%------------------------------------------------------------------------------
% File : Vampire-SAT---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 SAT
% Computer : n020.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 09:36:53 AM UTC 2026
% Result : Unsatisfiable 0.27s 0.33s
% Output : Refutation 0.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 15
% Syntax : Number of formulae : 46 ( 13 unt; 2 def)
% Number of atoms : 91 ( 13 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 90 ( 45 ~; 43 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 3 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 47 ( 0 sgn 47 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( product(X0,X1,compose(X0,X1))
| ~ defined(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/CAT001-0.ax',closure_of_composition) ).
fof(f2,axiom,
! [X2,X0,X1] :
( ~ product(X0,X1,X2)
| defined(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/CAT001-0.ax',associative_property1) ).
fof(f3,axiom,
! [X2,X3,X0,X1] :
( ~ product(X0,X1,X2)
| ~ defined(X2,X3)
| defined(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/CAT001-0.ax',associative_property2) ).
fof(f6,axiom,
! [X2,X3,X0,X1] :
( ~ product(X0,X1,X2)
| ~ defined(X3,X2)
| defined(X3,X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/CAT001-0.ax',category_theory_axiom3) ).
fof(f10,axiom,
! [X0] : identity_map(domain(X0)),
file('/export/starexec/sandbox2/benchmark/Axioms/CAT001-0.ax',domain_is_an_identity_map) ).
fof(f11,axiom,
! [X0] : identity_map(codomain(X0)),
file('/export/starexec/sandbox2/benchmark/Axioms/CAT001-0.ax',codomain_is_an_identity_map) ).
fof(f14,axiom,
! [X0] : product(X0,domain(X0),X0),
file('/export/starexec/sandbox2/benchmark/Axioms/CAT001-0.ax',product_on_domain) ).
fof(f15,axiom,
! [X0] : product(codomain(X0),X0,X0),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/CAT001-0.ax',identity1) ).
fof(f17,axiom,
! [X0,X1] :
( product(X0,X1,X0)
| ~ identity_map(X1)
| ~ defined(X0,X1) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/CAT001-0.ax',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(f238,plain,
! [X2,X0,X1] :
( ~ defined(X0,X1)
| ~ product(X0,X1,X2)
| compose(X0,X1) = X2 ),
inference(resolution,[],[f1,f18]) ).
fof(f244,plain,
! [X2,X0,X1] :
( ~ product(X0,X1,X2)
| compose(X0,X1) = X2 ),
inference(forward_subsumption_resolution,[],[f238,f2]) ).
fof(f318,plain,
! [X0,X1] :
( ~ defined(X0,X1)
| ~ identity_map(X1)
| compose(X0,X1) = X0 ),
inference(resolution,[],[f244,f17]) ).
fof(f320,plain,
! [X0,X1] :
( ~ defined(X0,X1)
| ~ identity_map(X0)
| compose(X0,X1) = X1 ),
inference(resolution,[],[f244,f16]) ).
fof(f445,plain,
! [X0,X1] :
( defined(domain(X0),X1)
| ~ defined(X0,X1) ),
inference(resolution,[],[f3,f14]) ).
fof(f648,plain,
! [X0,X1] :
( defined(X0,codomain(X1))
| ~ defined(X0,X1) ),
inference(resolution,[],[f6,f15]) ).
fof(f665,plain,
! [X0,X1] :
( ~ identity_map(codomain(X0))
| compose(X1,codomain(X0)) = X1
| ~ defined(X1,X0) ),
inference(resolution,[],[f318,f648]) ).
fof(f674,plain,
! [X0,X1] :
( ~ defined(X1,X0)
| compose(X1,codomain(X0)) = X1 ),
inference(forward_subsumption_resolution,[],[f665,f11]) ).
fof(f1540,plain,
! [X0,X1] :
( ~ identity_map(domain(X0))
| compose(domain(X0),X1) = X1
| ~ defined(X0,X1) ),
inference(resolution,[],[f320,f445]) ).
fof(f1544,plain,
! [X0,X1] :
( ~ defined(X0,X1)
| compose(domain(X0),X1) = X1 ),
inference(forward_subsumption_resolution,[],[f1540,f10]) ).
fof(f1632,definition,
( spl0_48
<=> defined(domain(a),b) ),
introduced(definition,[new_symbols(definition,[spl0_48])],[avatar_definition]) ).
fof(f1633,plain,
( defined(domain(a),b)
| ~ spl0_48 ),
inference(avatar_component_clause,[],[f1632]) ).
fof(f1634,plain,
( ~ defined(domain(a),b)
| spl0_48 ),
inference(avatar_component_clause,[],[f1632]) ).
fof(f1640,plain,
( ~ defined(a,b)
| spl0_48 ),
inference(resolution,[],[f1634,f445]) ).
fof(f1641,plain,
( $false
| spl0_48 ),
inference(forward_subsumption_resolution,[],[f1640,f19]) ).
