%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET199-6 : 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 : 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 08:36:02 AM UTC 2026
% Result : Unsatisfiable 32.24s 9.73s
% Output : CNFRefutation 32.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of formulae : 23 ( 12 unt; 0 def)
% Number of atoms : 38 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 30 ( 15 ~; 15 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 23 ( 0 sgn 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_greatest_lower_bound_3,axiom,
~ subclass(z,intersection(x,y)),
file('theBenchmark.p',prove_greatest_lower_bound_3) ).
cnf(c_36,plain,
~ subclass(z,intersection(x,y)),
inference(clausify,[status(thm)],[prove_greatest_lower_bound_3]) ).
fof(prove_greatest_lower_bound_2,axiom,
subclass(z,y),
file('theBenchmark.p',prove_greatest_lower_bound_2) ).
cnf(c_37,plain,
subclass(z,y),
inference(clausify,[status(thm)],[prove_greatest_lower_bound_2]) ).
fof(prove_greatest_lower_bound_1,axiom,
subclass(z,x),
file('theBenchmark.p',prove_greatest_lower_bound_1) ).
cnf(c_38,plain,
subclass(z,x),
inference(clausify,[status(thm)],[prove_greatest_lower_bound_1]) ).
fof(intersection3,axiom,
! [VAR_0,VAR_1,VAR_2] :
( member(VAR_0,intersection(VAR_1,VAR_2))
| ~ member(VAR_0,VAR_2)
| ~ member(VAR_0,VAR_1) ),
file('theBenchmark.p',intersection3) ).
cnf(c_122,plain,
( member(A,intersection(B,C))
| ~ member(A,C)
| ~ member(A,B) ),
inference(clausify,[status(thm)],[intersection3]) ).
fof(not_subclass_members2,axiom,
! [VAR_0,VAR_1] :
( subclass(VAR_0,VAR_1)
| ~ member(not_subclass_element(VAR_0,VAR_1),VAR_1) ),
file('theBenchmark.p',not_subclass_members2) ).
cnf(c_144,plain,
( subclass(A,B)
| ~ member(not_subclass_element(A,B),B) ),
inference(clausify,[status(thm)],[not_subclass_members2]) ).
fof(not_subclass_members1,axiom,
! [VAR_0,VAR_1] :
( subclass(VAR_0,VAR_1)
| member(not_subclass_element(VAR_0,VAR_1),VAR_0) ),
file('theBenchmark.p',not_subclass_members1) ).
cnf(c_145,plain,
( subclass(A,B)
| member(not_subclass_element(A,B),A) ),
inference(clausify,[status(thm)],[not_subclass_members1]) ).
fof(subclass_members,axiom,
! [VAR_0,VAR_1,VAR_2] :
( member(VAR_2,VAR_1)
| ~ member(VAR_2,VAR_0)
| ~ subclass(VAR_0,VAR_1) ),
file('theBenchmark.p',subclass_members) ).
cnf(c_146,plain,
( member(C,B)
| ~ member(C,A)
| ~ subclass(A,B) ),
inference(clausify,[status(thm)],[subclass_members]) ).
cnf(c_310,plain,
member(not_subclass_element(z,intersection(x,y)),z),
inference(resolve,[status(thm)],[c_145,c_36]) ).
cnf(c_322,plain,
( member(A,x)
| ~ member(A,z) ),
inference(resolve,[status(thm)],[c_146,c_38]) ).
cnf(c_323,plain,
( member(A,y)
| ~ member(A,z) ),
inference(resolve,[status(thm)],[c_146,c_37]) ).
cnf(c_510,plain,
member(not_subclass_element(z,intersection(x,y)),y),
inference(resolve,[status(thm)],[c_310,c_323]) ).
cnf(c_511,plain,
member(not_subclass_element(z,intersection(x,y)),x),
inference(resolve,[status(thm)],[c_310,c_322]) ).
cnf(c_592,plain,
( member(not_subclass_element(z,intersection(x,y)),intersection(A,y))
| ~ member(not_subclass_element(z,intersection(x,y)),A) ),
inference(resolve,[status(thm)],[c_510,c_122]) ).
cnf(c_22717,plain,
member(not_subclass_element(z,intersection(x,y)),intersection(x,y)),
inference(resolve,[status(thm)],[c_592,c_511]) ).
cnf(c_22731,plain,
subclass(z,intersection(x,y)),
inference(resolve,[status(thm)],[c_22717,c_144]) ).
cnf(c_22730,plain,
$false,
inference(resolve,[status(thm)],[c_36,c_22731]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET199-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.37 % Computer : n026.cluster.edu
% 0.08/0.37 % Model : x86_64 x86_64
% 0.08/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.37 % Memory : 8046.5625MB
% 0.08/0.37 % OS : Linux 6.8.0-71-generic
% 0.08/0.37 % CPULimit : 300
% 0.08/0.37 % WCLimit : 300
% 0.08/0.37 % DateTime : Sat Sep 26 07:22:10 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.08/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.37 % Process 393658 was started by sandbox on n026,
% 0.08/0.37 % Sat Sep 26 07:22:10 2026
% 0.08/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.02/0.38
% 0.02/0.38 % From the command line: assign(max_seconds, 300).
% 32.24/9.73
% 32.24/9.73 % given #500 (T,wt=9): 3628 member(omega,intersection(intersection(universal_class,universal_class),unordered_pair(omega,A))). [resolve(423,a,381,a)].
% 32.24/9.73
% 32.24/9.73 % given #1000 (F,wt=91): 16908 -member(A,complement(intersection(complement(intersection(cross_product(B,C),intersection(complement(intersection(D,cross_product(E,F))),complement(intersection(complement(D),complement(cross_product(E,F))))))),complement(intersection(complement(cross_product(B,C)),complement(intersection(complement(intersection(cross_product(E,F),D)),complement(intersection(complement(D),complement(cross_product(E,F))))))))))) | -member(A,intersection(complement(intersection(intersection(complement(intersection(cross_product(E,F),D)),complement(intersection(complement(D),complement(cross_product(E,F))))),cross_product(B,C))),complement(intersection(complement(cross_product(B,C)),complement(intersection(complement(intersection(cross_product(E,F),D)),complement(intersection(complement(D),complement(cross_product(E,F)))))))))). [para(115(a,2),16684(a,2,1,2,1,2,1,1,1))].
% 32.24/9.73
% 32.24/9.73 % SZS status Unsatisfiable for theBenchmark
% 32.24/9.73
% 32.24/9.73 % Proof 1 at 3.60 (+ 0.93) seconds.
% 32.24/9.73 % Length of proof is 15.
% 32.24/9.73 % Level of proof is 5.
% 32.24/9.73 % Maximum clause weight is 16.000.
% 32.24/9.73 % Given clauses 1312.
% 32.24/9.73
% 32.24/9.73 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------