%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWC253+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 02:43:40 PM UTC 2026
% Result : Theorem 0.25s 10.71s
% Output : CNFRefutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 12
% Syntax : Number of formulae : 80 ( 13 unt; 0 def)
% Number of atoms : 314 ( 127 equ)
% Maximal formula atoms : 28 ( 3 avg)
% Number of connectives : 370 ( 136 ~; 152 |; 33 &)
% ( 3 <=>; 46 =>; 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 : 91 ( 0 sgn 56 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( ( neq(X4,nil)
| ~ neq(X2,nil) )
& ( singletonP(X1)
| ? [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(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_12,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( ( neq(X4,nil)
| ~ neq(X2,nil) )
& ( singletonP(X1)
| ? [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_13,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( ( neq(X4,nil)
| ~ neq(X2,nil) )
& ( singletonP(X1)
| ? [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_12]) ).
fof(c_0_14,negated_conjecture,
! [X255,X256] :
( ( ~ singletonP(esk48_0)
| ~ neq(esk51_0,nil) )
& ( ~ singletonP(esk48_0)
| neq(esk49_0,nil) )
& ( ~ neq(nil,esk51_0)
| app(esk50_0,X256) != X255
| tl(esk51_0) != X256
| ~ ssList(X256)
| esk51_0 = X255
| ~ ssList(X255)
| ~ neq(esk51_0,nil) )
& ( ~ neq(nil,esk51_0)
| app(esk50_0,X256) != X255
| tl(esk51_0) != X256
| ~ ssList(X256)
| esk51_0 = X255
| ~ ssList(X255)
| 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_13])])])])])]) ).
cnf(c_0_15,negated_conjecture,
( neq(esk49_0,nil)
| neq(esk49_0,nil) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_16,negated_conjecture,
neq(esk49_0,nil),
inference(cn,[status(thm)],[c_0_15]) ).
cnf(c_0_17,negated_conjecture,
esk49_0 = esk51_0,
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_18,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_14]) ).
cnf(c_0_19,negated_conjecture,
esk48_0 = esk50_0,
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_20,negated_conjecture,
neq(esk51_0,nil),
inference(rw,[status(thm)],[c_0_16,c_0_17]) ).
fof(c_0_21,plain,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
inference(fof_simplification,[status(thm)],[ax15]) ).
cnf(c_0_22,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_18,c_0_19]),c_0_20])]) ).
fof(c_0_23,plain,
! [X109,X110] :
( ( ~ ssList(X109)
| ~ ssList(X110)
| neq(X109,X110)
| X109 = X110 )
& ( ~ ssList(X109)
| ~ ssList(X110)
| X109 != X110
| ~ neq(X109,X110) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_21])])])])]) ).
cnf(c_0_24,negated_conjecture,
ssList(esk49_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_25,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_22]) ).
cnf(c_0_26,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| neq(X1,X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_27,negated_conjecture,
ssList(esk51_0),
inference(rw,[status(thm)],[c_0_24,c_0_17]) ).
cnf(c_0_28,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[ax17]) ).
fof(c_0_29,plain,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> ssList(tl(X1)) ) ),
inference(fof_simplification,[status(thm)],[ax24]) ).
cnf(c_0_30,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_25,c_0_26]),c_0_27]),c_0_28])]) ).
fof(c_0_31,plain,
! [X127] :
( ssList(tl(X127))
| nil = X127
| ~ ssList(X127) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_29])])]) ).
cnf(c_0_32,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_30]) ).
cnf(c_0_33,plain,
( ~ ssList(X1)
| ssList(tl(X1))
| nil = X1 ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
fof(c_0_34,plain,
! [X130,X131] :
( ssList(app(X130,X131))
| ~ ssList(X131)
| ~ ssList(X130) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax26])])])]) ).
fof(c_0_35,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_36,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_32,c_0_33]),c_0_27])]) ).
cnf(c_0_37,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ssList(app(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_38,negated_conjecture,
ssList(esk48_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
fof(c_0_39,plain,
! [X230,X231] :
( tl(app(X230,X231)) = app(tl(X230),X231)
| 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_35])])])]) ).
