%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWC378-1 : 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 : n013.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 05:19:25 PM UTC 2026
% Result : Unsatisfiable 7.01s 4.65s
% Output : CNFRefutation 7.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 35
% Syntax : Number of clauses : 127 ( 50 unt; 14 nHn; 111 RR)
% Number of literals : 311 ( 84 equ; 182 neg)
% Maximal clause size : 7 ( 2 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 : 144 ( 22 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(co1_10,negated_conjecture,
app(sk6,sk5) = sk3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_10) ).
cnf(co1_6,negated_conjecture,
sk1 = sk3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_6) ).
cnf(co1_9,negated_conjecture,
app(sk5,sk6) = sk4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_9) ).
cnf(co1_5,negated_conjecture,
sk2 = sk4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_5) ).
cnf(clause119,axiom,
( nil = X2
| app(X1,X2) != nil
| ~ ssList(X2)
| ~ ssList(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause119) ).
cnf(co1_7,negated_conjecture,
ssList(sk5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_7) ).
cnf(co1_8,negated_conjecture,
ssList(sk6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_8) ).
cnf(clause74,axiom,
( app(nil,X1) = X1
| ~ ssList(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause74) ).
cnf(clause73,axiom,
( app(X1,nil) = X1
| ~ ssList(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause73) ).
cnf(clause118,axiom,
( nil = X1
| app(X1,X2) != nil
| ~ ssList(X2)
| ~ ssList(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause118) ).
cnf(clause145,axiom,
( app(X1,X2) = nil
| nil != X1
| nil != X2
| ~ ssList(X2)
| ~ ssList(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause145) ).
cnf(clause8,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause8) ).
cnf(clause179,axiom,
( app(app(X1,cons(X2,X3)),cons(X2,X4)) != X5
| ~ ssList(X4)
| ~ ssList(X3)
| ~ ssList(X1)
| ~ ssItem(X2)
| ~ duplicatefreeP(X5)
| ~ ssList(X5) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause179) ).
cnf(co1_13,negated_conjecture,
( ~ memberP(sk2,sk7)
| ~ memberP(sk1,sk7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_13) ).
cnf(co1_12,negated_conjecture,
( memberP(sk2,sk7)
| memberP(sk1,sk7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_12) ).
cnf(clause169,axiom,
( app(skaf42(X1,X2),cons(X2,skaf43(X2,X1))) = X1
| ~ memberP(X1,X2)
| ~ ssItem(X2)
| ~ ssList(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause169) ).
cnf(clause52,axiom,
ssList(skaf43(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause52) ).
cnf(clause53,axiom,
ssList(skaf42(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause53) ).
cnf(clause138,axiom,
( memberP(cons(X2,X3),X1)
| X1 != X2
| ~ ssList(X3)
| ~ ssItem(X2)
| ~ ssItem(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause138) ).
cnf(clause72,axiom,
( duplicatefreeP(X1)
| ssItem(X2)
| ~ ssList(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause72) ).
cnf(clause85,axiom,
( ssList(app(X2,X1))
| ~ ssList(X1)
| ~ ssList(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause85) ).
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(co1_2,negated_conjecture,
ssList(sk2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_2) ).
cnf(clause71,axiom,
( ~ memberP(nil,X1)
| ~ ssItem(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause71) ).
cnf(co1_11,negated_conjecture,
ssItem(sk7),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_11) ).
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(clause141,axiom,
( memberP(app(X3,X1),X2)
| ~ memberP(X1,X2)
| ~ ssList(X1)
| ~ ssList(X3)
| ~ ssItem(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause141) ).
cnf(clause158,axiom,
( memberP(X2,X3)
| memberP(X1,X3)
| ~ memberP(app(X1,X2),X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause158) ).
cnf(clause140,axiom,
( memberP(app(X1,X3),X2)
| ~ memberP(X1,X2)
| ~ ssList(X3)
| ~ ssList(X1)
| ~ ssItem(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause140) ).
cnf(co1_1,negated_conjecture,
ssList(sk1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_1) ).
