%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWC285-1 : TPTP v9.2.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n003.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 05:19:01 PM UTC 2026
% Result : Unsatisfiable 4.00s 3.22s
% Output : CNFRefutation 4.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 48
% Syntax : Number of clauses : 168 ( 38 unt; 46 nHn; 160 RR)
% Number of literals : 468 ( 168 equ; 257 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 9 con; 0-2 aty)
% Number of variables : 170 ( 10 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(co1_11,negated_conjecture,
app(app(sk6,cons(sk5,nil)),sk7) = sk1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_11) ).
cnf(co1_6,negated_conjecture,
sk1 = sk3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_6) ).
cnf(clause119,axiom,
( nil = X2
| app(X1,X2) != nil
| ~ ssList(X2)
| ~ ssList(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause119) ).
cnf(co1_10,negated_conjecture,
ssList(sk7),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_10) ).
cnf(clause118,axiom,
( nil = X1
| app(X1,X2) != nil
| ~ ssList(X2)
| ~ ssList(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause118) ).
cnf(clause85,axiom,
( ssList(app(X2,X1))
| ~ ssList(X1)
| ~ ssList(X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause85) ).
cnf(co1_9,negated_conjecture,
ssList(sk6),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_9) ).
cnf(clause86,axiom,
( ssList(cons(X1,X2))
| ~ ssItem(X1)
| ~ ssList(X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause86) ).
cnf(co1_8,negated_conjecture,
ssItem(sk5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_8) ).
cnf(clause8,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause8) ).
cnf(clause96,axiom,
( tl(cons(X1,X2)) = X2
| ~ ssItem(X1)
| ~ ssList(X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause96) ).
cnf(clause101,axiom,
( cons(skaf44(X1),nil) = X1
| ~ singletonP(X1)
| ~ ssList(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause101) ).
cnf(clause47,axiom,
ssItem(skaf44(X1)),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause47) ).
cnf(co1_1,negated_conjecture,
ssList(sk1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_1) ).
cnf(co1_13,negated_conjecture,
( memberP(sk6,sk8)
| memberP(sk7,sk8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_13) ).
cnf(clause97,axiom,
( hd(cons(X1,X2)) = X1
| ~ ssItem(X1)
| ~ ssList(X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause97) ).
cnf(co1_17,negated_conjecture,
( singletonP(sk3)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_17) ).
cnf(co1_2,negated_conjecture,
ssList(sk2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_2) ).
cnf(co1_5,negated_conjecture,
sk2 = sk4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_5) ).
cnf(clause100,axiom,
( neq(X2,X1)
| X2 = X1
| ~ ssList(X1)
| ~ ssList(X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause100) ).
cnf(clause71,axiom,
( ~ memberP(nil,X1)
| ~ ssItem(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause71) ).
cnf(co1_12,negated_conjecture,
ssItem(sk8),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_12) ).
cnf(clause104,axiom,
( cons(hd(X1),tl(X1)) = X1
| nil = X1
| ~ ssList(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause104) ).
cnf(clause171,axiom,
( X4 = X2
| cons(X1,X2) != cons(X3,X4)
| ~ ssItem(X3)
| ~ ssItem(X1)
| ~ ssList(X4)
| ~ ssList(X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause171) ).
cnf(clause109,axiom,
( cons(skaf83(X1),skaf82(X1)) = X1
| nil = X1
| ~ ssList(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause109) ).
cnf(clause12,axiom,
ssItem(skaf83(X1)),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause12) ).
cnf(clause13,axiom,
ssList(skaf82(X1)),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause13) ).
cnf(clause120,axiom,
( app(cons(X1,nil),X2) = cons(X1,X2)
| ~ ssItem(X1)
| ~ ssList(X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause120) ).
cnf(clause133,axiom,
( nil = X2
| tl(app(X2,X1)) = app(tl(X2),X1)
| ~ ssList(X1)
| ~ ssList(X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause133) ).
