%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : CAT005-4 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n005.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 06:55:55 AM UTC 2026
% Result : Unsatisfiable 0.09s 0.36s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of formulae : 31 ( 15 unt; 0 def)
% Number of atoms : 47 ( 19 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 34 ( 18 ~; 16 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 3 ( 1 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 : 19 ( 1 sgn 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_domain_of_a_is_d,axiom,
domain(a) != d,
file('theBenchmark.p',prove_domain_of_a_is_d) ).
cnf(c_4,plain,
domain(a) != d,
inference(clausify,[status(thm)],[prove_domain_of_a_is_d]) ).
fof(xd_equals_x,axiom,
! [VAR_0] :
( compose(VAR_0,d) = VAR_0
| ~ there_exists(compose(VAR_0,d)) ),
file('theBenchmark.p',xd_equals_x) ).
cnf(c_6,plain,
( compose(A,d) = A
| ~ there_exists(compose(A,d)) ),
inference(clausify,[status(thm)],[xd_equals_x]) ).
fof(ad_exists,axiom,
there_exists(compose(a,d)),
file('theBenchmark.p',ad_exists) ).
cnf(c_7,plain,
there_exists(compose(a,d)),
inference(clausify,[status(thm)],[ad_exists]) ).
fof(compose_codomain,axiom,
! [VAR_0] : compose(codomain(VAR_0),VAR_0) = VAR_0,
file('theBenchmark.p',compose_codomain) ).
cnf(c_8,plain,
compose(codomain(A),A) = A,
inference(clausify,[status(thm)],[compose_codomain]) ).
fof(compose_domain,axiom,
! [VAR_0] : compose(VAR_0,domain(VAR_0)) = VAR_0,
file('theBenchmark.p',compose_domain) ).
cnf(c_9,plain,
compose(A,domain(A)) = A,
inference(clausify,[status(thm)],[compose_domain]) ).
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_14,plain,
( domain(A) = codomain(B)
| ~ there_exists(compose(A,B)) ),
inference(clausify,[status(thm)],[domain_codomain_composition1]) ).
cnf(c_15,plain,
( codomain(B) = domain(A)
| ~ there_exists(compose(A,B)) ),
inference(copy,[status(thm)],[c_14]) ).
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_16,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_17,plain,
( there_exists(A)
| ~ there_exists(codomain(A)) ),
inference(clausify,[status(thm)],[codomain_has_elements]) ).
cnf(c_19,plain,
compose(a,d) = a,
inference(resolve,[status(thm)],[c_6,c_7]) ).
cnf(c_20,plain,
there_exists(a),
inference(paramod,[status(thm)],[c_19,c_7]) ).
cnf(c_63,plain,
( compose(codomain(d),d) = codomain(d)
| ~ there_exists(d) ),
inference(paramod,[status(thm)],[c_8,c_6]) ).
cnf(c_64,plain,
( d = codomain(d)
| ~ there_exists(d) ),
inference(paramod,[status(thm)],[c_8,c_63]) ).
cnf(c_21,plain,
( codomain(d) = d
| ~ there_exists(d) ),
inference(copy,[status(thm)],[c_64]) ).
cnf(c_31,plain,
( there_exists(domain(A))
| ~ there_exists(A) ),
inference(paramod,[status(thm)],[c_9,c_16]) ).
cnf(c_34,plain,
( codomain(d) = domain(a)
| ~ there_exists(a) ),
inference(paramod,[status(thm)],[c_19,c_15]) ).
cnf(c_35,plain,
there_exists(domain(a)),
inference(resolve,[status(thm)],[c_31,c_20]) ).
cnf(c_37,plain,
codomain(d) = domain(a),
inference(resolve,[status(thm)],[c_34,c_20]) ).
cnf(c_38,plain,
( domain(a) = d
| ~ there_exists(d) ),
inference(paramod,[status(thm)],[c_37,c_21]) ).
cnf(c_41,plain,
( there_exists(d)
| ~ there_exists(domain(a)) ),
inference(paramod,[status(thm)],[c_37,c_17]) ).
cnf(c_42,plain,
there_exists(d),
inference(resolve,[status(thm)],[c_41,c_35]) ).
cnf(c_61,plain,
domain(a) = d,
inference(resolve,[status(thm)],[c_38,c_42]) ).
cnf(c_62,plain,
$false,
inference(resolve,[status(thm)],[c_61,c_4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : CAT005-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.34 % Computer : n005.cluster.edu
% 0.09/0.34 % Model : x86_64 x86_64
% 0.09/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.34 % Memory : 8046.5625MB
% 0.09/0.34 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 26 22:48:31 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.35 % Process 3290512 was started by sandbox on n005,
% 0.09/0.35 % Sat Sep 26 22:48:31 2026
% 0.09/0.35 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.35
% 0.09/0.35 % From the command line: assign(max_seconds, 300).
% 0.09/0.36
% 0.09/0.36 % SZS status Unsatisfiable for theBenchmark
% 0.09/0.36
% 0.09/0.36 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.09/0.36 % Length of proof is 21.
% 0.09/0.36 % Level of proof is 7.
% 0.09/0.36 % Maximum clause weight is 21.000.
% 0.09/0.36 % Given clauses 28.
% 0.09/0.36
% 0.09/0.36 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------