%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SWX201-1 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n002.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 03:14:44 PM UTC 2026
% Result : Unsatisfiable 260.23s 46.77s
% Output : CNFRefutation 260.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 31
% Syntax : Number of clauses : 108 ( 108 unt; 0 nHn; 11 RR)
% Number of literals : 108 ( 107 equ; 4 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 12 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 22 ( 22 usr; 4 con; 0-5 aty)
% Number of variables : 241 ( 36 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(axiom_024,axiom,
msort(cons(X1,cons(X2,X3))) = aux3(X1,X2,X3,splitAtNat(div2(lengthNat(cons(X1,cons(X2,X3)))),cons(X1,cons(X2,X3)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_024) ).
cnf(axiom_016,axiom,
lengthNat(cons(X1,X2)) = s(lengthNat(X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_016) ).
cnf(axiom_021,axiom,
div2(s(s(X1))) = s(div2(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_021) ).
cnf(axiom,axiom,
aux(X1,X2,X3,pair2(X4,X5)) = pair2(cons(X2,X4),X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom) ).
cnf(axiom_006,axiom,
splitAtNat(z,X1) = pair2(nil,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_006) ).
cnf(axiom_008,axiom,
splitAtNat(s(X1),cons(X2,X3)) = aux(X1,X2,X3,splitAtNat(X1,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_008) ).
cnf(axiom_015,axiom,
lengthNat(nil) = z,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_015) ).
cnf(axiom_019,axiom,
div2(z) = z,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_019) ).
cnf(axiom_003,axiom,
aux3(X1,X2,X3,pair2(X4,X5)) = merge(msort(X4),msort(X5)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_003) ).
cnf(axiom_023,axiom,
msort(cons(X1,nil)) = cons(X1,nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_023) ).
cnf(axiom_014,axiom,
merge(cons(X1,X2),cons(X3,X4)) = aux2(X1,X2,X3,X4,leqNat(X1,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_014) ).
cnf(axiom_009,axiom,
leqNat(z,X1) = btrue,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_009) ).
cnf(axiom_001,axiom,
aux2(X1,X2,X3,X4,btrue) = cons(X1,merge(X2,cons(X3,X4))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_001) ).
cnf(axiom_011,axiom,
leqNat(s(X1),s(X2)) = leqNat(X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_011) ).
cnf(axiom_012,axiom,
merge(nil,X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_012) ).
cnf(axiom_010,axiom,
leqNat(s(X1),z) = bfalse,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_010) ).
cnf(axiom_002,axiom,
aux2(X1,X2,X3,X4,bfalse) = cons(X3,merge(cons(X1,X2),X4)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_002) ).
cnf(axiom_020,axiom,
div2(s(z)) = z,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_020) ).
cnf(axiom_026,axiom,
count(X1,cons(X2,X3)) = aux4(X1,X2,X3,eq(X2,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_026) ).
cnf(axiom_033,axiom,
eq(X1,X1) = btrue,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_033) ).
cnf(axiom_004,axiom,
aux4(X1,X2,X3,btrue) = s(count(X1,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_004) ).
cnf(axiom_027,axiom,
prop_msort_permutation_wrong1(X1,X2) = impl(eq2(leqNat(count(X2,X1),s(s(s(s(s(z)))))),bfalse),eq(count(X2,X1),count(s(X2),msort(X1)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_027) ).
cnf(axiom_013,axiom,
merge(cons(X1,X2),nil) = cons(X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_013) ).
cnf(axiom_032,axiom,
eq(s(X1),z) = bfalse,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_032) ).
cnf(axiom_005,axiom,
aux4(X1,X2,X3,bfalse) = count(X1,X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_005) ).
cnf(axiom_031,axiom,
eq(z,s(X1)) = bfalse,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_031) ).
cnf(goal,negated_conjecture,
eq2(prop_msort_permutation_wrong1(X1,X2),bfalse) != btrue,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal) ).
cnf(axiom_025,axiom,
count(X1,nil) = z,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_025) ).
cnf(axiom_034,axiom,
eq2(X1,X1) = btrue,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_034) ).
cnf(axiom_030,axiom,
eq(s(X1),s(X2)) = eq(X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_030) ).