cnf(clause141,axiom,
( memberP(app(X3,X1),X2)
| ~ memberP(X1,X2)
| ~ ssList(X1)
| ~ ssList(X3)
| ~ ssItem(X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause141) ).
cnf(clause149,axiom,
( app(app(X3,X2),X1) = app(X3,app(X2,X1))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause149) ).
cnf(clause161,axiom,
( memberP(X2,X3)
| X3 = X1
| ~ memberP(cons(X1,X2),X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause161) ).
cnf(clause75,axiom,
( ssList(tl(X1))
| nil = X1
| ~ ssList(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause75) ).
cnf(clause76,axiom,
( ssItem(hd(X1))
| nil = X1
| ~ ssList(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause76) ).
cnf(clause175,axiom,
( memberP(X4,X2)
| app(X1,cons(X2,X3)) != X4
| ~ ssList(X3)
| ~ ssList(X1)
| ~ ssItem(X2)
| ~ ssList(X4) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause175) ).
cnf(clause144,axiom,
( frontsegP(X3,X1)
| app(X1,X2) != X3
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause144) ).
cnf(clause150,axiom,
( X2 = X3
| app(X1,X2) != app(X1,X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause150) ).
cnf(clause132,axiom,
( app(X2,skaf45(X1,X2)) = X1
| ~ frontsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause132) ).
cnf(clause51,axiom,
ssList(skaf45(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause51) ).
cnf(clause173,axiom,
( segmentP(X4,X2)
| app(app(X1,X2),X3) != X4
| ~ ssList(X3)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X4) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause173) ).
cnf(clause74,axiom,
( app(nil,X1) = X1
| ~ ssList(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause74) ).
cnf(clause73,axiom,
( app(X1,nil) = X1
| ~ ssList(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause73) ).
cnf(clause127,axiom,
( X2 = X1
| ~ segmentP(X1,X2)
| ~ segmentP(X2,X1)
| ~ ssList(X1)
| ~ ssList(X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause127) ).
cnf(clause151,axiom,
( X1 = X3
| app(X1,X2) != app(X3,X2)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause151) ).
cnf(clause152,axiom,
( segmentP(X1,X3)
| ~ segmentP(X1,X2)
| ~ segmentP(X2,X3)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause152) ).
cnf(co1_7,negated_conjecture,
segmentP(sk4,sk3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_7) ).
cnf(clause80,axiom,
( nil = X1
| ~ segmentP(nil,X1)
| ~ ssList(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause80) ).
cnf(clause79,axiom,
( segmentP(nil,X1)
| nil != X1
| ~ ssList(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause79) ).
cnf(c_0_48,negated_conjecture,
app(app(sk6,cons(sk5,nil)),sk7) = sk1,
co1_11 ).
cnf(c_0_49,negated_conjecture,
sk1 = sk3,
co1_6 ).
cnf(c_0_50,axiom,
( nil = X2
| app(X1,X2) != nil
| ~ ssList(X2)
| ~ ssList(X1) ),
clause119 ).
cnf(c_0_51,negated_conjecture,
app(app(sk6,cons(sk5,nil)),sk7) = sk3,
inference(rw,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_52,negated_conjecture,
ssList(sk7),
co1_10 ).
cnf(c_0_53,axiom,
( nil = X1
| app(X1,X2) != nil
| ~ ssList(X2)
| ~ ssList(X1) ),
clause118 ).
cnf(c_0_54,negated_conjecture,
( sk7 = nil
| sk3 != nil
| ~ ssList(app(sk6,cons(sk5,nil))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_52])]) ).
cnf(c_0_55,axiom,
( ssList(app(X2,X1))
| ~ ssList(X1)
| ~ ssList(X2) ),
clause85 ).
cnf(c_0_56,negated_conjecture,
ssList(sk6),
co1_9 ).
