%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET257-6 : 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 : n004.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 08:36:07 AM UTC 2026
% Result : Unsatisfiable 12.27s 2.05s
% Output : CNFRefutation 12.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 26 ( 10 unt; 0 def)
% Number of atoms : 46 ( 10 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 37 ( 17 ~; 20 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-3 aty)
% Number of variables : 48 ( 2 sgn 15 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_restriction_property5_1,axiom,
restrict(cross_product(x,y),x,y) != cross_product(x,y),
file('theBenchmark.p',prove_restriction_property5_1) ).
cnf(c_36,plain,
restrict(cross_product(x,y),x,y) != cross_product(x,y),
inference(clausify,[status(thm)],[prove_restriction_property5_1]) ).
fof(restriction2,axiom,
! [VAR_0,VAR_1,VAR_2] : intersection(cross_product(VAR_0,VAR_1),VAR_2) = restrict(VAR_2,VAR_0,VAR_1),
file('theBenchmark.p',restriction2) ).
cnf(c_110,plain,
intersection(cross_product(A,B),C) = restrict(C,A,B),
inference(clausify,[status(thm)],[restriction2]) ).
cnf(c_111,plain,
restrict(A,B,C) = intersection(cross_product(B,C),A),
inference(copy,[status(thm)],[c_110]) ).
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_120,plain,
( member(A,intersection(B,C))
| ~ member(A,C)
| ~ member(A,B) ),
inference(clausify,[status(thm)],[intersection3]) ).
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_122,plain,
( member(A,B)
| ~ member(A,intersection(B,C)) ),
inference(clausify,[status(thm)],[intersection1]) ).
fof(subclass_implies_equal,axiom,
! [VAR_0,VAR_1] :
( VAR_0 = VAR_1
| ~ subclass(VAR_1,VAR_0)
| ~ subclass(VAR_0,VAR_1) ),
file('theBenchmark.p',subclass_implies_equal) ).
cnf(c_138,plain,
( A = B
| ~ subclass(B,A)
| ~ subclass(A,B) ),
inference(clausify,[status(thm)],[subclass_implies_equal]) ).
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_142,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_143,plain,
( subclass(A,B)
| member(not_subclass_element(A,B),A) ),
inference(clausify,[status(thm)],[not_subclass_members1]) ).
cnf(c_176,plain,
( member(A,intersection(B,B))
| ~ member(A,B) ),
inference(factor,[status(thm)],[c_120]) ).
cnf(c_208,plain,
intersection(cross_product(x,y),cross_product(x,y)) != cross_product(x,y),
inference(paramod,[status(thm)],[c_111,c_36]) ).
cnf(c_336,plain,
( member(not_subclass_element(intersection(A,B),C),A)
| subclass(intersection(A,B),C) ),
inference(resolve,[status(thm)],[c_143,c_122]) ).
cnf(c_392,plain,
( subclass(A,B)
| member(not_subclass_element(A,B),intersection(A,A)) ),
inference(resolve,[status(thm)],[c_176,c_143]) ).
cnf(c_7370,plain,
( subclass(A,intersection(A,A))
| subclass(A,intersection(A,A)) ),
inference(resolve,[status(thm)],[c_392,c_142]) ).
cnf(c_4206,plain,
subclass(A,intersection(A,A)),
inference(copy,[status(thm)],[c_7370]) ).
cnf(c_4241,plain,
( intersection(A,A) = A
| ~ subclass(intersection(A,A),A) ),
inference(resolve,[status(thm)],[c_4206,c_138]) ).
cnf(c_7371,plain,
( subclass(intersection(A,B),A)
| subclass(intersection(A,B),A) ),
inference(resolve,[status(thm)],[c_336,c_142]) ).
cnf(c_7354,plain,
subclass(intersection(A,B),A),
inference(copy,[status(thm)],[c_7371]) ).
cnf(c_7368,plain,
intersection(A,A) = A,
inference(resolve,[status(thm)],[c_7354,c_4241]) ).
cnf(c_7369,plain,
$false,
inference(resolve,[status(thm)],[c_7368,c_208]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET257-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.44 % Computer : n004.cluster.edu
% 0.19/0.44 % Model : x86_64 x86_64
% 0.19/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.44 % Memory : 8046.5625MB
% 0.19/0.44 % OS : Linux 6.8.0-71-generic
% 0.19/0.44 % CPULimit : 300
% 0.19/0.44 % WCLimit : 300
% 0.19/0.44 % DateTime : Sat Sep 26 07:24:21 UTC 2026
% 0.19/0.45 % CPUTime :
% 0.19/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.19/0.45 % Process 1104590 was started by sandbox on n004,
% 0.19/0.45 % Sat Sep 26 07:24:21 2026
% 0.19/0.45 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.19/0.46
% 0.19/0.46 % From the command line: assign(max_seconds, 300).
% 12.27/2.05
% 12.27/2.05 % given #500 (A,wt=22): 313 subclass(successor(A),union(A,singleton(A))). [resolve(139,a,91,a(flip))].
% 12.27/2.05
% 12.27/2.05 % SZS status Unsatisfiable for theBenchmark
% 12.27/2.05
% 12.27/2.05 % Proof 1 at 1.24 (+ 0.32) seconds.
% 12.27/2.05 % Length of proof is 17.
% 12.27/2.05 % Level of proof is 6.
% 12.27/2.05 % Maximum clause weight is 27.000.
% 12.27/2.05 % Given clauses 553.
% 12.27/2.05
% 12.27/2.05 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------