%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM852+1 : TPTP v9.3.1. Released v4.1.0.
% 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 : n003.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 08:10:11 AM UTC 2026
% Result : Theorem 96.65s 19.67s
% Output : Refutation 83.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 46
% Number of leaves : 66
% Syntax : Number of formulae : 954 ( 359 unt; 0 typ; 8 def)
% Number of atoms : 2236 (1068 equ; 0 cnn)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 6937 (1093 ~; 754 |; 40 &;4970 @)
% ( 4 <=>; 76 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% Number of symbols : 24 ( 21 usr; 6 con; 0-2 aty)
% Number of variables : 1503 ( 8 ^;1453 !; 34 ?;1503 :)
% ( 0 !>; 0 ?*; 0 @-; 8 @+)
% Comments :
%------------------------------------------------------------------------------
thf(greater_decl,type,
greater: $i > $i > $o ).
thf(vmul_decl,type,
vmul: $i > $i > $i ).
thf(vd481_decl,type,
vd481: $i ).
thf(vd469_decl,type,
vd469: $i ).
thf(vd480_decl,type,
vd480: $i ).
thf(leq_decl,type,
leq: $i > $i > $o ).
thf(vplus_decl,type,
vplus: $i > $i > $i ).
thf(vsucc_decl,type,
vsucc: $i > $i ).
thf(v1_decl,type,
v1: $i ).
thf(less_decl,type,
less: $i > $i > $o ).
thf(geq_decl,type,
geq: $i > $i > $o ).
thf(vskolem2_decl,type,
vskolem2: $i > $i ).
thf(vskolem9_decl,type,
vskolem9: $i > $i > $i ).
thf(sk1_decl,type,
sk1: $i > $i > $i ).
thf(sk2_decl,type,
sk2: $i > $i > $i ).
thf(sk3_decl,type,
sk3: $i > $i > $i ).
thf(sk4_decl,type,
sk4: $i > $i ).
thf(sk5_decl,type,
sk5: $i > $i > $i ).
thf(sk6_decl,type,
sk6: $i > $i ).
thf(sk7_decl,type,
sk7: $i > $i > $i ).
thf(sk8_decl,type,
sk8: $i > $i > $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ vplus ) @ ( B @ A ) )
= C ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
( B
= ( C @ ( A @ vplus ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
( A
= ( C @ ( B @ vplus ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( @+[A: $i > $i] :
! [B: $i] :
( ( B @ vsucc @ A )
= B ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( @+[A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ vplus ) @ ( C @ A ) )
= B ) ) ) ).
thf(sk6_def,definition,
( sk6
= ( @+[A: $i > $i] :
! [B: $i] :
( ( B @ vsucc @ A )
= B ) ) ) ).
thf(sk7_def,definition,
( sk7
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
( B
= ( C @ ( A @ vplus ) ) ) ) ) ).
thf(sk8_def,definition,
( sk8
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
( A
= ( C @ ( B @ vplus ) ) ) ) ) ).
thf(55,axiom,
vd481 @ ( vd480 @ less ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(antec(304), 482, 0)') ).
thf(250,plain,
vd481 @ ( vd480 @ less ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(26,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ less ) )
<=> ? [C: $i] :
( A
= ( C @ ( B @ vplus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','def(cond(conseq(axiom(3)), 12), 1)') ).
thf(153,plain,
! [A: $i,B: $i] :
( ( ? [C: $i] :
( A
= ( C @ ( B @ vplus ) ) )
=> ( A @ ( B @ less ) ) )
& ( ( A @ ( B @ less ) )
=> ? [C: $i] :
( A
= ( C @ ( B @ vplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(154,plain,
( ! [A: $i,B: $i] :
( ? [C: $i] :
( A
= ( C @ ( B @ vplus ) ) )
=> ( A @ ( B @ less ) ) )
& ! [A: $i,B: $i] :
( ( A @ ( B @ less ) )
=> ? [C: $i] :
( A
= ( C @ ( B @ vplus ) ) ) ) ),
inference(miniscope,[status(thm)],[153]) ).
thf(155,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( D @ less ) )
| ( C
!= ( E @ ( D @ vplus ) ) ) )
& ( ( A
= ( A @ ( B @ sk7 ) @ ( B @ vplus ) ) )
| ~ ( A @ ( B @ less ) ) ) ),
inference(cnf,[status(esa)],[154]) ).
thf(156,plain,
! [B: $i,A: $i] :
( ( A
= ( A @ ( B @ sk7 ) @ ( B @ vplus ) ) )
| ~ ( A @ ( B @ less ) ) ),
inference(cnfConj,[status(thm)],[155]) ).
thf(158,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ less ) )
| ( ( A @ ( B @ sk7 ) @ ( B @ vplus ) )
= A ) ),
inference(lifteq,[status(thm)],[156]) ).
thf(5036,plain,
! [B: $i,A: $i] :
( ( ( vd481 @ ( vd480 @ less ) )
!= ( A @ ( B @ less ) ) )
| ~ $true
| ( ( A @ ( B @ sk7 ) @ ( B @ vplus ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[250,158]) ).
thf(5037,plain,
! [B: $i,A: $i] :
( ( ( vd481 @ ( vd480 @ less ) )
!= ( A @ ( B @ less ) ) )
| ( ( A @ ( B @ sk7 ) @ ( B @ vplus ) )
= A ) ),
inference(simp,[status(thm)],[5036]) ).
thf(5038,plain,
( ( vd481 @ ( vd480 @ sk7 ) @ ( vd480 @ vplus ) )
= vd481 ),
inference(pattern_uni,[status(thm)],[5037:[bind(A,$thf( vd481 )),bind(B,$thf( vd480 ))]]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ vplus ) )
= ( B @ ( A @ vplus ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(61, 0), 0)') ).
thf(75,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ vplus ) )
= ( B @ ( A @ vplus ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(76,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ vplus ) )
= ( B @ ( A @ vplus ) ) ),
inference(cnf,[status(esa)],[75]) ).
thf(77,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ vplus ) )
= ( B @ ( A @ vplus ) ) ),
inference(lifteq,[status(thm)],[76]) ).
thf(7354,plain,
! [B: $i,A: $i] :
( ( ( vd481 @ ( vd480 @ sk7 ) @ ( vd480 @ vplus ) )
!= ( A @ ( B @ vplus ) ) )
| ( ( B @ ( A @ vplus ) )
= vd481 ) ),
inference(paramod_ordered,[status(thm)],[5038,77]) ).
thf(7355,plain,
( ( vd480 @ ( vd481 @ ( vd480 @ sk7 ) @ vplus ) )
= vd481 ),
inference(pattern_uni,[status(thm)],[7354:[bind(A,$thf( vd481 @ ( vd480 @ sk7 ) )),bind(B,$thf( vd480 ))]]) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( A != B )
=> ! [C: $i] :
( ( A @ ( C @ vplus ) )
!= ( B @ ( C @ vplus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(81, 0), 0)') ).
thf(84,plain,
! [A: $i,B: $i] :
( ( A != B )
=> ! [C: $i] :
( ( A @ ( C @ vplus ) )
!= ( B @ ( C @ vplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(85,plain,
! [A: $i,B: $i] :
( ( A != B )
=> ~ ? [C: $i] :
( ( A @ ( C @ vplus ) )
= ( B @ ( C @ vplus ) ) ) ),
inference(miniscope,[status(thm)],[84]) ).
thf(86,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ vplus ) )
!= ( B @ ( C @ vplus ) ) )
| ( A = B ) ),
inference(cnf,[status(esa)],[85]) ).
thf(87,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ vplus ) )
!= ( B @ ( C @ vplus ) ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[86]) ).
thf(88,plain,
? [A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ vplus ) @ ( B @ A ) )
= C ),
inference(detectInverse,[status(thm)],[87]) ).
thf(89,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ vplus ) @ ( A @ sk1 ) )
= B ),
inference(cnf,[status(esa)],[88]) ).
thf(708,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ vplus ) @ ( A @ sk1 ) )
= B ),
inference(lifteq,[status(thm)],[89]) ).
thf(7424,plain,
! [B: $i,A: $i] :
( ( ( vd481 @ ( vd480 @ sk7 ) @ ( vd480 @ vplus ) )
!= ( B @ ( A @ vplus ) ) )
| ( ( vd481 @ ( A @ sk1 ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[5038,708]) ).
thf(7425,plain,
( ( vd481 @ ( vd480 @ sk7 ) )
= ( vd481 @ ( vd480 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[7424:[bind(A,$thf( vd480 )),bind(B,$thf( vd481 @ ( vd480 @ sk7 ) ))]]) ).
thf(9096,plain,
( ( vd480 @ ( vd481 @ ( vd480 @ sk1 ) @ vplus ) )
= vd481 ),
inference(rewrite,[status(thm)],[7355,7425]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( ( v1 @ ( A @ vplus ) )
= ( A @ vsucc ) )
& ( ( B @ vsucc @ ( A @ vplus ) )
= ( B @ ( A @ vplus ) @ vsucc ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(conseq(axiom(3)), 3), and(holds(definiens(29), 45, 0), holds(definiens(29), 44, 0)))') ).
thf(63,plain,
! [A: $i,B: $i] :
( ( ( v1 @ ( A @ vplus ) )
= ( A @ vsucc ) )
& ( ( B @ vsucc @ ( A @ vplus ) )
= ( B @ ( A @ vplus ) @ vsucc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(64,plain,
( ! [A: $i] :
( ( v1 @ ( A @ vplus ) )
= ( A @ vsucc ) )
& ! [A: $i,B: $i] :
( ( B @ vsucc @ ( A @ vplus ) )
= ( B @ ( A @ vplus ) @ vsucc ) ) ),
inference(miniscope,[status(thm)],[63]) ).
thf(65,plain,
! [C: $i,B: $i,A: $i] :
( ( ( v1 @ ( C @ vplus ) )
= ( C @ vsucc ) )
& ( ( B @ vsucc @ ( A @ vplus ) )
= ( B @ ( A @ vplus ) @ vsucc ) ) ),
inference(cnf,[status(esa)],[64]) ).
thf(66,plain,
! [B: $i,A: $i] :
( ( B @ vsucc @ ( A @ vplus ) )
= ( B @ ( A @ vplus ) @ vsucc ) ),
inference(cnfConj,[status(thm)],[65]) ).
thf(68,plain,
! [B: $i,A: $i] :
( ( B @ vsucc @ ( A @ vplus ) )
= ( B @ ( A @ vplus ) @ vsucc ) ),
inference(lifteq,[status(thm)],[66]) ).
thf(157,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ less ) )
| ( A
!= ( C @ ( B @ vplus ) ) ) ),
inference(cnfConj,[status(thm)],[155]) ).
thf(159,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ less ) )
| ( A
!= ( C @ ( B @ vplus ) ) ) ),
inference(lifteq,[status(thm)],[157]) ).
thf(160,plain,
! [B: $i,A: $i] : ( B @ ( A @ vplus ) @ ( A @ less ) ),
inference(simp,[status(thm)],[159]) ).
thf(391,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ vsucc @ ( A @ vplus ) )
!= ( D @ ( C @ vplus ) ) )
| ( B @ ( A @ vplus ) @ vsucc @ ( C @ less ) ) ),
inference(paramod_ordered,[status(thm)],[68,160]) ).
thf(392,plain,
! [B: $i,A: $i] : ( B @ ( A @ vplus ) @ vsucc @ ( A @ less ) ),
inference(pattern_uni,[status(thm)],[391:[bind(A,$thf( A )),bind(B,$thf( E )),bind(C,$thf( A )),bind(D,$thf( E @ vsucc ))]]) ).
thf(394,plain,
! [B: $i,A: $i] : ( B @ ( A @ vplus ) @ vsucc @ ( A @ less ) ),
inference(simp,[status(thm)],[392]) ).
thf(26556,plain,
! [B: $i,A: $i] :
( ( ( vd480 @ ( vd481 @ ( vd480 @ sk1 ) @ vplus ) )
!= ( B @ ( A @ vplus ) ) )
| ( vd481 @ vsucc @ ( A @ less ) ) ),
inference(paramod_ordered,[status(thm)],[9096,394]) ).
thf(26557,plain,
vd481 @ vsucc @ ( vd481 @ ( vd480 @ sk1 ) @ less ),
inference(pattern_uni,[status(thm)],[26556:[bind(A,$thf( vd481 @ ( vd480 @ sk1 ) )),bind(B,$thf( vd480 ))]]) ).
thf(42,axiom,
vd480 @ ( vd481 @ greater ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(conseq_conjunct1(conseq(304)), 483, 0)') ).
thf(217,plain,
vd480 @ ( vd481 @ greater ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(46,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ greater ) )
=> ( A
= ( B @ ( A @ vskolem9 ) @ ( B @ vplus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(302, 0), 3)') ).
thf(226,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ greater ) )
=> ( A
= ( B @ ( A @ vskolem9 ) @ ( B @ vplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(227,plain,
! [B: $i,A: $i] :
( ( A
= ( B @ ( A @ vskolem9 ) @ ( B @ vplus ) ) )
| ~ ( B @ ( A @ greater ) ) ),
inference(cnf,[status(esa)],[226]) ).
thf(228,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ greater ) )
| ( ( B @ ( A @ vskolem9 ) @ ( B @ vplus ) )
= A ) ),
inference(lifteq,[status(thm)],[227]) ).
thf(9642,plain,
! [B: $i,A: $i] :
( ( ( vd480 @ ( vd481 @ greater ) )
!= ( B @ ( A @ greater ) ) )
| ~ $true
| ( ( B @ ( A @ vskolem9 ) @ ( B @ vplus ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[217,228]) ).
thf(9643,plain,
! [B: $i,A: $i] :
( ( ( vd480 @ ( vd481 @ greater ) )
!= ( B @ ( A @ greater ) ) )
| ( ( B @ ( A @ vskolem9 ) @ ( B @ vplus ) )
= A ) ),
inference(simp,[status(thm)],[9642]) ).
thf(9644,plain,
( ( vd480 @ ( vd481 @ vskolem9 ) @ ( vd480 @ vplus ) )
= vd481 ),
inference(pattern_uni,[status(thm)],[9643:[bind(A,$thf( vd481 )),bind(B,$thf( vd480 ))]]) ).
thf(15610,plain,
! [B: $i,A: $i] :
( ( ( vd480 @ ( vd481 @ vskolem9 ) @ ( vd480 @ vplus ) )
!= ( B @ ( A @ vplus ) ) )
| ( ( vd481 @ ( A @ sk1 ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[9644,708]) ).
thf(15611,plain,
( ( vd481 @ ( vd480 @ sk1 ) )
= ( vd480 @ ( vd481 @ vskolem9 ) ) ),
inference(pattern_uni,[status(thm)],[15610:[bind(A,$thf( vd480 )),bind(B,$thf( vd480 @ ( vd481 @ vskolem9 ) ))]]) ).
thf(29528,plain,
vd481 @ vsucc @ ( vd480 @ ( vd481 @ vskolem9 ) @ less ),
inference(rewrite,[status(thm)],[26557,15611]) ).
thf(15,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ leq ) )
<=> ( ( B = A )
| ( A @ ( B @ less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','def(cond(conseq(axiom(3)), 17), 1)') ).
thf(103,plain,
! [A: $i,B: $i] :
( ( ( ( B = A )
| ( A @ ( B @ less ) ) )
=> ( A @ ( B @ leq ) ) )
& ( ( A @ ( B @ leq ) )
=> ( ( B = A )
| ( A @ ( B @ less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(104,plain,
( ! [A: $i,B: $i] :
( ( ( B = A )
| ( A @ ( B @ less ) ) )
=> ( A @ ( B @ leq ) ) )
& ! [A: $i,B: $i] :
( ( A @ ( B @ leq ) )
=> ( ( B = A )
| ( A @ ( B @ less ) ) ) ) ),
inference(miniscope,[status(thm)],[103]) ).
thf(105,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( D @ leq ) )
| ( D != C ) )
& ( ( C @ ( D @ leq ) )
| ~ ( C @ ( D @ less ) ) )
& ( ( B = A )
| ( A @ ( B @ less ) )
| ~ ( A @ ( B @ leq ) ) ) ),
inference(cnf,[status(esa)],[104]) ).
thf(107,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ leq ) )
| ~ ( A @ ( B @ less ) ) ),
inference(cnfConj,[status(thm)],[105]) ).
thf(110,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ leq ) )
| ~ ( A @ ( B @ less ) ) ),
inference(simp,[status(thm)],[107]) ).
thf(29538,plain,
! [B: $i,A: $i] :
( ( ( vd481 @ vsucc @ ( vd480 @ ( vd481 @ vskolem9 ) @ less ) )
!= ( A @ ( B @ less ) ) )
| ( A @ ( B @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[29528,110]) ).
thf(29539,plain,
! [B: $i,A: $i] :
( ( ( vd481 @ vsucc @ ( vd480 @ ( vd481 @ vskolem9 ) @ less ) )
!= ( A @ ( B @ less ) ) )
| ( A @ ( B @ leq ) ) ),
inference(simp,[status(thm)],[29538]) ).
thf(29540,plain,
vd481 @ vsucc @ ( vd480 @ ( vd481 @ vskolem9 ) @ leq ),
inference(pattern_uni,[status(thm)],[29539:[bind(A,$thf( vd481 @ vsucc )),bind(B,$thf( vd480 @ ( vd481 @ vskolem9 ) ))]]) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ leq ) )
=> ( A @ ( B @ geq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(163, 0), 0)') ).
thf(96,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ leq ) )
=> ( A @ ( B @ geq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(97,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ geq ) )
| ~ ( B @ ( A @ leq ) ) ),
inference(cnf,[status(esa)],[96]) ).
thf(30925,plain,
! [B: $i,A: $i] :
( ( ( vd481 @ vsucc @ ( vd480 @ ( vd481 @ vskolem9 ) @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( A @ ( B @ geq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[29540,97]) ).
thf(30926,plain,
! [B: $i,A: $i] :
( ( ( vd481 @ vsucc @ ( vd480 @ ( vd481 @ vskolem9 ) @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( A @ ( B @ geq ) ) ),
inference(simp,[status(thm)],[30925]) ).
thf(30927,plain,
vd480 @ ( vd481 @ vskolem9 ) @ ( vd481 @ vsucc @ geq ),
inference(pattern_uni,[status(thm)],[30926:[bind(A,$thf( vd480 @ ( vd481 @ vskolem9 ) )),bind(B,$thf( vd481 @ vsucc ))]]) ).
thf(35,axiom,
! [A: $i,B: $i] : ( A @ ( B @ ( A @ vplus ) @ greater ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(189, 0), 0)') ).
thf(186,plain,
! [A: $i,B: $i] : ( A @ ( B @ ( A @ vplus ) @ greater ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(187,plain,
! [B: $i,A: $i] : ( A @ ( B @ ( A @ vplus ) @ greater ) ),
inference(cnf,[status(esa)],[186]) ).
thf(480,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ vplus ) )
!= ( D @ ( C @ vplus ) ) )
| ( C @ ( B @ ( A @ vplus ) @ greater ) ) ),
inference(paramod_ordered,[status(thm)],[77,187]) ).
thf(481,plain,
! [B: $i,A: $i] : ( B @ ( B @ ( A @ vplus ) @ greater ) ),
inference(pattern_uni,[status(thm)],[480:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A ))]]) ).
thf(15439,plain,
! [B: $i,A: $i] :
( ( ( vd480 @ ( vd481 @ vskolem9 ) @ ( vd480 @ vplus ) )
!= ( B @ ( A @ vplus ) ) )
| ( B @ ( vd481 @ greater ) ) ),
inference(paramod_ordered,[status(thm)],[9644,481]) ).
thf(15440,plain,
vd480 @ ( vd481 @ vskolem9 ) @ ( vd481 @ greater ),
inference(pattern_uni,[status(thm)],[15439:[bind(A,$thf( vd480 )),bind(B,$thf( vd480 @ ( vd481 @ vskolem9 ) ))]]) ).
thf(54,axiom,
! [A: $i,B: $i] :
( ~ ( B @ ( A @ less ) )
| ~ ( B @ ( A @ greater ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(130), 0), 2)') ).
thf(248,plain,
! [A: $i,B: $i] :
( ~ ( B @ ( A @ less ) )
| ~ ( B @ ( A @ greater ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(249,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ less ) )
| ~ ( B @ ( A @ greater ) ) ),
inference(cnf,[status(esa)],[248]) ).
thf(44,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ vmul ) )
= ( A @ ( B @ vmul ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(270, 0), 0)') ).
thf(221,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ vmul ) )
= ( A @ ( B @ vmul ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(222,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ vmul ) )
= ( A @ ( B @ vmul ) ) ),
inference(cnf,[status(esa)],[221]) ).
thf(223,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ vmul ) )
= ( A @ ( B @ vmul ) ) ),
inference(lifteq,[status(thm)],[222]) ).
thf(1,conjecture,
vd469 @ ( vd480 @ vmul ) @ ( vd469 @ ( vd481 @ vmul ) @ greater ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(conseq_conjunct1(conseq_conjunct2(conseq(304))), 484, 0)') ).
thf(2,negated_conjecture,
~ ( vd469 @ ( vd480 @ vmul ) @ ( vd469 @ ( vd481 @ vmul ) @ greater ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(60,plain,
~ ( vd469 @ ( vd480 @ vmul ) @ ( vd469 @ ( vd481 @ vmul ) @ greater ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(488,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ vplus ) @ greater ) )
!= ( vd469 @ ( vd480 @ vmul ) @ ( vd469 @ ( vd481 @ vmul ) @ greater ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[187,60]) ).
thf(489,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ vplus ) @ greater ) )
!= ( vd469 @ ( vd480 @ vmul ) @ ( vd469 @ ( vd481 @ vmul ) @ greater ) ) ),
inference(simp,[status(thm)],[488]) ).
thf(497,plain,
! [B: $i,A: $i] :
( ( A
!= ( vd469 @ ( vd480 @ vmul ) ) )
| ( ( B @ ( A @ vplus ) )
!= ( vd469 @ ( vd481 @ vmul ) ) ) ),
inference(simp,[status(thm)],[489]) ).
thf(501,plain,
! [A: $i] :
( ( A @ ( vd469 @ ( vd480 @ vmul ) @ vplus ) )
!= ( vd469 @ ( vd481 @ vmul ) ) ),
inference(simp,[status(thm)],[497]) ).
thf(5069,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk7 ) @ ( B @ vplus ) )
!= ( C @ ( vd469 @ ( vd480 @ vmul ) @ vplus ) ) )
| ( A
!= ( vd469 @ ( vd481 @ vmul ) ) )
| ~ ( A @ ( B @ less ) ) ),
inference(paramod_ordered,[status(thm)],[158,501]) ).
thf(5070,plain,
! [A: $i] :
( ( A
!= ( vd469 @ ( vd481 @ vmul ) ) )
| ~ ( A @ ( vd469 @ ( vd480 @ vmul ) @ less ) ) ),
inference(pattern_uni,[status(thm)],[5069:[bind(A,$thf( G )),bind(B,$thf( vd469 @ ( vd480 @ vmul ) )),bind(C,$thf( G @ ( vd469 @ ( vd480 @ vmul ) @ sk7 ) ))]]) ).
thf(5120,plain,
~ ( vd469 @ ( vd481 @ vmul ) @ ( vd469 @ ( vd480 @ vmul ) @ less ) ),
inference(simp,[status(thm)],[5070]) ).
thf(33244,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ vmul ) )
!= ( vd469 @ ( vd480 @ vmul ) ) )
| ~ ( vd469 @ ( vd481 @ vmul ) @ ( A @ ( B @ vmul ) @ less ) ) ),
inference(paramod_ordered,[status(thm)],[223,5120]) ).
thf(33245,plain,
~ ( vd469 @ ( vd481 @ vmul ) @ ( vd480 @ ( vd469 @ vmul ) @ less ) ),
inference(pattern_uni,[status(thm)],[33244:[bind(A,$thf( vd480 )),bind(B,$thf( vd469 ))]]) ).
thf(14,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ geq ) )
=> ( A @ ( B @ leq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(158, 0), 0)') ).
thf(101,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ geq ) )
=> ( A @ ( B @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(48,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ less ) )
=> ( A @ ( B @ greater ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(147, 0), 0)') ).
thf(231,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ less ) )
=> ( A @ ( B @ greater ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(232,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ greater ) )
| ~ ( B @ ( A @ less ) ) ),
inference(cnf,[status(esa)],[231]) ).
thf(29648,plain,
! [B: $i,A: $i] :
( ( ( vd481 @ vsucc @ ( vd480 @ ( vd481 @ vskolem9 ) @ less ) )
!= ( B @ ( A @ less ) ) )
| ( A @ ( B @ greater ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[29528,232]) ).
thf(29649,plain,
! [B: $i,A: $i] :
( ( ( vd481 @ vsucc @ ( vd480 @ ( vd481 @ vskolem9 ) @ less ) )
!= ( B @ ( A @ less ) ) )
| ( A @ ( B @ greater ) ) ),
inference(simp,[status(thm)],[29648]) ).
