%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET071+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 02:13:25 PM UTC 2026
% Result : Theorem 148.16s 22.06s
% Output : CNFRefutation 148.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 20
% Syntax : Number of formulae : 130 ( 40 unt; 0 def)
% Number of atoms : 326 ( 80 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 326 ( 130 ~; 137 |; 42 &)
% ( 10 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 6 con; 0-2 aty)
% Number of variables : 226 ( 33 sgn 87 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(regularity,axiom,
! [X1] :
( X1 != null_class
=> ? [X3] :
( disjoint(X3,X1)
& member(X3,X1)
& member(X3,universal_class) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET005+0.ax',regularity) ).
fof(unordered_pair_defn,axiom,
! [X3,X1,X2] :
( member(X3,unordered_pair(X1,X2))
<=> ( ( X3 = X2
| X3 = X1 )
& member(X3,universal_class) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET005+0.ax',unordered_pair_defn) ).
fof(disjoint_defn,axiom,
! [X1,X2] :
( disjoint(X1,X2)
<=> ! [X3] :
~ ( member(X3,X2)
& member(X3,X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET005+0.ax',disjoint_defn) ).
fof(ordered_pair_defn,axiom,
! [X1,X2] : ordered_pair(X1,X2) = unordered_pair(singleton(X1),unordered_pair(X1,singleton(X2))),
file('/export/starexec/sandbox2/benchmark/Axioms/SET005+0.ax',ordered_pair_defn) ).
fof(singleton_set_defn,axiom,
! [X1] : singleton(X1) = unordered_pair(X1,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/SET005+0.ax',singleton_set_defn) ).
fof(successor_defn,axiom,
! [X1] : successor(X1) = union(X1,singleton(X1)),
file('/export/starexec/sandbox2/benchmark/Axioms/SET005+0.ax',successor_defn) ).
fof(subclass_defn,axiom,
! [X1,X2] :
( subclass(X1,X2)
<=> ! [X3] :
( member(X3,X1)
=> member(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET005+0.ax',subclass_defn) ).
fof(union_defn,axiom,
! [X1,X2,X5] :
( member(X5,union(X1,X2))
<=> ( member(X5,X2)
| member(X5,X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET005+0.ax',union_defn) ).
fof(power_class_defn,axiom,
! [X3,X1] :
( member(X3,power_class(X1))
<=> ( subclass(X3,X1)
& member(X3,universal_class) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET005+0.ax',power_class_defn) ).
fof(successor_relation_defn2,axiom,
! [X1,X2] :
( member(ordered_pair(X1,X2),successor_relation)
<=> ( successor(X1) = X2
& member(X2,universal_class)
& member(X1,universal_class) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET005+0.ax',successor_relation_defn2) ).
fof(extensionality,axiom,
! [X1,X2] :
( X1 = X2
<=> ( subclass(X2,X1)
& subclass(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET005+0.ax',extensionality) ).
fof(class_elements_are_sets,axiom,
! [X1] : subclass(X1,universal_class),
file('/export/starexec/sandbox2/benchmark/Axioms/SET005+0.ax',class_elements_are_sets) ).
fof(null_class_defn,axiom,
! [X1] : ~ member(X1,null_class),
file('/export/starexec/sandbox2/benchmark/Axioms/SET005+0.ax',null_class_defn) ).
fof(power_class,axiom,
! [X3] :
( member(X3,universal_class)
=> member(power_class(X3),universal_class) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET005+0.ax',power_class) ).
fof(sum_class_defn,axiom,
! [X3,X1] :
( member(X3,sum_class(X1))
<=> ? [X2] :
( member(X2,X1)
& member(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET005+0.ax',sum_class_defn) ).
fof(cross_product_defn,axiom,
! [X3,X4,X1,X2] :
( member(ordered_pair(X3,X4),cross_product(X1,X2))
<=> ( member(X4,X2)
& member(X3,X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET005+0.ax',cross_product_defn) ).
fof(element_relation_defn,axiom,
! [X1,X2] :
( member(ordered_pair(X1,X2),element_relation)
<=> ( member(X1,X2)
& member(X2,universal_class) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET005+0.ax',element_relation_defn) ).
