%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWX240_1 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n004.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 64.34s 25.23s
% Output : Refutation 64.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 57
% Syntax : Number of formulae : 198 ( 137 unt; 0 typ; 0 def)
% Number of atoms : 351 ( 157 equ; 0 cnn)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 1222 ( 164 ~; 58 |; 16 &; 937 @)
% ( 9 <=>; 38 =>; 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 : 40 ( 37 usr; 9 con; 0-3 aty)
% Number of variables : 336 ( 0 ^; 316 !; 20 ?; 336 :)
% 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(assign_decl,type,
assign: $i > $i > $i ).
thf(ifThenElse_decl,type,
ifThenElse: $i > $i > $i > $i ).
thf(eval_decl,type,
eval: $i > $i > $o ).
thf(proj2IfThenElse_decl,type,
proj2IfThenElse: $i > $i ).
thf(skip_decl,type,
skip: $i ).
thf(proj1Assign_decl,type,
proj1Assign: $i > $i ).
thf(proj1Seq_decl,type,
proj1Seq: $i > $i ).
thf(seq_decl,type,
seq: $i > $i > $i ).
thf(proj1Var_decl,type,
proj1Var: $i > $i ).
thf(var_decl,type,
var: $i > $i ).
thf(proj1Low_decl,type,
proj1Low: $i > $i ).
thf(low_decl,type,
low: $i > $i ).
thf(secret_decl,type,
secret: $i > $o ).
thf(del_decl,type,
del: $i > $i > $i ).
thf(nil_decl,type,
nil: $i ).
thf(proj2Assign_decl,type,
proj2Assign: $i > $i ).
thf(proj2Seq_decl,type,
proj2Seq: $i > $i ).
thf(high_decl,type,
high: $i > $i ).
thf(proj1IfThenElse_decl,type,
proj1IfThenElse: $i > $i ).
thf(proj3IfThenElse_decl,type,
proj3IfThenElse: $i > $i ).
thf(proj1High_decl,type,
proj1High: $i > $i ).
thf(zero_decl,type,
zero: $i ).
thf(head_decl,type,
head: $i > $i ).
thf(tail_decl,type,
tail: $i > $i ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ nand ) )
!= fF ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_013) ).
thf(75,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ nand ) )
!= fF ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(76,plain,
~ ? [A: $i,B: $i] :
( ( B @ ( A @ nand ) )
= fF ),
inference(miniscope,[status(thm)],[75]) ).
thf(77,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ nand ) )
!= fF ),
inference(cnf,[status(esa)],[76]) ).
thf(78,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ nand ) )
!= fF ),
inference(lifteq,[status(thm)],[77]) ).
thf(30,axiom,
! [A: $i] : ( A @ high @ var @ secret ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_033) ).
thf(161,plain,
! [A: $i] : ( A @ high @ var @ secret ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(162,plain,
! [A: $i] : ( A @ high @ var @ secret ),
inference(cnf,[status(esa)],[161]) ).
thf(43,axiom,
( l
= ( zero @ low ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_040) ).
thf(212,plain,
( l
= ( zero @ low ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(213,plain,
( ( zero @ low )
= l ),
inference(lifteq,[status(thm)],[212]) ).
thf(20,axiom,
! [A: $i] :
~ ( A @ low @ var @ secret ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_034) ).
thf(125,plain,
! [A: $i] :
~ ( A @ low @ var @ secret ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(126,plain,
~ ? [A: $i] : ( A @ low @ var @ secret ),
inference(miniscope,[status(thm)],[125]) ).
thf(127,plain,
! [A: $i] :
~ ( A @ low @ var @ secret ),
inference(cnf,[status(esa)],[126]) ).
thf(318,plain,
! [A: $i] :
( ( ( zero @ low )
!= ( A @ low ) )
| ~ ( l @ var @ secret ) ),
inference(paramod_ordered,[status(thm)],[213,127]) ).
thf(319,plain,
~ ( l @ var @ secret ),
inference(pattern_uni,[status(thm)],[318:[bind(A,$thf( zero ))]]) ).
