%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWC183+1 : TPTP v9.2.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n027.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 05:18:38 PM UTC 2026
% Result : Theorem 1.69s 1.82s
% Output : CNFRefutation 1.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 21
% Syntax : Number of formulae : 132 ( 36 unt; 0 def)
% Number of atoms : 480 ( 146 equ)
% Maximal formula atoms : 34 ( 3 avg)
% Number of connectives : 586 ( 238 ~; 243 |; 46 &)
% ( 6 <=>; 53 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 9 con; 0-2 aty)
% Number of variables : 172 ( 0 sgn 100 !; 6 ?)
% 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
| ( ~ memberP(X6,X5)
& ~ memberP(X7,X5) ) ) ) )
| ( ! [X8] :
( ~ ssItem(X8)
| cons(X8,nil) != X3
| ~ memberP(X4,X8)
| ? [X9] :
( ssItem(X9)
& X8 != X9
& memberP(X4,X9)
& leq(X8,X9) ) )
& ( nil != X4
| nil != X3 ) ) ) ) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/SWC001+0.ax',ax82) ).
fof(ax16,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> ssList(cons(X2,X1)) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/SWC001+0.ax',ax5) ).
fof(ax26,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ssList(app(X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax26) ).
fof(ax17,axiom,
ssList(nil),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/Axioms/SWC001+0.ax',ax80) ).
fof(ax6,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( rearsegP(X1,X2)
<=> ? [X3] :
( ssList(X3)
& app(X3,X2) = X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax6) ).
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/sandbox/benchmark/Axioms/SWC001+0.ax',ax27) ).
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(ax3,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> ( memberP(X1,X2)
<=> ? [X3] :
( ssList(X3)
& ? [X4] :
( ssList(X4)
& app(X3,cons(X2,X4)) = X1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax3) ).
fof(ax83,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( nil = app(X1,X2)
<=> ( nil = X2
& nil = X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax83) ).
fof(ax36,axiom,
! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( memberP(app(X2,X3),X1)
<=> ( memberP(X2,X1)
| memberP(X3,X1) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax36) ).
fof(ax38,axiom,
! [X1] :
( ssItem(X1)
=> ~ memberP(nil,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax38) ).
fof(ax37,axiom,
! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssList(X3)
=> ( memberP(cons(X2,X3),X1)
<=> ( X1 = X2
| memberP(X3,X1) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax37) ).
fof(ax84,axiom,
! [X1] :
( ssList(X1)
=> app(X1,nil) = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax84) ).
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(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(ax24,axiom,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> ssList(tl(X1)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax24) ).
fof(c_0_21,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
| ( ~ memberP(X6,X5)
& ~ memberP(X7,X5) ) ) ) )
| ( ! [X8] :
( ~ ssItem(X8)
| cons(X8,nil) != X3
| ~ memberP(X4,X8)
| ? [X9] :
( ssItem(X9)
& X8 != X9
& memberP(X4,X9)
& leq(X8,X9) ) )
& ( nil != X4
| nil != X3 ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[co1])]) ).
fof(c_0_22,negated_conjecture,
! [X474] :
( 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
& ( memberP(esk53_0,esk52_0)
| memberP(esk54_0,esk52_0) )
& ( nil = esk51_0
| ssItem(esk55_0) )
& ( nil = esk50_0
| ssItem(esk55_0) )
& ( nil = esk51_0
| cons(esk55_0,nil) = esk50_0 )
& ( nil = esk50_0
| cons(esk55_0,nil) = esk50_0 )
& ( nil = esk51_0
| memberP(esk51_0,esk55_0) )
& ( nil = esk50_0
| memberP(esk51_0,esk55_0) )
& ( nil = esk51_0
| ~ ssItem(X474)
| esk55_0 = X474
| ~ memberP(esk51_0,X474)
| ~ leq(esk55_0,X474) )
& ( nil = esk50_0
| ~ ssItem(X474)
| esk55_0 = X474
| ~ memberP(esk51_0,X474)
| ~ leq(esk55_0,X474) ) ),
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(esk53_0,cons(esk52_0,nil)),esk54_0) = esk48_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]) ).
fof(c_0_25,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_26,negated_conjecture,
app(app(esk53_0,cons(esk52_0,nil)),esk54_0) = esk50_0,
inference(rw,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_27,plain,
( app(app(X1,X2),X3) = app(X1,app(X2,X3))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_28,negated_conjecture,
ssList(esk54_0),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_29,negated_conjecture,
ssList(esk53_0),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
fof(c_0_30,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_31,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_32,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_33,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_26,c_0_27]),c_0_28]),c_0_29])]) ).
