%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET017-6 : 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 : n020.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 08:35:20 AM UTC 2026
% Result : Unsatisfiable 0.13s 0.64s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 9
% Syntax : Number of formulae : 48 ( 32 unt; 0 def)
% Number of atoms : 66 ( 24 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 41 ( 23 ~; 18 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 4 ( 1 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 : 62 ( 15 sgn 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_left_cancellation_3,axiom,
y != z,
file('theBenchmark.p',prove_left_cancellation_3) ).
cnf(c_34,plain,
y != z,
inference(clausify,[status(thm)],[prove_left_cancellation_3]) ).
cnf(c_35,plain,
z != y,
inference(copy,[status(thm)],[c_34]) ).
fof(prove_left_cancellation_2,axiom,
member(ordered_pair(y,z),cross_product(universal_class,universal_class)),
file('theBenchmark.p',prove_left_cancellation_2) ).
cnf(c_36,plain,
member(ordered_pair(y,z),cross_product(universal_class,universal_class)),
inference(clausify,[status(thm)],[prove_left_cancellation_2]) ).
fof(prove_left_cancellation_1,axiom,
unordered_pair(x,y) = unordered_pair(x,z),
file('theBenchmark.p',prove_left_cancellation_1) ).
cnf(c_37,plain,
unordered_pair(x,y) = unordered_pair(x,z),
inference(clausify,[status(thm)],[prove_left_cancellation_1]) ).
cnf(c_38,plain,
unordered_pair(x,z) = unordered_pair(x,y),
inference(copy,[status(thm)],[c_37]) ).
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_108,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_109,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_110,plain,
unordered_pair(singleton(A),unordered_pair(A,singleton(B))) = ordered_pair(A,B),
inference(clausify,[status(thm)],[ordered_pair]) ).
cnf(c_111,plain,
ordered_pair(A,B) = unordered_pair(singleton(A),unordered_pair(A,singleton(B))),
inference(copy,[status(thm)],[c_110]) ).
fof(singleton_set,axiom,
! [VAR_0] : unordered_pair(VAR_0,VAR_0) = singleton(VAR_0),
file('theBenchmark.p',singleton_set) ).
cnf(c_112,plain,
unordered_pair(A,A) = singleton(A),
inference(clausify,[status(thm)],[singleton_set]) ).
cnf(c_113,plain,
singleton(A) = unordered_pair(A,A),
inference(copy,[status(thm)],[c_112]) ).
fof(unordered_pair3,axiom,
! [VAR_0,VAR_1] :
( member(VAR_0,unordered_pair(VAR_1,VAR_0))
| ~ member(VAR_0,universal_class) ),
file('theBenchmark.p',unordered_pair3) ).
cnf(c_115,plain,
( member(A,unordered_pair(B,A))
| ~ member(A,universal_class) ),
inference(clausify,[status(thm)],[unordered_pair3]) ).
fof(unordered_pair_member,axiom,
! [VAR_0,VAR_1,VAR_2] :
( VAR_0 = VAR_2
| VAR_0 = VAR_1
| ~ member(VAR_0,unordered_pair(VAR_1,VAR_2)) ),
file('theBenchmark.p',unordered_pair_member) ).
cnf(c_117,plain,
( A = C
| A = B
| ~ member(A,unordered_pair(B,C)) ),
inference(clausify,[status(thm)],[unordered_pair_member]) ).
cnf(c_1005,plain,
( member(A,C)
| ~ member(unordered_pair(singleton(A),unordered_pair(A,singleton(B))),cross_product(C,D)) ),
inference(paramod,[status(thm)],[c_111,c_109]) ).
cnf(c_1006,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_113,c_1005]) ).
cnf(c_188,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_113,c_1006]) ).
cnf(c_1007,plain,
( member(B,D)
| ~ member(unordered_pair(singleton(A),unordered_pair(A,singleton(B))),cross_product(C,D)) ),
inference(paramod,[status(thm)],[c_111,c_108]) ).
cnf(c_1008,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_113,c_1007]) ).
cnf(c_189,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_113,c_1008]) ).