thf(29650,plain,
vd480 @ ( vd481 @ vskolem9 ) @ ( vd481 @ vsucc @ greater ),
inference(pattern_uni,[status(thm)],[29649:[bind(A,$thf( vd480 @ ( vd481 @ vskolem9 ) )),bind(B,$thf( vd481 @ vsucc ))]]) ).
thf(41,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ greater ) )
=> ( v1 @ ( B @ vplus ) @ ( A @ geq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(234, 0), 0)') ).
thf(215,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ greater ) )
=> ( v1 @ ( B @ vplus ) @ ( A @ geq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(216,plain,
! [B: $i,A: $i] :
( ( v1 @ ( B @ vplus ) @ ( A @ geq ) )
| ~ ( B @ ( A @ greater ) ) ),
inference(cnf,[status(esa)],[215]) ).
thf(67,plain,
! [A: $i] :
( ( v1 @ ( A @ vplus ) )
= ( A @ vsucc ) ),
inference(cnfConj,[status(thm)],[65]) ).
thf(69,plain,
! [A: $i] :
( ( v1 @ ( A @ vplus ) )
= ( A @ vsucc ) ),
inference(lifteq,[status(thm)],[67]) ).
thf(70,plain,
! [A: $i] :
( ( v1 @ ( A @ vplus ) )
= ( A @ vsucc ) ),
inference(simp,[status(thm)],[69]) ).
thf(8252,plain,
! [B: $i,A: $i] :
( ( B @ vsucc @ ( A @ geq ) )
| ~ ( B @ ( A @ greater ) ) ),
inference(rewrite,[status(thm)],[216,70]) ).
thf(31020,plain,
! [B: $i,A: $i] :
( ( ( vd480 @ ( vd481 @ vskolem9 ) @ ( vd481 @ vsucc @ greater ) )
!= ( B @ ( A @ greater ) ) )
| ( B @ vsucc @ ( A @ geq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[29650,8252]) ).
thf(31021,plain,
! [B: $i,A: $i] :
( ( ( vd480 @ ( vd481 @ vskolem9 ) @ ( vd481 @ vsucc @ greater ) )
!= ( B @ ( A @ greater ) ) )
| ( B @ vsucc @ ( A @ geq ) ) ),
inference(simp,[status(thm)],[31020]) ).
thf(31022,plain,
vd480 @ ( vd481 @ vskolem9 ) @ vsucc @ ( vd481 @ vsucc @ geq ),
inference(pattern_uni,[status(thm)],[31021:[bind(A,$thf( vd481 @ vsucc )),bind(B,$thf( vd480 @ ( vd481 @ vskolem9 ) ))]]) ).
thf(102,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ leq ) )
| ~ ( B @ ( A @ geq ) ) ),
inference(cnf,[status(esa)],[101]) ).
thf(34112,plain,
! [B: $i,A: $i] :
( ( ( vd480 @ ( vd481 @ vskolem9 ) @ vsucc @ ( vd481 @ vsucc @ geq ) )
!= ( B @ ( A @ geq ) ) )
| ( A @ ( B @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[31022,102]) ).
thf(34113,plain,
! [B: $i,A: $i] :
( ( ( vd480 @ ( vd481 @ vskolem9 ) @ vsucc @ ( vd481 @ vsucc @ geq ) )
!= ( B @ ( A @ geq ) ) )
| ( A @ ( B @ leq ) ) ),
inference(simp,[status(thm)],[34112]) ).
thf(34114,plain,
vd481 @ vsucc @ ( vd480 @ ( vd481 @ vskolem9 ) @ vsucc @ leq ),
inference(pattern_uni,[status(thm)],[34113:[bind(A,$thf( vd481 @ vsucc )),bind(B,$thf( vd480 @ ( vd481 @ vskolem9 ) @ vsucc ))]]) ).
thf(26548,plain,
! [B: $i,A: $i] :
( ( ( vd480 @ ( vd481 @ vskolem9 ) @ ( vd480 @ vplus ) )
!= ( B @ ( A @ vplus ) ) )
| ( vd481 @ vsucc @ ( A @ less ) ) ),
inference(paramod_ordered,[status(thm)],[9644,394]) ).
thf(26549,plain,
vd481 @ vsucc @ ( vd480 @ less ),
inference(pattern_uni,[status(thm)],[26548:[bind(A,$thf( vd480 )),bind(B,$thf( vd480 @ ( vd481 @ vskolem9 ) ))]]) ).
thf(16,axiom,
! [A: $i,B: $i] :
( ( ( A @ vsucc )
= ( B @ vsucc ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(antec(axiom(3)), imp(antec(axiom(3))))') ).
thf(113,plain,
! [A: $i,B: $i] :
( ( ( A @ vsucc )
= ( B @ vsucc ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(114,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ vsucc )
!= ( B @ vsucc ) ) ),
inference(cnf,[status(esa)],[113]) ).
thf(115,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ vsucc )
!= ( B @ vsucc ) ) ),
inference(lifteq,[status(thm)],[114]) ).
thf(25,axiom,
! [A: $i,B: $i] :
( B
!= ( B @ ( A @ vplus ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(73, 0), 0)') ).
thf(149,plain,
! [A: $i,B: $i] :
( B
!= ( B @ ( A @ vplus ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(150,plain,
~ ? [A: $i,B: $i] :
( B
= ( B @ ( A @ vplus ) ) ),
inference(miniscope,[status(thm)],[149]) ).
thf(151,plain,
! [B: $i,A: $i] :
( B
!= ( B @ ( A @ vplus ) ) ),
inference(cnf,[status(esa)],[150]) ).
thf(152,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ vplus ) )
!= B ),
inference(lifteq,[status(thm)],[151]) ).
thf(380,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ vsucc @ ( A @ vplus ) )
!= ( D @ ( C @ vplus ) ) )
| ( ( B @ ( A @ vplus ) @ vsucc )
!= D ) ),
inference(paramod_ordered,[status(thm)],[68,152]) ).
thf(381,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ vplus ) @ vsucc )
!= ( B @ vsucc ) ),
inference(pattern_uni,[status(thm)],[380:[bind(A,$thf( A )),bind(B,$thf( E )),bind(C,$thf( A )),bind(D,$thf( E @ vsucc ))]]) ).
thf(382,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ vplus ) @ vsucc )
!= ( B @ vsucc ) ),
inference(simp,[status(thm)],[381]) ).
thf(25606,plain,
! [B: $i,A: $i] :
( ( ( vd480 @ ( vd481 @ vskolem9 ) @ ( vd480 @ vplus ) )
!= ( B @ ( A @ vplus ) ) )
| ( ( vd481 @ vsucc )
!= ( B @ vsucc ) ) ),
inference(paramod_ordered,[status(thm)],[9644,382]) ).
thf(25607,plain,
( ( vd480 @ ( vd481 @ vskolem9 ) @ vsucc )
!= ( vd481 @ vsucc ) ),
inference(pattern_uni,[status(thm)],[25606:[bind(A,$thf( vd480 )),bind(B,$thf( vd480 @ ( vd481 @ vskolem9 ) ))]]) ).
thf(31,axiom,
! [A: $i] :
( ( A @ ( v1 @ vplus ) )
= ( A @ vsucc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(43, 0), 0)') ).
thf(175,plain,
! [A: $i] :
( ( A @ ( v1 @ vplus ) )
= ( A @ vsucc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(176,plain,
! [A: $i] :
( ( A @ ( v1 @ vplus ) )
= ( A @ vsucc ) ),
inference(cnf,[status(esa)],[175]) ).
thf(177,plain,
! [A: $i] :
( ( A @ ( v1 @ vplus ) )
= ( A @ vsucc ) ),
inference(lifteq,[status(thm)],[176]) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ~ ? [C: $i] :
( B
= ( C @ ( A @ vplus ) ) )
| ~ ? [C: $i] :
( A
= ( C @ ( B @ vplus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(88), 0), 2)') ).
thf(78,plain,
! [A: $i,B: $i] :
( ~ ? [C: $i] :
( B
= ( C @ ( A @ vplus ) ) )
| ~ ? [C: $i] :
( A
= ( C @ ( B @ vplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(79,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B
!= ( D @ ( A @ vplus ) ) )
| ( A
!= ( C @ ( B @ vplus ) ) ) ),
inference(cnf,[status(esa)],[78]) ).
thf(80,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B
!= ( D @ ( A @ vplus ) ) )
| ( A
!= ( C @ ( B @ vplus ) ) ) ),
inference(lifteq,[status(thm)],[79]) ).
thf(81,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ vplus ) @ vplus ) )
!= A ),
inference(simp,[status(thm)],[80]) ).
thf(524,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( v1 @ vplus ) )
!= ( D @ ( C @ ( B @ vplus ) @ vplus ) ) )
| ( ( A @ vsucc )
!= B ) ),
inference(paramod_ordered,[status(thm)],[177,81]) ).
thf(532,plain,
! [C: $i,B: $i,A: $i] :
( ( C != A )
| ( ( B @ ( A @ vsucc @ vplus ) )
!= v1 ) ),
inference(simp,[status(thm)],[524]) ).
thf(538,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ vsucc @ vplus ) )
!= v1 ),
inference(simp,[status(thm)],[532]) ).
thf(623,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ vplus ) )
!= ( D @ ( C @ vsucc @ vplus ) ) )
| ( ( B @ ( A @ vplus ) )
!= v1 ) ),
inference(paramod_ordered,[status(thm)],[77,538]) ).
thf(624,plain,
! [B: $i,A: $i] :
( ( B @ vsucc @ ( A @ vplus ) )
!= v1 ),
inference(pattern_uni,[status(thm)],[623:[bind(A,$thf( A )),bind(B,$thf( E @ vsucc )),bind(C,$thf( E )),bind(D,$thf( A ))]]) ).
thf(631,plain,
! [B: $i,A: $i] :
( ( B @ vsucc @ ( A @ vplus ) )
!= v1 ),
inference(simp,[status(thm)],[624]) ).
thf(683,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ vplus ) @ vsucc )
!= v1 ),
inference(rewrite,[status(thm)],[631,68]) ).
thf(13,axiom,
! [A: $i] :
( ( A != v1 )
=> ( A
= ( A @ vskolem2 @ vsucc ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(20, 0), 0)') ).
thf(98,plain,
! [A: $i] :
( ( A != v1 )
=> ( A
= ( A @ vskolem2 @ vsucc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(99,plain,
! [A: $i] :
( ( A
= ( A @ vskolem2 @ vsucc ) )
| ( A = v1 ) ),
inference(cnf,[status(esa)],[98]) ).
thf(100,plain,
! [A: $i] :
( ( ( A @ vskolem2 @ vsucc )
= A )
| ( A = v1 ) ),
inference(lifteq,[status(thm)],[99]) ).
thf(389,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( v1 @ vplus ) )
!= ( C @ ( B @ vplus ) ) )
| ( A @ vsucc @ ( B @ less ) ) ),
inference(paramod_ordered,[status(thm)],[177,160]) ).
thf(390,plain,
! [A: $i] : ( A @ vsucc @ ( v1 @ less ) ),
inference(pattern_uni,[status(thm)],[389:[bind(A,$thf( A )),bind(B,$thf( v1 )),bind(C,$thf( A ))]]) ).
thf(1416,plain,
! [B: $i,A: $i] :
( ( ( A @ vskolem2 @ vsucc )
!= ( B @ vsucc ) )
| ( A @ ( v1 @ less ) )
| ( A = v1 ) ),
inference(paramod_ordered,[status(thm)],[100,390]) ).
thf(1417,plain,
! [A: $i] :
( ( A @ ( v1 @ less ) )
| ( A = v1 ) ),
inference(pattern_uni,[status(thm)],[1416:[bind(A,$thf( C )),bind(B,$thf( C @ vskolem2 ))]]) ).
thf(1448,plain,
! [A: $i] :
( ( A @ ( v1 @ less ) )
| ( A = v1 ) ),
inference(simp,[status(thm)],[1417]) ).
thf(40,axiom,
! [A: $i,B: $i] :
( ( ( v1 @ ( A @ vmul ) )
= A )
& ( ( B @ vsucc @ ( A @ vmul ) )
= ( A @ ( B @ ( A @ vmul ) @ vplus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(conseq(axiom(3)), 32), and(holds(definiens(249), 399, 0), holds(definiens(249), 398, 0)))') ).
thf(207,plain,
! [A: $i,B: $i] :
( ( ( v1 @ ( A @ vmul ) )
= A )
& ( ( B @ vsucc @ ( A @ vmul ) )
= ( A @ ( B @ ( A @ vmul ) @ vplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(208,plain,
( ! [A: $i] :
( ( v1 @ ( A @ vmul ) )
= A )
& ! [A: $i,B: $i] :
( ( B @ vsucc @ ( A @ vmul ) )
= ( A @ ( B @ ( A @ vmul ) @ vplus ) ) ) ),
inference(miniscope,[status(thm)],[207]) ).
thf(209,plain,
! [C: $i,B: $i,A: $i] :
( ( ( v1 @ ( C @ vmul ) )
= C )
& ( ( B @ vsucc @ ( A @ vmul ) )
= ( A @ ( B @ ( A @ vmul ) @ vplus ) ) ) ),
inference(cnf,[status(esa)],[208]) ).
thf(211,plain,
! [A: $i] :
( ( v1 @ ( A @ vmul ) )
= A ),
inference(cnfConj,[status(thm)],[209]) ).
thf(213,plain,
! [A: $i] :
( ( v1 @ ( A @ vmul ) )
= A ),
inference(lifteq,[status(thm)],[211]) ).
thf(214,plain,
! [A: $i] :
( ( v1 @ ( A @ vmul ) )
= A ),
inference(simp,[status(thm)],[213]) ).
thf(271,plain,
( ( ( vd469 @ ( vd480 @ vmul ) @ ( vd469 @ ( vd481 @ vmul ) @ greater ) )
!= ( vd480 @ ( vd481 @ greater ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[217,60]) ).
thf(272,plain,
( ( vd469 @ ( vd480 @ vmul ) @ ( vd469 @ ( vd481 @ vmul ) @ greater ) )
!= ( vd480 @ ( vd481 @ greater ) ) ),
inference(simp,[status(thm)],[271]) ).
thf(273,plain,
( ( ( vd469 @ ( vd480 @ vmul ) )
!= vd480 )
| ( ( vd469 @ ( vd481 @ vmul ) )
!= vd481 ) ),
inference(simp,[status(thm)],[272]) ).
thf(299,plain,
! [A: $i] :
( ( ( v1 @ ( A @ vmul ) )
!= ( vd469 @ ( vd481 @ vmul ) ) )
| ( ( vd469 @ ( vd480 @ vmul ) )
!= vd480 )
| ( A != vd481 ) ),
inference(paramod_ordered,[status(thm)],[214,273]) ).
thf(304,plain,
( ( v1 != vd469 )
| ( vd481 != vd481 )
| ( ( vd469 @ ( vd480 @ vmul ) )
!= vd480 ) ),
inference(simp,[status(thm)],[299]) ).
thf(307,plain,
( ( v1 != vd469 )
| ( ( vd469 @ ( vd480 @ vmul ) )
!= vd480 ) ),
inference(simp,[status(thm)],[304]) ).
thf(311,plain,
! [A: $i] :
( ( ( v1 @ ( A @ vmul ) )
!= ( vd469 @ ( vd480 @ vmul ) ) )
| ( v1 != vd469 )
| ( A != vd480 ) ),
inference(paramod_ordered,[status(thm)],[214,307]) ).
thf(313,plain,
( ( v1 != vd469 )
| ( vd480 != vd480 )
| ( v1 != vd469 ) ),
inference(simp,[status(thm)],[311]) ).
thf(314,plain,
v1 != vd469,
inference(simp,[status(thm)],[313]) ).
thf(1838,plain,
! [A: $i] :
( ( v1 != v1 )
| ( A != vd469 )
| ( A @ ( v1 @ less ) ) ),
inference(paramod_ordered,[status(thm)],[1448,314]) ).
thf(1839,plain,
! [A: $i] :
( ( A != vd469 )
| ( A @ ( v1 @ less ) ) ),
inference(pattern_uni,[status(thm)],[1838:[]]) ).
thf(1975,plain,
vd469 @ ( v1 @ less ),
inference(simp,[status(thm)],[1839]) ).
thf(4947,plain,
! [B: $i,A: $i] :
( ( ( vd469 @ ( v1 @ less ) )
!= ( A @ ( B @ less ) ) )
| ~ $true
| ( ( A @ ( B @ sk7 ) @ ( B @ vplus ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[1975,158]) ).
thf(4948,plain,
! [B: $i,A: $i] :
( ( ( vd469 @ ( v1 @ less ) )
!= ( A @ ( B @ less ) ) )
| ( ( A @ ( B @ sk7 ) @ ( B @ vplus ) )
= A ) ),
inference(simp,[status(thm)],[4947]) ).
thf(4949,plain,
( ( vd469 @ ( v1 @ sk7 ) @ ( v1 @ vplus ) )
= vd469 ),
inference(pattern_uni,[status(thm)],[4948:[bind(A,$thf( vd469 )),bind(B,$thf( v1 ))]]) ).
thf(5150,plain,
( ( vd469 @ ( v1 @ sk7 ) @ vsucc )
= vd469 ),
inference(rewrite,[status(thm)],[4949,177]) ).
thf(621,plain,
! [C: $i,B: $i,A: $i] :
( ( ( v1 @ ( A @ vplus ) )
!= ( C @ ( B @ vsucc @ vplus ) ) )
| ( ( A @ vsucc )
!= v1 ) ),
inference(paramod_ordered,[status(thm)],[70,538]) ).
thf(622,plain,
! [A: $i] :
( ( A @ vsucc @ vsucc )
!= v1 ),
inference(pattern_uni,[status(thm)],[621:[bind(A,$thf( D @ vsucc )),bind(B,$thf( D )),bind(C,$thf( v1 ))]]) ).
thf(635,plain,
! [A: $i] :
( ( A @ vsucc @ vsucc )
!= v1 ),
inference(simp,[status(thm)],[622]) ).
thf(5241,plain,
! [A: $i] :
( ( ( vd469 @ ( v1 @ sk7 ) @ vsucc )
!= ( A @ vsucc ) )
| ( ( vd469 @ vsucc )
!= v1 ) ),
inference(paramod_ordered,[status(thm)],[5150,635]) ).
thf(5242,plain,
( ( vd469 @ vsucc )
!= v1 ),
inference(pattern_uni,[status(thm)],[5241:[bind(A,$thf( vd469 @ ( v1 @ sk7 ) ))]]) ).
thf(18,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ vplus ) )
= ( C @ ( B @ vplus ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(202), 0), 1)') ).
thf(123,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ vplus ) )
= ( C @ ( B @ vplus ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(124,plain,
! [A: $i,B: $i] :
( ? [C: $i] :
( ( C @ ( A @ vplus ) )
= ( C @ ( B @ vplus ) ) )
=> ( A = B ) ),
inference(miniscope,[status(thm)],[123]) ).
thf(125,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ( ( C @ ( A @ vplus ) )
!= ( C @ ( B @ vplus ) ) ) ),
inference(cnf,[status(esa)],[124]) ).
thf(126,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ( ( C @ ( A @ vplus ) )
!= ( C @ ( B @ vplus ) ) ) ),
inference(lifteq,[status(thm)],[125]) ).
thf(127,plain,
? [A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ vplus ) @ ( C @ A ) )
= B ),
inference(detectInverse,[status(thm)],[126]) ).
thf(128,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ vplus ) @ ( B @ sk5 ) )
= A ),
inference(cnf,[status(esa)],[127]) ).
thf(3959,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ vplus ) @ ( B @ sk5 ) )
= A ),
inference(lifteq,[status(thm)],[128]) ).
thf(53,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ vplus ) @ ( C @ ( A @ vplus ) @ greater ) )
=> ( B @ ( A @ greater ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(202), 0), 2)') ).
thf(245,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ vplus ) @ ( C @ ( A @ vplus ) @ greater ) )
=> ( B @ ( A @ greater ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(246,plain,
! [A: $i,B: $i] :
( ? [C: $i] : ( C @ ( B @ vplus ) @ ( C @ ( A @ vplus ) @ greater ) )
=> ( B @ ( A @ greater ) ) ),
inference(miniscope,[status(thm)],[245]) ).
thf(247,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ greater ) )
| ~ ( C @ ( B @ vplus ) @ ( C @ ( A @ vplus ) @ greater ) ) ),
inference(cnf,[status(esa)],[246]) ).
thf(59,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( B @ ( A @ greater ) )
& ( D @ ( C @ geq ) ) )
| ( ( B @ ( A @ geq ) )
& ( D @ ( C @ greater ) ) ) )
=> ( D @ ( B @ vplus ) @ ( C @ ( A @ vplus ) @ greater ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(216), 0), 0)') ).
thf(267,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( B @ ( A @ greater ) )
& ( D @ ( C @ geq ) ) )
| ( ( B @ ( A @ geq ) )
& ( D @ ( C @ greater ) ) ) )
=> ( D @ ( B @ vplus ) @ ( C @ ( A @ vplus ) @ greater ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(268,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( B @ vplus ) @ ( C @ ( A @ vplus ) @ greater ) )
| ~ ( B @ ( A @ greater ) )
| ~ ( D @ ( C @ geq ) ) )
& ( ( D @ ( B @ vplus ) @ ( C @ ( A @ vplus ) @ greater ) )
| ~ ( B @ ( A @ geq ) )
| ~ ( D @ ( C @ greater ) ) ) ),
inference(cnf,[status(esa)],[267]) ).
thf(269,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ vplus ) @ ( C @ ( A @ vplus ) @ greater ) )
| ~ ( B @ ( A @ geq ) )
| ~ ( D @ ( C @ greater ) ) ),
inference(cnfConj,[status(thm)],[268]) ).
thf(692,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ vsucc @ ( A @ vplus ) )
!= ( D @ ( C @ vplus ) ) )
| ( ( B @ ( A @ vplus ) @ vsucc @ vsucc )
!= v1 ) ),
inference(paramod_ordered,[status(thm)],[68,683]) ).
thf(693,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ vplus ) @ vsucc @ vsucc )
!= v1 ),
inference(pattern_uni,[status(thm)],[692:[bind(A,$thf( A )),bind(B,$thf( E )),bind(C,$thf( A )),bind(D,$thf( E @ vsucc ))]]) ).
thf(694,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ vplus ) @ vsucc @ vsucc )
!= v1 ),
inference(simp,[status(thm)],[693]) ).
thf(7367,plain,
! [B: $i,A: $i] :
( ( ( vd481 @ ( vd480 @ sk7 ) @ ( vd480 @ vplus ) )
!= ( B @ ( A @ vplus ) ) )
| ( ( vd481 @ vsucc @ vsucc )
!= v1 ) ),
inference(paramod_ordered,[status(thm)],[5038,694]) ).
thf(7368,plain,
( ( vd481 @ vsucc @ vsucc )
!= v1 ),
inference(pattern_uni,[status(thm)],[7367:[bind(A,$thf( vd480 )),bind(B,$thf( vd481 @ ( vd480 @ sk7 ) ))]]) ).
thf(2063,plain,
! [A: $i] :
( ( v1 != v1 )
| ( vd469 @ ( A @ less ) )
| ( A @ ( v1 @ less ) ) ),
inference(paramod_ordered,[status(thm)],[1448,1975]) ).
thf(2064,plain,
! [A: $i] :
( ( vd469 @ ( A @ less ) )
| ( A @ ( v1 @ less ) ) ),
inference(pattern_uni,[status(thm)],[2063:[]]) ).
thf(16234,plain,
! [B: $i,A: $i] :
( ( ( vd480 @ ( vd481 @ greater ) )
!= ( B @ ( A @ greater ) ) )
| ~ ( B @ ( A @ less ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[217,249]) ).
thf(16235,plain,
! [B: $i,A: $i] :
( ( ( vd480 @ ( vd481 @ greater ) )
!= ( B @ ( A @ greater ) ) )
| ~ ( B @ ( A @ less ) ) ),
inference(simp,[status(thm)],[16234]) ).
thf(16236,plain,
~ ( vd480 @ ( vd481 @ less ) ),
inference(pattern_uni,[status(thm)],[16235:[bind(A,$thf( vd481 )),bind(B,$thf( vd480 ))]]) ).
thf(16419,plain,
! [A: $i] :
( ( ( A @ ( v1 @ less ) )
!= ( vd480 @ ( vd481 @ less ) ) )
| ~ $true
| ( vd469 @ ( A @ less ) ) ),
inference(paramod_ordered,[status(thm)],[2064,16236]) ).
thf(16420,plain,
! [A: $i] :
( ( ( A @ ( v1 @ less ) )
!= ( vd480 @ ( vd481 @ less ) ) )
| ( vd469 @ ( A @ less ) ) ),
inference(simp,[status(thm)],[16419]) ).
thf(16441,plain,
! [A: $i] :
( ( A != vd480 )
| ( v1 != vd481 )
| ( vd469 @ ( A @ less ) ) ),
inference(simp,[status(thm)],[16420]) ).
