%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : CAT010-10 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 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 : Sun Sep 27 06:55:57 AM UTC 2026
% Result : Unsatisfiable 0.16s 0.51s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 9
% Syntax : Number of formulae : 40 ( 40 unt; 0 def)
% Number of atoms : 40 ( 39 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-4 aty)
% Number of variables : 39 ( 3 sgn 15 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ifeq_axiom_001,axiom,
! [VAR_0,VAR_1,VAR_2] : ifeq2(VAR_0,VAR_0,VAR_1,VAR_2) = VAR_1,
file('theBenchmark.p',ifeq_axiom_001) ).
cnf(c_2,plain,
ifeq2(A,A,B,C) = B,
inference(clausify,[status(thm)],[ifeq_axiom_001]) ).
fof(ifeq_axiom_002,axiom,
! [VAR_0,VAR_1,VAR_2] : ifeq(VAR_0,VAR_0,VAR_1,VAR_2) = VAR_1,
file('theBenchmark.p',ifeq_axiom_002) ).
cnf(c_3,plain,
ifeq(A,A,B,C) = B,
inference(clausify,[status(thm)],[ifeq_axiom_002]) ).
fof(domain_has_elements,axiom,
! [VAR_0] : ifeq(there_exists(domain(VAR_0)),true,there_exists(VAR_0),true) = true,
file('theBenchmark.p',domain_has_elements) ).
cnf(c_7,plain,
ifeq(there_exists(domain(A)),true,there_exists(A),true) = true,
inference(clausify,[status(thm)],[domain_has_elements]) ).
fof(composition_implies_domain,axiom,
! [VAR_0,VAR_1] : ifeq(there_exists(compose(VAR_0,VAR_1)),true,there_exists(domain(VAR_0)),true) = true,
file('theBenchmark.p',composition_implies_domain) ).
cnf(c_9,plain,
ifeq(there_exists(compose(A,B)),true,there_exists(domain(A)),true) = true,
inference(clausify,[status(thm)],[composition_implies_domain]) ).
fof(domain_codomain_composition1,axiom,
! [VAR_0,VAR_1] : ifeq2(there_exists(compose(VAR_0,VAR_1)),true,domain(VAR_0),codomain(VAR_1)) = codomain(VAR_1),
file('theBenchmark.p',domain_codomain_composition1) ).
cnf(c_10,plain,
ifeq2(there_exists(compose(A,B)),true,domain(A),codomain(B)) = codomain(B),
inference(clausify,[status(thm)],[domain_codomain_composition1]) ).
fof(associativity_of_compose,axiom,
! [VAR_0,VAR_1,VAR_2] : compose(VAR_0,compose(VAR_1,VAR_2)) = compose(compose(VAR_0,VAR_1),VAR_2),
file('theBenchmark.p',associativity_of_compose) ).
cnf(c_12,plain,
compose(A,compose(B,C)) = compose(compose(A,B),C),
inference(clausify,[status(thm)],[associativity_of_compose]) ).
cnf(c_13,plain,
compose(compose(A,B),C) = compose(A,compose(B,C)),
inference(copy,[status(thm)],[c_12]) ).
fof(compose_codomain,axiom,
! [VAR_0] : compose(codomain(VAR_0),VAR_0) = VAR_0,
file('theBenchmark.p',compose_codomain) ).
cnf(c_15,plain,
compose(codomain(A),A) = A,
inference(clausify,[status(thm)],[compose_codomain]) ).
fof(ab_exists,axiom,
there_exists(compose(a,b)) = true,
file('theBenchmark.p',ab_exists) ).
cnf(c_16,plain,
there_exists(compose(a,b)) = true,
inference(clausify,[status(thm)],[ab_exists]) ).
fof(prove_codomain_of_ab_equals_codomain_of_a,axiom,
codomain(compose(a,b)) != codomain(a),
file('theBenchmark.p',prove_codomain_of_ab_equals_codomain_of_a) ).
cnf(c_17,plain,
codomain(compose(a,b)) != codomain(a),
inference(clausify,[status(thm)],[prove_codomain_of_ab_equals_codomain_of_a]) ).
cnf(c_19,plain,
ifeq2(there_exists(compose(A,compose(B,C))),true,domain(compose(A,B)),codomain(C)) = codomain(C),
inference(paramod,[status(thm)],[c_13,c_10]) ).
cnf(c_26,plain,
ifeq2(there_exists(A),true,domain(codomain(A)),codomain(A)) = codomain(A),
inference(paramod,[status(thm)],[c_15,c_10]) ).
