%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWC329-1 : 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 : n011.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 05:19:12 PM UTC 2026
% Result : Unsatisfiable 45.57s 26.84s
% Output : CNFRefutation 45.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 52
% Syntax : Number of clauses : 180 ( 37 unt; 36 nHn; 151 RR)
% Number of literals : 494 ( 141 equ; 302 neg)
% Maximal clause size : 7 ( 2 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 6 con; 0-2 aty)
% Number of variables : 253 ( 48 sgn)
% Comments :
%------------------------------------------------------------------------------
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(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(clause101,axiom,
( cons(skaf44(X1),nil) = X1
| ~ singletonP(X1)
| ~ ssList(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause101) ).
cnf(clause47,axiom,
ssItem(skaf44(X1)),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause47) ).
cnf(clause8,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause8) ).
cnf(clause85,axiom,
( ssList(app(X2,X1))
| ~ ssList(X1)
| ~ ssList(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause85) ).
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(clause116,axiom,
( singletonP(X2)
| cons(X1,nil) != X2
| ~ ssItem(X1)
| ~ ssList(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause116) ).
cnf(clause72,axiom,
( duplicatefreeP(X1)
| ssItem(X2)
| ~ ssList(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause72) ).
cnf(clause86,axiom,
( ssList(cons(X1,X2))
| ~ ssItem(X1)
| ~ ssList(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause86) ).
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(clause51,axiom,
ssList(skaf45(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause51) ).
cnf(clause74,axiom,
( app(nil,X1) = X1
| ~ ssList(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause74) ).
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(clause60,axiom,
( frontsegP(X1,nil)
| ~ ssList(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause60) ).
cnf(clause157,axiom,
( cons(X1,app(X2,X3)) = app(cons(X1,X2),X3)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause157) ).
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(clause151,axiom,
( X1 = X3
| app(X1,X2) != app(X3,X2)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause151) ).
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(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(clause131,axiom,
( app(skaf46(X1,X2),X2) = X1
| ~ rearsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause131) ).
cnf(clause50,axiom,
ssList(skaf46(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause50) ).
cnf(clause58,axiom,
( rearsegP(X1,nil)
| ~ ssList(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause58) ).
cnf(clause71,axiom,
( ~ memberP(nil,X1)
| ~ ssItem(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause71) ).
cnf(clause73,axiom,
( app(X1,nil) = X1
| ~ ssList(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause73) ).
cnf(co1_1,negated_conjecture,
ssList(sk1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_1) ).
cnf(co1_6,negated_conjecture,
sk1 = sk3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_6) ).
cnf(co1_8,negated_conjecture,
( ssItem(sk5)
| nil = sk3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_8) ).
cnf(clause104,axiom,
( cons(hd(X1),tl(X1)) = X1
| nil = X1
| ~ ssList(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause104) ).
cnf(clause97,axiom,
( hd(cons(X1,X2)) = X1
| ~ ssItem(X1)
| ~ ssList(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause97) ).
cnf(clause98,axiom,
( cons(X1,X2) != nil
| ~ ssItem(X1)
| ~ ssList(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause98) ).
cnf(clause96,axiom,
( tl(cons(X1,X2)) = X2
| ~ ssItem(X1)
| ~ ssList(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause96) ).
cnf(co1_12,negated_conjecture,
( cons(sk5,nil) = sk3
| nil = sk3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_12) ).
cnf(clause99,axiom,
( cons(X1,X2) != X2
| ~ ssItem(X1)
| ~ ssList(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause99) ).
cnf(co1_2,negated_conjecture,
ssList(sk2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_2) ).
cnf(co1_5,negated_conjecture,
sk2 = sk4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_5) ).
cnf(co1_7,negated_conjecture,
( ssItem(sk5)
| nil = sk4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_7) ).
cnf(co1_13,negated_conjecture,
( memberP(sk4,sk5)
| nil = sk3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_13) ).
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(co1_9,negated_conjecture,
( cons(sk5,nil) = sk3
| nil = sk4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_9) ).
cnf(co1_15,negated_conjecture,
( ~ segmentP(sk2,sk1)
| ~ equalelemsP(sk1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_15) ).
cnf(clause109,axiom,
( cons(skaf83(X1),skaf82(X1)) = X1
| nil = X1
| ~ ssList(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause109) ).
cnf(clause13,axiom,
ssList(skaf82(X1)),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause13) ).
cnf(clause1,axiom,
equalelemsP(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause1) ).
