%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET927+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 : n001.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 08:37:18 AM UTC 2026
% Result : Theorem 0.24s 0.68s
% Output : CNFRefutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 2
% Syntax : Number of formulae : 50 ( 5 unt; 0 def)
% Number of atoms : 146 ( 92 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 143 ( 47 ~; 81 |; 12 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 45 ( 4 sgn 9 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(l39_zfmisc_1,axiom,
! [A,B,C] :
( set_difference(unordered_pair(A,B),C) = singleton(A)
<=> ( ( A = B
| in(B,C) )
& ~ in(A,C) ) ),
file('theBenchmark.p',l39_zfmisc_1) ).
fof(t70_zfmisc_1,conjecture,
! [A,B,C] :
( set_difference(unordered_pair(A,B),C) = singleton(A)
<=> ( ( A = B
| in(B,C) )
& ~ in(A,C) ) ),
file('theBenchmark.p',t70_zfmisc_1) ).
fof(t70_zfmisc_1_neg,negated_conjecture,
~ ! [A,B,C] :
( set_difference(unordered_pair(A,B),C) = singleton(A)
<=> ( ( A = B
| in(B,C) )
& ~ in(A,C) ) ),
inference(assume_negation,[status(cth)],[t70_zfmisc_1]) ).
cnf(c_11,plain,
( ~ in(A,C)
| singleton(A) != set_difference(unordered_pair(A,B),C) ),
inference(clausify,[status(thm)],[l39_zfmisc_1]) ).
cnf(c_12,plain,
( ~ in(A,C)
| set_difference(unordered_pair(A,B),C) != singleton(A) ),
inference(copy,[status(thm)],[c_11]) ).
cnf(c_13,plain,
( B = A
| in(B,C)
| singleton(A) != set_difference(unordered_pair(A,B),C) ),
inference(clausify,[status(thm)],[l39_zfmisc_1]) ).
cnf(c_14,plain,
( B = A
| in(B,C)
| set_difference(unordered_pair(A,B),C) != singleton(A) ),
inference(copy,[status(thm)],[c_13]) ).
cnf(c_15,plain,
( ~ in(B,C)
| in(A,C)
| singleton(A) = set_difference(unordered_pair(A,B),C) ),
inference(clausify,[status(thm)],[l39_zfmisc_1]) ).
cnf(c_16,plain,
( ~ in(B,C)
| in(A,C)
| set_difference(unordered_pair(A,B),C) = singleton(A) ),
inference(copy,[status(thm)],[c_15]) ).
cnf(c_17,plain,
( B != A
| in(A,C)
| singleton(A) = set_difference(unordered_pair(A,B),C) ),
inference(clausify,[status(thm)],[l39_zfmisc_1]) ).
cnf(c_18,plain,
( B != A
| in(A,C)
| set_difference(unordered_pair(A,B),C) = singleton(A) ),
inference(copy,[status(thm)],[c_17]) ).
fof(nnf_6,plain,
? [A,B,C] :
( ( ( B != A
& ~ in(B,C) )
| in(A,C)
| singleton(A) != set_difference(unordered_pair(A,B),C) )
& ( ( ( B = A
| in(B,C) )
& ~ in(A,C) )
| singleton(A) = set_difference(unordered_pair(A,B),C) ) ),
inference(fof_nnf,[status(thm)],[t70_zfmisc_1_neg]) ).
fof(sk_t70_zfmisc_1_neg_sk,plain,
( ( ( sK1 != sK0
& ~ in(sK1,sK2) )
| in(sK0,sK2)
| singleton(sK0) != set_difference(unordered_pair(sK0,sK1),sK2) )
& ( ( ( sK1 = sK0
| in(sK1,sK2) )
& ~ in(sK0,sK2) )
| singleton(sK0) = set_difference(unordered_pair(sK0,sK1),sK2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(A,sK0),skolemize(B,sK1),skolemize(C,sK2)],[nnf_6]) ).
fof(sk_t70_zfmisc_1_neg,plain,
( ( sK1 != sK0
| in(sK0,sK2)
| singleton(sK0) != set_difference(unordered_pair(sK0,sK1),sK2) )
& ( ~ in(sK1,sK2)
| in(sK0,sK2)
| singleton(sK0) != set_difference(unordered_pair(sK0,sK1),sK2) )
& ( sK1 = sK0
| in(sK1,sK2)
| singleton(sK0) = set_difference(unordered_pair(sK0,sK1),sK2) )
& ( ~ in(sK0,sK2)
| singleton(sK0) = set_difference(unordered_pair(sK0,sK1),sK2) ) ),
inference(cnf_transformation,[status(thm)],[sk_t70_zfmisc_1_neg_sk]) ).
