%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWC397+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 : n026.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 05:19:29 PM UTC 2026
% Result : Theorem 1.77s 1.84s
% Output : CNFRefutation 1.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 15
% Syntax : Number of formulae : 89 ( 17 unt; 0 def)
% Number of atoms : 378 ( 103 equ)
% Maximal formula atoms : 19 ( 4 avg)
% Number of connectives : 466 ( 177 ~; 201 |; 37 &)
% ( 6 <=>; 45 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 8 con; 0-2 aty)
% Number of variables : 129 ( 0 sgn 77 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ! [X5] :
( ssItem(X5)
=> ( ~ memberP(X1,X5)
| memberP(X2,X5) ) )
| ( nil != X3
& nil = X4 )
| ( ! [X6] :
( ssItem(X6)
=> ! [X7] :
( ssList(X7)
=> ( app(cons(X6,nil),X7) != X3
| app(X7,cons(X6,nil)) != X4 ) ) )
& neq(X4,nil) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
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(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(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(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(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(ax16,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> ssList(cons(X2,X1)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax16) ).
fof(ax44,axiom,
! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( frontsegP(cons(X1,X3),cons(X2,X4))
<=> ( X1 = X2
& frontsegP(X3,X4) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax44) ).
fof(ax20,axiom,
! [X1] :
( ssList(X1)
=> ( nil = X1
| ? [X2] :
( ssList(X2)
& ? [X3] :
( ssItem(X3)
& cons(X3,X2) = X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax20) ).
fof(ax79,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( app(X3,X2) = app(X1,X2)
=> X3 = X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax79) ).
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(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(c_0_15,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ! [X5] :
( ssItem(X5)
=> ( ~ memberP(X1,X5)
| memberP(X2,X5) ) )
| ( nil != X3
& nil = X4 )
| ( ! [X6] :
( ssItem(X6)
=> ! [X7] :
( ssList(X7)
=> ( app(cons(X6,nil),X7) != X3
| app(X7,cons(X6,nil)) != X4 ) ) )
& neq(X4,nil) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[co1])]) ).
fof(c_0_16,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)
& memberP(esk48_0,esk52_0)
& ~ memberP(esk49_0,esk52_0)
& ( nil = esk50_0
| nil != esk51_0 )
& ( ssItem(esk53_0)
| ~ neq(esk51_0,nil) )
& ( ssList(esk54_0)
| ~ neq(esk51_0,nil) )
& ( app(cons(esk53_0,nil),esk54_0) = esk50_0
| ~ neq(esk51_0,nil) )
& ( app(esk54_0,cons(esk53_0,nil)) = esk51_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_15])])])]) ).
fof(c_0_17,plain,
! [X320,X321] :
( ( ~ neq(X320,X321)
| X320 != X321
| ~ ssList(X321)
| ~ ssList(X320) )
& ( X320 = X321
| neq(X320,X321)
| ~ ssList(X321)
| ~ ssList(X320) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax15])])])]) ).
cnf(c_0_18,negated_conjecture,
ssList(esk49_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_19,negated_conjecture,
esk49_0 = esk51_0,
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_20,negated_conjecture,
( app(cons(esk53_0,nil),esk54_0) = esk50_0
| ~ neq(esk51_0,nil) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_21,plain,
( X1 = X2
| neq(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_22,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[ax17]) ).
cnf(c_0_23,negated_conjecture,
ssList(esk51_0),
inference(rw,[status(thm)],[c_0_18,c_0_19]) ).
fof(c_0_24,plain,
! [X431,X432] :
( ~ ssList(X431)
| ~ ssItem(X432)
| cons(X432,X431) = app(cons(X432,nil),X431) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax81])])]) ).
cnf(c_0_25,negated_conjecture,
( ssItem(esk53_0)
| ~ neq(esk51_0,nil) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_26,negated_conjecture,
( ssList(esk54_0)
| ~ neq(esk51_0,nil) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_27,plain,
! [X343,X344,X345] :
( ~ ssList(X343)
| ~ ssList(X344)
| ~ ssItem(X345)
| cons(X345,app(X344,X343)) = app(cons(X345,X344),X343) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax27])])]) ).
