%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWC229+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 : 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 02:43:33 PM UTC 2026
% Result : Theorem 0.35s 0.71s
% Output : CNFRefutation 0.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 14
% Syntax : Number of formulae : 82 ( 13 unt; 0 def)
% Number of atoms : 338 ( 109 equ)
% Maximal formula atoms : 35 ( 4 avg)
% Number of connectives : 417 ( 161 ~; 169 |; 39 &)
% ( 3 <=>; 45 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 5 con; 0-3 aty)
% Number of variables : 113 ( 0 sgn 62 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( neq(X4,nil)
& ~ singletonP(X3) )
| ? [X5] :
( ? [X6] :
( ? [X7] :
( ! [X8] :
( ssItem(X8)
=> ( leq(X8,X5)
| ~ leq(X5,X8)
| ~ memberP(X7,X8)
| ~ memberP(X6,X8) ) )
& app(app(X6,cons(X5,nil)),X7) = X1
& ssList(X7) )
& ssList(X6) )
& ssItem(X5) )
| nil = X1
| ~ segmentP(X4,X3)
| X1 != X3
| X2 != X4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
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(ax25,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> tl(cons(X2,X1)) = X1 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax25) ).
fof(ax4,axiom,
! [X1] :
( ssList(X1)
=> ( singletonP(X1)
<=> ? [X2] :
( cons(X2,nil) = X1
& ssItem(X2) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax4) ).
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(ax17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax17) ).
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(ax22,axiom,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> ssItem(hd(X1)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax22) ).
fof(ax38,axiom,
! [X1] :
( ssItem(X1)
=> ~ memberP(nil,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax38) ).
fof(ax20,axiom,
! [X1] :
( ssList(X1)
=> ( ? [X2] :
( ? [X3] :
( cons(X3,X2) = X1
& ssItem(X3) )
& ssList(X2) )
| nil = X1 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax20) ).
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(ax28,axiom,
! [X1] :
( ssList(X1)
=> app(nil,X1) = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax28) ).
fof(ax54,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( ( segmentP(X2,X1)
& segmentP(X1,X2) )
=> X1 = X2 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax54) ).
fof(ax57,axiom,
! [X1] :
( ssList(X1)
=> segmentP(X1,nil) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax57) ).
fof(c_0_14,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( neq(X4,nil)
& ~ singletonP(X3) )
| ? [X5] :
( ? [X6] :
( ? [X7] :
( ! [X8] :
( ssItem(X8)
=> ( leq(X8,X5)
| ~ leq(X5,X8)
| ~ memberP(X7,X8)
| ~ memberP(X6,X8) ) )
& app(app(X6,cons(X5,nil)),X7) = X1
& ssList(X7) )
& ssList(X6) )
& ssItem(X5) )
| nil = X1
| ~ segmentP(X4,X3)
| X1 != X3
| X2 != X4 ) ) ) ) ),
inference(assume_negation,[status(cth)],[co1]) ).
fof(c_0_15,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( neq(X4,nil)
& ~ singletonP(X3) )
| ? [X5] :
( ? [X6] :
( ? [X7] :
( ! [X8] :
( ssItem(X8)
=> ( leq(X8,X5)
| ~ leq(X5,X8)
| ~ memberP(X7,X8)
| ~ memberP(X6,X8) ) )
& app(app(X6,cons(X5,nil)),X7) = X1
& ssList(X7) )
& ssList(X6) )
& ssItem(X5) )
| nil = X1
| ~ segmentP(X4,X3)
| X1 != X3
| X2 != X4 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_14]) ).
fof(c_0_16,negated_conjecture,
! [X257,X258,X259] :
( ( ~ neq(esk51_0,nil)
| singletonP(esk50_0) )
& ( ~ ssItem(X257)
| ~ ssList(X258)
| app(app(X258,cons(X257,nil)),X259) != esk48_0
| ~ ssList(X259)
| ~ leq(esk52_3(X257,X258,X259),X257) )
& ( ~ ssItem(X257)
| ~ ssList(X258)
| app(app(X258,cons(X257,nil)),X259) != esk48_0
| ~ ssList(X259)
| leq(X257,esk52_3(X257,X258,X259)) )
& ( ~ ssItem(X257)
| ~ ssList(X258)
| app(app(X258,cons(X257,nil)),X259) != esk48_0
| ~ ssList(X259)
| memberP(X259,esk52_3(X257,X258,X259)) )
& ( ~ ssItem(X257)
| ~ ssList(X258)
| app(app(X258,cons(X257,nil)),X259) != esk48_0
| ~ ssList(X259)
| memberP(X258,esk52_3(X257,X258,X259)) )
& ( ~ ssItem(X257)
| ~ ssList(X258)
| app(app(X258,cons(X257,nil)),X259) != esk48_0
| ~ ssList(X259)
| ssItem(esk52_3(X257,X258,X259)) )
& nil != esk48_0
& segmentP(esk51_0,esk50_0)
& esk48_0 = esk50_0
& esk49_0 = esk51_0
& ssList(esk51_0)
& ssList(esk50_0)
& ssList(esk49_0)
& ssList(esk48_0) ),
inference(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_15])])])])])]) ).
