%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWX201-1 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n020.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 : Sun Sep 27 09:15:16 AM UTC 2026
% Result : Unsatisfiable 65.81s 15.93s
% Output : Refutation 65.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 36
% Syntax : Number of formulae : 117 ( 107 unt; 0 typ; 0 def)
% Number of atoms : 130 ( 129 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 602 ( 25 ~; 13 |; 0 &; 564 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 24 ( 22 usr; 5 con; 0-5 aty)
% Number of variables : 190 ( 0 ^; 190 !; 0 ?; 190 :)
% Comments :
%------------------------------------------------------------------------------
thf(eq2_decl,type,
eq2: $i > $i > $i ).
thf(prop_msort_permutation_wrong1_decl,type,
prop_msort_permutation_wrong1: $i > $i > $i ).
thf(bfalse_decl,type,
bfalse: $i ).
thf(btrue_decl,type,
btrue: $i ).
thf(splitAtNat_decl,type,
splitAtNat: $i > $i > $i ).
thf(z_decl,type,
z: $i ).
thf(pair2_decl,type,
pair2: $i > $i > $i ).
thf(nil_decl,type,
nil: $i ).
thf(s_decl,type,
s: $i > $i ).
thf(count_decl,type,
count: $i > $i > $i ).
thf(div2_decl,type,
div2: $i > $i ).
thf(lengthNat_decl,type,
lengthNat: $i > $i ).
thf(leqNat_decl,type,
leqNat: $i > $i > $i ).
thf(cons_decl,type,
cons: $i > $i > $i ).
thf(aux4_decl,type,
aux4: $i > $i > $i > $i > $i ).
thf(eq_decl,type,
eq: $i > $i > $i ).
thf(aux_decl,type,
aux: $i > $i > $i > $i > $i ).
thf(merge_decl,type,
merge: $i > $i > $i ).
thf(aux2_decl,type,
aux2: $i > $i > $i > $i > $i > $i ).
thf(msort_decl,type,
msort: $i > $i ).
thf(aux3_decl,type,
aux3: $i > $i > $i > $i > $i ).
thf(impl_decl,type,
impl: $i > $i > $i ).
thf(10,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ cons ) @ ( A @ count ) )
= ( A @ ( B @ eq ) @ ( C @ ( B @ ( A @ aux4 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_026) ).
thf(56,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ cons ) @ ( A @ count ) )
= ( A @ ( B @ eq ) @ ( C @ ( B @ ( A @ aux4 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(8,axiom,
( ( z @ div2 )
= z ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_019) ).
thf(52,plain,
( ( z @ div2 )
= z ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(53,plain,
( ( z @ div2 )
= z ),
inference(lifteq,[status(thm)],[52]) ).
thf(2,axiom,
! [A: $i] :
( ( A @ ( z @ splitAtNat ) )
= ( A @ ( nil @ pair2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_006) ).
thf(40,plain,
! [A: $i] :
( ( A @ ( z @ splitAtNat ) )
= ( A @ ( nil @ pair2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(41,plain,
! [A: $i] :
( ( A @ ( nil @ pair2 ) )
= ( A @ ( z @ splitAtNat ) ) ),
inference(lifteq,[status(thm)],[40]) ).
thf(34,axiom,
! [A: $i] :
( ( z @ ( A @ s @ leqNat ) )
= bfalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_010) ).
thf(104,plain,
! [A: $i] :
( ( z @ ( A @ s @ leqNat ) )
= bfalse ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(105,plain,
! [A: $i] :
( ( z @ ( A @ s @ leqNat ) )
= bfalse ),
inference(lifteq,[status(thm)],[104]) ).
thf(4,axiom,
! [A: $i] :
( ( nil @ ( A @ count ) )
= z ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_025) ).
thf(44,plain,
! [A: $i] :
( ( nil @ ( A @ count ) )
= z ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(22,axiom,
( ( btrue @ ( bfalse @ eq2 ) )
= bfalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_028) ).