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(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(c_0_35,negated_conjecture,
app(sk6,sk5) = sk3,
co1_10 ).
cnf(c_0_36,negated_conjecture,
sk1 = sk3,
co1_6 ).
cnf(c_0_37,negated_conjecture,
app(sk5,sk6) = sk4,
co1_9 ).
cnf(c_0_38,negated_conjecture,
sk2 = sk4,
co1_5 ).
cnf(c_0_39,axiom,
( nil = X2
| app(X1,X2) != nil
| ~ ssList(X2)
| ~ ssList(X1) ),
clause119 ).
cnf(c_0_40,negated_conjecture,
app(sk6,sk5) = sk1,
inference(rw,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_41,negated_conjecture,
ssList(sk5),
co1_7 ).
cnf(c_0_42,negated_conjecture,
ssList(sk6),
co1_8 ).
cnf(c_0_43,negated_conjecture,
app(sk5,sk6) = sk2,
inference(rw,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_44,negated_conjecture,
( sk5 = nil
| sk1 != nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_41]),c_0_42])]) ).
cnf(c_0_45,axiom,
( app(nil,X1) = X1
| ~ ssList(X1) ),
clause74 ).
cnf(c_0_46,negated_conjecture,
( app(nil,sk6) = sk2
| sk1 != nil ),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_47,axiom,
( app(X1,nil) = X1
| ~ ssList(X1) ),
clause73 ).
cnf(c_0_48,negated_conjecture,
( app(sk6,nil) = sk1
| sk1 != nil ),
inference(spm,[status(thm)],[c_0_40,c_0_44]) ).
cnf(c_0_49,axiom,
( nil = X1
| app(X1,X2) != nil
| ~ ssList(X2)
| ~ ssList(X1) ),
clause118 ).
cnf(c_0_50,axiom,
( app(X1,X2) = nil
| nil != X1
| nil != X2
| ~ ssList(X2)
| ~ ssList(X1) ),
clause145 ).
cnf(c_0_51,axiom,
ssList(nil),
clause8 ).
cnf(c_0_52,negated_conjecture,
( sk6 = sk2
| sk1 != nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_42])]) ).
cnf(c_0_53,negated_conjecture,
( sk6 = sk1
| sk1 != nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_42])]) ).
cnf(c_0_54,negated_conjecture,
( sk6 = nil
| sk1 != nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_40]),c_0_41]),c_0_42])]) ).
cnf(c_0_55,plain,
app(nil,nil) = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_50])]),c_0_51])]) ).
cnf(c_0_56,axiom,
( app(app(X1,cons(X2,X3)),cons(X2,X4)) != X5
| ~ ssList(X4)
| ~ ssList(X3)
| ~ ssList(X1)
| ~ ssItem(X2)
| ~ duplicatefreeP(X5)
| ~ ssList(X5) ),
clause179 ).
cnf(c_0_57,negated_conjecture,
( ~ memberP(sk2,sk7)
| ~ memberP(sk1,sk7) ),
co1_13 ).
cnf(c_0_58,negated_conjecture,
( sk2 = sk1
| sk1 != nil ),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_59,negated_conjecture,
( memberP(sk2,sk7)
| memberP(sk1,sk7) ),
co1_12 ).
cnf(c_0_60,negated_conjecture,
( sk2 = nil
| sk1 != nil ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_54]),c_0_55]) ).
cnf(c_0_61,plain,
( ~ ssItem(X1)
| ~ ssList(app(app(X2,cons(X1,X3)),cons(X1,X4)))
| ~ ssList(X4)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ duplicatefreeP(app(app(X2,cons(X1,X3)),cons(X1,X4))) ),
inference(er,[status(thm)],[c_0_56]) ).
cnf(c_0_62,axiom,
( app(skaf42(X1,X2),cons(X2,skaf43(X2,X1))) = X1
| ~ memberP(X1,X2)
| ~ ssItem(X2)
| ~ ssList(X1) ),
clause169 ).
cnf(c_0_63,axiom,
ssList(skaf43(X1,X2)),
clause52 ).
cnf(c_0_64,axiom,
ssList(skaf42(X1,X2)),
clause53 ).
cnf(c_0_65,axiom,
( memberP(cons(X2,X3),X1)
| X1 != X2
| ~ ssList(X3)
| ~ ssItem(X2)
| ~ ssItem(X1) ),
clause138 ).
cnf(c_0_66,axiom,
( duplicatefreeP(X1)
| ssItem(X2)
| ~ ssList(X1) ),
clause72 ).
cnf(c_0_67,axiom,
( ssList(app(X2,X1))
| ~ ssList(X1)
| ~ ssList(X2) ),
clause85 ).
cnf(c_0_68,negated_conjecture,
( sk1 != nil
| ~ memberP(sk1,sk7) ),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_69,negated_conjecture,
( memberP(nil,sk7)
| memberP(sk1,sk7)
| sk1 != nil ),
inference(spm,[status(thm)],[c_0_59,c_0_60]) ).
cnf(c_0_70,plain,
( ~ memberP(X1,X2)
| ~ ssItem(X2)
| ~ ssList(app(X1,cons(X2,X3)))
| ~ ssList(X3)
| ~ ssList(X1)
| ~ duplicatefreeP(app(X1,cons(X2,X3))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_63]),c_0_64])]) ).