thf(336,plain,
! [A: $i] :
( ( ( A @ high @ var @ secret )
!= ( l @ var @ secret ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[162,319]) ).
thf(337,plain,
! [A: $i] :
( ( A @ high @ var @ secret )
!= ( l @ var @ secret ) ),
inference(simp,[status(thm)],[336]) ).
thf(340,plain,
! [A: $i] :
( ( A @ high @ var )
!= ( l @ var ) ),
inference(simp,[status(thm)],[337]) ).
thf(349,plain,
! [A: $i] :
( ( A @ high )
!= l ),
inference(simp,[status(thm)],[340]) ).
thf(48,axiom,
skip @ typeCorrect,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_035) ).
thf(230,plain,
skip @ typeCorrect,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(1,conjecture,
? [A: $i,B: $i] :
~ ( ( A @ typeCorrect )
=> ( ( A @ ( B @ run ) @ ( l @ elem ) )
<=> ( A @ ( B @ ( h @ cons ) @ run ) @ ( l @ elem ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal_057) ).
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(59,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(60,plain,
~ ~ ! [A: $i] :
( ( A @ typeCorrect )
=> ( ! [B: $i] :
( ( A @ ( B @ ( h @ cons ) @ run ) @ ( l @ elem ) )
=> ( A @ ( B @ run ) @ ( l @ elem ) ) )
& ! [B: $i] :
( ( A @ ( B @ run ) @ ( l @ elem ) )
=> ( A @ ( B @ ( h @ cons ) @ run ) @ ( l @ elem ) ) ) ) ),
inference(miniscope,[status(thm)],[59]) ).
thf(61,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ run ) @ ( l @ elem ) )
| ~ ( A @ ( C @ ( h @ cons ) @ run ) @ ( l @ elem ) )
| ~ ( A @ typeCorrect ) )
& ( ( A @ ( B @ ( h @ cons ) @ run ) @ ( l @ elem ) )
| ~ ( A @ ( B @ run ) @ ( l @ elem ) )
| ~ ( A @ typeCorrect ) ) ),
inference(cnf,[status(esa)],[60]) ).
thf(62,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( h @ cons ) @ run ) @ ( l @ elem ) )
| ~ ( A @ ( B @ run ) @ ( l @ elem ) )
| ~ ( A @ typeCorrect ) ),
inference(cnfConj,[status(thm)],[61]) ).
thf(280,plain,
! [B: $i,A: $i] :
( ( ( skip @ typeCorrect )
!= ( A @ typeCorrect ) )
| ( A @ ( B @ ( h @ cons ) @ run ) @ ( l @ elem ) )
| ~ ( A @ ( B @ run ) @ ( l @ elem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[230,62]) ).
thf(281,plain,
! [B: $i,A: $i] :
( ( ( skip @ typeCorrect )
!= ( A @ typeCorrect ) )
| ( A @ ( B @ ( h @ cons ) @ run ) @ ( l @ elem ) )
| ~ ( A @ ( B @ run ) @ ( l @ elem ) ) ),
inference(simp,[status(thm)],[280]) ).
thf(282,plain,
! [A: $i] :
( ( skip @ ( A @ ( h @ cons ) @ run ) @ ( l @ elem ) )
| ~ ( skip @ ( A @ run ) @ ( l @ elem ) ) ),
inference(pattern_uni,[status(thm)],[281:[bind(A,$thf( skip ))]]) ).
thf(286,plain,
! [A: $i] :
( ( skip @ ( A @ ( h @ cons ) @ run ) @ ( l @ elem ) )
| ~ ( skip @ ( A @ run ) @ ( l @ elem ) ) ),
inference(simp,[status(thm)],[282]) ).
thf(40,axiom,
! [A: $i] :
~ ( nil @ ( A @ elem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_042) ).
thf(197,plain,
! [A: $i] :
~ ( nil @ ( A @ elem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(198,plain,
~ ? [A: $i] : ( nil @ ( A @ elem ) ),
inference(miniscope,[status(thm)],[197]) ).