cnf(c_0_57,negated_conjecture,
( app(sk6,cons(sk5,nil)) = nil
| sk3 != nil
| ~ ssList(app(sk6,cons(sk5,nil))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_51]),c_0_52])]) ).
cnf(c_0_58,negated_conjecture,
( sk7 = nil
| sk3 != nil
| ~ ssList(cons(sk5,nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_56])]) ).
cnf(c_0_59,axiom,
( ssList(cons(X1,X2))
| ~ ssItem(X1)
| ~ ssList(X2) ),
clause86 ).
cnf(c_0_60,negated_conjecture,
ssItem(sk5),
co1_8 ).
cnf(c_0_61,axiom,
ssList(nil),
clause8 ).
cnf(c_0_62,negated_conjecture,
( app(sk6,cons(sk5,nil)) = nil
| sk3 != nil
| ~ ssList(cons(sk5,nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_55]),c_0_56])]) ).
cnf(c_0_63,axiom,
( tl(cons(X1,X2)) = X2
| ~ ssItem(X1)
| ~ ssList(X2) ),
clause96 ).
cnf(c_0_64,axiom,
( cons(skaf44(X1),nil) = X1
| ~ singletonP(X1)
| ~ ssList(X1) ),
clause101 ).
cnf(c_0_65,axiom,
ssItem(skaf44(X1)),
clause47 ).
cnf(c_0_66,negated_conjecture,
ssList(sk1),
co1_1 ).
cnf(c_0_67,negated_conjecture,
( memberP(sk6,sk8)
| memberP(sk7,sk8) ),
co1_13 ).
cnf(c_0_68,negated_conjecture,
( sk7 = nil
| sk3 != nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_60]),c_0_61])]) ).
cnf(c_0_69,negated_conjecture,
( sk6 = nil
| sk3 != nil
| ~ ssList(cons(sk5,nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_62]),c_0_56])]) ).
cnf(c_0_70,axiom,
( hd(cons(X1,X2)) = X1
| ~ ssItem(X1)
| ~ ssList(X2) ),
clause97 ).
cnf(c_0_71,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_63,c_0_64]),c_0_65]),c_0_61])]) ).
cnf(c_0_72,negated_conjecture,
( singletonP(sk3)
| ~ neq(sk4,nil) ),
co1_17 ).
cnf(c_0_73,negated_conjecture,
ssList(sk3),
inference(rw,[status(thm)],[c_0_66,c_0_49]) ).
cnf(c_0_74,negated_conjecture,
ssList(sk2),
co1_2 ).
cnf(c_0_75,negated_conjecture,
sk2 = sk4,
co1_5 ).
cnf(c_0_76,negated_conjecture,
( memberP(nil,sk8)
| memberP(sk6,sk8)
| sk3 != nil ),
inference(spm,[status(thm)],[c_0_67,c_0_68]) ).
cnf(c_0_77,negated_conjecture,
( sk6 = nil
| sk3 != nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_59]),c_0_60]),c_0_61])]) ).
cnf(c_0_78,plain,
( skaf44(X1) = hd(X1)
| ~ singletonP(X1)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_64]),c_0_65]),c_0_61])]) ).
cnf(c_0_79,negated_conjecture,
( tl(sk3) = nil
| ~ neq(sk4,nil) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_73])]) ).
cnf(c_0_80,axiom,
( neq(X2,X1)
| X2 = X1
| ~ ssList(X1)
| ~ ssList(X2) ),
clause100 ).
cnf(c_0_81,negated_conjecture,
ssList(sk4),
inference(rw,[status(thm)],[c_0_74,c_0_75]) ).
cnf(c_0_82,axiom,
( ~ memberP(nil,X1)
| ~ ssItem(X1) ),
clause71 ).
cnf(c_0_83,negated_conjecture,
( memberP(nil,sk8)
| sk3 != nil ),
inference(spm,[status(thm)],[c_0_76,c_0_77]) ).
cnf(c_0_84,negated_conjecture,
ssItem(sk8),
co1_12 ).
