%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : KRS191+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n008.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 166.41s 43.19s
% Output : Refutation 156.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 64
% Syntax : Number of formulae : 426 ( 133 unt; 0 typ; 31 def)
% Number of atoms : 1446 ( 386 equ; 0 cnn)
% Maximal formula atoms : 23 ( 3 avg)
% Number of connectives : 3645 ( 675 ~; 333 |; 199 &;2295 @)
% ( 28 <=>; 113 =>; 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 : 61 ( 58 usr; 40 con; 0-3 aty)
% Number of variables : 713 ( 23 ^; 477 !; 182 ?; 713 :)
% ( 0 !>; 0 ?*; 0 @-; 31 @+)
% Comments :
%------------------------------------------------------------------------------
thf(isa_decl,type,
isa: $i > $i > $o ).
thf(wtc_decl,type,
wtc: $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(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(eqv_decl,type,
eqv: $i ).
thf(esa_decl,type,
esa: $i ).
thf(sat_decl,type,
sat: $i ).
thf(tau_decl,type,
tau: $i ).
thf(mighta_decl,type,
mighta: $i > $i > $o ).
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(sk8_decl,type,
sk8: $i > $i > $i ).
thf(sk9_decl,type,
sk9: $i > $i > $i ).
thf(sk10_decl,type,
sk10: $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(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(sk45_decl,type,
sk45: $i > $i > $i ).
thf(sk46_decl,type,
sk46: $i > $i > $i ).
thf(sk49_decl,type,
sk49: $i > $i ).
thf(sk62_decl,type,
sk62: $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(sk8_def,definition,
( sk8
= ( ^ [A: $i,B: $i] :
@+[C: $i] : ( B @ ( C @ model ) ) ) ) ).
thf(sk9_def,definition,
( sk9
= ( ^ [A: $i,B: $i] :
@+[C: $i] : ( A @ ( C @ model ) ) ) ) ).
thf(sk10_def,definition,
( sk10
= ( ^ [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(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(sk45_def,definition,
( sk45
= ( ^ [A: $i,B: $i] :
@+[C: $i] : ( A @ ( C @ model ) ) ) ) ).
thf(sk46_def,definition,
( sk46
= ( ^ [A: $i,B: $i] :
@+[C: $i] : ( B @ ( C @ model ) ) ) ) ).
thf(sk49_def,definition,
( sk49
= ( ^ [A: $i] :
@+[B: $i] : ( A @ ( B @ model ) ) ) ) ).
thf(sk62_def,definition,
( sk62
= ( @+[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(sk63_def,definition,
( sk63
= ( @+[A: $i] : ( sk62 @ ( A @ model ) ) ) ) ).
thf(sk64_def,definition,
( sk64
= ( @+[A: $i] :
( ~ ! [B: $i] : ( A @ ( B @ model ) )
& ? [B: $i] :
( ( A @ ( B @ model ) )
& ~ ( sk62 @ ( B @ model ) ) )
& ! [B: $i] :
( ( sk62 @ ( B @ model ) )
=> ( A @ ( B @ model ) ) ) ) ) ) ).
thf(sk65_def,definition,
( sk65
= ( @+[A: $i] :
( ( sk64 @ ( A @ model ) )
& ~ ( sk62 @ ( A @ model ) ) ) ) ) ).
thf(sk66_def,definition,
( sk66
= ( @+[A: $i] :
~ ( sk64 @ ( A @ model ) ) ) ) ).
thf(sk67_def,definition,
( sk67
= ( @+[A: $i] :
! [B: $i] : ( A @ ( B @ model ) ) ) ) ).
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/sandbox2/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(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(172,plain,
sk36 @ ( sk38 @ model ),
inference(cnfConj,[status(thm)],[171]) ).
thf(174,plain,
( ~ ( sk37 @ ( sk40 @ model ) )
| ~ ( sk36 @ ( sk39 @ model ) ) ),
inference(cnfConj,[status(thm)],[171]) ).
thf(1089,plain,
( ( ( sk36 @ ( sk39 @ model ) )
!= ( sk36 @ ( sk38 @ model ) ) )
| ~ ( sk37 @ ( sk40 @ model ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[172,174]) ).
thf(1090,plain,
( ( ( sk36 @ ( sk39 @ model ) )
!= ( sk36 @ ( sk38 @ model ) ) )
| ~ ( sk37 @ ( sk40 @ model ) ) ),
inference(simp,[status(thm)],[1089]) ).
thf(1141,plain,
( ( sk36 != sk36 )
| ( sk39 != sk38 )
| ~ ( sk37 @ ( sk40 @ model ) ) ),
inference(simp,[status(thm)],[1090]) ).
thf(1147,plain,
( ( sk39 != sk38 )
| ~ ( sk37 @ ( sk40 @ model ) ) ),
inference(simp,[status(thm)],[1141]) ).
thf(10,axiom,
? [A: $i] :
! [B: $i] :
~ ( A @ ( B @ model ) ),
file('/export/starexec/sandbox2/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(6,axiom,
! [A: $i,B: $i] :
( ( ? [C: $i] : ( A @ ( C @ model ) )
=> ? [C: $i] : ( B @ ( C @ model ) ) )
<=> ( sap @ ( B @ ( A @ status ) ) ) ),
file('/export/starexec/sandbox2/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(16,axiom,
? [A: $i,B: $i,C: $i] :
( ? [D: $i] : ( C @ ( D @ model ) )
& ~ ( C @ ( A @ model ) )
& ( B @ ( A @ model ) ) ),
file('/export/starexec/sandbox2/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(160,plain,
sk32 @ ( sk33 @ model ),
inference(cnfConj,[status(thm)],[157]) ).
thf(3,axiom,
? [A: $i] :
( ? [B: $i] :
~ ( A @ ( B @ model ) )
& ? [B: $i] : ( A @ ( B @ model ) ) ),
file('/export/starexec/sandbox2/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(40,plain,
~ ( sk1 @ ( sk3 @ model ) ),
inference(cnfConj,[status(thm)],[38]) ).
thf(329,plain,
( ( ( sk32 @ ( sk33 @ model ) )
!= ( sk1 @ ( sk3 @ model ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[160,40]) ).
thf(330,plain,
( ( sk32 @ ( sk33 @ model ) )
!= ( sk1 @ ( sk3 @ model ) ) ),
inference(simp,[status(thm)],[329]) ).
thf(333,plain,
( ( sk32 != sk1 )
| ( sk33 != sk3 ) ),
inference(simp,[status(thm)],[330]) ).
thf(158,plain,
sk31 @ ( sk30 @ model ),
inference(cnfConj,[status(thm)],[157]) ).
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/sandbox2/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(57,plain,
( ! [A: $i,B: $i] :
( ( wca @ ( B @ ( A @ status ) ) )
=> ( ~ ! [C: $i] : ( B @ ( C @ model ) )
& ? [C: $i] : ( B @ ( C @ model ) )
& ~ ? [C: $i] : ( A @ ( C @ model ) ) ) )
& ! [A: $i,B: $i] :
( ( ~ ! [C: $i] : ( B @ ( C @ model ) )
& ? [C: $i] : ( B @ ( C @ model ) )
& ~ ? [C: $i] : ( A @ ( C @ model ) ) )
=> ( wca @ ( B @ ( A @ status ) ) ) ) ),
inference(miniscope,[status(thm)],[56]) ).
thf(58,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ~ ( F @ ( E @ ( F @ sk10 ) @ model ) )
| ~ ( wca @ ( F @ ( E @ status ) ) ) )
& ( ( F @ ( E @ ( F @ sk9 ) @ model ) )
| ~ ( wca @ ( F @ ( E @ status ) ) ) )
& ( ~ ( E @ ( G @ model ) )
| ~ ( wca @ ( F @ ( E @ status ) ) ) )
& ( ( wca @ ( B @ ( A @ status ) ) )
| ( B @ ( D @ model ) )
| ~ ( B @ ( C @ model ) )
| ( A @ ( A @ ( B @ sk8 ) @ model ) ) ) ),
inference(cnf,[status(esa)],[57]) ).
thf(60,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ model ) )
| ~ ( wca @ ( B @ ( A @ status ) ) ) ),
inference(cnfConj,[status(thm)],[58]) ).
thf(63,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ model ) )
| ~ ( wca @ ( B @ ( A @ status ) ) ) ),
inference(simp,[status(thm)],[60]) ).
thf(1872,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk31 @ ( sk30 @ model ) )
!= ( A @ ( C @ model ) ) )
| ~ $true
| ~ ( wca @ ( B @ ( A @ status ) ) ) ),
inference(paramod_ordered,[status(thm)],[158,63]) ).
thf(1873,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk31 @ ( sk30 @ model ) )
!= ( A @ ( C @ model ) ) )
| ~ ( wca @ ( B @ ( A @ status ) ) ) ),
inference(simp,[status(thm)],[1872]) ).
thf(1874,plain,
! [A: $i] :
~ ( wca @ ( A @ ( sk31 @ status ) ) ),
inference(pattern_uni,[status(thm)],[1873:[bind(A,$thf( sk31 )),bind(B,$thf( B )),bind(C,$thf( sk30 ))]]) ).
thf(1899,plain,
! [A: $i] :
~ ( wca @ ( A @ ( sk31 @ status ) ) ),
inference(simp,[status(thm)],[1874]) ).
