%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : KRS258+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 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 : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 07:44:56 AM UTC 2026
% Result : Theorem 12.13s 3.23s
% Output : Refutation 12.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 56
% Syntax : Number of formulae : 191 ( 81 unt; 0 typ; 23 def)
% Number of atoms : 667 ( 113 equ; 0 cnn)
% Maximal formula atoms : 23 ( 3 avg)
% Number of connectives : 1827 ( 237 ~; 71 |; 181 &;1209 @)
% ( 28 <=>; 99 =>; 0 <=; 2 <~>)
% Maximal formula depth : 21 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 53 ( 50 usr; 40 con; 0-3 aty)
% Number of variables : 447 ( 8 ^; 249 !; 167 ?; 447 :)
% ( 0 !>; 0 ?*; 0 @-; 23 @+)
% Comments :
%------------------------------------------------------------------------------
thf(mighta_decl,type,
mighta: $i > $i > $o ).
thf(eqv_decl,type,
eqv: $i ).
thf(thm_decl,type,
thm: $i ).
thf(model_decl,type,
model: $i > $i > $o ).
thf(status_decl,type,
status: $i > $i > $i > $o ).
thf(wth_decl,type,
wth: $i ).
thf(wca_decl,type,
wca: $i ).
thf(sap_decl,type,
sap: $i ).
thf(sca_decl,type,
sca: $i ).
thf(tac_decl,type,
tac: $i ).
thf(not_decl,type,
not: $i > $i ).
thf(csa_decl,type,
csa: $i ).
thf(xora_decl,type,
xora: $i > $i > $o ).
thf(wec_decl,type,
wec: $i ).
thf(nota_decl,type,
nota: $i > $i > $o ).
thf(eth_decl,type,
eth: $i ).
thf(uns_decl,type,
uns: $i ).
thf(isa_decl,type,
isa: $i > $i > $o ).
thf(noc_decl,type,
noc: $i ).
thf(nevera_decl,type,
nevera: $i > $i > $o ).
thf(unp_decl,type,
unp: $i ).
thf(tca_decl,type,
tca: $i ).
thf(cax_decl,type,
cax: $i ).
thf(esa_decl,type,
esa: $i ).
thf(sat_decl,type,
sat: $i ).
thf(tau_decl,type,
tau: $i ).
thf(wtc_decl,type,
wtc: $i ).
thf(sk1_decl,type,
sk1: $i ).
thf(sk2_decl,type,
sk2: $i ).
thf(sk3_decl,type,
sk3: $i ).
thf(sk4_decl,type,
sk4: $i > $i > $i ).
thf(sk5_decl,type,
sk5: $i > $i > $i ).
thf(sk6_decl,type,
sk6: $i > $i > $i ).
thf(sk7_decl,type,
sk7: $i > $i > $i ).
thf(sk18_decl,type,
sk18: $i ).
thf(sk30_decl,type,
sk30: $i ).
thf(sk31_decl,type,
sk31: $i ).
thf(sk32_decl,type,
sk32: $i ).
thf(sk33_decl,type,
sk33: $i ).
thf(sk36_decl,type,
sk36: $i ).
thf(sk37_decl,type,
sk37: $i ).
thf(sk38_decl,type,
sk38: $i ).
thf(sk39_decl,type,
sk39: $i ).
thf(sk40_decl,type,
sk40: $i ).
thf(sk41_decl,type,
sk41: $i ).
thf(sk63_decl,type,
sk63: $i ).
thf(sk64_decl,type,
sk64: $i ).
thf(sk65_decl,type,
sk65: $i ).
thf(sk66_decl,type,
sk66: $i ).
thf(sk67_decl,type,
sk67: $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
( ~ ! [B: $i] : ( A @ ( B @ model ) )
& ? [B: $i] : ( A @ ( B @ model ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] : ( sk1 @ ( A @ model ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: $i] :
~ ( sk1 @ ( A @ model ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ( ( B @ ( C @ model ) )
=> ( A @ ( C @ model ) ) ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( ^ [A: $i,B: $i] :
@+[C: $i] : ( B @ ( C @ model ) ) ) ) ).
thf(sk6_def,definition,
( sk6
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
( ~ ( B @ ( C @ model ) )
& ( A @ ( C @ model ) ) ) ) ) ).
thf(sk7_def,definition,
( sk7
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ( A @ ( C @ model ) ) ) ) ).
thf(sk18_def,definition,
( sk18
= ( @+[A: $i] :
~ ? [B: $i] : ( A @ ( B @ model ) ) ) ) ).
thf(sk30_def,definition,
( sk30
= ( @+[A: $i] :
( ? [B: $i] :
( ? [C: $i] : ( B @ ( C @ model ) )
& ~ ( B @ ( A @ model ) ) )
& ? [B: $i] : ( B @ ( A @ model ) ) ) ) ) ).
thf(sk31_def,definition,
( sk31
= ( @+[A: $i] : ( A @ ( sk30 @ model ) ) ) ) ).
thf(sk32_def,definition,
( sk32
= ( @+[A: $i] :
( ? [B: $i] : ( A @ ( B @ model ) )
& ~ ( A @ ( sk30 @ model ) ) ) ) ) ).
thf(sk33_def,definition,
( sk33
= ( @+[A: $i] : ( sk32 @ ( A @ model ) ) ) ) ).
thf(sk36_def,definition,
( sk36
= ( @+[A: $i] :
? [B: $i] :
( ( ~ ! [C: $i] : ( B @ ( C @ model ) )
| ~ ! [C: $i] : ( A @ ( C @ model ) ) )
& ? [C: $i] :
( ( B @ ( C @ model ) )
& ( A @ ( C @ model ) ) ) ) ) ) ).
thf(sk37_def,definition,
( sk37
= ( @+[A: $i] :
( ( ~ ! [B: $i] : ( A @ ( B @ model ) )
| ~ ! [B: $i] : ( sk36 @ ( B @ model ) ) )
& ? [B: $i] :
( ( A @ ( B @ model ) )
& ( sk36 @ ( B @ model ) ) ) ) ) ) ).
thf(sk38_def,definition,
( sk38
= ( @+[A: $i] :
( ( sk37 @ ( A @ model ) )
& ( sk36 @ ( A @ model ) ) ) ) ) ).
thf(sk39_def,definition,
( sk39
= ( @+[A: $i] :
~ ( sk36 @ ( A @ model ) ) ) ) ).
thf(sk40_def,definition,
( sk40
= ( @+[A: $i] :
~ ( sk37 @ ( A @ model ) ) ) ) ).
