%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET887+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 : n024.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 05:08:54 PM UTC 2026
% Result : Theorem 1.11s 1.61s
% Output : CNFRefutation 1.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 5
% Syntax : Number of formulae : 41 ( 10 unt; 0 def)
% Number of atoms : 128 ( 94 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 138 ( 51 ~; 62 |; 19 &)
% ( 5 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-3 aty)
% Number of variables : 72 ( 9 sgn 39 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t28_zfmisc_1,conjecture,
! [X1,X2,X3,X4] :
~ ( subset(unordered_pair(X1,X2),unordered_pair(X3,X4))
& X1 != X3
& X1 != X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_zfmisc_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(t8_zfmisc_1,axiom,
! [X1,X2,X3] :
( singleton(X1) = unordered_pair(X2,X3)
=> X1 = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_zfmisc_1) ).
fof(d2_tarski,axiom,
! [X1,X2,X3] :
( X3 = unordered_pair(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( X4 = X1
| X4 = X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_tarski) ).
fof(d1_xboole_0,axiom,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_xboole_0) ).
fof(c_0_5,negated_conjecture,
~ ! [X1,X2,X3,X4] :
~ ( subset(unordered_pair(X1,X2),unordered_pair(X3,X4))
& X1 != X3
& X1 != X4 ),
inference(assume_negation,[status(cth)],[t28_zfmisc_1]) ).
fof(c_0_6,plain,
! [X50,X51,X52] :
( ( ~ subset(X50,unordered_pair(X51,X52))
| X50 = empty_set
| X50 = singleton(X51)
| X50 = singleton(X52)
| X50 = unordered_pair(X51,X52) )
& ( X50 != empty_set
| subset(X50,unordered_pair(X51,X52)) )
& ( X50 != singleton(X51)
| subset(X50,unordered_pair(X51,X52)) )
& ( X50 != singleton(X52)
| subset(X50,unordered_pair(X51,X52)) )
& ( X50 != unordered_pair(X51,X52)
| subset(X50,unordered_pair(X51,X52)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l46_zfmisc_1])])]) ).
fof(c_0_7,negated_conjecture,
( subset(unordered_pair(esk5_0,esk6_0),unordered_pair(esk7_0,esk8_0))
& esk5_0 != esk7_0
& esk5_0 != esk8_0 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])]) ).
fof(c_0_8,plain,
! [X64,X65,X66] :
( singleton(X64) != unordered_pair(X65,X66)
| X64 = X65 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t8_zfmisc_1])]) ).
cnf(c_0_9,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_6]) ).
cnf(c_0_10,negated_conjecture,
subset(unordered_pair(esk5_0,esk6_0),unordered_pair(esk7_0,esk8_0)),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,plain,
( X1 = X2
| singleton(X1) != unordered_pair(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_12,negated_conjecture,
( unordered_pair(esk7_0,esk8_0) = unordered_pair(esk5_0,esk6_0)
| singleton(esk7_0) = unordered_pair(esk5_0,esk6_0)
| singleton(esk8_0) = unordered_pair(esk5_0,esk6_0)
| unordered_pair(esk5_0,esk6_0) = empty_set ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_13,negated_conjecture,
( unordered_pair(esk7_0,esk8_0) = unordered_pair(esk5_0,esk6_0)
| singleton(esk7_0) = unordered_pair(esk5_0,esk6_0)
| unordered_pair(esk5_0,esk6_0) = empty_set
| esk8_0 = X1
| unordered_pair(esk5_0,esk6_0) != unordered_pair(X1,X2) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_14,negated_conjecture,
esk5_0 != esk8_0,
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_15,plain,
! [X41,X42,X43,X44,X45,X46,X47,X48] :
( ( ~ in(X44,X43)
| X44 = X41
| X44 = X42
| X43 != unordered_pair(X41,X42) )
& ( X45 != X41
| in(X45,X43)
| X43 != unordered_pair(X41,X42) )
& ( X45 != X42
| in(X45,X43)
| X43 != unordered_pair(X41,X42) )
& ( esk2_3(X46,X47,X48) != X46
| ~ in(esk2_3(X46,X47,X48),X48)
| X48 = unordered_pair(X46,X47) )
& ( esk2_3(X46,X47,X48) != X47
| ~ in(esk2_3(X46,X47,X48),X48)
| X48 = unordered_pair(X46,X47) )
& ( in(esk2_3(X46,X47,X48),X48)
| esk2_3(X46,X47,X48) = X46
| esk2_3(X46,X47,X48) = X47
| X48 = unordered_pair(X46,X47) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[d2_tarski])])])])])]) ).
cnf(c_0_16,negated_conjecture,
( unordered_pair(esk7_0,esk8_0) = unordered_pair(esk5_0,esk6_0)
| singleton(esk7_0) = unordered_pair(esk5_0,esk6_0)
| unordered_pair(esk5_0,esk6_0) = empty_set ),
inference(sr,[status(thm)],[inference(er,[status(thm)],[c_0_13]),c_0_14]) ).
