TSTP Solution File: SWC166+1 by E-SAT---3.1.00
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%------------------------------------------------------------------------------
% File : E-SAT---3.1.00
% Problem : SWC166+1 : TPTP v8.2.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% 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 21 04:28:03 EDT 2024
% Result : Theorem 0.73s 0.54s
% Output : CNFRefutation 0.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 20
% Syntax : Number of formulae : 123 ( 27 unt; 0 def)
% Number of atoms : 384 ( 149 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 425 ( 164 ~; 165 |; 22 &)
% ( 5 <=>; 69 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 9 con; 0-2 aty)
% Number of variables : 143 ( 0 sgn 96 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ~ singletonP(X3)
| ! [X5] :
( ssItem(X5)
=> ! [X6] :
( ssItem(X6)
=> ! [X7] :
( ssList(X7)
=> ! [X8] :
( ssList(X8)
=> ( app(app(app(X7,cons(X5,nil)),cons(X6,nil)),X8) != X1
| neq(X5,X6) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
fof(ax1,axiom,
! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax1) ).
fof(ax82,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> app(app(X1,X2),X3) = app(X1,app(X2,X3)) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax82) ).
fof(ax16,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> ssList(cons(X2,X1)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax16) ).
fof(ax17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(ax81,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> cons(X2,X1) = app(cons(X2,nil),X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax81) ).
fof(ax27,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssItem(X3)
=> cons(X3,app(X2,X1)) = app(cons(X3,X2),X1) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax27) ).
fof(ax5,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( frontsegP(X1,X2)
<=> ? [X3] :
( ssList(X3)
& app(X2,X3) = X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax5) ).
fof(ax26,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ssList(app(X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax26) ).
fof(ax25,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> tl(cons(X2,X1)) = X1 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax25) ).
fof(ax4,axiom,
! [X1] :
( ssList(X1)
=> ( singletonP(X1)
<=> ? [X2] :
( ssItem(X2)
& cons(X2,nil) = X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax4) ).
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(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(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(ax80,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( app(X2,X3) = app(X2,X1)
=> X3 = X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax80) ).
fof(ax84,axiom,
! [X1] :
( ssList(X1)
=> app(X1,nil) = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax84) ).
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(ax24,axiom,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> ssList(tl(X1)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax24) ).
fof(ax21,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> nil != cons(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax21) ).
fof(ax28,axiom,
! [X1] :
( ssList(X1)
=> app(nil,X1) = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax28) ).
fof(c_0_20,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ~ singletonP(X3)
| ! [X5] :
( ssItem(X5)
=> ! [X6] :
( ssItem(X6)
=> ! [X7] :
( ssList(X7)
=> ! [X8] :
( ssList(X8)
=> ( app(app(app(X7,cons(X5,nil)),cons(X6,nil)),X8) != X1
| neq(X5,X6) ) ) ) ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[co1])]) ).
fof(c_0_21,plain,
! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
inference(fof_simplification,[status(thm)],[ax1]) ).
fof(c_0_22,negated_conjecture,
( ssList(esk1_0)
& ssList(esk2_0)
& ssList(esk3_0)
& ssList(esk4_0)
& esk2_0 = esk4_0
& esk1_0 = esk3_0
& singletonP(esk3_0)
& ssItem(esk5_0)
& ssItem(esk6_0)
& ssList(esk7_0)
& ssList(esk8_0)
& app(app(app(esk7_0,cons(esk5_0,nil)),cons(esk6_0,nil)),esk8_0) = esk1_0
& ~ neq(esk5_0,esk6_0) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_20])])])]) ).
fof(c_0_23,plain,
! [X17,X18] :
( ( ~ neq(X17,X18)
| X17 != X18
| ~ ssItem(X18)
| ~ ssItem(X17) )
& ( X17 = X18
| neq(X17,X18)
| ~ ssItem(X18)
| ~ ssItem(X17) ) ),
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_21])])])])]) ).