thf(sk41_def,definition,
( sk41
= ( @+[A: $i] :
! [B: $i] : ( A @ ( B @ model ) ) ) ) ).
thf(sk63_def,definition,
( sk63
= ( @+[A: $i] :
( ? [B: $i] :
( ~ ! [C: $i] : ( B @ ( C @ model ) )
& ? [C: $i] :
( ( B @ ( C @ model ) )
& ~ ( A @ ( C @ model ) ) )
& ! [C: $i] :
( ( A @ ( C @ model ) )
=> ( B @ ( C @ model ) ) ) )
& ? [B: $i] : ( A @ ( B @ model ) ) ) ) ) ).
thf(sk64_def,definition,
( sk64
= ( @+[A: $i] : ( sk63 @ ( A @ model ) ) ) ) ).
thf(sk65_def,definition,
( sk65
= ( @+[A: $i] :
( ~ ! [B: $i] : ( A @ ( B @ model ) )
& ? [B: $i] :
( ( A @ ( B @ model ) )
& ~ ( sk63 @ ( B @ model ) ) )
& ! [B: $i] :
( ( sk63 @ ( B @ model ) )
=> ( A @ ( B @ model ) ) ) ) ) ) ).
thf(sk66_def,definition,
( sk66
= ( @+[A: $i] :
( ( sk65 @ ( A @ model ) )
& ~ ( sk63 @ ( A @ model ) ) ) ) ) ).
thf(sk67_def,definition,
( sk67
= ( @+[A: $i] :
~ ( sk65 @ ( A @ model ) ) ) ) ).
thf(31,axiom,
? [A: $i,B: $i] :
( ? [C: $i] :
~ ( B @ ( C @ model ) )
& ? [C: $i] :
( ( B @ ( C @ model ) )
& ~ ( A @ ( C @ model ) ) )
& ! [C: $i] :
( ( A @ ( C @ model ) )
=> ( B @ ( C @ model ) ) )
& ? [C: $i] : ( A @ ( C @ model ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mixed_pair) ).
thf(269,plain,
? [A: $i,B: $i] :
( ? [C: $i] :
~ ( B @ ( C @ model ) )
& ? [C: $i] :
( ( B @ ( C @ model ) )
& ~ ( A @ ( C @ model ) ) )
& ! [C: $i] :
( ( A @ ( C @ model ) )
=> ( B @ ( C @ model ) ) )
& ? [C: $i] : ( A @ ( C @ model ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(270,plain,
? [A: $i] :
( ? [B: $i] :
( ~ ! [C: $i] : ( B @ ( C @ model ) )
& ? [C: $i] :
( ( B @ ( C @ model ) )
& ~ ( A @ ( C @ model ) ) )
& ! [C: $i] :
( ( A @ ( C @ model ) )
=> ( B @ ( C @ model ) ) ) )
& ? [B: $i] : ( A @ ( B @ model ) ) ),
inference(miniscope,[status(thm)],[269]) ).
thf(271,plain,
! [A: $i] :
( ~ ( sk65 @ ( sk67 @ model ) )
& ( sk65 @ ( sk66 @ model ) )
& ~ ( sk63 @ ( sk66 @ model ) )
& ( ( sk65 @ ( A @ model ) )
| ~ ( sk63 @ ( A @ model ) ) )
& ( sk63 @ ( sk64 @ model ) ) ),
inference(cnf,[status(esa)],[270]) ).
thf(273,plain,
sk63 @ ( sk64 @ model ),
inference(cnfConj,[status(thm)],[271]) ).
thf(272,plain,
~ ( sk63 @ ( sk66 @ model ) ),
inference(cnfConj,[status(thm)],[271]) ).
thf(471,plain,
( ( ( sk63 @ ( sk66 @ model ) )
!= ( sk63 @ ( sk64 @ model ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[273,272]) ).
thf(472,plain,
( ( sk63 @ ( sk66 @ model ) )
!= ( sk63 @ ( sk64 @ model ) ) ),
inference(simp,[status(thm)],[471]) ).
thf(475,plain,
( ( sk63 != sk63 )
| ( sk66 != sk64 ) ),
inference(simp,[status(thm)],[472]) ).
thf(481,plain,
sk66 != sk64,
inference(simp,[status(thm)],[475]) ).
thf(3,axiom,
? [A: $i] :
( ? [B: $i] :
~ ( A @ ( B @ model ) )
& ? [B: $i] : ( A @ ( B @ model ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satisfiable) ).
thf(36,plain,
? [A: $i] :
( ? [B: $i] :
~ ( A @ ( B @ model ) )
& ? [B: $i] : ( A @ ( B @ model ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(37,plain,
? [A: $i] :
( ~ ! [B: $i] : ( A @ ( B @ model ) )
& ? [B: $i] : ( A @ ( B @ model ) ) ),
inference(miniscope,[status(thm)],[36]) ).
thf(38,plain,
( ~ ( sk1 @ ( sk3 @ model ) )
& ( sk1 @ ( sk2 @ model ) ) ),
inference(cnf,[status(esa)],[37]) ).
thf(39,plain,
sk1 @ ( sk2 @ model ),
inference(cnfConj,[status(thm)],[38]) ).
thf(10,axiom,
? [A: $i] :
! [B: $i] :
~ ( A @ ( B @ model ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',contradiction) ).
thf(97,plain,
? [A: $i] :
! [B: $i] :
~ ( A @ ( B @ model ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(98,plain,
~ ! [A: $i] :
? [B: $i] : ( A @ ( B @ model ) ),
inference(miniscope,[status(thm)],[97]) ).
thf(99,plain,
! [A: $i] :
~ ( sk18 @ ( A @ model ) ),
inference(cnf,[status(esa)],[98]) ).
thf(693,plain,
! [A: $i] :
( ( ( sk1 @ ( sk2 @ model ) )
!= ( sk18 @ ( A @ model ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[39,99]) ).
thf(694,plain,
! [A: $i] :
( ( sk1 @ ( sk2 @ model ) )
!= ( sk18 @ ( A @ model ) ) ),
inference(simp,[status(thm)],[693]) ).
thf(699,plain,
! [A: $i] :
( ( sk18 != sk1 )
| ( sk2 != A ) ),
inference(simp,[status(thm)],[694]) ).
thf(709,plain,
sk18 != sk1,
inference(simp,[status(thm)],[699]) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ! [C: $i,D: $i] :
( ( A @ ( D @ ( C @ status ) ) )
<~> ( B @ ( D @ ( C @ status ) ) ) )
<=> ( B @ ( A @ xora ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',xora) ).
