%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : KRS195+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 : n017.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 171.89s 46.94s
% Output : Refutation 173.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 64
% Syntax : Number of formulae : 426 ( 133 unt; 0 typ; 31 def)
% Number of atoms : 1447 ( 387 equ; 0 cnn)
% Maximal formula atoms : 23 ( 3 avg)
% Number of connectives : 3647 ( 676 ~; 334 |; 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 : 729 ( 23 ^; 493 !; 182 ?; 729 :)
% ( 0 !>; 0 ?*; 0 @-; 31 @+)
% Comments :
%------------------------------------------------------------------------------
thf(isa_decl,type,
isa: $i > $i > $o ).
thf(tca_decl,type,
tca: $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(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(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(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(sk50_decl,type,
sk50: $i > $i > $i ).
thf(sk51_decl,type,
sk51: $i > $i > $i ).
thf(sk52_decl,type,
sk52: $i > $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(sk68_decl,type,
sk68: $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(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(sk50_def,definition,
( sk50
= ( ^ [A: $i,B: $i] :
@+[C: $i] : ( A @ ( C @ model ) ) ) ) ).
thf(sk51_def,definition,
( sk51
= ( ^ [A: $i,B: $i] :
@+[C: $i] : ( B @ ( C @ model ) ) ) ) ).
thf(sk52_def,definition,
( sk52
= ( ^ [A: $i] :
@+[B: $i] : ( A @ ( B @ model ) ) ) ) ).
thf(sk63_def,definition,
( sk63
= ( @+[A: $i] :
( ? [B: $i] :
( ~ ! [C: $i] : ( B @ ( C @ model ) )
& ? [C: $i] :
( ( B @ ( C @ model ) )
& ~ ( A @ ( C @ model ) ) )
& ! [C: $i] :
( ( A @ ( C @ model ) )
=> ( B @ ( C @ model ) ) ) )
& ? [B: $i] : ( A @ ( B @ model ) ) ) ) ) ).
thf(sk64_def,definition,
( sk64
= ( @+[A: $i] : ( sk63 @ ( A @ model ) ) ) ) ).
thf(sk65_def,definition,
( sk65
= ( @+[A: $i] :
( ~ ! [B: $i] : ( A @ ( B @ model ) )
& ? [B: $i] :
( ( A @ ( B @ model ) )
& ~ ( sk63 @ ( B @ model ) ) )
& ! [B: $i] :
( ( sk63 @ ( B @ model ) )
=> ( A @ ( B @ model ) ) ) ) ) ) ).
thf(sk66_def,definition,
( sk66
= ( @+[A: $i] :
( ( sk65 @ ( A @ model ) )
& ~ ( sk63 @ ( A @ model ) ) ) ) ) ).
thf(sk67_def,definition,
( sk67
= ( @+[A: $i] :
~ ( sk65 @ ( A @ model ) ) ) ) ).
thf(sk68_def,definition,
( sk68
= ( @+[A: $i] :
! [B: $i] : ( A @ ( B @ model ) ) ) ) ).
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(18,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(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(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(273,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(274,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)],[273]) ).
thf(275,plain,
! [A: $i] :
( ~ ( sk65 @ ( sk67 @ model ) )
& ( sk65 @ ( sk66 @ model ) )
& ~ ( sk63 @ ( sk66 @ model ) )
& ( ( sk65 @ ( A @ model ) )
| ~ ( sk63 @ ( A @ model ) ) )
& ( sk63 @ ( sk64 @ model ) ) ),
inference(cnf,[status(esa)],[274]) ).
thf(276,plain,
~ ( sk63 @ ( sk66 @ model ) ),
inference(cnfConj,[status(thm)],[275]) ).
thf(329,plain,
( ( ( sk63 @ ( sk66 @ model ) )
!= ( sk37 @ ( sk38 @ model ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[178,276]) ).
thf(330,plain,
( ( sk63 @ ( sk66 @ model ) )
!= ( sk37 @ ( sk38 @ model ) ) ),
inference(simp,[status(thm)],[329]) ).
thf(333,plain,
( ( sk63 != sk37 )
| ( sk66 != sk38 ) ),
inference(simp,[status(thm)],[330]) ).
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(1870,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk37 @ ( sk38 @ model ) )
!= ( A @ ( C @ model ) ) )
| ~ $true
| ~ ( wca @ ( B @ ( A @ status ) ) ) ),
inference(paramod_ordered,[status(thm)],[178,63]) ).
thf(1871,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk37 @ ( sk38 @ model ) )
!= ( A @ ( C @ model ) ) )
| ~ ( wca @ ( B @ ( A @ status ) ) ) ),
inference(simp,[status(thm)],[1870]) ).
thf(1872,plain,
! [A: $i] :
~ ( wca @ ( A @ ( sk37 @ status ) ) ),
inference(pattern_uni,[status(thm)],[1871:[bind(A,$thf( sk37 )),bind(B,$thf( B )),bind(C,$thf( sk38 ))]]) ).
thf(1899,plain,
! [A: $i] :
~ ( wca @ ( A @ ( sk37 @ status ) ) ),
inference(simp,[status(thm)],[1872]) ).
thf(277,plain,
sk63 @ ( sk64 @ model ),
inference(cnfConj,[status(thm)],[275]) ).
thf(473,plain,
( ( ( sk63 @ ( sk66 @ model ) )
!= ( sk63 @ ( sk64 @ model ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[277,276]) ).
thf(474,plain,
( ( sk63 @ ( sk66 @ model ) )
!= ( sk63 @ ( sk64 @ model ) ) ),
inference(simp,[status(thm)],[473]) ).
thf(477,plain,
( ( sk63 != sk63 )
| ( sk66 != sk64 ) ),
inference(simp,[status(thm)],[474]) ).
thf(481,plain,
sk66 != sk64,
inference(simp,[status(thm)],[477]) ).
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(39,plain,
sk1 @ ( sk2 @ model ),
inference(cnfConj,[status(thm)],[38]) ).
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/sandbox2/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(1109,plain,
( ( ( sk41 @ ( sk44 @ model ) )
!= ( sk41 @ ( sk43 @ model ) ) )
| ~ ( sk42 @ ( sk45 @ model ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[190,192]) ).
thf(1110,plain,
( ( ( sk41 @ ( sk44 @ model ) )
!= ( sk41 @ ( sk43 @ model ) ) )
| ~ ( sk42 @ ( sk45 @ model ) ) ),
inference(simp,[status(thm)],[1109]) ).
thf(1122,plain,
( ( sk41 != sk41 )
| ( sk44 != sk43 )
| ~ ( sk42 @ ( sk45 @ model ) ) ),
inference(simp,[status(thm)],[1110]) ).
thf(1142,plain,
( ( sk44 != sk43 )
| ~ ( sk42 @ ( sk45 @ model ) ) ),
inference(simp,[status(thm)],[1122]) ).
thf(1178,plain,
( ( ( sk42 @ ( sk45 @ model ) )
!= ( sk1 @ ( sk2 @ model ) ) )
| ( sk44 != sk43 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[39,1142]) ).
thf(1179,plain,
( ( ( sk42 @ ( sk45 @ model ) )
!= ( sk1 @ ( sk2 @ model ) ) )
| ( sk44 != sk43 ) ),
inference(simp,[status(thm)],[1178]) ).
