%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET890+1 : TPTP v9.2.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n007.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 05:08:55 PM UTC 2026
% Result : Theorem 1.30s 1.74s
% Output : CNFRefutation 1.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 35 ( 9 unt; 0 def)
% Number of atoms : 112 ( 37 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 127 ( 50 ~; 56 |; 14 &)
% ( 6 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 1 con; 0-3 aty)
% Number of variables : 81 ( 0 sgn 34 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d4_tarski,axiom,
! [X1,X2] :
( X2 = union(X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(X3,X4)
& in(X4,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_tarski) ).
fof(d1_tarski,axiom,
! [X1,X2] :
( X2 = singleton(X1)
<=> ! [X3] :
( in(X3,X2)
<=> X3 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).
fof(d3_tarski,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( in(X3,X1)
=> in(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(d10_xboole_0,axiom,
! [X1,X2] :
( X1 = X2
<=> ( subset(X1,X2)
& subset(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_xboole_0) ).
fof(t31_zfmisc_1,conjecture,
! [X1] : union(singleton(X1)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_zfmisc_1) ).
fof(c_0_5,plain,
! [X43,X44,X45,X47,X48,X49,X50,X52] :
( ( in(X45,esk3_3(X43,X44,X45))
| ~ in(X45,X44)
| X44 != union(X43) )
& ( in(esk3_3(X43,X44,X45),X43)
| ~ in(X45,X44)
| X44 != union(X43) )
& ( ~ in(X47,X48)
| ~ in(X48,X43)
| in(X47,X44)
| X44 != union(X43) )
& ( ~ in(esk4_2(X49,X50),X50)
| ~ in(esk4_2(X49,X50),X52)
| ~ in(X52,X49)
| X50 = union(X49) )
& ( in(esk4_2(X49,X50),esk5_2(X49,X50))
| in(esk4_2(X49,X50),X50)
| X50 = union(X49) )
& ( in(esk5_2(X49,X50),X49)
| in(esk4_2(X49,X50),X50)
| X50 = union(X49) ) ),
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)],[d4_tarski])])])])])]) ).
fof(c_0_6,plain,
! [X30,X31,X32,X33,X34,X35] :
( ( ~ in(X32,X31)
| X32 = X30
| X31 != singleton(X30) )
& ( X33 != X30
| in(X33,X31)
| X31 != singleton(X30) )
& ( ~ in(esk1_2(X34,X35),X35)
| esk1_2(X34,X35) != X34
| X35 = singleton(X34) )
& ( in(esk1_2(X34,X35),X35)
| esk1_2(X34,X35) = X34
| X35 = singleton(X34) ) ),
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)],[d1_tarski])])])])])]) ).
cnf(c_0_7,plain,
( in(X1,X4)
| ~ in(X1,X2)
| ~ in(X2,X3)
| X4 != union(X3) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_8,plain,
( in(X1,X3)
| X1 != X2
| X3 != singleton(X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_9,plain,
( X1 = X3
| ~ in(X1,X2)
| X2 != singleton(X3) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,plain,
( in(esk3_3(X1,X2,X3),X1)
| ~ in(X3,X2)
| X2 != union(X1) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
fof(c_0_11,plain,
! [X37,X38,X39,X40,X41] :
( ( ~ subset(X37,X38)
| ~ in(X39,X37)
| in(X39,X38) )
& ( in(esk2_2(X40,X41),X40)
| subset(X40,X41) )
& ( ~ in(esk2_2(X40,X41),X41)
| subset(X40,X41) ) ),
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)],[d3_tarski])])])])])]) ).
cnf(c_0_12,plain,
( in(X1,union(X2))
| ~ in(X3,X2)
| ~ in(X1,X3) ),
inference(er,[status(thm)],[c_0_7]) ).
cnf(c_0_13,plain,
in(X1,singleton(X1)),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_8])]) ).
cnf(c_0_14,plain,
( in(X1,esk3_3(X2,X3,X1))
| ~ in(X1,X3)
| X3 != union(X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_15,plain,
( X1 = X2
| ~ in(X1,singleton(X2)) ),
inference(er,[status(thm)],[c_0_9]) ).
cnf(c_0_16,plain,
( in(esk3_3(X1,union(X1),X2),X1)
| ~ in(X2,union(X1)) ),
inference(er,[status(thm)],[c_0_10]) ).
cnf(c_0_17,plain,
( subset(X1,X2)
| ~ in(esk2_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_18,plain,
( in(X1,union(singleton(X2)))
| ~ in(X1,X2) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_19,plain,
( in(X1,esk3_3(X2,union(X2),X1))
| ~ in(X1,union(X2)) ),
inference(er,[status(thm)],[c_0_14]) ).
cnf(c_0_20,plain,
( esk3_3(singleton(X1),union(singleton(X1)),X2) = X1
| ~ in(X2,union(singleton(X1))) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
fof(c_0_21,plain,
! [X28,X29] :
( ( subset(X28,X29)
| X28 != X29 )
& ( subset(X29,X28)
| X28 != X29 )
& ( ~ subset(X28,X29)
| ~ subset(X29,X28)
| X28 = X29 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d10_xboole_0])])]) ).
cnf(c_0_22,plain,
( subset(X1,union(singleton(X2)))
| ~ in(esk2_2(X1,union(singleton(X2))),X2) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_23,plain,
( in(esk2_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_24,plain,
( in(X1,X2)
| ~ in(X1,union(singleton(X2))) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
fof(c_0_25,negated_conjecture,
~ ! [X1] : union(singleton(X1)) = X1,
inference(assume_negation,[status(cth)],[t31_zfmisc_1]) ).
cnf(c_0_26,plain,
( X1 = X2
| ~ subset(X1,X2)
| ~ subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_27,plain,
subset(X1,union(singleton(X1))),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_28,plain,
( subset(union(singleton(X1)),X2)
| in(esk2_2(union(singleton(X1)),X2),X1) ),
inference(spm,[status(thm)],[c_0_24,c_0_23]) ).
fof(c_0_29,negated_conjecture,
union(singleton(esk8_0)) != esk8_0,
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_25])])]) ).
cnf(c_0_30,plain,
( union(singleton(X1)) = X1
| ~ subset(union(singleton(X1)),X1) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_31,plain,
subset(union(singleton(X1)),X1),
inference(spm,[status(thm)],[c_0_17,c_0_28]) ).
cnf(c_0_32,negated_conjecture,
union(singleton(esk8_0)) != esk8_0,
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_33,plain,
union(singleton(X1)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_30,c_0_31])]) ).
cnf(c_0_34,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_32,c_0_33])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : SET890+1 : TPTP v9.2.1. Released v3.2.0.
% 0.11/0.13 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.18/0.34 % Computer : n007.cluster.edu
% 0.18/0.34 % Model : x86_64 x86_64
% 0.18/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.34 % Memory : 8042.1875MB
% 0.18/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.34 % CPULimit : 300
% 0.18/0.34 % WCLimit : 300
% 0.18/0.34 % DateTime : Tue May 5 02:37:54 EDT 2026
% 0.18/0.34 % CPUTime :
% 0.18/0.35 % start to proof: theBenchmark
% 1.30/1.74 % Version : CSE_E---1.7
% 1.30/1.74 % Problem : theBenchmark.p
% 1.30/1.74 % SZS status Theorem for theBenchmark.p
% 1.30/1.74 % SZS output start CNFRefutation
% See solution above
% 1.30/1.74 % Total time : 1.369s
%------------------------------------------------------------------------------