cnf(c_0_28,negated_conjecture,
( app(cons(esk53_0,nil),esk54_0) = esk50_0
| esk51_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22]),c_0_23])]) ).
cnf(c_0_29,plain,
( cons(X2,X1) = app(cons(X2,nil),X1)
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_30,negated_conjecture,
( esk51_0 = nil
| ssItem(esk53_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_21]),c_0_22]),c_0_23])]) ).
cnf(c_0_31,negated_conjecture,
( esk51_0 = nil
| ssList(esk54_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_21]),c_0_22]),c_0_23])]) ).
fof(c_0_32,plain,
! [X231,X232,X234] :
( ( ssList(esk6_2(X231,X232))
| ~ frontsegP(X231,X232)
| ~ ssList(X232)
| ~ ssList(X231) )
& ( app(X232,esk6_2(X231,X232)) = X231
| ~ frontsegP(X231,X232)
| ~ ssList(X232)
| ~ ssList(X231) )
& ( ~ ssList(X234)
| app(X232,X234) != X231
| frontsegP(X231,X232)
| ~ ssList(X232)
| ~ ssList(X231) ) ),
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_33,plain,
! [X341,X342] :
( ~ ssList(X341)
| ~ ssList(X342)
| ssList(app(X341,X342)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax26])])]) ).
cnf(c_0_34,plain,
( cons(X3,app(X2,X1)) = app(cons(X3,X2),X1)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssItem(X3) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_35,negated_conjecture,
( cons(esk53_0,esk54_0) = esk50_0
| esk51_0 = nil ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30]),c_0_31]) ).
cnf(c_0_36,negated_conjecture,
( app(esk54_0,cons(esk53_0,nil)) = esk51_0
| ~ neq(esk51_0,nil) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_37,plain,
( frontsegP(X3,X2)
| ~ ssList(X1)
| app(X2,X1) != X3
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_38,plain,
( ssList(app(X1,X2))
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
fof(c_0_39,plain,
! [X362,X363,X364] :
( ( ~ memberP(app(X363,X364),X362)
| memberP(X363,X362)
| memberP(X364,X362)
| ~ ssList(X364)
| ~ ssList(X363)
| ~ ssItem(X362) )
& ( ~ memberP(X363,X362)
| memberP(app(X363,X364),X362)
| ~ ssList(X364)
| ~ ssList(X363)
| ~ ssItem(X362) )
& ( ~ memberP(X364,X362)
| memberP(app(X363,X364),X362)
| ~ ssList(X364)
| ~ ssList(X363)
| ~ ssItem(X362) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax36])])])]) ).
cnf(c_0_40,negated_conjecture,
memberP(esk48_0,esk52_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_41,negated_conjecture,
esk48_0 = esk50_0,
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_42,negated_conjecture,
ssList(esk48_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_43,negated_conjecture,
( cons(esk53_0,app(esk54_0,X1)) = app(esk50_0,X1)
| esk51_0 = nil
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_30]),c_0_31]) ).
cnf(c_0_44,negated_conjecture,
( app(esk54_0,cons(esk53_0,nil)) = esk51_0
| esk51_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_21]),c_0_22]),c_0_23])]) ).
fof(c_0_45,plain,
! [X322,X323] :
( ~ ssList(X322)
| ~ ssItem(X323)
| ssList(cons(X323,X322)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax16])])]) ).
fof(c_0_46,plain,
! [X378,X379,X380,X381] :
( ( X378 = X379
| ~ frontsegP(cons(X378,X380),cons(X379,X381))
| ~ ssList(X381)
| ~ ssList(X380)
| ~ ssItem(X379)
| ~ ssItem(X378) )
& ( frontsegP(X380,X381)
| ~ frontsegP(cons(X378,X380),cons(X379,X381))
| ~ ssList(X381)
| ~ ssList(X380)
| ~ ssItem(X379)
| ~ ssItem(X378) )
& ( X378 != X379
| ~ frontsegP(X380,X381)
| frontsegP(cons(X378,X380),cons(X379,X381))
| ~ ssList(X381)
| ~ ssList(X380)
| ~ ssItem(X379)
| ~ ssItem(X378) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax44])])])]) ).