cnf(c_0_17,plain,
( in(X1,X3)
| X1 != X2
| X3 != unordered_pair(X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_18,negated_conjecture,
( unordered_pair(esk7_0,esk8_0) = unordered_pair(esk5_0,esk6_0)
| unordered_pair(esk5_0,esk6_0) = empty_set
| esk7_0 = X1
| unordered_pair(esk5_0,esk6_0) != unordered_pair(X1,X2) ),
inference(spm,[status(thm)],[c_0_11,c_0_16]) ).
cnf(c_0_19,negated_conjecture,
esk5_0 != esk7_0,
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_20,plain,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[d1_xboole_0]) ).
cnf(c_0_21,plain,
( X1 = X3
| X1 = X4
| ~ in(X1,X2)
| X2 != unordered_pair(X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_22,plain,
in(X1,unordered_pair(X1,X2)),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_17])]) ).
cnf(c_0_23,negated_conjecture,
( unordered_pair(esk7_0,esk8_0) = unordered_pair(esk5_0,esk6_0)
| unordered_pair(esk5_0,esk6_0) = empty_set ),
inference(sr,[status(thm)],[inference(er,[status(thm)],[c_0_18]),c_0_19]) ).
fof(c_0_24,plain,
! [X37,X38,X39] :
( ( X37 != empty_set
| ~ in(X38,X37) )
& ( in(esk1_1(X39),X39)
| X39 = empty_set ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_20])])])])]) ).
cnf(c_0_25,plain,
( X1 = X2
| X1 = X3
| ~ in(X1,unordered_pair(X3,X2)) ),
inference(er,[status(thm)],[c_0_21]) ).
cnf(c_0_26,negated_conjecture,
( unordered_pair(esk5_0,esk6_0) = empty_set
| in(esk7_0,unordered_pair(esk5_0,esk6_0)) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_27,plain,
( X1 != empty_set
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_28,negated_conjecture,
( unordered_pair(esk5_0,esk6_0) = empty_set
| esk6_0 = esk7_0 ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_19]) ).
cnf(c_0_29,plain,
~ in(X1,empty_set),
inference(er,[status(thm)],[c_0_27]) ).
cnf(c_0_30,plain,
( in(X1,X3)
| X1 != X2
| X3 != unordered_pair(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_31,negated_conjecture,
esk6_0 = esk7_0,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_28]),c_0_29]) ).
cnf(c_0_32,plain,
in(X1,unordered_pair(X2,X1)),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_30])]) ).
cnf(c_0_33,negated_conjecture,
( unordered_pair(esk7_0,esk8_0) = unordered_pair(esk5_0,esk7_0)
| unordered_pair(esk5_0,esk7_0) = empty_set ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_23,c_0_31]),c_0_31]) ).
cnf(c_0_34,negated_conjecture,
( unordered_pair(esk5_0,esk7_0) = empty_set
| in(esk8_0,unordered_pair(esk5_0,esk7_0)) ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_35,negated_conjecture,
( unordered_pair(esk5_0,esk7_0) = empty_set
| esk8_0 = esk7_0 ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_34]),c_0_14]) ).
cnf(c_0_36,negated_conjecture,
esk8_0 = esk7_0,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_35]),c_0_29]) ).
cnf(c_0_37,negated_conjecture,
( unordered_pair(esk7_0,esk7_0) = unordered_pair(esk5_0,esk7_0)
| unordered_pair(esk5_0,esk7_0) = empty_set ),
inference(rw,[status(thm)],[c_0_33,c_0_36]) ).
cnf(c_0_38,negated_conjecture,
( unordered_pair(esk5_0,esk7_0) = empty_set
| X1 = esk7_0
| ~ in(X1,unordered_pair(esk5_0,esk7_0)) ),
inference(spm,[status(thm)],[c_0_25,c_0_37]) ).
cnf(c_0_39,negated_conjecture,
unordered_pair(esk5_0,esk7_0) = empty_set,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_22]),c_0_19]) ).
cnf(c_0_40,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_39]),c_0_29]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : SET887+1 : TPTP v9.2.1. Released v3.2.0.
% 0.00/0.06 % 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
% 0.06/0.24 % Computer : n024.cluster.edu
% 0.06/0.24 % Model : x86_64 x86_64
% 0.06/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.24 % Memory : 8042.1875MB
% 0.06/0.24 % OS : Linux 3.10.0-693.el7.x86_64
% 0.06/0.24 % CPULimit : 300
% 0.06/0.24 % WCLimit : 300
% 0.06/0.24 % DateTime : Mon May 4 21:38:26 EDT 2026
% 0.06/0.24 % CPUTime :
% 0.06/0.24 % start to proof: theBenchmark
% 1.11/1.61 % Version : CSE_E---1.7
% 1.11/1.61 % Problem : theBenchmark.p
% 1.11/1.61 % SZS status Theorem for theBenchmark.p
% 1.11/1.61 % SZS output start CNFRefutation
% See solution above
% 1.11/1.61 % Total time : 1.361s
%------------------------------------------------------------------------------