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/sandbox2/benchmark/theBenchmark.p',mixed_pair) ).
thf(271,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(272,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)],[271]) ).
thf(273,plain,
! [A: $i] :
( ~ ( sk64 @ ( sk66 @ model ) )
& ( sk64 @ ( sk65 @ model ) )
& ~ ( sk62 @ ( sk65 @ model ) )
& ( ( sk64 @ ( A @ model ) )
| ~ ( sk62 @ ( A @ model ) ) )
& ( sk62 @ ( sk63 @ model ) ) ),
inference(cnf,[status(esa)],[272]) ).
thf(275,plain,
sk64 @ ( sk65 @ model ),
inference(cnfConj,[status(thm)],[273]) ).
thf(274,plain,
~ ( sk62 @ ( sk65 @ model ) ),
inference(cnfConj,[status(thm)],[273]) ).
thf(471,plain,
( ( ( sk64 @ ( sk65 @ model ) )
!= ( sk62 @ ( sk65 @ model ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[275,274]) ).
thf(472,plain,
( ( sk64 @ ( sk65 @ model ) )
!= ( sk62 @ ( sk65 @ model ) ) ),
inference(simp,[status(thm)],[471]) ).
thf(475,plain,
( ( sk64 != sk62 )
| ( sk65 != sk65 ) ),
inference(simp,[status(thm)],[472]) ).
thf(481,plain,
sk64 != sk62,
inference(simp,[status(thm)],[475]) ).
thf(31,axiom,
? [A: $i] :
! [B: $i] : ( A @ ( B @ model ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tautology) ).
thf(279,plain,
? [A: $i] :
! [B: $i] : ( A @ ( B @ model ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(280,plain,
! [A: $i] : ( sk67 @ ( A @ model ) ),
inference(cnf,[status(esa)],[279]) ).
thf(1067,plain,
! [A: $i] :
( ( ( sk67 @ ( A @ model ) )
!= ( sk37 @ ( sk40 @ model ) ) )
| ~ $true
| ~ ( sk36 @ ( sk39 @ model ) ) ),
inference(paramod_ordered,[status(thm)],[280,174]) ).
thf(1068,plain,
! [A: $i] :
( ( ( sk67 @ ( A @ model ) )
!= ( sk37 @ ( sk40 @ model ) ) )
| ~ ( sk36 @ ( sk39 @ model ) ) ),
inference(simp,[status(thm)],[1067]) ).
thf(1122,plain,
! [A: $i] :
( ( sk67 != sk37 )
| ( A != sk40 )
| ~ ( sk36 @ ( sk39 @ model ) ) ),
inference(simp,[status(thm)],[1068]) ).
thf(1142,plain,
( ( sk67 != sk37 )
| ~ ( sk36 @ ( sk39 @ model ) ) ),
inference(simp,[status(thm)],[1122]) ).
thf(1178,plain,
( ( ( sk64 @ ( sk65 @ model ) )
!= ( sk36 @ ( sk39 @ model ) ) )
| ( sk67 != sk37 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[275,1142]) ).
thf(1179,plain,
( ( ( sk64 @ ( sk65 @ model ) )
!= ( sk36 @ ( sk39 @ model ) ) )
| ( sk67 != sk37 ) ),
inference(simp,[status(thm)],[1178]) ).
thf(1200,plain,
( ( sk64 != sk36 )
| ( sk65 != sk39 )
| ( sk67 != sk37 ) ),
inference(simp,[status(thm)],[1179]) ).
thf(1184,plain,
( ( ( sk36 @ ( sk39 @ model ) )
!= ( sk36 @ ( sk38 @ model ) ) )
| ( sk67 != sk37 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[172,1142]) ).
thf(1185,plain,
( ( ( sk36 @ ( sk39 @ model ) )
!= ( sk36 @ ( sk38 @ model ) ) )
| ( sk67 != sk37 ) ),
inference(simp,[status(thm)],[1184]) ).
thf(1208,plain,
( ( sk36 != sk36 )
| ( sk39 != sk38 )
| ( sk67 != sk37 ) ),
inference(simp,[status(thm)],[1185]) ).
thf(1211,plain,
( ( sk39 != sk38 )
| ( sk67 != sk37 ) ),
inference(simp,[status(thm)],[1208]) ).
thf(276,plain,
~ ( sk64 @ ( sk66 @ model ) ),
inference(cnfConj,[status(thm)],[273]) ).
thf(39,plain,
sk1 @ ( sk2 @ 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] :
( ( B @ ( C @ model ) )
& ( A @ ( C @ model ) ) )
<=> ( sat @ ( B @ ( A @ status ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sat) ).
thf(247,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)],[27]) ).
thf(173,plain,
sk37 @ ( sk38 @ model ),
inference(cnfConj,[status(thm)],[171]) ).
thf(1083,plain,
( ( ( sk37 @ ( sk40 @ model ) )
!= ( sk37 @ ( sk38 @ model ) ) )
| ~ $true
| ~ ( sk36 @ ( sk39 @ model ) ) ),
inference(paramod_ordered,[status(thm)],[173,174]) ).
thf(1084,plain,
( ( ( sk37 @ ( sk40 @ model ) )
!= ( sk37 @ ( sk38 @ model ) ) )
| ~ ( sk36 @ ( sk39 @ model ) ) ),
inference(simp,[status(thm)],[1083]) ).
thf(1132,plain,
( ( sk37 != sk37 )
| ( sk40 != sk38 )
| ~ ( sk36 @ ( sk39 @ model ) ) ),
inference(simp,[status(thm)],[1084]) ).
thf(1145,plain,
( ( sk40 != sk38 )
| ~ ( sk36 @ ( sk39 @ model ) ) ),
inference(simp,[status(thm)],[1132]) ).
thf(1278,plain,
( ( ( sk36 @ ( sk39 @ model ) )
!= ( sk36 @ ( sk38 @ model ) ) )
| ( sk40 != sk38 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[172,1145]) ).
thf(1279,plain,
( ( ( sk36 @ ( sk39 @ model ) )
!= ( sk36 @ ( sk38 @ model ) ) )
| ( sk40 != sk38 ) ),
inference(simp,[status(thm)],[1278]) ).
thf(1295,plain,
( ( sk36 != sk36 )
| ( sk39 != sk38 )
| ( sk40 != sk38 ) ),
inference(simp,[status(thm)],[1279]) ).
thf(1305,plain,
( ( sk39 != sk38 )
| ( sk40 != sk38 ) ),
inference(simp,[status(thm)],[1295]) ).
thf(483,plain,
( ( ( sk64 @ ( sk66 @ model ) )
!= ( sk37 @ ( sk38 @ model ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[173,276]) ).
thf(484,plain,
( ( sk64 @ ( sk66 @ model ) )
!= ( sk37 @ ( sk38 @ model ) ) ),
inference(simp,[status(thm)],[483]) ).
thf(500,plain,
( ( sk64 != sk37 )
| ( sk66 != sk38 ) ),
inference(simp,[status(thm)],[484]) ).
thf(725,plain,
! [A: $i] :
( ( ( sk67 @ ( A @ model ) )
!= ( sk64 @ ( sk66 @ model ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[280,276]) ).
thf(726,plain,
! [A: $i] :
( ( sk67 @ ( A @ model ) )
!= ( sk64 @ ( sk66 @ model ) ) ),
inference(simp,[status(thm)],[725]) ).
thf(740,plain,
! [A: $i] :
( ( sk67 != sk64 )
| ( A != sk66 ) ),
inference(simp,[status(thm)],[726]) ).
thf(747,plain,
sk67 != sk64,
inference(simp,[status(thm)],[740]) ).
