%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWC295+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 02:43:49 PM UTC 2026
% Result : Theorem 2.31s 0.85s
% Output : CNFRefutation 2.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 25
% Syntax : Number of formulae : 160 ( 26 unt; 0 def)
% Number of atoms : 632 ( 207 equ)
% Maximal formula atoms : 41 ( 3 avg)
% Number of connectives : 787 ( 315 ~; 319 |; 53 &)
% ( 5 <=>; 95 =>; 0 <=; 0 <~>)
% Maximal formula depth : 29 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 10 con; 0-2 aty)
% Number of variables : 213 ( 0 sgn 134 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( ( nil != X3
| nil != X4 )
& ! [X9] :
( ssItem(X9)
=> ( ? [X10] :
( leq(X9,X10)
& memberP(X4,X10)
& X9 != X10
& ssItem(X10) )
| ~ memberP(X4,X9)
| cons(X9,nil) != X3 ) ) )
| ! [X5] :
( ssItem(X5)
=> ! [X6] :
( ssList(X6)
=> ! [X7] :
( ssList(X7)
=> ( ! [X8] :
( ssItem(X8)
=> ( ( lt(X5,X8)
| ~ memberP(X7,X8) )
& ( lt(X8,X5)
| ~ memberP(X6,X8) ) ) )
| app(app(X6,cons(X5,nil)),X7) != X1 ) ) ) )
| X1 != X3
| X2 != X4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
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(ax26,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ssList(app(X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax26) ).
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(ax38,axiom,
! [X1] :
( ssItem(X1)
=> ~ memberP(nil,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax38) ).
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(ax3,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> ( memberP(X1,X2)
<=> ? [X3] :
( ? [X4] :
( app(X3,cons(X2,X4)) = X1
& ssList(X4) )
& ssList(X3) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax3) ).
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(ax37,axiom,
! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssList(X3)
=> ( memberP(cons(X2,X3),X1)
<=> ( memberP(X3,X1)
| X1 = X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax37) ).
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(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(ax41,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( ( frontsegP(X2,X1)
& frontsegP(X1,X2) )
=> X1 = X2 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax41) ).
fof(ax79,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( app(X3,X2) = app(X1,X2)
=> X3 = X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax79) ).
fof(ax36,axiom,
! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( memberP(app(X2,X3),X1)
<=> ( memberP(X3,X1)
| memberP(X2,X1) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax36) ).
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(ax23,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> hd(cons(X2,X1)) = X2 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax23) ).
fof(ax43,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( frontsegP(X1,X2)
=> frontsegP(app(X1,X3),X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax43) ).
fof(ax21,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> nil != cons(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax21) ).
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(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(ax25,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> tl(cons(X2,X1)) = X1 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax25) ).
fof(ax28,axiom,
! [X1] :
( ssList(X1)
=> app(nil,X1) = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax28) ).
fof(c_0_25,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( ( nil != X3
| nil != X4 )
& ! [X9] :
( ssItem(X9)
=> ( ? [X10] :
( leq(X9,X10)
& memberP(X4,X10)
& X9 != X10
& ssItem(X10) )
| ~ memberP(X4,X9)
| cons(X9,nil) != X3 ) ) )
| ! [X5] :
( ssItem(X5)
=> ! [X6] :
( ssList(X6)
=> ! [X7] :
( ssList(X7)
=> ( ! [X8] :
( ssItem(X8)
=> ( ( lt(X5,X8)
| ~ memberP(X7,X8) )
& ( lt(X8,X5)
| ~ memberP(X6,X8) ) ) )
| app(app(X6,cons(X5,nil)),X7) != X1 ) ) ) )
| X1 != X3
| X2 != X4 ) ) ) ) ),
inference(assume_negation,[status(cth)],[co1]) ).
fof(c_0_26,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( ( nil != X3
| nil != X4 )
& ! [X9] :
( ssItem(X9)
=> ( ? [X10] :
( leq(X9,X10)
& memberP(X4,X10)
& X9 != X10
& ssItem(X10) )
| ~ memberP(X4,X9)
| cons(X9,nil) != X3 ) ) )
| ! [X5] :
( ssItem(X5)
=> ! [X6] :
( ssList(X6)
=> ! [X7] :
( ssList(X7)
=> ( ! [X8] :
( ssItem(X8)
=> ( ( lt(X5,X8)
| ~ memberP(X7,X8) )
& ( lt(X8,X5)
| ~ memberP(X6,X8) ) ) )
| app(app(X6,cons(X5,nil)),X7) != X1 ) ) ) )
| X1 != X3
| X2 != X4 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_25]) ).
