%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWC232+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 : n018.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 05:18:49 PM UTC 2026
% Result : Theorem 4.54s 3.36s
% Output : CNFRefutation 4.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 21
% Syntax : Number of formulae : 130 ( 18 unt; 0 def)
% Number of atoms : 501 ( 183 equ)
% Maximal formula atoms : 46 ( 3 avg)
% Number of connectives : 618 ( 247 ~; 264 |; 43 &)
% ( 1 <=>; 63 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 8 con; 0-3 aty)
% Number of variables : 185 ( 0 sgn 97 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| nil = X1
| ? [X5] :
( ssItem(X5)
& ? [X6] :
( ssList(X6)
& ? [X7] :
( ssList(X7)
& app(app(X6,cons(X5,nil)),X7) = X1
& ! [X8] :
( ssItem(X8)
=> ( ~ memberP(X6,X8)
| ~ memberP(X7,X8)
| ~ leq(X5,X8)
| lt(X5,X8) ) ) ) ) )
| ( nil != X3
& ! [X9] :
( ssItem(X9)
=> ! [X10] :
( ssList(X10)
=> ! [X11] :
( ssList(X11)
=> ( app(app(X10,cons(X9,nil)),X11) != X3
| ? [X12] :
( ssItem(X12)
& ~ leq(X9,X12)
& memberP(X10,X12)
& memberP(X11,X12)
& lt(X9,X12) ) ) ) ) ) ) ) ) ) ) ),
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(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(ax16,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> ssList(cons(X2,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax16) ).
fof(ax17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(ax26,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ssList(app(X1,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax26) ).
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(ax25,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> tl(cons(X2,X1)) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax25) ).
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(ax24,axiom,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> ssList(tl(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax24) ).
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(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(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(ax78,axiom,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> cons(hd(X1),tl(X1)) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax78) ).
fof(ax22,axiom,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> ssItem(hd(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax22) ).
fof(ax21,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> nil != cons(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax21) ).
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(ax20,axiom,
! [X1] :
( ssList(X1)
=> ( nil = X1
| ? [X2] :
( ssList(X2)
& ? [X3] :
( ssItem(X3)
& cons(X3,X2) = X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax20) ).
fof(ax38,axiom,
! [X1] :
( ssItem(X1)
=> ~ memberP(nil,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax38) ).
fof(ax28,axiom,
! [X1] :
( ssList(X1)
=> app(nil,X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax28) ).
fof(c_0_21,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| nil = X1
| ? [X5] :
( ssItem(X5)
& ? [X6] :
( ssList(X6)
& ? [X7] :
( ssList(X7)
& app(app(X6,cons(X5,nil)),X7) = X1
& ! [X8] :
( ssItem(X8)
=> ( ~ memberP(X6,X8)
| ~ memberP(X7,X8)
| ~ leq(X5,X8)
| lt(X5,X8) ) ) ) ) )
| ( nil != X3
& ! [X9] :
( ssItem(X9)
=> ! [X10] :
( ssList(X10)
=> ! [X11] :
( ssList(X11)
=> ( app(app(X10,cons(X9,nil)),X11) != X3
| ? [X12] :
( ssItem(X12)
& ~ leq(X9,X12)
& memberP(X10,X12)
& memberP(X11,X12)
& lt(X9,X12) ) ) ) ) ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[co1])]) ).