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/sandbox2/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(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] :
( ( ( sk67 @ ( A @ model ) )
!= ( C @ ( B @ ( C @ sk7 ) @ model ) ) )
| ~ $true
| ~ ( wth @ ( C @ ( B @ status ) ) ) ),
inference(paramod_ordered,[status(thm)],[280,52]) ).
thf(858,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk67 @ ( A @ model ) )
!= ( C @ ( B @ ( C @ sk7 ) @ model ) ) )
| ~ ( wth @ ( C @ ( B @ status ) ) ) ),
inference(simp,[status(thm)],[857]) ).
thf(859,plain,
! [A: $i] :
~ ( wth @ ( sk67 @ ( A @ status ) ) ),
inference(pattern_uni,[status(thm)],[858:[bind(A,$thf( E @ ( sk67 @ sk7 ) )),bind(B,$thf( E )),bind(C,$thf( sk67 ))]]) ).
thf(913,plain,
! [A: $i] :
~ ( wth @ ( sk67 @ ( A @ status ) ) ),
inference(simp,[status(thm)],[859]) ).
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(33,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( A @ ( C @ model ) )
=> ( B @ ( C @ model ) ) )
<=> ( thm @ ( B @ ( A @ status ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm) ).
thf(288,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(429,plain,
( ( ( sk62 @ ( sk65 @ model ) )
!= ( sk36 @ ( sk38 @ model ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[172,274]) ).
thf(430,plain,
( ( sk62 @ ( sk65 @ model ) )
!= ( sk36 @ ( sk38 @ model ) ) ),
inference(simp,[status(thm)],[429]) ).
thf(436,plain,
( ( sk62 != sk36 )
| ( sk65 != sk38 ) ),
inference(simp,[status(thm)],[430]) ).
thf(1848,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk36 @ ( sk38 @ model ) )
!= ( A @ ( C @ model ) ) )
| ~ $true
| ~ ( wca @ ( B @ ( A @ status ) ) ) ),
inference(paramod_ordered,[status(thm)],[172,63]) ).
thf(1849,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk36 @ ( sk38 @ model ) )
!= ( A @ ( C @ model ) ) )
| ~ ( wca @ ( B @ ( A @ status ) ) ) ),
inference(simp,[status(thm)],[1848]) ).
thf(1850,plain,
! [A: $i] :
~ ( wca @ ( A @ ( sk36 @ status ) ) ),
inference(pattern_uni,[status(thm)],[1849:[bind(A,$thf( sk36 )),bind(B,$thf( B )),bind(C,$thf( sk38 ))]]) ).
thf(1904,plain,
! [A: $i] :
~ ( wca @ ( A @ ( sk36 @ status ) ) ),
inference(simp,[status(thm)],[1850]) ).
thf(1065,plain,
! [A: $i] :
( ( ( sk67 @ ( A @ model ) )
!= ( sk36 @ ( sk39 @ model ) ) )
| ~ ( sk37 @ ( sk40 @ model ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[280,174]) ).
thf(1066,plain,
! [A: $i] :
( ( ( sk67 @ ( A @ model ) )
!= ( sk36 @ ( sk39 @ model ) ) )
| ~ ( sk37 @ ( sk40 @ model ) ) ),
inference(simp,[status(thm)],[1065]) ).
thf(1129,plain,
! [A: $i] :
( ( sk67 != sk36 )
| ( A != sk39 )
| ~ ( sk37 @ ( sk40 @ model ) ) ),
inference(simp,[status(thm)],[1066]) ).
thf(1144,plain,
( ( sk67 != sk36 )
| ~ ( sk37 @ ( sk40 @ model ) ) ),
inference(simp,[status(thm)],[1129]) ).
thf(1234,plain,
( ( ( sk37 @ ( sk40 @ model ) )
!= ( sk37 @ ( sk38 @ model ) ) )
| ( sk67 != sk36 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[173,1144]) ).
thf(1235,plain,
( ( ( sk37 @ ( sk40 @ model ) )
!= ( sk37 @ ( sk38 @ model ) ) )
| ( sk67 != sk36 ) ),
inference(simp,[status(thm)],[1234]) ).
thf(1261,plain,
( ( sk37 != sk37 )
| ( sk40 != sk38 )
| ( sk67 != sk36 ) ),
inference(simp,[status(thm)],[1235]) ).
thf(1265,plain,
( ( sk40 != sk38 )
| ( sk67 != sk36 ) ),
inference(simp,[status(thm)],[1261]) ).
thf(23,axiom,
! [A: $i,B: $i] :
( ~ ? [C: $i] : ( A @ ( C @ model ) )
<=> ( cax @ ( B @ ( A @ status ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cax) ).
thf(209,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)],[23]) ).
thf(210,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)],[209]) ).
thf(211,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ~ ( C @ ( E @ model ) )
| ~ ( cax @ ( D @ ( C @ status ) ) ) )
& ( ( cax @ ( B @ ( A @ status ) ) )
| ( A @ ( A @ sk49 @ model ) ) ) ),
inference(cnf,[status(esa)],[210]) ).
thf(212,plain,
! [B: $i,A: $i] :
( ( cax @ ( B @ ( A @ status ) ) )
| ( A @ ( A @ sk49 @ model ) ) ),
inference(cnfConj,[status(thm)],[211]) ).
thf(1830,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk32 @ ( sk33 @ model ) )
!= ( A @ ( C @ model ) ) )
| ~ $true
| ~ ( wca @ ( B @ ( A @ status ) ) ) ),
inference(paramod_ordered,[status(thm)],[160,63]) ).
thf(1831,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk32 @ ( sk33 @ model ) )
!= ( A @ ( C @ model ) ) )
| ~ ( wca @ ( B @ ( A @ status ) ) ) ),
inference(simp,[status(thm)],[1830]) ).
thf(1832,plain,
! [A: $i] :
~ ( wca @ ( A @ ( sk32 @ status ) ) ),
inference(pattern_uni,[status(thm)],[1831:[bind(A,$thf( sk32 )),bind(B,$thf( B )),bind(C,$thf( sk33 ))]]) ).
thf(1893,plain,
! [A: $i] :
~ ( wca @ ( A @ ( sk32 @ status ) ) ),
inference(simp,[status(thm)],[1832]) ).
thf(1912,plain,
! [C: $i,B: $i,A: $i] :
( ( ( cax @ ( B @ ( A @ status ) ) )
!= ( wca @ ( C @ ( sk32 @ status ) ) ) )
| ~ $true
| ( A @ ( A @ sk49 @ model ) ) ),
inference(paramod_ordered,[status(thm)],[212,1893]) ).
thf(1913,plain,
! [C: $i,B: $i,A: $i] :
( ( ( cax @ ( B @ ( A @ status ) ) )
!= ( wca @ ( C @ ( sk32 @ status ) ) ) )
| ( A @ ( A @ sk49 @ model ) ) ),
inference(simp,[status(thm)],[1912]) ).
thf(1932,plain,
! [C: $i,B: $i,A: $i] :
( ( cax != wca )
| ( B != C )
| ( A != sk32 )
| ( A @ ( A @ sk49 @ model ) ) ),
inference(simp,[status(thm)],[1913]) ).
thf(1938,plain,
( ( cax != wca )
| ( sk32 @ ( sk32 @ sk49 @ model ) ) ),
inference(simp,[status(thm)],[1932]) ).
thf(159,plain,
~ ( sk32 @ ( sk30 @ model ) ),
inference(cnfConj,[status(thm)],[157]) ).
thf(2278,plain,
( ( ( sk32 @ ( sk32 @ sk49 @ model ) )
!= ( sk32 @ ( sk30 @ model ) ) )
| ~ $true
| ( cax != wca ) ),
inference(paramod_ordered,[status(thm)],[1938,159]) ).
thf(2279,plain,
( ( ( sk32 @ ( sk32 @ sk49 @ model ) )
!= ( sk32 @ ( sk30 @ model ) ) )
| ( cax != wca ) ),
inference(simp,[status(thm)],[2278]) ).
thf(2318,plain,
( ( sk32 != sk32 )
| ( ( sk32 @ sk49 )
!= sk30 )
| ( cax != wca ) ),
inference(simp,[status(thm)],[2279]) ).
thf(2328,plain,
( ( ( sk32 @ sk49 )
!= sk30 )
| ( cax != wca ) ),
inference(simp,[status(thm)],[2318]) ).
thf(495,plain,
( ( ( sk64 @ ( sk66 @ model ) )
!= ( sk1 @ ( sk2 @ model ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[39,276]) ).
thf(496,plain,
( ( sk64 @ ( sk66 @ model ) )
!= ( sk1 @ ( sk2 @ model ) ) ),
inference(simp,[status(thm)],[495]) ).