thf(199,plain,
! [A: $i] :
~ ( nil @ ( A @ elem ) ),
inference(cnf,[status(esa)],[198]) ).
thf(312,plain,
! [B: $i,A: $i] :
( ( ( skip @ ( A @ ( h @ cons ) @ run ) @ ( l @ elem ) )
!= ( nil @ ( B @ elem ) ) )
| ~ $true
| ~ ( skip @ ( A @ run ) @ ( l @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[286,199]) ).
thf(313,plain,
! [B: $i,A: $i] :
( ( ( skip @ ( A @ ( h @ cons ) @ run ) @ ( l @ elem ) )
!= ( nil @ ( B @ elem ) ) )
| ~ ( skip @ ( A @ run ) @ ( l @ elem ) ) ),
inference(simp,[status(thm)],[312]) ).
thf(315,plain,
! [B: $i,A: $i] :
( ( ( skip @ ( A @ ( h @ cons ) @ run ) )
!= nil )
| ( l != B )
| ~ ( skip @ ( A @ run ) @ ( l @ elem ) ) ),
inference(simp,[status(thm)],[313]) ).
thf(317,plain,
! [A: $i] :
( ( ( skip @ ( A @ ( h @ cons ) @ run ) )
!= nil )
| ~ ( skip @ ( A @ run ) @ ( l @ elem ) ) ),
inference(simp,[status(thm)],[315]) ).
thf(34,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ nand ) @ secret )
<=> ( ( B @ secret )
| ( A @ secret ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_032) ).
thf(173,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)],[34]) ).
thf(52,axiom,
( h
= ( zero @ high ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_041) ).
thf(249,plain,
( h
= ( zero @ high ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(250,plain,
( ( zero @ high )
= h ),
inference(lifteq,[status(thm)],[249]) ).
thf(334,plain,
! [A: $i] :
( ( ( zero @ high )
!= ( A @ high ) )
| ( h @ var @ secret ) ),
inference(paramod_ordered,[status(thm)],[250,162]) ).
thf(335,plain,
h @ var @ secret,
inference(pattern_uni,[status(thm)],[334:[bind(A,$thf( zero ))]]) ).
thf(344,plain,
! [A: $i] :
( ( ( A @ low @ var @ secret )
!= ( h @ var @ secret ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[335,127]) ).
thf(345,plain,
! [A: $i] :
( ( A @ low @ var @ secret )
!= ( h @ var @ secret ) ),
inference(simp,[status(thm)],[344]) ).
thf(347,plain,
! [A: $i] :
( ( A @ low @ var )
!= ( h @ var ) ),
inference(simp,[status(thm)],[345]) ).
thf(33,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ ifThenElse ) ) @ proj3IfThenElse )
= C ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_024) ).
thf(170,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ ifThenElse ) ) @ proj3IfThenElse )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(45,axiom,
! [A: $i,B: $i] :
( nil
!= ( B @ ( A @ cons ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_003) ).
thf(217,plain,
! [A: $i,B: $i] :
( nil
!= ( B @ ( A @ cons ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(57,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ cons ) @ tail )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_002) ).
thf(269,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ cons ) @ tail )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(27,axiom,
! [A: $i] :
( tT
!= ( A @ var ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_016) ).
thf(150,plain,
! [A: $i] :
( tT
!= ( A @ var ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(151,plain,
~ ? [A: $i] :
( tT
= ( A @ var ) ),
inference(miniscope,[status(thm)],[150]) ).
thf(152,plain,
! [A: $i] :
( tT
!= ( A @ var ) ),
inference(cnf,[status(esa)],[151]) ).
thf(153,plain,
! [A: $i] :
( ( A @ var )
!= tT ),
inference(lifteq,[status(thm)],[152]) ).
thf(36,axiom,
! [A: $i] :
( ( A
!= ( A @ proj2Nand @ ( A @ proj1Nand @ nand ) ) )
=> ( ( A
!= ( A @ proj1Var @ var ) )
=> ~ ( A @ secret ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_031) ).