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(clause12,axiom,
ssItem(skaf83(X1)),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause12) ).
cnf(clause56,axiom,
( segmentP(X1,nil)
| ~ ssList(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause56) ).
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(clause64,axiom,
( equalelemsP(cons(X1,nil))
| ~ ssItem(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause64) ).
cnf(co1_10,negated_conjecture,
( memberP(sk4,sk5)
| nil = sk4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_10) ).
cnf(c_0_52,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_53,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_52]) ).
cnf(c_0_54,axiom,
( app(skaf42(X1,X2),cons(X2,skaf43(X2,X1))) = X1
| ~ memberP(X1,X2)
| ~ ssItem(X2)
| ~ ssList(X1) ),
clause169 ).
cnf(c_0_55,axiom,
ssList(skaf43(X1,X2)),
clause52 ).
cnf(c_0_56,axiom,
ssList(skaf42(X1,X2)),
clause53 ).
cnf(c_0_57,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_53,c_0_54]),c_0_55]),c_0_56])]) ).
cnf(c_0_58,axiom,
( cons(skaf44(X1),nil) = X1
| ~ singletonP(X1)
| ~ ssList(X1) ),
clause101 ).
cnf(c_0_59,axiom,
ssItem(skaf44(X1)),
clause47 ).
cnf(c_0_60,axiom,
ssList(nil),
clause8 ).
cnf(c_0_61,axiom,
( ssList(app(X2,X1))
| ~ ssList(X1)
| ~ ssList(X2) ),
clause85 ).
cnf(c_0_62,axiom,
( memberP(cons(X2,X3),X1)
| X1 != X2
| ~ ssList(X3)
| ~ ssItem(X2)
| ~ ssItem(X1) ),
clause138 ).
cnf(c_0_63,plain,
( ~ memberP(X1,skaf44(X2))
| ~ singletonP(X2)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ duplicatefreeP(app(X1,X2)) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_59]),c_0_60])]),c_0_61]) ).
cnf(c_0_64,plain,
( memberP(cons(X1,X2),X1)
| ~ ssItem(X1)
| ~ ssList(X2) ),
inference(er,[status(thm)],[c_0_62]) ).
cnf(c_0_65,plain,
( ~ singletonP(X1)
| ~ ssList(cons(skaf44(X1),X2))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ duplicatefreeP(app(cons(skaf44(X1),X2),X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_59])]) ).
cnf(c_0_66,axiom,
( singletonP(X2)
| cons(X1,nil) != X2
| ~ ssItem(X1)
| ~ ssList(X2) ),
clause116 ).
cnf(c_0_67,axiom,
( duplicatefreeP(X1)
| ssItem(X2)
| ~ ssList(X1) ),
clause72 ).
cnf(c_0_68,axiom,
( ssList(cons(X1,X2))
| ~ ssItem(X1)
| ~ ssList(X2) ),
clause86 ).
cnf(c_0_69,plain,
( ~ singletonP(X1)
| ~ ssList(X1)
| ~ duplicatefreeP(app(X1,X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_58]),c_0_60])]) ).
cnf(c_0_70,axiom,
( app(cons(X1,nil),X2) = cons(X1,X2)
| ~ ssItem(X1)
| ~ ssList(X2) ),
clause120 ).
cnf(c_0_71,plain,
( singletonP(cons(X1,nil))
| ~ ssItem(X1)
| ~ ssList(cons(X1,nil)) ),
inference(er,[status(thm)],[c_0_66]) ).
cnf(c_0_72,plain,
( ssItem(X1)
| duplicatefreeP(cons(X2,X3))
| ~ ssItem(X2)
| ~ ssList(X3) ),
inference(spm,[status(thm)],[c_0_67,c_0_68]) ).
cnf(c_0_73,plain,
( ~ ssItem(X1)
| ~ ssList(cons(X1,nil))
| ~ duplicatefreeP(cons(X1,cons(X1,nil))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_71]) ).
cnf(c_0_74,plain,
( ssItem(X1)
| duplicatefreeP(cons(skaf44(X2),X3))
| ~ ssList(X3) ),
inference(spm,[status(thm)],[c_0_72,c_0_59]) ).
