%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWX212-1 : 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 : n011.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 09:15:18 AM UTC 2026
% Result : Unsatisfiable 17.77s 5.16s
% Output : Refutation 15.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 91
% Syntax : Number of formulae : 229 ( 214 unt; 0 typ; 0 def)
% Number of atoms : 260 ( 259 equ; 0 cnn)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 1436 ( 42 ~; 31 |; 0 &;1363 @)
% ( 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 : 27 ( 25 usr; 9 con; 0-4 aty)
% Number of variables : 417 ( 0 ^; 417 !; 0 ?; 417 :)
% Comments :
%------------------------------------------------------------------------------
thf(eq2_decl,type,
eq2: $i > $i > $i ).
thf(prop_koen_decl,type,
prop_koen: $i > $i > $i > $i ).
thf(bfalse_decl,type,
bfalse: $i ).
thf(btrue_decl,type,
btrue: $i ).
thf(z_decl,type,
z: $i > $i > $i ).
thf(y_decl,type,
y: $i > $i > $i ).
thf(nil2_decl,type,
nil2: $i ).
thf(x2_decl,type,
x2: $i > $i > $i ).
thf(x_decl,type,
x: $i > $i > $i ).
thf(atom_decl,type,
atom: $i > $i ).
thf(eps_decl,type,
eps: $i ).
thf(step_decl,type,
step: $i > $i > $i ).
thf(star_decl,type,
star: $i > $i ).
thf(aux2_decl,type,
aux2: $i > $i > $i > $i > $i ).
thf(eps2_decl,type,
eps2: $i > $i ).
thf(rec_decl,type,
rec: $i > $i > $i ).
thf(cons_decl,type,
cons: $i > $i > $i ).
thf(aux_decl,type,
aux: $i > $i > $i > $i ).
thf(eq_decl,type,
eq: $i > $i > $i ).
thf(nil_decl,type,
nil: $i ).
thf(andb_decl,type,
andb: $i > $i > $i ).
thf(orb_decl,type,
orb: $i > $i > $i ).
thf(c_decl,type,
c: $i ).
thf(a_decl,type,
a: $i ).
thf(b_decl,type,
b: $i ).
thf(31,axiom,
! [A: $i] :
( ( eps @ ( A @ atom @ z ) )
= ( A @ atom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_007) ).
thf(153,plain,
! [A: $i] :
( ( eps @ ( A @ atom @ z ) )
= ( A @ atom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(5,axiom,
! [B: $i,A: $i] :
( ( eps @ ( B @ ( A @ y ) @ x2 ) )
= ( eps @ ( B @ ( A @ y ) @ x ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_050) ).
thf(101,plain,
! [B: $i,A: $i] :
( ( eps @ ( B @ ( A @ y ) @ x2 ) )
= ( eps @ ( B @ ( A @ y ) @ x ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(79,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ prop_koen ) ) )
= ( C @ ( A @ ( B @ y ) @ rec ) @ ( C @ ( B @ ( A @ y ) @ rec ) @ eq2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_079) ).
thf(249,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ prop_koen ) ) )
= ( C @ ( A @ ( B @ y ) @ rec ) @ ( C @ ( B @ ( A @ y ) @ rec ) @ eq2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(71,axiom,
! [A: $i] :
( ( A @ ( bfalse @ andb ) )
= bfalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_064) ).
thf(233,plain,
! [A: $i] :
( ( A @ ( bfalse @ andb ) )
= bfalse ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(234,plain,
! [A: $i] :
( ( A @ ( bfalse @ andb ) )
= bfalse ),
inference(lifteq,[status(thm)],[233]) ).
thf(12,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ x ) @ ( A @ star @ z ) )
= ( C @ ( B @ x ) @ ( A @ star @ y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_027) ).
thf(115,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ x ) @ ( A @ star @ z ) )
= ( C @ ( B @ x ) @ ( A @ star @ y ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(63,axiom,
! [B: $i,A: $i] :
( ( B @ atom @ ( A @ star @ x2 ) )
= ( B @ atom @ ( A @ star @ x ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_057) ).
thf(217,plain,
! [B: $i,A: $i] :
( ( B @ atom @ ( A @ star @ x2 ) )
= ( B @ atom @ ( A @ star @ x ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(78,axiom,
( ( a @ ( b @ eq ) )
= bfalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_082) ).
thf(247,plain,
( ( a @ ( b @ eq ) )
= bfalse ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(89,axiom,
! [A: $i] :
( ( A @ star @ eps2 )
= btrue ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_068) ).
thf(269,plain,
! [A: $i] :
( ( A @ star @ eps2 )
= btrue ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(47,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ y ) @ ( eps @ x2 ) )
= ( B @ ( A @ y ) @ ( eps @ x ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_035) ).
thf(185,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ y ) @ ( eps @ x2 ) )
= ( B @ ( A @ y ) @ ( eps @ x ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(83,axiom,
( ( b @ ( a @ eq ) )
= bfalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_080) ).
thf(257,plain,
( ( b @ ( a @ eq ) )
= bfalse ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(17,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ x ) @ ( eps @ x2 ) )
= ( B @ ( A @ x ) @ ( eps @ x ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_034) ).
