%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEV517+1 : TPTP v9.2.1. Released v7.3.0.
% 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 : n022.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 05:15:20 PM UTC 2026
% Result : Theorem 12.58s 8.55s
% Output : CNFRefutation 12.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 30 ( 10 unt; 0 def)
% Number of atoms : 180 ( 11 equ)
% Maximal formula atoms : 105 ( 6 avg)
% Number of connectives : 221 ( 71 ~; 101 |; 39 &)
% ( 4 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 39 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 4 con; 0-3 aty)
% Number of variables : 63 ( 2 sgn 38 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(diff_elem_in_partition,conjecture,
! [X3,X1,X2,X11] :
( ( member(X3,difference(X1,X2))
& partition(X11,X1) )
=> ? [X12] :
( member(X12,difference(X11,singleton(X2)))
& member(X3,X12) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',diff_elem_in_partition) ).
fof(difference,axiom,
! [X2,X1,X4] :
( member(X2,difference(X4,X1))
<=> ( member(X2,X4)
& ~ member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',difference) ).
fof(partition,axiom,
! [X1,X4] :
( partition(X1,X4)
<=> ( ! [X3] :
( member(X3,X1)
=> subset(X3,X4) )
& ! [X3] :
( member(X3,X4)
=> ? [X5] :
( member(X5,X1)
& member(X3,X5) ) )
& ! [X3,X5] :
( ( member(X3,X1)
& member(X5,X1) )
=> ( ? [X6] :
( member(X6,X3)
& member(X6,X5) )
=> X3 = X5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+2.ax',partition) ).
fof(singleton,axiom,
! [X3,X1] :
( member(X3,singleton(X1))
<=> X3 = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',singleton) ).
fof(c_0_4,negated_conjecture,
~ ! [X3,X1,X2,X11] :
( ( member(X3,difference(X1,X2))
& partition(X11,X1) )
=> ? [X12] :
( member(X12,difference(X11,singleton(X2)))
& member(X3,X12) ) ),
inference(assume_negation,[status(cth)],[diff_elem_in_partition]) ).
fof(c_0_5,plain,
! [X2,X1,X4] :
( member(X2,difference(X4,X1))
<=> ( member(X2,X4)
& ~ member(X2,X1) ) ),
inference(fof_simplification,[status(thm)],[difference]) ).
fof(c_0_6,plain,
! [X127,X128,X129,X130,X132,X133,X134,X135,X136,X139] :
( ( ~ member(X129,X127)
| subset(X129,X128)
| ~ partition(X127,X128) )
& ( member(esk5_3(X127,X128,X130),X127)
| ~ member(X130,X128)
| ~ partition(X127,X128) )
& ( member(X130,esk5_3(X127,X128,X130))
| ~ member(X130,X128)
| ~ partition(X127,X128) )
& ( ~ member(X132,X127)
| ~ member(X133,X127)
| ~ member(X134,X132)
| ~ member(X134,X133)
| X132 = X133
| ~ partition(X127,X128) )
& ( member(esk8_2(X135,X136),X135)
| member(esk7_2(X135,X136),X136)
| member(esk6_2(X135,X136),X135)
| partition(X135,X136) )
& ( member(esk9_2(X135,X136),X135)
| member(esk7_2(X135,X136),X136)
| member(esk6_2(X135,X136),X135)
| partition(X135,X136) )
& ( member(esk10_2(X135,X136),esk8_2(X135,X136))
| member(esk7_2(X135,X136),X136)
| member(esk6_2(X135,X136),X135)