thf(1200,plain,
( ( sk42 != sk1 )
| ( sk45 != sk2 )
| ( sk44 != sk43 ) ),
inference(simp,[status(thm)],[1179]) ).
thf(31,axiom,
? [A: $i] :
! [B: $i] : ( A @ ( B @ model ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tautology) ).
thf(281,plain,
? [A: $i] :
! [B: $i] : ( A @ ( B @ model ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(282,plain,
! [A: $i] : ( sk68 @ ( A @ model ) ),
inference(cnf,[status(esa)],[281]) ).
thf(1188,plain,
! [A: $i] :
( ( ( sk68 @ ( A @ model ) )
!= ( sk42 @ ( sk45 @ model ) ) )
| ( sk44 != sk43 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[282,1142]) ).
thf(1189,plain,
! [A: $i] :
( ( ( sk68 @ ( A @ model ) )
!= ( sk42 @ ( sk45 @ model ) ) )
| ( sk44 != sk43 ) ),
inference(simp,[status(thm)],[1188]) ).
thf(1207,plain,
! [A: $i] :
( ( sk68 != sk42 )
| ( A != sk45 )
| ( sk44 != sk43 ) ),
inference(simp,[status(thm)],[1189]) ).
thf(1211,plain,
( ( sk68 != sk42 )
| ( sk44 != sk43 ) ),
inference(simp,[status(thm)],[1207]) ).
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(280,plain,
~ ( sk65 @ ( sk67 @ model ) ),
inference(cnfConj,[status(thm)],[275]) ).
thf(483,plain,
( ( ( sk65 @ ( sk67 @ model ) )
!= ( sk1 @ ( sk2 @ model ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[39,280]) ).
thf(484,plain,
( ( sk65 @ ( sk67 @ model ) )
!= ( sk1 @ ( sk2 @ model ) ) ),
inference(simp,[status(thm)],[483]) ).
thf(500,plain,
( ( sk65 != sk1 )
| ( sk67 != sk2 ) ),
inference(simp,[status(thm)],[484]) ).
thf(278,plain,
sk65 @ ( sk66 @ model ),
inference(cnfConj,[status(thm)],[275]) ).
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(685,plain,
! [A: $i] :
( ( ( sk65 @ ( sk66 @ model ) )
!= ( sk18 @ ( A @ model ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[278,99]) ).
thf(686,plain,
! [A: $i] :
( ( sk65 @ ( sk66 @ model ) )
!= ( sk18 @ ( A @ model ) ) ),
inference(simp,[status(thm)],[685]) ).
thf(698,plain,
! [A: $i] :
( ( sk65 != sk18 )
| ( sk66 != A ) ),
inference(simp,[status(thm)],[686]) ).
thf(709,plain,
sk65 != sk18,
inference(simp,[status(thm)],[698]) ).
thf(431,plain,
( ( ( sk63 @ ( sk66 @ model ) )
!= ( sk41 @ ( sk43 @ model ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[190,276]) ).
thf(432,plain,
( ( sk63 @ ( sk66 @ model ) )
!= ( sk41 @ ( sk43 @ model ) ) ),
inference(simp,[status(thm)],[431]) ).
thf(436,plain,
( ( sk63 != sk41 )
| ( sk66 != sk43 ) ),
inference(simp,[status(thm)],[432]) ).
thf(28,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(257,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(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(495,plain,
( ( ( sk65 @ ( sk67 @ model ) )
!= ( sk37 @ ( sk38 @ model ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[178,280]) ).
thf(496,plain,
( ( sk65 @ ( sk67 @ model ) )
!= ( sk37 @ ( sk38 @ model ) ) ),
inference(simp,[status(thm)],[495]) ).
thf(504,plain,
( ( sk65 != sk37 )
| ( sk67 != sk38 ) ),
inference(simp,[status(thm)],[496]) ).
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/sandbox2/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(1099,plain,
! [A: $i] :
( ( ( sk68 @ ( A @ model ) )
!= ( sk42 @ ( sk45 @ model ) ) )
| ~ $true
| ~ ( sk41 @ ( sk44 @ model ) ) ),
inference(paramod_ordered,[status(thm)],[282,192]) ).
thf(1100,plain,
! [A: $i] :
( ( ( sk68 @ ( A @ model ) )
!= ( sk42 @ ( sk45 @ model ) ) )
| ~ ( sk41 @ ( sk44 @ model ) ) ),
inference(simp,[status(thm)],[1099]) ).
thf(1124,plain,
! [A: $i] :
( ( sk68 != sk42 )
| ( A != sk45 )
| ~ ( sk41 @ ( sk44 @ model ) ) ),
inference(simp,[status(thm)],[1100]) ).
thf(1143,plain,
( ( sk68 != sk42 )
| ~ ( sk41 @ ( sk44 @ model ) ) ),
inference(simp,[status(thm)],[1124]) ).
thf(1242,plain,
! [A: $i] :
( ( ( sk68 @ ( A @ model ) )
!= ( sk41 @ ( sk44 @ model ) ) )
| ( sk68 != sk42 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[282,1143]) ).
thf(1243,plain,
! [A: $i] :
( ( ( sk68 @ ( A @ model ) )
!= ( sk41 @ ( sk44 @ model ) ) )
| ( sk68 != sk42 ) ),
inference(simp,[status(thm)],[1242]) ).
thf(1256,plain,
! [A: $i] :
( ( sk68 != sk41 )
| ( A != sk44 )
| ( sk68 != sk42 ) ),
inference(simp,[status(thm)],[1243]) ).
thf(1264,plain,
( ( sk68 != sk41 )
| ( sk68 != sk42 ) ),
inference(simp,[status(thm)],[1256]) ).
thf(176,plain,
sk36 @ ( sk35 @ model ),
inference(cnfConj,[status(thm)],[175]) ).
thf(1827,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk36 @ ( sk35 @ model ) )
!= ( A @ ( C @ model ) ) )
| ~ $true
| ~ ( wca @ ( B @ ( A @ status ) ) ) ),
inference(paramod_ordered,[status(thm)],[176,63]) ).
thf(1828,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk36 @ ( sk35 @ model ) )
!= ( A @ ( C @ model ) ) )
| ~ ( wca @ ( B @ ( A @ status ) ) ) ),
inference(simp,[status(thm)],[1827]) ).
thf(1829,plain,
! [A: $i] :
~ ( wca @ ( A @ ( sk36 @ status ) ) ),
inference(pattern_uni,[status(thm)],[1828:[bind(A,$thf( sk36 )),bind(B,$thf( B )),bind(C,$thf( sk35 ))]]) ).
thf(1892,plain,
! [A: $i] :
~ ( wca @ ( A @ ( sk36 @ status ) ) ),
inference(simp,[status(thm)],[1829]) ).
thf(1097,plain,
! [A: $i] :
( ( ( sk68 @ ( A @ model ) )
!= ( sk41 @ ( sk44 @ model ) ) )
| ~ ( sk42 @ ( sk45 @ model ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[282,192]) ).
thf(1098,plain,
! [A: $i] :
( ( ( sk68 @ ( A @ model ) )
!= ( sk41 @ ( sk44 @ model ) ) )
| ~ ( sk42 @ ( sk45 @ model ) ) ),
inference(simp,[status(thm)],[1097]) ).
