%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : CAT006-3 : 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 : n026.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 06:55:56 AM UTC 2026
% Result : Unsatisfiable 0.14s 0.40s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 28 ( 14 unt; 0 def)
% Number of atoms : 42 ( 16 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 33 ( 19 ~; 14 |; 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 : 16 ( 1 sgn 7 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_codomain_of_a_is_d,axiom,
codomain(a) != d,
file('theBenchmark.p',prove_codomain_of_a_is_d) ).
cnf(c_7,plain,
codomain(a) != d,
inference(clausify,[status(thm)],[prove_codomain_of_a_is_d]) ).
fof(dx_equals_x,axiom,
! [VAR_0] :
( compose(d,VAR_0) = VAR_0
| ~ there_exists(compose(d,VAR_0)) ),
file('theBenchmark.p',dx_equals_x) ).
cnf(c_8,plain,
( compose(d,A) = A
| ~ there_exists(compose(d,A)) ),
inference(clausify,[status(thm)],[dx_equals_x]) ).
fof(da_exists,axiom,
there_exists(compose(d,a)),
file('theBenchmark.p',da_exists) ).
cnf(c_10,plain,
there_exists(compose(d,a)),
inference(clausify,[status(thm)],[da_exists]) ).
fof(compose_domain,axiom,
! [VAR_0] : compose(VAR_0,domain(VAR_0)) = VAR_0,
file('theBenchmark.p',compose_domain) ).
cnf(c_18,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_23,plain,
( domain(A) = codomain(B)
| ~ there_exists(compose(A,B)) ),
inference(clausify,[status(thm)],[domain_codomain_composition1]) ).
cnf(c_24,plain,
( codomain(B) = domain(A)
| ~ there_exists(compose(A,B)) ),
inference(copy,[status(thm)],[c_23]) ).
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_25,plain,
( there_exists(domain(A))
| ~ there_exists(compose(A,B)) ),
inference(clausify,[status(thm)],[composition_implies_domain]) ).
fof(domain_has_elements,axiom,
! [VAR_0] :
( there_exists(VAR_0)
| ~ there_exists(domain(VAR_0)) ),
file('theBenchmark.p',domain_has_elements) ).
cnf(c_27,plain,
( there_exists(A)
| ~ there_exists(domain(A)) ),
inference(clausify,[status(thm)],[domain_has_elements]) ).
cnf(c_28,plain,
compose(d,a) = a,
inference(resolve,[status(thm)],[c_10,c_8]) ).
cnf(c_30,plain,
there_exists(a),
inference(paramod,[status(thm)],[c_28,c_10]) ).
cnf(c_57,plain,
( compose(d,domain(d)) = domain(d)
| ~ there_exists(d) ),
inference(paramod,[status(thm)],[c_18,c_8]) ).
cnf(c_58,plain,
( d = domain(d)
| ~ there_exists(d) ),
inference(paramod,[status(thm)],[c_18,c_57]) ).
cnf(c_37,plain,
( domain(d) = d
| ~ there_exists(d) ),
inference(copy,[status(thm)],[c_58]) ).
cnf(c_59,plain,
( codomain(a) = domain(d)
| ~ there_exists(a) ),
inference(paramod,[status(thm)],[c_28,c_24]) ).
cnf(c_52,plain,
codomain(a) = domain(d),
inference(resolve,[status(thm)],[c_30,c_59]) ).
cnf(c_60,plain,
( there_exists(domain(d))
| ~ there_exists(a) ),
inference(paramod,[status(thm)],[c_28,c_25]) ).
cnf(c_53,plain,
there_exists(domain(d)),
inference(resolve,[status(thm)],[c_30,c_60]) ).
cnf(c_54,plain,
domain(d) != d,
inference(paramod,[status(thm)],[c_52,c_7]) ).
cnf(c_55,plain,
~ there_exists(d),
inference(resolve,[status(thm)],[c_54,c_37]) ).
cnf(c_61,plain,
~ there_exists(domain(d)),
inference(resolve,[status(thm)],[c_27,c_55]) ).
cnf(c_56,plain,
$false,
inference(resolve,[status(thm)],[c_53,c_61]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : CAT006-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n026.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sat Sep 26 22:51:25 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.38 % Process 2133915 was started by sandbox on n026,
% 0.09/0.38 % Sat Sep 26 22:51:25 2026
% 0.09/0.38 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.14/0.38
% 0.14/0.38 % From the command line: assign(max_seconds, 300).
% 0.14/0.40
% 0.14/0.40 % SZS status Unsatisfiable for theBenchmark
% 0.14/0.40
% 0.14/0.40 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.14/0.40 % Length of proof is 16.
% 0.14/0.40 % Level of proof is 6.
% 0.14/0.40 % Maximum clause weight is 9.000.
% 0.14/0.40 % Given clauses 19.
% 0.14/0.40
% 0.14/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------