%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SWC409+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 : n007.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 02:46:13 PM UTC 2026
% Result : Theorem 2.51s 0.81s
% Output : CNFRefutation 2.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 15
% Syntax : Number of formulae : 102 ( 24 unt; 0 def)
% Number of atoms : 387 ( 113 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 455 ( 170 ~; 195 |; 38 &)
% ( 4 <=>; 48 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 6 con; 0-2 aty)
% Number of variables : 140 ( 0 sgn 75 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( nil = X4
& nil != X3 )
| ! [X7] :
( ssItem(X7)
=> ( memberP(X1,X7)
| ~ memberP(X2,X7) ) )
| ? [X5] :
( ? [X6] :
( app(cons(X5,nil),X6) = X4
& app(X6,cons(X5,nil)) != X3
& ssList(X6) )
& ssItem(X5) )
| X1 != X3
| X2 != X4 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
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(ax26,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ssList(app(X1,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax26) ).
fof(ax3,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> ( memberP(X1,X2)
<=> ? [X3] :
( ? [X4] :
( app(X3,cons(X2,X4)) = X1
& ssList(X4) )
& ssList(X3) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax3) ).
fof(ax16,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> ssList(cons(X2,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax16) ).
fof(ax85,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( nil != X1
=> hd(app(X1,X2)) = hd(X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax85) ).
fof(ax22,axiom,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> ssItem(hd(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax22) ).
fof(ax28,axiom,
! [X1] :
( ssList(X1)
=> app(nil,X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax28) ).
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(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(ax23,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> hd(cons(X2,X1)) = X2 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax23) ).
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(ax17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(ax36,axiom,
! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( memberP(app(X2,X3),X1)
<=> ( memberP(X3,X1)
| memberP(X2,X1) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax36) ).
fof(ax37,axiom,
! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssList(X3)
=> ( memberP(cons(X2,X3),X1)
<=> ( memberP(X3,X1)
| X1 = X2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax37) ).
fof(c_0_15,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( nil = X4
& nil != X3 )
| ! [X7] :
( ssItem(X7)
=> ( memberP(X1,X7)
| ~ memberP(X2,X7) ) )
| ? [X5] :
( ? [X6] :
( app(cons(X5,nil),X6) = X4
& app(X6,cons(X5,nil)) != X3
& ssList(X6) )
& ssItem(X5) )
| X1 != X3
| X2 != X4 ) ) ) ) ),
inference(assume_negation,[status(cth)],[co1]) ).
fof(c_0_16,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( nil = X4
& nil != X3 )
| ! [X7] :
( ssItem(X7)
=> ( memberP(X1,X7)
| ~ memberP(X2,X7) ) )
| ? [X5] :
( ? [X6] :
( app(cons(X5,nil),X6) = X4
& app(X6,cons(X5,nil)) != X3
& ssList(X6) )
& ssItem(X5) )
| X1 != X3
| X2 != X4 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_15]) ).
fof(c_0_17,negated_conjecture,
! [X256,X257] :
( ( nil != esk51_0
| nil = esk50_0 )
& ~ memberP(esk48_0,esk52_0)
& memberP(esk49_0,esk52_0)
& ssItem(esk52_0)
& ( app(cons(X256,nil),X257) != esk51_0
| app(X257,cons(X256,nil)) = esk50_0
| ~ ssList(X257)
| ~ ssItem(X256) )
& 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(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_16])])])])]) ).
fof(c_0_18,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_19,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_20,plain,
! [X12,X13,X16,X17] :
( ( ~ ssList(X12)
| ~ ssItem(X13)
| memberP(X12,X13)
| app(X16,cons(X13,X17)) != X12
| ~ ssList(X17)
| ~ ssList(X16) )
& ( ~ ssList(X12)
| ~ ssItem(X13)
| ~ memberP(X12,X13)
| app(esk3_2(X12,X13),cons(X13,esk4_2(X12,X13))) = X12 )
& ( ~ ssList(X12)
| ~ ssItem(X13)
| ~ memberP(X12,X13)
| ssList(esk4_2(X12,X13)) )
& ( ~ ssList(X12)
| ~ ssItem(X13)
| ~ memberP(X12,X13)
| ssList(esk3_2(X12,X13)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax3])])])])])]) ).
