%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWC413-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 02:44:19 PM UTC 2026
% Result : Unsatisfiable 0.14s 5.58s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 30
% Syntax : Number of formulae : 96 ( 16 unt; 0 def)
% Number of atoms : 271 ( 87 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 305 ( 130 ~; 173 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 11 con; 0-2 aty)
% Number of variables : 90 ( 0 sgn 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(co1_16,negated_conjecture,
( app(app(cons(X1,nil),cons(X2,nil)),X3) != sk4
| ~ ssList(X3)
| ~ ssItem(X2)
| ~ ssItem(X1)
| ssItem(sk8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_16) ).
cnf(co1_17,negated_conjecture,
( app(app(cons(X1,nil),cons(X2,nil)),X3) != sk4
| ~ ssList(X3)
| ~ ssItem(X2)
| ~ ssItem(X1)
| ssItem(sk9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_17) ).
cnf(co1_18,negated_conjecture,
( app(app(cons(X1,nil),cons(X2,nil)),X3) != sk4
| ~ ssList(X3)
| ~ ssItem(X2)
| ~ ssItem(X1)
| ssList(sk10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_18) ).
cnf(co1_5,negated_conjecture,
sk2 = sk4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_5) ).
cnf(co1_55,negated_conjecture,
( app(app(cons(sk11,nil),cons(sk12,nil)),sk13) = sk2
| app(app(cons(sk8,nil),cons(sk9,nil)),sk10) = sk4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_55) ).
cnf(co1_44,negated_conjecture,
( app(app(cons(sk11,nil),cons(sk12,nil)),sk13) = sk2
| ssItem(sk8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_44) ).
cnf(co1_43,negated_conjecture,
( ssList(sk13)
| ssItem(sk8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_43) ).
cnf(co1_37,negated_conjecture,
( ssItem(sk11)
| ssItem(sk8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_37) ).
cnf(co1_42,negated_conjecture,
( ssItem(sk12)
| ssItem(sk8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_42) ).
cnf(co1_50,negated_conjecture,
( app(app(cons(sk11,nil),cons(sk12,nil)),sk13) = sk2
| ssItem(sk9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_50) ).
cnf(co1_49,negated_conjecture,
( ssList(sk13)
| ssItem(sk9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_49) ).
cnf(co1_38,negated_conjecture,
( ssItem(sk11)
| ssItem(sk9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_38) ).
cnf(co1_45,negated_conjecture,
( ssItem(sk12)
| ssItem(sk9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_45) ).
cnf(co1_54,negated_conjecture,
( app(app(cons(sk11,nil),cons(sk12,nil)),sk13) = sk2
| ssList(sk10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_54) ).
cnf(co1_51,negated_conjecture,
( ssList(sk13)
| ssList(sk10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_51) ).
cnf(co1_39,negated_conjecture,
( ssItem(sk11)
| ssList(sk10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_39) ).
cnf(co1_46,negated_conjecture,
( ssItem(sk12)
| ssList(sk10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_46) ).
cnf(co1_52,negated_conjecture,
( ssList(sk13)
| app(app(cons(sk8,nil),cons(sk9,nil)),sk10) = sk4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_52) ).
cnf(co1_47,negated_conjecture,
( ssItem(sk12)
| app(app(cons(sk8,nil),cons(sk9,nil)),sk10) = sk4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_47) ).
cnf(co1_40,negated_conjecture,
( ssItem(sk11)
| app(app(cons(sk8,nil),cons(sk9,nil)),sk10) = sk4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_40) ).
cnf(co1_7,negated_conjecture,
( app(app(cons(X4,nil),cons(X5,nil)),X6) != sk4
| ~ ssList(X6)
| ~ ssItem(X5)
| ~ ssItem(X4)
| app(app(cons(X2,nil),cons(X1,nil)),X3) != sk1
| app(app(cons(X1,nil),cons(X2,nil)),X3) != sk2
| ~ ssList(X3)
| ~ ssItem(X2)
| ~ ssItem(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_7) ).
