%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWC170+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n016.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 02:43:18 PM UTC 2026
% Result : Theorem 0.69s 0.87s
% Output : CNFRefutation 0.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 48
% Number of leaves : 29
% Syntax : Number of formulae : 187 ( 32 unt; 0 def)
% Number of atoms : 660 ( 225 equ)
% Maximal formula atoms : 30 ( 3 avg)
% Number of connectives : 766 ( 293 ~; 312 |; 41 &)
% ( 11 <=>; 109 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 22 ( 22 usr; 9 con; 0-2 aty)
% Number of variables : 242 ( 0 sgn 154 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( neq(X4,nil)
& ~ singletonP(X3) )
| ! [X5] :
( ssItem(X5)
=> ! [X6] :
( ssItem(X6)
=> ! [X7] :
( ssList(X7)
=> ! [X8] :
( ssList(X8)
=> ( neq(X5,X6)
| app(app(app(X7,cons(X5,nil)),cons(X6,nil)),X8) != X1 ) ) ) ) )
| ~ segmentP(X4,X3)
| X1 != X3
| X2 != X4 ) ) ) ) ),
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] :
( app(X2,X3) = X1
& ssList(X3) ) ) ) ),
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(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(ax15,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax15) ).
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] :
( cons(X2,nil) = X1
& ssItem(X2) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax4) ).
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 = X1
& nil = X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax83) ).
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(ax13,axiom,
! [X1] :
( ssList(X1)
=> ( duplicatefreeP(X1)
<=> ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssItem(X3)
=> ! [X4] :
( ssList(X4)
=> ! [X5] :
( ssList(X5)
=> ! [X6] :
( ssList(X6)
=> ( app(app(X4,cons(X2,X5)),cons(X3,X6)) = X1
=> X2 != X3 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax13) ).
fof(ax71,axiom,
! [X1] :
( ssItem(X1)
=> duplicatefreeP(cons(X1,nil)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax71) ).
fof(ax28,axiom,
! [X1] :
( ssList(X1)
=> app(nil,X1) = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax28) ).
fof(ax21,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> nil != cons(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax21) ).
fof(ax23,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> hd(cons(X2,X1)) = X2 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax23) ).
fof(ax18,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> cons(X2,X1) != X1 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax18) ).
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(ax7,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( segmentP(X1,X2)
<=> ? [X3] :
( ? [X4] :
( app(app(X3,X2),X4) = X1
& ssList(X4) )
& ssList(X3) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax7) ).
fof(ax54,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( ( segmentP(X2,X1)
& segmentP(X1,X2) )
=> X1 = X2 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax54) ).
fof(ax57,axiom,
! [X1] :
( ssList(X1)
=> segmentP(X1,nil) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax57) ).
fof(ax58,axiom,
! [X1] :
( ssList(X1)
=> ( segmentP(nil,X1)
<=> nil = X1 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax58) ).
fof(c_0_29,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( neq(X4,nil)
& ~ singletonP(X3) )
| ! [X5] :
( ssItem(X5)
=> ! [X6] :
( ssItem(X6)
=> ! [X7] :
( ssList(X7)
=> ! [X8] :
( ssList(X8)
=> ( neq(X5,X6)
| app(app(app(X7,cons(X5,nil)),cons(X6,nil)),X8) != X1 ) ) ) ) )
| ~ segmentP(X4,X3)
| X1 != X3
| X2 != X4 ) ) ) ) ),
inference(assume_negation,[status(cth)],[co1]) ).
fof(c_0_30,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( neq(X4,nil)
& ~ singletonP(X3) )
| ! [X5] :
( ssItem(X5)
=> ! [X6] :
( ssItem(X6)
=> ! [X7] :
( ssList(X7)
=> ! [X8] :
( ssList(X8)
=> ( neq(X5,X6)
| app(app(app(X7,cons(X5,nil)),cons(X6,nil)),X8) != X1 ) ) ) ) )
| ~ segmentP(X4,X3)
| X1 != X3
| X2 != X4 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_29]) ).
fof(c_0_31,plain,
! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
inference(fof_simplification,[status(thm)],[ax1]) ).
fof(c_0_32,negated_conjecture,
( ( ~ neq(esk51_0,nil)
| singletonP(esk50_0) )
& ~ neq(esk52_0,esk53_0)
& app(app(app(esk54_0,cons(esk52_0,nil)),cons(esk53_0,nil)),esk55_0) = esk48_0
& ssList(esk55_0)
& ssList(esk54_0)
& ssItem(esk53_0)
& ssItem(esk52_0)
& segmentP(esk51_0,esk50_0)
& esk48_0 = esk50_0
& esk49_0 = esk51_0
& ssList(esk51_0)
& ssList(esk50_0)
& ssList(esk49_0)
& ssList(esk48_0) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_30])])])]) ).
fof(c_0_33,plain,
! [X9,X10] :
( ( ~ ssItem(X9)
| ~ ssItem(X10)
| neq(X9,X10)
| X9 = X10 )
& ( ~ ssItem(X9)
| ~ ssItem(X10)
| X9 != X10
| ~ neq(X9,X10) ) ),
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_31])])])])]) ).