cnf(c_1009,plain,
member(unordered_pair(singleton(y),unordered_pair(y,singleton(z))),cross_product(universal_class,universal_class)),
inference(paramod,[status(thm)],[c_111,c_36]) ).
cnf(c_1010,plain,
member(unordered_pair(unordered_pair(y,y),unordered_pair(y,singleton(z))),cross_product(universal_class,universal_class)),
inference(paramod,[status(thm)],[c_113,c_1009]) ).
cnf(c_198,plain,
member(unordered_pair(unordered_pair(y,y),unordered_pair(y,unordered_pair(z,z))),cross_product(universal_class,universal_class)),
inference(paramod,[status(thm)],[c_113,c_1010]) ).
cnf(c_1011,plain,
y != z,
inference(copy,[status(thm)],[c_35]) ).
cnf(c_1012,plain,
( y = A
| ~ member(y,unordered_pair(z,A)) ),
inference(resolve,[status(thm)],[c_117,c_1011]) ).
cnf(c_1013,plain,
y != z,
inference(copy,[status(thm)],[c_35]) ).
cnf(c_232,plain,
~ member(y,unordered_pair(z,z)),
inference(resolve,[status(thm)],[c_1012,c_1013]) ).
cnf(c_333,plain,
member(z,universal_class),
inference(resolve,[status(thm)],[c_198,c_189]) ).
cnf(c_334,plain,
member(y,universal_class),
inference(resolve,[status(thm)],[c_198,c_188]) ).
cnf(c_379,plain,
member(z,unordered_pair(A,z)),
inference(resolve,[status(thm)],[c_333,c_115]) ).
cnf(c_395,plain,
member(y,unordered_pair(A,y)),
inference(resolve,[status(thm)],[c_334,c_115]) ).
cnf(c_505,plain,
member(z,unordered_pair(x,y)),
inference(paramod,[status(thm)],[c_38,c_379]) ).
cnf(c_1014,plain,
( z = y
| z = x ),
inference(resolve,[status(thm)],[c_505,c_117]) ).
cnf(c_574,plain,
z = x,
inference(resolve,[status(thm)],[c_35,c_1014]) ).
cnf(c_1015,plain,
~ member(y,unordered_pair(x,z)),
inference(paramod,[status(thm)],[c_574,c_232]) ).
cnf(c_666,plain,
~ member(y,unordered_pair(x,x)),
inference(paramod,[status(thm)],[c_574,c_1015]) ).
cnf(c_1016,plain,
unordered_pair(x,x) = unordered_pair(x,y),
inference(paramod,[status(thm)],[c_574,c_38]) ).
cnf(c_669,plain,
unordered_pair(x,y) = unordered_pair(x,x),
inference(copy,[status(thm)],[c_1016]) ).
cnf(c_1017,plain,
member(y,unordered_pair(x,x)),
inference(paramod,[status(thm)],[c_669,c_395]) ).
cnf(c_1004,plain,
$false,
inference(resolve,[status(thm)],[c_666,c_1017]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET017-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.53 % Computer : n020.cluster.edu
% 0.09/0.53 % Model : x86_64 x86_64
% 0.09/0.53 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.53 % Memory : 8046.5625MB
% 0.09/0.53 % OS : Linux 6.8.0-71-generic
% 0.09/0.53 % CPULimit : 300
% 0.09/0.53 % WCLimit : 300
% 0.09/0.53 % DateTime : Sat Sep 26 06:52:20 UTC 2026
% 0.09/0.53 % CPUTime :
% 0.09/0.53 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.53 % Process 895303 was started by sandbox on n020,
% 0.09/0.53 % Sat Sep 26 06:52:20 2026
% 0.09/0.53 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.54
% 0.09/0.54 % From the command line: assign(max_seconds, 300).
% 0.13/0.64
% 0.13/0.64 % SZS status Unsatisfiable for theBenchmark
% 0.13/0.64
% 0.13/0.64 % Proof 1 at 0.08 (+ 0.01) seconds.
% 0.13/0.64 % Length of proof is 26.
% 0.13/0.64 % Level of proof is 8.
% 0.13/0.64 % Maximum clause weight is 16.000.
% 0.13/0.64 % Given clauses 189.
% 0.13/0.64
% 0.13/0.64 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------