cnf(c_0_34,plain,
( ssList(cons(X2,X1))
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_35,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[ax17]) ).
cnf(c_0_36,negated_conjecture,
ssItem(esk52_0),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
fof(c_0_37,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_38,plain,
( frontsegP(X3,X2)
| ~ ssList(X1)
| app(X2,X1) != X3
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_39,plain,
( ssList(app(X1,X2))
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_40,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_33,c_0_34]),c_0_35]),c_0_36])]) ).
cnf(c_0_41,plain,
( cons(X2,X1) = app(cons(X2,nil),X1)
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_42,plain,
( frontsegP(app(X1,X2),X1)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_38]),c_0_39]) ).
cnf(c_0_43,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_40,c_0_41]),c_0_28]),c_0_36])]) ).
cnf(c_0_44,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_42,c_0_43]),c_0_29])]) ).
cnf(c_0_45,negated_conjecture,
ssList(esk48_0),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
fof(c_0_46,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_47,plain,
( app(X1,esk6_2(X2,X1)) = X2
| ~ frontsegP(X2,X1)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_48,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_44,c_0_34]),c_0_28]),c_0_36])]) ).
cnf(c_0_49,negated_conjecture,
ssList(esk50_0),
inference(rw,[status(thm)],[c_0_45,c_0_24]) ).
cnf(c_0_50,plain,
( ssList(esk6_2(X1,X2))
| ~ frontsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_51,plain,
( X3 = X1
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| app(X2,X3) != app(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_52,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_47,c_0_48]),c_0_49]),c_0_29])]) ).
cnf(c_0_53,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_50,c_0_48]),c_0_29]),c_0_49])]) ).
cnf(c_0_54,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_51,c_0_52]),c_0_53]),c_0_29])]) ).
cnf(c_0_55,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_54,c_0_43]) ).
cnf(c_0_56,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_55,c_0_34]),c_0_28]),c_0_36])]) ).
fof(c_0_57,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_58,negated_conjecture,
( X1 = cons(esk52_0,esk54_0)
| app(esk53_0,X1) != esk50_0
| ~ ssList(X1) ),
inference(rw,[status(thm)],[c_0_54,c_0_56]) ).
cnf(c_0_59,plain,
( rearsegP(X3,X2)
| ~ ssList(X1)
| app(X1,X2) != X3
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_60,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_58,c_0_40]) ).
cnf(c_0_61,plain,
( rearsegP(app(X1,X2),X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_59]),c_0_39]) ).
fof(c_0_62,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_63,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_60,c_0_39]),c_0_28])]) ).
cnf(c_0_64,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_61,c_0_43]),c_0_29])]) ).
fof(c_0_65,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_66,plain,
( cons(X3,app(X2,X1)) = app(cons(X3,X2),X1)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssItem(X3) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_67,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_63,c_0_34]),c_0_35]),c_0_36])]) ).
cnf(c_0_68,plain,
( app(esk7_2(X1,X2),X2) = X1
| ~ rearsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_69,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_64,c_0_34]),c_0_28]),c_0_36])]) ).
cnf(c_0_70,plain,
( ssList(esk7_2(X1,X2))
| ~ rearsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_71,plain,
( ~ ssList(X1)
| ~ ssItem(X2)
| nil != cons(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_65]) ).
cnf(c_0_72,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_66,c_0_67]),c_0_35]),c_0_28]),c_0_36])]) ).
fof(c_0_73,plain,
! [X350] :
( ~ ssList(X350)
| app(nil,X350) = X350 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax28])]) ).
fof(c_0_74,plain,
! [X226,X227,X230,X231] :
( ( ssList(esk3_2(X226,X227))
| ~ memberP(X226,X227)
| ~ ssItem(X227)
| ~ ssList(X226) )
& ( ssList(esk4_2(X226,X227))
| ~ memberP(X226,X227)
| ~ ssItem(X227)
| ~ ssList(X226) )
& ( app(esk3_2(X226,X227),cons(X227,esk4_2(X226,X227))) = X226
| ~ memberP(X226,X227)
| ~ ssItem(X227)
| ~ ssList(X226) )
& ( ~ ssList(X230)
| ~ ssList(X231)
| app(X230,cons(X227,X231)) != X226
| memberP(X226,X227)
| ~ ssItem(X227)
| ~ ssList(X226) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax3])])])])]) ).
fof(c_0_75,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_76,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_68,c_0_69]),c_0_49])]) ).
cnf(c_0_77,negated_conjecture,
ssList(cons(esk52_0,esk54_0)),
inference(rw,[status(thm)],[c_0_53,c_0_56]) ).
cnf(c_0_78,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_70,c_0_69]),c_0_49])]) ).
