%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWC079-1 : 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 : n002.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 05:18:10 PM UTC 2026
% Result : Unsatisfiable 4.28s 3.25s
% Output : CNFRefutation 4.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 36
% Syntax : Number of clauses : 133 ( 24 unt; 36 nHn; 127 RR)
% Number of literals : 415 ( 124 equ; 256 neg)
% Maximal clause size : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 5 con; 0-2 aty)
% Number of variables : 160 ( 8 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(co1_7,negated_conjecture,
( neq(sk2,nil)
| neq(sk2,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_7) ).
cnf(co1_5,negated_conjecture,
sk2 = sk4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_5) ).
cnf(co1_12,negated_conjecture,
( sk3 = X1
| ~ ssList(X1)
| ~ ssItem(X2)
| cons(X2,nil) != X1
| hd(sk4) != X2
| ~ neq(nil,sk4)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_12) ).
cnf(co1_6,negated_conjecture,
sk1 = sk3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_6) ).
cnf(clause86,axiom,
( ssList(cons(X1,X2))
| ~ ssItem(X1)
| ~ ssList(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause86) ).
cnf(clause8,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause8) ).
cnf(clause97,axiom,
( hd(cons(X1,X2)) = X1
| ~ ssItem(X1)
| ~ ssList(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause97) ).
cnf(co1_2,negated_conjecture,
ssList(sk2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_2) ).
cnf(clause99,axiom,
( cons(X1,X2) != X2
| ~ ssItem(X1)
| ~ ssList(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause99) ).
cnf(clause171,axiom,
( X4 = X2
| cons(X1,X2) != cons(X3,X4)
| ~ ssItem(X3)
| ~ ssItem(X1)
| ~ ssList(X4)
| ~ ssList(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause171) ).
cnf(clause76,axiom,
( ssItem(hd(X1))
| nil = X1
| ~ ssList(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause76) ).
cnf(clause100,axiom,
( neq(X2,X1)
| X2 = X1
| ~ ssList(X1)
| ~ ssList(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause100) ).
cnf(co1_1,negated_conjecture,
ssList(sk1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_1) ).
cnf(clause96,axiom,
( tl(cons(X1,X2)) = X2
| ~ ssItem(X1)
| ~ ssList(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause96) ).
cnf(clause104,axiom,
( cons(hd(X1),tl(X1)) = X1
| nil = X1
| ~ ssList(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause104) ).
cnf(clause120,axiom,
( app(cons(X1,nil),X2) = cons(X1,X2)
| ~ ssItem(X1)
| ~ ssList(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause120) ).
cnf(clause109,axiom,
( cons(skaf83(X1),skaf82(X1)) = X1
| nil = X1
| ~ ssList(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause109) ).
cnf(clause12,axiom,
ssItem(skaf83(X1)),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause12) ).
cnf(clause13,axiom,
ssList(skaf82(X1)),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause13) ).
cnf(clause170,axiom,
( X1 = X3
| cons(X1,X2) != cons(X3,X4)
| ~ ssItem(X3)
| ~ ssItem(X1)
| ~ ssList(X4)
| ~ ssList(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause170) ).
cnf(clause98,axiom,
( cons(X1,X2) != nil
| ~ ssItem(X1)
| ~ ssList(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause98) ).
cnf(clause174,axiom,
( frontsegP(X2,X4)
| ~ frontsegP(cons(X1,X2),cons(X3,X4))
| ~ ssList(X4)
| ~ ssList(X2)
| ~ ssItem(X3)
| ~ ssItem(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause174) ).
cnf(clause144,axiom,
( frontsegP(X3,X1)
| app(X1,X2) != X3
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause144) ).
cnf(clause85,axiom,
( ssList(app(X2,X1))
| ~ ssList(X1)
| ~ ssList(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause85) ).
