%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : KRS193+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 : n020.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 07:44:51 AM UTC 2026
% Result : Theorem 107.02s 26.95s
% Output : Refutation 100.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 59
% Syntax : Number of formulae : 300 ( 109 unt; 0 typ; 26 def)
% Number of atoms : 997 ( 232 equ; 0 cnn)
% Maximal formula atoms : 23 ( 3 avg)
% Number of connectives : 2550 ( 421 ~; 166 |; 188 &;1638 @)
% ( 28 <=>; 107 =>; 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 : 56 ( 53 usr; 40 con; 0-3 aty)
% Number of variables : 536 ( 13 ^; 323 !; 174 ?; 536 :)
% ( 0 !>; 0 ?*; 0 @-; 26 @+)
% Comments :
%------------------------------------------------------------------------------
thf(isa_decl,type,
isa: $i > $i > $o ).
thf(cax_decl,type,
cax: $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(wtc_decl,type,
wtc: $i ).
thf(mighta_decl,type,
mighta: $i > $i > $o ).
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(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(eqv_decl,type,
eqv: $i ).
thf(esa_decl,type,
esa: $i ).
thf(sat_decl,type,
sat: $i ).
thf(tau_decl,type,
tau: $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(sk11_decl,type,
sk11: $i > $i > $i ).
thf(sk12_decl,type,
sk12: $i > $i > $i ).
thf(sk18_decl,type,
sk18: $i ).
thf(sk35_decl,type,
sk35: $i ).
thf(sk36_decl,type,
sk36: $i ).
thf(sk37_decl,type,
sk37: $i ).
thf(sk38_decl,type,
sk38: $i ).
thf(sk41_decl,type,
sk41: $i ).
thf(sk42_decl,type,
sk42: $i ).
thf(sk43_decl,type,
sk43: $i ).
thf(sk44_decl,type,
sk44: $i ).
thf(sk45_decl,type,
sk45: $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(sk68_decl,type,
sk68: $i ).
thf(sk69_decl,type,
sk69: $i ).
thf(sk73_decl,type,
sk73: $i > $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(sk11_def,definition,
( sk11
= ( ^ [A: $i,B: $i] :
@+[C: $i] : ( B @ ( C @ model ) ) ) ) ).
thf(sk12_def,definition,
( sk12
= ( ^ [A: $i,B: $i] :
@+[C: $i] : ( A @ ( C @ model ) ) ) ) ).
thf(sk18_def,definition,
( sk18
= ( @+[A: $i] :
~ ? [B: $i] : ( A @ ( B @ model ) ) ) ) ).
thf(sk35_def,definition,
( sk35
= ( @+[A: $i] :
( ? [B: $i] :
( ? [C: $i] : ( B @ ( C @ model ) )
& ~ ( B @ ( A @ model ) ) )
& ? [B: $i] : ( B @ ( A @ model ) ) ) ) ) ).
thf(sk36_def,definition,
( sk36
= ( @+[A: $i] : ( A @ ( sk35 @ model ) ) ) ) ).
thf(sk37_def,definition,
( sk37
= ( @+[A: $i] :
( ? [B: $i] : ( A @ ( B @ model ) )
& ~ ( A @ ( sk35 @ model ) ) ) ) ) ).
thf(sk38_def,definition,
( sk38
= ( @+[A: $i] : ( sk37 @ ( A @ model ) ) ) ) ).
thf(sk41_def,definition,
( sk41
= ( @+[A: $i] :
? [B: $i] :
( ( ~ ! [C: $i] : ( B @ ( C @ model ) )
| ~ ! [C: $i] : ( A @ ( C @ model ) ) )
& ? [C: $i] :
( ( B @ ( C @ model ) )
& ( A @ ( C @ model ) ) ) ) ) ) ).
thf(sk42_def,definition,
( sk42
= ( @+[A: $i] :
( ( ~ ! [B: $i] : ( A @ ( B @ model ) )
| ~ ! [B: $i] : ( sk41 @ ( B @ model ) ) )
& ? [B: $i] :
( ( A @ ( B @ model ) )
& ( sk41 @ ( B @ model ) ) ) ) ) ) ).
thf(sk43_def,definition,
( sk43
= ( @+[A: $i] :
( ( sk42 @ ( A @ model ) )
& ( sk41 @ ( A @ model ) ) ) ) ) ).
thf(sk44_def,definition,
( sk44
= ( @+[A: $i] :
~ ( sk41 @ ( A @ model ) ) ) ) ).
thf(sk45_def,definition,
( sk45
= ( @+[A: $i] :
~ ( sk42 @ ( A @ model ) ) ) ) ).
thf(sk64_def,definition,
( sk64
= ( @+[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(sk65_def,definition,
( sk65
= ( @+[A: $i] : ( sk64 @ ( A @ model ) ) ) ) ).
thf(sk66_def,definition,
( sk66
= ( @+[A: $i] :
( ~ ! [B: $i] : ( A @ ( B @ model ) )
& ? [B: $i] :
( ( A @ ( B @ model ) )
& ~ ( sk64 @ ( B @ model ) ) )
& ! [B: $i] :
( ( sk64 @ ( B @ model ) )
=> ( A @ ( B @ model ) ) ) ) ) ) ).
thf(sk67_def,definition,
( sk67
= ( @+[A: $i] :
( ( sk66 @ ( A @ model ) )
& ~ ( sk64 @ ( A @ model ) ) ) ) ) ).
thf(sk68_def,definition,
( sk68
= ( @+[A: $i] :
~ ( sk66 @ ( A @ model ) ) ) ) ).
thf(sk69_def,definition,
( sk69
= ( @+[A: $i] :
! [B: $i] : ( A @ ( B @ model ) ) ) ) ).
thf(sk73_def,definition,
( sk73
= ( ^ [A: $i] :
@+[B: $i] : ( A @ ( B @ model ) ) ) ) ).
thf(31,axiom,
? [A: $i] :
! [B: $i] : ( A @ ( B @ model ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tautology) ).
thf(283,plain,
? [A: $i] :
! [B: $i] : ( A @ ( B @ model ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(284,plain,
! [A: $i] : ( sk69 @ ( A @ model ) ),
inference(cnf,[status(esa)],[283]) ).
