%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET962+1 : TPTP v9.3.1. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n003.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 08:37:22 AM UTC 2026
% Result : Theorem 0.13s 0.38s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 5
% Syntax : Number of formulae : 40 ( 13 unt; 0 def)
% Number of atoms : 93 ( 33 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 78 ( 25 ~; 42 |; 6 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 76 ( 5 sgn 23 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(commutativity_k2_tarski,axiom,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
file('theBenchmark.p',commutativity_k2_tarski) ).
fof(d5_tarski,axiom,
! [A,B] : ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A)),
file('theBenchmark.p',d5_tarski) ).
fof(l55_zfmisc_1,axiom,
! [A,B,C,D] :
( in(ordered_pair(A,B),cartesian_product2(C,D))
<=> ( in(B,D)
& in(A,C) ) ),
file('theBenchmark.p',l55_zfmisc_1) ).
fof(t2_tarski,axiom,
! [A,B] :
( ! [C] :
( in(C,A)
<=> in(C,B) )
=> A = B ),
file('theBenchmark.p',t2_tarski) ).
fof(t115_zfmisc_1,conjecture,
! [A,B] :
( cartesian_product2(A,A) = cartesian_product2(B,B)
=> A = B ),
file('theBenchmark.p',t115_zfmisc_1) ).
fof(t115_zfmisc_1_neg,negated_conjecture,
~ ! [A,B] :
( cartesian_product2(A,A) = cartesian_product2(B,B)
=> A = B ),
inference(assume_negation,[status(cth)],[t115_zfmisc_1]) ).
cnf(c_11,plain,
unordered_pair(A,B) = unordered_pair(B,A),
inference(clausify,[status(thm)],[commutativity_k2_tarski]) ).
cnf(c_12,plain,
ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A)),
inference(clausify,[status(thm)],[d5_tarski]) ).
cnf(c_13,plain,
ordered_pair(A,B) = unordered_pair(singleton(A),unordered_pair(A,B)),
inference(paramod,[status(thm)],[c_11,c_12]) ).
cnf(c_18,plain,
( in(B,D)
| ~ in(ordered_pair(A,B),cartesian_product2(C,D)) ),
inference(clausify,[status(thm)],[l55_zfmisc_1]) ).
cnf(c_19,plain,
( in(B,D)
| ~ in(unordered_pair(singleton(A),unordered_pair(A,B)),cartesian_product2(C,D)) ),
inference(paramod,[status(thm)],[c_13,c_18]) ).
cnf(c_20,plain,
( ~ in(B,D)
| ~ in(A,C)
| in(ordered_pair(A,B),cartesian_product2(C,D)) ),
inference(clausify,[status(thm)],[l55_zfmisc_1]) ).
cnf(c_21,plain,
( ~ in(B,D)
| ~ in(A,C)
| in(unordered_pair(singleton(A),unordered_pair(A,B)),cartesian_product2(C,D)) ),
inference(paramod,[status(thm)],[c_13,c_20]) ).
fof(nnf_8,plain,
! [A,B] :
( B = A
| ? [C] :
( ( ~ in(C,B)
| ~ in(C,A) )
& ( in(C,B)
| in(C,A) ) ) ),
inference(fof_nnf,[status(thm)],[t2_tarski]) ).
fof(sk_t2_tarski_sk,plain,
! [A,B] :
( B = A
| ( ( ~ in(sK0(A,B),B)
| ~ in(sK0(A,B),A) )
& ( in(sK0(A,B),B)
| in(sK0(A,B),A) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(C,sK0(A,B))],[nnf_8]) ).
fof(sk_t2_tarski,plain,
( ! [VAR_0,VAR_1] :
( VAR_1 = VAR_0
| ~ in(sK0(VAR_0,VAR_1),VAR_1)
| ~ in(sK0(VAR_0,VAR_1),VAR_0) )
& ! [VAR_0,VAR_1] :
( VAR_1 = VAR_0
| in(sK0(VAR_0,VAR_1),VAR_1)
| in(sK0(VAR_0,VAR_1),VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_t2_tarski_sk]) ).
cnf(c_24,plain,
( B = A
| in(sK0(A,B),B)
| in(sK0(A,B),A) ),
inference(split_conjunct,[status(thm)],[sk_t2_tarski]) ).
cnf(c_25,plain,
( B = A
| ~ in(sK0(A,B),B)
| ~ in(sK0(A,B),A) ),
inference(split_conjunct,[status(thm)],[sk_t2_tarski]) ).
fof(nnf_9,plain,
? [A,B] :
( B != A
& cartesian_product2(B,B) = cartesian_product2(A,A) ),
inference(fof_nnf,[status(thm)],[t115_zfmisc_1_neg]) ).
fof(sk_t115_zfmisc_1_neg,plain,
( sK1 != sK2
& cartesian_product2(sK1,sK1) = cartesian_product2(sK2,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(A,sK2),skolemize(B,sK1)],[nnf_9]) ).
cnf(c_26,negated_conjecture,
cartesian_product2(sK1,sK1) = cartesian_product2(sK2,sK2),
inference(split_conjunct,[status(thm)],[sk_t115_zfmisc_1_neg]) ).
