%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWX222-1 : 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 : n018.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 09:15:20 AM UTC 2026
% Result : Unsatisfiable 7.81s 4.12s
% Output : Refutation 8.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 56
% Syntax : Number of formulae : 113 ( 103 unt; 0 typ; 0 def)
% Number of atoms : 127 ( 126 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 604 ( 16 ~; 14 |; 0 &; 574 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 28 ( 26 usr; 9 con; 0-4 aty)
% Number of variables : 236 ( 0 ^; 236 !; 0 ?; 236 :)
% Comments :
%------------------------------------------------------------------------------
thf(eq4_decl,type,
eq4: $i > $i > $i ).
thf(sat_synth_nf_k_decl,type,
sat_synth_nf_k: $i > $i ).
thf(bfalse_decl,type,
bfalse: $i ).
thf(btrue_decl,type,
btrue: $i ).
thf(tc_decl,type,
tc: $i > $i > $i > $i ).
thf(var_decl,type,
var: $i > $i ).
thf(aux_decl,type,
aux: $i > $i > $i > $i > $i ).
thf(index_decl,type,
index: $i > $i > $i ).
thf(eq3_decl,type,
eq3: $i > $i > $i ).
thf(eq2_decl,type,
eq2: $i > $i > $i ).
thf(nf_decl,type,
nf: $i > $i ).
thf(app_decl,type,
app: $i > $i > $i > $i ).
thf(andb_decl,type,
andb: $i > $i > $i ).
thf(just_decl,type,
just: $i > $i ).
thf(eq_decl,type,
eq: $i > $i > $i ).
thf(lam_decl,type,
lam: $i > $i ).
thf(cons_decl,type,
cons: $i > $i > $i ).
thf(suc_decl,type,
suc: $i > $i ).
thf(zero_decl,type,
zero: $i ).
thf(arr_decl,type,
arr: $i > $i > $i ).
thf(nil_decl,type,
nil: $i ).
thf(nothing_decl,type,
nothing: $i ).
thf(c_decl,type,
c: $i ).
thf(b_decl,type,
b: $i ).
thf(a_decl,type,
a: $i ).
thf(notb_decl,type,
notb: $i > $i ).
thf(16,axiom,
! [A: $i] :
( ( A @ ( A @ eq3 ) )
= btrue ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_053) ).
thf(88,plain,
! [A: $i] :
( ( A @ ( A @ eq3 ) )
= btrue ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(31,axiom,
! [B: $i,A: $i] :
( ( a @ ( B @ lam @ ( A @ tc ) ) )
= bfalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_016) ).
thf(120,plain,
! [B: $i,A: $i] :
( ( a @ ( B @ lam @ ( A @ tc ) ) )
= bfalse ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(47,axiom,
! [A: $i] :
( ( zero @ ( A @ suc @ eq2 ) )
= bfalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_031) ).
thf(153,plain,
! [A: $i] :
( ( zero @ ( A @ suc @ eq2 ) )
= bfalse ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(49,axiom,
! [B: $i,A: $i] :
( ( B @ var @ ( A @ lam @ eq3 ) )
= bfalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_048) ).
thf(157,plain,
! [B: $i,A: $i] :
( ( B @ var @ ( A @ lam @ eq3 ) )
= bfalse ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(2,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ var @ ( A @ tc ) ) )
= ( B @ ( A @ index ) @ ( B @ ( C @ ( A @ aux ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_019) ).
thf(60,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ var @ ( A @ tc ) ) )
= ( B @ ( A @ index ) @ ( B @ ( C @ ( A @ aux ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(7,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ suc @ ( B @ ( A @ cons ) @ index ) )
= ( C @ ( B @ index ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_006) ).
thf(70,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ suc @ ( B @ ( A @ cons ) @ index ) )
= ( C @ ( B @ index ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(18,axiom,
! [B: $i,A: $i] :
( ( b @ ( B @ lam @ ( A @ tc ) ) )
= bfalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_017) ).