thf(80,plain,
( ( btrue @ ( bfalse @ eq2 ) )
= bfalse ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(7,axiom,
( ( nil @ lengthNat )
= z ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_015) ).
thf(50,plain,
( ( nil @ lengthNat )
= z ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(18,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ pair2 ) @ ( C @ ( B @ ( A @ aux3 ) ) ) )
= ( E @ msort @ ( D @ msort @ merge ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_003) ).
thf(72,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ pair2 ) @ ( C @ ( B @ ( A @ aux3 ) ) ) )
= ( E @ msort @ ( D @ msort @ merge ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(16,axiom,
! [B: $i,A: $i] :
( ( B @ s @ ( A @ s @ eq ) )
= ( B @ ( A @ eq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_030) ).
thf(68,plain,
! [B: $i,A: $i] :
( ( B @ s @ ( A @ s @ eq ) )
= ( B @ ( A @ eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(69,plain,
! [B: $i,A: $i] :
( ( B @ s @ ( A @ s @ eq ) )
= ( B @ ( A @ eq ) ) ),
inference(lifteq,[status(thm)],[68]) ).
thf(26,axiom,
! [C: $i,B: $i,A: $i] :
( ( btrue @ ( C @ ( B @ ( A @ aux4 ) ) ) )
= ( C @ ( A @ count ) @ s ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_004) ).
thf(88,plain,
! [C: $i,B: $i,A: $i] :
( ( btrue @ ( C @ ( B @ ( A @ aux4 ) ) ) )
= ( C @ ( A @ count ) @ s ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(31,axiom,
! [A: $i] :
( ( A @ ( btrue @ impl ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_017) ).
thf(98,plain,
! [A: $i] :
( ( A @ ( btrue @ impl ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(99,plain,
! [A: $i] :
( ( A @ ( btrue @ impl ) )
= A ),
inference(lifteq,[status(thm)],[98]) ).
thf(27,axiom,
! [A: $i] :
( ( A @ ( bfalse @ impl ) )
= btrue ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_018) ).
thf(90,plain,
! [A: $i] :
( ( A @ ( bfalse @ impl ) )
= btrue ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(91,plain,
! [A: $i] :
( ( A @ ( bfalse @ impl ) )
= btrue ),
inference(lifteq,[status(thm)],[90]) ).
thf(147,plain,
! [B: $i,A: $i] :
( ( ( A @ ( btrue @ impl ) )
!= ( B @ ( bfalse @ impl ) ) )
| ( A = btrue ) ),
inference(paramod_ordered,[status(thm)],[99,91]) ).
thf(149,plain,
! [B: $i,A: $i] :
( ( A != B )
| ( btrue != bfalse )
| ( A = btrue ) ),
inference(simp,[status(thm)],[147]) ).
thf(151,plain,
! [A: $i] :
( ( btrue != bfalse )
| ( A = btrue ) ),
inference(simp,[status(thm)],[149]) ).
thf(35,axiom,
! [A: $i] :
( ( A @ ( A @ eq2 ) )
= btrue ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_034) ).
thf(106,plain,
! [A: $i] :
( ( A @ ( A @ eq2 ) )
= btrue ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(107,plain,
! [A: $i] :
( ( A @ ( A @ eq2 ) )
= btrue ),
inference(lifteq,[status(thm)],[106]) ).
thf(1,negated_conjecture,
! [B: $i,A: $i] :
( ( bfalse @ ( B @ ( A @ prop_msort_permutation_wrong1 ) @ eq2 ) )
!= btrue ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goal) ).
thf(37,plain,
! [B: $i,A: $i] :
( ( bfalse @ ( B @ ( A @ prop_msort_permutation_wrong1 ) @ eq2 ) )
!= btrue ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(38,plain,
! [B: $i,A: $i] :
( ( bfalse @ ( B @ ( A @ prop_msort_permutation_wrong1 ) @ eq2 ) )
!= btrue ),
inference(polarity_switch,[status(thm)],[37]) ).
