%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWC284+1 : TPTP v9.2.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 05:19:01 PM UTC 2026
% Result : Theorem 1.66s 1.82s
% Output : CNFRefutation 1.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 23
% Syntax : Number of formulae : 145 ( 37 unt; 0 def)
% Number of atoms : 483 ( 158 equ)
% Maximal formula atoms : 27 ( 3 avg)
% Number of connectives : 569 ( 231 ~; 234 |; 39 &)
% ( 5 <=>; 60 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 10 con; 0-2 aty)
% Number of variables : 174 ( 0 sgn 104 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ~ ssList(X4)
| X2 != X4
| X1 != X3
| ! [X5] :
( ssItem(X5)
=> ! [X6] :
( ssList(X6)
=> ! [X7] :
( ~ ssList(X7)
| app(app(X6,cons(X5,nil)),X7) != X1
| ! [X8] :
( ssItem(X8)
=> ( ( ~ memberP(X6,X8)
| leq(X8,X5) )
& ( ~ memberP(X7,X8)
| leq(X5,X8) ) ) ) ) ) )
| ( nil != X3
& nil = X4 )
| ( ! [X9] :
( ~ ssItem(X9)
| cons(X9,nil) != X3
| ~ memberP(X4,X9) )
& neq(X4,nil) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
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/sandbox2/benchmark/Axioms/SWC001+0.ax',ax82) ).
fof(ax16,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> ssList(cons(X2,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax16) ).
fof(ax5,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( frontsegP(X1,X2)
<=> ? [X3] :
( ssList(X3)
& app(X2,X3) = X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax5) ).
fof(ax26,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ssList(app(X1,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax26) ).
fof(ax17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(ax81,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> cons(X2,X1) = app(cons(X2,nil),X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax81) ).
fof(ax80,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( app(X2,X3) = app(X2,X1)
=> X3 = X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax80) ).
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(ax6,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( rearsegP(X1,X2)
<=> ? [X3] :
( ssList(X3)
& app(X3,X2) = X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax6) ).
fof(ax4,axiom,
! [X1] :
( ssList(X1)
=> ( singletonP(X1)
<=> ? [X2] :
( ssItem(X2)
& cons(X2,nil) = X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax4) ).
fof(ax25,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> tl(cons(X2,X1)) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax25) ).
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(ax27,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssItem(X3)
=> cons(X3,app(X2,X1)) = app(cons(X3,X2),X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax27) ).
fof(ax21,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> nil != cons(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax21) ).
fof(ax22,axiom,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> ssItem(hd(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax22) ).
fof(ax28,axiom,
! [X1] :
( ssList(X1)
=> app(nil,X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax28) ).
fof(ax23,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> hd(cons(X2,X1)) = X2 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax23) ).
fof(ax83,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( nil = app(X1,X2)
<=> ( nil = X2
& nil = X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax83) ).
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(ax19,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssItem(X3)
=> ! [X4] :
( ssItem(X4)
=> ( cons(X3,X1) = cons(X4,X2)
=> ( X3 = X4
& X2 = X1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax19) ).
fof(ax24,axiom,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> ssList(tl(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax24) ).
fof(ax38,axiom,
! [X1] :
( ssItem(X1)
=> ~ memberP(nil,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax38) ).
fof(c_0_23,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ~ ssList(X4)
| X2 != X4
| X1 != X3
| ! [X5] :
( ssItem(X5)
=> ! [X6] :
( ssList(X6)
=> ! [X7] :
( ~ ssList(X7)
| app(app(X6,cons(X5,nil)),X7) != X1
| ! [X8] :
( ssItem(X8)
=> ( ( ~ memberP(X6,X8)
| leq(X8,X5) )
& ( ~ memberP(X7,X8)
| leq(X5,X8) ) ) ) ) ) )
| ( nil != X3
& nil = X4 )
| ( ! [X9] :
( ~ ssItem(X9)
| cons(X9,nil) != X3
| ~ memberP(X4,X9) )
& neq(X4,nil) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[co1])]) ).