thf(106,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ xora ) )
=> ! [C: $i,D: $i] :
~ ( ( ( B @ ( D @ ( C @ status ) ) )
=> ( A @ ( D @ ( C @ status ) ) ) )
& ( ( A @ ( D @ ( C @ status ) ) )
=> ( B @ ( D @ ( C @ status ) ) ) ) ) )
& ( ! [C: $i,D: $i] :
~ ( ( ( B @ ( D @ ( C @ status ) ) )
=> ( A @ ( D @ ( C @ status ) ) ) )
& ( ( A @ ( D @ ( C @ status ) ) )
=> ( B @ ( D @ ( C @ status ) ) ) ) )
=> ( B @ ( A @ xora ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(18,axiom,
? [A: $i,B: $i] :
( ? [C: $i] :
( ~ ( B @ ( C @ model ) )
| ~ ( A @ ( C @ model ) ) )
& ? [C: $i] :
( ( B @ ( C @ model ) )
& ( A @ ( C @ model ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sat_non_taut_pair) ).
thf(169,plain,
? [A: $i,B: $i] :
( ? [C: $i] :
( ~ ( B @ ( C @ model ) )
| ~ ( A @ ( C @ model ) ) )
& ? [C: $i] :
( ( B @ ( C @ model ) )
& ( A @ ( C @ model ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( ? [C: $i] : ( B @ ( C @ model ) )
& ~ ? [C: $i] : ( A @ ( C @ model ) ) )
<=> ( sca @ ( B @ ( A @ status ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sca) ).
thf(73,plain,
! [A: $i,B: $i] :
( ( ( sca @ ( B @ ( A @ status ) ) )
=> ( ? [C: $i] : ( B @ ( C @ model ) )
& ~ ? [C: $i] : ( A @ ( C @ model ) ) ) )
& ( ( ? [C: $i] : ( B @ ( C @ model ) )
& ~ ? [C: $i] : ( A @ ( C @ model ) ) )
=> ( sca @ ( B @ ( A @ status ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(1,conjecture,
thm @ ( eqv @ mighta ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mighta_eqv_thm) ).
thf(2,negated_conjecture,
~ ( thm @ ( eqv @ mighta ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(35,plain,
~ ( thm @ ( eqv @ mighta ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(19,axiom,
? [A: $i] :
! [B: $i] : ( A @ ( B @ model ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tautology) ).
thf(175,plain,
? [A: $i] :
! [B: $i] : ( A @ ( B @ model ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(176,plain,
! [A: $i] : ( sk41 @ ( A @ model ) ),
inference(cnf,[status(esa)],[175]) ).
thf(16,axiom,
? [A: $i,B: $i,C: $i] :
( ? [D: $i] : ( C @ ( D @ model ) )
& ~ ( C @ ( A @ model ) )
& ( B @ ( A @ model ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',non_thm_spt) ).
thf(155,plain,
? [A: $i,B: $i,C: $i] :
( ? [D: $i] : ( C @ ( D @ model ) )
& ~ ( C @ ( A @ model ) )
& ( B @ ( A @ model ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(156,plain,
? [A: $i] :
( ? [B: $i] :
( ? [C: $i] : ( B @ ( C @ model ) )
& ~ ( B @ ( A @ model ) ) )
& ? [B: $i] : ( B @ ( A @ model ) ) ),
inference(miniscope,[status(thm)],[155]) ).
thf(157,plain,
( ( sk32 @ ( sk33 @ model ) )
& ~ ( sk32 @ ( sk30 @ model ) )
& ( sk31 @ ( sk30 @ model ) ) ),
inference(cnf,[status(esa)],[156]) ).
thf(159,plain,
~ ( sk32 @ ( sk30 @ model ) ),
inference(cnfConj,[status(thm)],[157]) ).
thf(715,plain,
! [A: $i] :
( ( ( sk41 @ ( A @ model ) )
!= ( sk32 @ ( sk30 @ model ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[176,159]) ).
thf(716,plain,
! [A: $i] :
( ( sk41 @ ( A @ model ) )
!= ( sk32 @ ( sk30 @ model ) ) ),
inference(simp,[status(thm)],[715]) ).
thf(742,plain,
! [A: $i] :
( ( sk41 != sk32 )
| ( A != sk30 ) ),
inference(simp,[status(thm)],[716]) ).
thf(749,plain,
sk41 != sk32,
inference(simp,[status(thm)],[742]) ).
thf(24,axiom,
! [A: $i,B: $i] :
( ( ! [C: $i] : ( B @ ( C @ model ) )
& ~ ? [C: $i] : ( A @ ( C @ model ) ) )
<=> ( tca @ ( B @ ( A @ status ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tca) ).
thf(210,plain,
! [A: $i,B: $i] :
( ( ( tca @ ( B @ ( A @ status ) ) )
=> ( ! [C: $i] : ( B @ ( C @ model ) )
& ~ ? [C: $i] : ( A @ ( C @ model ) ) ) )
& ( ( ! [C: $i] : ( B @ ( C @ model ) )
& ~ ? [C: $i] : ( A @ ( C @ model ) ) )
=> ( tca @ ( B @ ( A @ status ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(32,axiom,
! [A: $i,B: $i] :
( ? [C: $i,D: $i] :
( ( B @ ( D @ ( C @ status ) ) )
& ( A @ ( D @ ( C @ status ) ) ) )
<=> ( B @ ( A @ mighta ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mighta) ).
thf(277,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ mighta ) )
=> ? [C: $i,D: $i] :
( ( B @ ( D @ ( C @ status ) ) )
& ( A @ ( D @ ( C @ status ) ) ) ) )
& ( ? [C: $i,D: $i] :
( ( B @ ( D @ ( C @ status ) ) )
& ( A @ ( D @ ( C @ status ) ) ) )
=> ( B @ ( A @ mighta ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(276,plain,
~ ( sk65 @ ( sk67 @ model ) ),
inference(cnfConj,[status(thm)],[271]) ).
thf(40,plain,
~ ( sk1 @ ( sk3 @ model ) ),
inference(cnfConj,[status(thm)],[38]) ).
thf(305,plain,
( ( ( sk1 @ ( sk3 @ model ) )
!= ( sk1 @ ( sk2 @ model ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[39,40]) ).
thf(306,plain,
( ( sk1 @ ( sk3 @ model ) )
!= ( sk1 @ ( sk2 @ model ) ) ),
inference(simp,[status(thm)],[305]) ).
thf(307,plain,
( ( sk1 != sk1 )
| ( sk3 != sk2 ) ),
inference(simp,[status(thm)],[306]) ).