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(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(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(49,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( B @ sk6 ) @ model ) )
| ~ ( wth @ ( B @ ( A @ status ) ) ) ),
inference(cnfConj,[status(thm)],[43]) ).
thf(54,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( B @ sk6 ) @ model ) )
| ~ ( wth @ ( B @ ( A @ status ) ) ) ),
inference(simp,[status(thm)],[49]) ).
thf(13,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ model ) )
<=> ~ ( B @ not @ ( A @ model ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not) ).
thf(118,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)],[13]) ).
thf(119,plain,
( ! [A: $i,B: $i] :
( ~ ( B @ not @ ( A @ model ) )
=> ( B @ ( A @ model ) ) )
& ! [A: $i,B: $i] :
( ( B @ ( A @ model ) )
=> ~ ( B @ not @ ( A @ model ) ) ) ),
inference(miniscope,[status(thm)],[118]) ).
thf(120,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ model ) )
| ( D @ not @ ( C @ model ) ) )
& ( ~ ( B @ not @ ( A @ model ) )
| ~ ( B @ ( A @ model ) ) ) ),
inference(cnf,[status(esa)],[119]) ).
thf(122,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ model ) )
| ( B @ not @ ( A @ model ) ) ),
inference(cnfConj,[status(thm)],[120]) ).
thf(123,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ model ) )
| ( B @ not @ ( A @ model ) ) ),
inference(simp,[status(thm)],[122]) ).
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(30,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(275,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)],[30]) ).
thf(276,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)],[275]) ).
thf(277,plain,
! [A: $i] :
( ~ ( sk66 @ ( sk68 @ model ) )
& ( sk66 @ ( sk67 @ model ) )
& ~ ( sk64 @ ( sk67 @ model ) )
& ( ( sk66 @ ( A @ model ) )
| ~ ( sk64 @ ( A @ model ) ) )
& ( sk64 @ ( sk65 @ model ) ) ),
inference(cnf,[status(esa)],[276]) ).
thf(281,plain,
~ ( sk66 @ ( sk68 @ model ) ),
inference(cnfConj,[status(thm)],[277]) ).
thf(312,plain,
( ( ( sk66 @ ( sk68 @ model ) )
!= ( sk1 @ ( sk2 @ model ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[39,281]) ).
thf(313,plain,
( ( sk66 @ ( sk68 @ model ) )
!= ( sk1 @ ( sk2 @ model ) ) ),
inference(simp,[status(thm)],[312]) ).
thf(314,plain,
( ( sk66 != sk1 )
| ( sk68 != sk2 ) ),
inference(simp,[status(thm)],[313]) ).
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(67,plain,
( ! [A: $i,B: $i] :
( ( sap @ ( B @ ( A @ status ) ) )
=> ( ? [C: $i] : ( A @ ( C @ model ) )
=> ? [C: $i] : ( B @ ( C @ model ) ) ) )
& ! [A: $i,B: $i] :
( ( ? [C: $i] : ( A @ ( C @ model ) )
=> ? [C: $i] : ( B @ ( C @ model ) ) )
=> ( sap @ ( B @ ( A @ status ) ) ) ) ),
inference(miniscope,[status(thm)],[66]) ).
thf(68,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( D @ ( E @ sk12 ) @ model ) )
| ~ ( D @ ( F @ model ) )
| ~ ( sap @ ( E @ ( D @ status ) ) ) )
& ( ( sap @ ( B @ ( A @ status ) ) )
| ~ ( B @ ( C @ model ) ) )
& ( ( sap @ ( B @ ( A @ status ) ) )
| ( A @ ( A @ ( B @ sk11 ) @ model ) ) ) ),
inference(cnf,[status(esa)],[67]) ).
thf(69,plain,
! [B: $i,A: $i] :
( ( sap @ ( B @ ( A @ status ) ) )
| ( A @ ( A @ ( B @ sk11 ) @ model ) ) ),
inference(cnfConj,[status(thm)],[68]) ).
thf(18,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(173,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)],[18]) ).
thf(174,plain,
? [A: $i] :
( ? [B: $i] :
( ? [C: $i] : ( B @ ( C @ model ) )
& ~ ( B @ ( A @ model ) ) )
& ? [B: $i] : ( B @ ( A @ model ) ) ),
inference(miniscope,[status(thm)],[173]) ).
thf(175,plain,
( ( sk37 @ ( sk38 @ model ) )
& ~ ( sk37 @ ( sk35 @ model ) )
& ( sk36 @ ( sk35 @ model ) ) ),
inference(cnf,[status(esa)],[174]) ).
thf(178,plain,
sk37 @ ( sk38 @ model ),
inference(cnfConj,[status(thm)],[175]) ).
thf(329,plain,
( ( ( sk66 @ ( sk68 @ model ) )
!= ( sk37 @ ( sk38 @ model ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[178,281]) ).
