%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWC343-1 : 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 : n003.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 02:44:00 PM UTC 2026
% Result : Unsatisfiable 6.11s 1.44s
% Output : CNFRefutation 6.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 28
% Syntax : Number of clauses : 117 ( 25 unt; 39 nHn; 115 RR)
% Number of literals : 390 ( 152 equ; 242 neg)
% Maximal clause size : 7 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 6 con; 0-2 aty)
% Number of variables : 125 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(co1_15,negated_conjecture,
( ~ strictorderedP(sk1)
| app(sk1,X1) != sk2
| ~ ssList(X1)
| nil = sk1
| app(cons(sk6(X1),nil),sk7(X1)) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_15) ).
cnf(co1_9,negated_conjecture,
strictorderedP(sk3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_9) ).
cnf(co1_6,negated_conjecture,
sk1 = sk3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_6) ).
cnf(co1_14,negated_conjecture,
( ~ strictorderedP(sk1)
| app(sk1,X1) != sk2
| ~ ssList(X1)
| nil = sk1
| ssList(sk7(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_14) ).
cnf(clause144,axiom,
( ~ ssList(X3)
| ~ ssList(X1)
| ~ ssList(X2)
| app(X1,X2) != X3
| frontsegP(X3,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause144) ).
cnf(clause85,axiom,
( ~ ssList(X2)
| ~ ssList(X1)
| ssList(app(X2,X1)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause85) ).
cnf(co1_5,negated_conjecture,
sk2 = sk4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_5) ).
cnf(co1_8,negated_conjecture,
app(sk3,sk5) = sk4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_8) ).
cnf(co1_12,negated_conjecture,
( ~ strictorderedP(sk1)
| app(sk1,X1) != sk2
| ~ ssList(X1)
| nil = sk1
| ssItem(sk6(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_12) ).
cnf(co1_7,negated_conjecture,
ssList(sk5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_7) ).
cnf(co1_18,negated_conjecture,
( ~ strictorderedP(sk1)
| app(sk1,X1) != sk2
| ~ ssList(X1)
| nil = sk1
| app(sk9(X1),cons(sk8(X1),nil)) = sk1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_18) ).
cnf(co1_17,negated_conjecture,
( ~ strictorderedP(sk1)
| app(sk1,X1) != sk2
| ~ ssList(X1)
| nil = sk1
| ssList(sk9(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_17) ).
cnf(co1_16,negated_conjecture,
( ~ strictorderedP(sk1)
| app(sk1,X1) != sk2
| ~ ssList(X1)
| nil = sk1
| ssItem(sk8(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_16) ).
cnf(clause86,axiom,
( ~ ssList(X2)
| ~ ssItem(X1)
| ssList(cons(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause86) ).
cnf(co1_10,negated_conjecture,
( ~ lt(X3,X1)
| app(X4,cons(X3,nil)) != sk3
| ~ ssList(X4)
| ~ ssItem(X3)
| app(cons(X1,nil),X2) != sk5
| ~ ssList(X2)
| ~ ssItem(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_10) ).
cnf(clause132,axiom,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ frontsegP(X1,X2)
| app(X2,skaf45(X1,X2)) = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause132) ).
cnf(clause8,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause8) ).
cnf(co1_19,negated_conjecture,
( ~ strictorderedP(sk1)
| app(sk1,X1) != sk2
| ~ ssList(X1)
| nil = sk1
| lt(sk8(X1),sk6(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_19) ).
cnf(co1_11,negated_conjecture,
( nil != sk3
| nil = sk4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_11) ).
cnf(co1_24,negated_conjecture,
( nil != sk2
| ~ strictorderedP(sk1)
| app(sk1,X1) != sk2
| ~ ssList(X1)
| app(sk9(X1),cons(sk8(X1),nil)) = sk1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_24) ).
cnf(clause51,axiom,
ssList(skaf45(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause51) ).
cnf(co1_22,negated_conjecture,
( nil != sk2
| ~ strictorderedP(sk1)
| app(sk1,X1) != sk2
| ~ ssList(X1)
| ssItem(sk8(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_22) ).
cnf(co1_23,negated_conjecture,
( nil != sk2
| ~ strictorderedP(sk1)
| app(sk1,X1) != sk2
| ~ ssList(X1)
| ssList(sk9(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_23) ).