thf(184,plain,
! [A: $i] :
( ( A
!= ( A @ proj2Nand @ ( A @ proj1Nand @ nand ) ) )
=> ( ( A
!= ( A @ proj1Var @ var ) )
=> ~ ( A @ secret ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(15,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ seq ) @ proj1Seq )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_020) ).
thf(110,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ seq ) @ proj1Seq )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(28,axiom,
! [A: $i,B: $i] :
( skip
!= ( B @ ( A @ seq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_026) ).
thf(154,plain,
! [A: $i,B: $i] :
( skip
!= ( B @ ( A @ seq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(155,plain,
~ ? [A: $i,B: $i] :
( skip
= ( B @ ( A @ seq ) ) ),
inference(miniscope,[status(thm)],[154]) ).
thf(156,plain,
! [B: $i,A: $i] :
( skip
!= ( B @ ( A @ seq ) ) ),
inference(cnf,[status(esa)],[155]) ).
thf(157,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ seq ) )
!= skip ),
inference(lifteq,[status(thm)],[156]) ).
thf(50,axiom,
! [A: $i,B: $i,C: $i] :
( ( A = B )
=> ( ( C @ ( B @ cons ) @ ( A @ del ) )
= ( C @ ( A @ del ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_049) ).
thf(238,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)],[50]) ).
thf(18,axiom,
! [A: $i] :
( ( A @ var @ proj1Var )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_011) ).
thf(119,plain,
! [A: $i] :
( ( A @ var @ proj1Var )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(120,plain,
! [A: $i] :
( ( A @ var @ proj1Var )
= A ),
inference(cnf,[status(esa)],[119]) ).
thf(121,plain,
! [A: $i] :
( ( A @ var @ proj1Var )
= A ),
inference(lifteq,[status(thm)],[120]) ).
thf(342,plain,
( ( ( h @ var @ secret )
!= ( l @ var @ secret ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[335,319]) ).
thf(343,plain,
( ( h @ var @ secret )
!= ( l @ var @ secret ) ),
inference(simp,[status(thm)],[342]) ).
thf(346,plain,
( ( h @ var )
!= ( l @ var ) ),
inference(simp,[status(thm)],[343]) ).
thf(348,plain,
h != l,
inference(simp,[status(thm)],[346]) ).
thf(26,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ assign ) @ proj2Assign )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_019) ).
thf(147,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ assign ) @ proj2Assign )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(46,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ low @ assign ) @ typeCorrect )
<=> ~ ( A @ secret ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_037) ).
thf(221,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)],[46]) ).
thf(10,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ nand ) @ ( A @ eval ) )
<=> ( ~ ( C @ ( A @ eval ) )
| ~ ( B @ ( A @ eval ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_044) ).
thf(89,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)],[10]) ).
thf(51,axiom,
! [A: $i,B: $i] :
( ( B @ var @ ( A @ eval ) )
<=> ( A @ ( B @ elem ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_047) ).
thf(243,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)],[51]) ).
thf(5,axiom,
tT != fF,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_015) ).
thf(72,plain,
tT != fF,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(73,plain,
tT != fF,
inference(polarity_switch,[status(thm)],[72]) ).
thf(74,plain,
fF != tT,
inference(lifteq,[status(thm)],[73]) ).
thf(17,axiom,
! [A: $i] : ( tT @ ( A @ eval ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_045) ).
thf(117,plain,
! [A: $i] : ( tT @ ( A @ eval ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(9,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( A @ assign ) )
!= ( E @ ( D @ ( C @ ifThenElse ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_029) ).
thf(85,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)],[9]) ).
thf(3,axiom,
! [A: $i] :
( ( A @ suc @ proj1Suc )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_004) ).
thf(65,plain,
! [A: $i] :
( ( A @ suc @ proj1Suc )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(11,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ ifThenElse ) ) @ proj2IfThenElse )
= B ),
file('/export/starexec/sandbox/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)],[11]) ).
thf(14,axiom,
! [A: $i] :
~ ( fF @ ( A @ eval ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_046) ).
