%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SWC079+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 : n006.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 02:44:49 PM UTC 2026
% Result : Theorem 2.94s 1.02s
% Output : CNFRefutation 2.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 19
% Syntax : Number of formulae : 100 ( 13 unt; 0 def)
% Number of atoms : 407 ( 106 equ)
% Maximal formula atoms : 34 ( 4 avg)
% Number of connectives : 510 ( 203 ~; 200 |; 46 &)
% ( 5 <=>; 56 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-2 aty)
% Number of variables : 149 ( 0 sgn 83 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( ( neq(X4,nil)
| ~ neq(X2,nil) )
& ( ? [X6] :
( ? [X7] :
( neq(nil,X4)
& hd(X4) = X7
& cons(X7,nil) = X6
& ssItem(X7) )
& X3 != X6
& ssList(X6) )
| ? [X5] :
( segmentP(X1,X5)
& segmentP(X2,X5)
& neq(X5,nil)
& ssList(X5) )
| ~ neq(X2,nil) ) )
| X1 != X3
| X2 != X4 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
fof(ax26,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ssList(app(X1,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax26) ).
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(ax16,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> ssList(cons(X2,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax16) ).
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(ax17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(ax21,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> nil != cons(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax21) ).
fof(ax22,axiom,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> ssItem(hd(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax22) ).
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(ax23,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> hd(cons(X2,X1)) = X2 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax23) ).
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(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(ax78,axiom,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> cons(hd(X1),tl(X1)) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax78) ).
fof(ax24,axiom,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> ssList(tl(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax24) ).
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/sandbox2/benchmark/Axioms/SWC001+0.ax',ax56) ).
fof(ax28,axiom,
! [X1] :
( ssList(X1)
=> app(nil,X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax28) ).
fof(ax55,axiom,
! [X1] :
( ssList(X1)
=> segmentP(X1,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax55) ).
fof(ax58,axiom,
! [X1] :
( ssList(X1)
=> ( segmentP(nil,X1)
<=> nil = X1 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax58) ).
fof(ax57,axiom,
! [X1] :
( ssList(X1)
=> segmentP(X1,nil) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax57) ).
fof(c_0_19,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( ( neq(X4,nil)
| ~ neq(X2,nil) )
& ( ? [X6] :
( ? [X7] :
( neq(nil,X4)
& hd(X4) = X7
& cons(X7,nil) = X6
& ssItem(X7) )
& X3 != X6
& ssList(X6) )
| ? [X5] :
( segmentP(X1,X5)
& segmentP(X2,X5)
& neq(X5,nil)
& ssList(X5) )
| ~ neq(X2,nil) ) )
| X1 != X3
| X2 != X4 ) ) ) ) ),
inference(assume_negation,[status(cth)],[co1]) ).
fof(c_0_20,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( ( neq(X4,nil)
| ~ neq(X2,nil) )
& ( ? [X6] :
( ? [X7] :
( neq(nil,X4)
& hd(X4) = X7
& cons(X7,nil) = X6
& ssItem(X7) )
& X3 != X6
& ssList(X6) )
| ? [X5] :
( segmentP(X1,X5)
& segmentP(X2,X5)
& neq(X5,nil)
& ssList(X5) )
| ~ neq(X2,nil) ) )
| X1 != X3
| X2 != X4 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_19]) ).