cnf(c_19,negated_conjecture,
( ~ in(sK0,sK2)
| singleton(sK0) = set_difference(unordered_pair(sK0,sK1),sK2) ),
inference(split_conjunct,[status(thm)],[sk_t70_zfmisc_1_neg]) ).
cnf(c_20,negated_conjecture,
( ~ in(sK0,sK2)
| set_difference(unordered_pair(sK0,sK1),sK2) = singleton(sK0) ),
inference(copy,[status(thm)],[c_19]) ).
cnf(c_21,negated_conjecture,
( sK1 = sK0
| in(sK1,sK2)
| singleton(sK0) = set_difference(unordered_pair(sK0,sK1),sK2) ),
inference(split_conjunct,[status(thm)],[sk_t70_zfmisc_1_neg]) ).
cnf(c_22,negated_conjecture,
( sK1 = sK0
| in(sK1,sK2)
| set_difference(unordered_pair(sK0,sK1),sK2) = singleton(sK0) ),
inference(copy,[status(thm)],[c_21]) ).
cnf(c_23,negated_conjecture,
( ~ in(sK1,sK2)
| in(sK0,sK2)
| singleton(sK0) != set_difference(unordered_pair(sK0,sK1),sK2) ),
inference(split_conjunct,[status(thm)],[sk_t70_zfmisc_1_neg]) ).
cnf(c_24,negated_conjecture,
( ~ in(sK1,sK2)
| in(sK0,sK2)
| set_difference(unordered_pair(sK0,sK1),sK2) != singleton(sK0) ),
inference(copy,[status(thm)],[c_23]) ).
cnf(c_25,negated_conjecture,
( sK1 != sK0
| in(sK0,sK2)
| singleton(sK0) != set_difference(unordered_pair(sK0,sK1),sK2) ),
inference(split_conjunct,[status(thm)],[sk_t70_zfmisc_1_neg]) ).
cnf(c_26,negated_conjecture,
( sK1 != sK0
| in(sK0,sK2)
| set_difference(unordered_pair(sK0,sK1),sK2) != singleton(sK0) ),
inference(copy,[status(thm)],[c_25]) ).
cnf(c_30,plain,
( in(A,B)
| set_difference(unordered_pair(A,A),B) = singleton(A) ),
inference(xxres,[status(thm)],[c_18]) ).
cnf(c_31,plain,
( in(A,sK2)
| set_difference(unordered_pair(A,sK1),sK2) = singleton(A)
| sK1 = sK0
| set_difference(unordered_pair(sK0,sK1),sK2) = singleton(sK0) ),
inference(resolve,[status(thm)],[c_22,c_16]) ).
cnf(c_34,plain,
( in(sK0,sK2)
| sK1 = sK0
| set_difference(unordered_pair(sK0,sK1),sK2) = singleton(sK0) ),
inference(factor,[status(thm)],[c_31]) ).
cnf(c_38,plain,
( in(C,B)
| set_difference(unordered_pair(C,A),B) = singleton(C)
| set_difference(unordered_pair(A,A),B) = singleton(A) ),
inference(resolve,[status(thm)],[c_30,c_16]) ).
cnf(c_91,negated_conjecture,
( set_difference(unordered_pair(sK0,sK1),sK2) = singleton(sK0)
| sK1 = sK0
| set_difference(unordered_pair(sK0,sK1),sK2) = singleton(sK0) ),
inference(resolve,[status(thm)],[c_34,c_20]) ).
cnf(c_50,negated_conjecture,
( sK1 = sK0
| set_difference(unordered_pair(sK0,sK1),sK2) = singleton(sK0) ),
inference(copy,[status(thm)],[c_91]) ).
cnf(c_92,plain,
( sK1 = sK0
| in(sK1,sK2)
| sK1 = sK0 ),
inference(resolve,[status(thm)],[c_50,c_14]) ).
cnf(c_52,plain,
( in(sK1,sK2)
| sK1 = sK0 ),
inference(copy,[status(thm)],[c_92]) ).
cnf(c_56,plain,
( in(sK0,sK2)
| set_difference(unordered_pair(sK0,sK1),sK2) != singleton(sK0)
| sK1 = sK0 ),
inference(resolve,[status(thm)],[c_52,c_24]) ).
cnf(c_93,plain,
( sK1 = sK0
| in(sK0,sK2)
| sK1 = sK0 ),
inference(resolve,[status(thm)],[c_56,c_50]) ).
cnf(c_67,plain,
( in(sK0,sK2)
| sK1 = sK0 ),
inference(copy,[status(thm)],[c_93]) ).
cnf(c_70,plain,
( set_difference(unordered_pair(sK0,A),sK2) != singleton(sK0)
| sK1 = sK0 ),
inference(resolve,[status(thm)],[c_67,c_12]) ).