thf(330,plain,
( ( sk66 @ ( sk68 @ model ) )
!= ( sk37 @ ( sk38 @ model ) ) ),
inference(simp,[status(thm)],[329]) ).
thf(333,plain,
( ( sk66 != sk37 )
| ( sk68 != sk38 ) ),
inference(simp,[status(thm)],[330]) ).
thf(26,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(234,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)],[26]) ).
thf(278,plain,
sk66 @ ( sk67 @ model ),
inference(cnfConj,[status(thm)],[277]) ).
thf(473,plain,
( ( ( sk66 @ ( sk68 @ model ) )
!= ( sk66 @ ( sk67 @ model ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[278,281]) ).
thf(474,plain,
( ( sk66 @ ( sk68 @ model ) )
!= ( sk66 @ ( sk67 @ model ) ) ),
inference(simp,[status(thm)],[473]) ).
thf(477,plain,
( ( sk66 != sk66 )
| ( sk68 != sk67 ) ),
inference(simp,[status(thm)],[474]) ).
thf(481,plain,
sk68 != sk67,
inference(simp,[status(thm)],[477]) ).
thf(20,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(187,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)],[20]) ).
thf(188,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)],[187]) ).
thf(189,plain,
( ( ~ ( sk42 @ ( sk45 @ model ) )
| ~ ( sk41 @ ( sk44 @ model ) ) )
& ( sk42 @ ( sk43 @ model ) )
& ( sk41 @ ( sk43 @ model ) ) ),
inference(cnf,[status(esa)],[188]) ).
thf(190,plain,
sk41 @ ( sk43 @ model ),
inference(cnfConj,[status(thm)],[189]) ).
thf(192,plain,
( ~ ( sk42 @ ( sk45 @ model ) )
| ~ ( sk41 @ ( sk44 @ model ) ) ),
inference(cnfConj,[status(thm)],[189]) ).
thf(1067,plain,
! [A: $i] :
( ( ( sk69 @ ( A @ model ) )
!= ( sk42 @ ( sk45 @ model ) ) )
| ~ $true
| ~ ( sk41 @ ( sk44 @ model ) ) ),
inference(paramod_ordered,[status(thm)],[284,192]) ).
thf(1068,plain,
! [A: $i] :
( ( ( sk69 @ ( A @ model ) )
!= ( sk42 @ ( sk45 @ model ) ) )
| ~ ( sk41 @ ( sk44 @ model ) ) ),
inference(simp,[status(thm)],[1067]) ).
thf(1122,plain,
! [A: $i] :
( ( sk69 != sk42 )
| ( A != sk45 )
| ~ ( sk41 @ ( sk44 @ model ) ) ),
inference(simp,[status(thm)],[1068]) ).
thf(1142,plain,
( ( sk69 != sk42 )
| ~ ( sk41 @ ( sk44 @ model ) ) ),
inference(simp,[status(thm)],[1122]) ).
thf(1196,plain,
( ( ( sk41 @ ( sk44 @ model ) )
!= ( sk41 @ ( sk43 @ model ) ) )
| ( sk69 != sk42 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[190,1142]) ).
thf(1197,plain,
( ( ( sk41 @ ( sk44 @ model ) )
!= ( sk41 @ ( sk43 @ model ) ) )
| ( sk69 != sk42 ) ),
inference(simp,[status(thm)],[1196]) ).
thf(1206,plain,
( ( sk41 != sk41 )
| ( sk44 != sk43 )
| ( sk69 != sk42 ) ),
inference(simp,[status(thm)],[1197]) ).
thf(1211,plain,
( ( sk44 != sk43 )
| ( sk69 != sk42 ) ),
inference(simp,[status(thm)],[1206]) ).
thf(279,plain,
sk64 @ ( sk65 @ model ),
inference(cnfConj,[status(thm)],[277]) ).
thf(177,plain,
~ ( sk37 @ ( sk35 @ model ) ),
inference(cnfConj,[status(thm)],[175]) ).
thf(506,plain,
( ( ( sk64 @ ( sk65 @ model ) )
!= ( sk37 @ ( sk35 @ model ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[279,177]) ).
thf(507,plain,
( ( sk64 @ ( sk65 @ model ) )
!= ( sk37 @ ( sk35 @ model ) ) ),
inference(simp,[status(thm)],[506]) ).
thf(523,plain,
( ( sk64 != sk37 )
| ( sk65 != sk35 ) ),
inference(simp,[status(thm)],[507]) ).
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(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(247,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(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(282,plain,
~ ( sk64 @ ( sk67 @ model ) ),
inference(cnfConj,[status(thm)],[277]) ).
thf(483,plain,
( ( ( sk64 @ ( sk67 @ model ) )
!= ( sk1 @ ( sk2 @ model ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[39,282]) ).
thf(484,plain,
( ( sk64 @ ( sk67 @ model ) )
!= ( sk1 @ ( sk2 @ model ) ) ),
inference(simp,[status(thm)],[483]) ).
thf(500,plain,
( ( sk64 != sk1 )
| ( sk67 != sk2 ) ),
inference(simp,[status(thm)],[484]) ).
thf(717,plain,
! [A: $i] :
( ( ( sk69 @ ( A @ model ) )
!= ( sk1 @ ( sk3 @ model ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[284,40]) ).
thf(718,plain,
! [A: $i] :
( ( sk69 @ ( A @ model ) )
!= ( sk1 @ ( sk3 @ model ) ) ),
inference(simp,[status(thm)],[717]) ).
thf(740,plain,
! [A: $i] :
( ( sk69 != sk1 )
| ( A != sk3 ) ),
inference(simp,[status(thm)],[718]) ).