thf(1141,plain,
! [A: $i] :
( ( sk68 != sk41 )
| ( A != sk44 )
| ~ ( sk42 @ ( sk45 @ model ) ) ),
inference(simp,[status(thm)],[1098]) ).
thf(1147,plain,
( ( sk68 != sk41 )
| ~ ( sk42 @ ( sk45 @ model ) ) ),
inference(simp,[status(thm)],[1141]) ).
thf(23,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(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(213,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)],[212]) ).
thf(214,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ~ ( E @ ( F @ model ) )
| ( D @ ( D @ ( E @ sk51 ) @ model ) )
| ~ ( unp @ ( E @ ( D @ status ) ) ) )
& ( ( unp @ ( B @ ( A @ status ) ) )
| ( B @ ( A @ ( B @ sk50 ) @ model ) ) )
& ( ( unp @ ( B @ ( A @ status ) ) )
| ~ ( A @ ( C @ model ) ) ) ),
inference(cnf,[status(esa)],[213]) ).
thf(216,plain,
! [B: $i,A: $i] :
( ( unp @ ( B @ ( A @ status ) ) )
| ( B @ ( A @ ( B @ sk50 ) @ model ) ) ),
inference(cnfConj,[status(thm)],[214]) ).
thf(471,plain,
( ( ( sk63 @ ( sk64 @ model ) )
!= ( sk1 @ ( sk3 @ model ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[277,40]) ).
thf(472,plain,
( ( sk63 @ ( sk64 @ model ) )
!= ( sk1 @ ( sk3 @ model ) ) ),
inference(simp,[status(thm)],[471]) ).
thf(475,plain,
( ( sk63 != sk1 )
| ( sk64 != 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/sandbox2/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(1121,plain,
( ~ $true
| ( ( sk42 @ ( sk45 @ model ) )
!= ( sk41 @ ( sk44 @ model ) ) )
| ~ ( sk41 @ ( sk44 @ model ) ) ),
inference(eqfactor_ordered,[status(thm)],[192]) ).
thf(1135,plain,
( ( ( sk42 @ ( sk45 @ model ) )
!= ( sk41 @ ( sk44 @ model ) ) )
| ~ ( sk41 @ ( sk44 @ model ) ) ),
inference(simp,[status(thm)],[1121]) ).
thf(1573,plain,
( ( ( sk41 @ ( sk44 @ model ) )
!= ( sk41 @ ( sk43 @ model ) ) )
| ( ( sk42 @ ( sk45 @ model ) )
!= ( sk41 @ ( sk44 @ model ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[190,1135]) ).
thf(1574,plain,
( ( ( sk41 @ ( sk44 @ model ) )
!= ( sk41 @ ( sk43 @ model ) ) )
| ( ( sk42 @ ( sk45 @ model ) )
!= ( sk41 @ ( sk44 @ model ) ) ) ),
inference(simp,[status(thm)],[1573]) ).
thf(1603,plain,
( ( sk41 != sk41 )
| ( sk44 != sk43 )
| ( ( sk42 @ ( sk45 @ model ) )
!= ( sk41 @ ( sk44 @ model ) ) ) ),
inference(simp,[status(thm)],[1574]) ).
thf(1622,plain,
( ( sk44 != sk43 )
| ( ( sk42 @ ( sk45 @ model ) )
!= ( sk41 @ ( sk44 @ model ) ) ) ),
inference(simp,[status(thm)],[1603]) ).
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(29,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(265,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(1180,plain,
( ( ( sk65 @ ( sk66 @ model ) )
!= ( sk42 @ ( sk45 @ model ) ) )
| ( sk44 != sk43 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[278,1142]) ).
thf(1181,plain,
( ( ( sk65 @ ( sk66 @ model ) )
!= ( sk42 @ ( sk45 @ model ) ) )
| ( sk44 != sk43 ) ),
inference(simp,[status(thm)],[1180]) ).
thf(1206,plain,
( ( sk65 != sk42 )
| ( sk66 != sk45 )
| ( sk44 != sk43 ) ),
inference(simp,[status(thm)],[1181]) ).
thf(679,plain,
! [A: $i] :
( ( ( sk41 @ ( sk43 @ model ) )
!= ( sk18 @ ( A @ model ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[190,99]) ).
thf(680,plain,
! [A: $i] :
( ( sk41 @ ( sk43 @ model ) )
!= ( sk18 @ ( A @ model ) ) ),
inference(simp,[status(thm)],[679]) ).
thf(703,plain,
! [A: $i] :
( ( sk41 != sk18 )
| ( sk43 != A ) ),
inference(simp,[status(thm)],[680]) ).
thf(714,plain,
sk41 != sk18,
inference(simp,[status(thm)],[703]) ).
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(772,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk68 @ ( A @ model ) )
!= ( B @ ( B @ ( C @ sk6 ) @ model ) ) )
| ~ $true
| ~ ( wth @ ( C @ ( B @ status ) ) ) ),
inference(paramod_ordered,[status(thm)],[282,51]) ).
thf(773,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk68 @ ( A @ model ) )
!= ( B @ ( B @ ( C @ sk6 ) @ model ) ) )
| ~ ( wth @ ( C @ ( B @ status ) ) ) ),
inference(simp,[status(thm)],[772]) ).
thf(774,plain,
! [A: $i] :
~ ( wth @ ( A @ ( sk68 @ status ) ) ),
inference(pattern_uni,[status(thm)],[773:[bind(A,$thf( sk68 @ ( D @ sk6 ) )),bind(B,$thf( sk68 )),bind(C,$thf( D ))]]) ).
thf(798,plain,
! [A: $i] :
~ ( wth @ ( A @ ( sk68 @ status ) ) ),
inference(simp,[status(thm)],[774]) ).
thf(177,plain,
~ ( sk37 @ ( sk35 @ model ) ),
inference(cnfConj,[status(thm)],[175]) ).
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(1839,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(1840,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk1 @ ( sk2 @ model ) )
!= ( A @ ( C @ model ) ) )
| ~ ( wca @ ( B @ ( A @ status ) ) ) ),
inference(simp,[status(thm)],[1839]) ).
thf(1841,plain,
! [A: $i] :
~ ( wca @ ( A @ ( sk1 @ status ) ) ),
inference(pattern_uni,[status(thm)],[1840:[bind(A,$thf( sk1 )),bind(B,$thf( B )),bind(C,$thf( sk2 ))]]) ).
thf(1900,plain,
! [A: $i] :
~ ( wca @ ( A @ ( sk1 @ status ) ) ),
inference(simp,[status(thm)],[1841]) ).
thf(717,plain,
! [B: $i,A: $i] :
( ( ( sk68 @ ( A @ model ) )
!= ( sk18 @ ( B @ model ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[282,99]) ).
thf(718,plain,
! [B: $i,A: $i] :
( ( sk68 @ ( A @ model ) )
!= ( sk18 @ ( B @ model ) ) ),
inference(simp,[status(thm)],[717]) ).
thf(740,plain,
! [B: $i,A: $i] :
( ( sk68 != sk18 )
| ( A != B ) ),
inference(simp,[status(thm)],[718]) ).
thf(746,plain,
sk68 != sk18,
inference(simp,[status(thm)],[740]) ).
thf(1232,plain,
( ( ( sk41 @ ( sk44 @ model ) )
!= ( sk1 @ ( sk2 @ model ) ) )
| ( sk68 != sk42 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[39,1143]) ).
thf(1233,plain,
( ( ( sk41 @ ( sk44 @ model ) )
!= ( sk1 @ ( sk2 @ model ) ) )
| ( sk68 != sk42 ) ),
inference(simp,[status(thm)],[1232]) ).
thf(1255,plain,
( ( sk41 != sk1 )
| ( sk44 != sk2 )
| ( sk68 != sk42 ) ),
inference(simp,[status(thm)],[1233]) ).
thf(34,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(297,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)],[34]) ).
