%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWC412-1 : 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 : n029.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 05:19:34 PM UTC 2026
% Result : Unsatisfiable 1.63s 1.81s
% Output : CNFRefutation 1.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 38
% Syntax : Number of clauses : 111 ( 20 unt; 44 nHn; 111 RR)
% Number of literals : 338 ( 111 equ; 189 neg)
% Maximal clause size : 9 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 11 con; 0-2 aty)
% Number of variables : 124 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(co1_13,negated_conjecture,
( ssItem(sk12)
| ~ ssItem(X1)
| ~ ssItem(X2)
| ~ ssList(X3)
| app(app(cons(X1,nil),cons(X2,nil)),X3) != sk4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_13) ).
cnf(co1_5,negated_conjecture,
sk2 = sk4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_5) ).
cnf(co1_12,negated_conjecture,
( ssItem(sk11)
| ~ ssItem(X1)
| ~ ssItem(X2)
| ~ ssList(X3)
| app(app(cons(X1,nil),cons(X2,nil)),X3) != sk4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_12) ).
cnf(co1_14,negated_conjecture,
( ssList(sk13)
| ~ ssItem(X1)
| ~ ssItem(X2)
| ~ ssList(X3)
| app(app(cons(X1,nil),cons(X2,nil)),X3) != sk4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_14) ).
cnf(co1_16,negated_conjecture,
( ~ ssItem(X1)
| ~ ssItem(X2)
| ~ ssList(X3)
| app(app(cons(X1,nil),cons(X2,nil)),X3) != sk4
| app(app(cons(sk12,nil),sk13),cons(sk11,nil)) != sk1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_16) ).
cnf(co1_18,negated_conjecture,
( ssItem(sk6)
| app(app(cons(X2,nil),X3),cons(X1,nil)) = sk3
| ~ ssItem(X1)
| ~ ssItem(X2)
| ~ ssList(X3)
| app(app(cons(X1,nil),X3),cons(X2,nil)) != sk4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_18) ).
cnf(co1_6,negated_conjecture,
sk1 = sk3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_6) ).
cnf(co1_53,negated_conjecture,
( app(app(cons(sk5,nil),cons(sk6,nil)),sk7) = sk2
| ssItem(sk12) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_53) ).
cnf(co1_49,negated_conjecture,
( ssList(sk7)
| ssItem(sk12) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_49) ).
cnf(co1_26,negated_conjecture,
( ssItem(sk5)
| ssItem(sk12) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_26) ).
cnf(co1_43,negated_conjecture,
( ssItem(sk6)
| ssItem(sk12) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_43) ).
cnf(co1_48,negated_conjecture,
( app(app(cons(sk5,nil),cons(sk6,nil)),sk7) = sk2
| ssItem(sk11) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_48) ).
cnf(co1_47,negated_conjecture,
( ssList(sk7)
| ssItem(sk11) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_47) ).
cnf(co1_25,negated_conjecture,
( ssItem(sk5)
| ssItem(sk11) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_25) ).
cnf(co1_42,negated_conjecture,
( ssItem(sk6)
| ssItem(sk11) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_42) ).
cnf(co1_54,negated_conjecture,
( app(app(cons(sk5,nil),cons(sk6,nil)),sk7) = sk2
| ssList(sk13) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_54) ).
cnf(co1_50,negated_conjecture,
( ssList(sk7)
| ssList(sk13) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_50) ).
cnf(co1_27,negated_conjecture,
( ssItem(sk5)
| ssList(sk13) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_27) ).
cnf(co1_44,negated_conjecture,
( ssItem(sk6)
| ssList(sk13) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_44) ).
cnf(co1_56,negated_conjecture,
( app(app(cons(sk5,nil),cons(sk6,nil)),sk7) = sk2
| app(app(cons(sk12,nil),sk13),cons(sk11,nil)) != sk1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_56) ).
cnf(co1_52,negated_conjecture,
( ssList(sk7)
| app(app(cons(sk12,nil),sk13),cons(sk11,nil)) != sk1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_52) ).
