%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWC164-1 : 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 : n015.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 05:18:33 PM UTC 2026
% Result : Unsatisfiable 2.01s 1.90s
% Output : CNFRefutation 2.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 34
% Syntax : Number of clauses : 125 ( 36 unt; 18 nHn; 123 RR)
% Number of literals : 322 ( 120 equ; 190 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 8 con; 0-2 aty)
% Number of variables : 112 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(co1_11,negated_conjecture,
app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) = 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(clause118,axiom,
( nil = X1
| app(X1,X2) != nil
| ~ ssList(X2)
| ~ ssList(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause118) ).
cnf(co1_10,negated_conjecture,
ssList(sk8),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_10) ).
cnf(co1_12,negated_conjecture,
~ neq(sk5,sk6),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_12) ).
cnf(clause102,axiom,
( neq(X2,X1)
| X2 = X1
| ~ ssItem(X1)
| ~ ssItem(X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause102) ).
cnf(co1_7,negated_conjecture,
ssItem(sk5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_7) ).
cnf(co1_8,negated_conjecture,
ssItem(sk6),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_8) ).
cnf(clause85,axiom,
( ssList(app(X2,X1))
| ~ ssList(X1)
| ~ ssList(X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause85) ).
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(co1_9,negated_conjecture,
ssList(sk7),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_9) ).
cnf(clause119,axiom,
( nil = X2
| app(X1,X2) != nil
| ~ ssList(X2)
| ~ ssList(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause119) ).
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(clause86,axiom,
( ssList(cons(X1,X2))
| ~ ssItem(X1)
| ~ ssList(X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause86) ).
cnf(clause8,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause8) ).
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(clause157,axiom,
( cons(X1,app(X2,X3)) = app(cons(X1,X2),X3)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause157) ).
cnf(co1_1,negated_conjecture,
ssList(sk1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_1) ).
cnf(clause98,axiom,
( cons(X1,X2) != nil
| ~ ssItem(X1)
| ~ ssList(X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause98) ).
cnf(co1_18,negated_conjecture,
( cons(sk9,nil) = sk3
| nil = sk3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_18) ).
cnf(co1_14,negated_conjecture,
( ssItem(sk9)
| nil = sk3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_14) ).
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(clause71,axiom,
( ~ memberP(nil,X1)
| ~ ssItem(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause71) ).
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(clause74,axiom,
( app(nil,X1) = X1
| ~ ssList(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause74) ).
cnf(clause97,axiom,
( hd(cons(X1,X2)) = X1
| ~ ssItem(X1)
| ~ ssList(X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause97) ).
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(clause73,axiom,
( app(X1,nil) = X1
| ~ ssList(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause73) ).
cnf(clause123,axiom,
( nil = X2
| hd(app(X2,X1)) = hd(X2)
| ~ ssList(X1)
| ~ ssList(X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause123) ).
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(clause129,axiom,
( X2 = X1
| ~ frontsegP(X1,X2)
| ~ frontsegP(X2,X1)
| ~ ssList(X1)
| ~ ssList(X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause129) ).
cnf(clause104,axiom,
( cons(hd(X1),tl(X1)) = X1
| nil = X1
| ~ ssList(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause104) ).
cnf(clause75,axiom,
( ssList(tl(X1))
| nil = X1
| ~ ssList(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause75) ).
cnf(c_0_34,negated_conjecture,
app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) = sk1,
co1_11 ).
cnf(c_0_35,negated_conjecture,
sk1 = sk3,
co1_6 ).
cnf(c_0_36,axiom,
( nil = X1
| app(X1,X2) != nil
| ~ ssList(X2)
| ~ ssList(X1) ),
clause118 ).
cnf(c_0_37,negated_conjecture,
app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) = sk3,
inference(rw,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_38,negated_conjecture,
ssList(sk8),
co1_10 ).
cnf(c_0_39,negated_conjecture,
~ neq(sk5,sk6),
co1_12 ).
cnf(c_0_40,axiom,
( neq(X2,X1)
| X2 = X1
| ~ ssItem(X1)
| ~ ssItem(X2) ),
clause102 ).
cnf(c_0_41,negated_conjecture,
ssItem(sk5),
co1_7 ).
cnf(c_0_42,negated_conjecture,
ssItem(sk6),
co1_8 ).
cnf(c_0_43,negated_conjecture,
( app(app(sk7,cons(sk5,nil)),cons(sk6,nil)) = nil
| sk3 != nil
| ~ ssList(app(app(sk7,cons(sk5,nil)),cons(sk6,nil))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_38])]) ).
cnf(c_0_44,negated_conjecture,
sk6 = sk5,
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,negated_conjecture,
( app(app(sk7,cons(sk5,nil)),cons(sk5,nil)) = nil
| sk3 != nil
| ~ ssList(app(app(sk7,cons(sk5,nil)),cons(sk5,nil))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_43,c_0_44]),c_0_44]) ).
