%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET928+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 : n002.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 0.08s 0.41s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 30 ( 8 unt; 0 def)
% Number of atoms : 73 ( 25 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 74 ( 31 ~; 29 |; 11 &)
% ( 3 <=>; 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 : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 38 ( 2 sgn 16 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(commutativity_k2_tarski,axiom,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
file('theBenchmark.p',commutativity_k2_tarski) ).
fof(t55_zfmisc_1,axiom,
! [A,B,C] :
~ ( in(A,C)
& disjoint(unordered_pair(A,B),C) ),
file('theBenchmark.p',t55_zfmisc_1) ).
fof(t57_zfmisc_1,axiom,
! [A,B,C] :
~ ( ~ disjoint(unordered_pair(A,C),B)
& ~ in(C,B)
& ~ in(A,B) ),
file('theBenchmark.p',t57_zfmisc_1) ).
fof(t83_xboole_1,axiom,
! [A,B] :
( disjoint(A,B)
<=> set_difference(A,B) = A ),
file('theBenchmark.p',t83_xboole_1) ).
fof(t72_zfmisc_1,conjecture,
! [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(t72_zfmisc_1_neg,negated_conjecture,
~ ! [A,B,C] :
( set_difference(unordered_pair(A,B),C) = unordered_pair(A,B)
<=> ( ~ in(B,C)
& ~ in(A,C) ) ),
inference(assume_negation,[status(cth)],[t72_zfmisc_1]) ).
cnf(c_11,plain,
unordered_pair(A,B) = unordered_pair(B,A),
inference(clausify,[status(thm)],[commutativity_k2_tarski]) ).
cnf(c_15,plain,
( ~ in(A,C)
| ~ disjoint(unordered_pair(A,B),C) ),
inference(clausify,[status(thm)],[t55_zfmisc_1]) ).
cnf(c_16,plain,
( disjoint(unordered_pair(A,C),B)
| in(C,B)
| in(A,B) ),
inference(clausify,[status(thm)],[t57_zfmisc_1]) ).
cnf(c_17,plain,
( set_difference(A,B) = A
| ~ disjoint(A,B) ),
inference(clausify,[status(thm)],[t83_xboole_1]) ).
cnf(c_18,plain,
( set_difference(A,B) != A
| disjoint(A,B) ),
inference(clausify,[status(thm)],[t83_xboole_1]) ).
fof(nnf_9,plain,
? [A,B,C] :
( ( in(B,C)
| in(A,C)
| set_difference(unordered_pair(A,B),C) != unordered_pair(A,B) )
& ( ( ~ in(B,C)
& ~ in(A,C) )
| set_difference(unordered_pair(A,B),C) = unordered_pair(A,B) ) ),
inference(fof_nnf,[status(thm)],[t72_zfmisc_1_neg]) ).
fof(sk_t72_zfmisc_1_neg_sk,plain,
( ( in(sK1,sK2)
| in(sK0,sK2)
| set_difference(unordered_pair(sK0,sK1),sK2) != unordered_pair(sK0,sK1) )
& ( ( ~ in(sK1,sK2)
& ~ in(sK0,sK2) )
| set_difference(unordered_pair(sK0,sK1),sK2) = unordered_pair(sK0,sK1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(A,sK0),skolemize(B,sK1),skolemize(C,sK2)],[nnf_9]) ).
fof(sk_t72_zfmisc_1_neg,plain,
( ( in(sK1,sK2)
| in(sK0,sK2)
| set_difference(unordered_pair(sK0,sK1),sK2) != unordered_pair(sK0,sK1) )
& ( ~ in(sK1,sK2)
| set_difference(unordered_pair(sK0,sK1),sK2) = unordered_pair(sK0,sK1) )
& ( ~ in(sK0,sK2)
| set_difference(unordered_pair(sK0,sK1),sK2) = unordered_pair(sK0,sK1) ) ),
inference(cnf_transformation,[status(thm)],[sk_t72_zfmisc_1_neg_sk]) ).