fof(f1642,plain,
spl0_48,
inference(avatar_contradiction_clause,[],[f1641]) ).
fof(f1645,plain,
( domain(a) = compose(domain(a),codomain(b))
| ~ spl0_48 ),
inference(resolution,[],[f1633,f674]) ).
fof(f1853,definition,
( spl0_54
<=> defined(a,codomain(b)) ),
introduced(definition,[new_symbols(definition,[spl0_54])],[avatar_definition]) ).
fof(f1854,plain,
( defined(a,codomain(b))
| ~ spl0_54 ),
inference(avatar_component_clause,[],[f1853]) ).
fof(f1855,plain,
( ~ defined(a,codomain(b))
| spl0_54 ),
inference(avatar_component_clause,[],[f1853]) ).
fof(f1861,plain,
( ~ defined(a,b)
| spl0_54 ),
inference(resolution,[],[f1855,f648]) ).
fof(f1862,plain,
( $false
| spl0_54 ),
inference(forward_subsumption_resolution,[],[f1861,f19]) ).
fof(f1863,plain,
spl0_54,
inference(avatar_contradiction_clause,[],[f1862]) ).
fof(f1864,plain,
( codomain(b) = compose(domain(a),codomain(b))
| ~ spl0_54 ),
inference(resolution,[],[f1854,f1544]) ).
fof(f1869,plain,
( domain(a) = codomain(b)
| ~ spl0_48
| ~ spl0_54 ),
inference(forward_demodulation,[],[f1864,f1645]) ).
fof(f1870,plain,
( $false
| ~ spl0_48
| ~ spl0_54 ),
inference(forward_subsumption_resolution,[],[f1869,f20]) ).
fof(f1871,plain,
( ~ spl0_48
| ~ spl0_54 ),
inference(avatar_contradiction_clause,[],[f1870]) ).
cnf(s872,plain,
spl0_48,
inference(sat_conversion,[],[f1642]) ).
cnf(s980,plain,
spl0_54,
inference(sat_conversion,[],[f1863]) ).
cnf(s984,plain,
( ~ spl0_48
| ~ spl0_54 ),
inference(sat_conversion,[],[f1871]) ).
cnf(s985,plain,
~ spl0_48,
inference(rat,[],[s984,s980]) ).
cnf(s987,plain,
$false,
inference(rat,[],[s872,s985]) ).
fof(f1872,plain,
$false,
inference(avatar_sat_refutation,[],[s987]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : CAT008-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.22 % Computer : n020.cluster.edu
% 0.10/0.22 % Model : x86_64 x86_64
% 0.10/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.22 % Memory : 8046.5625MB
% 0.10/0.22 % OS : Linux 6.8.0-71-generic
% 0.10/0.22 % CPULimit : 300
% 0.10/0.22 % WCLimit : 300
% 0.10/0.22 % DateTime : Mon Sep 28 21:14:05 UTC 2026
% 0.10/0.22 % CPUTime :
% 0.10/0.22 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.27 Running first-order model finding
% 0.10/0.27 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.27/0.33 % (567946)Will run a generic schedule for satisfiability detection.
% 0.27/0.33 % (567953)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3015317023:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.27/0.33 % (567955)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2115337032:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.27/0.33 % (567952)% WARNING: option uhcvi not known.
% 0.27/0.33 % (567951)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=26706465_2999 on theBenchmark for (2999ds/0Mi)
% 0.27/0.33 % (567952)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1226513882:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.27/0.33 % TRYING [1]
% 0.27/0.33 % TRYING [2]
% 0.27/0.33 % (567954)dis+10_1_sil=32000:sp=arity:random_seed=1756355349:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.27/0.33 % TRYING [3]
% 0.27/0.33 % (567956)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1834867407:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.27/0.33 % (567957)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3080760693:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.27/0.33 % TRYING [4]
% 0.27/0.33 % (567953) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-567946-567953"...
% 0.27/0.33 % (567953)...printing done.
% 0.27/0.33 % (567953)Refutation found. Thanks to Tanya!
% 0.27/0.33 % SZS status Unsatisfiable for theBenchmark
% 0.27/0.33 % SZS output start Proof for theBenchmark
% See solution above
% 0.27/0.33 % (567953)------------------------------
% 0.27/0.33 % (567953)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.27/0.33 % (567953)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.27/0.33 % (567953)CaDiCaL version: 2.1.3
% 0.27/0.33 % (567953)Termination reason: Refutation
% 0.27/0.33 % (567953)Time elapsed: 0.029 s
% 0.27/0.33 % (567953)Peak memory usage: 12 MB
% 0.27/0.33 % (567953)Instructions burned: 48 (million)
% 0.27/0.33 % (567946)Success in time 0.052 s
% 0.27/0.33 % Vampire exiting
%------------------------------------------------------------------------------