cnf(axiom_017,axiom,
impl(btrue,X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_017) ).
cnf(c_0_31,axiom,
msort(cons(X1,cons(X2,X3))) = aux3(X1,X2,X3,splitAtNat(div2(lengthNat(cons(X1,cons(X2,X3)))),cons(X1,cons(X2,X3)))),
axiom_024 ).
cnf(c_0_32,axiom,
lengthNat(cons(X1,X2)) = s(lengthNat(X2)),
axiom_016 ).
cnf(c_0_33,axiom,
div2(s(s(X1))) = s(div2(X1)),
axiom_021 ).
cnf(c_0_34,axiom,
aux(X1,X2,X3,pair2(X4,X5)) = pair2(cons(X2,X4),X5),
axiom ).
cnf(c_0_35,axiom,
splitAtNat(z,X1) = pair2(nil,X1),
axiom_006 ).
cnf(c_0_36,plain,
aux3(X1,X2,X3,splitAtNat(s(div2(lengthNat(X3))),cons(X1,cons(X2,X3)))) = msort(cons(X1,cons(X2,X3))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_31,c_0_32]),c_0_32]),c_0_33]) ).
cnf(c_0_37,plain,
aux(X1,X2,X3,splitAtNat(z,X4)) = pair2(cons(X2,nil),X4),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_38,axiom,
splitAtNat(s(X1),cons(X2,X3)) = aux(X1,X2,X3,splitAtNat(X1,X3)),
axiom_008 ).
cnf(c_0_39,plain,
aux3(X1,X2,cons(X3,X4),splitAtNat(s(div2(s(lengthNat(X4)))),cons(X1,cons(X2,cons(X3,X4))))) = msort(cons(X1,cons(X2,cons(X3,X4)))),
inference(spm,[status(thm)],[c_0_36,c_0_32]) ).
cnf(c_0_40,plain,
splitAtNat(s(z),cons(X1,X2)) = pair2(cons(X1,nil),X2),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_41,axiom,
lengthNat(nil) = z,
axiom_015 ).
cnf(c_0_42,axiom,
div2(z) = z,
axiom_019 ).
cnf(c_0_43,axiom,
aux3(X1,X2,X3,pair2(X4,X5)) = merge(msort(X4),msort(X5)),
axiom_003 ).
cnf(c_0_44,axiom,
msort(cons(X1,nil)) = cons(X1,nil),
axiom_023 ).
cnf(c_0_45,axiom,
merge(cons(X1,X2),cons(X3,X4)) = aux2(X1,X2,X3,X4,leqNat(X1,X3)),
axiom_014 ).
cnf(c_0_46,axiom,
leqNat(z,X1) = btrue,
axiom_009 ).
cnf(c_0_47,axiom,
aux2(X1,X2,X3,X4,btrue) = cons(X1,merge(X2,cons(X3,X4))),
axiom_001 ).
cnf(c_0_48,axiom,
leqNat(s(X1),s(X2)) = leqNat(X1,X2),
axiom_011 ).
cnf(c_0_49,plain,
aux3(X1,X2,cons(X3,cons(X4,X5)),splitAtNat(s(s(div2(lengthNat(X5)))),cons(X1,cons(X2,cons(X3,cons(X4,X5)))))) = msort(cons(X1,cons(X2,cons(X3,cons(X4,X5))))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_32]),c_0_33]) ).
cnf(c_0_50,plain,
splitAtNat(s(s(z)),cons(X1,cons(X2,X3))) = pair2(cons(X1,cons(X2,nil)),X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_40]),c_0_34]) ).
cnf(c_0_51,plain,
merge(cons(X1,nil),cons(X2,nil)) = msort(cons(X1,cons(X2,nil))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_41]),c_0_42]),c_0_40]),c_0_43]),c_0_44]),c_0_44]) ).
cnf(c_0_52,plain,
merge(cons(z,X1),cons(X2,X3)) = cons(z,merge(X1,cons(X2,X3))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_47]) ).
cnf(c_0_53,axiom,
merge(nil,X1) = X1,
axiom_012 ).