thf(308,plain,
sk3 != sk2,
inference(simp,[status(thm)],[307]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( ? [C: $i] :
~ ( B @ ( C @ model ) )
& ? [C: $i] : ( B @ ( C @ model ) )
& ~ ? [C: $i] : ( A @ ( C @ model ) ) )
<=> ( wca @ ( B @ ( A @ status ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wca) ).
thf(56,plain,
! [A: $i,B: $i] :
( ( ( wca @ ( B @ ( A @ status ) ) )
=> ( ? [C: $i] :
~ ( B @ ( C @ model ) )
& ? [C: $i] : ( B @ ( C @ model ) )
& ~ ? [C: $i] : ( A @ ( C @ model ) ) ) )
& ( ( ? [C: $i] :
~ ( B @ ( C @ model ) )
& ? [C: $i] : ( B @ ( C @ model ) )
& ~ ? [C: $i] : ( A @ ( C @ model ) ) )
=> ( wca @ ( B @ ( A @ status ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(725,plain,
! [A: $i] :
( ( ( sk41 @ ( A @ model ) )
!= ( sk63 @ ( sk66 @ model ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[176,272]) ).
thf(726,plain,
! [A: $i] :
( ( sk41 @ ( A @ model ) )
!= ( sk63 @ ( sk66 @ model ) ) ),
inference(simp,[status(thm)],[725]) ).
thf(740,plain,
! [A: $i] :
( ( sk63 != sk41 )
| ( A != sk66 ) ),
inference(simp,[status(thm)],[726]) ).
thf(747,plain,
sk63 != sk41,
inference(simp,[status(thm)],[740]) ).
thf(21,axiom,
! [A: $i,B: $i] :
( ( ? [C: $i] :
( ( B @ not @ ( C @ model ) )
& ( A @ ( C @ model ) ) )
& ? [C: $i] :
( ( B @ ( C @ model ) )
& ( A @ ( C @ model ) ) ) )
<=> ( noc @ ( B @ ( A @ status ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',noc) ).
thf(184,plain,
! [A: $i,B: $i] :
( ( ( noc @ ( B @ ( A @ status ) ) )
=> ( ? [C: $i] :
( ( B @ not @ ( C @ model ) )
& ( A @ ( C @ model ) ) )
& ? [C: $i] :
( ( B @ ( C @ model ) )
& ( A @ ( C @ model ) ) ) ) )
& ( ( ? [C: $i] :
( ( B @ not @ ( C @ model ) )
& ( A @ ( C @ model ) ) )
& ? [C: $i] :
( ( B @ ( C @ model ) )
& ( A @ ( C @ model ) ) ) )
=> ( noc @ ( B @ ( A @ status ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(723,plain,
! [B: $i,A: $i] :
( ( ( sk41 @ ( A @ model ) )
!= ( sk18 @ ( B @ model ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[176,99]) ).
thf(724,plain,
! [B: $i,A: $i] :
( ( sk41 @ ( A @ model ) )
!= ( sk18 @ ( B @ model ) ) ),
inference(simp,[status(thm)],[723]) ).
thf(744,plain,
! [B: $i,A: $i] :
( ( sk41 != sk18 )
| ( A != B ) ),
inference(simp,[status(thm)],[724]) ).
thf(751,plain,
sk41 != sk18,
inference(simp,[status(thm)],[744]) ).
thf(22,axiom,
! [A: $i,B: $i] :
( ! [C: $i,D: $i] :
( ( A @ ( D @ ( C @ status ) ) )
=> ~ ( B @ ( D @ ( C @ status ) ) ) )
<=> ( B @ ( A @ nevera ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nevera) ).
thf(196,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ nevera ) )
=> ! [C: $i,D: $i] :
( ( A @ ( D @ ( C @ status ) ) )
=> ~ ( B @ ( D @ ( C @ status ) ) ) ) )
& ( ! [C: $i,D: $i] :
( ( A @ ( D @ ( C @ status ) ) )
=> ~ ( B @ ( D @ ( C @ status ) ) ) )
=> ( B @ ( A @ nevera ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(14,axiom,
! [A: $i,B: $i] :
( ? [C: $i,D: $i] :
( ~ ( B @ ( D @ ( C @ status ) ) )
& ( A @ ( D @ ( C @ status ) ) ) )
<=> ( B @ ( A @ nota ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nota) ).
thf(132,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ nota ) )
=> ? [C: $i,D: $i] :
( ~ ( B @ ( D @ ( C @ status ) ) )
& ( A @ ( D @ ( C @ status ) ) ) ) )
& ( ? [C: $i,D: $i] :
( ~ ( B @ ( D @ ( C @ status ) ) )
& ( A @ ( D @ ( C @ status ) ) ) )
=> ( B @ ( A @ nota ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ? [C: $i] :
( ( B @ not @ ( C @ model ) )
& ( A @ ( C @ model ) ) )
<=> ( csa @ ( B @ ( A @ status ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',csa) ).
thf(89,plain,
! [A: $i,B: $i] :
( ( ( csa @ ( B @ ( A @ status ) ) )
=> ? [C: $i] :
( ( B @ not @ ( C @ model ) )
& ( A @ ( C @ model ) ) ) )
& ( ? [C: $i] :
( ( B @ not @ ( C @ model ) )
& ( A @ ( C @ model ) ) )
=> ( csa @ ( B @ ( A @ status ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(28,axiom,
! [A: $i,B: $i] :
( ? [C: $i] :
( ( B @ ( C @ model ) )
& ( A @ ( C @ model ) ) )
<=> ( sat @ ( B @ ( A @ status ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sat) ).
thf(243,plain,
! [A: $i,B: $i] :
( ( ( sat @ ( B @ ( A @ status ) ) )
=> ? [C: $i] :
( ( B @ ( C @ model ) )
& ( A @ ( C @ model ) ) ) )
& ( ? [C: $i] :
( ( B @ ( C @ model ) )
& ( A @ ( C @ model ) ) )
=> ( sat @ ( B @ ( A @ status ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(274,plain,
sk65 @ ( sk66 @ model ),
inference(cnfConj,[status(thm)],[271]) ).
thf(517,plain,
( ( ( sk65 @ ( sk67 @ model ) )
!= ( sk65 @ ( sk66 @ model ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[274,276]) ).
thf(518,plain,
( ( sk65 @ ( sk67 @ model ) )
!= ( sk65 @ ( sk66 @ model ) ) ),
inference(simp,[status(thm)],[517]) ).
thf(521,plain,
( ( sk65 != sk65 )
| ( sk67 != sk66 ) ),
inference(simp,[status(thm)],[518]) ).
thf(527,plain,
sk67 != sk66,
inference(simp,[status(thm)],[521]) ).