cnf(c_77,plain,
( set_difference(unordered_pair(sK0,sK1),sK2) = singleton(sK0)
| set_difference(unordered_pair(sK0,A),sK2) = singleton(sK0)
| set_difference(unordered_pair(A,A),sK2) = singleton(A) ),
inference(resolve,[status(thm)],[c_38,c_20]) ).
cnf(c_81,plain,
( set_difference(unordered_pair(sK0,sK1),sK2) = singleton(sK0)
| set_difference(unordered_pair(sK1,sK1),sK2) = singleton(sK1) ),
inference(factor,[status(thm)],[c_77]) ).
cnf(c_94,plain,
( sK1 = sK0
| sK1 = sK0 ),
inference(resolve,[status(thm)],[c_70,c_50]) ).
cnf(c_84,plain,
sK1 = sK0,
inference(copy,[status(thm)],[c_94]) ).
cnf(c_95,plain,
( set_difference(unordered_pair(sK0,sK1),sK2) = singleton(sK0)
| set_difference(unordered_pair(sK0,sK1),sK2) = singleton(sK1) ),
inference(paramod,[status(thm)],[c_84,c_81]) ).
cnf(c_96,plain,
( set_difference(unordered_pair(sK0,sK1),sK2) = singleton(sK0)
| set_difference(unordered_pair(sK0,sK0),sK2) = singleton(sK1) ),
inference(paramod,[status(thm)],[c_84,c_95]) ).
cnf(c_97,plain,
( set_difference(unordered_pair(sK0,sK1),sK2) = singleton(sK0)
| set_difference(unordered_pair(sK0,sK0),sK2) = singleton(sK0) ),
inference(paramod,[status(thm)],[c_84,c_96]) ).
cnf(c_98,plain,
( set_difference(unordered_pair(sK0,sK0),sK2) = singleton(sK0)
| set_difference(unordered_pair(sK0,sK0),sK2) = singleton(sK0) ),
inference(paramod,[status(thm)],[c_84,c_97]) ).
cnf(c_85,plain,
set_difference(unordered_pair(sK0,sK0),sK2) = singleton(sK0),
inference(copy,[status(thm)],[c_98]) ).
cnf(c_99,negated_conjecture,
( sK1 != sK0
| in(sK0,sK2)
| set_difference(unordered_pair(sK0,sK0),sK2) != singleton(sK0) ),
inference(paramod,[status(thm)],[c_84,c_26]) ).
cnf(c_100,negated_conjecture,
( sK1 != sK0
| in(sK0,sK2)
| singleton(sK0) != singleton(sK0) ),
inference(paramod,[status(thm)],[c_85,c_99]) ).
cnf(c_101,negated_conjecture,
( sK0 != sK0
| in(sK0,sK2)
| singleton(sK0) != singleton(sK0) ),
inference(paramod,[status(thm)],[c_84,c_100]) ).
cnf(c_102,negated_conjecture,
( sK0 != sK0
| in(sK0,sK2) ),
inference(copy,[status(thm)],[c_101]) ).
cnf(c_86,negated_conjecture,
in(sK0,sK2),
inference(copy,[status(thm)],[c_102]) ).
cnf(c_89,plain,
set_difference(unordered_pair(sK0,A),sK2) != singleton(sK0),
inference(resolve,[status(thm)],[c_86,c_12]) ).
cnf(c_90,plain,
$false,
inference(resolve,[status(thm)],[c_89,c_85]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET927+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.64 % Computer : n001.cluster.edu
% 0.20/0.64 % Model : x86_64 x86_64
% 0.20/0.64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.64 % Memory : 8046.5625MB
% 0.20/0.64 % OS : Linux 6.8.0-71-generic
% 0.20/0.64 % CPULimit : 300
% 0.20/0.64 % WCLimit : 300
% 0.20/0.64 % DateTime : Sat Sep 26 08:31:42 UTC 2026
% 0.20/0.65 % CPUTime :
% 0.20/0.65 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.20/0.65 % Process 1378491 was started by sandbox on n001,
% 0.20/0.65 % Sat Sep 26 08:31:42 2026
% 0.20/0.65 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.24/0.66
% 0.24/0.66 % From the command line: assign(max_seconds, 300).
% 0.24/0.68
% 0.24/0.68 % SZS status Theorem for theBenchmark
% 0.24/0.68
% 0.24/0.68 % Proof 1 at 0.01 (+ 0.01) seconds.
% 0.24/0.68 % Length of proof is 34.
% 0.24/0.68 % Level of proof is 14.
% 0.24/0.68 % Maximum clause weight is 24.000.
% 0.24/0.68 % Given clauses 38.
% 0.24/0.68
% 0.24/0.68 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------