%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWC297+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 : n015.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 02:43:49 PM UTC 2026
% Result : Theorem 0.58s 0.74s
% Output : CNFRefutation 0.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 15
% Syntax : Number of formulae : 96 ( 23 unt; 0 def)
% Number of atoms : 350 ( 127 equ)
% Maximal formula atoms : 27 ( 3 avg)
% Number of connectives : 411 ( 157 ~; 152 |; 33 &)
% ( 3 <=>; 66 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 10 con; 0-2 aty)
% Number of variables : 117 ( 0 sgn 87 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( neq(X4,nil)
& ! [X9] :
( ssItem(X9)
=> ( ~ memberP(X4,X9)
| cons(X9,nil) != X3 ) ) )
| ( nil = X4
& nil != X3 )
| ! [X5] :
( ssItem(X5)
=> ! [X6] :
( ssList(X6)
=> ! [X7] :
( ssList(X7)
=> ( ! [X8] :
( ssItem(X8)
=> ( ( lt(X5,X8)
| ~ memberP(X7,X8) )
& ( lt(X8,X5)
| ~ memberP(X6,X8) ) ) )
| app(app(X6,cons(X5,nil)),X7) != X1 ) ) ) )
| X1 != X3
| X2 != X4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
fof(ax83,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( nil = app(X1,X2)
<=> ( nil = X1
& nil = X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax83) ).
fof(ax26,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ssList(app(X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax26) ).
fof(ax16,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> ssList(cons(X2,X1)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax16) ).
fof(ax17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(ax38,axiom,
! [X1] :
( ssItem(X1)
=> ~ memberP(nil,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax38) ).
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(ax82,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> app(app(X1,X2),X3) = app(X1,app(X2,X3)) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax82) ).
fof(ax86,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( nil != X1
=> tl(app(X1,X2)) = app(tl(X1),X2) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax86) ).
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(ax25,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> tl(cons(X2,X1)) = X1 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax25) ).
fof(ax24,axiom,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> ssList(tl(X1)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax24) ).
fof(ax21,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> nil != cons(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax21) ).
fof(ax28,axiom,
! [X1] :
( ssList(X1)
=> app(nil,X1) = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax28) ).
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(c_0_15,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( neq(X4,nil)
& ! [X9] :
( ssItem(X9)
=> ( ~ memberP(X4,X9)
| cons(X9,nil) != X3 ) ) )
| ( nil = X4
& nil != X3 )
| ! [X5] :
( ssItem(X5)
=> ! [X6] :
( ssList(X6)
=> ! [X7] :
( ssList(X7)
=> ( ! [X8] :
( ssItem(X8)
=> ( ( lt(X5,X8)
| ~ memberP(X7,X8) )
& ( lt(X8,X5)
| ~ memberP(X6,X8) ) ) )
| app(app(X6,cons(X5,nil)),X7) != X1 ) ) ) )
| 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)
=> ( ( neq(X4,nil)
& ! [X9] :
( ssItem(X9)
=> ( ~ memberP(X4,X9)
| cons(X9,nil) != X3 ) ) )
| ( nil = X4
& nil != X3 )
| ! [X5] :
( ssItem(X5)
=> ! [X6] :
( ssList(X6)
=> ! [X7] :
( ssList(X7)
=> ( ! [X8] :
( ssItem(X8)
=> ( ( lt(X5,X8)
| ~ memberP(X7,X8) )
& ( lt(X8,X5)
| ~ memberP(X6,X8) ) ) )
| app(app(X6,cons(X5,nil)),X7) != X1 ) ) ) )
| X1 != X3
| X2 != X4 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_15]) ).