cnf(c_0_54,plain,
aux2(s(X1),X2,s(X3),X4,leqNat(X1,X3)) = merge(cons(s(X1),X2),cons(s(X3),X4)),
inference(spm,[status(thm)],[c_0_45,c_0_48]) ).
cnf(c_0_55,plain,
merge(msort(cons(X1,cons(X2,nil))),msort(cons(X3,cons(X4,nil)))) = msort(cons(X1,cons(X2,cons(X3,cons(X4,nil))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_41]),c_0_42]),c_0_50]),c_0_43]) ).
cnf(c_0_56,plain,
msort(cons(z,cons(X1,nil))) = cons(z,cons(X1,nil)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_53]) ).
cnf(c_0_57,plain,
merge(cons(s(z),X1),cons(s(X2),X3)) = cons(s(z),merge(X1,cons(s(X2),X3))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_46]),c_0_47]) ).
cnf(c_0_58,axiom,
leqNat(s(X1),z) = bfalse,
axiom_010 ).
cnf(c_0_59,axiom,
aux2(X1,X2,X3,X4,bfalse) = cons(X3,merge(cons(X1,X2),X4)),
axiom_002 ).
cnf(c_0_60,axiom,
div2(s(z)) = z,
axiom_020 ).
cnf(c_0_61,axiom,
count(X1,cons(X2,X3)) = aux4(X1,X2,X3,eq(X2,X1)),
axiom_026 ).
cnf(c_0_62,axiom,
eq(X1,X1) = btrue,
axiom_033 ).
cnf(c_0_63,axiom,
aux4(X1,X2,X3,btrue) = s(count(X1,X3)),
axiom_004 ).
cnf(c_0_64,plain,
merge(msort(cons(X1,cons(X2,nil))),cons(z,cons(X3,nil))) = msort(cons(X1,cons(X2,cons(z,cons(X3,nil))))),
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_65,plain,
msort(cons(s(z),cons(s(X1),nil))) = cons(s(z),cons(s(X1),nil)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_57]),c_0_53]) ).
cnf(c_0_66,plain,
merge(cons(s(X1),X2),cons(z,X3)) = cons(z,merge(cons(s(X1),X2),X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_58]),c_0_59]) ).
cnf(c_0_67,plain,
merge(cons(X1,nil),msort(cons(X2,cons(X3,nil)))) = msort(cons(X1,cons(X2,cons(X3,nil)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_41]),c_0_60]),c_0_40]),c_0_43]),c_0_44]) ).
cnf(c_0_68,axiom,
prop_msort_permutation_wrong1(X1,X2) = impl(eq2(leqNat(count(X2,X1),s(s(s(s(s(z)))))),bfalse),eq(count(X2,X1),count(s(X2),msort(X1)))),
axiom_027 ).
cnf(c_0_69,plain,
count(X1,cons(X1,X2)) = s(count(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_63]) ).
cnf(c_0_70,plain,
cons(z,merge(cons(s(z),cons(s(X1),nil)),cons(X2,nil))) = msort(cons(s(z),cons(s(X1),cons(z,cons(X2,nil))))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_65]),c_0_66]) ).
cnf(c_0_71,axiom,
merge(cons(X1,X2),nil) = cons(X1,X2),
axiom_013 ).
cnf(c_0_72,plain,
merge(cons(z,cons(X1,nil)),msort(cons(X2,cons(X3,nil)))) = msort(cons(z,cons(X1,cons(X2,cons(X3,nil))))),
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_73,plain,
merge(cons(X1,nil),cons(s(z),cons(s(X2),nil))) = msort(cons(X1,cons(s(z),cons(s(X2),nil)))),
inference(spm,[status(thm)],[c_0_67,c_0_65]) ).
cnf(c_0_74,plain,
impl(eq2(leqNat(count(X1,X2),s(s(s(s(z))))),bfalse),eq(s(count(X1,X2)),count(s(X1),msort(cons(X1,X2))))) = prop_msort_permutation_wrong1(cons(X1,X2),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_48]) ).
