TSTP Solution File: SWC395+1 by E---3.1.00
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : SWC395+1 : TPTP v8.2.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n016.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 21 04:26:23 EDT 2024
% Result : Theorem 1.45s 0.64s
% Output : CNFRefutation 1.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 15
% Syntax : Number of formulae : 107 ( 17 unt; 0 def)
% Number of atoms : 429 ( 155 equ)
% Maximal formula atoms : 23 ( 4 avg)
% Number of connectives : 525 ( 203 ~; 223 |; 42 &)
% ( 5 <=>; 52 =>; 0 <=; 0 <~>)
% Maximal formula depth : 29 ( 5 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 126 ( 0 sgn 74 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ~ ssList(X4)
| X2 != X4
| X1 != X3
| ! [X5] :
( ~ ssItem(X5)
| ~ memberP(X1,X5)
| memberP(X2,X5) )
| ( nil != X3
& nil = X4 )
| ( ? [X6] :
( ssList(X6)
& X3 != X6
& ? [X7] :
( ssList(X7)
& ? [X8] :
( ssList(X8)
& tl(X4) = X7
& app(X7,X8) = X6
& ? [X9] :
( ssItem(X9)
& cons(X9,nil) = X8
& hd(X4) = X9
& neq(nil,X4) )
& neq(nil,X4) ) ) )
& neq(X4,nil) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
fof(ax26,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ssList(app(X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax26) ).
fof(ax24,axiom,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> ssList(tl(X1)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax24) ).
fof(ax16,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> ssList(cons(X2,X1)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax16) ).
fof(ax22,axiom,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> ssItem(hd(X1)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax22) ).
fof(ax17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(ax15,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax15) ).
fof(ax78,axiom,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> cons(hd(X1),tl(X1)) = X1 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax78) ).
fof(ax86,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( nil != X1
=> tl(app(X1,X2)) = app(tl(X1),X2) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax86) ).
fof(ax83,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( nil = app(X1,X2)
<=> ( nil = X2
& nil = X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax83) ).
fof(ax85,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( nil != X1
=> hd(app(X1,X2)) = hd(X1) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax85) ).
fof(ax21,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> nil != cons(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax21) ).
fof(ax37,axiom,
! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssList(X3)
=> ( memberP(cons(X2,X3),X1)
<=> ( X1 = X2
| memberP(X3,X1) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax37) ).
fof(ax36,axiom,
! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( memberP(app(X2,X3),X1)
<=> ( memberP(X2,X1)
| memberP(X3,X1) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax36) ).
fof(ax38,axiom,
! [X1] :
( ssItem(X1)
=> ~ memberP(nil,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax38) ).
fof(c_0_15,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ~ ssList(X4)
| X2 != X4
| X1 != X3
| ! [X5] :
( ~ ssItem(X5)
| ~ memberP(X1,X5)
| memberP(X2,X5) )
| ( nil != X3
& nil = X4 )
| ( ? [X6] :
( ssList(X6)
& X3 != X6
& ? [X7] :
( ssList(X7)
& ? [X8] :
( ssList(X8)
& tl(X4) = X7
& app(X7,X8) = X6
& ? [X9] :
( ssItem(X9)
& cons(X9,nil) = X8
& hd(X4) = X9
& neq(nil,X4) )
& neq(nil,X4) ) ) )
& neq(X4,nil) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[co1])]) ).
fof(c_0_16,negated_conjecture,
! [X15,X16,X17,X18] :
( ssList(esk1_0)
& ssList(esk2_0)
& ssList(esk3_0)
& ssList(esk4_0)
& esk2_0 = esk4_0
& esk1_0 = esk3_0
& ssItem(esk5_0)
& memberP(esk1_0,esk5_0)
& ~ memberP(esk2_0,esk5_0)
& ( nil = esk3_0
| nil != esk4_0 )
& ( ~ ssList(X15)
| esk3_0 = X15
| ~ ssList(X16)
| ~ ssList(X17)
| tl(esk4_0) != X16
| app(X16,X17) != X15
| ~ ssItem(X18)
| cons(X18,nil) != X17
| hd(esk4_0) != X18
| ~ neq(nil,esk4_0)
| ~ neq(nil,esk4_0)
| ~ neq(esk4_0,nil) ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_15])])])])]) ).