fof(element_relation,axiom,
subclass(element_relation,cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox2/benchmark/Axioms/SET005+0.ax',element_relation) ).
fof(unordered_pair,axiom,
! [X1,X2] : member(unordered_pair(X1,X2),universal_class),
file('/export/starexec/sandbox2/benchmark/Axioms/SET005+0.ax',unordered_pair) ).
fof(null_unordered_pair,conjecture,
! [X1,X2] :
( ( ~ member(X2,universal_class)
& ~ member(X1,universal_class) )
=> unordered_pair(X1,X2) = null_class ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',null_unordered_pair) ).
fof(c_0_20,plain,
! [X1] :
( X1 != null_class
=> ? [X3] :
( disjoint(X3,X1)
& member(X3,X1)
& member(X3,universal_class) ) ),
inference(fof_simplification,[status(thm)],[regularity]) ).
fof(c_0_21,plain,
! [X19,X20,X21] :
( ( member(X19,unordered_pair(X20,X21))
| ~ member(X19,universal_class)
| X19 != X21 )
& ( member(X19,unordered_pair(X20,X21))
| ~ member(X19,universal_class)
| X19 != X20 )
& ( ~ member(X19,unordered_pair(X20,X21))
| X19 = X21
| X19 = X20 )
& ( ~ member(X19,unordered_pair(X20,X21))
| member(X19,universal_class) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[unordered_pair_defn])])])]) ).
fof(c_0_22,plain,
! [X101] :
( ( X101 = null_class
| disjoint(esk6_1(X101),X101) )
& ( X101 = null_class
| member(esk6_1(X101),X101) )
& ( X101 = null_class
| member(esk6_1(X101),universal_class) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_20])])])]) ).
fof(c_0_23,plain,
! [X95,X96,X97,X98,X99] :
( ( disjoint(X98,X99)
| member(esk5_2(X98,X99),X99) )
& ( disjoint(X98,X99)
| member(esk5_2(X98,X99),X98) )
& ( ~ member(X97,X96)
| ~ member(X97,X95)
| ~ disjoint(X95,X96) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[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)],[disjoint_defn])])])])])])]) ).
cnf(c_0_24,plain,
( ~ member(X1,unordered_pair(X2,X3))
| X1 = X3
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_25,plain,
( X1 = null_class
| member(esk6_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
fof(c_0_26,plain,
! [X25,X26] : ordered_pair(X25,X26) = unordered_pair(singleton(X25),unordered_pair(X25,singleton(X26))),
inference(variable_rename,[status(thm)],[ordered_pair_defn]) ).
fof(c_0_27,plain,
! [X24] : singleton(X24) = unordered_pair(X24,X24),
inference(variable_rename,[status(thm)],[singleton_set_defn]) ).
cnf(c_0_28,plain,
( ~ member(X3,X2)
| ~ member(X3,X1)
| ~ disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_29,plain,
( X1 = null_class
| disjoint(esk6_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_30,plain,
( unordered_pair(X1,X2) = null_class
| esk6_1(unordered_pair(X1,X2)) = X2
| esk6_1(unordered_pair(X1,X2)) = X1 ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
fof(c_0_31,plain,
! [X62] : successor(X62) = union(X62,singleton(X62)),
inference(variable_rename,[status(thm)],[successor_defn]) ).
fof(c_0_32,plain,
! [X10,X11,X12,X13,X14] :
( ( subclass(X13,X14)
| ~ member(esk1_2(X13,X14),X14) )
& ( subclass(X13,X14)
| member(esk1_2(X13,X14),X13) )
& ( member(X12,X11)
| ~ member(X12,X10)
| ~ subclass(X10,X11) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[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)],[subclass_defn])])])])])])]) ).
fof(c_0_33,plain,
! [X59,X60,X61] :
( ( member(X61,union(X59,X60))
| ~ member(X61,X60) )
& ( member(X61,union(X59,X60))
| ~ member(X61,X59) )
& ( member(X61,X60)
| member(X61,X59)
| ~ member(X61,union(X59,X60)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[union_defn])])])]) ).