thf(39,plain,
! [B: $i,A: $i] :
( ( bfalse @ ( B @ ( A @ prop_msort_permutation_wrong1 ) @ eq2 ) )
!= btrue ),
inference(lifteq,[status(thm)],[38]) ).
thf(155,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ eq2 ) )
!= ( bfalse @ ( C @ ( B @ prop_msort_permutation_wrong1 ) @ eq2 ) ) )
| ( btrue != btrue ) ),
inference(paramod_ordered,[status(thm)],[107,39]) ).
thf(156,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ eq2 ) )
!= ( bfalse @ ( C @ ( B @ prop_msort_permutation_wrong1 ) @ eq2 ) ) ),
inference(simp,[status(thm)],[155]) ).
thf(161,plain,
! [C: $i,B: $i,A: $i] :
( ( A != bfalse )
| ( A
!= ( C @ ( B @ prop_msort_permutation_wrong1 ) ) ) ),
inference(simp,[status(thm)],[156]) ).
thf(165,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ prop_msort_permutation_wrong1 ) )
!= bfalse ),
inference(simp,[status(thm)],[161]) ).
thf(183,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( C @ ( B @ prop_msort_permutation_wrong1 ) ) )
| ( btrue != bfalse )
| ( btrue != bfalse ) ),
inference(paramod_ordered,[status(thm)],[151,165]) ).
thf(184,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( C @ ( B @ prop_msort_permutation_wrong1 ) ) )
| ( btrue != bfalse ) ),
inference(simp,[status(thm)],[183]) ).
thf(185,plain,
btrue != bfalse,
inference(pattern_uni,[status(thm)],[184:[bind(A,$thf( E @ ( D @ prop_msort_permutation_wrong1 ) )),bind(B,$thf( D )),bind(C,$thf( E ))]]) ).
thf(3,axiom,
! [A: $i] :
( ( nil @ ( A @ s @ splitAtNat ) )
= ( nil @ ( nil @ pair2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_007) ).
thf(42,plain,
! [A: $i] :
( ( nil @ ( A @ s @ splitAtNat ) )
= ( nil @ ( nil @ pair2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(5,axiom,
! [A: $i] :
( ( A @ s @ s @ div2 )
= ( A @ div2 @ s ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_021) ).
thf(46,plain,
! [A: $i] :
( ( A @ s @ s @ div2 )
= ( A @ div2 @ s ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(57,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ eq ) @ ( C @ ( B @ ( A @ aux4 ) ) ) )
= ( C @ ( B @ cons ) @ ( A @ count ) ) ),
inference(lifteq,[status(thm)],[56]) ).
thf(21,axiom,
( ( nil @ msort )
= nil ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_022) ).
thf(78,plain,
( ( nil @ msort )
= nil ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(24,axiom,
! [A: $i] :
( ( A @ s @ ( z @ eq ) )
= bfalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_031) ).
thf(84,plain,
! [A: $i] :
( ( A @ s @ ( z @ eq ) )
= bfalse ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(89,plain,
! [C: $i,B: $i,A: $i] :
( ( btrue @ ( C @ ( B @ ( A @ aux4 ) ) ) )
= ( C @ ( A @ count ) @ s ) ),
inference(lifteq,[status(thm)],[88]) ).
thf(19,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ cons ) @ lengthNat )
= ( B @ lengthNat @ s ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_016) ).
thf(74,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ cons ) @ lengthNat )
= ( B @ lengthNat @ s ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(30,axiom,
! [A: $i] :
( ( A @ ( z @ leqNat ) )
= btrue ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_009) ).
thf(96,plain,
! [A: $i] :
( ( A @ ( z @ leqNat ) )
= btrue ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(97,plain,
! [A: $i] :
( ( A @ ( z @ leqNat ) )
= btrue ),
inference(lifteq,[status(thm)],[96]) ).
thf(124,plain,
! [B: $i,A: $i] :
( ( ( z @ ( A @ s @ leqNat ) )
!= ( B @ ( z @ leqNat ) ) )
| ( btrue = bfalse ) ),
inference(paramod_ordered,[status(thm)],[105,97]) ).
