%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWC178+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n015.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 02:43:20 PM UTC 2026
% Result : Theorem 0.55s 0.54s
% Output : CNFRefutation 0.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 20
% Syntax : Number of formulae : 146 ( 42 unt; 0 def)
% Number of atoms : 458 ( 135 equ)
% Maximal formula atoms : 34 ( 3 avg)
% Number of connectives : 522 ( 210 ~; 200 |; 34 &)
% ( 7 <=>; 71 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 9 con; 0-2 aty)
% Number of variables : 151 ( 0 sgn 107 !; 1 ?)
% 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)
=> ( neq(X5,X6)
| ! [X7] :
( ssList(X7)
=> ! [X8] :
( ssList(X8)
=> app(app(app(X7,cons(X5,nil)),cons(X6,nil)),X8) != X1 ) ) ) ) )
| ~ segmentP(X4,X3)
| X1 != X3
| X2 != X4 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
fof(ax1,axiom,
! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/SWC001+0.ax',ax82) ).
fof(ax16,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> ssList(cons(X2,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax16) ).
fof(ax17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/Axioms/SWC001+0.ax',ax27) ).
fof(ax80,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( app(X2,X3) = app(X2,X1)
=> X3 = X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax80) ).
fof(ax26,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ssList(app(X1,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax26) ).
fof(ax25,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> tl(cons(X2,X1)) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax25) ).
fof(ax15,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax15) ).
fof(ax21,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> nil != cons(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax21) ).
fof(ax8,axiom,
! [X1] :
( ssList(X1)
=> ( cyclefreeP(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
=> ~ ( leq(X3,X2)
& leq(X2,X3) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax8) ).
fof(ax59,axiom,
! [X1] :
( ssItem(X1)
=> cyclefreeP(cons(X1,nil)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax59) ).
fof(ax4,axiom,
! [X1] :
( ssList(X1)
=> ( singletonP(X1)
<=> ? [X2] :
( cons(X2,nil) = X1
& ssItem(X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax4) ).
fof(ax28,axiom,
! [X1] :
( ssList(X1)
=> app(nil,X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax28) ).
fof(ax83,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( nil = app(X1,X2)
<=> ( nil = X1
& nil = X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax83) ).
fof(ax54,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( ( segmentP(X2,X1)
& segmentP(X1,X2) )
=> X1 = X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax54) ).
fof(ax31,axiom,
! [X1] :
( ssItem(X1)
=> leq(X1,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax31) ).
fof(ax57,axiom,
! [X1] :
( ssList(X1)
=> segmentP(X1,nil) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax57) ).
fof(c_0_20,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)
=> ( neq(X5,X6)
| ! [X7] :
( ssList(X7)
=> ! [X8] :
( ssList(X8)
=> 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_21,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)
=> ( neq(X5,X6)
| ! [X7] :
( ssList(X7)
=> ! [X8] :
( ssList(X8)
=> 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_20]) ).
fof(c_0_22,plain,
! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
inference(fof_simplification,[status(thm)],[ax1]) ).
fof(c_0_23,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_21])])])]) ).
fof(c_0_24,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_22])])])])]) ).
cnf(c_0_25,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_23]) ).
cnf(c_0_26,negated_conjecture,
esk48_0 = esk50_0,
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_27,negated_conjecture,
~ neq(esk52_0,esk53_0),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_28,plain,
( ~ ssItem(X1)
| ~ ssItem(X2)
| neq(X1,X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_29,negated_conjecture,
ssItem(esk53_0),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_30,negated_conjecture,
ssItem(esk52_0),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_31,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_25,c_0_26]) ).
cnf(c_0_32,negated_conjecture,
esk53_0 = esk52_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29]),c_0_30])]) ).
fof(c_0_33,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_34,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_31,c_0_32]) ).
cnf(c_0_35,plain,
( ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| app(app(X1,X2),X3) = app(X1,app(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_36,negated_conjecture,
ssList(esk54_0),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
fof(c_0_37,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_38,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_34,c_0_35]),c_0_36])]) ).
cnf(c_0_39,plain,
( ~ ssItem(X2)
| ~ ssList(X1)
| ssList(cons(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_40,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[ax17]) ).
fof(c_0_41,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_42,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_38,c_0_39]),c_0_40]),c_0_30])]) ).
