%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET929+1 : TPTP v9.3.1. Released v3.2.0.
% 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 08:37:19 AM UTC 2026
% Result : Theorem 0.14s 0.37s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 3
% Syntax : Number of formulae : 28 ( 6 unt; 0 def)
% Number of atoms : 69 ( 18 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 65 ( 24 ~; 28 |; 9 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 28 ( 2 sgn 11 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t37_xboole_1,axiom,
! [A,B] :
( set_difference(A,B) = empty_set
<=> subset(A,B) ),
file('theBenchmark.p',t37_xboole_1) ).
fof(t38_zfmisc_1,axiom,
! [A,B,C] :
( subset(unordered_pair(A,B),C)
<=> ( in(B,C)
& in(A,C) ) ),
file('theBenchmark.p',t38_zfmisc_1) ).
fof(t73_zfmisc_1,conjecture,
! [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(t73_zfmisc_1_neg,negated_conjecture,
~ ! [A,B,C] :
( set_difference(unordered_pair(A,B),C) = empty_set
<=> ( in(B,C)
& in(A,C) ) ),
inference(assume_negation,[status(cth)],[t73_zfmisc_1]) ).
cnf(c_15,plain,
( subset(A,B)
| set_difference(A,B) != empty_set ),
inference(clausify,[status(thm)],[t37_xboole_1]) ).
cnf(c_16,plain,
( ~ subset(A,B)
| set_difference(A,B) = empty_set ),
inference(clausify,[status(thm)],[t37_xboole_1]) ).
cnf(c_17,plain,
( in(A,C)
| ~ subset(unordered_pair(A,B),C) ),
inference(clausify,[status(thm)],[t38_zfmisc_1]) ).
cnf(c_18,plain,
( in(B,C)
| ~ subset(unordered_pair(A,B),C) ),
inference(clausify,[status(thm)],[t38_zfmisc_1]) ).
cnf(c_19,plain,
( ~ in(B,C)
| ~ in(A,C)
| subset(unordered_pair(A,B),C) ),
inference(clausify,[status(thm)],[t38_zfmisc_1]) ).
fof(nnf_8,plain,
? [A,B,C] :
( ( ~ in(B,C)
| ~ in(A,C)
| set_difference(unordered_pair(A,B),C) != empty_set )
& ( ( in(B,C)
& in(A,C) )
| set_difference(unordered_pair(A,B),C) = empty_set ) ),
inference(fof_nnf,[status(thm)],[t73_zfmisc_1_neg]) ).
fof(sk_t73_zfmisc_1_neg_sk,plain,
( ( ~ in(sK1,sK2)
| ~ in(sK0,sK2)
| set_difference(unordered_pair(sK0,sK1),sK2) != empty_set )
& ( ( in(sK1,sK2)
& in(sK0,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]) ).
fof(sk_t73_zfmisc_1_neg,plain,
( ( ~ in(sK1,sK2)
| ~ in(sK0,sK2)
| set_difference(unordered_pair(sK0,sK1),sK2) != empty_set )
& ( in(sK1,sK2)
| set_difference(unordered_pair(sK0,sK1),sK2) = empty_set )
& ( in(sK0,sK2)
| set_difference(unordered_pair(sK0,sK1),sK2) = empty_set ) ),
inference(cnf_transformation,[status(thm)],[sk_t73_zfmisc_1_neg_sk]) ).
cnf(c_20,negated_conjecture,
( in(sK0,sK2)
| set_difference(unordered_pair(sK0,sK1),sK2) = empty_set ),
inference(split_conjunct,[status(thm)],[sk_t73_zfmisc_1_neg]) ).
cnf(c_21,negated_conjecture,
( in(sK1,sK2)
| set_difference(unordered_pair(sK0,sK1),sK2) = empty_set ),
inference(split_conjunct,[status(thm)],[sk_t73_zfmisc_1_neg]) ).
cnf(c_22,negated_conjecture,
( ~ in(sK1,sK2)
| ~ in(sK0,sK2)
| set_difference(unordered_pair(sK0,sK1),sK2) != empty_set ),
inference(split_conjunct,[status(thm)],[sk_t73_zfmisc_1_neg]) ).
cnf(c_28,plain,
( subset(unordered_pair(sK0,sK1),sK2)
| in(sK0,sK2) ),
inference(resolve,[status(thm)],[c_20,c_15]) ).
cnf(c_32,plain,
( subset(unordered_pair(sK0,sK1),sK2)
| in(sK1,sK2) ),
inference(resolve,[status(thm)],[c_21,c_15]) ).
cnf(c_89,plain,
( in(sK0,sK2)
| in(sK0,sK2) ),
inference(resolve,[status(thm)],[c_28,c_17]) ).
cnf(c_61,plain,
in(sK0,sK2),
inference(copy,[status(thm)],[c_89]) ).
cnf(c_63,negated_conjecture,
( ~ in(sK1,sK2)
| set_difference(unordered_pair(sK0,sK1),sK2) != empty_set ),
inference(resolve,[status(thm)],[c_61,c_22]) ).
cnf(c_72,plain,
( ~ in(A,sK2)
| subset(unordered_pair(A,sK1),sK2)
| subset(unordered_pair(sK0,sK1),sK2) ),
inference(resolve,[status(thm)],[c_32,c_19]) ).
cnf(c_90,plain,
( in(sK1,sK2)
| in(sK1,sK2) ),
inference(resolve,[status(thm)],[c_32,c_18]) ).
cnf(c_75,plain,
in(sK1,sK2),
inference(copy,[status(thm)],[c_90]) ).
cnf(c_91,plain,
( ~ in(sK0,sK2)
| subset(unordered_pair(sK0,sK1),sK2) ),
inference(factor,[status(thm)],[c_72]) ).
cnf(c_76,plain,
subset(unordered_pair(sK0,sK1),sK2),
inference(resolve,[status(thm)],[c_61,c_91]) ).
cnf(c_77,negated_conjecture,
set_difference(unordered_pair(sK0,sK1),sK2) != empty_set,
inference(resolve,[status(thm)],[c_75,c_63]) ).
cnf(c_92,plain,
set_difference(unordered_pair(sK0,sK1),sK2) = empty_set,
inference(resolve,[status(thm)],[c_76,c_16]) ).
cnf(c_88,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_77,c_92]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET929+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n004.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Sat Sep 26 08:26:21 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.10/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.36 % Process 1238191 was started by sandbox2 on n004,
% 0.10/0.36 % Sat Sep 26 08:26:21 2026
% 0.10/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.36
% 0.10/0.36 % From the command line: assign(max_seconds, 300).
% 0.14/0.37
% 0.14/0.37 % SZS status Theorem for theBenchmark
% 0.14/0.37
% 0.14/0.37 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.14/0.37 % Length of proof is 20.
% 0.14/0.37 % Level of proof is 6.
% 0.14/0.37 % Maximum clause weight is 28.000.
% 0.14/0.37 % Given clauses 38.
% 0.14/0.37
% 0.14/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------