cnf(clause138,axiom,
( ~ ssItem(X1)
| ~ ssItem(X2)
| ~ ssList(X3)
| X1 != X2
| memberP(cons(X2,X3),X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause138) ).
cnf(clause73,axiom,
( ~ ssList(X1)
| app(X1,nil) = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause73) ).
cnf(clause141,axiom,
( ~ ssItem(X2)
| ~ ssList(X3)
| ~ ssList(X1)
| ~ memberP(X1,X2)
| memberP(app(X3,X1),X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause141) ).
cnf(clause71,axiom,
( ~ ssItem(X1)
| ~ memberP(nil,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause71) ).
cnf(co1_1,negated_conjecture,
ssList(sk1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_1) ).
cnf(c_0_28,negated_conjecture,
( ~ strictorderedP(sk1)
| app(sk1,X1) != sk2
| ~ ssList(X1)
| nil = sk1
| app(cons(sk6(X1),nil),sk7(X1)) = X1 ),
inference(fof_simplification,[status(thm)],[co1_15]) ).
cnf(c_0_29,negated_conjecture,
strictorderedP(sk3),
co1_9 ).
cnf(c_0_30,negated_conjecture,
sk1 = sk3,
co1_6 ).
cnf(c_0_31,negated_conjecture,
( ~ strictorderedP(sk1)
| app(sk1,X1) != sk2
| ~ ssList(X1)
| nil = sk1
| ssList(sk7(X1)) ),
inference(fof_simplification,[status(thm)],[co1_14]) ).
cnf(c_0_32,plain,
( ~ ssList(X3)
| ~ ssList(X1)
| ~ ssList(X2)
| app(X1,X2) != X3
| frontsegP(X3,X1) ),
inference(fof_simplification,[status(thm)],[clause144]) ).
cnf(c_0_33,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ssList(app(X2,X1)) ),
inference(fof_simplification,[status(thm)],[clause85]) ).
cnf(c_0_34,negated_conjecture,
( ~ strictorderedP(sk1)
| app(sk1,X1) != sk2
| ~ ssList(X1)
| nil = sk1
| app(cons(sk6(X1),nil),sk7(X1)) = X1 ),
c_0_28 ).
cnf(c_0_35,negated_conjecture,
sk2 = sk4,
co1_5 ).
cnf(c_0_36,negated_conjecture,
strictorderedP(sk1),
inference(rw,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_37,negated_conjecture,
app(sk3,sk5) = sk4,
co1_8 ).
cnf(c_0_38,negated_conjecture,
( ~ strictorderedP(sk1)
| app(sk1,X1) != sk2
| ~ ssList(X1)
| nil = sk1
| ssList(sk7(X1)) ),
c_0_31 ).
cnf(c_0_39,negated_conjecture,
( ~ strictorderedP(sk1)
| app(sk1,X1) != sk2
| ~ ssList(X1)
| nil = sk1
| ssItem(sk6(X1)) ),
inference(fof_simplification,[status(thm)],[co1_12]) ).
cnf(c_0_40,plain,
( ~ ssList(X3)
| ~ ssList(X1)
| ~ ssList(X2)
| app(X1,X2) != X3
| frontsegP(X3,X1) ),
c_0_32 ).
cnf(c_0_41,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ssList(app(X2,X1)) ),
c_0_33 ).
cnf(c_0_42,negated_conjecture,
( ~ ssList(X1)
| app(sk1,X1) != sk4
| nil = sk1
| app(cons(sk6(X1),nil),sk7(X1)) = X1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_35]),c_0_36])]) ).
cnf(c_0_43,negated_conjecture,
app(sk1,sk5) = sk4,
inference(rw,[status(thm)],[c_0_37,c_0_30]) ).
cnf(c_0_44,negated_conjecture,
ssList(sk5),
co1_7 ).
cnf(c_0_45,negated_conjecture,
( ~ ssList(X1)
| app(sk1,X1) != sk4
| ssList(sk7(X1))
| nil = sk1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_38,c_0_35]),c_0_36])]) ).
cnf(c_0_46,negated_conjecture,
( ~ strictorderedP(sk1)
| app(sk1,X1) != sk2
| ~ ssList(X1)
| nil = sk1
| ssItem(sk6(X1)) ),
c_0_39 ).