cnf(c_0_43,plain,
( ~ ssItem(X2)
| ~ ssList(X1)
| cons(X2,X1) = app(cons(X2,nil),X1) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_44,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_42,c_0_43]),c_0_30])]) ).
cnf(c_0_45,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_44,c_0_39]),c_0_40]),c_0_30])]) ).
cnf(c_0_46,negated_conjecture,
ssList(esk55_0),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_47,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_35,c_0_45]),c_0_46]),c_0_36])]) ).
cnf(c_0_48,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_47,c_0_39]),c_0_30])]) ).
fof(c_0_49,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_50,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_48,c_0_39]),c_0_40]),c_0_30])]) ).
cnf(c_0_51,plain,
( ~ ssItem(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| cons(X3,app(X2,X1)) = app(cons(X3,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_52,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_50,c_0_51]),c_0_46]),c_0_30])]) ).
fof(c_0_53,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])])])]) ).
cnf(c_0_54,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_52,c_0_39]),c_0_40]),c_0_30])]) ).
cnf(c_0_55,plain,
( app(X2,X3) != app(X2,X1)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| X3 = X1 ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_56,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_54,c_0_43]),c_0_46]),c_0_30])]) ).
cnf(c_0_57,negated_conjecture,
( ~ ssList(X1)
| ~ ssList(cons(esk52_0,cons(esk52_0,esk55_0)))
| app(esk54_0,X1) != esk50_0
| X1 = cons(esk52_0,cons(esk52_0,esk55_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_36])]) ).
cnf(c_0_58,negated_conjecture,
( ~ ssList(cons(esk52_0,cons(esk52_0,esk55_0)))
| ~ ssList(app(cons(esk52_0,cons(esk52_0,nil)),esk55_0))
| app(cons(esk52_0,cons(esk52_0,nil)),esk55_0) = cons(esk52_0,cons(esk52_0,esk55_0)) ),
inference(spm,[status(thm)],[c_0_57,c_0_50]) ).
cnf(c_0_59,negated_conjecture,
( ~ ssList(cons(esk52_0,esk55_0))
| ~ ssList(app(cons(esk52_0,cons(esk52_0,nil)),esk55_0))
| app(cons(esk52_0,cons(esk52_0,nil)),esk55_0) = cons(esk52_0,cons(esk52_0,esk55_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_39]),c_0_30])]) ).
fof(c_0_60,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_61,negated_conjecture,
( ~ ssList(app(cons(esk52_0,cons(esk52_0,nil)),esk55_0))
| app(cons(esk52_0,cons(esk52_0,nil)),esk55_0) = cons(esk52_0,cons(esk52_0,esk55_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_39]),c_0_46]),c_0_30])]) ).
cnf(c_0_62,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ssList(app(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
cnf(c_0_63,negated_conjecture,
( ~ ssList(cons(esk52_0,cons(esk52_0,nil)))
| app(cons(esk52_0,cons(esk52_0,nil)),esk55_0) = cons(esk52_0,cons(esk52_0,esk55_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_46])]) ).
cnf(c_0_64,negated_conjecture,
( ~ ssList(cons(esk52_0,nil))
| app(cons(esk52_0,cons(esk52_0,nil)),esk55_0) = cons(esk52_0,cons(esk52_0,esk55_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_39]),c_0_30])]) ).
cnf(c_0_65,negated_conjecture,
app(cons(esk52_0,cons(esk52_0,nil)),esk55_0) = cons(esk52_0,cons(esk52_0,esk55_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_39]),c_0_40]),c_0_30])]) ).
cnf(c_0_66,negated_conjecture,
( ~ ssList(cons(esk52_0,nil))
| cons(esk52_0,app(cons(esk52_0,nil),esk55_0)) = cons(esk52_0,cons(esk52_0,esk55_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_65]),c_0_46]),c_0_30])]) ).
fof(c_0_67,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])])])]) ).
cnf(c_0_68,negated_conjecture,
cons(esk52_0,app(cons(esk52_0,nil),esk55_0)) = cons(esk52_0,cons(esk52_0,esk55_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_39]),c_0_40]),c_0_30])]) ).
cnf(c_0_69,plain,
( ~ ssItem(X2)
| ~ ssList(X1)
| tl(cons(X2,X1)) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_67]) ).