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/sandbox2/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(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(2372,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk68 @ ( A @ model ) )
!= ( C @ ( B @ ( C @ sk10 ) @ model ) ) )
| ~ $true
| ~ ( wca @ ( C @ ( B @ status ) ) ) ),
inference(paramod_ordered,[status(thm)],[282,65]) ).
thf(2373,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk68 @ ( A @ model ) )
!= ( C @ ( B @ ( C @ sk10 ) @ model ) ) )
| ~ ( wca @ ( C @ ( B @ status ) ) ) ),
inference(simp,[status(thm)],[2372]) ).
thf(2374,plain,
! [A: $i] :
~ ( wca @ ( sk68 @ ( A @ status ) ) ),
inference(pattern_uni,[status(thm)],[2373:[bind(A,$thf( E @ ( sk68 @ sk10 ) )),bind(B,$thf( E )),bind(C,$thf( sk68 ))]]) ).
thf(2414,plain,
! [A: $i] :
~ ( wca @ ( sk68 @ ( A @ status ) ) ),
inference(simp,[status(thm)],[2374]) ).
thf(191,plain,
sk42 @ ( sk43 @ model ),
inference(cnfConj,[status(thm)],[189]) ).
thf(1176,plain,
( ( ( sk42 @ ( sk45 @ model ) )
!= ( sk42 @ ( sk43 @ model ) ) )
| ( sk44 != sk43 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[191,1142]) ).
thf(1177,plain,
( ( ( sk42 @ ( sk45 @ model ) )
!= ( sk42 @ ( sk43 @ model ) ) )
| ( sk44 != sk43 ) ),
inference(simp,[status(thm)],[1176]) ).
thf(1205,plain,
( ( sk42 != sk42 )
| ( sk45 != sk43 )
| ( sk44 != sk43 ) ),
inference(simp,[status(thm)],[1177]) ).
thf(1210,plain,
( ( sk45 != sk43 )
| ( sk44 != sk43 ) ),
inference(simp,[status(thm)],[1205]) ).
thf(693,plain,
! [A: $i] :
( ( ( sk37 @ ( sk38 @ model ) )
!= ( sk18 @ ( A @ model ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[178,99]) ).
thf(694,plain,
! [A: $i] :
( ( sk37 @ ( sk38 @ model ) )
!= ( sk18 @ ( A @ model ) ) ),
inference(simp,[status(thm)],[693]) ).
thf(699,plain,
! [A: $i] :
( ( sk37 != sk18 )
| ( sk38 != A ) ),
inference(simp,[status(thm)],[694]) ).
thf(710,plain,
sk37 != sk18,
inference(simp,[status(thm)],[699]) ).
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(1252,plain,
( ( ( sk63 @ ( sk64 @ model ) )
!= ( sk41 @ ( sk44 @ model ) ) )
| ( sk68 != sk42 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[277,1143]) ).
thf(1253,plain,
( ( ( sk63 @ ( sk64 @ model ) )
!= ( sk41 @ ( sk44 @ model ) ) )
| ( sk68 != sk42 ) ),
inference(simp,[status(thm)],[1252]) ).
thf(1259,plain,
( ( sk63 != sk41 )
| ( sk64 != sk44 )
| ( sk68 != sk42 ) ),
inference(simp,[status(thm)],[1253]) ).
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(491,plain,
( ( ( sk65 @ ( sk67 @ model ) )
!= ( sk36 @ ( sk35 @ model ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[176,280]) ).
thf(492,plain,
( ( sk65 @ ( sk67 @ model ) )
!= ( sk36 @ ( sk35 @ model ) ) ),
inference(simp,[status(thm)],[491]) ).
thf(499,plain,
( ( sk65 != sk36 )
| ( sk67 != sk35 ) ),
inference(simp,[status(thm)],[492]) ).
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/sandbox2/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(14,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(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(25,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ model ) )
<~> ( B @ not @ ( A @ model ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',completeness) ).
thf(225,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(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,
( ( ( sk65 @ ( sk67 @ model ) )
!= ( sk41 @ ( sk43 @ model ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[190,280]) ).
thf(490,plain,
( ( sk65 @ ( sk67 @ model ) )
!= ( sk41 @ ( sk43 @ model ) ) ),
inference(simp,[status(thm)],[489]) ).
thf(503,plain,
( ( sk65 != sk41 )
| ( sk67 != sk43 ) ),
inference(simp,[status(thm)],[490]) ).
thf(877,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk68 @ ( A @ model ) )
!= ( C @ ( B @ ( C @ sk7 ) @ model ) ) )
| ~ $true
| ~ ( wth @ ( C @ ( B @ status ) ) ) ),
inference(paramod_ordered,[status(thm)],[282,52]) ).
thf(878,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk68 @ ( A @ model ) )
!= ( C @ ( B @ ( C @ sk7 ) @ model ) ) )
| ~ ( wth @ ( C @ ( B @ status ) ) ) ),
inference(simp,[status(thm)],[877]) ).
thf(879,plain,
! [A: $i] :
~ ( wth @ ( sk68 @ ( A @ status ) ) ),
inference(pattern_uni,[status(thm)],[878:[bind(A,$thf( E @ ( sk68 @ sk7 ) )),bind(B,$thf( E )),bind(C,$thf( sk68 ))]]) ).
thf(911,plain,
! [A: $i] :
~ ( wth @ ( sk68 @ ( A @ status ) ) ),
inference(simp,[status(thm)],[879]) ).
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(24,axiom,
! [A: $i,B: $i] :
( ~ ? [C: $i] : ( A @ ( C @ model ) )
<=> ( cax @ ( B @ ( A @ status ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cax) ).
thf(219,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)],[24]) ).
thf(220,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)],[219]) ).
thf(221,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ~ ( C @ ( E @ model ) )
| ~ ( cax @ ( D @ ( C @ status ) ) ) )
& ( ( cax @ ( B @ ( A @ status ) ) )
| ( A @ ( A @ sk52 @ model ) ) ) ),
inference(cnf,[status(esa)],[220]) ).
thf(222,plain,
! [B: $i,A: $i] :
( ( cax @ ( B @ ( A @ status ) ) )
| ( A @ ( A @ sk52 @ model ) ) ),
inference(cnfConj,[status(thm)],[221]) ).
thf(1830,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk42 @ ( sk43 @ model ) )
!= ( A @ ( C @ model ) ) )
| ~ $true
| ~ ( wca @ ( B @ ( A @ status ) ) ) ),
inference(paramod_ordered,[status(thm)],[191,63]) ).
thf(1831,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk42 @ ( sk43 @ model ) )
!= ( A @ ( C @ model ) ) )
| ~ ( wca @ ( B @ ( A @ status ) ) ) ),
inference(simp,[status(thm)],[1830]) ).