cnf(c_0_75,axiom,
ssList(skaf45(X1,X2)),
clause51 ).
cnf(c_0_76,plain,
( ~ singletonP(X1)
| ~ ssList(X1)
| ~ duplicatefreeP(cons(skaf44(X1),X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_58]),c_0_59])]) ).
cnf(c_0_77,plain,
( ssItem(X1)
| duplicatefreeP(cons(skaf44(X2),skaf45(X3,X4))) ),
inference(spm,[status(thm)],[c_0_74,c_0_75]) ).
cnf(c_0_78,axiom,
( app(nil,X1) = X1
| ~ ssList(X1) ),
clause74 ).
cnf(c_0_79,axiom,
( app(X2,skaf45(X1,X2)) = X1
| ~ frontsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
clause132 ).
cnf(c_0_80,axiom,
( frontsegP(X1,nil)
| ~ ssList(X1) ),
clause60 ).
cnf(c_0_81,axiom,
( cons(X1,app(X2,X3)) = app(cons(X1,X2),X3)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
clause157 ).
cnf(c_0_82,axiom,
( app(X1,X2) = nil
| nil != X1
| nil != X2
| ~ ssList(X2)
| ~ ssList(X1) ),
clause145 ).
cnf(c_0_83,plain,
( ssItem(X1)
| ~ singletonP(skaf45(X2,X3)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_77]),c_0_75])]) ).
cnf(c_0_84,plain,
( skaf45(X1,nil) = X1
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_79]),c_0_75]),c_0_60])]),c_0_80]) ).
cnf(c_0_85,plain,
( ssList(cons(X1,app(X2,X3)))
| ~ ssItem(X1)
| ~ ssList(X3)
| ~ ssList(X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_81]),c_0_68]) ).
cnf(c_0_86,plain,
app(nil,nil) = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_82])]),c_0_60])]) ).
cnf(c_0_87,plain,
( ssItem(X1)
| ~ singletonP(X2)
| ~ ssList(X2) ),
inference(spm,[status(thm)],[c_0_83,c_0_84]) ).
cnf(c_0_88,plain,
( ssList(cons(X1,nil))
| ~ ssItem(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_86]),c_0_60])]) ).
cnf(c_0_89,axiom,
( X1 = X3
| app(X1,X2) != app(X3,X2)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
clause151 ).
cnf(c_0_90,plain,
( ssItem(X1)
| ~ ssItem(X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_71]),c_0_88]) ).
cnf(c_0_91,plain,
( X1 = nil
| app(X1,nil) != nil
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_86]),c_0_60])]) ).
cnf(c_0_92,axiom,
( app(app(X3,X2),X1) = app(X3,app(X2,X1))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
clause149 ).
cnf(c_0_93,axiom,
( memberP(app(X1,X3),X2)
| ~ memberP(X1,X2)
| ~ ssList(X3)
| ~ ssList(X1)
| ~ ssItem(X2) ),
clause140 ).
cnf(c_0_94,plain,
ssItem(X1),
inference(spm,[status(thm)],[c_0_90,c_0_59]) ).
cnf(c_0_95,plain,
( app(X1,X2) = nil
| app(X1,app(X2,nil)) != nil
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_92]),c_0_60])]),c_0_61]) ).
cnf(c_0_96,axiom,
( app(skaf46(X1,X2),X2) = X1
| ~ rearsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
clause131 ).
cnf(c_0_97,axiom,
ssList(skaf46(X1,X2)),
clause50 ).
cnf(c_0_98,axiom,
( rearsegP(X1,nil)
| ~ ssList(X1) ),
clause58 ).
cnf(c_0_99,axiom,
( ~ memberP(nil,X1)
| ~ ssItem(X1) ),
clause71 ).
cnf(c_0_100,axiom,
( app(X1,nil) = X1
| ~ ssList(X1) ),
clause73 ).
cnf(c_0_101,plain,
( ssList(app(X1,app(X2,X3)))
| ~ ssList(X3)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_92]),c_0_61]) ).
cnf(c_0_102,negated_conjecture,
ssList(sk1),
co1_1 ).
cnf(c_0_103,negated_conjecture,
sk1 = sk3,
co1_6 ).
cnf(c_0_104,negated_conjecture,
( ssItem(sk5)
| nil = sk3 ),
co1_8 ).
