%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET959+1 : TPTP v9.3.1. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n004.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 0.08s 0.38s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 4
% Syntax : Number of formulae : 58 ( 10 unt; 0 def)
% Number of atoms : 156 ( 63 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 150 ( 52 ~; 73 |; 19 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 2 con; 0-2 aty)
% Number of variables : 81 ( 0 sgn 43 !; 7 ?)
% 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(t2_tarski,axiom,
! [A,B] :
( ! [C] :
( in(C,A)
<=> in(C,B) )
=> A = B ),
file('theBenchmark.p',t2_tarski) ).
fof(t112_zfmisc_1,conjecture,
! [A,B] :
( ( ! [C,D] :
( in(ordered_pair(C,D),A)
<=> in(ordered_pair(C,D),B) )
& ! [C] :
~ ( ! [D,E] : C != ordered_pair(D,E)
& in(C,B) )
& ! [C] :
~ ( ! [D,E] : C != ordered_pair(D,E)
& in(C,A) ) )
=> A = B ),
file('theBenchmark.p',t112_zfmisc_1) ).
fof(t112_zfmisc_1_neg,negated_conjecture,
~ ! [A,B] :
( ( ! [C,D] :
( in(ordered_pair(C,D),A)
<=> in(ordered_pair(C,D),B) )
& ! [C] :
~ ( ! [D,E] : C != ordered_pair(D,E)
& in(C,B) )
& ! [C] :
~ ( ! [D,E] : C != ordered_pair(D,E)
& in(C,A) ) )
=> A = B ),
inference(assume_negation,[status(cth)],[t112_zfmisc_1]) ).
cnf(c_10,plain,
unordered_pair(A,B) = unordered_pair(B,A),
inference(clausify,[status(thm)],[commutativity_k2_tarski]) ).
cnf(c_11,plain,
ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A)),
inference(clausify,[status(thm)],[d5_tarski]) ).
fof(nnf_7,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_7]) ).
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_16,plain,
( B = A
| in(sK0(A,B),B)
| in(sK0(A,B),A) ),
inference(split_conjunct,[status(thm)],[sk_t2_tarski]) ).
cnf(c_17,plain,
( B = A
| ~ in(sK0(A,B),B)
| ~ in(sK0(A,B),A) ),
inference(split_conjunct,[status(thm)],[sk_t2_tarski]) ).
fof(nnf_8,plain,
? [A,B] :
( B != A
& ! [C,D] :
( ( ~ in(ordered_pair(C,D),B)
| in(ordered_pair(C,D),A) )
& ( in(ordered_pair(C,D),B)
| ~ in(ordered_pair(C,D),A) ) )
& ! [X3] :
( ? [X4,E] : ordered_pair(X4,E) = X3
| ~ in(X3,B) )
& ! [X0] :
( ? [X1,X2] : ordered_pair(X1,X2) = X0
| ~ in(X0,A) ) ),
inference(fof_nnf,[status(thm)],[t112_zfmisc_1_neg]) ).
fof(sk_t112_zfmisc_1_neg,plain,
( sK4 != sK1
& ! [C,D] :
( ( ~ in(ordered_pair(C,D),sK4)
| in(ordered_pair(C,D),sK1) )
& ( in(ordered_pair(C,D),sK4)
| ~ in(ordered_pair(C,D),sK1) ) )
& ! [X3] :
( ordered_pair(sK5(X3),sK6(X3)) = X3
| ~ in(X3,sK4) )
& ! [X0] :
( ordered_pair(sK2(X0),sK3(X0)) = X0
| ~ in(X0,sK1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3,sK4,sK5,sK6]),skolemize(A,sK1),skolemize(B,sK4),skolemize(X1,sK2(X0)),skolemize(X2,sK3(X0)),skolemize(X4,sK5(X3)),skolemize(E,sK6(X3))],[nnf_8]) ).
