%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET600+3 : TPTP v9.2.1. Released v2.2.0.
% 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 : n026.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 05:08:05 PM UTC 2026
% Result : Theorem 1.27s 1.71s
% Output : CNFRefutation 1.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of formulae : 41 ( 12 unt; 0 def)
% Number of atoms : 111 ( 47 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 108 ( 38 ~; 48 |; 14 &)
% ( 7 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 66 ( 8 sgn 38 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(empty_set_defn,axiom,
! [X1] : ~ member(X1,empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_set_defn) ).
fof(prove_th59,conjecture,
! [X1,X2] :
( union(X1,X2) = empty_set
<=> ( X1 = empty_set
& X2 = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th59) ).
fof(subset_defn,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( member(X3,X1)
=> member(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_defn) ).
fof(union_defn,axiom,
! [X1,X2,X3] :
( member(X3,union(X1,X2))
<=> ( member(X3,X1)
| member(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_defn) ).
fof(equal_defn,axiom,
! [X1,X2] :
( X1 = X2
<=> ( subset(X1,X2)
& subset(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_defn) ).
fof(equal_member_defn,axiom,
! [X1,X2] :
( X1 = X2
<=> ! [X3] :
( member(X3,X1)
<=> member(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_member_defn) ).
fof(commutativity_of_union,axiom,
! [X1,X2] : union(X1,X2) = union(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_union) ).
fof(c_0_7,plain,
! [X1] : ~ member(X1,empty_set),
inference(fof_simplification,[status(thm)],[empty_set_defn]) ).
fof(c_0_8,negated_conjecture,
~ ! [X1,X2] :
( union(X1,X2) = empty_set
<=> ( X1 = empty_set
& X2 = empty_set ) ),
inference(assume_negation,[status(cth)],[prove_th59]) ).
fof(c_0_9,plain,
! [X26] : ~ member(X26,empty_set),
inference(variable_rename,[status(thm)],[c_0_7]) ).
fof(c_0_10,plain,
! [X31,X32,X33,X34,X35] :
( ( ~ subset(X31,X32)
| ~ member(X33,X31)
| member(X33,X32) )
& ( member(esk1_2(X34,X35),X34)
| subset(X34,X35) )
& ( ~ member(esk1_2(X34,X35),X35)
| subset(X34,X35) ) ),
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)],[subset_defn])])])])])]) ).
fof(c_0_11,plain,
! [X23,X24,X25] :
( ( ~ member(X25,union(X23,X24))
| member(X25,X23)
| member(X25,X24) )
& ( ~ member(X25,X23)
| member(X25,union(X23,X24)) )
& ( ~ member(X25,X24)
| member(X25,union(X23,X24)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[union_defn])])]) ).
fof(c_0_12,negated_conjecture,
( ( union(esk4_0,esk5_0) != empty_set
| esk4_0 != empty_set
| esk5_0 != empty_set )
& ( esk4_0 = empty_set
| union(esk4_0,esk5_0) = empty_set )
& ( esk5_0 = empty_set
| union(esk4_0,esk5_0) = empty_set ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])])]) ).
fof(c_0_13,plain,
! [X27,X28] :
( ( subset(X27,X28)
| X27 != X28 )
& ( subset(X28,X27)
| X27 != X28 )
& ( ~ subset(X27,X28)
| ~ subset(X28,X27)
| X27 = X28 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[equal_defn])])]) ).
cnf(c_0_14,plain,
~ member(X1,empty_set),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,plain,
( member(esk1_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,plain,
( member(X1,union(X3,X2))
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_17,negated_conjecture,
( esk5_0 = empty_set
| union(esk4_0,esk5_0) = empty_set ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_18,plain,
! [X42,X43,X44,X45,X46,X47] :
( ( ~ member(X44,X42)
| member(X44,X43)
| X42 != X43 )
& ( ~ member(X45,X43)
| member(X45,X42)
| X42 != X43 )
& ( ~ member(esk3_2(X46,X47),X46)
| ~ member(esk3_2(X46,X47),X47)
| X46 = X47 )
& ( member(esk3_2(X46,X47),X46)
| member(esk3_2(X46,X47),X47)
| 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)],[equal_member_defn])])])])])]) ).
cnf(c_0_19,plain,
( X1 = X2
| ~ subset(X1,X2)
| ~ subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_20,plain,
subset(empty_set,X1),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_21,negated_conjecture,
( esk5_0 = empty_set
| ~ member(X1,esk5_0) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_14]) ).
cnf(c_0_22,plain,
( member(X1,union(X2,X3))
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_23,negated_conjecture,
( esk4_0 = empty_set
| union(esk4_0,esk5_0) = empty_set ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_24,plain,
( member(esk3_2(X1,X2),X1)
| member(esk3_2(X1,X2),X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_25,plain,
( X1 = empty_set
| ~ subset(X1,empty_set) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_26,negated_conjecture,
( esk5_0 = empty_set
| subset(esk5_0,X1) ),
inference(spm,[status(thm)],[c_0_21,c_0_15]) ).
fof(c_0_27,plain,
! [X29,X30] : union(X29,X30) = union(X30,X29),
inference(variable_rename,[status(thm)],[commutativity_of_union]) ).
cnf(c_0_28,negated_conjecture,
( esk4_0 = empty_set
| ~ member(X1,esk4_0) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_14]) ).
cnf(c_0_29,plain,
( member(X1,X2)
| member(X1,X3)
| ~ member(X1,union(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_30,plain,
( empty_set = X1
| member(esk3_2(empty_set,X1),X1) ),
inference(spm,[status(thm)],[c_0_14,c_0_24]) ).
cnf(c_0_31,negated_conjecture,
( union(esk4_0,esk5_0) != empty_set
| esk4_0 != empty_set
| esk5_0 != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_32,negated_conjecture,
esk5_0 = empty_set,
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_33,plain,
union(X1,X2) = union(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_34,negated_conjecture,
( esk4_0 = empty_set
| subset(esk4_0,X1) ),
inference(spm,[status(thm)],[c_0_28,c_0_15]) ).
cnf(c_0_35,plain,
( union(X1,X2) = empty_set
| member(esk3_2(empty_set,union(X1,X2)),X1)
| member(esk3_2(empty_set,union(X1,X2)),X2) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_36,negated_conjecture,
( union(empty_set,esk4_0) != empty_set
| esk4_0 != empty_set ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_31,c_0_32]),c_0_33]),c_0_32])]) ).
cnf(c_0_37,negated_conjecture,
esk4_0 = empty_set,
inference(spm,[status(thm)],[c_0_25,c_0_34]) ).
cnf(c_0_38,plain,
( union(X1,empty_set) = empty_set
| member(esk3_2(empty_set,union(X1,empty_set)),X1) ),
inference(spm,[status(thm)],[c_0_14,c_0_35]) ).
cnf(c_0_39,negated_conjecture,
union(empty_set,empty_set) != empty_set,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_36,c_0_37]),c_0_37])]) ).
cnf(c_0_40,plain,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_38]),c_0_39]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET600+3 : TPTP v9.2.1. Released v2.2.0.
% 0.00/0.12 % 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
% 0.15/0.32 % Computer : n026.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Tue May 5 02:29:08 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.27/1.71 % Version : CSE_E---1.7
% 1.27/1.71 % Problem : theBenchmark.p
% 1.27/1.71 % SZS status Theorem for theBenchmark.p
% 1.27/1.71 % SZS output start CNFRefutation
% See solution above
% 1.27/1.71 % Total time : 1.371s
%------------------------------------------------------------------------------