cnf(c_0_75,plain,
lengthNat(msort(cons(s(z),cons(s(X1),cons(z,cons(X2,nil)))))) = s(lengthNat(merge(cons(s(z),cons(s(X1),nil)),cons(X2,nil)))),
inference(spm,[status(thm)],[c_0_32,c_0_70]) ).
cnf(c_0_76,plain,
splitAtNat(s(s(s(z))),cons(X1,cons(X2,cons(X3,X4)))) = pair2(cons(X1,cons(X2,cons(X3,nil))),X4),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_50]),c_0_34]) ).
cnf(c_0_77,plain,
aux3(X1,X2,cons(X3,msort(cons(s(z),cons(s(X4),cons(z,cons(X5,nil)))))),splitAtNat(s(s(div2(lengthNat(merge(cons(s(z),cons(s(X4),nil)),cons(X5,nil)))))),cons(X1,cons(X2,cons(X3,msort(cons(s(z),cons(s(X4),cons(z,cons(X5,nil)))))))))) = msort(cons(X1,cons(X2,cons(X3,msort(cons(s(z),cons(s(X4),cons(z,cons(X5,nil))))))))),
inference(spm,[status(thm)],[c_0_49,c_0_70]) ).
cnf(c_0_78,plain,
msort(cons(s(z),cons(s(X1),cons(z,cons(z,nil))))) = cons(z,cons(z,cons(s(z),cons(s(X1),nil)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_66]),c_0_71]) ).
cnf(c_0_79,plain,
msort(cons(z,cons(X1,cons(s(z),cons(s(X2),nil))))) = cons(z,msort(cons(X1,cons(s(z),cons(s(X2),nil))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_65]),c_0_52]),c_0_73]) ).
cnf(c_0_80,plain,
msort(cons(z,cons(s(z),cons(s(X1),nil)))) = cons(z,cons(s(z),cons(s(X1),nil))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_73]),c_0_53]) ).
cnf(c_0_81,plain,
merge(cons(X1,nil),cons(z,cons(X2,nil))) = msort(cons(X1,cons(z,cons(X2,nil)))),
inference(spm,[status(thm)],[c_0_67,c_0_56]) ).
cnf(c_0_82,plain,
impl(eq2(leqNat(count(X1,X2),s(s(s(z)))),bfalse),eq(s(s(count(X1,X2))),count(s(X1),msort(cons(X1,cons(X1,X2)))))) = prop_msort_permutation_wrong1(cons(X1,cons(X1,X2)),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_69]),c_0_48]) ).
cnf(c_0_83,plain,
aux3(X1,X2,cons(X3,cons(X4,msort(cons(s(z),cons(s(X5),cons(z,cons(X6,nil))))))),splitAtNat(s(s(div2(s(lengthNat(merge(cons(s(z),cons(s(X5),nil)),cons(X6,nil))))))),cons(X1,cons(X2,cons(X3,cons(X4,msort(cons(s(z),cons(s(X5),cons(z,cons(X6,nil))))))))))) = msort(cons(X1,cons(X2,cons(X3,cons(X4,msort(cons(s(z),cons(s(X5),cons(z,cons(X6,nil)))))))))),
inference(spm,[status(thm)],[c_0_49,c_0_75]) ).
cnf(c_0_84,plain,
splitAtNat(s(s(s(s(z)))),cons(X1,cons(X2,cons(X3,cons(X4,X5))))) = pair2(cons(X1,cons(X2,cons(X3,cons(X4,nil)))),X5),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_76]),c_0_34]) ).
cnf(c_0_85,plain,
merge(msort(cons(X1,cons(X2,cons(X3,nil)))),cons(z,cons(z,cons(s(z),cons(s(X4),nil))))) = msort(cons(X1,cons(X2,cons(X3,cons(z,cons(z,cons(s(z),cons(s(X4),nil)))))))),
inference(rw,[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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78]),c_0_66]),c_0_71]),c_0_32]),c_0_32]),c_0_32]),c_0_41]),c_0_33]),c_0_60]),c_0_76]),c_0_43]),c_0_79]),c_0_80]) ).
cnf(c_0_86,plain,
msort(cons(z,cons(z,cons(X1,nil)))) = cons(z,cons(z,cons(X1,nil))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_81]),c_0_53]) ).
