%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWC061+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 : n008.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 02:42:49 PM UTC 2026
% Result : Theorem 0.24s 5.97s
% Output : CNFRefutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 19
% Syntax : Number of formulae : 126 ( 20 unt; 0 def)
% Number of atoms : 449 ( 173 equ)
% Maximal formula atoms : 30 ( 3 avg)
% Number of connectives : 548 ( 225 ~; 220 |; 38 &)
% ( 3 <=>; 62 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 159 ( 0 sgn 98 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ( ( ? [X7] :
( segmentP(X1,X7)
& segmentP(X2,X7)
& neq(X7,nil)
& ssList(X7) )
| ~ neq(X2,nil) )
& ( nil = X1
| nil != X2 ) )
| ( neq(X4,nil)
& ! [X5] :
( ssItem(X5)
=> ! [X6] :
( app(X6,cons(X5,nil)) != X3
| app(cons(X5,nil),X6) != X4
| ~ ssList(X6) ) ) )
| ( nil = X4
& nil != X3 )
| X1 != X3
| X2 != X4
| ~ ssList(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(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(ax21,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> nil != cons(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax21) ).
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(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(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(ax84,axiom,
! [X1] :
( ssList(X1)
=> app(X1,nil) = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax84) ).
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(ax26,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ssList(app(X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax26) ).
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(ax78,axiom,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> cons(hd(X1),tl(X1)) = X1 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax78) ).
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(ax56,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( segmentP(X1,X2)
=> segmentP(app(app(X3,X1),X4),X2) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax56) ).
fof(ax28,axiom,
! [X1] :
( ssList(X1)
=> app(nil,X1) = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax28) ).
fof(ax19,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssItem(X3)
=> ! [X4] :
( ssItem(X4)
=> ( cons(X3,X1) = cons(X4,X2)
=> ( X2 = X1
& X3 = X4 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax19) ).
fof(ax55,axiom,
! [X1] :
( ssList(X1)
=> segmentP(X1,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax55) ).
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(c_0_19,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ( ( ? [X7] :
( segmentP(X1,X7)
& segmentP(X2,X7)
& neq(X7,nil)
& ssList(X7) )
| ~ neq(X2,nil) )
& ( nil = X1
| nil != X2 ) )
| ( neq(X4,nil)
& ! [X5] :
( ssItem(X5)
=> ! [X6] :
( app(X6,cons(X5,nil)) != X3
| app(cons(X5,nil),X6) != X4
| ~ ssList(X6) ) ) )
| ( nil = X4
& nil != X3 )
| X1 != X3
| X2 != X4
| ~ ssList(X4) ) ) ) ),
inference(assume_negation,[status(cth)],[co1]) ).
fof(c_0_20,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ( ( ? [X7] :
( segmentP(X1,X7)
& segmentP(X2,X7)
& neq(X7,nil)
& ssList(X7) )
| ~ neq(X2,nil) )
& ( nil = X1
| nil != X2 ) )
| ( neq(X4,nil)
& ! [X5] :
( ssItem(X5)
=> ! [X6] :
( app(X6,cons(X5,nil)) != X3
| app(cons(X5,nil),X6) != X4
| ~ ssList(X6) ) ) )
| ( nil = X4
& nil != X3 )
| X1 != X3
| X2 != X4
| ~ ssList(X4) ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_19]) ).
fof(c_0_21,negated_conjecture,
! [X14] :
( ( nil != esk1_0
| ~ segmentP(esk1_0,X14)
| ~ segmentP(esk2_0,X14)
| ~ neq(X14,nil)
| ~ ssList(X14) )
& ( nil != esk1_0
| neq(esk2_0,nil) )
& ( nil = esk2_0
| ~ segmentP(esk1_0,X14)
| ~ segmentP(esk2_0,X14)
| ~ neq(X14,nil)
| ~ ssList(X14) )
& ( nil = esk2_0
| neq(esk2_0,nil) )
& ( ~ neq(esk4_0,nil)
| app(esk6_0,cons(esk5_0,nil)) = esk3_0 )
& ( ~ neq(esk4_0,nil)
| app(cons(esk5_0,nil),esk6_0) = esk4_0 )
& ( ~ neq(esk4_0,nil)
| ssList(esk6_0) )
& ( ~ neq(esk4_0,nil)
| ssItem(esk5_0) )
& ( nil != esk4_0
| nil = esk3_0 )
& esk1_0 = esk3_0
& esk2_0 = esk4_0
& ssList(esk4_0)
& ssList(esk3_0)
& ssList(esk2_0)
& ssList(esk1_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_20])])])])])]) ).