cnf(co1_29,negated_conjecture,
( ssItem(sk5)
| app(app(cons(sk12,nil),sk13),cons(sk11,nil)) != sk1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_29) ).
cnf(co1_46,negated_conjecture,
( ssItem(sk6)
| app(app(cons(sk12,nil),sk13),cons(sk11,nil)) != sk1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_46) ).
cnf(co1_17,negated_conjecture,
( ssItem(sk5)
| app(app(cons(X2,nil),X3),cons(X1,nil)) = sk3
| ~ ssItem(X1)
| ~ ssItem(X2)
| ~ ssList(X3)
| app(app(cons(X1,nil),X3),cons(X2,nil)) != sk4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_17) ).
cnf(co1_19,negated_conjecture,
( ssList(sk7)
| app(app(cons(X2,nil),X3),cons(X1,nil)) = sk3
| ~ ssItem(X1)
| ~ ssItem(X2)
| ~ ssList(X3)
| app(app(cons(X1,nil),X3),cons(X2,nil)) != sk4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_19) ).
cnf(co1_15,negated_conjecture,
( app(app(cons(sk11,nil),sk13),cons(sk12,nil)) = sk2
| ~ ssItem(X1)
| ~ ssItem(X2)
| ~ ssList(X3)
| app(app(cons(X1,nil),cons(X2,nil)),X3) != sk4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_15) ).
cnf(co1_45,negated_conjecture,
( ssItem(sk6)
| app(app(cons(sk11,nil),sk13),cons(sk12,nil)) = sk2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_45) ).
cnf(co1_28,negated_conjecture,
( ssItem(sk5)
| app(app(cons(sk11,nil),sk13),cons(sk12,nil)) = sk2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_28) ).
cnf(co1_51,negated_conjecture,
( ssList(sk7)
| app(app(cons(sk11,nil),sk13),cons(sk12,nil)) = sk2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_51) ).
cnf(co1_20,negated_conjecture,
( app(app(cons(sk5,nil),cons(sk6,nil)),sk7) = sk2
| app(app(cons(X2,nil),X3),cons(X1,nil)) = sk3
| ~ ssItem(X1)
| ~ ssItem(X2)
| ~ ssList(X3)
| app(app(cons(X1,nil),X3),cons(X2,nil)) != sk4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_20) ).
cnf(co1_55,negated_conjecture,
( app(app(cons(sk5,nil),cons(sk6,nil)),sk7) = sk2
| app(app(cons(sk11,nil),sk13),cons(sk12,nil)) = sk2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_55) ).
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(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(clause97,axiom,
( hd(cons(X1,X2)) = X1
| ~ ssItem(X1)
| ~ ssList(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause97) ).
cnf(clause85,axiom,
( ssList(app(X2,X1))
| ~ ssList(X1)
| ~ ssList(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause85) ).
cnf(clause86,axiom,
( ssList(cons(X1,X2))
| ~ ssItem(X1)
| ~ ssList(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause86) ).
cnf(clause8,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause8) ).
cnf(co1_7,negated_conjecture,
( app(app(cons(X5,nil),X6),cons(X4,nil)) = sk3
| ~ ssItem(X1)
| ~ ssItem(X2)
| ~ ssList(X3)
| app(app(cons(X1,nil),cons(X2,nil)),X3) != sk4
| ~ ssItem(X4)
| ~ ssItem(X5)
| ~ ssList(X6)
| app(app(cons(X4,nil),X6),cons(X5,nil)) != sk4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_7) ).
cnf(c_0_38,negated_conjecture,
( ssItem(sk12)
| ~ ssItem(X1)
| ~ ssItem(X2)
| ~ ssList(X3)
| app(app(cons(X1,nil),cons(X2,nil)),X3) != sk4 ),
co1_13 ).
cnf(c_0_39,negated_conjecture,
sk2 = sk4,
co1_5 ).
cnf(c_0_40,negated_conjecture,
( ssItem(sk11)
| ~ ssItem(X1)
| ~ ssItem(X2)
| ~ ssList(X3)
| app(app(cons(X1,nil),cons(X2,nil)),X3) != sk4 ),
co1_12 ).