fof(c_0_24,negated_conjecture,
( ssList(esk48_0)
& ssList(esk49_0)
& ssList(esk50_0)
& ssList(esk51_0)
& esk49_0 = esk51_0
& esk48_0 = esk50_0
& ssItem(esk52_0)
& ssList(esk53_0)
& ssList(esk54_0)
& app(app(esk53_0,cons(esk52_0,nil)),esk54_0) = esk48_0
& ssItem(esk55_0)
& ( memberP(esk54_0,esk55_0)
| memberP(esk53_0,esk55_0) )
& ( ~ leq(esk52_0,esk55_0)
| memberP(esk53_0,esk55_0) )
& ( memberP(esk54_0,esk55_0)
| ~ leq(esk55_0,esk52_0) )
& ( ~ leq(esk52_0,esk55_0)
| ~ leq(esk55_0,esk52_0) )
& ( nil = esk50_0
| nil != esk51_0 )
& ( ssItem(esk56_0)
| ~ neq(esk51_0,nil) )
& ( cons(esk56_0,nil) = esk50_0
| ~ neq(esk51_0,nil) )
& ( memberP(esk51_0,esk56_0)
| ~ neq(esk51_0,nil) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_23])])])]) ).
cnf(c_0_25,negated_conjecture,
app(app(esk53_0,cons(esk52_0,nil)),esk54_0) = esk48_0,
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_26,negated_conjecture,
esk48_0 = esk50_0,
inference(split_conjunct,[status(thm)],[c_0_24]) ).
fof(c_0_27,plain,
! [X437,X438,X439] :
( ~ ssList(X437)
| ~ ssList(X438)
| ~ ssList(X439)
| app(app(X437,X438),X439) = app(X437,app(X438,X439)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax82])])]) ).
cnf(c_0_28,negated_conjecture,
app(app(esk53_0,cons(esk52_0,nil)),esk54_0) = esk50_0,
inference(rw,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_29,plain,
( app(app(X1,X2),X3) = app(X1,app(X2,X3))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_30,negated_conjecture,
ssList(esk54_0),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_31,negated_conjecture,
ssList(esk53_0),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
fof(c_0_32,plain,
! [X326,X327] :
( ~ ssList(X326)
| ~ ssItem(X327)
| ssList(cons(X327,X326)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax16])])]) ).
fof(c_0_33,plain,
! [X235,X236,X238] :
( ( ssList(esk6_2(X235,X236))
| ~ frontsegP(X235,X236)
| ~ ssList(X236)
| ~ ssList(X235) )
& ( app(X236,esk6_2(X235,X236)) = X235
| ~ frontsegP(X235,X236)
| ~ ssList(X236)
| ~ ssList(X235) )
& ( ~ ssList(X238)
| app(X236,X238) != X235
| frontsegP(X235,X236)
| ~ ssList(X236)
| ~ ssList(X235) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax5])])])])]) ).
fof(c_0_34,plain,
! [X345,X346] :
( ~ ssList(X345)
| ~ ssList(X346)
| ssList(app(X345,X346)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax26])])]) ).
cnf(c_0_35,negated_conjecture,
( app(esk53_0,app(cons(esk52_0,nil),esk54_0)) = esk50_0
| ~ ssList(cons(esk52_0,nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30]),c_0_31])]) ).
cnf(c_0_36,plain,
( ssList(cons(X2,X1))
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_37,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[ax17]) ).
cnf(c_0_38,negated_conjecture,
ssItem(esk52_0),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
fof(c_0_39,plain,
! [X435,X436] :
( ~ ssList(X435)
| ~ ssItem(X436)
| cons(X436,X435) = app(cons(X436,nil),X435) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax81])])]) ).
cnf(c_0_40,plain,
( frontsegP(X3,X2)
| ~ ssList(X1)
| app(X2,X1) != X3
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_41,plain,
( ssList(app(X1,X2))
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_42,negated_conjecture,
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_35,c_0_36]),c_0_37]),c_0_38])]) ).
cnf(c_0_43,plain,
( cons(X2,X1) = app(cons(X2,nil),X1)
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_44,plain,
( frontsegP(app(X1,X2),X1)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_40]),c_0_41]) ).
cnf(c_0_45,negated_conjecture,
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_42,c_0_43]),c_0_30]),c_0_38])]) ).
cnf(c_0_46,negated_conjecture,
( frontsegP(esk50_0,esk53_0)
| ~ ssList(cons(esk52_0,esk54_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_31])]) ).