cnf(clause137,axiom,
( frontsegP(app(X1,X3),X2)
| ~ frontsegP(X1,X2)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause137) ).
cnf(clause74,axiom,
( app(nil,X1) = X1
| ~ ssList(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause74) ).
cnf(co1_11,negated_conjecture,
( ~ ssList(X1)
| ~ neq(X1,nil)
| ~ segmentP(sk2,X1)
| ~ segmentP(sk1,X1)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_11) ).
cnf(clause173,axiom,
( segmentP(X4,X2)
| app(app(X1,X2),X3) != X4
| ~ ssList(X3)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X4) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause173) ).
cnf(clause149,axiom,
( app(app(X3,X2),X1) = app(X3,app(X2,X1))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause149) ).
cnf(clause132,axiom,
( app(X2,skaf45(X1,X2)) = X1
| ~ frontsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause132) ).
cnf(clause51,axiom,
ssList(skaf45(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause51) ).
cnf(clause178,axiom,
( frontsegP(cons(X3,X1),cons(X4,X2))
| ~ frontsegP(X1,X2)
| X3 != X4
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X4)
| ~ ssItem(X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause178) ).
cnf(clause57,axiom,
( segmentP(X1,X1)
| ~ ssList(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause57) ).
cnf(clause75,axiom,
( ssList(tl(X1))
| nil = X1
| ~ ssList(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause75) ).
cnf(clause79,axiom,
( segmentP(nil,X1)
| nil != X1
| ~ ssList(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause79) ).
cnf(clause56,axiom,
( segmentP(X1,nil)
| ~ ssList(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause56) ).
cnf(c_0_36,negated_conjecture,
neq(sk2,nil),
inference(fof_simplification,[status(thm)],[co1_7]) ).
cnf(c_0_37,negated_conjecture,
neq(sk2,nil),
c_0_36 ).
cnf(c_0_38,negated_conjecture,
sk2 = sk4,
co1_5 ).
cnf(c_0_39,negated_conjecture,
( sk3 = X1
| ~ ssList(X1)
| ~ ssItem(X2)
| cons(X2,nil) != X1
| hd(sk4) != X2
| ~ neq(nil,sk4)
| ~ neq(sk4,nil) ),
co1_12 ).
cnf(c_0_40,negated_conjecture,
sk1 = sk3,
co1_6 ).
cnf(c_0_41,negated_conjecture,
neq(sk4,nil),
inference(rw,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_42,negated_conjecture,
( cons(hd(sk4),nil) = sk1
| ~ neq(nil,sk4)
| ~ ssItem(hd(sk4))
| ~ ssList(cons(hd(sk4),nil)) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_39,c_0_40]),c_0_41])])])]) ).
cnf(c_0_43,axiom,
( ssList(cons(X1,X2))
| ~ ssItem(X1)
| ~ ssList(X2) ),
clause86 ).
cnf(c_0_44,axiom,
ssList(nil),
clause8 ).
cnf(c_0_45,axiom,
( hd(cons(X1,X2)) = X1
| ~ ssItem(X1)
| ~ ssList(X2) ),
clause97 ).
cnf(c_0_46,negated_conjecture,
( cons(hd(sk4),nil) = sk1
| ~ neq(nil,sk4)
| ~ ssItem(hd(sk4)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_44])]) ).
cnf(c_0_47,negated_conjecture,
ssList(sk2),
co1_2 ).
cnf(c_0_48,axiom,
( cons(X1,X2) != X2
| ~ ssItem(X1)
| ~ ssList(X2) ),
clause99 ).
cnf(c_0_49,axiom,
( X4 = X2
| cons(X1,X2) != cons(X3,X4)
| ~ ssItem(X3)
| ~ ssItem(X1)
| ~ ssList(X4)
| ~ ssList(X2) ),
clause171 ).
cnf(c_0_50,negated_conjecture,
( hd(sk1) = hd(sk4)
| ~ neq(nil,sk4)
| ~ ssItem(hd(sk4)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_44])]) ).
