%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET931+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 : n013.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 05:09:00 PM UTC 2026
% Result : Theorem 1.26s 1.71s
% Output : CNFRefutation 1.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 4
% Syntax : Number of formulae : 36 ( 8 unt; 0 def)
% Number of atoms : 112 ( 83 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 129 ( 53 ~; 54 |; 18 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 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 : 44 ( 11 sgn 19 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t75_zfmisc_1,conjecture,
! [X1,X2,X3] :
( set_difference(X1,unordered_pair(X2,X3)) = empty_set
<=> ~ ( X1 != empty_set
& X1 != singleton(X2)
& X1 != singleton(X3)
& X1 != unordered_pair(X2,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t75_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(l46_zfmisc_1,axiom,
! [X1,X2,X3] :
( subset(X1,unordered_pair(X2,X3))
<=> ~ ( X1 != empty_set
& X1 != singleton(X2)
& X1 != singleton(X3)
& X1 != unordered_pair(X2,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l46_zfmisc_1) ).
fof(reflexivity_r1_tarski,axiom,
! [X1,X2] : subset(X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(c_0_4,negated_conjecture,
~ ! [X1,X2,X3] :
( set_difference(X1,unordered_pair(X2,X3)) = empty_set
<=> ~ ( X1 != empty_set
& X1 != singleton(X2)
& X1 != singleton(X3)
& X1 != unordered_pair(X2,X3) ) ),
inference(assume_negation,[status(cth)],[t75_zfmisc_1]) ).
fof(c_0_5,plain,
! [X26,X27] :
( ( set_difference(X26,X27) != empty_set
| subset(X26,X27) )
& ( ~ subset(X26,X27)
| set_difference(X26,X27) = empty_set ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t37_xboole_1])]) ).
fof(c_0_6,negated_conjecture,
( ( esk3_0 != empty_set
| set_difference(esk3_0,unordered_pair(esk4_0,esk5_0)) != empty_set )
& ( esk3_0 != singleton(esk4_0)
| set_difference(esk3_0,unordered_pair(esk4_0,esk5_0)) != empty_set )
& ( esk3_0 != singleton(esk5_0)
| set_difference(esk3_0,unordered_pair(esk4_0,esk5_0)) != empty_set )
& ( esk3_0 != unordered_pair(esk4_0,esk5_0)
| set_difference(esk3_0,unordered_pair(esk4_0,esk5_0)) != empty_set )
& ( set_difference(esk3_0,unordered_pair(esk4_0,esk5_0)) = empty_set
| esk3_0 = empty_set
| esk3_0 = singleton(esk4_0)
| esk3_0 = singleton(esk5_0)
| esk3_0 = unordered_pair(esk4_0,esk5_0) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])])]) ).
fof(c_0_7,plain,
! [X20,X21,X22] :
( ( ~ subset(X20,unordered_pair(X21,X22))
| X20 = empty_set
| X20 = singleton(X21)
| X20 = singleton(X22)
| X20 = unordered_pair(X21,X22) )
& ( X20 != empty_set
| subset(X20,unordered_pair(X21,X22)) )
& ( X20 != singleton(X21)
| subset(X20,unordered_pair(X21,X22)) )
& ( X20 != singleton(X22)
| subset(X20,unordered_pair(X21,X22)) )
& ( X20 != unordered_pair(X21,X22)
| subset(X20,unordered_pair(X21,X22)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l46_zfmisc_1])])]) ).
cnf(c_0_8,plain,
( subset(X1,X2)
| set_difference(X1,X2) != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_9,negated_conjecture,
( set_difference(esk3_0,unordered_pair(esk4_0,esk5_0)) = empty_set
| esk3_0 = empty_set
| esk3_0 = singleton(esk4_0)
| esk3_0 = singleton(esk5_0)
| esk3_0 = unordered_pair(esk4_0,esk5_0) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,plain,
( subset(X1,unordered_pair(X3,X2))
| X1 != singleton(X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,plain,
( X1 = empty_set
| X1 = singleton(X2)
| X1 = singleton(X3)
| X1 = unordered_pair(X2,X3)
| ~ subset(X1,unordered_pair(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,negated_conjecture,
( unordered_pair(esk4_0,esk5_0) = esk3_0
| singleton(esk5_0) = esk3_0
| singleton(esk4_0) = esk3_0
| esk3_0 = empty_set
| subset(esk3_0,unordered_pair(esk4_0,esk5_0)) ),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_13,negated_conjecture,
( esk3_0 != singleton(esk5_0)
| set_difference(esk3_0,unordered_pair(esk4_0,esk5_0)) != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_14,plain,
( set_difference(X1,X2) = empty_set
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_15,plain,
subset(singleton(X1),unordered_pair(X2,X1)),
inference(er,[status(thm)],[c_0_10]) ).