cnf(c_0_17,negated_conjecture,
( esk3_0 = X1
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| tl(esk4_0) != X2
| app(X2,X3) != X1
| ~ ssItem(X4)
| cons(X4,nil) != X3
| hd(esk4_0) != X4
| ~ neq(nil,esk4_0)
| ~ neq(nil,esk4_0)
| ~ neq(esk4_0,nil) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_18,plain,
! [X87,X88] :
( ~ ssList(X87)
| ~ ssList(X88)
| ssList(app(X87,X88)) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax26])])])]) ).
fof(c_0_19,plain,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> ssList(tl(X1)) ) ),
inference(fof_simplification,[status(thm)],[ax24]) ).
cnf(c_0_20,negated_conjecture,
( esk3_0 = X1
| hd(esk4_0) != X4
| tl(esk4_0) != X2
| app(X2,X3) != X1
| cons(X4,nil) != X3
| ~ ssItem(X4)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ neq(nil,esk4_0)
| ~ neq(esk4_0,nil) ),
inference(cn,[status(thm)],[c_0_17]) ).
cnf(c_0_21,plain,
( ssList(app(X1,X2))
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
fof(c_0_22,plain,
! [X110] :
( ~ ssList(X110)
| nil = X110
| ssList(tl(X110)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_19])])]) ).
cnf(c_0_23,negated_conjecture,
ssList(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_24,negated_conjecture,
esk2_0 = esk4_0,
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_25,negated_conjecture,
( app(tl(esk4_0),cons(hd(esk4_0),nil)) = esk3_0
| ~ ssList(cons(hd(esk4_0),nil))
| ~ ssList(tl(esk4_0))
| ~ neq(nil,esk4_0)
| ~ neq(esk4_0,nil)
| ~ ssItem(hd(esk4_0)) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_20])])])]),c_0_21]) ).
cnf(c_0_26,plain,
( nil = X1
| ssList(tl(X1))
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_27,negated_conjecture,
ssList(esk4_0),
inference(rw,[status(thm)],[c_0_23,c_0_24]) ).
fof(c_0_28,plain,
! [X48,X49] :
( ~ ssList(X48)
| ~ ssItem(X49)
| ssList(cons(X49,X48)) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax16])])])]) ).
fof(c_0_29,plain,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> ssItem(hd(X1)) ) ),
inference(fof_simplification,[status(thm)],[ax22]) ).
cnf(c_0_30,negated_conjecture,
( app(tl(esk4_0),cons(hd(esk4_0),nil)) = esk3_0
| esk4_0 = nil
| ~ ssList(cons(hd(esk4_0),nil))
| ~ neq(nil,esk4_0)
| ~ neq(esk4_0,nil)
| ~ ssItem(hd(esk4_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27])]) ).
cnf(c_0_31,plain,
( ssList(cons(X2,X1))
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_32,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[ax17]) ).
fof(c_0_33,plain,
! [X28] :
( ~ ssList(X28)
| nil = X28
| ssItem(hd(X28)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_29])])]) ).
fof(c_0_34,plain,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
inference(fof_simplification,[status(thm)],[ax15]) ).
fof(c_0_35,plain,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> cons(hd(X1),tl(X1)) = X1 ) ),
inference(fof_simplification,[status(thm)],[ax78]) ).
fof(c_0_36,plain,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( nil != X1
=> tl(app(X1,X2)) = app(tl(X1),X2) ) ) ),
inference(fof_simplification,[status(thm)],[ax86]) ).
cnf(c_0_37,negated_conjecture,
( app(tl(esk4_0),cons(hd(esk4_0),nil)) = esk3_0
| esk4_0 = nil
| ~ neq(nil,esk4_0)
| ~ neq(esk4_0,nil)
| ~ ssItem(hd(esk4_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32])]) ).
cnf(c_0_38,plain,
( nil = X1
| ssItem(hd(X1))
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
fof(c_0_39,plain,
! [X21,X22] :
( ( ~ neq(X21,X22)
| X21 != X22
| ~ ssList(X22)
| ~ ssList(X21) )
& ( X21 = X22
| neq(X21,X22)
| ~ ssList(X22)
| ~ ssList(X21) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_34])])])])]) ).