cnf(c_0_41,negated_conjecture,
( ssList(sk13)
| ~ ssItem(X1)
| ~ ssItem(X2)
| ~ ssList(X3)
| app(app(cons(X1,nil),cons(X2,nil)),X3) != sk4 ),
co1_14 ).
cnf(c_0_42,negated_conjecture,
( ~ ssItem(X1)
| ~ ssItem(X2)
| ~ ssList(X3)
| app(app(cons(X1,nil),cons(X2,nil)),X3) != sk4
| app(app(cons(sk12,nil),sk13),cons(sk11,nil)) != sk1 ),
co1_16 ).
cnf(c_0_43,negated_conjecture,
( ssItem(sk6)
| app(app(cons(X2,nil),X3),cons(X1,nil)) = sk3
| ~ ssItem(X1)
| ~ ssItem(X2)
| ~ ssList(X3)
| app(app(cons(X1,nil),X3),cons(X2,nil)) != sk4 ),
co1_18 ).
cnf(c_0_44,negated_conjecture,
sk1 = sk3,
co1_6 ).
cnf(c_0_45,negated_conjecture,
( ssItem(sk12)
| app(app(cons(X1,nil),cons(X2,nil)),X3) != sk2
| ~ ssItem(X2)
| ~ ssItem(X1)
| ~ ssList(X3) ),
inference(rw,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_46,negated_conjecture,
( app(app(cons(sk5,nil),cons(sk6,nil)),sk7) = sk2
| ssItem(sk12) ),
co1_53 ).
cnf(c_0_47,negated_conjecture,
( ssList(sk7)
| ssItem(sk12) ),
co1_49 ).
cnf(c_0_48,negated_conjecture,
( ssItem(sk5)
| ssItem(sk12) ),
co1_26 ).
cnf(c_0_49,negated_conjecture,
( ssItem(sk6)
| ssItem(sk12) ),
co1_43 ).
cnf(c_0_50,negated_conjecture,
( ssItem(sk11)
| app(app(cons(X1,nil),cons(X2,nil)),X3) != sk2
| ~ ssItem(X2)
| ~ ssItem(X1)
| ~ ssList(X3) ),
inference(rw,[status(thm)],[c_0_40,c_0_39]) ).
cnf(c_0_51,negated_conjecture,
( app(app(cons(sk5,nil),cons(sk6,nil)),sk7) = sk2
| ssItem(sk11) ),
co1_48 ).
cnf(c_0_52,negated_conjecture,
( ssList(sk7)
| ssItem(sk11) ),
co1_47 ).
cnf(c_0_53,negated_conjecture,
( ssItem(sk5)
| ssItem(sk11) ),
co1_25 ).
cnf(c_0_54,negated_conjecture,
( ssItem(sk6)
| ssItem(sk11) ),
co1_42 ).
cnf(c_0_55,negated_conjecture,
( ssList(sk13)
| app(app(cons(X1,nil),cons(X2,nil)),X3) != sk2
| ~ ssItem(X2)
| ~ ssItem(X1)
| ~ ssList(X3) ),
inference(rw,[status(thm)],[c_0_41,c_0_39]) ).
cnf(c_0_56,negated_conjecture,
( app(app(cons(sk5,nil),cons(sk6,nil)),sk7) = sk2
| ssList(sk13) ),
co1_54 ).
cnf(c_0_57,negated_conjecture,
( ssList(sk7)
| ssList(sk13) ),
co1_50 ).
cnf(c_0_58,negated_conjecture,
( ssItem(sk5)
| ssList(sk13) ),
co1_27 ).
cnf(c_0_59,negated_conjecture,
( ssItem(sk6)
| ssList(sk13) ),
co1_44 ).
cnf(c_0_60,negated_conjecture,
( app(app(cons(sk12,nil),sk13),cons(sk11,nil)) != sk1
| app(app(cons(X1,nil),cons(X2,nil)),X3) != sk2
| ~ ssItem(X2)
| ~ ssItem(X1)
| ~ ssList(X3) ),
inference(rw,[status(thm)],[c_0_42,c_0_39]) ).
