%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWX241_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 : n010.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 09:15:23 AM UTC 2026
% Result : Theorem 56.18s 12.14s
% Output : Refutation 48.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 65
% Syntax : Number of formulae : 132 ( 99 unt; 0 typ; 0 def)
% Number of atoms : 203 ( 107 equ; 0 cnn)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 714 ( 70 ~; 9 |; 15 &; 573 @)
% ( 10 <=>; 37 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 42 ( 40 usr; 8 con; 0-3 aty)
% Number of variables : 282 ( 0 ^; 276 !; 6 ?; 282 :)
% Comments :
%------------------------------------------------------------------------------
thf(typeCorrect_decl,type,
typeCorrect: $i > $o ).
thf(elem_decl,type,
elem: $i > $i > $o ).
thf(l_decl,type,
l: $i ).
thf(run_decl,type,
run: $i > $i > $i ).
thf(cons_decl,type,
cons: $i > $i > $i ).
thf(h_decl,type,
h: $i ).
thf(proj1Suc_decl,type,
proj1Suc: $i > $i ).
thf(suc_decl,type,
suc: $i > $i ).
thf(nand_decl,type,
nand: $i > $i > $i ).
thf(tT_decl,type,
tT: $i ).
thf(fF_decl,type,
fF: $i ).
thf(proj1Nand_decl,type,
proj1Nand: $i > $i ).
thf(proj2Nand_decl,type,
proj2Nand: $i > $i ).
thf(skip_decl,type,
skip: $i ).
thf(seq_decl,type,
seq: $i > $i > $i ).
thf(proj2IfThenElse_decl,type,
proj2IfThenElse: $i > $i ).
thf(ifThenElse_decl,type,
ifThenElse: $i > $i > $i > $i ).
thf(var_decl,type,
var: $i > $i ).
thf(secret_decl,type,
secret: $i > $o ).
thf(eval_decl,type,
eval: $i > $i > $o ).
thf(assign_decl,type,
assign: $i > $i > $i ).
thf(while_decl,type,
while: $i > $i > $i ).
thf(proj1Seq_decl,type,
proj1Seq: $i > $i ).
thf(proj1IfThenElse_decl,type,
proj1IfThenElse: $i > $i ).
thf(del_decl,type,
del: $i > $i > $i ).
thf(nil_decl,type,
nil: $i ).
thf(high_decl,type,
high: $i > $i ).
thf(low_decl,type,
low: $i > $i ).
thf(proj1Var_decl,type,
proj1Var: $i > $i ).
thf(proj1While_decl,type,
proj1While: $i > $i ).
thf(proj1High_decl,type,
proj1High: $i > $i ).
thf(proj2While_decl,type,
proj2While: $i > $i ).
thf(zero_decl,type,
zero: $i ).
thf(proj1Assign_decl,type,
proj1Assign: $i > $i ).
thf(proj2Assign_decl,type,
proj2Assign: $i > $i ).
thf(proj2Seq_decl,type,
proj2Seq: $i > $i ).
thf(proj3IfThenElse_decl,type,
proj3IfThenElse: $i > $i ).
thf(proj1Low_decl,type,
proj1Low: $i > $i ).
thf(head_decl,type,
head: $i > $i ).
thf(tail_decl,type,
tail: $i > $i ).
thf(20,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ ifThenElse ) ) @ proj1IfThenElse )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_022) ).
thf(138,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ ifThenElse ) ) @ proj1IfThenElse )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(52,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ low @ assign ) @ typeCorrect )
<=> ~ ( A @ secret ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_043) ).
thf(247,plain,
! [A: $i,B: $i] :
( ( ~ ( A @ secret )
=> ( A @ ( B @ low @ assign ) @ typeCorrect ) )
& ( ( A @ ( B @ low @ assign ) @ typeCorrect )
=> ~ ( A @ secret ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(3,axiom,
! [A: $i] :
( ( A @ suc @ proj1Suc )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_004) ).
thf(73,plain,
! [A: $i] :
( ( A @ suc @ proj1Suc )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(39,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( A @ assign ) )
!= ( D @ ( C @ seq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_031) ).
thf(204,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( A @ assign ) )
!= ( D @ ( C @ seq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(30,axiom,
! [A: $i] :
( zero
!= ( A @ suc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_005) ).
thf(175,plain,
! [A: $i] :
( zero
!= ( A @ suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(36,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( A @ assign ) )
!= ( E @ ( D @ ( C @ ifThenElse ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_032) ).