fof(c_0_47,plain,
! [X330] :
( ( ssList(esk44_1(X330))
| nil = X330
| ~ ssList(X330) )
& ( ssItem(esk45_1(X330))
| nil = X330
| ~ ssList(X330) )
& ( cons(esk45_1(X330),esk44_1(X330)) = X330
| nil = X330
| ~ ssList(X330) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax20])])])]) ).
cnf(c_0_48,plain,
( frontsegP(app(X1,X2),X1)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_37]),c_0_38]) ).
cnf(c_0_49,plain,
( memberP(app(X1,X3),X2)
| ~ memberP(X1,X2)
| ~ ssList(X3)
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_50,negated_conjecture,
memberP(esk50_0,esk52_0),
inference(rw,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_51,negated_conjecture,
ssList(esk50_0),
inference(rw,[status(thm)],[c_0_42,c_0_41]) ).
cnf(c_0_52,negated_conjecture,
ssItem(esk52_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_53,negated_conjecture,
( app(esk50_0,cons(esk53_0,nil)) = cons(esk53_0,esk51_0)
| esk51_0 = nil
| ~ ssList(cons(esk53_0,nil)) ),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_54,plain,
( ssList(cons(X2,X1))
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
fof(c_0_55,plain,
! [X425,X426,X427] :
( ~ ssList(X425)
| ~ ssList(X426)
| ~ ssList(X427)
| app(X427,X426) != app(X425,X426)
| X427 = X425 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax79])])]) ).
fof(c_0_56,plain,
! [X346] :
( ~ ssList(X346)
| app(nil,X346) = X346 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax28])]) ).
cnf(c_0_57,plain,
( X1 = X2
| ~ frontsegP(cons(X1,X3),cons(X2,X4))
| ~ ssList(X4)
| ~ ssList(X3)
| ~ ssItem(X2)
| ~ ssItem(X1) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_58,plain,
( cons(esk45_1(X1),esk44_1(X1)) = X1
| nil = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_59,plain,
( ssItem(esk45_1(X1))
| nil = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_60,plain,
( ssList(esk44_1(X1))
| nil = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_61,negated_conjecture,
( esk51_0 = nil
| frontsegP(esk50_0,cons(esk53_0,nil))
| ~ ssList(cons(esk53_0,nil)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_28]),c_0_31]) ).
fof(c_0_62,plain,
! [X222,X223,X226,X227] :
( ( ssList(esk3_2(X222,X223))
| ~ memberP(X222,X223)
| ~ ssItem(X223)
| ~ ssList(X222) )
& ( ssList(esk4_2(X222,X223))
| ~ memberP(X222,X223)
| ~ ssItem(X223)
| ~ ssList(X222) )
& ( app(esk3_2(X222,X223),cons(X223,esk4_2(X222,X223))) = X222
| ~ memberP(X222,X223)
| ~ ssItem(X223)
| ~ ssList(X222) )
& ( ~ ssList(X226)
| ~ ssList(X227)
| app(X226,cons(X223,X227)) != X222
| memberP(X222,X223)
| ~ ssItem(X223)
| ~ ssList(X222) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax3])])])])]) ).
cnf(c_0_63,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_49,c_0_50]),c_0_51]),c_0_52])]) ).
cnf(c_0_64,negated_conjecture,
( app(esk50_0,cons(esk53_0,nil)) = cons(esk53_0,esk51_0)
| esk51_0 = nil ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_22])]),c_0_30]) ).
cnf(c_0_65,plain,
( X3 = X1
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| app(X3,X2) != app(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_66,plain,
( app(nil,X1) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_67,plain,
( esk45_1(X1) = X2
| nil = X1
| ~ frontsegP(X1,cons(X2,X3))
| ~ ssList(X3)
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_59]),c_0_60]) ).
cnf(c_0_68,negated_conjecture,
( esk51_0 = nil
| frontsegP(esk50_0,cons(esk53_0,nil)) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_54]),c_0_22])]),c_0_30]) ).
cnf(c_0_69,negated_conjecture,
( nil = esk50_0
| nil != esk51_0 ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_70,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_62]) ).