cnf(c_0_70,negated_conjecture,
cons(esk52_0,cons(esk52_0,app(nil,esk55_0))) = cons(esk52_0,cons(esk52_0,esk55_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_51]),c_0_40]),c_0_46]),c_0_30])]) ).
cnf(c_0_71,negated_conjecture,
( ~ ssList(app(cons(esk52_0,nil),esk55_0))
| tl(cons(esk52_0,cons(esk52_0,esk55_0))) = app(cons(esk52_0,nil),esk55_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_68]),c_0_30])]) ).
cnf(c_0_72,negated_conjecture,
( ~ ssList(cons(esk52_0,nil))
| ~ ssList(app(esk54_0,cons(esk52_0,nil)))
| app(app(esk54_0,cons(esk52_0,nil)),app(cons(esk52_0,nil),esk55_0)) = esk50_0 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_35]),c_0_46])]),c_0_32]),c_0_32]) ).
cnf(c_0_73,negated_conjecture,
( ~ ssList(app(cons(esk52_0,nil),cons(esk52_0,nil)))
| app(esk54_0,app(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_35,c_0_42]),c_0_46]),c_0_36])]) ).
cnf(c_0_74,negated_conjecture,
( ~ ssList(cons(esk52_0,app(nil,esk55_0)))
| tl(cons(esk52_0,cons(esk52_0,esk55_0))) = cons(esk52_0,app(nil,esk55_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_30])]) ).
cnf(c_0_75,negated_conjecture,
( ~ ssList(cons(esk52_0,esk55_0))
| tl(cons(esk52_0,cons(esk52_0,esk55_0))) = cons(esk52_0,esk55_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_43]),c_0_46]),c_0_30])]) ).
cnf(c_0_76,negated_conjecture,
( ~ ssList(app(esk54_0,cons(esk52_0,nil)))
| app(app(esk54_0,cons(esk52_0,nil)),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_72,c_0_39]),c_0_40]),c_0_30])]) ).
cnf(c_0_77,negated_conjecture,
( ~ ssList(cons(esk52_0,cons(esk52_0,nil)))
| ssList(cons(esk52_0,cons(esk52_0,esk55_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_65]),c_0_46])]) ).
cnf(c_0_78,negated_conjecture,
( ~ ssList(cons(esk52_0,nil))
| app(esk54_0,app(app(cons(esk52_0,nil),cons(esk52_0,nil)),esk55_0)) = esk50_0 ),
inference(spm,[status(thm)],[c_0_73,c_0_62]) ).
cnf(c_0_79,negated_conjecture,
( ~ ssList(app(nil,esk55_0))
| tl(cons(esk52_0,cons(esk52_0,esk55_0))) = cons(esk52_0,app(nil,esk55_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_39]),c_0_30])]) ).
cnf(c_0_80,negated_conjecture,
tl(cons(esk52_0,cons(esk52_0,esk55_0))) = cons(esk52_0,esk55_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_39]),c_0_46]),c_0_30])]) ).
cnf(c_0_81,negated_conjecture,
( ~ ssList(cons(esk52_0,nil))
| app(app(esk54_0,cons(esk52_0,nil)),app(cons(esk52_0,nil),esk55_0)) = esk50_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_62]),c_0_36])]) ).
fof(c_0_82,plain,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
inference(fof_simplification,[status(thm)],[ax15]) ).
cnf(c_0_83,negated_conjecture,
( ~ ssList(cons(esk52_0,nil))
| ssList(cons(esk52_0,cons(esk52_0,esk55_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_39]),c_0_30])]) ).
cnf(c_0_84,negated_conjecture,
app(esk54_0,app(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_78,c_0_39]),c_0_40]),c_0_30])]) ).
cnf(c_0_85,negated_conjecture,
( ~ ssList(cons(esk52_0,nil))
| tl(cons(esk52_0,cons(esk52_0,esk55_0))) = app(cons(esk52_0,nil),esk55_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_62]),c_0_46])]) ).
cnf(c_0_86,negated_conjecture,
( ~ ssList(app(nil,esk55_0))
| cons(esk52_0,app(nil,esk55_0)) = cons(esk52_0,esk55_0) ),
inference(rw,[status(thm)],[c_0_79,c_0_80]) ).