fof(c_0_24,plain,
! [X59,X60,X61] :
( ~ ssList(X59)
| ~ ssList(X60)
| ~ ssList(X61)
| app(app(X59,X60),X61) = app(X59,app(X60,X61)) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax82])])])]) ).
cnf(c_0_25,negated_conjecture,
~ neq(esk5_0,esk6_0),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_26,plain,
( X1 = X2
| neq(X1,X2)
| ~ ssItem(X2)
| ~ ssItem(X1) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_27,negated_conjecture,
ssItem(esk6_0),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_28,negated_conjecture,
ssItem(esk5_0),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_29,negated_conjecture,
app(app(app(esk7_0,cons(esk5_0,nil)),cons(esk6_0,nil)),esk8_0) = esk1_0,
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_30,plain,
( app(app(X1,X2),X3) = app(X1,app(X2,X3))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_31,negated_conjecture,
esk6_0 = esk5_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27]),c_0_28])]) ).
cnf(c_0_32,negated_conjecture,
ssList(esk7_0),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
fof(c_0_33,plain,
! [X69,X70] :
( ~ ssList(X69)
| ~ ssItem(X70)
| ssList(cons(X70,X69)) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax16])])])]) ).
cnf(c_0_34,negated_conjecture,
( app(app(esk7_0,app(cons(esk5_0,nil),cons(esk5_0,nil))),esk8_0) = esk1_0
| ~ ssList(cons(esk5_0,nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31]),c_0_31]),c_0_32])]) ).
cnf(c_0_35,plain,
( ssList(cons(X2,X1))
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_36,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[ax17]) ).
fof(c_0_37,plain,
! [X57,X58] :
( ~ ssList(X57)
| ~ ssItem(X58)
| cons(X58,X57) = app(cons(X58,nil),X57) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax81])])])]) ).
cnf(c_0_38,negated_conjecture,
app(app(esk7_0,app(cons(esk5_0,nil),cons(esk5_0,nil))),esk8_0) = esk1_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36]),c_0_28])]) ).
cnf(c_0_39,plain,
( cons(X2,X1) = app(cons(X2,nil),X1)
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_40,negated_conjecture,
( app(app(esk7_0,cons(esk5_0,cons(esk5_0,nil))),esk8_0) = esk1_0
| ~ ssList(cons(esk5_0,nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_28])]) ).
cnf(c_0_41,negated_conjecture,
app(app(esk7_0,cons(esk5_0,cons(esk5_0,nil))),esk8_0) = esk1_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_35]),c_0_36]),c_0_28])]) ).
cnf(c_0_42,negated_conjecture,
ssList(esk8_0),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_43,negated_conjecture,
( app(esk7_0,app(cons(esk5_0,cons(esk5_0,nil)),esk8_0)) = esk1_0
| ~ ssList(cons(esk5_0,cons(esk5_0,nil))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_41]),c_0_42]),c_0_32])]) ).
cnf(c_0_44,negated_conjecture,
( app(esk7_0,app(cons(esk5_0,cons(esk5_0,nil)),esk8_0)) = esk1_0
| ~ ssList(cons(esk5_0,nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_35]),c_0_28])]) ).
fof(c_0_45,plain,
! [X37,X38,X39] :
( ~ ssList(X37)
| ~ ssList(X38)
| ~ ssItem(X39)
| cons(X39,app(X38,X37)) = app(cons(X39,X38),X37) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax27])])])]) ).
cnf(c_0_46,negated_conjecture,
app(esk7_0,app(cons(esk5_0,cons(esk5_0,nil)),esk8_0)) = esk1_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_35]),c_0_36]),c_0_28])]) ).
