%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET158-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n006.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 08:35:56 AM UTC 2026
% Result : Unsatisfiable 0.14s 0.49s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 4
% Syntax : Number of formulae : 12 ( 10 unt; 0 def)
% Number of atoms : 14 ( 3 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 7 ( 5 ~; 2 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 4 ( 0 sgn 2 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_corollary_to_complement_axiom_3,axiom,
y = z,
file('theBenchmark.p',prove_corollary_to_complement_axiom_3) ).
cnf(c_36,plain,
y = z,
inference(clausify,[status(thm)],[prove_corollary_to_complement_axiom_3]) ).
cnf(c_37,plain,
z = y,
inference(copy,[status(thm)],[c_36]) ).
fof(prove_corollary_to_complement_axiom_2,axiom,
member(z,complement(x)),
file('theBenchmark.p',prove_corollary_to_complement_axiom_2) ).
cnf(c_38,plain,
member(z,complement(x)),
inference(clausify,[status(thm)],[prove_corollary_to_complement_axiom_2]) ).
cnf(c_39,plain,
member(y,complement(x)),
inference(paramod,[status(thm)],[c_37,c_38]) ).
fof(prove_corollary_to_complement_axiom_1,axiom,
member(y,x),
file('theBenchmark.p',prove_corollary_to_complement_axiom_1) ).
cnf(c_40,plain,
member(y,x),
inference(clausify,[status(thm)],[prove_corollary_to_complement_axiom_1]) ).
fof(complement1,axiom,
! [VAR_0,VAR_1] :
( ~ member(VAR_0,VAR_1)
| ~ member(VAR_0,complement(VAR_1)) ),
file('theBenchmark.p',complement1) ).
cnf(c_123,plain,
( ~ member(A,B)
| ~ member(A,complement(B)) ),
inference(clausify,[status(thm)],[complement1]) ).
cnf(c_264,plain,
~ member(y,x),
inference(resolve,[status(thm)],[c_123,c_39]) ).
cnf(c_263,plain,
$false,
inference(resolve,[status(thm)],[c_40,c_264]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SET158-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.39 % Computer : n006.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Sat Sep 26 07:13:55 UTC 2026
% 0.11/0.40 % CPUTime :
% 0.14/0.40 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.14/0.40 % Process 651108 was started by sandbox on n006,
% 0.14/0.40 % Sat Sep 26 07:13:55 2026
% 0.14/0.40 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.14/0.41
% 0.14/0.41 % From the command line: assign(max_seconds, 300).
% 0.14/0.49
% 0.14/0.49 % SZS status Unsatisfiable for theBenchmark
% 0.14/0.49
% 0.14/0.49 % Proof 1 at 0.03 (+ 0.00) seconds.
% 0.14/0.49 % Length of proof is 7.
% 0.14/0.49 % Level of proof is 3.
% 0.14/0.49 % Maximum clause weight is 7.000.
% 0.14/0.49 % Given clauses 28.
% 0.14/0.49
% 0.14/0.49 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------