fof(c_0_17,negated_conjecture,
( ( ~ neq(esk51_0,nil)
| memberP(esk51_0,esk56_0) )
& ( ~ neq(esk51_0,nil)
| cons(esk56_0,nil) = esk50_0 )
& ( ~ neq(esk51_0,nil)
| ssItem(esk56_0) )
& ( nil != esk51_0
| nil = esk50_0 )
& ( ~ lt(esk55_0,esk52_0)
| ~ lt(esk52_0,esk55_0) )
& ( ~ lt(esk55_0,esk52_0)
| memberP(esk54_0,esk55_0) )
& ( memberP(esk53_0,esk55_0)
| ~ lt(esk52_0,esk55_0) )
& ( memberP(esk53_0,esk55_0)
| memberP(esk54_0,esk55_0) )
& ssItem(esk55_0)
& app(app(esk53_0,cons(esk52_0,nil)),esk54_0) = esk48_0
& ssList(esk54_0)
& ssList(esk53_0)
& ssItem(esk52_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(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_16])])])])]) ).
fof(c_0_18,plain,
! [X228,X229] :
( ( ~ ssList(X228)
| ~ ssList(X229)
| nil = app(X228,X229)
| nil != X228
| nil != X229 )
& ( ~ ssList(X228)
| ~ ssList(X229)
| nil != app(X228,X229)
| nil = X228 )
& ( ~ ssList(X228)
| ~ ssList(X229)
| nil != app(X228,X229)
| nil = X229 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax83])])])])]) ).
cnf(c_0_19,negated_conjecture,
app(app(esk53_0,cons(esk52_0,nil)),esk54_0) = esk48_0,
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_20,negated_conjecture,
esk48_0 = esk50_0,
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_21,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| nil != app(X2,X1)
| nil = X1 ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_22,negated_conjecture,
app(app(esk53_0,cons(esk52_0,nil)),esk54_0) = esk50_0,
inference(rw,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_23,negated_conjecture,
ssList(esk54_0),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_24,plain,
! [X133,X134] :
( ssList(app(X133,X134))
| ~ ssList(X134)
| ~ ssList(X133) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax26])])])]) ).
cnf(c_0_25,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| nil != app(X1,X2)
| nil = X1 ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_26,negated_conjecture,
( ~ ssList(app(esk53_0,cons(esk52_0,nil)))
| esk50_0 != nil
| esk54_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23])]) ).
cnf(c_0_27,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ssList(app(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_28,negated_conjecture,
ssList(esk53_0),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_29,plain,
! [X114,X115] :
( ssList(cons(X115,X114))
| ~ ssItem(X115)
| ~ ssList(X114) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax16])])])]) ).
cnf(c_0_30,negated_conjecture,
( ~ ssList(app(esk53_0,cons(esk52_0,nil)))
| esk50_0 != nil
| app(esk53_0,cons(esk52_0,nil)) = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_22]),c_0_23])]) ).
cnf(c_0_31,negated_conjecture,
( ~ ssList(cons(esk52_0,nil))
| esk50_0 != nil
| esk54_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28])]) ).
cnf(c_0_32,plain,
( ~ ssItem(X2)
| ~ ssList(X1)
| ssList(cons(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_33,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[ax17]) ).
cnf(c_0_34,negated_conjecture,
ssItem(esk52_0),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_35,negated_conjecture,
( ~ ssList(cons(esk52_0,nil))
| esk50_0 != nil
| app(esk53_0,cons(esk52_0,nil)) = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_27]),c_0_28])]) ).
fof(c_0_36,plain,
! [X1] :
( ssItem(X1)
=> ~ memberP(nil,X1) ),
inference(fof_simplification,[status(thm)],[ax38]) ).
cnf(c_0_37,negated_conjecture,
( memberP(esk53_0,esk55_0)
| memberP(esk54_0,esk55_0) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_38,negated_conjecture,
( esk50_0 != nil
| esk54_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_33]),c_0_34])]) ).
cnf(c_0_39,negated_conjecture,
( ~ ssList(cons(esk52_0,nil))
| esk50_0 != nil
| esk53_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_35]),c_0_28])]) ).
fof(c_0_40,plain,
! [X160] :
( ~ memberP(nil,X160)
| ~ ssItem(X160) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_36])])]) ).