thf(92,plain,
! [B: $i,A: $i] :
( ( b @ ( B @ lam @ ( A @ tc ) ) )
= bfalse ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(56,axiom,
! [A: $i] :
( ( A @ sat_synth_nf_k )
= ( b @ ( b @ arr ) @ ( a @ arr ) @ ( A @ ( nil @ tc ) ) @ ( A @ nf @ andb ) @ notb ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_020) ).
thf(173,plain,
! [A: $i] :
( ( A @ sat_synth_nf_k )
= ( b @ ( b @ arr ) @ ( a @ arr ) @ ( A @ ( nil @ tc ) ) @ ( A @ nf @ andb ) @ notb ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(30,axiom,
! [B: $i,A: $i] :
( ( B @ lam @ ( A @ var @ eq3 ) )
= bfalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_050) ).
thf(118,plain,
! [B: $i,A: $i] :
( ( B @ lam @ ( A @ var @ eq3 ) )
= bfalse ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(13,axiom,
! [A: $i] :
( ( A @ ( nil @ index ) )
= nothing ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_004) ).
thf(82,plain,
! [A: $i] :
( ( A @ ( nil @ index ) )
= nothing ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(46,axiom,
( ( c @ ( b @ eq ) )
= bfalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_024) ).
thf(151,plain,
( ( c @ ( b @ eq ) )
= bfalse ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(1,negated_conjecture,
! [A: $i] :
( ( bfalse @ ( A @ sat_synth_nf_k @ eq4 ) )
!= btrue ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goal) ).
thf(57,plain,
! [A: $i] :
( ( bfalse @ ( A @ sat_synth_nf_k @ eq4 ) )
!= btrue ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(11,axiom,
! [B: $i,A: $i] :
( ( B @ suc @ ( A @ suc @ eq2 ) )
= ( B @ ( A @ eq2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_029) ).
thf(78,plain,
! [B: $i,A: $i] :
( ( B @ suc @ ( A @ suc @ eq2 ) )
= ( B @ ( A @ eq2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(52,axiom,
( ( bfalse @ ( btrue @ eq4 ) )
= bfalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_028) ).
thf(164,plain,
( ( bfalse @ ( btrue @ eq4 ) )
= bfalse ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(14,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( C @ ( B @ app ) ) @ ( A @ tc ) ) )
= ( D @ ( C @ ( A @ tc ) ) @ ( E @ ( D @ arr ) @ ( B @ ( A @ tc ) ) @ andb ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_014) ).
thf(84,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( C @ ( B @ app ) ) @ ( A @ tc ) ) )
= ( D @ ( C @ ( A @ tc ) ) @ ( E @ ( D @ arr ) @ ( B @ ( A @ tc ) ) @ andb ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(44,axiom,
! [C: $i,B: $i,A: $i] :
( ( nothing @ ( C @ ( B @ ( A @ aux ) ) ) )
= bfalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom) ).
thf(147,plain,
! [C: $i,B: $i,A: $i] :
( ( nothing @ ( C @ ( B @ ( A @ aux ) ) ) )
= bfalse ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(37,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ arr ) @ ( b @ eq ) )
= bfalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_038) ).
thf(132,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ arr ) @ ( b @ eq ) )
= bfalse ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(29,axiom,
! [A: $i] :
( ( A @ ( A @ eq2 ) )
= btrue ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_052) ).
thf(116,plain,
! [A: $i] :
( ( A @ ( A @ eq2 ) )
= btrue ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(9,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ var @ app ) ) @ nf )
= ( B @ nf @ ( A @ var @ nf @ andb ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_011) ).
thf(74,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ var @ app ) ) @ nf )
= ( B @ nf @ ( A @ var @ nf @ andb ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(54,axiom,
! [A: $i] :
( ( A @ ( bfalse @ andb ) )
= bfalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_008) ).
thf(169,plain,
! [A: $i] :
( ( A @ ( bfalse @ andb ) )
= bfalse ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(41,axiom,
( ( btrue @ ( bfalse @ eq4 ) )
= bfalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_027) ).