cnf(c_0_34,negated_conjecture,
app(app(app(esk54_0,cons(esk52_0,nil)),cons(esk53_0,nil)),esk55_0) = esk48_0,
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_35,negated_conjecture,
esk48_0 = esk50_0,
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_36,negated_conjecture,
~ neq(esk52_0,esk53_0),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_37,plain,
( ~ ssItem(X1)
| ~ ssItem(X2)
| neq(X1,X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_38,negated_conjecture,
ssItem(esk53_0),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_39,negated_conjecture,
ssItem(esk52_0),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_40,negated_conjecture,
app(app(app(esk54_0,cons(esk52_0,nil)),cons(esk53_0,nil)),esk55_0) = esk50_0,
inference(rw,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_41,negated_conjecture,
esk53_0 = esk52_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_38]),c_0_39])]) ).
fof(c_0_42,plain,
! [X224,X225,X226] :
( app(app(X224,X225),X226) = app(X224,app(X225,X226))
| ~ ssList(X226)
| ~ ssList(X225)
| ~ ssList(X224) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax82])])])]) ).
cnf(c_0_43,negated_conjecture,
app(app(app(esk54_0,cons(esk52_0,nil)),cons(esk52_0,nil)),esk55_0) = esk50_0,
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_44,plain,
( ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| app(app(X1,X2),X3) = app(X1,app(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_45,negated_conjecture,
ssList(esk54_0),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
fof(c_0_46,plain,
! [X113,X114] :
( ssList(cons(X114,X113))
| ~ ssItem(X114)
| ~ ssList(X113) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax16])])])]) ).
cnf(c_0_47,negated_conjecture,
( ~ ssList(cons(esk52_0,nil))
| app(app(esk54_0,app(cons(esk52_0,nil),cons(esk52_0,nil))),esk55_0) = esk50_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_45])]) ).
cnf(c_0_48,plain,
( ~ ssItem(X2)
| ~ ssList(X1)
| ssList(cons(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_49,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[ax17]) ).
fof(c_0_50,plain,
! [X222,X223] :
( cons(X223,X222) = app(cons(X223,nil),X222)
| ~ ssItem(X223)
| ~ ssList(X222) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax81])])])]) ).
cnf(c_0_51,negated_conjecture,
app(app(esk54_0,app(cons(esk52_0,nil),cons(esk52_0,nil))),esk55_0) = esk50_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_49]),c_0_39])]) ).
cnf(c_0_52,plain,
( ~ ssItem(X2)
| ~ ssList(X1)
| cons(X2,X1) = app(cons(X2,nil),X1) ),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
cnf(c_0_53,negated_conjecture,
( ~ ssList(cons(esk52_0,nil))
| app(app(esk54_0,cons(esk52_0,cons(esk52_0,nil))),esk55_0) = esk50_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_39])]) ).
cnf(c_0_54,negated_conjecture,
app(app(esk54_0,cons(esk52_0,cons(esk52_0,nil))),esk55_0) = esk50_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_48]),c_0_49]),c_0_39])]) ).
cnf(c_0_55,negated_conjecture,
ssList(esk55_0),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_56,negated_conjecture,
( ~ ssList(cons(esk52_0,cons(esk52_0,nil)))
| app(esk54_0,app(cons(esk52_0,cons(esk52_0,nil)),esk55_0)) = esk50_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_54]),c_0_55]),c_0_45])]) ).
cnf(c_0_57,negated_conjecture,
( ~ ssList(cons(esk52_0,nil))
| app(esk54_0,app(cons(esk52_0,cons(esk52_0,nil)),esk55_0)) = esk50_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_48]),c_0_39])]) ).
fof(c_0_58,plain,
! [X134,X135,X136] :
( cons(X136,app(X135,X134)) = app(cons(X136,X135),X134)
| ~ ssItem(X136)
| ~ ssList(X135)
| ~ ssList(X134) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax27])])])]) ).
cnf(c_0_59,negated_conjecture,
app(esk54_0,app(cons(esk52_0,cons(esk52_0,nil)),esk55_0)) = esk50_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_48]),c_0_49]),c_0_39])]) ).
cnf(c_0_60,plain,
( ~ ssItem(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| cons(X3,app(X2,X1)) = app(cons(X3,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
fof(c_0_61,plain,
! [X22,X23,X25] :
( ( ~ ssList(X22)
| ~ ssList(X23)
| frontsegP(X22,X23)
| app(X23,X25) != X22
| ~ ssList(X25) )
& ( ~ ssList(X22)
| ~ ssList(X23)
| ~ frontsegP(X22,X23)
| app(X23,esk6_2(X22,X23)) = X22 )
& ( ~ ssList(X22)
| ~ ssList(X23)
| ~ frontsegP(X22,X23)
| ssList(esk6_2(X22,X23)) ) ),
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_62,plain,
! [X132,X133] :
( ssList(app(X132,X133))
| ~ ssList(X133)
| ~ ssList(X132) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax26])])])]) ).
cnf(c_0_63,negated_conjecture,
( ~ ssList(cons(esk52_0,nil))
| app(esk54_0,cons(esk52_0,app(cons(esk52_0,nil),esk55_0))) = esk50_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_55]),c_0_39])]) ).