thf(125,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ x ) @ ( eps @ x2 ) )
= ( B @ ( A @ x ) @ ( eps @ x ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(52,axiom,
! [A: $i] :
( ( nil2 @ ( A @ star @ z ) )
= nil2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_024) ).
thf(195,plain,
! [A: $i] :
( ( nil2 @ ( A @ star @ z ) )
= nil2 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(196,plain,
! [A: $i] :
( ( nil2 @ ( A @ star @ z ) )
= nil2 ),
inference(lifteq,[status(thm)],[195]) ).
thf(33,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ y ) @ eps2 )
= ( B @ eps2 @ ( A @ eps2 @ andb ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_067) ).
thf(157,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ y ) @ eps2 )
= ( B @ eps2 @ ( A @ eps2 @ andb ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(49,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ x ) @ ( B @ ( A @ y ) @ z ) )
= ( D @ ( C @ x ) @ ( B @ ( A @ y ) @ y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_021) ).
thf(189,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ x ) @ ( B @ ( A @ y ) @ z ) )
= ( D @ ( C @ x ) @ ( B @ ( A @ y ) @ y ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(85,axiom,
! [A: $i] :
( ( A @ ( btrue @ andb ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_063) ).
thf(261,plain,
! [A: $i] :
( ( A @ ( btrue @ andb ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(62,axiom,
! [A: $i] :
( ( A @ ( eps @ step ) )
= nil2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_076) ).
thf(215,plain,
! [A: $i] :
( ( A @ ( eps @ step ) )
= nil2 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(216,plain,
! [A: $i] :
( ( A @ ( eps @ step ) )
= nil2 ),
inference(lifteq,[status(thm)],[215]) ).
thf(44,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ atom @ ( B @ ( A @ x ) @ z ) )
= ( C @ atom @ ( B @ ( A @ x ) @ y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_014) ).
thf(179,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ atom @ ( B @ ( A @ x ) @ z ) )
= ( C @ atom @ ( B @ ( A @ x ) @ y ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(73,axiom,
( ( btrue @ ( bfalse @ eq2 ) )
= bfalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_086) ).
thf(237,plain,
( ( btrue @ ( bfalse @ eq2 ) )
= bfalse ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(238,plain,
( ( btrue @ ( bfalse @ eq2 ) )
= bfalse ),
inference(lifteq,[status(thm)],[237]) ).
thf(15,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ star @ ( B @ ( A @ y ) @ x2 ) )
= ( C @ star @ ( B @ ( A @ y ) @ x ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_054) ).
thf(121,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ star @ ( B @ ( A @ y ) @ x2 ) )
= ( C @ star @ ( B @ ( A @ y ) @ x ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(60,axiom,
! [B: $i,A: $i] :
( ( B @ atom @ ( A @ atom @ x2 ) )
= ( B @ atom @ ( A @ atom @ x ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_039) ).
thf(211,plain,
! [B: $i,A: $i] :
( ( B @ atom @ ( A @ atom @ x2 ) )
= ( B @ atom @ ( A @ atom @ x ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(81,axiom,
( ( nil2 @ eps2 )
= bfalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_069) ).
thf(253,plain,
( ( nil2 @ eps2 )
= bfalse ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(28,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ star @ ( B @ ( A @ y ) @ z ) )
= ( C @ star @ ( B @ ( A @ y ) @ y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_023) ).
thf(147,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ star @ ( B @ ( A @ y ) @ z ) )
= ( C @ star @ ( B @ ( A @ y ) @ y ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(65,axiom,
! [B: $i,A: $i] :
( ( B @ star @ ( A @ atom @ z ) )
= ( B @ star @ ( A @ atom @ y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_011) ).
thf(221,plain,
! [B: $i,A: $i] :
( ( B @ star @ ( A @ atom @ z ) )
= ( B @ star @ ( A @ atom @ y ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(20,axiom,
( ( nil2 @ ( eps @ x2 ) )
= eps ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_031) ).
thf(131,plain,
( ( nil2 @ ( eps @ x2 ) )
= eps ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(132,plain,
( ( nil2 @ ( eps @ x2 ) )
= eps ),
inference(lifteq,[status(thm)],[131]) ).
thf(21,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ y ) @ ( B @ ( A @ x ) @ z ) )
= ( D @ ( C @ y ) @ ( B @ ( A @ x ) @ y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_016) ).
thf(133,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ y ) @ ( B @ ( A @ x ) @ z ) )
= ( D @ ( C @ y ) @ ( B @ ( A @ x ) @ y ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(76,axiom,
( ( eps @ eps2 )
= btrue ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_065) ).
thf(243,plain,
( ( eps @ eps2 )
= btrue ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(87,axiom,
! [A: $i] :
( ( A @ ( bfalse @ orb ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_062) ).
thf(265,plain,
! [A: $i] :
( ( A @ ( bfalse @ orb ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(57,axiom,
( ( eps @ ( eps @ x2 ) )
= ( eps @ ( eps @ x ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_032) ).