cnf(c_18,negated_conjecture,
( ordered_pair(sK2(A),sK3(A)) = A
| ~ in(A,sK1) ),
inference(split_conjunct,[status(thm)],[sk_t112_zfmisc_1_neg]) ).
cnf(c_80,negated_conjecture,
( unordered_pair(unordered_pair(sK2(A),sK3(A)),singleton(sK2(A))) = A
| ~ in(A,sK1) ),
inference(paramod,[status(thm)],[c_11,c_18]) ).
cnf(c_19,negated_conjecture,
( unordered_pair(singleton(sK2(A)),unordered_pair(sK2(A),sK3(A))) = A
| ~ in(A,sK1) ),
inference(paramod,[status(thm)],[c_10,c_80]) ).
cnf(c_20,negated_conjecture,
( ordered_pair(sK5(A),sK6(A)) = A
| ~ in(A,sK4) ),
inference(split_conjunct,[status(thm)],[sk_t112_zfmisc_1_neg]) ).
cnf(c_81,negated_conjecture,
( unordered_pair(unordered_pair(sK5(A),sK6(A)),singleton(sK5(A))) = A
| ~ in(A,sK4) ),
inference(paramod,[status(thm)],[c_11,c_20]) ).
cnf(c_21,negated_conjecture,
( unordered_pair(singleton(sK5(A)),unordered_pair(sK5(A),sK6(A))) = A
| ~ in(A,sK4) ),
inference(paramod,[status(thm)],[c_10,c_81]) ).
cnf(c_22,negated_conjecture,
( in(ordered_pair(A,B),sK4)
| ~ in(ordered_pair(A,B),sK1) ),
inference(split_conjunct,[status(thm)],[sk_t112_zfmisc_1_neg]) ).
cnf(c_82,negated_conjecture,
( in(ordered_pair(A,B),sK4)
| ~ in(unordered_pair(unordered_pair(A,B),singleton(A)),sK1) ),
inference(paramod,[status(thm)],[c_11,c_22]) ).
cnf(c_23,negated_conjecture,
( in(unordered_pair(unordered_pair(A,B),singleton(A)),sK4)
| ~ in(unordered_pair(unordered_pair(A,B),singleton(A)),sK1) ),
inference(paramod,[status(thm)],[c_11,c_82]) ).
cnf(c_24,negated_conjecture,
( ~ in(ordered_pair(A,B),sK4)
| in(ordered_pair(A,B),sK1) ),
inference(split_conjunct,[status(thm)],[sk_t112_zfmisc_1_neg]) ).
cnf(c_83,negated_conjecture,
( ~ in(ordered_pair(A,B),sK4)
| in(unordered_pair(unordered_pair(A,B),singleton(A)),sK1) ),
inference(paramod,[status(thm)],[c_11,c_24]) ).
cnf(c_25,negated_conjecture,
( ~ in(unordered_pair(unordered_pair(A,B),singleton(A)),sK4)
| in(unordered_pair(unordered_pair(A,B),singleton(A)),sK1) ),
inference(paramod,[status(thm)],[c_11,c_83]) ).
cnf(c_26,negated_conjecture,
sK4 != sK1,
inference(split_conjunct,[status(thm)],[sk_t112_zfmisc_1_neg]) ).
cnf(c_32,plain,
( sK1 = A
| in(sK0(A,sK1),A)
| unordered_pair(singleton(sK2(sK0(A,sK1))),unordered_pair(sK2(sK0(A,sK1)),sK3(sK0(A,sK1)))) = sK0(A,sK1) ),
inference(resolve,[status(thm)],[c_19,c_16]) ).
cnf(c_37,plain,
( in(unordered_pair(unordered_pair(A,B),singleton(A)),sK4)
| ~ in(unordered_pair(singleton(A),unordered_pair(A,B)),sK1) ),
inference(paramod,[status(thm)],[c_10,c_23]) ).