thf(34,axiom,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( A @ ( C @ model ) )
<=> ( B @ ( C @ model ) ) )
& ? [C: $i] : ( A @ ( C @ model ) ) )
<=> ( eqv @ ( B @ ( A @ status ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eqv) ).
thf(292,plain,
! [A: $i,B: $i] :
( ( ( eqv @ ( B @ ( A @ status ) ) )
=> ( ! [C: $i] :
( ( ( B @ ( C @ model ) )
=> ( A @ ( C @ model ) ) )
& ( ( A @ ( C @ model ) )
=> ( B @ ( C @ model ) ) ) )
& ? [C: $i] : ( A @ ( C @ model ) ) ) )
& ( ( ! [C: $i] :
( ( ( B @ ( C @ model ) )
=> ( A @ ( C @ model ) ) )
& ( ( A @ ( C @ model ) )
=> ( B @ ( C @ model ) ) ) )
& ? [C: $i] : ( A @ ( C @ model ) ) )
=> ( eqv @ ( B @ ( A @ status ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(515,plain,
( ( ( sk65 @ ( sk66 @ model ) )
!= ( sk63 @ ( sk66 @ model ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[274,272]) ).
thf(516,plain,
( ( sk65 @ ( sk66 @ model ) )
!= ( sk63 @ ( sk66 @ model ) ) ),
inference(simp,[status(thm)],[515]) ).
thf(524,plain,
( ( sk65 != sk63 )
| ( sk66 != sk66 ) ),
inference(simp,[status(thm)],[516]) ).
thf(529,plain,
sk65 != sk63,
inference(simp,[status(thm)],[524]) ).
thf(158,plain,
sk31 @ ( sk30 @ model ),
inference(cnfConj,[status(thm)],[157]) ).
thf(695,plain,
! [A: $i] :
( ( ( sk31 @ ( sk30 @ model ) )
!= ( sk18 @ ( A @ model ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[158,99]) ).
thf(696,plain,
! [A: $i] :
( ( sk31 @ ( sk30 @ model ) )
!= ( sk18 @ ( A @ model ) ) ),
inference(simp,[status(thm)],[695]) ).
thf(703,plain,
! [A: $i] :
( ( sk31 != sk18 )
| ( sk30 != A ) ),
inference(simp,[status(thm)],[696]) ).
thf(714,plain,
sk31 != sk18,
inference(simp,[status(thm)],[703]) ).
thf(160,plain,
sk32 @ ( sk33 @ model ),
inference(cnfConj,[status(thm)],[157]) ).
thf(325,plain,
( ( ( sk32 @ ( sk33 @ model ) )
!= ( sk32 @ ( sk30 @ model ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[160,159]) ).
thf(326,plain,
( ( sk32 @ ( sk33 @ model ) )
!= ( sk32 @ ( sk30 @ model ) ) ),
inference(simp,[status(thm)],[325]) ).
thf(331,plain,
( ( sk32 != sk32 )
| ( sk33 != sk30 ) ),
inference(simp,[status(thm)],[326]) ).
thf(334,plain,
sk33 != sk30,
inference(simp,[status(thm)],[331]) ).
thf(315,plain,
( ( ( sk32 @ ( sk30 @ model ) )
!= ( sk31 @ ( sk30 @ model ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[158,159]) ).
thf(316,plain,
( ( sk32 @ ( sk30 @ model ) )
!= ( sk31 @ ( sk30 @ model ) ) ),
inference(simp,[status(thm)],[315]) ).
thf(321,plain,
( ( sk32 != sk31 )
| ( sk30 != sk30 ) ),
inference(simp,[status(thm)],[316]) ).
thf(324,plain,
sk32 != sk31,
inference(simp,[status(thm)],[321]) ).
thf(33,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( A @ ( C @ model ) )
=> ( B @ ( C @ model ) ) )
<=> ( thm @ ( B @ ( A @ status ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm) ).
thf(285,plain,
! [A: $i,B: $i] :
( ( ( thm @ ( B @ ( A @ status ) ) )
=> ! [C: $i] :
( ( A @ ( C @ model ) )
=> ( B @ ( C @ model ) ) ) )
& ( ! [C: $i] :
( ( A @ ( C @ model ) )
=> ( B @ ( C @ model ) ) )
=> ( thm @ ( B @ ( A @ status ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(26,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ model ) )
<~> ( B @ not @ ( A @ model ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',completeness) ).
thf(224,plain,
! [A: $i,B: $i] :
~ ( ( ( B @ not @ ( A @ model ) )
=> ( B @ ( A @ model ) ) )
& ( ( B @ ( A @ model ) )
=> ( B @ not @ ( A @ model ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(170,plain,
? [A: $i,B: $i] :
( ( ~ ! [C: $i] : ( B @ ( C @ model ) )
| ~ ! [C: $i] : ( A @ ( C @ model ) ) )
& ? [C: $i] :
( ( B @ ( C @ model ) )
& ( A @ ( C @ model ) ) ) ),
inference(miniscope,[status(thm)],[169]) ).
thf(171,plain,
( ( ~ ( sk37 @ ( sk40 @ model ) )
| ~ ( sk36 @ ( sk39 @ model ) ) )
& ( sk37 @ ( sk38 @ model ) )
& ( sk36 @ ( sk38 @ model ) ) ),
inference(cnf,[status(esa)],[170]) ).
thf(173,plain,
sk37 @ ( sk38 @ model ),
inference(cnfConj,[status(thm)],[171]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( ? [C: $i] :
~ ( B @ ( C @ model ) )
& ? [C: $i] :
( ~ ( A @ ( C @ model ) )
& ( B @ ( C @ model ) ) )
& ! [C: $i] :
( ( A @ ( C @ model ) )
=> ( B @ ( C @ model ) ) )
& ? [C: $i] : ( A @ ( C @ model ) ) )
<=> ( wth @ ( B @ ( A @ status ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wth) ).
thf(41,plain,
! [A: $i,B: $i] :
( ( ( wth @ ( B @ ( A @ status ) ) )
=> ( ? [C: $i] :
~ ( B @ ( C @ model ) )
& ? [C: $i] :
( ~ ( A @ ( C @ model ) )
& ( B @ ( C @ model ) ) )
& ! [C: $i] :
( ( A @ ( C @ model ) )
=> ( B @ ( C @ model ) ) )
& ? [C: $i] : ( A @ ( C @ model ) ) ) )
& ( ( ? [C: $i] :
~ ( B @ ( C @ model ) )
& ? [C: $i] :
( ~ ( A @ ( C @ model ) )
& ( B @ ( C @ model ) ) )
& ! [C: $i] :
( ( A @ ( C @ model ) )
=> ( B @ ( C @ model ) ) )
& ? [C: $i] : ( A @ ( C @ model ) ) )
=> ( wth @ ( B @ ( A @ status ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(727,plain,
! [A: $i] :
( ( ( sk41 @ ( A @ model ) )
!= ( sk65 @ ( sk67 @ model ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[176,276]) ).