thf(205,plain,
( ( eps @ ( eps @ x2 ) )
= ( eps @ ( eps @ x ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(206,plain,
( ( eps @ ( eps @ x ) )
= ( eps @ ( eps @ x2 ) ) ),
inference(lifteq,[status(thm)],[205]) ).
thf(248,plain,
( ( a @ ( b @ eq ) )
= bfalse ),
inference(lifteq,[status(thm)],[247]) ).
thf(13,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ atom @ ( B @ ( A @ y ) @ z ) )
= ( C @ atom @ ( B @ ( A @ y ) @ y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_020) ).
thf(117,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ atom @ ( B @ ( A @ y ) @ z ) )
= ( C @ atom @ ( B @ ( A @ y ) @ y ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(270,plain,
! [A: $i] :
( ( A @ star @ eps2 )
= btrue ),
inference(lifteq,[status(thm)],[269]) ).
thf(55,axiom,
! [A: $i] :
( ( nil2 @ ( A @ atom @ x2 ) )
= ( A @ atom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_037) ).
thf(201,plain,
! [A: $i] :
( ( nil2 @ ( A @ atom @ x2 ) )
= ( A @ atom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(84,axiom,
( ( bfalse @ ( btrue @ eq2 ) )
= bfalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_087) ).
thf(259,plain,
( ( bfalse @ ( btrue @ eq2 ) )
= bfalse ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(260,plain,
( ( bfalse @ ( btrue @ eq2 ) )
= bfalse ),
inference(lifteq,[status(thm)],[259]) ).
thf(23,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ y ) @ ( A @ star @ x2 ) )
= ( C @ ( B @ y ) @ ( A @ star @ x ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_059) ).
thf(137,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ y ) @ ( A @ star @ x2 ) )
= ( C @ ( B @ y ) @ ( A @ star @ x ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(37,axiom,
! [B: $i,A: $i] :
( ( B @ atom @ ( A @ star @ z ) )
= ( B @ atom @ ( A @ star @ y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_026) ).
thf(165,plain,
! [B: $i,A: $i] :
( ( B @ atom @ ( A @ star @ z ) )
= ( B @ atom @ ( A @ star @ y ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(1,negated_conjecture,
! [C: $i,B: $i,A: $i] :
( ( bfalse @ ( C @ ( B @ ( A @ prop_koen ) ) @ eq2 ) )
!= btrue ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goal) ).
thf(92,plain,
! [C: $i,B: $i,A: $i] :
( ( bfalse @ ( C @ ( B @ ( A @ prop_koen ) ) @ eq2 ) )
!= btrue ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(69,axiom,
( ( a @ ( c @ eq ) )
= bfalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_084) ).
thf(229,plain,
( ( a @ ( c @ eq ) )
= bfalse ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(80,axiom,
( ( c @ ( b @ eq ) )
= bfalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_083) ).
thf(251,plain,
( ( c @ ( b @ eq ) )
= bfalse ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(252,plain,
( ( c @ ( b @ eq ) )
= bfalse ),
inference(lifteq,[status(thm)],[251]) ).
thf(53,axiom,
! [B: $i,A: $i] :
( ( nil2 @ ( B @ ( A @ y ) @ x2 ) )
= ( B @ ( A @ y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_049) ).
thf(197,plain,
! [B: $i,A: $i] :
( ( nil2 @ ( B @ ( A @ y ) @ x2 ) )
= ( B @ ( A @ y ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(3,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ atom @ ( B @ ( A @ x ) @ x2 ) )
= ( C @ atom @ ( B @ ( A @ x ) @ x ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_045) ).
thf(97,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ atom @ ( B @ ( A @ x ) @ x2 ) )
= ( C @ atom @ ( B @ ( A @ x ) @ x ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(39,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ y ) @ ( A @ atom @ z ) )
= ( C @ ( B @ y ) @ ( A @ atom @ y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_010) ).
thf(169,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ y ) @ ( A @ atom @ z ) )
= ( C @ ( B @ y ) @ ( A @ atom @ y ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(25,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ atom @ step ) )
= ( B @ ( A @ eq ) @ ( A @ ( B @ aux ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_071) ).
thf(141,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ atom @ step ) )
= ( B @ ( A @ eq ) @ ( A @ ( B @ aux ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(51,axiom,
! [B: $i,A: $i] :
( ( B @ atom @ ( A @ atom @ z ) )
= ( B @ atom @ ( A @ atom @ y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_008) ).
thf(193,plain,
! [B: $i,A: $i] :
( ( B @ atom @ ( A @ atom @ z ) )
= ( B @ atom @ ( A @ atom @ y ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(2,axiom,
! [B: $i,A: $i] :
( ( nil2 @ ( B @ ( A @ y ) @ z ) )
= nil2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_018) ).
thf(95,plain,
! [B: $i,A: $i] :
( ( nil2 @ ( B @ ( A @ y ) @ z ) )
= nil2 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(96,plain,
! [B: $i,A: $i] :
( ( nil2 @ ( B @ ( A @ y ) @ z ) )
= nil2 ),
inference(lifteq,[status(thm)],[95]) ).