cnf(c_0_51,axiom,
( ssItem(hd(X1))
| nil = X1
| ~ ssList(X1) ),
clause76 ).
cnf(c_0_52,negated_conjecture,
ssList(sk4),
inference(rw,[status(thm)],[c_0_47,c_0_38]) ).
cnf(c_0_53,negated_conjecture,
( sk1 != nil
| ~ neq(nil,sk4)
| ~ ssItem(hd(sk4)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_46]),c_0_44])]) ).
cnf(c_0_54,negated_conjecture,
( X1 = nil
| cons(X2,X1) != sk1
| ~ neq(nil,sk4)
| ~ ssItem(hd(sk4))
| ~ ssItem(X2)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_46]),c_0_44])]) ).
cnf(c_0_55,axiom,
( neq(X2,X1)
| X2 = X1
| ~ ssList(X1)
| ~ ssList(X2) ),
clause100 ).
cnf(c_0_56,negated_conjecture,
( hd(sk1) = hd(sk4)
| sk4 = nil
| ~ neq(nil,sk4) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_52])]) ).
cnf(c_0_57,negated_conjecture,
ssList(sk1),
co1_1 ).
cnf(c_0_58,negated_conjecture,
( sk4 = nil
| sk1 != nil
| ~ neq(nil,sk4) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_51]),c_0_52])]) ).
cnf(c_0_59,axiom,
( tl(cons(X1,X2)) = X2
| ~ ssItem(X1)
| ~ ssList(X2) ),
clause96 ).
cnf(c_0_60,negated_conjecture,
( sk4 = nil
| X1 = nil
| cons(X2,X1) != sk1
| ~ ssItem(hd(sk4))
| ~ ssItem(X2)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_44]),c_0_52])]) ).
cnf(c_0_61,negated_conjecture,
( sk4 = nil
| ssItem(hd(sk4))
| ~ neq(nil,sk4) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_56]),c_0_57])]),c_0_58]) ).
cnf(c_0_62,axiom,
( cons(hd(X1),tl(X1)) = X1
| nil = X1
| ~ ssList(X1) ),
clause104 ).
cnf(c_0_63,negated_conjecture,
( tl(sk1) = nil
| ~ neq(nil,sk4)
| ~ ssItem(hd(sk4)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_46]),c_0_44])]) ).
cnf(c_0_64,negated_conjecture,
( sk4 = nil
| X1 = nil
| cons(X2,X1) != sk1
| ~ neq(nil,sk4)
| ~ ssItem(X2)
| ~ ssList(X1) ),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_65,axiom,
( app(cons(X1,nil),X2) = cons(X1,X2)
| ~ ssItem(X1)
| ~ ssList(X2) ),
clause120 ).
cnf(c_0_66,negated_conjecture,
( cons(hd(sk1),nil) = sk1
| ~ neq(nil,sk4)
| ~ ssItem(hd(sk4)) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_57])]),c_0_53]) ).
cnf(c_0_67,negated_conjecture,
( sk4 = nil
| X1 = nil
| cons(X2,X1) != sk1
| ~ ssItem(X2)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_55]),c_0_44]),c_0_52])]) ).
cnf(c_0_68,axiom,
( cons(skaf83(X1),skaf82(X1)) = X1
| nil = X1
| ~ ssList(X1) ),
clause109 ).
cnf(c_0_69,axiom,
ssItem(skaf83(X1)),
clause12 ).
cnf(c_0_70,axiom,
ssList(skaf82(X1)),
clause13 ).
cnf(c_0_71,negated_conjecture,
( sk4 = nil
| sk1 != nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_55]),c_0_44]),c_0_52])]) ).
