%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : CAT009-4 : 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 : 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 : Sun Sep 27 06:55:57 AM UTC 2026
% Result : Unsatisfiable 0.17s 5.50s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of formulae : 28 ( 17 unt; 0 def)
% Number of atoms : 39 ( 18 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 24 ( 13 ~; 11 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 29 ( 1 sgn 9 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_domain_of_ab_equals_domain_of_b,axiom,
domain(compose(a,b)) != domain(b),
file('theBenchmark.p',prove_domain_of_ab_equals_domain_of_b) ).
cnf(c_4,plain,
domain(compose(a,b)) != domain(b),
inference(clausify,[status(thm)],[prove_domain_of_ab_equals_domain_of_b]) ).
fof(ab_exists,axiom,
there_exists(compose(a,b)),
file('theBenchmark.p',ab_exists) ).
cnf(c_5,plain,
there_exists(compose(a,b)),
inference(clausify,[status(thm)],[ab_exists]) ).
fof(compose_domain,axiom,
! [VAR_0] : compose(VAR_0,domain(VAR_0)) = VAR_0,
file('theBenchmark.p',compose_domain) ).
cnf(c_7,plain,
compose(A,domain(A)) = A,
inference(clausify,[status(thm)],[compose_domain]) ).
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_8,plain,
compose(A,compose(B,C)) = compose(compose(A,B),C),
inference(clausify,[status(thm)],[associativity_of_compose]) ).
cnf(c_9,plain,
compose(compose(A,B),C) = compose(A,compose(B,C)),
inference(copy,[status(thm)],[c_8]) ).
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_12,plain,
( domain(A) = codomain(B)
| ~ there_exists(compose(A,B)) ),
inference(clausify,[status(thm)],[domain_codomain_composition1]) ).
cnf(c_13,plain,
( codomain(B) = domain(A)
| ~ there_exists(compose(A,B)) ),
inference(copy,[status(thm)],[c_12]) ).
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_14,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_15,plain,
( there_exists(A)
| ~ there_exists(codomain(A)) ),
inference(clausify,[status(thm)],[codomain_has_elements]) ).
cnf(c_20,plain,
codomain(b) = domain(a),
inference(resolve,[status(thm)],[c_13,c_5]) ).
cnf(c_22,plain,
( codomain(domain(A)) = domain(A)
| ~ there_exists(A) ),
inference(paramod,[status(thm)],[c_7,c_13]) ).
cnf(c_23,plain,
( codomain(C) = domain(compose(A,B))
| ~ there_exists(compose(A,compose(B,C))) ),
inference(paramod,[status(thm)],[c_9,c_13]) ).
cnf(c_24,plain,
there_exists(domain(a)),
inference(resolve,[status(thm)],[c_14,c_5]) ).
cnf(c_43,plain,
( there_exists(b)
| ~ there_exists(domain(a)) ),
inference(paramod,[status(thm)],[c_20,c_15]) ).
cnf(c_47,plain,
there_exists(b),
inference(resolve,[status(thm)],[c_43,c_24]) ).
cnf(c_53,plain,
codomain(domain(b)) = domain(b),
inference(resolve,[status(thm)],[c_22,c_47]) ).
cnf(c_58,plain,
( codomain(domain(B)) = domain(compose(A,B))
| ~ there_exists(compose(A,B)) ),
inference(paramod,[status(thm)],[c_7,c_23]) ).
cnf(c_168,plain,
codomain(domain(b)) = domain(compose(a,b)),
inference(resolve,[status(thm)],[c_58,c_5]) ).
cnf(c_169,plain,
domain(b) = domain(compose(a,b)),
inference(paramod,[status(thm)],[c_53,c_168]) ).
cnf(c_166,plain,
domain(compose(a,b)) = domain(b),
inference(copy,[status(thm)],[c_169]) ).
cnf(c_167,plain,
$false,
inference(resolve,[status(thm)],[c_166,c_4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : CAT009-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/5.45 % Computer : n009.cluster.edu
% 0.17/5.45 % Model : x86_64 x86_64
% 0.17/5.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/5.45 % Memory : 8046.5625MB
% 0.17/5.45 % OS : Linux 6.8.0-71-generic
% 0.17/5.45 % CPULimit : 300
% 0.17/5.45 % WCLimit : 300
% 0.17/5.45 % DateTime : Sat Sep 26 22:49:21 UTC 2026
% 0.17/5.45 % CPUTime :
% 0.17/5.46 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/5.46 % Process 1316354 was started by sandbox2 on n009,
% 0.17/5.46 % Sat Sep 26 22:49:21 2026
% 0.17/5.46 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.17/5.46
% 0.17/5.46 % From the command line: assign(max_seconds, 300).
% 0.17/5.50
% 0.17/5.50 % SZS status Unsatisfiable for theBenchmark
% 0.17/5.50
% 0.17/5.50 % Proof 1 at 0.02 (+ 0.01) seconds.
% 0.17/5.50 % Length of proof is 19.
% 0.17/5.50 % Level of proof is 7.
% 0.17/5.50 % Maximum clause weight is 36.000.
% 0.17/5.50 % Given clauses 50.
% 0.17/5.50
% 0.17/5.50 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------