fof(c_0_21,negated_conjecture,
! [X256,X257,X258] :
( ( ~ neq(nil,esk51_0)
| hd(esk51_0) != X258
| cons(X258,nil) != X257
| ~ ssItem(X258)
| esk50_0 = X257
| ~ ssList(X257)
| ~ neq(esk51_0,nil) )
& ( ~ neq(nil,esk51_0)
| hd(esk51_0) != X258
| cons(X258,nil) != X257
| ~ ssItem(X258)
| esk50_0 = X257
| ~ ssList(X257)
| neq(esk49_0,nil) )
& ( ~ segmentP(esk48_0,X256)
| ~ segmentP(esk49_0,X256)
| ~ neq(X256,nil)
| ~ ssList(X256)
| ~ neq(esk51_0,nil) )
& ( ~ segmentP(esk48_0,X256)
| ~ segmentP(esk49_0,X256)
| ~ neq(X256,nil)
| ~ ssList(X256)
| neq(esk49_0,nil) )
& ( neq(esk49_0,nil)
| ~ neq(esk51_0,nil) )
& ( neq(esk49_0,nil)
| neq(esk49_0,nil) )
& 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_20])])])])])]) ).
fof(c_0_22,plain,
! [X131,X132] :
( ssList(app(X131,X132))
| ~ ssList(X132)
| ~ ssList(X131) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax26])])])]) ).
fof(c_0_23,plain,
! [X133,X134,X135] :
( cons(X135,app(X134,X133)) = app(cons(X135,X134),X133)
| ~ ssItem(X135)
| ~ ssList(X134)
| ~ ssList(X133) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax27])])])]) ).
fof(c_0_24,plain,
! [X112,X113] :
( ssList(cons(X113,X112))
| ~ ssItem(X113)
| ~ ssList(X112) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax16])])])]) ).
fof(c_0_25,plain,
! [X226,X227] :
( ( ~ ssList(X226)
| ~ ssList(X227)
| nil = app(X226,X227)
| nil != X226
| nil != X227 )
& ( ~ ssList(X226)
| ~ ssList(X227)
| nil != app(X226,X227)
| nil = X226 )
& ( ~ ssList(X226)
| ~ ssList(X227)
| nil != app(X226,X227)
| nil = X227 ) ),
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_26,negated_conjecture,
( neq(esk49_0,nil)
| neq(esk49_0,nil) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_27,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ssList(app(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_28,plain,
( ~ ssItem(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| cons(X3,app(X2,X1)) = app(cons(X3,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_29,plain,
( ~ ssItem(X2)
| ~ ssList(X1)
| ssList(cons(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_30,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| nil != X2
| nil != X1
| nil = app(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_31,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[ax17]) ).
fof(c_0_32,plain,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> nil != cons(X2,X1) ) ),
inference(fof_simplification,[status(thm)],[ax21]) ).
cnf(c_0_33,negated_conjecture,
neq(esk49_0,nil),
inference(cn,[status(thm)],[c_0_26]) ).
cnf(c_0_34,negated_conjecture,
esk49_0 = esk51_0,
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_35,plain,
( ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ssList(cons(X1,app(X2,X3))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29]) ).
cnf(c_0_36,plain,
app(nil,nil) = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_30])]),c_0_31])]) ).
fof(c_0_37,plain,
! [X123,X124] :
( nil != cons(X124,X123)
| ~ ssItem(X124)
| ~ ssList(X123) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_32])])])]) ).
cnf(c_0_38,negated_conjecture,
( ~ neq(nil,esk51_0)
| hd(esk51_0) != X2
| cons(X2,nil) != X1
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ neq(esk51_0,nil)
| esk50_0 = X1 ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_39,negated_conjecture,
esk48_0 = esk50_0,
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_40,negated_conjecture,
neq(esk51_0,nil),
inference(rw,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_41,plain,
( ~ ssItem(X1)
| ssList(cons(X1,nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_31])]) ).
fof(c_0_42,plain,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> ssItem(hd(X1)) ) ),
inference(fof_simplification,[status(thm)],[ax22]) ).
fof(c_0_43,plain,
! [X21,X22,X24] :
( ( ~ ssList(X21)
| ~ ssList(X22)
| frontsegP(X21,X22)
| app(X22,X24) != X21
| ~ ssList(X24) )
& ( ~ ssList(X21)
| ~ ssList(X22)
| ~ frontsegP(X21,X22)
| app(X22,esk6_2(X21,X22)) = X21 )
& ( ~ ssList(X21)
| ~ ssList(X22)
| ~ frontsegP(X21,X22)
| ssList(esk6_2(X21,X22)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax5])])])])])]) ).