cnf(co1_19,negated_conjecture,
( app(app(cons(X1,nil),cons(X2,nil)),X3) != sk4
| ~ ssList(X3)
| ~ ssItem(X2)
| ~ ssItem(X1)
| app(app(cons(sk8,nil),cons(sk9,nil)),sk10) = sk4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_19) ).
cnf(co1_56,negated_conjecture,
( app(app(cons(sk11,nil),cons(sk12,nil)),sk13) = sk2
| app(app(cons(sk9,nil),cons(sk8,nil)),sk10) = sk3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_56) ).
cnf(co1_6,negated_conjecture,
sk1 = sk3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_6) ).
cnf(co1_48,negated_conjecture,
( ssItem(sk12)
| app(app(cons(sk9,nil),cons(sk8,nil)),sk10) = sk3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_48) ).
cnf(co1_41,negated_conjecture,
( ssItem(sk11)
| app(app(cons(sk9,nil),cons(sk8,nil)),sk10) = sk3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_41) ).
cnf(co1_53,negated_conjecture,
( ssList(sk13)
| app(app(cons(sk9,nil),cons(sk8,nil)),sk10) = sk3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_53) ).
cnf(co1_20,negated_conjecture,
( app(app(cons(X1,nil),cons(X2,nil)),X3) != sk4
| ~ ssList(X3)
| ~ ssItem(X2)
| ~ ssItem(X1)
| app(app(cons(sk9,nil),cons(sk8,nil)),sk10) = sk3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_20) ).
cnf(c_0_28,negated_conjecture,
( app(app(cons(X1,nil),cons(X2,nil)),X3) != sk4
| ~ ssList(X3)
| ~ ssItem(X2)
| ~ ssItem(X1)
| ssItem(sk8) ),
inference(fof_simplification,[status(thm)],[co1_16]) ).
cnf(c_0_29,negated_conjecture,
( app(app(cons(X1,nil),cons(X2,nil)),X3) != sk4
| ~ ssList(X3)
| ~ ssItem(X2)
| ~ ssItem(X1)
| ssItem(sk9) ),
inference(fof_simplification,[status(thm)],[co1_17]) ).
cnf(c_0_30,negated_conjecture,
( app(app(cons(X1,nil),cons(X2,nil)),X3) != sk4
| ~ ssList(X3)
| ~ ssItem(X2)
| ~ ssItem(X1)
| ssList(sk10) ),
inference(fof_simplification,[status(thm)],[co1_18]) ).
cnf(c_0_31,negated_conjecture,
( app(app(cons(X1,nil),cons(X2,nil)),X3) != sk4
| ~ ssList(X3)
| ~ ssItem(X2)
| ~ ssItem(X1)
| ssItem(sk8) ),
c_0_28 ).
cnf(c_0_32,negated_conjecture,
sk2 = sk4,
co1_5 ).
cnf(c_0_33,negated_conjecture,
( app(app(cons(X1,nil),cons(X2,nil)),X3) != sk4
| ~ ssList(X3)
| ~ ssItem(X2)
| ~ ssItem(X1)
| ssItem(sk9) ),
c_0_29 ).
cnf(c_0_34,negated_conjecture,
( app(app(cons(X1,nil),cons(X2,nil)),X3) != sk4
| ~ ssList(X3)
| ~ ssItem(X2)
| ~ ssItem(X1)
| ssList(sk10) ),
c_0_30 ).
fof(c_0_35,plain,
( ~ epred3_0
<=> ! [X4,X5,X6] :
( app(app(cons(X4,nil),cons(X5,nil)),X6) != sk2
| ~ ssItem(X5)
| ~ ssItem(X4)
| ~ ssList(X6) ) ),
introduced(definition) ).
cnf(c_0_36,negated_conjecture,
( app(app(cons(sk11,nil),cons(sk12,nil)),sk13) = sk2
| app(app(cons(sk8,nil),cons(sk9,nil)),sk10) = sk4 ),
co1_55 ).
cnf(c_0_37,negated_conjecture,
( ~ ssList(X3)
| ~ ssItem(X1)
| ~ ssItem(X2)
| app(app(cons(X1,nil),cons(X2,nil)),X3) != sk2
| ssItem(sk8) ),
inference(rw,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_38,negated_conjecture,
( app(app(cons(sk11,nil),cons(sk12,nil)),sk13) = sk2
| ssItem(sk8) ),
co1_44 ).