cnf(c_0_85,plain,
( ssItem(hd(X1))
| ~ singletonP(X1)
| ~ ssList(X1) ),
inference(spm,[status(thm)],[c_0_65,c_0_78]) ).
cnf(c_0_86,axiom,
( cons(hd(X1),tl(X1)) = X1
| nil = X1
| ~ ssList(X1) ),
clause104 ).
cnf(c_0_87,negated_conjecture,
( tl(sk3) = nil
| sk4 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_80]),c_0_81]),c_0_61])]) ).
cnf(c_0_88,negated_conjecture,
sk3 != nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_83]),c_0_84])]) ).
cnf(c_0_89,negated_conjecture,
( ssItem(hd(sk3))
| ~ neq(sk4,nil) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_72]),c_0_73])]) ).
cnf(c_0_90,axiom,
( X4 = X2
| cons(X1,X2) != cons(X3,X4)
| ~ ssItem(X3)
| ~ ssItem(X1)
| ~ ssList(X4)
| ~ ssList(X2) ),
clause171 ).
cnf(c_0_91,negated_conjecture,
( cons(hd(sk3),nil) = sk3
| sk4 = nil ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_87]),c_0_73])]),c_0_88]) ).
cnf(c_0_92,negated_conjecture,
( sk4 = nil
| ssItem(hd(sk3)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_80]),c_0_81]),c_0_61])]) ).
cnf(c_0_93,negated_conjecture,
( sk4 = nil
| nil = X1
| cons(X2,X1) != sk3
| ~ ssItem(X2)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_91]),c_0_61])]),c_0_92]) ).
cnf(c_0_94,axiom,
( cons(skaf83(X1),skaf82(X1)) = X1
| nil = X1
| ~ ssList(X1) ),
clause109 ).
cnf(c_0_95,axiom,
ssItem(skaf83(X1)),
clause12 ).
cnf(c_0_96,axiom,
ssList(skaf82(X1)),
clause13 ).
cnf(c_0_97,negated_conjecture,
( skaf82(sk3) = nil
| sk4 = nil ),
inference(sr,[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_93,c_0_94]),c_0_95]),c_0_96])])]),c_0_73])]),c_0_88]) ).
cnf(c_0_98,negated_conjecture,
( cons(skaf83(sk3),nil) = sk3
| sk4 = nil ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_97]),c_0_73])]),c_0_88]) ).
cnf(c_0_99,axiom,
( app(cons(X1,nil),X2) = cons(X1,X2)
| ~ ssItem(X1)
| ~ ssList(X2) ),
clause120 ).
cnf(c_0_100,negated_conjecture,
( skaf83(sk3) = hd(sk3)
| sk4 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_98]),c_0_95]),c_0_61])]) ).
cnf(c_0_101,negated_conjecture,
( cons(hd(sk3),X1) = app(sk3,X1)
| sk4 = nil
| ~ ssItem(hd(sk3))
| ~ ssList(X1) ),
inference(spm,[status(thm)],[c_0_99,c_0_91]) ).
cnf(c_0_102,negated_conjecture,
( cons(hd(sk3),skaf82(sk3)) = sk3
| sk4 = nil ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_100]),c_0_73])]),c_0_88]) ).
cnf(c_0_103,axiom,
( nil = X2
| tl(app(X2,X1)) = app(tl(X2),X1)
| ~ ssList(X1)
| ~ ssList(X2) ),
clause133 ).
cnf(c_0_104,negated_conjecture,
( app(sk3,skaf82(sk3)) = sk3
| sk4 = nil ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_102]),c_0_96])]),c_0_92]) ).
cnf(c_0_105,negated_conjecture,
( app(tl(sk3),skaf82(sk3)) = tl(sk3)
| sk4 = nil ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_104]),c_0_73]),c_0_96])]),c_0_88]) ).
cnf(c_0_106,axiom,
( memberP(app(X3,X1),X2)
| ~ memberP(X1,X2)
| ~ ssList(X1)
| ~ ssList(X3)
| ~ ssItem(X2) ),
clause141 ).