cnf(c_0_40,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_36,c_0_37]),c_0_38])]) ).
cnf(c_0_41,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| tl(app(X1,X2)) = app(tl(X1),X2)
| nil = X1 ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_42,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_40,c_0_33]),c_0_27])]) ).
fof(c_0_43,plain,
! [X214,X215,X216] :
( X216 = X214
| app(X216,X215) != app(X214,X215)
| ~ ssList(X216)
| ~ ssList(X215)
| ~ ssList(X214) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax79])])])]) ).
cnf(c_0_44,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_41,c_0_42]),c_0_38])]) ).
cnf(c_0_45,plain,
( app(X3,X2) != app(X1,X2)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| X3 = X1 ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_46,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_44,c_0_33]),c_0_27])]) ).
fof(c_0_47,plain,
! [X135] :
( app(nil,X135) = X135
| ~ ssList(X135) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax28])])]) ).
cnf(c_0_48,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_45,c_0_46]) ).
cnf(c_0_49,plain,
( ~ ssList(X1)
| app(nil,X1) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
fof(c_0_50,plain,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> cons(hd(X1),tl(X1)) = X1 ) ),
inference(fof_simplification,[status(thm)],[ax78]) ).
cnf(c_0_51,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_48,c_0_49]),c_0_28])]) ).
fof(c_0_52,plain,
! [X17,X19] :
( ( ~ ssList(X17)
| singletonP(X17)
| cons(X19,nil) != X17
| ~ ssItem(X19) )
& ( ~ ssList(X17)
| ~ singletonP(X17)
| cons(esk5_1(X17),nil) = X17 )
& ( ~ ssList(X17)
| ~ singletonP(X17)
| ssItem(esk5_1(X17)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax4])])])])])]) ).
fof(c_0_53,plain,
! [X213] :
( cons(hd(X213),tl(X213)) = X213
| nil = X213
| ~ ssList(X213) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_50])])]) ).
cnf(c_0_54,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_51,c_0_33]),c_0_38])]) ).
cnf(c_0_55,plain,
( ~ ssList(X2)
| cons(X1,nil) != X2
| ~ ssItem(X1)
| singletonP(X2) ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_56,plain,
( ~ ssList(X1)
| cons(hd(X1),tl(X1)) = X1
| nil = X1 ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_57,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_54,c_0_33]),c_0_27])]) ).
cnf(c_0_58,negated_conjecture,
( ~ singletonP(esk48_0)
| ~ neq(esk51_0,nil) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
fof(c_0_59,plain,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> ssItem(hd(X1)) ) ),
inference(fof_simplification,[status(thm)],[ax22]) ).
cnf(c_0_60,plain,
( ~ ssItem(X1)
| ~ ssList(cons(X1,nil))
| singletonP(cons(X1,nil)) ),
inference(er,[status(thm)],[c_0_55]) ).
cnf(c_0_61,negated_conjecture,
( esk48_0 = nil
| esk51_0 = nil
| cons(hd(esk48_0),nil) = esk48_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_38])]) ).
cnf(c_0_62,negated_conjecture,
~ singletonP(esk48_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_58,c_0_20])]) ).
fof(c_0_63,plain,
! [X124] :
( ssItem(hd(X124))
| nil = X124
| ~ ssList(X124) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_59])])]) ).
cnf(c_0_64,negated_conjecture,
( ~ ssItem(hd(esk48_0))
| esk51_0 = nil
| esk48_0 = nil ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_38])]),c_0_62]) ).
cnf(c_0_65,plain,
( ~ ssList(X1)
| ssItem(hd(X1))
| nil = X1 ),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
cnf(c_0_66,negated_conjecture,
( esk48_0 = nil
| esk51_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_65]),c_0_38])]) ).
cnf(c_0_67,negated_conjecture,
( esk51_0 = nil
| app(nil,tl(esk51_0)) = esk51_0 ),
inference(spm,[status(thm)],[c_0_42,c_0_66]) ).
fof(c_0_68,plain,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> cons(X2,X1) != X1 ) ),
inference(fof_simplification,[status(thm)],[ax18]) ).