cnf(c_0_79,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_71,c_0_72]),c_0_36])]) ).
cnf(c_0_80,plain,
( app(nil,X1) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_73]) ).
cnf(c_0_81,plain,
( memberP(X4,X3)
| ~ ssList(X1)
| ~ ssList(X2)
| app(X1,cons(X3,X2)) != X4
| ~ ssItem(X3)
| ~ ssList(X4) ),
inference(split_conjunct,[status(thm)],[c_0_74]) ).
cnf(c_0_82,plain,
( nil = X1
| nil != app(X2,X1)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_75]) ).
cnf(c_0_83,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_76,c_0_77])]) ).
cnf(c_0_84,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_78,c_0_34]),c_0_28]),c_0_36])]) ).
cnf(c_0_85,negated_conjecture,
cons(esk52_0,esk54_0) != nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_80]),c_0_28])]) ).
fof(c_0_86,plain,
! [X366,X367,X368] :
( ( ~ memberP(app(X367,X368),X366)
| memberP(X367,X366)
| memberP(X368,X366)
| ~ ssList(X368)
| ~ ssList(X367)
| ~ ssItem(X366) )
& ( ~ memberP(X367,X366)
| memberP(app(X367,X368),X366)
| ~ ssList(X368)
| ~ ssList(X367)
| ~ ssItem(X366) )
& ( ~ memberP(X368,X366)
| memberP(app(X367,X368),X366)
| ~ ssList(X368)
| ~ ssList(X367)
| ~ ssItem(X366) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax36])])])]) ).
cnf(c_0_87,plain,
( memberP(app(X1,cons(X2,X3)),X2)
| ~ ssList(app(X1,cons(X2,X3)))
| ~ ssList(X3)
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(er,[status(thm)],[c_0_81]) ).
cnf(c_0_88,negated_conjecture,
( nil = esk50_0
| cons(esk55_0,nil) = esk50_0 ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_89,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_82,c_0_83]),c_0_84]),c_0_77])]),c_0_85]) ).
cnf(c_0_90,negated_conjecture,
( nil = esk50_0
| ssItem(esk55_0) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_91,plain,
( memberP(app(X1,X3),X2)
| ~ memberP(X1,X2)
| ~ ssList(X3)
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_86]) ).
cnf(c_0_92,negated_conjecture,
memberP(esk50_0,esk52_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_43]),c_0_49]),c_0_28]),c_0_29]),c_0_36])]) ).
cnf(c_0_93,negated_conjecture,
cons(esk55_0,nil) = esk50_0,
inference(sr,[status(thm)],[c_0_88,c_0_89]) ).
cnf(c_0_94,negated_conjecture,
ssItem(esk55_0),
inference(sr,[status(thm)],[c_0_90,c_0_89]) ).
fof(c_0_95,plain,
! [X1] :
( ssItem(X1)
=> ~ memberP(nil,X1) ),
inference(fof_simplification,[status(thm)],[ax38]) ).
fof(c_0_96,plain,
! [X369,X370,X371] :
( ( ~ memberP(cons(X370,X371),X369)
| X369 = X370
| memberP(X371,X369)
| ~ ssList(X371)
| ~ ssItem(X370)
| ~ ssItem(X369) )
& ( X369 != X370
| memberP(cons(X370,X371),X369)
| ~ ssList(X371)
| ~ ssItem(X370)
| ~ ssItem(X369) )
& ( ~ memberP(X371,X369)
| memberP(cons(X370,X371),X369)
| ~ ssList(X371)
| ~ ssItem(X370)
| ~ ssItem(X369) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax37])])])]) ).
cnf(c_0_97,negated_conjecture,
( memberP(app(esk50_0,X1),esk52_0)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_92]),c_0_49]),c_0_36])]) ).
cnf(c_0_98,negated_conjecture,
( app(esk50_0,X1) = cons(esk55_0,X1)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_93]),c_0_94])]) ).
fof(c_0_99,plain,
! [X442] :
( ~ ssList(X442)
| app(X442,nil) = X442 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax84])]) ).
fof(c_0_100,plain,
! [X372] :
( ~ ssItem(X372)
| ~ memberP(nil,X372) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_95])]) ).
cnf(c_0_101,plain,
( X3 = X1
| memberP(X2,X3)
| ~ memberP(cons(X1,X2),X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X3) ),
inference(split_conjunct,[status(thm)],[c_0_96]) ).
cnf(c_0_102,negated_conjecture,
( memberP(cons(esk55_0,X1),esk52_0)
| ~ ssList(X1) ),
inference(spm,[status(thm)],[c_0_97,c_0_98]) ).