fof(c_0_34,plain,
! [X79,X80] :
( ( member(X79,power_class(X80))
| ~ subclass(X79,X80)
| ~ member(X79,universal_class) )
& ( ~ member(X79,power_class(X80))
| subclass(X79,X80) )
& ( ~ member(X79,power_class(X80))
| member(X79,universal_class) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[power_class_defn])])])]) ).
fof(c_0_35,plain,
! [X63,X64] :
( ( member(ordered_pair(X63,X64),successor_relation)
| successor(X63) != X64
| ~ member(X64,universal_class)
| ~ member(X63,universal_class) )
& ( ~ member(ordered_pair(X63,X64),successor_relation)
| successor(X63) = X64 )
& ( ~ member(ordered_pair(X63,X64),successor_relation)
| member(X64,universal_class) )
& ( ~ member(ordered_pair(X63,X64),successor_relation)
| member(X63,universal_class) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[successor_relation_defn2])])])]) ).
cnf(c_0_36,plain,
ordered_pair(X1,X2) = unordered_pair(singleton(X1),unordered_pair(X1,singleton(X2))),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_37,plain,
singleton(X1) = unordered_pair(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_38,plain,
( ~ member(X2,X1)
| ~ member(X2,esk6_1(X1))
| X1 = null_class ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_39,plain,
( unordered_pair(X1,X1) = null_class
| esk6_1(unordered_pair(X1,X1)) = X1 ),
inference(er,[status(thm)],[inference(ef,[status(thm)],[c_0_30])]) ).
cnf(c_0_40,plain,
successor(X1) = union(X1,singleton(X1)),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
fof(c_0_41,plain,
! [X17,X18] :
( ( X17 = X18
| ~ subclass(X18,X17)
| ~ subclass(X17,X18) )
& ( X17 != X18
| subclass(X18,X17) )
& ( X17 != X18
| subclass(X17,X18) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[extensionality])])])]) ).
fof(c_0_42,plain,
! [X16] : subclass(X16,universal_class),
inference(variable_rename,[status(thm)],[class_elements_are_sets]) ).
cnf(c_0_43,plain,
( ~ member(esk1_2(X1,X2),X2)
| subclass(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_44,plain,
( ~ member(X1,X2)
| member(X1,union(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_45,plain,
( ~ subclass(X1,X2)
| ~ member(X1,universal_class)
| member(X1,power_class(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_46,plain,
( ~ member(ordered_pair(X2,X1),successor_relation)
| member(X1,universal_class) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_47,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_36,c_0_37]),c_0_37]) ).
cnf(c_0_48,plain,
( X1 = null_class
| member(esk6_1(X1),universal_class) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_49,plain,
( ~ member(X2,X1)
| ~ member(X2,unordered_pair(X1,X1))
| unordered_pair(X1,X1) = null_class ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_50,plain,
( successor(X1) != X2
| ~ member(X2,universal_class)
| ~ member(X1,universal_class)
| member(ordered_pair(X1,X2),successor_relation) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_51,plain,
successor(X1) = union(X1,unordered_pair(X1,X1)),
inference(rw,[status(thm)],[c_0_40,c_0_37]) ).
cnf(c_0_52,plain,
( ~ subclass(X2,X1)
| ~ subclass(X1,X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_53,plain,
subclass(X1,universal_class),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_54,plain,
( ~ member(esk1_2(X1,union(X2,X3)),X2)
| subclass(X1,union(X2,X3)) ),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_55,plain,
( subclass(X1,X2)
| member(esk1_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
fof(c_0_56,plain,
! [X1] : ~ member(X1,null_class),
inference(fof_simplification,[status(thm)],[null_class_defn]) ).
cnf(c_0_57,plain,
( ~ member(X1,universal_class)
| X1 != X2
| member(X1,unordered_pair(X3,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
fof(c_0_58,plain,
! [X81] :
( member(power_class(X81),universal_class)
| ~ member(X81,universal_class) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[power_class])])]) ).
cnf(c_0_59,plain,
( ~ subclass(esk1_2(X1,power_class(X2)),X2)
| ~ member(esk1_2(X1,power_class(X2)),universal_class)
| subclass(X1,power_class(X2)) ),
inference(spm,[status(thm)],[c_0_43,c_0_45]) ).