fof(c_0_40,plain,
! [X47] :
( ~ ssList(X47)
| nil = X47
| cons(hd(X47),tl(X47)) = X47 ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_35])])]) ).
fof(c_0_41,plain,
! [X108,X109] :
( ~ ssList(X108)
| ~ ssList(X109)
| nil = X108
| tl(app(X108,X109)) = app(tl(X108),X109) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_36])])])]) ).
fof(c_0_42,plain,
! [X34,X35] :
( ( nil = X35
| nil != app(X34,X35)
| ~ ssList(X35)
| ~ ssList(X34) )
& ( nil = X34
| nil != app(X34,X35)
| ~ ssList(X35)
| ~ ssList(X34) )
& ( nil != X35
| nil != X34
| nil = app(X34,X35)
| ~ ssList(X35)
| ~ ssList(X34) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax83])])])])]) ).
cnf(c_0_43,negated_conjecture,
( app(tl(esk4_0),cons(hd(esk4_0),nil)) = esk3_0
| esk4_0 = nil
| ~ neq(nil,esk4_0)
| ~ neq(esk4_0,nil) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_27])]) ).
cnf(c_0_44,plain,
( X1 = X2
| neq(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_45,plain,
( nil = X1
| cons(hd(X1),tl(X1)) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_46,plain,
( nil = X1
| tl(app(X1,X2)) = app(tl(X1),X2)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_47,plain,
( nil = X1
| nil != app(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_48,negated_conjecture,
( app(tl(esk4_0),cons(hd(esk4_0),nil)) = esk3_0
| esk4_0 = nil
| ~ neq(esk4_0,nil) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_27]),c_0_32])]) ).
cnf(c_0_49,plain,
( cons(hd(app(X1,X2)),app(tl(X1),X2)) = app(X1,X2)
| nil = X1
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_21]),c_0_47]) ).
cnf(c_0_50,negated_conjecture,
( app(tl(esk4_0),cons(hd(esk4_0),nil)) = esk3_0
| esk4_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_44]),c_0_32]),c_0_27])]) ).
cnf(c_0_51,negated_conjecture,
( cons(hd(app(esk4_0,cons(hd(esk4_0),nil))),esk3_0) = app(esk4_0,cons(hd(esk4_0),nil))
| esk4_0 = nil
| ~ ssList(cons(hd(esk4_0),nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_27])]) ).
fof(c_0_52,plain,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( nil != X1
=> hd(app(X1,X2)) = hd(X1) ) ) ),
inference(fof_simplification,[status(thm)],[ax85]) ).
cnf(c_0_53,negated_conjecture,
( cons(hd(app(esk4_0,cons(hd(esk4_0),nil))),esk3_0) = app(esk4_0,cons(hd(esk4_0),nil))
| esk4_0 = nil
| ~ ssItem(hd(esk4_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_31]),c_0_32])]) ).
fof(c_0_54,plain,
! [X37,X38] :
( ~ ssList(X37)
| ~ ssList(X38)
| nil = X37
| hd(app(X37,X38)) = hd(X37) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_52])])])]) ).
fof(c_0_55,plain,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> nil != cons(X2,X1) ) ),
inference(fof_simplification,[status(thm)],[ax21]) ).
cnf(c_0_56,negated_conjecture,
( cons(hd(app(esk4_0,cons(hd(esk4_0),nil))),esk3_0) = app(esk4_0,cons(hd(esk4_0),nil))
| esk4_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_38]),c_0_27])]) ).
cnf(c_0_57,plain,
( nil = X1
| hd(app(X1,X2)) = hd(X1)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
fof(c_0_58,plain,
! [X26,X27] :
( ~ ssList(X26)
| ~ ssItem(X27)
| nil != cons(X27,X26) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_55])])])]) ).
cnf(c_0_59,negated_conjecture,
ssList(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_60,negated_conjecture,
esk1_0 = esk3_0,
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_61,negated_conjecture,
( app(esk4_0,cons(hd(esk4_0),nil)) = cons(hd(esk4_0),esk3_0)
| esk4_0 = nil
| ~ ssList(cons(hd(esk4_0),nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_27])]) ).