cnf(c_0_87,plain,
impl(eq2(leqNat(count(X1,X2),s(s(z))),bfalse),eq(s(s(s(count(X1,X2)))),count(s(X1),msort(cons(X1,cons(X1,cons(X1,X2))))))) = prop_msort_permutation_wrong1(cons(X1,cons(X1,cons(X1,X2))),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_69]),c_0_48]) ).
cnf(c_0_88,plain,
merge(msort(cons(X1,cons(X2,cons(X3,cons(X4,nil))))),cons(z,cons(z,cons(s(z),cons(s(X5),nil))))) = msort(cons(X1,cons(X2,cons(X3,cons(X4,cons(z,cons(z,cons(s(z),cons(s(X5),nil))))))))),
inference(rw,[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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_78]),c_0_66]),c_0_71]),c_0_32]),c_0_32]),c_0_32]),c_0_41]),c_0_33]),c_0_33]),c_0_42]),c_0_84]),c_0_43]),c_0_79]),c_0_80]) ).
cnf(c_0_89,plain,
msort(cons(z,cons(X1,cons(z,cons(X2,nil))))) = cons(z,msort(cons(X1,cons(z,cons(X2,nil))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_56]),c_0_52]),c_0_81]) ).
cnf(c_0_90,axiom,
eq(s(X1),z) = bfalse,
axiom_032 ).
cnf(c_0_91,axiom,
aux4(X1,X2,X3,bfalse) = count(X1,X3),
axiom_005 ).
cnf(c_0_92,plain,
cons(z,cons(z,merge(cons(X1,nil),cons(z,cons(z,cons(s(z),cons(s(X2),nil))))))) = msort(cons(z,cons(z,cons(X1,cons(z,cons(z,cons(s(z),cons(s(X2),nil)))))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_86]),c_0_52]),c_0_52]) ).
cnf(c_0_93,axiom,
eq(z,s(X1)) = bfalse,
axiom_031 ).
cnf(c_0_94,negated_conjecture,
eq2(prop_msort_permutation_wrong1(X1,X2),bfalse) != btrue,
inference(fof_simplification,[status(thm)],[goal]) ).
cnf(c_0_95,plain,
impl(eq2(leqNat(count(X1,X2),s(z)),bfalse),eq(s(s(s(s(count(X1,X2))))),count(s(X1),msort(cons(X1,cons(X1,cons(X1,cons(X1,X2)))))))) = prop_msort_permutation_wrong1(cons(X1,cons(X1,cons(X1,cons(X1,X2)))),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_69]),c_0_48]) ).
cnf(c_0_96,plain,
msort(cons(z,cons(X1,cons(z,cons(X2,cons(z,cons(z,cons(s(z),cons(s(X3),nil))))))))) = cons(z,msort(cons(X1,cons(z,cons(X2,cons(z,cons(z,cons(s(z),cons(s(X3),nil))))))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_89]),c_0_52]),c_0_85]) ).
cnf(c_0_97,plain,
count(z,cons(s(X1),X2)) = count(z,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_90]),c_0_91]) ).
cnf(c_0_98,axiom,
count(X1,nil) = z,
axiom_025 ).
cnf(c_0_99,axiom,
eq2(X1,X1) = btrue,
axiom_034 ).
cnf(c_0_100,plain,
msort(cons(z,cons(z,cons(z,cons(z,cons(z,cons(s(z),cons(s(X1),nil)))))))) = cons(z,cons(z,cons(z,cons(z,cons(z,cons(s(z),cons(s(X1),nil))))))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_52]),c_0_53]) ).
cnf(c_0_101,plain,
count(s(X1),cons(z,X2)) = count(s(X1),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_93]),c_0_91]) ).
cnf(c_0_102,axiom,
eq(s(X1),s(X2)) = eq(X1,X2),
axiom_030 ).
cnf(c_0_103,axiom,
impl(btrue,X1) = X1,
axiom_017 ).
cnf(c_0_104,negated_conjecture,
eq2(prop_msort_permutation_wrong1(X1,X2),bfalse) != btrue,
c_0_94 ).