cnf(c_0_21,negated_conjecture,
memberP(esk49_0,esk52_0),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_22,negated_conjecture,
esk49_0 = esk51_0,
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_23,negated_conjecture,
ssList(esk49_0),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_24,plain,
( ~ ssList(X3)
| ~ ssList(X2)
| app(X2,X1) != X3
| ~ ssList(X1)
| frontsegP(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_25,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ssList(app(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_26,plain,
( ~ ssList(X1)
| ~ ssItem(X2)
| ~ memberP(X1,X2)
| app(esk3_2(X1,X2),cons(X2,esk4_2(X1,X2))) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_27,negated_conjecture,
memberP(esk51_0,esk52_0),
inference(rw,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_28,negated_conjecture,
ssList(esk51_0),
inference(rw,[status(thm)],[c_0_23,c_0_22]) ).
cnf(c_0_29,negated_conjecture,
ssItem(esk52_0),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_30,plain,
( ~ ssList(X1)
| ~ ssItem(X2)
| ~ memberP(X1,X2)
| ssList(esk3_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_31,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| frontsegP(app(X1,X2),X1) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_24]),c_0_25]) ).
cnf(c_0_32,negated_conjecture,
app(esk3_2(esk51_0,esk52_0),cons(esk52_0,esk4_2(esk51_0,esk52_0))) = esk51_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28]),c_0_29])]) ).
cnf(c_0_33,negated_conjecture,
ssList(esk3_2(esk51_0,esk52_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_27]),c_0_28]),c_0_29])]) ).
fof(c_0_34,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])])])]) ).
cnf(c_0_35,plain,
( ~ ssList(X1)
| ~ ssItem(X2)
| ~ memberP(X1,X2)
| ssList(esk4_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
fof(c_0_36,plain,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( nil != X1
=> hd(app(X1,X2)) = hd(X1) ) ) ),
inference(fof_simplification,[status(thm)],[ax85]) ).
cnf(c_0_37,negated_conjecture,
( ~ ssList(cons(esk52_0,esk4_2(esk51_0,esk52_0)))
| frontsegP(esk51_0,esk3_2(esk51_0,esk52_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_33])]) ).
cnf(c_0_38,plain,
( ~ ssItem(X2)
| ~ ssList(X1)
| ssList(cons(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_39,negated_conjecture,
ssList(esk4_2(esk51_0,esk52_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_27]),c_0_28]),c_0_29])]) ).
fof(c_0_40,plain,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> ssItem(hd(X1)) ) ),
inference(fof_simplification,[status(thm)],[ax22]) ).
fof(c_0_41,plain,
! [X229,X230] :
( hd(app(X229,X230)) = hd(X229)
| nil = X229
| ~ ssList(X230)
| ~ ssList(X229) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_36])])])]) ).
cnf(c_0_42,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ~ frontsegP(X2,X1)
| app(X1,esk6_2(X2,X1)) = X2 ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_43,negated_conjecture,
frontsegP(esk51_0,esk3_2(esk51_0,esk52_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_39]),c_0_29])]) ).
cnf(c_0_44,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ frontsegP(X1,X2)
| ssList(esk6_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
fof(c_0_45,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_40])])]) ).
cnf(c_0_46,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| hd(app(X1,X2)) = hd(X1)
| nil = X1 ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_47,negated_conjecture,
app(esk3_2(esk51_0,esk52_0),esk6_2(esk51_0,esk3_2(esk51_0,esk52_0))) = esk51_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_28]),c_0_33])]) ).
cnf(c_0_48,negated_conjecture,
ssList(esk6_2(esk51_0,esk3_2(esk51_0,esk52_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_43]),c_0_33]),c_0_28])]) ).