cnf(c_0_64,plain,
( ~ ssList(X3)
| ~ ssList(X2)
| app(X2,X1) != X3
| ~ ssList(X1)
| frontsegP(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
cnf(c_0_65,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ssList(app(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_66,negated_conjecture,
app(esk54_0,cons(esk52_0,app(cons(esk52_0,nil),esk55_0))) = esk50_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_48]),c_0_49]),c_0_39])]) ).
cnf(c_0_67,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| frontsegP(app(X1,X2),X1) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_64]),c_0_65]) ).
cnf(c_0_68,negated_conjecture,
app(esk54_0,cons(esk52_0,cons(esk52_0,esk55_0))) = esk50_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_52]),c_0_55]),c_0_39])]) ).
cnf(c_0_69,negated_conjecture,
( ~ ssList(cons(esk52_0,cons(esk52_0,esk55_0)))
| frontsegP(esk50_0,esk54_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_68]),c_0_45])]) ).
fof(c_0_70,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_71,negated_conjecture,
( ~ ssList(cons(esk52_0,esk55_0))
| frontsegP(esk50_0,esk54_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_48]),c_0_39])]) ).
cnf(c_0_72,negated_conjecture,
ssList(esk48_0),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
fof(c_0_73,plain,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
inference(fof_simplification,[status(thm)],[ax15]) ).
fof(c_0_74,plain,
! [X232,X233] :
( tl(app(X232,X233)) = app(tl(X232),X233)
| nil = X232
| ~ ssList(X233)
| ~ ssList(X232) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_70])])])]) ).
cnf(c_0_75,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ~ frontsegP(X2,X1)
| app(X1,esk6_2(X2,X1)) = X2 ),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
cnf(c_0_76,negated_conjecture,
frontsegP(esk50_0,esk54_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_48]),c_0_55]),c_0_39])]) ).
cnf(c_0_77,negated_conjecture,
ssList(esk50_0),
inference(rw,[status(thm)],[c_0_72,c_0_35]) ).
cnf(c_0_78,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ frontsegP(X1,X2)
| ssList(esk6_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
fof(c_0_79,plain,
! [X130,X131] :
( tl(cons(X131,X130)) = X130
| ~ ssItem(X131)
| ~ ssList(X130) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax25])])])]) ).
fof(c_0_80,plain,
! [X19,X21] :
( ( ~ ssList(X19)
| singletonP(X19)
| cons(X21,nil) != X19
| ~ ssItem(X21) )
& ( ~ ssList(X19)
| ~ singletonP(X19)
| cons(esk5_1(X19),nil) = X19 )
& ( ~ ssList(X19)
| ~ singletonP(X19)
| ssItem(esk5_1(X19)) ) ),
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_81,plain,
! [X111,X112] :
( ( ~ ssList(X111)
| ~ ssList(X112)
| neq(X111,X112)
| X111 = X112 )
& ( ~ ssList(X111)
| ~ ssList(X112)
| X111 != X112
| ~ neq(X111,X112) ) ),
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_73])])])])]) ).
cnf(c_0_82,negated_conjecture,
ssList(esk49_0),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_83,negated_conjecture,
esk49_0 = esk51_0,
inference(split_conjunct,[status(thm)],[c_0_32]) ).
fof(c_0_84,plain,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( nil != X1
=> hd(app(X1,X2)) = hd(X1) ) ) ),
inference(fof_simplification,[status(thm)],[ax85]) ).
fof(c_0_85,plain,
! [X227,X228] :
( ( ~ ssList(X227)
| ~ ssList(X228)
| nil = app(X227,X228)
| nil != X227
| nil != X228 )
& ( ~ ssList(X227)
| ~ ssList(X228)
| nil != app(X227,X228)
| nil = X227 )
& ( ~ ssList(X227)
| ~ ssList(X228)
| nil != app(X227,X228)
| nil = X228 ) ),
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_86,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| tl(app(X1,X2)) = app(tl(X1),X2)
| nil = X1 ),
inference(split_conjunct,[status(thm)],[c_0_74]) ).
cnf(c_0_87,negated_conjecture,
app(esk54_0,esk6_2(esk50_0,esk54_0)) = esk50_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_76]),c_0_77]),c_0_45])]) ).
cnf(c_0_88,negated_conjecture,
ssList(esk6_2(esk50_0,esk54_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_76]),c_0_45]),c_0_77])]) ).
cnf(c_0_89,plain,
( ~ ssItem(X2)
| ~ ssList(X1)
| tl(cons(X2,X1)) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_79]) ).
cnf(c_0_90,plain,
( ~ ssList(X1)
| ~ singletonP(X1)
| cons(esk5_1(X1),nil) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_80]) ).
cnf(c_0_91,plain,
( ~ ssList(X1)
| ~ singletonP(X1)
| ssItem(esk5_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_80]) ).
cnf(c_0_92,negated_conjecture,
( ~ neq(esk51_0,nil)
| singletonP(esk50_0) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_93,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| neq(X1,X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_81]) ).
cnf(c_0_94,negated_conjecture,
ssList(esk51_0),
inference(rw,[status(thm)],[c_0_82,c_0_83]) ).
fof(c_0_95,plain,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> cons(hd(X1),tl(X1)) = X1 ) ),
inference(fof_simplification,[status(thm)],[ax78]) ).
fof(c_0_96,plain,
! [X230,X231] :
( hd(app(X230,X231)) = hd(X230)
| nil = X230
| ~ ssList(X231)
| ~ ssList(X230) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_84])])])]) ).