thf(1832,plain,
! [A: $i] :
~ ( wca @ ( A @ ( sk42 @ status ) ) ),
inference(pattern_uni,[status(thm)],[1831:[bind(A,$thf( sk42 )),bind(B,$thf( B )),bind(C,$thf( sk43 ))]]) ).
thf(1894,plain,
! [A: $i] :
~ ( wca @ ( A @ ( sk42 @ status ) ) ),
inference(simp,[status(thm)],[1832]) ).
thf(1982,plain,
! [C: $i,B: $i,A: $i] :
( ( ( cax @ ( B @ ( A @ status ) ) )
!= ( wca @ ( C @ ( sk42 @ status ) ) ) )
| ~ $true
| ( A @ ( A @ sk52 @ model ) ) ),
inference(paramod_ordered,[status(thm)],[222,1894]) ).
thf(1983,plain,
! [C: $i,B: $i,A: $i] :
( ( ( cax @ ( B @ ( A @ status ) ) )
!= ( wca @ ( C @ ( sk42 @ status ) ) ) )
| ( A @ ( A @ sk52 @ model ) ) ),
inference(simp,[status(thm)],[1982]) ).
thf(1986,plain,
! [C: $i,B: $i,A: $i] :
( ( cax != wca )
| ( B != C )
| ( A != sk42 )
| ( A @ ( A @ sk52 @ model ) ) ),
inference(simp,[status(thm)],[1983]) ).
thf(1991,plain,
( ( cax != wca )
| ( sk42 @ ( sk42 @ sk52 @ model ) ) ),
inference(simp,[status(thm)],[1986]) ).
thf(1198,plain,
( ( ( sk63 @ ( sk64 @ model ) )
!= ( sk42 @ ( sk45 @ model ) ) )
| ( sk44 != sk43 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[277,1142]) ).
thf(1199,plain,
( ( ( sk63 @ ( sk64 @ model ) )
!= ( sk42 @ ( sk45 @ model ) ) )
| ( sk44 != sk43 ) ),
inference(simp,[status(thm)],[1198]) ).
thf(1202,plain,
( ( sk63 != sk42 )
| ( sk64 != sk45 )
| ( sk44 != sk43 ) ),
inference(simp,[status(thm)],[1199]) ).
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/sandbox2/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(505,plain,
( ( ( sk65 @ ( sk67 @ model ) )
!= ( sk65 @ ( sk66 @ model ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[278,280]) ).
thf(506,plain,
( ( sk65 @ ( sk67 @ model ) )
!= ( sk65 @ ( sk66 @ model ) ) ),
inference(simp,[status(thm)],[505]) ).
thf(525,plain,
( ( sk65 != sk65 )
| ( sk67 != sk66 ) ),
inference(simp,[status(thm)],[506]) ).
thf(530,plain,
sk67 != sk66,
inference(simp,[status(thm)],[525]) ).
thf(715,plain,
! [A: $i] :
( ( ( sk68 @ ( A @ model ) )
!= ( sk65 @ ( sk67 @ model ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[282,280]) ).
thf(716,plain,
! [A: $i] :
( ( sk68 @ ( A @ model ) )
!= ( sk65 @ ( sk67 @ model ) ) ),
inference(simp,[status(thm)],[715]) ).
thf(743,plain,
! [A: $i] :
( ( sk68 != sk65 )
| ( A != sk67 ) ),
inference(simp,[status(thm)],[716]) ).
thf(750,plain,
sk68 != sk65,
inference(simp,[status(thm)],[743]) ).
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] :
( ( ( sk1 @ ( sk2 @ model ) )
!= ( sk18 @ ( A @ model ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[39,99]) ).
thf(672,plain,
! [A: $i] :
( ( sk1 @ ( sk2 @ model ) )
!= ( sk18 @ ( A @ model ) ) ),
inference(simp,[status(thm)],[671]) ).
thf(700,plain,
! [A: $i] :
( ( sk18 != sk1 )
| ( sk2 != A ) ),
inference(simp,[status(thm)],[672]) ).
thf(711,plain,
sk18 != sk1,
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(13,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ model ) )
<=> ~ ( B @ not @ ( A @ model ) ) ),
file('/export/starexec/sandbox2/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(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(695,plain,
! [A: $i] :
( ( ( sk63 @ ( sk64 @ model ) )
!= ( sk18 @ ( A @ model ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[277,99]) ).
thf(696,plain,
! [A: $i] :
( ( sk63 @ ( sk64 @ model ) )
!= ( sk18 @ ( A @ model ) ) ),
inference(simp,[status(thm)],[695]) ).
thf(702,plain,
! [A: $i] :
( ( sk63 != sk18 )
| ( sk64 != A ) ),
inference(simp,[status(thm)],[696]) ).
thf(713,plain,
sk63 != sk18,
inference(simp,[status(thm)],[702]) ).
thf(1867,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk41 @ ( sk43 @ model ) )
!= ( A @ ( C @ model ) ) )
| ~ $true
| ~ ( wca @ ( B @ ( A @ status ) ) ) ),
inference(paramod_ordered,[status(thm)],[190,63]) ).
thf(1868,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk41 @ ( sk43 @ model ) )
!= ( A @ ( C @ model ) ) )
| ~ ( wca @ ( B @ ( A @ status ) ) ) ),
inference(simp,[status(thm)],[1867]) ).
thf(1869,plain,
! [A: $i] :
~ ( wca @ ( A @ ( sk41 @ status ) ) ),
inference(pattern_uni,[status(thm)],[1868:[bind(A,$thf( sk41 )),bind(B,$thf( B )),bind(C,$thf( sk43 ))]]) ).
thf(1897,plain,
! [A: $i] :
~ ( wca @ ( A @ ( sk41 @ status ) ) ),
inference(simp,[status(thm)],[1869]) ).
thf(1234,plain,
( ( ( sk65 @ ( sk66 @ model ) )
!= ( sk41 @ ( sk44 @ model ) ) )
| ( sk68 != sk42 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[278,1143]) ).
thf(1235,plain,
( ( ( sk65 @ ( sk66 @ model ) )
!= ( sk41 @ ( sk44 @ model ) ) )
| ( sk68 != sk42 ) ),
inference(simp,[status(thm)],[1234]) ).
thf(1258,plain,
( ( sk65 != sk41 )
| ( sk66 != sk44 )
| ( sk68 != sk42 ) ),
inference(simp,[status(thm)],[1235]) ).