fof(c_0_71,plain,
! [X365,X366,X367] :
( ( ~ memberP(cons(X366,X367),X365)
| X365 = X366
| memberP(X367,X365)
| ~ ssList(X367)
| ~ ssItem(X366)
| ~ ssItem(X365) )
& ( X365 != X366
| memberP(cons(X366,X367),X365)
| ~ ssList(X367)
| ~ ssItem(X366)
| ~ ssItem(X365) )
& ( ~ memberP(X367,X365)
| memberP(cons(X366,X367),X365)
| ~ ssList(X367)
| ~ ssItem(X366)
| ~ ssItem(X365) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax37])])])]) ).
cnf(c_0_72,negated_conjecture,
( esk51_0 = nil
| memberP(cons(esk53_0,esk51_0),esk52_0)
| ~ ssList(cons(esk53_0,nil)) ),
inference(spm,[status(thm)],[c_0_63,c_0_64]) ).
cnf(c_0_73,negated_conjecture,
~ memberP(esk49_0,esk52_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_74,plain,
( X1 = nil
| app(X1,X2) != X2
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_22])]) ).
cnf(c_0_75,negated_conjecture,
( esk45_1(esk50_0) = esk53_0
| esk50_0 = nil ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_68]),c_0_22]),c_0_51])]),c_0_30]),c_0_69]) ).
cnf(c_0_76,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_70]) ).
cnf(c_0_77,plain,
( X3 = X1
| memberP(X2,X3)
| ~ memberP(cons(X1,X2),X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X3) ),
inference(split_conjunct,[status(thm)],[c_0_71]) ).
cnf(c_0_78,negated_conjecture,
( esk51_0 = nil
| memberP(cons(esk53_0,esk51_0),esk52_0) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_54]),c_0_22])]),c_0_30]) ).
cnf(c_0_79,negated_conjecture,
~ memberP(esk51_0,esk52_0),
inference(rw,[status(thm)],[c_0_73,c_0_19]) ).
cnf(c_0_80,negated_conjecture,
( esk50_0 = nil
| cons(esk53_0,esk51_0) != cons(esk53_0,nil)
| ~ ssList(cons(esk53_0,nil)) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_64]),c_0_51])]),c_0_69]) ).
cnf(c_0_81,negated_conjecture,
( esk50_0 = nil
| ssItem(esk53_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_75]),c_0_51])]) ).
cnf(c_0_82,negated_conjecture,
( esk51_0 = nil
| memberP(esk51_0,esk53_0) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_44]),c_0_23]),c_0_22])]),c_0_30]),c_0_31]) ).
cnf(c_0_83,negated_conjecture,
( esk51_0 = nil
| esk53_0 = esk52_0 ),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78]),c_0_23]),c_0_52])]),c_0_79]),c_0_30]) ).
cnf(c_0_84,negated_conjecture,
( esk50_0 = nil
| cons(esk53_0,esk51_0) != cons(esk53_0,nil) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_54]),c_0_22])]),c_0_81]) ).
cnf(c_0_85,negated_conjecture,
esk51_0 = nil,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_83]),c_0_79]) ).
cnf(c_0_86,negated_conjecture,
esk50_0 = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_84,c_0_85])]) ).
cnf(c_0_87,negated_conjecture,
~ memberP(nil,esk52_0),
inference(rw,[status(thm)],[c_0_79,c_0_85]) ).
cnf(c_0_88,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_50,c_0_86]),c_0_87]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SWC397+1 : TPTP v9.2.1. Released v2.4.0.
% 0.00/0.11 % 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
% 0.13/0.31 % Computer : n026.cluster.edu
% 0.13/0.31 % Model : x86_64 x86_64
% 0.13/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.31 % Memory : 8042.1875MB
% 0.13/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.31 % CPULimit : 300
% 0.13/0.31 % WCLimit : 300
% 0.13/0.31 % DateTime : Tue May 5 04:48:23 EDT 2026
% 0.13/0.32 % CPUTime :
% 0.13/0.33 % start to proof: theBenchmark
% 1.77/1.84 % Version : CSE_E---1.7
% 1.77/1.84 % Problem : theBenchmark.p
% 1.77/1.84 % SZS status Theorem for theBenchmark.p
% 1.77/1.84 % SZS output start CNFRefutation
% See solution above
% 1.77/1.84 % Total time : 1.373s
%------------------------------------------------------------------------------