cnf(c_0_47,negated_conjecture,
( ~ strictorderedP(sk1)
| app(sk1,X1) != sk2
| ~ ssList(X1)
| nil = sk1
| app(sk9(X1),cons(sk8(X1),nil)) = sk1 ),
inference(fof_simplification,[status(thm)],[co1_18]) ).
cnf(c_0_48,negated_conjecture,
( ~ strictorderedP(sk1)
| app(sk1,X1) != sk2
| ~ ssList(X1)
| nil = sk1
| ssList(sk9(X1)) ),
inference(fof_simplification,[status(thm)],[co1_17]) ).
cnf(c_0_49,negated_conjecture,
( ~ strictorderedP(sk1)
| app(sk1,X1) != sk2
| ~ ssList(X1)
| nil = sk1
| ssItem(sk8(X1)) ),
inference(fof_simplification,[status(thm)],[co1_16]) ).
cnf(c_0_50,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| frontsegP(app(X1,X2),X1) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_40]),c_0_41]) ).
cnf(c_0_51,negated_conjecture,
( nil = sk1
| app(cons(sk6(sk5),nil),sk7(sk5)) = sk5 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_44])]) ).
cnf(c_0_52,negated_conjecture,
( ssList(sk7(sk5))
| nil = sk1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_43]),c_0_44])]) ).
cnf(c_0_53,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| ssList(cons(X1,X2)) ),
inference(fof_simplification,[status(thm)],[clause86]) ).
cnf(c_0_54,negated_conjecture,
( ~ ssList(X1)
| app(sk1,X1) != sk4
| ssItem(sk6(X1))
| nil = sk1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_46,c_0_35]),c_0_36])]) ).
cnf(c_0_55,negated_conjecture,
( ~ lt(X3,X1)
| app(X4,cons(X3,nil)) != sk3
| ~ ssList(X4)
| ~ ssItem(X3)
| app(cons(X1,nil),X2) != sk5
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(fof_simplification,[status(thm)],[co1_10]) ).
cnf(c_0_56,negated_conjecture,
( ~ strictorderedP(sk1)
| app(sk1,X1) != sk2
| ~ ssList(X1)
| nil = sk1
| app(sk9(X1),cons(sk8(X1),nil)) = sk1 ),
c_0_47 ).
cnf(c_0_57,negated_conjecture,
( ~ strictorderedP(sk1)
| app(sk1,X1) != sk2
| ~ ssList(X1)
| nil = sk1
| ssList(sk9(X1)) ),
c_0_48 ).
cnf(c_0_58,negated_conjecture,
( ~ strictorderedP(sk1)
| app(sk1,X1) != sk2
| ~ ssList(X1)
| nil = sk1
| ssItem(sk8(X1)) ),
c_0_49 ).
cnf(c_0_59,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ frontsegP(X1,X2)
| app(X2,skaf45(X1,X2)) = X1 ),
inference(fof_simplification,[status(thm)],[clause132]) ).
cnf(c_0_60,negated_conjecture,
( ~ ssList(cons(sk6(sk5),nil))
| frontsegP(sk5,cons(sk6(sk5),nil))
| nil = sk1 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_52]) ).
cnf(c_0_61,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| ssList(cons(X1,X2)) ),
c_0_53 ).
cnf(c_0_62,axiom,
ssList(nil),
clause8 ).
cnf(c_0_63,negated_conjecture,
( ssItem(sk6(sk5))
| nil = sk1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_43]),c_0_44])]) ).
cnf(c_0_64,negated_conjecture,
( ~ strictorderedP(sk1)
| app(sk1,X1) != sk2
| ~ ssList(X1)
| nil = sk1
| lt(sk8(X1),sk6(X1)) ),
inference(fof_simplification,[status(thm)],[co1_19]) ).
cnf(c_0_65,negated_conjecture,
( ~ lt(X3,X1)
| app(X4,cons(X3,nil)) != sk3
| ~ ssList(X4)
| ~ ssItem(X3)
| app(cons(X1,nil),X2) != sk5
| ~ ssList(X2)
| ~ ssItem(X1) ),
c_0_55 ).
cnf(c_0_66,negated_conjecture,
( ~ ssList(X1)
| app(sk1,X1) != sk4
| nil = sk1
| app(sk9(X1),cons(sk8(X1),nil)) = sk1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_56,c_0_35]),c_0_36])]) ).