cnf(c_0_72,negated_conjecture,
( cons(hd(sk1),X1) = app(sk1,X1)
| ~ neq(nil,sk4)
| ~ ssItem(hd(sk1))
| ~ ssItem(hd(sk4))
| ~ ssList(X1) ),
inference(spm,[status(thm)],[c_0_65,c_0_66]) ).
cnf(c_0_73,negated_conjecture,
( skaf82(sk1) = nil
| sk4 = nil ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[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_69]),c_0_70])])]),c_0_57])]),c_0_71]) ).
cnf(c_0_74,negated_conjecture,
( app(sk1,nil) = sk1
| ~ neq(nil,sk4)
| ~ ssItem(hd(sk4))
| ~ ssItem(hd(sk1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_72]),c_0_44])]) ).
cnf(c_0_75,axiom,
( X1 = X3
| cons(X1,X2) != cons(X3,X4)
| ~ ssItem(X3)
| ~ ssItem(X1)
| ~ ssList(X4)
| ~ ssList(X2) ),
clause170 ).
cnf(c_0_76,axiom,
( cons(X1,X2) != nil
| ~ ssItem(X1)
| ~ ssList(X2) ),
clause98 ).
cnf(c_0_77,axiom,
( frontsegP(X2,X4)
| ~ frontsegP(cons(X1,X2),cons(X3,X4))
| ~ ssList(X4)
| ~ ssList(X2)
| ~ ssItem(X3)
| ~ ssItem(X1) ),
clause174 ).
cnf(c_0_78,negated_conjecture,
( cons(skaf83(sk1),nil) = sk1
| sk4 = nil ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_73]),c_0_57])]),c_0_71]) ).
cnf(c_0_79,axiom,
( frontsegP(X3,X1)
| app(X1,X2) != X3
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X3) ),
clause144 ).
cnf(c_0_80,axiom,
( ssList(app(X2,X1))
| ~ ssList(X1)
| ~ ssList(X2) ),
clause85 ).
cnf(c_0_81,negated_conjecture,
( app(sk1,nil) = sk1
| sk4 = nil
| ~ neq(nil,sk4) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_56]),c_0_61]) ).
cnf(c_0_82,plain,
( skaf83(cons(X1,X2)) = X1
| ~ ssItem(X1)
| ~ ssList(X2) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_68]),c_0_69]),c_0_70])])]),c_0_43]),c_0_76]) ).
cnf(c_0_83,negated_conjecture,
( sk4 = nil
| frontsegP(nil,X1)
| ~ frontsegP(sk1,cons(X2,X1))
| ~ ssItem(X2)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78]),c_0_69]),c_0_44])]) ).
cnf(c_0_84,negated_conjecture,
( cons(skaf83(sk1),X1) = app(sk1,X1)
| sk4 = nil
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_78]),c_0_69])]) ).
cnf(c_0_85,plain,
( frontsegP(app(X1,X2),X1)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_79]),c_0_80]) ).
cnf(c_0_86,negated_conjecture,
( app(sk1,nil) = sk1
| sk4 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_55]),c_0_44]),c_0_52])]) ).
cnf(c_0_87,negated_conjecture,
( skaf83(sk1) = hd(sk4)
| ~ neq(nil,sk4)
| ~ ssItem(hd(sk4)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_46]),c_0_44])]) ).
cnf(c_0_88,axiom,
( frontsegP(app(X1,X3),X2)
| ~ frontsegP(X1,X2)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1) ),
clause137 ).
cnf(c_0_89,axiom,
( app(nil,X1) = X1
| ~ ssList(X1) ),
clause74 ).
cnf(c_0_90,negated_conjecture,
( sk4 = nil
| frontsegP(nil,X1)
| ~ frontsegP(sk1,app(sk1,X1))
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_84]),c_0_69])]) ).
cnf(c_0_91,negated_conjecture,
( app(sk1,skaf82(sk1)) = sk1
| sk4 = nil ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_84]),c_0_57]),c_0_70])]),c_0_71]) ).