thf(16473,plain,
( ( v1 != vd481 )
| ( vd469 @ ( vd480 @ less ) ) ),
inference(simp,[status(thm)],[16441]) ).
thf(22159,plain,
! [B: $i,A: $i] :
( ( ( vd469 @ ( vd480 @ less ) )
!= ( A @ ( B @ less ) ) )
| ( A @ ( B @ leq ) )
| ~ $true
| ( v1 != vd481 ) ),
inference(paramod_ordered,[status(thm)],[16473,110]) ).
thf(22160,plain,
! [B: $i,A: $i] :
( ( ( vd469 @ ( vd480 @ less ) )
!= ( A @ ( B @ less ) ) )
| ( A @ ( B @ leq ) )
| ( v1 != vd481 ) ),
inference(simp,[status(thm)],[22159]) ).
thf(22161,plain,
( ( vd469 @ ( vd480 @ leq ) )
| ( v1 != vd481 ) ),
inference(pattern_uni,[status(thm)],[22160:[bind(A,$thf( vd469 )),bind(B,$thf( vd480 ))]]) ).
thf(25573,plain,
! [A: $i] :
( ( v1 != v1 )
| ( vd469 @ ( vd480 @ leq ) )
| ( A != vd481 )
| ( A @ ( v1 @ less ) ) ),
inference(paramod_ordered,[status(thm)],[1448,22161]) ).
thf(25574,plain,
! [A: $i] :
( ( vd469 @ ( vd480 @ leq ) )
| ( A != vd481 )
| ( A @ ( v1 @ less ) ) ),
inference(pattern_uni,[status(thm)],[25573:[]]) ).
thf(25596,plain,
( ( vd469 @ ( vd480 @ leq ) )
| ( vd481 @ ( v1 @ less ) ) ),
inference(simp,[status(thm)],[25574]) ).
thf(29209,plain,
! [B: $i,A: $i] :
( ( ( vd481 @ ( v1 @ less ) )
!= ( B @ ( A @ less ) ) )
| ( A @ ( B @ greater ) )
| ~ $true
| ( vd469 @ ( vd480 @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[25596,232]) ).
thf(29210,plain,
! [B: $i,A: $i] :
( ( ( vd481 @ ( v1 @ less ) )
!= ( B @ ( A @ less ) ) )
| ( A @ ( B @ greater ) )
| ( vd469 @ ( vd480 @ leq ) ) ),
inference(simp,[status(thm)],[29209]) ).
thf(29211,plain,
( ( v1 @ ( vd481 @ greater ) )
| ( vd469 @ ( vd480 @ leq ) ) ),
inference(pattern_uni,[status(thm)],[29210:[bind(A,$thf( v1 )),bind(B,$thf( vd481 ))]]) ).
thf(32272,plain,
! [B: $i,A: $i] :
( ( ( vd469 @ ( vd480 @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( A @ ( B @ geq ) )
| ~ $true
| ( v1 @ ( vd481 @ greater ) ) ),
inference(paramod_ordered,[status(thm)],[29211,97]) ).
thf(32273,plain,
! [B: $i,A: $i] :
( ( ( vd469 @ ( vd480 @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( A @ ( B @ geq ) )
| ( v1 @ ( vd481 @ greater ) ) ),
inference(simp,[status(thm)],[32272]) ).
thf(32274,plain,
( ( vd480 @ ( vd469 @ geq ) )
| ( v1 @ ( vd481 @ greater ) ) ),
inference(pattern_uni,[status(thm)],[32273:[bind(A,$thf( vd480 )),bind(B,$thf( vd469 ))]]) ).
thf(22,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ vsucc @ vplus ) )
= ( B @ ( A @ vplus ) @ vsucc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(52, 0), 0)') ).
thf(140,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ vsucc @ vplus ) )
= ( B @ ( A @ vplus ) @ vsucc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(141,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ vsucc @ vplus ) )
= ( B @ ( A @ vplus ) @ vsucc ) ),
inference(cnf,[status(esa)],[140]) ).
thf(142,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ vsucc @ vplus ) )
= ( B @ ( A @ vplus ) @ vsucc ) ),
inference(lifteq,[status(thm)],[141]) ).
thf(43,axiom,
! [A: $i] :
( ( A @ ( v1 @ vmul ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(253, 0), 0)') ).
thf(218,plain,
! [A: $i] :
( ( A @ ( v1 @ vmul ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(219,plain,
! [A: $i] :
( ( A @ ( v1 @ vmul ) )
= A ),
inference(cnf,[status(esa)],[218]) ).
thf(220,plain,
! [A: $i] :
( ( A @ ( v1 @ vmul ) )
= A ),
inference(lifteq,[status(thm)],[219]) ).
thf(319,plain,
! [A: $i] :
( ( ( A @ ( v1 @ vmul ) )
!= ( vd469 @ ( vd481 @ vmul ) ) )
| ~ ( vd469 @ ( vd480 @ vmul ) @ ( A @ greater ) ) ),
inference(paramod_ordered,[status(thm)],[220,60]) ).
thf(326,plain,
! [A: $i] :
( ( A != vd469 )
| ( v1 != vd481 )
| ~ ( vd469 @ ( vd480 @ vmul ) @ ( A @ greater ) ) ),
inference(simp,[status(thm)],[319]) ).
thf(330,plain,
( ( v1 != vd481 )
| ~ ( vd469 @ ( vd480 @ vmul ) @ ( vd469 @ greater ) ) ),
inference(simp,[status(thm)],[326]) ).
thf(776,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ ( A @ vplus ) @ greater ) )
!= ( vd469 @ ( vd480 @ vmul ) @ ( vd469 @ greater ) ) )
| ( v1 != vd481 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[481,330]) ).
thf(777,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ ( A @ vplus ) @ greater ) )
!= ( vd469 @ ( vd480 @ vmul ) @ ( vd469 @ greater ) ) )
| ( v1 != vd481 ) ),
inference(simp,[status(thm)],[776]) ).
thf(792,plain,
! [B: $i,A: $i] :
( ( B
!= ( vd469 @ ( vd480 @ vmul ) ) )
| ( ( B @ ( A @ vplus ) )
!= vd469 )
| ( v1 != vd481 ) ),
inference(simp,[status(thm)],[777]) ).
thf(797,plain,
! [A: $i] :
( ( ( vd469 @ ( vd480 @ vmul ) @ ( A @ vplus ) )
!= vd469 )
| ( v1 != vd481 ) ),
inference(simp,[status(thm)],[792]) ).
thf(20,axiom,
! [A: $i,B: $i] :
( ( A != B )
=> ( ( A @ vsucc )
!= ( B @ vsucc ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(6, 0), 0)') ).
thf(131,plain,
! [A: $i,B: $i] :
( ( A != B )
=> ( ( A @ vsucc )
!= ( B @ vsucc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(132,plain,
! [B: $i,A: $i] :
( ( ( A @ vsucc )
!= ( B @ vsucc ) )
| ( A = B ) ),
inference(cnf,[status(esa)],[131]) ).
thf(133,plain,
! [B: $i,A: $i] :
( ( ( A @ vsucc )
!= ( B @ vsucc ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[132]) ).
thf(134,plain,
? [A: $i > $i] :
! [B: $i] :
( ( B @ vsucc @ A )
= B ),
inference(detectInverse,[status(thm)],[133]) ).
thf(135,plain,
! [A: $i] :
( ( A @ vsucc @ sk6 )
= A ),
inference(cnf,[status(esa)],[134]) ).
thf(338,plain,
! [A: $i] :
( ( A @ vsucc @ sk6 )
= A ),
inference(lifteq,[status(thm)],[135]) ).
thf(5210,plain,
! [A: $i] :
( ( ( vd469 @ ( v1 @ sk7 ) @ vsucc )
!= ( A @ vsucc ) )
| ( ( vd469 @ sk6 )
= A ) ),
inference(paramod_ordered,[status(thm)],[5150,338]) ).
thf(5211,plain,
( ( vd469 @ ( v1 @ sk7 ) )
= ( vd469 @ sk6 ) ),
inference(pattern_uni,[status(thm)],[5210:[bind(A,$thf( vd469 @ ( v1 @ sk7 ) ))]]) ).
thf(5679,plain,
( ( vd469 @ sk6 @ vsucc )
= vd469 ),
inference(rewrite,[status(thm)],[5150,5211]) ).
thf(116,plain,
? [A: $i > $i] :
! [B: $i] :
( ( B @ vsucc @ A )
= B ),
inference(detectInverse,[status(thm)],[115]) ).
thf(117,plain,
! [A: $i] :
( ( A @ vsucc @ sk4 )
= A ),
inference(cnf,[status(esa)],[116]) ).
thf(337,plain,
! [A: $i] :
( ( A @ vsucc @ sk4 )
= A ),
inference(lifteq,[status(thm)],[117]) ).
thf(5878,plain,
! [A: $i] :
( ( ( vd469 @ sk6 @ vsucc )
!= ( A @ vsucc ) )
| ( ( vd469 @ sk4 )
= A ) ),
inference(paramod_ordered,[status(thm)],[5679,337]) ).
thf(5879,plain,
( ( vd469 @ sk6 )
= ( vd469 @ sk4 ) ),
inference(pattern_uni,[status(thm)],[5878:[bind(A,$thf( vd469 @ sk6 ))]]) ).
thf(6180,plain,
( ( vd469 @ sk4 @ vsucc )
= vd469 ),
inference(rewrite,[status(thm)],[5679,5879]) ).
thf(8256,plain,
! [B: $i,A: $i] :
( ( ( vd480 @ ( vd481 @ greater ) )
!= ( B @ ( A @ greater ) ) )
| ( B @ vsucc @ ( A @ geq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[217,8252]) ).
thf(8257,plain,
! [B: $i,A: $i] :
( ( ( vd480 @ ( vd481 @ greater ) )
!= ( B @ ( A @ greater ) ) )
| ( B @ vsucc @ ( A @ geq ) ) ),
inference(simp,[status(thm)],[8256]) ).
thf(8258,plain,
vd480 @ vsucc @ ( vd481 @ geq ),
inference(pattern_uni,[status(thm)],[8257:[bind(A,$thf( vd481 )),bind(B,$thf( vd480 ))]]) ).
thf(8336,plain,
( ( ( vd469 @ sk4 @ vsucc )
!= ( vd480 @ vsucc ) )
| ( vd469 @ ( vd481 @ geq ) ) ),
inference(paramod_ordered,[status(thm)],[6180,8258]) ).
thf(8342,plain,
( ( ( vd469 @ sk4 )
!= vd480 )
| ( vd469 @ ( vd481 @ geq ) ) ),
inference(simp,[status(thm)],[8336]) ).
thf(411,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ vplus ) )
!= ( D @ ( C @ vplus ) ) )
| ( B @ ( A @ vplus ) @ ( C @ less ) ) ),
inference(paramod_ordered,[status(thm)],[77,160]) ).
thf(412,plain,
! [B: $i,A: $i] : ( B @ ( A @ vplus ) @ ( B @ less ) ),
inference(pattern_uni,[status(thm)],[411:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A ))]]) ).
thf(7363,plain,
! [B: $i,A: $i] :
( ( ( vd481 @ ( vd480 @ sk7 ) @ ( vd480 @ vplus ) )
!= ( B @ ( A @ vplus ) ) )
| ( vd481 @ ( B @ less ) ) ),
inference(paramod_ordered,[status(thm)],[5038,412]) ).
thf(7364,plain,
vd481 @ ( vd481 @ ( vd480 @ sk7 ) @ less ),
inference(pattern_uni,[status(thm)],[7363:[bind(A,$thf( vd480 )),bind(B,$thf( vd481 @ ( vd480 @ sk7 ) ))]]) ).
thf(9090,plain,
vd481 @ ( vd481 @ ( vd480 @ sk1 ) @ less ),
inference(rewrite,[status(thm)],[7364,7425]) ).
thf(492,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( v1 @ vplus ) )
!= ( C @ ( B @ vplus ) ) )
| ( B @ ( A @ vsucc @ greater ) ) ),
inference(paramod_ordered,[status(thm)],[177,187]) ).
thf(493,plain,
! [A: $i] : ( v1 @ ( A @ vsucc @ greater ) ),
inference(pattern_uni,[status(thm)],[492:[bind(A,$thf( A )),bind(B,$thf( v1 )),bind(C,$thf( A ))]]) ).
thf(5168,plain,
! [A: $i] :
( ( ( vd469 @ ( v1 @ sk7 ) @ vsucc )
!= ( A @ vsucc ) )
| ( v1 @ ( vd469 @ greater ) ) ),
inference(paramod_ordered,[status(thm)],[5150,493]) ).
thf(5169,plain,
v1 @ ( vd469 @ greater ),
inference(pattern_uni,[status(thm)],[5168:[bind(A,$thf( vd469 @ ( v1 @ sk7 ) ))]]) ).
thf(16249,plain,
! [B: $i,A: $i] :
( ( ( v1 @ ( vd469 @ greater ) )
!= ( B @ ( A @ greater ) ) )
| ~ ( B @ ( A @ less ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5169,249]) ).
thf(16250,plain,
! [B: $i,A: $i] :
( ( ( v1 @ ( vd469 @ greater ) )
!= ( B @ ( A @ greater ) ) )
| ~ ( B @ ( A @ less ) ) ),
inference(simp,[status(thm)],[16249]) ).
thf(16251,plain,
~ ( v1 @ ( vd469 @ less ) ),
inference(pattern_uni,[status(thm)],[16250:[bind(A,$thf( vd469 )),bind(B,$thf( v1 ))]]) ).
thf(16499,plain,
( ( ( vd481 @ ( vd481 @ ( vd480 @ sk1 ) @ less ) )
!= ( v1 @ ( vd469 @ less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9090,16251]) ).
thf(16500,plain,
( ( vd481 @ ( vd481 @ ( vd480 @ sk1 ) @ less ) )
!= ( v1 @ ( vd469 @ less ) ) ),
inference(simp,[status(thm)],[16499]) ).
thf(16559,plain,
( ( v1 != vd481 )
| ( ( vd481 @ ( vd480 @ sk1 ) )
!= vd469 ) ),
inference(simp,[status(thm)],[16500]) ).
thf(30112,plain,
( ( v1 != vd481 )
| ( ( vd480 @ ( vd481 @ vskolem9 ) )
!= vd469 ) ),
inference(rewrite,[status(thm)],[16559,15611]) ).
thf(628,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ vsucc @ ( A @ vplus ) )
!= ( D @ ( C @ vsucc @ vplus ) ) )
| ( ( B @ ( A @ vplus ) @ vsucc )
!= v1 ) ),
inference(paramod_ordered,[status(thm)],[68,538]) ).
thf(629,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ vsucc @ vplus ) @ vsucc )
!= v1 ),
inference(pattern_uni,[status(thm)],[628:[bind(A,$thf( E @ vsucc )),bind(B,$thf( F )),bind(C,$thf( E )),bind(D,$thf( F @ vsucc ))]]) ).
thf(633,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ vsucc @ vplus ) @ vsucc )
!= v1 ),
inference(simp,[status(thm)],[629]) ).
thf(1030,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ vsucc @ ( A @ vplus ) )
!= ( D @ ( C @ vsucc @ vplus ) ) )
| ( ( B @ ( A @ vplus ) @ vsucc @ vsucc )
!= v1 ) ),
inference(paramod_ordered,[status(thm)],[68,633]) ).
thf(1031,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ vsucc @ vplus ) @ vsucc @ vsucc )
!= v1 ),
inference(pattern_uni,[status(thm)],[1030:[bind(A,$thf( E @ vsucc )),bind(B,$thf( F )),bind(C,$thf( E )),bind(D,$thf( F @ vsucc ))]]) ).
thf(1036,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ vsucc @ vplus ) @ vsucc @ vsucc )
!= v1 ),
inference(simp,[status(thm)],[1031]) ).
thf(1507,plain,
! [C: $i,B: $i,A: $i] :
( ( ( v1 @ ( A @ vplus ) )
!= ( C @ ( B @ vsucc @ vplus ) ) )
| ( ( A @ vsucc @ vsucc @ vsucc )
!= v1 ) ),
inference(paramod_ordered,[status(thm)],[70,1036]) ).
thf(1508,plain,
! [A: $i] :
( ( A @ vsucc @ vsucc @ vsucc @ vsucc )
!= v1 ),
inference(pattern_uni,[status(thm)],[1507:[bind(A,$thf( D @ vsucc )),bind(B,$thf( D )),bind(C,$thf( v1 ))]]) ).
thf(1530,plain,
! [A: $i] :
( ( A @ vsucc @ vsucc @ vsucc @ vsucc )
!= v1 ),
inference(simp,[status(thm)],[1508]) ).
thf(5191,plain,
! [A: $i] :
( ( ( vd469 @ ( v1 @ sk7 ) @ vsucc )
!= ( A @ vsucc ) )
| ( ( vd469 @ vsucc @ vsucc @ vsucc )
!= v1 ) ),
inference(paramod_ordered,[status(thm)],[5150,1530]) ).
thf(5192,plain,
( ( vd469 @ vsucc @ vsucc @ vsucc )
!= v1 ),
inference(pattern_uni,[status(thm)],[5191:[bind(A,$thf( vd469 @ ( v1 @ sk7 ) ))]]) ).
thf(30,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ vplus ) @ ( C @ ( A @ vplus ) @ less ) )
=> ( B @ ( A @ less ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(202), 0), 0)') ).
thf(172,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ vplus ) @ ( C @ ( A @ vplus ) @ less ) )
=> ( B @ ( A @ less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(173,plain,
! [A: $i,B: $i] :
( ? [C: $i] : ( C @ ( B @ vplus ) @ ( C @ ( A @ vplus ) @ less ) )
=> ( B @ ( A @ less ) ) ),
inference(miniscope,[status(thm)],[172]) ).
thf(174,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ less ) )
| ~ ( C @ ( B @ vplus ) @ ( C @ ( A @ vplus ) @ less ) ) ),
inference(cnf,[status(esa)],[173]) ).
thf(16330,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ vsucc @ ( v1 @ less ) )
!= ( C @ ( B @ less ) ) )
| ~ $true
| ~ ( C @ ( B @ greater ) ) ),
inference(paramod_ordered,[status(thm)],[390,249]) ).
thf(16331,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ vsucc @ ( v1 @ less ) )
!= ( C @ ( B @ less ) ) )
| ~ ( C @ ( B @ greater ) ) ),
inference(simp,[status(thm)],[16330]) ).
thf(16332,plain,
! [A: $i] :
~ ( A @ vsucc @ ( v1 @ greater ) ),
inference(pattern_uni,[status(thm)],[16331:[bind(A,$thf( D )),bind(B,$thf( v1 )),bind(C,$thf( D @ vsucc ))]]) ).
thf(16351,plain,
! [A: $i] :
~ ( A @ vsucc @ ( v1 @ greater ) ),
inference(simp,[status(thm)],[16332]) ).
thf(28,axiom,
! [A: $i] :
( ( A @ vsucc )
!= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(12, 0), 0)') ).
thf(165,plain,
! [A: $i] :
( ( A @ vsucc )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(166,plain,
~ ? [A: $i] :
( ( A @ vsucc )
= A ),
inference(miniscope,[status(thm)],[165]) ).
thf(167,plain,
! [A: $i] :
( ( A @ vsucc )
!= A ),
inference(cnf,[status(esa)],[166]) ).
thf(168,plain,
! [A: $i] :
( ( A @ vsucc )
!= A ),
inference(lifteq,[status(thm)],[167]) ).
thf(5233,plain,
! [A: $i] :
( ( ( vd469 @ ( v1 @ sk7 ) @ vsucc )
!= ( A @ vsucc ) )
| ( vd469 != A ) ),
inference(paramod_ordered,[status(thm)],[5150,168]) ).
thf(5234,plain,
( ( vd469 @ ( v1 @ sk7 ) )
!= vd469 ),
inference(pattern_uni,[status(thm)],[5233:[bind(A,$thf( vd469 @ ( v1 @ sk7 ) ))]]) ).
thf(5681,plain,
( ( vd469 @ sk6 )
!= vd469 ),
inference(rewrite,[status(thm)],[5234,5211]) ).
thf(6182,plain,
( ( vd469 @ sk4 )
!= vd469 ),
inference(rewrite,[status(thm)],[5681,5879]) ).
thf(490,plain,
! [C: $i,B: $i,A: $i] :
( ( ( v1 @ ( A @ vplus ) )
!= ( C @ ( B @ vplus ) ) )
| ( B @ ( A @ vsucc @ greater ) ) ),
inference(paramod_ordered,[status(thm)],[70,187]) ).
thf(491,plain,
! [A: $i] : ( A @ ( A @ vsucc @ greater ) ),
inference(pattern_uni,[status(thm)],[490:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( v1 ))]]) ).
thf(5880,plain,
! [A: $i] :
( ( ( vd469 @ sk6 @ vsucc )
!= ( A @ vsucc ) )
| ( A @ ( vd469 @ greater ) ) ),
inference(paramod_ordered,[status(thm)],[5679,491]) ).
thf(5881,plain,
vd469 @ sk6 @ ( vd469 @ greater ),
inference(pattern_uni,[status(thm)],[5880:[bind(A,$thf( vd469 @ sk6 ))]]) ).
thf(6217,plain,
vd469 @ sk4 @ ( vd469 @ greater ),
inference(rewrite,[status(thm)],[5881,5879]) ).
thf(8287,plain,
! [B: $i,A: $i] :
( ( ( vd469 @ sk4 @ ( vd469 @ greater ) )
!= ( B @ ( A @ greater ) ) )
| ( B @ vsucc @ ( A @ geq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6217,8252]) ).
thf(8288,plain,
! [B: $i,A: $i] :
( ( ( vd469 @ sk4 @ ( vd469 @ greater ) )
!= ( B @ ( A @ greater ) ) )
| ( B @ vsucc @ ( A @ geq ) ) ),
inference(simp,[status(thm)],[8287]) ).
thf(8289,plain,
vd469 @ sk4 @ vsucc @ ( vd469 @ geq ),
inference(pattern_uni,[status(thm)],[8288:[bind(A,$thf( vd469 )),bind(B,$thf( vd469 @ sk4 ))]]) ).
thf(8603,plain,
vd469 @ ( vd469 @ geq ),
inference(rewrite,[status(thm)],[8289,6180]) ).
thf(39,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ greater ) )
<=> ? [C: $i] :
( B
= ( C @ ( A @ vplus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','def(cond(conseq(axiom(3)), 11), 1)') ).
thf(199,plain,
! [A: $i,B: $i] :
( ( ? [C: $i] :
( B
= ( C @ ( A @ vplus ) ) )
=> ( A @ ( B @ greater ) ) )
& ( ( A @ ( B @ greater ) )
=> ? [C: $i] :
( B
= ( C @ ( A @ vplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(200,plain,
( ! [A: $i,B: $i] :
( ? [C: $i] :
( B
= ( C @ ( A @ vplus ) ) )
=> ( A @ ( B @ greater ) ) )
& ! [A: $i,B: $i] :
( ( A @ ( B @ greater ) )
=> ? [C: $i] :
( B
= ( C @ ( A @ vplus ) ) ) ) ),
inference(miniscope,[status(thm)],[199]) ).
thf(201,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( D @ greater ) )
| ( D
!= ( E @ ( C @ vplus ) ) ) )
& ( ( B
= ( A @ ( B @ sk8 ) @ ( A @ vplus ) ) )
| ~ ( A @ ( B @ greater ) ) ) ),
inference(cnf,[status(esa)],[200]) ).
thf(202,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ ( B @ sk8 ) @ ( A @ vplus ) ) )
| ~ ( A @ ( B @ greater ) ) ),
inference(cnfConj,[status(thm)],[201]) ).
thf(204,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ greater ) )
| ( ( A @ ( B @ sk8 ) @ ( A @ vplus ) )
= B ) ),
inference(lifteq,[status(thm)],[202]) ).
thf(7563,plain,
! [B: $i,A: $i] :
( ( ( vd480 @ ( vd481 @ greater ) )
!= ( A @ ( B @ greater ) ) )
| ~ $true
| ( ( A @ ( B @ sk8 ) @ ( A @ vplus ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[217,204]) ).
thf(7564,plain,
! [B: $i,A: $i] :
( ( ( vd480 @ ( vd481 @ greater ) )
!= ( A @ ( B @ greater ) ) )
| ( ( A @ ( B @ sk8 ) @ ( A @ vplus ) )
= B ) ),
inference(simp,[status(thm)],[7563]) ).
thf(7565,plain,
( ( vd480 @ ( vd481 @ sk8 ) @ ( vd480 @ vplus ) )
= vd481 ),
inference(pattern_uni,[status(thm)],[7564:[bind(A,$thf( vd480 )),bind(B,$thf( vd481 ))]]) ).
thf(10283,plain,
! [B: $i,A: $i] :
( ( ( vd480 @ ( vd481 @ sk8 ) @ ( vd480 @ vplus ) )
!= ( B @ ( A @ vplus ) ) )
| ( ( vd481 @ ( A @ sk1 ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[7565,708]) ).