fof(c_0_27,negated_conjecture,
! [X264] :
( ( ~ leq(esk56_0,X264)
| ~ memberP(esk51_0,X264)
| esk56_0 = X264
| ~ ssItem(X264)
| nil = esk50_0 )
& ( ~ leq(esk56_0,X264)
| ~ memberP(esk51_0,X264)
| esk56_0 = X264
| ~ ssItem(X264)
| nil = esk51_0 )
& ( memberP(esk51_0,esk56_0)
| nil = esk50_0 )
& ( memberP(esk51_0,esk56_0)
| nil = esk51_0 )
& ( cons(esk56_0,nil) = esk50_0
| nil = esk50_0 )
& ( cons(esk56_0,nil) = esk50_0
| nil = esk51_0 )
& ( ssItem(esk56_0)
| nil = esk50_0 )
& ( ssItem(esk56_0)
| nil = esk51_0 )
& ( ~ lt(esk55_0,esk52_0)
| ~ lt(esk52_0,esk55_0) )
& ( ~ lt(esk55_0,esk52_0)
| memberP(esk54_0,esk55_0) )
& ( memberP(esk53_0,esk55_0)
| ~ lt(esk52_0,esk55_0) )
& ( memberP(esk53_0,esk55_0)
| memberP(esk54_0,esk55_0) )
& ssItem(esk55_0)
& app(app(esk53_0,cons(esk52_0,nil)),esk54_0) = esk48_0
& ssList(esk54_0)
& ssList(esk53_0)
& ssItem(esk52_0)
& esk48_0 = esk50_0
& esk49_0 = esk51_0
& ssList(esk51_0)
& ssList(esk50_0)
& ssList(esk49_0)
& ssList(esk48_0) ),
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_26])])])])])]) ).
fof(c_0_28,plain,
! [X229,X230] :
( ( ~ ssList(X229)
| ~ ssList(X230)
| nil = app(X229,X230)
| nil != X229
| nil != X230 )
& ( ~ ssList(X229)
| ~ ssList(X230)
| nil != app(X229,X230)
| nil = X229 )
& ( ~ ssList(X229)
| ~ ssList(X230)
| nil != app(X229,X230)
| nil = X230 ) ),
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_29,negated_conjecture,
app(app(esk53_0,cons(esk52_0,nil)),esk54_0) = esk48_0,
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_30,negated_conjecture,
esk48_0 = esk50_0,
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_31,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| nil != app(X2,X1)
| nil = X1 ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_32,negated_conjecture,
app(app(esk53_0,cons(esk52_0,nil)),esk54_0) = esk50_0,
inference(rw,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_33,negated_conjecture,
ssList(esk54_0),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
fof(c_0_34,plain,
! [X134,X135] :
( ssList(app(X134,X135))
| ~ ssList(X135)
| ~ ssList(X134) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax26])])])]) ).
cnf(c_0_35,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| nil != app(X1,X2)
| nil = X1 ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_36,negated_conjecture,
( ~ ssList(app(esk53_0,cons(esk52_0,nil)))
| esk50_0 != nil
| esk54_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_33])]) ).
cnf(c_0_37,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ssList(app(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_38,negated_conjecture,
ssList(esk53_0),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
fof(c_0_39,plain,
! [X115,X116] :
( ssList(cons(X116,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)],[ax16])])])]) ).
cnf(c_0_40,negated_conjecture,
( ~ ssList(app(esk53_0,cons(esk52_0,nil)))
| esk50_0 != nil
| app(esk53_0,cons(esk52_0,nil)) = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_32]),c_0_33])]) ).
cnf(c_0_41,negated_conjecture,
( ~ ssList(cons(esk52_0,nil))
| esk50_0 != nil
| esk54_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_38])]) ).
cnf(c_0_42,plain,
( ~ ssItem(X2)
| ~ ssList(X1)
| ssList(cons(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_43,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[ax17]) ).
cnf(c_0_44,negated_conjecture,
ssItem(esk52_0),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_45,negated_conjecture,
( ~ ssList(cons(esk52_0,nil))
| esk50_0 != nil
| app(esk53_0,cons(esk52_0,nil)) = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_37]),c_0_38])]) ).
fof(c_0_46,plain,
! [X1] :
( ssItem(X1)
=> ~ memberP(nil,X1) ),
inference(fof_simplification,[status(thm)],[ax38]) ).
cnf(c_0_47,negated_conjecture,
( memberP(esk53_0,esk55_0)
| memberP(esk54_0,esk55_0) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_48,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_41,c_0_42]),c_0_43]),c_0_44])]) ).
cnf(c_0_49,negated_conjecture,
( ~ ssList(cons(esk52_0,nil))
| esk50_0 != nil
| esk53_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_45]),c_0_38])]) ).
fof(c_0_50,plain,
! [X161] :
( ~ memberP(nil,X161)
| ~ ssItem(X161) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_46])])]) ).
cnf(c_0_51,negated_conjecture,
( esk50_0 != nil
| memberP(esk53_0,esk55_0)
| memberP(nil,esk55_0) ),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_52,negated_conjecture,
( esk50_0 != nil
| esk53_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_42]),c_0_43]),c_0_44])]) ).