cnf(c_0_22,negated_conjecture,
( ~ neq(esk4_0,nil)
| app(esk6_0,cons(esk5_0,nil)) = esk3_0 ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_23,negated_conjecture,
esk1_0 = esk3_0,
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_24,negated_conjecture,
( nil != esk1_0
| neq(esk2_0,nil) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_25,negated_conjecture,
esk2_0 = esk4_0,
inference(split_conjunct,[status(thm)],[c_0_21]) ).
fof(c_0_26,plain,
! [X45,X46] :
( ( ~ ssList(X45)
| ~ ssList(X46)
| nil = app(X45,X46)
| nil != X45
| nil != X46 )
& ( ~ ssList(X45)
| ~ ssList(X46)
| nil != app(X45,X46)
| nil = X45 )
& ( ~ ssList(X45)
| ~ ssList(X46)
| nil != app(X45,X46)
| nil = X46 ) ),
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_27,negated_conjecture,
( ~ neq(esk4_0,nil)
| app(esk6_0,cons(esk5_0,nil)) = esk1_0 ),
inference(rw,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_28,negated_conjecture,
( esk1_0 != nil
| neq(esk4_0,nil) ),
inference(rw,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_29,negated_conjecture,
( ~ neq(esk4_0,nil)
| ssList(esk6_0) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_30,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| nil != app(X1,X2)
| nil = X1 ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_31,negated_conjecture,
( esk1_0 != nil
| app(esk6_0,cons(esk5_0,nil)) = esk1_0 ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_32,negated_conjecture,
( esk1_0 != nil
| ssList(esk6_0) ),
inference(spm,[status(thm)],[c_0_29,c_0_28]) ).
fof(c_0_33,plain,
! [X48,X49] :
( ssList(cons(X49,X48))
| ~ ssItem(X49)
| ~ ssList(X48) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax16])])])]) ).
cnf(c_0_34,negated_conjecture,
( ~ neq(esk4_0,nil)
| ssItem(esk5_0) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_35,negated_conjecture,
( ~ ssList(cons(esk5_0,nil))
| esk1_0 != nil
| esk6_0 = nil ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32]) ).
cnf(c_0_36,plain,
( ~ ssItem(X2)
| ~ ssList(X1)
| ssList(cons(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_37,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[ax17]) ).
cnf(c_0_38,negated_conjecture,
( esk1_0 != nil
| ssItem(esk5_0) ),
inference(spm,[status(thm)],[c_0_34,c_0_28]) ).
cnf(c_0_39,negated_conjecture,
( esk1_0 != nil
| esk6_0 = nil ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37])]),c_0_38]) ).
fof(c_0_40,plain,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> nil != cons(X2,X1) ) ),
inference(fof_simplification,[status(thm)],[ax21]) ).
cnf(c_0_41,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| nil != app(X2,X1)
| nil = X1 ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_42,negated_conjecture,
( esk1_0 != nil
| app(nil,cons(esk5_0,nil)) = esk1_0 ),
inference(spm,[status(thm)],[c_0_31,c_0_39]) ).
fof(c_0_43,plain,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
inference(fof_simplification,[status(thm)],[ax15]) ).
fof(c_0_44,plain,
! [X40,X41] :
( nil != cons(X41,X40)
| ~ ssItem(X41)
| ~ ssList(X40) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_40])])])]) ).
cnf(c_0_45,negated_conjecture,
( ~ ssList(cons(esk5_0,nil))
| esk1_0 != nil
| cons(esk5_0,nil) = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_37])]) ).
fof(c_0_46,plain,
! [X35,X36] :
( ( ~ ssList(X35)
| ~ ssList(X36)
| neq(X35,X36)
| X35 = X36 )
& ( ~ ssList(X35)
| ~ ssList(X36)
| X35 != X36
| ~ neq(X35,X36) ) ),
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_43])])])])]) ).