cnf(c_0_47,plain,
( cons(X3,app(X2,X1)) = app(cons(X3,X2),X1)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssItem(X3) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
fof(c_0_48,plain,
! [X21,X22,X24] :
( ( ssList(esk9_2(X21,X22))
| ~ frontsegP(X21,X22)
| ~ ssList(X22)
| ~ ssList(X21) )
& ( app(X22,esk9_2(X21,X22)) = X21
| ~ frontsegP(X21,X22)
| ~ ssList(X22)
| ~ ssList(X21) )
& ( ~ ssList(X24)
| app(X22,X24) != X21
| frontsegP(X21,X22)
| ~ ssList(X22)
| ~ ssList(X21) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax5])])])])])]) ).
fof(c_0_49,plain,
! [X35,X36] :
( ~ ssList(X35)
| ~ ssList(X36)
| ssList(app(X35,X36)) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax26])])])]) ).
cnf(c_0_50,negated_conjecture,
( app(esk7_0,cons(esk5_0,app(cons(esk5_0,nil),esk8_0))) = esk1_0
| ~ ssList(cons(esk5_0,nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_42]),c_0_28])]) ).
cnf(c_0_51,plain,
( frontsegP(X3,X2)
| ~ ssList(X1)
| app(X2,X1) != X3
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_52,plain,
( ssList(app(X1,X2))
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_53,negated_conjecture,
app(esk7_0,cons(esk5_0,app(cons(esk5_0,nil),esk8_0))) = esk1_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_35]),c_0_36]),c_0_28])]) ).
cnf(c_0_54,plain,
( frontsegP(app(X1,X2),X1)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_51]),c_0_52]) ).
cnf(c_0_55,negated_conjecture,
app(esk7_0,cons(esk5_0,cons(esk5_0,esk8_0))) = esk1_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_39]),c_0_42]),c_0_28])]) ).
cnf(c_0_56,negated_conjecture,
( frontsegP(esk1_0,esk7_0)
| ~ ssList(cons(esk5_0,cons(esk5_0,esk8_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_32])]) ).
fof(c_0_57,plain,
! [X134,X135] :
( ~ ssList(X134)
| ~ ssItem(X135)
| tl(cons(X135,X134)) = X134 ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax25])])])]) ).
fof(c_0_58,plain,
! [X96,X98] :
( ( ssItem(esk17_1(X96))
| ~ singletonP(X96)
| ~ ssList(X96) )
& ( cons(esk17_1(X96),nil) = X96
| ~ singletonP(X96)
| ~ ssList(X96) )
& ( ~ ssItem(X98)
| cons(X98,nil) != X96
| singletonP(X96)
| ~ ssList(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(fof_nnf,[status(thm)],[ax4])])])])])]) ).
fof(c_0_59,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_60,negated_conjecture,
( frontsegP(esk1_0,esk7_0)
| ~ ssList(cons(esk5_0,esk8_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_35]),c_0_28])]) ).
cnf(c_0_61,plain,
( tl(cons(X2,X1)) = X1
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_62,plain,
( cons(esk17_1(X1),nil) = X1
| ~ singletonP(X1)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_63,plain,
( ssItem(esk17_1(X1))
| ~ singletonP(X1)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_64,negated_conjecture,
singletonP(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_65,negated_conjecture,
esk1_0 = esk3_0,
inference(split_conjunct,[status(thm)],[c_0_22]) ).
fof(c_0_66,plain,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( nil != X1
=> hd(app(X1,X2)) = hd(X1) ) ) ),
inference(fof_simplification,[status(thm)],[ax85]) ).
fof(c_0_67,plain,
! [X67,X68] :
( ~ ssList(X67)
| ~ ssList(X68)
| nil = X67
| tl(app(X67,X68)) = app(tl(X67),X68) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_59])])])]) ).
cnf(c_0_68,plain,
( app(X1,esk9_2(X2,X1)) = X2
| ~ frontsegP(X2,X1)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_69,negated_conjecture,
frontsegP(esk1_0,esk7_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_35]),c_0_42]),c_0_28])]) ).
cnf(c_0_70,negated_conjecture,
ssList(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_71,plain,
( tl(X1) = nil
| ~ singletonP(X1)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_36])]),c_0_63]) ).