fof(c_0_22,negated_conjecture,
! [X476,X477,X478,X483] :
( ssList(esk48_0)
& ssList(esk49_0)
& ssList(esk50_0)
& ssList(esk51_0)
& esk49_0 = esk51_0
& esk48_0 = esk50_0
& nil != esk48_0
& ( ssItem(esk52_3(X476,X477,X478))
| ~ ssList(X478)
| app(app(X477,cons(X476,nil)),X478) != esk48_0
| ~ ssList(X477)
| ~ ssItem(X476) )
& ( memberP(X477,esk52_3(X476,X477,X478))
| ~ ssList(X478)
| app(app(X477,cons(X476,nil)),X478) != esk48_0
| ~ ssList(X477)
| ~ ssItem(X476) )
& ( memberP(X478,esk52_3(X476,X477,X478))
| ~ ssList(X478)
| app(app(X477,cons(X476,nil)),X478) != esk48_0
| ~ ssList(X477)
| ~ ssItem(X476) )
& ( leq(X476,esk52_3(X476,X477,X478))
| ~ ssList(X478)
| app(app(X477,cons(X476,nil)),X478) != esk48_0
| ~ ssList(X477)
| ~ ssItem(X476) )
& ( ~ lt(X476,esk52_3(X476,X477,X478))
| ~ ssList(X478)
| app(app(X477,cons(X476,nil)),X478) != esk48_0
| ~ ssList(X477)
| ~ ssItem(X476) )
& ( ssItem(esk53_0)
| nil = esk50_0 )
& ( ssList(esk54_0)
| nil = esk50_0 )
& ( ssList(esk55_0)
| nil = esk50_0 )
& ( app(app(esk54_0,cons(esk53_0,nil)),esk55_0) = esk50_0
| nil = esk50_0 )
& ( ~ ssItem(X483)
| leq(esk53_0,X483)
| ~ memberP(esk54_0,X483)
| ~ memberP(esk55_0,X483)
| ~ lt(esk53_0,X483)
| nil = esk50_0 ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_21])])])])]) ).
cnf(c_0_23,negated_conjecture,
( app(app(esk54_0,cons(esk53_0,nil)),esk55_0) = esk50_0
| nil = esk50_0 ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_24,negated_conjecture,
esk48_0 = esk50_0,
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_25,negated_conjecture,
nil != esk48_0,
inference(split_conjunct,[status(thm)],[c_0_22]) ).
fof(c_0_26,plain,
! [X443,X444,X445] :
( ~ ssList(X443)
| ~ ssList(X444)
| ~ ssList(X445)
| app(app(X443,X444),X445) = app(X443,app(X444,X445)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax82])])]) ).
cnf(c_0_27,negated_conjecture,
( ssList(esk55_0)
| nil = esk50_0 ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_28,negated_conjecture,
( ssList(esk54_0)
| nil = esk50_0 ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_29,negated_conjecture,
app(app(esk54_0,cons(esk53_0,nil)),esk55_0) = esk48_0,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_23,c_0_24]),c_0_24]),c_0_25]) ).
cnf(c_0_30,plain,
( app(app(X1,X2),X3) = app(X1,app(X2,X3))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_31,negated_conjecture,
ssList(esk55_0),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_24]),c_0_25]) ).
cnf(c_0_32,negated_conjecture,
ssList(esk54_0),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_28,c_0_24]),c_0_25]) ).
fof(c_0_33,plain,
! [X441,X442] :
( ~ ssList(X441)
| ~ ssItem(X442)
| cons(X442,X441) = app(cons(X442,nil),X441) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax81])])]) ).
cnf(c_0_34,negated_conjecture,
( ssItem(esk53_0)
| nil = esk50_0 ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
fof(c_0_35,plain,
! [X438,X439,X440] :
( ~ ssList(X438)
| ~ ssList(X439)
| ~ ssList(X440)
| app(X439,X440) != app(X439,X438)
| X440 = X438 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax80])])]) ).
cnf(c_0_36,negated_conjecture,
( app(esk54_0,app(cons(esk53_0,nil),esk55_0)) = esk48_0
| ~ ssList(cons(esk53_0,nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31]),c_0_32])]) ).
cnf(c_0_37,plain,
( cons(X2,X1) = app(cons(X2,nil),X1)
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_38,negated_conjecture,
ssItem(esk53_0),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_24]),c_0_25]) ).
cnf(c_0_39,plain,
( X3 = X1
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| app(X2,X3) != app(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_40,negated_conjecture,
( app(esk54_0,cons(esk53_0,esk55_0)) = esk48_0
| ~ ssList(cons(esk53_0,nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_31]),c_0_38])]) ).
fof(c_0_41,plain,
! [X332,X333] :
( ~ ssList(X332)
| ~ ssItem(X333)
| ssList(cons(X333,X332)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax16])])]) ).
cnf(c_0_42,negated_conjecture,
( X1 = cons(esk53_0,esk55_0)
| app(esk54_0,X1) != esk48_0
| ~ ssList(cons(esk53_0,esk55_0))
| ~ ssList(cons(esk53_0,nil))
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_32])]) ).