cnf(c_0_62,plain,
( ~ ssList(X1)
| ~ ssItem(X2)
| nil != cons(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_63,negated_conjecture,
ssList(esk3_0),
inference(rw,[status(thm)],[c_0_59,c_0_60]) ).
cnf(c_0_64,negated_conjecture,
( app(esk4_0,cons(hd(esk4_0),nil)) = cons(hd(esk4_0),esk3_0)
| esk4_0 = nil
| ~ ssItem(hd(esk4_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_31]),c_0_32])]) ).
cnf(c_0_65,negated_conjecture,
( esk4_0 = nil
| app(esk4_0,cons(hd(esk4_0),nil)) != nil
| ~ ssItem(hd(app(esk4_0,cons(hd(esk4_0),nil)))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_56]),c_0_63])]) ).
cnf(c_0_66,negated_conjecture,
( app(esk4_0,cons(hd(esk4_0),nil)) = cons(hd(esk4_0),esk3_0)
| esk4_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_38]),c_0_27])]) ).
cnf(c_0_67,negated_conjecture,
( esk4_0 = nil
| app(esk4_0,cons(hd(esk4_0),nil)) != nil
| ~ ssList(cons(hd(esk4_0),nil))
| ~ ssItem(hd(esk4_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_57]),c_0_27])]) ).
fof(c_0_68,plain,
! [X122,X123,X124] :
( ( ~ memberP(cons(X123,X124),X122)
| X122 = X123
| memberP(X124,X122)
| ~ ssList(X124)
| ~ ssItem(X123)
| ~ ssItem(X122) )
& ( X122 != X123
| memberP(cons(X123,X124),X122)
| ~ ssList(X124)
| ~ ssItem(X123)
| ~ ssItem(X122) )
& ( ~ memberP(X124,X122)
| memberP(cons(X123,X124),X122)
| ~ ssList(X124)
| ~ ssItem(X123)
| ~ ssItem(X122) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax37])])])])]) ).
cnf(c_0_69,negated_conjecture,
memberP(esk1_0,esk5_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_70,negated_conjecture,
( hd(cons(hd(esk4_0),esk3_0)) = hd(esk4_0)
| esk4_0 = nil
| ~ ssList(cons(hd(esk4_0),nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_66]),c_0_27])]) ).
cnf(c_0_71,negated_conjecture,
( esk4_0 = nil
| ssList(cons(hd(esk4_0),esk3_0))
| ~ ssList(cons(hd(esk4_0),nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_66]),c_0_27])]) ).
cnf(c_0_72,negated_conjecture,
( esk4_0 = nil
| app(esk4_0,cons(hd(esk4_0),nil)) != nil
| ~ ssItem(hd(esk4_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_31]),c_0_32])]) ).
cnf(c_0_73,plain,
( memberP(cons(X3,X1),X2)
| ~ memberP(X1,X2)
| ~ ssList(X1)
| ~ ssItem(X3)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_68]) ).
cnf(c_0_74,negated_conjecture,
memberP(esk3_0,esk5_0),
inference(rw,[status(thm)],[c_0_69,c_0_60]) ).
cnf(c_0_75,negated_conjecture,
ssItem(esk5_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_76,negated_conjecture,
( hd(cons(hd(esk4_0),esk3_0)) = hd(esk4_0)
| esk4_0 = nil
| ~ ssItem(hd(esk4_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_31]),c_0_32])]) ).
cnf(c_0_77,negated_conjecture,
( esk4_0 = nil
| ssList(cons(hd(esk4_0),esk3_0))
| ~ ssItem(hd(esk4_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_31]),c_0_32])]) ).
cnf(c_0_78,negated_conjecture,
( esk4_0 = nil
| app(esk4_0,cons(hd(esk4_0),nil)) != nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_38]),c_0_27])]) ).
cnf(c_0_79,negated_conjecture,
( memberP(cons(X1,esk3_0),esk5_0)
| ~ ssItem(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_74]),c_0_63]),c_0_75])]) ).
cnf(c_0_80,negated_conjecture,
( hd(cons(hd(esk4_0),esk3_0)) = hd(esk4_0)
| esk4_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_38]),c_0_27])]) ).
cnf(c_0_81,negated_conjecture,
( esk4_0 = nil
| ssList(cons(hd(esk4_0),esk3_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_38]),c_0_27])]) ).