cnf(c_0_92,negated_conjecture,
( sk4 = nil
| frontsegP(sk1,sk1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_86]),c_0_44]),c_0_57])]) ).
cnf(c_0_93,negated_conjecture,
( skaf83(sk1) = hd(sk1)
| sk4 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_78]),c_0_69]),c_0_44])]) ).
cnf(c_0_94,negated_conjecture,
( ~ ssList(X1)
| ~ neq(X1,nil)
| ~ segmentP(sk2,X1)
| ~ segmentP(sk1,X1)
| ~ neq(sk4,nil) ),
co1_11 ).
cnf(c_0_95,axiom,
( segmentP(X4,X2)
| app(app(X1,X2),X3) != X4
| ~ ssList(X3)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X4) ),
clause173 ).
cnf(c_0_96,axiom,
( app(app(X3,X2),X1) = app(X3,app(X2,X1))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
clause149 ).
cnf(c_0_97,negated_conjecture,
( cons(hd(sk4),skaf82(sk1)) = sk1
| ~ neq(nil,sk4)
| ~ ssItem(hd(sk4)) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_87]),c_0_57])]),c_0_53]) ).
cnf(c_0_98,plain,
( frontsegP(X1,X2)
| ~ frontsegP(nil,X2)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_89]),c_0_44])]) ).
cnf(c_0_99,negated_conjecture,
( sk4 = nil
| frontsegP(nil,skaf82(sk1)) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_91]),c_0_70])]),c_0_92]) ).
cnf(c_0_100,negated_conjecture,
( cons(hd(sk1),skaf82(sk1)) = sk1
| sk4 = nil ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_93]),c_0_57])]),c_0_71]) ).
cnf(c_0_101,negated_conjecture,
( sk4 = nil
| ssItem(hd(sk1)) ),
inference(spm,[status(thm)],[c_0_69,c_0_93]) ).
cnf(c_0_102,negated_conjecture,
( ~ neq(X1,nil)
| ~ segmentP(sk1,X1)
| ~ segmentP(sk4,X1)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_94,c_0_38]),c_0_41])]) ).
cnf(c_0_103,plain,
( segmentP(app(app(X1,X2),X3),X2)
| ~ ssList(app(app(X1,X2),X3))
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(er,[status(thm)],[c_0_95]) ).
cnf(c_0_104,axiom,
( app(X2,skaf45(X1,X2)) = X1
| ~ frontsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
clause132 ).
cnf(c_0_105,axiom,
ssList(skaf45(X1,X2)),
clause51 ).
cnf(c_0_106,plain,
( app(nil,app(X1,X2)) = app(X1,X2)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_89]),c_0_44])]) ).
cnf(c_0_107,axiom,
( frontsegP(cons(X3,X1),cons(X4,X2))
| ~ frontsegP(X1,X2)
| X3 != X4
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X4)
| ~ ssItem(X3) ),
clause178 ).
cnf(c_0_108,negated_conjecture,
( skaf82(sk1) = tl(sk1)
| ~ neq(nil,sk4)
| ~ ssItem(hd(sk4)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_97]),c_0_70])]) ).
cnf(c_0_109,negated_conjecture,
( sk4 = nil
| frontsegP(X1,skaf82(sk1))
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_99]),c_0_70])]) ).
cnf(c_0_110,negated_conjecture,
( skaf82(sk1) = tl(sk1)
| sk4 = nil ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_100]),c_0_70])]),c_0_101]) ).
cnf(c_0_111,negated_conjecture,
( nil = X1
| ~ segmentP(sk1,X1)
| ~ segmentP(sk4,X1)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_55]),c_0_44])]) ).
cnf(c_0_112,axiom,
( segmentP(X1,X1)
| ~ ssList(X1) ),
clause57 ).
cnf(c_0_113,plain,
( segmentP(X1,X2)
| ~ frontsegP(X1,app(X3,X2))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_104]),c_0_105])]),c_0_80]) ).