thf(747,plain,
sk69 != sk1,
inference(simp,[status(thm)],[740]) ).
thf(45,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ ( B @ sk7 ) @ model ) )
| ~ ( wth @ ( B @ ( A @ status ) ) ) ),
inference(cnfConj,[status(thm)],[43]) ).
thf(52,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ ( B @ sk7 ) @ model ) )
| ~ ( wth @ ( B @ ( A @ status ) ) ) ),
inference(simp,[status(thm)],[45]) ).
thf(857,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk69 @ ( A @ model ) )
!= ( C @ ( B @ ( C @ sk7 ) @ model ) ) )
| ~ $true
| ~ ( wth @ ( C @ ( B @ status ) ) ) ),
inference(paramod_ordered,[status(thm)],[284,52]) ).
thf(858,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk69 @ ( A @ model ) )
!= ( C @ ( B @ ( C @ sk7 ) @ model ) ) )
| ~ ( wth @ ( C @ ( B @ status ) ) ) ),
inference(simp,[status(thm)],[857]) ).
thf(859,plain,
! [A: $i] :
~ ( wth @ ( sk69 @ ( A @ status ) ) ),
inference(pattern_uni,[status(thm)],[858:[bind(A,$thf( E @ ( sk69 @ sk7 ) )),bind(B,$thf( E )),bind(C,$thf( sk69 ))]]) ).
thf(913,plain,
! [A: $i] :
~ ( wth @ ( sk69 @ ( A @ status ) ) ),
inference(simp,[status(thm)],[859]) ).
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(673,plain,
! [A: $i] :
( ( ( sk1 @ ( sk2 @ model ) )
!= ( sk18 @ ( A @ model ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[39,99]) ).
thf(674,plain,
! [A: $i] :
( ( sk1 @ ( sk2 @ model ) )
!= ( sk18 @ ( A @ model ) ) ),
inference(simp,[status(thm)],[673]) ).
thf(699,plain,
! [A: $i] :
( ( sk18 != sk1 )
| ( sk2 != A ) ),
inference(simp,[status(thm)],[674]) ).
thf(709,plain,
sk18 != sk1,
inference(simp,[status(thm)],[699]) ).
thf(431,plain,
( ( ( sk66 @ ( sk68 @ model ) )
!= ( sk41 @ ( sk43 @ model ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[190,281]) ).
thf(432,plain,
( ( sk66 @ ( sk68 @ model ) )
!= ( sk41 @ ( sk43 @ model ) ) ),
inference(simp,[status(thm)],[431]) ).
thf(436,plain,
( ( sk66 != sk41 )
| ( sk68 != sk43 ) ),
inference(simp,[status(thm)],[432]) ).
thf(485,plain,
( ( ( sk64 @ ( sk67 @ model ) )
!= ( sk41 @ ( sk43 @ model ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[190,282]) ).
thf(486,plain,
( ( sk64 @ ( sk67 @ model ) )
!= ( sk41 @ ( sk43 @ model ) ) ),
inference(simp,[status(thm)],[485]) ).
thf(504,plain,
( ( sk64 != sk41 )
| ( sk67 != sk43 ) ),
inference(simp,[status(thm)],[486]) ).
thf(12,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(110,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)],[12]) ).
thf(715,plain,
! [B: $i,A: $i] :
( ( ( sk69 @ ( A @ model ) )
!= ( sk18 @ ( B @ model ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[284,99]) ).
thf(716,plain,
! [B: $i,A: $i] :
( ( sk69 @ ( A @ model ) )
!= ( sk18 @ ( B @ model ) ) ),
inference(simp,[status(thm)],[715]) ).
thf(743,plain,
! [B: $i,A: $i] :
( ( sk69 != sk18 )
| ( A != B ) ),
inference(simp,[status(thm)],[716]) ).
thf(751,plain,
sk69 != sk18,
inference(simp,[status(thm)],[743]) ).
thf(471,plain,
( ( ( sk66 @ ( sk67 @ model ) )
!= ( sk1 @ ( sk3 @ model ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[278,40]) ).
thf(472,plain,
( ( sk66 @ ( sk67 @ model ) )
!= ( sk1 @ ( sk3 @ model ) ) ),
inference(simp,[status(thm)],[471]) ).
thf(475,plain,
( ( sk66 != sk1 )
| ( sk67 != sk3 ) ),
inference(simp,[status(thm)],[472]) ).
thf(19,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(179,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)],[19]) ).
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(292,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(520,plain,
( ( ( sk64 @ ( sk67 @ model ) )
!= ( sk64 @ ( sk65 @ model ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[279,282]) ).
thf(521,plain,
( ( sk64 @ ( sk67 @ model ) )
!= ( sk64 @ ( sk65 @ model ) ) ),
inference(simp,[status(thm)],[520]) ).
thf(525,plain,
( ( sk64 != sk64 )
| ( sk67 != sk65 ) ),
inference(simp,[status(thm)],[521]) ).
thf(529,plain,
sk67 != sk65,
inference(simp,[status(thm)],[525]) ).
thf(675,plain,
! [A: $i] :
( ( ( sk41 @ ( sk43 @ model ) )
!= ( sk18 @ ( A @ model ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[190,99]) ).
thf(676,plain,
! [A: $i] :
( ( sk41 @ ( sk43 @ model ) )
!= ( sk18 @ ( A @ model ) ) ),
inference(simp,[status(thm)],[675]) ).
thf(703,plain,
! [A: $i] :
( ( sk41 != sk18 )
| ( sk43 != A ) ),
inference(simp,[status(thm)],[676]) ).