cnf(c_0_105,plain,
prop_msort_permutation_wrong1(cons(z,cons(z,cons(z,cons(z,cons(z,cons(z,cons(s(z),cons(s(X1),nil)))))))),z) = eq(s(s(s(s(s(z))))),count(s(z),cons(s(X1),nil))),
inference(rw,[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)],[inference(rw,[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)],[inference(rw,[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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_96]),c_0_69]),c_0_69]),c_0_97]),c_0_97]),c_0_98]),c_0_48]),c_0_58]),c_0_99]),c_0_69]),c_0_69]),c_0_97]),c_0_97]),c_0_98]),c_0_100]),c_0_101]),c_0_101]),c_0_101]),c_0_101]),c_0_101]),c_0_101]),c_0_69]),c_0_102]),c_0_103]) ).
cnf(c_0_106,negated_conjecture,
eq2(eq(s(s(s(s(s(z))))),count(s(z),cons(s(X1),nil))),bfalse) != btrue,
inference(spm,[status(thm)],[c_0_104,c_0_105]) ).
cnf(c_0_107,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_69]),c_0_98]),c_0_102]),c_0_90]),c_0_99])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWX201-1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.56 % Computer : n002.cluster.edu
% 0.11/0.56 % Model : x86_64 x86_64
% 0.11/0.56 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.56 % Memory : 8046.5625MB
% 0.11/0.56 % OS : Linux 6.8.0-71-generic
% 0.11/0.56 % CPULimit : 300
% 0.11/0.56 % WCLimit : 300
% 0.11/0.56 % DateTime : Mon Sep 21 10:36:17 UTC 2026
% 0.11/0.56 % CPUTime :
% 0.11/0.56 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.60 Running first-order theorem proving
% 0.14/0.60 Running: /export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p
% 260.23/46.77 % Version: 3.5.1
% 260.23/46.77 % Preprocessing class: FSMSSMSSSSSNFFN.
% 260.23/46.77 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 260.23/46.77 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 260.23/46.77 % Starting new_bool_3 with 300s (1) cores
% 260.23/46.77 % Starting new_bool_1 with 300s (1) cores
% 260.23/46.77 % Starting sh5l with 300s (1) cores
% 260.23/46.77 % new_bool_3 with pid 3074253 completed with status 9
% 260.23/46.77 % new_bool_1 with pid 3074254 completed with status 9
% 260.23/46.77 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 3074252 completed with status 0
% 260.23/46.77 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 260.23/46.77 % Preprocessing class: FSMSSMSSSSSNFFN.
% 260.23/46.77 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 260.23/46.77 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 260.23/46.77 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 260.23/46.77 % No SInE strategy applied
% 260.23/46.77 % Search class: FUUPM-FFMM32-DFFFFFNN
% 260.23/46.77 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 260.23/46.77 % Starting SubtermCWHack with 136s (1) cores
% 260.23/46.77 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 260.23/46.77 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 260.23/46.77 % Starting new_bool_3 with 136s (1) cores
% 260.23/46.77 % Starting new_bool_1 with 136s (1) cores
% 260.23/46.77 % new_bool_1 with pid 3074260 completed with status 0
% 260.23/46.77 % Result found by new_bool_1
% 260.23/46.77 % Preprocessing class: FSMSSMSSSSSNFFN.
% 260.23/46.77 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 260.23/46.77 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 260.23/46.77 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 260.23/46.77 % No SInE strategy applied
% 260.23/46.77 % Search class: FUUPM-FFMM32-DFFFFFNN
% 260.23/46.77 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 260.23/46.77 % Starting SubtermCWHack with 136s (1) cores
% 260.23/46.77 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 260.23/46.77 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 260.23/46.77 % Starting new_bool_3 with 136s (1) cores
% 260.23/46.77 % Starting new_bool_1 with 136s (1) cores
% 260.23/46.77 % Preprocessing time : 0.001 s
% 260.23/46.77 % Presaturation interreduction done
% 260.23/46.77
% 260.23/46.77 % Proof found!