cnf(c_0_41,negated_conjecture,
( esk50_0 != nil
| memberP(esk53_0,esk55_0)
| memberP(nil,esk55_0) ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_42,negated_conjecture,
( esk50_0 != nil
| esk53_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_32]),c_0_33]),c_0_34])]) ).
fof(c_0_43,plain,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
inference(fof_simplification,[status(thm)],[ax15]) ).
cnf(c_0_44,plain,
( ~ memberP(nil,X1)
| ~ ssItem(X1) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_45,negated_conjecture,
( esk50_0 != nil
| memberP(nil,esk55_0) ),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_46,negated_conjecture,
ssItem(esk55_0),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_47,plain,
! [X225,X226,X227] :
( app(app(X225,X226),X227) = app(X225,app(X226,X227))
| ~ ssList(X227)
| ~ ssList(X226)
| ~ ssList(X225) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax82])])])]) ).
fof(c_0_48,plain,
! [X112,X113] :
( ( ~ ssList(X112)
| ~ ssList(X113)
| neq(X112,X113)
| X112 = X113 )
& ( ~ ssList(X112)
| ~ ssList(X113)
| X112 != X113
| ~ neq(X112,X113) ) ),
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_43])])])])]) ).
cnf(c_0_49,negated_conjecture,
ssList(esk49_0),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_50,negated_conjecture,
esk49_0 = esk51_0,
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_51,negated_conjecture,
esk50_0 != nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_46])]) ).
cnf(c_0_52,negated_conjecture,
( nil != esk51_0
| nil = esk50_0 ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_53,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_54,plain,
( ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| app(app(X1,X2),X3) = app(X1,app(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
fof(c_0_55,plain,
! [X223,X224] :
( cons(X224,X223) = app(cons(X224,nil),X223)
| ~ ssItem(X224)
| ~ ssList(X223) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax81])])])]) ).
fof(c_0_56,plain,
! [X131,X132] :
( tl(cons(X132,X131)) = X131
| ~ ssItem(X132)
| ~ ssList(X131) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax25])])])]) ).
cnf(c_0_57,negated_conjecture,
( ~ neq(esk51_0,nil)
| cons(esk56_0,nil) = esk50_0 ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_58,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| neq(X1,X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_59,negated_conjecture,
ssList(esk51_0),
inference(rw,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_60,negated_conjecture,
esk51_0 != nil,
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_61,negated_conjecture,
( ~ neq(esk51_0,nil)
| ssItem(esk56_0) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_62,plain,
! [X233,X234] :
( tl(app(X233,X234)) = app(tl(X233),X234)
| nil = X233
| ~ ssList(X234)
| ~ ssList(X233) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_53])])])]) ).
cnf(c_0_63,negated_conjecture,
( ~ ssList(cons(esk52_0,nil))
| app(esk53_0,app(cons(esk52_0,nil),esk54_0)) = esk50_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_54]),c_0_23]),c_0_28])]) ).
cnf(c_0_64,plain,
( ~ ssItem(X2)
| ~ ssList(X1)
| cons(X2,X1) = app(cons(X2,nil),X1) ),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_65,plain,
( ~ ssItem(X2)
| ~ ssList(X1)
| tl(cons(X2,X1)) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_66,negated_conjecture,
cons(esk56_0,nil) = esk50_0,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_33]),c_0_59])]),c_0_60]) ).
cnf(c_0_67,negated_conjecture,
ssItem(esk56_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_58]),c_0_33]),c_0_59])]),c_0_60]) ).
cnf(c_0_68,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| tl(app(X1,X2)) = app(tl(X1),X2)
| nil = X1 ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_69,negated_conjecture,
( ~ ssList(cons(esk52_0,nil))
| app(esk53_0,cons(esk52_0,esk54_0)) = esk50_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_23]),c_0_34])]) ).
cnf(c_0_70,negated_conjecture,
tl(esk50_0) = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_33]),c_0_67])]) ).