cnf(c_0_97,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| nil != app(X1,X2)
| nil = X1 ),
inference(split_conjunct,[status(thm)],[c_0_85]) ).
cnf(c_0_98,negated_conjecture,
( esk54_0 = nil
| app(tl(esk54_0),esk6_2(esk50_0,esk54_0)) = tl(esk50_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_87]),c_0_88]),c_0_45])]) ).
cnf(c_0_99,plain,
( ~ ssList(X1)
| ~ singletonP(X1)
| tl(X1) = nil ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_90]),c_0_49])]),c_0_91]) ).
cnf(c_0_100,negated_conjecture,
( singletonP(esk50_0)
| esk51_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_93]),c_0_49]),c_0_94])]) ).
fof(c_0_101,plain,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> ssList(tl(X1)) ) ),
inference(fof_simplification,[status(thm)],[ax24]) ).
fof(c_0_102,plain,
! [X1] :
( ssList(X1)
=> ( duplicatefreeP(X1)
<=> ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssItem(X3)
=> ! [X4] :
( ssList(X4)
=> ! [X5] :
( ssList(X5)
=> ! [X6] :
( ssList(X6)
=> ( app(app(X4,cons(X2,X5)),cons(X3,X6)) = X1
=> X2 != X3 ) ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[ax13]) ).
fof(c_0_103,plain,
! [X215] :
( cons(hd(X215),tl(X215)) = X215
| nil = X215
| ~ ssList(X215) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_95])])]) ).
cnf(c_0_104,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| hd(app(X1,X2)) = hd(X1)
| nil = X1 ),
inference(split_conjunct,[status(thm)],[c_0_96]) ).
cnf(c_0_105,negated_conjecture,
( ~ ssList(tl(esk54_0))
| tl(esk50_0) != nil
| esk54_0 = nil
| tl(esk54_0) = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_98]),c_0_88])]) ).
cnf(c_0_106,negated_conjecture,
( esk51_0 = nil
| tl(esk50_0) = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_100]),c_0_77])]) ).
fof(c_0_107,plain,
! [X129] :
( ssList(tl(X129))
| nil = X129
| ~ ssList(X129) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_101])])]) ).
fof(c_0_108,plain,
! [X91,X92,X93,X94,X95,X96] :
( ( ~ ssList(X91)
| duplicatefreeP(X91)
| esk35_1(X91) = esk36_1(X91) )
& ( ~ ssList(X91)
| duplicatefreeP(X91)
| app(app(esk37_1(X91),cons(esk35_1(X91),esk38_1(X91))),cons(esk36_1(X91),esk39_1(X91))) = X91 )
& ( ~ ssList(X91)
| duplicatefreeP(X91)
| ssList(esk39_1(X91)) )
& ( ~ ssList(X91)
| duplicatefreeP(X91)
| ssList(esk38_1(X91)) )
& ( ~ ssList(X91)
| duplicatefreeP(X91)
| ssList(esk37_1(X91)) )
& ( ~ ssList(X91)
| duplicatefreeP(X91)
| ssItem(esk36_1(X91)) )
& ( ~ ssList(X91)
| duplicatefreeP(X91)
| ssItem(esk35_1(X91)) )
& ( ~ ssList(X91)
| X92 != X93
| app(app(X94,cons(X92,X95)),cons(X93,X96)) != X91
| ~ ssList(X96)
| ~ ssList(X95)
| ~ ssList(X94)
| ~ ssItem(X93)
| ~ ssItem(X92)
| ~ duplicatefreeP(X91) ) ),
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)],[c_0_102])])])])])]) ).
cnf(c_0_109,plain,
( ~ ssList(X1)
| cons(hd(X1),tl(X1)) = X1
| nil = X1 ),
inference(split_conjunct,[status(thm)],[c_0_103]) ).
cnf(c_0_110,negated_conjecture,
( esk54_0 = nil
| hd(esk54_0) = hd(esk50_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_87]),c_0_88]),c_0_45])]) ).
cnf(c_0_111,negated_conjecture,
( ~ ssList(tl(esk54_0))
| esk54_0 = nil
| esk51_0 = nil
| tl(esk54_0) = nil ),
inference(spm,[status(thm)],[c_0_105,c_0_106]) ).
cnf(c_0_112,plain,
( ~ ssList(X1)
| ssList(tl(X1))
| nil = X1 ),
inference(split_conjunct,[status(thm)],[c_0_107]) ).
cnf(c_0_113,plain,
( ~ ssList(X1)
| X2 != X3
| app(app(X4,cons(X2,X5)),cons(X3,X6)) != X1
| ~ ssList(X6)
| ~ ssList(X5)
| ~ ssList(X4)
| ~ ssItem(X3)
| ~ ssItem(X2)
| ~ duplicatefreeP(X1) ),
inference(split_conjunct,[status(thm)],[c_0_108]) ).
cnf(c_0_114,negated_conjecture,
( esk54_0 = nil
| cons(hd(esk50_0),tl(esk54_0)) = esk54_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_110]),c_0_45])]) ).
cnf(c_0_115,negated_conjecture,
( esk51_0 = nil
| esk54_0 = nil
| tl(esk54_0) = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_112]),c_0_45])]) ).
fof(c_0_116,plain,
! [X207] :
( duplicatefreeP(cons(X207,nil))
| ~ ssItem(X207) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax71])])]) ).