fof(c_0_53,plain,
! [X226,X227,X228] :
( app(app(X226,X227),X228) = app(X226,app(X227,X228))
| ~ ssList(X228)
| ~ ssList(X227)
| ~ ssList(X226) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax82])])])]) ).
cnf(c_0_54,plain,
( ~ memberP(nil,X1)
| ~ ssItem(X1) ),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
cnf(c_0_55,negated_conjecture,
( esk50_0 != nil
| memberP(nil,esk55_0) ),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_56,negated_conjecture,
ssItem(esk55_0),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
fof(c_0_57,plain,
! [X15,X16,X19,X20] :
( ( ~ ssList(X15)
| ~ ssItem(X16)
| memberP(X15,X16)
| app(X19,cons(X16,X20)) != X15
| ~ ssList(X20)
| ~ ssList(X19) )
& ( ~ ssList(X15)
| ~ ssItem(X16)
| ~ memberP(X15,X16)
| app(esk3_2(X15,X16),cons(X16,esk4_2(X15,X16))) = X15 )
& ( ~ ssList(X15)
| ~ ssItem(X16)
| ~ memberP(X15,X16)
| ssList(esk4_2(X15,X16)) )
& ( ~ ssList(X15)
| ~ ssItem(X16)
| ~ memberP(X15,X16)
| ssList(esk3_2(X15,X16)) ) ),
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)],[ax3])])])])])]) ).
cnf(c_0_58,plain,
( ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| app(app(X1,X2),X3) = app(X1,app(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
fof(c_0_59,plain,
! [X224,X225] :
( cons(X225,X224) = app(cons(X225,nil),X224)
| ~ ssItem(X225)
| ~ ssList(X224) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax81])])])]) ).
fof(c_0_60,plain,
! [X158,X159,X160] :
( ( ~ ssItem(X158)
| ~ ssItem(X159)
| ~ ssList(X160)
| memberP(cons(X159,X160),X158)
| ~ memberP(X160,X158) )
& ( ~ ssItem(X158)
| ~ ssItem(X159)
| ~ ssList(X160)
| memberP(cons(X159,X160),X158)
| X158 != X159 )
& ( ~ ssItem(X158)
| ~ ssItem(X159)
| ~ ssList(X160)
| memberP(X160,X158)
| X158 = X159
| ~ memberP(cons(X159,X160),X158) ) ),
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_61,negated_conjecture,
( cons(esk56_0,nil) = esk50_0
| nil = esk50_0 ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_62,negated_conjecture,
esk50_0 != nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_56])]) ).
cnf(c_0_63,negated_conjecture,
( ssItem(esk56_0)
| nil = esk50_0 ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_64,plain,
( ~ ssList(X4)
| ~ ssItem(X3)
| app(X1,cons(X3,X2)) != X4
| ~ ssList(X2)
| ~ ssList(X1)
| memberP(X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_65,negated_conjecture,
( ~ ssList(cons(esk52_0,nil))
| app(esk53_0,app(cons(esk52_0,nil),esk54_0)) = esk50_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_58]),c_0_33]),c_0_38])]) ).
cnf(c_0_66,plain,
( ~ ssItem(X2)
| ~ ssList(X1)
| cons(X2,X1) = app(cons(X2,nil),X1) ),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
cnf(c_0_67,negated_conjecture,
ssList(esk48_0),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_68,plain,
( ~ ssItem(X3)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ memberP(cons(X1,X2),X3)
| memberP(X2,X3)
| X3 = X1 ),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
cnf(c_0_69,negated_conjecture,
cons(esk56_0,nil) = esk50_0,
inference(sr,[status(thm)],[c_0_61,c_0_62]) ).
cnf(c_0_70,negated_conjecture,
ssItem(esk56_0),
inference(sr,[status(thm)],[c_0_63,c_0_62]) ).
cnf(c_0_71,plain,
( ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X3)
| ~ ssList(app(X1,cons(X2,X3)))
| memberP(app(X1,cons(X2,X3)),X2) ),
inference(er,[status(thm)],[c_0_64]) ).
cnf(c_0_72,negated_conjecture,
( ~ ssList(cons(esk52_0,nil))
| app(esk53_0,cons(esk52_0,esk54_0)) = esk50_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_33]),c_0_44])]) ).
cnf(c_0_73,negated_conjecture,
ssList(esk50_0),
inference(rw,[status(thm)],[c_0_67,c_0_30]) ).
fof(c_0_74,plain,
! [X24,X25,X27] :
( ( ~ ssList(X24)
| ~ ssList(X25)
| frontsegP(X24,X25)
| app(X25,X27) != X24
| ~ ssList(X27) )
& ( ~ ssList(X24)
| ~ ssList(X25)
| ~ frontsegP(X24,X25)
| app(X25,esk6_2(X24,X25)) = X24 )
& ( ~ ssList(X24)
| ~ ssList(X25)
| ~ frontsegP(X24,X25)
| ssList(esk6_2(X24,X25)) ) ),
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_75,plain,
! [X221,X222,X223] :
( X223 = X221
| app(X222,X223) != app(X222,X221)
| ~ ssList(X223)
| ~ ssList(X222)
| ~ ssList(X221) ),
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,
! [X231] :
( app(X231,nil) = X231
| ~ ssList(X231) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax84])])]) ).