cnf(c_0_82,negated_conjecture,
( esk4_0 = nil
| cons(hd(esk4_0),esk3_0) != nil ),
inference(spm,[status(thm)],[c_0_78,c_0_66]) ).
cnf(c_0_83,negated_conjecture,
( esk4_0 = nil
| memberP(app(esk4_0,cons(hd(esk4_0),nil)),esk5_0)
| ~ ssItem(hd(app(esk4_0,cons(hd(esk4_0),nil)))) ),
inference(spm,[status(thm)],[c_0_79,c_0_56]) ).
cnf(c_0_84,negated_conjecture,
( esk4_0 = nil
| ssItem(hd(esk4_0)) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_80]),c_0_81]),c_0_82]) ).
fof(c_0_85,plain,
! [X119,X120,X121] :
( ( ~ memberP(app(X120,X121),X119)
| memberP(X120,X119)
| memberP(X121,X119)
| ~ ssList(X121)
| ~ ssList(X120)
| ~ ssItem(X119) )
& ( ~ memberP(X120,X119)
| memberP(app(X120,X121),X119)
| ~ ssList(X121)
| ~ ssList(X120)
| ~ ssItem(X119) )
& ( ~ memberP(X121,X119)
| memberP(app(X120,X121),X119)
| ~ ssList(X121)
| ~ ssList(X120)
| ~ ssItem(X119) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax36])])])])]) ).
cnf(c_0_86,negated_conjecture,
( esk4_0 = nil
| memberP(app(esk4_0,cons(hd(esk4_0),nil)),esk5_0)
| ~ ssList(cons(hd(esk4_0),nil)) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_57]),c_0_27])]),c_0_84]) ).
cnf(c_0_87,negated_conjecture,
~ memberP(esk2_0,esk5_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_88,plain,
( memberP(X1,X3)
| memberP(X2,X3)
| ~ memberP(app(X1,X2),X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X3) ),
inference(split_conjunct,[status(thm)],[c_0_85]) ).
cnf(c_0_89,negated_conjecture,
( esk4_0 = nil
| memberP(app(esk4_0,cons(hd(esk4_0),nil)),esk5_0) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_31]),c_0_32])]),c_0_84]) ).
cnf(c_0_90,negated_conjecture,
~ memberP(esk4_0,esk5_0),
inference(rw,[status(thm)],[c_0_87,c_0_24]) ).
cnf(c_0_91,plain,
( memberP(cons(X2,X3),X1)
| X1 != X2
| ~ ssList(X3)
| ~ ssItem(X2)
| ~ ssItem(X1) ),
inference(split_conjunct,[status(thm)],[c_0_68]) ).
cnf(c_0_92,negated_conjecture,
( esk4_0 = nil
| memberP(cons(hd(esk4_0),nil),esk5_0)
| ~ ssList(cons(hd(esk4_0),nil)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_89]),c_0_27]),c_0_75])]),c_0_90]) ).
fof(c_0_93,plain,
! [X1] :
( ssItem(X1)
=> ~ memberP(nil,X1) ),
inference(fof_simplification,[status(thm)],[ax38]) ).
cnf(c_0_94,plain,
( memberP(cons(X1,X2),X1)
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(er,[status(thm)],[c_0_91]) ).
cnf(c_0_95,plain,
( X3 = X1
| memberP(X2,X3)
| ~ memberP(cons(X1,X2),X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X3) ),
inference(split_conjunct,[status(thm)],[c_0_68]) ).
cnf(c_0_96,negated_conjecture,
( esk4_0 = nil
| memberP(cons(hd(esk4_0),nil),esk5_0) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_31]),c_0_32])]),c_0_84]) ).
fof(c_0_97,plain,
! [X125] :
( ~ ssItem(X125)
| ~ memberP(nil,X125) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_93])])]) ).
cnf(c_0_98,plain,
( nil = X1
| memberP(X1,hd(X1))
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_45]),c_0_38]),c_0_26]) ).
cnf(c_0_99,negated_conjecture,
( hd(esk4_0) = esk5_0
| esk4_0 = nil
| memberP(nil,esk5_0) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_96]),c_0_32]),c_0_75])]),c_0_84]) ).