thf(107,plain,
! [A: $i] :
~ ( fF @ ( A @ eval ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(108,plain,
~ ? [A: $i] : ( fF @ ( A @ eval ) ),
inference(miniscope,[status(thm)],[107]) ).
thf(109,plain,
! [A: $i] :
~ ( fF @ ( A @ eval ) ),
inference(cnf,[status(esa)],[108]) ).
thf(19,axiom,
! [A: $i] :
( ( A @ low @ proj1Low )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_007) ).
thf(122,plain,
! [A: $i] :
( ( A @ low @ proj1Low )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(123,plain,
! [A: $i] :
( ( A @ low @ proj1Low )
= A ),
inference(cnf,[status(esa)],[122]) ).
thf(124,plain,
! [A: $i] :
( ( A @ low @ proj1Low )
= A ),
inference(lifteq,[status(thm)],[123]) ).
thf(22,axiom,
! [A: $i] :
( fF
!= ( A @ var ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_017) ).
thf(131,plain,
! [A: $i] :
( fF
!= ( A @ var ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(132,plain,
~ ? [A: $i] :
( fF
= ( A @ var ) ),
inference(miniscope,[status(thm)],[131]) ).
thf(133,plain,
! [A: $i] :
( fF
!= ( A @ var ) ),
inference(cnf,[status(esa)],[132]) ).
thf(134,plain,
! [A: $i] :
( ( A @ var )
!= fF ),
inference(lifteq,[status(thm)],[133]) ).
thf(21,axiom,
! [A: $i] :
( ( nil @ ( A @ del ) )
= nil ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_048) ).
thf(128,plain,
! [A: $i] :
( ( nil @ ( A @ del ) )
= nil ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(32,axiom,
! [A: $i,B: $i] :
( ( A @ high )
!= ( B @ low ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_008) ).
thf(166,plain,
! [A: $i,B: $i] :
( ( A @ high )
!= ( B @ low ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(63,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ run ) @ ( l @ elem ) )
| ~ ( A @ ( B @ ( h @ cons ) @ run ) @ ( l @ elem ) )
| ~ ( A @ typeCorrect ) ),
inference(cnfConj,[status(thm)],[61]) ).
thf(64,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ run ) @ ( l @ elem ) )
| ~ ( A @ ( B @ ( h @ cons ) @ run ) @ ( l @ elem ) )
| ~ ( A @ typeCorrect ) ),
inference(simp,[status(thm)],[63]) ).
thf(55,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( A @ eval ) )
=> ( ( C @ ( B @ assign ) @ ( A @ run ) )
= ( A @ ( B @ cons ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_052) ).
thf(259,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)],[55]) ).
thf(38,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( C @ ( A @ eval ) )
=> ( ( C @ ( B @ assign ) @ ( A @ run ) )
= ( A @ ( B @ del ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_053) ).
thf(191,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)],[38]) ).
thf(402,plain,
! [A: $i] :
( ( A @ low )
!= h ),
inference(simp,[status(thm)],[347]) ).
thf(118,plain,
! [A: $i] : ( tT @ ( A @ eval ) ),
inference(cnf,[status(esa)],[117]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ nand ) )
!= tT ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_012) ).
thf(68,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ nand ) )
!= tT ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(69,plain,
~ ? [A: $i,B: $i] :
( ( B @ ( A @ nand ) )
= tT ),
inference(miniscope,[status(thm)],[68]) ).
thf(70,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ nand ) )
!= tT ),
inference(cnf,[status(esa)],[69]) ).
thf(71,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ nand ) )
!= tT ),
inference(lifteq,[status(thm)],[70]) ).
thf(35,axiom,
! [A: $i] :
( ( A @ high @ proj1High )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_006) ).
thf(181,plain,
! [A: $i] :
( ( A @ high @ proj1High )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(37,axiom,
! [A: $i] :
( zero
!= ( A @ suc ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_005) ).
thf(187,plain,
! [A: $i] :
( zero
!= ( A @ suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(16,axiom,
! [A: $i,B: $i,C: $i] :
( skip
!= ( C @ ( B @ ( A @ ifThenElse ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_027) ).