cnf(c_0_67,negated_conjecture,
( ~ ssList(X1)
| app(sk1,X1) != sk4
| ssList(sk9(X1))
| nil = sk1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_57,c_0_35]),c_0_36])]) ).
cnf(c_0_68,negated_conjecture,
( ~ ssList(X1)
| app(sk1,X1) != sk4
| ssItem(sk8(X1))
| nil = sk1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_58,c_0_35]),c_0_36])]) ).
cnf(c_0_69,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ frontsegP(X1,X2)
| app(X2,skaf45(X1,X2)) = X1 ),
c_0_59 ).
cnf(c_0_70,negated_conjecture,
( frontsegP(sk5,cons(sk6(sk5),nil))
| nil = sk1 ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_62])]),c_0_63]) ).
cnf(c_0_71,negated_conjecture,
( ~ strictorderedP(sk1)
| app(sk1,X1) != sk2
| ~ ssList(X1)
| nil = sk1
| lt(sk8(X1),sk6(X1)) ),
c_0_64 ).
cnf(c_0_72,negated_conjecture,
( nil != sk3
| nil = sk4 ),
inference(fof_simplification,[status(thm)],[co1_11]) ).
cnf(c_0_73,negated_conjecture,
( ~ ssList(X4)
| ~ ssList(X1)
| ~ ssItem(X3)
| ~ ssItem(X2)
| ~ lt(X2,X3)
| app(cons(X3,nil),X4) != sk5
| app(X1,cons(X2,nil)) != sk1 ),
inference(rw,[status(thm)],[c_0_65,c_0_30]) ).
cnf(c_0_74,negated_conjecture,
( nil = sk1
| app(sk9(sk5),cons(sk8(sk5),nil)) = sk1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_43]),c_0_44])]) ).
cnf(c_0_75,negated_conjecture,
( ssList(sk9(sk5))
| nil = sk1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_43]),c_0_44])]) ).
cnf(c_0_76,negated_conjecture,
( ssItem(sk8(sk5))
| nil = sk1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_43]),c_0_44])]) ).
cnf(c_0_77,negated_conjecture,
( ~ ssList(cons(sk6(sk5),nil))
| nil = sk1
| app(cons(sk6(sk5),nil),skaf45(sk5,cons(sk6(sk5),nil))) = sk5 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_44])]) ).
cnf(c_0_78,negated_conjecture,
( ~ ssList(X1)
| app(sk1,X1) != sk4
| lt(sk8(X1),sk6(X1))
| nil = sk1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_71,c_0_35]),c_0_36])]) ).
cnf(c_0_79,negated_conjecture,
( nil != sk2
| ~ strictorderedP(sk1)
| app(sk1,X1) != sk2
| ~ ssList(X1)
| app(sk9(X1),cons(sk8(X1),nil)) = sk1 ),
inference(fof_simplification,[status(thm)],[co1_24]) ).
cnf(c_0_80,negated_conjecture,
( nil != sk3
| nil = sk4 ),
c_0_72 ).
cnf(c_0_81,negated_conjecture,
( ~ ssList(X2)
| ~ ssItem(X1)
| ~ lt(sk8(sk5),X1)
| app(cons(X1,nil),X2) != sk5
| nil = sk1 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_74]),c_0_75]),c_0_76]) ).
cnf(c_0_82,negated_conjecture,
( nil = sk1
| app(cons(sk6(sk5),nil),skaf45(sk5,cons(sk6(sk5),nil))) = sk5 ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_61]),c_0_62])]),c_0_63]) ).
cnf(c_0_83,axiom,
ssList(skaf45(X1,X2)),
clause51 ).
cnf(c_0_84,negated_conjecture,
( lt(sk8(sk5),sk6(sk5))
| nil = sk1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_43]),c_0_44])]) ).
cnf(c_0_85,negated_conjecture,
( nil != sk2
| ~ strictorderedP(sk1)
| app(sk1,X1) != sk2
| ~ ssList(X1)
| ssItem(sk8(X1)) ),
inference(fof_simplification,[status(thm)],[co1_22]) ).
cnf(c_0_86,negated_conjecture,
( nil != sk2
| ~ strictorderedP(sk1)
| app(sk1,X1) != sk2
| ~ ssList(X1)
| ssList(sk9(X1)) ),
inference(fof_simplification,[status(thm)],[co1_23]) ).
