%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET930+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 : n005.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 1.26s 1.71s
% Output : CNFRefutation 1.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 37 ( 12 unt; 0 def)
% Number of atoms : 99 ( 51 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 116 ( 54 ~; 34 |; 21 &)
% ( 5 <=>; 2 =>; 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 : 68 ( 2 sgn 40 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(l39_zfmisc_1,axiom,
! [X1,X2,X3] :
( set_difference(unordered_pair(X1,X2),X3) = singleton(X1)
<=> ( ~ in(X1,X3)
& ( in(X2,X3)
| X1 = X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l39_zfmisc_1) ).
fof(t72_zfmisc_1,axiom,
! [X1,X2,X3] :
( set_difference(unordered_pair(X1,X2),X3) = unordered_pair(X1,X2)
<=> ( ~ in(X1,X3)
& ~ in(X2,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t72_zfmisc_1) ).
fof(antisymmetry_r2_hidden,axiom,
! [X1,X2] :
( in(X1,X2)
=> ~ in(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(t74_zfmisc_1,conjecture,
! [X1,X2,X3] :
~ ( set_difference(unordered_pair(X1,X2),X3) != empty_set
& set_difference(unordered_pair(X1,X2),X3) != singleton(X1)
& set_difference(unordered_pair(X1,X2),X3) != singleton(X2)
& set_difference(unordered_pair(X1,X2),X3) != unordered_pair(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t74_zfmisc_1) ).
fof(t73_zfmisc_1,axiom,
! [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(commutativity_k2_tarski,axiom,
! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(c_0_6,plain,
! [X1,X2,X3] :
( set_difference(unordered_pair(X1,X2),X3) = singleton(X1)
<=> ( ~ in(X1,X3)
& ( in(X2,X3)
| X1 = X2 ) ) ),
inference(fof_simplification,[status(thm)],[l39_zfmisc_1]) ).
fof(c_0_7,plain,
! [X26,X27,X28] :
( ( ~ in(X26,X28)
| set_difference(unordered_pair(X26,X27),X28) != singleton(X26) )
& ( in(X27,X28)
| X26 = X27
| set_difference(unordered_pair(X26,X27),X28) != singleton(X26) )
& ( ~ in(X27,X28)
| in(X26,X28)
| set_difference(unordered_pair(X26,X27),X28) = singleton(X26) )
& ( X26 != X27
| in(X26,X28)
| set_difference(unordered_pair(X26,X27),X28) = singleton(X26) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])]) ).
fof(c_0_8,plain,
! [X1,X2,X3] :
( set_difference(unordered_pair(X1,X2),X3) = unordered_pair(X1,X2)
<=> ( ~ in(X1,X3)
& ~ in(X2,X3) ) ),
inference(fof_simplification,[status(thm)],[t72_zfmisc_1]) ).
fof(c_0_9,plain,
! [X1,X2] :
( in(X1,X2)
=> ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[antisymmetry_r2_hidden]) ).
cnf(c_0_10,plain,
( in(X1,X3)
| set_difference(unordered_pair(X1,X2),X3) = singleton(X1)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_11,plain,
! [X31,X32,X33] :
( ( ~ in(X31,X33)
| set_difference(unordered_pair(X31,X32),X33) != unordered_pair(X31,X32) )
& ( ~ in(X32,X33)
| set_difference(unordered_pair(X31,X32),X33) != unordered_pair(X31,X32) )
& ( in(X31,X33)
| in(X32,X33)
| set_difference(unordered_pair(X31,X32),X33) = unordered_pair(X31,X32) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])]) ).
fof(c_0_12,plain,
! [X22,X23] :
( ~ in(X22,X23)
| ~ in(X23,X22) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])]) ).
cnf(c_0_13,plain,
( set_difference(unordered_pair(X1,X1),X2) = singleton(X1)
| in(X1,X2) ),
inference(er,[status(thm)],[c_0_10]) ).
