%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET930+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 : n018.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 08:37:19 AM UTC 2026
% Result : Theorem 0.13s 0.38s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 30 ( 13 unt; 0 def)
% Number of atoms : 65 ( 37 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 71 ( 36 ~; 17 |; 15 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 36 ( 0 sgn 17 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(commutativity_k2_tarski,axiom,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
file('theBenchmark.p',commutativity_k2_tarski) ).
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(t72_zfmisc_1,axiom,
! [A,B,C] :
( set_difference(unordered_pair(A,B),C) = unordered_pair(A,B)
<=> ( ~ in(B,C)
& ~ in(A,C) ) ),
file('theBenchmark.p',t72_zfmisc_1) ).
fof(t73_zfmisc_1,axiom,
! [A,B,C] :
( set_difference(unordered_pair(A,B),C) = empty_set
<=> ( in(B,C)
& in(A,C) ) ),
file('theBenchmark.p',t73_zfmisc_1) ).
fof(t74_zfmisc_1,conjecture,
! [A,B,C] :
~ ( set_difference(unordered_pair(A,B),C) != unordered_pair(A,B)
& set_difference(unordered_pair(A,B),C) != singleton(B)
& set_difference(unordered_pair(A,B),C) != singleton(A)
& set_difference(unordered_pair(A,B),C) != empty_set ),
file('theBenchmark.p',t74_zfmisc_1) ).
fof(t74_zfmisc_1_neg,negated_conjecture,
~ ! [A,B,C] :
~ ( set_difference(unordered_pair(A,B),C) != unordered_pair(A,B)
& set_difference(unordered_pair(A,B),C) != singleton(B)
& set_difference(unordered_pair(A,B),C) != singleton(A)
& set_difference(unordered_pair(A,B),C) != empty_set ),
inference(assume_negation,[status(cth)],[t74_zfmisc_1]) ).
cnf(c_10,plain,
unordered_pair(A,B) = unordered_pair(B,A),
inference(clausify,[status(thm)],[commutativity_k2_tarski]) ).
cnf(c_16,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_17,plain,
( ~ in(B,C)
| in(A,C)
| set_difference(unordered_pair(A,B),C) = singleton(A) ),
inference(copy,[status(thm)],[c_16]) ).
cnf(c_24,plain,
( in(B,C)
| in(A,C)
| set_difference(unordered_pair(A,B),C) = unordered_pair(A,B) ),
inference(clausify,[status(thm)],[t72_zfmisc_1]) ).
cnf(c_27,plain,
( ~ in(B,C)
| ~ in(A,C)
| set_difference(unordered_pair(A,B),C) = empty_set ),
inference(clausify,[status(thm)],[t73_zfmisc_1]) ).
fof(nnf_8,plain,
? [A,B,C] :
( set_difference(unordered_pair(A,B),C) != unordered_pair(A,B)
& singleton(B) != set_difference(unordered_pair(A,B),C)
& singleton(A) != set_difference(unordered_pair(A,B),C)
& set_difference(unordered_pair(A,B),C) != empty_set ),
inference(fof_nnf,[status(thm)],[t74_zfmisc_1_neg]) ).
fof(sk_t74_zfmisc_1_neg,plain,
( set_difference(unordered_pair(sK0,sK1),sK2) != unordered_pair(sK0,sK1)
& singleton(sK1) != set_difference(unordered_pair(sK0,sK1),sK2)
& singleton(sK0) != set_difference(unordered_pair(sK0,sK1),sK2)
& set_difference(unordered_pair(sK0,sK1),sK2) != empty_set ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(A,sK0),skolemize(B,sK1),skolemize(C,sK2)],[nnf_8]) ).
cnf(c_28,negated_conjecture,
set_difference(unordered_pair(sK0,sK1),sK2) != empty_set,
inference(split_conjunct,[status(thm)],[sk_t74_zfmisc_1_neg]) ).
cnf(c_29,negated_conjecture,
singleton(sK0) != set_difference(unordered_pair(sK0,sK1),sK2),
inference(split_conjunct,[status(thm)],[sk_t74_zfmisc_1_neg]) ).
cnf(c_30,negated_conjecture,
set_difference(unordered_pair(sK0,sK1),sK2) != singleton(sK0),
inference(copy,[status(thm)],[c_29]) ).
cnf(c_31,negated_conjecture,
singleton(sK1) != set_difference(unordered_pair(sK0,sK1),sK2),
inference(split_conjunct,[status(thm)],[sk_t74_zfmisc_1_neg]) ).
cnf(c_32,negated_conjecture,
set_difference(unordered_pair(sK0,sK1),sK2) != singleton(sK1),
inference(copy,[status(thm)],[c_31]) ).
cnf(c_33,negated_conjecture,
set_difference(unordered_pair(sK0,sK1),sK2) != unordered_pair(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_t74_zfmisc_1_neg]) ).
cnf(c_61,plain,
set_difference(unordered_pair(sK1,sK0),sK2) != singleton(sK1),
inference(paramod,[status(thm)],[c_10,c_32]) ).
cnf(c_62,plain,
( in(sK1,sK2)
| in(sK0,sK2) ),
inference(resolve,[status(thm)],[c_33,c_24]) ).
cnf(c_170,plain,
( in(A,sK2)
| set_difference(unordered_pair(A,sK0),sK2) = singleton(A)
| in(sK1,sK2) ),
inference(resolve,[status(thm)],[c_62,c_17]) ).
cnf(c_178,plain,
( in(A,sK2)
| set_difference(unordered_pair(A,sK1),sK2) = singleton(A)
| in(sK0,sK2) ),
inference(resolve,[status(thm)],[c_62,c_17]) ).
cnf(c_192,plain,
( set_difference(unordered_pair(sK1,sK0),sK2) = singleton(sK1)
| in(sK1,sK2) ),
inference(factor,[status(thm)],[c_170]) ).
cnf(c_181,plain,
in(sK1,sK2),
inference(resolve,[status(thm)],[c_61,c_192]) ).
cnf(c_193,plain,
( set_difference(unordered_pair(sK0,sK1),sK2) = singleton(sK0)
| in(sK0,sK2) ),
inference(factor,[status(thm)],[c_178]) ).
cnf(c_182,negated_conjecture,
in(sK0,sK2),
inference(resolve,[status(thm)],[c_30,c_193]) ).
cnf(c_194,negated_conjecture,
( ~ in(sK1,sK2)
| ~ in(sK0,sK2) ),
inference(resolve,[status(thm)],[c_27,c_28]) ).
cnf(c_195,negated_conjecture,
~ in(sK0,sK2),
inference(resolve,[status(thm)],[c_194,c_181]) ).
cnf(c_191,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_182,c_195]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET930+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n018.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 26 08:28:36 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.35 % Process 4192848 was started by sandbox on n018,
% 0.09/0.35 % Sat Sep 26 08:28:36 2026
% 0.09/0.35 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.36
% 0.09/0.36 % From the command line: assign(max_seconds, 300).
% 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 (+ 0.01) seconds.
% 0.13/0.38 % Length of proof is 23.
% 0.13/0.38 % Level of proof is 5.
% 0.13/0.38 % Maximum clause weight is 30.000.
% 0.13/0.38 % Given clauses 31.
% 0.13/0.38
% 0.13/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------