%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWC015+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 : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 02:42:37 PM UTC 2026
% Result : Theorem 0.20s 0.51s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 13
% Syntax : Number of formulae : 91 ( 12 unt; 0 def)
% Number of atoms : 376 ( 162 equ)
% Maximal formula atoms : 34 ( 4 avg)
% Number of connectives : 452 ( 167 ~; 188 |; 42 &)
% ( 3 <=>; 52 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-2 aty)
% Number of variables : 116 ( 0 sgn 64 !; 13 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( ( neq(X4,nil)
| ~ neq(X2,nil) )
& ( ? [X7] :
( ? [X8] :
( app(cons(X7,nil),X8) = X2
& cons(X7,nil) = X1
& ssList(X8) )
& ssItem(X7) )
| ? [X5] :
( ? [X6] :
( neq(nil,X4)
& app(X3,X6) = X5
& tl(X4) = X6
& ssList(X6) )
& X4 != X5
& ssList(X5) )
| ~ neq(X2,nil) ) )
| 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(ax24,axiom,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> ssList(tl(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax24) ).
fof(ax26,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ssList(app(X1,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax26) ).
fof(ax86,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( nil != X1
=> tl(app(X1,X2)) = app(tl(X1),X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax86) ).
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(ax79,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( app(X3,X2) = app(X1,X2)
=> X3 = X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax79) ).
fof(ax28,axiom,
! [X1] :
( ssList(X1)
=> app(nil,X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax28) ).
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(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(ax22,axiom,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> ssItem(hd(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax22) ).
fof(ax18,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> cons(X2,X1) != X1 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax18) ).
fof(c_0_13,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( ( neq(X4,nil)
| ~ neq(X2,nil) )
& ( ? [X7] :
( ? [X8] :
( app(cons(X7,nil),X8) = X2
& cons(X7,nil) = X1
& ssList(X8) )
& ssItem(X7) )
| ? [X5] :
( ? [X6] :
( neq(nil,X4)
& app(X3,X6) = X5
& tl(X4) = X6
& ssList(X6) )
& X4 != X5
& ssList(X5) )
| ~ neq(X2,nil) ) )
| X1 != X3
| X2 != X4 ) ) ) ) ),
inference(assume_negation,[status(cth)],[co1]) ).
fof(c_0_14,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( ( neq(X4,nil)
| ~ neq(X2,nil) )
& ( ? [X7] :
( ? [X8] :
( app(cons(X7,nil),X8) = X2
& cons(X7,nil) = X1
& ssList(X8) )
& ssItem(X7) )
| ? [X5] :
( ? [X6] :
( neq(nil,X4)
& app(X3,X6) = X5
& tl(X4) = X6
& ssList(X6) )
& X4 != X5
& ssList(X5) )
| ~ neq(X2,nil) ) )
| X1 != X3
| X2 != X4 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_13]) ).
fof(c_0_15,negated_conjecture,
! [X257,X258,X259,X260] :
( ( app(cons(X259,nil),X260) != esk49_0
| cons(X259,nil) != esk48_0
| ~ ssList(X260)
| ~ ssItem(X259)
| ~ neq(esk51_0,nil) )
& ( app(cons(X259,nil),X260) != esk49_0
| cons(X259,nil) != esk48_0
| ~ ssList(X260)
| ~ ssItem(X259)
| neq(esk49_0,nil) )
& ( ~ neq(nil,esk51_0)
| app(esk50_0,X258) != X257
| tl(esk51_0) != X258
| ~ ssList(X258)
| esk51_0 = X257
| ~ ssList(X257)
| ~ neq(esk51_0,nil) )
& ( ~ neq(nil,esk51_0)
| app(esk50_0,X258) != X257
| tl(esk51_0) != X258
| ~ ssList(X258)
| esk51_0 = X257
| ~ ssList(X257)
| 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_14])])])])])]) ).
cnf(c_0_16,negated_conjecture,
( neq(esk49_0,nil)
| neq(esk49_0,nil) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_17,negated_conjecture,
neq(esk49_0,nil),
inference(cn,[status(thm)],[c_0_16]) ).