fof(c_0_17,plain,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
inference(fof_simplification,[status(thm)],[ax15]) ).
fof(c_0_18,plain,
! [X130,X131] :
( tl(cons(X131,X130)) = X130
| ~ ssItem(X131)
| ~ ssList(X130) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax25])])])]) ).
fof(c_0_19,plain,
! [X19,X21] :
( ( ~ ssList(X19)
| singletonP(X19)
| cons(X21,nil) != X19
| ~ ssItem(X21) )
& ( ~ ssList(X19)
| ~ singletonP(X19)
| cons(esk5_1(X19),nil) = X19 )
& ( ~ ssList(X19)
| ~ singletonP(X19)
| ssItem(esk5_1(X19)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax4])])])])])]) ).
cnf(c_0_20,negated_conjecture,
( ~ neq(esk51_0,nil)
| singletonP(esk50_0) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_21,negated_conjecture,
esk48_0 = esk50_0,
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_22,plain,
! [X111,X112] :
( ( ~ ssList(X111)
| ~ ssList(X112)
| neq(X111,X112)
| X111 = X112 )
& ( ~ ssList(X111)
| ~ ssList(X112)
| X111 != X112
| ~ neq(X111,X112) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_17])])])])]) ).
cnf(c_0_23,negated_conjecture,
ssList(esk49_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_24,negated_conjecture,
esk49_0 = esk51_0,
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_25,plain,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> cons(hd(X1),tl(X1)) = X1 ) ),
inference(fof_simplification,[status(thm)],[ax78]) ).
cnf(c_0_26,plain,
( ~ ssItem(X2)
| ~ ssList(X1)
| tl(cons(X2,X1)) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_27,plain,
( ~ ssList(X1)
| ~ singletonP(X1)
| cons(esk5_1(X1),nil) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_28,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[ax17]) ).
cnf(c_0_29,plain,
( ~ ssList(X1)
| ~ singletonP(X1)
| ssItem(esk5_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_30,negated_conjecture,
( ~ neq(esk51_0,nil)
| singletonP(esk48_0) ),
inference(rw,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_31,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| neq(X1,X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_32,negated_conjecture,
ssList(esk51_0),
inference(rw,[status(thm)],[c_0_23,c_0_24]) ).
fof(c_0_33,plain,
! [X215] :
( cons(hd(X215),tl(X215)) = X215
| nil = X215
| ~ ssList(X215) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_25])])]) ).
cnf(c_0_34,plain,
( ~ ssList(X1)
| ~ singletonP(X1)
| tl(X1) = nil ),
inference(csr,[status(thm)],[inference(cn,[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_35,negated_conjecture,
( singletonP(esk48_0)
| esk51_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_28]),c_0_32])]) ).
cnf(c_0_36,negated_conjecture,
ssList(esk48_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_37,plain,
! [X117,X118,X119,X120] :
( ( ~ ssList(X117)
| ~ ssList(X118)
| ~ ssItem(X119)
| ~ ssItem(X120)
| cons(X119,X117) != cons(X120,X118)
| X118 = X117 )
& ( ~ ssList(X117)
| ~ ssList(X118)
| ~ ssItem(X119)
| ~ ssItem(X120)
| cons(X119,X117) != cons(X120,X118)
| X119 = X120 ) ),
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_38,plain,
( ~ ssList(X1)
| cons(hd(X1),tl(X1)) = X1
| nil = X1 ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_39,negated_conjecture,
( esk51_0 = nil
| tl(esk48_0) = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36])]) ).
cnf(c_0_40,negated_conjecture,
nil != esk48_0,
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_41,plain,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> ssItem(hd(X1)) ) ),
inference(fof_simplification,[status(thm)],[ax22]) ).