fof(c_0_87,plain,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> nil != cons(X2,X1) ) ),
inference(fof_simplification,[status(thm)],[ax21]) ).
fof(c_0_88,plain,
! [X36,X37,X38,X39,X40,X41] :
( ( ~ ssList(X36)
| cyclefreeP(X36)
| leq(esk11_1(X36),esk10_1(X36)) )
& ( ~ ssList(X36)
| cyclefreeP(X36)
| leq(esk10_1(X36),esk11_1(X36)) )
& ( ~ ssList(X36)
| cyclefreeP(X36)
| app(app(esk12_1(X36),cons(esk10_1(X36),esk13_1(X36))),cons(esk11_1(X36),esk14_1(X36))) = X36 )
& ( ~ ssList(X36)
| cyclefreeP(X36)
| ssList(esk14_1(X36)) )
& ( ~ ssList(X36)
| cyclefreeP(X36)
| ssList(esk13_1(X36)) )
& ( ~ ssList(X36)
| cyclefreeP(X36)
| ssList(esk12_1(X36)) )
& ( ~ ssList(X36)
| cyclefreeP(X36)
| ssItem(esk11_1(X36)) )
& ( ~ ssList(X36)
| cyclefreeP(X36)
| ssItem(esk10_1(X36)) )
& ( ~ ssList(X36)
| ~ leq(X38,X37)
| ~ leq(X37,X38)
| app(app(X39,cons(X37,X40)),cons(X38,X41)) != X36
| ~ ssList(X41)
| ~ ssList(X40)
| ~ ssList(X39)
| ~ ssItem(X38)
| ~ ssItem(X37)
| ~ cyclefreeP(X36) ) ),
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)],[ax8])])])])])]) ).
cnf(c_0_89,negated_conjecture,
app(app(esk54_0,cons(esk52_0,nil)),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_81,c_0_39]),c_0_40]),c_0_30])]) ).
fof(c_0_90,plain,
! [X198] :
( cyclefreeP(cons(X198,nil))
| ~ ssItem(X198) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax59])])]) ).
fof(c_0_91,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_92,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_82])])])])]) ).
cnf(c_0_93,negated_conjecture,
ssList(esk49_0),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_94,negated_conjecture,
esk49_0 = esk51_0,
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_95,negated_conjecture,
ssList(cons(esk52_0,cons(esk52_0,esk55_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_39]),c_0_40]),c_0_30])]) ).
cnf(c_0_96,negated_conjecture,
( ~ ssList(cons(esk52_0,nil))
| app(esk54_0,app(cons(esk52_0,nil),app(cons(esk52_0,nil),esk55_0))) = esk50_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_35]),c_0_46])]) ).
cnf(c_0_97,negated_conjecture,
( ~ ssList(cons(esk52_0,nil))
| app(cons(esk52_0,nil),esk55_0) = cons(esk52_0,esk55_0) ),
inference(rw,[status(thm)],[c_0_85,c_0_80]) ).
cnf(c_0_98,negated_conjecture,
cons(esk52_0,app(nil,esk55_0)) = cons(esk52_0,esk55_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_62]),c_0_46]),c_0_40])]) ).
fof(c_0_99,plain,
! [X137] :
( app(nil,X137) = X137
| ~ ssList(X137) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax28])])]) ).
fof(c_0_100,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_87])])])]) ).
cnf(c_0_101,plain,
( ~ ssList(X1)
| ~ leq(X3,X2)
| ~ leq(X2,X3)
| app(app(X4,cons(X2,X5)),cons(X3,X6)) != X1
| ~ ssList(X6)
| ~ ssList(X5)
| ~ ssList(X4)
| ~ ssItem(X3)
| ~ ssItem(X2)
| ~ cyclefreeP(X1) ),
inference(split_conjunct,[status(thm)],[c_0_88]) ).
cnf(c_0_102,negated_conjecture,
app(app(esk54_0,cons(esk52_0,nil)),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_89,c_0_43]),c_0_46]),c_0_30])]) ).
cnf(c_0_103,negated_conjecture,
ssList(esk48_0),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_104,plain,
( ~ ssItem(X1)
| cyclefreeP(cons(X1,nil)) ),
inference(split_conjunct,[status(thm)],[c_0_90]) ).
cnf(c_0_105,plain,
( ~ ssList(X1)
| ~ singletonP(X1)
| cons(esk5_1(X1),nil) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_91]) ).