cnf(c_0_49,plain,
( ~ ssList(X1)
| ssItem(hd(X1))
| nil = X1 ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_50,negated_conjecture,
( esk3_2(esk51_0,esk52_0) = nil
| hd(esk3_2(esk51_0,esk52_0)) = hd(esk51_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_48]),c_0_33])]) ).
fof(c_0_51,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_52,negated_conjecture,
( ssItem(hd(esk51_0))
| esk3_2(esk51_0,esk52_0) = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_33])]) ).
fof(c_0_53,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])])])]) ).
cnf(c_0_54,plain,
( ~ ssList(X1)
| app(nil,X1) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_55,negated_conjecture,
( ssItem(hd(esk51_0))
| app(nil,cons(esk52_0,esk4_2(esk51_0,esk52_0))) = esk51_0 ),
inference(spm,[status(thm)],[c_0_32,c_0_52]) ).
cnf(c_0_56,negated_conjecture,
( app(cons(X1,nil),X2) != esk51_0
| ~ ssList(X2)
| ~ ssItem(X1)
| app(X2,cons(X1,nil)) = esk50_0 ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_57,plain,
( ~ ssItem(X2)
| ~ ssList(X1)
| cons(X2,X1) = app(cons(X2,nil),X1) ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
fof(c_0_58,plain,
! [X120] :
( ( ~ ssList(X120)
| nil = X120
| cons(esk45_1(X120),esk44_1(X120)) = X120 )
& ( ~ ssList(X120)
| nil = X120
| ssItem(esk45_1(X120)) )
& ( ~ ssList(X120)
| nil = X120
| ssList(esk44_1(X120)) ) ),
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_59,negated_conjecture,
( ~ ssList(cons(esk52_0,esk4_2(esk51_0,esk52_0)))
| ssItem(hd(esk51_0))
| cons(esk52_0,esk4_2(esk51_0,esk52_0)) = esk51_0 ),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_60,negated_conjecture,
( ~ ssItem(X2)
| ~ ssList(X1)
| cons(X2,X1) != esk51_0
| app(X1,cons(X2,nil)) = esk50_0 ),
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_61,plain,
( ~ ssList(X1)
| nil = X1
| cons(esk45_1(X1),esk44_1(X1)) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
fof(c_0_62,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_63,plain,
( ~ ssList(X4)
| ~ ssItem(X3)
| app(X1,cons(X3,X2)) != X4
| ~ ssList(X2)
| ~ ssList(X1)
| memberP(X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_64,negated_conjecture,
( ssItem(hd(esk51_0))
| cons(esk52_0,esk4_2(esk51_0,esk52_0)) = esk51_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_38]),c_0_39]),c_0_29])]) ).
cnf(c_0_65,negated_conjecture,
ssList(esk48_0),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_66,negated_conjecture,
esk48_0 = esk50_0,
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_67,negated_conjecture,
~ memberP(esk48_0,esk52_0),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_68,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])])])]) ).
cnf(c_0_69,negated_conjecture,
( ~ ssItem(esk45_1(esk51_0))
| ~ ssList(esk44_1(esk51_0))
| esk51_0 = nil
| app(esk44_1(esk51_0),cons(esk45_1(esk51_0),nil)) = esk50_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61])]),c_0_28])]) ).
cnf(c_0_70,plain,
( ~ ssList(X1)
| nil = X1
| ssList(esk44_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_71,plain,
( ~ ssItem(X2)
| ~ ssList(X1)
| hd(cons(X2,X1)) = X2 ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_72,plain,
( ~ ssList(X1)
| nil = X1
| ssItem(esk45_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_73,plain,
( ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X3)
| ~ ssList(app(X1,cons(X2,X3)))
| memberP(app(X1,cons(X2,X3)),X2) ),
inference(er,[status(thm)],[c_0_63]) ).
cnf(c_0_74,negated_conjecture,
( ssItem(hd(esk51_0))
| app(esk4_2(esk51_0,esk52_0),cons(esk52_0,nil)) = esk50_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_64]),c_0_39]),c_0_29])]) ).
cnf(c_0_75,negated_conjecture,
ssList(esk50_0),
inference(rw,[status(thm)],[c_0_65,c_0_66]) ).