cnf(c_0_107,negated_conjecture,
( app(nil,skaf82(sk3)) = nil
| sk4 = nil ),
inference(spm,[status(thm)],[c_0_105,c_0_87]) ).
cnf(c_0_108,axiom,
( app(app(X3,X2),X1) = app(X3,app(X2,X1))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
clause149 ).
cnf(c_0_109,negated_conjecture,
( sk4 = nil
| ~ memberP(skaf82(sk3),X1)
| ~ ssItem(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_107]),c_0_61]),c_0_96])]),c_0_82]) ).
cnf(c_0_110,plain,
( skaf82(X1) = tl(X1)
| nil = X1
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_94]),c_0_95]),c_0_96])]) ).
cnf(c_0_111,axiom,
( memberP(X2,X3)
| X3 = X1
| ~ memberP(cons(X1,X2),X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X3) ),
clause161 ).
cnf(c_0_112,axiom,
( ssList(tl(X1))
| nil = X1
| ~ ssList(X1) ),
clause75 ).
cnf(c_0_113,axiom,
( ssItem(hd(X1))
| nil = X1
| ~ ssList(X1) ),
clause76 ).
cnf(c_0_114,axiom,
( memberP(X4,X2)
| app(X1,cons(X2,X3)) != X4
| ~ ssList(X3)
| ~ ssList(X1)
| ~ ssItem(X2)
| ~ ssList(X4) ),
clause175 ).
cnf(c_0_115,negated_conjecture,
( app(sk6,app(cons(sk5,nil),sk7)) = sk3
| ~ ssList(cons(sk5,nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_108]),c_0_56]),c_0_52])]) ).
cnf(c_0_116,axiom,
( frontsegP(X3,X1)
| app(X1,X2) != X3
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X3) ),
clause144 ).
cnf(c_0_117,negated_conjecture,
( sk4 = nil
| ~ memberP(tl(sk3),X1)
| ~ ssItem(X1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_110]),c_0_73])]),c_0_88]) ).
cnf(c_0_118,plain,
( hd(X1) = X2
| nil = X1
| memberP(tl(X1),X2)
| ~ memberP(X1,X2)
| ~ ssItem(X2)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_86]),c_0_112]),c_0_113]) ).
cnf(c_0_119,plain,
( memberP(app(X1,cons(X2,X3)),X2)
| ~ ssItem(X2)
| ~ ssList(app(X1,cons(X2,X3)))
| ~ ssList(X3)
| ~ ssList(X1) ),
inference(er,[status(thm)],[c_0_114]) ).
cnf(c_0_120,negated_conjecture,
( app(sk6,cons(sk5,sk7)) = sk3
| ~ ssList(cons(sk5,nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_99]),c_0_60]),c_0_52])]) ).
cnf(c_0_121,axiom,
( X2 = X3
| app(X1,X2) != app(X1,X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X3) ),
clause150 ).
cnf(c_0_122,axiom,
( app(X2,skaf45(X1,X2)) = X1
| ~ frontsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
clause132 ).
cnf(c_0_123,axiom,
ssList(skaf45(X1,X2)),
clause51 ).
cnf(c_0_124,plain,
( frontsegP(app(X1,X2),X1)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_116]),c_0_55]) ).
cnf(c_0_125,negated_conjecture,
( hd(sk3) = X1
| sk4 = nil
| ~ memberP(sk3,X1)
| ~ ssItem(X1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_117,c_0_118]),c_0_73])]),c_0_88]) ).
cnf(c_0_126,negated_conjecture,
( memberP(sk3,sk5)
| ~ ssList(cons(sk5,nil)) ),
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_119,c_0_120]),c_0_60]),c_0_73]),c_0_52]),c_0_56])]) ).
cnf(c_0_127,plain,
( skaf45(app(X1,X2),X1) = X2
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_121,c_0_122]),c_0_123])])]),c_0_55]),c_0_124]) ).