thf(141,plain,
( ( btrue @ ( bfalse @ eq4 ) )
= bfalse ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(26,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( F @ ( B @ ( D @ app ) ) @ ( E @ ( A @ ( C @ app ) ) @ eq3 ) )
= bfalse )
| ( ( D @ ( C @ eq3 ) )
!= btrue )
| ( ( B @ ( A @ eq3 ) )
!= bfalse ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_041) ).
thf(109,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( F @ ( B @ ( D @ app ) ) @ ( E @ ( A @ ( C @ app ) ) @ eq3 ) )
= bfalse )
| ( ( D @ ( C @ eq3 ) )
!= btrue )
| ( ( B @ ( A @ eq3 ) )
!= bfalse ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(33,axiom,
! [B: $i,A: $i] :
( ( c @ ( B @ lam @ ( A @ tc ) ) )
= bfalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_018) ).
thf(124,plain,
! [B: $i,A: $i] :
( ( c @ ( B @ lam @ ( A @ tc ) ) )
= bfalse ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(20,axiom,
( ( b @ ( a @ eq ) )
= bfalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_021) ).
thf(96,plain,
( ( b @ ( a @ eq ) )
= bfalse ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(38,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ var @ ( C @ ( B @ ( A @ app ) ) @ eq3 ) )
= bfalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_046) ).
thf(134,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ var @ ( C @ ( B @ ( A @ app ) ) @ eq3 ) )
= bfalse ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(35,axiom,
( ( btrue @ notb )
= bfalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_002) ).
thf(128,plain,
( ( btrue @ notb )
= bfalse ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(24,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ app ) ) @ ( A @ lam @ eq3 ) )
= bfalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_047) ).
thf(105,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ app ) ) @ ( A @ lam @ eq3 ) )
= bfalse ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(53,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( F @ ( E @ ( B @ app ) ) @ ( D @ ( C @ ( A @ app ) ) @ eq3 ) )
= bfalse )
| ( ( B @ ( A @ eq3 ) )
!= bfalse ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_040) ).
thf(166,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( F @ ( E @ ( B @ app ) ) @ ( D @ ( C @ ( A @ app ) ) @ eq3 ) )
= bfalse )
| ( ( B @ ( A @ eq3 ) )
!= bfalse ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(51,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( F @ ( D @ ( B @ app ) ) @ ( E @ ( C @ ( A @ app ) ) @ eq3 ) )
= ( F @ ( E @ eq ) ) )
| ( ( D @ ( C @ eq3 ) )
!= btrue )
| ( ( B @ ( A @ eq3 ) )
!= btrue ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_042) ).
thf(161,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( F @ ( D @ ( B @ app ) ) @ ( E @ ( C @ ( A @ app ) ) @ eq3 ) )
= ( F @ ( E @ eq ) ) )
| ( ( D @ ( C @ eq3 ) )
!= btrue )
| ( ( B @ ( A @ eq3 ) )
!= btrue ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(4,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( C @ ( B @ ( A @ app ) ) @ app ) ) @ nf )
= ( D @ nf @ ( C @ ( B @ ( A @ app ) ) @ nf @ andb ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_010) ).
thf(64,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( C @ ( B @ ( A @ app ) ) @ app ) ) @ nf )
= ( D @ nf @ ( C @ ( B @ ( A @ app ) ) @ nf @ andb ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(45,axiom,
! [A: $i] :
( ( A @ ( A @ eq ) )
= btrue ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_051) ).
thf(149,plain,
! [A: $i] :
( ( A @ ( A @ eq ) )
= btrue ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(15,axiom,
( ( b @ ( c @ eq ) )
= bfalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_026) ).
thf(86,plain,
( ( b @ ( c @ eq ) )
= bfalse ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(50,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ lam @ app ) ) @ nf )
= bfalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_009) ).
thf(159,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ lam @ app ) ) @ nf )
= bfalse ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(10,axiom,
! [A: $i] :
( ( A @ lam @ nf )
= ( A @ nf ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_012) ).
thf(76,plain,
! [A: $i] :
( ( A @ lam @ nf )
= ( A @ nf ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(21,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ arr ) @ ( a @ eq ) )
= bfalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_037) ).