cnf(c_0_47,negated_conjecture,
ssList(esk48_0),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
fof(c_0_48,plain,
! [X432,X433,X434] :
( ~ ssList(X432)
| ~ ssList(X433)
| ~ ssList(X434)
| app(X433,X434) != app(X433,X432)
| X434 = X432 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax80])])]) ).
cnf(c_0_49,plain,
( app(X1,esk6_2(X2,X1)) = X2
| ~ frontsegP(X2,X1)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_50,negated_conjecture,
frontsegP(esk50_0,esk53_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_36]),c_0_30]),c_0_38])]) ).
cnf(c_0_51,negated_conjecture,
ssList(esk50_0),
inference(rw,[status(thm)],[c_0_47,c_0_26]) ).
cnf(c_0_52,plain,
( ssList(esk6_2(X1,X2))
| ~ frontsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_53,plain,
( X3 = X1
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| app(X2,X3) != app(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_54,negated_conjecture,
app(esk53_0,esk6_2(esk50_0,esk53_0)) = esk50_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_51]),c_0_31])]) ).
cnf(c_0_55,negated_conjecture,
ssList(esk6_2(esk50_0,esk53_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_50]),c_0_31]),c_0_51])]) ).
cnf(c_0_56,negated_conjecture,
( X1 = esk6_2(esk50_0,esk53_0)
| app(esk53_0,X1) != esk50_0
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_55]),c_0_31])]) ).
cnf(c_0_57,negated_conjecture,
( esk6_2(esk50_0,esk53_0) = cons(esk52_0,esk54_0)
| ~ ssList(cons(esk52_0,esk54_0)) ),
inference(spm,[status(thm)],[c_0_56,c_0_45]) ).
cnf(c_0_58,negated_conjecture,
esk6_2(esk50_0,esk53_0) = cons(esk52_0,esk54_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_36]),c_0_30]),c_0_38])]) ).
fof(c_0_59,plain,
! [X324,X325] :
( ( ~ neq(X324,X325)
| X324 != X325
| ~ ssList(X325)
| ~ ssList(X324) )
& ( X324 = X325
| neq(X324,X325)
| ~ ssList(X325)
| ~ ssList(X324) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax15])])])]) ).
cnf(c_0_60,negated_conjecture,
ssList(esk49_0),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_61,negated_conjecture,
esk49_0 = esk51_0,
inference(split_conjunct,[status(thm)],[c_0_24]) ).
fof(c_0_62,plain,
! [X239,X240,X242] :
( ( ssList(esk7_2(X239,X240))
| ~ rearsegP(X239,X240)
| ~ ssList(X240)
| ~ ssList(X239) )
& ( app(esk7_2(X239,X240),X240) = X239
| ~ rearsegP(X239,X240)
| ~ ssList(X240)
| ~ ssList(X239) )
& ( ~ ssList(X242)
| app(X242,X240) != X239
| rearsegP(X239,X240)
| ~ ssList(X240)
| ~ ssList(X239) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax6])])])])]) ).
cnf(c_0_63,negated_conjecture,
( X1 = cons(esk52_0,esk54_0)
| app(esk53_0,X1) != esk50_0
| ~ ssList(X1) ),
inference(rw,[status(thm)],[c_0_56,c_0_58]) ).
fof(c_0_64,plain,
! [X232,X234] :
( ( ssItem(esk5_1(X232))
| ~ singletonP(X232)
| ~ ssList(X232) )
& ( cons(esk5_1(X232),nil) = X232
| ~ singletonP(X232)
| ~ ssList(X232) )
& ( ~ ssItem(X234)
| cons(X234,nil) != X232
| singletonP(X232)
| ~ ssList(X232) ) ),
inference(distribute,[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_65,plain,
! [X343,X344] :
( ~ ssList(X343)
| ~ ssItem(X344)
| tl(cons(X344,X343)) = X343 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax25])])]) ).
cnf(c_0_66,negated_conjecture,
( cons(esk56_0,nil) = esk50_0
| ~ neq(esk51_0,nil) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_67,plain,
( X1 = X2
| neq(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
cnf(c_0_68,negated_conjecture,
ssList(esk51_0),
inference(rw,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_69,negated_conjecture,
( ssItem(esk56_0)
| ~ neq(esk51_0,nil) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_70,plain,
( rearsegP(X3,X2)
| ~ ssList(X1)
| app(X1,X2) != X3
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_71,negated_conjecture,
( app(cons(esk52_0,nil),esk54_0) = cons(esk52_0,esk54_0)
| ~ ssList(app(cons(esk52_0,nil),esk54_0)) ),
inference(spm,[status(thm)],[c_0_63,c_0_42]) ).