cnf(c_0_76,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[ax17]) ).
cnf(c_0_77,negated_conjecture,
~ memberP(esk50_0,esk52_0),
inference(rw,[status(thm)],[c_0_67,c_0_66]) ).
cnf(c_0_78,plain,
( ~ ssItem(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| cons(X3,app(X2,X1)) = app(cons(X3,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_68]) ).
cnf(c_0_79,negated_conjecture,
( ~ ssItem(esk45_1(esk51_0))
| esk51_0 = nil
| app(esk44_1(esk51_0),cons(esk45_1(esk51_0),nil)) = esk50_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_28])]) ).
cnf(c_0_80,plain,
( ~ ssList(X1)
| nil = X1
| esk45_1(X1) = hd(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_61]),c_0_72]),c_0_70]) ).
cnf(c_0_81,negated_conjecture,
ssItem(hd(esk51_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_74]),c_0_75]),c_0_76]),c_0_39]),c_0_29])]),c_0_77]) ).
cnf(c_0_82,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| nil = X1
| cons(esk45_1(X1),app(esk44_1(X1),X2)) = app(X1,X2) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_61]),c_0_72]),c_0_70]) ).
cnf(c_0_83,negated_conjecture,
( esk51_0 = nil
| app(esk44_1(esk51_0),cons(hd(esk51_0),nil)) = esk50_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_80]),c_0_81]),c_0_28])]) ).
fof(c_0_84,plain,
! [X152,X153,X154] :
( ( ~ ssItem(X152)
| ~ ssList(X153)
| ~ ssList(X154)
| memberP(app(X153,X154),X152)
| ~ memberP(X154,X152) )
& ( ~ ssItem(X152)
| ~ ssList(X153)
| ~ ssList(X154)
| memberP(app(X153,X154),X152)
| ~ memberP(X153,X152) )
& ( ~ ssItem(X152)
| ~ ssList(X153)
| ~ ssList(X154)
| memberP(X154,X152)
| memberP(X153,X152)
| ~ memberP(app(X153,X154),X152) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax36])])])])]) ).
cnf(c_0_85,negated_conjecture,
( ~ ssList(cons(hd(esk51_0),nil))
| esk51_0 = nil
| cons(esk45_1(esk51_0),esk50_0) = app(esk51_0,cons(hd(esk51_0),nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_83]),c_0_28])]) ).
cnf(c_0_86,plain,
( ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X3)
| ~ memberP(X1,X2)
| memberP(app(X1,X3),X2) ),
inference(split_conjunct,[status(thm)],[c_0_84]) ).
cnf(c_0_87,negated_conjecture,
( esk51_0 = nil
| cons(esk45_1(esk51_0),esk50_0) = app(esk51_0,cons(hd(esk51_0),nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_38]),c_0_76]),c_0_81])]) ).
cnf(c_0_88,negated_conjecture,
( ~ ssList(X1)
| memberP(app(esk51_0,X1),esk52_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_27]),c_0_28]),c_0_29])]) ).
cnf(c_0_89,negated_conjecture,
( esk51_0 = nil
| app(esk51_0,cons(hd(esk51_0),nil)) = cons(hd(esk51_0),esk50_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_80]),c_0_28])]) ).
fof(c_0_90,plain,
! [X155,X156,X157] :
( ( ~ ssItem(X155)
| ~ ssItem(X156)
| ~ ssList(X157)
| memberP(cons(X156,X157),X155)
| ~ memberP(X157,X155) )
& ( ~ ssItem(X155)
| ~ ssItem(X156)
| ~ ssList(X157)
| memberP(cons(X156,X157),X155)
| X155 != X156 )
& ( ~ ssItem(X155)
| ~ ssItem(X156)
| ~ ssList(X157)
| memberP(X157,X155)
| X155 = X156
| ~ memberP(cons(X156,X157),X155) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax37])])])])]) ).