cnf(c_0_128,negated_conjecture,
( hd(sk3) = sk5
| sk4 = nil
| ~ ssList(cons(sk5,nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_125,c_0_126]),c_0_60])]) ).
cnf(c_0_129,negated_conjecture,
( skaf45(sk3,sk6) = cons(sk5,sk7)
| ~ ssList(cons(sk5,sk7))
| ~ ssList(cons(sk5,nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_127,c_0_120]),c_0_56])]) ).
cnf(c_0_130,negated_conjecture,
( skaf45(sk3,sk6) = app(cons(sk5,nil),sk7)
| ~ ssList(app(cons(sk5,nil),sk7))
| ~ ssList(cons(sk5,nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_127,c_0_115]),c_0_56])]) ).
cnf(c_0_131,negated_conjecture,
( cons(sk5,nil) = sk3
| sk4 = nil
| ~ ssList(cons(sk5,nil)) ),
inference(spm,[status(thm)],[c_0_91,c_0_128]) ).
cnf(c_0_132,negated_conjecture,
( app(cons(sk5,nil),sk7) = cons(sk5,sk7)
| ~ ssList(app(cons(sk5,nil),sk7))
| ~ ssList(cons(sk5,sk7))
| ~ ssList(cons(sk5,nil)) ),
inference(spm,[status(thm)],[c_0_129,c_0_130]) ).
cnf(c_0_133,axiom,
( segmentP(X4,X2)
| app(app(X1,X2),X3) != X4
| ~ ssList(X3)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X4) ),
clause173 ).
cnf(c_0_134,negated_conjecture,
( cons(sk5,nil) = sk3
| sk4 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_131,c_0_59]),c_0_60]),c_0_61])]) ).
cnf(c_0_135,negated_conjecture,
( app(cons(sk5,nil),sk7) = cons(sk5,sk7)
| ~ ssList(cons(sk5,sk7))
| ~ ssList(cons(sk5,nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_132,c_0_55]),c_0_52])]) ).
cnf(c_0_136,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_133]) ).
cnf(c_0_137,axiom,
( app(nil,X1) = X1
| ~ ssList(X1) ),
clause74 ).
cnf(c_0_138,axiom,
( app(X1,nil) = X1
| ~ ssList(X1) ),
clause73 ).
cnf(c_0_139,negated_conjecture,
( app(sk6,app(sk3,sk7)) = sk3
| sk4 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_134]),c_0_73])]) ).
cnf(c_0_140,negated_conjecture,
( app(sk3,sk7) = cons(sk5,sk7)
| sk4 = nil
| ~ ssList(cons(sk5,sk7)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_135,c_0_134]),c_0_73])]) ).
cnf(c_0_141,plain,
( segmentP(app(X1,X2),X1)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_136,c_0_137]),c_0_61])]),c_0_55]) ).
cnf(c_0_142,plain,
( segmentP(app(X1,X2),X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_136,c_0_138]),c_0_61])]),c_0_55]) ).
cnf(c_0_143,negated_conjecture,
( app(sk6,cons(sk5,sk7)) = sk3
| sk4 = nil
| ~ ssList(cons(sk5,sk7)) ),
inference(spm,[status(thm)],[c_0_139,c_0_140]) ).
cnf(c_0_144,axiom,
( X2 = X1
| ~ segmentP(X1,X2)
| ~ segmentP(X2,X1)
| ~ ssList(X1)
| ~ ssList(X2) ),
clause127 ).
cnf(c_0_145,negated_conjecture,
( sk4 = nil
| segmentP(cons(sk5,sk7),sk3)
| ~ ssList(cons(sk5,sk7)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_141,c_0_140]),c_0_52]),c_0_73])]) ).
cnf(c_0_146,negated_conjecture,
( sk4 = nil
| segmentP(sk3,cons(sk5,sk7))
| ~ ssList(cons(sk5,sk7)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_142,c_0_143]),c_0_56])]) ).
