%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWC099+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 : n010.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 02:43:00 PM UTC 2026
% Result : Theorem 1.32s 0.66s
% Output : CNFRefutation 1.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 17
% Syntax : Number of formulae : 98 ( 14 unt; 0 def)
% Number of atoms : 383 ( 95 equ)
% Maximal formula atoms : 23 ( 3 avg)
% Number of connectives : 484 ( 199 ~; 192 |; 45 &)
% ( 6 <=>; 42 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-2 aty)
% Number of variables : 140 ( 0 sgn 71 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( ( ( frontsegP(X2,X1)
& neq(X1,nil) )
| ~ neq(X2,nil) )
& ( nil = X1
| nil != X2 ) )
| ? [X5] :
( equalelemsP(X5)
& segmentP(X5,X3)
& frontsegP(X4,X5)
& neq(X3,X5)
& ssList(X5) )
| ~ equalelemsP(X3)
| ~ frontsegP(X4,X3)
| X1 != X3
| X2 != X4 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
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(ax17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(ax46,axiom,
! [X1] :
( ssList(X1)
=> ( frontsegP(nil,X1)
<=> nil = X1 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax46) ).
fof(ax18,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> cons(X2,X1) != X1 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax18) ).
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(ax57,axiom,
! [X1] :
( ssList(X1)
=> segmentP(X1,nil) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax57) ).
fof(ax84,axiom,
! [X1] :
( ssList(X1)
=> app(X1,nil) = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax84) ).
fof(ax26,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ssList(app(X1,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax26) ).
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(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(ax73,axiom,
! [X1] :
( ssItem(X1)
=> equalelemsP(cons(X1,nil)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax73) ).
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(ax16,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> ssList(cons(X2,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax16) ).
fof(ax5,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( frontsegP(X1,X2)
<=> ? [X3] :
( app(X2,X3) = X1
& ssList(X3) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax5) ).
fof(ax20,axiom,
! [X1] :
( ssList(X1)
=> ( ? [X2] :
( ? [X3] :
( cons(X3,X2) = X1
& ssItem(X3) )
& ssList(X2) )
| nil = X1 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax20) ).
fof(c_0_17,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( ( ( frontsegP(X2,X1)
& neq(X1,nil) )
| ~ neq(X2,nil) )
& ( nil = X1
| nil != X2 ) )
| ? [X5] :
( equalelemsP(X5)
& segmentP(X5,X3)
& frontsegP(X4,X5)
& neq(X3,X5)
& ssList(X5) )
| ~ equalelemsP(X3)
| ~ frontsegP(X4,X3)
| X1 != X3
| X2 != X4 ) ) ) ) ),
inference(assume_negation,[status(cth)],[co1]) ).
fof(c_0_18,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( ( ( frontsegP(X2,X1)
& neq(X1,nil) )
| ~ neq(X2,nil) )
& ( nil = X1
| nil != X2 ) )
| ? [X5] :
( equalelemsP(X5)
& segmentP(X5,X3)
& frontsegP(X4,X5)
& neq(X3,X5)
& ssList(X5) )
| ~ equalelemsP(X3)
| ~ frontsegP(X4,X3)
| X1 != X3
| X2 != X4 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_17]) ).
fof(c_0_19,negated_conjecture,
! [X255] :
( ( nil != esk48_0
| ~ frontsegP(esk49_0,esk48_0)
| ~ neq(esk48_0,nil) )
& ( nil != esk48_0
| neq(esk49_0,nil) )
& ( nil = esk49_0
| ~ frontsegP(esk49_0,esk48_0)
| ~ neq(esk48_0,nil) )
& ( nil = esk49_0
| neq(esk49_0,nil) )
& ( ~ equalelemsP(X255)
| ~ segmentP(X255,esk50_0)
| ~ frontsegP(esk51_0,X255)
| ~ neq(esk50_0,X255)
| ~ ssList(X255) )
& equalelemsP(esk50_0)
& frontsegP(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(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_18])])])])])]) ).
cnf(c_0_20,negated_conjecture,
frontsegP(esk51_0,esk50_0),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_21,negated_conjecture,
esk49_0 = esk51_0,
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_22,negated_conjecture,
esk48_0 = esk50_0,
inference(split_conjunct,[status(thm)],[c_0_19]) ).
fof(c_0_23,plain,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
inference(fof_simplification,[status(thm)],[ax15]) ).
cnf(c_0_24,negated_conjecture,
( ~ frontsegP(esk49_0,esk48_0)
| ~ neq(esk48_0,nil)
| nil = esk49_0 ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_25,negated_conjecture,
frontsegP(esk49_0,esk48_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_20,c_0_21]),c_0_22]) ).