cnf(c_0_91,negated_conjecture,
( ~ ssList(cons(hd(esk51_0),nil))
| memberP(cons(hd(esk51_0),esk50_0),esk52_0)
| esk51_0 = nil ),
inference(spm,[status(thm)],[c_0_88,c_0_89]) ).
cnf(c_0_92,negated_conjecture,
( ~ ssList(esk44_1(esk51_0))
| memberP(esk50_0,hd(esk51_0))
| esk51_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_83]),c_0_75]),c_0_76]),c_0_81])]) ).
cnf(c_0_93,plain,
( ~ ssItem(X3)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ memberP(cons(X1,X2),X3)
| memberP(X2,X3)
| X3 = X1 ),
inference(split_conjunct,[status(thm)],[c_0_90]) ).
cnf(c_0_94,negated_conjecture,
( memberP(cons(hd(esk51_0),esk50_0),esk52_0)
| esk51_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_38]),c_0_76]),c_0_81])]) ).
cnf(c_0_95,negated_conjecture,
( memberP(esk50_0,hd(esk51_0))
| esk51_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_70]),c_0_28])]) ).
cnf(c_0_96,negated_conjecture,
( esk51_0 = nil
| hd(esk51_0) = esk52_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_93,c_0_94]),c_0_75]),c_0_29]),c_0_81])]),c_0_77]) ).
cnf(c_0_97,negated_conjecture,
( nil != esk51_0
| nil = esk50_0 ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_98,negated_conjecture,
esk51_0 = nil,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_96]),c_0_77]) ).
cnf(c_0_99,negated_conjecture,
esk50_0 = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_97,c_0_98])]) ).
cnf(c_0_100,negated_conjecture,
~ memberP(nil,esk52_0),
inference(rw,[status(thm)],[c_0_77,c_0_99]) ).
cnf(c_0_101,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_98]),c_0_100]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC409+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.37 % Computer : n007.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Mon Sep 21 08:20:21 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 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
% 2.51/0.81 % Version: 3.5.1
% 2.51/0.81 % Preprocessing class: FSLSSMSSSSSNFFN.
% 2.51/0.81 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.51/0.81 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 2.51/0.81 % Starting new_bool_3 with 300s (1) cores
% 2.51/0.81 % Starting new_bool_1 with 300s (1) cores
% 2.51/0.81 % Starting sh5l with 300s (1) cores
% 2.51/0.81 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 634293 completed with status 0
% 2.51/0.81 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 2.51/0.81 % Preprocessing class: FSLSSMSSSSSNFFN.
% 2.51/0.81 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.51/0.81 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 2.51/0.81 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 2.51/0.81 % No SInE strategy applied
% 2.51/0.81 % Search class: FGHSF-FSLM21-MFFFFFNN
% 2.51/0.81 % Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 2.51/0.81 % Starting SubtermCWHack with 136s (1) cores
% 2.51/0.81 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 2.51/0.81 % Starting G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4d with 136s (1) cores
% 2.51/0.81 % Starting G-E--_110_C45_F1_PI_SE_CS_SP_PS_S4S with 136s (1) cores
% 2.51/0.81 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_TT_S0Y with 136s (1) cores
% 2.51/0.81 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 634302 completed with status 0
% 2.51/0.81 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 2.51/0.81 % Preprocessing class: FSLSSMSSSSSNFFN.
% 2.51/0.81 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.51/0.81 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 2.51/0.81 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 2.51/0.81 % No SInE strategy applied
% 2.51/0.81 % Search class: FGHSF-FSLM21-MFFFFFNN
% 2.51/0.81 % Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 2.51/0.81 % Starting SubtermCWHack with 136s (1) cores
% 2.51/0.81 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 2.51/0.81 % Preprocessing time : 0.004 s
% 2.51/0.81 % Presaturation interreduction done
% 2.51/0.81
% 2.51/0.81 % Proof found!