cnf(c_0_117,plain,
( ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X3)
| ~ ssList(X4)
| ~ ssList(app(app(X1,cons(X2,X3)),cons(X2,X4)))
| ~ duplicatefreeP(app(app(X1,cons(X2,X3)),cons(X2,X4))) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_113])]) ).
cnf(c_0_118,negated_conjecture,
( esk54_0 = nil
| esk51_0 = nil
| cons(hd(esk50_0),nil) = esk54_0 ),
inference(spm,[status(thm)],[c_0_114,c_0_115]) ).
cnf(c_0_119,negated_conjecture,
( esk50_0 = nil
| esk51_0 = nil
| cons(hd(esk50_0),nil) = esk50_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_106]),c_0_77])]) ).
cnf(c_0_120,negated_conjecture,
( esk50_0 != nil
| esk54_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_87]),c_0_88]),c_0_45])]) ).
cnf(c_0_121,plain,
( ~ ssItem(X1)
| duplicatefreeP(cons(X1,nil)) ),
inference(split_conjunct,[status(thm)],[c_0_116]) ).
cnf(c_0_122,negated_conjecture,
( ~ ssList(X1)
| ~ ssList(cons(esk52_0,esk55_0))
| ~ ssList(app(esk50_0,cons(esk52_0,X1)))
| ~ duplicatefreeP(app(esk50_0,cons(esk52_0,X1))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_117,c_0_68]),c_0_45]),c_0_39])]) ).
cnf(c_0_123,negated_conjecture,
( esk54_0 = esk50_0
| esk51_0 = nil
| esk54_0 = nil ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_119]),c_0_120]) ).
cnf(c_0_124,plain,
( ~ ssList(X1)
| ~ singletonP(X1)
| duplicatefreeP(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_121,c_0_90]),c_0_91]) ).
cnf(c_0_125,negated_conjecture,
( ~ ssList(X1)
| ~ ssList(app(esk50_0,cons(esk52_0,X1)))
| ~ duplicatefreeP(app(esk50_0,cons(esk52_0,X1))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_122,c_0_48]),c_0_55]),c_0_39])]) ).
cnf(c_0_126,negated_conjecture,
( esk54_0 = nil
| esk51_0 = nil
| app(esk50_0,cons(esk52_0,cons(esk52_0,esk55_0))) = esk50_0 ),
inference(spm,[status(thm)],[c_0_68,c_0_123]) ).
cnf(c_0_127,negated_conjecture,
( duplicatefreeP(esk50_0)
| esk51_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_124,c_0_100]),c_0_77])]) ).
cnf(c_0_128,negated_conjecture,
( ~ ssList(cons(esk52_0,esk55_0))
| esk51_0 = nil
| esk54_0 = nil ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_125,c_0_126]),c_0_77])]),c_0_127]) ).
fof(c_0_129,plain,
! [X137] :
( app(nil,X137) = X137
| ~ ssList(X137) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax28])])]) ).
cnf(c_0_130,negated_conjecture,
( esk54_0 = nil
| esk51_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_48]),c_0_55]),c_0_39])]) ).
fof(c_0_131,plain,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> nil != cons(X2,X1) ) ),
inference(fof_simplification,[status(thm)],[ax21]) ).
cnf(c_0_132,plain,
( ~ ssList(X1)
| app(nil,X1) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_129]) ).
cnf(c_0_133,negated_conjecture,
( esk51_0 = nil
| app(nil,cons(esk52_0,cons(esk52_0,esk55_0))) = esk50_0 ),
inference(spm,[status(thm)],[c_0_68,c_0_130]) ).
fof(c_0_134,plain,
! [X124,X125] :
( nil != cons(X125,X124)
| ~ ssItem(X125)
| ~ ssList(X124) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_131])])])]) ).
cnf(c_0_135,negated_conjecture,
( ~ ssList(cons(esk52_0,cons(esk52_0,esk55_0)))
| esk51_0 = nil
| cons(esk52_0,cons(esk52_0,esk55_0)) = esk50_0 ),
inference(spm,[status(thm)],[c_0_132,c_0_133]) ).
cnf(c_0_136,plain,
( nil != cons(X2,X1)
| ~ ssItem(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_134]) ).
fof(c_0_137,plain,
! [X127,X128] :
( hd(cons(X128,X127)) = X128
| ~ ssItem(X128)
| ~ ssList(X127) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax23])])])]) ).
cnf(c_0_138,negated_conjecture,
( ~ ssList(cons(esk52_0,esk55_0))
| esk51_0 = nil
| cons(esk52_0,cons(esk52_0,esk55_0)) = esk50_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_135,c_0_48]),c_0_39])]) ).
cnf(c_0_139,plain,
( ~ ssItem(X1)
| ~ ssList(X2)
| cons(hd(cons(X1,X2)),X2) = cons(X1,X2) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_89]),c_0_48]),c_0_136]) ).
cnf(c_0_140,plain,
( ~ ssItem(X2)
| ~ ssList(X1)
| hd(cons(X2,X1)) = X2 ),
inference(split_conjunct,[status(thm)],[c_0_137]) ).
cnf(c_0_141,negated_conjecture,
( esk51_0 = nil
| cons(esk52_0,cons(esk52_0,esk55_0)) = esk50_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_138,c_0_48]),c_0_55]),c_0_39])]) ).