cnf(c_0_60,plain,
( ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X1,X1))),successor_relation)
| member(X1,universal_class) ),
inference(rw,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_61,plain,
( member(X1,universal_class)
| unordered_pair(X1,X1) = null_class ),
inference(spm,[status(thm)],[c_0_48,c_0_39]) ).
cnf(c_0_62,plain,
( ~ member(esk6_1(unordered_pair(X1,X1)),X1)
| unordered_pair(X1,X1) = null_class ),
inference(spm,[status(thm)],[c_0_49,c_0_25]) ).
cnf(c_0_63,plain,
( ~ member(X1,universal_class)
| ~ member(X2,universal_class)
| union(X1,unordered_pair(X1,X1)) != X2
| member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),successor_relation) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_50,c_0_51]),c_0_47]) ).
cnf(c_0_64,plain,
( ~ subclass(universal_class,X1)
| universal_class = X1 ),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_65,plain,
subclass(X1,union(X1,X2)),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
fof(c_0_66,plain,
! [X46] : ~ member(X46,null_class),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_56])]) ).
fof(c_0_67,plain,
! [X72,X73,X75,X76,X77] :
( ( member(X75,sum_class(X76))
| ~ member(X77,X76)
| ~ member(X75,X77) )
& ( ~ member(X72,sum_class(X73))
| member(esk3_2(X72,X73),X73) )
& ( ~ member(X72,sum_class(X73))
| member(X72,esk3_2(X72,X73)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[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)],[sum_class_defn])])])])])])]) ).
cnf(c_0_68,plain,
( ~ member(X1,universal_class)
| member(X1,unordered_pair(X2,X1)) ),
inference(er,[status(thm)],[c_0_57]) ).
cnf(c_0_69,plain,
( ~ member(X1,universal_class)
| member(power_class(X1),universal_class) ),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_70,plain,
( ~ member(esk1_2(X1,power_class(universal_class)),universal_class)
| subclass(X1,power_class(universal_class)) ),
inference(spm,[status(thm)],[c_0_59,c_0_53]) ).
cnf(c_0_71,plain,
( ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,null_class)),successor_relation)
| member(X1,universal_class) ),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_72,plain,
null_class = unordered_pair(universal_class,universal_class),
inference(spm,[status(thm)],[c_0_62,c_0_48]) ).
cnf(c_0_73,plain,
( ~ member(X1,universal_class)
| ~ member(union(X1,unordered_pair(X1,X1)),universal_class)
| member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(union(X1,unordered_pair(X1,X1)),union(X1,unordered_pair(X1,X1))))),successor_relation) ),
inference(er,[status(thm)],[c_0_63]) ).
cnf(c_0_74,plain,
union(universal_class,X1) = universal_class,
inference(spm,[status(thm)],[c_0_64,c_0_65]) ).
cnf(c_0_75,plain,
~ member(X1,null_class),
inference(split_conjunct,[status(thm)],[c_0_66]) ).
cnf(c_0_76,plain,
( ~ member(X1,sum_class(X2))
| member(esk3_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_67]) ).
fof(c_0_77,plain,
! [X27,X28,X29,X30] :
( ( member(ordered_pair(X27,X28),cross_product(X29,X30))
| ~ member(X28,X30)
| ~ member(X27,X29) )
& ( ~ member(ordered_pair(X27,X28),cross_product(X29,X30))
| member(X28,X30) )
& ( ~ member(ordered_pair(X27,X28),cross_product(X29,X30))
| member(X27,X29) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cross_product_defn])])])]) ).
fof(c_0_78,plain,
! [X36,X37] :
( ( member(ordered_pair(X36,X37),element_relation)
| ~ member(X36,X37)
| ~ member(X37,universal_class) )
& ( ~ member(ordered_pair(X36,X37),element_relation)
| member(X36,X37) )
& ( ~ member(ordered_pair(X36,X37),element_relation)
| member(X37,universal_class) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[element_relation_defn])])])]) ).
cnf(c_0_79,plain,
( ~ member(X2,X3)
| ~ member(X1,X2)
| member(X1,sum_class(X3)) ),
inference(split_conjunct,[status(thm)],[c_0_67]) ).