cnf(c_0_43,plain,
( ssList(cons(X2,X1))
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_44,negated_conjecture,
( X1 = cons(esk53_0,esk55_0)
| app(esk54_0,X1) != esk48_0
| ~ ssList(cons(esk53_0,nil))
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_31]),c_0_38])]) ).
cnf(c_0_45,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[ax17]) ).
cnf(c_0_46,negated_conjecture,
( X1 = cons(esk53_0,esk55_0)
| app(esk54_0,X1) != esk48_0
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_43]),c_0_45]),c_0_38])]) ).
fof(c_0_47,plain,
! [X351,X352] :
( ~ ssList(X351)
| ~ ssList(X352)
| ssList(app(X351,X352)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax26])])]) ).
fof(c_0_48,plain,
! [X353,X354,X355] :
( ~ ssList(X353)
| ~ ssList(X354)
| ~ ssItem(X355)
| cons(X355,app(X354,X353)) = app(cons(X355,X354),X353) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax27])])]) ).
cnf(c_0_49,negated_conjecture,
( app(cons(esk53_0,nil),esk55_0) = cons(esk53_0,esk55_0)
| ~ ssList(app(cons(esk53_0,nil),esk55_0))
| ~ ssList(cons(esk53_0,nil)) ),
inference(spm,[status(thm)],[c_0_46,c_0_36]) ).
cnf(c_0_50,plain,
( ssList(app(X1,X2))
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
fof(c_0_51,plain,
! [X349,X350] :
( ~ ssList(X349)
| ~ ssItem(X350)
| tl(cons(X350,X349)) = X349 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax25])])]) ).
cnf(c_0_52,plain,
( cons(X3,app(X2,X1)) = app(cons(X3,X2),X1)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssItem(X3) ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_53,negated_conjecture,
( app(cons(esk53_0,nil),esk55_0) = cons(esk53_0,esk55_0)
| ~ ssList(cons(esk53_0,nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_31])]) ).
cnf(c_0_54,plain,
( tl(cons(X2,X1)) = X1
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_55,negated_conjecture,
( cons(esk53_0,app(nil,esk55_0)) = cons(esk53_0,esk55_0)
| ~ ssList(cons(esk53_0,nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_45]),c_0_31]),c_0_38])]) ).
cnf(c_0_56,negated_conjecture,
( tl(cons(esk53_0,esk55_0)) = app(nil,esk55_0)
| ~ ssList(app(nil,esk55_0))
| ~ ssList(cons(esk53_0,nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_38])]) ).
cnf(c_0_57,negated_conjecture,
( app(nil,esk55_0) = esk55_0
| ~ ssList(app(nil,esk55_0))
| ~ ssList(cons(esk53_0,nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_56]),c_0_31]),c_0_38])]) ).
fof(c_0_58,plain,
! [X435,X436,X437] :
( ~ ssList(X435)
| ~ ssList(X436)
| ~ ssList(X437)
| app(X437,X436) != app(X435,X436)
| X437 = X435 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax79])])]) ).
cnf(c_0_59,negated_conjecture,
( app(nil,esk55_0) = esk55_0
| ~ ssList(cons(esk53_0,nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_50]),c_0_31]),c_0_45])]) ).
cnf(c_0_60,plain,
( X3 = X1
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| app(X3,X2) != app(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_61,negated_conjecture,
app(nil,esk55_0) = esk55_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_43]),c_0_45]),c_0_38])]) ).
cnf(c_0_62,negated_conjecture,
( X1 = nil
| app(X1,esk55_0) != esk55_0
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_45]),c_0_31])]) ).
fof(c_0_63,plain,
! [X348] :
( ~ ssList(X348)
| nil = X348
| ssList(tl(X348)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax24])]) ).
fof(c_0_64,plain,
! [X451,X452] :
( ~ ssList(X451)
| ~ ssList(X452)
| nil = X451
| tl(app(X451,X452)) = app(tl(X451),X452) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax86])])]) ).
fof(c_0_65,plain,
! [X446,X447] :
( ( nil = X447
| nil != app(X446,X447)
| ~ ssList(X447)
| ~ ssList(X446) )
& ( nil = X446
| nil != app(X446,X447)
| ~ ssList(X447)
| ~ ssList(X446) )
& ( nil != X447
| nil != X446
| nil = app(X446,X447)
| ~ ssList(X447)
| ~ ssList(X446) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax83])])])]) ).
