%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET929+1 : TPTP v9.2.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n028.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 05:08:59 PM UTC 2026
% Result : Theorem 1.23s 1.71s
% Output : CNFRefutation 1.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 23 ( 4 unt; 0 def)
% Number of atoms : 60 ( 13 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 62 ( 25 ~; 25 |; 8 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 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 : 29 ( 2 sgn 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t73_zfmisc_1,conjecture,
! [X1,X2,X3] :
( set_difference(unordered_pair(X1,X2),X3) = empty_set
<=> ( in(X1,X3)
& in(X2,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t73_zfmisc_1) ).
fof(t37_xboole_1,axiom,
! [X1,X2] :
( set_difference(X1,X2) = empty_set
<=> subset(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_xboole_1) ).
fof(t38_zfmisc_1,axiom,
! [X1,X2,X3] :
( subset(unordered_pair(X1,X2),X3)
<=> ( in(X1,X3)
& in(X2,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t38_zfmisc_1) ).
fof(c_0_3,negated_conjecture,
~ ! [X1,X2,X3] :
( set_difference(unordered_pair(X1,X2),X3) = empty_set
<=> ( in(X1,X3)
& in(X2,X3) ) ),
inference(assume_negation,[status(cth)],[t73_zfmisc_1]) ).
fof(c_0_4,negated_conjecture,
( ( set_difference(unordered_pair(esk3_0,esk4_0),esk5_0) != empty_set
| ~ in(esk3_0,esk5_0)
| ~ in(esk4_0,esk5_0) )
& ( in(esk3_0,esk5_0)
| set_difference(unordered_pair(esk3_0,esk4_0),esk5_0) = empty_set )
& ( in(esk4_0,esk5_0)
| set_difference(unordered_pair(esk3_0,esk4_0),esk5_0) = empty_set ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])])]) ).
fof(c_0_5,plain,
! [X27,X28] :
( ( set_difference(X27,X28) != empty_set
| subset(X27,X28) )
& ( ~ subset(X27,X28)
| set_difference(X27,X28) = empty_set ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t37_xboole_1])]) ).
cnf(c_0_6,negated_conjecture,
( set_difference(unordered_pair(esk3_0,esk4_0),esk5_0) != empty_set
| ~ in(esk3_0,esk5_0)
| ~ in(esk4_0,esk5_0) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_7,plain,
( set_difference(X1,X2) = empty_set
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
fof(c_0_8,plain,
! [X29,X30,X31] :
( ( in(X29,X31)
| ~ subset(unordered_pair(X29,X30),X31) )
& ( in(X30,X31)
| ~ subset(unordered_pair(X29,X30),X31) )
& ( ~ in(X29,X31)
| ~ in(X30,X31)
| subset(unordered_pair(X29,X30),X31) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t38_zfmisc_1])])]) ).
cnf(c_0_9,plain,
( subset(X1,X2)
| set_difference(X1,X2) != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_10,negated_conjecture,
( in(esk4_0,esk5_0)
| set_difference(unordered_pair(esk3_0,esk4_0),esk5_0) = empty_set ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_11,negated_conjecture,
( ~ subset(unordered_pair(esk3_0,esk4_0),esk5_0)
| ~ in(esk3_0,esk5_0)
| ~ in(esk4_0,esk5_0) ),
inference(spm,[status(thm)],[c_0_6,c_0_7]) ).
cnf(c_0_12,plain,
( subset(unordered_pair(X1,X3),X2)
| ~ in(X1,X2)
| ~ in(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,plain,
( in(X1,X2)
| ~ subset(unordered_pair(X3,X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_14,negated_conjecture,
( subset(unordered_pair(esk3_0,esk4_0),esk5_0)
| in(esk4_0,esk5_0) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_15,negated_conjecture,
( in(esk3_0,esk5_0)
| set_difference(unordered_pair(esk3_0,esk4_0),esk5_0) = empty_set ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_16,negated_conjecture,
( ~ in(esk3_0,esk5_0)
| ~ in(esk4_0,esk5_0) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_17,negated_conjecture,
in(esk4_0,esk5_0),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_18,negated_conjecture,
( subset(unordered_pair(esk3_0,esk4_0),esk5_0)
| in(esk3_0,esk5_0) ),
inference(spm,[status(thm)],[c_0_9,c_0_15]) ).
cnf(c_0_19,negated_conjecture,
~ in(esk3_0,esk5_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_16,c_0_17])]) ).
cnf(c_0_20,plain,
( in(X1,X2)
| ~ subset(unordered_pair(X1,X3),X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_21,negated_conjecture,
subset(unordered_pair(esk3_0,esk4_0),esk5_0),
inference(sr,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_22,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_19]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SET929+1 : TPTP v9.2.1. Released v3.2.0.
% 0.00/0.11 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.14/0.32 % Computer : n028.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Tue May 5 02:40:30 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.33 % start to proof: theBenchmark
% 1.23/1.71 % Version : CSE_E---1.7
% 1.23/1.71 % Problem : theBenchmark.p
% 1.23/1.71 % SZS status Theorem for theBenchmark.p
% 1.23/1.71 % SZS output start CNFRefutation
% See solution above
% 1.23/1.71 % Total time : 1.371s
%------------------------------------------------------------------------------