thf(728,plain,
! [A: $i] :
( ( sk41 @ ( A @ model ) )
!= ( sk65 @ ( sk67 @ model ) ) ),
inference(simp,[status(thm)],[727]) ).
thf(743,plain,
! [A: $i] :
( ( sk65 != sk41 )
| ( A != sk67 ) ),
inference(simp,[status(thm)],[728]) ).
thf(750,plain,
sk65 != sk41,
inference(simp,[status(thm)],[743]) ).
thf(17,axiom,
! [A: $i,B: $i] :
( ( ! [C: $i] : ( B @ not @ ( C @ model ) )
& ! [C: $i] : ( A @ ( C @ model ) ) )
<=> ( uns @ ( B @ ( A @ status ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',uns) ).
thf(161,plain,
! [A: $i,B: $i] :
( ( ( uns @ ( B @ ( A @ status ) ) )
=> ( ! [C: $i] : ( B @ not @ ( C @ model ) )
& ! [C: $i] : ( A @ ( C @ model ) ) ) )
& ( ( ! [C: $i] : ( B @ not @ ( C @ model ) )
& ! [C: $i] : ( A @ ( C @ model ) ) )
=> ( uns @ ( B @ ( A @ status ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(671,plain,
! [A: $i] :
( ( ( sk37 @ ( sk38 @ model ) )
!= ( sk18 @ ( A @ model ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[173,99]) ).
thf(672,plain,
! [A: $i] :
( ( sk37 @ ( sk38 @ model ) )
!= ( sk18 @ ( A @ model ) ) ),
inference(simp,[status(thm)],[671]) ).
thf(700,plain,
! [A: $i] :
( ( sk37 != sk18 )
| ( sk38 != A ) ),
inference(simp,[status(thm)],[672]) ).
thf(711,plain,
sk37 != sk18,
inference(simp,[status(thm)],[700]) ).
thf(30,axiom,
! [A: $i,B: $i] :
( ( ! [C: $i] : ( B @ ( C @ model ) )
& ? [C: $i] :
~ ( A @ ( C @ model ) )
& ? [C: $i] : ( A @ ( C @ model ) ) )
<=> ( wtc @ ( B @ ( A @ status ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wtc) ).
thf(259,plain,
! [A: $i,B: $i] :
( ( ( wtc @ ( B @ ( A @ status ) ) )
=> ( ! [C: $i] : ( B @ ( C @ model ) )
& ? [C: $i] :
~ ( A @ ( C @ model ) )
& ? [C: $i] : ( A @ ( C @ model ) ) ) )
& ( ( ! [C: $i] : ( B @ ( C @ model ) )
& ? [C: $i] :
~ ( A @ ( C @ model ) )
& ? [C: $i] : ( A @ ( C @ model ) ) )
=> ( wtc @ ( B @ ( A @ status ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(687,plain,
! [A: $i] :
( ( ( sk32 @ ( sk33 @ model ) )
!= ( sk18 @ ( A @ model ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[160,99]) ).
thf(688,plain,
! [A: $i] :
( ( sk32 @ ( sk33 @ model ) )
!= ( sk18 @ ( A @ model ) ) ),
inference(simp,[status(thm)],[687]) ).
thf(702,plain,
! [A: $i] :
( ( sk32 != sk18 )
| ( sk33 != A ) ),
inference(simp,[status(thm)],[688]) ).
thf(713,plain,
sk32 != sk18,
inference(simp,[status(thm)],[702]) ).
thf(172,plain,
sk36 @ ( sk38 @ model ),
inference(cnfConj,[status(thm)],[171]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( ! [C: $i] : ( B @ ( C @ model ) )
& ? [C: $i] : ( A @ ( C @ model ) ) )
<=> ( tac @ ( B @ ( A @ status ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tac) ).
thf(81,plain,
! [A: $i,B: $i] :
( ( ( tac @ ( B @ ( A @ status ) ) )
=> ( ! [C: $i] : ( B @ ( C @ model ) )
& ? [C: $i] : ( A @ ( C @ model ) ) ) )
& ( ( ! [C: $i] : ( B @ ( C @ model ) )
& ? [C: $i] : ( A @ ( C @ model ) ) )
=> ( tac @ ( B @ ( A @ status ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(15,axiom,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( A @ ( C @ model ) )
<=> ( B @ ( C @ model ) ) )
& ? [C: $i] :
~ ( A @ ( C @ model ) )
& ? [C: $i] : ( A @ ( C @ model ) ) )
<=> ( eth @ ( B @ ( A @ status ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eth) ).
thf(140,plain,
! [A: $i,B: $i] :
( ( ( eth @ ( B @ ( A @ status ) ) )
=> ( ! [C: $i] :
( ( ( B @ ( C @ model ) )
=> ( A @ ( C @ model ) ) )
& ( ( A @ ( C @ model ) )
=> ( B @ ( C @ model ) ) ) )
& ? [C: $i] :
~ ( A @ ( C @ model ) )
& ? [C: $i] : ( A @ ( C @ model ) ) ) )
& ( ( ! [C: $i] :
( ( ( B @ ( C @ model ) )
=> ( A @ ( C @ model ) ) )
& ( ( A @ ( C @ model ) )
=> ( B @ ( C @ model ) ) ) )
& ? [C: $i] :
~ ( A @ ( C @ model ) )
& ? [C: $i] : ( A @ ( C @ model ) ) )
=> ( eth @ ( B @ ( A @ status ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( ? [C: $i] : ( A @ ( C @ model ) )
=> ? [C: $i] : ( B @ ( C @ model ) ) )
<=> ( sap @ ( B @ ( A @ status ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sap) ).
thf(66,plain,
! [A: $i,B: $i] :
( ( ( sap @ ( B @ ( A @ status ) ) )
=> ( ? [C: $i] : ( A @ ( C @ model ) )
=> ? [C: $i] : ( B @ ( C @ model ) ) ) )
& ( ( ? [C: $i] : ( A @ ( C @ model ) )
=> ? [C: $i] : ( B @ ( C @ model ) ) )
=> ( sap @ ( B @ ( A @ status ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(29,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( B @ ( C @ model ) )
& ( A @ ( C @ model ) ) )
<=> ( tau @ ( B @ ( A @ status ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tau) ).
