%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : CAT018-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n003.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 06:56:00 AM UTC 2026
% Result : Unsatisfiable 7.28s 1.36s
% Output : CNFRefutation 7.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 12
% Syntax : Number of formulae : 46 ( 24 unt; 0 def)
% Number of atoms : 74 ( 27 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 60 ( 32 ~; 28 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 52 ( 3 sgn 17 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(existence_and_equality_implies_equivalence1,axiom,
! [VAR_0,VAR_1] :
( equivalent(VAR_0,VAR_1)
| VAR_0 != VAR_1
| ~ there_exists(VAR_0) ),
file('theBenchmark.p',existence_and_equality_implies_equivalence1) ).
cnf(c_1,plain,
( equivalent(A,B)
| A != B
| ~ there_exists(A) ),
inference(clausify,[status(thm)],[existence_and_equality_implies_equivalence1]) ).
fof(equivalence_implies_existence3,axiom,
! [VAR_0,VAR_1] :
( there_exists(VAR_1)
| ~ equivalent(VAR_0,VAR_1) ),
file('theBenchmark.p',equivalence_implies_existence3) ).
cnf(c_4,plain,
( there_exists(B)
| ~ equivalent(A,B) ),
inference(clausify,[status(thm)],[equivalence_implies_existence3]) ).
cnf(c_6,plain,
( B != A
| ~ there_exists(B)
| there_exists(A) ),
inference(resolve,[status(thm)],[c_4,c_1]) ).
fof(prove_a_bc_exists,axiom,
~ there_exists(compose(a,compose(b,c))),
file('theBenchmark.p',prove_a_bc_exists) ).
cnf(c_7,plain,
~ there_exists(compose(a,compose(b,c))),
inference(clausify,[status(thm)],[prove_a_bc_exists]) ).
fof(assume_bc_exists,axiom,
there_exists(compose(b,c)),
file('theBenchmark.p',assume_bc_exists) ).
cnf(c_8,plain,
there_exists(compose(b,c)),
inference(clausify,[status(thm)],[assume_bc_exists]) ).
fof(assume_ab_exists,axiom,
there_exists(compose(a,b)),
file('theBenchmark.p',assume_ab_exists) ).
cnf(c_9,plain,
there_exists(compose(a,b)),
inference(clausify,[status(thm)],[assume_ab_exists]) ).
fof(composition_implies_codomain,axiom,
! [VAR_0,VAR_1] :
( there_exists(codomain(VAR_0))
| ~ there_exists(compose(VAR_0,VAR_1)) ),
file('theBenchmark.p',composition_implies_codomain) ).
cnf(c_15,plain,
( there_exists(codomain(A))
| ~ there_exists(compose(A,B)) ),
inference(clausify,[status(thm)],[composition_implies_codomain]) ).
fof(compose_codomain,axiom,
! [VAR_0] : compose(codomain(VAR_0),VAR_0) = VAR_0,
file('theBenchmark.p',compose_codomain) ).
cnf(c_16,plain,
compose(codomain(A),A) = A,
inference(clausify,[status(thm)],[compose_codomain]) ).
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_18,plain,
compose(A,compose(B,C)) = compose(compose(A,B),C),
inference(clausify,[status(thm)],[associativity_of_compose]) ).
cnf(c_19,plain,
compose(compose(A,B),C) = compose(A,compose(B,C)),
inference(copy,[status(thm)],[c_18]) ).
fof(domain_codomain_composition2,axiom,
! [VAR_0,VAR_1] :
( there_exists(compose(VAR_0,VAR_1))
| domain(VAR_0) != codomain(VAR_1)
| ~ there_exists(domain(VAR_0)) ),
file('theBenchmark.p',domain_codomain_composition2) ).
cnf(c_20,plain,
( there_exists(compose(A,B))
| domain(A) != codomain(B)
| ~ there_exists(domain(A)) ),
inference(clausify,[status(thm)],[domain_codomain_composition2]) ).
cnf(c_21,plain,
( there_exists(compose(A,B))
| codomain(B) != domain(A)
| ~ there_exists(domain(A)) ),
inference(copy,[status(thm)],[c_20]) ).
fof(domain_codomain_composition1,axiom,
! [VAR_0,VAR_1] :
( domain(VAR_0) = codomain(VAR_1)
| ~ there_exists(compose(VAR_0,VAR_1)) ),
file('theBenchmark.p',domain_codomain_composition1) ).