thf(9,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ y ) @ step ) )
= ( A @ eps2 @ ( B @ ( A @ ( C @ aux2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_073) ).
thf(109,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ y ) @ step ) )
= ( A @ eps2 @ ( B @ ( A @ ( C @ aux2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(93,plain,
! [C: $i,B: $i,A: $i] :
( ( bfalse @ ( C @ ( B @ ( A @ prop_koen ) ) @ eq2 ) )
!= btrue ),
inference(polarity_switch,[status(thm)],[92]) ).
thf(94,plain,
! [C: $i,B: $i,A: $i] :
( ( bfalse @ ( C @ ( B @ ( A @ prop_koen ) ) @ eq2 ) )
!= btrue ),
inference(lifteq,[status(thm)],[93]) ).
thf(326,plain,
! [C: $i,B: $i,A: $i] :
( ( ( bfalse @ ( C @ ( B @ ( A @ prop_koen ) ) @ eq2 ) )
!= ( bfalse @ ( btrue @ eq2 ) ) )
| ( btrue != bfalse ) ),
inference(paramod_ordered,[status(thm)],[260,94]) ).
thf(327,plain,
! [C: $i,B: $i,A: $i] :
( ( bfalse != bfalse )
| ( ( C @ ( B @ ( A @ prop_koen ) ) )
!= btrue )
| ( btrue != bfalse ) ),
inference(simp,[status(thm)],[326]) ).
thf(328,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ prop_koen ) ) )
!= btrue )
| ( btrue != bfalse ) ),
inference(simp,[status(thm)],[327]) ).
thf(16,axiom,
! [A: $i] :
( ( A @ ( nil2 @ z ) )
= nil2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_004) ).
thf(123,plain,
! [A: $i] :
( ( A @ ( nil2 @ z ) )
= nil2 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(124,plain,
! [A: $i] :
( ( A @ ( nil2 @ z ) )
= nil2 ),
inference(lifteq,[status(thm)],[123]) ).
thf(67,axiom,
! [B: $i,A: $i] :
( ( B @ star @ ( A @ star @ x2 ) )
= ( B @ star @ ( A @ star @ x ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_060) ).
thf(225,plain,
! [B: $i,A: $i] :
( ( B @ star @ ( A @ star @ x2 ) )
= ( B @ star @ ( A @ star @ x ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(41,axiom,
! [A: $i] :
( ( A @ star @ ( eps @ x2 ) )
= ( A @ star @ ( eps @ x ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_036) ).
thf(173,plain,
! [A: $i] :
( ( A @ star @ ( eps @ x2 ) )
= ( A @ star @ ( eps @ x ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(19,axiom,
! [A: $i] :
( ( nil2 @ ( A @ atom @ z ) )
= nil2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_006) ).
thf(129,plain,
! [A: $i] :
( ( nil2 @ ( A @ atom @ z ) )
= nil2 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(98,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ atom @ ( B @ ( A @ x ) @ x ) )
= ( C @ atom @ ( B @ ( A @ x ) @ x2 ) ) ),
inference(lifteq,[status(thm)],[97]) ).
thf(356,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ atom @ ( B @ ( A @ x ) @ x ) )
!= ( eps @ ( eps @ x ) ) )
| ( ( C @ atom @ ( B @ ( A @ x ) @ x2 ) )
= ( eps @ ( eps @ x2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[206,98]) ).
thf(360,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ atom )
!= eps )
| ( ( B @ ( A @ x ) )
!= eps )
| ( ( C @ atom @ ( B @ ( A @ x ) @ x2 ) )
= ( eps @ ( eps @ x2 ) ) ) ),
inference(simp,[status(thm)],[356]) ).
thf(7,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ y ) @ ( B @ ( A @ y ) @ z ) )
= ( D @ ( C @ y ) @ ( B @ ( A @ y ) @ y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_022) ).
thf(105,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ y ) @ ( B @ ( A @ y ) @ z ) )
= ( D @ ( C @ y ) @ ( B @ ( A @ y ) @ y ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(244,plain,
( ( eps @ eps2 )
= btrue ),
inference(lifteq,[status(thm)],[243]) ).
thf(35,axiom,
! [A: $i] :
( ( A @ atom @ ( eps @ x2 ) )
= ( A @ atom @ ( eps @ x ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_033) ).
thf(161,plain,
! [A: $i] :
( ( A @ atom @ ( eps @ x2 ) )
= ( A @ atom @ ( eps @ x ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(29,axiom,
! [A: $i] :
( ( A @ ( nil2 @ step ) )
= nil2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_075) ).
thf(149,plain,
! [A: $i] :
( ( A @ ( nil2 @ step ) )
= nil2 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(42,axiom,
! [A: $i] :
( ( A @ ( eps @ z ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_005) ).
thf(175,plain,
! [A: $i] :
( ( A @ ( eps @ z ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(176,plain,
! [A: $i] :
( ( A @ ( eps @ z ) )
= A ),
inference(lifteq,[status(thm)],[175]) ).
thf(50,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ x ) @ step ) )
= ( C @ ( B @ step ) @ ( C @ ( A @ step ) @ x ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_072) ).