cnf(c_0_77,negated_conjecture,
( ~ ssItem(X1)
| ~ memberP(esk50_0,X1)
| esk56_0 = X1 ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_43]),c_0_70])]),c_0_54]) ).
cnf(c_0_78,negated_conjecture,
( ~ ssList(cons(esk52_0,nil))
| memberP(esk50_0,esk52_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_73]),c_0_33]),c_0_38]),c_0_44])]) ).
cnf(c_0_79,plain,
( ~ ssList(X3)
| ~ ssList(X2)
| app(X2,X1) != X3
| ~ ssList(X1)
| frontsegP(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_74]) ).
cnf(c_0_80,plain,
( app(X2,X3) != app(X2,X1)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| X3 = X1 ),
inference(split_conjunct,[status(thm)],[c_0_75]) ).
cnf(c_0_81,plain,
( ~ ssList(X1)
| app(X1,nil) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_76]) ).
cnf(c_0_82,negated_conjecture,
( ~ ssList(cons(esk52_0,nil))
| esk52_0 = esk56_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78]),c_0_44])]) ).
fof(c_0_83,plain,
! [X165,X166] :
( X165 = X166
| ~ frontsegP(X166,X165)
| ~ frontsegP(X165,X166)
| ~ ssList(X166)
| ~ ssList(X165) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax41])])])]) ).
cnf(c_0_84,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| frontsegP(app(X1,X2),X1) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_79]),c_0_37]) ).
cnf(c_0_85,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_80,c_0_81]),c_0_43])]) ).
fof(c_0_86,plain,
! [X218,X219,X220] :
( X220 = X218
| app(X220,X219) != app(X218,X219)
| ~ ssList(X220)
| ~ ssList(X219)
| ~ ssList(X218) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax79])])])]) ).
fof(c_0_87,plain,
! [X155,X156,X157] :
( ( ~ ssItem(X155)
| ~ ssList(X156)
| ~ ssList(X157)
| memberP(app(X156,X157),X155)
| ~ memberP(X157,X155) )
& ( ~ ssItem(X155)
| ~ ssList(X156)
| ~ ssList(X157)
| memberP(app(X156,X157),X155)
| ~ memberP(X156,X155) )
& ( ~ ssItem(X155)
| ~ ssList(X156)
| ~ ssList(X157)
| memberP(X157,X155)
| memberP(X156,X155)
| ~ memberP(app(X156,X157),X155) ) ),
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_88,negated_conjecture,
esk52_0 = esk56_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_42]),c_0_43]),c_0_44])]) ).
fof(c_0_89,plain,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( nil != X1
=> hd(app(X1,X2)) = hd(X1) ) ) ),
inference(fof_simplification,[status(thm)],[ax85]) ).
fof(c_0_90,plain,
! [X129,X130] :
( hd(cons(X130,X129)) = X130
| ~ ssItem(X130)
| ~ ssList(X129) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax23])])])]) ).
cnf(c_0_91,plain,
( ~ frontsegP(X2,X1)
| ~ frontsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_83]) ).
cnf(c_0_92,negated_conjecture,
( ~ ssList(app(esk53_0,cons(esk52_0,nil)))
| frontsegP(esk50_0,app(esk53_0,cons(esk52_0,nil))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_32]),c_0_33])]) ).
fof(c_0_93,plain,
! [X168,X169,X170] :
( frontsegP(app(X168,X170),X169)
| ~ frontsegP(X168,X169)
| ~ ssList(X170)
| ~ ssList(X169)
| ~ ssList(X168) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax43])])])]) ).
fof(c_0_94,plain,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> nil != cons(X2,X1) ) ),
inference(fof_simplification,[status(thm)],[ax21]) ).
cnf(c_0_95,negated_conjecture,
( ~ ssList(cons(esk52_0,nil))
| ~ ssList(cons(esk52_0,esk54_0))
| esk53_0 != esk50_0
| cons(esk52_0,esk54_0) = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_72]),c_0_38])]) ).
cnf(c_0_96,plain,
( app(X3,X2) != app(X1,X2)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| X3 = X1 ),
inference(split_conjunct,[status(thm)],[c_0_86]) ).
cnf(c_0_97,negated_conjecture,
( ~ ssList(X1)
| app(esk50_0,X1) = cons(esk56_0,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_69]),c_0_70])]) ).
cnf(c_0_98,plain,
( ~ ssItem(X2)
| ~ ssList(X3)
| ~ ssList(X1)
| ~ memberP(X1,X2)
| memberP(app(X3,X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_87]) ).