thf(251,plain,
! [A: $i,B: $i] :
( ( ( tau @ ( B @ ( A @ status ) ) )
=> ! [C: $i] :
( ( B @ ( C @ model ) )
& ( A @ ( C @ model ) ) ) )
& ( ! [C: $i] :
( ( B @ ( C @ model ) )
& ( A @ ( C @ model ) ) )
=> ( tau @ ( B @ ( A @ status ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(42,plain,
( ! [A: $i,B: $i] :
( ( wth @ ( B @ ( A @ status ) ) )
=> ( ~ ! [C: $i] : ( B @ ( C @ model ) )
& ? [C: $i] :
( ~ ( A @ ( C @ model ) )
& ( B @ ( C @ model ) ) )
& ! [C: $i] :
( ( A @ ( C @ model ) )
=> ( B @ ( C @ model ) ) )
& ? [C: $i] : ( A @ ( C @ model ) ) ) )
& ! [A: $i,B: $i] :
( ( ~ ! [C: $i] : ( B @ ( C @ model ) )
& ? [C: $i] :
( ~ ( A @ ( C @ model ) )
& ( B @ ( C @ model ) ) )
& ! [C: $i] :
( ( A @ ( C @ model ) )
=> ( B @ ( C @ model ) ) )
& ? [C: $i] : ( A @ ( C @ model ) ) )
=> ( wth @ ( B @ ( A @ status ) ) ) ) ),
inference(miniscope,[status(thm)],[41]) ).
thf(43,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ~ ( G @ ( F @ ( G @ sk7 ) @ model ) )
| ~ ( wth @ ( G @ ( F @ status ) ) ) )
& ( ~ ( F @ ( F @ ( G @ sk6 ) @ model ) )
| ~ ( wth @ ( G @ ( F @ status ) ) ) )
& ( ( G @ ( F @ ( G @ sk6 ) @ model ) )
| ~ ( wth @ ( G @ ( F @ status ) ) ) )
& ( ( G @ ( H @ model ) )
| ~ ( F @ ( H @ model ) )
| ~ ( wth @ ( G @ ( F @ status ) ) ) )
& ( ( F @ ( F @ ( G @ sk5 ) @ model ) )
| ~ ( wth @ ( G @ ( F @ status ) ) ) )
& ( ( wth @ ( B @ ( A @ status ) ) )
| ( B @ ( E @ model ) )
| ( A @ ( D @ model ) )
| ~ ( B @ ( D @ model ) )
| ~ ( B @ ( A @ ( B @ sk4 ) @ model ) )
| ~ ( A @ ( C @ model ) ) )
& ( ( wth @ ( B @ ( A @ status ) ) )
| ( B @ ( E @ model ) )
| ( A @ ( D @ model ) )
| ~ ( B @ ( D @ model ) )
| ( A @ ( A @ ( B @ sk4 ) @ model ) )
| ~ ( A @ ( C @ model ) ) ) ),
inference(cnf,[status(esa)],[42]) ).
thf(48,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( wth @ ( B @ ( A @ status ) ) )
| ( B @ ( E @ model ) )
| ( A @ ( D @ model ) )
| ~ ( B @ ( D @ model ) )
| ~ ( B @ ( A @ ( B @ sk4 ) @ model ) )
| ~ ( A @ ( C @ model ) ) ),
inference(cnfConj,[status(thm)],[43]) ).
thf(689,plain,
! [A: $i] :
( ( ( sk36 @ ( sk38 @ model ) )
!= ( sk18 @ ( A @ model ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[172,99]) ).
thf(690,plain,
! [A: $i] :
( ( sk36 @ ( sk38 @ model ) )
!= ( sk18 @ ( A @ model ) ) ),
inference(simp,[status(thm)],[689]) ).
thf(701,plain,
! [A: $i] :
( ( sk36 != sk18 )
| ( sk38 != A ) ),
inference(simp,[status(thm)],[690]) ).
thf(712,plain,
sk36 != sk18,
inference(simp,[status(thm)],[701]) ).
thf(691,plain,
! [A: $i] :
( ( ( sk65 @ ( sk66 @ model ) )
!= ( sk18 @ ( A @ model ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[274,99]) ).
thf(692,plain,
! [A: $i] :
( ( sk65 @ ( sk66 @ model ) )
!= ( sk18 @ ( A @ model ) ) ),
inference(simp,[status(thm)],[691]) ).
thf(697,plain,
! [A: $i] :
( ( sk65 != sk18 )
| ( sk66 != A ) ),
inference(simp,[status(thm)],[692]) ).
thf(707,plain,
sk65 != sk18,
inference(simp,[status(thm)],[697]) ).
thf(50,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( wth @ ( B @ ( A @ status ) ) )
| ( B @ ( E @ model ) )
| ( A @ ( D @ model ) )
| ~ ( B @ ( D @ model ) )
| ( A @ ( A @ ( B @ sk4 ) @ model ) )
| ~ ( A @ ( C @ model ) ) ),
inference(cnfConj,[status(thm)],[43]) ).
thf(20,axiom,
! [A: $i,B: $i] :
( ! [C: $i,D: $i] :
( ( A @ ( D @ ( C @ status ) ) )
=> ( B @ ( D @ ( C @ status ) ) ) )
<=> ( B @ ( A @ isa ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',isa) ).
thf(177,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ isa ) )
=> ! [C: $i,D: $i] :
( ( A @ ( D @ ( C @ status ) ) )
=> ( B @ ( D @ ( C @ status ) ) ) ) )
& ( ! [C: $i,D: $i] :
( ( A @ ( D @ ( C @ status ) ) )
=> ( B @ ( D @ ( C @ status ) ) ) )
=> ( B @ ( A @ isa ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(27,axiom,
! [A: $i,B: $i] :
( ( ? [C: $i] : ( A @ ( C @ model ) )
<=> ? [C: $i] : ( B @ ( C @ model ) ) )
<=> ( esa @ ( B @ ( A @ status ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',esa) ).
thf(231,plain,
! [A: $i,B: $i] :
( ( ( esa @ ( B @ ( A @ status ) ) )
=> ( ( ? [C: $i] : ( B @ ( C @ model ) )
=> ? [C: $i] : ( A @ ( C @ model ) ) )
& ( ? [C: $i] : ( A @ ( C @ model ) )
=> ? [C: $i] : ( B @ ( C @ model ) ) ) ) )
& ( ( ( ? [C: $i] : ( B @ ( C @ model ) )
=> ? [C: $i] : ( A @ ( C @ model ) ) )
& ( ? [C: $i] : ( A @ ( C @ model ) )
=> ? [C: $i] : ( B @ ( C @ model ) ) ) )
=> ( esa @ ( B @ ( A @ status ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(23,axiom,
! [A: $i,B: $i] :
( ( ~ ? [C: $i] : ( A @ ( C @ model ) )
=> ~ ? [C: $i] : ( B @ ( C @ model ) ) )
<=> ( unp @ ( B @ ( A @ status ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unp) ).