thf(714,plain,
sk41 != sk18,
inference(simp,[status(thm)],[703]) ).
thf(325,plain,
( ( ( sk37 @ ( sk38 @ model ) )
!= ( sk37 @ ( sk35 @ model ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[178,177]) ).
thf(326,plain,
( ( sk37 @ ( sk38 @ model ) )
!= ( sk37 @ ( sk35 @ model ) ) ),
inference(simp,[status(thm)],[325]) ).
thf(331,plain,
( ( sk37 != sk37 )
| ( sk38 != sk35 ) ),
inference(simp,[status(thm)],[326]) ).
thf(334,plain,
sk38 != sk35,
inference(simp,[status(thm)],[331]) ).
thf(34,axiom,
! [A: $i,B: $i] :
( ~ ? [C: $i] : ( A @ ( C @ model ) )
<=> ( cax @ ( B @ ( A @ status ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cax) ).
thf(299,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)],[34]) ).
thf(300,plain,
( ! [A: $i] :
( ? [B: $i] : ( cax @ ( B @ ( A @ status ) ) )
=> ~ ? [B: $i] : ( A @ ( B @ model ) ) )
& ! [A: $i] :
( ~ ? [B: $i] : ( A @ ( B @ model ) )
=> ! [B: $i] : ( cax @ ( B @ ( A @ status ) ) ) ) ),
inference(miniscope,[status(thm)],[299]) ).
thf(301,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ~ ( C @ ( E @ model ) )
| ~ ( cax @ ( D @ ( C @ status ) ) ) )
& ( ( cax @ ( B @ ( A @ status ) ) )
| ( A @ ( A @ sk73 @ model ) ) ) ),
inference(cnf,[status(esa)],[300]) ).
thf(302,plain,
! [B: $i,A: $i] :
( ( cax @ ( B @ ( A @ status ) ) )
| ( A @ ( A @ sk73 @ model ) ) ),
inference(cnfConj,[status(thm)],[301]) ).
thf(15,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(137,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)],[15]) ).
thf(671,plain,
! [A: $i] :
( ( ( sk64 @ ( sk65 @ model ) )
!= ( sk18 @ ( A @ model ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[279,99]) ).
thf(672,plain,
! [A: $i] :
( ( sk64 @ ( sk65 @ model ) )
!= ( sk18 @ ( A @ model ) ) ),
inference(simp,[status(thm)],[671]) ).
thf(700,plain,
! [A: $i] :
( ( sk64 != sk18 )
| ( sk65 != A ) ),
inference(simp,[status(thm)],[672]) ).
thf(710,plain,
sk64 != sk18,
inference(simp,[status(thm)],[700]) ).
thf(176,plain,
sk36 @ ( sk35 @ model ),
inference(cnfConj,[status(thm)],[175]) ).
thf(315,plain,
( ( ( sk37 @ ( sk35 @ model ) )
!= ( sk36 @ ( sk35 @ model ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[176,177]) ).
thf(316,plain,
( ( sk37 @ ( sk35 @ model ) )
!= ( sk36 @ ( sk35 @ model ) ) ),
inference(simp,[status(thm)],[315]) ).
thf(321,plain,
( ( sk37 != sk36 )
| ( sk35 != sk35 ) ),
inference(simp,[status(thm)],[316]) ).
thf(324,plain,
sk37 != sk36,
inference(simp,[status(thm)],[321]) ).
thf(32,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(285,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)],[32]) ).
thf(44,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ model ) )
| ~ ( A @ ( C @ model ) )
| ~ ( wth @ ( B @ ( A @ status ) ) ) ),
inference(cnfConj,[status(thm)],[43]) ).
thf(53,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ model ) )
| ~ ( A @ ( C @ model ) )
| ~ ( wth @ ( B @ ( A @ status ) ) ) ),
inference(simp,[status(thm)],[44]) ).
thf(191,plain,
sk42 @ ( sk43 @ model ),
inference(cnfConj,[status(thm)],[189]) ).
thf(491,plain,
( ( ( sk64 @ ( sk67 @ model ) )
!= ( sk42 @ ( sk43 @ model ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[191,282]) ).
thf(492,plain,
( ( sk64 @ ( sk67 @ model ) )
!= ( sk42 @ ( sk43 @ model ) ) ),
inference(simp,[status(thm)],[491]) ).
thf(499,plain,
( ( sk64 != sk42 )
| ( sk67 != sk43 ) ),
inference(simp,[status(thm)],[492]) ).
thf(14,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(124,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)],[14]) ).
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(193,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(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(212,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(450,plain,
( ( ( sk42 @ ( sk43 @ model ) )
!= ( sk1 @ ( sk3 @ model ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[191,40]) ).
thf(451,plain,
( ( sk42 @ ( sk43 @ model ) )
!= ( sk1 @ ( sk3 @ model ) ) ),
inference(simp,[status(thm)],[450]) ).
thf(457,plain,
( ( sk42 != sk1 )
| ( sk43 != sk3 ) ),
inference(simp,[status(thm)],[451]) ).
thf(489,plain,
( ( ( sk64 @ ( sk67 @ model ) )
!= ( sk36 @ ( sk35 @ model ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[176,282]) ).
thf(490,plain,
( ( sk64 @ ( sk67 @ model ) )
!= ( sk36 @ ( sk35 @ model ) ) ),
inference(simp,[status(thm)],[489]) ).
thf(503,plain,
( ( sk64 != sk36 )
| ( sk67 != sk35 ) ),
inference(simp,[status(thm)],[490]) ).