cnf(c_0_105,axiom,
( cons(hd(X1),tl(X1)) = X1
| nil = X1
| ~ ssList(X1) ),
clause104 ).
cnf(c_0_106,axiom,
( hd(cons(X1,X2)) = X1
| ~ ssItem(X1)
| ~ ssList(X2) ),
clause97 ).
cnf(c_0_107,axiom,
( cons(X1,X2) != nil
| ~ ssItem(X1)
| ~ ssList(X2) ),
clause98 ).
cnf(c_0_108,axiom,
( tl(cons(X1,X2)) = X2
| ~ ssItem(X1)
| ~ ssList(X2) ),
clause96 ).
cnf(c_0_109,plain,
( memberP(app(X1,X2),X3)
| ~ memberP(X1,X3)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_93,c_0_94])]) ).
cnf(c_0_110,plain,
( app(X1,skaf46(X2,nil)) = nil
| app(X1,X2) != nil
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_96]),c_0_97]),c_0_60])]),c_0_98]) ).
cnf(c_0_111,plain,
~ memberP(nil,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_99,c_0_94])]) ).
cnf(c_0_112,plain,
( app(X1,app(X2,nil)) = app(X1,X2)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_92]),c_0_60])]),c_0_61]) ).
cnf(c_0_113,plain,
( ssList(app(X1,nil))
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_86]),c_0_60])]) ).
cnf(c_0_114,negated_conjecture,
( cons(sk5,nil) = sk3
| nil = sk3 ),
co1_12 ).
cnf(c_0_115,negated_conjecture,
ssList(sk3),
inference(rw,[status(thm)],[c_0_102,c_0_103]) ).
cnf(c_0_116,negated_conjecture,
( sk3 = nil
| ssItem(X1)
| duplicatefreeP(cons(sk5,X2))
| ~ ssList(X2) ),
inference(spm,[status(thm)],[c_0_72,c_0_104]) ).
cnf(c_0_117,axiom,
( cons(X1,X2) != X2
| ~ ssItem(X1)
| ~ ssList(X2) ),
clause99 ).
cnf(c_0_118,plain,
( cons(X1,tl(cons(X1,X2))) = cons(X1,X2)
| ~ ssItem(X1)
| ~ ssList(X2) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_106]),c_0_68]),c_0_107]) ).
cnf(c_0_119,plain,
( tl(X1) = nil
| ~ singletonP(X1)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_58]),c_0_59]),c_0_60])]) ).
cnf(c_0_120,plain,
( app(X1,X2) != nil
| ~ memberP(X1,X3)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_110]),c_0_97])]),c_0_111]) ).
cnf(c_0_121,plain,
( app(nil,X1) = app(X1,nil)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_112]),c_0_60])]),c_0_113]) ).
cnf(c_0_122,negated_conjecture,
ssList(sk2),
co1_2 ).
cnf(c_0_123,negated_conjecture,
sk2 = sk4,
co1_5 ).
cnf(c_0_124,negated_conjecture,
( sk3 = nil
| ~ duplicatefreeP(cons(sk5,sk3)) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_114]),c_0_115])]),c_0_104]) ).
cnf(c_0_125,negated_conjecture,
( sk3 = nil
| ssItem(X1)
| duplicatefreeP(cons(sk5,sk3)) ),
inference(spm,[status(thm)],[c_0_116,c_0_115]) ).
cnf(c_0_126,plain,
( tl(cons(X1,X2)) != cons(X1,X2)
| ~ ssItem(X1)
| ~ ssList(tl(cons(X1,X2)))
| ~ ssList(X2) ),
inference(spm,[status(thm)],[c_0_117,c_0_118]) ).
cnf(c_0_127,plain,
( tl(cons(X1,nil)) = nil
| ~ ssItem(X1)
| ~ ssList(cons(X1,nil)) ),
inference(spm,[status(thm)],[c_0_119,c_0_71]) ).
cnf(c_0_128,negated_conjecture,
( ssItem(sk5)
| nil = sk4 ),
co1_7 ).
cnf(c_0_129,plain,
( app(nil,X1) != nil
| ~ memberP(X1,X2)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_120,c_0_121]),c_0_60])]) ).
cnf(c_0_130,negated_conjecture,
( memberP(sk4,sk5)
| nil = sk3 ),
co1_13 ).