cnf(c_39,plain,
( ~ in(unordered_pair(singleton(A),unordered_pair(A,B)),sK4)
| in(unordered_pair(unordered_pair(A,B),singleton(A)),sK1) ),
inference(paramod,[status(thm)],[c_10,c_25]) ).
cnf(c_84,negated_conjecture,
( unordered_pair(singleton(sK5(sK0(sK4,sK1))),unordered_pair(sK5(sK0(sK4,sK1)),sK6(sK0(sK4,sK1)))) = sK0(sK4,sK1)
| sK1 = sK4
| unordered_pair(singleton(sK2(sK0(sK4,sK1))),unordered_pair(sK2(sK0(sK4,sK1)),sK3(sK0(sK4,sK1)))) = sK0(sK4,sK1) ),
inference(resolve,[status(thm)],[c_32,c_21]) ).
cnf(c_85,negated_conjecture,
( unordered_pair(singleton(sK5(sK0(sK4,sK1))),unordered_pair(sK5(sK0(sK4,sK1)),sK6(sK0(sK4,sK1)))) = sK0(sK4,sK1)
| sK4 = sK1
| unordered_pair(singleton(sK2(sK0(sK4,sK1))),unordered_pair(sK2(sK0(sK4,sK1)),sK3(sK0(sK4,sK1)))) = sK0(sK4,sK1) ),
inference(copy,[status(thm)],[c_84]) ).
cnf(c_43,negated_conjecture,
( unordered_pair(singleton(sK5(sK0(sK4,sK1))),unordered_pair(sK5(sK0(sK4,sK1)),sK6(sK0(sK4,sK1)))) = sK0(sK4,sK1)
| unordered_pair(singleton(sK2(sK0(sK4,sK1))),unordered_pair(sK2(sK0(sK4,sK1)),sK3(sK0(sK4,sK1)))) = sK0(sK4,sK1) ),
inference(resolve,[status(thm)],[c_26,c_85]) ).
cnf(c_86,plain,
( ~ in(sK0(sK4,sK1),sK4)
| in(unordered_pair(unordered_pair(sK5(sK0(sK4,sK1)),sK6(sK0(sK4,sK1))),singleton(sK5(sK0(sK4,sK1)))),sK1)
| unordered_pair(singleton(sK2(sK0(sK4,sK1))),unordered_pair(sK2(sK0(sK4,sK1)),sK3(sK0(sK4,sK1)))) = sK0(sK4,sK1) ),
inference(paramod,[status(thm)],[c_43,c_39]) ).
cnf(c_52,plain,
( ~ in(sK0(sK4,sK1),sK4)
| in(unordered_pair(singleton(sK5(sK0(sK4,sK1))),unordered_pair(sK5(sK0(sK4,sK1)),sK6(sK0(sK4,sK1)))),sK1)
| unordered_pair(singleton(sK2(sK0(sK4,sK1))),unordered_pair(sK2(sK0(sK4,sK1)),sK3(sK0(sK4,sK1)))) = sK0(sK4,sK1) ),
inference(paramod,[status(thm)],[c_10,c_86]) ).
cnf(c_87,plain,
( sK1 = sK4
| unordered_pair(singleton(sK2(sK0(sK4,sK1))),unordered_pair(sK2(sK0(sK4,sK1)),sK3(sK0(sK4,sK1)))) = sK0(sK4,sK1)
| in(unordered_pair(singleton(sK5(sK0(sK4,sK1))),unordered_pair(sK5(sK0(sK4,sK1)),sK6(sK0(sK4,sK1)))),sK1)
| unordered_pair(singleton(sK2(sK0(sK4,sK1))),unordered_pair(sK2(sK0(sK4,sK1)),sK3(sK0(sK4,sK1)))) = sK0(sK4,sK1) ),
inference(resolve,[status(thm)],[c_52,c_32]) ).