cnf(c_0_39,negated_conjecture,
( ssList(sk13)
| ssItem(sk8) ),
co1_43 ).
cnf(c_0_40,negated_conjecture,
( ssItem(sk11)
| ssItem(sk8) ),
co1_37 ).
cnf(c_0_41,negated_conjecture,
( ssItem(sk12)
| ssItem(sk8) ),
co1_42 ).
cnf(c_0_42,negated_conjecture,
( ~ ssList(X3)
| ~ ssItem(X1)
| ~ ssItem(X2)
| app(app(cons(X1,nil),cons(X2,nil)),X3) != sk2
| ssItem(sk9) ),
inference(rw,[status(thm)],[c_0_33,c_0_32]) ).
cnf(c_0_43,negated_conjecture,
( app(app(cons(sk11,nil),cons(sk12,nil)),sk13) = sk2
| ssItem(sk9) ),
co1_50 ).
cnf(c_0_44,negated_conjecture,
( ssList(sk13)
| ssItem(sk9) ),
co1_49 ).
cnf(c_0_45,negated_conjecture,
( ssItem(sk11)
| ssItem(sk9) ),
co1_38 ).
cnf(c_0_46,negated_conjecture,
( ssItem(sk12)
| ssItem(sk9) ),
co1_45 ).
cnf(c_0_47,negated_conjecture,
( ~ ssList(X3)
| ~ ssItem(X1)
| ~ ssItem(X2)
| app(app(cons(X1,nil),cons(X2,nil)),X3) != sk2
| ssList(sk10) ),
inference(rw,[status(thm)],[c_0_34,c_0_32]) ).
cnf(c_0_48,negated_conjecture,
( app(app(cons(sk11,nil),cons(sk12,nil)),sk13) = sk2
| ssList(sk10) ),
co1_54 ).
cnf(c_0_49,negated_conjecture,
( ssList(sk13)
| ssList(sk10) ),
co1_51 ).
cnf(c_0_50,negated_conjecture,
( ssItem(sk11)
| ssList(sk10) ),
co1_39 ).
cnf(c_0_51,negated_conjecture,
( ssItem(sk12)
| ssList(sk10) ),
co1_46 ).
cnf(c_0_52,negated_conjecture,
( ssList(sk13)
| app(app(cons(sk8,nil),cons(sk9,nil)),sk10) = sk4 ),
co1_52 ).
cnf(c_0_53,negated_conjecture,
( ssItem(sk12)
| app(app(cons(sk8,nil),cons(sk9,nil)),sk10) = sk4 ),
co1_47 ).
cnf(c_0_54,negated_conjecture,
( ssItem(sk11)
| app(app(cons(sk8,nil),cons(sk9,nil)),sk10) = sk4 ),
co1_40 ).
cnf(c_0_55,negated_conjecture,
( app(app(cons(X4,nil),cons(X5,nil)),X6) != sk4
| ~ ssList(X6)
| ~ ssItem(X5)
| ~ ssItem(X4)
| app(app(cons(X2,nil),cons(X1,nil)),X3) != sk1
| app(app(cons(X1,nil),cons(X2,nil)),X3) != sk2
| ~ ssList(X3)
| ~ ssItem(X2)
| ~ ssItem(X1) ),
inference(fof_simplification,[status(thm)],[co1_7]) ).
cnf(c_0_56,negated_conjecture,
( ~ ssList(X3)
| ~ ssItem(X2)
| ~ ssItem(X1)
| app(app(cons(X1,nil),cons(X2,nil)),X3) != sk2
| epred3_0 ),
inference(split_equiv,[status(thm)],[c_0_35]) ).
cnf(c_0_57,negated_conjecture,
( app(app(cons(sk11,nil),cons(sk12,nil)),sk13) = sk2
| app(app(cons(sk8,nil),cons(sk9,nil)),sk10) = sk2 ),
inference(rw,[status(thm)],[c_0_36,c_0_32]) ).
cnf(c_0_58,negated_conjecture,
ssItem(sk8),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_39]),c_0_40]),c_0_41]) ).