cnf(c_0_106,plain,
( ~ ssList(X1)
| ~ singletonP(X1)
| ssItem(esk5_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_91]) ).
cnf(c_0_107,negated_conjecture,
( ~ neq(esk51_0,nil)
| singletonP(esk50_0) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_108,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| neq(X1,X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_92]) ).
cnf(c_0_109,negated_conjecture,
ssList(esk51_0),
inference(rw,[status(thm)],[c_0_93,c_0_94]) ).
cnf(c_0_110,negated_conjecture,
( ~ ssList(X1)
| app(esk54_0,X1) != esk50_0
| X1 = cons(esk52_0,cons(esk52_0,esk55_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_57,c_0_95])]) ).
cnf(c_0_111,negated_conjecture,
app(esk54_0,app(cons(esk52_0,nil),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_96,c_0_39]),c_0_40]),c_0_30])]) ).
cnf(c_0_112,negated_conjecture,
app(cons(esk52_0,nil),esk55_0) = cons(esk52_0,esk55_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_39]),c_0_40]),c_0_30])]) ).
cnf(c_0_113,negated_conjecture,
( ~ ssList(app(nil,esk55_0))
| ssList(cons(esk52_0,esk55_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_98]),c_0_30])]) ).
cnf(c_0_114,plain,
( ~ ssList(X1)
| app(nil,X1) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_99]) ).
cnf(c_0_115,plain,
( nil != cons(X2,X1)
| ~ ssItem(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_100]) ).
cnf(c_0_116,negated_conjecture,
( ~ ssList(X1)
| ~ cyclefreeP(X1)
| ~ leq(esk52_0,esk52_0)
| esk50_0 != X1 ),
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_101,c_0_102]),c_0_46]),c_0_40]),c_0_36]),c_0_30])]) ).
cnf(c_0_117,negated_conjecture,
ssList(esk50_0),
inference(rw,[status(thm)],[c_0_103,c_0_26]) ).
cnf(c_0_118,plain,
( ~ ssList(X1)
| ~ singletonP(X1)
| cyclefreeP(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_105]),c_0_106]) ).
cnf(c_0_119,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_107,c_0_108]),c_0_40]),c_0_109])]) ).
fof(c_0_120,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_121,negated_conjecture,
( ~ ssList(app(cons(esk52_0,nil),cons(esk52_0,esk55_0)))
| app(cons(esk52_0,nil),cons(esk52_0,esk55_0)) = cons(esk52_0,cons(esk52_0,esk55_0)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_111]),c_0_112]),c_0_112]) ).
cnf(c_0_122,negated_conjecture,
ssList(cons(esk52_0,esk55_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_114]),c_0_46])]) ).
cnf(c_0_123,negated_conjecture,
( ~ ssList(cons(esk52_0,app(nil,esk55_0)))
| cons(esk52_0,cons(esk52_0,esk55_0)) != nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_70]),c_0_30])]) ).
fof(c_0_124,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_125,negated_conjecture,
( ~ cyclefreeP(esk50_0)
| ~ leq(esk52_0,esk52_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_116]),c_0_117])]) ).
cnf(c_0_126,negated_conjecture,
( cyclefreeP(esk50_0)
| esk51_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_119]),c_0_117])]) ).
fof(c_0_127,plain,
! [X143] :
( leq(X143,X143)
| ~ ssItem(X143) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax31])])]) ).
cnf(c_0_128,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| nil != app(X2,X1)
| nil = X1 ),
inference(split_conjunct,[status(thm)],[c_0_120]) ).
cnf(c_0_129,negated_conjecture,
app(esk54_0,app(cons(esk52_0,nil),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_111,c_0_43]),c_0_46]),c_0_30])]) ).
cnf(c_0_130,negated_conjecture,
( ~ ssList(cons(esk52_0,nil))
| app(cons(esk52_0,nil),cons(esk52_0,esk55_0)) = cons(esk52_0,cons(esk52_0,esk55_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_121,c_0_62]),c_0_122])]) ).
cnf(c_0_131,negated_conjecture,
( ~ ssList(cons(esk52_0,esk55_0))
| cons(esk52_0,cons(esk52_0,esk55_0)) != nil ),
inference(rw,[status(thm)],[c_0_123,c_0_98]) ).