cnf(c_0_69,negated_conjecture,
( ~ ssList(tl(esk51_0))
| esk51_0 = nil
| tl(esk51_0) = esk51_0 ),
inference(spm,[status(thm)],[c_0_49,c_0_67]) ).
fof(c_0_70,plain,
! [X113,X114] :
( cons(X114,X113) != X113
| ~ ssItem(X114)
| ~ ssList(X113) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_68])])])]) ).
cnf(c_0_71,negated_conjecture,
( esk51_0 = nil
| tl(esk51_0) = esk51_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_33]),c_0_27])]) ).
cnf(c_0_72,plain,
( cons(X2,X1) != X1
| ~ ssItem(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_70]) ).
cnf(c_0_73,negated_conjecture,
( esk51_0 = nil
| cons(hd(esk51_0),esk51_0) = esk51_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_71]),c_0_27])]) ).
cnf(c_0_74,negated_conjecture,
( ~ ssItem(hd(esk51_0))
| esk51_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_27])]) ).
cnf(c_0_75,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| X1 != X2
| ~ neq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_76,negated_conjecture,
esk51_0 = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_65]),c_0_27])]) ).
cnf(c_0_77,plain,
( ~ neq(X1,X1)
| ~ ssList(X1) ),
inference(er,[status(thm)],[c_0_75]) ).
cnf(c_0_78,negated_conjecture,
neq(nil,nil),
inference(rw,[status(thm)],[c_0_20,c_0_76]) ).
cnf(c_0_79,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78]),c_0_28])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWC253+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.19/10.48 % Computer : n010.cluster.edu
% 0.19/10.48 % Model : x86_64 x86_64
% 0.19/10.48 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/10.48 % Memory : 8046.5625MB
% 0.19/10.48 % OS : Linux 6.8.0-71-generic
% 0.19/10.48 % CPULimit : 300
% 0.19/10.48 % WCLimit : 300
% 0.19/10.48 % DateTime : Mon Sep 21 08:09:21 UTC 2026
% 0.19/10.48 % CPUTime :
% 0.19/10.48 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.25/10.54 Running first-order theorem proving
% 0.25/10.54 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
% 0.25/10.71 % Version: 3.5.1
% 0.25/10.71 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.25/10.71 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.25/10.71 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.25/10.71 % Starting new_bool_3 with 300s (1) cores
% 0.25/10.71 % Starting new_bool_1 with 300s (1) cores
% 0.25/10.71 % Starting sh5l with 300s (1) cores
% 0.25/10.71 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 436323 completed with status 0
% 0.25/10.71 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 0.25/10.71 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.25/10.71 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.25/10.71 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.25/10.71 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.25/10.71 % No SInE strategy applied
% 0.25/10.71 % Search class: FGHSF-FSLM21-MFFFFFNN
% 0.25/10.71 % Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 0.25/10.71 % Starting SubtermCWHack with 136s (1) cores
% 0.25/10.71 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.25/10.71 % Starting G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4d with 136s (1) cores
% 0.25/10.71 % Starting G-E--_110_C45_F1_PI_SE_CS_SP_PS_S4S with 136s (1) cores
% 0.25/10.71 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_TT_S0Y with 136s (1) cores
% 0.25/10.71 % G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4d with pid 436331 completed with status 0
% 0.25/10.71 % Result found by G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4d
% 0.25/10.71 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.25/10.71 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.25/10.71 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.25/10.71 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.25/10.71 % No SInE strategy applied
% 0.25/10.71 % Search class: FGHSF-FSLM21-MFFFFFNN
% 0.25/10.71 % Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 0.25/10.71 % Starting SubtermCWHack with 136s (1) cores
% 0.25/10.71 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.25/10.71 % Starting G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4d with 136s (1) cores
% 0.25/10.71 % Preprocessing time : 0.006 s
% 0.25/10.71
% 0.25/10.71 % Proof found!