| partition(X135,X136) )
& ( member(esk10_2(X135,X136),esk9_2(X135,X136))
| member(esk7_2(X135,X136),X136)
| member(esk6_2(X135,X136),X135)
| partition(X135,X136) )
& ( esk8_2(X135,X136) != esk9_2(X135,X136)
| member(esk7_2(X135,X136),X136)
| member(esk6_2(X135,X136),X135)
| partition(X135,X136) )
& ( member(esk8_2(X135,X136),X135)
| ~ member(X139,X135)
| ~ member(esk7_2(X135,X136),X139)
| member(esk6_2(X135,X136),X135)
| partition(X135,X136) )
& ( member(esk9_2(X135,X136),X135)
| ~ member(X139,X135)
| ~ member(esk7_2(X135,X136),X139)
| member(esk6_2(X135,X136),X135)
| partition(X135,X136) )
& ( member(esk10_2(X135,X136),esk8_2(X135,X136))
| ~ member(X139,X135)
| ~ member(esk7_2(X135,X136),X139)
| member(esk6_2(X135,X136),X135)
| partition(X135,X136) )
& ( member(esk10_2(X135,X136),esk9_2(X135,X136))
| ~ member(X139,X135)
| ~ member(esk7_2(X135,X136),X139)
| member(esk6_2(X135,X136),X135)
| partition(X135,X136) )
& ( esk8_2(X135,X136) != esk9_2(X135,X136)
| ~ member(X139,X135)
| ~ member(esk7_2(X135,X136),X139)
| member(esk6_2(X135,X136),X135)
| partition(X135,X136) )
& ( member(esk8_2(X135,X136),X135)
| member(esk7_2(X135,X136),X136)
| ~ subset(esk6_2(X135,X136),X136)
| partition(X135,X136) )
& ( member(esk9_2(X135,X136),X135)
| member(esk7_2(X135,X136),X136)
| ~ subset(esk6_2(X135,X136),X136)
| partition(X135,X136) )
& ( member(esk10_2(X135,X136),esk8_2(X135,X136))
| member(esk7_2(X135,X136),X136)
| ~ subset(esk6_2(X135,X136),X136)
| partition(X135,X136) )
& ( member(esk10_2(X135,X136),esk9_2(X135,X136))
| member(esk7_2(X135,X136),X136)
| ~ subset(esk6_2(X135,X136),X136)
| partition(X135,X136) )
& ( esk8_2(X135,X136) != esk9_2(X135,X136)
| member(esk7_2(X135,X136),X136)
| ~ subset(esk6_2(X135,X136),X136)
| partition(X135,X136) )
& ( member(esk8_2(X135,X136),X135)
| ~ member(X139,X135)
| ~ member(esk7_2(X135,X136),X139)
| ~ subset(esk6_2(X135,X136),X136)
| partition(X135,X136) )
& ( member(esk9_2(X135,X136),X135)
| ~ member(X139,X135)
| ~ member(esk7_2(X135,X136),X139)
| ~ subset(esk6_2(X135,X136),X136)
| partition(X135,X136) )
& ( member(esk10_2(X135,X136),esk8_2(X135,X136))
| ~ member(X139,X135)
| ~ member(esk7_2(X135,X136),X139)
| ~ subset(esk6_2(X135,X136),X136)
| partition(X135,X136) )
& ( member(esk10_2(X135,X136),esk9_2(X135,X136))
| ~ member(X139,X135)
| ~ member(esk7_2(X135,X136),X139)
| ~ subset(esk6_2(X135,X136),X136)
| partition(X135,X136) )
& ( esk8_2(X135,X136) != esk9_2(X135,X136)
| ~ member(X139,X135)
| ~ member(esk7_2(X135,X136),X139)
| ~ subset(esk6_2(X135,X136),X136)
| partition(X135,X136) ) ),
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)],[partition])])])])])]) ).
fof(c_0_7,negated_conjecture,
! [X183] :
( member(esk19_0,difference(esk20_0,esk21_0))
& partition(esk22_0,esk20_0)
& ( ~ member(X183,difference(esk22_0,singleton(esk21_0)))
| ~ member(esk19_0,X183) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])])]) ).