fof(c_0_103,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_104,plain,
( app(X1,nil) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_99]) ).
cnf(c_0_105,plain,
( ~ ssItem(X1)
| ~ memberP(nil,X1) ),
inference(split_conjunct,[status(thm)],[c_0_100]) ).
cnf(c_0_106,negated_conjecture,
( esk52_0 = esk55_0
| memberP(X1,esk52_0)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_102]),c_0_36]),c_0_94])]) ).
cnf(c_0_107,plain,
( tl(cons(X2,X1)) = X1
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_103]) ).
cnf(c_0_108,plain,
( X1 = nil
| app(X2,X1) != X2
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_104]),c_0_35])]) ).
fof(c_0_109,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_110,negated_conjecture,
esk52_0 = esk55_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_106]),c_0_36]),c_0_35])]) ).
cnf(c_0_111,negated_conjecture,
( tl(esk50_0) = nil
| esk50_0 = nil ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_88]),c_0_35])]),c_0_90]) ).
cnf(c_0_112,negated_conjecture,
( esk54_0 = nil
| app(esk53_0,cons(esk52_0,nil)) != esk50_0
| ~ ssList(app(esk53_0,cons(esk52_0,nil))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_26]),c_0_28])]) ).
cnf(c_0_113,plain,
( nil = X1
| tl(app(X1,X2)) = app(tl(X1),X2)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_109]) ).
cnf(c_0_114,negated_conjecture,
app(esk53_0,cons(esk55_0,esk54_0)) = esk50_0,
inference(rw,[status(thm)],[c_0_43,c_0_110]) ).
cnf(c_0_115,negated_conjecture,
tl(esk50_0) = nil,
inference(sr,[status(thm)],[c_0_111,c_0_89]) ).
cnf(c_0_116,negated_conjecture,
ssList(cons(esk55_0,esk54_0)),
inference(rw,[status(thm)],[c_0_77,c_0_110]) ).
cnf(c_0_117,negated_conjecture,
( esk54_0 = nil
| app(esk53_0,cons(esk52_0,nil)) != esk50_0
| ~ ssList(cons(esk52_0,nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_39]),c_0_29])]) ).
cnf(c_0_118,negated_conjecture,
( app(tl(esk53_0),cons(esk55_0,esk54_0)) = nil
| 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_113,c_0_114]),c_0_115]),c_0_116]),c_0_29])]) ).
cnf(c_0_119,negated_conjecture,
cons(esk55_0,esk54_0) != nil,
inference(rw,[status(thm)],[c_0_85,c_0_110]) ).
fof(c_0_120,plain,
! [X342] :
( ~ ssList(X342)
| nil = X342
| ssList(tl(X342)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax24])]) ).
cnf(c_0_121,negated_conjecture,
( esk54_0 = nil
| app(esk53_0,cons(esk52_0,nil)) != esk50_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_117,c_0_34]),c_0_35]),c_0_36])]) ).
cnf(c_0_122,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_82,c_0_118]),c_0_116])]),c_0_119]) ).
cnf(c_0_123,plain,
( nil = X1
| ssList(tl(X1))
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_120]) ).
cnf(c_0_124,negated_conjecture,
( esk54_0 = nil
| app(esk53_0,esk50_0) != esk50_0 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_121,c_0_110]),c_0_93]) ).
cnf(c_0_125,negated_conjecture,
esk53_0 = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_122,c_0_123]),c_0_29])]) ).
cnf(c_0_126,negated_conjecture,
( memberP(esk53_0,esk52_0)
| memberP(esk54_0,esk52_0) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_127,negated_conjecture,
( esk54_0 = nil
| app(nil,esk50_0) != esk50_0 ),
inference(rw,[status(thm)],[c_0_124,c_0_125]) ).
cnf(c_0_128,negated_conjecture,
( memberP(esk54_0,esk55_0)
| memberP(esk53_0,esk55_0) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_126,c_0_110]),c_0_110]) ).
cnf(c_0_129,negated_conjecture,
esk54_0 = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_127,c_0_80]),c_0_49])]) ).
cnf(c_0_130,negated_conjecture,
memberP(nil,esk55_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_128,c_0_125]),c_0_129])]) ).
cnf(c_0_131,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_130]),c_0_94])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWC183+1 : TPTP v9.2.1. Released v2.4.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.33 % Computer : n027.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 04:31:50 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.69/1.82 % Version : CSE_E---1.7
% 1.69/1.82 % Problem : theBenchmark.p
% 1.69/1.82 % SZS status Theorem for theBenchmark.p
% 1.69/1.82 % SZS output start CNFRefutation
% See solution above
% 1.69/1.83 % Total time : 1.372s
%------------------------------------------------------------------------------