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(27,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(245,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(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(1406,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( sk36 @ ( sk35 @ model ) )
!= ( B @ ( C @ model ) ) )
| ( wca @ ( B @ ( A @ status ) ) )
| ( B @ ( D @ model ) )
| ~ $true
| ( A @ ( A @ ( B @ sk8 ) @ model ) ) ),
inference(paramod_ordered,[status(thm)],[176,59]) ).
thf(1407,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( sk36 @ ( sk35 @ model ) )
!= ( B @ ( C @ model ) ) )
| ( wca @ ( B @ ( A @ status ) ) )
| ( B @ ( D @ model ) )
| ( A @ ( A @ ( B @ sk8 ) @ model ) ) ),
inference(simp,[status(thm)],[1406]) ).
thf(1408,plain,
! [B: $i,A: $i] :
( ( wca @ ( sk36 @ ( A @ status ) ) )
| ( sk36 @ ( B @ model ) )
| ( A @ ( A @ ( sk36 @ sk8 ) @ model ) ) ),
inference(pattern_uni,[status(thm)],[1407:[bind(A,$thf( A )),bind(B,$thf( sk36 )),bind(C,$thf( sk35 ))]]) ).
thf(1490,plain,
! [B: $i,A: $i] :
( ( wca @ ( sk36 @ ( A @ status ) ) )
| ( sk36 @ ( B @ model ) )
| ( A @ ( A @ ( sk36 @ sk8 ) @ model ) ) ),
inference(simp,[status(thm)],[1408]) ).
thf(1762,plain,
! [B: $i,A: $i] :
( ~ $true
| ( ( sk36 @ ( B @ model ) )
!= ( A @ ( A @ ( sk36 @ sk8 ) @ model ) ) )
| ( wca @ ( sk36 @ ( A @ status ) ) )
| ( A @ ( A @ ( sk36 @ sk8 ) @ model ) ) ),
inference(eqfactor_ordered,[status(thm)],[1490]) ).
thf(1781,plain,
( ( wca @ ( sk36 @ ( sk36 @ status ) ) )
| ( sk36 @ ( sk36 @ ( sk36 @ sk8 ) @ model ) ) ),
inference(pattern_uni,[status(thm)],[1762:[bind(A,$thf( sk36 )),bind(B,$thf( sk36 @ ( sk36 @ sk8 ) ))]]) ).
thf(2024,plain,
( $false
| ( sk36 @ ( sk36 @ ( sk36 @ sk8 ) @ model ) ) ),
inference(rewrite,[status(thm)],[1781,1892]) ).
thf(2025,plain,
sk36 @ ( sk36 @ ( sk36 @ sk8 ) @ model ),
inference(simp,[status(thm)],[2024]) ).
thf(319,plain,
( ( ( sk63 @ ( sk66 @ model ) )
!= ( sk36 @ ( sk35 @ model ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[176,276]) ).
thf(320,plain,
( ( sk63 @ ( sk66 @ model ) )
!= ( sk36 @ ( sk35 @ model ) ) ),
inference(simp,[status(thm)],[319]) ).
thf(323,plain,
( ( sk63 != sk36 )
| ( sk66 != sk35 ) ),
inference(simp,[status(thm)],[320]) ).
thf(517,plain,
( ( ( sk65 @ ( sk66 @ model ) )
!= ( sk1 @ ( sk3 @ model ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[278,40]) ).
thf(518,plain,
( ( sk65 @ ( sk66 @ model ) )
!= ( sk1 @ ( sk3 @ model ) ) ),
inference(simp,[status(thm)],[517]) ).
thf(521,plain,
( ( sk65 != sk1 )
| ( sk66 != sk3 ) ),
inference(simp,[status(thm)],[518]) ).
thf(452,plain,
( ( ( sk63 @ ( sk66 @ model ) )
!= ( sk42 @ ( sk43 @ model ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[191,276]) ).
thf(453,plain,
( ( sk63 @ ( sk66 @ model ) )
!= ( sk42 @ ( sk43 @ model ) ) ),
inference(simp,[status(thm)],[452]) ).
thf(455,plain,
( ( sk63 != sk42 )
| ( sk66 != sk43 ) ),
inference(simp,[status(thm)],[453]) ).
thf(1,conjecture,
thm @ ( tca @ isa ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',isa_tca_thm) ).
thf(2,negated_conjecture,
~ ( thm @ ( tca @ isa ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(35,plain,
~ ( thm @ ( tca @ isa ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(1196,plain,
( ( ( sk42 @ ( sk45 @ model ) )
!= ( sk37 @ ( sk38 @ model ) ) )
| ( sk44 != sk43 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[178,1142]) ).
thf(1197,plain,
( ( ( sk42 @ ( sk45 @ model ) )
!= ( sk37 @ ( sk38 @ model ) ) )
| ( sk44 != sk43 ) ),
inference(simp,[status(thm)],[1196]) ).
thf(1208,plain,
( ( sk42 != sk37 )
| ( sk45 != sk38 )
| ( sk44 != sk43 ) ),
inference(simp,[status(thm)],[1197]) ).
thf(738,plain,
! [A: $i] :
( ( ( sk68 @ ( A @ model ) )
!= ( sk37 @ ( sk35 @ model ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[282,177]) ).
thf(739,plain,
! [A: $i] :
( ( sk68 @ ( A @ model ) )
!= ( sk37 @ ( sk35 @ model ) ) ),
inference(simp,[status(thm)],[738]) ).
thf(742,plain,
! [A: $i] :
( ( sk68 != sk37 )
| ( A != sk35 ) ),
inference(simp,[status(thm)],[739]) ).
thf(749,plain,
sk68 != sk37,
inference(simp,[status(thm)],[742]) ).
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(1075,plain,
( ( ( sk42 @ ( sk45 @ model ) )
!= ( sk42 @ ( sk43 @ model ) ) )
| ~ $true
| ~ ( sk41 @ ( sk44 @ model ) ) ),
inference(paramod_ordered,[status(thm)],[191,192]) ).
thf(1076,plain,
( ( ( sk42 @ ( sk45 @ model ) )
!= ( sk42 @ ( sk43 @ model ) ) )
| ~ ( sk41 @ ( sk44 @ model ) ) ),
inference(simp,[status(thm)],[1075]) ).
thf(1130,plain,
( ( sk42 != sk42 )
| ( sk45 != sk43 )
| ~ ( sk41 @ ( sk44 @ model ) ) ),
inference(simp,[status(thm)],[1076]) ).
thf(1145,plain,
( ( sk45 != sk43 )
| ~ ( sk41 @ ( sk44 @ model ) ) ),
inference(simp,[status(thm)],[1130]) ).
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] :
( ( ( sk42 @ ( sk43 @ model ) )
!= ( sk18 @ ( A @ model ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[191,99]) ).
thf(684,plain,
! [A: $i] :
( ( sk42 @ ( sk43 @ model ) )
!= ( sk18 @ ( A @ model ) ) ),
inference(simp,[status(thm)],[683]) ).
thf(701,plain,
! [A: $i] :
( ( sk42 != sk18 )
| ( sk43 != A ) ),
inference(simp,[status(thm)],[684]) ).
thf(712,plain,
sk42 != sk18,
inference(simp,[status(thm)],[701]) ).