cnf(c_0_46,axiom,
( ssList(app(X2,X1))
| ~ ssList(X1)
| ~ ssList(X2) ),
clause85 ).
cnf(c_0_47,negated_conjecture,
app(app(app(sk7,cons(sk5,nil)),cons(sk5,nil)),sk8) = sk3,
inference(rw,[status(thm)],[c_0_37,c_0_44]) ).
cnf(c_0_48,axiom,
( app(app(X3,X2),X1) = app(X3,app(X2,X1))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
clause149 ).
cnf(c_0_49,negated_conjecture,
ssList(sk7),
co1_9 ).
cnf(c_0_50,axiom,
( nil = X2
| app(X1,X2) != nil
| ~ ssList(X2)
| ~ ssList(X1) ),
clause119 ).
cnf(c_0_51,negated_conjecture,
( app(app(sk7,cons(sk5,nil)),cons(sk5,nil)) = nil
| sk3 != nil
| ~ ssList(app(sk7,cons(sk5,nil)))
| ~ ssList(cons(sk5,nil)) ),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_52,negated_conjecture,
( app(app(sk7,app(cons(sk5,nil),cons(sk5,nil))),sk8) = sk3
| ~ ssList(cons(sk5,nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_49])]) ).
cnf(c_0_53,axiom,
( app(cons(X1,nil),X2) = cons(X1,X2)
| ~ ssItem(X1)
| ~ ssList(X2) ),
clause120 ).
cnf(c_0_54,negated_conjecture,
( cons(sk5,nil) = nil
| sk3 != nil
| ~ ssList(app(sk7,cons(sk5,nil)))
| ~ ssList(cons(sk5,nil)) ),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_55,negated_conjecture,
( app(app(sk7,cons(sk5,cons(sk5,nil))),sk8) = sk3
| ~ ssList(cons(sk5,nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_41])]) ).
cnf(c_0_56,negated_conjecture,
( cons(sk5,nil) = nil
| sk3 != nil
| ~ ssList(cons(sk5,nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_46]),c_0_49])]) ).
cnf(c_0_57,axiom,
( ssList(cons(X1,X2))
| ~ ssItem(X1)
| ~ ssList(X2) ),
clause86 ).
cnf(c_0_58,axiom,
ssList(nil),
clause8 ).
cnf(c_0_59,axiom,
( memberP(X4,X2)
| app(X1,cons(X2,X3)) != X4
| ~ ssList(X3)
| ~ ssList(X1)
| ~ ssItem(X2)
| ~ ssList(X4) ),
clause175 ).
cnf(c_0_60,negated_conjecture,
( app(sk7,app(cons(sk5,cons(sk5,nil)),sk8)) = sk3
| ~ ssList(cons(sk5,cons(sk5,nil)))
| ~ ssList(cons(sk5,nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_55]),c_0_49]),c_0_38])]) ).
cnf(c_0_61,axiom,
( cons(X1,app(X2,X3)) = app(cons(X1,X2),X3)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
clause157 ).
cnf(c_0_62,negated_conjecture,
ssList(sk1),
co1_1 ).
cnf(c_0_63,axiom,
( cons(X1,X2) != nil
| ~ ssItem(X1)
| ~ ssList(X2) ),
clause98 ).
cnf(c_0_64,negated_conjecture,
( cons(sk5,nil) = nil
| sk3 != nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_41]),c_0_58])]) ).
cnf(c_0_65,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_59]) ).
cnf(c_0_66,negated_conjecture,
( app(sk7,cons(sk5,app(cons(sk5,nil),sk8))) = sk3
| ~ ssList(cons(sk5,cons(sk5,nil)))
| ~ ssList(cons(sk5,nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_41]),c_0_38])]) ).
cnf(c_0_67,negated_conjecture,
ssList(sk3),
inference(rw,[status(thm)],[c_0_62,c_0_35]) ).
cnf(c_0_68,negated_conjecture,
( cons(sk9,nil) = sk3
| nil = sk3 ),
co1_18 ).
cnf(c_0_69,negated_conjecture,
sk3 != nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_41]),c_0_58])]) ).
cnf(c_0_70,negated_conjecture,
( ssItem(sk9)
| nil = sk3 ),
co1_14 ).
cnf(c_0_71,negated_conjecture,
( memberP(sk3,sk5)
| ~ ssList(app(cons(sk5,nil),sk8))
| ~ ssList(cons(sk5,cons(sk5,nil)))
| ~ ssList(cons(sk5,nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_41]),c_0_67]),c_0_49])]) ).
cnf(c_0_72,axiom,
( memberP(X2,X3)
| X3 = X1
| ~ memberP(cons(X1,X2),X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X3) ),
clause161 ).