thf(126,plain,
! [B: $i,A: $i] :
( ( z != B )
| ( ( A @ s )
!= z )
| ( btrue = bfalse ) ),
inference(simp,[status(thm)],[124]) ).
thf(128,plain,
! [A: $i] :
( ( ( A @ s )
!= z )
| ( btrue = bfalse ) ),
inference(simp,[status(thm)],[126]) ).
thf(307,plain,
! [A: $i] :
( ( A @ s )
!= z ),
inference(simplifyReflect,[status(thm)],[128,185]) ).
thf(12,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ cons ) @ ( B @ ( A @ cons ) @ merge ) )
= ( C @ ( A @ leqNat ) @ ( D @ ( C @ ( B @ ( A @ aux2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_014) ).
thf(60,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ cons ) @ ( B @ ( A @ cons ) @ merge ) )
= ( C @ ( A @ leqNat ) @ ( D @ ( C @ ( B @ ( A @ aux2 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(85,plain,
! [A: $i] :
( ( A @ s @ ( z @ eq ) )
= bfalse ),
inference(lifteq,[status(thm)],[84]) ).
thf(33,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( btrue @ ( D @ ( C @ ( B @ ( A @ aux2 ) ) ) ) )
= ( D @ ( C @ cons ) @ ( B @ merge ) @ ( A @ cons ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_001) ).
thf(102,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( btrue @ ( D @ ( C @ ( B @ ( A @ aux2 ) ) ) ) )
= ( D @ ( C @ cons ) @ ( B @ merge ) @ ( A @ cons ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(17,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ pair2 ) @ ( C @ ( B @ ( A @ aux ) ) ) )
= ( E @ ( D @ ( B @ cons ) @ pair2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom) ).
thf(70,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ pair2 ) @ ( C @ ( B @ ( A @ aux ) ) ) )
= ( E @ ( D @ ( B @ cons ) @ pair2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(28,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ prop_msort_permutation_wrong1 ) )
= ( A @ msort @ ( B @ s @ count ) @ ( A @ ( B @ count ) @ eq ) @ ( bfalse @ ( z @ s @ s @ s @ s @ s @ ( A @ ( B @ count ) @ leqNat ) @ eq2 ) @ impl ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_027) ).
thf(92,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ prop_msort_permutation_wrong1 ) )
= ( A @ msort @ ( B @ s @ count ) @ ( A @ ( B @ count ) @ eq ) @ ( bfalse @ ( z @ s @ s @ s @ s @ s @ ( A @ ( B @ count ) @ leqNat ) @ eq2 ) @ impl ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(14,axiom,
! [A: $i] :
( ( nil @ ( A @ cons ) @ msort )
= ( nil @ ( A @ cons ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_023) ).
thf(64,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ msort )
= ( nil @ ( A @ cons ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(65,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ msort )
= ( nil @ ( A @ cons ) ) ),
inference(lifteq,[status(thm)],[64]) ).
thf(36,axiom,
! [A: $i] :
( ( z @ ( A @ s @ eq ) )
= bfalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_032) ).
thf(108,plain,
! [A: $i] :
( ( z @ ( A @ s @ eq ) )
= bfalse ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(109,plain,
! [A: $i] :
( ( z @ ( A @ s @ eq ) )
= bfalse ),
inference(lifteq,[status(thm)],[108]) ).
thf(20,axiom,
! [B: $i,A: $i] :
( ( nil @ ( B @ ( A @ cons ) @ merge ) )
= ( B @ ( A @ cons ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_013) ).
thf(76,plain,
! [B: $i,A: $i] :
( ( nil @ ( B @ ( A @ cons ) @ merge ) )
= ( B @ ( A @ cons ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(77,plain,
! [B: $i,A: $i] :
( ( nil @ ( B @ ( A @ cons ) @ merge ) )
= ( B @ ( A @ cons ) ) ),
inference(lifteq,[status(thm)],[76]) ).