cnf(c_0_72,plain,
( singletonP(X2)
| ~ ssItem(X1)
| cons(X1,nil) != X2
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
fof(c_0_73,plain,
! [X428] :
( ~ ssList(X428)
| nil = X428
| cons(hd(X428),tl(X428)) = X428 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax78])]) ).
cnf(c_0_74,plain,
( tl(cons(X2,X1)) = X1
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_65]) ).
cnf(c_0_75,negated_conjecture,
( cons(esk56_0,nil) = esk50_0
| esk51_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_67]),c_0_37]),c_0_68])]) ).
cnf(c_0_76,negated_conjecture,
( esk51_0 = nil
| ssItem(esk56_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_67]),c_0_37]),c_0_68])]) ).
cnf(c_0_77,plain,
( rearsegP(app(X1,X2),X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_70]),c_0_41]) ).
fof(c_0_78,plain,
! [X347,X348,X349] :
( ~ ssList(X347)
| ~ ssList(X348)
| ~ ssItem(X349)
| cons(X349,app(X348,X347)) = app(cons(X349,X348),X347) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax27])])]) ).
cnf(c_0_79,negated_conjecture,
( app(cons(esk52_0,nil),esk54_0) = cons(esk52_0,esk54_0)
| ~ ssList(cons(esk52_0,nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_41]),c_0_30])]) ).
cnf(c_0_80,plain,
( singletonP(cons(X1,nil))
| ~ ssList(cons(X1,nil))
| ~ ssItem(X1) ),
inference(er,[status(thm)],[c_0_72]) ).
cnf(c_0_81,plain,
( nil = X1
| cons(hd(X1),tl(X1)) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_73]) ).
cnf(c_0_82,negated_conjecture,
( tl(esk50_0) = nil
| esk51_0 = nil ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_37])]),c_0_76]) ).
cnf(c_0_83,negated_conjecture,
( nil = esk50_0
| nil != esk51_0 ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_84,negated_conjecture,
( rearsegP(esk50_0,cons(esk52_0,esk54_0))
| ~ ssList(cons(esk52_0,esk54_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_45]),c_0_31])]) ).
fof(c_0_85,plain,
! [X337,X338] :
( ~ ssList(X337)
| ~ ssItem(X338)
| nil != cons(X338,X337) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax21])])]) ).
cnf(c_0_86,plain,
( cons(X3,app(X2,X1)) = app(cons(X3,X2),X1)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssItem(X3) ),
inference(split_conjunct,[status(thm)],[c_0_78]) ).
cnf(c_0_87,negated_conjecture,
app(cons(esk52_0,nil),esk54_0) = cons(esk52_0,esk54_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_36]),c_0_37]),c_0_38])]) ).
cnf(c_0_88,plain,
( singletonP(cons(X1,nil))
| ~ ssItem(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_36]),c_0_37])]) ).
cnf(c_0_89,negated_conjecture,
( cons(hd(esk50_0),nil) = esk50_0
| esk50_0 = nil ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_82]),c_0_51])]),c_0_83]) ).
fof(c_0_90,plain,
! [X339] :
( ~ ssList(X339)
| nil = X339
| ssItem(hd(X339)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax22])]) ).
cnf(c_0_91,plain,
( app(esk7_2(X1,X2),X2) = X1
| ~ rearsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_92,negated_conjecture,
rearsegP(esk50_0,cons(esk52_0,esk54_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_36]),c_0_30]),c_0_38])]) ).
cnf(c_0_93,plain,
( ssList(esk7_2(X1,X2))
| ~ rearsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_94,plain,
( ~ ssList(X1)
| ~ ssItem(X2)
| nil != cons(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_85]) ).
cnf(c_0_95,negated_conjecture,
cons(esk52_0,app(nil,esk54_0)) = cons(esk52_0,esk54_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_87]),c_0_37]),c_0_30]),c_0_38])]) ).
fof(c_0_96,plain,
! [X350] :
( ~ ssList(X350)
| app(nil,X350) = X350 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax28])]) ).
fof(c_0_97,plain,
! [X340,X341] :
( ~ ssList(X340)
| ~ ssItem(X341)
| hd(cons(X341,X340)) = X341 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax23])])]) ).