cnf(c_0_14,plain,
( in(X1,X2)
| in(X3,X2)
| set_difference(unordered_pair(X1,X3),X2) = unordered_pair(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_15,negated_conjecture,
~ ! [X1,X2,X3] :
~ ( set_difference(unordered_pair(X1,X2),X3) != empty_set
& set_difference(unordered_pair(X1,X2),X3) != singleton(X1)
& set_difference(unordered_pair(X1,X2),X3) != singleton(X2)
& set_difference(unordered_pair(X1,X2),X3) != unordered_pair(X1,X2) ),
inference(assume_negation,[status(cth)],[t74_zfmisc_1]) ).
cnf(c_0_16,plain,
( ~ in(X1,X2)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_17,plain,
( unordered_pair(X1,X1) = singleton(X1)
| in(X1,X2) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
fof(c_0_18,negated_conjecture,
( set_difference(unordered_pair(esk3_0,esk4_0),esk5_0) != empty_set
& set_difference(unordered_pair(esk3_0,esk4_0),esk5_0) != singleton(esk3_0)
& set_difference(unordered_pair(esk3_0,esk4_0),esk5_0) != singleton(esk4_0)
& set_difference(unordered_pair(esk3_0,esk4_0),esk5_0) != unordered_pair(esk3_0,esk4_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_15])])]) ).
fof(c_0_19,plain,
! [X34,X35,X36] :
( ( in(X34,X36)
| set_difference(unordered_pair(X34,X35),X36) != empty_set )
& ( in(X35,X36)
| set_difference(unordered_pair(X34,X35),X36) != empty_set )
& ( ~ in(X34,X36)
| ~ in(X35,X36)
| set_difference(unordered_pair(X34,X35),X36) = empty_set ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t73_zfmisc_1])])]) ).
cnf(c_0_20,plain,
( unordered_pair(X1,X1) = singleton(X1)
| ~ in(X2,X1) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_21,negated_conjecture,
set_difference(unordered_pair(esk3_0,esk4_0),esk5_0) != empty_set,
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_22,plain,
( set_difference(unordered_pair(X1,X3),X2) = empty_set
| ~ in(X1,X2)
| ~ in(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_23,plain,
( unordered_pair(X1,X1) = singleton(X1)
| unordered_pair(X2,X2) = singleton(X2) ),
inference(spm,[status(thm)],[c_0_20,c_0_17]) ).
fof(c_0_24,plain,
! [X24,X25] : unordered_pair(X24,X25) = unordered_pair(X25,X24),
inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).
cnf(c_0_25,negated_conjecture,
set_difference(unordered_pair(esk3_0,esk4_0),esk5_0) != singleton(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_26,plain,
( in(X3,X2)
| set_difference(unordered_pair(X3,X1),X2) = singleton(X3)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_27,negated_conjecture,
( ~ in(esk4_0,esk5_0)
| ~ in(esk3_0,esk5_0) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_28,negated_conjecture,
set_difference(unordered_pair(esk3_0,esk4_0),esk5_0) != singleton(esk4_0),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_29,plain,
unordered_pair(X1,X1) = singleton(X1),
inference(ef,[status(thm)],[c_0_23]) ).
cnf(c_0_30,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_31,negated_conjecture,
set_difference(unordered_pair(esk3_0,esk4_0),esk5_0) != unordered_pair(esk3_0,esk4_0),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_32,negated_conjecture,
~ in(esk4_0,esk5_0),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27]) ).
cnf(c_0_33,negated_conjecture,
set_difference(unordered_pair(esk3_0,esk4_0),esk5_0) != unordered_pair(esk4_0,esk4_0),
inference(rw,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_34,plain,
( set_difference(unordered_pair(X1,X2),X3) = singleton(X2)
| in(X2,X3)
| ~ in(X1,X3) ),
inference(spm,[status(thm)],[c_0_26,c_0_30]) ).
cnf(c_0_35,negated_conjecture,
in(esk3_0,esk5_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_14]),c_0_32]) ).
cnf(c_0_36,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_29]),c_0_35])]),c_0_32]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SET930+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 : n005.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 02:40:15 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.33 % 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
% 1.26/1.71 % Total time : 1.370s
%------------------------------------------------------------------------------