thf(195,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( A @ assign ) )
!= ( E @ ( D @ ( C @ ifThenElse ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(18,axiom,
! [A: $i,B: $i] :
( skip
!= ( B @ ( A @ while ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_030) ).
thf(131,plain,
! [A: $i,B: $i] :
( skip
!= ( B @ ( A @ while ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(33,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( A @ seq ) )
!= ( E @ ( D @ ( C @ ifThenElse ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_034) ).
thf(185,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( A @ seq ) )
!= ( E @ ( D @ ( C @ ifThenElse ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(61,axiom,
! [A: $i,B: $i] : ( A @ ( B @ high @ assign ) @ typeCorrect ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_042) ).
thf(288,plain,
! [A: $i,B: $i] : ( A @ ( B @ high @ assign ) @ typeCorrect ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(34,axiom,
! [A: $i] :
~ ( A @ low @ var @ secret ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_040) ).
thf(189,plain,
! [A: $i] :
~ ( A @ low @ var @ secret ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(9,axiom,
! [A: $i,B: $i] :
( skip
!= ( B @ ( A @ seq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_028) ).
thf(93,plain,
! [A: $i,B: $i] :
( skip
!= ( B @ ( A @ seq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(31,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ assign ) @ proj1Assign )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_018) ).
thf(179,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ assign ) @ proj1Assign )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(41,axiom,
! [A: $i] :
( fF
!= ( A @ var ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_017) ).
thf(211,plain,
! [A: $i] :
( fF
!= ( A @ var ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(53,axiom,
! [A: $i,B: $i,C: $i] :
( ( A = B )
=> ( ( C @ ( B @ cons ) @ ( A @ del ) )
= ( C @ ( A @ del ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_056) ).
thf(253,plain,
! [A: $i,B: $i,C: $i] :
( ( A = B )
=> ( ( C @ ( B @ cons ) @ ( A @ del ) )
= ( C @ ( A @ del ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(44,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( C @ ( A @ eval ) )
=> ( ( C @ ( B @ assign ) @ ( A @ run ) )
= ( A @ ( B @ del ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_060) ).
thf(221,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( C @ ( A @ eval ) )
=> ( ( C @ ( B @ assign ) @ ( A @ run ) )
= ( A @ ( B @ del ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(56,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ while ) @ typeCorrect )
<=> ( B @ typeCorrect ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_046) ).
thf(265,plain,
! [A: $i,B: $i] :
( ( ( B @ typeCorrect )
=> ( B @ ( A @ while ) @ typeCorrect ) )
& ( ( B @ ( A @ while ) @ typeCorrect )
=> ( B @ typeCorrect ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(14,axiom,
! [A: $i] :
~ ( fF @ ( A @ eval ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_053) ).
thf(116,plain,
! [A: $i] :
~ ( fF @ ( A @ eval ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(51,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( B @ ( A @ eval ) )
=> ( ( D @ ( C @ ( B @ ifThenElse ) ) @ ( A @ run ) )
= ( D @ ( A @ run ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_063) ).
thf(243,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( B @ ( A @ eval ) )
=> ( ( D @ ( C @ ( B @ ifThenElse ) ) @ ( A @ run ) )
= ( D @ ( A @ run ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(48,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ cons ) @ head )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_001) ).
thf(233,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ cons ) @ head )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(38,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ ifThenElse ) ) @ proj3IfThenElse )
= C ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_024) ).
thf(201,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ ifThenElse ) ) @ proj3IfThenElse )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(63,axiom,
! [A: $i,B: $i] :
( ( B @ var @ ( A @ eval ) )
<=> ( A @ ( B @ elem ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_054) ).
thf(297,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ elem ) )
=> ( B @ var @ ( A @ eval ) ) )
& ( ( B @ var @ ( A @ eval ) )
=> ( A @ ( B @ elem ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(35,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ seq ) @ proj2Seq )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_021) ).
thf(192,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ seq ) @ proj2Seq )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(59,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ cons ) @ ( A @ elem ) )
<=> ( ( C @ ( A @ elem ) )
| ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_050) ).
thf(275,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( C @ ( A @ elem ) )
| ( B = A ) )
=> ( C @ ( B @ cons ) @ ( A @ elem ) ) )
& ( ( C @ ( B @ cons ) @ ( A @ elem ) )
=> ( ( C @ ( A @ elem ) )
| ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(10,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ ifThenElse ) ) @ proj2IfThenElse )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_023) ).