thf(191,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ x ) @ step ) )
= ( C @ ( B @ step ) @ ( C @ ( A @ step ) @ x ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(56,axiom,
! [A: $i] :
( ( A @ ( nil2 @ x2 ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_030) ).
thf(203,plain,
! [A: $i] :
( ( A @ ( nil2 @ x2 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(204,plain,
! [A: $i] :
( ( A @ ( nil2 @ x2 ) )
= A ),
inference(lifteq,[status(thm)],[203]) ).
thf(72,axiom,
! [A: $i] :
( ( A @ ( btrue @ orb ) )
= btrue ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_061) ).
thf(235,plain,
! [A: $i] :
( ( A @ ( btrue @ orb ) )
= btrue ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(236,plain,
! [A: $i] :
( ( A @ ( btrue @ orb ) )
= btrue ),
inference(lifteq,[status(thm)],[235]) ).
thf(45,axiom,
! [B: $i,A: $i] :
( ( eps @ ( B @ ( A @ x ) @ z ) )
= ( B @ ( A @ x ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_013) ).
thf(181,plain,
! [B: $i,A: $i] :
( ( eps @ ( B @ ( A @ x ) @ z ) )
= ( B @ ( A @ x ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(34,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ y ) @ ( A @ atom @ x2 ) )
= ( C @ ( B @ y ) @ ( A @ atom @ x ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_041) ).
thf(159,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ y ) @ ( A @ atom @ x2 ) )
= ( C @ ( B @ y ) @ ( A @ atom @ x ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(48,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ y ) @ ( B @ ( A @ x ) @ x2 ) )
= ( D @ ( C @ y ) @ ( B @ ( A @ x ) @ x ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_047) ).
thf(187,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ y ) @ ( B @ ( A @ x ) @ x2 ) )
= ( D @ ( C @ y ) @ ( B @ ( A @ x ) @ x ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(11,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ cons ) @ ( A @ rec ) )
= ( C @ ( B @ ( A @ step ) @ rec ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_078) ).
thf(113,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ cons ) @ ( A @ rec ) )
= ( C @ ( B @ ( A @ step ) @ rec ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(64,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ x ) @ ( A @ atom @ x2 ) )
= ( C @ ( B @ x ) @ ( A @ atom @ x ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_040) ).
thf(219,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ x ) @ ( A @ atom @ x2 ) )
= ( C @ ( B @ x ) @ ( A @ atom @ x ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(230,plain,
( ( a @ ( c @ eq ) )
= bfalse ),
inference(lifteq,[status(thm)],[229]) ).
thf(77,axiom,
! [A: $i] :
( ( A @ ( A @ eq2 ) )
= btrue ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_089) ).
thf(245,plain,
! [A: $i] :
( ( A @ ( A @ eq2 ) )
= btrue ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(90,axiom,
( ( c @ ( a @ eq ) )
= bfalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_081) ).
thf(271,plain,
( ( c @ ( a @ eq ) )
= bfalse ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(6,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ star @ step ) )
= ( A @ star @ ( B @ ( A @ step ) @ y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_074) ).
thf(103,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ star @ step ) )
= ( A @ star @ ( B @ ( A @ step ) @ y ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(61,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ x ) @ eps2 )
= ( B @ eps2 @ ( A @ eps2 @ orb ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_066) ).
thf(213,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ x ) @ eps2 )
= ( B @ eps2 @ ( A @ eps2 @ orb ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(32,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ x ) @ ( B @ ( A @ x ) @ x2 ) )
= ( D @ ( C @ x ) @ ( B @ ( A @ x ) @ x ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_046) ).
thf(155,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ x ) @ ( B @ ( A @ x ) @ x2 ) )
= ( D @ ( C @ x ) @ ( B @ ( A @ x ) @ x ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(130,plain,
! [A: $i] :
( ( nil2 @ ( A @ atom @ z ) )
= nil2 ),
inference(lifteq,[status(thm)],[129]) ).
thf(66,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ atom @ ( B @ ( A @ y ) @ x2 ) )
= ( C @ atom @ ( B @ ( A @ y ) @ x ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_051) ).
thf(223,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ atom @ ( B @ ( A @ y ) @ x2 ) )
= ( C @ atom @ ( B @ ( A @ y ) @ x ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(22,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ x ) @ ( A @ star @ x2 ) )
= ( C @ ( B @ x ) @ ( A @ star @ x ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_058) ).
thf(135,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ x ) @ ( A @ star @ x2 ) )
= ( C @ ( B @ x ) @ ( A @ star @ x ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(88,axiom,
! [A: $i] :
( ( A @ atom @ eps2 )
= bfalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_070) ).
thf(267,plain,
! [A: $i] :
( ( A @ atom @ eps2 )
= bfalse ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(75,axiom,
( ( b @ ( c @ eq ) )
= bfalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_085) ).
thf(241,plain,
( ( b @ ( c @ eq ) )
= bfalse ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(38,axiom,
! [A: $i] :
( ( eps @ ( A @ star @ x2 ) )
= ( eps @ ( A @ star @ x ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_056) ).