fof(c_0_26,plain,
! [X109,X110] :
( ( ~ ssList(X109)
| ~ ssList(X110)
| neq(X109,X110)
| X109 = X110 )
& ( ~ ssList(X109)
| ~ ssList(X110)
| X109 != X110
| ~ neq(X109,X110) ) ),
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_23])])])])]) ).
cnf(c_0_27,negated_conjecture,
( ~ neq(esk48_0,nil)
| esk49_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_25])]) ).
cnf(c_0_28,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| neq(X1,X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_29,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[ax17]) ).
cnf(c_0_30,negated_conjecture,
ssList(esk48_0),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
fof(c_0_31,plain,
! [X172] :
( ( ~ ssList(X172)
| frontsegP(nil,X172)
| nil != X172 )
& ( ~ ssList(X172)
| nil = X172
| ~ frontsegP(nil,X172) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax46])])])]) ).
cnf(c_0_32,negated_conjecture,
( esk49_0 = nil
| esk48_0 = nil ),
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,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> cons(X2,X1) != X1 ) ),
inference(fof_simplification,[status(thm)],[ax18]) ).
fof(c_0_34,plain,
! [X220,X221] :
( cons(X221,X220) = app(cons(X221,nil),X220)
| ~ ssItem(X221)
| ~ ssList(X220) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax81])])])]) ).
fof(c_0_35,plain,
! [X132,X133,X134] :
( cons(X134,app(X133,X132)) = app(cons(X134,X133),X132)
| ~ ssItem(X134)
| ~ ssList(X133)
| ~ ssList(X132) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax27])])])]) ).
cnf(c_0_36,plain,
( ~ ssList(X1)
| ~ frontsegP(nil,X1)
| nil = X1 ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_37,negated_conjecture,
( frontsegP(nil,esk48_0)
| esk48_0 = nil ),
inference(spm,[status(thm)],[c_0_25,c_0_32]) ).
fof(c_0_38,plain,
! [X194] :
( segmentP(X194,nil)
| ~ ssList(X194) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax57])])]) ).
fof(c_0_39,plain,
! [X113,X114] :
( cons(X114,X113) != 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)],[c_0_33])])])]) ).
cnf(c_0_40,plain,
( ~ ssItem(X2)
| ~ ssList(X1)
| cons(X2,X1) = app(cons(X2,nil),X1) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_41,plain,
( ~ ssItem(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| cons(X3,app(X2,X1)) = app(cons(X3,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_42,negated_conjecture,
( ~ equalelemsP(X1)
| ~ segmentP(X1,esk50_0)
| ~ frontsegP(esk51_0,X1)
| ~ neq(esk50_0,X1)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_43,negated_conjecture,
esk48_0 = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_30])]) ).
cnf(c_0_44,plain,
( ~ ssList(X1)
| segmentP(X1,nil) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_45,plain,
( cons(X2,X1) != X1
| ~ ssItem(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_46,plain,
( ~ ssItem(X1)
| ~ ssList(X2)
| cons(X1,app(nil,X2)) = cons(X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_29])]) ).
fof(c_0_47,plain,
! [X227] :
( app(X227,nil) = X227
| ~ ssList(X227) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax84])])]) ).
fof(c_0_48,plain,
! [X130,X131] :
( ssList(app(X130,X131))
| ~ ssList(X131)
| ~ ssList(X130) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax26])])])]) ).
fof(c_0_49,plain,
! [X222,X223,X224] :
( app(app(X222,X223),X224) = app(X222,app(X223,X224))
| ~ ssList(X224)
| ~ ssList(X223)
| ~ ssList(X222) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax82])])])]) ).
fof(c_0_50,plain,
! [X225,X226] :
( ( ~ ssList(X225)
| ~ ssList(X226)
| nil = app(X225,X226)
| nil != X225
| nil != X226 )
& ( ~ ssList(X225)
| ~ ssList(X226)
| nil != app(X225,X226)
| nil = X225 )
& ( ~ ssList(X225)
| ~ ssList(X226)
| nil != app(X225,X226)
| nil = X226 ) ),
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_51,negated_conjecture,
( ~ neq(nil,X1)
| ~ ssList(X1)
| ~ frontsegP(esk49_0,X1)
| ~ equalelemsP(X1) ),
inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_42,c_0_22]),c_0_43]),c_0_22]),c_0_43]),c_0_21]),c_0_44]) ).