thf(113,plain,
! [A: $i,B: $i,C: $i] :
( skip
!= ( C @ ( B @ ( A @ ifThenElse ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(12,axiom,
! [A: $i,B: $i] :
( skip
!= ( B @ ( A @ assign ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_025) ).
thf(100,plain,
! [A: $i,B: $i] :
( skip
!= ( B @ ( A @ assign ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(101,plain,
~ ? [A: $i,B: $i] :
( skip
= ( B @ ( A @ assign ) ) ),
inference(miniscope,[status(thm)],[100]) ).
thf(102,plain,
! [B: $i,A: $i] :
( skip
!= ( B @ ( A @ assign ) ) ),
inference(cnf,[status(esa)],[101]) ).
thf(103,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ assign ) )
!= skip ),
inference(lifteq,[status(thm)],[102]) ).
thf(53,axiom,
! [A: $i,B: $i,C: $i] :
( ( A != B )
=> ( ( C @ ( B @ cons ) @ ( A @ del ) )
= ( C @ ( A @ del ) @ ( B @ cons ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_050) ).
thf(251,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)],[53]) ).
thf(129,plain,
! [A: $i] :
( ( nil @ ( A @ del ) )
= nil ),
inference(cnf,[status(esa)],[128]) ).
thf(130,plain,
! [A: $i] :
( ( nil @ ( A @ del ) )
= nil ),
inference(lifteq,[status(thm)],[129]) ).
thf(23,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ nand ) )
!= ( C @ var ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_014) ).
thf(135,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ nand ) )
!= ( C @ var ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(294,plain,
! [B: $i,A: $i] :
( ( ( skip @ ( A @ ( h @ cons ) @ run ) @ ( l @ elem ) )
!= ( skip @ ( B @ run ) @ ( l @ elem ) ) )
| ( skip @ ( B @ ( h @ cons ) @ run ) @ ( l @ elem ) )
| ~ $true
| ~ ( skip @ ( A @ run ) @ ( l @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[286,286]) ).
thf(295,plain,
! [B: $i,A: $i] :
( ( ( skip @ ( A @ ( h @ cons ) @ run ) @ ( l @ elem ) )
!= ( skip @ ( B @ run ) @ ( l @ elem ) ) )
| ( skip @ ( B @ ( h @ cons ) @ run ) @ ( l @ elem ) )
| ~ ( skip @ ( A @ run ) @ ( l @ elem ) ) ),
inference(simp,[status(thm)],[294]) ).
thf(296,plain,
! [A: $i] :
( ( skip @ ( A @ ( h @ cons ) @ ( h @ cons ) @ run ) @ ( l @ elem ) )
| ~ ( skip @ ( A @ run ) @ ( l @ elem ) ) ),
inference(pattern_uni,[status(thm)],[295:[bind(A,$thf( D )),bind(B,$thf( D @ ( h @ cons ) ))]]) ).
thf(299,plain,
! [A: $i] :
( ( skip @ ( A @ ( h @ cons ) @ ( h @ cons ) @ run ) @ ( l @ elem ) )
| ~ ( skip @ ( A @ run ) @ ( l @ elem ) ) ),
inference(simp,[status(thm)],[296]) ).
thf(54,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( B @ ( A @ eval ) )
=> ( ( D @ ( C @ ( B @ ifThenElse ) ) @ ( A @ run ) )
= ( D @ ( A @ run ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_056) ).
thf(255,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)],[54]) ).
thf(39,axiom,
! [A: $i] :
( ( skip @ ( A @ run ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_051) ).
thf(194,plain,
! [A: $i] :
( ( skip @ ( A @ run ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(323,plain,
! [B: $i,A: $i] :
( ( ( skip @ ( A @ ( h @ cons ) @ run ) @ ( l @ elem ) )
!= ( skip @ ( B @ run ) @ ( l @ elem ) ) )
| ( ( skip @ ( B @ ( h @ cons ) @ run ) )
!= nil )
| ~ $true
| ~ ( skip @ ( A @ run ) @ ( l @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[286,317]) ).