thf(98,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ arr ) @ ( a @ eq ) )
= bfalse ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(23,axiom,
! [B: $i,A: $i] :
( ( b @ ( B @ ( A @ arr ) @ eq ) )
= bfalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_035) ).
thf(103,plain,
! [B: $i,A: $i] :
( ( b @ ( B @ ( A @ arr ) @ eq ) )
= bfalse ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(5,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ just @ ( C @ ( B @ ( A @ aux ) ) ) )
= ( B @ ( D @ eq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_001) ).
thf(66,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ just @ ( C @ ( B @ ( A @ aux ) ) ) )
= ( B @ ( D @ eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(48,axiom,
! [B: $i,A: $i] :
( ( c @ ( B @ ( A @ arr ) @ eq ) )
= bfalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_036) ).
thf(155,plain,
! [B: $i,A: $i] :
( ( c @ ( B @ ( A @ arr ) @ eq ) )
= bfalse ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(36,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ arr ) @ ( c @ eq ) )
= bfalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_039) ).
thf(130,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ arr ) @ ( c @ eq ) )
= bfalse ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(12,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ arr ) @ ( B @ lam @ ( A @ tc ) ) )
= ( D @ ( B @ ( A @ ( C @ cons ) @ tc ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_015) ).
thf(80,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ arr ) @ ( B @ lam @ ( A @ tc ) ) )
= ( D @ ( B @ ( A @ ( C @ cons ) @ tc ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(27,axiom,
! [B: $i,A: $i] :
( ( a @ ( B @ ( A @ arr ) @ eq ) )
= bfalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_034) ).
thf(112,plain,
! [B: $i,A: $i] :
( ( a @ ( B @ ( A @ arr ) @ eq ) )
= bfalse ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(43,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ lam @ ( C @ ( B @ ( A @ app ) ) @ eq3 ) )
= bfalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_045) ).
thf(145,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ lam @ ( C @ ( B @ ( A @ app ) ) @ eq3 ) )
= bfalse ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(8,axiom,
! [B: $i,A: $i] :
( ( zero @ ( B @ ( A @ cons ) @ index ) )
= ( A @ just ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_005) ).
thf(72,plain,
! [B: $i,A: $i] :
( ( zero @ ( B @ ( A @ cons ) @ index ) )
= ( A @ just ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(42,axiom,
( ( a @ ( c @ eq ) )
= bfalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_025) ).
thf(143,plain,
( ( a @ ( c @ eq ) )
= bfalse ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(28,axiom,
( ( a @ ( b @ eq ) )
= bfalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_023) ).
thf(114,plain,
( ( a @ ( b @ eq ) )
= bfalse ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(55,axiom,
! [A: $i] :
( ( A @ suc @ ( zero @ eq2 ) )
= bfalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_030) ).
thf(171,plain,
! [A: $i] :
( ( A @ suc @ ( zero @ eq2 ) )
= bfalse ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(40,axiom,
! [A: $i] :
( ( A @ ( A @ eq4 ) )
= btrue ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_054) ).
thf(139,plain,
! [A: $i] :
( ( A @ ( A @ eq4 ) )
= btrue ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(25,axiom,
! [A: $i] :
( ( A @ ( btrue @ andb ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_007) ).
thf(107,plain,
! [A: $i] :
( ( A @ ( btrue @ andb ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(19,axiom,
! [A: $i] :
( ( A @ var @ nf )
= btrue ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_013) ).
thf(94,plain,
! [A: $i] :
( ( A @ var @ nf )
= btrue ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(34,axiom,
( ( bfalse @ notb )
= btrue ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_003) ).
thf(126,plain,
( ( bfalse @ notb )
= btrue ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(39,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( B @ arr ) @ ( C @ ( A @ arr ) @ eq ) )
= ( D @ ( C @ eq ) ) )
| ( ( B @ ( A @ eq ) )
!= btrue ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_033) ).