cnf(c_0_18,negated_conjecture,
esk49_0 = esk51_0,
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_19,negated_conjecture,
( ~ neq(nil,esk51_0)
| app(esk50_0,X2) != X1
| tl(esk51_0) != X2
| ~ ssList(X2)
| ~ ssList(X1)
| ~ neq(esk51_0,nil)
| esk51_0 = X1 ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_20,negated_conjecture,
esk48_0 = esk50_0,
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_21,negated_conjecture,
neq(esk51_0,nil),
inference(rw,[status(thm)],[c_0_17,c_0_18]) ).
fof(c_0_22,plain,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
inference(fof_simplification,[status(thm)],[ax15]) ).
cnf(c_0_23,negated_conjecture,
( ~ neq(nil,esk51_0)
| ~ ssList(X1)
| ~ ssList(X2)
| tl(esk51_0) != X2
| app(esk48_0,X2) != X1
| esk51_0 = X1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_19,c_0_20]),c_0_21])]) ).
fof(c_0_24,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_22])])])])]) ).
cnf(c_0_25,negated_conjecture,
ssList(esk49_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_26,negated_conjecture,
( ~ neq(nil,esk51_0)
| ~ ssList(X1)
| ~ ssList(tl(esk51_0))
| app(esk48_0,tl(esk51_0)) != X1
| esk51_0 = X1 ),
inference(er,[status(thm)],[c_0_23]) ).
cnf(c_0_27,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| neq(X1,X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_28,negated_conjecture,
ssList(esk51_0),
inference(rw,[status(thm)],[c_0_25,c_0_18]) ).
cnf(c_0_29,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[ax17]) ).
fof(c_0_30,plain,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> ssList(tl(X1)) ) ),
inference(fof_simplification,[status(thm)],[ax24]) ).
cnf(c_0_31,negated_conjecture,
( ~ ssList(X1)
| ~ ssList(tl(esk51_0))
| app(esk48_0,tl(esk51_0)) != X1
| esk51_0 = X1
| esk51_0 = nil ),
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])]) ).
fof(c_0_32,plain,
! [X129] :
( ssList(tl(X129))
| nil = X129
| ~ ssList(X129) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_30])])]) ).
cnf(c_0_33,negated_conjecture,
( ~ ssList(tl(esk51_0))
| ~ ssList(app(esk48_0,tl(esk51_0)))
| esk51_0 = nil
| app(esk48_0,tl(esk51_0)) = esk51_0 ),
inference(er,[status(thm)],[c_0_31]) ).
cnf(c_0_34,plain,
( ~ ssList(X1)
| ssList(tl(X1))
| nil = X1 ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
fof(c_0_35,plain,
! [X132,X133] :
( ssList(app(X132,X133))
| ~ ssList(X133)
| ~ ssList(X132) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax26])])])]) ).
fof(c_0_36,plain,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( nil != X1
=> tl(app(X1,X2)) = app(tl(X1),X2) ) ) ),
inference(fof_simplification,[status(thm)],[ax86]) ).
cnf(c_0_37,negated_conjecture,
( ~ ssList(app(esk48_0,tl(esk51_0)))
| esk51_0 = nil
| app(esk48_0,tl(esk51_0)) = esk51_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_28])]) ).
cnf(c_0_38,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ssList(app(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_39,negated_conjecture,
ssList(esk48_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_40,plain,
! [X232,X233] :
( tl(app(X232,X233)) = app(tl(X232),X233)
| nil = X232
| ~ ssList(X233)
| ~ ssList(X232) ),
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_41,negated_conjecture,
( ~ ssList(tl(esk51_0))
| esk51_0 = nil
| app(esk48_0,tl(esk51_0)) = esk51_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_39])]) ).
cnf(c_0_42,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| tl(app(X1,X2)) = app(tl(X1),X2)
| nil = X1 ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_43,negated_conjecture,
( esk51_0 = nil
| app(esk48_0,tl(esk51_0)) = esk51_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_34]),c_0_28])]) ).
fof(c_0_44,plain,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( nil != X1
=> hd(app(X1,X2)) = hd(X1) ) ) ),
inference(fof_simplification,[status(thm)],[ax85]) ).
fof(c_0_45,plain,
! [X216,X217,X218] :
( X218 = X216
| app(X218,X217) != app(X216,X217)
| ~ ssList(X218)
| ~ ssList(X217)
| ~ ssList(X216) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax79])])])]) ).
cnf(c_0_46,negated_conjecture,
( ~ ssList(tl(esk51_0))
| esk48_0 = nil
| esk51_0 = nil
| app(tl(esk48_0),tl(esk51_0)) = tl(esk51_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_39])]) ).