cnf(c_0_80,plain,
( ~ member(X1,universal_class)
| member(power_class(X1),unordered_pair(X2,power_class(X1))) ),
inference(spm,[status(thm)],[c_0_68,c_0_69]) ).
cnf(c_0_81,plain,
subclass(universal_class,power_class(universal_class)),
inference(spm,[status(thm)],[c_0_70,c_0_55]) ).
cnf(c_0_82,plain,
( ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(universal_class,universal_class))),successor_relation)
| member(X1,universal_class) ),
inference(spm,[status(thm)],[c_0_71,c_0_72]) ).
cnf(c_0_83,plain,
( ~ member(universal_class,universal_class)
| member(unordered_pair(unordered_pair(universal_class,universal_class),unordered_pair(universal_class,unordered_pair(universal_class,universal_class))),successor_relation) ),
inference(spm,[status(thm)],[c_0_73,c_0_74]) ).
cnf(c_0_84,plain,
~ member(X1,sum_class(null_class)),
inference(spm,[status(thm)],[c_0_75,c_0_76]) ).
cnf(c_0_85,plain,
( ~ member(ordered_pair(X1,X3),cross_product(X2,X4))
| member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_77]) ).
cnf(c_0_86,plain,
( ~ member(X3,X1)
| ~ subclass(X1,X2)
| member(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_87,plain,
subclass(element_relation,cross_product(universal_class,universal_class)),
inference(split_conjunct,[status(thm)],[element_relation]) ).
cnf(c_0_88,plain,
( ~ member(X2,X1)
| ~ member(X1,universal_class)
| member(ordered_pair(X2,X1),element_relation) ),
inference(split_conjunct,[status(thm)],[c_0_78]) ).
cnf(c_0_89,plain,
( ~ member(X3,universal_class)
| ~ member(X1,power_class(X3))
| member(X1,sum_class(unordered_pair(X2,power_class(X3)))) ),
inference(spm,[status(thm)],[c_0_79,c_0_80]) ).
cnf(c_0_90,plain,
power_class(universal_class) = universal_class,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_81]),c_0_53])]) ).
cnf(c_0_91,plain,
( ~ member(universal_class,universal_class)
| member(X1,universal_class) ),
inference(spm,[status(thm)],[c_0_82,c_0_83]) ).
cnf(c_0_92,plain,
sum_class(null_class) = null_class,
inference(spm,[status(thm)],[c_0_84,c_0_25]) ).
cnf(c_0_93,plain,
( ~ member(X1,universal_class)
| X1 != X2
| member(X1,unordered_pair(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_94,plain,
( ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X3,X3))),cross_product(X2,X4))
| member(X1,X2) ),
inference(rw,[status(thm)],[c_0_85,c_0_47]) ).
cnf(c_0_95,plain,
( member(X1,universal_class)
| unordered_pair(X1,X1) = unordered_pair(universal_class,universal_class) ),
inference(rw,[status(thm)],[c_0_61,c_0_72]) ).
cnf(c_0_96,plain,
( ~ member(X1,element_relation)
| member(X1,cross_product(universal_class,universal_class)) ),
inference(spm,[status(thm)],[c_0_86,c_0_87]) ).
cnf(c_0_97,plain,
( ~ member(X1,universal_class)
| ~ member(X2,X1)
| member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X1,X1))),element_relation) ),
inference(rw,[status(thm)],[c_0_88,c_0_47]) ).
cnf(c_0_98,plain,
( ~ member(universal_class,universal_class)
| member(X1,sum_class(unordered_pair(X2,universal_class))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_90]),c_0_91]) ).
cnf(c_0_99,plain,
sum_class(unordered_pair(universal_class,universal_class)) = unordered_pair(universal_class,universal_class),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_92,c_0_72]),c_0_72]) ).
cnf(c_0_100,plain,
~ member(X1,unordered_pair(universal_class,universal_class)),
inference(rw,[status(thm)],[c_0_75,c_0_72]) ).
cnf(c_0_101,plain,
( ~ member(X1,universal_class)
| member(X1,unordered_pair(X1,X2)) ),
inference(er,[status(thm)],[c_0_93]) ).