fof(c_0_8,plain,
! [X101,X102,X103] :
( ( member(X101,X103)
| ~ member(X101,difference(X103,X102)) )
& ( ~ member(X101,X102)
| ~ member(X101,difference(X103,X102)) )
& ( ~ member(X101,X103)
| member(X101,X102)
| member(X101,difference(X103,X102)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])]) ).
cnf(c_0_9,plain,
( member(X1,esk5_3(X2,X3,X1))
| ~ member(X1,X3)
| ~ partition(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,negated_conjecture,
partition(esk22_0,esk20_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,plain,
( member(X1,X2)
| ~ member(X1,difference(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_12,negated_conjecture,
member(esk19_0,difference(esk20_0,esk21_0)),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_13,plain,
( member(esk5_3(X1,X2,X3),X1)
| ~ member(X3,X2)
| ~ partition(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_14,negated_conjecture,
( member(X1,esk5_3(esk22_0,esk20_0,X1))
| ~ member(X1,esk20_0) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_15,negated_conjecture,
member(esk19_0,esk20_0),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_16,negated_conjecture,
( member(esk5_3(esk22_0,esk20_0,X1),esk22_0)
| ~ member(X1,esk20_0) ),
inference(spm,[status(thm)],[c_0_13,c_0_10]) ).
cnf(c_0_17,negated_conjecture,
( ~ member(X1,difference(esk22_0,singleton(esk21_0)))
| ~ member(esk19_0,X1) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_18,negated_conjecture,
member(esk19_0,esk5_3(esk22_0,esk20_0,esk19_0)),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_19,plain,
( member(X1,X3)
| member(X1,difference(X2,X3))
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_20,negated_conjecture,
member(esk5_3(esk22_0,esk20_0,esk19_0),esk22_0),
inference(spm,[status(thm)],[c_0_16,c_0_15]) ).
fof(c_0_21,plain,
! [X104,X105] :
( ( ~ member(X104,singleton(X105))
| X104 = X105 )
& ( X104 != X105
| member(X104,singleton(X105)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[singleton])]) ).
cnf(c_0_22,negated_conjecture,
~ member(esk5_3(esk22_0,esk20_0,esk19_0),difference(esk22_0,singleton(esk21_0))),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_23,negated_conjecture,
( member(esk5_3(esk22_0,esk20_0,esk19_0),difference(esk22_0,X1))
| member(esk5_3(esk22_0,esk20_0,esk19_0),X1) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_24,plain,
( X1 = X2
| ~ member(X1,singleton(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_25,negated_conjecture,
member(esk5_3(esk22_0,esk20_0,esk19_0),singleton(esk21_0)),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_26,plain,
( ~ member(X1,X2)
| ~ member(X1,difference(X3,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_27,negated_conjecture,
esk5_3(esk22_0,esk20_0,esk19_0) = esk21_0,
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_28,negated_conjecture,
~ member(esk19_0,esk21_0),
inference(spm,[status(thm)],[c_0_26,c_0_12]) ).
cnf(c_0_29,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_18,c_0_27]),c_0_28]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.14 % Problem : SEV517+1 : TPTP v9.2.1. Released v7.3.0.
% 0.10/0.14 % 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
% 0.16/0.35 % Computer : n022.cluster.edu
% 0.16/0.35 % Model : x86_64 x86_64
% 0.16/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.35 % Memory : 8042.1875MB
% 0.16/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.35 % CPULimit : 300
% 0.16/0.35 % WCLimit : 300
% 0.16/0.35 % DateTime : Tue May 5 04:06:51 EDT 2026
% 0.16/0.35 % CPUTime :
% 0.13/0.36 % start to proof: theBenchmark
% 12.58/8.55 % Version : CSE_E---1.7
% 12.58/8.55 % Problem : theBenchmark.p
% 12.58/8.55 % SZS status Theorem for theBenchmark.p
% 12.58/8.55 % SZS output start CNFRefutation
% See solution above
% 12.69/8.60 % Total time : 6.386s
%------------------------------------------------------------------------------