fof(c_0_52,plain,
! [X206] :
( equalelemsP(cons(X206,nil))
| ~ ssItem(X206) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax73])])]) ).
cnf(c_0_53,plain,
( ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(app(nil,X2))
| cons(X1,X2) != app(nil,X2) ),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_54,plain,
( ~ ssList(X1)
| app(X1,nil) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
fof(c_0_55,plain,
! [X17,X19] :
( ( ~ ssList(X17)
| singletonP(X17)
| cons(X19,nil) != X17
| ~ ssItem(X19) )
& ( ~ ssList(X17)
| ~ singletonP(X17)
| cons(esk5_1(X17),nil) = X17 )
& ( ~ ssList(X17)
| ~ singletonP(X17)
| ssItem(esk5_1(X17)) ) ),
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])])])])])]) ).
cnf(c_0_56,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ssList(app(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_57,plain,
( ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| app(app(X1,X2),X3) = app(X1,app(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_58,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| nil != X2
| nil != X1
| nil = app(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
cnf(c_0_59,negated_conjecture,
( ~ ssList(X1)
| ~ frontsegP(esk49_0,X1)
| ~ equalelemsP(X1)
| nil = X1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_28]),c_0_29])]) ).
cnf(c_0_60,plain,
( ~ ssItem(X1)
| equalelemsP(cons(X1,nil)) ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_61,plain,
( ~ ssItem(X1)
| cons(X1,nil) != nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_29])]) ).
cnf(c_0_62,plain,
( ~ ssList(X2)
| cons(X1,nil) != X2
| ~ ssItem(X1)
| singletonP(X2) ),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_63,plain,
( ~ ssList(X1)
| ~ singletonP(X1)
| cons(esk5_1(X1),nil) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_64,plain,
( ~ ssList(X1)
| ~ singletonP(X1)
| ssItem(esk5_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_65,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ssList(app(X1,app(X2,X3))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_56]) ).
cnf(c_0_66,plain,
app(nil,nil) = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_58])]),c_0_29])]) ).
fof(c_0_67,plain,
! [X111,X112] :
( ssList(cons(X112,X111))
| ~ ssItem(X112)
| ~ ssList(X111) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax16])])])]) ).
cnf(c_0_68,negated_conjecture,
( ~ ssItem(X1)
| ~ ssList(cons(X1,nil))
| ~ frontsegP(esk49_0,cons(X1,nil)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_61]) ).
cnf(c_0_69,plain,
( ~ ssItem(X1)
| ~ ssList(cons(X1,nil))
| singletonP(cons(X1,nil)) ),
inference(er,[status(thm)],[c_0_62]) ).
cnf(c_0_70,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ singletonP(X1)
| cons(esk5_1(X1),X2) = app(X1,X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_63]),c_0_64]) ).
cnf(c_0_71,plain,
( ~ ssList(X1)
| ssList(app(X1,nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_29])]) ).
cnf(c_0_72,plain,
( ~ ssItem(X2)
| ~ ssList(X1)
| ssList(cons(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_67]) ).
fof(c_0_73,plain,
! [X20,X21,X23] :
( ( ~ ssList(X20)
| ~ ssList(X21)
| frontsegP(X20,X21)
| app(X21,X23) != X20
| ~ ssList(X23) )
& ( ~ ssList(X20)
| ~ ssList(X21)
| ~ frontsegP(X20,X21)
| app(X21,esk6_2(X20,X21)) = X20 )
& ( ~ ssList(X20)
| ~ ssList(X21)
| ~ frontsegP(X20,X21)
| ssList(esk6_2(X20,X21)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax5])])])])])]) ).
cnf(c_0_74,negated_conjecture,
( ~ ssList(X1)
| ~ singletonP(X1)
| ~ frontsegP(esk49_0,X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_63]),c_0_64]) ).
cnf(c_0_75,plain,
( ~ ssList(X1)
| ~ singletonP(X1)
| singletonP(app(X1,nil)) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_29])]),c_0_64]),c_0_71]) ).
cnf(c_0_76,plain,
( ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ssList(cons(X1,app(X2,X3))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_41]),c_0_72]) ).
cnf(c_0_77,plain,
( ~ ssList(X3)
| ~ ssList(X2)
| app(X2,X1) != X3
| ~ ssList(X1)
| frontsegP(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_73]) ).
cnf(c_0_78,negated_conjecture,
( ~ ssList(X1)
| ~ singletonP(X1)
| ~ frontsegP(esk49_0,app(X1,nil)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_71]) ).
cnf(c_0_79,plain,
( ~ ssItem(X1)
| ssList(cons(X1,nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_66]),c_0_29])]) ).