cnf(c_0_99,negated_conjecture,
app(app(esk53_0,esk50_0),esk54_0) = esk50_0,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_88]),c_0_69]) ).
fof(c_0_100,plain,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> cons(hd(X1),tl(X1)) = X1 ) ),
inference(fof_simplification,[status(thm)],[ax78]) ).
fof(c_0_101,plain,
! [X232,X233] :
( hd(app(X232,X233)) = hd(X232)
| 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_89])])])]) ).
cnf(c_0_102,plain,
( ~ ssItem(X2)
| ~ ssList(X1)
| hd(cons(X2,X1)) = X2 ),
inference(split_conjunct,[status(thm)],[c_0_90]) ).
cnf(c_0_103,negated_conjecture,
( ~ ssList(app(esk53_0,cons(esk52_0,nil)))
| ~ frontsegP(app(esk53_0,cons(esk52_0,nil)),esk50_0)
| app(esk53_0,cons(esk52_0,nil)) = esk50_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_92]),c_0_73])]) ).
cnf(c_0_104,plain,
( ~ frontsegP(X1,X2)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| frontsegP(app(X1,X3),X2) ),
inference(split_conjunct,[status(thm)],[c_0_93]) ).
fof(c_0_105,plain,
! [X126,X127] :
( nil != cons(X127,X126)
| ~ ssItem(X127)
| ~ ssList(X126) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_94])])])]) ).
cnf(c_0_106,negated_conjecture,
( ~ ssList(cons(esk52_0,nil))
| esk53_0 != esk50_0
| cons(esk52_0,esk54_0) = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_42]),c_0_33]),c_0_44])]) ).
cnf(c_0_107,negated_conjecture,
( ~ ssList(X1)
| ~ ssList(X2)
| app(X1,X2) != cons(esk56_0,X2)
| X1 = esk50_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_97]),c_0_73])]) ).
cnf(c_0_108,plain,
( ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X3)
| ~ memberP(X1,X2)
| memberP(app(X1,X3),X2) ),
inference(split_conjunct,[status(thm)],[c_0_87]) ).
cnf(c_0_109,negated_conjecture,
app(esk53_0,app(esk50_0,esk54_0)) = esk50_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_88]),c_0_69]),c_0_69]),c_0_73])]) ).
cnf(c_0_110,negated_conjecture,
( ~ ssItem(X1)
| ~ ssList(app(esk53_0,esk50_0))
| ~ memberP(esk54_0,X1)
| memberP(esk50_0,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_99]),c_0_33])]) ).
fof(c_0_111,plain,
! [X217] :
( cons(hd(X217),tl(X217)) = X217
| nil = X217
| ~ ssList(X217) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_100])])]) ).
cnf(c_0_112,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| hd(app(X1,X2)) = hd(X1)
| nil = X1 ),
inference(split_conjunct,[status(thm)],[c_0_101]) ).
cnf(c_0_113,negated_conjecture,
hd(esk50_0) = esk56_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_69]),c_0_43]),c_0_70])]) ).
cnf(c_0_114,negated_conjecture,
( ~ ssList(cons(esk52_0,nil))
| ~ ssList(app(esk53_0,cons(esk52_0,nil)))
| ~ frontsegP(esk53_0,esk50_0)
| app(esk53_0,cons(esk52_0,nil)) = esk50_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_104]),c_0_73]),c_0_38])]) ).
cnf(c_0_115,plain,
( nil != cons(X2,X1)
| ~ ssItem(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_105]) ).
cnf(c_0_116,negated_conjecture,
( esk53_0 != esk50_0
| cons(esk52_0,esk54_0) = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_42]),c_0_43]),c_0_44])]) ).
cnf(c_0_117,negated_conjecture,
( ~ ssList(app(esk53_0,cons(esk52_0,nil)))
| cons(esk56_0,esk54_0) != esk50_0
| app(esk53_0,cons(esk52_0,nil)) = esk50_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_32]),c_0_33])]) ).
cnf(c_0_118,negated_conjecture,
( ~ ssItem(X1)
| ~ ssList(app(esk50_0,esk54_0))
| ~ memberP(esk53_0,X1)
| memberP(esk50_0,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_109]),c_0_38])]) ).
cnf(c_0_119,negated_conjecture,
( ~ ssList(app(esk53_0,esk50_0))
| memberP(esk50_0,esk55_0)
| memberP(esk53_0,esk55_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_47]),c_0_56])]) ).
cnf(c_0_120,plain,
( ~ ssList(X1)
| cons(hd(X1),tl(X1)) = X1
| nil = X1 ),
inference(split_conjunct,[status(thm)],[c_0_111]) ).
cnf(c_0_121,negated_conjecture,
( ~ ssList(cons(esk52_0,nil))
| ~ ssList(cons(esk52_0,esk54_0))
| esk53_0 = nil
| hd(esk53_0) = esk56_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_72]),c_0_113]),c_0_38])]) ).