cnf(c_0_47,plain,
( nil != cons(X2,X1)
| ~ ssItem(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_48,negated_conjecture,
( esk1_0 != nil
| cons(esk5_0,nil) = nil ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_36]),c_0_37])]),c_0_38]) ).
cnf(c_0_49,negated_conjecture,
( nil != esk4_0
| nil = esk3_0 ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_50,negated_conjecture,
( nil = esk2_0
| neq(esk2_0,nil) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_51,negated_conjecture,
( ~ neq(esk4_0,nil)
| app(cons(esk5_0,nil),esk6_0) = esk4_0 ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_52,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| neq(X1,X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_53,negated_conjecture,
ssList(esk4_0),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_54,negated_conjecture,
esk1_0 != nil,
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_37])]),c_0_38]) ).
cnf(c_0_55,negated_conjecture,
( esk4_0 != nil
| esk1_0 = nil ),
inference(rw,[status(thm)],[c_0_49,c_0_23]) ).
cnf(c_0_56,negated_conjecture,
( neq(esk4_0,nil)
| esk4_0 = nil ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_50,c_0_25]),c_0_25]) ).
fof(c_0_57,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_58,negated_conjecture,
( esk4_0 = nil
| app(cons(esk5_0,nil),esk6_0) = esk4_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_37]),c_0_53])]) ).
cnf(c_0_59,negated_conjecture,
esk4_0 != nil,
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
fof(c_0_60,plain,
! [X43,X44] :
( cons(X44,X43) = app(cons(X44,nil),X43)
| ~ ssItem(X44)
| ~ ssList(X43) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax81])])])]) ).
cnf(c_0_61,negated_conjecture,
( ssList(esk6_0)
| esk4_0 = nil ),
inference(spm,[status(thm)],[c_0_29,c_0_56]) ).
cnf(c_0_62,negated_conjecture,
( ssItem(esk5_0)
| esk4_0 = nil ),
inference(spm,[status(thm)],[c_0_34,c_0_56]) ).
fof(c_0_63,plain,
! [X86,X87] :
( tl(app(X86,X87)) = app(tl(X86),X87)
| nil = X86
| ~ ssList(X87)
| ~ ssList(X86) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_57])])])]) ).
fof(c_0_64,plain,
! [X47] :
( app(X47,nil) = X47
| ~ ssList(X47) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax84])])]) ).
fof(c_0_65,plain,
! [X129,X130] :
( tl(cons(X130,X129)) = X129
| ~ ssItem(X130)
| ~ ssList(X129) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax25])])])]) ).
cnf(c_0_66,negated_conjecture,
app(cons(esk5_0,nil),esk6_0) = esk4_0,
inference(sr,[status(thm)],[c_0_58,c_0_59]) ).
cnf(c_0_67,plain,
( ~ ssItem(X2)
| ~ ssList(X1)
| cons(X2,X1) = app(cons(X2,nil),X1) ),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
cnf(c_0_68,negated_conjecture,
ssList(esk6_0),
inference(sr,[status(thm)],[c_0_61,c_0_59]) ).
cnf(c_0_69,negated_conjecture,
ssItem(esk5_0),
inference(sr,[status(thm)],[c_0_62,c_0_59]) ).
cnf(c_0_70,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| tl(app(X1,X2)) = app(tl(X1),X2)
| nil = X1 ),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
cnf(c_0_71,plain,
( ~ ssList(X1)
| app(X1,nil) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
cnf(c_0_72,plain,
( ~ ssItem(X2)
| ~ ssList(X1)
| tl(cons(X2,X1)) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_65]) ).
cnf(c_0_73,negated_conjecture,
cons(esk5_0,esk6_0) = esk4_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_67]),c_0_68]),c_0_69])]) ).
fof(c_0_74,plain,
! [X56,X57] :
( ssList(app(X56,X57))
| ~ ssList(X57)
| ~ ssList(X56) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax26])])])]) ).
fof(c_0_75,plain,
! [X64,X65,X66] :
( X66 = X64
| app(X65,X66) != app(X65,X64)
| ~ ssList(X66)
| ~ ssList(X65)
| ~ ssList(X64) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax80])])])]) ).