cnf(c_0_71,axiom,
( cons(skaf83(X1),skaf82(X1)) = X1
| nil = X1
| ~ ssList(X1) ),
clause109 ).
cnf(c_0_72,axiom,
ssItem(skaf83(X1)),
clause12 ).
cnf(c_0_73,axiom,
ssList(skaf82(X1)),
clause13 ).
cnf(c_0_74,plain,
( memberP(cons(X1,X2),X1)
| ~ ssItem(X1)
| ~ ssList(X2) ),
inference(er,[status(thm)],[c_0_65]) ).
cnf(c_0_75,plain,
( ssItem(X1)
| duplicatefreeP(app(X2,X3))
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(spm,[status(thm)],[c_0_66,c_0_67]) ).
cnf(c_0_76,negated_conjecture,
ssList(sk2),
co1_2 ).
cnf(c_0_77,negated_conjecture,
( sk6 = nil
| sk2 != nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_43]),c_0_42]),c_0_41])]) ).
cnf(c_0_78,axiom,
( ~ memberP(nil,X1)
| ~ ssItem(X1) ),
clause71 ).
cnf(c_0_79,negated_conjecture,
( memberP(nil,sk7)
| sk1 != nil ),
inference(spm,[status(thm)],[c_0_68,c_0_69]) ).
cnf(c_0_80,negated_conjecture,
ssItem(sk7),
co1_11 ).
cnf(c_0_81,plain,
( nil = X1
| ~ memberP(X2,skaf83(X1))
| ~ ssList(X2)
| ~ ssList(X1)
| ~ duplicatefreeP(app(X2,X1)) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_72]),c_0_73])]),c_0_67]) ).
cnf(c_0_82,plain,
( nil = X1
| memberP(X1,skaf83(X1))
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_71]),c_0_72]),c_0_73])]) ).
cnf(c_0_83,negated_conjecture,
( ssItem(X1)
| duplicatefreeP(app(sk2,X2))
| ~ ssList(X2) ),
inference(spm,[status(thm)],[c_0_75,c_0_76]) ).
cnf(c_0_84,negated_conjecture,
( app(nil,sk5) = sk1
| sk2 != nil ),
inference(spm,[status(thm)],[c_0_40,c_0_77]) ).
cnf(c_0_85,negated_conjecture,
( sk5 = nil
| sk2 != nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_43]),c_0_42]),c_0_41])]) ).
cnf(c_0_86,negated_conjecture,
sk1 != nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_79]),c_0_80])]) ).
cnf(c_0_87,axiom,
( app(app(X3,X2),X1) = app(X3,app(X2,X1))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
clause149 ).
cnf(c_0_88,plain,
( nil = X1
| ~ ssList(X1)
| ~ duplicatefreeP(app(X1,X1)) ),
inference(spm,[status(thm)],[c_0_81,c_0_82]) ).
cnf(c_0_89,negated_conjecture,
( ssItem(X1)
| duplicatefreeP(app(sk2,sk2)) ),
inference(spm,[status(thm)],[c_0_83,c_0_76]) ).
cnf(c_0_90,negated_conjecture,
sk2 != nil,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_85]),c_0_55]),c_0_86]) ).
cnf(c_0_91,negated_conjecture,
( app(sk6,app(sk5,X1)) = app(sk1,X1)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_40]),c_0_42]),c_0_41])]) ).
cnf(c_0_92,axiom,
( memberP(app(X3,X1),X2)
| ~ memberP(X1,X2)
| ~ ssList(X1)
| ~ ssList(X3)
| ~ ssItem(X2) ),
clause141 ).
cnf(c_0_93,negated_conjecture,
ssItem(X1),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_89]),c_0_76])]),c_0_90]) ).
cnf(c_0_94,negated_conjecture,
( app(sk5,app(sk6,X1)) = app(sk2,X1)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_43]),c_0_41]),c_0_42])]) ).
cnf(c_0_95,negated_conjecture,
app(sk6,sk2) = app(sk1,sk6),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_43]),c_0_42])]) ).
cnf(c_0_96,axiom,
( memberP(X2,X3)
| memberP(X1,X3)
| ~ memberP(app(X1,X2),X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X3) ),
clause158 ).
cnf(c_0_97,plain,
( memberP(app(X1,X2),X3)
| ~ memberP(X2,X3)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_92,c_0_93])]) ).
cnf(c_0_98,negated_conjecture,
app(sk5,app(sk1,sk6)) = app(sk2,sk2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_95]),c_0_76])]) ).
cnf(c_0_99,negated_conjecture,
ssList(app(sk1,sk6)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_95]),c_0_42]),c_0_76])]) ).