cnf(c_0_80,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| frontsegP(app(X1,X2),X1) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_77]),c_0_56]) ).
fof(c_0_81,plain,
! [X119] :
( ( ~ ssList(X119)
| nil = X119
| cons(esk45_1(X119),esk44_1(X119)) = X119 )
& ( ~ ssList(X119)
| nil = X119
| ssItem(esk45_1(X119)) )
& ( ~ ssList(X119)
| nil = X119
| ssList(esk44_1(X119)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax20])])])])]) ).
cnf(c_0_82,negated_conjecture,
( ~ ssItem(X1)
| ~ frontsegP(esk49_0,app(cons(X1,nil),nil)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_69]),c_0_79]) ).
cnf(c_0_83,plain,
( ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(cons(X1,nil))
| frontsegP(cons(X1,X2),cons(X1,nil)) ),
inference(spm,[status(thm)],[c_0_80,c_0_40]) ).
cnf(c_0_84,plain,
( ~ ssList(X1)
| nil = X1
| cons(esk45_1(X1),esk44_1(X1)) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_81]) ).
cnf(c_0_85,plain,
( ~ ssList(X1)
| nil = X1
| ssItem(esk45_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_81]) ).
cnf(c_0_86,plain,
( ~ ssList(X1)
| nil = X1
| ssList(esk44_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_81]) ).
cnf(c_0_87,negated_conjecture,
( ~ ssItem(X1)
| ~ frontsegP(esk49_0,cons(X1,nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_41]),c_0_66]),c_0_29])]) ).
cnf(c_0_88,plain,
( ~ ssList(X1)
| ~ ssList(cons(esk45_1(X1),nil))
| frontsegP(X1,cons(esk45_1(X1),nil))
| nil = X1 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_84]),c_0_85]),c_0_86]) ).
cnf(c_0_89,negated_conjecture,
ssList(esk49_0),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_90,negated_conjecture,
( nil != esk48_0
| ~ frontsegP(esk49_0,esk48_0)
| ~ neq(esk48_0,nil) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_91,negated_conjecture,
( nil != esk48_0
| neq(esk49_0,nil) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_92,negated_conjecture,
( ~ ssItem(esk45_1(esk49_0))
| esk49_0 = nil ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_88]),c_0_89])]),c_0_79]) ).
cnf(c_0_93,negated_conjecture,
( ~ neq(esk48_0,nil)
| esk48_0 != nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_90,c_0_25])]) ).
cnf(c_0_94,negated_conjecture,
neq(esk49_0,nil),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_91,c_0_43])]) ).
cnf(c_0_95,negated_conjecture,
esk49_0 = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_85]),c_0_89])]) ).
cnf(c_0_96,negated_conjecture,
~ neq(nil,nil),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_93,c_0_43]),c_0_43])]) ).
cnf(c_0_97,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_94,c_0_95]),c_0_96]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC099+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n010.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 21 07:55:55 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.44 Running first-order theorem proving
% 0.14/0.44 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
% 1.32/0.66 % Version: 3.5.1
% 1.32/0.66 % Preprocessing class: FSLSSMSSSSSNFFN.
% 1.32/0.66 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.32/0.66 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 1.32/0.66 % Starting new_bool_3 with 300s (1) cores
% 1.32/0.66 % Starting new_bool_1 with 300s (1) cores
% 1.32/0.66 % Starting sh5l with 300s (1) cores
% 1.32/0.66 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 415876 completed with status 0
% 1.32/0.66 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 1.32/0.66 % Preprocessing class: FSLSSMSSSSSNFFN.
% 1.32/0.66 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.32/0.66 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 1.32/0.66 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.32/0.66 % No SInE strategy applied
% 1.32/0.66 % Search class: FGHSF-FSLM21-MFFFFFNN
% 1.32/0.66 % Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 1.32/0.66 % Starting SubtermCWHack with 136s (1) cores
% 1.32/0.66 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 1.32/0.66 % Starting G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4d with 136s (1) cores
% 1.32/0.66 % Starting G-E--_110_C45_F1_PI_SE_CS_SP_PS_S4S with 136s (1) cores
% 1.32/0.66 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_TT_S0Y with 136s (1) cores
% 1.32/0.66 % SubtermCWHack with pid 415883 completed with status 0
% 1.32/0.66 % Result found by SubtermCWHack
% 1.32/0.66 % Preprocessing class: FSLSSMSSSSSNFFN.
