%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET949+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n013.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 08:37:21 AM UTC 2026
% Result : Theorem 0.09s 0.45s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 23 ( 10 unt; 0 def)
% Number of atoms : 100 ( 48 equ)
% Maximal formula atoms : 28 ( 4 avg)
% Number of connectives : 128 ( 51 ~; 48 |; 27 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 3 con; 0-4 aty)
% Number of variables : 108 ( 6 sgn 70 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(commutativity_k2_tarski,axiom,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
file('theBenchmark.p',commutativity_k2_tarski) ).
fof(d2_zfmisc_1,axiom,
! [A,B,C] :
( C = cartesian_product2(A,B)
<=> ! [D] :
( in(D,C)
<=> ? [E,F] :
( D = ordered_pair(E,F)
& in(F,B)
& in(E,A) ) ) ),
file('theBenchmark.p',d2_zfmisc_1) ).
fof(d5_tarski,axiom,
! [A,B] : ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A)),
file('theBenchmark.p',d5_tarski) ).
fof(t102_zfmisc_1,conjecture,
! [A,B,C] :
~ ( ! [D,E] : ordered_pair(D,E) != A
& in(A,cartesian_product2(B,C)) ),
file('theBenchmark.p',t102_zfmisc_1) ).
fof(t102_zfmisc_1_neg,negated_conjecture,
~ ! [A,B,C] :
~ ( ! [D,E] : ordered_pair(D,E) != A
& in(A,cartesian_product2(B,C)) ),
inference(assume_negation,[status(cth)],[t102_zfmisc_1]) ).
cnf(c_10,plain,
unordered_pair(A,B) = unordered_pair(B,A),
inference(clausify,[status(thm)],[commutativity_k2_tarski]) ).
fof(nnf_3,plain,
! [A,B,C] :
( ( ? [D] :
( ( ! [E,F] :
( ordered_pair(E,F) != D
| ~ in(F,B)
| ~ in(E,A) )
| ~ in(D,C) )
& ( ? [X5,X6] :
( ordered_pair(X5,X6) = D
& in(X6,B)
& in(X5,A) )
| in(D,C) ) )
| cartesian_product2(A,B) = C )
& ( ! [X0] :
( ( ! [X3,X4] :
( ordered_pair(X3,X4) != X0
| ~ in(X4,B)
| ~ in(X3,A) )
| in(X0,C) )
& ( ? [X1,X2] :
( ordered_pair(X1,X2) = X0
& in(X2,B)
& in(X1,A) )
| ~ in(X0,C) ) )
| cartesian_product2(A,B) != C ) ),
inference(fof_nnf,[status(thm)],[d2_zfmisc_1]) ).
fof(sk_d2_zfmisc_1_sk,plain,
! [A,B,C] :
( ( ( ( ! [E,F] :
( ordered_pair(E,F) != sK5(A,B,C)
| ~ in(F,B)
| ~ in(E,A) )
| ~ in(sK5(A,B,C),C) )
& ( ( ordered_pair(sK6(A,B,C),sK7(A,B,C)) = sK5(A,B,C)
& in(sK7(A,B,C),B)
& in(sK6(A,B,C),A) )
| in(sK5(A,B,C),C) ) )
| cartesian_product2(A,B) = C )
& ( ! [X0] :
( ( ! [X3,X4] :
( ordered_pair(X3,X4) != X0
| ~ in(X4,B)
| ~ in(X3,A) )
| in(X0,C) )
& ( ( ordered_pair(sK0(A,B,C,X0),sK1(A,B,C,X0)) = X0
& in(sK1(A,B,C,X0),B)
& in(sK0(A,B,C,X0),A) )
| ~ in(X0,C) ) )
| cartesian_product2(A,B) != C ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK5,sK6,sK7]),skolemize(X1,sK0(A,B,C,X0)),skolemize(X2,sK1(A,B,C,X0)),skolemize(D,sK5(A,B,C)),skolemize(X5,sK6(A,B,C)),skolemize(X6,sK7(A,B,C))],[nnf_3]) ).
fof(sk_d2_zfmisc_1,plain,
( ! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4] :
( ordered_pair(VAR_3,VAR_4) != sK5(VAR_0,VAR_1,VAR_2)
| ~ in(VAR_4,VAR_1)
| ~ in(VAR_3,VAR_0)
| ~ in(sK5(VAR_0,VAR_1,VAR_2),VAR_2)
| cartesian_product2(VAR_0,VAR_1) = VAR_2 )
& ! [VAR_0,VAR_1,VAR_2] :
( ordered_pair(sK6(VAR_0,VAR_1,VAR_2),sK7(VAR_0,VAR_1,VAR_2)) = sK5(VAR_0,VAR_1,VAR_2)
| in(sK5(VAR_0,VAR_1,VAR_2),VAR_2)
| cartesian_product2(VAR_0,VAR_1) = VAR_2 )
& ! [VAR_0,VAR_1,VAR_2] :
( in(sK7(VAR_0,VAR_1,VAR_2),VAR_1)
| in(sK5(VAR_0,VAR_1,VAR_2),VAR_2)
| cartesian_product2(VAR_0,VAR_1) = VAR_2 )
& ! [VAR_0,VAR_1,VAR_2] :
( in(sK6(VAR_0,VAR_1,VAR_2),VAR_0)
| in(sK5(VAR_0,VAR_1,VAR_2),VAR_2)
| cartesian_product2(VAR_0,VAR_1) = VAR_2 )
& ! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5] :
( ordered_pair(VAR_4,VAR_5) != VAR_3
| ~ in(VAR_5,VAR_1)
| ~ in(VAR_4,VAR_0)
| in(VAR_3,VAR_2)
| cartesian_product2(VAR_0,VAR_1) != VAR_2 )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ordered_pair(sK0(VAR_0,VAR_1,VAR_2,VAR_3),sK1(VAR_0,VAR_1,VAR_2,VAR_3)) = VAR_3
| ~ in(VAR_3,VAR_2)
| cartesian_product2(VAR_0,VAR_1) != VAR_2 )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( in(sK1(VAR_0,VAR_1,VAR_2,VAR_3),VAR_1)
| ~ in(VAR_3,VAR_2)
| cartesian_product2(VAR_0,VAR_1) != VAR_2 )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( in(sK0(VAR_0,VAR_1,VAR_2,VAR_3),VAR_0)
| ~ in(VAR_3,VAR_2)
| cartesian_product2(VAR_0,VAR_1) != VAR_2 ) ),
inference(cnf_transformation,[status(thm)],[sk_d2_zfmisc_1_sk]) ).