cnf(c_0_16,negated_conjecture,
( unordered_pair(esk4_0,esk5_0) = esk3_0
| singleton(esk4_0) = esk3_0
| singleton(esk5_0) = esk3_0
| esk3_0 = empty_set ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_17,plain,
( subset(X1,unordered_pair(X2,X3))
| X1 != singleton(X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_18,negated_conjecture,
( singleton(esk5_0) != esk3_0
| ~ subset(esk3_0,unordered_pair(esk4_0,esk5_0)) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_19,negated_conjecture,
( unordered_pair(esk4_0,esk5_0) = esk3_0
| singleton(esk4_0) = esk3_0
| esk3_0 = empty_set
| subset(esk3_0,unordered_pair(X1,esk5_0)) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_20,negated_conjecture,
( esk3_0 != singleton(esk4_0)
| set_difference(esk3_0,unordered_pair(esk4_0,esk5_0)) != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_21,plain,
subset(singleton(X1),unordered_pair(X1,X2)),
inference(er,[status(thm)],[c_0_17]) ).
cnf(c_0_22,negated_conjecture,
( unordered_pair(esk4_0,esk5_0) = esk3_0
| singleton(esk4_0) = esk3_0
| esk3_0 = empty_set ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_16]) ).
cnf(c_0_23,negated_conjecture,
( esk3_0 != unordered_pair(esk4_0,esk5_0)
| set_difference(esk3_0,unordered_pair(esk4_0,esk5_0)) != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_24,negated_conjecture,
( singleton(esk4_0) != esk3_0
| ~ subset(esk3_0,unordered_pair(esk4_0,esk5_0)) ),
inference(spm,[status(thm)],[c_0_20,c_0_14]) ).
cnf(c_0_25,negated_conjecture,
( unordered_pair(esk4_0,esk5_0) = esk3_0
| esk3_0 = empty_set
| subset(esk3_0,unordered_pair(esk4_0,X1)) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
fof(c_0_26,plain,
! [X25] : subset(X25,X25),
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[reflexivity_r1_tarski])]) ).
cnf(c_0_27,negated_conjecture,
( esk3_0 != empty_set
| set_difference(esk3_0,unordered_pair(esk4_0,esk5_0)) != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_28,negated_conjecture,
( unordered_pair(esk4_0,esk5_0) != esk3_0
| ~ subset(esk3_0,unordered_pair(esk4_0,esk5_0)) ),
inference(spm,[status(thm)],[c_0_23,c_0_14]) ).
cnf(c_0_29,negated_conjecture,
( unordered_pair(esk4_0,esk5_0) = esk3_0
| esk3_0 = empty_set ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_22]) ).
cnf(c_0_30,plain,
subset(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_31,plain,
( subset(X1,unordered_pair(X2,X3))
| X1 != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_32,negated_conjecture,
( esk3_0 != empty_set
| ~ subset(esk3_0,unordered_pair(esk4_0,esk5_0)) ),
inference(spm,[status(thm)],[c_0_27,c_0_14]) ).
cnf(c_0_33,negated_conjecture,
esk3_0 = empty_set,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30])]) ).
cnf(c_0_34,plain,
subset(empty_set,unordered_pair(X1,X2)),
inference(er,[status(thm)],[c_0_31]) ).
cnf(c_0_35,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_32,c_0_33]),c_0_33]),c_0_34])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET931+1 : TPTP v9.2.1. Released v3.2.0.
% 0.00/0.12 % 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
% 0.15/0.33 % Computer : n013.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue May 5 02:40:11 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.26/1.71 % Version : CSE_E---1.7
% 1.26/1.71 % Problem : theBenchmark.p
% 1.26/1.71 % SZS status Theorem for theBenchmark.p
% 1.26/1.71 % SZS output start CNFRefutation
% See solution above
% 1.26/1.72 % Total time : 1.368s
%------------------------------------------------------------------------------