cnf(c_0_66,negated_conjecture,
( app(esk54_0,cons(esk53_0,nil)) = nil
| esk55_0 != esk48_0
| ~ ssList(app(esk54_0,cons(esk53_0,nil))) ),
inference(spm,[status(thm)],[c_0_62,c_0_29]) ).
fof(c_0_67,plain,
! [X449,X450] :
( ~ ssList(X449)
| ~ ssList(X450)
| nil = X449
| hd(app(X449,X450)) = hd(X449) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax85])])]) ).
fof(c_0_68,plain,
! [X434] :
( ~ ssList(X434)
| nil = X434
| cons(hd(X434),tl(X434)) = X434 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax78])]) ).
cnf(c_0_69,plain,
( nil = X1
| ssList(tl(X1))
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
cnf(c_0_70,plain,
( nil = X1
| tl(app(X1,X2)) = app(tl(X1),X2)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
cnf(c_0_71,plain,
( nil = X1
| nil != app(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_65]) ).
cnf(c_0_72,plain,
( nil = X1
| nil != app(X2,X1)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_65]) ).
cnf(c_0_73,negated_conjecture,
( app(esk54_0,cons(esk53_0,nil)) = nil
| esk55_0 != esk48_0
| ~ ssList(cons(esk53_0,nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_50]),c_0_32])]) ).
fof(c_0_74,plain,
! [X345] :
( ~ ssList(X345)
| nil = X345
| ssItem(hd(X345)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax22])]) ).
cnf(c_0_75,plain,
( nil = X1
| hd(app(X1,X2)) = hd(X1)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_67]) ).
cnf(c_0_76,plain,
( nil = X1
| cons(hd(X1),tl(X1)) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_68]) ).
cnf(c_0_77,plain,
( nil = X1
| ssList(app(tl(X1),X2))
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_50]),c_0_71]) ).
cnf(c_0_78,negated_conjecture,
( app(tl(app(esk54_0,cons(esk53_0,nil))),esk55_0) = tl(esk48_0)
| app(esk54_0,cons(esk53_0,nil)) = nil
| ~ ssList(app(esk54_0,cons(esk53_0,nil))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_29]),c_0_31])]) ).
fof(c_0_79,plain,
! [X343,X344] :
( ~ ssList(X343)
| ~ ssItem(X344)
| nil != cons(X344,X343) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax21])])]) ).
cnf(c_0_80,negated_conjecture,
( cons(esk53_0,nil) = nil
| esk55_0 != esk48_0
| ~ ssList(cons(esk53_0,nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_32])]) ).
cnf(c_0_81,plain,
( nil = X1
| ssItem(hd(X1))
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_74]) ).
cnf(c_0_82,negated_conjecture,
( hd(app(esk54_0,cons(esk53_0,nil))) = hd(esk48_0)
| app(esk54_0,cons(esk53_0,nil)) = nil
| ~ ssList(app(esk54_0,cons(esk53_0,nil))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_29]),c_0_31])]) ).
cnf(c_0_83,plain,
( cons(hd(app(X1,X2)),app(tl(X1),X2)) = app(X1,X2)
| nil = X1
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_70]),c_0_50]),c_0_71]) ).
cnf(c_0_84,negated_conjecture,
( app(esk54_0,cons(esk53_0,nil)) = nil
| ssList(tl(esk48_0))
| ~ ssList(app(esk54_0,cons(esk53_0,nil))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78]),c_0_31])]) ).
cnf(c_0_85,plain,
( ~ ssList(X1)
| ~ ssItem(X2)
| nil != cons(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_79]) ).
cnf(c_0_86,negated_conjecture,
( cons(esk53_0,nil) = nil
| esk55_0 != esk48_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_43]),c_0_45]),c_0_38])]) ).
cnf(c_0_87,negated_conjecture,
( app(esk54_0,cons(esk53_0,nil)) = nil
| ssItem(hd(esk48_0))
| ~ ssList(app(esk54_0,cons(esk53_0,nil))) ),
inference(spm,[status(thm)],[c_0_81,c_0_82]) ).