cnf(c_0_72,negated_conjecture,
singletonP(esk1_0),
inference(rw,[status(thm)],[c_0_64,c_0_65]) ).
cnf(c_0_73,plain,
( ssList(esk9_2(X1,X2))
| ~ frontsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
fof(c_0_74,plain,
! [X62,X63] :
( ( nil = X63
| nil != app(X62,X63)
| ~ ssList(X63)
| ~ ssList(X62) )
& ( nil = X62
| nil != app(X62,X63)
| ~ ssList(X63)
| ~ ssList(X62) )
& ( nil != X63
| nil != X62
| nil = app(X62,X63)
| ~ ssList(X63)
| ~ ssList(X62) ) ),
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])])])])]) ).
fof(c_0_75,plain,
! [X54,X55,X56] :
( ~ ssList(X54)
| ~ ssList(X55)
| ~ ssList(X56)
| app(X55,X56) != app(X55,X54)
| X56 = X54 ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax80])])])]) ).
fof(c_0_76,plain,
! [X64] :
( ~ ssList(X64)
| app(X64,nil) = X64 ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax84])])]) ).
fof(c_0_77,plain,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> cons(hd(X1),tl(X1)) = X1 ) ),
inference(fof_simplification,[status(thm)],[ax78]) ).
fof(c_0_78,plain,
! [X65,X66] :
( ~ ssList(X65)
| ~ ssList(X66)
| nil = X65
| hd(app(X65,X66)) = hd(X65) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_66])])])]) ).
cnf(c_0_79,plain,
( nil = X1
| tl(app(X1,X2)) = app(tl(X1),X2)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_67]) ).
cnf(c_0_80,negated_conjecture,
app(esk7_0,esk9_2(esk1_0,esk7_0)) = esk1_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_70]),c_0_32])]) ).
cnf(c_0_81,negated_conjecture,
tl(esk1_0) = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_70])]) ).
cnf(c_0_82,negated_conjecture,
ssList(esk9_2(esk1_0,esk7_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_69]),c_0_32]),c_0_70])]) ).
fof(c_0_83,plain,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> ssList(tl(X1)) ) ),
inference(fof_simplification,[status(thm)],[ax24]) ).
cnf(c_0_84,plain,
( nil = X1
| nil != app(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_74]) ).
cnf(c_0_85,plain,
( X3 = X1
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| app(X2,X3) != app(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_75]) ).
cnf(c_0_86,plain,
( app(X1,nil) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_76]) ).
fof(c_0_87,plain,
! [X132] :
( ~ ssList(X132)
| nil = X132
| cons(hd(X132),tl(X132)) = X132 ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_77])])]) ).
cnf(c_0_88,plain,
( nil = X1
| hd(app(X1,X2)) = hd(X1)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_78]) ).
cnf(c_0_89,negated_conjecture,
( app(tl(esk7_0),esk9_2(esk1_0,esk7_0)) = nil
| esk7_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_80]),c_0_81]),c_0_82]),c_0_32])]) ).
fof(c_0_90,plain,
! [X133] :
( ~ ssList(X133)
| nil = X133
| ssList(tl(X133)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_83])])]) ).
cnf(c_0_91,negated_conjecture,
( esk7_0 = nil
| esk1_0 != nil
| ~ ssList(app(cons(esk5_0,cons(esk5_0,nil)),esk8_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_46]),c_0_32])]) ).
cnf(c_0_92,plain,
( X1 = nil
| app(X2,X1) != X2
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_86]),c_0_36])]) ).
cnf(c_0_93,plain,
( nil = X1
| cons(hd(X1),tl(X1)) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_87]) ).
cnf(c_0_94,negated_conjecture,
( hd(esk7_0) = hd(esk1_0)
| esk7_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_80]),c_0_82]),c_0_32])]) ).
cnf(c_0_95,negated_conjecture,
( tl(esk7_0) = nil
| esk7_0 = nil
| ~ ssList(tl(esk7_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_89]),c_0_82])]) ).
cnf(c_0_96,plain,
( nil = X1
| ssList(tl(X1))
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_90]) ).