% 1.32/0.66 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.32/0.66 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 1.32/0.66 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.32/0.66 % No SInE strategy applied
% 1.32/0.66 % Search class: FGHSF-FSLM21-MFFFFFNN
% 1.32/0.66 % Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 1.32/0.66 % Starting SubtermCWHack with 136s (1) cores
% 1.32/0.66 % Preprocessing time : 0.003 s
% 1.32/0.66
% 1.32/0.66 % Proof found!
% 1.32/0.66 % SZS status Theorem
% 1.32/0.66 % SZS output start CNFRefutation
% See solution above
% 1.32/0.66 % Parsed axioms : 96
% 1.32/0.66 % Removed by relevancy pruning/SinE : 0
% 1.32/0.66 % Initial clauses : 203
% 1.32/0.66 % Removed in clause preprocessing : 2
% 1.32/0.66 % Initial clauses in saturation : 201
% 1.32/0.66 % Processed clauses : 1906
% 1.32/0.66 % ...of these trivial : 0
% 1.32/0.66 % ...subsumed : 1323
% 1.32/0.66 % ...remaining for further processing : 583
% 1.32/0.66 % Other redundant clauses eliminated : 182
% 1.32/0.66 % Clauses deleted for lack of memory : 0
% 1.32/0.66 % Backward-subsumed : 26
% 1.32/0.66 % Backward-rewritten : 26
% 1.32/0.66 % Generated clauses : 6963
% 1.32/0.66 % ...of the previous two non-redundant : 6289
% 1.32/0.66 % ...aggressively subsumed : 0
% 1.32/0.66 % Contextual simplify-reflections : 282
% 1.32/0.66 % Paramodulations : 6776
% 1.32/0.66 % Factorizations : 0
% 1.32/0.66 % NegExts : 0
% 1.32/0.66 % Equation resolutions : 189
% 1.32/0.66 % Disequality decompositions : 0
% 1.32/0.66 % Total rewrite steps : 2720
% 1.32/0.66 % ...of those cached : 2698
% 1.32/0.66 % Propositional unsat checks : 0
% 1.32/0.66 % Propositional check models : 0
% 1.32/0.66 % Propositional check unsatisfiable : 0
% 1.32/0.66 % Propositional clauses : 0
% 1.32/0.66 % Propositional clauses after purity: 0
% 1.32/0.66 % Propositional unsat core size : 0
% 1.32/0.66 % Propositional preprocessing time : 0.000
% 1.32/0.66 % Propositional encoding time : 0.000
% 1.32/0.66 % Propositional solver time : 0.000
% 1.32/0.66 % Success case prop preproc time : 0.000
% 1.32/0.66 % Success case prop encoding time : 0.000
% 1.32/0.66 % Success case prop solver time : 0.000
% 1.32/0.66 % Current number of processed clauses : 508
% 1.32/0.66 % Positive orientable unit clauses : 19
% 1.32/0.66 % Positive unorientable unit clauses: 0
% 1.32/0.66 % Negative unit clauses : 3
% 1.32/0.66 % Non-unit-clauses : 486
% 1.32/0.66 % Current number of unprocessed clauses: 4434
% 1.32/0.66 % ...number of literals in the above : 27482
% 1.32/0.66 % Current number of archived formulas : 0
% 1.32/0.66 % Current number of archived clauses : 52
% 1.32/0.66 % Clause-clause subsumption calls (NU) : 76745
% 1.32/0.66 % Rec. Clause-clause subsumption calls : 20781
% 1.32/0.66 % Non-unit clause-clause subsumptions : 1469
% 1.32/0.66 % Unit Clause-clause subsumption calls : 133
% 1.32/0.66 % Rewrite failures with RHS unbound : 0
% 1.32/0.66 % BW rewrite match attempts : 7
% 1.32/0.66 % BW rewrite match successes : 7
% 1.32/0.66 % Condensation attempts : 0
% 1.32/0.66 % Condensation successes : 0
% 1.32/0.66 % Termbank termtop insertions : 137762
% 1.32/0.66 % Search garbage collected termcells : 4314
% 1.32/0.66
% 1.32/0.66 % -------------------------------------------------
% 1.32/0.66 % User time : 0.189 s
% 1.32/0.66 % System time : 0.009 s
% 1.32/0.66 % Total time : 0.198 s
% 1.32/0.66 % Maximum resident set size: 4272 pages
% 1.32/0.66
% 1.32/0.66 % -------------------------------------------------
% 1.32/0.66 % User time : 0.734 s
% 1.32/0.66 % System time : 0.029 s
% 1.32/0.66 % Total time : 0.763 s
% 1.32/0.66 % Maximum resident set size: 4608 pages
% 1.32/0.66 % E exiting
%------------------------------------------------------------------------------