cnf(c_0_132,plain,
( ~ segmentP(X2,X1)
| ~ segmentP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_124]) ).
cnf(c_0_133,negated_conjecture,
segmentP(esk51_0,esk50_0),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_134,negated_conjecture,
( ~ leq(esk52_0,esk52_0)
| esk51_0 = nil ),
inference(spm,[status(thm)],[c_0_125,c_0_126]) ).
cnf(c_0_135,plain,
( ~ ssItem(X1)
| leq(X1,X1) ),
inference(split_conjunct,[status(thm)],[c_0_127]) ).
cnf(c_0_136,negated_conjecture,
( ~ ssList(app(cons(esk52_0,nil),cons(esk52_0,esk55_0)))
| esk50_0 != nil
| app(cons(esk52_0,nil),cons(esk52_0,esk55_0)) = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_129]),c_0_36])]) ).
cnf(c_0_137,negated_conjecture,
app(cons(esk52_0,nil),cons(esk52_0,esk55_0)) = cons(esk52_0,cons(esk52_0,esk55_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_39]),c_0_40]),c_0_30])]) ).
cnf(c_0_138,negated_conjecture,
cons(esk52_0,cons(esk52_0,esk55_0)) != nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_131,c_0_122])]) ).
cnf(c_0_139,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_132,c_0_133]),c_0_109]),c_0_117])]) ).
cnf(c_0_140,negated_conjecture,
esk51_0 = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_134,c_0_135]),c_0_30])]) ).
cnf(c_0_141,negated_conjecture,
esk50_0 != nil,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_136,c_0_137]),c_0_137]),c_0_95])]),c_0_138]) ).
fof(c_0_142,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_143,negated_conjecture,
~ segmentP(esk50_0,nil),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_139,c_0_140]),c_0_140]),c_0_141]) ).
cnf(c_0_144,plain,
( ~ ssList(X1)
| segmentP(X1,nil) ),
inference(split_conjunct,[status(thm)],[c_0_142]) ).
cnf(c_0_145,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_143,c_0_144]),c_0_117])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC178+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.36 % Computer : n015.cluster.edu
% 0.12/0.36 % Model : x86_64 x86_64
% 0.12/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.36 % Memory : 8046.5625MB
% 0.12/0.36 % OS : Linux 6.8.0-71-generic
% 0.12/0.36 % CPULimit : 300
% 0.12/0.36 % WCLimit : 300
% 0.12/0.36 % DateTime : Mon Sep 21 08:05:20 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/0.43 Running first-order theorem proving
% 0.15/0.43 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.55/0.54 % Version: 3.5.1
% 0.55/0.54 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.55/0.54 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.55/0.54 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.55/0.54 % Starting new_bool_3 with 300s (1) cores
% 0.55/0.54 % Starting new_bool_1 with 300s (1) cores
% 0.55/0.54 % Starting sh5l with 300s (1) cores
% 0.55/0.54 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 992852 completed with status 0
% 0.55/0.54 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 0.55/0.54 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.55/0.54 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.55/0.54 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.55/0.54 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.55/0.54 % No SInE strategy applied
% 0.55/0.54 % Search class: FGHSF-FSLM21-MFFFFFNN
% 0.55/0.54 % Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 0.55/0.54 % Starting SubtermCWHack with 136s (1) cores
% 0.55/0.54 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.55/0.54 % Starting G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4d with 136s (1) cores
% 0.55/0.54 % Starting G-E--_110_C45_F1_PI_SE_CS_SP_PS_S4S with 136s (1) cores
% 0.55/0.54 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_TT_S0Y with 136s (1) cores
% 0.55/0.54 % G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4d with pid 992861 completed with status 0
% 0.55/0.54 % Result found by G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4d
% 0.55/0.54 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.55/0.54 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.55/0.54 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.55/0.54 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.55/0.54 % No SInE strategy applied
% 0.55/0.54 % Search class: FGHSF-FSLM21-MFFFFFNN
% 0.55/0.54 % Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 0.55/0.54 % Starting SubtermCWHack with 136s (1) cores
% 0.55/0.54 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.55/0.54 % Starting G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4d with 136s (1) cores
% 0.55/0.54 % Preprocessing time : 0.002 s
% 0.55/0.54
% 0.55/0.54 % Proof found!