fof(c_0_88,plain,
! [X336,X337,X338,X339] :
( ( X338 = X339
| cons(X338,X336) != cons(X339,X337)
| ~ ssItem(X339)
| ~ ssItem(X338)
| ~ ssList(X337)
| ~ ssList(X336) )
& ( X337 = X336
| cons(X338,X336) != cons(X339,X337)
| ~ ssItem(X339)
| ~ ssItem(X338)
| ~ ssList(X337)
| ~ ssList(X336) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax19])])])]) ).
fof(c_0_89,plain,
! [X340] :
( ( ssList(esk44_1(X340))
| nil = X340
| ~ ssList(X340) )
& ( ssItem(esk45_1(X340))
| nil = X340
| ~ ssList(X340) )
& ( cons(esk45_1(X340),esk44_1(X340)) = X340
| nil = X340
| ~ ssList(X340) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax20])])])]) ).
cnf(c_0_90,negated_conjecture,
( app(esk54_0,cons(esk53_0,nil)) = nil
| cons(hd(esk48_0),tl(esk48_0)) = esk48_0
| ~ ssList(app(esk54_0,cons(esk53_0,nil))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_78]),c_0_29]),c_0_29]),c_0_31])]) ).
cnf(c_0_91,negated_conjecture,
( app(esk54_0,cons(esk53_0,nil)) = nil
| ssList(tl(esk48_0))
| ~ ssList(cons(esk53_0,nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_50]),c_0_32])]) ).
cnf(c_0_92,negated_conjecture,
esk55_0 != esk48_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_86]),c_0_45]),c_0_38])]) ).
cnf(c_0_93,negated_conjecture,
( app(esk54_0,cons(esk53_0,nil)) = nil
| ssItem(hd(esk48_0))
| ~ ssList(cons(esk53_0,nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_50]),c_0_32])]) ).
cnf(c_0_94,plain,
( X1 = X2
| cons(X3,X2) != cons(X4,X1)
| ~ ssItem(X4)
| ~ ssItem(X3)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_88]) ).
cnf(c_0_95,plain,
( cons(esk45_1(X1),esk44_1(X1)) = X1
| nil = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_89]) ).
cnf(c_0_96,plain,
( ssItem(esk45_1(X1))
| nil = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_89]) ).
cnf(c_0_97,negated_conjecture,
( cons(hd(esk48_0),tl(esk48_0)) = esk48_0
| app(esk54_0,cons(esk53_0,nil)) = nil
| ~ ssList(cons(esk53_0,nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_50]),c_0_32])]) ).
cnf(c_0_98,negated_conjecture,
( ssList(tl(esk48_0))
| ~ ssList(cons(esk53_0,nil)) ),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_91]),c_0_61]),c_0_92]) ).
cnf(c_0_99,negated_conjecture,
( ssItem(hd(esk48_0))
| ~ ssList(cons(esk53_0,nil)) ),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_93]),c_0_61]),c_0_92]) ).
cnf(c_0_100,plain,
( esk44_1(cons(X1,X2)) = X2
| ~ ssList(esk44_1(cons(X1,X2)))
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_95])]),c_0_96]),c_0_43]),c_0_85]) ).
cnf(c_0_101,negated_conjecture,
( cons(hd(esk48_0),tl(esk48_0)) = esk48_0
| ~ ssList(cons(esk53_0,nil)) ),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_97]),c_0_61]),c_0_92]) ).
cnf(c_0_102,negated_conjecture,
ssList(tl(esk48_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_43]),c_0_45]),c_0_38])]) ).
cnf(c_0_103,negated_conjecture,
ssItem(hd(esk48_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_43]),c_0_45]),c_0_38])]) ).
cnf(c_0_104,plain,
( nil = app(X2,X1)
| nil != X1
| nil != X2
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_65]) ).
cnf(c_0_105,negated_conjecture,
( esk44_1(esk48_0) = tl(esk48_0)
| ~ ssList(cons(esk53_0,nil))
| ~ ssList(esk44_1(esk48_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_101]),c_0_102]),c_0_103])]) ).
fof(c_0_106,plain,
! [X1] :
( ssItem(X1)
=> ~ memberP(nil,X1) ),
inference(fof_simplification,[status(thm)],[ax38]) ).
fof(c_0_107,plain,
! [X356] :
( ~ ssList(X356)
| app(nil,X356) = X356 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax28])]) ).