thf(10284,plain,
( ( vd480 @ ( vd481 @ sk8 ) )
= ( vd481 @ ( vd480 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[10283:[bind(A,$thf( vd480 )),bind(B,$thf( vd480 @ ( vd481 @ sk8 ) ))]]) ).
thf(28550,plain,
( ( vd480 @ ( vd481 @ sk8 ) )
= ( vd480 @ ( vd481 @ vskolem9 ) ) ),
inference(rewrite,[status(thm)],[10284,15611]) ).
thf(25610,plain,
! [B: $i,A: $i] :
( ( ( vd480 @ ( vd481 @ ( vd480 @ sk1 ) @ vplus ) )
!= ( B @ ( A @ vplus ) ) )
| ( ( vd481 @ vsucc )
!= ( B @ vsucc ) ) ),
inference(paramod_ordered,[status(thm)],[9096,382]) ).
thf(25611,plain,
( ( vd480 @ vsucc )
!= ( vd481 @ vsucc ) ),
inference(pattern_uni,[status(thm)],[25610:[bind(A,$thf( vd481 @ ( vd480 @ sk1 ) )),bind(B,$thf( vd480 ))]]) ).
thf(34,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ greater ) )
=> ( vd469 @ ( B @ vmul ) @ ( vd469 @ ( B @ ( A @ vskolem9 ) @ vmul ) @ ( vd469 @ ( B @ vmul ) @ vplus ) @ greater ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(302, 0), 0)') ).
thf(184,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ greater ) )
=> ( vd469 @ ( B @ vmul ) @ ( vd469 @ ( B @ ( A @ vskolem9 ) @ vmul ) @ ( vd469 @ ( B @ vmul ) @ vplus ) @ greater ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(494,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ vsucc @ ( A @ vplus ) )
!= ( D @ ( C @ vplus ) ) )
| ( C @ ( B @ ( A @ vplus ) @ vsucc @ greater ) ) ),
inference(paramod_ordered,[status(thm)],[68,187]) ).
thf(495,plain,
! [B: $i,A: $i] : ( A @ ( B @ ( A @ vplus ) @ vsucc @ greater ) ),
inference(pattern_uni,[status(thm)],[494:[bind(A,$thf( A )),bind(B,$thf( E )),bind(C,$thf( A )),bind(D,$thf( E @ vsucc ))]]) ).
thf(504,plain,
! [B: $i,A: $i] : ( A @ ( B @ ( A @ vplus ) @ vsucc @ greater ) ),
inference(simp,[status(thm)],[495]) ).
thf(745,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ vsucc @ ( A @ vplus ) )
!= ( C @ ( vd469 @ ( vd480 @ vmul ) @ vplus ) ) )
| ( ( B @ ( A @ vplus ) @ vsucc )
!= ( vd469 @ ( vd481 @ vmul ) ) ) ),
inference(paramod_ordered,[status(thm)],[68,501]) ).
thf(746,plain,
! [A: $i] :
( ( A @ ( vd469 @ ( vd480 @ vmul ) @ vplus ) @ vsucc )
!= ( vd469 @ ( vd481 @ vmul ) ) ),
inference(pattern_uni,[status(thm)],[745:[bind(A,$thf( vd469 @ ( vd480 @ vmul ) )),bind(B,$thf( F )),bind(C,$thf( F @ vsucc ))]]) ).
thf(751,plain,
! [A: $i] :
( ( A @ ( vd469 @ ( vd480 @ vmul ) @ vplus ) @ vsucc )
!= ( vd469 @ ( vd481 @ vmul ) ) ),
inference(simp,[status(thm)],[746]) ).
thf(1284,plain,
! [B: $i,A: $i] :
( ( ( v1 @ ( A @ vplus ) )
!= ( B @ ( vd469 @ ( vd480 @ vmul ) @ vplus ) ) )
| ( ( A @ vsucc @ vsucc )
!= ( vd469 @ ( vd481 @ vmul ) ) ) ),
inference(paramod_ordered,[status(thm)],[70,751]) ).
thf(1285,plain,
( ( vd469 @ ( vd480 @ vmul ) @ vsucc @ vsucc )
!= ( vd469 @ ( vd481 @ vmul ) ) ),
inference(pattern_uni,[status(thm)],[1284:[bind(A,$thf( vd469 @ ( vd480 @ vmul ) )),bind(B,$thf( v1 ))]]) ).
thf(1320,plain,
! [A: $i] :
( ( ( A @ ( v1 @ vmul ) )
!= ( vd469 @ ( vd480 @ vmul ) ) )
| ( ( A @ vsucc @ vsucc )
!= ( vd469 @ ( vd481 @ vmul ) ) ) ),
inference(paramod_ordered,[status(thm)],[220,1285]) ).
thf(1324,plain,
! [A: $i] :
( ( A != vd469 )
| ( v1 != vd480 )
| ( ( A @ vsucc @ vsucc )
!= ( vd469 @ ( vd481 @ vmul ) ) ) ),
inference(simp,[status(thm)],[1320]) ).
thf(1330,plain,
( ( v1 != vd480 )
| ( ( vd469 @ ( vd481 @ vmul ) )
!= ( vd469 @ vsucc @ vsucc ) ) ),
inference(simp,[status(thm)],[1324]) ).
thf(106,plain,
! [B: $i,A: $i] :
( ( B = A )
| ( A @ ( B @ less ) )
| ~ ( A @ ( B @ leq ) ) ),
inference(cnfConj,[status(thm)],[105]) ).
thf(109,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ less ) )
| ~ ( A @ ( B @ leq ) )
| ( B = A ) ),
inference(lifteq,[status(thm)],[106]) ).
thf(2765,plain,
! [B: $i,A: $i] :
( ( A != v1 )
| ( B != vd469 )
| ( A @ ( B @ less ) )
| ~ ( A @ ( B @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[109,314]) ).
thf(2766,plain,
! [A: $i] :
( ( A != vd469 )
| ( v1 @ ( A @ less ) )
| ~ ( v1 @ ( A @ leq ) ) ),
inference(pattern_uni,[status(thm)],[2765:[bind(A,$thf( v1 ))]]) ).
thf(3274,plain,
( ( v1 @ ( vd469 @ less ) )
| ~ ( v1 @ ( vd469 @ leq ) ) ),
inference(simp,[status(thm)],[2766]) ).
thf(16479,plain,
( $false
| ~ ( v1 @ ( vd469 @ leq ) ) ),
inference(rewrite,[status(thm)],[3274,16251]) ).
thf(16480,plain,
~ ( v1 @ ( vd469 @ leq ) ),
inference(simp,[status(thm)],[16479]) ).
thf(210,plain,
! [B: $i,A: $i] :
( ( B @ vsucc @ ( A @ vmul ) )
= ( A @ ( B @ ( A @ vmul ) @ vplus ) ) ),
inference(cnfConj,[status(thm)],[209]) ).
thf(212,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ vmul ) @ vplus ) )
= ( B @ vsucc @ ( A @ vmul ) ) ),
inference(lifteq,[status(thm)],[210]) ).
thf(16522,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ vplus ) @ ( B @ less ) )
!= ( v1 @ ( vd469 @ less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[412,16251]) ).
thf(16523,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ vplus ) @ ( B @ less ) )
!= ( v1 @ ( vd469 @ less ) ) ),
inference(simp,[status(thm)],[16522]) ).
thf(16565,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ vplus ) )
!= v1 )
| ( B != vd469 ) ),
inference(simp,[status(thm)],[16523]) ).
thf(16586,plain,
! [A: $i] :
( ( vd469 @ ( A @ vplus ) )
!= v1 ),
inference(simp,[status(thm)],[16565]) ).
thf(22805,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ vmul ) @ vplus ) )
!= ( vd469 @ ( C @ vplus ) ) )
| ( ( B @ vsucc @ ( A @ vmul ) )
!= v1 ) ),
inference(paramod_ordered,[status(thm)],[212,16586]) ).
thf(22806,plain,
! [A: $i] :
( ( A @ vsucc @ ( vd469 @ vmul ) )
!= v1 ),
inference(pattern_uni,[status(thm)],[22805:[bind(A,$thf( vd469 )),bind(B,$thf( E )),bind(C,$thf( E @ ( vd469 @ vmul ) ))]]) ).
thf(22864,plain,
! [A: $i] :
( ( A @ vsucc @ ( vd469 @ vmul ) )
!= v1 ),
inference(simp,[status(thm)],[22806]) ).
thf(35267,plain,
! [A: $i] :
( ( ( vd469 @ sk4 @ vsucc )
!= ( A @ vsucc ) )
| ( ( vd469 @ ( vd469 @ vmul ) )
!= v1 ) ),
inference(paramod_ordered,[status(thm)],[6180,22864]) ).
thf(35268,plain,
( ( vd469 @ ( vd469 @ vmul ) )
!= v1 ),
inference(pattern_uni,[status(thm)],[35267:[bind(A,$thf( vd469 @ sk4 ))]]) ).
thf(35361,plain,
! [A: $i] :
( ( A
!= ( vd469 @ ( vd469 @ vmul ) ) )
| ( v1 != v1 )
| ( A @ ( v1 @ less ) ) ),
inference(paramod_ordered,[status(thm)],[1448,35268]) ).
thf(35362,plain,
! [A: $i] :
( ( A
!= ( vd469 @ ( vd469 @ vmul ) ) )
| ( A @ ( v1 @ less ) ) ),
inference(simp,[status(thm)],[35361]) ).
thf(35363,plain,
vd469 @ ( vd469 @ vmul ) @ ( v1 @ less ),
inference(pattern_uni,[status(thm)],[35362:[bind(A,$thf( vd469 @ ( vd469 @ vmul ) ))]]) ).
thf(35508,plain,
! [B: $i,A: $i] :
( ( ( vd469 @ ( vd469 @ vmul ) @ ( v1 @ less ) )
!= ( B @ ( A @ less ) ) )
| ( A @ ( B @ greater ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[35363,232]) ).
thf(35509,plain,
! [B: $i,A: $i] :
( ( ( vd469 @ ( vd469 @ vmul ) @ ( v1 @ less ) )
!= ( B @ ( A @ less ) ) )
| ( A @ ( B @ greater ) ) ),
inference(simp,[status(thm)],[35508]) ).
thf(35510,plain,
v1 @ ( vd469 @ ( vd469 @ vmul ) @ greater ),
inference(pattern_uni,[status(thm)],[35509:[bind(A,$thf( v1 )),bind(B,$thf( vd469 @ ( vd469 @ vmul ) ))]]) ).
thf(38,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ greater ) )
=> ( ( vd469 @ ( A @ vmul ) )
= ( vd469 @ ( B @ ( A @ vskolem9 ) @ ( B @ vplus ) @ vmul ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(302, 0), 2)') ).
thf(196,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ greater ) )
=> ( ( vd469 @ ( A @ vmul ) )
= ( vd469 @ ( B @ ( A @ vskolem9 ) @ ( B @ vplus ) @ vmul ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(26806,plain,
! [B: $i,A: $i] :
( ( ( vd481 @ vsucc @ ( vd480 @ less ) )
!= ( B @ ( A @ less ) ) )
| ( A @ ( B @ greater ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[26549,232]) ).
thf(26807,plain,
! [B: $i,A: $i] :
( ( ( vd481 @ vsucc @ ( vd480 @ less ) )
!= ( B @ ( A @ less ) ) )
| ( A @ ( B @ greater ) ) ),
inference(simp,[status(thm)],[26806]) ).
thf(26808,plain,
vd480 @ ( vd481 @ vsucc @ greater ),
inference(pattern_uni,[status(thm)],[26807:[bind(A,$thf( vd480 )),bind(B,$thf( vd481 @ vsucc ))]]) ).
thf(27115,plain,
! [B: $i,A: $i] :
( ( ( vd480 @ ( vd481 @ vsucc @ greater ) )
!= ( B @ ( A @ greater ) ) )
| ( B @ vsucc @ ( A @ geq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[26808,8252]) ).
thf(27116,plain,
! [B: $i,A: $i] :
( ( ( vd480 @ ( vd481 @ vsucc @ greater ) )
!= ( B @ ( A @ greater ) ) )
| ( B @ vsucc @ ( A @ geq ) ) ),
inference(simp,[status(thm)],[27115]) ).
thf(27117,plain,
vd480 @ vsucc @ ( vd481 @ vsucc @ geq ),
inference(pattern_uni,[status(thm)],[27116:[bind(A,$thf( vd481 @ vsucc )),bind(B,$thf( vd480 ))]]) ).
thf(28104,plain,
! [B: $i,A: $i] :
( ( ( vd480 @ vsucc @ ( vd481 @ vsucc @ geq ) )
!= ( B @ ( A @ geq ) ) )
| ( A @ ( B @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[27117,102]) ).
thf(28105,plain,
! [B: $i,A: $i] :
( ( ( vd480 @ vsucc @ ( vd481 @ vsucc @ geq ) )
!= ( B @ ( A @ geq ) ) )
| ( A @ ( B @ leq ) ) ),
inference(simp,[status(thm)],[28104]) ).
thf(28106,plain,
vd481 @ vsucc @ ( vd480 @ vsucc @ leq ),
inference(pattern_uni,[status(thm)],[28105:[bind(A,$thf( vd481 @ vsucc )),bind(B,$thf( vd480 @ vsucc ))]]) ).
thf(559,plain,
! [A: $i] :
( ( ( A @ ( A @ vsucc @ greater ) )
!= ( vd469 @ ( vd480 @ vmul ) @ ( vd469 @ greater ) ) )
| ( v1 != vd481 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[491,330]) ).
thf(560,plain,
! [A: $i] :
( ( ( A @ ( A @ vsucc @ greater ) )
!= ( vd469 @ ( vd480 @ vmul ) @ ( vd469 @ greater ) ) )
| ( v1 != vd481 ) ),
inference(simp,[status(thm)],[559]) ).
thf(566,plain,
! [A: $i] :
( ( A
!= ( vd469 @ ( vd480 @ vmul ) ) )
| ( ( A @ vsucc )
!= vd469 )
| ( v1 != vd481 ) ),
inference(simp,[status(thm)],[560]) ).
thf(570,plain,
( ( ( vd469 @ ( vd480 @ vmul ) @ vsucc )
!= vd469 )
| ( v1 != vd481 ) ),
inference(simp,[status(thm)],[566]) ).
thf(387,plain,
! [C: $i,B: $i,A: $i] :
( ( ( v1 @ ( A @ vplus ) )
!= ( C @ ( B @ vplus ) ) )
| ( A @ vsucc @ ( B @ less ) ) ),
inference(paramod_ordered,[status(thm)],[70,160]) ).
thf(388,plain,
! [A: $i] : ( A @ vsucc @ ( A @ less ) ),
inference(pattern_uni,[status(thm)],[387:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( v1 ))]]) ).
thf(5151,plain,
! [A: $i] :
( ( ( vd469 @ ( v1 @ sk7 ) @ vsucc )
!= ( A @ vsucc ) )
| ( vd469 @ ( A @ less ) ) ),
inference(paramod_ordered,[status(thm)],[5150,388]) ).
thf(5152,plain,
vd469 @ ( vd469 @ ( v1 @ sk7 ) @ less ),
inference(pattern_uni,[status(thm)],[5151:[bind(A,$thf( vd469 @ ( v1 @ sk7 ) ))]]) ).
thf(5683,plain,
vd469 @ ( vd469 @ sk6 @ less ),
inference(rewrite,[status(thm)],[5152,5211]) ).
thf(6179,plain,
vd469 @ ( vd469 @ sk4 @ less ),
inference(rewrite,[status(thm)],[5683,5879]) ).
thf(16300,plain,
! [B: $i,A: $i] :
( ( ( vd469 @ ( vd469 @ sk4 @ less ) )
!= ( B @ ( A @ less ) ) )
| ~ $true
| ~ ( B @ ( A @ greater ) ) ),
inference(paramod_ordered,[status(thm)],[6179,249]) ).
thf(16301,plain,
! [B: $i,A: $i] :
( ( ( vd469 @ ( vd469 @ sk4 @ less ) )
!= ( B @ ( A @ less ) ) )
| ~ ( B @ ( A @ greater ) ) ),
inference(simp,[status(thm)],[16300]) ).
thf(16302,plain,
~ ( vd469 @ ( vd469 @ sk4 @ greater ) ),
inference(pattern_uni,[status(thm)],[16301:[bind(A,$thf( vd469 @ sk4 )),bind(B,$thf( vd469 ))]]) ).
thf(17163,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ ( A @ vplus ) @ greater ) )
!= ( vd469 @ ( vd469 @ sk4 @ greater ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[481,16302]) ).
thf(17164,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ vplus ) @ greater ) )
!= ( vd469 @ ( vd469 @ sk4 @ greater ) ) ),
inference(simp,[status(thm)],[17163]) ).
thf(17224,plain,
! [B: $i,A: $i] :
( ( B != vd469 )
| ( ( B @ ( A @ vplus ) )
!= ( vd469 @ sk4 ) ) ),
inference(simp,[status(thm)],[17164]) ).
thf(17234,plain,
! [A: $i] :
( ( vd469 @ ( A @ vplus ) )
!= ( vd469 @ sk4 ) ),
inference(simp,[status(thm)],[17224]) ).
thf(709,plain,
! [C: $i,B: $i,A: $i] :
( ( ( v1 @ ( A @ vplus ) )
!= ( C @ ( B @ vplus ) ) )
| ( ( A @ vsucc @ ( B @ sk1 ) )
= C ) ),
inference(paramod_ordered,[status(thm)],[70,708]) ).
thf(710,plain,
! [A: $i] :
( ( A @ vsucc @ ( A @ sk1 ) )
= v1 ),
inference(pattern_uni,[status(thm)],[709:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( v1 ))]]) ).
thf(5807,plain,
! [A: $i] :
( ( ( vd469 @ sk6 @ vsucc )
!= ( A @ vsucc ) )
| ( ( vd469 @ ( A @ sk1 ) )
= v1 ) ),
inference(paramod_ordered,[status(thm)],[5679,710]) ).
thf(5808,plain,
( ( vd469 @ ( vd469 @ sk6 @ sk1 ) )
= v1 ),
inference(pattern_uni,[status(thm)],[5807:[bind(A,$thf( vd469 @ sk6 ))]]) ).
thf(6905,plain,
( ( vd469 @ ( vd469 @ sk4 @ sk1 ) )
= v1 ),
inference(rewrite,[status(thm)],[5808,5879]) ).
thf(320,plain,
! [A: $i] :
( ( ( A @ ( v1 @ vmul ) )
!= ( vd469 @ ( vd480 @ vmul ) ) )
| ~ ( A @ ( vd469 @ ( vd481 @ vmul ) @ greater ) ) ),
inference(paramod_ordered,[status(thm)],[220,60]) ).
thf(323,plain,
! [A: $i] :
( ( A != vd469 )
| ( v1 != vd480 )
| ~ ( A @ ( vd469 @ ( vd481 @ vmul ) @ greater ) ) ),
inference(simp,[status(thm)],[320]) ).
thf(329,plain,
( ( v1 != vd480 )
| ~ ( vd469 @ ( vd469 @ ( vd481 @ vmul ) @ greater ) ) ),
inference(simp,[status(thm)],[323]) ).
thf(563,plain,
! [A: $i] :
( ( ( A @ ( A @ vsucc @ greater ) )
!= ( vd469 @ ( vd469 @ ( vd481 @ vmul ) @ greater ) ) )
| ( v1 != vd480 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[491,329]) ).
thf(564,plain,
! [A: $i] :
( ( ( A @ ( A @ vsucc @ greater ) )
!= ( vd469 @ ( vd469 @ ( vd481 @ vmul ) @ greater ) ) )
| ( v1 != vd480 ) ),
inference(simp,[status(thm)],[563]) ).
thf(568,plain,
! [A: $i] :
( ( A != vd469 )
| ( ( A @ vsucc )
!= ( vd469 @ ( vd481 @ vmul ) ) )
| ( v1 != vd480 ) ),
inference(simp,[status(thm)],[564]) ).
thf(572,plain,
( ( ( vd469 @ ( vd481 @ vmul ) )
!= ( vd469 @ vsucc ) )
| ( v1 != vd480 ) ),
inference(simp,[status(thm)],[568]) ).
thf(1764,plain,
! [A: $i] :
( ( v1 != v1 )
| ( ( vd469 @ ( vd481 @ vmul ) )
!= ( vd469 @ vsucc ) )
| ( A != vd480 )
| ( A @ ( v1 @ less ) ) ),
inference(paramod_ordered,[status(thm)],[1448,572]) ).
thf(1765,plain,
! [A: $i] :
( ( ( vd469 @ ( vd481 @ vmul ) )
!= ( vd469 @ vsucc ) )
| ( A != vd480 )
| ( A @ ( v1 @ less ) ) ),
inference(pattern_uni,[status(thm)],[1764:[]]) ).
thf(2049,plain,
( ( ( vd469 @ ( vd481 @ vmul ) )
!= ( vd469 @ vsucc ) )
| ( vd480 @ ( v1 @ less ) ) ),
inference(simp,[status(thm)],[1765]) ).
thf(11,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ vplus ) @ vplus ) )
= ( C @ ( B @ vplus ) @ ( A @ vplus ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(33, 0), 0)') ).
thf(93,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ vplus ) @ vplus ) )
= ( C @ ( B @ vplus ) @ ( A @ vplus ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(321,plain,
! [A: $i] :
( ( ( A @ ( v1 @ vmul ) )
!= ( vd469 @ ( vd481 @ vmul ) ) )
| ( ( vd469 @ ( vd480 @ vmul ) )
!= vd480 )
| ( A != vd481 ) ),
inference(paramod_ordered,[status(thm)],[220,273]) ).
thf(325,plain,
( ( vd469 != vd481 )
| ( v1 != vd481 )
| ( ( vd469 @ ( vd480 @ vmul ) )
!= vd480 ) ),
inference(simp,[status(thm)],[321]) ).
thf(57,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ geq ) )
<=> ( ( B = A )
| ( A @ ( B @ greater ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','def(cond(conseq(axiom(3)), 16), 1)') ).
thf(254,plain,
! [A: $i,B: $i] :
( ( ( ( B = A )
| ( A @ ( B @ greater ) ) )
=> ( A @ ( B @ geq ) ) )
& ( ( A @ ( B @ geq ) )
=> ( ( B = A )
| ( A @ ( B @ greater ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(255,plain,
( ! [A: $i,B: $i] :
( ( ( B = A )
| ( A @ ( B @ greater ) ) )
=> ( A @ ( B @ geq ) ) )
& ! [A: $i,B: $i] :
( ( A @ ( B @ geq ) )
=> ( ( B = A )
| ( A @ ( B @ greater ) ) ) ) ),
inference(miniscope,[status(thm)],[254]) ).
thf(256,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( D @ geq ) )
| ( D != C ) )
& ( ( C @ ( D @ geq ) )
| ~ ( C @ ( D @ greater ) ) )
& ( ( B = A )
| ( A @ ( B @ greater ) )
| ~ ( A @ ( B @ geq ) ) ) ),
inference(cnf,[status(esa)],[255]) ).
thf(258,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ geq ) )
| ~ ( A @ ( B @ greater ) ) ),
inference(cnfConj,[status(thm)],[256]) ).
thf(261,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ geq ) )
| ~ ( A @ ( B @ greater ) ) ),
inference(simp,[status(thm)],[258]) ).
thf(27,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( ( B @ ( A @ less ) )
& ( C @ ( B @ leq ) ) )
| ( ( B @ ( A @ leq ) )
& ( C @ ( B @ less ) ) ) )
=> ( C @ ( A @ less ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(177), 0), 0)') ).
thf(161,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( B @ ( A @ less ) )
& ( C @ ( B @ leq ) ) )
| ( ( B @ ( A @ leq ) )
& ( C @ ( B @ less ) ) ) )
=> ( C @ ( A @ less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(162,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ less ) )
| ~ ( B @ ( A @ less ) )
| ~ ( C @ ( B @ leq ) ) )
& ( ( C @ ( A @ less ) )
| ~ ( B @ ( A @ leq ) )
| ~ ( C @ ( B @ less ) ) ) ),
inference(cnf,[status(esa)],[161]) ).
thf(164,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ less ) )
| ~ ( B @ ( A @ less ) )
| ~ ( C @ ( B @ leq ) ) ),
inference(cnfConj,[status(thm)],[162]) ).
thf(32,axiom,
! [A: $i] : ( v1 @ ( A @ geq ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(228, 0), 0)') ).
thf(178,plain,
! [A: $i] : ( v1 @ ( A @ geq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(179,plain,
! [A: $i] : ( v1 @ ( A @ geq ) ),
inference(cnf,[status(esa)],[178]) ).
thf(26719,plain,
! [B: $i,A: $i] :
( ( ( vd481 @ vsucc @ ( vd480 @ less ) )
!= ( B @ ( A @ less ) ) )
| ~ $true
| ~ ( B @ ( A @ greater ) ) ),
inference(paramod_ordered,[status(thm)],[26549,249]) ).
thf(26720,plain,
! [B: $i,A: $i] :
( ( ( vd481 @ vsucc @ ( vd480 @ less ) )
!= ( B @ ( A @ less ) ) )
| ~ ( B @ ( A @ greater ) ) ),
inference(simp,[status(thm)],[26719]) ).
