%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET238-6 : 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 : 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 08:36:05 AM UTC 2026
% Result : Unsatisfiable 0.15s 10.49s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of formulae : 35 ( 28 unt; 0 def)
% Number of atoms : 42 ( 19 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 22 ( 15 ~; 7 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 4 con; 0-3 aty)
% Number of variables : 51 ( 9 sgn 15 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_corollary_to_restriction_alternate_defn1_2,axiom,
~ member(ordered_pair(first(z),second(z)),restrict(xr,x,y)),
file('theBenchmark.p',prove_corollary_to_restriction_alternate_defn1_2) ).
cnf(c_36,plain,
~ member(ordered_pair(first(z),second(z)),restrict(xr,x,y)),
inference(clausify,[status(thm)],[prove_corollary_to_restriction_alternate_defn1_2]) ).
fof(prove_corollary_to_restriction_alternate_defn1_1,axiom,
member(z,restrict(xr,x,y)),
file('theBenchmark.p',prove_corollary_to_restriction_alternate_defn1_1) ).
cnf(c_37,plain,
member(z,restrict(xr,x,y)),
inference(clausify,[status(thm)],[prove_corollary_to_restriction_alternate_defn1_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_111,plain,
intersection(cross_product(A,B),C) = restrict(C,A,B),
inference(clausify,[status(thm)],[restriction2]) ).
cnf(c_112,plain,
restrict(A,B,C) = intersection(cross_product(B,C),A),
inference(copy,[status(thm)],[c_111]) ).
fof(restriction1,axiom,
! [VAR_0,VAR_1,VAR_2] : intersection(VAR_0,cross_product(VAR_1,VAR_2)) = restrict(VAR_0,VAR_1,VAR_2),
file('theBenchmark.p',restriction1) ).
cnf(c_113,plain,
intersection(A,cross_product(B,C)) = restrict(A,B,C),
inference(clausify,[status(thm)],[restriction1]) ).
cnf(c_449,plain,
intersection(A,cross_product(B,C)) = intersection(cross_product(B,C),A),
inference(paramod,[status(thm)],[c_112,c_113]) ).
cnf(c_114,plain,
intersection(cross_product(A,B),C) = intersection(C,cross_product(A,B)),
inference(copy,[status(thm)],[c_449]) ).
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_122,plain,
( member(A,C)
| ~ member(A,intersection(B,C)) ),
inference(clausify,[status(thm)],[intersection2]) ).
fof(cartesian_product4,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ordered_pair(first(VAR_0),second(VAR_0)) = VAR_0
| ~ member(VAR_0,cross_product(VAR_1,VAR_2)) ),
file('theBenchmark.p',cartesian_product4) ).
cnf(c_127,plain,
( ordered_pair(first(A),second(A)) = A
| ~ member(A,cross_product(B,C)) ),
inference(clausify,[status(thm)],[cartesian_product4]) ).
fof(ordered_pair,axiom,
! [VAR_0,VAR_1] : unordered_pair(singleton(VAR_0),unordered_pair(VAR_0,singleton(VAR_1))) = ordered_pair(VAR_0,VAR_1),
file('theBenchmark.p',ordered_pair) ).
cnf(c_131,plain,
unordered_pair(singleton(A),unordered_pair(A,singleton(B))) = ordered_pair(A,B),
inference(clausify,[status(thm)],[ordered_pair]) ).
cnf(c_132,plain,
ordered_pair(A,B) = unordered_pair(singleton(A),unordered_pair(A,singleton(B))),
inference(copy,[status(thm)],[c_131]) ).
fof(singleton_set,axiom,
! [VAR_0] : unordered_pair(VAR_0,VAR_0) = singleton(VAR_0),
file('theBenchmark.p',singleton_set) ).
cnf(c_133,plain,
unordered_pair(A,A) = singleton(A),
inference(clausify,[status(thm)],[singleton_set]) ).
cnf(c_134,plain,
singleton(A) = unordered_pair(A,A),
inference(copy,[status(thm)],[c_133]) ).
cnf(c_450,plain,
member(z,intersection(cross_product(x,y),xr)),
inference(paramod,[status(thm)],[c_112,c_37]) ).