fof(c_0_47,plain,
! [X230,X231] :
( hd(app(X230,X231)) = hd(X230)
| nil = X230
| ~ ssList(X231)
| ~ ssList(X230) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_44])])])]) ).
cnf(c_0_48,plain,
( app(X3,X2) != app(X1,X2)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| X3 = X1 ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_49,negated_conjecture,
( esk51_0 = nil
| esk48_0 = nil
| app(tl(esk48_0),tl(esk51_0)) = tl(esk51_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_34]),c_0_28])]) ).
fof(c_0_50,plain,
! [X137] :
( app(nil,X137) = X137
| ~ ssList(X137) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax28])])]) ).
fof(c_0_51,plain,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> cons(hd(X1),tl(X1)) = X1 ) ),
inference(fof_simplification,[status(thm)],[ax78]) ).
cnf(c_0_52,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| hd(app(X1,X2)) = hd(X1)
| nil = X1 ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_53,negated_conjecture,
( ~ ssList(X1)
| ~ ssList(tl(esk51_0))
| ~ ssList(tl(esk48_0))
| app(X1,tl(esk51_0)) != tl(esk51_0)
| esk48_0 = nil
| esk51_0 = nil
| X1 = tl(esk48_0) ),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_54,plain,
( ~ ssList(X1)
| app(nil,X1) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
cnf(c_0_55,negated_conjecture,
( app(cons(X1,nil),X2) != esk49_0
| cons(X1,nil) != esk48_0
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ neq(esk51_0,nil) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_56,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])])])])])]) ).
fof(c_0_57,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_51])])]) ).
cnf(c_0_58,negated_conjecture,
( ~ ssList(tl(esk51_0))
| esk48_0 = nil
| esk51_0 = nil
| hd(esk48_0) = hd(esk51_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_43]),c_0_39])]) ).
cnf(c_0_59,negated_conjecture,
( ~ ssList(tl(esk51_0))
| ~ ssList(tl(esk48_0))
| esk51_0 = nil
| esk48_0 = nil
| tl(esk48_0) = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_29])]) ).
fof(c_0_60,plain,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> ssItem(hd(X1)) ) ),
inference(fof_simplification,[status(thm)],[ax22]) ).
cnf(c_0_61,negated_conjecture,
( ~ ssItem(X1)
| ~ ssList(X2)
| cons(X1,nil) != esk48_0
| app(cons(X1,nil),X2) != esk51_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_55,c_0_18]),c_0_21])]) ).
cnf(c_0_62,plain,
( ~ ssList(X1)
| ~ singletonP(X1)
| cons(esk5_1(X1),nil) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_63,plain,
( ~ ssList(X1)
| ~ singletonP(X1)
| ssItem(esk5_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_64,plain,
( ~ ssList(X1)
| cons(hd(X1),tl(X1)) = X1
| nil = X1 ),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_65,negated_conjecture,
( esk51_0 = nil
| esk48_0 = nil
| hd(esk48_0) = hd(esk51_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_34]),c_0_28])]) ).
cnf(c_0_66,negated_conjecture,
( ~ ssList(tl(esk51_0))
| esk48_0 = nil
| esk51_0 = nil
| tl(esk48_0) = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_34]),c_0_39])]) ).
fof(c_0_67,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_60])])]) ).
cnf(c_0_68,negated_conjecture,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ singletonP(X1)
| X1 != esk48_0
| app(X1,X2) != esk51_0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_63]) ).
cnf(c_0_69,plain,
( ~ ssList(X2)
| cons(X1,nil) != X2
| ~ ssItem(X1)
| singletonP(X2) ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_70,negated_conjecture,
( esk48_0 = nil
| esk51_0 = nil
| cons(hd(esk51_0),tl(esk48_0)) = esk48_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_65]),c_0_39])]) ).
cnf(c_0_71,negated_conjecture,
( esk51_0 = nil
| esk48_0 = nil
| tl(esk48_0) = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_34]),c_0_28])]) ).
cnf(c_0_72,plain,
( ~ ssList(X1)
| ssItem(hd(X1))
| nil = X1 ),
inference(split_conjunct,[status(thm)],[c_0_67]) ).
cnf(c_0_73,negated_conjecture,
( ~ ssList(tl(esk51_0))
| ~ singletonP(esk48_0)
| esk51_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_43]),c_0_39])]) ).