cnf(c_0_100,plain,
( ~ ssItem(X1)
| ~ memberP(nil,X1) ),
inference(split_conjunct,[status(thm)],[c_0_97]) ).
cnf(c_0_101,negated_conjecture,
( esk4_0 = nil
| memberP(nil,esk5_0) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_99]),c_0_27])]),c_0_90]) ).
cnf(c_0_102,negated_conjecture,
( nil = esk3_0
| nil != esk4_0 ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_103,negated_conjecture,
esk4_0 = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_101]),c_0_75])]) ).
cnf(c_0_104,negated_conjecture,
esk3_0 = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_102,c_0_103])]) ).
cnf(c_0_105,negated_conjecture,
~ memberP(nil,esk5_0),
inference(rw,[status(thm)],[c_0_90,c_0_103]) ).
cnf(c_0_106,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_74,c_0_104]),c_0_105]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SWC395+1 : TPTP v8.2.0. Released v2.4.0.
% 0.10/0.13 % Command : run_E %s %d THM
% 0.12/0.35 % Computer : n016.cluster.edu
% 0.12/0.35 % Model : x86_64 x86_64
% 0.12/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.35 % Memory : 8042.1875MB
% 0.12/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.35 % CPULimit : 300
% 0.12/0.35 % WCLimit : 300
% 0.12/0.35 % DateTime : Sun May 19 02:40:37 EDT 2024
% 0.12/0.35 % CPUTime :
% 0.19/0.46 Running first-order theorem proving
% 0.19/0.46 Running: /export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p
% 1.45/0.64 # Version: 3.1.0
% 1.45/0.64 # Preprocessing class: FSLSSMSSSSSNFFN.
% 1.45/0.64 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.45/0.64 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 1.45/0.64 # Starting new_bool_3 with 300s (1) cores
% 1.45/0.64 # Starting new_bool_1 with 300s (1) cores
% 1.45/0.64 # Starting sh5l with 300s (1) cores
% 1.45/0.64 # sh5l with pid 22079 completed with status 0
% 1.45/0.64 # Result found by sh5l
% 1.45/0.64 # Preprocessing class: FSLSSMSSSSSNFFN.
% 1.45/0.64 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.45/0.64 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 1.45/0.64 # Starting new_bool_3 with 300s (1) cores
% 1.45/0.64 # Starting new_bool_1 with 300s (1) cores
% 1.45/0.64 # Starting sh5l with 300s (1) cores
% 1.45/0.64 # SinE strategy is gf500_gu_R04_F100_L20000
% 1.45/0.64 # Search class: FGHSF-FSLM21-MFFFFFNN
% 1.45/0.64 # Scheduled 11 strats onto 1 cores with 300 seconds (300 total)
% 1.45/0.64 # Starting G-E--_208_C18_SOS_F1_SE_CS_SP_PS_S4c with 28s (1) cores
% 1.45/0.64 # G-E--_208_C18_SOS_F1_SE_CS_SP_PS_S4c with pid 22082 completed with status 0
% 1.45/0.64 # Result found by G-E--_208_C18_SOS_F1_SE_CS_SP_PS_S4c
% 1.45/0.64 # Preprocessing class: FSLSSMSSSSSNFFN.
% 1.45/0.64 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.45/0.64 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 1.45/0.64 # Starting new_bool_3 with 300s (1) cores
% 1.45/0.64 # Starting new_bool_1 with 300s (1) cores
% 1.45/0.64 # Starting sh5l with 300s (1) cores
% 1.45/0.64 # SinE strategy is gf500_gu_R04_F100_L20000
% 1.45/0.64 # Search class: FGHSF-FSLM21-MFFFFFNN
% 1.45/0.64 # Scheduled 11 strats onto 1 cores with 300 seconds (300 total)
% 1.45/0.64 # Starting G-E--_208_C18_SOS_F1_SE_CS_SP_PS_S4c with 28s (1) cores
% 1.45/0.64 # Preprocessing time : 0.003 s
% 1.45/0.64 # Presaturation interreduction done
% 1.45/0.64
% 1.45/0.64 # Proof found!