cnf(c_27,negated_conjecture,
sK1 != sK2,
inference(split_conjunct,[status(thm)],[sk_t115_zfmisc_1_neg]) ).
cnf(c_29,plain,
( ~ in(A,B)
| in(unordered_pair(singleton(A),unordered_pair(A,A)),cartesian_product2(B,B)) ),
inference(factor,[status(thm)],[c_21]) ).
cnf(c_32,plain,
( in(B,D)
| ~ in(unordered_pair(singleton(A),unordered_pair(B,A)),cartesian_product2(C,D)) ),
inference(paramod,[status(thm)],[c_11,c_19]) ).
cnf(c_167,plain,
( B = A
| in(sK0(A,B),B)
| ~ in(C,D)
| in(unordered_pair(singleton(sK0(A,B)),unordered_pair(sK0(A,B),C)),cartesian_product2(A,D)) ),
inference(resolve,[status(thm)],[c_21,c_24]) ).
cnf(c_40,plain,
( D = C
| in(sK0(C,D),D)
| B = A
| in(sK0(A,B),B)
| in(unordered_pair(singleton(sK0(A,B)),unordered_pair(sK0(A,B),sK0(C,D))),cartesian_product2(A,C)) ),
inference(resolve,[status(thm)],[c_167,c_24]) ).
cnf(c_168,plain,
( B = A
| B = A
| in(sK0(A,B),B)
| in(unordered_pair(singleton(sK0(A,B)),unordered_pair(sK0(A,B),sK0(A,B))),cartesian_product2(A,A)) ),
inference(factor,[status(thm)],[c_40]) ).
cnf(c_43,plain,
( B = A
| in(sK0(A,B),B)
| in(unordered_pair(singleton(sK0(A,B)),unordered_pair(sK0(A,B),sK0(A,B))),cartesian_product2(A,A)) ),
inference(copy,[status(thm)],[c_168]) ).
cnf(c_72,plain,
( in(B,sK1)
| ~ in(unordered_pair(singleton(A),unordered_pair(B,A)),cartesian_product2(sK2,sK2)) ),
inference(paramod,[status(thm)],[c_26,c_32]) ).
cnf(c_169,plain,
( in(sK0(sK2,A),sK1)
| A = sK2
| in(sK0(sK2,A),A) ),
inference(resolve,[status(thm)],[c_43,c_72]) ).
cnf(c_97,plain,
( in(sK0(sK2,A),sK1)
| sK2 = A
| in(sK0(sK2,A),A) ),
inference(copy,[status(thm)],[c_169]) ).
cnf(c_170,plain,
( sK2 = sK1
| in(sK0(sK2,sK1),sK1) ),
inference(factor,[status(thm)],[c_97]) ).
cnf(c_171,plain,
( sK1 = sK2
| in(sK0(sK2,sK1),sK1) ),
inference(copy,[status(thm)],[c_170]) ).
cnf(c_104,negated_conjecture,
in(sK0(sK2,sK1),sK1),
inference(resolve,[status(thm)],[c_27,c_171]) ).
cnf(c_172,plain,
in(unordered_pair(singleton(sK0(sK2,sK1)),unordered_pair(sK0(sK2,sK1),sK0(sK2,sK1))),cartesian_product2(sK1,sK1)),
inference(resolve,[status(thm)],[c_104,c_29]) ).
cnf(c_117,plain,
in(unordered_pair(singleton(sK0(sK2,sK1)),unordered_pair(sK0(sK2,sK1),sK0(sK2,sK1))),cartesian_product2(sK2,sK2)),
inference(paramod,[status(thm)],[c_26,c_172]) ).
cnf(c_173,plain,
( sK1 = sK2
| ~ in(sK0(sK2,sK1),sK2) ),
inference(resolve,[status(thm)],[c_104,c_25]) ).
cnf(c_118,negated_conjecture,
~ in(sK0(sK2,sK1),sK2),
inference(resolve,[status(thm)],[c_27,c_173]) ).
cnf(c_165,plain,
~ in(unordered_pair(singleton(A),unordered_pair(sK0(sK2,sK1),A)),cartesian_product2(B,sK2)),
inference(resolve,[status(thm)],[c_32,c_118]) ).
cnf(c_166,plain,
$false,
inference(resolve,[status(thm)],[c_165,c_117]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET962+1 : TPTP v9.3.1. Bugfixed v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.35 % Computer : n003.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Sat Sep 26 08:29:08 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.07/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.07/0.35 % Process 2444280 was started by sandbox on n003,
% 0.07/0.35 % Sat Sep 26 08:29:08 2026
% 0.07/0.35 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.07/0.36
% 0.07/0.36 % From the command line: assign(max_seconds, 300).
% 0.13/0.38
% 0.13/0.38 % Assigning unary symbol singleton kb_weight 0 and highest precedence (12).
% 0.13/0.38
% 0.13/0.38 % SZS status Theorem for theBenchmark
% 0.13/0.38
% 0.13/0.38 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.13/0.38 % Length of proof is 27.
% 0.13/0.38 % Level of proof is 10.
% 0.13/0.38 % Maximum clause weight is 57.000.
% 0.13/0.38 % Given clauses 47.
% 0.13/0.38
% 0.13/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------