cnf(c_0_59,negated_conjecture,
ssItem(sk9),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_44]),c_0_45]),c_0_46]) ).
cnf(c_0_60,negated_conjecture,
ssList(sk10),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_49]),c_0_50]),c_0_51]) ).
cnf(c_0_61,negated_conjecture,
( ssList(sk13)
| app(app(cons(sk8,nil),cons(sk9,nil)),sk10) = sk2 ),
inference(rw,[status(thm)],[c_0_52,c_0_32]) ).
cnf(c_0_62,negated_conjecture,
( ssItem(sk12)
| app(app(cons(sk8,nil),cons(sk9,nil)),sk10) = sk2 ),
inference(rw,[status(thm)],[c_0_53,c_0_32]) ).
cnf(c_0_63,negated_conjecture,
( ssItem(sk11)
| app(app(cons(sk8,nil),cons(sk9,nil)),sk10) = sk2 ),
inference(rw,[status(thm)],[c_0_54,c_0_32]) ).
fof(c_0_64,plain,
( ~ epred4_0
<=> ! [X1,X2,X3] :
( app(app(cons(X2,nil),cons(X1,nil)),X3) != sk1
| app(app(cons(X1,nil),cons(X2,nil)),X3) != sk2
| ~ ssItem(X2)
| ~ ssItem(X1)
| ~ ssList(X3) ) ),
introduced(definition) ).
cnf(c_0_65,negated_conjecture,
( app(app(cons(X4,nil),cons(X5,nil)),X6) != sk4
| ~ ssList(X6)
| ~ ssItem(X5)
| ~ ssItem(X4)
| app(app(cons(X2,nil),cons(X1,nil)),X3) != sk1
| app(app(cons(X1,nil),cons(X2,nil)),X3) != sk2
| ~ ssList(X3)
| ~ ssItem(X2)
| ~ ssItem(X1) ),
c_0_55 ).
cnf(c_0_66,negated_conjecture,
( epred3_0
| app(app(cons(sk11,nil),cons(sk12,nil)),sk13) = sk2 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_58]),c_0_59]),c_0_60])]) ).
cnf(c_0_67,negated_conjecture,
( ssList(sk13)
| epred3_0 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_61]),c_0_60])]),c_0_44]),c_0_39]) ).
cnf(c_0_68,negated_conjecture,
( ssItem(sk12)
| epred3_0 ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_62]),c_0_58]),c_0_60])]),c_0_46]) ).
cnf(c_0_69,negated_conjecture,
( ssItem(sk11)
| epred3_0 ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_63]),c_0_58]),c_0_60])]),c_0_45]) ).
cnf(c_0_70,negated_conjecture,
( app(app(cons(X1,nil),cons(X2,nil)),X3) != sk4
| ~ ssList(X3)
| ~ ssItem(X2)
| ~ ssItem(X1)
| app(app(cons(sk8,nil),cons(sk9,nil)),sk10) = sk4 ),
inference(fof_simplification,[status(thm)],[co1_19]) ).
cnf(c_0_71,negated_conjecture,
( ~ epred3_0
| ~ epred4_0 ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(rw,[status(thm)],[c_0_65,c_0_32]),c_0_35]),c_0_64]) ).
cnf(c_0_72,negated_conjecture,
epred3_0,
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_66]),c_0_67]),c_0_68]),c_0_69]) ).
cnf(c_0_73,negated_conjecture,
( app(app(cons(sk11,nil),cons(sk12,nil)),sk13) = sk2
| app(app(cons(sk9,nil),cons(sk8,nil)),sk10) = sk3 ),
co1_56 ).
cnf(c_0_74,negated_conjecture,
sk1 = sk3,
co1_6 ).
cnf(c_0_75,negated_conjecture,
( ssItem(sk12)
| app(app(cons(sk9,nil),cons(sk8,nil)),sk10) = sk3 ),
co1_48 ).
cnf(c_0_76,negated_conjecture,
( ssItem(sk11)
| app(app(cons(sk9,nil),cons(sk8,nil)),sk10) = sk3 ),
co1_41 ).