% 1.45/0.64 # SZS status Theorem
% 1.45/0.64 # SZS output start CNFRefutation
% See solution above
% 1.45/0.64 # Parsed axioms : 96
% 1.45/0.64 # Removed by relevancy pruning/SinE : 8
% 1.45/0.64 # Initial clauses : 178
% 1.45/0.64 # Removed in clause preprocessing : 2
% 1.45/0.64 # Initial clauses in saturation : 176
% 1.45/0.64 # Processed clauses : 1285
% 1.45/0.64 # ...of these trivial : 13
% 1.45/0.64 # ...subsumed : 407
% 1.45/0.64 # ...remaining for further processing : 865
% 1.45/0.64 # Other redundant clauses eliminated : 67
% 1.45/0.64 # Clauses deleted for lack of memory : 0
% 1.45/0.64 # Backward-subsumed : 223
% 1.45/0.64 # Backward-rewritten : 158
% 1.45/0.64 # Generated clauses : 3765
% 1.45/0.64 # ...of the previous two non-redundant : 3124
% 1.45/0.64 # ...aggressively subsumed : 0
% 1.45/0.64 # Contextual simplify-reflections : 177
% 1.45/0.64 # Paramodulations : 3696
% 1.45/0.64 # Factorizations : 0
% 1.45/0.64 # NegExts : 0
% 1.45/0.64 # Equation resolutions : 73
% 1.45/0.64 # Disequality decompositions : 0
% 1.45/0.64 # Total rewrite steps : 2985
% 1.45/0.64 # ...of those cached : 2937
% 1.45/0.64 # Propositional unsat checks : 0
% 1.45/0.64 # Propositional check models : 0
% 1.45/0.64 # Propositional check unsatisfiable : 0
% 1.45/0.64 # Propositional clauses : 0
% 1.45/0.64 # Propositional clauses after purity: 0
% 1.45/0.64 # Propositional unsat core size : 0
% 1.45/0.64 # Propositional preprocessing time : 0.000
% 1.45/0.64 # Propositional encoding time : 0.000
% 1.45/0.64 # Propositional solver time : 0.000
% 1.45/0.64 # Success case prop preproc time : 0.000
% 1.45/0.64 # Success case prop encoding time : 0.000
% 1.45/0.64 # Success case prop solver time : 0.000
% 1.45/0.64 # Current number of processed clauses : 293
% 1.45/0.64 # Positive orientable unit clauses : 26
% 1.45/0.64 # Positive unorientable unit clauses: 0
% 1.45/0.64 # Negative unit clauses : 2
% 1.45/0.64 # Non-unit-clauses : 265
% 1.45/0.64 # Current number of unprocessed clauses: 2024
% 1.45/0.64 # ...number of literals in the above : 12158
% 1.45/0.64 # Current number of archived formulas : 0
% 1.45/0.64 # Current number of archived clauses : 551
% 1.45/0.64 # Clause-clause subsumption calls (NU) : 49119
% 1.45/0.64 # Rec. Clause-clause subsumption calls : 14853
% 1.45/0.64 # Non-unit clause-clause subsumptions : 807
% 1.45/0.64 # Unit Clause-clause subsumption calls : 1642
% 1.45/0.64 # Rewrite failures with RHS unbound : 0
% 1.45/0.64 # BW rewrite match attempts : 11
% 1.45/0.64 # BW rewrite match successes : 11
% 1.45/0.64 # Condensation attempts : 0
% 1.45/0.64 # Condensation successes : 0
% 1.45/0.64 # Termbank termtop insertions : 87884
% 1.45/0.64 # Search garbage collected termcells : 3948
% 1.45/0.64
% 1.45/0.64 # -------------------------------------------------
% 1.45/0.64 # User time : 0.162 s
% 1.45/0.64 # System time : 0.009 s
% 1.45/0.64 # Total time : 0.170 s
% 1.45/0.64 # Maximum resident set size: 2440 pages
% 1.45/0.64
% 1.45/0.64 # -------------------------------------------------
% 1.45/0.64 # User time : 0.165 s
% 1.45/0.64 # System time : 0.009 s
% 1.45/0.64 # Total time : 0.174 s
% 1.45/0.64 # Maximum resident set size: 1832 pages
% 1.45/0.64 % E---3.1 exiting
% 1.45/0.64 % E exiting
%------------------------------------------------------------------------------