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/sandbox2/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(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,
( ( ( sk65 @ ( sk67 @ model ) )
!= ( sk42 @ ( sk43 @ model ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[191,280]) ).
thf(494,plain,
( ( sk65 @ ( sk67 @ model ) )
!= ( sk42 @ ( sk43 @ model ) ) ),
inference(simp,[status(thm)],[493]) ).
thf(502,plain,
( ( sk65 != sk42 )
| ( sk67 != sk43 ) ),
inference(simp,[status(thm)],[494]) ).
thf(1873,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk63 @ ( sk64 @ model ) )
!= ( A @ ( C @ model ) ) )
| ~ $true
| ~ ( wca @ ( B @ ( A @ status ) ) ) ),
inference(paramod_ordered,[status(thm)],[277,63]) ).
thf(1874,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk63 @ ( sk64 @ model ) )
!= ( A @ ( C @ model ) ) )
| ~ ( wca @ ( B @ ( A @ status ) ) ) ),
inference(simp,[status(thm)],[1873]) ).
thf(1875,plain,
! [A: $i] :
~ ( wca @ ( A @ ( sk63 @ status ) ) ),
inference(pattern_uni,[status(thm)],[1874:[bind(A,$thf( sk63 )),bind(B,$thf( B )),bind(C,$thf( sk64 ))]]) ).
thf(1901,plain,
! [A: $i] :
~ ( wca @ ( A @ ( sk63 @ status ) ) ),
inference(simp,[status(thm)],[1875]) ).
thf(1250,plain,
( ( ( sk41 @ ( sk44 @ model ) )
!= ( sk37 @ ( sk38 @ model ) ) )
| ( sk68 != sk42 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[178,1143]) ).
thf(1251,plain,
( ( ( sk41 @ ( sk44 @ model ) )
!= ( sk37 @ ( sk38 @ model ) ) )
| ( sk68 != sk42 ) ),
inference(simp,[status(thm)],[1250]) ).
thf(1257,plain,
( ( sk41 != sk37 )
| ( sk44 != sk38 )
| ( sk68 != sk42 ) ),
inference(simp,[status(thm)],[1251]) ).
thf(312,plain,
( ( ( sk63 @ ( sk66 @ model ) )
!= ( sk1 @ ( sk2 @ model ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[39,276]) ).
thf(313,plain,
( ( sk63 @ ( sk66 @ model ) )
!= ( sk1 @ ( sk2 @ model ) ) ),
inference(simp,[status(thm)],[312]) ).
thf(314,plain,
( ( sk63 != sk1 )
| ( sk66 != sk2 ) ),
inference(simp,[status(thm)],[313]) ).
thf(1954,plain,
! [C: $i,B: $i,A: $i] :
( ( ( cax @ ( B @ ( A @ status ) ) )
!= ( wca @ ( C @ ( sk36 @ status ) ) ) )
| ~ $true
| ( A @ ( A @ sk52 @ model ) ) ),
inference(paramod_ordered,[status(thm)],[222,1892]) ).
thf(1955,plain,
! [C: $i,B: $i,A: $i] :
( ( ( cax @ ( B @ ( A @ status ) ) )
!= ( wca @ ( C @ ( sk36 @ status ) ) ) )
| ( A @ ( A @ sk52 @ model ) ) ),
inference(simp,[status(thm)],[1954]) ).
thf(1960,plain,
! [C: $i,B: $i,A: $i] :
( ( cax != wca )
| ( B != C )
| ( A != sk36 )
| ( A @ ( A @ sk52 @ model ) ) ),
inference(simp,[status(thm)],[1955]) ).
thf(1966,plain,
( ( cax != wca )
| ( sk36 @ ( sk36 @ sk52 @ model ) ) ),
inference(simp,[status(thm)],[1960]) ).
thf(515,plain,
( ( ( sk65 @ ( sk66 @ model ) )
!= ( sk37 @ ( sk35 @ model ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[278,177]) ).
thf(516,plain,
( ( sk65 @ ( sk66 @ model ) )
!= ( sk37 @ ( sk35 @ model ) ) ),
inference(simp,[status(thm)],[515]) ).
thf(524,plain,
( ( sk65 != sk37 )
| ( sk66 != sk35 ) ),
inference(simp,[status(thm)],[516]) ).
thf(721,plain,
! [A: $i] :
( ( ( sk68 @ ( A @ model ) )
!= ( sk63 @ ( sk66 @ model ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[282,276]) ).
thf(722,plain,
! [A: $i] :
( ( sk68 @ ( A @ model ) )
!= ( sk63 @ ( sk66 @ model ) ) ),
inference(simp,[status(thm)],[721]) ).
thf(741,plain,
! [A: $i] :
( ( sk68 != sk63 )
| ( A != sk66 ) ),
inference(simp,[status(thm)],[722]) ).
thf(748,plain,
sk68 != sk63,
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/sandbox2/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(1561,plain,
! [A: $i] :
( ( ( sk68 @ ( A @ model ) )
!= ( sk41 @ ( sk44 @ model ) ) )
| ( ( sk42 @ ( sk45 @ model ) )
!= ( sk41 @ ( sk44 @ model ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[282,1135]) ).
thf(1562,plain,
! [A: $i] :
( ( ( sk68 @ ( A @ model ) )
!= ( sk41 @ ( sk44 @ model ) ) )
| ( ( sk42 @ ( sk45 @ model ) )
!= ( sk41 @ ( sk44 @ model ) ) ) ),
inference(simp,[status(thm)],[1561]) ).
thf(1594,plain,
! [A: $i] :
( ( sk68 != sk41 )
| ( A != sk44 )
| ( ( sk42 @ ( sk45 @ model ) )
!= ( sk41 @ ( sk44 @ model ) ) ) ),
inference(simp,[status(thm)],[1562]) ).
thf(1629,plain,
( ( sk68 != sk41 )
| ( ( sk42 @ ( sk45 @ model ) )
!= ( sk41 @ ( sk44 @ model ) ) ) ),
inference(simp,[status(thm)],[1594]) ).
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(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(290,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(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,
( ( ( sk63 @ ( sk64 @ model ) )
!= ( sk37 @ ( sk35 @ model ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[277,177]) ).
thf(470,plain,
( ( sk63 @ ( sk64 @ model ) )
!= ( sk37 @ ( sk35 @ model ) ) ),
inference(simp,[status(thm)],[469]) ).
thf(478,plain,
( ( sk63 != sk37 )
| ( sk64 != sk35 ) ),
inference(simp,[status(thm)],[470]) ).
thf(719,plain,
! [A: $i] :
( ( ( sk68 @ ( A @ model ) )
!= ( sk1 @ ( sk3 @ model ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[282,40]) ).
thf(720,plain,
! [A: $i] :
( ( sk68 @ ( A @ model ) )
!= ( sk1 @ ( sk3 @ model ) ) ),
inference(simp,[status(thm)],[719]) ).
thf(744,plain,
! [A: $i] :
( ( sk68 != sk1 )
| ( A != sk3 ) ),
inference(simp,[status(thm)],[720]) ).
thf(752,plain,
sk68 != sk1,
inference(simp,[status(thm)],[744]) ).
thf(1282,plain,
! [A: $i] :
( ( ( sk68 @ ( A @ model ) )
!= ( sk41 @ ( sk44 @ model ) ) )
| ( sk45 != sk43 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[282,1145]) ).
thf(1283,plain,
! [A: $i] :
( ( ( sk68 @ ( A @ model ) )
!= ( sk41 @ ( sk44 @ model ) ) )
| ( sk45 != sk43 ) ),
inference(simp,[status(thm)],[1282]) ).
thf(1296,plain,
! [A: $i] :
( ( sk68 != sk41 )
| ( A != sk44 )
| ( sk45 != sk43 ) ),
inference(simp,[status(thm)],[1283]) ).
thf(1303,plain,
( ( sk68 != sk41 )
| ( sk45 != sk43 ) ),
inference(simp,[status(thm)],[1296]) ).
thf(1856,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( sk68 @ ( A @ model ) )
!= ( B @ ( D @ model ) ) )
| ~ $true
| ~ ( wca @ ( C @ ( B @ status ) ) ) ),
inference(paramod_ordered,[status(thm)],[282,63]) ).