cnf(c_0_77,negated_conjecture,
( ssList(sk13)
| app(app(cons(sk9,nil),cons(sk8,nil)),sk10) = sk3 ),
co1_53 ).
cnf(c_0_78,negated_conjecture,
( app(app(cons(X1,nil),cons(X2,nil)),X3) != sk4
| ~ ssList(X3)
| ~ ssItem(X2)
| ~ ssItem(X1)
| app(app(cons(sk9,nil),cons(sk8,nil)),sk10) = sk3 ),
inference(fof_simplification,[status(thm)],[co1_20]) ).
cnf(c_0_79,negated_conjecture,
( app(app(cons(X1,nil),cons(X2,nil)),X3) != sk4
| ~ ssList(X3)
| ~ ssItem(X2)
| ~ ssItem(X1)
| app(app(cons(sk8,nil),cons(sk9,nil)),sk10) = sk4 ),
c_0_70 ).
cnf(c_0_80,negated_conjecture,
( ~ ssList(X3)
| ~ ssItem(X2)
| ~ ssItem(X1)
| app(app(cons(X2,nil),cons(X1,nil)),X3) != sk1
| app(app(cons(X1,nil),cons(X2,nil)),X3) != sk2
| epred4_0 ),
inference(split_equiv,[status(thm)],[c_0_64]) ).
cnf(c_0_81,negated_conjecture,
~ epred4_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_71,c_0_72])]) ).
cnf(c_0_82,negated_conjecture,
( app(app(cons(sk11,nil),cons(sk12,nil)),sk13) = sk2
| app(app(cons(sk9,nil),cons(sk8,nil)),sk10) = sk1 ),
inference(rw,[status(thm)],[c_0_73,c_0_74]) ).
cnf(c_0_83,negated_conjecture,
( ssItem(sk12)
| app(app(cons(sk9,nil),cons(sk8,nil)),sk10) = sk1 ),
inference(rw,[status(thm)],[c_0_75,c_0_74]) ).
cnf(c_0_84,negated_conjecture,
( ssItem(sk11)
| app(app(cons(sk9,nil),cons(sk8,nil)),sk10) = sk1 ),
inference(rw,[status(thm)],[c_0_76,c_0_74]) ).
cnf(c_0_85,negated_conjecture,
( ssList(sk13)
| app(app(cons(sk9,nil),cons(sk8,nil)),sk10) = sk1 ),
inference(rw,[status(thm)],[c_0_77,c_0_74]) ).
cnf(c_0_86,negated_conjecture,
( app(app(cons(X1,nil),cons(X2,nil)),X3) != sk4
| ~ ssList(X3)
| ~ ssItem(X2)
| ~ ssItem(X1)
| app(app(cons(sk9,nil),cons(sk8,nil)),sk10) = sk3 ),
c_0_78 ).
cnf(c_0_87,negated_conjecture,
( ~ ssList(X3)
| ~ ssItem(X1)
| ~ ssItem(X2)
| app(app(cons(X1,nil),cons(X2,nil)),X3) != sk2
| app(app(cons(sk8,nil),cons(sk9,nil)),sk10) = sk2 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_79,c_0_32]),c_0_32]) ).
cnf(c_0_88,negated_conjecture,
app(app(cons(sk11,nil),cons(sk12,nil)),sk13) = sk2,
inference(csr,[status(thm)],[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_80,c_0_57]),c_0_58]),c_0_59]),c_0_60])]),c_0_81]),c_0_82]) ).
cnf(c_0_89,negated_conjecture,
ssItem(sk12),
inference(csr,[status(thm)],[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_80,c_0_62]),c_0_58]),c_0_59]),c_0_60])]),c_0_81]),c_0_83]) ).
cnf(c_0_90,negated_conjecture,
ssItem(sk11),
inference(csr,[status(thm)],[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_80,c_0_63]),c_0_58]),c_0_59]),c_0_60])]),c_0_81]),c_0_84]) ).
cnf(c_0_91,negated_conjecture,
ssList(sk13),
inference(csr,[status(thm)],[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_80,c_0_61]),c_0_58]),c_0_59]),c_0_60])]),c_0_81]),c_0_85]) ).