thf(324,plain,
! [B: $i,A: $i] :
( ( ( skip @ ( A @ ( h @ cons ) @ run ) @ ( l @ elem ) )
!= ( skip @ ( B @ run ) @ ( l @ elem ) ) )
| ( ( skip @ ( B @ ( h @ cons ) @ run ) )
!= nil )
| ~ ( skip @ ( A @ run ) @ ( l @ elem ) ) ),
inference(simp,[status(thm)],[323]) ).
thf(325,plain,
! [A: $i] :
( ( ( skip @ ( A @ ( h @ cons ) @ ( h @ cons ) @ run ) )
!= nil )
| ~ ( skip @ ( A @ run ) @ ( l @ elem ) ) ),
inference(pattern_uni,[status(thm)],[324:[bind(A,$thf( D )),bind(B,$thf( D @ ( h @ cons ) ))]]) ).
thf(327,plain,
! [A: $i] :
( ( ( skip @ ( A @ ( h @ cons ) @ ( h @ cons ) @ run ) )
!= nil )
| ~ ( skip @ ( A @ run ) @ ( l @ elem ) ) ),
inference(simp,[status(thm)],[325]) ).
thf(66,plain,
! [A: $i] :
( ( A @ suc @ proj1Suc )
= A ),
inference(cnf,[status(esa)],[65]) ).
thf(67,plain,
! [A: $i] :
( ( A @ suc @ proj1Suc )
= A ),
inference(lifteq,[status(thm)],[66]) ).
thf(25,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( A @ seq ) )
!= ( E @ ( D @ ( C @ ifThenElse ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_030) ).
thf(143,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)],[25]) ).
thf(13,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ assign ) @ proj1Assign )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_018) ).
thf(104,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ assign ) @ proj1Assign )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(49,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ seq ) @ typeCorrect )
<=> ( ( B @ typeCorrect )
& ( A @ typeCorrect ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_038) ).
thf(231,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)],[49]) ).
thf(29,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ seq ) @ proj2Seq )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_021) ).
thf(158,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ seq ) @ proj2Seq )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(24,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( A @ assign ) )
!= ( D @ ( C @ seq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_028) ).
thf(139,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( A @ assign ) )
!= ( D @ ( C @ seq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(58,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( A @ eval ) )
=> ( ( D @ ( C @ ( B @ ifThenElse ) ) @ ( A @ run ) )
= ( C @ ( A @ run ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_055) ).
thf(272,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)],[58]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ nand ) @ proj2Nand )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_010) ).
thf(82,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ nand ) @ proj2Nand )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(44,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ cons ) @ head )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_001) ).
thf(214,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ cons ) @ head )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(56,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ ifThenElse ) ) @ typeCorrect )
<=> ( ( C @ typeCorrect )
& ( B @ typeCorrect ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_039) ).
thf(262,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)],[56]) ).
thf(188,plain,
~ ? [A: $i] :
( zero
= ( A @ suc ) ),
inference(miniscope,[status(thm)],[187]) ).
thf(189,plain,
! [A: $i] :
( zero
!= ( A @ suc ) ),
inference(cnf,[status(esa)],[188]) ).
thf(190,plain,
! [A: $i] :
( ( A @ suc )
!= zero ),
inference(lifteq,[status(thm)],[189]) ).
thf(42,axiom,
! [A: $i,B: $i] : ( A @ ( B @ high @ assign ) @ typeCorrect ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_036) ).
thf(210,plain,
! [A: $i,B: $i] : ( A @ ( B @ high @ assign ) @ typeCorrect ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ nand ) @ proj1Nand )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_009) ).
thf(79,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ nand ) @ proj1Nand )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(31,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ ifThenElse ) ) @ proj1IfThenElse )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_022) ).
thf(163,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ ifThenElse ) ) @ proj1IfThenElse )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(41,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ cons ) @ ( A @ elem ) )
<=> ( ( C @ ( A @ elem ) )
| ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_043) ).
thf(200,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)],[41]) ).