cnf(c_0_61,negated_conjecture,
( app(app(cons(sk5,nil),cons(sk6,nil)),sk7) = sk2
| app(app(cons(sk12,nil),sk13),cons(sk11,nil)) != sk1 ),
co1_56 ).
cnf(c_0_62,negated_conjecture,
( ssList(sk7)
| app(app(cons(sk12,nil),sk13),cons(sk11,nil)) != sk1 ),
co1_52 ).
cnf(c_0_63,negated_conjecture,
( ssItem(sk5)
| app(app(cons(sk12,nil),sk13),cons(sk11,nil)) != sk1 ),
co1_29 ).
cnf(c_0_64,negated_conjecture,
( ssItem(sk6)
| app(app(cons(sk12,nil),sk13),cons(sk11,nil)) != sk1 ),
co1_46 ).
cnf(c_0_65,negated_conjecture,
( ssItem(sk5)
| app(app(cons(X2,nil),X3),cons(X1,nil)) = sk3
| ~ ssItem(X1)
| ~ ssItem(X2)
| ~ ssList(X3)
| app(app(cons(X1,nil),X3),cons(X2,nil)) != sk4 ),
co1_17 ).
cnf(c_0_66,negated_conjecture,
( ssList(sk7)
| app(app(cons(X2,nil),X3),cons(X1,nil)) = sk3
| ~ ssItem(X1)
| ~ ssItem(X2)
| ~ ssList(X3)
| app(app(cons(X1,nil),X3),cons(X2,nil)) != sk4 ),
co1_19 ).
cnf(c_0_67,negated_conjecture,
( app(app(cons(sk11,nil),sk13),cons(sk12,nil)) = sk2
| ~ ssItem(X1)
| ~ ssItem(X2)
| ~ ssList(X3)
| app(app(cons(X1,nil),cons(X2,nil)),X3) != sk4 ),
co1_15 ).
cnf(c_0_68,negated_conjecture,
( app(app(cons(X1,nil),X2),cons(X3,nil)) = sk1
| ssItem(sk6)
| app(app(cons(X3,nil),X2),cons(X1,nil)) != sk2
| ~ ssItem(X1)
| ~ ssItem(X3)
| ~ ssList(X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_43,c_0_44]),c_0_39]) ).
cnf(c_0_69,negated_conjecture,
( ssItem(sk6)
| app(app(cons(sk11,nil),sk13),cons(sk12,nil)) = sk2 ),
co1_45 ).
cnf(c_0_70,negated_conjecture,
ssItem(sk12),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_47]),c_0_48]),c_0_49]) ).
cnf(c_0_71,negated_conjecture,
ssItem(sk11),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_52]),c_0_53]),c_0_54]) ).
cnf(c_0_72,negated_conjecture,
ssList(sk13),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_57]),c_0_58]),c_0_59]) ).
cnf(c_0_73,negated_conjecture,
app(app(cons(sk12,nil),sk13),cons(sk11,nil)) != sk1,
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_62]),c_0_63]),c_0_64]) ).
cnf(c_0_74,negated_conjecture,
( app(app(cons(X1,nil),X2),cons(X3,nil)) = sk1
| ssItem(sk5)
| app(app(cons(X3,nil),X2),cons(X1,nil)) != sk2
| ~ ssItem(X1)
| ~ ssItem(X3)
| ~ ssList(X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_65,c_0_44]),c_0_39]) ).
cnf(c_0_75,negated_conjecture,
( ssItem(sk5)
| app(app(cons(sk11,nil),sk13),cons(sk12,nil)) = sk2 ),
co1_28 ).
cnf(c_0_76,negated_conjecture,
( app(app(cons(X1,nil),X2),cons(X3,nil)) = sk1
| ssList(sk7)
| app(app(cons(X3,nil),X2),cons(X1,nil)) != sk2
| ~ ssItem(X1)
| ~ ssItem(X3)
| ~ ssList(X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_66,c_0_44]),c_0_39]) ).
cnf(c_0_77,negated_conjecture,
( ssList(sk7)
| app(app(cons(sk11,nil),sk13),cons(sk12,nil)) = sk2 ),
co1_51 ).