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(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(205,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(309,plain,
( ( ( sk37 @ ( sk35 @ model ) )
!= ( sk1 @ ( sk2 @ model ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[39,177]) ).
thf(310,plain,
( ( sk37 @ ( sk35 @ model ) )
!= ( sk1 @ ( sk2 @ model ) ) ),
inference(simp,[status(thm)],[309]) ).
thf(311,plain,
( ( sk37 != sk1 )
| ( sk35 != sk2 ) ),
inference(simp,[status(thm)],[310]) ).
thf(730,plain,
! [A: $i] :
( ( ( sk69 @ ( A @ model ) )
!= ( sk64 @ ( sk67 @ model ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[284,282]) ).
thf(731,plain,
! [A: $i] :
( ( sk69 @ ( A @ model ) )
!= ( sk64 @ ( sk67 @ model ) ) ),
inference(simp,[status(thm)],[730]) ).
thf(742,plain,
! [A: $i] :
( ( sk69 != sk64 )
| ( A != sk67 ) ),
inference(simp,[status(thm)],[731]) ).
thf(750,plain,
sk69 != sk64,
inference(simp,[status(thm)],[742]) ).
thf(679,plain,
! [A: $i] :
( ( ( sk36 @ ( sk35 @ model ) )
!= ( sk18 @ ( A @ model ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[176,99]) ).
thf(680,plain,
! [A: $i] :
( ( sk36 @ ( sk35 @ model ) )
!= ( sk18 @ ( A @ model ) ) ),
inference(simp,[status(thm)],[679]) ).
thf(701,plain,
! [A: $i] :
( ( sk36 != sk18 )
| ( sk35 != A ) ),
inference(simp,[status(thm)],[680]) ).
thf(711,plain,
sk36 != sk18,
inference(simp,[status(thm)],[701]) ).
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(259,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(1172,plain,
! [A: $i] :
( ( ( sk69 @ ( A @ model ) )
!= ( sk41 @ ( sk44 @ model ) ) )
| ( sk69 != sk42 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[284,1142]) ).
thf(1173,plain,
! [A: $i] :
( ( ( sk69 @ ( A @ model ) )
!= ( sk41 @ ( sk44 @ model ) ) )
| ( sk69 != sk42 ) ),
inference(simp,[status(thm)],[1172]) ).
thf(1201,plain,
! [A: $i] :
( ( sk69 != sk41 )
| ( A != sk44 )
| ( sk69 != sk42 ) ),
inference(simp,[status(thm)],[1173]) ).
thf(1209,plain,
( ( sk69 != sk41 )
| ( sk69 != sk42 ) ),
inference(simp,[status(thm)],[1201]) ).
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(219,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(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(1113,plain,
( ( ( sk41 @ ( sk44 @ model ) )
!= ( sk41 @ ( sk43 @ model ) ) )
| ~ ( sk42 @ ( sk45 @ model ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[190,192]) ).
thf(1114,plain,
( ( ( sk41 @ ( sk44 @ model ) )
!= ( sk41 @ ( sk43 @ model ) ) )
| ~ ( sk42 @ ( sk45 @ model ) ) ),
inference(simp,[status(thm)],[1113]) ).
thf(1126,plain,
( ( sk41 != sk41 )
| ( sk44 != sk43 )
| ~ ( sk42 @ ( sk45 @ model ) ) ),
inference(simp,[status(thm)],[1114]) ).
thf(1144,plain,
( ( sk44 != sk43 )
| ~ ( sk42 @ ( sk45 @ model ) ) ),
inference(simp,[status(thm)],[1126]) ).
thf(429,plain,
( ( ( sk41 @ ( sk43 @ model ) )
!= ( sk1 @ ( sk3 @ model ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[190,40]) ).
thf(430,plain,
( ( sk41 @ ( sk43 @ model ) )
!= ( sk1 @ ( sk3 @ model ) ) ),
inference(simp,[status(thm)],[429]) ).
thf(434,plain,
( ( sk41 != sk1 )
| ( sk43 != sk3 ) ),
inference(simp,[status(thm)],[430]) ).
thf(319,plain,
( ( ( sk66 @ ( sk68 @ model ) )
!= ( sk36 @ ( sk35 @ model ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[176,281]) ).
thf(320,plain,
( ( sk66 @ ( sk68 @ model ) )
!= ( sk36 @ ( sk35 @ model ) ) ),
inference(simp,[status(thm)],[319]) ).
thf(323,plain,
( ( sk66 != sk36 )
| ( sk68 != sk35 ) ),
inference(simp,[status(thm)],[320]) ).
thf(452,plain,
( ( ( sk66 @ ( sk68 @ model ) )
!= ( sk42 @ ( sk43 @ model ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[191,281]) ).
thf(453,plain,
( ( sk66 @ ( sk68 @ model ) )
!= ( sk42 @ ( sk43 @ model ) ) ),
inference(simp,[status(thm)],[452]) ).
thf(455,plain,
( ( sk66 != sk42 )
| ( sk68 != sk43 ) ),
inference(simp,[status(thm)],[453]) ).