cnf(c_0_108,plain,
( ssList(cons(X1,app(X2,X3)))
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_52]),c_0_43]) ).
cnf(c_0_109,plain,
app(nil,nil) = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_104])]),c_0_45])]) ).
cnf(c_0_110,plain,
( X1 = X2
| cons(X1,X3) != cons(X2,X4)
| ~ ssItem(X2)
| ~ ssItem(X1)
| ~ ssList(X4)
| ~ ssList(X3) ),
inference(split_conjunct,[status(thm)],[c_0_88]) ).
cnf(c_0_111,negated_conjecture,
( esk44_1(esk48_0) = tl(esk48_0)
| ~ ssList(esk44_1(esk48_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_43]),c_0_45]),c_0_38])]) ).
cnf(c_0_112,plain,
( ssList(esk44_1(X1))
| nil = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_89]) ).
cnf(c_0_113,negated_conjecture,
ssList(esk48_0),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
fof(c_0_114,plain,
! [X378] :
( ~ ssItem(X378)
| ~ memberP(nil,X378) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_106])]) ).
cnf(c_0_115,negated_conjecture,
( memberP(X1,esk52_3(X2,X1,X3))
| ~ ssList(X3)
| app(app(X1,cons(X2,nil)),X3) != esk48_0
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_116,plain,
( app(nil,X1) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_107]) ).
cnf(c_0_117,plain,
( ssList(cons(X1,nil))
| ~ ssItem(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_109]),c_0_45])]) ).
cnf(c_0_118,negated_conjecture,
( ssItem(esk52_3(X1,X2,X3))
| ~ ssList(X3)
| app(app(X2,cons(X1,nil)),X3) != esk48_0
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_119,plain,
( esk45_1(cons(X1,X2)) = X1
| ~ ssList(esk44_1(cons(X1,X2)))
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_95])]),c_0_96]),c_0_43]),c_0_85]) ).
cnf(c_0_120,negated_conjecture,
esk44_1(esk48_0) = tl(esk48_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_112]),c_0_113])]),c_0_25]) ).
cnf(c_0_121,plain,
( ~ ssItem(X1)
| ~ memberP(nil,X1) ),
inference(split_conjunct,[status(thm)],[c_0_114]) ).
cnf(c_0_122,negated_conjecture,
( memberP(nil,esk52_3(X1,nil,X2))
| app(cons(X1,nil),X2) != esk48_0
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_116]),c_0_45])]),c_0_117]) ).
cnf(c_0_123,negated_conjecture,
( ssItem(esk52_3(X1,nil,X2))
| app(cons(X1,nil),X2) != esk48_0
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_116]),c_0_45])]),c_0_117]) ).
cnf(c_0_124,negated_conjecture,
( esk45_1(esk48_0) = hd(esk48_0)
| ~ ssList(cons(esk53_0,nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_119,c_0_101]),c_0_102]),c_0_103])]),c_0_120]),c_0_102])]) ).
cnf(c_0_125,negated_conjecture,
( app(cons(X1,nil),X2) != esk48_0
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_121,c_0_122]),c_0_123]) ).
cnf(c_0_126,negated_conjecture,
esk45_1(esk48_0) = hd(esk48_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_124,c_0_43]),c_0_45]),c_0_38])]) ).
cnf(c_0_127,negated_conjecture,
( cons(X1,X2) != esk48_0
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(spm,[status(thm)],[c_0_125,c_0_37]) ).
cnf(c_0_128,negated_conjecture,
cons(hd(esk48_0),tl(esk48_0)) = esk48_0,
inference(rw,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_120]),c_0_113])]),c_0_25]),c_0_126]) ).
cnf(c_0_129,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_127,c_0_128]),c_0_102]),c_0_103])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWC232+1 : TPTP v9.2.1. Released v2.4.0.
% 0.00/0.12 % 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
% 0.15/0.33 % Computer : n018.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue May 5 04:36:32 EDT 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.35 % start to proof: theBenchmark
% 4.54/3.36 % Version : CSE_E---1.7
% 4.54/3.36 % Problem : theBenchmark.p
% 4.54/3.36 % SZS status Theorem for theBenchmark.p
% 4.54/3.36 % SZS output start CNFRefutation
% See solution above
% 4.54/3.37 % Total time : 2.370s
%------------------------------------------------------------------------------