cnf(c_0_76,plain,
( ~ ssList(X1)
| nil = X1
| app(tl(X1),nil) = tl(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_37])]) ).
cnf(c_0_77,negated_conjecture,
tl(esk4_0) = esk6_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_68]),c_0_69])]) ).
cnf(c_0_78,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ssList(app(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_74]) ).
fof(c_0_79,plain,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> cons(hd(X1),tl(X1)) = X1 ) ),
inference(fof_simplification,[status(thm)],[ax78]) ).
fof(c_0_80,plain,
! [X58,X59,X60] :
( cons(X60,app(X59,X58)) = app(cons(X60,X59),X58)
| ~ ssItem(X60)
| ~ ssList(X59)
| ~ ssList(X58) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax27])])])]) ).
cnf(c_0_81,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_82,negated_conjecture,
app(esk6_0,nil) = esk6_0,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_77]),c_0_53])]),c_0_59]) ).
cnf(c_0_83,negated_conjecture,
( esk4_0 = nil
| app(esk6_0,cons(esk5_0,nil)) = esk1_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_52]),c_0_37]),c_0_53])]) ).
fof(c_0_84,plain,
! [X27,X28,X29,X30] :
( segmentP(app(app(X29,X27),X30),X28)
| ~ segmentP(X27,X28)
| ~ ssList(X30)
| ~ ssList(X29)
| ~ ssList(X28)
| ~ ssList(X27) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax56])])])]) ).
cnf(c_0_85,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| nil = X1
| app(app(tl(X1),X2),nil) = app(tl(X1),X2) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_70]),c_0_78]),c_0_30]) ).
fof(c_0_86,plain,
! [X42] :
( app(nil,X42) = X42
| ~ ssList(X42) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax28])])]) ).
fof(c_0_87,plain,
! [X127] :
( cons(hd(X127),tl(X127)) = X127
| nil = X127
| ~ ssList(X127) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_79])])]) ).
cnf(c_0_88,plain,
( ~ ssItem(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| cons(X3,app(X2,X1)) = app(cons(X3,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_80]) ).
cnf(c_0_89,negated_conjecture,
( ~ ssList(X1)
| app(esk6_0,X1) != esk6_0
| X1 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_82]),c_0_37]),c_0_68])]) ).
cnf(c_0_90,negated_conjecture,
app(esk6_0,cons(esk5_0,nil)) = esk1_0,
inference(sr,[status(thm)],[c_0_83,c_0_59]) ).
cnf(c_0_91,plain,
( ~ segmentP(X1,X2)
| ~ ssList(X4)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| segmentP(app(app(X3,X1),X4),X2) ),
inference(split_conjunct,[status(thm)],[c_0_84]) ).
cnf(c_0_92,negated_conjecture,
( ~ ssList(X1)
| app(app(esk6_0,X1),nil) = app(esk6_0,X1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_77]),c_0_53])]),c_0_59]) ).
cnf(c_0_93,plain,
( ~ ssList(X1)
| app(nil,X1) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_86]) ).
fof(c_0_94,plain,
! [X52,X53,X54,X55] :
( ( ~ ssList(X52)
| ~ ssList(X53)
| ~ ssItem(X54)
| ~ ssItem(X55)
| cons(X54,X52) != cons(X55,X53)
| X53 = X52 )
& ( ~ ssList(X52)
| ~ ssList(X53)
| ~ ssItem(X54)
| ~ ssItem(X55)
| cons(X54,X52) != cons(X55,X53)
| X54 = X55 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax19])])])])]) ).
cnf(c_0_95,plain,
( ~ ssList(X1)
| cons(hd(X1),tl(X1)) = X1
| nil = X1 ),
inference(split_conjunct,[status(thm)],[c_0_87]) ).
cnf(c_0_96,negated_conjecture,
( ~ ssList(X1)
| cons(esk5_0,app(esk6_0,X1)) = app(esk4_0,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_73]),c_0_68]),c_0_69])]) ).
cnf(c_0_97,negated_conjecture,
( ~ ssList(cons(esk5_0,nil))
| esk6_0 != esk1_0
| cons(esk5_0,nil) = nil ),
inference(spm,[status(thm)],[c_0_89,c_0_90]) ).