thf(45,plain,
! [A: $i] :
( ( nil @ ( A @ count ) )
= z ),
inference(lifteq,[status(thm)],[44]) ).
thf(9,axiom,
! [B: $i,A: $i] :
( ( B @ s @ ( A @ s @ leqNat ) )
= ( B @ ( A @ leqNat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_011) ).
thf(54,plain,
! [B: $i,A: $i] :
( ( B @ s @ ( A @ s @ leqNat ) )
= ( B @ ( A @ leqNat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(6,axiom,
( ( z @ s @ div2 )
= z ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_020) ).
thf(48,plain,
( ( z @ s @ div2 )
= z ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(49,plain,
( ( z @ s @ div2 )
= z ),
inference(lifteq,[status(thm)],[48]) ).
thf(25,axiom,
( ( bfalse @ ( btrue @ eq2 ) )
= bfalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_029) ).
thf(86,plain,
( ( bfalse @ ( btrue @ eq2 ) )
= bfalse ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(81,plain,
( ( btrue @ ( bfalse @ eq2 ) )
= bfalse ),
inference(lifteq,[status(thm)],[80]) ).
thf(15,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ cons ) @ ( A @ cons ) @ msort )
= ( C @ ( B @ cons ) @ ( A @ cons ) @ ( C @ ( B @ cons ) @ ( A @ cons ) @ lengthNat @ div2 @ splitAtNat ) @ ( C @ ( B @ ( A @ aux3 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_024) ).
thf(66,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ cons ) @ ( A @ cons ) @ msort )
= ( C @ ( B @ cons ) @ ( A @ cons ) @ ( C @ ( B @ cons ) @ ( A @ cons ) @ lengthNat @ div2 @ splitAtNat ) @ ( C @ ( B @ ( A @ aux3 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(13,axiom,
! [A: $i] :
( ( A @ ( nil @ merge ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_012) ).
thf(62,plain,
! [A: $i] :
( ( A @ ( nil @ merge ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(63,plain,
! [A: $i] :
( ( A @ ( nil @ merge ) )
= A ),
inference(lifteq,[status(thm)],[62]) ).
thf(29,axiom,
! [A: $i] :
( ( A @ ( A @ eq ) )
= btrue ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_033) ).
thf(94,plain,
! [A: $i] :
( ( A @ ( A @ eq ) )
= btrue ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(95,plain,
! [A: $i] :
( ( A @ ( A @ eq ) )
= btrue ),
inference(lifteq,[status(thm)],[94]) ).
thf(87,plain,
( ( bfalse @ ( btrue @ eq2 ) )
= bfalse ),
inference(lifteq,[status(thm)],[86]) ).
thf(55,plain,
! [B: $i,A: $i] :
( ( B @ s @ ( A @ s @ leqNat ) )
= ( B @ ( A @ leqNat ) ) ),
inference(lifteq,[status(thm)],[54]) ).
thf(75,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ cons ) @ lengthNat )
= ( B @ lengthNat @ s ) ),
inference(lifteq,[status(thm)],[74]) ).
thf(11,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ cons ) @ ( A @ s @ splitAtNat ) )
= ( C @ ( A @ splitAtNat ) @ ( C @ ( B @ ( A @ aux ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_008) ).
thf(58,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ cons ) @ ( A @ s @ splitAtNat ) )
= ( C @ ( A @ splitAtNat ) @ ( C @ ( B @ ( A @ aux ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(23,axiom,
! [C: $i,B: $i,A: $i] :
( ( bfalse @ ( C @ ( B @ ( A @ aux4 ) ) ) )
= ( C @ ( A @ count ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_005) ).
thf(82,plain,
! [C: $i,B: $i,A: $i] :
( ( bfalse @ ( C @ ( B @ ( A @ aux4 ) ) ) )
= ( C @ ( A @ count ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(43,plain,
! [A: $i] :
( ( nil @ ( A @ s @ splitAtNat ) )
= ( nil @ ( nil @ pair2 ) ) ),
inference(lifteq,[status(thm)],[42]) ).
