%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU151+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n016.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 08:45:12 AM UTC 2026
% Result : Theorem 0.53s 26.10s
% Output : CNFRefutation 0.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 7
% Syntax : Number of formulae : 51 ( 26 unt; 0 def)
% Number of atoms : 131 ( 99 equ)
% Maximal formula atoms : 20 ( 2 avg)
% Number of connectives : 136 ( 56 ~; 53 |; 23 &)
% ( 3 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-3 aty)
% Number of variables : 107 ( 11 sgn 50 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(commutativity_k2_tarski,axiom,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
file('theBenchmark.p',commutativity_k2_tarski) ).
fof(d1_xboole_0,axiom,
! [A] :
( A = empty_set
<=> ! [B] : ~ in(B,A) ),
file('theBenchmark.p',d1_xboole_0) ).
fof(d2_tarski,axiom,
! [A,B,C] :
( C = unordered_pair(A,B)
<=> ! [D] :
( in(D,C)
<=> ( D = B
| D = A ) ) ),
file('theBenchmark.p',d2_tarski) ).
fof(l1_zfmisc_1,axiom,
! [A] : singleton(A) != empty_set,
file('theBenchmark.p',l1_zfmisc_1) ).
fof(t69_enumset1,axiom,
! [A] : unordered_pair(A,A) = singleton(A),
file('theBenchmark.p',t69_enumset1) ).
fof(t9_zfmisc_1,axiom,
! [A,B,C] :
( singleton(A) = unordered_pair(B,C)
=> B = C ),
file('theBenchmark.p',t9_zfmisc_1) ).
fof(t10_zfmisc_1,conjecture,
! [A,B,C,D] :
~ ( A != D
& A != C
& unordered_pair(A,B) = unordered_pair(C,D) ),
file('theBenchmark.p',t10_zfmisc_1) ).
fof(t10_zfmisc_1_neg,negated_conjecture,
~ ! [A,B,C,D] :
~ ( A != D
& A != C
& unordered_pair(A,B) = unordered_pair(C,D) ),
inference(assume_negation,[status(cth)],[t10_zfmisc_1]) ).
cnf(c_75,plain,
unordered_pair(A,B) = unordered_pair(B,A),
inference(clausify,[status(thm)],[commutativity_k2_tarski]) ).
cnf(c_85,plain,
( ~ in(B,A)
| empty_set != A ),
inference(clausify,[status(thm)],[d1_xboole_0]) ).
fof(nnf_10,plain,
! [A,B,C] :
( ( ? [D] :
( ( ( D != B
& D != A )
| ~ in(D,C) )
& ( D = B
| D = A
| in(D,C) ) )
| unordered_pair(A,B) = C )
& ( ! [X0] :
( ( ( X0 != B
& X0 != A )
| in(X0,C) )
& ( X0 = B
| X0 = A
| ~ in(X0,C) ) )
| unordered_pair(A,B) != C ) ),
inference(fof_nnf,[status(thm)],[d2_tarski]) ).
fof(sk_d2_tarski_sk,plain,
! [A,B,C] :
( ( ( ( ( sK0(A,B,C) != B
& sK0(A,B,C) != A )
| ~ in(sK0(A,B,C),C) )
& ( sK0(A,B,C) = B
| sK0(A,B,C) = A
| in(sK0(A,B,C),C) ) )
| unordered_pair(A,B) = C )
& ( ! [X0] :
( ( ( X0 != B
& X0 != A )
| in(X0,C) )
& ( X0 = B
| X0 = A
| ~ in(X0,C) ) )
| unordered_pair(A,B) != C ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(D,sK0(A,B,C))],[nnf_10]) ).