fof(c_0_44,plain,
! [X126,X127] :
( hd(cons(X127,X126)) = X127
| ~ ssItem(X127)
| ~ ssList(X126) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax23])])])]) ).
cnf(c_0_45,plain,
( nil != cons(X2,X1)
| ~ ssItem(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_46,negated_conjecture,
( ~ ssItem(hd(esk51_0))
| ~ neq(nil,esk51_0)
| cons(hd(esk51_0),nil) = esk48_0 ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_38,c_0_39]),c_0_40])])])]),c_0_41]) ).
fof(c_0_47,plain,
! [X125] :
( ssItem(hd(X125))
| nil = X125
| ~ ssList(X125) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_42])])]) ).
fof(c_0_48,plain,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
inference(fof_simplification,[status(thm)],[ax15]) ).
cnf(c_0_49,plain,
( ~ ssList(X3)
| ~ ssList(X2)
| app(X2,X1) != X3
| ~ ssList(X1)
| frontsegP(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
fof(c_0_50,plain,
! [X221,X222] :
( cons(X222,X221) = app(cons(X222,nil),X221)
| ~ ssItem(X222)
| ~ ssList(X221) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax81])])])]) ).
fof(c_0_51,plain,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> cons(hd(X1),tl(X1)) = X1 ) ),
inference(fof_simplification,[status(thm)],[ax78]) ).
fof(c_0_52,plain,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> ssList(tl(X1)) ) ),
inference(fof_simplification,[status(thm)],[ax24]) ).
cnf(c_0_53,plain,
( ~ ssItem(X2)
| ~ ssList(X1)
| hd(cons(X2,X1)) = X2 ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_54,negated_conjecture,
( ~ ssItem(hd(esk51_0))
| ~ neq(nil,esk51_0)
| esk48_0 != nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_31])]) ).
cnf(c_0_55,plain,
( ~ ssList(X1)
| ssItem(hd(X1))
| nil = X1 ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_56,negated_conjecture,
ssList(esk51_0),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
fof(c_0_57,plain,
! [X110,X111] :
( ( ~ ssList(X110)
| ~ ssList(X111)
| neq(X110,X111)
| X110 = X111 )
& ( ~ ssList(X110)
| ~ ssList(X111)
| X110 != X111
| ~ neq(X110,X111) ) ),
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_48])])])])]) ).
cnf(c_0_58,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| frontsegP(app(X1,X2),X1) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_49]),c_0_27]) ).
cnf(c_0_59,plain,
( ~ ssItem(X2)
| ~ ssList(X1)
| cons(X2,X1) = app(cons(X2,nil),X1) ),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
fof(c_0_60,plain,
! [X214] :
( cons(hd(X214),tl(X214)) = X214
| nil = X214
| ~ ssList(X214) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_51])])]) ).
fof(c_0_61,plain,
! [X128] :
( ssList(tl(X128))
| nil = X128
| ~ ssList(X128) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_52])])]) ).
cnf(c_0_62,negated_conjecture,
( ~ ssItem(hd(esk51_0))
| ~ neq(nil,esk51_0)
| hd(esk48_0) = hd(esk51_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_46]),c_0_31])]) ).
cnf(c_0_63,negated_conjecture,
( ~ neq(nil,esk51_0)
| esk48_0 != nil
| esk51_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_56])]) ).
cnf(c_0_64,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| neq(X1,X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
fof(c_0_65,plain,
! [X191,X192,X193,X194] :
( segmentP(app(app(X193,X191),X194),X192)
| ~ segmentP(X191,X192)
| ~ ssList(X194)
| ~ ssList(X193)
| ~ ssList(X192)
| ~ ssList(X191) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax56])])])]) ).