thf(504,plain,
( ( sk64 != sk1 )
| ( sk66 != sk2 ) ),
inference(simp,[status(thm)],[496]) ).
thf(1851,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk1 @ ( sk2 @ model ) )
!= ( A @ ( C @ model ) ) )
| ~ $true
| ~ ( wca @ ( B @ ( A @ status ) ) ) ),
inference(paramod_ordered,[status(thm)],[39,63]) ).
thf(1852,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk1 @ ( sk2 @ model ) )
!= ( A @ ( C @ model ) ) )
| ~ ( wca @ ( B @ ( A @ status ) ) ) ),
inference(simp,[status(thm)],[1851]) ).
thf(1853,plain,
! [A: $i] :
~ ( wca @ ( A @ ( sk1 @ status ) ) ),
inference(pattern_uni,[status(thm)],[1852:[bind(A,$thf( sk1 )),bind(B,$thf( B )),bind(C,$thf( sk2 ))]]) ).
thf(1907,plain,
! [A: $i] :
~ ( wca @ ( A @ ( sk1 @ status ) ) ),
inference(simp,[status(thm)],[1853]) ).
thf(723,plain,
! [B: $i,A: $i] :
( ( ( sk67 @ ( A @ model ) )
!= ( sk18 @ ( B @ model ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[280,99]) ).
thf(724,plain,
! [B: $i,A: $i] :
( ( sk67 @ ( A @ model ) )
!= ( sk18 @ ( B @ model ) ) ),
inference(simp,[status(thm)],[723]) ).
thf(744,plain,
! [B: $i,A: $i] :
( ( sk67 != sk18 )
| ( A != B ) ),
inference(simp,[status(thm)],[724]) ).
thf(751,plain,
sk67 != sk18,
inference(simp,[status(thm)],[744]) ).
thf(62,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ ( B @ sk10 ) @ model ) )
| ~ ( wca @ ( B @ ( A @ status ) ) ) ),
inference(cnfConj,[status(thm)],[58]) ).
thf(65,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ ( B @ sk10 ) @ model ) )
| ~ ( wca @ ( B @ ( A @ status ) ) ) ),
inference(simp,[status(thm)],[62]) ).
thf(2529,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk67 @ ( A @ model ) )
!= ( C @ ( B @ ( C @ sk10 ) @ model ) ) )
| ~ $true
| ~ ( wca @ ( C @ ( B @ status ) ) ) ),
inference(paramod_ordered,[status(thm)],[280,65]) ).
thf(2530,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk67 @ ( A @ model ) )
!= ( C @ ( B @ ( C @ sk10 ) @ model ) ) )
| ~ ( wca @ ( C @ ( B @ status ) ) ) ),
inference(simp,[status(thm)],[2529]) ).
thf(2531,plain,
! [A: $i] :
~ ( wca @ ( sk67 @ ( A @ status ) ) ),
inference(pattern_uni,[status(thm)],[2530:[bind(A,$thf( E @ ( sk67 @ sk10 ) )),bind(B,$thf( E )),bind(C,$thf( sk67 ))]]) ).
thf(2616,plain,
! [A: $i] :
~ ( wca @ ( sk67 @ ( A @ status ) ) ),
inference(simp,[status(thm)],[2531]) ).
thf(1121,plain,
( ~ $true
| ( ( sk37 @ ( sk40 @ model ) )
!= ( sk36 @ ( sk39 @ model ) ) )
| ~ ( sk36 @ ( sk39 @ model ) ) ),
inference(eqfactor_ordered,[status(thm)],[174]) ).
thf(1136,plain,
( ( ( sk37 @ ( sk40 @ model ) )
!= ( sk36 @ ( sk39 @ model ) ) )
| ~ ( sk36 @ ( sk39 @ model ) ) ),
inference(simp,[status(thm)],[1121]) ).
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/sandbox2/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(14,axiom,
! [A: $i,B: $i] :
( ? [C: $i,D: $i] :
( ~ ( B @ ( D @ ( C @ status ) ) )
& ( A @ ( D @ ( C @ status ) ) ) )
<=> ( B @ ( A @ nota ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/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(1196,plain,
( ( ( sk36 @ ( sk39 @ model ) )
!= ( sk31 @ ( sk30 @ model ) ) )
| ( sk67 != sk37 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[158,1142]) ).
thf(1197,plain,
( ( ( sk36 @ ( sk39 @ model ) )
!= ( sk31 @ ( sk30 @ model ) ) )
| ( sk67 != sk37 ) ),
inference(simp,[status(thm)],[1196]) ).
thf(1206,plain,
( ( sk36 != sk31 )
| ( sk39 != sk30 )
| ( sk67 != sk37 ) ),
inference(simp,[status(thm)],[1197]) ).
thf(277,plain,
sk62 @ ( sk63 @ model ),
inference(cnfConj,[status(thm)],[273]) ).
thf(518,plain,
( ( ( sk62 @ ( sk65 @ model ) )
!= ( sk62 @ ( sk63 @ model ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[277,274]) ).
thf(519,plain,
( ( sk62 @ ( sk65 @ model ) )
!= ( sk62 @ ( sk63 @ model ) ) ),
inference(simp,[status(thm)],[518]) ).
thf(524,plain,
( ( sk62 != sk62 )
| ( sk65 != sk63 ) ),
inference(simp,[status(thm)],[519]) ).
thf(529,plain,
sk65 != sk63,
inference(simp,[status(thm)],[524]) ).
thf(22,axiom,
! [A: $i,B: $i] :
( ( ! [C: $i] : ( B @ ( C @ model ) )
& ~ ? [C: $i] : ( A @ ( C @ model ) ) )
<=> ( tca @ ( B @ ( A @ status ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tca) ).
thf(201,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)],[22]) ).
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(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(1232,plain,
( ( ( sk64 @ ( sk65 @ model ) )
!= ( sk37 @ ( sk40 @ model ) ) )
| ( sk67 != sk36 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[275,1144]) ).
thf(1233,plain,
( ( ( sk64 @ ( sk65 @ model ) )
!= ( sk37 @ ( sk40 @ model ) ) )
| ( sk67 != sk36 ) ),
inference(simp,[status(thm)],[1232]) ).
thf(1255,plain,
( ( sk64 != sk37 )
| ( sk65 != sk40 )
| ( sk67 != sk36 ) ),
inference(simp,[status(thm)],[1233]) ).
thf(1553,plain,
( ( ( sk36 @ ( sk39 @ model ) )
!= ( sk36 @ ( sk38 @ model ) ) )
| ( ( sk37 @ ( sk40 @ model ) )
!= ( sk36 @ ( sk39 @ model ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[172,1136]) ).
thf(1554,plain,
( ( ( sk36 @ ( sk39 @ model ) )
!= ( sk36 @ ( sk38 @ model ) ) )
| ( ( sk37 @ ( sk40 @ model ) )
!= ( sk36 @ ( sk39 @ model ) ) ) ),
inference(simp,[status(thm)],[1553]) ).
thf(1586,plain,
( ( sk36 != sk36 )
| ( sk39 != sk38 )
| ( ( sk37 @ ( sk40 @ model ) )
!= ( sk36 @ ( sk39 @ model ) ) ) ),
inference(simp,[status(thm)],[1554]) ).
thf(1624,plain,
( ( sk39 != sk38 )
| ( ( sk37 @ ( sk40 @ model ) )
!= ( sk36 @ ( sk39 @ model ) ) ) ),
inference(simp,[status(thm)],[1586]) ).
thf(506,plain,
( ( ( sk62 @ ( sk63 @ model ) )
!= ( sk32 @ ( sk30 @ model ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[277,159]) ).
thf(507,plain,
( ( sk62 @ ( sk63 @ model ) )
!= ( sk32 @ ( sk30 @ model ) ) ),
inference(simp,[status(thm)],[506]) ).
thf(522,plain,
( ( sk62 != sk32 )
| ( sk63 != sk30 ) ),
inference(simp,[status(thm)],[507]) ).
thf(440,plain,
( ( ( sk37 @ ( sk38 @ model ) )
!= ( sk32 @ ( sk30 @ model ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[173,159]) ).
thf(441,plain,
( ( sk37 @ ( sk38 @ model ) )
!= ( sk32 @ ( sk30 @ model ) ) ),
inference(simp,[status(thm)],[440]) ).
thf(456,plain,
( ( sk37 != sk32 )
| ( sk38 != sk30 ) ),
inference(simp,[status(thm)],[441]) ).