% 260.23/46.77 % SZS status Unsatisfiable
% 260.23/46.77 % SZS output start CNFRefutation
% See solution above
% 260.23/46.77 % Parsed axioms : 36
% 260.23/46.77 % Removed by relevancy pruning/SinE : 0
% 260.23/46.77 % Initial clauses : 36
% 260.23/46.77 % Removed in clause preprocessing : 0
% 260.23/46.77 % Initial clauses in saturation : 36
% 260.23/46.77 % Processed clauses : 26596
% 260.23/46.77 % ...of these trivial : 6537
% 260.23/46.77 % ...subsumed : 8359
% 260.23/46.77 % ...remaining for further processing : 11700
% 260.23/46.77 % Other redundant clauses eliminated : 0
% 260.23/46.77 % Clauses deleted for lack of memory : 0
% 260.23/46.77 % Backward-subsumed : 0
% 260.23/46.77 % Backward-rewritten : 1390
% 260.23/46.77 % Generated clauses : 976130
% 260.23/46.77 % ...of the previous two non-redundant : 926740
% 260.23/46.77 % ...aggressively subsumed : 0
% 260.23/46.77 % Contextual simplify-reflections : 0
% 260.23/46.77 % Paramodulations : 976130
% 260.23/46.77 % Factorizations : 0
% 260.23/46.77 % NegExts : 0
% 260.23/46.77 % Equation resolutions : 0
% 260.23/46.77 % Disequality decompositions : 0
% 260.23/46.77 % Total rewrite steps : 516392
% 260.23/46.77 % ...of those cached : 427897
% 260.23/46.77 % Propositional unsat checks : 2
% 260.23/46.77 % Propositional check models : 2
% 260.23/46.77 % Propositional check unsatisfiable : 0
% 260.23/46.77 % Propositional clauses : 0
% 260.23/46.77 % Propositional clauses after purity: 0
% 260.23/46.77 % Propositional unsat core size : 0
% 260.23/46.77 % Propositional preprocessing time : 0.000
% 260.23/46.77 % Propositional encoding time : 8.958
% 260.23/46.77 % Propositional solver time : 0.075
% 260.23/46.77 % Success case prop preproc time : 0.000
% 260.23/46.77 % Success case prop encoding time : 0.000
% 260.23/46.77 % Success case prop solver time : 0.000
% 260.23/46.77 % Current number of processed clauses : 10274
% 260.23/46.77 % Positive orientable unit clauses : 10271
% 260.23/46.77 % Positive unorientable unit clauses: 0
% 260.23/46.77 % Negative unit clauses : 3
% 260.23/46.77 % Non-unit-clauses : 0
% 260.23/46.77 % Current number of unprocessed clauses: 898597
% 260.23/46.77 % ...number of literals in the above : 898597
% 260.23/46.77 % Current number of archived formulas : 0
% 260.23/46.77 % Current number of archived clauses : 1426
% 260.23/46.77 % Clause-clause subsumption calls (NU) : 0
% 260.23/46.77 % Rec. Clause-clause subsumption calls : 0
% 260.23/46.77 % Non-unit clause-clause subsumptions : 0
% 260.23/46.77 % Unit Clause-clause subsumption calls : 3
% 260.23/46.77 % Rewrite failures with RHS unbound : 0
% 260.23/46.77 % BW rewrite match attempts : 7097771
% 260.23/46.77 % BW rewrite match successes : 1289
% 260.23/46.77 % Condensation attempts : 0
% 260.23/46.77 % Condensation successes : 0
% 260.23/46.77 % Termbank termtop insertions : 86724125
% 260.23/46.77 % Search garbage collected termcells : 2
% 260.23/46.77
% 260.23/46.77 % -------------------------------------------------
% 260.23/46.77 % User time : 43.973 s
% 260.23/46.77 % System time : 1.444 s
% 260.23/46.77 % Total time : 45.418 s
% 260.23/46.77 % Maximum resident set size: 3404 pages
% 260.23/46.77
% 260.23/46.77 % -------------------------------------------------
% 260.23/46.77 % User time : 222.084 s
% 260.23/46.77 % System time : 6.895 s
% 260.23/46.77 % Total time : 228.980 s
% 260.23/46.77 % Maximum resident set size: 4608 pages
% 260.23/46.77 % E exiting
%------------------------------------------------------------------------------