cnf(c_0_98,negated_conjecture,
( ~ segmentP(esk1_0,X1)
| ~ segmentP(esk2_0,X1)
| ~ neq(X1,nil)
| ~ ssList(X1)
| nil = esk2_0 ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_99,negated_conjecture,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ segmentP(X1,X2)
| segmentP(app(esk6_0,X1),X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_92]),c_0_37]),c_0_68])]) ).
fof(c_0_100,plain,
! [X26] :
( segmentP(X26,X26)
| ~ ssList(X26) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax55])])]) ).
cnf(c_0_101,plain,
( ~ ssList(X1)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ segmentP(X1,X3)
| segmentP(app(X1,X2),X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_93]),c_0_37])]) ).
cnf(c_0_102,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X3)
| ~ ssItem(X4)
| cons(X3,X2) != cons(X4,X1)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_94]) ).
cnf(c_0_103,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| nil = X1
| cons(hd(app(X1,X2)),app(tl(X1),X2)) = app(X1,X2) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_70]),c_0_78]),c_0_30]) ).
cnf(c_0_104,negated_conjecture,
( ~ ssList(cons(esk5_0,nil))
| app(esk4_0,cons(esk5_0,nil)) = cons(esk5_0,esk1_0) ),
inference(spm,[status(thm)],[c_0_96,c_0_90]) ).
cnf(c_0_105,negated_conjecture,
( esk6_0 != esk1_0
| cons(esk5_0,nil) = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_36]),c_0_37]),c_0_69])]) ).
cnf(c_0_106,negated_conjecture,
( ~ neq(X1,nil)
| ~ ssList(X1)
| ~ segmentP(esk4_0,X1)
| ~ segmentP(esk1_0,X1) ),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_98,c_0_25]),c_0_25]),c_0_59]) ).
cnf(c_0_107,negated_conjecture,
( ~ ssList(X1)
| ~ ssList(cons(esk5_0,nil))
| ~ segmentP(cons(esk5_0,nil),X1)
| segmentP(esk1_0,X1) ),
inference(spm,[status(thm)],[c_0_99,c_0_90]) ).
cnf(c_0_108,plain,
( ~ ssList(X1)
| segmentP(X1,X1) ),
inference(split_conjunct,[status(thm)],[c_0_100]) ).
cnf(c_0_109,negated_conjecture,
( ~ ssList(X1)
| ~ ssList(cons(esk5_0,nil))
| ~ segmentP(cons(esk5_0,nil),X1)
| segmentP(esk4_0,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_66]),c_0_68])]) ).
cnf(c_0_110,negated_conjecture,
( ~ ssItem(X2)
| ~ ssList(X1)
| cons(X2,X1) != esk4_0
| esk6_0 = X1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_73]),c_0_68]),c_0_69])]) ).
cnf(c_0_111,negated_conjecture,
( ~ ssList(cons(esk5_0,nil))
| cons(hd(cons(esk5_0,esk1_0)),esk1_0) = cons(esk5_0,esk1_0) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_104]),c_0_77]),c_0_90]),c_0_53])]),c_0_59]) ).
cnf(c_0_112,negated_conjecture,
ssList(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_113,negated_conjecture,
esk6_0 != esk1_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_105]),c_0_37]),c_0_69])]) ).
fof(c_0_114,plain,
! [X88,X89] :
( hd(cons(X89,X88)) = X89
| ~ ssItem(X89)
| ~ ssList(X88) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax23])])])]) ).
cnf(c_0_115,negated_conjecture,
( ~ ssList(X1)
| ~ segmentP(esk4_0,X1)
| ~ segmentP(esk1_0,X1)
| X1 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_52]),c_0_37])]) ).
cnf(c_0_116,negated_conjecture,
( ~ ssList(cons(esk5_0,nil))
| segmentP(esk1_0,cons(esk5_0,nil)) ),
inference(spm,[status(thm)],[c_0_107,c_0_108]) ).
cnf(c_0_117,negated_conjecture,
( ~ ssList(cons(esk5_0,nil))
| segmentP(esk4_0,cons(esk5_0,nil)) ),
inference(spm,[status(thm)],[c_0_109,c_0_108]) ).