cnf(c_0_147,axiom,
( X1 = X3
| app(X1,X2) != app(X3,X2)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
clause151 ).
cnf(c_0_148,negated_conjecture,
( cons(sk5,sk7) = sk3
| sk4 = nil
| ~ ssList(cons(sk5,sk7)) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_144,c_0_145]),c_0_73])]),c_0_146]) ).
cnf(c_0_149,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_147,c_0_137]),c_0_61])]) ).
cnf(c_0_150,negated_conjecture,
( cons(sk5,sk7) = sk3
| sk4 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_148,c_0_59]),c_0_60]),c_0_52])]) ).
cnf(c_0_151,negated_conjecture,
( sk6 = nil
| cons(sk5,sk7) != sk3
| ~ ssList(cons(sk5,sk7))
| ~ ssList(cons(sk5,nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_149,c_0_120]),c_0_56])]) ).
cnf(c_0_152,negated_conjecture,
( tl(sk3) = sk7
| sk4 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_150]),c_0_60]),c_0_52])]) ).
cnf(c_0_153,negated_conjecture,
( sk6 = nil
| cons(sk5,sk7) != sk3
| ~ ssList(cons(sk5,nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_151,c_0_59]),c_0_60]),c_0_52])]) ).
cnf(c_0_154,negated_conjecture,
( sk4 = nil
| ~ memberP(sk7,X1)
| ~ ssItem(X1) ),
inference(spm,[status(thm)],[c_0_117,c_0_152]) ).
cnf(c_0_155,negated_conjecture,
( sk6 = nil
| cons(sk5,sk7) != sk3 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_153,c_0_59]),c_0_60]),c_0_61])]) ).
cnf(c_0_156,axiom,
( segmentP(X1,X3)
| ~ segmentP(X1,X2)
| ~ segmentP(X2,X3)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1) ),
clause152 ).
cnf(c_0_157,negated_conjecture,
segmentP(sk4,sk3),
co1_7 ).
cnf(c_0_158,negated_conjecture,
( sk4 = nil
| memberP(sk6,sk8) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_154,c_0_67]),c_0_84])]) ).
cnf(c_0_159,negated_conjecture,
( sk4 = nil
| sk6 = nil ),
inference(spm,[status(thm)],[c_0_155,c_0_150]) ).
cnf(c_0_160,axiom,
( nil = X1
| ~ segmentP(nil,X1)
| ~ ssList(X1) ),
clause80 ).
cnf(c_0_161,negated_conjecture,
( segmentP(X1,sk3)
| ~ segmentP(X1,sk4)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_156,c_0_157]),c_0_73]),c_0_81])]) ).
cnf(c_0_162,negated_conjecture,
( sk4 = nil
| memberP(nil,sk8) ),
inference(spm,[status(thm)],[c_0_158,c_0_159]) ).
cnf(c_0_163,axiom,
( segmentP(nil,X1)
| nil != X1
| ~ ssList(X1) ),
clause79 ).
cnf(c_0_164,negated_conjecture,
~ segmentP(nil,sk4),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_160,c_0_161]),c_0_73]),c_0_61])]),c_0_88]) ).
cnf(c_0_165,negated_conjecture,
sk4 = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_162]),c_0_84])]) ).
cnf(c_0_166,plain,
segmentP(nil,nil),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_163]),c_0_61])]) ).
cnf(c_0_167,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_164,c_0_165]),c_0_166])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SWC285-1 : TPTP v9.2.1. Released v2.4.0.
% 0.00/0.11 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.14/0.32 % Computer : n003.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Tue May 5 04:41:41 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.33 % start to proof: theBenchmark
% 4.00/3.22 % Version : CSE_E---1.7
% 4.00/3.22 % Problem : theBenchmark.p
% 4.00/3.22 % SZS status Unsatisfiable for theBenchmark.p
% 4.00/3.22 % SZS output start CNFRefutation
% See solution above
% 4.00/3.23 % Total time : 2.372s
%------------------------------------------------------------------------------