%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : CAT009-1 : 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 : 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 09:36:54 AM UTC 2026
% Result : Unsatisfiable 0.25s 0.36s
% Output : Refutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 14
% Syntax : Number of formulae : 40 ( 11 unt; 0 def)
% Number of atoms : 98 ( 15 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 100 ( 42 ~; 58 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 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 : 74 ( 74 !; 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] :
( ~ defined(X3,X2)
| ~ product(X0,X1,X2)
| defined(X3,X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/CAT001-0.ax',category_theory_axiom3) ).
fof(f7,axiom,
! [X2,X3,X0,X1,X4] :
( ~ defined(X3,X2)
| ~ product(X3,X0,X4)
| ~ product(X0,X1,X2)
| defined(X4,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/CAT001-0.ax',category_theory_axiom4) ).
fof(f9,axiom,
! [X2,X0,X1] :
( ~ defined(X0,X1)
| ~ defined(X1,X2)
| ~ identity_map(X1)
| defined(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/CAT001-0.ax',category_theory_axiom6) ).
fof(f10,axiom,
! [X0] : identity_map(domain(X0)),
file('/export/starexec/sandbox2/benchmark/Axioms/CAT001-0.ax',domain_is_an_identity_map) ).
fof(f12,axiom,
! [X0] : defined(X0,domain(X0)),
file('/export/starexec/sandbox2/benchmark/Axioms/CAT001-0.ax',mapping_from_x_to_its_domain) ).
fof(f14,axiom,
! [X0] : product(X0,domain(X0),X0),
file('/export/starexec/sandbox2/benchmark/Axioms/CAT001-0.ax',product_on_domain) ).
fof(f16,axiom,
! [X0,X1] :
( ~ defined(X0,X1)
| ~ identity_map(X0)
| product(X0,X1,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/CAT001-0.ax',identity1) ).
fof(f17,axiom,
! [X0,X1] :
( ~ defined(X0,X1)
| ~ identity_map(X1)
| product(X0,X1,X0) ),
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(b,a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ba_defined) ).
fof(f20,negated_conjecture,
domain(compose(b,a)) != domain(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_domain_of_ba_equals_domain_of_a) ).
fof(f21,plain,
! [X2,X0,X1] :
( ~ defined(X1,X2)
| ~ defined(X0,X1)
| identity_map(X1)
| defined(X0,X2) ),
inference(consistent_polarity_flipping,[],[f9]) ).
fof(f22,plain,
! [X0] : ~ identity_map(domain(X0)),
inference(consistent_polarity_flipping,[],[f10]) ).
fof(f24,plain,
! [X0,X1] :
( product(X0,X1,X1)
| identity_map(X0)
| ~ defined(X0,X1) ),
inference(consistent_polarity_flipping,[],[f16]) ).
fof(f25,plain,
! [X0,X1] :
( product(X0,X1,X0)
| identity_map(X1)
| ~ defined(X0,X1) ),
inference(consistent_polarity_flipping,[],[f17]) ).
fof(f31,plain,
! [X0,X1] :
( ~ defined(X0,X1)
| defined(domain(X0),X1) ),
inference(resolution,[],[f3,f14]) ).
fof(f36,plain,
! [X0,X1] :
( ~ product(X0,X1,a)
| defined(b,X0) ),
inference(resolution,[],[f6,f19]) ).
fof(f39,plain,
! [X0,X1] :
( ~ product(X0,domain(X0),X1)
| X0 = X1 ),
inference(resolution,[],[f18,f14]) ).
fof(f43,plain,
! [X2,X0,X1] :
( ~ product(X0,X1,X2)
| X1 = X2
| identity_map(X0)
| ~ defined(X0,X1) ),
inference(resolution,[],[f18,f24]) ).
fof(f44,plain,
! [X2,X0,X1] :
( ~ product(X0,X1,X2)
| X1 = X2
| identity_map(X0) ),
inference(forward_subsumption_resolution,[],[f43,f2]) ).
fof(f48,plain,
! [X0,X1] :
( defined(X0,domain(X1))
| identity_map(X1)
| ~ defined(X0,X1) ),
inference(resolution,[],[f21,f12]) ).
fof(f67,plain,
! [X2,X0,X1] :
( ~ product(b,X0,X1)
| ~ product(X0,X2,a)
| defined(X1,X2) ),
inference(resolution,[],[f7,f19]) ).
fof(f112,plain,
! [X0] :
( domain(X0) = X0
| identity_map(X0)
| ~ defined(X0,domain(X0)) ),
inference(resolution,[],[f39,f24]) ).
fof(f113,plain,
! [X0] :
( identity_map(X0)
| domain(X0) = X0 ),
inference(forward_subsumption_resolution,[],[f112,f12]) ).
