%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET060-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n012.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 08:35:32 AM UTC 2026
% Result : Unsatisfiable 0.03s 10.35s
% Output : CNFRefutation 0.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of formulae : 12 ( 6 unt; 0 def)
% Number of atoms : 18 ( 0 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 15 ( 9 ~; 6 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 16 ( 2 sgn 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_special_classes_lemma_1,axiom,
member(y,intersection(complement(x),x)),
file('theBenchmark.p',prove_special_classes_lemma_1) ).
cnf(c_34,plain,
member(y,intersection(complement(x),x)),
inference(clausify,[status(thm)],[prove_special_classes_lemma_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_95,plain,
( ~ member(A,B)
| ~ member(A,complement(B)) ),
inference(clausify,[status(thm)],[complement1]) ).
fof(intersection2,axiom,
! [VAR_0,VAR_1,VAR_2] :
( member(VAR_0,VAR_2)
| ~ member(VAR_0,intersection(VAR_1,VAR_2)) ),
file('theBenchmark.p',intersection2) ).
cnf(c_97,plain,
( member(A,C)
| ~ member(A,intersection(B,C)) ),
inference(clausify,[status(thm)],[intersection2]) ).
fof(intersection1,axiom,
! [VAR_0,VAR_1,VAR_2] :
( member(VAR_0,VAR_1)
| ~ member(VAR_0,intersection(VAR_1,VAR_2)) ),
file('theBenchmark.p',intersection1) ).
cnf(c_98,plain,
( member(A,B)
| ~ member(A,intersection(B,C)) ),
inference(clausify,[status(thm)],[intersection1]) ).
cnf(c_193,plain,
member(y,x),
inference(resolve,[status(thm)],[c_97,c_34]) ).
cnf(c_195,plain,
member(y,complement(x)),
inference(resolve,[status(thm)],[c_98,c_34]) ).
cnf(c_380,plain,
~ member(y,complement(x)),
inference(resolve,[status(thm)],[c_95,c_193]) ).
cnf(c_379,plain,
$false,
inference(resolve,[status(thm)],[c_195,c_380]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SET060-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.02 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.03/10.32 % Computer : n012.cluster.edu
% 0.03/10.32 % Model : x86_64 x86_64
% 0.03/10.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/10.32 % Memory : 8046.5625MB
% 0.03/10.32 % OS : Linux 6.8.0-71-generic
% 0.03/10.32 % CPULimit : 300
% 0.03/10.32 % WCLimit : 300
% 0.03/10.32 % DateTime : Sat Sep 26 07:00:33 UTC 2026
% 0.03/10.33 % CPUTime :
% 0.03/10.33 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.03/10.33 % Process 4144849 was started by sandbox2 on n012,
% 0.03/10.33 % Sat Sep 26 07:00:33 2026
% 0.03/10.33 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.03/10.33
% 0.03/10.33 % From the command line: assign(max_seconds, 300).
% 0.03/10.35
% 0.03/10.35 % SZS status Unsatisfiable for theBenchmark
% 0.03/10.35
% 0.03/10.35 % Proof 1 at 0.01 (+ 0.01) seconds.
% 0.03/10.35 % Length of proof is 7.
% 0.03/10.35 % Level of proof is 2.
% 0.03/10.35 % Maximum clause weight is 21.000.
% 0.03/10.35 % Given clauses 105.
% 0.03/10.35
% 0.03/10.35 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------