (771811)Refutation found. Thanks to Tanya!
% 3.67/1.26 % SZS status Unsatisfiable for theBenchmark
% 3.67/1.26 % SZS output start Proof for theBenchmark
% See solution above
% 3.67/1.26 % (771811)------------------------------
% 3.67/1.26 % (771811)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.67/1.26 % (771811)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.67/1.26 % (771811)CaDiCaL version: 2.1.3
% 3.67/1.26 % (771811)Termination reason: Refutation
% 3.67/1.26 % (771811)Time elapsed: 0.005 s
% 3.67/1.26 % (771811)Peak memory usage: 88 MB
% 3.67/1.26 % (771811)Instructions burned: 6 (million)
% 3.67/1.26 % (771811)------------------------------
% 3.67/1.26 % (771811)------------------------------
% 3.67/1.26 % (771676)Success in time 0.438 s
% 3.67/1.26 % Vampire exiting
%------------------------------------------------------------------------------