% 0.55/0.54 % SZS status Theorem
% 0.55/0.54 % SZS output start CNFRefutation
% See solution above
% 0.55/0.54 % Parsed axioms : 96
% 0.55/0.54 % Removed by relevancy pruning/SinE : 0
% 0.55/0.54 % Initial clauses : 204
% 0.55/0.54 % Removed in clause preprocessing : 2
% 0.55/0.54 % Initial clauses in saturation : 202
% 0.55/0.54 % Processed clauses : 1050
% 0.55/0.54 % ...of these trivial : 15
% 0.55/0.54 % ...subsumed : 317
% 0.55/0.54 % ...remaining for further processing : 718
% 0.55/0.54 % Other redundant clauses eliminated : 86
% 0.55/0.54 % Clauses deleted for lack of memory : 0
% 0.55/0.54 % Backward-subsumed : 112
% 0.55/0.54 % Backward-rewritten : 178
% 0.55/0.54 % Generated clauses : 3235
% 0.55/0.54 % ...of the previous two non-redundant : 2931
% 0.55/0.54 % ...aggressively subsumed : 0
% 0.55/0.54 % Contextual simplify-reflections : 59
% 0.55/0.54 % Paramodulations : 3105
% 0.55/0.54 % Factorizations : 0
% 0.55/0.54 % NegExts : 0
% 0.55/0.54 % Equation resolutions : 129
% 0.55/0.54 % Disequality decompositions : 0
% 0.55/0.54 % Total rewrite steps : 3054
% 0.55/0.54 % ...of those cached : 2972
% 0.55/0.54 % Propositional unsat checks : 0
% 0.55/0.54 % Propositional check models : 0
% 0.55/0.54 % Propositional check unsatisfiable : 0
% 0.55/0.54 % Propositional clauses : 0
% 0.55/0.54 % Propositional clauses after purity: 0
% 0.55/0.54 % Propositional unsat core size : 0
% 0.55/0.54 % Propositional preprocessing time : 0.000
% 0.55/0.54 % Propositional encoding time : 0.000
% 0.55/0.54 % Propositional solver time : 0.000
% 0.55/0.54 % Success case prop preproc time : 0.000
% 0.55/0.54 % Success case prop encoding time : 0.000
% 0.55/0.54 % Success case prop solver time : 0.000
% 0.55/0.54 % Current number of processed clauses : 421
% 0.55/0.54 % Positive orientable unit clauses : 75
% 0.55/0.54 % Positive unorientable unit clauses: 0
% 0.55/0.54 % Negative unit clauses : 11
% 0.55/0.54 % Non-unit-clauses : 335
% 0.55/0.54 % Current number of unprocessed clauses: 1940
% 0.55/0.54 % ...number of literals in the above : 12311
% 0.55/0.54 % Current number of archived formulas : 0
% 0.55/0.54 % Current number of archived clauses : 291
% 0.55/0.54 % Clause-clause subsumption calls (NU) : 27297
% 0.55/0.54 % Rec. Clause-clause subsumption calls : 14894
% 0.55/0.54 % Non-unit clause-clause subsumptions : 382
% 0.55/0.54 % Unit Clause-clause subsumption calls : 1332
% 0.55/0.54 % Rewrite failures with RHS unbound : 0
% 0.55/0.54 % BW rewrite match attempts : 95
% 0.55/0.54 % BW rewrite match successes : 58
% 0.55/0.54 % Condensation attempts : 0
% 0.55/0.54 % Condensation successes : 0
% 0.55/0.54 % Termbank termtop insertions : 88431
% 0.55/0.54 % Search garbage collected termcells : 4306
% 0.55/0.54
% 0.55/0.54 % -------------------------------------------------
% 0.55/0.54 % User time : 0.080 s
% 0.55/0.54 % System time : 0.008 s
% 0.55/0.54 % Total time : 0.088 s
% 0.55/0.54 % Maximum resident set size: 4272 pages
% 0.55/0.54
% 0.55/0.54 % -------------------------------------------------
% 0.55/0.54 % User time : 0.342 s
% 0.55/0.54 % System time : 0.031 s
% 0.55/0.54 % Total time : 0.373 s
% 0.55/0.54 % Maximum resident set size: 4864 pages
% 0.55/0.54 % E exiting
%------------------------------------------------------------------------------