thf(26721,plain,
~ ( vd481 @ vsucc @ ( vd480 @ greater ) ),
inference(pattern_uni,[status(thm)],[26720:[bind(A,$thf( vd480 )),bind(B,$thf( vd481 @ vsucc ))]]) ).
thf(26907,plain,
! [A: $i] :
( ( ( A @ ( A @ vsucc @ greater ) )
!= ( vd481 @ vsucc @ ( vd480 @ greater ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[491,26721]) ).
thf(26908,plain,
! [A: $i] :
( ( A @ ( A @ vsucc @ greater ) )
!= ( vd481 @ vsucc @ ( vd480 @ greater ) ) ),
inference(simp,[status(thm)],[26907]) ).
thf(26925,plain,
! [A: $i] :
( ( A
!= ( vd481 @ vsucc ) )
| ( ( A @ vsucc )
!= vd480 ) ),
inference(simp,[status(thm)],[26908]) ).
thf(26938,plain,
( ( vd481 @ vsucc @ vsucc )
!= vd480 ),
inference(simp,[status(thm)],[26925]) ).
thf(50,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ less ) )
| ( B @ ( A @ greater ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(130), 0), 0)') ).
thf(236,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ less ) )
| ( B @ ( A @ greater ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(237,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ less ) )
| ( B @ ( A @ greater ) )
| ( A = B ) ),
inference(cnf,[status(esa)],[236]) ).
thf(238,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ less ) )
| ( B @ ( A @ greater ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[237]) ).
thf(3980,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( v1 @ vplus ) )
!= ( C @ ( B @ vplus ) ) )
| ( ( A @ vsucc @ ( C @ sk5 ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[177,3959]) ).
thf(3981,plain,
! [A: $i] :
( ( A @ vsucc @ ( A @ sk5 ) )
= v1 ),
inference(pattern_uni,[status(thm)],[3980:[bind(A,$thf( A )),bind(B,$thf( v1 )),bind(C,$thf( A ))]]) ).
thf(5834,plain,
! [A: $i] :
( ( ( vd469 @ sk6 @ vsucc )
!= ( A @ vsucc ) )
| ( ( vd469 @ ( A @ sk5 ) )
= v1 ) ),
inference(paramod_ordered,[status(thm)],[5679,3981]) ).
thf(5835,plain,
( ( vd469 @ ( vd469 @ sk6 @ sk5 ) )
= v1 ),
inference(pattern_uni,[status(thm)],[5834:[bind(A,$thf( vd469 @ sk6 ))]]) ).
thf(6964,plain,
( ( vd469 @ ( vd469 @ sk4 @ sk5 ) )
= v1 ),
inference(rewrite,[status(thm)],[5835,5879]) ).
thf(29529,plain,
! [B: $i,A: $i] :
( ( ( vd481 @ vsucc @ ( vd480 @ ( vd481 @ vskolem9 ) @ less ) )
!= ( B @ ( A @ less ) ) )
| ~ $true
| ~ ( B @ ( A @ greater ) ) ),
inference(paramod_ordered,[status(thm)],[29528,249]) ).
thf(29530,plain,
! [B: $i,A: $i] :
( ( ( vd481 @ vsucc @ ( vd480 @ ( vd481 @ vskolem9 ) @ less ) )
!= ( B @ ( A @ less ) ) )
| ~ ( B @ ( A @ greater ) ) ),
inference(simp,[status(thm)],[29529]) ).
thf(29531,plain,
~ ( vd481 @ vsucc @ ( vd480 @ ( vd481 @ vskolem9 ) @ greater ) ),
inference(pattern_uni,[status(thm)],[29530:[bind(A,$thf( vd480 @ ( vd481 @ vskolem9 ) )),bind(B,$thf( vd481 @ vsucc ))]]) ).
thf(30822,plain,
! [A: $i] :
( ( ( A @ ( A @ vsucc @ greater ) )
!= ( vd481 @ vsucc @ ( vd480 @ ( vd481 @ vskolem9 ) @ greater ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[491,29531]) ).
thf(30823,plain,
! [A: $i] :
( ( A @ ( A @ vsucc @ greater ) )
!= ( vd481 @ vsucc @ ( vd480 @ ( vd481 @ vskolem9 ) @ greater ) ) ),
inference(simp,[status(thm)],[30822]) ).
thf(30847,plain,
! [A: $i] :
( ( A
!= ( vd481 @ vsucc ) )
| ( ( A @ vsucc )
!= ( vd480 @ ( vd481 @ vskolem9 ) ) ) ),
inference(simp,[status(thm)],[30823]) ).
thf(30870,plain,
( ( vd480 @ ( vd481 @ vskolem9 ) )
!= ( vd481 @ vsucc @ vsucc ) ),
inference(simp,[status(thm)],[30847]) ).
thf(16384,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ vplus ) @ ( A @ less ) )
!= ( vd480 @ ( vd481 @ less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[160,16236]) ).
thf(16385,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ vplus ) @ ( A @ less ) )
!= ( vd480 @ ( vd481 @ less ) ) ),
inference(simp,[status(thm)],[16384]) ).
thf(16455,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ vplus ) )
!= vd480 )
| ( A != vd481 ) ),
inference(simp,[status(thm)],[16385]) ).
thf(16463,plain,
! [A: $i] :
( ( A @ ( vd481 @ vplus ) )
!= vd480 ),
inference(simp,[status(thm)],[16455]) ).
thf(56,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ vplus ) @ ( A @ vmul ) )
= ( C @ ( A @ vmul ) @ ( B @ ( A @ vmul ) @ vplus ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(281, 0), 0)') ).
thf(251,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ vplus ) @ ( A @ vmul ) )
= ( C @ ( A @ vmul ) @ ( B @ ( A @ vmul ) @ vplus ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(252,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ vplus ) @ ( A @ vmul ) )
= ( C @ ( A @ vmul ) @ ( B @ ( A @ vmul ) @ vplus ) ) ),
inference(cnf,[status(esa)],[251]) ).
thf(253,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ vmul ) @ ( B @ ( A @ vmul ) @ vplus ) )
= ( C @ ( B @ vplus ) @ ( A @ vmul ) ) ),
inference(lifteq,[status(thm)],[252]) ).
thf(1052,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ vsucc @ ( A @ vplus ) )
!= ( D @ ( C @ vplus ) ) )
| ( ( B @ ( A @ vplus ) @ vsucc @ vsucc @ vsucc )
!= v1 ) ),
inference(paramod_ordered,[status(thm)],[68,694]) ).
thf(1053,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ vplus ) @ vsucc @ vsucc @ vsucc )
!= v1 ),
inference(pattern_uni,[status(thm)],[1052:[bind(A,$thf( A )),bind(B,$thf( E )),bind(C,$thf( A )),bind(D,$thf( E @ vsucc ))]]) ).
thf(1056,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ vplus ) @ vsucc @ vsucc @ vsucc )
!= v1 ),
inference(simp,[status(thm)],[1053]) ).
thf(7412,plain,
! [B: $i,A: $i] :
( ( ( vd481 @ ( vd480 @ sk7 ) @ ( vd480 @ vplus ) )
!= ( B @ ( A @ vplus ) ) )
| ( ( vd481 @ vsucc @ vsucc @ vsucc )
!= v1 ) ),
inference(paramod_ordered,[status(thm)],[5038,1056]) ).
thf(7413,plain,
( ( vd481 @ vsucc @ vsucc @ vsucc )
!= v1 ),
inference(pattern_uni,[status(thm)],[7412:[bind(A,$thf( vd480 )),bind(B,$thf( vd481 @ ( vd480 @ sk7 ) ))]]) ).
thf(15457,plain,
! [B: $i,A: $i] :
( ( ( vd480 @ ( vd481 @ vskolem9 ) @ ( vd480 @ vplus ) )
!= ( B @ ( A @ vplus ) ) )
| ( vd481 != B ) ),
inference(paramod_ordered,[status(thm)],[9644,152]) ).
thf(15458,plain,
( ( vd480 @ ( vd481 @ vskolem9 ) )
!= vd481 ),
inference(pattern_uni,[status(thm)],[15457:[bind(A,$thf( vd480 )),bind(B,$thf( vd480 @ ( vd481 @ vskolem9 ) ))]]) ).
thf(486,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ vplus ) @ greater ) )
!= ( vd469 @ ( vd480 @ vmul ) @ ( vd469 @ greater ) ) )
| ( v1 != vd481 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[187,330]) ).
thf(487,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ vplus ) @ greater ) )
!= ( vd469 @ ( vd480 @ vmul ) @ ( vd469 @ greater ) ) )
| ( v1 != vd481 ) ),
inference(simp,[status(thm)],[486]) ).
thf(498,plain,
! [B: $i,A: $i] :
( ( A
!= ( vd469 @ ( vd480 @ vmul ) ) )
| ( ( B @ ( A @ vplus ) )
!= vd469 )
| ( v1 != vd481 ) ),
inference(simp,[status(thm)],[487]) ).
thf(502,plain,
! [A: $i] :
( ( ( A @ ( vd469 @ ( vd480 @ vmul ) @ vplus ) )
!= vd469 )
| ( v1 != vd481 ) ),
inference(simp,[status(thm)],[498]) ).
thf(5034,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk7 ) @ ( B @ vplus ) )
!= ( C @ ( vd469 @ ( vd480 @ vmul ) @ vplus ) ) )
| ( A != vd469 )
| ( v1 != vd481 )
| ~ ( A @ ( B @ less ) ) ),
inference(paramod_ordered,[status(thm)],[158,502]) ).
thf(5035,plain,
! [A: $i] :
( ( A != vd469 )
| ( v1 != vd481 )
| ~ ( A @ ( vd469 @ ( vd480 @ vmul ) @ less ) ) ),
inference(pattern_uni,[status(thm)],[5034:[bind(A,$thf( G )),bind(B,$thf( vd469 @ ( vd480 @ vmul ) )),bind(C,$thf( G @ ( vd469 @ ( vd480 @ vmul ) @ sk7 ) ))]]) ).
thf(5101,plain,
( ( v1 != vd481 )
| ~ ( vd469 @ ( vd469 @ ( vd480 @ vmul ) @ less ) ) ),
inference(simp,[status(thm)],[5035]) ).
thf(531,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ vsucc @ vplus ) @ vplus ) )
!= ( A @ ( v1 @ vplus ) ) ),
inference(simp,[status(thm)],[524]) ).
thf(537,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ vsucc @ vplus ) @ vplus ) )
!= ( A @ ( v1 @ vplus ) ) ),
inference(simp,[status(thm)],[531]) ).
thf(94,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ vplus ) @ vplus ) )
= ( C @ ( B @ vplus ) @ ( A @ vplus ) ) ),
inference(cnf,[status(esa)],[93]) ).
thf(95,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ vplus ) @ vplus ) )
= ( C @ ( B @ vplus ) @ ( A @ vplus ) ) ),
inference(lifteq,[status(thm)],[94]) ).
thf(32619,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ vplus ) @ ( A @ vsucc @ vplus ) )
!= ( A @ vsucc ) ),
inference(rewrite,[status(thm)],[537,177,95]) ).
thf(5306,plain,
( ( ( vd469 @ ( vd480 @ vmul ) @ ( vd469 @ greater ) )
!= ( v1 @ ( vd469 @ greater ) ) )
| ( v1 != vd481 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5169,330]) ).
thf(5307,plain,
( ( ( vd469 @ ( vd480 @ vmul ) @ ( vd469 @ greater ) )
!= ( v1 @ ( vd469 @ greater ) ) )
| ( v1 != vd481 ) ),
inference(simp,[status(thm)],[5306]) ).
thf(5318,plain,
( ( ( vd469 @ ( vd480 @ vmul ) )
!= v1 )
| ( vd469 != vd469 )
| ( v1 != vd481 ) ),
inference(simp,[status(thm)],[5307]) ).
thf(5321,plain,
( ( ( vd469 @ ( vd480 @ vmul ) )
!= v1 )
| ( v1 != vd481 ) ),
inference(simp,[status(thm)],[5318]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ~ ? [C: $i] :
( A
= ( C @ ( B @ vplus ) ) )
| ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(88), 0), 3)') ).
thf(71,plain,
! [A: $i,B: $i] :
( ~ ? [C: $i] :
( A
= ( C @ ( B @ vplus ) ) )
| ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(72,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( C @ ( B @ vplus ) ) )
| ( A != B ) ),
inference(cnf,[status(esa)],[71]) ).
thf(73,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( C @ ( B @ vplus ) ) )
| ( A != B ) ),
inference(lifteq,[status(thm)],[72]) ).
thf(74,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ vplus ) )
!= A ),
inference(simp,[status(thm)],[73]) ).
thf(8259,plain,
! [B: $i,A: $i] :
( ( ( v1 @ ( vd469 @ greater ) )
!= ( B @ ( A @ greater ) ) )
| ( B @ vsucc @ ( A @ geq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5169,8252]) ).
thf(8260,plain,
! [B: $i,A: $i] :
( ( ( v1 @ ( vd469 @ greater ) )
!= ( B @ ( A @ greater ) ) )
| ( B @ vsucc @ ( A @ geq ) ) ),
inference(simp,[status(thm)],[8259]) ).
thf(8261,plain,
v1 @ vsucc @ ( vd469 @ geq ),
inference(pattern_uni,[status(thm)],[8260:[bind(A,$thf( vd469 )),bind(B,$thf( v1 ))]]) ).
thf(3,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ leq ) )
& ( C @ ( B @ leq ) ) )
=> ( C @ ( A @ leq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(184, 0), 0)') ).
thf(61,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ leq ) )
& ( C @ ( B @ leq ) ) )
=> ( C @ ( A @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(62,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ leq ) )
| ~ ( B @ ( A @ leq ) )
| ~ ( C @ ( B @ leq ) ) ),
inference(cnf,[status(esa)],[61]) ).
thf(287,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ leq ) )
!= ( E @ ( D @ leq ) ) )
| ( F @ ( D @ leq ) )
| ~ $true
| ~ ( F @ ( E @ leq ) )
| ~ ( B @ ( A @ leq ) )
| ~ ( C @ ( B @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[62,62]) ).
thf(288,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ leq ) )
!= ( E @ ( D @ leq ) ) )
| ( F @ ( D @ leq ) )
| ~ ( F @ ( E @ leq ) )
| ~ ( B @ ( A @ leq ) )
| ~ ( C @ ( B @ leq ) ) ),
inference(simp,[status(thm)],[287]) ).
thf(289,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( A @ leq ) )
| ~ ( D @ ( C @ leq ) )
| ~ ( B @ ( A @ leq ) )
| ~ ( C @ ( B @ leq ) ) ),
inference(pattern_uni,[status(thm)],[288:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( A )),bind(E,$thf( C ))]]) ).
thf(292,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( A @ leq ) )
| ~ ( D @ ( C @ leq ) )
| ~ ( B @ ( A @ leq ) )
| ~ ( C @ ( B @ leq ) ) ),
inference(simp,[status(thm)],[289]) ).
thf(49,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ vsucc @ vmul ) )
= ( B @ ( B @ ( A @ vmul ) @ vplus ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(261, 0), 0)') ).
thf(233,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ vsucc @ vmul ) )
= ( B @ ( B @ ( A @ vmul ) @ vplus ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(8654,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ vmul ) )
!= ( vd469 @ ( vd480 @ vmul ) ) )
| ( ( A @ ( B @ vmul ) )
!= v1 )
| ( v1 != vd481 ) ),
inference(paramod_ordered,[status(thm)],[223,5321]) ).
thf(8655,plain,
( ( ( vd480 @ ( vd469 @ vmul ) )
!= v1 )
| ( v1 != vd481 ) ),
inference(pattern_uni,[status(thm)],[8654:[bind(A,$thf( vd480 )),bind(B,$thf( vd469 ))]]) ).
thf(270,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ vplus ) @ ( C @ ( A @ vplus ) @ greater ) )
| ~ ( B @ ( A @ greater ) )
| ~ ( D @ ( C @ geq ) ) ),
inference(cnfConj,[status(thm)],[268]) ).
thf(28551,plain,
( ( vd481 @ ( vd480 @ sk7 ) )
= ( vd480 @ ( vd481 @ vskolem9 ) ) ),
inference(rewrite,[status(thm)],[7425,15611]) ).
thf(234,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ vsucc @ vmul ) )
= ( B @ ( B @ ( A @ vmul ) @ vplus ) ) ),
inference(cnf,[status(esa)],[233]) ).
thf(235,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ vmul ) @ vplus ) )
= ( B @ ( A @ vsucc @ vmul ) ) ),
inference(lifteq,[status(thm)],[234]) ).
thf(11044,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ ( A @ vmul ) @ vplus ) )
!= ( C @ ( vd469 @ ( vd480 @ vmul ) @ vplus ) ) )
| ( ( B @ ( A @ vsucc @ vmul ) )
!= ( vd469 @ ( vd481 @ vmul ) ) ) ),
inference(paramod_ordered,[status(thm)],[235,501]) ).
thf(11045,plain,
( ( vd469 @ ( vd480 @ vsucc @ vmul ) )
!= ( vd469 @ ( vd481 @ vmul ) ) ),
inference(pattern_uni,[status(thm)],[11044:[bind(A,$thf( vd480 )),bind(B,$thf( vd469 )),bind(C,$thf( vd469 ))]]) ).
thf(33971,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ vmul ) )
!= ( vd469 @ ( vd480 @ vsucc @ vmul ) ) )
| ( ( A @ ( B @ vmul ) )
!= ( vd469 @ ( vd481 @ vmul ) ) ) ),
inference(paramod_ordered,[status(thm)],[223,11045]) ).
thf(33972,plain,
( ( vd480 @ vsucc @ ( vd469 @ vmul ) )
!= ( vd469 @ ( vd481 @ vmul ) ) ),
inference(pattern_uni,[status(thm)],[33971:[bind(A,$thf( vd480 @ vsucc )),bind(B,$thf( vd469 ))]]) ).
thf(16225,plain,
! [B: $i,A: $i] :
( ( ( vd480 @ ( vd481 @ vskolem9 ) @ ( vd481 @ greater ) )
!= ( B @ ( A @ greater ) ) )
| ~ ( B @ ( A @ less ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[15440,249]) ).
thf(16226,plain,
! [B: $i,A: $i] :
( ( ( vd480 @ ( vd481 @ vskolem9 ) @ ( vd481 @ greater ) )
!= ( B @ ( A @ greater ) ) )
| ~ ( B @ ( A @ less ) ) ),
inference(simp,[status(thm)],[16225]) ).
thf(16227,plain,
~ ( vd480 @ ( vd481 @ vskolem9 ) @ ( vd481 @ less ) ),
inference(pattern_uni,[status(thm)],[16226:[bind(A,$thf( vd481 )),bind(B,$thf( vd480 @ ( vd481 @ vskolem9 ) ))]]) ).
thf(16411,plain,
( ( ( vd469 @ ( vd469 @ sk4 @ less ) )
!= ( vd480 @ ( vd481 @ less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6179,16236]) ).
thf(16412,plain,
( ( vd469 @ ( vd469 @ sk4 @ less ) )
!= ( vd480 @ ( vd481 @ less ) ) ),
inference(simp,[status(thm)],[16411]) ).
thf(16460,plain,
( ( vd480 != vd469 )
| ( ( vd469 @ sk4 )
!= vd481 ) ),
inference(simp,[status(thm)],[16412]) ).
thf(257,plain,
! [B: $i,A: $i] :
( ( B = A )
| ( A @ ( B @ greater ) )
| ~ ( A @ ( B @ geq ) ) ),
inference(cnfConj,[status(thm)],[256]) ).
thf(260,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ greater ) )
| ~ ( A @ ( B @ geq ) )
| ( B = A ) ),
inference(lifteq,[status(thm)],[257]) ).
thf(37,axiom,
! [A: $i,B: $i] :
( ( A = B )
=> ( ( vd469 @ ( A @ vmul ) )
= ( vd469 @ ( B @ vmul ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(303, 0), 0)') ).
thf(192,plain,
! [A: $i,B: $i] :
( ( A = B )
=> ( ( vd469 @ ( A @ vmul ) )
= ( vd469 @ ( B @ vmul ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(15539,plain,
! [B: $i,A: $i] :
( ( ( vd480 @ ( vd481 @ vskolem9 ) @ ( vd480 @ vplus ) )
!= ( B @ ( A @ vplus ) ) )
| ( vd481 @ ( B @ less ) ) ),
inference(paramod_ordered,[status(thm)],[9644,412]) ).
thf(15540,plain,
vd481 @ ( vd480 @ ( vd481 @ vskolem9 ) @ less ),
inference(pattern_uni,[status(thm)],[15539:[bind(A,$thf( vd480 )),bind(B,$thf( vd480 @ ( vd481 @ vskolem9 ) ))]]) ).
thf(16014,plain,
! [B: $i,A: $i] :
( ( ( vd481 @ ( vd480 @ ( vd481 @ vskolem9 ) @ less ) )
!= ( A @ ( B @ less ) ) )
| ( A @ ( B @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[15540,110]) ).
thf(16015,plain,
! [B: $i,A: $i] :
( ( ( vd481 @ ( vd480 @ ( vd481 @ vskolem9 ) @ less ) )
!= ( A @ ( B @ less ) ) )
| ( A @ ( B @ leq ) ) ),
inference(simp,[status(thm)],[16014]) ).
thf(16016,plain,
vd481 @ ( vd480 @ ( vd481 @ vskolem9 ) @ leq ),
inference(pattern_uni,[status(thm)],[16015:[bind(A,$thf( vd481 )),bind(B,$thf( vd480 @ ( vd481 @ vskolem9 ) ))]]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( v1 @ ( B @ vplus ) @ ( A @ less ) )
=> ( B @ ( A @ leq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(241, 0), 0)') ).
thf(82,plain,
! [A: $i,B: $i] :
( ( v1 @ ( B @ vplus ) @ ( A @ less ) )
=> ( B @ ( A @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(83,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ leq ) )
| ~ ( v1 @ ( B @ vplus ) @ ( A @ less ) ) ),
inference(cnf,[status(esa)],[82]) ).
thf(598,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ leq ) )
| ~ ( B @ vsucc @ ( A @ less ) ) ),
inference(rewrite,[status(thm)],[83,70]) ).
thf(26728,plain,
! [B: $i,A: $i] :
( ( ( vd481 @ vsucc @ ( vd480 @ less ) )
!= ( A @ ( B @ less ) ) )
| ( A @ ( B @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[26549,110]) ).
thf(26729,plain,
! [B: $i,A: $i] :
( ( ( vd481 @ vsucc @ ( vd480 @ less ) )
!= ( A @ ( B @ less ) ) )
| ( A @ ( B @ leq ) ) ),
inference(simp,[status(thm)],[26728]) ).
thf(26730,plain,
vd481 @ vsucc @ ( vd480 @ leq ),
inference(pattern_uni,[status(thm)],[26729:[bind(A,$thf( vd481 @ vsucc )),bind(B,$thf( vd480 ))]]) ).
thf(26981,plain,
! [B: $i,A: $i] :
( ( ( vd481 @ vsucc @ ( vd480 @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( A @ ( B @ geq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[26730,97]) ).
thf(26982,plain,
! [B: $i,A: $i] :
( ( ( vd481 @ vsucc @ ( vd480 @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( A @ ( B @ geq ) ) ),
inference(simp,[status(thm)],[26981]) ).
thf(26983,plain,
vd480 @ ( vd481 @ vsucc @ geq ),
inference(pattern_uni,[status(thm)],[26982:[bind(A,$thf( vd480 )),bind(B,$thf( vd481 @ vsucc ))]]) ).
thf(1701,plain,
! [A: $i] :
( ( v1 != v1 )
| ( A != vd480 )
| ~ ( vd469 @ ( vd469 @ ( vd481 @ vmul ) @ greater ) )
| ( A @ ( v1 @ less ) ) ),
inference(paramod_ordered,[status(thm)],[1448,329]) ).
thf(1702,plain,
! [A: $i] :
( ( A != vd480 )
| ~ ( vd469 @ ( vd469 @ ( vd481 @ vmul ) @ greater ) )
| ( A @ ( v1 @ less ) ) ),
inference(pattern_uni,[status(thm)],[1701:[]]) ).
thf(2032,plain,
( ~ ( vd469 @ ( vd469 @ ( vd481 @ vmul ) @ greater ) )
| ( vd480 @ ( v1 @ less ) ) ),
inference(simp,[status(thm)],[1702]) ).
thf(3483,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ vsucc @ ( A @ less ) )
!= ( B @ ( C @ less ) ) )
| ( B @ ( C @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[388,110]) ).
thf(3484,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ vsucc @ ( A @ less ) )
!= ( B @ ( C @ less ) ) )
| ( B @ ( C @ leq ) ) ),
inference(simp,[status(thm)],[3483]) ).
thf(3485,plain,
! [A: $i] : ( A @ vsucc @ ( A @ leq ) ),
inference(pattern_uni,[status(thm)],[3484:[bind(A,$thf( D )),bind(B,$thf( D @ vsucc )),bind(C,$thf( D ))]]) ).