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(267,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(493,plain,
( ( ( sk66 @ ( sk67 @ model ) )
!= ( sk64 @ ( sk67 @ model ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[278,282]) ).
thf(494,plain,
( ( sk66 @ ( sk67 @ model ) )
!= ( sk64 @ ( sk67 @ model ) ) ),
inference(simp,[status(thm)],[493]) ).
thf(502,plain,
( ( sk66 != sk64 )
| ( sk67 != sk67 ) ),
inference(simp,[status(thm)],[494]) ).
thf(505,plain,
sk66 != sk64,
inference(simp,[status(thm)],[502]) ).
thf(1,conjecture,
thm @ ( cax @ isa ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',isa_cax_thm) ).
thf(2,negated_conjecture,
~ ( thm @ ( cax @ isa ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(35,plain,
~ ( thm @ ( cax @ isa ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
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(683,plain,
! [A: $i] :
( ( ( sk66 @ ( sk67 @ model ) )
!= ( sk18 @ ( A @ model ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[278,99]) ).
thf(684,plain,
! [A: $i] :
( ( sk66 @ ( sk67 @ model ) )
!= ( sk18 @ ( A @ model ) ) ),
inference(simp,[status(thm)],[683]) ).
thf(702,plain,
! [A: $i] :
( ( sk66 != sk18 )
| ( sk67 != A ) ),
inference(simp,[status(thm)],[684]) ).
thf(712,plain,
sk66 != sk18,
inference(simp,[status(thm)],[702]) ).
thf(16,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(150,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)],[16]) ).
thf(677,plain,
! [A: $i] :
( ( ( sk37 @ ( sk38 @ model ) )
!= ( sk18 @ ( A @ model ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[178,99]) ).
thf(678,plain,
! [A: $i] :
( ( sk37 @ ( sk38 @ model ) )
!= ( sk18 @ ( A @ model ) ) ),
inference(simp,[status(thm)],[677]) ).
thf(697,plain,
! [A: $i] :
( ( sk37 != sk18 )
| ( sk38 != A ) ),
inference(simp,[status(thm)],[678]) ).
thf(707,plain,
sk37 != 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(508,plain,
( ( ( sk64 @ ( sk65 @ model ) )
!= ( sk1 @ ( sk3 @ model ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[279,40]) ).
thf(509,plain,
( ( sk64 @ ( sk65 @ model ) )
!= ( sk1 @ ( sk3 @ model ) ) ),
inference(simp,[status(thm)],[508]) ).
thf(524,plain,
( ( sk64 != sk1 )
| ( sk65 != sk3 ) ),
inference(simp,[status(thm)],[509]) ).
thf(738,plain,
! [A: $i] :
( ( ( sk69 @ ( A @ model ) )
!= ( sk37 @ ( sk35 @ model ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[284,177]) ).
thf(739,plain,
! [A: $i] :
( ( sk69 @ ( A @ model ) )
!= ( sk37 @ ( sk35 @ model ) ) ),
inference(simp,[status(thm)],[738]) ).
thf(741,plain,
! [A: $i] :
( ( sk69 != sk37 )
| ( A != sk35 ) ),
inference(simp,[status(thm)],[739]) ).
thf(748,plain,
sk69 != sk37,
inference(simp,[status(thm)],[741]) ).
thf(17,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(158,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)],[17]) ).
thf(47,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ sk5 ) @ model ) )
| ~ ( wth @ ( B @ ( A @ status ) ) ) ),
inference(cnfConj,[status(thm)],[43]) ).
thf(55,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ sk5 ) @ model ) )
| ~ ( wth @ ( B @ ( A @ status ) ) ) ),
inference(simp,[status(thm)],[47]) ).
thf(427,plain,
( ( ( sk41 @ ( sk43 @ model ) )
!= ( sk37 @ ( sk35 @ model ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[190,177]) ).
thf(428,plain,
( ( sk41 @ ( sk43 @ model ) )
!= ( sk37 @ ( sk35 @ model ) ) ),
inference(simp,[status(thm)],[427]) ).
thf(433,plain,
( ( sk41 != sk37 )
| ( sk43 != sk35 ) ),
inference(simp,[status(thm)],[428]) ).
thf(469,plain,
( ( ( sk66 @ ( sk67 @ model ) )
!= ( sk37 @ ( sk35 @ model ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[278,177]) ).
thf(470,plain,
( ( sk66 @ ( sk67 @ model ) )
!= ( sk37 @ ( sk35 @ model ) ) ),
inference(simp,[status(thm)],[469]) ).
thf(478,plain,
( ( sk66 != sk37 )
| ( sk67 != sk35 ) ),
inference(simp,[status(thm)],[470]) ).
thf(719,plain,
! [A: $i] :
( ( ( sk69 @ ( A @ model ) )
!= ( sk66 @ ( sk68 @ model ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[284,281]) ).
thf(720,plain,
! [A: $i] :
( ( sk69 @ ( A @ model ) )
!= ( sk66 @ ( sk68 @ model ) ) ),
inference(simp,[status(thm)],[719]) ).
thf(744,plain,
! [A: $i] :
( ( sk69 != sk66 )
| ( A != sk68 ) ),
inference(simp,[status(thm)],[720]) ).
thf(752,plain,
sk69 != sk66,
inference(simp,[status(thm)],[744]) ).