cnf(c_0_131,negated_conjecture,
ssList(sk4),
inference(rw,[status(thm)],[c_0_122,c_0_123]) ).
cnf(c_0_132,axiom,
( X4 = X2
| cons(X1,X2) != cons(X3,X4)
| ~ ssItem(X3)
| ~ ssItem(X1)
| ~ ssList(X4)
| ~ ssList(X2) ),
clause171 ).
cnf(c_0_133,negated_conjecture,
( sk3 = nil
| ssItem(X1) ),
inference(spm,[status(thm)],[c_0_124,c_0_125]) ).
cnf(c_0_134,plain,
( cons(X1,nil) != nil
| ~ ssItem(X1)
| ~ ssList(cons(X1,nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_126,c_0_127]),c_0_60])]) ).
cnf(c_0_135,negated_conjecture,
( cons(sk5,nil) = sk3
| nil = sk4 ),
co1_9 ).
cnf(c_0_136,negated_conjecture,
( sk4 = nil
| ssItem(X1)
| duplicatefreeP(cons(sk5,X2))
| ~ ssList(X2) ),
inference(spm,[status(thm)],[c_0_72,c_0_128]) ).
cnf(c_0_137,negated_conjecture,
( ~ segmentP(sk2,sk1)
| ~ equalelemsP(sk1) ),
co1_15 ).
cnf(c_0_138,negated_conjecture,
( sk3 = nil
| app(nil,sk4) != nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_129,c_0_130]),c_0_131])]) ).
cnf(c_0_139,negated_conjecture,
( sk3 = nil
| X1 = nil
| cons(X2,X1) != sk3
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_132,c_0_114]),c_0_60])]),c_0_133]),c_0_133]) ).
cnf(c_0_140,axiom,
( cons(skaf83(X1),skaf82(X1)) = X1
| nil = X1
| ~ ssList(X1) ),
clause109 ).
cnf(c_0_141,axiom,
ssList(skaf82(X1)),
clause13 ).
cnf(c_0_142,plain,
( cons(X1,nil) != nil
| ~ ssItem(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_134,c_0_68]),c_0_60])]) ).
cnf(c_0_143,plain,
( cons(skaf44(X1),X2) = app(X1,X2)
| ~ singletonP(X1)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_58]),c_0_59])]) ).
cnf(c_0_144,negated_conjecture,
( sk4 = nil
| ~ duplicatefreeP(cons(sk5,sk3)) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_135]),c_0_115])]),c_0_128]) ).
cnf(c_0_145,negated_conjecture,
( sk4 = nil
| ssItem(X1)
| duplicatefreeP(cons(sk5,sk3)) ),
inference(spm,[status(thm)],[c_0_136,c_0_115]) ).
cnf(c_0_146,negated_conjecture,
( ~ segmentP(sk4,sk3)
| ~ equalelemsP(sk3) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_137,c_0_103]),c_0_123]),c_0_103]) ).
cnf(c_0_147,negated_conjecture,
( sk3 = nil
| sk4 != nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_138,c_0_78]),c_0_131])]) ).
cnf(c_0_148,axiom,
equalelemsP(nil),
clause1 ).
cnf(c_0_149,negated_conjecture,
( skaf82(sk3) = nil
| sk3 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_139,c_0_140]),c_0_141])])]),c_0_115])]) ).
cnf(c_0_150,axiom,
( X1 = X3
| cons(X1,X2) != cons(X3,X4)
| ~ ssItem(X3)
| ~ ssItem(X1)
| ~ ssList(X4)
| ~ ssList(X2) ),
clause170 ).
cnf(c_0_151,axiom,
ssItem(skaf83(X1)),
clause12 ).
cnf(c_0_152,plain,
( app(X1,nil) != nil
| ~ singletonP(X1)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_142,c_0_143]),c_0_59]),c_0_60])]) ).
cnf(c_0_153,negated_conjecture,
( sk4 = nil
| singletonP(sk3) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_135]),c_0_115])]),c_0_128]) ).
cnf(c_0_154,negated_conjecture,
( sk4 = nil
| ssItem(X1) ),
inference(spm,[status(thm)],[c_0_144,c_0_145]) ).
cnf(c_0_155,negated_conjecture,
( sk4 != nil
| ~ segmentP(sk4,nil) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_146,c_0_147]),c_0_148])]) ).