cnf(c_0_87,plain,
( ~ ssItem(X1)
| ~ ssItem(X2)
| ~ ssList(X3)
| X1 != X2
| memberP(cons(X2,X3),X1) ),
inference(fof_simplification,[status(thm)],[clause138]) ).
cnf(c_0_88,negated_conjecture,
( nil != sk2
| ~ strictorderedP(sk1)
| app(sk1,X1) != sk2
| ~ ssList(X1)
| app(sk9(X1),cons(sk8(X1),nil)) = sk1 ),
c_0_79 ).
cnf(c_0_89,negated_conjecture,
( nil != sk1
| nil = sk4 ),
inference(rw,[status(thm)],[c_0_80,c_0_30]) ).
cnf(c_0_90,negated_conjecture,
nil = sk1,
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_82]),c_0_83])]),c_0_63]),c_0_84]) ).
cnf(c_0_91,plain,
( ~ ssList(X1)
| app(X1,nil) = X1 ),
inference(fof_simplification,[status(thm)],[clause73]) ).
cnf(c_0_92,negated_conjecture,
( nil != sk2
| ~ strictorderedP(sk1)
| app(sk1,X1) != sk2
| ~ ssList(X1)
| ssItem(sk8(X1)) ),
c_0_85 ).
cnf(c_0_93,negated_conjecture,
( nil != sk2
| ~ strictorderedP(sk1)
| app(sk1,X1) != sk2
| ~ ssList(X1)
| ssList(sk9(X1)) ),
c_0_86 ).
cnf(c_0_94,plain,
( ~ ssItem(X2)
| ~ ssList(X3)
| ~ ssList(X1)
| ~ memberP(X1,X2)
| memberP(app(X3,X1),X2) ),
inference(fof_simplification,[status(thm)],[clause141]) ).
cnf(c_0_95,plain,
( ~ ssItem(X1)
| ~ ssItem(X2)
| ~ ssList(X3)
| X1 != X2
| memberP(cons(X2,X3),X1) ),
c_0_87 ).
cnf(c_0_96,negated_conjecture,
( ~ ssList(X1)
| nil != sk4
| app(sk1,X1) != sk4
| app(sk9(X1),cons(sk8(X1),nil)) = sk1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_88,c_0_35]),c_0_35]),c_0_36])]) ).
cnf(c_0_97,negated_conjecture,
sk4 = sk1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_89,c_0_90]),c_0_90])]) ).
cnf(c_0_98,plain,
( ~ ssList(X1)
| app(X1,nil) = X1 ),
c_0_91 ).
cnf(c_0_99,negated_conjecture,
( ~ ssList(X1)
| nil != sk4
| app(sk1,X1) != sk4
| ssItem(sk8(X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_92,c_0_35]),c_0_35]),c_0_36])]) ).
cnf(c_0_100,negated_conjecture,
( ~ ssList(X1)
| nil != sk4
| app(sk1,X1) != sk4
| ssList(sk9(X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_93,c_0_35]),c_0_35]),c_0_36])]) ).
cnf(c_0_101,plain,
( ~ ssItem(X1)
| ~ memberP(nil,X1) ),
inference(fof_simplification,[status(thm)],[clause71]) ).
cnf(c_0_102,plain,
( ~ ssItem(X2)
| ~ ssList(X3)
| ~ ssList(X1)
| ~ memberP(X1,X2)
| memberP(app(X3,X1),X2) ),
c_0_94 ).
cnf(c_0_103,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| memberP(cons(X1,X2),X1) ),
inference(er,[status(thm)],[c_0_95]) ).
cnf(c_0_104,negated_conjecture,
( ~ ssList(X1)
| app(sk1,X1) != sk1
| app(sk9(X1),cons(sk8(X1),sk1)) = sk1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_96,c_0_90]),c_0_90]),c_0_97]),c_0_97])]) ).
cnf(c_0_105,plain,
( ~ ssList(X1)
| app(X1,sk1) = X1 ),
inference(rw,[status(thm)],[c_0_98,c_0_90]) ).
cnf(c_0_106,negated_conjecture,
ssList(sk1),
co1_1 ).
cnf(c_0_107,negated_conjecture,
( ~ ssList(X1)
| app(sk1,X1) != sk1
| ssItem(sk8(X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_99,c_0_90]),c_0_97]),c_0_97])]) ).