cnf(c_0_102,plain,
( ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(universal_class,unordered_pair(X3,X3))),cross_product(X2,X4))
| member(universal_class,X2)
| member(X1,universal_class) ),
inference(spm,[status(thm)],[c_0_94,c_0_95]) ).
cnf(c_0_103,plain,
( ~ member(X1,X2)
| ~ member(X2,universal_class)
| member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),cross_product(universal_class,universal_class)) ),
inference(spm,[status(thm)],[c_0_96,c_0_97]) ).
cnf(c_0_104,plain,
~ member(universal_class,universal_class),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_99]),c_0_100]) ).
fof(c_0_105,plain,
! [X22,X23] : member(unordered_pair(X22,X23),universal_class),
inference(variable_rename,[status(thm)],[unordered_pair]) ).
cnf(c_0_106,plain,
( member(esk6_1(X1),unordered_pair(esk6_1(X1),X2))
| X1 = null_class ),
inference(spm,[status(thm)],[c_0_101,c_0_48]) ).
fof(c_0_107,negated_conjecture,
~ ! [X1,X2] :
( ( ~ member(X2,universal_class)
& ~ member(X1,universal_class) )
=> unordered_pair(X1,X2) = null_class ),
inference(assume_negation,[status(cth)],[null_unordered_pair]) ).
cnf(c_0_108,plain,
( ~ member(universal_class,X1)
| ~ member(X1,universal_class) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_103]),c_0_104]) ).
cnf(c_0_109,plain,
member(unordered_pair(X1,X2),universal_class),
inference(split_conjunct,[status(thm)],[c_0_105]) ).
cnf(c_0_110,plain,
( member(esk6_1(X1),unordered_pair(esk6_1(X1),X2))
| X1 = unordered_pair(universal_class,universal_class) ),
inference(rw,[status(thm)],[c_0_106,c_0_72]) ).
cnf(c_0_111,plain,
( esk6_1(unordered_pair(X1,X2)) = X1
| esk6_1(unordered_pair(X1,X2)) = X2
| unordered_pair(X1,X2) = unordered_pair(universal_class,universal_class) ),
inference(rw,[status(thm)],[c_0_30,c_0_72]) ).
fof(c_0_112,negated_conjecture,
~ ! [X1,X2] :
( ( ~ member(X2,universal_class)
& ~ member(X1,universal_class) )
=> unordered_pair(X1,X2) = null_class ),
inference(fof_simplification,[status(thm)],[c_0_107]) ).
cnf(c_0_113,plain,
~ member(universal_class,unordered_pair(X1,X2)),
inference(spm,[status(thm)],[c_0_108,c_0_109]) ).
cnf(c_0_114,plain,
( member(X1,unordered_pair(X1,X3))
| esk6_1(unordered_pair(X1,X2)) = X2
| unordered_pair(X1,X2) = unordered_pair(universal_class,universal_class) ),
inference(spm,[status(thm)],[c_0_110,c_0_111]) ).
cnf(c_0_115,plain,
( member(esk6_1(X1),unordered_pair(X2,esk6_1(X1)))
| X1 = null_class ),
inference(spm,[status(thm)],[c_0_68,c_0_48]) ).
fof(c_0_116,negated_conjecture,
( unordered_pair(esk8_0,esk9_0) != null_class
& ~ member(esk9_0,universal_class)
& ~ member(esk8_0,universal_class) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_112])])])]) ).
cnf(c_0_117,plain,
( member(esk6_1(X1),universal_class)
| X1 = unordered_pair(universal_class,universal_class) ),
inference(rw,[status(thm)],[c_0_48,c_0_72]) ).
cnf(c_0_118,plain,
( esk6_1(unordered_pair(universal_class,X1)) = X1
| unordered_pair(universal_class,X1) = unordered_pair(universal_class,universal_class) ),
inference(spm,[status(thm)],[c_0_113,c_0_114]) ).
cnf(c_0_119,plain,
( member(esk6_1(X1),unordered_pair(X2,esk6_1(X1)))
| X1 = unordered_pair(universal_class,universal_class) ),
inference(rw,[status(thm)],[c_0_115,c_0_72]) ).
cnf(c_0_120,negated_conjecture,
~ member(esk9_0,universal_class),
inference(split_conjunct,[status(thm)],[c_0_116]) ).