fof(sk_d2_tarski,plain,
( ! [VAR_0,VAR_1,VAR_2] :
( sK0(VAR_0,VAR_1,VAR_2) != VAR_1
| ~ in(sK0(VAR_0,VAR_1,VAR_2),VAR_2)
| unordered_pair(VAR_0,VAR_1) = VAR_2 )
& ! [VAR_0,VAR_1,VAR_2] :
( sK0(VAR_0,VAR_1,VAR_2) != VAR_0
| ~ in(sK0(VAR_0,VAR_1,VAR_2),VAR_2)
| unordered_pair(VAR_0,VAR_1) = VAR_2 )
& ! [VAR_0,VAR_1,VAR_2] :
( sK0(VAR_0,VAR_1,VAR_2) = VAR_1
| sK0(VAR_0,VAR_1,VAR_2) = VAR_0
| in(sK0(VAR_0,VAR_1,VAR_2),VAR_2)
| unordered_pair(VAR_0,VAR_1) = VAR_2 )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( VAR_3 != VAR_1
| in(VAR_3,VAR_2)
| unordered_pair(VAR_0,VAR_1) != VAR_2 )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( VAR_3 != VAR_0
| in(VAR_3,VAR_2)
| unordered_pair(VAR_0,VAR_1) != VAR_2 )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( VAR_3 = VAR_1
| VAR_3 = VAR_0
| ~ in(VAR_3,VAR_2)
| unordered_pair(VAR_0,VAR_1) != VAR_2 ) ),
inference(cnf_transformation,[status(thm)],[sk_d2_tarski_sk]) ).
cnf(c_91,plain,
( D = B
| D = A
| ~ in(D,C)
| unordered_pair(A,B) != C ),
inference(split_conjunct,[status(thm)],[sk_d2_tarski]) ).
cnf(c_92,plain,
( D != A
| in(D,C)
| unordered_pair(A,B) != C ),
inference(split_conjunct,[status(thm)],[sk_d2_tarski]) ).
cnf(c_94,plain,
( sK0(A,B,C) = B
| sK0(A,B,C) = A
| in(sK0(A,B,C),C)
| unordered_pair(A,B) = C ),
inference(split_conjunct,[status(thm)],[sk_d2_tarski]) ).
cnf(c_129,plain,
singleton(A) != empty_set,
inference(clausify,[status(thm)],[l1_zfmisc_1]) ).
cnf(c_172,plain,
singleton(A) = unordered_pair(A,A),
inference(clausify,[status(thm)],[t69_enumset1]) ).
cnf(c_184,plain,
( C = B
| singleton(A) != unordered_pair(B,C) ),
inference(clausify,[status(thm)],[t9_zfmisc_1]) ).
cnf(c_2001,plain,
( C = B
| unordered_pair(A,A) != unordered_pair(B,C) ),
inference(paramod,[status(thm)],[c_172,c_184]) ).
cnf(c_185,plain,
( B = A
| unordered_pair(A,B) != unordered_pair(C,C) ),
inference(copy,[status(thm)],[c_2001]) ).
fof(nnf_72,plain,
? [A,B,C,D] :
( D != A
& C != A
& unordered_pair(C,D) = unordered_pair(A,B) ),
inference(fof_nnf,[status(thm)],[t10_zfmisc_1_neg]) ).
fof(sk_t10_zfmisc_1_neg,plain,
( sK2 != sK3
& sK1 != sK3
& unordered_pair(sK1,sK2) = unordered_pair(sK3,sK4) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3,sK4]),skolemize(A,sK3),skolemize(B,sK4),skolemize(C,sK1),skolemize(D,sK2)],[nnf_72]) ).
cnf(c_186,negated_conjecture,
unordered_pair(sK1,sK2) = unordered_pair(sK3,sK4),
inference(split_conjunct,[status(thm)],[sk_t10_zfmisc_1_neg]) ).
cnf(c_187,negated_conjecture,
sK1 != sK3,
inference(split_conjunct,[status(thm)],[sk_t10_zfmisc_1_neg]) ).
cnf(c_188,negated_conjecture,
sK2 != sK3,
inference(split_conjunct,[status(thm)],[sk_t10_zfmisc_1_neg]) ).
cnf(c_194,plain,
( sK0(A,A,B) = A
| in(sK0(A,A,B),B)
| unordered_pair(A,A) = B ),
inference(factor,[status(thm)],[c_94]) ).
cnf(c_230,plain,
unordered_pair(A,A) != empty_set,
inference(paramod,[status(thm)],[c_172,c_129]) ).
cnf(c_235,plain,
~ in(A,empty_set),
inference(xxres,[status(thm)],[c_85]) ).
cnf(c_242,plain,
( A = B
| A = C
| ~ in(A,unordered_pair(B,C)) ),
inference(resolve,[status(thm)],[c_91,c_75]) ).
cnf(c_246,plain,
( A != C
| in(A,unordered_pair(B,C)) ),
inference(resolve,[status(thm)],[c_92,c_75]) ).