cnf(c_0_74,plain,
( ~ ssItem(X1)
| ~ ssList(cons(X1,nil))
| singletonP(cons(X1,nil)) ),
inference(er,[status(thm)],[c_0_69]) ).
cnf(c_0_75,negated_conjecture,
( esk51_0 = nil
| esk48_0 = nil
| cons(hd(esk51_0),nil) = esk48_0 ),
inference(spm,[status(thm)],[c_0_70,c_0_71]) ).
cnf(c_0_76,negated_conjecture,
( ssItem(hd(esk51_0))
| esk48_0 = nil
| esk51_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_65]),c_0_39])]) ).
cnf(c_0_77,negated_conjecture,
( ~ singletonP(esk48_0)
| esk51_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_34]),c_0_28])]) ).
fof(c_0_78,plain,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> cons(X2,X1) != X1 ) ),
inference(fof_simplification,[status(thm)],[ax18]) ).
cnf(c_0_79,negated_conjecture,
( esk48_0 = nil
| esk51_0 = nil ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_39])]),c_0_76]),c_0_77]) ).
fof(c_0_80,plain,
! [X115,X116] :
( cons(X116,X115) != X115
| ~ ssItem(X116)
| ~ ssList(X115) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_78])])])]) ).
cnf(c_0_81,negated_conjecture,
( esk51_0 = nil
| app(nil,tl(esk51_0)) = esk51_0 ),
inference(spm,[status(thm)],[c_0_43,c_0_79]) ).
cnf(c_0_82,plain,
( cons(X2,X1) != X1
| ~ ssItem(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_80]) ).
cnf(c_0_83,negated_conjecture,
( ~ ssList(tl(esk51_0))
| esk51_0 = nil
| tl(esk51_0) = esk51_0 ),
inference(spm,[status(thm)],[c_0_54,c_0_81]) ).
cnf(c_0_84,plain,
( ~ ssList(X1)
| tl(X1) != X1
| nil = X1 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_64]),c_0_72]),c_0_34]) ).
cnf(c_0_85,negated_conjecture,
( esk51_0 = nil
| tl(esk51_0) = esk51_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_34]),c_0_28])]) ).
cnf(c_0_86,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| X1 != X2
| ~ neq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_87,negated_conjecture,
esk51_0 = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_85]),c_0_28])]) ).
cnf(c_0_88,plain,
( ~ neq(X1,X1)
| ~ ssList(X1) ),
inference(er,[status(thm)],[c_0_86]) ).
cnf(c_0_89,negated_conjecture,
neq(nil,nil),
inference(rw,[status(thm)],[c_0_21,c_0_87]) ).
cnf(c_0_90,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_89]),c_0_29])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC015+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.36 % Computer : n018.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Mon Sep 21 07:51:30 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.08/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.41 Running first-order theorem proving
% 0.08/0.41 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
% 0.20/0.51 % Version: 3.5.1
% 0.20/0.51 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.20/0.51 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.51 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.20/0.51 % Starting new_bool_3 with 300s (1) cores
% 0.20/0.51 % Starting new_bool_1 with 300s (1) cores
% 0.20/0.51 % Starting sh5l with 300s (1) cores
% 0.20/0.51 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 1379656 completed with status 0
% 0.20/0.51 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 0.20/0.51 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.20/0.51 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.51 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.20/0.51 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.20/0.51 % No SInE strategy applied
% 0.20/0.51 % Search class: FGHSF-FSLM21-MFFFFFNN
% 0.20/0.51 % Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 0.20/0.51 % Starting SubtermCWHack with 136s (1) cores
% 0.20/0.51 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.20/0.51 % Starting G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4d with 136s (1) cores
% 0.20/0.51 % Starting G-E--_110_C45_F1_PI_SE_CS_SP_PS_S4S with 136s (1) cores
% 0.20/0.51 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_TT_S0Y with 136s (1) cores
% 0.20/0.51 % G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4d with pid 1379669 completed with status 0
% 0.20/0.51 % Result found by G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4d
% 0.20/0.51 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.20/0.51 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.51 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.20/0.51 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.20/0.51 % No SInE strategy applied
% 0.20/0.51 % Search class: FGHSF-FSLM21-MFFFFFNN
% 0.20/0.51 % Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 0.20/0.51 % Starting SubtermCWHack with 136s (1) cores
% 0.20/0.51 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.20/0.51 % Starting G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4d with 136s (1) cores
% 0.20/0.51 % Preprocessing time : 0.004 s
% 0.20/0.51
% 0.20/0.51 % Proof found!