cnf(c_19,negated_conjecture,
( ~ in(sK0,sK2)
| set_difference(unordered_pair(sK0,sK1),sK2) = unordered_pair(sK0,sK1) ),
inference(split_conjunct,[status(thm)],[sk_t72_zfmisc_1_neg]) ).
cnf(c_20,negated_conjecture,
( ~ in(sK1,sK2)
| set_difference(unordered_pair(sK0,sK1),sK2) = unordered_pair(sK0,sK1) ),
inference(split_conjunct,[status(thm)],[sk_t72_zfmisc_1_neg]) ).
cnf(c_21,negated_conjecture,
( in(sK1,sK2)
| in(sK0,sK2)
| set_difference(unordered_pair(sK0,sK1),sK2) != unordered_pair(sK0,sK1) ),
inference(split_conjunct,[status(thm)],[sk_t72_zfmisc_1_neg]) ).
cnf(c_24,plain,
( ~ in(B,C)
| ~ disjoint(unordered_pair(A,B),C) ),
inference(paramod,[status(thm)],[c_11,c_15]) ).
cnf(c_27,plain,
( in(B,C)
| in(A,C)
| set_difference(unordered_pair(A,B),C) = unordered_pair(A,B) ),
inference(resolve,[status(thm)],[c_17,c_16]) ).
cnf(c_62,plain,
( set_difference(unordered_pair(sK0,sK1),sK2) = unordered_pair(sK0,sK1)
| in(A,sK2)
| set_difference(unordered_pair(sK0,A),sK2) = unordered_pair(sK0,A) ),
inference(resolve,[status(thm)],[c_27,c_19]) ).
cnf(c_74,plain,
( in(sK1,sK2)
| set_difference(unordered_pair(sK0,sK1),sK2) = unordered_pair(sK0,sK1) ),
inference(factor,[status(thm)],[c_62]) ).
cnf(c_164,negated_conjecture,
( set_difference(unordered_pair(sK0,sK1),sK2) = unordered_pair(sK0,sK1)
| set_difference(unordered_pair(sK0,sK1),sK2) = unordered_pair(sK0,sK1) ),
inference(resolve,[status(thm)],[c_74,c_20]) ).
cnf(c_114,negated_conjecture,
set_difference(unordered_pair(sK0,sK1),sK2) = unordered_pair(sK0,sK1),
inference(copy,[status(thm)],[c_164]) ).
cnf(c_165,negated_conjecture,
( in(sK1,sK2)
| in(sK0,sK2)
| unordered_pair(sK0,sK1) != unordered_pair(sK0,sK1) ),
inference(paramod,[status(thm)],[c_114,c_21]) ).
cnf(c_115,negated_conjecture,
( in(sK1,sK2)
| in(sK0,sK2) ),
inference(copy,[status(thm)],[c_165]) ).
cnf(c_122,plain,
disjoint(unordered_pair(sK0,sK1),sK2),
inference(resolve,[status(thm)],[c_114,c_18]) ).
cnf(c_160,plain,
~ in(sK1,sK2),
inference(resolve,[status(thm)],[c_122,c_24]) ).
cnf(c_161,plain,
~ in(sK0,sK2),
inference(resolve,[status(thm)],[c_122,c_15]) ).
cnf(c_166,negated_conjecture,
in(sK1,sK2),
inference(resolve,[status(thm)],[c_161,c_115]) ).
cnf(c_163,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_160,c_166]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET928+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n002.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sat Sep 26 08:28:37 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.37 % Process 1255141 was started by sandbox2 on n002,
% 0.08/0.37 % Sat Sep 26 08:28:37 2026
% 0.08/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.08/0.37
% 0.08/0.37 % From the command line: assign(max_seconds, 300).
% 0.08/0.41
% 0.08/0.41 % SZS status Theorem for theBenchmark
% 0.08/0.41
% 0.08/0.41 % Proof 1 at 0.01 (+ 0.01) seconds.
% 0.08/0.41 % Length of proof is 23.
% 0.08/0.41 % Level of proof is 8.
% 0.08/0.41 % Maximum clause weight is 21.000.
% 0.08/0.41 % Given clauses 46.
% 0.08/0.41
% 0.08/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------