thf(97,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ ifThenElse ) ) @ proj2IfThenElse )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(60,axiom,
! [A: $i] :
~ ( nil @ ( A @ elem ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_049) ).
thf(285,plain,
! [A: $i] :
~ ( nil @ ( A @ elem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(45,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ while ) @ ( A @ run ) )
= ( skip @ ( C @ ( B @ while ) @ ( C @ seq ) @ ( B @ ifThenElse ) ) @ ( A @ run ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_064) ).
thf(224,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ while ) @ ( A @ run ) )
= ( skip @ ( C @ ( B @ while ) @ ( C @ seq ) @ ( B @ ifThenElse ) ) @ ( A @ run ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(28,axiom,
! [A: $i] :
( ( A @ high @ proj1High )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_006) ).
thf(169,plain,
! [A: $i] :
( ( A @ high @ proj1High )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(21,axiom,
! [A: $i] :
( ( nil @ ( A @ del ) )
= nil ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_055) ).
thf(141,plain,
! [A: $i] :
( ( nil @ ( A @ del ) )
= nil ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(23,axiom,
! [A: $i] :
( ( A
!= ( A @ proj2Nand @ ( A @ proj1Nand @ nand ) ) )
=> ( ( A
!= ( A @ proj1Var @ var ) )
=> ~ ( A @ secret ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_037) ).
thf(148,plain,
! [A: $i] :
( ( A
!= ( A @ proj2Nand @ ( A @ proj1Nand @ nand ) ) )
=> ( ( A
!= ( A @ proj1Var @ var ) )
=> ~ ( A @ secret ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(27,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ nand ) @ ( A @ eval ) )
<=> ( ~ ( C @ ( A @ eval ) )
| ~ ( B @ ( A @ eval ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_051) ).
thf(161,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ~ ( C @ ( A @ eval ) )
| ~ ( B @ ( A @ eval ) ) )
=> ( C @ ( B @ nand ) @ ( A @ eval ) ) )
& ( ( C @ ( B @ nand ) @ ( A @ eval ) )
=> ( ~ ( C @ ( A @ eval ) )
| ~ ( B @ ( A @ eval ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(66,axiom,
( h
= ( zero @ high ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_048) ).
thf(313,plain,
( h
= ( zero @ high ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(22,axiom,
! [A: $i,B: $i] :
( ( A @ high )
!= ( B @ low ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_008) ).
thf(144,plain,
! [A: $i,B: $i] :
( ( A @ high )
!= ( B @ low ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(49,axiom,
! [A: $i,B: $i] :
( nil
!= ( B @ ( A @ cons ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_003) ).
thf(236,plain,
! [A: $i,B: $i] :
( nil
!= ( B @ ( A @ cons ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(29,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ while ) @ proj2While )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_026) ).
thf(172,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ while ) @ proj2While )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(43,axiom,
! [A: $i] : ( tT @ ( A @ eval ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_052) ).
thf(219,plain,
! [A: $i] : ( tT @ ( A @ eval ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ nand ) )
!= tT ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_012) ).
thf(76,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ nand ) )
!= tT ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(64,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ seq ) @ ( A @ run ) )
= ( C @ ( B @ ( A @ run ) @ run ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_061) ).
thf(303,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ seq ) @ ( A @ run ) )
= ( C @ ( B @ ( A @ run ) @ run ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(57,axiom,
skip @ typeCorrect,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_041) ).
thf(271,plain,
skip @ typeCorrect,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(40,axiom,
! [A: $i] :
( ( A @ low @ proj1Low )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_007) ).
thf(208,plain,
! [A: $i] :
( ( A @ low @ proj1Low )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(50,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ cons ) @ tail )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_002) ).
thf(240,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ cons ) @ tail )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(25,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ while ) @ proj1While )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_025) ).
thf(155,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ while ) @ proj1While )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(65,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ seq ) @ typeCorrect )
<=> ( ( B @ typeCorrect )
& ( A @ typeCorrect ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_044) ).
thf(306,plain,
! [A: $i,B: $i] :
( ( ( ( B @ typeCorrect )
& ( A @ typeCorrect ) )
=> ( B @ ( A @ seq ) @ typeCorrect ) )
& ( ( B @ ( A @ seq ) @ typeCorrect )
=> ( ( B @ typeCorrect )
& ( A @ typeCorrect ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(19,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ seq ) @ proj1Seq )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_020) ).