cnf(c_0_108,negated_conjecture,
( ~ ssList(X1)
| app(sk1,X1) != sk1
| ssList(sk9(X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_100,c_0_90]),c_0_97]),c_0_97])]) ).
cnf(c_0_109,plain,
( ~ ssItem(X1)
| ~ memberP(nil,X1) ),
c_0_101 ).
cnf(c_0_110,plain,
( ~ ssList(X3)
| ~ ssList(X1)
| ~ ssItem(X2)
| memberP(app(X1,cons(X2,X3)),X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_103]),c_0_61]) ).
cnf(c_0_111,negated_conjecture,
app(sk9(sk1),cons(sk8(sk1),sk1)) = sk1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_105]),c_0_106])]) ).
cnf(c_0_112,negated_conjecture,
ssItem(sk8(sk1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_105]),c_0_106])]) ).
cnf(c_0_113,negated_conjecture,
ssList(sk9(sk1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_105]),c_0_106])]) ).
cnf(c_0_114,plain,
( ~ ssItem(X1)
| ~ memberP(sk1,X1) ),
inference(rw,[status(thm)],[c_0_109,c_0_90]) ).
cnf(c_0_115,negated_conjecture,
memberP(sk1,sk8(sk1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_111]),c_0_112]),c_0_113]),c_0_106])]) ).
cnf(c_0_116,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_115]),c_0_112])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWC343-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.18/0.44 % Computer : n003.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.45 % CPULimit : 300
% 0.18/0.45 % WCLimit : 300
% 0.18/0.45 % DateTime : Mon Sep 21 08:19:00 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.45 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.28/0.52 Running first-order theorem proving
% 0.28/0.52 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
% 6.11/1.44 % Version: 3.5.1
% 6.11/1.44 % Preprocessing class: FSLSSMSMSSSNFFN.
% 6.11/1.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 6.11/1.44 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 6.11/1.44 % Starting new_bool_3 with 300s (1) cores
% 6.11/1.44 % Starting new_bool_1 with 300s (1) cores
% 6.11/1.44 % Starting sh5l with 300s (1) cores
% 6.11/1.44 % C07_19_nc_SOS_SAT001_MinMin_p005000_rr with pid 3836309 completed with status 0
% 6.11/1.44 % Result found by C07_19_nc_SOS_SAT001_MinMin_p005000_rr
% 6.11/1.44 % Preprocessing class: FSLSSMSMSSSNFFN.
% 6.11/1.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 6.11/1.44 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 6.11/1.44 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 6.11/1.44 % No SInE strategy applied
% 6.11/1.44 % Search class: FGHSM-FSLM21-MFFFFFNN
% 6.11/1.44 % Scheduled 10 strats onto 5 cores with 1500 seconds (1500 total)
% 6.11/1.44 % Starting SubtermCWHack with 136s (1) cores
% 6.11/1.44 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 6.11/1.44 % Starting G-E--_107_C45_F1_PI_AE_Q7_CS_SP_PS_S0Y with 136s (1) cores
% 6.11/1.44 % Starting G-E--_200_B02_F1_SE_CS_SP_PI_S2k with 136s (1) cores
% 6.11/1.44 % Starting G-E--_301_C18_F1_URBAN_S5PRR_RG_S04BN with 136s (1) cores
% 6.11/1.44 % G-E--_200_B02_F1_SE_CS_SP_PI_S2k with pid 3836319 completed with status 0
% 6.11/1.44 % Result found by G-E--_200_B02_F1_SE_CS_SP_PI_S2k
% 6.11/1.44 % Preprocessing class: FSLSSMSMSSSNFFN.
% 6.11/1.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 6.11/1.44 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 6.11/1.44 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 6.11/1.44 % No SInE strategy applied
% 6.11/1.44 % Search class: FGHSM-FSLM21-MFFFFFNN
% 6.11/1.44 % Scheduled 10 strats onto 5 cores with 1500 seconds (1500 total)
% 6.11/1.44 % Starting SubtermCWHack with 136s (1) cores
% 6.11/1.44 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 6.11/1.44 % Starting G-E--_107_C45_F1_PI_AE_Q7_CS_SP_PS_S0Y with 136s (1) cores
% 6.11/1.44 % Starting G-E--_200_B02_F1_SE_CS_SP_PI_S2k with 136s (1) cores
% 6.11/1.44 % Preprocessing time : 0.005 s
% 6.11/1.44
% 6.11/1.44 % Proof found!