fof(c_0_66,plain,
! [X136] :
( app(nil,X136) = X136
| ~ ssList(X136) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax28])])]) ).
cnf(c_0_67,plain,
( ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(cons(X1,nil))
| frontsegP(cons(X1,X2),cons(X1,nil)) ),
inference(spm,[status(thm)],[c_0_58,c_0_59]) ).
cnf(c_0_68,plain,
( ~ ssList(X1)
| cons(hd(X1),tl(X1)) = X1
| nil = X1 ),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
cnf(c_0_69,plain,
( ~ ssList(X1)
| ssList(tl(X1))
| nil = X1 ),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
cnf(c_0_70,negated_conjecture,
( ~ neq(nil,esk51_0)
| esk51_0 = nil
| hd(esk48_0) = hd(esk51_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_55]),c_0_56])]) ).
cnf(c_0_71,negated_conjecture,
ssList(esk48_0),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_72,negated_conjecture,
( esk48_0 != nil
| esk51_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_56]),c_0_31])]) ).
cnf(c_0_73,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_65]) ).
cnf(c_0_74,plain,
( ~ ssList(X1)
| app(nil,X1) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_66]) ).
cnf(c_0_75,plain,
( ~ ssList(X1)
| ~ ssList(cons(hd(X1),nil))
| frontsegP(X1,cons(hd(X1),nil))
| nil = X1 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_68]),c_0_55]),c_0_69]) ).
cnf(c_0_76,negated_conjecture,
( ~ neq(nil,esk51_0)
| ssItem(hd(esk51_0))
| esk51_0 = nil ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_70]),c_0_71])]),c_0_72]) ).
cnf(c_0_77,negated_conjecture,
( ~ segmentP(esk48_0,X1)
| ~ segmentP(esk49_0,X1)
| ~ neq(X1,nil)
| ~ ssList(X1)
| ~ neq(esk51_0,nil) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_78,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_73,c_0_74]),c_0_31])]) ).
cnf(c_0_79,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ~ frontsegP(X2,X1)
| app(X1,esk6_2(X2,X1)) = X2 ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_80,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ frontsegP(X1,X2)
| ssList(esk6_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_81,negated_conjecture,
( ~ neq(nil,esk51_0)
| frontsegP(esk51_0,esk48_0)
| esk51_0 = nil ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_46]),c_0_71]),c_0_56])]),c_0_76]) ).
cnf(c_0_82,negated_conjecture,
( ~ neq(X1,nil)
| ~ ssList(X1)
| ~ segmentP(esk51_0,X1)
| ~ segmentP(esk48_0,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_77,c_0_34]),c_0_40])]) ).
fof(c_0_83,plain,
! [X190] :
( segmentP(X190,X190)
| ~ ssList(X190) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax55])])]) ).
cnf(c_0_84,plain,
( ~ ssList(X1)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ frontsegP(X1,X3)
| ~ segmentP(X3,X2)
| segmentP(X1,X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_79]),c_0_80]) ).
cnf(c_0_85,negated_conjecture,
( frontsegP(esk51_0,esk48_0)
| esk51_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_64]),c_0_56]),c_0_31])]) ).
cnf(c_0_86,negated_conjecture,
( ~ ssList(X1)
| ~ segmentP(esk51_0,X1)
| ~ segmentP(esk48_0,X1)
| X1 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_64]),c_0_31])]) ).
cnf(c_0_87,plain,
( ~ ssList(X1)
| segmentP(X1,X1) ),
inference(split_conjunct,[status(thm)],[c_0_83]) ).
cnf(c_0_88,negated_conjecture,
( ~ ssList(X1)
| ~ segmentP(esk48_0,X1)
| segmentP(esk51_0,X1)
| esk51_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_85]),c_0_71]),c_0_56])]) ).
fof(c_0_89,plain,
! [X196] :
( ( ~ ssList(X196)
| segmentP(nil,X196)
| nil != X196 )
& ( ~ ssList(X196)
| nil = X196
| ~ segmentP(nil,X196) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax58])])])]) ).