thf(3519,plain,
! [A: $i] : ( A @ vsucc @ ( A @ leq ) ),
inference(simp,[status(thm)],[3485]) ).
thf(5200,plain,
! [A: $i] :
( ( ( vd469 @ ( v1 @ sk7 ) @ vsucc )
!= ( A @ vsucc ) )
| ( vd469 @ ( A @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[5150,3519]) ).
thf(5201,plain,
vd469 @ ( vd469 @ ( v1 @ sk7 ) @ leq ),
inference(pattern_uni,[status(thm)],[5200:[bind(A,$thf( vd469 @ ( v1 @ sk7 ) ))]]) ).
thf(5680,plain,
vd469 @ ( vd469 @ sk6 @ leq ),
inference(rewrite,[status(thm)],[5201,5211]) ).
thf(6178,plain,
vd469 @ ( vd469 @ sk4 @ leq ),
inference(rewrite,[status(thm)],[5680,5879]) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ? [C: $i] :
( B
= ( C @ ( A @ vplus ) ) )
| ? [C: $i] :
( A
= ( C @ ( B @ vplus ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(88), 0), 0)') ).
thf(90,plain,
! [A: $i,B: $i] :
( ? [C: $i] :
( B
= ( C @ ( A @ vplus ) ) )
| ? [C: $i] :
( A
= ( C @ ( B @ vplus ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(91,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ ( B @ sk3 ) @ ( A @ vplus ) ) )
| ( A
= ( A @ ( B @ sk2 ) @ ( B @ vplus ) ) )
| ( A = B ) ),
inference(cnf,[status(esa)],[90]) ).
thf(92,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ sk3 ) @ ( A @ vplus ) )
= B )
| ( ( A @ ( B @ sk2 ) @ ( B @ vplus ) )
= A )
| ( A = B ) ),
inference(lifteq,[status(thm)],[91]) ).
thf(31009,plain,
! [B: $i,A: $i] :
( ( ( vd480 @ ( vd481 @ vskolem9 ) @ ( vd481 @ vsucc @ greater ) )
!= ( B @ ( A @ greater ) ) )
| ~ ( B @ ( A @ less ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[29650,249]) ).
thf(31010,plain,
! [B: $i,A: $i] :
( ( ( vd480 @ ( vd481 @ vskolem9 ) @ ( vd481 @ vsucc @ greater ) )
!= ( B @ ( A @ greater ) ) )
| ~ ( B @ ( A @ less ) ) ),
inference(simp,[status(thm)],[31009]) ).
thf(31011,plain,
~ ( vd480 @ ( vd481 @ vskolem9 ) @ ( vd481 @ vsucc @ less ) ),
inference(pattern_uni,[status(thm)],[31010:[bind(A,$thf( vd481 @ vsucc )),bind(B,$thf( vd480 @ ( vd481 @ vskolem9 ) ))]]) ).
thf(45,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ greater ) )
& ( D @ ( C @ greater ) ) )
=> ( D @ ( B @ vplus ) @ ( C @ ( A @ vplus ) @ greater ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(209, 0), 0)') ).
thf(224,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ greater ) )
& ( D @ ( C @ greater ) ) )
=> ( D @ ( B @ vplus ) @ ( C @ ( A @ vplus ) @ greater ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(47,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ greater ) )
=> ( A @ ( B @ less ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(140, 0), 0)') ).
thf(229,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ greater ) )
=> ( A @ ( B @ less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(1290,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ vplus ) )
!= ( C @ ( vd469 @ ( vd480 @ vmul ) @ vplus ) ) )
| ( ( B @ ( A @ vplus ) @ vsucc )
!= ( vd469 @ ( vd481 @ vmul ) ) ) ),
inference(paramod_ordered,[status(thm)],[77,751]) ).
thf(1291,plain,
! [A: $i] :
( ( vd469 @ ( vd480 @ vmul ) @ ( A @ vplus ) @ vsucc )
!= ( vd469 @ ( vd481 @ vmul ) ) ),
inference(pattern_uni,[status(thm)],[1290:[bind(A,$thf( A )),bind(B,$thf( vd469 @ ( vd480 @ vmul ) )),bind(C,$thf( A ))]]) ).
thf(15737,plain,
! [B: $i,A: $i] :
( ( ( vd480 @ ( vd481 @ vskolem9 ) @ ( vd481 @ greater ) )
!= ( B @ ( A @ greater ) ) )
| ( B @ vsucc @ ( A @ geq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[15440,8252]) ).
thf(15738,plain,
! [B: $i,A: $i] :
( ( ( vd480 @ ( vd481 @ vskolem9 ) @ ( vd481 @ greater ) )
!= ( B @ ( A @ greater ) ) )
| ( B @ vsucc @ ( A @ geq ) ) ),
inference(simp,[status(thm)],[15737]) ).
thf(15739,plain,
vd480 @ ( vd481 @ vskolem9 ) @ vsucc @ ( vd481 @ geq ),
inference(pattern_uni,[status(thm)],[15738:[bind(A,$thf( vd481 )),bind(B,$thf( vd480 @ ( vd481 @ vskolem9 ) ))]]) ).
thf(8315,plain,
! [B: $i,A: $i] :
( ( ( vd480 @ vsucc @ ( vd481 @ geq ) )
!= ( B @ ( A @ geq ) ) )
| ( A @ ( B @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[8258,102]) ).
thf(8316,plain,
! [B: $i,A: $i] :
( ( ( vd480 @ vsucc @ ( vd481 @ geq ) )
!= ( B @ ( A @ geq ) ) )
| ( A @ ( B @ leq ) ) ),
inference(simp,[status(thm)],[8315]) ).
thf(8317,plain,
vd481 @ ( vd480 @ vsucc @ leq ),
inference(pattern_uni,[status(thm)],[8316:[bind(A,$thf( vd481 )),bind(B,$thf( vd480 @ vsucc ))]]) ).
thf(8407,plain,
( ( ( vd469 @ sk4 @ vsucc )
!= ( vd480 @ vsucc ) )
| ( vd481 @ ( vd469 @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[6180,8317]) ).
thf(8422,plain,
( ( ( vd469 @ sk4 )
!= vd480 )
| ( vd481 @ ( vd469 @ leq ) ) ),
inference(simp,[status(thm)],[8407]) ).
thf(16791,plain,
( ( ( v1 @ ( vd469 @ leq ) )
!= ( vd481 @ ( vd469 @ leq ) ) )
| ~ $true
| ( ( vd469 @ sk4 )
!= vd480 ) ),
inference(paramod_ordered,[status(thm)],[8422,16480]) ).
thf(16792,plain,
( ( ( v1 @ ( vd469 @ leq ) )
!= ( vd481 @ ( vd469 @ leq ) ) )
| ( ( vd469 @ sk4 )
!= vd480 ) ),
inference(simp,[status(thm)],[16791]) ).
thf(16822,plain,
( ( v1 != vd481 )
| ( vd469 != vd469 )
| ( ( vd469 @ sk4 )
!= vd480 ) ),
inference(simp,[status(thm)],[16792]) ).
thf(16833,plain,
( ( v1 != vd481 )
| ( ( vd469 @ sk4 )
!= vd480 ) ),
inference(simp,[status(thm)],[16822]) ).
thf(36,axiom,
! [A: $i,B: $i] :
( ~ ( B @ ( A @ greater ) )
| ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(130), 0), 3)') ).
thf(188,plain,
! [A: $i,B: $i] :
( ~ ( B @ ( A @ greater ) )
| ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(29,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ less ) )
=> ( C @ ( B @ vplus ) @ ( C @ ( A @ vplus ) @ less ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(193), 0), 0)') ).
thf(169,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ less ) )
=> ( C @ ( B @ vplus ) @ ( C @ ( A @ vplus ) @ less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(16421,plain,
! [A: $i] :
( ( ( vd469 @ ( A @ less ) )
!= ( vd480 @ ( vd481 @ less ) ) )
| ~ $true
| ( A @ ( v1 @ less ) ) ),
inference(paramod_ordered,[status(thm)],[2064,16236]) ).
thf(16422,plain,
! [A: $i] :
( ( ( vd469 @ ( A @ less ) )
!= ( vd480 @ ( vd481 @ less ) ) )
| ( A @ ( v1 @ less ) ) ),
inference(simp,[status(thm)],[16421]) ).
thf(16458,plain,
! [A: $i] :
( ( vd480 != vd469 )
| ( A != vd481 )
| ( A @ ( v1 @ less ) ) ),
inference(simp,[status(thm)],[16422]) ).
thf(16464,plain,
( ( vd480 != vd469 )
| ( vd481 @ ( v1 @ less ) ) ),
inference(simp,[status(thm)],[16458]) ).
thf(22120,plain,
! [B: $i,A: $i] :
( ( ( vd481 @ ( v1 @ less ) )
!= ( B @ ( A @ less ) ) )
| ( A @ ( B @ greater ) )
| ~ $true
| ( vd480 != vd469 ) ),
inference(paramod_ordered,[status(thm)],[16464,232]) ).
thf(22121,plain,
! [B: $i,A: $i] :
( ( ( vd481 @ ( v1 @ less ) )
!= ( B @ ( A @ less ) ) )
| ( A @ ( B @ greater ) )
| ( vd480 != vd469 ) ),
inference(simp,[status(thm)],[22120]) ).
thf(22122,plain,
( ( v1 @ ( vd481 @ greater ) )
| ( vd480 != vd469 ) ),
inference(pattern_uni,[status(thm)],[22121:[bind(A,$thf( v1 )),bind(B,$thf( vd481 ))]]) ).
thf(548,plain,
! [A: $i] :
( ( ( v1 @ ( A @ vsucc @ greater ) )
!= ( vd469 @ ( vd480 @ vmul ) @ ( vd469 @ ( vd481 @ vmul ) @ greater ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[493,60]) ).
thf(549,plain,
! [A: $i] :
( ( v1 @ ( A @ vsucc @ greater ) )
!= ( vd469 @ ( vd480 @ vmul ) @ ( vd469 @ ( vd481 @ vmul ) @ greater ) ) ),
inference(simp,[status(thm)],[548]) ).
thf(554,plain,
! [A: $i] :
( ( ( vd469 @ ( vd480 @ vmul ) )
!= v1 )
| ( ( A @ vsucc )
!= ( vd469 @ ( vd481 @ vmul ) ) ) ),
inference(simp,[status(thm)],[549]) ).
thf(25542,plain,
! [B: $i,A: $i] :
( ( ( vd469 @ ( vd480 @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( A @ ( B @ geq ) )
| ~ $true
| ( v1 != vd481 ) ),
inference(paramod_ordered,[status(thm)],[22161,97]) ).
thf(25543,plain,
! [B: $i,A: $i] :
( ( ( vd469 @ ( vd480 @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( A @ ( B @ geq ) )
| ( v1 != vd481 ) ),
inference(simp,[status(thm)],[25542]) ).
thf(25544,plain,
( ( vd480 @ ( vd469 @ geq ) )
| ( v1 != vd481 ) ),
inference(pattern_uni,[status(thm)],[25543:[bind(A,$thf( vd480 )),bind(B,$thf( vd469 ))]]) ).
thf(322,plain,
! [A: $i] :
( ( ( A @ ( v1 @ vmul ) )
!= ( vd469 @ ( vd480 @ vmul ) ) )
| ( A != vd480 )
| ( ( vd469 @ ( vd481 @ vmul ) )
!= vd481 ) ),
inference(paramod_ordered,[status(thm)],[220,273]) ).
thf(328,plain,
( ( vd480 != vd469 )
| ( v1 != vd480 )
| ( ( vd469 @ ( vd481 @ vmul ) )
!= vd481 ) ),
inference(simp,[status(thm)],[322]) ).
thf(35906,plain,
! [B: $i,A: $i] :
( ( ( v1 @ ( vd469 @ ( vd469 @ vmul ) @ greater ) )
!= ( B @ ( A @ greater ) ) )
| ( B @ vsucc @ ( A @ geq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[35510,8252]) ).
thf(35907,plain,
! [B: $i,A: $i] :
( ( ( v1 @ ( vd469 @ ( vd469 @ vmul ) @ greater ) )
!= ( B @ ( A @ greater ) ) )
| ( B @ vsucc @ ( A @ geq ) ) ),
inference(simp,[status(thm)],[35906]) ).
thf(35908,plain,
v1 @ vsucc @ ( vd469 @ ( vd469 @ vmul ) @ geq ),
inference(pattern_uni,[status(thm)],[35907:[bind(A,$thf( vd469 @ ( vd469 @ vmul ) )),bind(B,$thf( v1 ))]]) ).
thf(225,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ vplus ) @ ( C @ ( A @ vplus ) @ greater ) )
| ~ ( B @ ( A @ greater ) )
| ~ ( D @ ( C @ greater ) ) ),
inference(cnf,[status(esa)],[224]) ).
thf(3594,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ vsucc @ ( A @ leq ) )
!= ( C @ ( B @ leq ) ) )
| ( B @ ( C @ geq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3519,97]) ).
thf(3595,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ vsucc @ ( A @ leq ) )
!= ( C @ ( B @ leq ) ) )
| ( B @ ( C @ geq ) ) ),
inference(simp,[status(thm)],[3594]) ).
thf(3596,plain,
! [A: $i] : ( A @ ( A @ vsucc @ geq ) ),
inference(pattern_uni,[status(thm)],[3595:[bind(A,$thf( D )),bind(B,$thf( D )),bind(C,$thf( D @ vsucc ))]]) ).
thf(3622,plain,
! [A: $i] : ( A @ ( A @ vsucc @ geq ) ),
inference(simp,[status(thm)],[3596]) ).
thf(22150,plain,
! [B: $i,A: $i] :
( ( ( vd469 @ ( vd480 @ less ) )
!= ( B @ ( A @ less ) ) )
| ~ $true
| ~ ( B @ ( A @ greater ) )
| ( v1 != vd481 ) ),
inference(paramod_ordered,[status(thm)],[16473,249]) ).
thf(22151,plain,
! [B: $i,A: $i] :
( ( ( vd469 @ ( vd480 @ less ) )
!= ( B @ ( A @ less ) ) )
| ~ ( B @ ( A @ greater ) )
| ( v1 != vd481 ) ),
inference(simp,[status(thm)],[22150]) ).
thf(22152,plain,
( ~ ( vd469 @ ( vd480 @ greater ) )
| ( v1 != vd481 ) ),
inference(pattern_uni,[status(thm)],[22151:[bind(A,$thf( vd480 )),bind(B,$thf( vd469 ))]]) ).
thf(25069,plain,
! [A: $i] :
( ( ( A @ ( A @ vsucc @ greater ) )
!= ( vd469 @ ( vd480 @ greater ) ) )
| ~ $true
| ( v1 != vd481 ) ),
inference(paramod_ordered,[status(thm)],[491,22152]) ).
thf(25070,plain,
! [A: $i] :
( ( ( A @ ( A @ vsucc @ greater ) )
!= ( vd469 @ ( vd480 @ greater ) ) )
| ( v1 != vd481 ) ),
inference(simp,[status(thm)],[25069]) ).
thf(25079,plain,
! [A: $i] :
( ( A != vd469 )
| ( ( A @ vsucc )
!= vd480 )
| ( v1 != vd481 ) ),
inference(simp,[status(thm)],[25070]) ).
thf(25101,plain,
( ( ( vd469 @ vsucc )
!= vd480 )
| ( v1 != vd481 ) ),
inference(simp,[status(thm)],[25079]) ).
thf(7321,plain,
! [B: $i,A: $i] :
( ( ( vd481 @ ( vd480 @ sk7 ) @ ( vd480 @ vplus ) )
!= ( B @ ( A @ vplus ) ) )
| ( vd481 != B ) ),
inference(paramod_ordered,[status(thm)],[5038,152]) ).
thf(7322,plain,
( ( vd481 @ ( vd480 @ sk7 ) )
!= vd481 ),
inference(pattern_uni,[status(thm)],[7321:[bind(A,$thf( vd480 )),bind(B,$thf( vd481 @ ( vd480 @ sk7 ) ))]]) ).
thf(9089,plain,
( ( vd481 @ ( vd480 @ sk1 ) )
!= vd481 ),
inference(rewrite,[status(thm)],[7322,7425]) ).
thf(9340,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ vplus ) @ ( A @ sk1 ) )
!= ( vd481 @ ( vd480 @ sk1 ) ) )
| ( B != vd481 ) ),
inference(paramod_ordered,[status(thm)],[708,9089]) ).
thf(9344,plain,
! [A: $i] :
( ( ( vd481 @ ( A @ vplus ) )
!= vd481 )
| ( A != vd480 ) ),
inference(simp,[status(thm)],[9340]) ).
thf(9348,plain,
( ( vd481 @ ( vd480 @ vplus ) )
!= vd481 ),
inference(simp,[status(thm)],[9344]) ).
thf(1542,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( C @ ( B @ vsucc @ vplus ) ) )
| ( v1 != v1 )
| ( A @ ( v1 @ less ) ) ),
inference(paramod_ordered,[status(thm)],[1448,538]) ).
thf(1543,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( C @ ( B @ vsucc @ vplus ) ) )
| ( A @ ( v1 @ less ) ) ),
inference(simp,[status(thm)],[1542]) ).
thf(1544,plain,
! [B: $i,A: $i] : ( A @ ( B @ vsucc @ vplus ) @ ( v1 @ less ) ),
inference(pattern_uni,[status(thm)],[1543:[bind(A,$thf( E @ ( F @ vsucc @ vplus ) )),bind(B,$thf( F )),bind(C,$thf( E ))]]) ).
thf(1948,plain,
! [B: $i,A: $i] : ( A @ ( B @ vsucc @ vplus ) @ ( v1 @ less ) ),
inference(simp,[status(thm)],[1544]) ).
thf(3666,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ vplus ) )
!= ( C @ ( D @ vsucc @ vplus ) ) )
| ( B @ ( A @ vplus ) @ ( v1 @ less ) ) ),
inference(paramod_ordered,[status(thm)],[77,1948]) ).
thf(3667,plain,
! [B: $i,A: $i] : ( B @ vsucc @ ( A @ vplus ) @ ( v1 @ less ) ),
inference(pattern_uni,[status(thm)],[3666:[bind(A,$thf( A )),bind(B,$thf( E @ vsucc )),bind(C,$thf( A )),bind(D,$thf( E ))]]) ).
thf(3704,plain,
! [B: $i,A: $i] : ( B @ vsucc @ ( A @ vplus ) @ ( v1 @ less ) ),
inference(simp,[status(thm)],[3667]) ).
thf(4068,plain,
! [B: $i,A: $i] : ( B @ ( A @ vplus ) @ vsucc @ ( v1 @ less ) ),
inference(rewrite,[status(thm)],[3704,68]) ).
thf(19,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ less ) )
& ( C @ ( B @ less ) ) )
=> ( C @ ( A @ less ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(168, 0), 0)') ).
thf(129,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ less ) )
& ( C @ ( B @ less ) ) )
=> ( C @ ( A @ less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(5926,plain,
! [B: $i,A: $i] :
( ( ( vd469 @ ( vd469 @ sk6 @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( A @ ( B @ geq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5680,97]) ).
thf(5927,plain,
! [B: $i,A: $i] :
( ( ( vd469 @ ( vd469 @ sk6 @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( A @ ( B @ geq ) ) ),
inference(simp,[status(thm)],[5926]) ).
thf(5928,plain,
vd469 @ sk6 @ ( vd469 @ geq ),
inference(pattern_uni,[status(thm)],[5927:[bind(A,$thf( vd469 @ sk6 )),bind(B,$thf( vd469 ))]]) ).
thf(6450,plain,
vd469 @ sk4 @ ( vd469 @ geq ),
inference(rewrite,[status(thm)],[5928,5879]) ).
thf(8268,plain,
! [C: $i,B: $i,A: $i] :
( ( ( v1 @ ( A @ vsucc @ greater ) )
!= ( C @ ( B @ greater ) ) )
| ( C @ vsucc @ ( B @ geq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[493,8252]) ).
thf(8269,plain,
! [C: $i,B: $i,A: $i] :
( ( ( v1 @ ( A @ vsucc @ greater ) )
!= ( C @ ( B @ greater ) ) )
| ( C @ vsucc @ ( B @ geq ) ) ),
inference(simp,[status(thm)],[8268]) ).
thf(8270,plain,
! [A: $i] : ( v1 @ vsucc @ ( A @ vsucc @ geq ) ),
inference(pattern_uni,[status(thm)],[8269:[bind(A,$thf( D )),bind(B,$thf( D @ vsucc )),bind(C,$thf( v1 ))]]) ).
thf(8307,plain,
! [A: $i] : ( v1 @ vsucc @ ( A @ vsucc @ geq ) ),
inference(simp,[status(thm)],[8270]) ).
thf(22223,plain,
! [A: $i] :
( ( v1 != v1 )
| ( A != vd481 )
| ( vd469 @ ( vd480 @ less ) )
| ( A @ ( v1 @ less ) ) ),
inference(paramod_ordered,[status(thm)],[1448,16473]) ).
thf(22224,plain,
! [A: $i] :
( ( A != vd481 )
| ( vd469 @ ( vd480 @ less ) )
| ( A @ ( v1 @ less ) ) ),
inference(pattern_uni,[status(thm)],[22223:[]]) ).
thf(22250,plain,
( ( vd469 @ ( vd480 @ less ) )
| ( vd481 @ ( v1 @ less ) ) ),
inference(simp,[status(thm)],[22224]) ).
thf(28829,plain,
! [B: $i,A: $i] :
( ( ( vd481 @ ( v1 @ less ) )
!= ( B @ ( A @ less ) ) )
| ( A @ ( B @ greater ) )
| ~ $true
| ( vd469 @ ( vd480 @ less ) ) ),
inference(paramod_ordered,[status(thm)],[22250,232]) ).
thf(28830,plain,
! [B: $i,A: $i] :
( ( ( vd481 @ ( v1 @ less ) )
!= ( B @ ( A @ less ) ) )
| ( A @ ( B @ greater ) )
| ( vd469 @ ( vd480 @ less ) ) ),
inference(simp,[status(thm)],[28829]) ).
thf(28831,plain,
( ( v1 @ ( vd481 @ greater ) )
| ( vd469 @ ( vd480 @ less ) ) ),
inference(pattern_uni,[status(thm)],[28830:[bind(A,$thf( v1 )),bind(B,$thf( vd481 ))]]) ).
thf(478,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ vplus ) @ greater ) )
!= ( vd469 @ ( vd469 @ ( vd481 @ vmul ) @ greater ) ) )
| ( v1 != vd480 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[187,329]) ).
thf(479,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ vplus ) @ greater ) )
!= ( vd469 @ ( vd469 @ ( vd481 @ vmul ) @ greater ) ) )
| ( v1 != vd480 ) ),
inference(simp,[status(thm)],[478]) ).
thf(499,plain,
! [B: $i,A: $i] :
( ( A != vd469 )
| ( ( B @ ( A @ vplus ) )
!= ( vd469 @ ( vd481 @ vmul ) ) )
| ( v1 != vd480 ) ),
inference(simp,[status(thm)],[479]) ).
thf(503,plain,
! [A: $i] :
( ( ( A @ ( vd469 @ vplus ) )
!= ( vd469 @ ( vd481 @ vmul ) ) )
| ( v1 != vd480 ) ),
inference(simp,[status(thm)],[499]) ).
thf(9371,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ vplus ) )
!= ( vd481 @ ( vd480 @ vplus ) ) )
| ( ( B @ ( A @ vplus ) )
!= vd481 ) ),
inference(paramod_ordered,[status(thm)],[77,9348]) ).
thf(9372,plain,
( ( vd480 @ ( vd481 @ vplus ) )
!= vd481 ),
inference(pattern_uni,[status(thm)],[9371:[bind(A,$thf( vd481 )),bind(B,$thf( vd480 ))]]) ).
thf(15524,plain,
! [B: $i,A: $i] :
( ( ( vd480 @ ( vd481 @ vskolem9 ) @ ( vd480 @ vplus ) )
!= ( A @ ( B @ vplus ) ) )
| ( ( B @ ( A @ vplus ) )
= vd481 ) ),
inference(paramod_ordered,[status(thm)],[9644,77]) ).
thf(15525,plain,
( ( vd480 @ ( vd480 @ ( vd481 @ vskolem9 ) @ vplus ) )
= vd481 ),
inference(pattern_uni,[status(thm)],[15524:[bind(A,$thf( vd480 @ ( vd481 @ vskolem9 ) )),bind(B,$thf( vd480 ))]]) ).
thf(26078,plain,
! [B: $i,A: $i] :
( ( ( vd480 @ ( vd480 @ ( vd481 @ vskolem9 ) @ vplus ) )
!= ( B @ ( A @ vplus ) ) )
| ( ( vd481 @ ( A @ sk1 ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[15525,708]) ).
thf(26079,plain,
( ( vd481 @ ( vd480 @ ( vd481 @ vskolem9 ) @ sk1 ) )
= vd480 ),
inference(pattern_uni,[status(thm)],[26078:[bind(A,$thf( vd480 @ ( vd481 @ vskolem9 ) )),bind(B,$thf( vd480 ))]]) ).