cnf(c_0_156,axiom,
( segmentP(X1,nil)
| ~ ssList(X1) ),
clause56 ).
cnf(c_0_157,negated_conjecture,
( cons(skaf83(sk3),nil) = sk3
| sk3 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_140,c_0_149]),c_0_115])]) ).
cnf(c_0_158,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_150,c_0_140]),c_0_151]),c_0_141])])]),c_0_68]),c_0_107]) ).
cnf(c_0_159,negated_conjecture,
( sk4 = nil
| app(sk3,nil) != nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_152,c_0_153]),c_0_115])]) ).
cnf(c_0_160,negated_conjecture,
( app(sk3,X1) = cons(sk5,X1)
| sk4 = nil
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_135]),c_0_154]) ).
cnf(c_0_161,negated_conjecture,
sk4 != nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_155,c_0_156]),c_0_131])]) ).
cnf(c_0_162,axiom,
( segmentP(X4,X2)
| app(app(X1,X2),X3) != X4
| ~ ssList(X3)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X4) ),
clause173 ).
cnf(c_0_163,negated_conjecture,
( cons(skaf83(sk3),X1) = app(sk3,X1)
| sk3 = nil
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_157]),c_0_151])]) ).
cnf(c_0_164,negated_conjecture,
( skaf83(sk3) = sk5
| sk4 = nil ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_158,c_0_135]),c_0_60])]),c_0_154]) ).
cnf(c_0_165,negated_conjecture,
( sk4 = nil
| cons(sk5,nil) != nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_159,c_0_160]),c_0_60])]) ).
cnf(c_0_166,negated_conjecture,
cons(sk5,nil) = sk3,
inference(sr,[status(thm)],[c_0_135,c_0_161]) ).
cnf(c_0_167,axiom,
( equalelemsP(cons(X1,nil))
| ~ ssItem(X1) ),
clause64 ).
cnf(c_0_168,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_162]) ).
cnf(c_0_169,negated_conjecture,
( app(skaf42(X1,skaf83(sk3)),app(sk3,skaf43(skaf83(sk3),X1))) = X1
| sk3 = nil
| ~ memberP(X1,skaf83(sk3))
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_163]),c_0_151]),c_0_55])]) ).
cnf(c_0_170,negated_conjecture,
skaf83(sk3) = sk5,
inference(sr,[status(thm)],[c_0_164,c_0_161]) ).
cnf(c_0_171,negated_conjecture,
sk3 != nil,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_165,c_0_166]),c_0_161]) ).
cnf(c_0_172,negated_conjecture,
( sk3 = nil
| equalelemsP(sk3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_167,c_0_114]),c_0_104]) ).
cnf(c_0_173,plain,
( segmentP(app(X1,app(X2,X3)),X2)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_168,c_0_92]),c_0_101]) ).
cnf(c_0_174,negated_conjecture,
( app(skaf42(X1,sk5),app(sk3,skaf43(sk5,X1))) = X1
| ~ memberP(X1,sk5)
| ~ ssList(X1) ),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_169,c_0_170]),c_0_170]),c_0_170]),c_0_171]) ).
cnf(c_0_175,negated_conjecture,
( memberP(sk4,sk5)
| nil = sk4 ),
co1_10 ).
cnf(c_0_176,negated_conjecture,
( sk3 = nil
| ~ segmentP(sk4,sk3) ),
inference(spm,[status(thm)],[c_0_146,c_0_172]) ).
cnf(c_0_177,negated_conjecture,
( segmentP(X1,sk3)
| ~ memberP(X1,sk5)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_173,c_0_174]),c_0_55]),c_0_115]),c_0_56])]) ).
cnf(c_0_178,negated_conjecture,
memberP(sk4,sk5),
inference(sr,[status(thm)],[c_0_175,c_0_161]) ).
cnf(c_0_179,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_176,c_0_177]),c_0_178]),c_0_131])]),c_0_171]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWC329-1 : 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 : n011.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 04:44:32 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 45.57/26.84 % Version : CSE_E---1.7
% 45.57/26.84 % Problem : theBenchmark.p
% 45.57/26.84 % SZS status Unsatisfiable for theBenchmark.p
% 45.57/26.84 % SZS output start CNFRefutation
% See solution above
% 45.67/27.02 % Total time : 20.404s
%------------------------------------------------------------------------------