cnf(c_0_114,negated_conjecture,
( app(nil,sk1) = sk1
| sk4 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_91]),c_0_57]),c_0_70])]) ).
cnf(c_0_115,plain,
( frontsegP(cons(X1,X2),cons(X1,X3))
| ~ frontsegP(X2,X3)
| ~ ssItem(X1)
| ~ ssList(X3)
| ~ ssList(X2) ),
inference(er,[status(thm)],[c_0_107]) ).
cnf(c_0_116,negated_conjecture,
( cons(hd(sk4),tl(sk1)) = sk1
| sk4 = nil
| ~ neq(nil,sk4) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_56]),c_0_57])]),c_0_71]) ).
cnf(c_0_117,negated_conjecture,
( ssList(tl(sk1))
| ~ neq(nil,sk4)
| ~ ssItem(hd(sk4)) ),
inference(spm,[status(thm)],[c_0_70,c_0_108]) ).
cnf(c_0_118,negated_conjecture,
( sk4 = nil
| frontsegP(X1,tl(sk1))
| ~ ssList(X1) ),
inference(spm,[status(thm)],[c_0_109,c_0_110]) ).
cnf(c_0_119,negated_conjecture,
( sk1 = nil
| ~ segmentP(sk4,sk1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_112]),c_0_57])]) ).
cnf(c_0_120,negated_conjecture,
( sk4 = nil
| segmentP(X1,sk1)
| ~ frontsegP(X1,sk1)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_114]),c_0_57]),c_0_44])]) ).
cnf(c_0_121,negated_conjecture,
( sk4 = nil
| frontsegP(cons(hd(sk4),X1),sk1)
| ~ neq(nil,sk4)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_116]),c_0_117]),c_0_61]),c_0_118]) ).
cnf(c_0_122,negated_conjecture,
( sk4 = nil
| ~ frontsegP(sk4,sk1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_119,c_0_120]),c_0_52])]),c_0_71]) ).
cnf(c_0_123,negated_conjecture,
( sk4 = nil
| ~ neq(nil,sk4)
| ~ ssList(tl(sk4)) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_121,c_0_62]),c_0_52])]),c_0_122]) ).
cnf(c_0_124,axiom,
( ssList(tl(X1))
| nil = X1
| ~ ssList(X1) ),
clause75 ).
cnf(c_0_125,negated_conjecture,
( sk4 = nil
| ~ neq(nil,sk4) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_123,c_0_124]),c_0_52])]) ).
cnf(c_0_126,axiom,
( segmentP(nil,X1)
| nil != X1
| ~ ssList(X1) ),
clause79 ).
cnf(c_0_127,negated_conjecture,
( ~ segmentP(sk1,sk4)
| ~ segmentP(sk4,sk4) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_41]),c_0_52])]) ).
cnf(c_0_128,negated_conjecture,
sk4 = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_125,c_0_55]),c_0_44]),c_0_52])]) ).
cnf(c_0_129,plain,
segmentP(nil,nil),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_126]),c_0_44])]) ).
cnf(c_0_130,negated_conjecture,
~ segmentP(sk1,nil),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_127,c_0_128]),c_0_128]),c_0_128]),c_0_129])]) ).
cnf(c_0_131,axiom,
( segmentP(X1,nil)
| ~ ssList(X1) ),
clause56 ).
cnf(c_0_132,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_131]),c_0_57])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWC079-1 : 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
% 0.15/0.32 % Computer : n002.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Tue May 5 04:23:16 EDT 2026
% 0.15/0.32 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 4.28/3.25 % Version : CSE_E---1.7
% 4.28/3.25 % Problem : theBenchmark.p
% 4.28/3.25 % SZS status Unsatisfiable for theBenchmark.p
% 4.28/3.25 % SZS output start CNFRefutation
% See solution above
% 4.28/3.27 % Total time : 2.372s
%------------------------------------------------------------------------------