fof(c_0_71,plain,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> ssList(tl(X1)) ) ),
inference(fof_simplification,[status(thm)],[ax24]) ).
cnf(c_0_72,negated_conjecture,
( ~ ssList(cons(esk52_0,nil))
| ~ ssList(cons(esk52_0,esk54_0))
| esk53_0 = nil
| app(tl(esk53_0),cons(esk52_0,esk54_0)) = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_70]),c_0_28])]) ).
fof(c_0_73,plain,
! [X130] :
( ssList(tl(X130))
| nil = X130
| ~ ssList(X130) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_71])])]) ).
cnf(c_0_74,negated_conjecture,
( ~ ssList(tl(esk53_0))
| ~ ssList(cons(esk52_0,nil))
| ~ ssList(cons(esk52_0,esk54_0))
| esk53_0 = nil
| cons(esk52_0,esk54_0) = nil ),
inference(spm,[status(thm)],[c_0_21,c_0_72]) ).
cnf(c_0_75,plain,
( ~ ssList(X1)
| ssList(tl(X1))
| nil = X1 ),
inference(split_conjunct,[status(thm)],[c_0_73]) ).
fof(c_0_76,plain,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> nil != cons(X2,X1) ) ),
inference(fof_simplification,[status(thm)],[ax21]) ).
cnf(c_0_77,negated_conjecture,
( ~ ssList(cons(esk52_0,nil))
| ~ ssList(cons(esk52_0,esk54_0))
| esk53_0 = nil
| cons(esk52_0,esk54_0) = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_28])]) ).
fof(c_0_78,plain,
! [X125,X126] :
( nil != cons(X126,X125)
| ~ ssItem(X126)
| ~ ssList(X125) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_76])])])]) ).
cnf(c_0_79,negated_conjecture,
( ~ ssList(cons(esk52_0,nil))
| esk53_0 = nil
| cons(esk52_0,esk54_0) = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_32]),c_0_23]),c_0_34])]) ).
cnf(c_0_80,plain,
( nil != cons(X2,X1)
| ~ ssItem(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_78]) ).
cnf(c_0_81,negated_conjecture,
( esk53_0 = nil
| cons(esk52_0,esk54_0) = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_32]),c_0_33]),c_0_34])]) ).
cnf(c_0_82,negated_conjecture,
esk53_0 = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_81]),c_0_23]),c_0_34])]) ).
fof(c_0_83,plain,
! [X138] :
( app(nil,X138) = X138
| ~ ssList(X138) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax28])])]) ).
cnf(c_0_84,negated_conjecture,
app(app(nil,cons(esk52_0,nil)),esk54_0) = esk50_0,
inference(spm,[status(thm)],[c_0_22,c_0_82]) ).
cnf(c_0_85,plain,
( ~ ssList(X1)
| app(nil,X1) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_83]) ).
fof(c_0_86,plain,
! [X118,X119,X120,X121] :
( ( ~ ssList(X118)
| ~ ssList(X119)
| ~ ssItem(X120)
| ~ ssItem(X121)
| cons(X120,X118) != cons(X121,X119)
| X119 = X118 )
& ( ~ ssList(X118)
| ~ ssList(X119)
| ~ ssItem(X120)
| ~ ssItem(X121)
| cons(X120,X118) != cons(X121,X119)
| X120 = X121 ) ),
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_87,negated_conjecture,
( ~ ssList(cons(esk52_0,nil))
| app(cons(esk52_0,nil),esk54_0) = esk50_0 ),
inference(spm,[status(thm)],[c_0_84,c_0_85]) ).
cnf(c_0_88,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X3)
| ~ ssItem(X4)
| cons(X3,X2) != cons(X4,X1)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_86]) ).
cnf(c_0_89,negated_conjecture,
( ~ ssList(cons(esk52_0,nil))
| cons(esk52_0,esk54_0) = esk50_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_87]),c_0_23]),c_0_34])]) ).