thf(47,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ seq ) @ ( A @ run ) )
= ( C @ ( B @ ( A @ run ) @ run ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_054) ).
thf(227,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)],[47]) ).
thf(300,plain,
! [B: $i,A: $i] :
( ( ( skip @ typeCorrect )
!= ( A @ typeCorrect ) )
| ( A @ ( B @ run ) @ ( l @ elem ) )
| ~ ( A @ ( B @ ( h @ cons ) @ run ) @ ( l @ elem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[230,64]) ).
thf(301,plain,
! [B: $i,A: $i] :
( ( ( skip @ typeCorrect )
!= ( A @ typeCorrect ) )
| ( A @ ( B @ run ) @ ( l @ elem ) )
| ~ ( A @ ( B @ ( h @ cons ) @ run ) @ ( l @ elem ) ) ),
inference(simp,[status(thm)],[300]) ).
thf(302,plain,
! [A: $i] :
( ( skip @ ( A @ run ) @ ( l @ elem ) )
| ~ ( skip @ ( A @ ( h @ cons ) @ run ) @ ( l @ elem ) ) ),
inference(pattern_uni,[status(thm)],[301:[bind(A,$thf( skip ))]]) ).
thf(309,plain,
! [A: $i] :
( ( skip @ ( A @ run ) @ ( l @ elem ) )
| ~ ( skip @ ( A @ ( h @ cons ) @ run ) @ ( l @ elem ) ) ),
inference(simp,[status(thm)],[302]) ).
thf(16600,plain,
$false,
inference(e,[status(thm)],[78,349,317,173,347,249,170,217,269,340,153,184,110,125,157,238,121,348,147,221,89,243,74,117,85,197,65,97,109,124,212,134,128,166,161,64,286,259,191,402,59,118,71,335,181,187,113,230,103,213,251,130,135,299,162,255,194,150,327,67,199,127,154,72,143,104,250,231,319,158,139,75,119,272,346,82,214,262,190,210,107,79,131,68,62,163,200,227,122,309,100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWX240_1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.13/10.83 % Computer : n004.cluster.edu
% 0.13/10.83 % Model : x86_64 x86_64
% 0.13/10.83 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/10.83 % Memory : 8046.5625MB
% 0.13/10.83 % OS : Linux 6.8.0-71-generic
% 0.13/10.84 % CPULimit : 300
% 0.13/10.84 % WCLimit : 300
% 0.13/10.84 % DateTime : Sat Sep 26 17:02:03 UTC 2026
% 0.13/10.84 % CPUTime :
% 0.13/10.84 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.97/11.44 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.29/11.66 % [INFO] Parsing done (223ms).
% 1.29/11.68 % [INFO] Running in sequential loop mode.
% 2.07/12.08 % [INFO] eprover registered as external prover.
% 2.07/12.09 % [INFO] Scanning for conjecture ...
% 2.41/12.21 % [INFO] Found a conjecture (or negated_conjecture) and 56 axioms. Running axiom selection ...
% 2.63/12.31 % [INFO] Axiom selection finished. Selected 56 axioms (removed 0 axioms).
% 2.63/12.39 % [INFO] Problem is first-order (TPTP FOF).
% 2.88/12.40 % [INFO] Type checking passed.
% 2.88/12.40 % [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 ...
% 64.34/25.23 % External prover 'e' found a proof!
% 64.34/25.23 % [INFO] Killing All external provers ...
% 64.34/25.23 % Time passed: 14244ms (effective reasoning time: 13543ms)
% 64.34/25.23 % 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)>
% 64.34/25.23 % Axioms used in derivation (56): axiom_010, axiom_028, axiom_023, axiom_012, axiom_001, axiom_044, axiom_011, 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_056, axiom_027, axiom_005, axiom_045, axiom_038, axiom_031, axiom_015, axiom_004, axiom_055, axiom_033, axiom_022, 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
% 64.34/25.23 % No. of inferences in proof: 198
% 64.34/25.23 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 14244 ms resp. 13543 ms w/o parsing
% 64.34/25.28 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 64.34/25.28 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------