cnf(c_0_90,negated_conjecture,
( ~ segmentP(esk51_0,esk48_0)
| esk48_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_87]),c_0_71])]) ).
cnf(c_0_91,negated_conjecture,
( segmentP(esk51_0,esk48_0)
| esk51_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_87]),c_0_71])]) ).
cnf(c_0_92,plain,
( ~ ssList(X1)
| nil != X1
| segmentP(nil,X1) ),
inference(split_conjunct,[status(thm)],[c_0_89]) ).
cnf(c_0_93,negated_conjecture,
( ~ segmentP(esk51_0,esk51_0)
| ~ segmentP(esk48_0,esk51_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_40]),c_0_56])]) ).
cnf(c_0_94,negated_conjecture,
esk51_0 = nil,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_91]),c_0_72]) ).
cnf(c_0_95,plain,
segmentP(nil,nil),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_92]),c_0_31])]) ).
fof(c_0_96,plain,
! [X195] :
( segmentP(X195,nil)
| ~ ssList(X195) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax57])])]) ).
cnf(c_0_97,negated_conjecture,
~ segmentP(esk48_0,nil),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_93,c_0_94]),c_0_94]),c_0_94]),c_0_95])]) ).
cnf(c_0_98,plain,
( ~ ssList(X1)
| segmentP(X1,nil) ),
inference(split_conjunct,[status(thm)],[c_0_96]) ).
cnf(c_0_99,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_98]),c_0_71])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC079+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 : n006.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 07:53:42 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.42 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
% 2.94/1.02 % Version: 3.5.1
% 2.94/1.02 % Preprocessing class: FSLSSMSSSSSNFFN.
% 2.94/1.02 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.94/1.02 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 2.94/1.02 % Starting new_bool_3 with 300s (1) cores
% 2.94/1.02 % Starting new_bool_1 with 300s (1) cores
% 2.94/1.02 % Starting sh5l with 300s (1) cores
% 2.94/1.02 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 2359194 completed with status 0
% 2.94/1.02 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 2.94/1.02 % Preprocessing class: FSLSSMSSSSSNFFN.
% 2.94/1.02 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.94/1.02 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 2.94/1.02 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 2.94/1.02 % No SInE strategy applied
% 2.94/1.02 % Search class: FGHSF-FSLM21-MFFFFFNN
% 2.94/1.02 % Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 2.94/1.02 % Starting SubtermCWHack with 136s (1) cores
% 2.94/1.02 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 2.94/1.02 % Starting G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4d with 136s (1) cores
% 2.94/1.02 % Starting G-E--_110_C45_F1_PI_SE_CS_SP_PS_S4S with 136s (1) cores
% 2.94/1.02 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_TT_S0Y with 136s (1) cores
% 2.94/1.02 % SubtermCWHack with pid 2359207 completed with status 0
% 2.94/1.02 % Result found by SubtermCWHack
% 2.94/1.02 % Preprocessing class: FSLSSMSSSSSNFFN.
% 2.94/1.02 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.94/1.02 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 2.94/1.02 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 2.94/1.02 % No SInE strategy applied
% 2.94/1.02 % Search class: FGHSF-FSLM21-MFFFFFNN
% 2.94/1.02 % Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 2.94/1.02 % Starting SubtermCWHack with 136s (1) cores
% 2.94/1.02 % Preprocessing time : 0.002 s
% 2.94/1.02
% 2.94/1.02 % Proof found!