cnf(c_0_90,negated_conjecture,
( ~ ssItem(X2)
| ~ ssList(X1)
| cons(X2,X1) != esk50_0
| nil = X1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_66]),c_0_33]),c_0_67])]) ).
cnf(c_0_91,negated_conjecture,
cons(esk52_0,esk54_0) = esk50_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_32]),c_0_33]),c_0_34])]) ).
cnf(c_0_92,negated_conjecture,
( memberP(nil,esk55_0)
| memberP(esk54_0,esk55_0) ),
inference(rw,[status(thm)],[c_0_37,c_0_82]) ).
cnf(c_0_93,negated_conjecture,
esk54_0 = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_91]),c_0_23]),c_0_34])]) ).
cnf(c_0_94,negated_conjecture,
memberP(nil,esk55_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_92,c_0_93])]) ).
cnf(c_0_95,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_94]),c_0_46])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWC297+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.20/0.45 % Computer : n015.cluster.edu
% 0.20/0.45 % Model : x86_64 x86_64
% 0.20/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.45 % Memory : 8046.5625MB
% 0.20/0.45 % OS : Linux 6.8.0-71-generic
% 0.20/0.45 % CPULimit : 300
% 0.20/0.45 % WCLimit : 300
% 0.20/0.45 % DateTime : Mon Sep 21 08:16:20 UTC 2026
% 0.20/0.45 % CPUTime :
% 0.20/0.45 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.24/0.52 Running first-order theorem proving
% 0.24/0.52 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
% 0.58/0.74 % Version: 3.5.1
% 0.58/0.74 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.58/0.74 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.58/0.74 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.58/0.74 % Starting new_bool_3 with 300s (1) cores
% 0.58/0.74 % Starting new_bool_1 with 300s (1) cores
% 0.58/0.74 % Starting sh5l with 300s (1) cores
% 0.58/0.74 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 1012081 completed with status 0
% 0.58/0.74 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 0.58/0.74 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.58/0.74 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.58/0.74 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.58/0.74 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.58/0.74 % No SInE strategy applied
% 0.58/0.74 % Search class: FGHSF-FSLM21-MFFFFFNN
% 0.58/0.74 % Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 0.58/0.74 % Starting SubtermCWHack with 136s (1) cores
% 0.58/0.74 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.58/0.74 % Starting G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4d with 136s (1) cores
% 0.58/0.74 % Starting G-E--_110_C45_F1_PI_SE_CS_SP_PS_S4S with 136s (1) cores
% 0.58/0.74 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_TT_S0Y with 136s (1) cores
% 0.58/0.74 % G-E--_208_C18_F1_SE_CS_SP_PS_TT_S0Y with pid 1012092 completed with status 0
% 0.58/0.74 % Result found by G-E--_208_C18_F1_SE_CS_SP_PS_TT_S0Y
% 0.58/0.74 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.58/0.74 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.58/0.74 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.58/0.74 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.58/0.74 % No SInE strategy applied
% 0.58/0.74 % Search class: FGHSF-FSLM21-MFFFFFNN
% 0.58/0.74 % Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 0.58/0.74 % Starting SubtermCWHack with 136s (1) cores
% 0.58/0.74 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.58/0.74 % Starting G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4d with 136s (1) cores
% 0.58/0.74 % Starting G-E--_110_C45_F1_PI_SE_CS_SP_PS_S4S with 136s (1) cores
% 0.58/0.74 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_TT_S0Y with 136s (1) cores
% 0.58/0.74 % Preprocessing time : 0.006 s
% 0.58/0.74 % Presaturation interreduction done
% 0.58/0.74
% 0.58/0.74 % Proof found!