thf(167,plain,
! [A: $i] :
( ( eps @ ( A @ star @ x2 ) )
= ( eps @ ( A @ star @ x ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(82,axiom,
! [B: $i,A: $i] :
( ( btrue @ ( B @ ( A @ aux ) ) )
= eps ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom) ).
thf(255,plain,
! [B: $i,A: $i] :
( ( btrue @ ( B @ ( A @ aux ) ) )
= eps ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(59,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ x ) @ ( B @ ( A @ y ) @ x2 ) )
= ( D @ ( C @ x ) @ ( B @ ( A @ y ) @ x ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_052) ).
thf(209,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ x ) @ ( B @ ( A @ y ) @ x2 ) )
= ( D @ ( C @ x ) @ ( B @ ( A @ y ) @ x ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(27,axiom,
! [A: $i] :
( ( nil @ ( A @ rec ) )
= ( A @ eps2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_077) ).
thf(145,plain,
! [A: $i] :
( ( nil @ ( A @ rec ) )
= ( A @ eps2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(150,plain,
! [A: $i] :
( ( A @ ( nil2 @ step ) )
= nil2 ),
inference(lifteq,[status(thm)],[149]) ).
thf(86,axiom,
! [A: $i] :
( ( A @ ( A @ eq ) )
= btrue ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_088) ).
thf(263,plain,
! [A: $i] :
( ( A @ ( A @ eq ) )
= btrue ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(54,axiom,
! [B: $i,A: $i] :
( ( nil2 @ ( B @ ( A @ x ) @ x2 ) )
= ( B @ ( A @ x ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_043) ).
thf(199,plain,
! [B: $i,A: $i] :
( ( nil2 @ ( B @ ( A @ x ) @ x2 ) )
= ( B @ ( A @ x ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(43,axiom,
! [B: $i,A: $i] :
( ( nil2 @ ( B @ ( A @ x ) @ z ) )
= nil2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_012) ).
thf(177,plain,
! [B: $i,A: $i] :
( ( nil2 @ ( B @ ( A @ x ) @ z ) )
= nil2 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(246,plain,
! [A: $i] :
( ( A @ ( A @ eq2 ) )
= btrue ),
inference(lifteq,[status(thm)],[245]) ).
thf(492,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ eq2 ) )
!= ( bfalse @ ( D @ ( C @ ( B @ prop_koen ) ) @ eq2 ) ) )
| ( btrue != btrue ) ),
inference(paramod_ordered,[status(thm)],[246,94]) ).
thf(493,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ eq2 ) )
!= ( bfalse @ ( D @ ( C @ ( B @ prop_koen ) ) @ eq2 ) ) ),
inference(simp,[status(thm)],[492]) ).
thf(494,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A != bfalse )
| ( A
!= ( D @ ( C @ ( B @ prop_koen ) ) ) ) ),
inference(simp,[status(thm)],[493]) ).
thf(502,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ prop_koen ) ) )
!= bfalse ),
inference(simp,[status(thm)],[494]) ).
thf(18,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ star @ ( B @ ( A @ x ) @ z ) )
= ( C @ star @ ( B @ ( A @ x ) @ y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_017) ).
thf(127,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ star @ ( B @ ( A @ x ) @ z ) )
= ( C @ star @ ( B @ ( A @ x ) @ y ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(26,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ x ) @ ( A @ atom @ z ) )
= ( C @ ( B @ x ) @ ( A @ atom @ y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_009) ).
thf(143,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ x ) @ ( A @ atom @ z ) )
= ( C @ ( B @ x ) @ ( A @ atom @ y ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(70,axiom,
! [C: $i,B: $i,A: $i] :
( ( bfalse @ ( C @ ( B @ ( A @ aux2 ) ) ) )
= ( nil2 @ ( C @ ( A @ ( B @ step ) @ y ) @ x ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_003) ).
thf(231,plain,
! [C: $i,B: $i,A: $i] :
( ( bfalse @ ( C @ ( B @ ( A @ aux2 ) ) ) )
= ( nil2 @ ( C @ ( A @ ( B @ step ) @ y ) @ x ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(4,axiom,
! [A: $i] :
( ( eps @ ( A @ atom @ x2 ) )
= ( eps @ ( A @ atom @ x ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_038) ).
thf(99,plain,
! [A: $i] :
( ( eps @ ( A @ atom @ x2 ) )
= ( eps @ ( A @ atom @ x ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(258,plain,
( ( b @ ( a @ eq ) )
= bfalse ),
inference(lifteq,[status(thm)],[257]) ).
thf(40,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ y ) @ ( A @ star @ z ) )
= ( C @ ( B @ y ) @ ( A @ star @ y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_028) ).
thf(171,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ y ) @ ( A @ star @ z ) )
= ( C @ ( B @ y ) @ ( A @ star @ y ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(24,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ star @ ( B @ ( A @ x ) @ x2 ) )
= ( C @ star @ ( B @ ( A @ x ) @ x ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_048) ).
thf(139,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ star @ ( B @ ( A @ x ) @ x2 ) )
= ( C @ star @ ( B @ ( A @ x ) @ x ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(14,axiom,
! [A: $i] :
( ( eps @ ( A @ star @ z ) )
= ( A @ star ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_025) ).