cnf(c_0_142,plain,
( ~ ssList(X1)
| ~ singletonP(X1)
| cons(hd(X1),nil) = X1 ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_139,c_0_90]),c_0_49])]),c_0_91]) ).
cnf(c_0_143,negated_conjecture,
( ~ ssList(cons(esk52_0,esk55_0))
| esk51_0 = nil
| hd(esk50_0) = esk52_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_140,c_0_141]),c_0_39])]) ).
cnf(c_0_144,negated_conjecture,
( esk51_0 = nil
| cons(hd(esk50_0),nil) = esk50_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_142,c_0_100]),c_0_77])]) ).
cnf(c_0_145,negated_conjecture,
( esk51_0 = nil
| hd(esk50_0) = esk52_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_143,c_0_48]),c_0_55]),c_0_39])]) ).
cnf(c_0_146,negated_conjecture,
( esk51_0 = nil
| cons(esk52_0,nil) = esk50_0 ),
inference(spm,[status(thm)],[c_0_144,c_0_145]) ).
fof(c_0_147,plain,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> cons(X2,X1) != X1 ) ),
inference(fof_simplification,[status(thm)],[ax18]) ).
fof(c_0_148,plain,
! [X219,X220,X221] :
( X221 = X219
| app(X220,X221) != app(X220,X219)
| ~ ssList(X221)
| ~ ssList(X220)
| ~ ssList(X219) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax80])])])]) ).
fof(c_0_149,plain,
! [X229] :
( app(X229,nil) = X229
| ~ ssList(X229) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax84])])]) ).
cnf(c_0_150,negated_conjecture,
( esk51_0 = nil
| app(app(app(esk54_0,esk50_0),esk50_0),esk55_0) = esk50_0 ),
inference(spm,[status(thm)],[c_0_43,c_0_146]) ).
cnf(c_0_151,negated_conjecture,
( esk51_0 = nil
| app(esk54_0,esk50_0) = esk50_0 ),
inference(spm,[status(thm)],[c_0_68,c_0_141]) ).
fof(c_0_152,plain,
! [X115,X116] :
( cons(X116,X115) != X115
| ~ ssItem(X116)
| ~ ssList(X115) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_147])])])]) ).
fof(c_0_153,plain,
! [X30,X31,X34,X35] :
( ( ~ ssList(X30)
| ~ ssList(X31)
| segmentP(X30,X31)
| app(app(X34,X31),X35) != X30
| ~ ssList(X35)
| ~ ssList(X34) )
& ( ~ ssList(X30)
| ~ ssList(X31)
| ~ segmentP(X30,X31)
| app(app(esk8_2(X30,X31),X31),esk9_2(X30,X31)) = X30 )
& ( ~ ssList(X30)
| ~ ssList(X31)
| ~ segmentP(X30,X31)
| ssList(esk9_2(X30,X31)) )
& ( ~ ssList(X30)
| ~ ssList(X31)
| ~ segmentP(X30,X31)
| ssList(esk8_2(X30,X31)) ) ),
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)],[ax7])])])])])]) ).
cnf(c_0_154,plain,
( app(X2,X3) != app(X2,X1)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| X3 = X1 ),
inference(split_conjunct,[status(thm)],[c_0_148]) ).
cnf(c_0_155,plain,
( ~ ssList(X1)
| app(X1,nil) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_149]) ).
cnf(c_0_156,negated_conjecture,
( esk51_0 = nil
| app(app(esk50_0,esk50_0),esk55_0) = esk50_0 ),
inference(spm,[status(thm)],[c_0_150,c_0_151]) ).
cnf(c_0_157,plain,
( cons(X2,X1) != X1
| ~ ssItem(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_152]) ).
cnf(c_0_158,plain,
( ~ ssItem(X1)
| ~ ssList(X2)
| cons(X1,tl(cons(X1,X2))) = cons(X1,X2) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_140]),c_0_48]),c_0_136]) ).
cnf(c_0_159,plain,
( ~ ssList(X4)
| ~ ssList(X3)
| app(app(X1,X3),X2) != X4
| ~ ssList(X2)
| ~ ssList(X1)
| segmentP(X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_153]) ).
cnf(c_0_160,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| app(X2,X1) != X2
| X1 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_154,c_0_155]),c_0_49])]) ).
cnf(c_0_161,negated_conjecture,
( esk51_0 = nil
| app(esk50_0,app(esk50_0,esk55_0)) = esk50_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_156]),c_0_55]),c_0_77])]) ).
cnf(c_0_162,plain,
( ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(tl(cons(X1,X2)))
| tl(cons(X1,X2)) != cons(X1,X2) ),
inference(spm,[status(thm)],[c_0_157,c_0_158]) ).
cnf(c_0_163,plain,
( ~ ssList(X1)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(app(app(X1,X2),X3))
| segmentP(app(app(X1,X2),X3),X2) ),
inference(er,[status(thm)],[c_0_159]) ).
fof(c_0_164,plain,
! [X189,X190] :
( X189 = X190
| ~ segmentP(X190,X189)
| ~ segmentP(X189,X190)
| ~ ssList(X190)
| ~ ssList(X189) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax54])])])]) ).