cnf(c_247,plain,
( A != B
| in(A,unordered_pair(B,C)) ),
inference(xxres,[status(thm)],[c_92]) ).
cnf(c_2002,plain,
( sK0(A,A,empty_set) = A
| unordered_pair(A,A) = empty_set ),
inference(resolve,[status(thm)],[c_235,c_194]) ).
cnf(c_1394,plain,
sK0(A,A,empty_set) = A,
inference(resolve,[status(thm)],[c_230,c_2002]) ).
cnf(c_2003,plain,
in(sK0(A,A,empty_set),unordered_pair(B,A)),
inference(resolve,[status(thm)],[c_246,c_1394]) ).
cnf(c_1738,plain,
in(A,unordered_pair(B,A)),
inference(paramod,[status(thm)],[c_1394,c_2003]) ).
cnf(c_2004,plain,
in(sK0(A,A,empty_set),unordered_pair(A,B)),
inference(resolve,[status(thm)],[c_247,c_1394]) ).
cnf(c_1742,plain,
in(A,unordered_pair(A,B)),
inference(paramod,[status(thm)],[c_1394,c_2004]) ).
cnf(c_1782,plain,
in(sK2,unordered_pair(sK3,sK4)),
inference(paramod,[status(thm)],[c_186,c_1738]) ).
cnf(c_1808,plain,
in(sK1,unordered_pair(sK3,sK4)),
inference(paramod,[status(thm)],[c_186,c_1742]) ).
cnf(c_2005,plain,
( sK2 = sK3
| sK2 = sK4 ),
inference(resolve,[status(thm)],[c_1782,c_242]) ).
cnf(c_1810,negated_conjecture,
sK2 = sK4,
inference(resolve,[status(thm)],[c_188,c_2005]) ).
cnf(c_1818,negated_conjecture,
sK4 != sK3,
inference(paramod,[status(thm)],[c_1810,c_188]) ).
cnf(c_2006,negated_conjecture,
unordered_pair(sK1,sK4) = unordered_pair(sK3,sK4),
inference(paramod,[status(thm)],[c_1810,c_186]) ).
cnf(c_1819,negated_conjecture,
unordered_pair(sK4,sK1) = unordered_pair(sK3,sK4),
inference(paramod,[status(thm)],[c_75,c_2006]) ).
cnf(c_2007,plain,
( sK1 = sK3
| sK1 = sK4 ),
inference(resolve,[status(thm)],[c_1808,c_242]) ).
cnf(c_1821,negated_conjecture,
sK1 = sK4,
inference(resolve,[status(thm)],[c_187,c_2007]) ).
cnf(c_1822,negated_conjecture,
unordered_pair(sK4,sK4) = unordered_pair(sK3,sK4),
inference(paramod,[status(thm)],[c_1821,c_1819]) ).
cnf(c_2008,plain,
( B = A
| unordered_pair(C,C) != unordered_pair(A,B) ),
inference(copy,[status(thm)],[c_185]) ).
cnf(c_2009,negated_conjecture,
sK4 = sK3,
inference(resolve,[status(thm)],[c_1822,c_2008]) ).
cnf(c_2000,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_1818,c_2009]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU151+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/5.38 % Computer : n016.cluster.edu
% 0.09/5.38 % Model : x86_64 x86_64
% 0.09/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.38 % Memory : 8046.5625MB
% 0.09/5.38 % OS : Linux 6.8.0-71-generic
% 0.12/25.65 % CPULimit : 300
% 0.12/25.65 % WCLimit : 300
% 0.12/25.65 % DateTime : Sat Sep 26 08:44:03 UTC 2026
% 0.53/25.65 % CPUTime :
% 0.53/25.66 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.53/25.66 % Process 1289329 was started by sandbox2 on n002,
% 0.53/25.66 % Sat Sep 26 08:44:03 2026
% 0.53/25.66 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.53/25.67
% 0.53/25.67 % From the command line: assign(max_seconds, 300).
% 0.53/26.10
% 0.53/26.10 % SZS status Theorem for theBenchmark
% 0.53/26.10
% 0.53/26.10 % Proof 1 at 0.30 (+ 0.10) seconds.
% 0.53/26.10 % Length of proof is 36.
% 0.53/26.10 % Level of proof is 9.
% 0.53/26.10 % Maximum clause weight is 33.000.
% 0.53/26.10 % Given clauses 227.
% 0.53/26.10
% 0.53/26.10 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------