thf(119,plain,
! [A: $i] :
( ( eps @ ( A @ star @ z ) )
= ( A @ star ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(58,axiom,
! [B: $i,A: $i] :
( ( eps @ ( B @ ( A @ y ) @ z ) )
= ( B @ ( A @ y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_019) ).
thf(207,plain,
! [B: $i,A: $i] :
( ( eps @ ( B @ ( A @ y ) @ z ) )
= ( B @ ( A @ y ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(272,plain,
( ( c @ ( a @ eq ) )
= bfalse ),
inference(lifteq,[status(thm)],[271]) ).
thf(367,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ atom @ ( B @ ( A @ x ) @ x2 ) )
!= ( nil2 @ ( eps @ x2 ) ) )
| ( ( eps @ ( eps @ x2 ) )
= eps )
| ( ( C @ atom )
!= eps )
| ( ( B @ ( A @ x ) )
!= eps ) ),
inference(paramod_ordered,[status(thm)],[360,132]) ).
thf(377,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ atom )
!= nil2 )
| ( ( B @ ( A @ x ) )
!= eps )
| ( ( C @ atom )
!= eps )
| ( ( B @ ( A @ x ) )
!= eps )
| ( ( eps @ ( eps @ x2 ) )
= eps ) ),
inference(simp,[status(thm)],[367]) ).
thf(383,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ atom )
!= nil2 )
| ( ( C @ atom )
!= eps )
| ( ( B @ ( A @ x ) )
!= eps )
| ( ( eps @ ( eps @ x2 ) )
= eps ) ),
inference(simp,[status(thm)],[377]) ).
thf(30,axiom,
! [B: $i,A: $i] :
( ( B @ star @ ( A @ star @ z ) )
= ( B @ star @ ( A @ star @ y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_029) ).
thf(151,plain,
! [B: $i,A: $i] :
( ( B @ star @ ( A @ star @ z ) )
= ( B @ star @ ( A @ star @ y ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(46,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ x ) @ ( B @ ( A @ x ) @ z ) )
= ( D @ ( C @ x ) @ ( B @ ( A @ x ) @ y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_015) ).
thf(183,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ x ) @ ( B @ ( A @ x ) @ z ) )
= ( D @ ( C @ x ) @ ( B @ ( A @ x ) @ y ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(91,axiom,
! [B: $i,A: $i] :
( ( bfalse @ ( B @ ( A @ aux ) ) )
= nil2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_001) ).
thf(273,plain,
! [B: $i,A: $i] :
( ( bfalse @ ( B @ ( A @ aux ) ) )
= nil2 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(8,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ y ) @ ( B @ ( A @ y ) @ x2 ) )
= ( D @ ( C @ y ) @ ( B @ ( A @ y ) @ x ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_053) ).
thf(107,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ y ) @ ( B @ ( A @ y ) @ x2 ) )
= ( D @ ( C @ y ) @ ( B @ ( A @ y ) @ x ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(268,plain,
! [A: $i] :
( ( A @ atom @ eps2 )
= bfalse ),
inference(lifteq,[status(thm)],[267]) ).
thf(100,plain,
! [A: $i] :
( ( eps @ ( A @ atom @ x ) )
= ( eps @ ( A @ atom @ x2 ) ) ),
inference(lifteq,[status(thm)],[99]) ).
thf(428,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( eps @ ( A @ atom @ x ) )
!= ( C @ ( B @ x ) ) )
| ( ( D @ atom )
!= nil2 )
| ( ( D @ atom )
!= eps )
| ( ( eps @ ( A @ atom @ x2 ) )
!= eps )
| ( ( eps @ ( eps @ x2 ) )
= eps ) ),
inference(paramod_ordered,[status(thm)],[100,383]) ).
thf(429,plain,
! [B: $i,A: $i] :
( ( ( A @ atom )
!= nil2 )
| ( ( A @ atom )
!= eps )
| ( ( eps @ ( B @ atom @ x2 ) )
!= eps )
| ( ( eps @ ( eps @ x2 ) )
= eps ) ),
inference(pattern_uni,[status(thm)],[428:[bind(A,$thf( E )),bind(B,$thf( E @ atom )),bind(C,$thf( eps ))]]) ).
thf(437,plain,
! [B: $i,A: $i] :
( ( ( A @ atom )
!= nil2 )
| ( ( A @ atom )
!= eps )
| ( ( eps @ ( B @ atom @ x2 ) )
!= eps )
| ( ( eps @ ( eps @ x2 ) )
= eps ) ),
inference(simp,[status(thm)],[429]) ).
thf(74,axiom,
! [C: $i,B: $i,A: $i] :
( ( btrue @ ( C @ ( B @ ( A @ aux2 ) ) ) )
= ( A @ ( C @ step ) @ ( C @ ( A @ ( B @ step ) @ y ) @ x ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_002) ).