cnf(c_0_122,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ~ frontsegP(X1,app(X1,X2))
| app(X1,X2) = X1 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_84]),c_0_37]) ).
cnf(c_0_123,negated_conjecture,
( ~ ssList(cons(esk52_0,nil))
| ~ frontsegP(esk53_0,esk50_0)
| app(esk53_0,cons(esk52_0,nil)) = esk50_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_37]),c_0_38])]) ).
cnf(c_0_124,negated_conjecture,
esk53_0 != esk50_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_116]),c_0_33]),c_0_44])]) ).
fof(c_0_125,plain,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> ssList(tl(X1)) ) ),
inference(fof_simplification,[status(thm)],[ax24]) ).
fof(c_0_126,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_127,negated_conjecture,
( ~ ssList(cons(esk52_0,nil))
| cons(esk56_0,esk54_0) != esk50_0
| app(esk53_0,cons(esk52_0,nil)) = esk50_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_117,c_0_37]),c_0_38])]) ).
fof(c_0_128,plain,
! [X132,X133] :
( tl(cons(X133,X132)) = X132
| ~ ssItem(X133)
| ~ ssList(X132) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax25])])])]) ).
cnf(c_0_129,negated_conjecture,
( ~ ssList(app(esk53_0,esk50_0))
| ~ ssList(app(esk50_0,esk54_0))
| memberP(esk50_0,esk55_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_119]),c_0_56])]) ).
cnf(c_0_130,plain,
( ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(cons(X1,nil))
| frontsegP(cons(X1,X2),cons(X1,nil)) ),
inference(spm,[status(thm)],[c_0_84,c_0_66]) ).
cnf(c_0_131,negated_conjecture,
( ~ ssList(cons(esk52_0,nil))
| ~ ssList(cons(esk52_0,esk54_0))
| esk53_0 = nil
| cons(esk56_0,tl(esk53_0)) = esk53_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_120,c_0_121]),c_0_38])]) ).
cnf(c_0_132,negated_conjecture,
~ frontsegP(esk53_0,esk50_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_122,c_0_123]),c_0_38]),c_0_88]),c_0_69]),c_0_73])]),c_0_124]) ).
fof(c_0_133,plain,
! [X131] :
( ssList(tl(X131))
| nil = X131
| ~ ssList(X131) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_125])])]) ).
fof(c_0_134,plain,
! [X234,X235] :
( tl(app(X234,X235)) = app(tl(X234),X235)
| nil = X234
| ~ ssList(X235)
| ~ ssList(X234) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_126])])])]) ).
cnf(c_0_135,negated_conjecture,
( cons(esk56_0,esk54_0) != esk50_0
| app(esk53_0,esk50_0) = esk50_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_127,c_0_88]),c_0_69]),c_0_69]),c_0_73])]) ).
cnf(c_0_136,plain,
( ~ ssItem(X2)
| ~ ssList(X1)
| tl(cons(X2,X1)) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_128]) ).
cnf(c_0_137,negated_conjecture,
( ~ ssList(app(esk53_0,esk50_0))
| ~ ssList(app(esk50_0,esk54_0))
| esk55_0 = esk56_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_129]),c_0_56])]) ).
cnf(c_0_138,negated_conjecture,
( ~ ssList(app(esk53_0,cons(esk52_0,nil)))
| app(esk53_0,cons(esk52_0,nil)) != esk50_0
| esk54_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_32]),c_0_33])]) ).
cnf(c_0_139,negated_conjecture,
( ~ ssList(tl(esk53_0))
| ~ ssList(cons(esk56_0,esk54_0))
| esk53_0 = nil ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_131]),c_0_69]),c_0_69]),c_0_73]),c_0_70]),c_0_88]),c_0_88]),c_0_69]),c_0_73])]),c_0_132]) ).
cnf(c_0_140,plain,
( ~ ssList(X1)
| ssList(tl(X1))
| nil = X1 ),
inference(split_conjunct,[status(thm)],[c_0_133]) ).
cnf(c_0_141,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| tl(app(X1,X2)) = app(tl(X1),X2)
| nil = X1 ),
inference(split_conjunct,[status(thm)],[c_0_134]) ).
cnf(c_0_142,negated_conjecture,
( cons(esk56_0,esk54_0) != esk50_0
| app(esk50_0,esk54_0) = esk50_0 ),
inference(spm,[status(thm)],[c_0_99,c_0_135]) ).
cnf(c_0_143,negated_conjecture,
tl(esk50_0) = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_136,c_0_69]),c_0_43]),c_0_70])]) ).
cnf(c_0_144,negated_conjecture,
( ~ ssList(app(esk50_0,esk54_0))
| esk55_0 = esk56_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_137,c_0_37]),c_0_73]),c_0_38])]) ).
