%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET204-6 : 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 08:36:02 AM UTC 2026
% Result : Unsatisfiable 0.12s 0.45s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of formulae : 36 ( 20 unt; 0 def)
% Number of atoms : 57 ( 6 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 47 ( 26 ~; 21 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 71 ( 12 sgn 15 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_cross_product_property2_2,axiom,
~ member(ordered_pair(v,u),cross_product(y,x)),
file('theBenchmark.p',prove_cross_product_property2_2) ).
cnf(c_36,plain,
~ member(ordered_pair(v,u),cross_product(y,x)),
inference(clausify,[status(thm)],[prove_cross_product_property2_2]) ).
fof(prove_cross_product_property2_1,axiom,
member(ordered_pair(u,v),cross_product(x,y)),
file('theBenchmark.p',prove_cross_product_property2_1) ).
cnf(c_37,plain,
member(ordered_pair(u,v),cross_product(x,y)),
inference(clausify,[status(thm)],[prove_cross_product_property2_1]) ).
fof(cartesian_product3,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( member(ordered_pair(VAR_0,VAR_2),cross_product(VAR_1,VAR_3))
| ~ member(VAR_2,VAR_3)
| ~ member(VAR_0,VAR_1) ),
file('theBenchmark.p',cartesian_product3) ).
cnf(c_128,plain,
( member(ordered_pair(A,C),cross_product(B,D))
| ~ member(C,D)
| ~ member(A,B) ),
inference(clausify,[status(thm)],[cartesian_product3]) ).
fof(cartesian_product2,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( member(VAR_1,VAR_3)
| ~ member(ordered_pair(VAR_0,VAR_1),cross_product(VAR_2,VAR_3)) ),
file('theBenchmark.p',cartesian_product2) ).
cnf(c_129,plain,
( member(B,D)
| ~ member(ordered_pair(A,B),cross_product(C,D)) ),
inference(clausify,[status(thm)],[cartesian_product2]) ).
fof(cartesian_product1,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( member(VAR_0,VAR_2)
| ~ member(ordered_pair(VAR_0,VAR_1),cross_product(VAR_2,VAR_3)) ),
file('theBenchmark.p',cartesian_product1) ).
cnf(c_130,plain,
( member(A,C)
| ~ member(ordered_pair(A,B),cross_product(C,D)) ),
inference(clausify,[status(thm)],[cartesian_product1]) ).
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_555,plain,
( member(A,C)
| ~ member(unordered_pair(singleton(A),unordered_pair(A,singleton(B))),cross_product(C,D)) ),
inference(paramod,[status(thm)],[c_132,c_130]) ).
cnf(c_556,plain,
( member(A,C)
| ~ member(unordered_pair(unordered_pair(A,A),unordered_pair(A,singleton(B))),cross_product(C,D)) ),
inference(paramod,[status(thm)],[c_134,c_555]) ).
cnf(c_234,plain,
( member(A,C)
| ~ member(unordered_pair(unordered_pair(A,A),unordered_pair(A,unordered_pair(B,B))),cross_product(C,D)) ),
inference(paramod,[status(thm)],[c_134,c_556]) ).
cnf(c_557,plain,
( member(B,D)
| ~ member(unordered_pair(singleton(A),unordered_pair(A,singleton(B))),cross_product(C,D)) ),
inference(paramod,[status(thm)],[c_132,c_129]) ).
cnf(c_558,plain,
( member(B,D)
| ~ member(unordered_pair(unordered_pair(A,A),unordered_pair(A,singleton(B))),cross_product(C,D)) ),
inference(paramod,[status(thm)],[c_134,c_557]) ).
cnf(c_235,plain,
( member(B,D)
| ~ member(unordered_pair(unordered_pair(A,A),unordered_pair(A,unordered_pair(B,B))),cross_product(C,D)) ),
inference(paramod,[status(thm)],[c_134,c_558]) ).
cnf(c_559,plain,
( member(unordered_pair(singleton(A),unordered_pair(A,singleton(C))),cross_product(B,D))
| ~ member(C,D)
| ~ member(A,B) ),
inference(paramod,[status(thm)],[c_132,c_128]) ).