thf(239,plain,
! [C: $i,B: $i,A: $i] :
( ( btrue @ ( C @ ( B @ ( A @ aux2 ) ) ) )
= ( A @ ( C @ step ) @ ( C @ ( A @ ( B @ step ) @ y ) @ x ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(242,plain,
( ( b @ ( c @ eq ) )
= bfalse ),
inference(lifteq,[status(thm)],[241]) ).
thf(36,axiom,
! [A: $i] :
( ( nil2 @ ( A @ star @ x2 ) )
= ( A @ star ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_055) ).
thf(163,plain,
! [A: $i] :
( ( nil2 @ ( A @ star @ x2 ) )
= ( A @ star ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(254,plain,
( ( nil2 @ eps2 )
= bfalse ),
inference(lifteq,[status(thm)],[253]) ).
thf(275,plain,
( ( ( eps @ eps2 )
!= ( nil2 @ eps2 ) )
| ( btrue = bfalse ) ),
inference(paramod_ordered,[status(thm)],[254,244]) ).
thf(277,plain,
( ( eps != nil2 )
| ( btrue = bfalse ) ),
inference(simp,[status(thm)],[275]) ).
thf(10,axiom,
! [B: $i,A: $i] :
( ( eps @ ( B @ ( A @ x ) @ x2 ) )
= ( eps @ ( B @ ( A @ x ) @ x ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_044) ).
thf(111,plain,
! [B: $i,A: $i] :
( ( eps @ ( B @ ( A @ x ) @ x2 ) )
= ( eps @ ( B @ ( A @ x ) @ x ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(68,axiom,
! [B: $i,A: $i] :
( ( B @ star @ ( A @ atom @ x2 ) )
= ( B @ star @ ( A @ atom @ x ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_042) ).
thf(227,plain,
! [B: $i,A: $i] :
( ( B @ star @ ( A @ atom @ x2 ) )
= ( B @ star @ ( A @ atom @ x ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(1911,plain,
$false,
inference(e,[status(thm)],[153,101,249,234,115,217,247,269,185,257,125,196,157,189,261,216,179,238,121,211,253,147,221,132,133,243,265,206,233,248,117,270,201,260,137,165,92,229,252,197,97,169,141,193,96,109,328,124,225,173,129,237,360,205,105,244,161,149,176,191,204,259,236,181,159,187,113,219,230,245,98,271,103,213,251,155,130,223,135,267,241,167,255,209,123,145,150,95,263,199,177,502,127,175,143,231,99,203,258,171,139,119,207,272,383,235,246,151,183,273,107,268,195,437,94,239,242,131,163,277,111,215,100,254,227]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWX212-1 : 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
% 0.11/0.39 % Computer : n011.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Sat Sep 26 16:56:44 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 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
% 0.85/0.98 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.40/1.21 % [INFO] Parsing done (218ms).
% 1.40/1.22 % [INFO] Running in sequential loop mode.
% 2.13/1.62 % [INFO] eprover registered as external prover.
% 2.13/1.62 % [INFO] Scanning for conjecture ...
% 2.32/1.74 % [INFO] Found a conjecture (or negated_conjecture) and 90 axioms. Running axiom selection ...
% 2.48/1.85 % [INFO] Axiom selection finished. Selected 90 axioms (removed 0 axioms).
% 2.73/1.93 % [INFO] Problem is propositional (TPTP CNF).
% 2.73/1.94 % [INFO] Type checking passed.
% 2.73/1.94 % [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 ...
% 17.77/5.15 % External prover 'e' found a proof!
% 17.77/5.16 % [INFO] Killing All external provers ...
% 17.77/5.16 % Time passed: 4619ms (effective reasoning time: 3932ms)
% 17.77/5.16 % Axioms used in derivation (90): axiom_028, axiom_083, axiom_069, axiom_041, axiom_029, axiom_036, axiom_025, axiom_039, axiom_024, axiom_009, axiom_089, axiom_040, axiom_046, axiom_017, axiom_057, axiom_035, axiom_050, axiom_067, axiom_051, axiom_073, axiom_078, axiom_061, axiom_084, axiom_010, axiom_021, axiom_032, axiom_054, axiom_002, axiom_013, axiom_043, axiom_006, axiom_079, axiom_023, axiom_049, axiom_080, axiom_034, axiom_016, axiom_056, axiom_076, axiom_027, axiom_005, axiom_045, axiom_065, axiom_038, axiom_012, axiom_062, axiom_072, axiom_001, axiom_068, axiom_087, axiom_059, axiom_044, axiom_031, axiom_086, axiom_015, axiom_004, axiom_055, axiom_033, axiom_022, axiom_075, axiom_063, axiom_011, axiom_082, axiom, axiom_026, axiom_052, axiom_037, axiom_071, axiom_020, axiom_060, axiom_048, axiom_030, axiom_074, axiom_019, axiom_085, axiom_008, axiom_003, axiom_042, axiom_014, axiom_066, axiom_077, axiom_070, axiom_047, axiom_007, axiom_081, axiom_088, axiom_018, axiom_058, axiom_053, axiom_064
% 17.77/5.16 % No. of inferences in proof: 229
% 17.77/5.16 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 4619 ms resp. 3932 ms w/o parsing
% 15.79/5.29 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 15.79/5.29 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------