thf(146,plain,
! [A: $i] :
( ( nil @ ( A @ s @ splitAtNat ) )
= ( nil @ ( z @ splitAtNat ) ) ),
inference(rewrite,[status(thm)],[43,41]) ).
thf(51,plain,
( ( nil @ lengthNat )
= z ),
inference(lifteq,[status(thm)],[50]) ).
thf(79,plain,
( ( nil @ msort )
= nil ),
inference(lifteq,[status(thm)],[78]) ).
thf(47,plain,
! [A: $i] :
( ( A @ s @ s @ div2 )
= ( A @ div2 @ s ) ),
inference(lifteq,[status(thm)],[46]) ).
thf(83,plain,
! [C: $i,B: $i,A: $i] :
( ( bfalse @ ( C @ ( B @ ( A @ aux4 ) ) ) )
= ( C @ ( A @ count ) ) ),
inference(lifteq,[status(thm)],[82]) ).
thf(32,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( bfalse @ ( D @ ( C @ ( B @ ( A @ aux2 ) ) ) ) )
= ( D @ ( B @ ( A @ cons ) @ merge ) @ ( C @ cons ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_002) ).
thf(100,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( bfalse @ ( D @ ( C @ ( B @ ( A @ aux2 ) ) ) ) )
= ( D @ ( B @ ( A @ cons ) @ merge ) @ ( C @ cons ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(8539,plain,
$false,
inference(e,[status(thm)],[56,52,53,41,105,44,80,50,72,69,88,185,42,37,46,57,78,106,84,89,74,307,60,85,102,70,165,92,65,97,109,77,96,45,64,54,49,86,81,76,39,98,91,66,108,48,63,95,99,87,104,40,55,75,58,82,146,51,107,79,94,47,68,62,90,83,100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWX201-1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.12 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.23/0.56 % Computer : n020.cluster.edu
% 0.23/0.56 % Model : x86_64 x86_64
% 0.23/0.56 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.23/0.56 % Memory : 8046.5625MB
% 0.23/0.56 % OS : Linux 6.8.0-71-generic
% 0.23/0.56 % CPULimit : 300
% 0.23/0.56 % WCLimit : 300
% 0.23/0.56 % DateTime : Sat Sep 26 16:56:04 UTC 2026
% 0.23/0.57 % CPUTime :
% 0.23/0.57 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 1.47/1.41 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 2.07/1.70 % [INFO] Parsing done (289ms).
% 2.07/1.72 % [INFO] Running in sequential loop mode.
% 3.16/2.33 % [INFO] eprover registered as external prover.
% 3.16/2.34 % [INFO] Scanning for conjecture ...
% 3.36/2.48 % [INFO] Found a conjecture (or negated_conjecture) and 35 axioms. Running axiom selection ...
% 3.71/2.60 % [INFO] Axiom selection finished. Selected 35 axioms (removed 0 axioms).
% 3.71/2.67 % [INFO] Problem is propositional (TPTP CNF).
% 3.71/2.67 % [INFO] Type checking passed.
% 3.71/2.68 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 65.81/15.92 % External prover 'e' found a proof!
% 65.81/15.92 % [INFO] Killing All external provers ...
% 65.81/15.93 % Time passed: 15147ms (effective reasoning time: 14197ms)
% 65.81/15.93 % Axioms used in derivation (35): axiom_024, axiom_010, axiom_002, axiom_028, axiom_023, axiom_034, axiom_005, axiom_012, axiom_001, axiom_030, axiom_029, axiom_025, axiom_003, axiom_014, axiom_007, axiom_018, axiom_009, axiom_017, axiom_021, axiom_032, axiom_013, axiom_006, axiom_016, axiom_027, axiom_031, axiom_015, axiom_004, axiom_033, axiom_022, axiom, axiom_011, axiom_026, axiom_020, axiom_019, axiom_008
% 65.81/15.93 % No. of inferences in proof: 117
% 65.81/15.93 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 15147 ms resp. 14197 ms w/o parsing
% 65.81/16.01 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 65.81/16.01 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------