fof(f133,plain,
! [X0,X1] :
( ~ defined(X1,X0)
| identity_map(X1)
| identity_map(X0)
| X0 = X1 ),
inference(resolution,[],[f44,f25]) ).
fof(f157,plain,
! [X0,X1] :
( defined(domain(X1),domain(X0))
| ~ defined(X1,X0)
| identity_map(X0) ),
inference(resolution,[],[f48,f31]) ).
fof(f168,plain,
! [X0,X1] :
( ~ product(X0,X1,a)
| defined(compose(b,X0),X1)
| ~ defined(b,X0) ),
inference(resolution,[],[f67,f1]) ).
fof(f170,plain,
! [X0,X1] :
( ~ product(X0,X1,a)
| defined(compose(b,X0),X1) ),
inference(forward_subsumption_resolution,[],[f168,f36]) ).
fof(f302,plain,
! [X0] : domain(X0) = domain(domain(X0)),
inference(resolution,[],[f113,f22]) ).
fof(f371,plain,
defined(compose(b,a),domain(a)),
inference(resolution,[],[f170,f14]) ).
fof(f632,plain,
! [X0,X1] :
( ~ defined(X0,X1)
| identity_map(X1)
| identity_map(domain(X0))
| identity_map(domain(X1))
| domain(X0) = domain(X1) ),
inference(resolution,[],[f157,f133]) ).
fof(f637,plain,
! [X0,X1] :
( ~ defined(X0,X1)
| identity_map(X1)
| identity_map(domain(X0))
| domain(X0) = domain(X1) ),
inference(forward_subsumption_resolution,[],[f632,f22]) ).
fof(f641,plain,
! [X0,X1] :
( ~ defined(X0,X1)
| identity_map(X1)
| domain(X0) = domain(X1) ),
inference(forward_subsumption_resolution,[],[f637,f22]) ).
fof(f3756,plain,
( identity_map(domain(a))
| domain(compose(b,a)) = domain(domain(a)) ),
inference(resolution,[],[f641,f371]) ).
fof(f3825,plain,
domain(compose(b,a)) = domain(domain(a)),
inference(forward_subsumption_resolution,[],[f3756,f22]) ).
fof(f3850,plain,
domain(compose(b,a)) = domain(a),
inference(forward_demodulation,[],[f3825,f302]) ).
fof(f3871,plain,
$false,
inference(forward_subsumption_resolution,[],[f3850,f20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : CAT009-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.22 % Computer : n009.cluster.edu
% 0.08/0.22 % Model : x86_64 x86_64
% 0.08/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.22 % Memory : 8046.5625MB
% 0.08/0.22 % OS : Linux 6.8.0-71-generic
% 0.08/0.22 % CPULimit : 300
% 0.08/0.22 % WCLimit : 300
% 0.08/0.22 % DateTime : Mon Sep 28 21:13:15 UTC 2026
% 0.08/0.22 % CPUTime :
% 0.08/0.22 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.27 Running first-order model finding
% 0.08/0.27 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
% 0.25/0.36 % (3484249)Will run a generic schedule for satisfiability detection.
% 0.25/0.36 % (3484255)% WARNING: option uhcvi not known.
% 0.25/0.36 % (3484255)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3335523852:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.25/0.36 % (3484254)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3061305367_2999 on theBenchmark for (2999ds/0Mi)
% 0.25/0.36 % TRYING [1]
% 0.25/0.36 % TRYING [2]
% 0.25/0.36 % TRYING [3]
% 0.25/0.36 % TRYING [4]
% 0.25/0.36 % (3484256)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1270780988:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.25/0.36 % (3484258)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1716829405:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.25/0.36 % (3484257)dis+10_1_sil=32000:sp=arity:random_seed=2955072803:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.25/0.36 % (3484259)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2603988959:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.25/0.36 % (3484260)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2895579662:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.25/0.36 % TRYING [5]
% 0.25/0.36 % (3484255) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3484249-3484255"...
% 0.25/0.36 % (3484255)...printing done.
% 0.25/0.36 % (3484255)Refutation found. Thanks to Tanya!
% 0.25/0.36 % SZS status Unsatisfiable for theBenchmark
% 0.25/0.36 % SZS output start Proof for theBenchmark
% See solution above
% 0.25/0.36 % (3484255)------------------------------
% 0.25/0.36 % (3484255)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.25/0.36 % (3484255)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.25/0.36 % (3484255)CaDiCaL version: 2.1.3
% 0.25/0.36 % (3484255)Termination reason: Refutation
% 0.25/0.36 % (3484255)Time elapsed: 0.051 s
% 0.25/0.36 % (3484255)Peak memory usage: 12 MB
% 0.25/0.36 % (3484255)Instructions burned: 110 (million)
% 0.25/0.36 % (3484249)Success in time 0.072 s
% 0.25/0.36 % Vampire exiting
%------------------------------------------------------------------------------