cnf(c_0_121,plain,
( member(X1,universal_class)
| unordered_pair(universal_class,X1) = unordered_pair(universal_class,universal_class) ),
inference(spm,[status(thm)],[c_0_117,c_0_118]) ).
cnf(c_0_122,plain,
( member(X2,unordered_pair(X3,X2))
| esk6_1(unordered_pair(X1,X2)) = X1
| unordered_pair(X1,X2) = unordered_pair(universal_class,universal_class) ),
inference(spm,[status(thm)],[c_0_119,c_0_111]) ).
cnf(c_0_123,negated_conjecture,
unordered_pair(universal_class,esk9_0) = unordered_pair(universal_class,universal_class),
inference(spm,[status(thm)],[c_0_120,c_0_121]) ).
cnf(c_0_124,negated_conjecture,
unordered_pair(esk8_0,esk9_0) != null_class,
inference(split_conjunct,[status(thm)],[c_0_116]) ).
cnf(c_0_125,negated_conjecture,
( esk6_1(unordered_pair(X1,esk9_0)) = X1
| unordered_pair(X1,esk9_0) = unordered_pair(universal_class,universal_class) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_122,c_0_123]),c_0_100]) ).
cnf(c_0_126,negated_conjecture,
unordered_pair(esk8_0,esk9_0) != unordered_pair(universal_class,universal_class),
inference(rw,[status(thm)],[c_0_124,c_0_72]) ).
cnf(c_0_127,negated_conjecture,
( member(X1,universal_class)
| unordered_pair(X1,esk9_0) = unordered_pair(universal_class,universal_class) ),
inference(spm,[status(thm)],[c_0_117,c_0_125]) ).
cnf(c_0_128,negated_conjecture,
~ member(esk8_0,universal_class),
inference(split_conjunct,[status(thm)],[c_0_116]) ).
cnf(c_0_129,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_126,c_0_127]),c_0_128]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET071+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.37 % Computer : n002.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Mon Sep 21 04:52:31 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.43 Running first-order theorem proving
% 0.09/0.43 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 148.16/22.06 % Version: 3.5.1
% 148.16/22.06 % Preprocessing class: FSMSSMSSSSSNFFN.
% 148.16/22.06 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 148.16/22.06 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 148.16/22.06 % Starting new_bool_3 with 300s (1) cores
% 148.16/22.06 % Starting new_bool_1 with 300s (1) cores
% 148.16/22.06 % Starting sh5l with 300s (1) cores
% 148.16/22.06 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 2466153 completed with status 0
% 148.16/22.06 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 148.16/22.06 % Preprocessing class: FSMSSMSSSSSNFFN.
% 148.16/22.06 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 148.16/22.06 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 148.16/22.06 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 148.16/22.06 % No SInE strategy applied
% 148.16/22.06 % Search class: FGHSM-FFMS21-DFFFFFNN
% 148.16/22.06 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 148.16/22.06 % Starting SubtermCWHack with 136s (1) cores
% 148.16/22.06 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 148.16/22.06 % Starting sh3 with 271s (1) cores
% 148.16/22.06 % Starting ho_unfolding_3 with 271s (1) cores
% 148.16/22.06 % Starting new_ho_10_cnf2 with 271s (1) cores
% 148.16/22.06 % sh3 with pid 2466161 completed with status 0
% 148.16/22.06 % Result found by sh3
% 148.16/22.06 % Preprocessing class: FSMSSMSSSSSNFFN.
% 148.16/22.06 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 148.16/22.06 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 148.16/22.06 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 148.16/22.06 % No SInE strategy applied
% 148.16/22.06 % Search class: FGHSM-FFMS21-DFFFFFNN
% 148.16/22.06 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 148.16/22.06 % Starting SubtermCWHack with 136s (1) cores
% 148.16/22.06 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 148.16/22.06 % Starting sh3 with 271s (1) cores
% 148.16/22.06 % Preprocessing time : 0.002 s
% 148.16/22.06 % Presaturation interreduction done
% 148.16/22.06
% 148.16/22.06 % Proof found!