cnf(c_0_92,negated_conjecture,
( ~ ssList(X3)
| ~ ssItem(X1)
| ~ ssItem(X2)
| app(app(cons(X1,nil),cons(X2,nil)),X3) != sk2
| app(app(cons(sk9,nil),cons(sk8,nil)),sk10) = sk1 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_86,c_0_74]),c_0_32]) ).
cnf(c_0_93,negated_conjecture,
app(app(cons(sk8,nil),cons(sk9,nil)),sk10) = sk2,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_88]),c_0_89]),c_0_90]),c_0_91])]) ).
cnf(c_0_94,negated_conjecture,
app(app(cons(sk9,nil),cons(sk8,nil)),sk10) = sk1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_88]),c_0_89]),c_0_90]),c_0_91])]) ).
cnf(c_0_95,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[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_80,c_0_93]),c_0_58]),c_0_59]),c_0_60])]),c_0_81]),c_0_94])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC413-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/5.38 % Computer : n005.cluster.edu
% 0.10/5.38 % Model : x86_64 x86_64
% 0.10/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.38 % Memory : 8046.5625MB
% 0.10/5.38 % OS : Linux 6.8.0-71-generic
% 0.10/5.38 % CPULimit : 300
% 0.10/5.38 % WCLimit : 300
% 0.10/5.38 % DateTime : Mon Sep 21 08:22:54 UTC 2026
% 0.10/5.38 % CPUTime :
% 0.10/5.38 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/5.42 Running first-order theorem proving
% 0.14/5.42 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/5.58 % Version: 3.5.1
% 0.14/5.58 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.14/5.58 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/5.58 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.14/5.58 % Starting new_bool_3 with 300s (1) cores
% 0.14/5.58 % Starting new_bool_1 with 300s (1) cores
% 0.14/5.58 % Starting sh5l with 300s (1) cores
% 0.14/5.58 % C07_19_nc_SOS_SAT001_MinMin_p005000_rr with pid 3008778 completed with status 0
% 0.14/5.58 % Result found by C07_19_nc_SOS_SAT001_MinMin_p005000_rr
% 0.14/5.58 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.14/5.58 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/5.58 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.14/5.58 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.14/5.58 % No SInE strategy applied
% 0.14/5.58 % Search class: FGHSM-FSLM21-MFFFFFNN
% 0.14/5.58 % Scheduled 10 strats onto 5 cores with 1500 seconds (1500 total)
% 0.14/5.58 % Starting SubtermCWHack with 136s (1) cores
% 0.14/5.58 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 0.14/5.58 % Starting G-E--_107_C45_F1_PI_AE_Q7_CS_SP_PS_S0Y with 136s (1) cores
% 0.14/5.58 % Starting G-E--_200_B02_F1_SE_CS_SP_PI_S2k with 136s (1) cores
% 0.14/5.58 % Starting G-E--_301_C18_F1_URBAN_S5PRR_RG_S04BN with 136s (1) cores
% 0.14/5.58 % G-E--_107_C45_F1_PI_AE_Q7_CS_SP_PS_S0Y with pid 3008796 completed with status 0
% 0.14/5.58 % Result found by G-E--_107_C45_F1_PI_AE_Q7_CS_SP_PS_S0Y
% 0.14/5.58 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.14/5.58 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/5.58 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.14/5.58 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.14/5.58 % No SInE strategy applied
% 0.14/5.58 % Search class: FGHSM-FSLM21-MFFFFFNN
% 0.14/5.58 % Scheduled 10 strats onto 5 cores with 1500 seconds (1500 total)
% 0.14/5.58 % Starting SubtermCWHack with 136s (1) cores
% 0.14/5.58 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 0.14/5.58 % Starting G-E--_107_C45_F1_PI_AE_Q7_CS_SP_PS_S0Y with 136s (1) cores
% 0.14/5.58 % Preprocessing time : 0.005 s
% 0.14/5.58 % Presaturation interreduction done
% 0.14/5.58
% 0.14/5.58 % Proof found!