cnf(c_0_42,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X3)
| ~ ssItem(X4)
| cons(X3,X2) != cons(X4,X1)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_43,negated_conjecture,
( esk51_0 = nil
| cons(hd(esk48_0),nil) = esk48_0 ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_36])]),c_0_40]) ).
fof(c_0_44,plain,
! [X126] :
( ssItem(hd(X126))
| nil = X126
| ~ ssList(X126) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_41])])]) ).
fof(c_0_45,plain,
! [X1] :
( ssItem(X1)
=> ~ memberP(nil,X1) ),
inference(fof_simplification,[status(thm)],[ax38]) ).
cnf(c_0_46,negated_conjecture,
( ~ ssItem(X2)
| ~ ssItem(hd(esk48_0))
| ~ ssList(X1)
| cons(X2,X1) != esk48_0
| nil = X1
| esk51_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_28])]) ).
cnf(c_0_47,plain,
( ~ ssList(X1)
| ssItem(hd(X1))
| nil = X1 ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
fof(c_0_48,plain,
! [X121] :
( ( ~ ssList(X121)
| nil = X121
| cons(esk45_1(X121),esk44_1(X121)) = X121 )
& ( ~ ssList(X121)
| nil = X121
| ssItem(esk45_1(X121)) )
& ( ~ ssList(X121)
| nil = X121
| ssList(esk44_1(X121)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax20])])])])]) ).
fof(c_0_49,plain,
! [X159] :
( ~ memberP(nil,X159)
| ~ ssItem(X159) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_45])])]) ).
cnf(c_0_50,negated_conjecture,
( ~ ssItem(X2)
| ~ ssList(X1)
| cons(X2,X1) != esk48_0
| nil = X1
| esk51_0 = nil ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_36])]),c_0_40]) ).
cnf(c_0_51,plain,
( ~ ssList(X1)
| nil = X1
| cons(esk45_1(X1),esk44_1(X1)) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
fof(c_0_52,plain,
! [X222,X223] :
( cons(X223,X222) = app(cons(X223,nil),X222)
| ~ ssItem(X223)
| ~ ssList(X222) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax81])])])]) ).
cnf(c_0_53,plain,
( ~ memberP(nil,X1)
| ~ ssItem(X1) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_54,negated_conjecture,
( ~ ssItem(X2)
| ~ ssList(X3)
| app(app(X3,cons(X2,nil)),X1) != esk48_0
| ~ ssList(X1)
| memberP(X1,esk52_3(X2,X3,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_55,negated_conjecture,
( ~ ssItem(esk45_1(esk48_0))
| ~ ssList(esk44_1(esk48_0))
| esk51_0 = nil
| esk44_1(esk48_0) = nil ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51])]),c_0_36])]),c_0_40]) ).
cnf(c_0_56,plain,
( ~ ssList(X1)
| nil = X1
| ssItem(esk45_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_57,plain,
( ~ ssItem(X2)
| ~ ssList(X1)
| cons(X2,X1) = app(cons(X2,nil),X1) ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_58,negated_conjecture,
( ~ ssItem(X2)
| ~ ssItem(esk52_3(X2,X1,nil))
| ~ ssList(X1)
| app(app(X1,cons(X2,nil)),nil) != esk48_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_28])]) ).
cnf(c_0_59,negated_conjecture,
( ~ ssItem(X1)
| ~ ssList(X2)
| app(app(X2,cons(X1,nil)),X3) != esk48_0
| ~ ssList(X3)
| ssItem(esk52_3(X1,X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_60,plain,
! [X137] :
( app(nil,X137) = X137
| ~ ssList(X137) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax28])])]) ).
cnf(c_0_61,negated_conjecture,
( ~ ssList(esk44_1(esk48_0))
| esk51_0 = nil
| esk44_1(esk48_0) = nil ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_36])]),c_0_40]) ).
cnf(c_0_62,plain,
( ~ ssList(X1)
| nil = X1
| ssList(esk44_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_63,negated_conjecture,
( ~ ssItem(hd(esk48_0))
| ~ ssList(X1)
| esk51_0 = nil
| cons(hd(esk48_0),X1) = app(esk48_0,X1) ),
inference(spm,[status(thm)],[c_0_57,c_0_43]) ).
cnf(c_0_64,negated_conjecture,
( ~ ssItem(X2)
| ~ ssList(X1)
| app(app(X1,cons(X2,nil)),nil) != esk48_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_28])]) ).
cnf(c_0_65,plain,
( ~ ssList(X1)
| app(nil,X1) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
cnf(c_0_66,negated_conjecture,
( esk51_0 = nil
| esk44_1(esk48_0) = nil ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_36])]),c_0_40]) ).