cnf(c_0_97,negated_conjecture,
( esk7_0 = nil
| esk1_0 != nil
| ~ ssList(cons(esk5_0,cons(esk5_0,nil))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_52]),c_0_42])]) ).
cnf(c_0_98,negated_conjecture,
( cons(esk5_0,cons(esk5_0,esk8_0)) = nil
| esk7_0 != esk1_0
| ~ ssList(cons(esk5_0,cons(esk5_0,esk8_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_55]),c_0_32])]) ).
cnf(c_0_99,negated_conjecture,
( cons(hd(esk1_0),tl(esk7_0)) = esk7_0
| esk7_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_94]),c_0_32])]) ).
cnf(c_0_100,negated_conjecture,
( tl(esk7_0) = nil
| esk7_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_96]),c_0_32])]) ).
cnf(c_0_101,negated_conjecture,
( esk7_0 = nil
| esk1_0 != nil
| ~ ssList(cons(esk5_0,nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_35]),c_0_28])]) ).
fof(c_0_102,plain,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> nil != cons(X2,X1) ) ),
inference(fof_simplification,[status(thm)],[ax21]) ).
cnf(c_0_103,negated_conjecture,
( cons(esk5_0,cons(esk5_0,esk8_0)) = nil
| esk7_0 != esk1_0
| ~ ssList(cons(esk5_0,esk8_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_35]),c_0_28])]) ).
cnf(c_0_104,negated_conjecture,
( cons(hd(esk1_0),nil) = esk1_0
| esk1_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_81]),c_0_70])]) ).
cnf(c_0_105,negated_conjecture,
( cons(hd(esk1_0),nil) = esk7_0
| esk7_0 = nil ),
inference(spm,[status(thm)],[c_0_99,c_0_100]) ).
cnf(c_0_106,negated_conjecture,
( esk7_0 = nil
| esk1_0 != nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_35]),c_0_36]),c_0_28])]) ).
fof(c_0_107,plain,
! [X80,X81] :
( ~ ssList(X80)
| ~ ssItem(X81)
| nil != cons(X81,X80) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_102])])])]) ).
cnf(c_0_108,negated_conjecture,
( cons(esk5_0,cons(esk5_0,esk8_0)) = nil
| esk7_0 != esk1_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_35]),c_0_42]),c_0_28])]) ).
cnf(c_0_109,negated_conjecture,
( esk7_0 = nil
| esk7_0 = esk1_0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_105]),c_0_106]) ).
cnf(c_0_110,plain,
( ~ ssList(X1)
| ~ ssItem(X2)
| nil != cons(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_107]) ).
cnf(c_0_111,negated_conjecture,
( cons(esk5_0,cons(esk5_0,esk8_0)) = nil
| esk7_0 = nil ),
inference(spm,[status(thm)],[c_0_108,c_0_109]) ).
cnf(c_0_112,negated_conjecture,
( esk7_0 = nil
| ~ ssList(cons(esk5_0,esk8_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_111]),c_0_28])]) ).
fof(c_0_113,plain,
! [X40] :
( ~ ssList(X40)
| app(nil,X40) = X40 ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax28])])]) ).
cnf(c_0_114,negated_conjecture,
esk7_0 = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_35]),c_0_42]),c_0_28])]) ).
cnf(c_0_115,plain,
( app(nil,X1) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_113]) ).
cnf(c_0_116,negated_conjecture,
app(nil,cons(esk5_0,cons(esk5_0,esk8_0))) = esk1_0,
inference(rw,[status(thm)],[c_0_55,c_0_114]) ).
cnf(c_0_117,negated_conjecture,
( cons(esk5_0,cons(esk5_0,esk8_0)) = esk1_0
| ~ ssList(cons(esk5_0,cons(esk5_0,esk8_0))) ),
inference(spm,[status(thm)],[c_0_115,c_0_116]) ).