thf(203,plain,
! [A: $i,B: $i] :
( ( ( unp @ ( B @ ( A @ status ) ) )
=> ( ~ ? [C: $i] : ( A @ ( C @ model ) )
=> ~ ? [C: $i] : ( B @ ( C @ model ) ) ) )
& ( ( ~ ? [C: $i] : ( A @ ( C @ model ) )
=> ~ ? [C: $i] : ( B @ ( C @ model ) ) )
=> ( unp @ ( B @ ( A @ status ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(25,axiom,
! [A: $i,B: $i] :
( ~ ? [C: $i] : ( A @ ( C @ model ) )
<=> ( cax @ ( B @ ( A @ status ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cax) ).
thf(218,plain,
! [A: $i,B: $i] :
( ( ( cax @ ( B @ ( A @ status ) ) )
=> ~ ? [C: $i] : ( A @ ( C @ model ) ) )
& ( ~ ? [C: $i] : ( A @ ( C @ model ) )
=> ( cax @ ( B @ ( A @ status ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(738,plain,
! [A: $i] :
( ( ( sk41 @ ( A @ model ) )
!= ( sk1 @ ( sk3 @ model ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[176,40]) ).
thf(739,plain,
! [A: $i] :
( ( sk41 @ ( A @ model ) )
!= ( sk1 @ ( sk3 @ model ) ) ),
inference(simp,[status(thm)],[738]) ).
thf(741,plain,
! [A: $i] :
( ( sk41 != sk1 )
| ( A != sk3 ) ),
inference(simp,[status(thm)],[739]) ).
thf(748,plain,
sk41 != sk1,
inference(simp,[status(thm)],[741]) ).
thf(13,axiom,
! [A: $i,B: $i] :
( ( ? [C: $i] :
( ~ ( A @ ( C @ model ) )
& ( B @ ( C @ model ) ) )
& ! [C: $i] :
( ( A @ ( C @ model ) )
=> ( B @ ( C @ model ) ) )
& ? [C: $i] : ( A @ ( C @ model ) ) )
<=> ( wec @ ( B @ ( A @ status ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wec) ).
thf(119,plain,
! [A: $i,B: $i] :
( ( ( wec @ ( B @ ( A @ status ) ) )
=> ( ? [C: $i] :
( ~ ( A @ ( C @ model ) )
& ( B @ ( C @ model ) ) )
& ! [C: $i] :
( ( A @ ( C @ model ) )
=> ( B @ ( C @ model ) ) )
& ? [C: $i] : ( A @ ( C @ model ) ) ) )
& ( ( ? [C: $i] :
( ~ ( A @ ( C @ model ) )
& ( B @ ( C @ model ) ) )
& ! [C: $i] :
( ( A @ ( C @ model ) )
=> ( B @ ( C @ model ) ) )
& ? [C: $i] : ( A @ ( C @ model ) ) )
=> ( wec @ ( B @ ( A @ status ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(46,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ sk6 ) @ model ) )
| ~ ( wth @ ( B @ ( A @ status ) ) ) ),
inference(cnfConj,[status(thm)],[43]) ).
thf(51,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ sk6 ) @ model ) )
| ~ ( wth @ ( B @ ( A @ status ) ) ) ),
inference(simp,[status(thm)],[46]) ).
thf(685,plain,
! [A: $i] :
( ( ( sk63 @ ( sk64 @ model ) )
!= ( sk18 @ ( A @ model ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[273,99]) ).
thf(686,plain,
! [A: $i] :
( ( sk63 @ ( sk64 @ model ) )
!= ( sk18 @ ( A @ model ) ) ),
inference(simp,[status(thm)],[685]) ).
thf(698,plain,
! [A: $i] :
( ( sk63 != sk18 )
| ( sk64 != A ) ),
inference(simp,[status(thm)],[686]) ).
thf(708,plain,
sk63 != sk18,
inference(simp,[status(thm)],[698]) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ model ) )
<=> ~ ( B @ not @ ( A @ model ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not) ).
thf(100,plain,
! [A: $i,B: $i] :
( ( ~ ( B @ not @ ( A @ model ) )
=> ( B @ ( A @ model ) ) )
& ( ( B @ ( A @ model ) )
=> ~ ( B @ not @ ( A @ model ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(1065,plain,
$false,
inference(e,[status(thm)],[481,709,106,169,73,35,749,175,210,277,276,308,269,56,747,184,751,196,132,89,243,527,292,529,714,334,160,97,324,285,224,173,41,750,161,176,711,259,713,159,172,274,81,39,140,66,251,155,48,712,707,50,177,231,99,203,218,748,40,158,119,272,36,51,273,708,100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KRS258+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.06 % 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
% 0.11/0.37 % Computer : n018.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Fri Sep 25 19:52:20 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 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
% 0.61/0.68 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.02/0.82 % [INFO] Parsing done (136ms).
% 1.02/0.83 % [INFO] Running in sequential loop mode.
% 1.40/1.04 % [INFO] eprover registered as external prover.
% 1.40/1.05 % [INFO] Scanning for conjecture ...
% 1.76/1.09 % [INFO] Found a conjecture (or negated_conjecture) and 32 axioms. Running axiom selection ...
% 1.76/1.13 % [INFO] Axiom selection finished. Selected 32 axioms (removed 0 axioms).
% 2.03/1.19 % [INFO] Problem is first-order (TPTP FOF).
% 2.03/1.20 % [INFO] Type checking passed.
% 2.16/1.20 % [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 ...
% 12.13/3.23 % External prover 'e' found a proof!
% 12.13/3.23 % [INFO] Killing All external provers ...
% 12.13/3.23 % Time passed: 2768ms (effective reasoning time: 2399ms)
% 12.13/3.23 % 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)>
% 12.13/3.23 % Axioms used in derivation (32): wec, completeness, contradiction, tau, wtc, sat_non_taut_pair, satisfiable, wth, sat, sap, nevera, noc, tca, eth, thm, uns, nota, sca, csa, mighta, wca, eqv, isa, cax, tautology, tac, non_thm_spt, xora, not, unp, esa, mixed_pair
% 12.13/3.23 % No. of inferences in proof: 168
% 12.13/3.23 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2768 ms resp. 2399 ms w/o parsing
% 12.63/3.31 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 12.63/3.31 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------