% 2.51/0.81 % SZS status Theorem
% 2.51/0.81 % SZS output start CNFRefutation
% See solution above
% 2.51/0.81 % Parsed axioms : 96
% 2.51/0.81 % Removed by relevancy pruning/SinE : 0
% 2.51/0.81 % Initial clauses : 201
% 2.51/0.81 % Removed in clause preprocessing : 2
% 2.51/0.81 % Initial clauses in saturation : 199
% 2.51/0.81 % Processed clauses : 1673
% 2.51/0.81 % ...of these trivial : 3
% 2.51/0.81 % ...subsumed : 718
% 2.51/0.81 % ...remaining for further processing : 951
% 2.51/0.81 % Other redundant clauses eliminated : 147
% 2.51/0.81 % Clauses deleted for lack of memory : 0
% 2.51/0.81 % Backward-subsumed : 104
% 2.51/0.81 % Backward-rewritten : 208
% 2.51/0.81 % Generated clauses : 5432
% 2.51/0.81 % ...of the previous two non-redundant : 5030
% 2.51/0.81 % ...aggressively subsumed : 0
% 2.51/0.81 % Contextual simplify-reflections : 203
% 2.51/0.81 % Paramodulations : 5280
% 2.51/0.81 % Factorizations : 0
% 2.51/0.81 % NegExts : 0
% 2.51/0.81 % Equation resolutions : 154
% 2.51/0.81 % Disequality decompositions : 0
% 2.51/0.81 % Total rewrite steps : 3754
% 2.51/0.81 % ...of those cached : 3715
% 2.51/0.81 % Propositional unsat checks : 0
% 2.51/0.81 % Propositional check models : 0
% 2.51/0.81 % Propositional check unsatisfiable : 0
% 2.51/0.81 % Propositional clauses : 0
% 2.51/0.81 % Propositional clauses after purity: 0
% 2.51/0.81 % Propositional unsat core size : 0
% 2.51/0.81 % Propositional preprocessing time : 0.000
% 2.51/0.81 % Propositional encoding time : 0.000
% 2.51/0.81 % Propositional solver time : 0.000
% 2.51/0.81 % Success case prop preproc time : 0.000
% 2.51/0.81 % Success case prop encoding time : 0.000
% 2.51/0.81 % Success case prop solver time : 0.000
% 2.51/0.81 % Current number of processed clauses : 423
% 2.51/0.81 % Positive orientable unit clauses : 29
% 2.51/0.81 % Positive unorientable unit clauses: 0
% 2.51/0.81 % Negative unit clauses : 4
% 2.51/0.81 % Non-unit-clauses : 390
% 2.51/0.81 % Current number of unprocessed clauses: 3609
% 2.51/0.81 % ...number of literals in the above : 21361
% 2.51/0.81 % Current number of archived formulas : 0
% 2.51/0.81 % Current number of archived clauses : 505
% 2.51/0.81 % Clause-clause subsumption calls (NU) : 66173
% 2.51/0.81 % Rec. Clause-clause subsumption calls : 16711
% 2.51/0.81 % Non-unit clause-clause subsumptions : 824
% 2.51/0.81 % Unit Clause-clause subsumption calls : 355
% 2.51/0.81 % Rewrite failures with RHS unbound : 0
% 2.51/0.81 % BW rewrite match attempts : 11
% 2.51/0.81 % BW rewrite match successes : 11
% 2.51/0.81 % Condensation attempts : 0
% 2.51/0.81 % Condensation successes : 0
% 2.51/0.81 % Termbank termtop insertions : 120016
% 2.51/0.81 % Search garbage collected termcells : 4298
% 2.51/0.81
% 2.51/0.81 % -------------------------------------------------
% 2.51/0.81 % User time : 0.233 s
% 2.51/0.81 % System time : 0.007 s
% 2.51/0.81 % Total time : 0.240 s
% 2.51/0.81 % Maximum resident set size: 4272 pages
% 2.51/0.81
% 2.51/0.81 % -------------------------------------------------
% 2.51/0.81 % User time : 1.496 s
% 2.51/0.81 % System time : 0.063 s
% 2.51/0.81 % Total time : 1.559 s
% 2.51/0.81 % Maximum resident set size: 4864 pages
% 2.51/0.81 % E exiting
%------------------------------------------------------------------------------