cnf(c_88,plain,
( sK4 = sK1
| unordered_pair(singleton(sK2(sK0(sK4,sK1))),unordered_pair(sK2(sK0(sK4,sK1)),sK3(sK0(sK4,sK1)))) = sK0(sK4,sK1)
| in(unordered_pair(singleton(sK5(sK0(sK4,sK1))),unordered_pair(sK5(sK0(sK4,sK1)),sK6(sK0(sK4,sK1)))),sK1)
| unordered_pair(singleton(sK2(sK0(sK4,sK1))),unordered_pair(sK2(sK0(sK4,sK1)),sK3(sK0(sK4,sK1)))) = sK0(sK4,sK1) ),
inference(copy,[status(thm)],[c_87]) ).
cnf(c_89,plain,
( sK4 = sK1
| in(unordered_pair(singleton(sK5(sK0(sK4,sK1))),unordered_pair(sK5(sK0(sK4,sK1)),sK6(sK0(sK4,sK1)))),sK1)
| unordered_pair(singleton(sK2(sK0(sK4,sK1))),unordered_pair(sK2(sK0(sK4,sK1)),sK3(sK0(sK4,sK1)))) = sK0(sK4,sK1) ),
inference(copy,[status(thm)],[c_88]) ).
cnf(c_57,negated_conjecture,
( in(unordered_pair(singleton(sK5(sK0(sK4,sK1))),unordered_pair(sK5(sK0(sK4,sK1)),sK6(sK0(sK4,sK1)))),sK1)
| unordered_pair(singleton(sK2(sK0(sK4,sK1))),unordered_pair(sK2(sK0(sK4,sK1)),sK3(sK0(sK4,sK1)))) = sK0(sK4,sK1) ),
inference(resolve,[status(thm)],[c_26,c_89]) ).
cnf(c_90,plain,
( in(sK0(sK4,sK1),sK1)
| unordered_pair(singleton(sK2(sK0(sK4,sK1))),unordered_pair(sK2(sK0(sK4,sK1)),sK3(sK0(sK4,sK1)))) = sK0(sK4,sK1)
| unordered_pair(singleton(sK2(sK0(sK4,sK1))),unordered_pair(sK2(sK0(sK4,sK1)),sK3(sK0(sK4,sK1)))) = sK0(sK4,sK1) ),
inference(paramod,[status(thm)],[c_43,c_57]) ).
cnf(c_61,plain,
( in(sK0(sK4,sK1),sK1)
| unordered_pair(singleton(sK2(sK0(sK4,sK1))),unordered_pair(sK2(sK0(sK4,sK1)),sK3(sK0(sK4,sK1)))) = sK0(sK4,sK1) ),
inference(copy,[status(thm)],[c_90]) ).
cnf(c_91,negated_conjecture,
( unordered_pair(singleton(sK2(sK0(sK4,sK1))),unordered_pair(sK2(sK0(sK4,sK1)),sK3(sK0(sK4,sK1)))) = sK0(sK4,sK1)
| unordered_pair(singleton(sK2(sK0(sK4,sK1))),unordered_pair(sK2(sK0(sK4,sK1)),sK3(sK0(sK4,sK1)))) = sK0(sK4,sK1) ),
inference(resolve,[status(thm)],[c_61,c_19]) ).
cnf(c_65,negated_conjecture,
unordered_pair(singleton(sK2(sK0(sK4,sK1))),unordered_pair(sK2(sK0(sK4,sK1)),sK3(sK0(sK4,sK1)))) = sK0(sK4,sK1),
inference(copy,[status(thm)],[c_91]) ).
cnf(c_92,plain,
( in(unordered_pair(unordered_pair(sK2(sK0(sK4,sK1)),sK3(sK0(sK4,sK1))),singleton(sK2(sK0(sK4,sK1)))),sK4)
| ~ in(sK0(sK4,sK1),sK1) ),
inference(paramod,[status(thm)],[c_65,c_37]) ).