% 0.14/5.58 % SZS status Unsatisfiable
% 0.14/5.58 % SZS output start CNFRefutation
% See solution above
% 0.14/5.58 % Parsed axioms : 241
% 0.14/5.58 % Removed by relevancy pruning/SinE : 0
% 0.14/5.58 % Initial clauses : 241
% 0.14/5.58 % Removed in clause preprocessing : 0
% 0.14/5.58 % Initial clauses in saturation : 241
% 0.14/5.58 % Processed clauses : 596
% 0.14/5.58 % ...of these trivial : 4
% 0.14/5.58 % ...subsumed : 39
% 0.14/5.58 % ...remaining for further processing : 552
% 0.14/5.58 % Other redundant clauses eliminated : 85
% 0.14/5.58 % Clauses deleted for lack of memory : 0
% 0.14/5.58 % Backward-subsumed : 25
% 0.14/5.58 % Backward-rewritten : 47
% 0.14/5.58 % Generated clauses : 2052
% 0.14/5.58 % ...of the previous two non-redundant : 1808
% 0.14/5.58 % ...aggressively subsumed : 0
% 0.14/5.58 % Contextual simplify-reflections : 38
% 0.14/5.58 % Paramodulations : 1943
% 0.14/5.58 % Factorizations : 0
% 0.14/5.58 % NegExts : 0
% 0.14/5.58 % Equation resolutions : 103
% 0.14/5.58 % Disequality decompositions : 0
% 0.14/5.58 % Total rewrite steps : 1203
% 0.14/5.58 % ...of those cached : 1078
% 0.14/5.58 % Propositional unsat checks : 0
% 0.14/5.58 % Propositional check models : 0
% 0.14/5.58 % Propositional check unsatisfiable : 0
% 0.14/5.58 % Propositional clauses : 0
% 0.14/5.58 % Propositional clauses after purity: 0
% 0.14/5.58 % Propositional unsat core size : 0
% 0.14/5.58 % Propositional preprocessing time : 0.000
% 0.14/5.58 % Propositional encoding time : 0.000
% 0.14/5.58 % Propositional solver time : 0.000
% 0.14/5.58 % Success case prop preproc time : 0.000
% 0.14/5.58 % Success case prop encoding time : 0.000
% 0.14/5.58 % Success case prop solver time : 0.000
% 0.14/5.58 % Current number of processed clauses : 234
% 0.14/5.58 % Positive orientable unit clauses : 70
% 0.14/5.58 % Positive unorientable unit clauses: 0
% 0.14/5.58 % Negative unit clauses : 6
% 0.14/5.58 % Non-unit-clauses : 158
% 0.14/5.58 % Current number of unprocessed clauses: 1521
% 0.14/5.58 % ...number of literals in the above : 9695
% 0.14/5.58 % Current number of archived formulas : 0
% 0.14/5.58 % Current number of archived clauses : 311
% 0.14/5.58 % Clause-clause subsumption calls (NU) : 19138
% 0.14/5.58 % Rec. Clause-clause subsumption calls : 3307
% 0.14/5.58 % Non-unit clause-clause subsumptions : 83
% 0.14/5.58 % Unit Clause-clause subsumption calls : 1170
% 0.14/5.58 % Rewrite failures with RHS unbound : 0
% 0.14/5.58 % BW rewrite match attempts : 16
% 0.14/5.58 % BW rewrite match successes : 14
% 0.14/5.58 % Condensation attempts : 0
% 0.14/5.58 % Condensation successes : 0
% 0.14/5.58 % Termbank termtop insertions : 53538
% 0.14/5.58 % Search garbage collected termcells : 601
% 0.14/5.58
% 0.14/5.58 % -------------------------------------------------
% 0.14/5.58 % User time : 0.081 s
% 0.14/5.58 % System time : 0.004 s
% 0.14/5.58 % Total time : 0.085 s
% 0.14/5.58 % Maximum resident set size: 3796 pages
% 0.14/5.58
% 0.14/5.58 % -------------------------------------------------
% 0.14/5.58 % User time : 0.365 s
% 0.14/5.58 % System time : 0.044 s
% 0.14/5.58 % Total time : 0.408 s
% 0.14/5.58 % Maximum resident set size: 4864 pages
% 0.14/5.58 % E exiting
%------------------------------------------------------------------------------