cnf(c_0_67,negated_conjecture,
( ~ ssItem(hd(esk48_0))
| esk51_0 = nil
| app(esk48_0,nil) = esk48_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_63]),c_0_28])]) ).
fof(c_0_68,plain,
! [X189,X190] :
( X189 = X190
| ~ segmentP(X190,X189)
| ~ segmentP(X189,X190)
| ~ ssList(X190)
| ~ ssList(X189) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax54])])])]) ).
cnf(c_0_69,negated_conjecture,
segmentP(esk51_0,esk50_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_70,negated_conjecture,
( ~ ssItem(X1)
| ~ ssList(cons(X1,nil))
| app(cons(X1,nil),nil) != esk48_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_65]),c_0_28])]) ).
cnf(c_0_71,negated_conjecture,
( esk51_0 = nil
| cons(esk45_1(esk48_0),nil) = esk48_0 ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_66]),c_0_36])]),c_0_40]) ).
cnf(c_0_72,negated_conjecture,
( esk51_0 = nil
| app(esk48_0,nil) = esk48_0 ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_47]),c_0_36])]),c_0_40]) ).
cnf(c_0_73,plain,
( ~ segmentP(X2,X1)
| ~ segmentP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_68]) ).
cnf(c_0_74,negated_conjecture,
segmentP(esk51_0,esk48_0),
inference(rw,[status(thm)],[c_0_69,c_0_21]) ).
cnf(c_0_75,negated_conjecture,
( ~ ssItem(esk45_1(esk48_0))
| esk51_0 = nil ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_36])]),c_0_72]) ).
cnf(c_0_76,negated_conjecture,
( ~ segmentP(esk48_0,esk51_0)
| esk51_0 = esk48_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_74]),c_0_32]),c_0_36])]) ).
cnf(c_0_77,negated_conjecture,
esk51_0 = nil,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_56]),c_0_36])]),c_0_40]) ).
fof(c_0_78,plain,
! [X196] :
( segmentP(X196,nil)
| ~ ssList(X196) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax57])])]) ).
cnf(c_0_79,negated_conjecture,
~ segmentP(esk48_0,nil),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_76,c_0_77]),c_0_77]),c_0_40]) ).
cnf(c_0_80,plain,
( ~ ssList(X1)
| segmentP(X1,nil) ),
inference(split_conjunct,[status(thm)],[c_0_78]) ).
cnf(c_0_81,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_80]),c_0_36])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWC229+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.19/0.45 % Computer : n006.cluster.edu
% 0.19/0.45 % Model : x86_64 x86_64
% 0.19/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.45 % Memory : 8046.5625MB
% 0.19/0.45 % OS : Linux 6.8.0-71-generic
% 0.19/0.45 % CPULimit : 300
% 0.19/0.45 % WCLimit : 300
% 0.19/0.45 % DateTime : Mon Sep 21 08:06:27 UTC 2026
% 0.19/0.46 % CPUTime :
% 0.19/0.46 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.24/0.53 Running first-order theorem proving
% 0.24/0.53 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
% 0.35/0.71 % Version: 3.5.1
% 0.35/0.71 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.35/0.71 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.35/0.71 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.35/0.71 % Starting new_bool_3 with 300s (1) cores
% 0.35/0.71 % Starting new_bool_1 with 300s (1) cores
% 0.35/0.71 % Starting sh5l with 300s (1) cores
% 0.35/0.71 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 2384956 completed with status 0
% 0.35/0.71 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 0.35/0.71 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.35/0.71 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.35/0.71 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.35/0.71 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.35/0.71 % No SInE strategy applied
% 0.35/0.71 % Search class: FGHSF-FSLM31-MFFFFFNN
% 0.35/0.71 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.35/0.71 % Starting SubtermCWHack with 136s (1) cores
% 0.35/0.71 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.35/0.71 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 0.35/0.71 % Starting SAT001_MinMin_p005000_rr_RG with 136s (1) cores
% 0.35/0.71 % Starting G-E--_301_C18_F1_URBAN_S5PRR_RG_S070I with 136s (1) cores
% 0.35/0.71 % G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with pid 2384964 completed with status 0
% 0.35/0.71 % Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y
% 0.35/0.71 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.35/0.71 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.35/0.71 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.35/0.71 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.35/0.71 % No SInE strategy applied
% 0.35/0.71 % Search class: FGHSF-FSLM31-MFFFFFNN
% 0.35/0.71 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.35/0.71 % Starting SubtermCWHack with 136s (1) cores
% 0.35/0.71 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.35/0.71 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 0.35/0.71 % Preprocessing time : 0.006 s
% 0.35/0.71 % Presaturation interreduction done
% 0.35/0.71
% 0.35/0.71 % Proof found!