cnf(c_22,plain,
( domain(A) = codomain(B)
| ~ there_exists(compose(A,B)) ),
inference(clausify,[status(thm)],[domain_codomain_composition1]) ).
cnf(c_23,plain,
( codomain(B) = domain(A)
| ~ there_exists(compose(A,B)) ),
inference(copy,[status(thm)],[c_22]) ).
fof(composition_implies_domain,axiom,
! [VAR_0,VAR_1] :
( there_exists(domain(VAR_0))
| ~ there_exists(compose(VAR_0,VAR_1)) ),
file('theBenchmark.p',composition_implies_domain) ).
cnf(c_24,plain,
( there_exists(domain(A))
| ~ there_exists(compose(A,B)) ),
inference(clausify,[status(thm)],[composition_implies_domain]) ).
fof(codomain_has_elements,axiom,
! [VAR_0] :
( there_exists(VAR_0)
| ~ there_exists(codomain(VAR_0)) ),
file('theBenchmark.p',codomain_has_elements) ).
cnf(c_25,plain,
( there_exists(A)
| ~ there_exists(codomain(A)) ),
inference(clausify,[status(thm)],[codomain_has_elements]) ).
cnf(c_27,plain,
( compose(b,c) != A
| there_exists(A) ),
inference(resolve,[status(thm)],[c_8,c_6]) ).
cnf(c_36,plain,
there_exists(codomain(b)),
inference(resolve,[status(thm)],[c_15,c_8]) ).
cnf(c_5232,plain,
compose(A,B) = compose(codomain(A),compose(A,B)),
inference(paramod,[status(thm)],[c_16,c_19]) ).
cnf(c_43,plain,
compose(codomain(A),compose(A,B)) = compose(A,B),
inference(copy,[status(thm)],[c_5232]) ).
cnf(c_52,plain,
codomain(b) = domain(a),
inference(resolve,[status(thm)],[c_23,c_9]) ).
cnf(c_5233,plain,
( codomain(A) = domain(codomain(A))
| ~ there_exists(A) ),
inference(paramod,[status(thm)],[c_16,c_23]) ).
cnf(c_54,plain,
( domain(codomain(A)) = codomain(A)
| ~ there_exists(A) ),
inference(copy,[status(thm)],[c_5233]) ).
cnf(c_57,plain,
there_exists(domain(a)),
inference(resolve,[status(thm)],[c_24,c_9]) ).
cnf(c_86,plain,
there_exists(b),
inference(resolve,[status(thm)],[c_36,c_25]) ).
cnf(c_5234,plain,
( there_exists(compose(a,A))
| codomain(A) != domain(a) ),
inference(resolve,[status(thm)],[c_21,c_57]) ).
cnf(c_144,plain,
codomain(compose(b,c)) != domain(a),
inference(resolve,[status(thm)],[c_5234,c_7]) ).
cnf(c_5235,plain,
( A != compose(b,c)
| there_exists(A) ),
inference(copy,[status(thm)],[c_27]) ).
cnf(c_323,plain,
there_exists(compose(codomain(b),compose(b,c))),
inference(resolve,[status(thm)],[c_43,c_5235]) ).
cnf(c_865,plain,
domain(codomain(b)) = codomain(b),
inference(resolve,[status(thm)],[c_54,c_86]) ).
cnf(c_1667,plain,
domain(codomain(b)) = domain(a),
inference(paramod,[status(thm)],[c_52,c_865]) ).
cnf(c_5214,plain,
codomain(compose(b,c)) = domain(codomain(b)),
inference(resolve,[status(thm)],[c_323,c_23]) ).
cnf(c_5236,plain,
domain(codomain(b)) != domain(a),
inference(paramod,[status(thm)],[c_5214,c_144]) ).
cnf(c_5231,plain,
$false,
inference(resolve,[status(thm)],[c_1667,c_5236]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : CAT018-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n003.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 22:51:55 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 3976347 was started by sandbox2 on n003,
% 0.09/0.36 % Sat Sep 26 22:51:55 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.37
% 0.09/0.37 % From the command line: assign(max_seconds, 300).
% 7.28/1.36
% 7.28/1.36 % SZS status Unsatisfiable for theBenchmark
% 7.28/1.36
% 7.28/1.36 % Proof 1 at 0.76 (+ 0.21) seconds.
% 7.28/1.36 % Length of proof is 29.
% 7.28/1.36 % Level of proof is 5.
% 7.28/1.36 % Maximum clause weight is 30.000.
% 7.28/1.36 % Given clauses 324.
% 7.28/1.36
% 7.28/1.36 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------