cnf(c_189,plain,
ifeq(true,true,there_exists(domain(a)),true) = true,
inference(paramod,[status(thm)],[c_16,c_9]) ).
cnf(c_33,plain,
there_exists(domain(a)) = true,
inference(paramod,[status(thm)],[c_3,c_189]) ).
cnf(c_190,plain,
ifeq2(true,true,domain(a),codomain(b)) = codomain(b),
inference(paramod,[status(thm)],[c_16,c_10]) ).
cnf(c_191,plain,
domain(a) = codomain(b),
inference(paramod,[status(thm)],[c_2,c_190]) ).
cnf(c_34,plain,
codomain(b) = domain(a),
inference(copy,[status(thm)],[c_191]) ).
cnf(c_38,plain,
ifeq2(there_exists(compose(A,B)),true,domain(compose(codomain(compose(A,B)),A)),codomain(B)) = codomain(B),
inference(paramod,[status(thm)],[c_15,c_19]) ).
cnf(c_192,plain,
ifeq2(true,true,domain(codomain(compose(a,b))),codomain(compose(a,b))) = codomain(compose(a,b)),
inference(paramod,[status(thm)],[c_16,c_26]) ).
cnf(c_112,plain,
domain(codomain(compose(a,b))) = codomain(compose(a,b)),
inference(paramod,[status(thm)],[c_2,c_192]) ).
cnf(c_193,plain,
ifeq2(true,true,domain(compose(codomain(compose(a,b)),a)),codomain(b)) = codomain(b),
inference(paramod,[status(thm)],[c_16,c_38]) ).
cnf(c_194,plain,
ifeq2(true,true,domain(compose(codomain(compose(a,b)),a)),domain(a)) = codomain(b),
inference(paramod,[status(thm)],[c_34,c_193]) ).
cnf(c_195,plain,
domain(compose(codomain(compose(a,b)),a)) = codomain(b),
inference(paramod,[status(thm)],[c_2,c_194]) ).
cnf(c_156,plain,
domain(compose(codomain(compose(a,b)),a)) = domain(a),
inference(paramod,[status(thm)],[c_34,c_195]) ).
cnf(c_196,plain,
ifeq(there_exists(domain(a)),true,there_exists(compose(codomain(compose(a,b)),a)),true) = true,
inference(paramod,[status(thm)],[c_156,c_7]) ).
cnf(c_197,plain,
ifeq(true,true,there_exists(compose(codomain(compose(a,b)),a)),true) = true,
inference(paramod,[status(thm)],[c_33,c_196]) ).
cnf(c_183,plain,
there_exists(compose(codomain(compose(a,b)),a)) = true,
inference(paramod,[status(thm)],[c_3,c_197]) ).
cnf(c_198,plain,
ifeq2(true,true,domain(codomain(compose(a,b))),codomain(a)) = codomain(a),
inference(paramod,[status(thm)],[c_183,c_10]) ).
cnf(c_199,plain,
ifeq2(true,true,codomain(compose(a,b)),codomain(a)) = codomain(a),
inference(paramod,[status(thm)],[c_112,c_198]) ).
cnf(c_187,plain,
codomain(compose(a,b)) = codomain(a),
inference(paramod,[status(thm)],[c_2,c_199]) ).
cnf(c_188,plain,
$false,
inference(resolve,[status(thm)],[c_187,c_17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : CAT010-10 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.42 % Computer : n020.cluster.edu
% 0.16/0.42 % Model : x86_64 x86_64
% 0.16/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.42 % Memory : 8046.5625MB
% 0.16/0.42 % OS : Linux 6.8.0-71-generic
% 0.16/0.42 % CPULimit : 300
% 0.16/0.42 % WCLimit : 300
% 0.16/0.42 % DateTime : Sat Sep 26 22:49:48 UTC 2026
% 0.16/0.42 % CPUTime :
% 0.16/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/0.43 % Process 2720197 was started by sandbox2 on n020,
% 0.16/0.43 % Sat Sep 26 22:49:48 2026
% 0.16/0.43 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.16/0.43
% 0.16/0.43 % From the command line: assign(max_seconds, 300).
% 0.16/0.51
% 0.16/0.51 % SZS status Unsatisfiable for theBenchmark
% 0.16/0.51
% 0.16/0.51 % Proof 1 at 0.05 (+ 0.02) seconds.
% 0.16/0.51 % Length of proof is 20.
% 0.16/0.51 % Level of proof is 7.
% 0.16/0.51 % Maximum clause weight is 30.000.
% 0.16/0.51 % Given clauses 77.
% 0.16/0.51
% 0.16/0.51 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------