thf(135,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ seq ) @ proj1Seq )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(5,axiom,
tT != fF,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_015) ).
thf(80,plain,
tT != fF,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(13,axiom,
! [A: $i,B: $i,C: $i] :
( skip
!= ( C @ ( B @ ( A @ ifThenElse ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_029) ).
thf(112,plain,
! [A: $i,B: $i,C: $i] :
( skip
!= ( C @ ( B @ ( A @ ifThenElse ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(16,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( B @ ( A @ ifThenElse ) ) )
!= ( E @ ( D @ while ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_036) ).
thf(123,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( B @ ( A @ ifThenElse ) ) )
!= ( E @ ( D @ while ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(1,conjecture,
? [A: $i,B: $i] :
~ ( ( A @ typeCorrect )
=> ( ( A @ ( B @ run ) @ ( l @ elem ) )
<=> ( A @ ( B @ ( h @ cons ) @ run ) @ ( l @ elem ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goal_065) ).
thf(2,negated_conjecture,
~ ? [A: $i,B: $i] :
~ ( ( A @ typeCorrect )
=> ( ( A @ ( B @ run ) @ ( l @ elem ) )
<=> ( A @ ( B @ ( h @ cons ) @ run ) @ ( l @ elem ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(67,plain,
~ ? [A: $i,B: $i] :
~ ( ( A @ typeCorrect )
=> ( ( ( A @ ( B @ ( h @ cons ) @ run ) @ ( l @ elem ) )
=> ( A @ ( B @ run ) @ ( l @ elem ) ) )
& ( ( A @ ( B @ run ) @ ( l @ elem ) )
=> ( A @ ( B @ ( h @ cons ) @ run ) @ ( l @ elem ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(37,axiom,
! [A: $i] : ( A @ high @ var @ secret ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_039) ).
thf(199,plain,
! [A: $i] : ( A @ high @ var @ secret ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(32,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ assign ) @ proj2Assign )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_019) ).
thf(182,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ assign ) @ proj2Assign )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(17,axiom,
! [A: $i] :
( tT
!= ( A @ var ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_016) ).
thf(127,plain,
! [A: $i] :
( tT
!= ( A @ var ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(47,axiom,
( l
= ( zero @ low ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_047) ).
thf(231,plain,
( l
= ( zero @ low ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ nand ) @ proj1Nand )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_009) ).
thf(87,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ nand ) @ proj1Nand )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ nand ) @ secret )
<=> ( ( B @ secret )
| ( A @ secret ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_038) ).
thf(104,plain,
! [A: $i,B: $i] :
( ( ( ( B @ secret )
| ( A @ secret ) )
=> ( B @ ( A @ nand ) @ secret ) )
& ( ( B @ ( A @ nand ) @ secret )
=> ( ( B @ secret )
| ( A @ secret ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(54,axiom,
! [A: $i,B: $i,C: $i] :
( ( A != B )
=> ( ( C @ ( B @ cons ) @ ( A @ del ) )
= ( C @ ( A @ del ) @ ( B @ cons ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_057) ).
thf(258,plain,
! [A: $i,B: $i,C: $i] :
( ( A != B )
=> ( ( C @ ( B @ cons ) @ ( A @ del ) )
= ( C @ ( A @ del ) @ ( B @ cons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(26,axiom,
! [A: $i] :
( ( A @ var @ proj1Var )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_011) ).
thf(158,plain,
! [A: $i] :
( ( A @ var @ proj1Var )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(58,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( A @ eval ) )
=> ( ( C @ ( B @ assign ) @ ( A @ run ) )
= ( A @ ( B @ cons ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_059) ).
thf(272,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( A @ eval ) )
=> ( ( C @ ( B @ assign ) @ ( A @ run ) )
= ( A @ ( B @ cons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(62,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ ifThenElse ) ) @ typeCorrect )
<=> ( ( C @ typeCorrect )
& ( B @ typeCorrect ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_045) ).
thf(290,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( C @ typeCorrect )
& ( B @ typeCorrect ) )
=> ( C @ ( B @ ( A @ ifThenElse ) ) @ typeCorrect ) )
& ( ( C @ ( B @ ( A @ ifThenElse ) ) @ typeCorrect )
=> ( ( C @ typeCorrect )
& ( B @ typeCorrect ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(15,axiom,
! [A: $i,B: $i] :
( skip
!= ( B @ ( A @ assign ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_027) ).