cnf(c_0_165,negated_conjecture,
( ~ ssList(app(esk50_0,esk55_0))
| esk51_0 = nil
| app(esk50_0,esk55_0) = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_160,c_0_161]),c_0_77])]) ).
cnf(c_0_166,plain,
( ~ ssList(X1)
| ~ ssList(tl(X1))
| ~ singletonP(X1)
| tl(X1) != X1 ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_162,c_0_90]),c_0_49])]),c_0_91]) ).
cnf(c_0_167,negated_conjecture,
( ~ ssList(cons(esk52_0,nil))
| ~ ssList(app(esk54_0,cons(esk52_0,nil)))
| segmentP(esk50_0,cons(esk52_0,nil)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_163,c_0_40]),c_0_77]),c_0_55])]),c_0_41]),c_0_41]) ).
cnf(c_0_168,plain,
( ~ segmentP(X2,X1)
| ~ segmentP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_164]) ).
cnf(c_0_169,negated_conjecture,
segmentP(esk51_0,esk50_0),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_170,negated_conjecture,
( esk51_0 = nil
| app(esk50_0,esk55_0) = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_165,c_0_65]),c_0_55]),c_0_77])]) ).
cnf(c_0_171,negated_conjecture,
( esk50_0 != nil
| esk51_0 = nil ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_166,c_0_106]),c_0_49]),c_0_77])]),c_0_100]) ).
cnf(c_0_172,negated_conjecture,
( ~ ssList(app(esk54_0,cons(esk52_0,nil)))
| segmentP(esk50_0,cons(esk52_0,nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_167,c_0_48]),c_0_49]),c_0_39])]) ).
cnf(c_0_173,negated_conjecture,
( ~ segmentP(esk50_0,esk51_0)
| esk50_0 = esk51_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_168,c_0_169]),c_0_94]),c_0_77])]) ).
cnf(c_0_174,negated_conjecture,
esk51_0 = nil,
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_170]),c_0_55]),c_0_77])]),c_0_171]) ).
fof(c_0_175,plain,
! [X196] :
( segmentP(X196,nil)
| ~ ssList(X196) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax57])])]) ).
cnf(c_0_176,negated_conjecture,
( ~ ssList(cons(esk52_0,nil))
| segmentP(esk50_0,cons(esk52_0,nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_172,c_0_65]),c_0_45])]) ).
cnf(c_0_177,negated_conjecture,
( ~ segmentP(esk50_0,nil)
| esk50_0 = nil ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_173,c_0_174]),c_0_174]) ).
cnf(c_0_178,plain,
( ~ ssList(X1)
| segmentP(X1,nil) ),
inference(split_conjunct,[status(thm)],[c_0_175]) ).
fof(c_0_179,plain,
! [X197] :
( ( ~ ssList(X197)
| segmentP(nil,X197)
| nil != X197 )
& ( ~ ssList(X197)
| nil = X197
| ~ segmentP(nil,X197) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax58])])])]) ).
cnf(c_0_180,negated_conjecture,
segmentP(esk50_0,cons(esk52_0,nil)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_176,c_0_48]),c_0_49]),c_0_39])]) ).
cnf(c_0_181,negated_conjecture,
esk50_0 = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_177,c_0_178]),c_0_77])]) ).
cnf(c_0_182,plain,
( ~ ssList(X1)
| ~ segmentP(nil,X1)
| nil = X1 ),
inference(split_conjunct,[status(thm)],[c_0_179]) ).
cnf(c_0_183,negated_conjecture,
segmentP(nil,cons(esk52_0,nil)),
inference(rw,[status(thm)],[c_0_180,c_0_181]) ).
cnf(c_0_184,negated_conjecture,
( ~ ssList(cons(esk52_0,nil))
| cons(esk52_0,nil) = nil ),
inference(spm,[status(thm)],[c_0_182,c_0_183]) ).
cnf(c_0_185,negated_conjecture,
cons(esk52_0,nil) = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_184,c_0_48]),c_0_49]),c_0_39])]) ).
cnf(c_0_186,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_136,c_0_185]),c_0_49]),c_0_39])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWC170+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.20/0.46 % Computer : n016.cluster.edu
% 0.20/0.46 % Model : x86_64 x86_64
% 0.20/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.46 % Memory : 8046.5625MB
% 0.20/0.46 % OS : Linux 6.8.0-71-generic
% 0.20/0.46 % CPULimit : 300
% 0.20/0.46 % WCLimit : 300
% 0.20/0.46 % DateTime : Mon Sep 21 08:05:53 UTC 2026
% 0.20/0.47 % CPUTime :
% 0.20/0.47 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.24/0.55 Running first-order theorem proving
% 0.24/0.56 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
% 0.69/0.87 % Version: 3.5.1
% 0.69/0.87 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.69/0.87 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.69/0.87 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.69/0.87 % Starting new_bool_3 with 300s (1) cores
% 0.69/0.87 % Starting new_bool_1 with 300s (1) cores
% 0.69/0.87 % Starting sh5l with 300s (1) cores
% 0.69/0.87 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 1969593 completed with status 0
% 0.69/0.87 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 0.69/0.87 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.69/0.87 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.69/0.87 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.69/0.87 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.69/0.87 % No SInE strategy applied
% 0.69/0.87 % Search class: FGHSF-FSLM21-MFFFFFNN
% 0.69/0.87 % Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 0.69/0.87 % Starting SubtermCWHack with 136s (1) cores
% 0.69/0.87 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.69/0.87 % Starting G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4d with 136s (1) cores
% 0.69/0.87 % Starting G-E--_110_C45_F1_PI_SE_CS_SP_PS_S4S with 136s (1) cores
% 0.69/0.87 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_TT_S0Y with 136s (1) cores
% 0.69/0.87 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 1969601 completed with status 0
% 0.69/0.87 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 0.69/0.87 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.69/0.87 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.69/0.87 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.69/0.87 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.69/0.87 % No SInE strategy applied
% 0.69/0.87 % Search class: FGHSF-FSLM21-MFFFFFNN
% 0.69/0.87 % Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 0.69/0.87 % Starting SubtermCWHack with 136s (1) cores
% 0.69/0.87 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.69/0.87 % Preprocessing time : 0.006 s
% 0.69/0.87 % Presaturation interreduction done
% 0.69/0.87
% 0.69/0.87 % Proof found!