% 0.35/0.71 % SZS status Theorem
% 0.35/0.71 % SZS output start CNFRefutation
% See solution above
% 0.35/0.71 % Parsed axioms : 96
% 0.35/0.71 % Removed by relevancy pruning/SinE : 0
% 0.35/0.71 % Initial clauses : 204
% 0.35/0.71 % Removed in clause preprocessing : 2
% 0.35/0.71 % Initial clauses in saturation : 202
% 0.35/0.71 % Processed clauses : 668
% 0.35/0.71 % ...of these trivial : 2
% 0.35/0.71 % ...subsumed : 160
% 0.35/0.71 % ...remaining for further processing : 506
% 0.35/0.71 % Other redundant clauses eliminated : 63
% 0.35/0.71 % Clauses deleted for lack of memory : 0
% 0.35/0.71 % Backward-subsumed : 20
% 0.35/0.71 % Backward-rewritten : 67
% 0.35/0.71 % Generated clauses : 883
% 0.35/0.71 % ...of the previous two non-redundant : 718
% 0.35/0.71 % ...aggressively subsumed : 0
% 0.35/0.71 % Contextual simplify-reflections : 30
% 0.35/0.71 % Paramodulations : 817
% 0.35/0.71 % Factorizations : 0
% 0.35/0.71 % NegExts : 0
% 0.35/0.71 % Equation resolutions : 68
% 0.35/0.71 % Disequality decompositions : 0
% 0.35/0.71 % Total rewrite steps : 550
% 0.35/0.71 % ...of those cached : 537
% 0.35/0.71 % Propositional unsat checks : 0
% 0.35/0.71 % Propositional check models : 0
% 0.35/0.71 % Propositional check unsatisfiable : 0
% 0.35/0.71 % Propositional clauses : 0
% 0.35/0.71 % Propositional clauses after purity: 0
% 0.35/0.71 % Propositional unsat core size : 0
% 0.35/0.71 % Propositional preprocessing time : 0.000
% 0.35/0.71 % Propositional encoding time : 0.000
% 0.35/0.71 % Propositional solver time : 0.000
% 0.35/0.71 % Success case prop preproc time : 0.000
% 0.35/0.71 % Success case prop encoding time : 0.000
% 0.35/0.71 % Success case prop solver time : 0.000
% 0.35/0.71 % Current number of processed clauses : 200
% 0.35/0.71 % Positive orientable unit clauses : 20
% 0.35/0.71 % Positive unorientable unit clauses: 0
% 0.35/0.71 % Negative unit clauses : 4
% 0.35/0.71 % Non-unit-clauses : 176
% 0.35/0.71 % Current number of unprocessed clauses: 448
% 0.35/0.71 % ...number of literals in the above : 2650
% 0.35/0.71 % Current number of archived formulas : 0
% 0.35/0.71 % Current number of archived clauses : 283
% 0.35/0.71 % Clause-clause subsumption calls (NU) : 23100
% 0.35/0.71 % Rec. Clause-clause subsumption calls : 6651
% 0.35/0.71 % Non-unit clause-clause subsumptions : 182
% 0.35/0.71 % Unit Clause-clause subsumption calls : 85
% 0.35/0.71 % Rewrite failures with RHS unbound : 0
% 0.35/0.71 % BW rewrite match attempts : 3
% 0.35/0.71 % BW rewrite match successes : 3
% 0.35/0.71 % Condensation attempts : 0
% 0.35/0.71 % Condensation successes : 0
% 0.35/0.71 % Termbank termtop insertions : 33737
% 0.35/0.71 % Search garbage collected termcells : 4379
% 0.35/0.71
% 0.35/0.71 % -------------------------------------------------
% 0.35/0.71 % User time : 0.099 s
% 0.35/0.71 % System time : 0.011 s
% 0.35/0.71 % Total time : 0.110 s
% 0.35/0.71 % Maximum resident set size: 4476 pages
% 0.35/0.71
% 0.35/0.71 % -------------------------------------------------
% 0.35/0.71 % User time : 0.440 s
% 0.35/0.71 % System time : 0.033 s
% 0.35/0.71 % Total time : 0.473 s
% 0.35/0.71 % Maximum resident set size: 4608 pages
% 0.35/0.71 % E exiting
%------------------------------------------------------------------------------