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(1250,plain,
( ( ( sk37 @ ( sk40 @ model ) )
!= ( sk31 @ ( sk30 @ model ) ) )
| ( sk67 != sk36 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[158,1144]) ).
thf(1251,plain,
( ( ( sk37 @ ( sk40 @ model ) )
!= ( sk31 @ ( sk30 @ model ) ) )
| ( sk67 != sk36 ) ),
inference(simp,[status(thm)],[1250]) ).
thf(1259,plain,
( ( sk37 != sk31 )
| ( sk40 != sk30 )
| ( sk67 != sk36 ) ),
inference(simp,[status(thm)],[1251]) ).
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(1186,plain,
( ( ( sk36 @ ( sk39 @ model ) )
!= ( sk1 @ ( sk2 @ model ) ) )
| ( sk67 != sk37 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[39,1142]) ).
thf(1187,plain,
( ( ( sk36 @ ( sk39 @ model ) )
!= ( sk1 @ ( sk2 @ model ) ) )
| ( sk67 != sk37 ) ),
inference(simp,[status(thm)],[1186]) ).
thf(1207,plain,
( ( sk36 != sk1 )
| ( sk39 != sk2 )
| ( sk67 != sk37 ) ),
inference(simp,[status(thm)],[1187]) ).
thf(489,plain,
( ( ( sk64 @ ( sk66 @ model ) )
!= ( sk32 @ ( sk33 @ model ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[160,276]) ).
thf(490,plain,
( ( sk64 @ ( sk66 @ model ) )
!= ( sk32 @ ( sk33 @ model ) ) ),
inference(simp,[status(thm)],[489]) ).
thf(503,plain,
( ( sk64 != sk32 )
| ( sk66 != sk33 ) ),
inference(simp,[status(thm)],[490]) ).
thf(1525,plain,
! [A: $i] :
( ( ( sk67 @ ( A @ model ) )
!= ( sk36 @ ( sk39 @ model ) ) )
| ( ( sk37 @ ( sk40 @ model ) )
!= ( sk36 @ ( sk39 @ model ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[280,1136]) ).
thf(1526,plain,
! [A: $i] :
( ( ( sk67 @ ( A @ model ) )
!= ( sk36 @ ( sk39 @ model ) ) )
| ( ( sk37 @ ( sk40 @ model ) )
!= ( sk36 @ ( sk39 @ model ) ) ) ),
inference(simp,[status(thm)],[1525]) ).
thf(1589,plain,
! [A: $i] :
( ( sk67 != sk36 )
| ( A != sk39 )
| ( ( sk37 @ ( sk40 @ model ) )
!= ( sk36 @ ( sk39 @ model ) ) ) ),
inference(simp,[status(thm)],[1526]) ).
thf(1627,plain,
( ( sk67 != sk36 )
| ( ( sk37 @ ( sk40 @ model ) )
!= ( sk36 @ ( sk39 @ model ) ) ) ),
inference(simp,[status(thm)],[1589]) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( ? [C: $i] : ( B @ ( C @ model ) )
& ~ ? [C: $i] : ( A @ ( C @ model ) ) )
<=> ( sca @ ( B @ ( A @ status ) ) ) ),
file('/export/starexec/sandbox2/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(11,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ model ) )
<=> ~ ( B @ not @ ( A @ model ) ) ),
file('/export/starexec/sandbox2/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(101,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)],[100]) ).
thf(102,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)],[101]) ).
thf(104,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ model ) )
| ( B @ not @ ( A @ model ) ) ),
inference(cnfConj,[status(thm)],[102]) ).
thf(105,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ model ) )
| ( B @ not @ ( A @ model ) ) ),
inference(simp,[status(thm)],[104]) ).
thf(309,plain,
( ( ( sk32 @ ( sk30 @ model ) )
!= ( sk1 @ ( sk2 @ model ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[39,159]) ).
thf(310,plain,
( ( sk32 @ ( sk30 @ model ) )
!= ( sk1 @ ( sk2 @ model ) ) ),
inference(simp,[status(thm)],[309]) ).
thf(311,plain,
( ( sk32 != sk1 )
| ( sk30 != sk2 ) ),
inference(simp,[status(thm)],[310]) ).
thf(1833,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk64 @ ( sk65 @ model ) )
!= ( A @ ( C @ model ) ) )
| ~ $true
| ~ ( wca @ ( B @ ( A @ status ) ) ) ),
inference(paramod_ordered,[status(thm)],[275,63]) ).
thf(1834,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk64 @ ( sk65 @ model ) )
!= ( A @ ( C @ model ) ) )
| ~ ( wca @ ( B @ ( A @ status ) ) ) ),
inference(simp,[status(thm)],[1833]) ).
thf(1835,plain,
! [A: $i] :
~ ( wca @ ( A @ ( sk64 @ status ) ) ),
inference(pattern_uni,[status(thm)],[1834:[bind(A,$thf( sk64 )),bind(B,$thf( B )),bind(C,$thf( sk65 ))]]) ).
thf(1895,plain,
! [A: $i] :
~ ( wca @ ( A @ ( sk64 @ status ) ) ),
inference(simp,[status(thm)],[1835]) ).
thf(727,plain,
! [A: $i] :
( ( ( sk67 @ ( A @ model ) )
!= ( sk62 @ ( sk65 @ model ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[280,274]) ).
thf(728,plain,
! [A: $i] :
( ( sk67 @ ( A @ model ) )
!= ( sk62 @ ( sk65 @ model ) ) ),
inference(simp,[status(thm)],[727]) ).
thf(743,plain,
! [A: $i] :
( ( sk67 != sk62 )
| ( A != sk65 ) ),
inference(simp,[status(thm)],[728]) ).
thf(750,plain,
sk67 != sk62,
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/sandbox2/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(61,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( B @ sk9 ) @ model ) )
| ~ ( wca @ ( B @ ( A @ status ) ) ) ),
inference(cnfConj,[status(thm)],[58]) ).
thf(64,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( B @ sk9 ) @ model ) )
| ~ ( wca @ ( B @ ( A @ status ) ) ) ),
inference(simp,[status(thm)],[61]) ).
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(59,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( wca @ ( B @ ( A @ status ) ) )
| ( B @ ( D @ model ) )
| ~ ( B @ ( C @ model ) )
| ( A @ ( A @ ( B @ sk8 ) @ model ) ) ),
inference(cnfConj,[status(thm)],[58]) ).
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/sandbox2/benchmark/theBenchmark.p',isa) ).
thf(281,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(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(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(1836,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk37 @ ( sk38 @ model ) )
!= ( A @ ( C @ model ) ) )
| ~ $true
| ~ ( wca @ ( B @ ( A @ status ) ) ) ),
inference(paramod_ordered,[status(thm)],[173,63]) ).
thf(1837,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk37 @ ( sk38 @ model ) )
!= ( A @ ( C @ model ) ) )
| ~ ( wca @ ( B @ ( A @ status ) ) ) ),
inference(simp,[status(thm)],[1836]) ).
thf(1838,plain,
! [A: $i] :
~ ( wca @ ( A @ ( sk37 @ status ) ) ),
inference(pattern_uni,[status(thm)],[1837:[bind(A,$thf( sk37 )),bind(B,$thf( B )),bind(C,$thf( sk38 ))]]) ).
thf(1897,plain,
! [A: $i] :
~ ( wca @ ( A @ ( sk37 @ status ) ) ),
inference(simp,[status(thm)],[1838]) ).
thf(1240,plain,
( ( ( sk37 @ ( sk40 @ model ) )
!= ( sk1 @ ( sk2 @ model ) ) )
| ( sk67 != sk36 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[39,1144]) ).
thf(1241,plain,
( ( ( sk37 @ ( sk40 @ model ) )
!= ( sk1 @ ( sk2 @ model ) ) )
| ( sk67 != sk36 ) ),
inference(simp,[status(thm)],[1240]) ).
thf(1258,plain,
( ( sk37 != sk1 )
| ( sk40 != sk2 )
| ( sk67 != sk36 ) ),
inference(simp,[status(thm)],[1241]) ).
thf(20,axiom,
! [A: $i,B: $i] :
( ! [C: $i,D: $i] :
( ( A @ ( D @ ( C @ status ) ) )
=> ~ ( B @ ( D @ ( C @ status ) ) ) )
<=> ( B @ ( A @ nevera ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nevera) ).
thf(187,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)],[20]) ).
thf(1172,plain,
! [A: $i] :
( ( ( sk67 @ ( A @ model ) )
!= ( sk36 @ ( sk39 @ model ) ) )
| ( sk67 != sk37 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[280,1142]) ).