thf(1857,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( sk68 @ ( A @ model ) )
!= ( B @ ( D @ model ) ) )
| ~ ( wca @ ( C @ ( B @ status ) ) ) ),
inference(simp,[status(thm)],[1856]) ).
thf(1858,plain,
! [A: $i] :
~ ( wca @ ( A @ ( sk68 @ status ) ) ),
inference(pattern_uni,[status(thm)],[1857:[bind(A,$thf( A )),bind(B,$thf( sk68 )),bind(C,$thf( C )),bind(D,$thf( A ))]]) ).
thf(1891,plain,
! [A: $i] :
~ ( wca @ ( A @ ( sk68 @ status ) ) ),
inference(simp,[status(thm)],[1858]) ).
thf(2010,plain,
! [C: $i,B: $i,A: $i] :
( ( ( cax @ ( B @ ( A @ status ) ) )
!= ( wca @ ( C @ ( sk41 @ status ) ) ) )
| ~ $true
| ( A @ ( A @ sk52 @ model ) ) ),
inference(paramod_ordered,[status(thm)],[222,1897]) ).
thf(2011,plain,
! [C: $i,B: $i,A: $i] :
( ( ( cax @ ( B @ ( A @ status ) ) )
!= ( wca @ ( C @ ( sk41 @ status ) ) ) )
| ( A @ ( A @ sk52 @ model ) ) ),
inference(simp,[status(thm)],[2010]) ).
thf(2013,plain,
! [C: $i,B: $i,A: $i] :
( ( cax != wca )
| ( B != C )
| ( A != sk41 )
| ( A @ ( A @ sk52 @ model ) ) ),
inference(simp,[status(thm)],[2011]) ).
thf(2021,plain,
( ( cax != wca )
| ( sk41 @ ( sk41 @ sk52 @ model ) ) ),
inference(simp,[status(thm)],[2013]) ).
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(283,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(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(519,plain,
( ( ( sk65 @ ( sk66 @ model ) )
!= ( sk63 @ ( sk66 @ model ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[278,276]) ).
thf(520,plain,
( ( sk65 @ ( sk66 @ model ) )
!= ( sk63 @ ( sk66 @ model ) ) ),
inference(simp,[status(thm)],[519]) ).
thf(523,plain,
( ( sk65 != sk63 )
| ( sk66 != sk66 ) ),
inference(simp,[status(thm)],[520]) ).
thf(528,plain,
sk65 != sk63,
inference(simp,[status(thm)],[523]) ).
thf(1842,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk65 @ ( sk66 @ model ) )
!= ( A @ ( C @ model ) ) )
| ~ $true
| ~ ( wca @ ( B @ ( A @ status ) ) ) ),
inference(paramod_ordered,[status(thm)],[278,63]) ).
thf(1843,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk65 @ ( sk66 @ model ) )
!= ( A @ ( C @ model ) ) )
| ~ ( wca @ ( B @ ( A @ status ) ) ) ),
inference(simp,[status(thm)],[1842]) ).
thf(1844,plain,
! [A: $i] :
~ ( wca @ ( A @ ( sk65 @ status ) ) ),
inference(pattern_uni,[status(thm)],[1843:[bind(A,$thf( sk65 )),bind(B,$thf( B )),bind(C,$thf( sk66 ))]]) ).
thf(1902,plain,
! [A: $i] :
~ ( wca @ ( A @ ( sk65 @ status ) ) ),
inference(simp,[status(thm)],[1844]) ).
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(1174,plain,
( ( ( sk42 @ ( sk45 @ model ) )
!= ( sk36 @ ( sk35 @ model ) ) )
| ( sk44 != sk43 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[176,1142]) ).
thf(1175,plain,
( ( ( sk42 @ ( sk45 @ model ) )
!= ( sk36 @ ( sk35 @ model ) ) )
| ( sk44 != sk43 ) ),
inference(simp,[status(thm)],[1174]) ).
thf(1204,plain,
( ( sk42 != sk36 )
| ( sk45 != sk35 )
| ( sk44 != sk43 ) ),
inference(simp,[status(thm)],[1175]) ).
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(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/sandbox2/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(681,plain,
! [A: $i] :
( ( ( sk36 @ ( sk35 @ model ) )
!= ( sk18 @ ( A @ model ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[176,99]) ).
thf(682,plain,
! [A: $i] :
( ( sk36 @ ( sk35 @ model ) )
!= ( sk18 @ ( A @ model ) ) ),
inference(simp,[status(thm)],[681]) ).
thf(697,plain,
! [A: $i] :
( ( sk36 != sk18 )
| ( sk35 != A ) ),
inference(simp,[status(thm)],[682]) ).
thf(708,plain,
sk36 != sk18,
inference(simp,[status(thm)],[697]) ).
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/sandbox2/benchmark/theBenchmark.p',eqv) ).
thf(232,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(97919,plain,
$false,
inference(e,[status(thm)],[69,333,1899,481,1200,1211,276,308,1142,56,500,709,436,257,52,504,110,1264,1892,1147,216,475,179,280,1622,89,265,1206,714,798,334,1900,746,1255,297,192,137,2414,65,97,1210,710,324,1143,1259,53,499,193,212,124,225,457,41,503,173,911,73,1991,1202,205,311,530,1135,750,64,176,191,711,281,59,118,54,713,1897,1258,187,219,1894,81,245,39,434,2025,323,66,521,278,455,35,1208,749,123,1145,48,712,63,282,150,50,177,502,1901,1257,314,99,1966,524,748,40,158,1629,55,290,433,478,752,36,51,273,190,1303,1891,2021,283,332,528,178,277,1902,322,1490,1204,222,454,100,708,232]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : KRS195+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.12 % 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
% 0.23/0.48 % Computer : n017.cluster.edu
% 0.23/0.48 % Model : x86_64 x86_64
% 0.23/0.48 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.23/0.48 % Memory : 8046.5625MB
% 0.23/0.48 % OS : Linux 6.8.0-71-generic
% 0.23/0.48 % CPULimit : 300
% 0.23/0.48 % WCLimit : 300
% 0.23/0.48 % DateTime : Fri Sep 25 19:39:17 UTC 2026
% 0.23/0.49 % CPUTime :
% 0.23/0.49 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
% 1.45/1.34 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.98/1.70 % [INFO] Parsing done (345ms).
% 2.37/1.72 % [INFO] Running in sequential loop mode.
% 3.37/2.35 % [INFO] eprover registered as external prover.
% 3.37/2.36 % [INFO] Scanning for conjecture ...
% 3.57/2.49 % [INFO] Found a conjecture (or negated_conjecture) and 32 axioms. Running axiom selection ...
% 3.76/2.59 % [INFO] Axiom selection finished. Selected 32 axioms (removed 0 axioms).
% 4.18/2.73 % [INFO] Problem is first-order (TPTP FOF).
% 4.18/2.75 % [INFO] Type checking passed.
% 4.18/2.76 % [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 ...
% 171.89/46.94 % External prover 'e' found a proof!
% 171.89/46.94 % [INFO] Killing All external provers ...
% 171.89/46.94 % Time passed: 46245ms (effective reasoning time: 45213ms)
% 171.89/46.94 % 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)>
% 171.89/46.94 % 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
% 171.89/46.94 % No. of inferences in proof: 395
% 171.89/46.94 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 46245 ms resp. 45213 ms w/o parsing
% 173.90/47.19 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 173.90/47.20 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------