thf(136,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( B @ arr ) @ ( C @ ( A @ arr ) @ eq ) )
= ( D @ ( C @ eq ) ) )
| ( ( B @ ( A @ eq ) )
!= btrue ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(6,axiom,
! [B: $i,A: $i] :
( ( B @ lam @ ( A @ lam @ eq3 ) )
= ( B @ ( A @ eq3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_043) ).
thf(68,plain,
! [B: $i,A: $i] :
( ( B @ lam @ ( A @ lam @ eq3 ) )
= ( B @ ( A @ eq3 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(3,axiom,
! [B: $i,A: $i] :
( ( B @ var @ ( A @ var @ eq3 ) )
= ( B @ ( A @ eq2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_044) ).
thf(62,plain,
! [B: $i,A: $i] :
( ( B @ var @ ( A @ var @ eq3 ) )
= ( B @ ( A @ eq2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(17,axiom,
( ( c @ ( a @ eq ) )
= bfalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_022) ).
thf(90,plain,
( ( c @ ( a @ eq ) )
= bfalse ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(32,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ app ) ) @ ( A @ var @ eq3 ) )
= bfalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_049) ).
thf(122,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ app ) ) @ ( A @ var @ eq3 ) )
= bfalse ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(22,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( B @ arr ) @ ( C @ ( A @ arr ) @ eq ) )
= bfalse )
| ( ( B @ ( A @ eq ) )
!= bfalse ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_032) ).
thf(100,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( B @ arr ) @ ( C @ ( A @ arr ) @ eq ) )
= bfalse )
| ( ( B @ ( A @ eq ) )
!= bfalse ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(179,plain,
$false,
inference(e,[status(thm)],[88,120,153,157,60,70,92,173,118,82,151,57,78,164,84,147,132,116,74,169,141,109,124,96,134,128,105,166,161,64,149,86,159,76,98,103,66,155,130,80,112,145,72,143,114,171,139,107,94,126,136,68,62,90,122,100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWX222-1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.07 % 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
% 0.12/0.39 % Computer : n018.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Sat Sep 26 17:01:21 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 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
% 1.48/1.30 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 2.05/1.63 % [INFO] Parsing done (327ms).
% 2.05/1.66 % [INFO] Running in sequential loop mode.
% 3.41/2.33 % [INFO] eprover registered as external prover.
% 3.41/2.34 % [INFO] Scanning for conjecture ...
% 3.76/2.50 % [INFO] Found a conjecture (or negated_conjecture) and 55 axioms. Running axiom selection ...
% 3.95/2.63 % [INFO] Axiom selection finished. Selected 55 axioms (removed 0 axioms).
% 4.19/2.74 % [INFO] Problem is propositional (TPTP CNF).
% 4.19/2.75 % [INFO] Type checking passed.
% 4.19/2.76 % [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 ...
% 7.81/4.11 % External prover 'e' found a proof!
% 7.81/4.11 % [INFO] Killing All external provers ...
% 7.81/4.11 % Time passed: 3494ms (effective reasoning time: 2444ms)
% 7.81/4.12 % Axioms used in derivation (55): axiom_010, axiom_028, axiom_023, axiom_012, axiom_001, axiom_044, axiom_041, axiom_029, axiom_036, axiom_025, axiom_014, axiom_039, axiom_024, axiom_009, axiom_040, axiom_046, axiom_017, axiom_035, axiom_050, axiom_051, axiom_021, axiom_032, axiom_054, axiom_002, axiom_013, axiom_043, axiom_006, axiom_049, axiom_034, axiom_016, axiom_027, axiom_005, axiom_045, axiom_038, axiom_031, axiom_015, axiom_004, axiom_033, axiom_022, axiom, axiom_011, axiom_026, axiom_052, axiom_037, axiom_020, axiom_048, axiom_030, axiom_019, axiom_008, axiom_003, axiom_042, axiom_047, axiom_007, axiom_018, axiom_053
% 7.81/4.12 % No. of inferences in proof: 113
% 7.81/4.12 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3494 ms resp. 2444 ms w/o parsing
% 8.23/4.27 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 8.23/4.27 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------