% 0.58/0.74 % SZS status Theorem
% 0.58/0.74 % SZS output start CNFRefutation
% See solution above
% 0.58/0.74 % Parsed axioms : 96
% 0.58/0.74 % Removed by relevancy pruning/SinE : 0
% 0.58/0.74 % Initial clauses : 209
% 0.58/0.74 % Removed in clause preprocessing : 2
% 0.58/0.74 % Initial clauses in saturation : 207
% 0.58/0.74 % Processed clauses : 834
% 0.58/0.74 % ...of these trivial : 7
% 0.58/0.74 % ...subsumed : 179
% 0.58/0.74 % ...remaining for further processing : 648
% 0.58/0.74 % Other redundant clauses eliminated : 98
% 0.58/0.74 % Clauses deleted for lack of memory : 0
% 0.58/0.74 % Backward-subsumed : 50
% 0.58/0.74 % Backward-rewritten : 75
% 0.58/0.74 % Generated clauses : 2265
% 0.58/0.74 % ...of the previous two non-redundant : 2010
% 0.58/0.74 % ...aggressively subsumed : 0
% 0.58/0.74 % Contextual simplify-reflections : 51
% 0.58/0.74 % Paramodulations : 2164
% 0.58/0.74 % Factorizations : 0
% 0.58/0.74 % NegExts : 0
% 0.58/0.74 % Equation resolutions : 103
% 0.58/0.74 % Disequality decompositions : 0
% 0.58/0.74 % Total rewrite steps : 1945
% 0.58/0.74 % ...of those cached : 1899
% 0.58/0.74 % Propositional unsat checks : 0
% 0.58/0.74 % Propositional check models : 0
% 0.58/0.74 % Propositional check unsatisfiable : 0
% 0.58/0.74 % Propositional clauses : 0
% 0.58/0.74 % Propositional clauses after purity: 0
% 0.58/0.74 % Propositional unsat core size : 0
% 0.58/0.74 % Propositional preprocessing time : 0.000
% 0.58/0.74 % Propositional encoding time : 0.000
% 0.58/0.74 % Propositional solver time : 0.000
% 0.58/0.74 % Success case prop preproc time : 0.000
% 0.58/0.74 % Success case prop encoding time : 0.000
% 0.58/0.74 % Success case prop solver time : 0.000
% 0.58/0.74 % Current number of processed clauses : 299
% 0.58/0.74 % Positive orientable unit clauses : 47
% 0.58/0.74 % Positive unorientable unit clauses: 0
% 0.58/0.74 % Negative unit clauses : 7
% 0.58/0.74 % Non-unit-clauses : 245
% 0.58/0.74 % Current number of unprocessed clauses: 1523
% 0.58/0.74 % ...number of literals in the above : 9811
% 0.58/0.74 % Current number of archived formulas : 0
% 0.58/0.74 % Current number of archived clauses : 326
% 0.58/0.74 % Clause-clause subsumption calls (NU) : 25775
% 0.58/0.74 % Rec. Clause-clause subsumption calls : 6834
% 0.58/0.74 % Non-unit clause-clause subsumptions : 197
% 0.58/0.74 % Unit Clause-clause subsumption calls : 513
% 0.58/0.74 % Rewrite failures with RHS unbound : 0
% 0.58/0.74 % BW rewrite match attempts : 13
% 0.58/0.74 % BW rewrite match successes : 13
% 0.58/0.74 % Condensation attempts : 0
% 0.58/0.74 % Condensation successes : 0
% 0.58/0.74 % Termbank termtop insertions : 61737
% 0.58/0.74 % Search garbage collected termcells : 4402
% 0.58/0.74
% 0.58/0.74 % -------------------------------------------------
% 0.58/0.74 % User time : 0.177 s
% 0.58/0.74 % System time : 0.007 s
% 0.58/0.74 % Total time : 0.185 s
% 0.58/0.74 % Maximum resident set size: 4276 pages
% 0.58/0.74
% 0.58/0.74 % -------------------------------------------------
% 0.58/0.74 % User time : 0.813 s
% 0.58/0.74 % System time : 0.047 s
% 0.58/0.74 % Total time : 0.860 s
% 0.58/0.74 % Maximum resident set size: 4608 pages
% 0.58/0.74 % E exiting
%------------------------------------------------------------------------------