cnf(c_0_145,negated_conjecture,
( ~ ssList(cons(esk52_0,nil))
| app(esk53_0,cons(esk52_0,nil)) != esk50_0
| esk54_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_138,c_0_37]),c_0_38])]) ).
cnf(c_0_146,negated_conjecture,
( ~ ssList(cons(esk56_0,esk54_0))
| esk53_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_139,c_0_140]),c_0_38])]) ).
cnf(c_0_147,negated_conjecture,
( cons(esk56_0,esk54_0) != esk50_0
| app(nil,esk54_0) = nil ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_141,c_0_142]),c_0_143]),c_0_143]),c_0_33]),c_0_73])]),c_0_62]) ).
cnf(c_0_148,negated_conjecture,
esk55_0 = esk56_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_144,c_0_37]),c_0_33]),c_0_73])]) ).
cnf(c_0_149,negated_conjecture,
( app(esk53_0,esk50_0) != esk50_0
| esk54_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_145,c_0_88]),c_0_69]),c_0_69]),c_0_73])]) ).
cnf(c_0_150,negated_conjecture,
esk53_0 = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_146,c_0_42]),c_0_33]),c_0_70])]) ).
fof(c_0_151,plain,
! [X139] :
( app(nil,X139) = X139
| ~ ssList(X139) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax28])])]) ).
cnf(c_0_152,negated_conjecture,
( ~ ssItem(X1)
| ~ memberP(esk54_0,X1)
| cons(esk56_0,esk54_0) != esk50_0 ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_147]),c_0_43]),c_0_33])]),c_0_54]) ).
cnf(c_0_153,negated_conjecture,
( memberP(esk53_0,esk56_0)
| memberP(esk54_0,esk56_0) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_47,c_0_148]),c_0_148]) ).
cnf(c_0_154,negated_conjecture,
( app(nil,esk50_0) != esk50_0
| esk54_0 = nil ),
inference(rw,[status(thm)],[c_0_149,c_0_150]) ).
cnf(c_0_155,plain,
( ~ ssList(X1)
| app(nil,X1) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_151]) ).
cnf(c_0_156,negated_conjecture,
( cons(esk56_0,esk54_0) != esk50_0
| memberP(esk53_0,esk56_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_152,c_0_153]),c_0_70])]) ).
cnf(c_0_157,negated_conjecture,
esk54_0 = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_154,c_0_155]),c_0_73])]) ).
cnf(c_0_158,negated_conjecture,
memberP(nil,esk56_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_156,c_0_150]),c_0_157]),c_0_69])]) ).
cnf(c_0_159,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_158]),c_0_70])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWC295+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.19/0.44 % Computer : n016.cluster.edu
% 0.19/0.44 % Model : x86_64 x86_64
% 0.19/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.44 % Memory : 8046.5625MB
% 0.19/0.44 % OS : Linux 6.8.0-71-generic
% 0.19/0.44 % CPULimit : 300
% 0.19/0.44 % WCLimit : 300
% 0.19/0.44 % DateTime : Mon Sep 21 08:17:52 UTC 2026
% 0.19/0.44 % CPUTime :
% 0.19/0.44 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.19/0.51 Running first-order theorem proving
% 0.27/0.51 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
% 2.31/0.85 % Version: 3.5.1
% 2.31/0.85 % Preprocessing class: FSLSSMSSSSSNFFN.
% 2.31/0.85 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.31/0.85 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 2.31/0.85 % Starting new_bool_3 with 300s (1) cores
% 2.31/0.85 % Starting new_bool_1 with 300s (1) cores
% 2.31/0.85 % Starting sh5l with 300s (1) cores
% 2.31/0.85 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 1990060 completed with status 0
% 2.31/0.85 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 2.31/0.85 % Preprocessing class: FSLSSMSSSSSNFFN.
% 2.31/0.85 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.31/0.85 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 2.31/0.85 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 2.31/0.85 % No SInE strategy applied
% 2.31/0.85 % Search class: FGHSF-FSLM21-MFFFFFNN
% 2.31/0.85 % Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 2.31/0.85 % Starting SubtermCWHack with 136s (1) cores
% 2.31/0.85 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 2.31/0.85 % Starting G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4d with 136s (1) cores
% 2.31/0.85 % Starting G-E--_110_C45_F1_PI_SE_CS_SP_PS_S4S with 136s (1) cores
% 2.31/0.85 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_TT_S0Y with 136s (1) cores
% 2.31/0.85 % G-E--_208_C18_F1_SE_CS_SP_PS_TT_S0Y with pid 1990070 completed with status 0
% 2.31/0.85 % Result found by G-E--_208_C18_F1_SE_CS_SP_PS_TT_S0Y
% 2.31/0.85 % Preprocessing class: FSLSSMSSSSSNFFN.