% 0.25/10.71 % SZS status Theorem
% 0.25/10.71 % SZS output start CNFRefutation
% See solution above
% 0.25/10.71 % Parsed axioms : 96
% 0.25/10.71 % Removed by relevancy pruning/SinE : 0
% 0.25/10.71 % Initial clauses : 202
% 0.25/10.71 % Removed in clause preprocessing : 2
% 0.25/10.71 % Initial clauses in saturation : 200
% 0.25/10.71 % Processed clauses : 397
% 0.25/10.71 % ...of these trivial : 5
% 0.25/10.71 % ...subsumed : 46
% 0.25/10.71 % ...remaining for further processing : 346
% 0.25/10.71 % Other redundant clauses eliminated : 69
% 0.25/10.71 % Clauses deleted for lack of memory : 0
% 0.25/10.71 % Backward-subsumed : 87
% 0.25/10.71 % Backward-rewritten : 36
% 0.25/10.71 % Generated clauses : 1068
% 0.25/10.71 % ...of the previous two non-redundant : 894
% 0.25/10.71 % ...aggressively subsumed : 0
% 0.25/10.71 % Contextual simplify-reflections : 14
% 0.25/10.71 % Paramodulations : 971
% 0.25/10.71 % Factorizations : 0
% 0.25/10.71 % NegExts : 0
% 0.25/10.71 % Equation resolutions : 97
% 0.25/10.71 % Disequality decompositions : 0
% 0.25/10.71 % Total rewrite steps : 622
% 0.25/10.71 % ...of those cached : 605
% 0.25/10.71 % Propositional unsat checks : 0
% 0.25/10.71 % Propositional check models : 0
% 0.25/10.71 % Propositional check unsatisfiable : 0
% 0.25/10.71 % Propositional clauses : 0
% 0.25/10.71 % Propositional clauses after purity: 0
% 0.25/10.71 % Propositional unsat core size : 0
% 0.25/10.71 % Propositional preprocessing time : 0.000
% 0.25/10.71 % Propositional encoding time : 0.000
% 0.25/10.71 % Propositional solver time : 0.000
% 0.25/10.71 % Success case prop preproc time : 0.000
% 0.25/10.71 % Success case prop encoding time : 0.000
% 0.25/10.71 % Success case prop solver time : 0.000
% 0.25/10.71 % Current number of processed clauses : 217
% 0.25/10.71 % Positive orientable unit clauses : 23
% 0.25/10.71 % Positive unorientable unit clauses: 0
% 0.25/10.71 % Negative unit clauses : 3
% 0.25/10.71 % Non-unit-clauses : 191
% 0.25/10.71 % Current number of unprocessed clauses: 672
% 0.25/10.71 % ...number of literals in the above : 4790
% 0.25/10.71 % Current number of archived formulas : 0
% 0.25/10.71 % Current number of archived clauses : 123
% 0.25/10.71 % Clause-clause subsumption calls (NU) : 14906
% 0.25/10.71 % Rec. Clause-clause subsumption calls : 2452
% 0.25/10.71 % Non-unit clause-clause subsumptions : 145
% 0.25/10.71 % Unit Clause-clause subsumption calls : 140
% 0.25/10.71 % Rewrite failures with RHS unbound : 0
% 0.25/10.71 % BW rewrite match attempts : 7
% 0.25/10.71 % BW rewrite match successes : 7
% 0.25/10.71 % Condensation attempts : 0
% 0.25/10.71 % Condensation successes : 0
% 0.25/10.71 % Termbank termtop insertions : 39444
% 0.25/10.71 % Search garbage collected termcells : 4314
% 0.25/10.71
% 0.25/10.71 % -------------------------------------------------
% 0.25/10.71 % User time : 0.110 s
% 0.25/10.71 % System time : 0.008 s
% 0.25/10.71 % Total time : 0.118 s
% 0.25/10.71 % Maximum resident set size: 4272 pages
% 0.25/10.71
% 0.25/10.71 % -------------------------------------------------
% 0.25/10.71 % User time : 0.395 s
% 0.25/10.71 % System time : 0.038 s
% 0.25/10.71 % Total time : 0.433 s
% 0.25/10.71 % Maximum resident set size: 4864 pages
% 0.25/10.71 % E exiting
%------------------------------------------------------------------------------