% 2.94/1.02 % SZS status Theorem
% 2.94/1.02 % SZS output start CNFRefutation
% See solution above
% 2.94/1.02 % Parsed axioms : 96
% 2.94/1.02 % Removed by relevancy pruning/SinE : 0
% 2.94/1.02 % Initial clauses : 202
% 2.94/1.02 % Removed in clause preprocessing : 2
% 2.94/1.02 % Initial clauses in saturation : 200
% 2.94/1.02 % Processed clauses : 4606
% 2.94/1.02 % ...of these trivial : 3
% 2.94/1.02 % ...subsumed : 3493
% 2.94/1.02 % ...remaining for further processing : 1110
% 2.94/1.02 % Other redundant clauses eliminated : 372
% 2.94/1.02 % Clauses deleted for lack of memory : 0
% 2.94/1.02 % Backward-subsumed : 74
% 2.94/1.02 % Backward-rewritten : 224
% 2.94/1.02 % Generated clauses : 28490
% 2.94/1.02 % ...of the previous two non-redundant : 26340
% 2.94/1.02 % ...aggressively subsumed : 0
% 2.94/1.02 % Contextual simplify-reflections : 533
% 2.94/1.02 % Paramodulations : 28109
% 2.94/1.02 % Factorizations : 0
% 2.94/1.02 % NegExts : 0
% 2.94/1.02 % Equation resolutions : 384
% 2.94/1.02 % Disequality decompositions : 0
% 2.94/1.02 % Total rewrite steps : 14320
% 2.94/1.02 % ...of those cached : 14300
% 2.94/1.02 % Propositional unsat checks : 0
% 2.94/1.02 % Propositional check models : 0
% 2.94/1.02 % Propositional check unsatisfiable : 0
% 2.94/1.02 % Propositional clauses : 0
% 2.94/1.02 % Propositional clauses after purity: 0
% 2.94/1.02 % Propositional unsat core size : 0
% 2.94/1.02 % Propositional preprocessing time : 0.000
% 2.94/1.02 % Propositional encoding time : 0.000
% 2.94/1.02 % Propositional solver time : 0.000
% 2.94/1.02 % Success case prop preproc time : 0.000
% 2.94/1.02 % Success case prop encoding time : 0.000
% 2.94/1.02 % Success case prop solver time : 0.000
% 2.94/1.02 % Current number of processed clauses : 788
% 2.94/1.02 % Positive orientable unit clauses : 19
% 2.94/1.02 % Positive unorientable unit clauses: 0
% 2.94/1.02 % Negative unit clauses : 3
% 2.94/1.02 % Non-unit-clauses : 766
% 2.94/1.02 % Current number of unprocessed clauses: 21751
% 2.94/1.02 % ...number of literals in the above : 133140
% 2.94/1.02 % Current number of archived formulas : 0
% 2.94/1.02 % Current number of archived clauses : 298
% 2.94/1.02 % Clause-clause subsumption calls (NU) : 180904
% 2.94/1.02 % Rec. Clause-clause subsumption calls : 65630
% 2.94/1.02 % Non-unit clause-clause subsumptions : 3756
% 2.94/1.02 % Unit Clause-clause subsumption calls : 556
% 2.94/1.02 % Rewrite failures with RHS unbound : 0
% 2.94/1.02 % BW rewrite match attempts : 5
% 2.94/1.02 % BW rewrite match successes : 5
% 2.94/1.02 % Condensation attempts : 0
% 2.94/1.02 % Condensation successes : 0
% 2.94/1.02 % Termbank termtop insertions : 528712
% 2.94/1.02 % Search garbage collected termcells : 4345
% 2.94/1.02
% 2.94/1.02 % -------------------------------------------------
% 2.94/1.02 % User time : 0.550 s
% 2.94/1.02 % System time : 0.020 s
% 2.94/1.02 % Total time : 0.570 s
% 2.94/1.02 % Maximum resident set size: 4272 pages
% 2.94/1.02
% 2.94/1.02 % -------------------------------------------------
% 2.94/1.02 % User time : 1.733 s
% 2.94/1.02 % System time : 0.068 s
% 2.94/1.02 % Total time : 1.801 s
% 2.94/1.02 % Maximum resident set size: 4608 pages
% 2.94/1.02 % E exiting
%------------------------------------------------------------------------------