thf(52,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ greater ) )
=> ( ( vd469 @ ( B @ ( A @ vskolem9 ) @ ( B @ vplus ) @ vmul ) )
= ( vd469 @ ( B @ ( A @ vskolem9 ) @ vmul ) @ ( vd469 @ ( B @ vmul ) @ vplus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(302, 0), 1)') ).
thf(242,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ greater ) )
=> ( ( vd469 @ ( B @ ( A @ vskolem9 ) @ ( B @ vplus ) @ vmul ) )
= ( vd469 @ ( B @ ( A @ vskolem9 ) @ vmul ) @ ( vd469 @ ( B @ vmul ) @ vplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(243,plain,
! [B: $i,A: $i] :
( ( ( vd469 @ ( B @ ( A @ vskolem9 ) @ ( B @ vplus ) @ vmul ) )
= ( vd469 @ ( B @ ( A @ vskolem9 ) @ vmul ) @ ( vd469 @ ( B @ vmul ) @ vplus ) ) )
| ~ ( B @ ( A @ greater ) ) ),
inference(cnf,[status(esa)],[242]) ).
thf(244,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ greater ) )
| ( ( vd469 @ ( B @ ( A @ vskolem9 ) @ vmul ) @ ( vd469 @ ( B @ vmul ) @ vplus ) )
= ( vd469 @ ( B @ ( A @ vskolem9 ) @ ( B @ vplus ) @ vmul ) ) ) ),
inference(lifteq,[status(thm)],[243]) ).
thf(58,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ vmul ) @ vmul ) )
= ( C @ ( B @ vmul ) @ ( A @ vmul ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(290, 0), 0)') ).
thf(264,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ vmul ) @ vmul ) )
= ( C @ ( B @ vmul ) @ ( A @ vmul ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(265,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ vmul ) @ vmul ) )
= ( C @ ( B @ vmul ) @ ( A @ vmul ) ) ),
inference(cnf,[status(esa)],[264]) ).
thf(266,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ vmul ) @ vmul ) )
= ( C @ ( B @ vmul ) @ ( A @ vmul ) ) ),
inference(lifteq,[status(thm)],[265]) ).
thf(1019,plain,
! [C: $i,B: $i,A: $i] :
( ( ( v1 @ ( A @ vplus ) )
!= ( C @ ( B @ vsucc @ vplus ) ) )
| ( ( A @ vsucc @ vsucc )
!= v1 ) ),
inference(paramod_ordered,[status(thm)],[70,633]) ).
thf(1020,plain,
! [A: $i] :
( ( A @ vsucc @ vsucc @ vsucc )
!= v1 ),
inference(pattern_uni,[status(thm)],[1019:[bind(A,$thf( D @ vsucc )),bind(B,$thf( D )),bind(C,$thf( v1 ))]]) ).
thf(1038,plain,
! [A: $i] :
( ( A @ vsucc @ vsucc @ vsucc )
!= v1 ),
inference(simp,[status(thm)],[1020]) ).
thf(5208,plain,
! [A: $i] :
( ( ( vd469 @ ( v1 @ sk7 ) @ vsucc )
!= ( A @ vsucc ) )
| ( ( vd469 @ vsucc @ vsucc )
!= v1 ) ),
inference(paramod_ordered,[status(thm)],[5150,1038]) ).
thf(5209,plain,
( ( vd469 @ vsucc @ vsucc )
!= v1 ),
inference(pattern_uni,[status(thm)],[5208:[bind(A,$thf( vd469 @ ( v1 @ sk7 ) ))]]) ).
thf(786,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ vplus ) )
!= ( D @ ( C @ vplus ) ) )
| ( D @ ( A @ ( B @ vplus ) @ greater ) ) ),
inference(paramod_ordered,[status(thm)],[77,481]) ).
thf(787,plain,
! [B: $i,A: $i] : ( B @ ( A @ ( B @ vplus ) @ greater ) ),
inference(pattern_uni,[status(thm)],[786:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(17201,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( B @ vplus ) @ greater ) )
!= ( vd469 @ ( vd469 @ sk4 @ greater ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[787,16302]) ).
thf(17202,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( B @ vplus ) @ greater ) )
!= ( vd469 @ ( vd469 @ sk4 @ greater ) ) ),
inference(simp,[status(thm)],[17201]) ).
thf(17225,plain,
! [B: $i,A: $i] :
( ( B != vd469 )
| ( ( A @ ( B @ vplus ) )
!= ( vd469 @ sk4 ) ) ),
inference(simp,[status(thm)],[17202]) ).
thf(17235,plain,
! [A: $i] :
( ( A @ ( vd469 @ vplus ) )
!= ( vd469 @ sk4 ) ),
inference(simp,[status(thm)],[17225]) ).
thf(3960,plain,
! [C: $i,B: $i,A: $i] :
( ( ( v1 @ ( A @ vplus ) )
!= ( C @ ( B @ vplus ) ) )
| ( ( A @ vsucc @ ( C @ sk5 ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[70,3959]) ).
thf(3961,plain,
! [A: $i] :
( ( A @ vsucc @ ( v1 @ sk5 ) )
= A ),
inference(pattern_uni,[status(thm)],[3960:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( v1 ))]]) ).
thf(5849,plain,
! [A: $i] :
( ( ( vd469 @ sk6 @ vsucc )
!= ( A @ vsucc ) )
| ( ( vd469 @ ( v1 @ sk5 ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[5679,3961]) ).
thf(5850,plain,
( ( vd469 @ ( v1 @ sk5 ) )
= ( vd469 @ sk6 ) ),
inference(pattern_uni,[status(thm)],[5849:[bind(A,$thf( vd469 @ sk6 ))]]) ).
thf(7009,plain,
( ( vd469 @ ( v1 @ sk5 ) )
= ( vd469 @ sk4 ) ),
inference(rewrite,[status(thm)],[5850,5879]) ).
thf(7026,plain,
! [A: $i] :
( ( ( vd469 @ ( v1 @ sk5 ) )
!= ( A @ vsucc @ ( A @ sk5 ) ) )
| ( ( vd469 @ sk4 )
= v1 ) ),
inference(paramod_ordered,[status(thm)],[7009,3981]) ).
thf(7041,plain,
! [A: $i] :
( ( ( A @ vsucc )
!= vd469 )
| ( v1 != A )
| ( ( vd469 @ sk4 )
= v1 ) ),
inference(simp,[status(thm)],[7026]) ).
thf(7046,plain,
( ( ( v1 @ vsucc )
!= vd469 )
| ( ( vd469 @ sk4 )
= v1 ) ),
inference(simp,[status(thm)],[7041]) ).
thf(22236,plain,
! [B: $i,A: $i] :
( ( ( vd469 @ ( vd480 @ less ) )
!= ( B @ ( A @ less ) ) )
| ( A @ ( B @ greater ) )
| ~ $true
| ( v1 != vd481 ) ),
inference(paramod_ordered,[status(thm)],[16473,232]) ).
thf(22237,plain,
! [B: $i,A: $i] :
( ( ( vd469 @ ( vd480 @ less ) )
!= ( B @ ( A @ less ) ) )
| ( A @ ( B @ greater ) )
| ( v1 != vd481 ) ),
inference(simp,[status(thm)],[22236]) ).
thf(22238,plain,
( ( vd480 @ ( vd469 @ greater ) )
| ( v1 != vd481 ) ),
inference(pattern_uni,[status(thm)],[22237:[bind(A,$thf( vd480 )),bind(B,$thf( vd469 ))]]) ).
thf(26503,plain,
! [A: $i] :
( ( v1 != v1 )
| ( vd480 @ ( vd469 @ greater ) )
| ( A != vd481 )
| ( A @ ( v1 @ less ) ) ),
inference(paramod_ordered,[status(thm)],[1448,22238]) ).
thf(26504,plain,
! [A: $i] :
( ( vd480 @ ( vd469 @ greater ) )
| ( A != vd481 )
| ( A @ ( v1 @ less ) ) ),
inference(pattern_uni,[status(thm)],[26503:[]]) ).
thf(26528,plain,
( ( vd480 @ ( vd469 @ greater ) )
| ( vd481 @ ( v1 @ less ) ) ),
inference(simp,[status(thm)],[26504]) ).
thf(25364,plain,
! [B: $i,A: $i] :
( ( ( v1 @ ( vd481 @ greater ) )
!= ( B @ ( A @ greater ) ) )
| ~ ( B @ ( A @ less ) )
| ~ $true
| ( vd480 != vd469 ) ),
inference(paramod_ordered,[status(thm)],[22122,249]) ).
thf(25365,plain,
! [B: $i,A: $i] :
( ( ( v1 @ ( vd481 @ greater ) )
!= ( B @ ( A @ greater ) ) )
| ~ ( B @ ( A @ less ) )
| ( vd480 != vd469 ) ),
inference(simp,[status(thm)],[25364]) ).
thf(25366,plain,
( ~ ( v1 @ ( vd481 @ less ) )
| ( vd480 != vd469 ) ),
inference(pattern_uni,[status(thm)],[25365:[bind(A,$thf( vd481 )),bind(B,$thf( v1 ))]]) ).
thf(3504,plain,
! [B: $i,A: $i] :
( ( ( vd481 @ ( vd480 @ less ) )
!= ( A @ ( B @ less ) ) )
| ( A @ ( B @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[250,110]) ).
thf(3505,plain,
! [B: $i,A: $i] :
( ( ( vd481 @ ( vd480 @ less ) )
!= ( A @ ( B @ less ) ) )
| ( A @ ( B @ leq ) ) ),
inference(simp,[status(thm)],[3504]) ).
thf(3506,plain,
vd481 @ ( vd480 @ leq ),
inference(pattern_uni,[status(thm)],[3505:[bind(A,$thf( vd481 )),bind(B,$thf( vd480 ))]]) ).
thf(3521,plain,
! [B: $i,A: $i] :
( ( ( vd481 @ ( vd480 @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( A @ ( B @ geq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3506,97]) ).
thf(3522,plain,
! [B: $i,A: $i] :
( ( ( vd481 @ ( vd480 @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( A @ ( B @ geq ) ) ),
inference(simp,[status(thm)],[3521]) ).
thf(3523,plain,
vd480 @ ( vd481 @ geq ),
inference(pattern_uni,[status(thm)],[3522:[bind(A,$thf( vd480 )),bind(B,$thf( vd481 ))]]) ).
thf(33918,plain,
( ( vd469 != vd469 )
| ( ( vd480 @ vsucc )
!= vd481 ) ),
inference(simp,[status(thm)],[11045]) ).
thf(34036,plain,
( ( vd480 @ vsucc )
!= vd481 ),
inference(simp,[status(thm)],[33918]) ).
thf(373,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ vsucc @ ( A @ vplus ) )
!= ( D @ ( C @ vplus ) ) )
| ( ( B @ ( A @ vplus ) @ vsucc )
!= C ) ),
inference(paramod_ordered,[status(thm)],[68,74]) ).
thf(374,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ vplus ) @ vsucc )
!= A ),
inference(pattern_uni,[status(thm)],[373:[bind(A,$thf( A )),bind(B,$thf( E )),bind(C,$thf( A )),bind(D,$thf( E @ vsucc ))]]) ).
thf(375,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ vplus ) @ vsucc )
!= A ),
inference(simp,[status(thm)],[374]) ).
thf(15023,plain,
! [A: $i] :
( ( ( A @ vsucc @ sk4 )
!= ( vd469 @ sk4 ) )
| ( A != vd480 )
| ( vd481 @ ( vd469 @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[337,8422]) ).
thf(15025,plain,
( ( ( vd480 @ vsucc )
!= vd469 )
| ( vd481 @ ( vd469 @ leq ) ) ),
inference(simp,[status(thm)],[15023]) ).
thf(33,axiom,
! [A: $i] :
( ( A @ vsucc )
!= v1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(restrictor(axiom(1)), holds(scope(axiom(1)), 2, 0))') ).
thf(180,plain,
! [A: $i] :
( ( A @ vsucc )
!= v1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(688,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ vplus ) )
!= ( D @ ( C @ vplus ) ) )
| ( ( A @ ( B @ vplus ) @ vsucc )
!= v1 ) ),
inference(paramod_ordered,[status(thm)],[77,683]) ).
thf(689,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ vplus ) @ vsucc )
!= v1 ),
inference(pattern_uni,[status(thm)],[688:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(189,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ greater ) )
| ( A != B ) ),
inference(cnf,[status(esa)],[188]) ).
thf(190,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ greater ) )
| ( A != B ) ),
inference(lifteq,[status(thm)],[189]) ).
thf(191,plain,
! [A: $i] :
~ ( A @ ( A @ greater ) ),
inference(simp,[status(thm)],[190]) ).
thf(284,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ leq ) )
!= ( F @ ( E @ leq ) ) )
| ( F @ ( D @ leq ) )
| ~ ( E @ ( D @ leq ) )
| ~ $true
| ~ ( B @ ( A @ leq ) )
| ~ ( C @ ( B @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[62,62]) ).
thf(285,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ leq ) )
!= ( F @ ( E @ leq ) ) )
| ( F @ ( D @ leq ) )
| ~ ( E @ ( D @ leq ) )
| ~ ( B @ ( A @ leq ) )
| ~ ( C @ ( B @ leq ) ) ),
inference(simp,[status(thm)],[284]) ).
thf(286,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ leq ) )
| ~ ( A @ ( D @ leq ) )
| ~ ( B @ ( A @ leq ) )
| ~ ( C @ ( B @ leq ) ) ),
inference(pattern_uni,[status(thm)],[285:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( A )),bind(F,$thf( C ))]]) ).
thf(17,axiom,
! [A: $i,B: $i,C: $i] :
( ( A = B )
=> ( ( C @ ( A @ vplus ) )
= ( C @ ( B @ vplus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(193), 0), 1)') ).
thf(118,plain,
! [A: $i,B: $i,C: $i] :
( ( A = B )
=> ( ( C @ ( A @ vplus ) )
= ( C @ ( B @ vplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(25869,plain,
! [B: $i,A: $i] :
( ( ( vd480 @ ( vd480 @ ( vd481 @ vskolem9 ) @ vplus ) )
!= ( B @ ( A @ vplus ) ) )
| ( ( vd481 @ ( B @ sk5 ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[15525,3959]) ).
thf(25870,plain,
( ( vd481 @ ( vd480 @ sk5 ) )
= ( vd480 @ ( vd481 @ vskolem9 ) ) ),
inference(pattern_uni,[status(thm)],[25869:[bind(A,$thf( vd480 @ ( vd481 @ vskolem9 ) )),bind(B,$thf( vd480 ))]]) ).
thf(5716,plain,
! [A: $i] :
( ( ( A @ vsucc @ sk6 )
!= ( vd469 @ sk6 ) )
| ( A != vd469 ) ),
inference(paramod_ordered,[status(thm)],[338,5681]) ).
thf(5721,plain,
( ( vd469 @ vsucc )
!= vd469 ),
inference(simp,[status(thm)],[5716]) ).
thf(5736,plain,
! [A: $i] :
( ( ( A @ vskolem2 @ vsucc )
!= ( vd469 @ vsucc ) )
| ( A != vd469 )
| ( A = v1 ) ),
inference(paramod_ordered,[status(thm)],[100,5721]) ).
thf(5738,plain,
( ( ( vd469 @ vskolem2 )
!= vd469 )
| ( v1 = vd469 ) ),
inference(simp,[status(thm)],[5736]) ).
thf(6949,plain,
( ( vd469 @ vskolem2 )
!= vd469 ),
inference(simplifyReflect,[status(thm)],[5738,314]) ).
thf(33970,plain,
( ( ( vd469 @ sk4 @ vsucc )
!= ( vd480 @ vsucc ) )
| ( ( vd469 @ ( vd469 @ vmul ) )
!= ( vd469 @ ( vd481 @ vmul ) ) ) ),
inference(paramod_ordered,[status(thm)],[6180,11045]) ).
thf(34001,plain,
( ( ( vd469 @ sk4 )
!= vd480 )
| ( vd469 != vd469 )
| ( vd469 != vd481 ) ),
inference(simp,[status(thm)],[33970]) ).
thf(34033,plain,
( ( ( vd469 @ sk4 )
!= vd480 )
| ( vd469 != vd481 ) ),
inference(simp,[status(thm)],[34001]) ).
thf(23,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ geq ) )
& ( D @ ( C @ geq ) ) )
=> ( D @ ( B @ vplus ) @ ( C @ ( A @ vplus ) @ geq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(223, 0), 0)') ).
thf(143,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ geq ) )
& ( D @ ( C @ geq ) ) )
=> ( D @ ( B @ vplus ) @ ( C @ ( A @ vplus ) @ geq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(144,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ vplus ) @ ( C @ ( A @ vplus ) @ geq ) )
| ~ ( B @ ( A @ geq ) )
| ~ ( D @ ( C @ geq ) ) ),
inference(cnf,[status(esa)],[143]) ).
thf(16803,plain,
( ( ( vd481 @ ( vd480 @ vsucc @ leq ) )
!= ( v1 @ ( vd469 @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[8317,16480]) ).
thf(16804,plain,
( ( vd481 @ ( vd480 @ vsucc @ leq ) )
!= ( v1 @ ( vd469 @ leq ) ) ),
inference(simp,[status(thm)],[16803]) ).
thf(16823,plain,
( ( v1 != vd481 )
| ( ( vd480 @ vsucc )
!= vd469 ) ),
inference(simp,[status(thm)],[16804]) ).
thf(1784,plain,
! [A: $i] :
( ( v1 != v1 )
| ( A != vd481 )
| ~ ( vd469 @ ( vd480 @ vmul ) @ ( vd469 @ greater ) )
| ( A @ ( v1 @ less ) ) ),
inference(paramod_ordered,[status(thm)],[1448,330]) ).
thf(1785,plain,
! [A: $i] :
( ( A != vd481 )
| ~ ( vd469 @ ( vd480 @ vmul ) @ ( vd469 @ greater ) )
| ( A @ ( v1 @ less ) ) ),
inference(pattern_uni,[status(thm)],[1784:[]]) ).
thf(2055,plain,
( ~ ( vd469 @ ( vd480 @ vmul ) @ ( vd469 @ greater ) )
| ( vd481 @ ( v1 @ less ) ) ),
inference(simp,[status(thm)],[1785]) ).
thf(7307,plain,
! [B: $i,A: $i] :
( ( ( vd481 @ ( vd480 @ sk7 ) @ ( vd480 @ vplus ) )
!= ( B @ ( A @ vplus ) ) )
| ( B @ ( vd481 @ greater ) ) ),
inference(paramod_ordered,[status(thm)],[5038,481]) ).
thf(7308,plain,
vd481 @ ( vd480 @ sk7 ) @ ( vd481 @ greater ),
inference(pattern_uni,[status(thm)],[7307:[bind(A,$thf( vd480 )),bind(B,$thf( vd481 @ ( vd480 @ sk7 ) ))]]) ).
thf(9091,plain,
vd481 @ ( vd480 @ sk1 ) @ ( vd481 @ greater ),
inference(rewrite,[status(thm)],[7308,7425]) ).
thf(16228,plain,
! [B: $i,A: $i] :
( ( ( vd481 @ ( vd480 @ sk1 ) @ ( vd481 @ greater ) )
!= ( B @ ( A @ greater ) ) )
| ~ ( B @ ( A @ less ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9091,249]) ).
thf(16229,plain,
! [B: $i,A: $i] :
( ( ( vd481 @ ( vd480 @ sk1 ) @ ( vd481 @ greater ) )
!= ( B @ ( A @ greater ) ) )
| ~ ( B @ ( A @ less ) ) ),
inference(simp,[status(thm)],[16228]) ).
thf(16230,plain,
~ ( vd481 @ ( vd480 @ sk1 ) @ ( vd481 @ less ) ),
inference(pattern_uni,[status(thm)],[16229:[bind(A,$thf( vd481 )),bind(B,$thf( vd481 @ ( vd480 @ sk1 ) ))]]) ).
thf(20547,plain,
! [A: $i] :
( ( ( A @ vsucc @ ( A @ less ) )
!= ( vd481 @ ( vd480 @ sk1 ) @ ( vd481 @ less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[388,16230]) ).
thf(20548,plain,
! [A: $i] :
( ( A @ vsucc @ ( A @ less ) )
!= ( vd481 @ ( vd480 @ sk1 ) @ ( vd481 @ less ) ) ),
inference(simp,[status(thm)],[20547]) ).
thf(20635,plain,
! [A: $i] :
( ( ( A @ vsucc )
!= ( vd481 @ ( vd480 @ sk1 ) ) )
| ( A != vd481 ) ),
inference(simp,[status(thm)],[20548]) ).
thf(20650,plain,
( ( vd481 @ ( vd480 @ sk1 ) )
!= ( vd481 @ vsucc ) ),
inference(simp,[status(thm)],[20635]) ).
thf(21879,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ vplus ) @ ( A @ sk1 ) )
!= ( vd481 @ ( vd480 @ sk1 ) ) )
| ( B
!= ( vd481 @ vsucc ) ) ),
inference(paramod_ordered,[status(thm)],[708,20650]) ).
thf(21886,plain,
! [A: $i] :
( ( ( vd481 @ vsucc @ ( A @ vplus ) )
!= vd481 )
| ( A != vd480 ) ),
inference(simp,[status(thm)],[21879]) ).
thf(21902,plain,
( ( vd481 @ vsucc @ ( vd480 @ vplus ) )
!= vd481 ),
inference(simp,[status(thm)],[21886]) ).
thf(23691,plain,
( ( vd481 @ ( vd480 @ vplus ) @ vsucc )
!= vd481 ),
inference(rewrite,[status(thm)],[21902,68]) ).
thf(23750,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ vplus ) )
!= ( vd481 @ ( vd480 @ vplus ) ) )
| ( ( B @ ( A @ vplus ) @ vsucc )
!= vd481 ) ),
inference(paramod_ordered,[status(thm)],[77,23691]) ).
thf(23751,plain,
( ( vd480 @ ( vd481 @ vplus ) @ vsucc )
!= vd481 ),
inference(pattern_uni,[status(thm)],[23750:[bind(A,$thf( vd481 )),bind(B,$thf( vd480 ))]]) ).
thf(22034,plain,
! [B: $i,A: $i] :
( ( ( vd481 @ ( v1 @ less ) )
!= ( B @ ( A @ less ) ) )
| ~ $true
| ~ ( B @ ( A @ greater ) )
| ( vd480 != vd469 ) ),
inference(paramod_ordered,[status(thm)],[16464,249]) ).
thf(22035,plain,
! [B: $i,A: $i] :
( ( ( vd481 @ ( v1 @ less ) )
!= ( B @ ( A @ less ) ) )
| ~ ( B @ ( A @ greater ) )
| ( vd480 != vd469 ) ),
inference(simp,[status(thm)],[22034]) ).
thf(22036,plain,
( ~ ( vd481 @ ( v1 @ greater ) )
| ( vd480 != vd469 ) ),
inference(pattern_uni,[status(thm)],[22035:[bind(A,$thf( v1 )),bind(B,$thf( vd481 ))]]) ).
thf(230,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ less ) )
| ~ ( B @ ( A @ greater ) ) ),
inference(cnf,[status(esa)],[229]) ).
thf(34586,plain,
! [A: $i] :
( ( ( A @ vsucc @ sk4 )
!= ( vd469 @ sk4 ) )
| ( A != vd480 )
| ( vd469 != vd481 ) ),
inference(paramod_ordered,[status(thm)],[337,34033]) ).
thf(34588,plain,
( ( ( vd480 @ vsucc )
!= vd469 )
| ( vd469 != vd481 ) ),
inference(simp,[status(thm)],[34586]) ).
thf(16336,plain,
! [B: $i,A: $i] :
( ( ( vd481 @ ( vd480 @ ( vd481 @ vskolem9 ) @ less ) )
!= ( B @ ( A @ less ) ) )
| ~ $true
| ~ ( B @ ( A @ greater ) ) ),
inference(paramod_ordered,[status(thm)],[15540,249]) ).
thf(16337,plain,
! [B: $i,A: $i] :
( ( ( vd481 @ ( vd480 @ ( vd481 @ vskolem9 ) @ less ) )
!= ( B @ ( A @ less ) ) )
| ~ ( B @ ( A @ greater ) ) ),
inference(simp,[status(thm)],[16336]) ).
thf(16338,plain,
~ ( vd481 @ ( vd480 @ ( vd481 @ vskolem9 ) @ greater ) ),
inference(pattern_uni,[status(thm)],[16337:[bind(A,$thf( vd480 @ ( vd481 @ vskolem9 ) )),bind(B,$thf( vd481 ))]]) ).
thf(482,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ vplus ) )
!= ( D @ ( C @ vplus ) ) )
| ( C @ ( A @ ( B @ vplus ) @ greater ) ) ),
inference(paramod_ordered,[status(thm)],[77,187]) ).