cnf(c_0_73,negated_conjecture,
cons(sk9,nil) = sk3,
inference(sr,[status(thm)],[c_0_68,c_0_69]) ).
cnf(c_0_74,negated_conjecture,
ssItem(sk9),
inference(sr,[status(thm)],[c_0_70,c_0_69]) ).
cnf(c_0_75,axiom,
( ~ memberP(nil,X1)
| ~ ssItem(X1) ),
clause71 ).
cnf(c_0_76,negated_conjecture,
( memberP(sk3,sk5)
| ~ ssList(cons(sk5,cons(sk5,nil)))
| ~ ssList(cons(sk5,nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_46]),c_0_38])]) ).
cnf(c_0_77,negated_conjecture,
( sk9 = X1
| ~ memberP(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_72,c_0_73]),c_0_74]),c_0_58])]),c_0_75]) ).
cnf(c_0_78,negated_conjecture,
( memberP(sk3,sk5)
| ~ ssList(cons(sk5,nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_57]),c_0_41])]) ).
cnf(c_0_79,negated_conjecture,
( sk5 = sk9
| ~ ssList(cons(sk5,nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78]),c_0_41])]) ).
cnf(c_0_80,negated_conjecture,
( app(app(sk7,cons(sk5,app(nil,cons(sk5,nil)))),sk8) = sk3
| ~ ssList(cons(sk5,nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_61]),c_0_41]),c_0_58])]) ).
cnf(c_0_81,negated_conjecture,
sk5 = sk9,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_57]),c_0_41]),c_0_58])]) ).
cnf(c_0_82,negated_conjecture,
app(app(sk7,cons(sk9,app(nil,sk3))),sk8) = sk3,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_80,c_0_81]),c_0_81]),c_0_73]),c_0_81]),c_0_73]),c_0_67])]) ).
cnf(c_0_83,negated_conjecture,
( app(sk3,X1) = cons(sk9,X1)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_73]),c_0_74])]) ).
cnf(c_0_84,negated_conjecture,
( app(sk7,app(cons(sk9,app(nil,sk3)),sk8)) = sk3
| ~ ssList(cons(sk9,app(nil,sk3))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_82]),c_0_49]),c_0_38])]) ).
cnf(c_0_85,negated_conjecture,
( ssList(cons(sk9,X1))
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_83]),c_0_67])]) ).
cnf(c_0_86,axiom,
( frontsegP(X3,X1)
| app(X1,X2) != X3
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X3) ),
clause144 ).
cnf(c_0_87,negated_conjecture,
( app(sk7,cons(sk9,app(app(nil,sk3),sk8))) = sk3
| ~ ssList(app(nil,sk3)) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_61]),c_0_74]),c_0_38])]),c_0_85]) ).
cnf(c_0_88,axiom,
( app(nil,X1) = X1
| ~ ssList(X1) ),
clause74 ).
cnf(c_0_89,plain,
( frontsegP(app(X1,X2),X1)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_86]),c_0_46]) ).
cnf(c_0_90,negated_conjecture,
app(sk7,cons(sk9,app(sk3,sk8))) = sk3,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_88]),c_0_67])]) ).
cnf(c_0_91,axiom,
( hd(cons(X1,X2)) = X1
| ~ ssItem(X1)
| ~ ssList(X2) ),
clause97 ).
cnf(c_0_92,axiom,
( X2 = X3
| app(X1,X2) != app(X1,X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X3) ),
clause150 ).
cnf(c_0_93,axiom,
( app(X1,nil) = X1
| ~ ssList(X1) ),
clause73 ).
cnf(c_0_94,axiom,
( nil = X2
| hd(app(X2,X1)) = hd(X2)
| ~ ssList(X1)
| ~ ssList(X2) ),
clause123 ).
cnf(c_0_95,axiom,
( app(X2,skaf45(X1,X2)) = X1
| ~ frontsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
clause132 ).
cnf(c_0_96,axiom,
ssList(skaf45(X1,X2)),
clause51 ).
cnf(c_0_97,negated_conjecture,
( frontsegP(sk3,sk7)
| ~ ssList(cons(sk9,app(sk3,sk8))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_90]),c_0_49])]) ).
cnf(c_0_98,negated_conjecture,
( hd(sk3) = sk9
| sk3 = nil ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_68]),c_0_58])]),c_0_70]) ).
cnf(c_0_99,plain,
( X1 = nil
| app(X2,X1) != X2
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_93]),c_0_58])]) ).
cnf(c_0_100,axiom,
( X2 = X1
| ~ frontsegP(X1,X2)
| ~ frontsegP(X2,X1)
| ~ ssList(X1)
| ~ ssList(X2) ),
clause129 ).
cnf(c_0_101,plain,
( hd(X1) = hd(X2)
| nil = X2
| ~ frontsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_95]),c_0_96])]) ).