cnf(c_0_118,negated_conjecture,
( cons(esk5_0,cons(esk5_0,esk8_0)) = esk1_0
| ~ ssList(cons(esk5_0,esk8_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_117,c_0_35]),c_0_28])]) ).
cnf(c_0_119,negated_conjecture,
cons(esk5_0,cons(esk5_0,esk8_0)) = esk1_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_35]),c_0_42]),c_0_28])]) ).
cnf(c_0_120,negated_conjecture,
( cons(esk5_0,esk8_0) = nil
| ~ ssList(cons(esk5_0,esk8_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_119]),c_0_81]),c_0_28])]) ).
cnf(c_0_121,negated_conjecture,
cons(esk5_0,esk8_0) = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_120,c_0_35]),c_0_42]),c_0_28])]) ).
cnf(c_0_122,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_121]),c_0_42]),c_0_28])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SWC166+1 : TPTP v8.2.0. Released v2.4.0.
% 0.04/0.14 % Command : run_E %s %d THM
% 0.14/0.35 % Computer : n026.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sun May 19 03:04:53 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.20/0.47 Running first-order model finding
% 0.20/0.47 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --satauto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.73/0.54 # Version: 3.1.0
% 0.73/0.54 # Preprocessing class: FSLSSMSSSSSNFFN.
% 0.73/0.54 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.73/0.54 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.73/0.54 # Starting new_bool_3 with 300s (1) cores
% 0.73/0.54 # Starting new_bool_1 with 300s (1) cores
% 0.73/0.54 # Starting sh5l with 300s (1) cores
% 0.73/0.54 # sh5l with pid 25253 completed with status 0
% 0.73/0.54 # Result found by sh5l
% 0.73/0.54 # Preprocessing class: FSLSSMSSSSSNFFN.
% 0.73/0.54 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.73/0.54 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.73/0.54 # Starting new_bool_3 with 300s (1) cores
% 0.73/0.54 # Starting new_bool_1 with 300s (1) cores
% 0.73/0.54 # Starting sh5l with 300s (1) cores
% 0.73/0.54 # SinE strategy is gf500_gu_R04_F100_L20000
% 0.73/0.54 # Search class: FGHSF-FSLM21-MFFFFFNN
% 0.73/0.54 # Scheduled 11 strats onto 1 cores with 300 seconds (300 total)
% 0.73/0.54 # Starting G-E--_208_C18_SOS_F1_SE_CS_SP_PS_S4c with 28s (1) cores
% 0.73/0.54 # G-E--_208_C18_SOS_F1_SE_CS_SP_PS_S4c with pid 25256 completed with status 0
% 0.73/0.54 # Result found by G-E--_208_C18_SOS_F1_SE_CS_SP_PS_S4c
% 0.73/0.54 # Preprocessing class: FSLSSMSSSSSNFFN.
% 0.73/0.54 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.73/0.54 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.73/0.54 # Starting new_bool_3 with 300s (1) cores
% 0.73/0.54 # Starting new_bool_1 with 300s (1) cores
% 0.73/0.54 # Starting sh5l with 300s (1) cores
% 0.73/0.54 # SinE strategy is gf500_gu_R04_F100_L20000
% 0.73/0.54 # Search class: FGHSF-FSLM21-MFFFFFNN
% 0.73/0.54 # Scheduled 11 strats onto 1 cores with 300 seconds (300 total)
% 0.73/0.54 # Starting G-E--_208_C18_SOS_F1_SE_CS_SP_PS_S4c with 28s (1) cores
% 0.73/0.54 # Preprocessing time : 0.002 s
% 0.73/0.54 # Presaturation interreduction done
% 0.73/0.54
% 0.73/0.54 # Proof found!