thf(1173,plain,
! [A: $i] :
( ( ( sk67 @ ( A @ model ) )
!= ( sk36 @ ( sk39 @ model ) ) )
| ( sk67 != sk37 ) ),
inference(simp,[status(thm)],[1172]) ).
thf(1201,plain,
! [A: $i] :
( ( sk67 != sk36 )
| ( A != sk39 )
| ( sk67 != sk37 ) ),
inference(simp,[status(thm)],[1173]) ).
thf(1209,plain,
( ( sk67 != sk36 )
| ( sk67 != sk37 ) ),
inference(simp,[status(thm)],[1201]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( ! [C: $i] : ( B @ ( C @ model ) )
& ? [C: $i] : ( A @ ( C @ model ) ) )
<=> ( tac @ ( B @ ( A @ status ) ) ) ),
file('/export/starexec/sandbox2/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(1473,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( sk31 @ ( sk30 @ model ) )
!= ( B @ ( C @ model ) ) )
| ( wca @ ( B @ ( A @ status ) ) )
| ( B @ ( D @ model ) )
| ~ $true
| ( A @ ( A @ ( B @ sk8 ) @ model ) ) ),
inference(paramod_ordered,[status(thm)],[158,59]) ).
thf(1474,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( sk31 @ ( sk30 @ model ) )
!= ( B @ ( C @ model ) ) )
| ( wca @ ( B @ ( A @ status ) ) )
| ( B @ ( D @ model ) )
| ( A @ ( A @ ( B @ sk8 ) @ model ) ) ),
inference(simp,[status(thm)],[1473]) ).
thf(1475,plain,
! [B: $i,A: $i] :
( ( wca @ ( sk31 @ ( A @ status ) ) )
| ( sk31 @ ( B @ model ) )
| ( A @ ( A @ ( sk31 @ sk8 ) @ model ) ) ),
inference(pattern_uni,[status(thm)],[1474:[bind(A,$thf( A )),bind(B,$thf( sk31 )),bind(C,$thf( sk30 ))]]) ).
thf(1491,plain,
! [B: $i,A: $i] :
( ( wca @ ( sk31 @ ( A @ status ) ) )
| ( sk31 @ ( B @ model ) )
| ( A @ ( A @ ( sk31 @ sk8 ) @ model ) ) ),
inference(simp,[status(thm)],[1475]) ).
thf(1925,plain,
! [C: $i,B: $i,A: $i] :
( ( ( wca @ ( sk31 @ ( A @ status ) ) )
!= ( wca @ ( C @ ( sk32 @ status ) ) ) )
| ~ $true
| ( sk31 @ ( B @ model ) )
| ( A @ ( A @ ( sk31 @ sk8 ) @ model ) ) ),
inference(paramod_ordered,[status(thm)],[1491,1893]) ).
thf(1926,plain,
! [C: $i,B: $i,A: $i] :
( ( ( wca @ ( sk31 @ ( A @ status ) ) )
!= ( wca @ ( C @ ( sk32 @ status ) ) ) )
| ( sk31 @ ( B @ model ) )
| ( A @ ( A @ ( sk31 @ sk8 ) @ model ) ) ),
inference(simp,[status(thm)],[1925]) ).
thf(1927,plain,
! [A: $i] :
( ( sk31 @ ( A @ model ) )
| ( sk32 @ ( sk32 @ ( sk31 @ sk8 ) @ model ) ) ),
inference(pattern_uni,[status(thm)],[1926:[bind(A,$thf( sk32 )),bind(B,$thf( B )),bind(C,$thf( sk31 ))]]) ).
thf(1933,plain,
! [A: $i] :
( ( sk31 @ ( A @ model ) )
| ( sk32 @ ( sk32 @ ( sk31 @ sk8 ) @ model ) ) ),
inference(simp,[status(thm)],[1927]) ).
thf(431,plain,
( ( ( sk36 @ ( sk38 @ model ) )
!= ( sk1 @ ( sk3 @ model ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[172,40]) ).
thf(432,plain,
( ( sk36 @ ( sk38 @ model ) )
!= ( sk1 @ ( sk3 @ model ) ) ),
inference(simp,[status(thm)],[431]) ).
thf(434,plain,
( ( sk36 != sk1 )
| ( sk38 != sk3 ) ),
inference(simp,[status(thm)],[432]) ).
thf(461,plain,
( ( ( sk64 @ ( sk65 @ model ) )
!= ( sk32 @ ( sk30 @ model ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[275,159]) ).
thf(462,plain,
( ( sk64 @ ( sk65 @ model ) )
!= ( sk32 @ ( sk30 @ model ) ) ),
inference(simp,[status(thm)],[461]) ).
thf(477,plain,
( ( sk64 != sk32 )
| ( sk65 != sk30 ) ),
inference(simp,[status(thm)],[462]) ).
thf(1762,plain,
! [B: $i,A: $i] :
( ~ $true
| ( ( sk31 @ ( B @ model ) )
!= ( A @ ( A @ ( sk31 @ sk8 ) @ model ) ) )
| ( wca @ ( sk31 @ ( A @ status ) ) )
| ( A @ ( A @ ( sk31 @ sk8 ) @ model ) ) ),
inference(eqfactor_ordered,[status(thm)],[1491]) ).
thf(1770,plain,
( ( wca @ ( sk31 @ ( sk31 @ status ) ) )
| ( sk31 @ ( sk31 @ ( sk31 @ sk8 ) @ model ) ) ),
inference(pattern_uni,[status(thm)],[1762:[bind(A,$thf( sk31 )),bind(B,$thf( sk31 @ ( sk31 @ sk8 ) ))]]) ).
thf(2024,plain,
( $false
| ( sk31 @ ( sk31 @ ( sk31 @ sk8 ) @ model ) ) ),
inference(rewrite,[status(thm)],[1770,1899]) ).
thf(2025,plain,
sk31 @ ( sk31 @ ( sk31 @ sk8 ) @ model ),
inference(simp,[status(thm)],[2024]) ).
thf(319,plain,
( ( ( sk31 @ ( sk30 @ model ) )
!= ( sk1 @ ( sk3 @ model ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[158,40]) ).
thf(320,plain,
( ( sk31 @ ( sk30 @ model ) )
!= ( sk1 @ ( sk3 @ model ) ) ),
inference(simp,[status(thm)],[319]) ).
thf(323,plain,
( ( sk31 != sk1 )
| ( sk30 != sk3 ) ),
inference(simp,[status(thm)],[320]) ).
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/sandbox2/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(21,axiom,
! [A: $i,B: $i] :
( ( ~ ? [C: $i] : ( A @ ( C @ model ) )
=> ~ ? [C: $i] : ( B @ ( C @ model ) ) )
<=> ( unp @ ( B @ ( A @ status ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unp) ).
thf(194,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)],[21]) ).
thf(195,plain,
( ! [A: $i,B: $i] :
( ( unp @ ( 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 ) ) )
=> ( unp @ ( B @ ( A @ status ) ) ) ) ),
inference(miniscope,[status(thm)],[194]) ).
thf(196,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ~ ( E @ ( F @ model ) )
| ( D @ ( D @ ( E @ sk46 ) @ model ) )
| ~ ( unp @ ( E @ ( D @ status ) ) ) )
& ( ( unp @ ( B @ ( A @ status ) ) )
| ( B @ ( A @ ( B @ sk45 ) @ model ) ) )
& ( ( unp @ ( B @ ( A @ status ) ) )
| ~ ( A @ ( C @ model ) ) ) ),
inference(cnf,[status(esa)],[195]) ).
thf(198,plain,
! [B: $i,A: $i] :
( ( unp @ ( B @ ( A @ status ) ) )
| ( B @ ( A @ ( B @ sk45 ) @ model ) ) ),
inference(cnfConj,[status(thm)],[196]) ).