cnf(c_0_100,plain,
( memberP(X1,X2)
| memberP(X3,X2)
| ~ memberP(app(X1,X3),X2)
| ~ ssList(X3)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_96,c_0_93])]) ).
cnf(c_0_101,negated_conjecture,
( memberP(app(sk2,sk2),X1)
| ~ memberP(app(sk1,sk6),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_98]),c_0_41]),c_0_99])]) ).
cnf(c_0_102,axiom,
( memberP(app(X1,X3),X2)
| ~ memberP(X1,X2)
| ~ ssList(X3)
| ~ ssList(X1)
| ~ ssItem(X2) ),
clause140 ).
cnf(c_0_103,negated_conjecture,
( memberP(sk2,X1)
| ~ memberP(app(sk1,sk6),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_101]),c_0_76])]) ).
cnf(c_0_104,plain,
( memberP(app(X1,X2),X3)
| ~ memberP(X1,X3)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_102,c_0_93])]) ).
cnf(c_0_105,negated_conjecture,
ssList(sk1),
co1_1 ).
cnf(c_0_106,negated_conjecture,
( memberP(sk2,X1)
| ~ memberP(sk1,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_104]),c_0_42]),c_0_105])]) ).
cnf(c_0_107,axiom,
( frontsegP(X3,X1)
| app(X1,X2) != X3
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X3) ),
clause144 ).
cnf(c_0_108,axiom,
( app(X2,skaf45(X1,X2)) = X1
| ~ frontsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
clause132 ).
cnf(c_0_109,axiom,
ssList(skaf45(X1,X2)),
clause51 ).
cnf(c_0_110,negated_conjecture,
~ memberP(sk1,sk7),
inference(spm,[status(thm)],[c_0_57,c_0_106]) ).
cnf(c_0_111,plain,
( frontsegP(app(X1,X2),X1)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_107]),c_0_67]) ).
cnf(c_0_112,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_87,c_0_45]),c_0_51])]) ).
cnf(c_0_113,negated_conjecture,
app(sk5,sk1) = app(sk2,sk5),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_40]),c_0_41])]) ).
cnf(c_0_114,plain,
( memberP(X1,X2)
| ~ memberP(X3,X2)
| ~ frontsegP(X1,X3)
| ~ ssList(X3)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_108]),c_0_109])]) ).
cnf(c_0_115,negated_conjecture,
memberP(sk2,sk7),
inference(sr,[status(thm)],[c_0_59,c_0_110]) ).
cnf(c_0_116,plain,
( frontsegP(app(X1,app(X2,X3)),app(X1,X2))
| ~ ssList(X3)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_87]),c_0_67]) ).
cnf(c_0_117,negated_conjecture,
app(nil,app(sk2,sk5)) = app(sk2,sk5),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_113]),c_0_41]),c_0_105])]) ).
cnf(c_0_118,negated_conjecture,
app(nil,sk2) = sk2,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_43]),c_0_41]),c_0_42])]) ).
cnf(c_0_119,negated_conjecture,
app(sk6,app(sk2,sk5)) = app(sk1,sk1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_113]),c_0_105])]) ).
cnf(c_0_120,negated_conjecture,
ssList(app(sk2,sk5)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_113]),c_0_41]),c_0_105])]) ).
cnf(c_0_121,negated_conjecture,
( memberP(X1,sk7)
| ~ frontsegP(X1,sk2)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_115]),c_0_76])]) ).
cnf(c_0_122,negated_conjecture,
frontsegP(app(sk2,sk5),sk2),
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_116,c_0_117]),c_0_118]),c_0_41]),c_0_51]),c_0_76])]) ).
cnf(c_0_123,negated_conjecture,
( memberP(app(sk1,sk1),X1)
| ~ memberP(app(sk2,sk5),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_119]),c_0_42]),c_0_120])]) ).
cnf(c_0_124,negated_conjecture,
memberP(app(sk2,sk5),sk7),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_121,c_0_122]),c_0_120])]) ).
cnf(c_0_125,negated_conjecture,
memberP(app(sk1,sk1),sk7),
inference(spm,[status(thm)],[c_0_123,c_0_124]) ).
cnf(c_0_126,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_125]),c_0_105])]),c_0_110]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWC378-1 : 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
% 0.16/0.33 % Computer : n013.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 04:49:11 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 7.01/4.65 % Version : CSE_E---1.7
% 7.01/4.65 % Problem : theBenchmark.p
% 7.01/4.65 % SZS status Unsatisfiable for theBenchmark.p
% 7.01/4.65 % SZS output start CNFRefutation
% See solution above
% 7.01/4.68 % Total time : 3.370s
%------------------------------------------------------------------------------