cnf(c_93,plain,
( in(unordered_pair(singleton(sK2(sK0(sK4,sK1))),unordered_pair(sK2(sK0(sK4,sK1)),sK3(sK0(sK4,sK1)))),sK4)
| ~ in(sK0(sK4,sK1),sK1) ),
inference(paramod,[status(thm)],[c_10,c_92]) ).
cnf(c_72,plain,
( in(sK0(sK4,sK1),sK4)
| ~ in(sK0(sK4,sK1),sK1) ),
inference(paramod,[status(thm)],[c_65,c_93]) ).
cnf(c_94,plain,
( ~ in(sK0(sK4,sK1),sK4)
| in(unordered_pair(unordered_pair(sK2(sK0(sK4,sK1)),sK3(sK0(sK4,sK1))),singleton(sK2(sK0(sK4,sK1)))),sK1) ),
inference(paramod,[status(thm)],[c_65,c_39]) ).
cnf(c_95,plain,
( ~ in(sK0(sK4,sK1),sK4)
| in(unordered_pair(singleton(sK2(sK0(sK4,sK1))),unordered_pair(sK2(sK0(sK4,sK1)),sK3(sK0(sK4,sK1)))),sK1) ),
inference(paramod,[status(thm)],[c_10,c_94]) ).
cnf(c_74,plain,
( ~ in(sK0(sK4,sK1),sK4)
| in(sK0(sK4,sK1),sK1) ),
inference(paramod,[status(thm)],[c_65,c_95]) ).
cnf(c_96,plain,
( sK1 = sK4
| in(sK0(sK4,sK1),sK4)
| in(sK0(sK4,sK1),sK4) ),
inference(resolve,[status(thm)],[c_72,c_16]) ).
cnf(c_97,plain,
( sK4 = sK1
| in(sK0(sK4,sK1),sK4)
| in(sK0(sK4,sK1),sK4) ),
inference(copy,[status(thm)],[c_96]) ).
cnf(c_98,plain,
( sK4 = sK1
| in(sK0(sK4,sK1),sK4) ),
inference(copy,[status(thm)],[c_97]) ).
cnf(c_76,negated_conjecture,
in(sK0(sK4,sK1),sK4),
inference(resolve,[status(thm)],[c_26,c_98]) ).
cnf(c_77,plain,
in(sK0(sK4,sK1),sK1),
inference(resolve,[status(thm)],[c_76,c_74]) ).
cnf(c_99,plain,
( sK1 = sK4
| ~ in(sK0(sK4,sK1),sK1) ),
inference(resolve,[status(thm)],[c_76,c_17]) ).
cnf(c_100,plain,
( sK4 = sK1
| ~ in(sK0(sK4,sK1),sK1) ),
inference(copy,[status(thm)],[c_99]) ).
cnf(c_101,plain,
sK4 = sK1,
inference(resolve,[status(thm)],[c_77,c_100]) ).
cnf(c_79,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_26,c_101]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET959+1 : TPTP v9.3.1. Bugfixed v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n004.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Sat Sep 26 08:27:36 UTC 2026
% 0.08/0.34 % CPUTime :
% 0.08/0.34 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.34 % Process 1241410 was started by sandbox2 on n004,
% 0.08/0.34 % Sat Sep 26 08:27:36 2026
% 0.08/0.34 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.08/0.35
% 0.08/0.35 % From the command line: assign(max_seconds, 300).
% 0.08/0.38
% 0.08/0.38 % SZS status Theorem for theBenchmark
% 0.08/0.38
% 0.08/0.38 % Proof 1 at 0.01 (+ 0.01) seconds.
% 0.08/0.38 % Length of proof is 30.
% 0.08/0.38 % Level of proof is 12.
% 0.08/0.38 % Maximum clause weight is 76.000.
% 0.08/0.38 % Given clauses 49.
% 0.08/0.38
% 0.08/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------