% 6.11/1.44 % SZS status Unsatisfiable
% 6.11/1.44 % SZS output start CNFRefutation
% See solution above
% 6.11/1.44 % Parsed axioms : 210
% 6.11/1.44 % Removed by relevancy pruning/SinE : 0
% 6.11/1.44 % Initial clauses : 210
% 6.11/1.44 % Removed in clause preprocessing : 0
% 6.11/1.44 % Initial clauses in saturation : 210
% 6.11/1.44 % Processed clauses : 4063
% 6.11/1.44 % ...of these trivial : 115
% 6.11/1.44 % ...subsumed : 2531
% 6.11/1.44 % ...remaining for further processing : 1417
% 6.11/1.44 % Other redundant clauses eliminated : 621
% 6.11/1.44 % Clauses deleted for lack of memory : 0
% 6.11/1.44 % Backward-subsumed : 75
% 6.11/1.44 % Backward-rewritten : 830
% 6.11/1.44 % Generated clauses : 16190
% 6.11/1.44 % ...of the previous two non-redundant : 14635
% 6.11/1.44 % ...aggressively subsumed : 0
% 6.11/1.44 % Contextual simplify-reflections : 334
% 6.11/1.44 % Paramodulations : 15560
% 6.11/1.44 % Factorizations : 1
% 6.11/1.44 % NegExts : 0
% 6.11/1.44 % Equation resolutions : 630
% 6.11/1.44 % Disequality decompositions : 0
% 6.11/1.44 % Total rewrite steps : 17913
% 6.11/1.44 % ...of those cached : 17600
% 6.11/1.44 % Propositional unsat checks : 0
% 6.11/1.44 % Propositional check models : 0
% 6.11/1.44 % Propositional check unsatisfiable : 0
% 6.11/1.44 % Propositional clauses : 0
% 6.11/1.44 % Propositional clauses after purity: 0
% 6.11/1.44 % Propositional unsat core size : 0
% 6.11/1.44 % Propositional preprocessing time : 0.000
% 6.11/1.44 % Propositional encoding time : 0.000
% 6.11/1.44 % Propositional solver time : 0.000
% 6.11/1.44 % Success case prop preproc time : 0.000
% 6.11/1.44 % Success case prop encoding time : 0.000
% 6.11/1.44 % Success case prop solver time : 0.000
% 6.11/1.44 % Current number of processed clauses : 489
% 6.11/1.44 % Positive orientable unit clauses : 77
% 6.11/1.44 % Positive unorientable unit clauses: 0
% 6.11/1.44 % Negative unit clauses : 7
% 6.11/1.44 % Non-unit-clauses : 405
% 6.11/1.44 % Current number of unprocessed clauses: 9595
% 6.11/1.44 % ...number of literals in the above : 56345
% 6.11/1.44 % Current number of archived formulas : 0
% 6.11/1.44 % Current number of archived clauses : 905
% 6.11/1.44 % Clause-clause subsumption calls (NU) : 241376
% 6.11/1.44 % Rec. Clause-clause subsumption calls : 76395
% 6.11/1.44 % Non-unit clause-clause subsumptions : 2242
% 6.11/1.44 % Unit Clause-clause subsumption calls : 8299
% 6.11/1.44 % Rewrite failures with RHS unbound : 0
% 6.11/1.44 % BW rewrite match attempts : 32
% 6.11/1.44 % BW rewrite match successes : 31
% 6.11/1.44 % Condensation attempts : 0
% 6.11/1.44 % Condensation successes : 0
% 6.11/1.44 % Termbank termtop insertions : 322002
% 6.11/1.44 % Search garbage collected termcells : 597
% 6.11/1.44
% 6.11/1.44 % -------------------------------------------------
% 6.11/1.44 % User time : 0.850 s
% 6.11/1.44 % System time : 0.021 s
% 6.11/1.44 % Total time : 0.871 s
% 6.11/1.44 % Maximum resident set size: 4080 pages
% 6.11/1.44
% 6.11/1.44 % -------------------------------------------------
% 6.11/1.44 % User time : 4.212 s
% 6.11/1.44 % System time : 0.159 s
% 6.11/1.44 % Total time : 4.371 s
% 6.11/1.44 % Maximum resident set size: 5120 pages
% 6.11/1.44 % E exiting
%------------------------------------------------------------------------------