% 0.69/0.87 % SZS status Theorem
% 0.69/0.87 % SZS output start CNFRefutation
% See solution above
% 0.69/0.87 % Parsed axioms : 96
% 0.69/0.87 % Removed by relevancy pruning/SinE : 0
% 0.69/0.87 % Initial clauses : 204
% 0.69/0.87 % Removed in clause preprocessing : 2
% 0.69/0.87 % Initial clauses in saturation : 202
% 0.69/0.87 % Processed clauses : 1151
% 0.69/0.87 % ...of these trivial : 17
% 0.69/0.87 % ...subsumed : 328
% 0.69/0.87 % ...remaining for further processing : 806
% 0.69/0.87 % Other redundant clauses eliminated : 70
% 0.69/0.87 % Clauses deleted for lack of memory : 0
% 0.69/0.87 % Backward-subsumed : 86
% 0.69/0.87 % Backward-rewritten : 230
% 0.69/0.87 % Generated clauses : 3027
% 0.69/0.87 % ...of the previous two non-redundant : 2735
% 0.69/0.87 % ...aggressively subsumed : 0
% 0.69/0.87 % Contextual simplify-reflections : 84
% 0.69/0.87 % Paramodulations : 2953
% 0.69/0.87 % Factorizations : 1
% 0.69/0.87 % NegExts : 0
% 0.69/0.87 % Equation resolutions : 75
% 0.69/0.87 % Disequality decompositions : 0
% 0.69/0.87 % Total rewrite steps : 3009
% 0.69/0.87 % ...of those cached : 2943
% 0.69/0.87 % Propositional unsat checks : 0
% 0.69/0.87 % Propositional check models : 0
% 0.69/0.87 % Propositional check unsatisfiable : 0
% 0.69/0.87 % Propositional clauses : 0
% 0.69/0.87 % Propositional clauses after purity: 0
% 0.69/0.87 % Propositional unsat core size : 0
% 0.69/0.87 % Propositional preprocessing time : 0.000
% 0.69/0.87 % Propositional encoding time : 0.000
% 0.69/0.87 % Propositional solver time : 0.000
% 0.69/0.87 % Success case prop preproc time : 0.000
% 0.69/0.87 % Success case prop encoding time : 0.000
% 0.69/0.87 % Success case prop solver time : 0.000
% 0.69/0.87 % Current number of processed clauses : 271
% 0.69/0.87 % Positive orientable unit clauses : 41
% 0.69/0.87 % Positive unorientable unit clauses: 0
% 0.69/0.87 % Negative unit clauses : 4
% 0.69/0.87 % Non-unit-clauses : 226
% 0.69/0.87 % Current number of unprocessed clauses: 1939
% 0.69/0.87 % ...number of literals in the above : 9938
% 0.69/0.87 % Current number of archived formulas : 0
% 0.69/0.87 % Current number of archived clauses : 512
% 0.69/0.87 % Clause-clause subsumption calls (NU) : 35942
% 0.69/0.87 % Rec. Clause-clause subsumption calls : 13642
% 0.69/0.87 % Non-unit clause-clause subsumptions : 469
% 0.69/0.87 % Unit Clause-clause subsumption calls : 857
% 0.69/0.87 % Rewrite failures with RHS unbound : 0
% 0.69/0.87 % BW rewrite match attempts : 52
% 0.69/0.87 % BW rewrite match successes : 28
% 0.69/0.87 % Condensation attempts : 0
% 0.69/0.87 % Condensation successes : 0
% 0.69/0.87 % Termbank termtop insertions : 77413
% 0.69/0.87 % Search garbage collected termcells : 4307
% 0.69/0.87
% 0.69/0.87 % -------------------------------------------------
% 0.69/0.87 % User time : 0.219 s
% 0.69/0.87 % System time : 0.018 s
% 0.69/0.87 % Total time : 0.237 s
% 0.69/0.87 % Maximum resident set size: 3972 pages
% 0.69/0.87
% 0.69/0.87 % -------------------------------------------------
% 0.69/0.87 % User time : 0.847 s
% 0.69/0.87 % System time : 0.047 s
% 0.69/0.87 % Total time : 0.894 s
% 0.69/0.87 % Maximum resident set size: 4608 pages
% 0.69/0.87 % E exiting
%------------------------------------------------------------------------------