cnf(c_0_98,plain,
( cons(esk5_1(X1),nil) = X1
| ~ singletonP(X1)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
cnf(c_0_99,plain,
( ssItem(esk5_1(X1))
| ~ singletonP(X1)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
cnf(c_0_100,negated_conjecture,
( esk50_0 = nil
| singletonP(esk50_0)
| ~ ssItem(hd(esk50_0)) ),
inference(spm,[status(thm)],[c_0_88,c_0_89]) ).
cnf(c_0_101,plain,
( nil = X1
| ssItem(hd(X1))
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_90]) ).
fof(c_0_102,plain,
! [X440,X441] :
( ( nil = X441
| nil != app(X440,X441)
| ~ ssList(X441)
| ~ ssList(X440) )
& ( nil = X440
| nil != app(X440,X441)
| ~ ssList(X441)
| ~ ssList(X440) )
& ( nil != X441
| nil != X440
| nil = app(X440,X441)
| ~ ssList(X441)
| ~ ssList(X440) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax83])])])]) ).
cnf(c_0_103,negated_conjecture,
( app(esk7_2(esk50_0,cons(esk52_0,esk54_0)),cons(esk52_0,esk54_0)) = esk50_0
| ~ ssList(cons(esk52_0,esk54_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_92]),c_0_51])]) ).
cnf(c_0_104,negated_conjecture,
ssList(cons(esk52_0,esk54_0)),
inference(rw,[status(thm)],[c_0_55,c_0_58]) ).
cnf(c_0_105,negated_conjecture,
( ssList(esk7_2(esk50_0,cons(esk52_0,esk54_0)))
| ~ ssList(cons(esk52_0,esk54_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_92]),c_0_51])]) ).
cnf(c_0_106,negated_conjecture,
( cons(esk52_0,esk54_0) != nil
| ~ ssList(app(nil,esk54_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_95]),c_0_38])]) ).
cnf(c_0_107,plain,
( app(nil,X1) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_96]) ).
cnf(c_0_108,plain,
( hd(cons(X2,X1)) = X2
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_97]) ).
cnf(c_0_109,plain,
( tl(X1) = nil
| ~ singletonP(X1)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_98]),c_0_37])]),c_0_99]) ).
cnf(c_0_110,negated_conjecture,
( esk50_0 = nil
| singletonP(esk50_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_101]),c_0_51])]) ).
cnf(c_0_111,plain,
( nil = X1
| nil != app(X2,X1)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_102]) ).
cnf(c_0_112,negated_conjecture,
app(esk7_2(esk50_0,cons(esk52_0,esk54_0)),cons(esk52_0,esk54_0)) = esk50_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_103,c_0_104])]) ).
cnf(c_0_113,negated_conjecture,
ssList(esk7_2(esk50_0,cons(esk52_0,esk54_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_36]),c_0_30]),c_0_38])]) ).
cnf(c_0_114,negated_conjecture,
cons(esk52_0,esk54_0) != nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_107]),c_0_30])]) ).
cnf(c_0_115,plain,
( esk5_1(X1) = hd(X1)
| ~ singletonP(X1)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_98]),c_0_37])]),c_0_99]) ).
fof(c_0_116,plain,
! [X445,X446] :
( ~ ssList(X445)
| ~ ssList(X446)
| nil = X445
| tl(app(X445,X446)) = app(tl(X445),X446) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax86])])]) ).
cnf(c_0_117,negated_conjecture,
( tl(esk50_0) = nil
| esk50_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_110]),c_0_51])]) ).
cnf(c_0_118,negated_conjecture,
esk50_0 != nil,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_112]),c_0_113]),c_0_104])]),c_0_114]) ).
cnf(c_0_119,plain,
( ssItem(hd(X1))
| ~ singletonP(X1)
| ~ ssList(X1) ),
inference(spm,[status(thm)],[c_0_99,c_0_115]) ).
cnf(c_0_120,plain,
( nil = X1
| tl(app(X1,X2)) = app(tl(X1),X2)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_116]) ).
cnf(c_0_121,negated_conjecture,
tl(esk50_0) = nil,
inference(sr,[status(thm)],[c_0_117,c_0_118]) ).