thf(119,plain,
! [A: $i,B: $i] :
( skip
!= ( B @ ( A @ assign ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(24,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( A @ seq ) )
!= ( D @ ( C @ while ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_035) ).
thf(151,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( A @ seq ) )
!= ( D @ ( C @ while ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(55,axiom,
! [A: $i] :
( ( skip @ ( A @ run ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_058) ).
thf(262,plain,
! [A: $i] :
( ( skip @ ( A @ run ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ nand ) @ proj2Nand )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_010) ).
thf(90,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ nand ) @ proj2Nand )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(46,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( A @ eval ) )
=> ( ( D @ ( C @ ( B @ ifThenElse ) ) @ ( A @ run ) )
= ( C @ ( A @ run ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_062) ).
thf(227,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( A @ eval ) )
=> ( ( D @ ( C @ ( B @ ifThenElse ) ) @ ( A @ run ) )
= ( C @ ( A @ run ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ nand ) )
!= fF ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_013) ).
thf(83,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ nand ) )
!= fF ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(42,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( A @ assign ) )
!= ( D @ ( C @ while ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_033) ).
thf(215,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( A @ assign ) )
!= ( D @ ( C @ while ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(11,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ nand ) )
!= ( C @ var ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_014) ).
thf(100,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ nand ) )
!= ( C @ var ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(17170,plain,
$false,
inference(e,[status(thm)],[138,247,73,204,175,195,131,185,288,189,93,179,211,253,221,265,116,243,233,201,297,192,275,97,285,224,169,141,148,161,313,144,236,172,219,76,303,271,208,240,155,306,135,80,112,123,67,199,182,127,231,87,104,258,158,272,290,119,151,262,90,227,83,215,100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWX241_1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.08 % 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
% 0.14/0.40 % Computer : n010.cluster.edu
% 0.14/0.40 % Model : x86_64 x86_64
% 0.14/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.40 % Memory : 8046.5625MB
% 0.14/0.40 % OS : Linux 6.8.0-71-generic
% 0.14/0.40 % CPULimit : 300
% 0.14/0.40 % WCLimit : 300
% 0.14/0.40 % DateTime : Sat Sep 26 17:02:54 UTC 2026
% 0.14/0.41 % CPUTime :
% 0.14/0.41 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
% 0.87/0.98 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.42/1.21 % [INFO] Parsing done (225ms).
% 1.42/1.23 % [INFO] Running in sequential loop mode.
% 2.13/1.64 % [INFO] eprover registered as external prover.
% 2.13/1.65 % [INFO] Scanning for conjecture ...
% 2.35/1.76 % [INFO] Found a conjecture (or negated_conjecture) and 64 axioms. Running axiom selection ...
% 2.50/1.86 % [INFO] Axiom selection finished. Selected 64 axioms (removed 0 axioms).
% 2.76/1.95 % [INFO] Problem is first-order (TPTP FOF).
% 2.76/1.96 % [INFO] Type checking passed.
% 2.76/1.96 % [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 ...
% 56.18/12.13 % External prover 'e' found a proof!
% 56.18/12.14 % [INFO] Killing All external provers ...
% 56.18/12.14 % Time passed: 11592ms (effective reasoning time: 10905ms)
% 56.18/12.14 % Solved by 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)>
% 56.18/12.14 % Axioms used in derivation (64): axiom_028, axiom_023, axiom_001, axiom_041, axiom_029, axiom_036, axiom_025, axiom_014, axiom_039, axiom_024, axiom_009, axiom_040, axiom_046, axiom_017, axiom_057, axiom_035, axiom_050, axiom_051, axiom_061, axiom_010, axiom_021, axiom_032, axiom_054, axiom_002, axiom_013, axiom_043, axiom_006, axiom_049, axiom_034, axiom_016, axiom_056, axiom_027, axiom_005, axiom_045, axiom_038, axiom_012, axiom_062, axiom_059, axiom_044, axiom_031, axiom_015, axiom_004, axiom_055, axiom_033, axiom_022, axiom_063, axiom_011, axiom_026, axiom_052, axiom_037, axiom_020, axiom_060, axiom_048, axiom_030, axiom_019, axiom_008, axiom_003, axiom_042, axiom_047, axiom_007, axiom_018, axiom_058, axiom_053, axiom_064
% 56.18/12.14 % No. of inferences in proof: 132
% 56.18/12.14 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 11592 ms resp. 10905 ms w/o parsing
% 48.13/12.21 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 48.13/12.21 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------