cnf(c_0_118,negated_conjecture,
( ~ ssItem(hd(cons(esk5_0,esk1_0)))
| ~ ssList(cons(esk5_0,nil))
| cons(esk5_0,esk1_0) != esk4_0 ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_111]),c_0_112])]),c_0_113]) ).
cnf(c_0_119,plain,
( ~ ssItem(X2)
| ~ ssList(X1)
| hd(cons(X2,X1)) = X2 ),
inference(split_conjunct,[status(thm)],[c_0_114]) ).
cnf(c_0_120,negated_conjecture,
( ~ ssList(cons(esk5_0,nil))
| cons(esk5_0,nil) = nil ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_116]),c_0_117]) ).
cnf(c_0_121,negated_conjecture,
( ~ ssList(cons(esk5_0,nil))
| cons(esk5_0,esk1_0) != esk4_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_119]),c_0_69]),c_0_112])]) ).
cnf(c_0_122,negated_conjecture,
cons(esk5_0,nil) = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_120,c_0_36]),c_0_37]),c_0_69])]) ).
cnf(c_0_123,negated_conjecture,
app(esk4_0,nil) = esk4_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_71]),c_0_73]),c_0_37]),c_0_68])]) ).
cnf(c_0_124,negated_conjecture,
cons(esk5_0,esk1_0) != esk4_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_121,c_0_36]),c_0_37]),c_0_69])]) ).
cnf(c_0_125,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_104,c_0_122]),c_0_123]),c_0_122]),c_0_37])]),c_0_124]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWC061+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.20/5.67 % Computer : n008.cluster.edu
% 0.20/5.67 % Model : x86_64 x86_64
% 0.20/5.67 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/5.67 % Memory : 8046.5625MB
% 0.20/5.67 % OS : Linux 6.8.0-71-generic
% 0.20/5.68 % CPULimit : 300
% 0.20/5.68 % WCLimit : 300
% 0.20/5.68 % DateTime : Mon Sep 21 07:53:45 UTC 2026
% 0.20/5.68 % CPUTime :
% 0.20/5.68 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.24/5.73 Running first-order theorem proving
% 0.24/5.73 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
% 0.24/5.97 % Version: 3.5.1
% 0.24/5.97 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.24/5.97 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/5.97 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.24/5.97 % Starting new_bool_3 with 300s (1) cores
% 0.24/5.97 % Starting new_bool_1 with 300s (1) cores
% 0.24/5.97 % Starting sh5l with 300s (1) cores
% 0.24/5.97 % sh5l with pid 524294 completed with status 0
% 0.24/5.97 % Result found by sh5l
% 0.24/5.97 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.24/5.97 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/5.97 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.24/5.97 % Starting new_bool_3 with 300s (1) cores
% 0.24/5.97 % Starting new_bool_1 with 300s (1) cores
% 0.24/5.97 % Starting sh5l with 300s (1) cores
% 0.24/5.97 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.24/5.97 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.24/5.97 % Search class: FGHSF-FSLM21-MFFFFFNN
% 0.24/5.97 % Scheduled 11 strats onto 1 cores with 300 seconds (300 total)
% 0.24/5.97 % Starting SubtermCWHack with 28s (1) cores
% 0.24/5.97 % SubtermCWHack with pid 524297 completed with status 0
% 0.24/5.97 % Result found by SubtermCWHack
% 0.24/5.97 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.24/5.97 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/5.97 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.24/5.97 % Starting new_bool_3 with 300s (1) cores
% 0.24/5.97 % Starting new_bool_1 with 300s (1) cores
% 0.24/5.97 % Starting sh5l with 300s (1) cores
% 0.24/5.97 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.24/5.97 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.24/5.97 % Search class: FGHSF-FSLM21-MFFFFFNN
% 0.24/5.97 % Scheduled 11 strats onto 1 cores with 300 seconds (300 total)
% 0.24/5.97 % Starting SubtermCWHack with 28s (1) cores
% 0.24/5.97 % Preprocessing time : 0.005 s
% 0.24/5.97
% 0.24/5.97 % Proof found!