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(755,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk69 @ ( A @ model ) )
!= ( B @ ( B @ ( C @ sk6 ) @ model ) ) )
| ~ $true
| ~ ( wth @ ( C @ ( B @ status ) ) ) ),
inference(paramod_ordered,[status(thm)],[284,51]) ).
thf(756,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk69 @ ( A @ model ) )
!= ( B @ ( B @ ( C @ sk6 ) @ model ) ) )
| ~ ( wth @ ( C @ ( B @ status ) ) ) ),
inference(simp,[status(thm)],[755]) ).
thf(757,plain,
! [A: $i] :
~ ( wth @ ( A @ ( sk69 @ status ) ) ),
inference(pattern_uni,[status(thm)],[756:[bind(A,$thf( sk69 @ ( D @ sk6 ) )),bind(B,$thf( sk69 )),bind(C,$thf( D ))]]) ).
thf(801,plain,
! [A: $i] :
~ ( wth @ ( A @ ( sk69 @ status ) ) ),
inference(simp,[status(thm)],[757]) ).
thf(327,plain,
( ( ( sk37 @ ( sk38 @ model ) )
!= ( sk1 @ ( sk3 @ model ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[178,40]) ).
thf(328,plain,
( ( sk37 @ ( sk38 @ model ) )
!= ( sk1 @ ( sk3 @ model ) ) ),
inference(simp,[status(thm)],[327]) ).
thf(332,plain,
( ( sk37 != sk1 )
| ( sk38 != sk3 ) ),
inference(simp,[status(thm)],[328]) ).
thf(487,plain,
( ( ( sk64 @ ( sk67 @ model ) )
!= ( sk37 @ ( sk38 @ model ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[178,282]) ).
thf(488,plain,
( ( sk64 @ ( sk67 @ model ) )
!= ( sk37 @ ( sk38 @ model ) ) ),
inference(simp,[status(thm)],[487]) ).
thf(501,plain,
( ( sk64 != sk37 )
| ( sk67 != sk38 ) ),
inference(simp,[status(thm)],[488]) ).
thf(25,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ model ) )
<~> ( B @ not @ ( A @ model ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',completeness) ).
thf(227,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)],[25]) ).
thf(317,plain,
( ( ( sk36 @ ( sk35 @ model ) )
!= ( sk1 @ ( sk3 @ model ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[176,40]) ).
thf(318,plain,
( ( sk36 @ ( sk35 @ model ) )
!= ( sk1 @ ( sk3 @ model ) ) ),
inference(simp,[status(thm)],[317]) ).
thf(322,plain,
( ( sk36 != sk1 )
| ( sk35 != sk3 ) ),
inference(simp,[status(thm)],[318]) ).
thf(448,plain,
( ( ( sk42 @ ( sk43 @ model ) )
!= ( sk37 @ ( sk35 @ model ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[191,177]) ).
thf(449,plain,
( ( sk42 @ ( sk43 @ model ) )
!= ( sk37 @ ( sk35 @ model ) ) ),
inference(simp,[status(thm)],[448]) ).
thf(454,plain,
( ( sk42 != sk37 )
| ( sk43 != sk35 ) ),
inference(simp,[status(thm)],[449]) ).
thf(681,plain,
! [A: $i] :
( ( ( sk42 @ ( sk43 @ model ) )
!= ( sk18 @ ( A @ model ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[191,99]) ).
thf(682,plain,
! [A: $i] :
( ( sk42 @ ( sk43 @ model ) )
!= ( sk18 @ ( A @ model ) ) ),
inference(simp,[status(thm)],[681]) ).
thf(698,plain,
! [A: $i] :
( ( sk42 != sk18 )
| ( sk43 != A ) ),
inference(simp,[status(thm)],[682]) ).
thf(708,plain,
sk42 != sk18,
inference(simp,[status(thm)],[698]) ).
thf(11,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(100,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)],[11]) ).
thf(80790,plain,
$false,
inference(e,[status(thm)],[284,89,54,123,314,69,333,234,481,1211,523,308,247,1142,56,500,747,913,709,436,52,504,110,751,475,179,292,529,714,334,302,192,275,137,97,710,324,285,53,499,124,193,212,457,173,41,503,73,205,311,750,279,176,191,711,118,281,259,187,1209,219,81,1144,39,434,323,66,278,455,299,267,505,35,48,712,282,150,707,50,177,99,524,748,40,158,55,433,478,752,36,51,190,801,283,332,178,501,227,322,454,708,100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : KRS193+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.11 % 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
% 0.22/0.48 % Computer : n020.cluster.edu
% 0.22/0.48 % Model : x86_64 x86_64
% 0.22/0.48 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.22/0.48 % Memory : 8046.5625MB
% 0.22/0.48 % OS : Linux 6.8.0-71-generic
% 0.22/0.48 % CPULimit : 300
% 0.22/0.48 % WCLimit : 300
% 0.22/0.48 % DateTime : Fri Sep 25 19:44:33 UTC 2026
% 0.22/0.48 % CPUTime :
% 0.22/0.48 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
% 1.28/1.17 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.71/1.49 % [INFO] Parsing done (319ms).
% 2.07/1.51 % [INFO] Running in sequential loop mode.
% 2.96/2.11 % [INFO] eprover registered as external prover.
% 2.96/2.13 % [INFO] Scanning for conjecture ...
% 3.28/2.25 % [INFO] Found a conjecture (or negated_conjecture) and 32 axioms. Running axiom selection ...
% 3.43/2.34 % [INFO] Axiom selection finished. Selected 32 axioms (removed 0 axioms).
% 3.65/2.47 % [INFO] Problem is first-order (TPTP FOF).
% 3.65/2.49 % [INFO] Type checking passed.
% 3.65/2.49 % [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 ...
% 107.02/26.94 % External prover 'e' found a proof!
% 107.02/26.94 % [INFO] Killing All external provers ...
% 107.02/26.94 % Time passed: 26336ms (effective reasoning time: 25421ms)
% 107.02/26.94 % 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)>
% 107.02/26.95 % 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
% 107.02/26.95 % No. of inferences in proof: 274
% 107.02/26.95 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 26336 ms resp. 25421 ms w/o parsing
% 100.47/27.02 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 100.47/27.02 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------