cnf(c_560,plain,
( member(unordered_pair(unordered_pair(A,A),unordered_pair(A,singleton(C))),cross_product(B,D))
| ~ member(C,D)
| ~ member(A,B) ),
inference(paramod,[status(thm)],[c_134,c_559]) ).
cnf(c_236,plain,
( member(unordered_pair(unordered_pair(A,A),unordered_pair(A,unordered_pair(C,C))),cross_product(B,D))
| ~ member(C,D)
| ~ member(A,B) ),
inference(paramod,[status(thm)],[c_134,c_560]) ).
cnf(c_561,plain,
member(unordered_pair(singleton(u),unordered_pair(u,singleton(v))),cross_product(x,y)),
inference(paramod,[status(thm)],[c_132,c_37]) ).
cnf(c_562,plain,
member(unordered_pair(unordered_pair(u,u),unordered_pair(u,singleton(v))),cross_product(x,y)),
inference(paramod,[status(thm)],[c_134,c_561]) ).
cnf(c_251,plain,
member(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v))),cross_product(x,y)),
inference(paramod,[status(thm)],[c_134,c_562]) ).
cnf(c_563,plain,
~ member(unordered_pair(singleton(v),unordered_pair(v,singleton(u))),cross_product(y,x)),
inference(paramod,[status(thm)],[c_132,c_36]) ).
cnf(c_564,plain,
~ member(unordered_pair(unordered_pair(v,v),unordered_pair(v,singleton(u))),cross_product(y,x)),
inference(paramod,[status(thm)],[c_134,c_563]) ).
cnf(c_252,plain,
~ member(unordered_pair(unordered_pair(v,v),unordered_pair(v,unordered_pair(u,u))),cross_product(y,x)),
inference(paramod,[status(thm)],[c_134,c_564]) ).
cnf(c_467,plain,
member(v,y),
inference(resolve,[status(thm)],[c_251,c_235]) ).
cnf(c_468,plain,
member(u,x),
inference(resolve,[status(thm)],[c_251,c_234]) ).
cnf(c_565,plain,
( member(unordered_pair(unordered_pair(v,v),unordered_pair(v,unordered_pair(A,A))),cross_product(y,B))
| ~ member(A,B) ),
inference(resolve,[status(thm)],[c_236,c_467]) ).
cnf(c_566,plain,
member(unordered_pair(unordered_pair(v,v),unordered_pair(v,unordered_pair(u,u))),cross_product(y,x)),
inference(resolve,[status(thm)],[c_565,c_468]) ).
cnf(c_554,plain,
$false,
inference(resolve,[status(thm)],[c_252,c_566]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET204-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.33 % Computer : n006.cluster.edu
% 0.07/0.33 % Model : x86_64 x86_64
% 0.07/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.33 % Memory : 8046.5625MB
% 0.07/0.33 % OS : Linux 6.8.0-71-generic
% 0.07/0.33 % CPULimit : 300
% 0.07/0.33 % WCLimit : 300
% 0.07/0.33 % DateTime : Sat Sep 26 07:19:11 UTC 2026
% 0.07/0.34 % CPUTime :
% 0.07/0.34 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.07/0.34 % Process 668196 was started by sandbox on n006,
% 0.07/0.34 % Sat Sep 26 07:19:11 2026
% 0.07/0.34 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.07/0.34
% 0.07/0.34 % From the command line: assign(max_seconds, 300).
% 0.12/0.45
% 0.12/0.45 % SZS status Unsatisfiable for theBenchmark
% 0.12/0.45
% 0.12/0.45 % Proof 1 at 0.08 (+ 0.02) seconds.
% 0.12/0.45 % Length of proof is 17.
% 0.12/0.45 % Level of proof is 4.
% 0.12/0.45 % Maximum clause weight is 54.000.
% 0.12/0.45 % Given clauses 132.
% 0.12/0.45
% 0.12/0.45 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------