% 0.24/5.97 % SZS status Theorem
% 0.24/5.97 % SZS output start CNFRefutation
% See solution above
% 0.24/5.97 % Parsed axioms : 96
% 0.24/5.97 % Removed by relevancy pruning/SinE : 12
% 0.24/5.97 % Initial clauses : 171
% 0.24/5.97 % Removed in clause preprocessing : 2
% 0.24/5.97 % Initial clauses in saturation : 169
% 0.24/5.97 % Processed clauses : 1008
% 0.24/5.97 % ...of these trivial : 5
% 0.24/5.97 % ...subsumed : 433
% 0.24/5.97 % ...remaining for further processing : 570
% 0.24/5.97 % Other redundant clauses eliminated : 98
% 0.24/5.97 % Clauses deleted for lack of memory : 0
% 0.24/5.97 % Backward-subsumed : 57
% 0.24/5.97 % Backward-rewritten : 122
% 0.24/5.97 % Generated clauses : 3244
% 0.24/5.97 % ...of the previous two non-redundant : 2670
% 0.24/5.97 % ...aggressively subsumed : 0
% 0.24/5.97 % Contextual simplify-reflections : 65
% 0.24/5.97 % Paramodulations : 3137
% 0.24/5.97 % Factorizations : 0
% 0.24/5.97 % NegExts : 0
% 0.24/5.97 % Equation resolutions : 103
% 0.24/5.97 % Disequality decompositions : 0
% 0.24/5.97 % Total rewrite steps : 2721
% 0.24/5.97 % ...of those cached : 2671
% 0.24/5.97 % Propositional unsat checks : 0
% 0.24/5.97 % Propositional check models : 0
% 0.24/5.97 % Propositional check unsatisfiable : 0
% 0.24/5.97 % Propositional clauses : 0
% 0.24/5.97 % Propositional clauses after purity: 0
% 0.24/5.97 % Propositional unsat core size : 0
% 0.24/5.97 % Propositional preprocessing time : 0.000
% 0.24/5.97 % Propositional encoding time : 0.000
% 0.24/5.97 % Propositional solver time : 0.000
% 0.24/5.97 % Success case prop preproc time : 0.000
% 0.24/5.97 % Success case prop encoding time : 0.000
% 0.24/5.97 % Success case prop solver time : 0.000
% 0.24/5.97 % Current number of processed clauses : 368
% 0.24/5.97 % Positive orientable unit clauses : 51
% 0.24/5.97 % Positive unorientable unit clauses: 0
% 0.24/5.97 % Negative unit clauses : 15
% 0.24/5.97 % Non-unit-clauses : 302
% 0.24/5.97 % Current number of unprocessed clauses: 1721
% 0.24/5.97 % ...number of literals in the above : 9589
% 0.24/5.97 % Current number of archived formulas : 0
% 0.24/5.97 % Current number of archived clauses : 184
% 0.24/5.97 % Clause-clause subsumption calls (NU) : 22958
% 0.24/5.97 % Rec. Clause-clause subsumption calls : 11874
% 0.24/5.97 % Non-unit clause-clause subsumptions : 452
% 0.24/5.97 % Unit Clause-clause subsumption calls : 1160
% 0.24/5.97 % Rewrite failures with RHS unbound : 0
% 0.24/5.97 % BW rewrite match attempts : 21
% 0.24/5.97 % BW rewrite match successes : 21
% 0.24/5.97 % Condensation attempts : 0
% 0.24/5.97 % Condensation successes : 0
% 0.24/5.97 % Termbank termtop insertions : 71829
% 0.24/5.97 % Search garbage collected termcells : 3702
% 0.24/5.97
% 0.24/5.97 % -------------------------------------------------
% 0.24/5.97 % User time : 0.164 s
% 0.24/5.97 % System time : 0.012 s
% 0.24/5.97 % Total time : 0.177 s
% 0.24/5.97 % Maximum resident set size: 4016 pages
% 0.24/5.97
% 0.24/5.97 % -------------------------------------------------
% 0.24/5.97 % User time : 0.168 s
% 0.24/5.97 % System time : 0.016 s
% 0.24/5.97 % Total time : 0.185 s
% 0.24/5.97 % Maximum resident set size: 4864 pages
% 0.24/5.97 % E exiting
%------------------------------------------------------------------------------