% 0.20/0.51 % SZS status Theorem
% 0.20/0.51 % SZS output start CNFRefutation
% See solution above
% 0.20/0.51 % Parsed axioms : 96
% 0.20/0.51 % Removed by relevancy pruning/SinE : 0
% 0.20/0.51 % Initial clauses : 202
% 0.20/0.51 % Removed in clause preprocessing : 2
% 0.20/0.51 % Initial clauses in saturation : 200
% 0.20/0.51 % Processed clauses : 412
% 0.20/0.51 % ...of these trivial : 5
% 0.20/0.51 % ...subsumed : 42
% 0.20/0.51 % ...remaining for further processing : 365
% 0.20/0.51 % Other redundant clauses eliminated : 69
% 0.20/0.51 % Clauses deleted for lack of memory : 0
% 0.20/0.51 % Backward-subsumed : 116
% 0.20/0.51 % Backward-rewritten : 28
% 0.20/0.51 % Generated clauses : 1109
% 0.20/0.51 % ...of the previous two non-redundant : 956
% 0.20/0.51 % ...aggressively subsumed : 0
% 0.20/0.51 % Contextual simplify-reflections : 24
% 0.20/0.51 % Paramodulations : 1014
% 0.20/0.51 % Factorizations : 0
% 0.20/0.51 % NegExts : 0
% 0.20/0.51 % Equation resolutions : 95
% 0.20/0.51 % Disequality decompositions : 0
% 0.20/0.51 % Total rewrite steps : 527
% 0.20/0.51 % ...of those cached : 510
% 0.20/0.51 % Propositional unsat checks : 0
% 0.20/0.51 % Propositional check models : 0
% 0.20/0.51 % Propositional check unsatisfiable : 0
% 0.20/0.51 % Propositional clauses : 0
% 0.20/0.51 % Propositional clauses after purity: 0
% 0.20/0.51 % Propositional unsat core size : 0
% 0.20/0.51 % Propositional preprocessing time : 0.000
% 0.20/0.51 % Propositional encoding time : 0.000
% 0.20/0.51 % Propositional solver time : 0.000
% 0.20/0.51 % Success case prop preproc time : 0.000
% 0.20/0.51 % Success case prop encoding time : 0.000
% 0.20/0.51 % Success case prop solver time : 0.000
% 0.20/0.51 % Current number of processed clauses : 215
% 0.20/0.51 % Positive orientable unit clauses : 23
% 0.20/0.51 % Positive unorientable unit clauses: 0
% 0.20/0.51 % Negative unit clauses : 2
% 0.20/0.51 % Non-unit-clauses : 190
% 0.20/0.51 % Current number of unprocessed clauses: 716
% 0.20/0.51 % ...number of literals in the above : 5348
% 0.20/0.51 % Current number of archived formulas : 0
% 0.20/0.51 % Current number of archived clauses : 144
% 0.20/0.51 % Clause-clause subsumption calls (NU) : 16344
% 0.20/0.51 % Rec. Clause-clause subsumption calls : 2457
% 0.20/0.51 % Non-unit clause-clause subsumptions : 179
% 0.20/0.51 % Unit Clause-clause subsumption calls : 136
% 0.20/0.51 % Rewrite failures with RHS unbound : 0
% 0.20/0.51 % BW rewrite match attempts : 6
% 0.20/0.51 % BW rewrite match successes : 6
% 0.20/0.51 % Condensation attempts : 0
% 0.20/0.51 % Condensation successes : 0
% 0.20/0.51 % Termbank termtop insertions : 41084
% 0.20/0.51 % Search garbage collected termcells : 4356
% 0.20/0.51
% 0.20/0.51 % -------------------------------------------------
% 0.20/0.51 % User time : 0.074 s
% 0.20/0.51 % System time : 0.006 s
% 0.20/0.51 % Total time : 0.080 s
% 0.20/0.51 % Maximum resident set size: 4272 pages
% 0.20/0.51
% 0.20/0.51 % -------------------------------------------------
% 0.20/0.51 % User time : 0.297 s
% 0.20/0.51 % System time : 0.028 s
% 0.20/0.51 % Total time : 0.325 s
% 0.20/0.51 % Maximum resident set size: 4864 pages
% 0.20/0.51 % E exiting
%------------------------------------------------------------------------------