%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : CAT006-4 : 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 : 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 06:55:56 AM UTC 2026
% Result : Unsatisfiable 0.09s 0.39s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of formulae : 28 ( 13 unt; 0 def)
% Number of atoms : 43 ( 17 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 32 ( 17 ~; 15 |; 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_4,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_5,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_7,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_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(domain_has_elements,axiom,
! [VAR_0] :
( there_exists(VAR_0)
| ~ there_exists(domain(VAR_0)) ),
file('theBenchmark.p',domain_has_elements) ).
cnf(c_18,plain,
( there_exists(A)
| ~ there_exists(domain(A)) ),
inference(clausify,[status(thm)],[domain_has_elements]) ).
cnf(c_19,plain,
compose(d,a) = a,
inference(resolve,[status(thm)],[c_5,c_7]) ).
cnf(c_20,plain,
there_exists(a),
inference(paramod,[status(thm)],[c_19,c_7]) ).
cnf(c_81,plain,
( compose(d,domain(d)) = domain(d)
| ~ there_exists(d) ),
inference(paramod,[status(thm)],[c_9,c_5]) ).
cnf(c_82,plain,
( d = domain(d)
| ~ there_exists(d) ),
inference(paramod,[status(thm)],[c_9,c_81]) ).
cnf(c_22,plain,
( domain(d) = d
| ~ there_exists(d) ),
inference(copy,[status(thm)],[c_82]) ).
cnf(c_34,plain,
( codomain(a) = domain(d)
| ~ there_exists(a) ),
inference(paramod,[status(thm)],[c_19,c_15]) ).
cnf(c_35,plain,
( there_exists(domain(d))
| ~ there_exists(a) ),
inference(paramod,[status(thm)],[c_19,c_16]) ).
cnf(c_39,plain,
there_exists(domain(d)),
inference(resolve,[status(thm)],[c_35,c_20]) ).
cnf(c_41,plain,
there_exists(d),
inference(resolve,[status(thm)],[c_18,c_39]) ).
cnf(c_44,plain,
domain(d) = d,
inference(resolve,[status(thm)],[c_22,c_41]) ).
cnf(c_45,plain,
( codomain(a) = d
| ~ there_exists(a) ),
inference(paramod,[status(thm)],[c_44,c_34]) ).
cnf(c_79,plain,
codomain(a) = d,
inference(resolve,[status(thm)],[c_45,c_20]) ).
cnf(c_80,plain,
$false,
inference(resolve,[status(thm)],[c_79,c_4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : CAT006-4 : 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 : n005.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 22:48:47 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 3291744 was started by sandbox2 on n005,
% 0.09/0.36 % Sat Sep 26 22:48:47 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).
% 0.09/0.39
% 0.09/0.39 % SZS status Unsatisfiable for theBenchmark
% 0.09/0.39
% 0.09/0.39 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.09/0.39 % Length of proof is 19.
% 0.09/0.39 % Level of proof is 8.
% 0.09/0.39 % Maximum clause weight is 9.000.
% 0.09/0.39 % Given clauses 39.
% 0.09/0.39
% 0.09/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------