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] :
( ( ( sk67 @ ( A @ model ) )
!= ( B @ ( B @ ( C @ sk6 ) @ model ) ) )
| ~ $true
| ~ ( wth @ ( C @ ( B @ status ) ) ) ),
inference(paramod_ordered,[status(thm)],[280,51]) ).
thf(756,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk67 @ ( A @ model ) )
!= ( B @ ( B @ ( C @ sk6 ) @ model ) ) )
| ~ ( wth @ ( C @ ( B @ status ) ) ) ),
inference(simp,[status(thm)],[755]) ).
thf(757,plain,
! [A: $i] :
~ ( wth @ ( A @ ( sk67 @ status ) ) ),
inference(pattern_uni,[status(thm)],[756:[bind(A,$thf( sk67 @ ( D @ sk6 ) )),bind(B,$thf( sk67 )),bind(C,$thf( D ))]]) ).
thf(799,plain,
! [A: $i] :
~ ( wth @ ( A @ ( sk67 @ status ) ) ),
inference(simp,[status(thm)],[757]) ).
thf(1820,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( sk67 @ ( A @ model ) )
!= ( B @ ( D @ model ) ) )
| ~ $true
| ~ ( wca @ ( C @ ( B @ status ) ) ) ),
inference(paramod_ordered,[status(thm)],[280,63]) ).
thf(1821,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( sk67 @ ( A @ model ) )
!= ( B @ ( D @ model ) ) )
| ~ ( wca @ ( C @ ( B @ status ) ) ) ),
inference(simp,[status(thm)],[1820]) ).
thf(1822,plain,
! [A: $i] :
~ ( wca @ ( A @ ( sk67 @ status ) ) ),
inference(pattern_uni,[status(thm)],[1821:[bind(A,$thf( A )),bind(B,$thf( sk67 )),bind(C,$thf( C )),bind(D,$thf( A ))]]) ).
thf(1909,plain,
! [A: $i] :
~ ( wca @ ( A @ ( sk67 @ status ) ) ),
inference(simp,[status(thm)],[1822]) ).
thf(450,plain,
( ( ( sk62 @ ( sk65 @ model ) )
!= ( sk37 @ ( sk38 @ model ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[173,274]) ).
thf(451,plain,
( ( sk62 @ ( sk65 @ model ) )
!= ( sk37 @ ( sk38 @ model ) ) ),
inference(simp,[status(thm)],[450]) ).
thf(455,plain,
( ( sk62 != sk37 )
| ( sk65 != sk38 ) ),
inference(simp,[status(thm)],[451]) ).
thf(491,plain,
( ( ( sk64 @ ( sk66 @ model ) )
!= ( sk64 @ ( sk65 @ model ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[275,276]) ).
thf(492,plain,
( ( sk64 @ ( sk66 @ model ) )
!= ( sk64 @ ( sk65 @ model ) ) ),
inference(simp,[status(thm)],[491]) ).
thf(499,plain,
( ( sk64 != sk64 )
| ( sk66 != sk65 ) ),
inference(simp,[status(thm)],[492]) ).
thf(505,plain,
sk66 != sk65,
inference(simp,[status(thm)],[499]) ).
thf(1,conjecture,
thm @ ( wtc @ isa ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',isa_wtc_thm) ).
thf(2,negated_conjecture,
~ ( thm @ ( wtc @ isa ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(35,plain,
~ ( thm @ ( wtc @ isa ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(1198,plain,
( ( ( sk62 @ ( sk63 @ model ) )
!= ( sk36 @ ( sk39 @ model ) ) )
| ( sk67 != sk37 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[277,1142]) ).
thf(1199,plain,
( ( ( sk62 @ ( sk63 @ model ) )
!= ( sk36 @ ( sk39 @ model ) ) )
| ( sk67 != sk37 ) ),
inference(simp,[status(thm)],[1198]) ).
thf(1203,plain,
( ( sk62 != sk36 )
| ( sk63 != sk39 )
| ( sk67 != sk37 ) ),
inference(simp,[status(thm)],[1199]) ).
thf(1881,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk62 @ ( sk63 @ model ) )
!= ( A @ ( C @ model ) ) )
| ~ $true
| ~ ( wca @ ( B @ ( A @ status ) ) ) ),
inference(paramod_ordered,[status(thm)],[277,63]) ).
thf(1882,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk62 @ ( sk63 @ model ) )
!= ( A @ ( C @ model ) ) )
| ~ ( wca @ ( B @ ( A @ status ) ) ) ),
inference(simp,[status(thm)],[1881]) ).
thf(1883,plain,
! [A: $i] :
~ ( wca @ ( A @ ( sk62 @ status ) ) ),
inference(pattern_uni,[status(thm)],[1882:[bind(A,$thf( sk62 )),bind(B,$thf( B )),bind(C,$thf( sk63 ))]]) ).
thf(1905,plain,
! [A: $i] :
~ ( wca @ ( A @ ( sk62 @ status ) ) ),
inference(simp,[status(thm)],[1883]) ).
thf(28,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( B @ ( C @ model ) )
& ( A @ ( C @ model ) ) )
<=> ( tau @ ( B @ ( A @ status ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tau) ).
thf(255,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)],[28]) ).
thf(715,plain,
! [A: $i] :
( ( ( sk67 @ ( A @ model ) )
!= ( sk32 @ ( sk30 @ model ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[280,159]) ).
thf(716,plain,
! [A: $i] :
( ( sk67 @ ( A @ model ) )
!= ( sk32 @ ( sk30 @ model ) ) ),
inference(simp,[status(thm)],[715]) ).
thf(742,plain,
! [A: $i] :
( ( sk67 != sk32 )
| ( A != sk30 ) ),
inference(simp,[status(thm)],[716]) ).
thf(749,plain,
sk67 != sk32,
inference(simp,[status(thm)],[742]) ).
thf(689,plain,
! [A: $i] :
( ( ( sk64 @ ( sk65 @ model ) )
!= ( sk18 @ ( A @ model ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[275,99]) ).
thf(690,plain,
! [A: $i] :
( ( sk64 @ ( sk65 @ model ) )
!= ( sk18 @ ( A @ model ) ) ),
inference(simp,[status(thm)],[689]) ).
thf(701,plain,
! [A: $i] :
( ( sk64 != sk18 )
| ( sk65 != A ) ),
inference(simp,[status(thm)],[690]) ).
thf(712,plain,
sk64 != sk18,
inference(simp,[status(thm)],[701]) ).
thf(34,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/sandbox2/benchmark/theBenchmark.p',wtc) ).
thf(295,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)],[34]) ).
thf(691,plain,
! [A: $i] :
( ( ( sk36 @ ( sk38 @ model ) )
!= ( sk18 @ ( A @ model ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[172,99]) ).
thf(692,plain,
! [A: $i] :
( ( sk36 @ ( sk38 @ model ) )
!= ( sk18 @ ( A @ model ) ) ),
inference(simp,[status(thm)],[691]) ).
thf(697,plain,
! [A: $i] :
( ( sk36 != sk18 )
| ( sk38 != A ) ),
inference(simp,[status(thm)],[692]) ).
thf(707,plain,
sk36 != sk18,
inference(simp,[status(thm)],[697]) ).
thf(29,axiom,
! [A: $i,B: $i] :
( ? [C: $i,D: $i] :
( ( B @ ( D @ ( C @ status ) ) )
& ( A @ ( D @ ( C @ status ) ) ) )
<=> ( B @ ( A @ mighta ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mighta) ).
thf(263,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)],[29]) ).
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(520,plain,
( ( ( sk62 @ ( sk63 @ model ) )
!= ( sk1 @ ( sk3 @ model ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[277,40]) ).
thf(521,plain,
( ( sk62 @ ( sk63 @ model ) )
!= ( sk1 @ ( sk3 @ model ) ) ),
inference(simp,[status(thm)],[520]) ).
thf(525,plain,
( ( sk62 != sk1 )
| ( sk63 != sk3 ) ),
inference(simp,[status(thm)],[521]) ).
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(493,plain,
( ( ( sk64 @ ( sk66 @ model ) )
!= ( sk36 @ ( sk38 @ model ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[172,276]) ).
thf(494,plain,
( ( sk64 @ ( sk66 @ model ) )
!= ( sk36 @ ( sk38 @ model ) ) ),
inference(simp,[status(thm)],[493]) ).
thf(502,plain,
( ( sk64 != sk36 )
| ( sk66 != sk38 ) ),
inference(simp,[status(thm)],[494]) ).
thf(1230,plain,
( ( ( sk37 @ ( sk40 @ model ) )
!= ( sk32 @ ( sk33 @ model ) ) )
| ( sk67 != sk36 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[160,1144]) ).
thf(1231,plain,
( ( ( sk37 @ ( sk40 @ model ) )
!= ( sk32 @ ( sk33 @ model ) ) )
| ( sk67 != sk36 ) ),
inference(simp,[status(thm)],[1230]) ).
thf(1257,plain,
( ( sk37 != sk32 )
| ( sk40 != sk33 )
| ( sk67 != sk36 ) ),
inference(simp,[status(thm)],[1231]) ).
thf(19,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/sandbox2/benchmark/theBenchmark.p',noc) ).
thf(175,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)],[19]) ).
thf(312,plain,
( ( ( sk62 @ ( sk65 @ model ) )
!= ( sk1 @ ( sk2 @ model ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[39,274]) ).
thf(313,plain,
( ( sk62 @ ( sk65 @ model ) )
!= ( sk1 @ ( sk2 @ model ) ) ),
inference(simp,[status(thm)],[312]) ).
thf(314,plain,
( ( sk62 != sk1 )
| ( sk65 != sk2 ) ),
inference(simp,[status(thm)],[313]) ).
thf(738,plain,
! [A: $i] :
( ( ( sk67 @ ( A @ model ) )
!= ( sk1 @ ( sk3 @ model ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[280,40]) ).
thf(739,plain,
! [A: $i] :
( ( sk67 @ ( A @ model ) )
!= ( sk1 @ ( sk3 @ model ) ) ),
inference(simp,[status(thm)],[738]) ).
thf(741,plain,
! [A: $i] :
( ( sk67 != sk1 )
| ( A != sk3 ) ),
inference(simp,[status(thm)],[739]) ).
thf(748,plain,
sk67 != sk1,
inference(simp,[status(thm)],[741]) ).