cnf(c_0_102,negated_conjecture,
( frontsegP(sk3,sk7)
| ~ ssList(app(sk3,sk8)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_57]),c_0_74])]) ).
cnf(c_0_103,negated_conjecture,
hd(sk3) = sk9,
inference(sr,[status(thm)],[c_0_98,c_0_69]) ).
cnf(c_0_104,negated_conjecture,
( cons(sk9,app(sk3,sk8)) = nil
| sk7 != sk3
| ~ ssList(cons(sk9,app(sk3,sk8))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_90]),c_0_49])]) ).
cnf(c_0_105,negated_conjecture,
( cons(sk9,X1) != nil
| ~ ssList(X1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_83]),c_0_67])]),c_0_69]) ).
cnf(c_0_106,negated_conjecture,
app(app(app(sk7,sk3),sk3),sk8) = sk3,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_47,c_0_81]),c_0_73]),c_0_81]),c_0_73]) ).
cnf(c_0_107,plain,
( app(X1,X2) = X1
| ~ frontsegP(X1,app(X1,X2))
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_89]),c_0_46]) ).
cnf(c_0_108,axiom,
( cons(hd(X1),tl(X1)) = X1
| nil = X1
| ~ ssList(X1) ),
clause104 ).
cnf(c_0_109,negated_conjecture,
( hd(sk7) = sk9
| sk7 = nil
| ~ ssList(app(sk3,sk8)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_102]),c_0_103]),c_0_49]),c_0_67])]) ).
cnf(c_0_110,negated_conjecture,
( sk7 != sk3
| ~ ssList(app(sk3,sk8)) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_57]),c_0_74])]),c_0_105]) ).
cnf(c_0_111,negated_conjecture,
( app(app(sk7,sk3),app(sk3,sk8)) = sk3
| ~ ssList(app(sk7,sk3)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_106]),c_0_67]),c_0_38])]) ).
cnf(c_0_112,negated_conjecture,
( cons(sk9,X1) = sk3
| ~ frontsegP(sk3,cons(sk9,X1))
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_83]),c_0_67])]) ).
cnf(c_0_113,negated_conjecture,
( cons(sk9,tl(sk7)) = sk7
| sk7 = nil
| ~ ssList(app(sk3,sk8)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_109]),c_0_49])]) ).
cnf(c_0_114,negated_conjecture,
sk7 != sk3,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_46]),c_0_67]),c_0_38])]) ).
cnf(c_0_115,negated_conjecture,
( app(sk3,sk8) = nil
| app(sk7,sk3) != sk3
| ~ ssList(app(sk3,sk8))
| ~ ssList(app(sk7,sk3)) ),
inference(spm,[status(thm)],[c_0_99,c_0_111]) ).
cnf(c_0_116,negated_conjecture,
( sk7 = nil
| ~ ssList(app(sk3,sk8))
| ~ ssList(tl(sk7)) ),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_113]),c_0_114]),c_0_102]) ).
cnf(c_0_117,axiom,
( ssList(tl(X1))
| nil = X1
| ~ ssList(X1) ),
clause75 ).
cnf(c_0_118,negated_conjecture,
( app(sk3,sk8) = nil
| app(sk7,sk3) != sk3
| ~ ssList(app(sk3,sk8)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_46]),c_0_49]),c_0_67])]) ).
cnf(c_0_119,negated_conjecture,
( sk7 = nil
| ~ ssList(app(sk3,sk8)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_117]),c_0_49])]) ).
cnf(c_0_120,negated_conjecture,
( app(sk3,sk8) = nil
| app(sk7,sk3) != sk3 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_46]),c_0_67]),c_0_38])]) ).
cnf(c_0_121,negated_conjecture,
sk7 = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_119,c_0_46]),c_0_67]),c_0_38])]) ).
cnf(c_0_122,negated_conjecture,
( app(sk3,sk8) = nil
| app(nil,sk3) != sk3 ),
inference(rw,[status(thm)],[c_0_120,c_0_121]) ).
cnf(c_0_123,negated_conjecture,
app(nil,sk3) != sk3,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_122]),c_0_38]),c_0_67])]),c_0_69]) ).
cnf(c_0_124,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_123,c_0_88]),c_0_67])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWC164-1 : TPTP v9.2.1. Released v2.4.0.
% 0.00/0.12 % 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
% 0.15/0.32 % Computer : n015.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 04:30:47 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 2.01/1.90 % Version : CSE_E---1.7
% 2.01/1.90 % Problem : theBenchmark.p
% 2.01/1.90 % SZS status Unsatisfiable for theBenchmark.p
% 2.01/1.90 % SZS output start CNFRefutation
% See solution above
% 2.01/1.91 % Total time : 1.373s
%------------------------------------------------------------------------------