% 2.31/0.85 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.31/0.85 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 2.31/0.85 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 2.31/0.85 % No SInE strategy applied
% 2.31/0.85 % Search class: FGHSF-FSLM21-MFFFFFNN
% 2.31/0.85 % Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 2.31/0.85 % Starting SubtermCWHack with 136s (1) cores
% 2.31/0.85 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 2.31/0.85 % Starting G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4d with 136s (1) cores
% 2.31/0.85 % Starting G-E--_110_C45_F1_PI_SE_CS_SP_PS_S4S with 136s (1) cores
% 2.31/0.85 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_TT_S0Y with 136s (1) cores
% 2.31/0.85 % Preprocessing time : 0.006 s
% 2.31/0.85 % Presaturation interreduction done
% 2.31/0.85
% 2.31/0.85 % Proof found!
% 2.31/0.85 % SZS status Theorem
% 2.31/0.85 % SZS output start CNFRefutation
% See solution above
% 2.31/0.85 % Parsed axioms : 96
% 2.31/0.85 % Removed by relevancy pruning/SinE : 0
% 2.31/0.85 % Initial clauses : 213
% 2.31/0.85 % Removed in clause preprocessing : 2
% 2.31/0.85 % Initial clauses in saturation : 211
% 2.31/0.85 % Processed clauses : 1260
% 2.31/0.85 % ...of these trivial : 14
% 2.31/0.85 % ...subsumed : 430
% 2.31/0.85 % ...remaining for further processing : 816
% 2.31/0.85 % Other redundant clauses eliminated : 102
% 2.31/0.85 % Clauses deleted for lack of memory : 0
% 2.31/0.85 % Backward-subsumed : 100
% 2.31/0.85 % Backward-rewritten : 137
% 2.31/0.85 % Generated clauses : 3401
% 2.31/0.85 % ...of the previous two non-redundant : 2988
% 2.31/0.85 % ...aggressively subsumed : 0
% 2.31/0.85 % Contextual simplify-reflections : 93
% 2.31/0.85 % Paramodulations : 3286
% 2.31/0.85 % Factorizations : 0
% 2.31/0.85 % NegExts : 0
% 2.31/0.85 % Equation resolutions : 107
% 2.31/0.85 % Disequality decompositions : 0
% 2.31/0.85 % Total rewrite steps : 3761
% 2.31/0.85 % ...of those cached : 3708
% 2.31/0.85 % Propositional unsat checks : 0
% 2.31/0.85 % Propositional check models : 0
% 2.31/0.85 % Propositional check unsatisfiable : 0
% 2.31/0.85 % Propositional clauses : 0
% 2.31/0.85 % Propositional clauses after purity: 0
% 2.31/0.85 % Propositional unsat core size : 0
% 2.31/0.85 % Propositional preprocessing time : 0.000
% 2.31/0.85 % Propositional encoding time : 0.000
% 2.31/0.85 % Propositional solver time : 0.000
% 2.31/0.85 % Success case prop preproc time : 0.000
% 2.31/0.85 % Success case prop encoding time : 0.000
% 2.31/0.85 % Success case prop solver time : 0.000
% 2.31/0.85 % Current number of processed clauses : 341
% 2.31/0.85 % Positive orientable unit clauses : 49
% 2.31/0.85 % Positive unorientable unit clauses: 0
% 2.31/0.85 % Negative unit clauses : 6
% 2.31/0.85 % Non-unit-clauses : 286
% 2.31/0.85 % Current number of unprocessed clauses: 2093
% 2.31/0.85 % ...number of literals in the above : 12977
% 2.31/0.85 % Current number of archived formulas : 0
% 2.31/0.85 % Current number of archived clauses : 452
% 2.31/0.85 % Clause-clause subsumption calls (NU) : 34167
% 2.31/0.85 % Rec. Clause-clause subsumption calls : 10618
% 2.31/0.85 % Non-unit clause-clause subsumptions : 447
% 2.31/0.85 % Unit Clause-clause subsumption calls : 1151
% 2.31/0.85 % Rewrite failures with RHS unbound : 0
% 2.31/0.85 % BW rewrite match attempts : 23
% 2.31/0.85 % BW rewrite match successes : 23
% 2.31/0.85 % Condensation attempts : 0
% 2.31/0.85 % Condensation successes : 0
% 2.31/0.85 % Termbank termtop insertions : 81509
% 2.31/0.85 % Search garbage collected termcells : 4458
% 2.31/0.85
% 2.31/0.85 % -------------------------------------------------
% 2.31/0.85 % User time : 0.231 s
% 2.31/0.85 % System time : 0.012 s
% 2.31/0.85 % Total time : 0.243 s
% 2.31/0.85 % Maximum resident set size: 4276 pages
% 2.31/0.85
% 2.31/0.85 % -------------------------------------------------
% 2.31/0.85 % User time : 1.389 s
% 2.31/0.85 % System time : 0.068 s
% 2.31/0.85 % Total time : 1.457 s
% 2.31/0.85 % Maximum resident set size: 4608 pages
% 2.31/0.85 % E exiting
%------------------------------------------------------------------------------