% 0.73/0.54 # SZS status Theorem
% 0.73/0.54 # SZS output start CNFRefutation
% See solution above
% 0.73/0.54 # Parsed axioms : 96
% 0.73/0.54 # Removed by relevancy pruning/SinE : 10
% 0.73/0.54 # Initial clauses : 173
% 0.73/0.54 # Removed in clause preprocessing : 2
% 0.73/0.54 # Initial clauses in saturation : 171
% 0.73/0.54 # Processed clauses : 676
% 0.73/0.54 # ...of these trivial : 5
% 0.73/0.54 # ...subsumed : 115
% 0.73/0.54 # ...remaining for further processing : 556
% 0.73/0.54 # Other redundant clauses eliminated : 58
% 0.73/0.54 # Clauses deleted for lack of memory : 0
% 0.73/0.54 # Backward-subsumed : 49
% 0.73/0.54 # Backward-rewritten : 77
% 0.73/0.54 # Generated clauses : 1527
% 0.73/0.54 # ...of the previous two non-redundant : 1335
% 0.73/0.54 # ...aggressively subsumed : 0
% 0.73/0.54 # Contextual simplify-reflections : 29
% 0.73/0.54 # Paramodulations : 1463
% 0.73/0.54 # Factorizations : 1
% 0.73/0.54 # NegExts : 0
% 0.73/0.54 # Equation resolutions : 63
% 0.73/0.54 # Disequality decompositions : 0
% 0.73/0.54 # Total rewrite steps : 1575
% 0.73/0.54 # ...of those cached : 1523
% 0.73/0.54 # Propositional unsat checks : 0
% 0.73/0.54 # Propositional check models : 0
% 0.73/0.54 # Propositional check unsatisfiable : 0
% 0.73/0.54 # Propositional clauses : 0
% 0.73/0.54 # Propositional clauses after purity: 0
% 0.73/0.54 # Propositional unsat core size : 0
% 0.73/0.54 # Propositional preprocessing time : 0.000
% 0.73/0.54 # Propositional encoding time : 0.000
% 0.73/0.54 # Propositional solver time : 0.000
% 0.73/0.54 # Success case prop preproc time : 0.000
% 0.73/0.54 # Success case prop encoding time : 0.000
% 0.73/0.54 # Success case prop solver time : 0.000
% 0.73/0.54 # Current number of processed clauses : 245
% 0.73/0.54 # Positive orientable unit clauses : 56
% 0.73/0.54 # Positive unorientable unit clauses: 0
% 0.73/0.54 # Negative unit clauses : 4
% 0.73/0.54 # Non-unit-clauses : 185
% 0.73/0.54 # Current number of unprocessed clauses: 951
% 0.73/0.54 # ...number of literals in the above : 5295
% 0.73/0.54 # Current number of archived formulas : 0
% 0.73/0.54 # Current number of archived clauses : 292
% 0.73/0.54 # Clause-clause subsumption calls (NU) : 15790
% 0.73/0.54 # Rec. Clause-clause subsumption calls : 5289
% 0.73/0.54 # Non-unit clause-clause subsumptions : 158
% 0.73/0.54 # Unit Clause-clause subsumption calls : 357
% 0.73/0.54 # Rewrite failures with RHS unbound : 0
% 0.73/0.54 # BW rewrite match attempts : 23
% 0.73/0.54 # BW rewrite match successes : 15
% 0.73/0.54 # Condensation attempts : 0
% 0.73/0.54 # Condensation successes : 0
% 0.73/0.54 # Termbank termtop insertions : 45746
% 0.73/0.54 # Search garbage collected termcells : 3703
% 0.73/0.54
% 0.73/0.54 # -------------------------------------------------
% 0.73/0.54 # User time : 0.052 s
% 0.73/0.54 # System time : 0.004 s
% 0.73/0.54 # Total time : 0.056 s
% 0.73/0.54 # Maximum resident set size: 2456 pages
% 0.73/0.54
% 0.73/0.54 # -------------------------------------------------
% 0.73/0.54 # User time : 0.055 s
% 0.73/0.54 # System time : 0.007 s
% 0.73/0.54 # Total time : 0.061 s
% 0.73/0.54 # Maximum resident set size: 1824 pages
% 0.73/0.54 % E---3.1 exiting
%------------------------------------------------------------------------------