cnf(c_0_78,negated_conjecture,
( app(app(cons(sk5,nil),cons(sk6,nil)),sk7) = sk2
| app(app(cons(X2,nil),X3),cons(X1,nil)) = sk3
| ~ ssItem(X1)
| ~ ssItem(X2)
| ~ ssList(X3)
| app(app(cons(X1,nil),X3),cons(X2,nil)) != sk4 ),
co1_20 ).
cnf(c_0_79,negated_conjecture,
( app(app(cons(sk11,nil),sk13),cons(sk12,nil)) = sk2
| app(app(cons(X1,nil),cons(X2,nil)),X3) != sk2
| ~ ssItem(X2)
| ~ ssItem(X1)
| ~ ssList(X3) ),
inference(rw,[status(thm)],[c_0_67,c_0_39]) ).
cnf(c_0_80,negated_conjecture,
( app(app(cons(sk5,nil),cons(sk6,nil)),sk7) = sk2
| app(app(cons(sk11,nil),sk13),cons(sk12,nil)) = sk2 ),
co1_55 ).
cnf(c_0_81,negated_conjecture,
ssItem(sk6),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_70]),c_0_71]),c_0_72])]),c_0_73]) ).
cnf(c_0_82,negated_conjecture,
ssItem(sk5),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_70]),c_0_71]),c_0_72])]),c_0_73]) ).
cnf(c_0_83,negated_conjecture,
ssList(sk7),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_77]),c_0_70]),c_0_71]),c_0_72])]),c_0_73]) ).
cnf(c_0_84,negated_conjecture,
( app(app(cons(sk5,nil),cons(sk6,nil)),sk7) = sk2
| app(app(cons(X1,nil),X2),cons(X3,nil)) = sk1
| app(app(cons(X3,nil),X2),cons(X1,nil)) != sk2
| ~ ssItem(X1)
| ~ ssItem(X3)
| ~ ssList(X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_78,c_0_44]),c_0_39]) ).
cnf(c_0_85,negated_conjecture,
app(app(cons(sk11,nil),sk13),cons(sk12,nil)) = sk2,
inference(cn,[status(thm)],[inference(rw,[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_82]),c_0_83])]) ).
cnf(c_0_86,negated_conjecture,
app(app(cons(sk5,nil),cons(sk6,nil)),sk7) = sk2,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_85]),c_0_70]),c_0_71]),c_0_72])]),c_0_73]) ).
cnf(c_0_87,axiom,
( app(cons(X1,nil),X2) = cons(X1,X2)
| ~ ssItem(X1)
| ~ ssList(X2) ),
clause120 ).
cnf(c_0_88,axiom,
( cons(X1,app(X2,X3)) = app(cons(X1,X2),X3)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
clause157 ).
cnf(c_0_89,negated_conjecture,
( app(cons(sk5,cons(sk6,nil)),sk7) = sk2
| ~ ssList(cons(sk6,nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_87]),c_0_82])]) ).
cnf(c_0_90,negated_conjecture,
( cons(sk5,app(cons(sk6,nil),sk7)) = sk2
| ~ ssList(cons(sk6,nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_89]),c_0_82]),c_0_83])]) ).
cnf(c_0_91,negated_conjecture,
app(cons(sk11,sk13),cons(sk12,nil)) = sk2,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_87]),c_0_71]),c_0_72])]) ).
cnf(c_0_92,axiom,
( hd(cons(X1,X2)) = X1
| ~ ssItem(X1)
| ~ ssList(X2) ),
clause97 ).
cnf(c_0_93,negated_conjecture,
( cons(sk5,cons(sk6,sk7)) = sk2
| ~ ssList(cons(sk6,nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_87]),c_0_81]),c_0_83])]) ).
cnf(c_0_94,negated_conjecture,
( cons(sk11,app(sk13,cons(sk12,nil))) = sk2
| ~ ssList(cons(sk12,nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_91]),c_0_71]),c_0_72])]) ).
cnf(c_0_95,negated_conjecture,
( hd(sk2) = sk5
| ~ ssList(cons(sk6,sk7))
| ~ ssList(cons(sk6,nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_93]),c_0_82])]) ).