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(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/sandbox2/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(26,axiom,
! [A: $i,B: $i] :
( ( ? [C: $i] : ( A @ ( C @ model ) )
<=> ? [C: $i] : ( B @ ( C @ model ) ) )
<=> ( esa @ ( B @ ( A @ status ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',esa) ).
thf(235,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)],[26]) ).
thf(419,plain,
( ( ( sk36 @ ( sk38 @ model ) )
!= ( sk32 @ ( sk30 @ model ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[172,159]) ).
thf(420,plain,
( ( sk36 @ ( sk38 @ model ) )
!= ( sk32 @ ( sk30 @ model ) ) ),
inference(simp,[status(thm)],[419]) ).
thf(433,plain,
( ( sk36 != sk32 )
| ( sk38 != sk30 ) ),
inference(simp,[status(thm)],[420]) ).
thf(473,plain,
( ( ( sk64 @ ( sk65 @ model ) )
!= ( sk1 @ ( sk3 @ model ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[275,40]) ).
thf(474,plain,
( ( sk64 @ ( sk65 @ model ) )
!= ( sk1 @ ( sk3 @ model ) ) ),
inference(simp,[status(thm)],[473]) ).
thf(478,plain,
( ( sk64 != sk1 )
| ( sk65 != sk3 ) ),
inference(simp,[status(thm)],[474]) ).
thf(327,plain,
( ( ( sk62 @ ( sk65 @ model ) )
!= ( sk32 @ ( sk33 @ model ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[160,274]) ).
thf(328,plain,
( ( sk62 @ ( sk65 @ model ) )
!= ( sk32 @ ( sk33 @ model ) ) ),
inference(simp,[status(thm)],[327]) ).
thf(332,plain,
( ( sk62 != sk32 )
| ( sk65 != sk33 ) ),
inference(simp,[status(thm)],[328]) ).
thf(497,plain,
( ( ( sk64 @ ( sk66 @ model ) )
!= ( sk31 @ ( sk30 @ model ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[158,276]) ).
thf(498,plain,
( ( sk64 @ ( sk66 @ model ) )
!= ( sk31 @ ( sk30 @ model ) ) ),
inference(simp,[status(thm)],[497]) ).
thf(501,plain,
( ( sk64 != sk31 )
| ( sk66 != sk30 ) ),
inference(simp,[status(thm)],[498]) ).
thf(317,plain,
( ( ( sk62 @ ( sk65 @ model ) )
!= ( sk31 @ ( sk30 @ model ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[158,274]) ).
thf(318,plain,
( ( sk62 @ ( sk65 @ model ) )
!= ( sk31 @ ( sk30 @ model ) ) ),
inference(simp,[status(thm)],[317]) ).
thf(322,plain,
( ( sk62 != sk31 )
| ( sk65 != sk30 ) ),
inference(simp,[status(thm)],[318]) ).
thf(24,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ model ) )
<~> ( B @ not @ ( A @ model ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',completeness) ).
thf(215,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)],[24]) ).
thf(1176,plain,
( ( ( sk36 @ ( sk39 @ model ) )
!= ( sk32 @ ( sk33 @ model ) ) )
| ( sk67 != sk37 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[160,1142]) ).
thf(1177,plain,
( ( ( sk36 @ ( sk39 @ model ) )
!= ( sk32 @ ( sk33 @ model ) ) )
| ( sk67 != sk37 ) ),
inference(simp,[status(thm)],[1176]) ).
thf(1204,plain,
( ( sk36 != sk32 )
| ( sk39 != sk33 )
| ( sk67 != sk37 ) ),
inference(simp,[status(thm)],[1177]) ).
thf(25,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/sandbox2/benchmark/theBenchmark.p',eqv) ).
thf(222,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)],[25]) ).
thf(452,plain,
( ( ( sk37 @ ( sk38 @ model ) )
!= ( sk1 @ ( sk3 @ model ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[173,40]) ).
thf(453,plain,
( ( sk37 @ ( sk38 @ model ) )
!= ( sk1 @ ( sk3 @ model ) ) ),
inference(simp,[status(thm)],[452]) ).
thf(454,plain,
( ( sk37 != sk1 )
| ( sk38 != sk3 ) ),
inference(simp,[status(thm)],[453]) ).
thf(685,plain,
! [A: $i] :
( ( ( sk62 @ ( sk63 @ model ) )
!= ( sk18 @ ( A @ model ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[277,99]) ).
thf(686,plain,
! [A: $i] :
( ( sk62 @ ( sk63 @ model ) )
!= ( sk18 @ ( A @ model ) ) ),
inference(simp,[status(thm)],[685]) ).
thf(698,plain,
! [A: $i] :
( ( sk62 != sk18 )
| ( sk63 != A ) ),
inference(simp,[status(thm)],[686]) ).
thf(708,plain,
sk62 != sk18,
inference(simp,[status(thm)],[698]) ).
thf(128813,plain,
$false,
inference(e,[status(thm)],[1147,99,69,333,1899,481,1200,1211,276,308,247,1142,1305,56,500,747,913,174,709,288,436,1904,1265,52,2328,504,1907,751,2616,1136,106,280,132,89,1206,529,201,714,334,1255,160,275,1938,65,97,1624,522,456,324,1259,53,169,1207,212,173,41,503,1627,73,105,311,1895,750,161,279,64,711,59,281,54,713,1897,1258,159,187,1209,172,274,81,1933,1144,271,39,434,477,2025,323,140,66,155,198,799,1909,455,505,35,1203,1905,255,209,749,1145,194,712,63,295,707,263,48,525,50,502,1257,175,314,748,40,158,55,1491,119,235,433,478,1893,36,51,332,277,501,322,215,1204,222,454,708,100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KRS191+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.17/0.41 % Computer : n008.cluster.edu
% 0.17/0.41 % Model : x86_64 x86_64
% 0.17/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.41 % Memory : 8046.5625MB
% 0.17/0.41 % OS : Linux 6.8.0-71-generic
% 0.17/0.41 % CPULimit : 300
% 0.17/0.41 % WCLimit : 300
% 0.17/0.41 % DateTime : Fri Sep 25 19:44:39 UTC 2026
% 0.17/0.42 % CPUTime :
% 0.17/0.42 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.69/0.72 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.90/0.86 % [INFO] Parsing done (138ms).
% 0.90/0.87 % [INFO] Running in sequential loop mode.
% 1.50/1.09 % [INFO] eprover registered as external prover.
% 1.50/1.09 % [INFO] Scanning for conjecture ...
% 1.77/1.14 % [INFO] Found a conjecture (or negated_conjecture) and 32 axioms. Running axiom selection ...
% 1.77/1.18 % [INFO] Axiom selection finished. Selected 32 axioms (removed 0 axioms).
% 1.97/1.23 % [INFO] Problem is first-order (TPTP FOF).
% 1.97/1.24 % [INFO] Type checking passed.
% 1.97/1.24 % [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 ...
% 166.41/43.18 % External prover 'e' found a proof!
% 166.41/43.18 % [INFO] Killing All external provers ...
% 166.41/43.18 % Time passed: 42682ms (effective reasoning time: 42308ms)
% 166.41/43.18 % 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)>
% 166.41/43.19 % 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
% 166.41/43.19 % No. of inferences in proof: 395
% 166.41/43.19 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 42682 ms resp. 42308 ms w/o parsing
% 156.67/43.33 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 156.67/43.34 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------