% 148.16/22.06 % SZS status Theorem
% 148.16/22.06 % SZS output start CNFRefutation
% See solution above
% 148.16/22.06 % Parsed axioms : 44
% 148.16/22.06 % Removed by relevancy pruning/SinE : 0
% 148.16/22.06 % Initial clauses : 92
% 148.16/22.06 % Removed in clause preprocessing : 8
% 148.16/22.06 % Initial clauses in saturation : 84
% 148.16/22.06 % Processed clauses : 44227
% 148.16/22.06 % ...of these trivial : 199
% 148.16/22.06 % ...subsumed : 38787
% 148.16/22.06 % ...remaining for further processing : 5241
% 148.16/22.06 % Other redundant clauses eliminated : 74
% 148.16/22.06 % Clauses deleted for lack of memory : 0
% 148.16/22.06 % Backward-subsumed : 576
% 148.16/22.06 % Backward-rewritten : 210
% 148.16/22.06 % Generated clauses : 951278
% 148.16/22.06 % ...of the previous two non-redundant : 901565
% 148.16/22.06 % ...aggressively subsumed : 0
% 148.16/22.06 % Contextual simplify-reflections : 83
% 148.16/22.06 % Paramodulations : 950698
% 148.16/22.06 % Factorizations : 506
% 148.16/22.06 % NegExts : 0
% 148.16/22.06 % Equation resolutions : 74
% 148.16/22.06 % Disequality decompositions : 0
% 148.16/22.06 % Total rewrite steps : 521966
% 148.16/22.06 % ...of those cached : 517773
% 148.16/22.06 % Propositional unsat checks : 1
% 148.16/22.06 % Propositional check models : 0
% 148.16/22.06 % Propositional check unsatisfiable : 0
% 148.16/22.06 % Propositional clauses : 0
% 148.16/22.06 % Propositional clauses after purity: 0
% 148.16/22.06 % Propositional unsat core size : 0
% 148.16/22.06 % Propositional preprocessing time : 0.000
% 148.16/22.06 % Propositional encoding time : 2.685
% 148.16/22.06 % Propositional solver time : 1.424
% 148.16/22.06 % Success case prop preproc time : 0.000
% 148.16/22.06 % Success case prop encoding time : 0.000
% 148.16/22.06 % Success case prop solver time : 0.000
% 148.16/22.06 % Current number of processed clauses : 4366
% 148.16/22.06 % Positive orientable unit clauses : 158
% 148.16/22.06 % Positive unorientable unit clauses: 0
% 148.16/22.06 % Negative unit clauses : 417
% 148.16/22.06 % Non-unit-clauses : 3791
% 148.16/22.06 % Current number of unprocessed clauses: 855495
% 148.16/22.06 % ...number of literals in the above : 3243982
% 148.16/22.06 % Current number of archived formulas : 0
% 148.16/22.06 % Current number of archived clauses : 877
% 148.16/22.06 % Clause-clause subsumption calls (NU) : 2132391
% 148.16/22.06 % Rec. Clause-clause subsumption calls : 974076
% 148.16/22.06 % Non-unit clause-clause subsumptions : 11951
% 148.16/22.06 % Unit Clause-clause subsumption calls : 437128
% 148.16/22.06 % Rewrite failures with RHS unbound : 0
% 148.16/22.06 % BW rewrite match attempts : 343
% 148.16/22.06 % BW rewrite match successes : 43
% 148.16/22.06 % Condensation attempts : 0
% 148.16/22.06 % Condensation successes : 0
% 148.16/22.06 % Termbank termtop insertions : 44890721
% 148.16/22.06 % Search garbage collected termcells : 977
% 148.16/22.06
% 148.16/22.06 % -------------------------------------------------
% 148.16/22.06 % User time : 20.001 s
% 148.16/22.06 % System time : 0.917 s
% 148.16/22.06 % Total time : 20.918 s
% 148.16/22.06 % Maximum resident set size: 3896 pages
% 148.16/22.06
% 148.16/22.06 % -------------------------------------------------
% 148.16/22.06 % User time : 102.127 s
% 148.16/22.06 % System time : 3.585 s
% 148.16/22.06 % Total time : 105.712 s
% 148.16/22.06 % Maximum resident set size: 4608 pages
% 148.16/22.06 % E exiting
%------------------------------------------------------------------------------