cnf(c_231,plain,
member(z,intersection(xr,cross_product(x,y))),
inference(paramod,[status(thm)],[c_114,c_450]) ).
cnf(c_451,plain,
~ member(unordered_pair(singleton(first(z)),unordered_pair(first(z),singleton(second(z)))),restrict(xr,x,y)),
inference(paramod,[status(thm)],[c_132,c_36]) ).
cnf(c_452,plain,
~ member(unordered_pair(unordered_pair(first(z),first(z)),unordered_pair(first(z),singleton(second(z)))),restrict(xr,x,y)),
inference(paramod,[status(thm)],[c_134,c_451]) ).
cnf(c_453,plain,
~ member(unordered_pair(unordered_pair(first(z),first(z)),unordered_pair(first(z),unordered_pair(second(z),second(z)))),restrict(xr,x,y)),
inference(paramod,[status(thm)],[c_134,c_452]) ).
cnf(c_454,plain,
~ member(unordered_pair(unordered_pair(first(z),first(z)),unordered_pair(first(z),unordered_pair(second(z),second(z)))),intersection(cross_product(x,y),xr)),
inference(paramod,[status(thm)],[c_112,c_453]) ).
cnf(c_232,plain,
~ member(unordered_pair(unordered_pair(first(z),first(z)),unordered_pair(first(z),unordered_pair(second(z),second(z)))),intersection(xr,cross_product(x,y))),
inference(paramod,[status(thm)],[c_114,c_454]) ).
cnf(c_455,plain,
( unordered_pair(singleton(first(A)),unordered_pair(first(A),singleton(second(A)))) = A
| ~ member(A,cross_product(B,C)) ),
inference(paramod,[status(thm)],[c_132,c_127]) ).
cnf(c_456,plain,
( unordered_pair(unordered_pair(first(A),first(A)),unordered_pair(first(A),singleton(second(A)))) = A
| ~ member(A,cross_product(B,C)) ),
inference(paramod,[status(thm)],[c_134,c_455]) ).
cnf(c_239,plain,
( unordered_pair(unordered_pair(first(A),first(A)),unordered_pair(first(A),unordered_pair(second(A),second(A)))) = A
| ~ member(A,cross_product(B,C)) ),
inference(paramod,[status(thm)],[c_134,c_456]) ).
cnf(c_377,plain,
member(z,cross_product(x,y)),
inference(resolve,[status(thm)],[c_231,c_122]) ).
cnf(c_441,plain,
unordered_pair(unordered_pair(first(z),first(z)),unordered_pair(first(z),unordered_pair(second(z),second(z)))) = z,
inference(resolve,[status(thm)],[c_377,c_239]) ).
cnf(c_457,plain,
~ member(z,intersection(xr,cross_product(x,y))),
inference(paramod,[status(thm)],[c_441,c_232]) ).
cnf(c_448,plain,
$false,
inference(resolve,[status(thm)],[c_231,c_457]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET238-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/10.39 % Computer : n005.cluster.edu
% 0.10/10.39 % Model : x86_64 x86_64
% 0.10/10.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/10.39 % Memory : 8046.5625MB
% 0.10/10.39 % OS : Linux 6.8.0-71-generic
% 0.10/10.39 % CPULimit : 300
% 0.10/10.39 % WCLimit : 300
% 0.10/10.39 % DateTime : Sat Sep 26 07:22:27 UTC 2026
% 0.10/10.39 % CPUTime :
% 0.10/10.39 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/10.39 % Process 1546820 was started by sandbox2 on n005,
% 0.10/10.39 % Sat Sep 26 07:22:27 2026
% 0.10/10.39 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.15/10.40
% 0.15/10.40 % From the command line: assign(max_seconds, 300).
% 0.15/10.49
% 0.15/10.49 % SZS status Unsatisfiable for theBenchmark
% 0.15/10.49
% 0.15/10.49 % Proof 1 at 0.06 (+ 0.01) seconds.
% 0.15/10.49 % Length of proof is 18.
% 0.15/10.49 % Level of proof is 6.
% 0.15/10.49 % Maximum clause weight is 21.000.
% 0.15/10.49 % Given clauses 135.
% 0.15/10.49
% 0.15/10.49 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------