cnf(c_0_96,negated_conjecture,
( hd(sk2) = sk11
| ~ ssList(app(sk13,cons(sk12,nil)))
| ~ ssList(cons(sk12,nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_94]),c_0_71])]) ).
cnf(c_0_97,negated_conjecture,
( sk11 = sk5
| ~ ssList(app(sk13,cons(sk12,nil)))
| ~ ssList(cons(sk6,sk7))
| ~ ssList(cons(sk6,nil))
| ~ ssList(cons(sk12,nil)) ),
inference(spm,[status(thm)],[c_0_95,c_0_96]) ).
cnf(c_0_98,axiom,
( ssList(app(X2,X1))
| ~ ssList(X1)
| ~ ssList(X2) ),
clause85 ).
cnf(c_0_99,negated_conjecture,
( sk11 = sk5
| ~ ssList(cons(sk6,sk7))
| ~ ssList(cons(sk6,nil))
| ~ ssList(cons(sk12,nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_98]),c_0_72])]) ).
cnf(c_0_100,axiom,
( ssList(cons(X1,X2))
| ~ ssItem(X1)
| ~ ssList(X2) ),
clause86 ).
cnf(c_0_101,axiom,
ssList(nil),
clause8 ).
cnf(c_0_102,negated_conjecture,
( sk11 = sk5
| ~ ssList(cons(sk6,sk7))
| ~ ssList(cons(sk6,nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_100]),c_0_70]),c_0_101])]) ).
cnf(c_0_103,negated_conjecture,
( sk11 = sk5
| ~ ssList(cons(sk6,nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_100]),c_0_81]),c_0_83])]) ).
cnf(c_0_104,negated_conjecture,
( app(app(cons(X5,nil),X6),cons(X4,nil)) = sk3
| ~ ssItem(X1)
| ~ ssItem(X2)
| ~ ssList(X3)
| app(app(cons(X1,nil),cons(X2,nil)),X3) != sk4
| ~ ssItem(X4)
| ~ ssItem(X5)
| ~ ssList(X6)
| app(app(cons(X4,nil),X6),cons(X5,nil)) != sk4 ),
co1_7 ).
cnf(c_0_105,negated_conjecture,
sk11 = sk5,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_100]),c_0_81]),c_0_101])]) ).
cnf(c_0_106,negated_conjecture,
( app(app(cons(X1,nil),X2),cons(X3,nil)) = sk1
| app(app(cons(X3,nil),X2),cons(X1,nil)) != sk2
| app(app(cons(X4,nil),cons(X5,nil)),X6) != sk2
| ~ ssItem(X1)
| ~ ssItem(X3)
| ~ ssItem(X5)
| ~ ssItem(X4)
| ~ ssList(X2)
| ~ ssList(X6) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_104,c_0_44]),c_0_39]),c_0_39]) ).
cnf(c_0_107,negated_conjecture,
app(app(cons(sk5,nil),sk13),cons(sk12,nil)) = sk2,
inference(rw,[status(thm)],[c_0_85,c_0_105]) ).
cnf(c_0_108,negated_conjecture,
app(app(cons(sk12,nil),sk13),cons(sk5,nil)) != sk1,
inference(rw,[status(thm)],[c_0_73,c_0_105]) ).
cnf(c_0_109,negated_conjecture,
( app(app(cons(X1,nil),cons(X2,nil)),X3) != sk2
| ~ ssItem(X2)
| ~ ssItem(X1)
| ~ ssList(X3) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_107]),c_0_70]),c_0_82]),c_0_72])]),c_0_108]) ).
cnf(c_0_110,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_86]),c_0_81]),c_0_82]),c_0_83])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWC412-1 : 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 : n029.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 04:49:14 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.63/1.81 % Version : CSE_E---1.7
% 1.63/1.81 % Problem : theBenchmark.p
% 1.63/1.81 % SZS status Unsatisfiable for theBenchmark.p
% 1.63/1.81 % SZS output start CNFRefutation
% See solution above
% 1.63/1.81 % Total time : 1.374s
%------------------------------------------------------------------------------