fof(c_0_122,plain,
! [X330,X331,X332,X333] :
( ( X332 = X333
| cons(X332,X330) != cons(X333,X331)
| ~ ssItem(X333)
| ~ ssItem(X332)
| ~ ssList(X331)
| ~ ssList(X330) )
& ( X331 = X330
| cons(X332,X330) != cons(X333,X331)
| ~ ssItem(X333)
| ~ ssItem(X332)
| ~ ssList(X331)
| ~ ssList(X330) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax19])])])]) ).
cnf(c_0_123,negated_conjecture,
( esk50_0 = nil
| ssItem(hd(esk50_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_119,c_0_110]),c_0_51])]) ).
cnf(c_0_124,negated_conjecture,
( app(tl(esk53_0),cons(esk52_0,esk54_0)) = nil
| esk53_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_120,c_0_45]),c_0_31])]),c_0_121]),c_0_104])]) ).
fof(c_0_125,plain,
! [X342] :
( ~ ssList(X342)
| nil = X342
| ssList(tl(X342)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax24])]) ).
cnf(c_0_126,plain,
( X1 = X2
| cons(X3,X2) != cons(X4,X1)
| ~ ssItem(X4)
| ~ ssItem(X3)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_122]) ).
cnf(c_0_127,negated_conjecture,
cons(hd(esk50_0),nil) = esk50_0,
inference(sr,[status(thm)],[c_0_89,c_0_118]) ).
cnf(c_0_128,negated_conjecture,
ssItem(hd(esk50_0)),
inference(sr,[status(thm)],[c_0_123,c_0_118]) ).
cnf(c_0_129,negated_conjecture,
( esk53_0 = nil
| ~ ssList(tl(esk53_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_124]),c_0_104])]),c_0_114]) ).
cnf(c_0_130,plain,
( nil = X1
| ssList(tl(X1))
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_125]) ).
cnf(c_0_131,negated_conjecture,
( X1 = nil
| cons(X2,X1) != esk50_0
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_126,c_0_127]),c_0_37]),c_0_128])]) ).
cnf(c_0_132,negated_conjecture,
esk53_0 = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_129,c_0_130]),c_0_31])]) ).
cnf(c_0_133,negated_conjecture,
( app(nil,esk54_0) = nil
| cons(esk52_0,esk54_0) != esk50_0
| ~ ssList(app(nil,esk54_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_131,c_0_95]),c_0_38])]) ).
cnf(c_0_134,negated_conjecture,
app(nil,cons(esk52_0,esk54_0)) = esk50_0,
inference(rw,[status(thm)],[c_0_45,c_0_132]) ).
fof(c_0_135,plain,
! [X1] :
( ssItem(X1)
=> ~ memberP(nil,X1) ),
inference(fof_simplification,[status(thm)],[ax38]) ).
cnf(c_0_136,negated_conjecture,
( esk54_0 = nil
| cons(esk52_0,esk54_0) != esk50_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_133,c_0_107]),c_0_30])]) ).
cnf(c_0_137,negated_conjecture,
cons(esk52_0,esk54_0) = esk50_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_134]),c_0_104])]) ).
fof(c_0_138,plain,
! [X372] :
( ~ ssItem(X372)
| ~ memberP(nil,X372) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_135])]) ).
cnf(c_0_139,negated_conjecture,
( memberP(esk54_0,esk55_0)
| memberP(esk53_0,esk55_0) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_140,negated_conjecture,
esk54_0 = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_136,c_0_137])]) ).
cnf(c_0_141,plain,
( ~ ssItem(X1)
| ~ memberP(nil,X1) ),
inference(split_conjunct,[status(thm)],[c_0_138]) ).
cnf(c_0_142,negated_conjecture,
memberP(nil,esk55_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_139,c_0_132]),c_0_140])]) ).
cnf(c_0_143,negated_conjecture,
ssItem(esk55_0),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_144,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_141,c_0_142]),c_0_143])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SWC284+1 : TPTP v9.2.1. Released v2.4.0.
% 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.34 % Computer : n017.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Tue May 5 04:41:13 EDT 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.35 % start to proof: theBenchmark
% 1.66/1.82 % Version : CSE_E---1.7
% 1.66/1.82 % Problem : theBenchmark.p
% 1.66/1.82 % SZS status Theorem for theBenchmark.p
% 1.66/1.82 % SZS output start CNFRefutation
% See solution above
% 1.66/1.83 % Total time : 1.373s
%------------------------------------------------------------------------------