cnf(c_13,plain,
( ordered_pair(sK0(A,B,C,D),sK1(A,B,C,D)) = D
| ~ in(D,C)
| cartesian_product2(A,B) != C ),
inference(split_conjunct,[status(thm)],[sk_d2_zfmisc_1]) ).
cnf(c_20,plain,
ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A)),
inference(clausify,[status(thm)],[d5_tarski]) ).
fof(nnf_8,plain,
? [A,B,C] :
( ! [D,E] : ordered_pair(D,E) != A
& in(A,cartesian_product2(B,C)) ),
inference(fof_nnf,[status(thm)],[t102_zfmisc_1_neg]) ).
fof(sk_t102_zfmisc_1_neg,plain,
( ! [D,E] : ordered_pair(D,E) != sK2
& in(sK2,cartesian_product2(sK3,sK4)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4]),skolemize(A,sK2),skolemize(B,sK3),skolemize(C,sK4)],[nnf_8]) ).
cnf(c_25,negated_conjecture,
in(sK2,cartesian_product2(sK3,sK4)),
inference(split_conjunct,[status(thm)],[sk_t102_zfmisc_1_neg]) ).
cnf(c_26,negated_conjecture,
ordered_pair(A,B) != sK2,
inference(split_conjunct,[status(thm)],[sk_t102_zfmisc_1_neg]) ).
cnf(c_27,negated_conjecture,
unordered_pair(unordered_pair(A,B),singleton(A)) != sK2,
inference(paramod,[status(thm)],[c_20,c_26]) ).
cnf(c_105,plain,
( unordered_pair(unordered_pair(sK0(A,B,C,D),sK1(A,B,C,D)),singleton(sK0(A,B,C,D))) = D
| ~ in(D,C)
| cartesian_product2(A,B) != C ),
inference(paramod,[status(thm)],[c_20,c_13]) ).
cnf(c_36,plain,
( unordered_pair(singleton(sK0(A,B,C,D)),unordered_pair(sK0(A,B,C,D),sK1(A,B,C,D))) = D
| ~ in(D,C)
| cartesian_product2(A,B) != C ),
inference(paramod,[status(thm)],[c_10,c_105]) ).
cnf(c_50,plain,
unordered_pair(singleton(A),unordered_pair(A,B)) != sK2,
inference(paramod,[status(thm)],[c_10,c_27]) ).
cnf(c_106,negated_conjecture,
( unordered_pair(singleton(sK0(A,B,cartesian_product2(sK3,sK4),sK2)),unordered_pair(sK0(A,B,cartesian_product2(sK3,sK4),sK2),sK1(A,B,cartesian_product2(sK3,sK4),sK2))) = sK2
| cartesian_product2(A,B) != cartesian_product2(sK3,sK4) ),
inference(resolve,[status(thm)],[c_36,c_25]) ).
cnf(c_107,negated_conjecture,
( unordered_pair(singleton(sK0(A,B,cartesian_product2(sK3,sK4),sK2)),unordered_pair(sK0(A,B,cartesian_product2(sK3,sK4),sK2),sK1(A,B,cartesian_product2(sK3,sK4),sK2))) = sK2
| cartesian_product2(sK3,sK4) != cartesian_product2(A,B) ),
inference(copy,[status(thm)],[c_106]) ).
cnf(c_98,negated_conjecture,
cartesian_product2(sK3,sK4) != cartesian_product2(A,B),
inference(resolve,[status(thm)],[c_50,c_107]) ).
cnf(c_104,plain,
$false,
inference(xxres,[status(thm)],[c_98]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET949+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.41 % Computer : n013.cluster.edu
% 0.09/0.41 % Model : x86_64 x86_64
% 0.09/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.41 % Memory : 8046.5625MB
% 0.09/0.41 % OS : Linux 6.8.0-71-generic
% 0.09/0.41 % CPULimit : 300
% 0.09/0.41 % WCLimit : 300
% 0.09/0.41 % DateTime : Sat Sep 26 08:26:21 UTC 2026
% 0.09/0.41 % CPUTime :
% 0.09/0.41 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.41 % Process 2329347 was started by sandbox on n013,
% 0.09/0.41 % Sat Sep 26 08:26:21 2026
% 0.09/0.41 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.42
% 0.09/0.42 % From the command line: assign(max_seconds, 300).
% 0.09/0.45
% 0.09/0.45 % SZS status Theorem for theBenchmark
% 0.09/0.45
% 0.09/0.45 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.09/0.45 % Length of proof is 14.
% 0.09/0.45 % Level of proof is 5.
% 0.09/0.45 % Maximum clause weight is 28.000.
% 0.09/0.45 % Given clauses 27.
% 0.09/0.45
% 0.09/0.45 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------