thf(483,plain,
! [B: $i,A: $i] : ( A @ ( A @ ( B @ vplus ) @ greater ) ),
inference(pattern_uni,[status(thm)],[482:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(26402,plain,
! [B: $i,A: $i] :
( ( ( vd480 @ ( vd469 @ greater ) )
!= ( B @ ( A @ greater ) ) )
| ~ ( B @ ( A @ less ) )
| ~ $true
| ( v1 != vd481 ) ),
inference(paramod_ordered,[status(thm)],[22238,249]) ).
thf(26403,plain,
! [B: $i,A: $i] :
( ( ( vd480 @ ( vd469 @ greater ) )
!= ( B @ ( A @ greater ) ) )
| ~ ( B @ ( A @ less ) )
| ( v1 != vd481 ) ),
inference(simp,[status(thm)],[26402]) ).
thf(26404,plain,
( ~ ( vd480 @ ( vd469 @ less ) )
| ( v1 != vd481 ) ),
inference(pattern_uni,[status(thm)],[26403:[bind(A,$thf( vd469 )),bind(B,$thf( vd480 ))]]) ).
thf(739,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ vplus ) )
!= ( C @ ( vd469 @ ( vd480 @ vmul ) @ vplus ) ) )
| ( ( B @ ( A @ vplus ) )
!= ( vd469 @ ( vd481 @ vmul ) ) ) ),
inference(paramod_ordered,[status(thm)],[77,501]) ).
thf(740,plain,
! [A: $i] :
( ( vd469 @ ( vd480 @ vmul ) @ ( A @ vplus ) )
!= ( vd469 @ ( vd481 @ vmul ) ) ),
inference(pattern_uni,[status(thm)],[739:[bind(A,$thf( A )),bind(B,$thf( vd469 @ ( vd480 @ vmul ) )),bind(C,$thf( A ))]]) ).
thf(755,plain,
! [B: $i,A: $i] :
( ( ( A @ ( v1 @ vmul ) )
!= ( vd469 @ ( vd480 @ vmul ) ) )
| ( ( A @ ( B @ vplus ) )
!= ( vd469 @ ( vd481 @ vmul ) ) ) ),
inference(paramod_ordered,[status(thm)],[220,740]) ).
thf(768,plain,
! [B: $i,A: $i] :
( ( A != vd469 )
| ( v1 != vd480 )
| ( ( A @ ( B @ vplus ) )
!= ( vd469 @ ( vd481 @ vmul ) ) ) ),
inference(simp,[status(thm)],[755]) ).
thf(769,plain,
! [A: $i] :
( ( v1 != vd480 )
| ( ( vd469 @ ( A @ vplus ) )
!= ( vd469 @ ( vd481 @ vmul ) ) ) ),
inference(simp,[status(thm)],[768]) ).
thf(197,plain,
! [B: $i,A: $i] :
( ( ( vd469 @ ( A @ vmul ) )
= ( vd469 @ ( B @ ( A @ vskolem9 ) @ ( B @ vplus ) @ vmul ) ) )
| ~ ( B @ ( A @ greater ) ) ),
inference(cnf,[status(esa)],[196]) ).
thf(198,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ greater ) )
| ( ( vd469 @ ( B @ ( A @ vskolem9 ) @ ( B @ vplus ) @ vmul ) )
= ( vd469 @ ( A @ vmul ) ) ) ),
inference(lifteq,[status(thm)],[197]) ).
thf(130,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ less ) )
| ~ ( B @ ( A @ less ) )
| ~ ( C @ ( B @ less ) ) ),
inference(cnf,[status(esa)],[129]) ).
thf(16405,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ vplus ) @ ( B @ less ) )
!= ( vd480 @ ( vd481 @ less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[412,16236]) ).
thf(16406,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ vplus ) @ ( B @ less ) )
!= ( vd480 @ ( vd481 @ less ) ) ),
inference(simp,[status(thm)],[16405]) ).
thf(16442,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ vplus ) )
!= vd480 )
| ( B != vd481 ) ),
inference(simp,[status(thm)],[16406]) ).
thf(16474,plain,
! [A: $i] :
( ( vd481 @ ( A @ vplus ) )
!= vd480 ),
inference(simp,[status(thm)],[16442]) ).
thf(5247,plain,
! [A: $i] :
( ( ( vd469 @ ( v1 @ sk7 ) @ vsucc )
!= ( A @ vsucc ) )
| ( ( vd469 @ sk4 )
= A ) ),
inference(paramod_ordered,[status(thm)],[5150,337]) ).
thf(5248,plain,
( ( vd469 @ ( v1 @ sk7 ) )
= ( vd469 @ sk4 ) ),
inference(pattern_uni,[status(thm)],[5247:[bind(A,$thf( vd469 @ ( v1 @ sk7 ) ))]]) ).
thf(28522,plain,
! [A: $i] :
( ( v1 != v1 )
| ( vd480 @ ( vd469 @ geq ) )
| ( A != vd481 )
| ( A @ ( v1 @ less ) ) ),
inference(paramod_ordered,[status(thm)],[1448,25544]) ).
thf(28523,plain,
! [A: $i] :
( ( vd480 @ ( vd469 @ geq ) )
| ( A != vd481 )
| ( A @ ( v1 @ less ) ) ),
inference(pattern_uni,[status(thm)],[28522:[]]) ).
thf(28533,plain,
( ( vd480 @ ( vd469 @ geq ) )
| ( vd481 @ ( v1 @ less ) ) ),
inference(simp,[status(thm)],[28523]) ).
thf(16303,plain,
! [B: $i,A: $i] :
( ( ( vd469 @ sk4 @ ( vd469 @ greater ) )
!= ( B @ ( A @ greater ) ) )
| ~ ( B @ ( A @ less ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6217,249]) ).
thf(16304,plain,
! [B: $i,A: $i] :
( ( ( vd469 @ sk4 @ ( vd469 @ greater ) )
!= ( B @ ( A @ greater ) ) )
| ~ ( B @ ( A @ less ) ) ),
inference(simp,[status(thm)],[16303]) ).
thf(16305,plain,
~ ( vd469 @ sk4 @ ( vd469 @ less ) ),
inference(pattern_uni,[status(thm)],[16304:[bind(A,$thf( vd469 )),bind(B,$thf( vd469 @ sk4 ))]]) ).
thf(606,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ vsucc @ ( v1 @ less ) )
!= ( C @ vsucc @ ( B @ less ) ) )
| ( C @ ( B @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[390,598]) ).
thf(607,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ vsucc @ ( v1 @ less ) )
!= ( C @ vsucc @ ( B @ less ) ) )
| ( C @ ( B @ leq ) ) ),
inference(simp,[status(thm)],[606]) ).
thf(608,plain,
! [A: $i] : ( A @ ( v1 @ leq ) ),
inference(pattern_uni,[status(thm)],[607:[bind(A,$thf( A )),bind(B,$thf( v1 )),bind(C,$thf( A ))]]) ).
thf(51,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ greater ) )
=> ( C @ ( B @ vplus ) @ ( C @ ( A @ vplus ) @ greater ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(193), 0), 2)') ).
thf(239,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ greater ) )
=> ( C @ ( B @ vplus ) @ ( C @ ( A @ vplus ) @ greater ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(240,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ greater ) )
=> ! [C: $i] : ( C @ ( B @ vplus ) @ ( C @ ( A @ vplus ) @ greater ) ) ),
inference(miniscope,[status(thm)],[239]) ).
thf(241,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ vplus ) @ ( C @ ( A @ vplus ) @ greater ) )
| ~ ( B @ ( A @ greater ) ) ),
inference(cnf,[status(esa)],[240]) ).
thf(35390,plain,
! [B: $i,A: $i] :
( ( ( vd469 @ ( vd469 @ vmul ) @ ( v1 @ less ) )
!= ( B @ ( A @ less ) ) )
| ~ $true
| ~ ( B @ ( A @ greater ) ) ),
inference(paramod_ordered,[status(thm)],[35363,249]) ).
thf(35391,plain,
! [B: $i,A: $i] :
( ( ( vd469 @ ( vd469 @ vmul ) @ ( v1 @ less ) )
!= ( B @ ( A @ less ) ) )
| ~ ( B @ ( A @ greater ) ) ),
inference(simp,[status(thm)],[35390]) ).
thf(35392,plain,
~ ( vd469 @ ( vd469 @ vmul ) @ ( v1 @ greater ) ),
inference(pattern_uni,[status(thm)],[35391:[bind(A,$thf( v1 )),bind(B,$thf( vd469 @ ( vd469 @ vmul ) ))]]) ).
thf(35653,plain,
! [A: $i] :
( ( ( A @ ( A @ vsucc @ greater ) )
!= ( vd469 @ ( vd469 @ vmul ) @ ( v1 @ greater ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[491,35392]) ).
thf(35654,plain,
! [A: $i] :
( ( A @ ( A @ vsucc @ greater ) )
!= ( vd469 @ ( vd469 @ vmul ) @ ( v1 @ greater ) ) ),
inference(simp,[status(thm)],[35653]) ).
thf(35659,plain,
! [A: $i] :
( ( A
!= ( vd469 @ ( vd469 @ vmul ) ) )
| ( ( A @ vsucc )
!= v1 ) ),
inference(simp,[status(thm)],[35654]) ).
thf(35689,plain,
( ( vd469 @ ( vd469 @ vmul ) @ vsucc )
!= v1 ),
inference(simp,[status(thm)],[35659]) ).
thf(13983,plain,
! [A: $i] :
( ( ( A @ vsucc @ sk4 )
!= ( vd469 @ sk4 ) )
| ( A != vd480 )
| ( vd469 @ ( vd481 @ geq ) ) ),
inference(paramod_ordered,[status(thm)],[337,8342]) ).
thf(13985,plain,
( ( ( vd480 @ vsucc )
!= vd469 )
| ( vd469 @ ( vd481 @ geq ) ) ),
inference(simp,[status(thm)],[13983]) ).
thf(108,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ leq ) )
| ( B != A ) ),
inference(cnfConj,[status(thm)],[105]) ).
thf(111,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ leq ) )
| ( B != A ) ),
inference(lifteq,[status(thm)],[108]) ).
thf(112,plain,
! [A: $i] : ( A @ ( A @ leq ) ),
inference(simp,[status(thm)],[111]) ).
thf(8066,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ vmul ) @ vplus ) )
!= ( C @ ( vd469 @ ( vd480 @ vmul ) @ vplus ) ) )
| ( ( B @ vsucc @ ( A @ vmul ) )
!= ( vd469 @ ( vd481 @ vmul ) ) ) ),
inference(paramod_ordered,[status(thm)],[212,501]) ).
thf(8067,plain,
( ( vd469 @ vsucc @ ( vd480 @ vmul ) )
!= ( vd469 @ ( vd481 @ vmul ) ) ),
inference(pattern_uni,[status(thm)],[8066:[bind(A,$thf( vd480 )),bind(B,$thf( vd469 )),bind(C,$thf( vd480 ))]]) ).
thf(16380,plain,
( ( ( vd469 @ ( v1 @ less ) )
!= ( vd480 @ ( vd481 @ less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1975,16236]) ).
thf(16381,plain,
( ( vd469 @ ( v1 @ less ) )
!= ( vd480 @ ( vd481 @ less ) ) ),
inference(simp,[status(thm)],[16380]) ).
thf(16457,plain,
( ( vd480 != vd469 )
| ( v1 != vd481 ) ),
inference(simp,[status(thm)],[16381]) ).
thf(24,axiom,
! [A: $i,B: $i] :
( ~ ? [C: $i] :
( B
= ( C @ ( A @ vplus ) ) )
| ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(88), 0), 1)') ).
thf(145,plain,
! [A: $i,B: $i] :
( ~ ? [C: $i] :
( B
= ( C @ ( A @ vplus ) ) )
| ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(1048,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ vplus ) )
!= ( D @ ( C @ vplus ) ) )
| ( ( A @ ( B @ vplus ) @ vsucc @ vsucc )
!= v1 ) ),
inference(paramod_ordered,[status(thm)],[77,694]) ).
thf(1049,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ vplus ) @ vsucc @ vsucc )
!= v1 ),
inference(pattern_uni,[status(thm)],[1048:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(8348,plain,
! [B: $i,A: $i] :
( ( ( v1 @ vsucc @ ( vd469 @ geq ) )
!= ( B @ ( A @ geq ) ) )
| ( A @ ( B @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[8261,102]) ).
thf(8349,plain,
! [B: $i,A: $i] :
( ( ( v1 @ vsucc @ ( vd469 @ geq ) )
!= ( B @ ( A @ geq ) ) )
| ( A @ ( B @ leq ) ) ),
inference(simp,[status(thm)],[8348]) ).
thf(8350,plain,
vd469 @ ( v1 @ vsucc @ leq ),
inference(pattern_uni,[status(thm)],[8349:[bind(A,$thf( vd469 )),bind(B,$thf( v1 @ vsucc ))]]) ).
thf(259,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ geq ) )
| ( B != A ) ),
inference(cnfConj,[status(thm)],[256]) ).
thf(262,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ geq ) )
| ( B != A ) ),
inference(lifteq,[status(thm)],[259]) ).
thf(263,plain,
! [A: $i] : ( A @ ( A @ geq ) ),
inference(simp,[status(thm)],[262]) ).
thf(561,plain,
! [A: $i] :
( ( ( A @ ( A @ vsucc @ greater ) )
!= ( vd469 @ ( vd480 @ vmul ) @ ( vd469 @ ( vd481 @ vmul ) @ greater ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[491,60]) ).
thf(562,plain,
! [A: $i] :
( ( A @ ( A @ vsucc @ greater ) )
!= ( vd469 @ ( vd480 @ vmul ) @ ( vd469 @ ( vd481 @ vmul ) @ greater ) ) ),
inference(simp,[status(thm)],[561]) ).
thf(567,plain,
! [A: $i] :
( ( A
!= ( vd469 @ ( vd480 @ vmul ) ) )
| ( ( A @ vsucc )
!= ( vd469 @ ( vd481 @ vmul ) ) ) ),
inference(simp,[status(thm)],[562]) ).
thf(571,plain,
( ( vd469 @ ( vd480 @ vmul ) @ vsucc )
!= ( vd469 @ ( vd481 @ vmul ) ) ),
inference(simp,[status(thm)],[567]) ).
thf(8724,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ vmul ) )
!= ( vd469 @ ( vd480 @ vmul ) ) )
| ( ( A @ ( B @ vmul ) @ vsucc )
!= ( vd469 @ ( vd481 @ vmul ) ) ) ),
inference(paramod_ordered,[status(thm)],[223,571]) ).
thf(8725,plain,
( ( vd480 @ ( vd469 @ vmul ) @ vsucc )
!= ( vd469 @ ( vd481 @ vmul ) ) ),
inference(pattern_uni,[status(thm)],[8724:[bind(A,$thf( vd480 )),bind(B,$thf( vd469 ))]]) ).
thf(16388,plain,
! [A: $i] :
( ( ( A @ vsucc @ ( A @ less ) )
!= ( vd480 @ ( vd481 @ less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[388,16236]) ).
thf(16389,plain,
! [A: $i] :
( ( A @ vsucc @ ( A @ less ) )
!= ( vd480 @ ( vd481 @ less ) ) ),
inference(simp,[status(thm)],[16388]) ).
thf(16449,plain,
! [A: $i] :
( ( ( A @ vsucc )
!= vd480 )
| ( A != vd481 ) ),
inference(simp,[status(thm)],[16389]) ).
thf(16461,plain,
( ( vd481 @ vsucc )
!= vd480 ),
inference(simp,[status(thm)],[16449]) ).
thf(7581,plain,
! [B: $i,A: $i] :
( ( ( v1 @ ( vd469 @ greater ) )
!= ( A @ ( B @ greater ) ) )
| ~ $true
| ( ( A @ ( B @ sk8 ) @ ( A @ vplus ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[5169,204]) ).
thf(7582,plain,
! [B: $i,A: $i] :
( ( ( v1 @ ( vd469 @ greater ) )
!= ( A @ ( B @ greater ) ) )
| ( ( A @ ( B @ sk8 ) @ ( A @ vplus ) )
= B ) ),
inference(simp,[status(thm)],[7581]) ).
thf(7583,plain,
( ( v1 @ ( vd469 @ sk8 ) @ ( v1 @ vplus ) )
= vd469 ),
inference(pattern_uni,[status(thm)],[7582:[bind(A,$thf( v1 )),bind(B,$thf( vd469 ))]]) ).
thf(10447,plain,
( ( v1 @ ( vd469 @ sk8 ) @ vsucc )
= vd469 ),
inference(rewrite,[status(thm)],[7583,177]) ).
thf(10532,plain,
! [A: $i] :
( ( ( v1 @ ( vd469 @ sk8 ) @ vsucc )
!= ( A @ vsucc ) )
| ( ( vd469 @ sk6 )
= A ) ),
inference(paramod_ordered,[status(thm)],[10447,338]) ).
thf(10533,plain,
( ( v1 @ ( vd469 @ sk8 ) )
= ( vd469 @ sk6 ) ),
inference(pattern_uni,[status(thm)],[10532:[bind(A,$thf( v1 @ ( vd469 @ sk8 ) ))]]) ).
thf(11198,plain,
( ( v1 @ ( vd469 @ sk8 ) )
= ( vd469 @ sk4 ) ),
inference(rewrite,[status(thm)],[10533,5879]) ).
thf(29762,plain,
! [B: $i,A: $i] :
( ( ( vd481 @ ( v1 @ less ) )
!= ( B @ ( A @ less ) ) )
| ( A @ ( B @ greater ) )
| ~ $true
| ( vd480 @ ( vd469 @ greater ) ) ),
inference(paramod_ordered,[status(thm)],[26528,232]) ).
thf(29763,plain,
! [B: $i,A: $i] :
( ( ( vd481 @ ( v1 @ less ) )
!= ( B @ ( A @ less ) ) )
| ( A @ ( B @ greater ) )
| ( vd480 @ ( vd469 @ greater ) ) ),
inference(simp,[status(thm)],[29762]) ).
thf(29764,plain,
( ( v1 @ ( vd481 @ greater ) )
| ( vd480 @ ( vd469 @ greater ) ) ),
inference(pattern_uni,[status(thm)],[29763:[bind(A,$thf( v1 )),bind(B,$thf( vd481 ))]]) ).
thf(527,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ vsucc @ ( A @ vplus ) )
!= ( E @ ( D @ ( C @ vplus ) @ vplus ) ) )
| ( ( B @ ( A @ vplus ) @ vsucc )
!= C ) ),
inference(paramod_ordered,[status(thm)],[68,81]) ).
thf(528,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ vplus ) @ vplus ) @ vsucc )
!= A ),
inference(pattern_uni,[status(thm)],[527:[bind(A,$thf( G @ ( F @ vplus ) )),bind(B,$thf( H )),bind(C,$thf( F )),bind(D,$thf( G )),bind(E,$thf( H @ vsucc ))]]) ).
thf(533,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ vplus ) @ vplus ) @ vsucc )
!= A ),
inference(simp,[status(thm)],[528]) ).
thf(30513,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ vplus ) @ ( A @ vplus ) @ vsucc )
!= A ),
inference(rewrite,[status(thm)],[533,95]) ).
thf(27104,plain,
! [B: $i,A: $i] :
( ( ( vd480 @ ( vd481 @ vsucc @ greater ) )
!= ( B @ ( A @ greater ) ) )
| ~ ( B @ ( A @ less ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[26808,249]) ).
thf(27105,plain,
! [B: $i,A: $i] :
( ( ( vd480 @ ( vd481 @ vsucc @ greater ) )
!= ( B @ ( A @ greater ) ) )
| ~ ( B @ ( A @ less ) ) ),
inference(simp,[status(thm)],[27104]) ).
thf(27106,plain,
~ ( vd480 @ ( vd481 @ vsucc @ less ) ),
inference(pattern_uni,[status(thm)],[27105:[bind(A,$thf( vd481 @ vsucc )),bind(B,$thf( vd480 ))]]) ).
thf(35893,plain,
! [B: $i,A: $i] :
( ( ( v1 @ ( vd469 @ ( vd469 @ vmul ) @ greater ) )
!= ( B @ ( A @ greater ) ) )
| ~ ( B @ ( A @ less ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[35510,249]) ).
thf(35894,plain,
! [B: $i,A: $i] :
( ( ( v1 @ ( vd469 @ ( vd469 @ vmul ) @ greater ) )
!= ( B @ ( A @ greater ) ) )
| ~ ( B @ ( A @ less ) ) ),
inference(simp,[status(thm)],[35893]) ).
thf(35895,plain,
~ ( v1 @ ( vd469 @ ( vd469 @ vmul ) @ less ) ),
inference(pattern_uni,[status(thm)],[35894:[bind(A,$thf( vd469 @ ( vd469 @ vmul ) )),bind(B,$thf( v1 ))]]) ).
thf(16264,plain,
! [C: $i,B: $i,A: $i] :
( ( ( v1 @ ( A @ vsucc @ greater ) )
!= ( C @ ( B @ greater ) ) )
| ~ ( C @ ( B @ less ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[493,249]) ).
thf(16265,plain,
! [C: $i,B: $i,A: $i] :
( ( ( v1 @ ( A @ vsucc @ greater ) )
!= ( C @ ( B @ greater ) ) )
| ~ ( C @ ( B @ less ) ) ),
inference(simp,[status(thm)],[16264]) ).
thf(16266,plain,
! [A: $i] :
~ ( v1 @ ( A @ vsucc @ less ) ),
inference(pattern_uni,[status(thm)],[16265:[bind(A,$thf( D )),bind(B,$thf( D @ vsucc )),bind(C,$thf( v1 ))]]) ).
thf(16350,plain,
! [A: $i] :
~ ( v1 @ ( A @ vsucc @ less ) ),
inference(simp,[status(thm)],[16266]) ).
thf(16119,plain,
! [B: $i,A: $i] :
( ( ( vd481 @ ( vd480 @ ( vd481 @ vskolem9 ) @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( A @ ( B @ geq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[16016,97]) ).
thf(16120,plain,
! [B: $i,A: $i] :
( ( ( vd481 @ ( vd480 @ ( vd481 @ vskolem9 ) @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( A @ ( B @ geq ) ) ),
inference(simp,[status(thm)],[16119]) ).
thf(16121,plain,
vd480 @ ( vd481 @ vskolem9 ) @ ( vd481 @ geq ),
inference(pattern_uni,[status(thm)],[16120:[bind(A,$thf( vd480 @ ( vd481 @ vskolem9 ) )),bind(B,$thf( vd481 ))]]) ).
thf(516,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ vplus ) )
!= ( E @ ( D @ ( C @ vplus ) @ vplus ) ) )
| ( ( B @ ( A @ vplus ) )
!= C ) ),
inference(paramod_ordered,[status(thm)],[77,81]) ).
thf(517,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ vplus ) @ ( A @ vplus ) )
!= B ),
inference(pattern_uni,[status(thm)],[516:[bind(A,$thf( A )),bind(B,$thf( G @ ( F @ vplus ) )),bind(C,$thf( F )),bind(D,$thf( G )),bind(E,$thf( A ))]]) ).
thf(539,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ vplus ) @ ( A @ vplus ) )
!= B ),
inference(simp,[status(thm)],[517]) ).
thf(17216,plain,
! [A: $i] :
( ( ( A @ ( A @ vsucc @ greater ) )
!= ( vd469 @ ( vd469 @ sk4 @ greater ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[491,16302]) ).
thf(17217,plain,
! [A: $i] :
( ( A @ ( A @ vsucc @ greater ) )
!= ( vd469 @ ( vd469 @ sk4 @ greater ) ) ),
inference(simp,[status(thm)],[17216]) ).
thf(17230,plain,
! [A: $i] :
( ( A != vd469 )
| ( ( A @ vsucc )
!= ( vd469 @ sk4 ) ) ),
inference(simp,[status(thm)],[17217]) ).
thf(17237,plain,
( ( vd469 @ sk4 )
!= ( vd469 @ vsucc ) ),
inference(simp,[status(thm)],[17230]) ).
thf(17389,plain,
! [A: $i] :
( ( ( A @ vsucc @ sk4 )
!= ( vd469 @ sk4 ) )
| ( A
!= ( vd469 @ vsucc ) ) ),
inference(paramod_ordered,[status(thm)],[337,17237]) ).
thf(17391,plain,
( ( vd469 @ vsucc @ vsucc )
!= vd469 ),
inference(simp,[status(thm)],[17389]) ).
thf(1321,plain,
! [A: $i] :
( ( ( A @ ( v1 @ vmul ) )
!= ( vd469 @ ( vd481 @ vmul ) ) )
| ( A
!= ( vd469 @ ( vd480 @ vmul ) @ vsucc @ vsucc ) ) ),
inference(paramod_ordered,[status(thm)],[220,1285]) ).
thf(1326,plain,
( ( ( vd469 @ ( vd480 @ vmul ) @ vsucc @ vsucc )
!= vd469 )
| ( v1 != vd481 ) ),
inference(simp,[status(thm)],[1321]) ).
thf(20706,plain,
! [A: $i] :
( ( ( A @ vsucc @ sk4 )
!= ( vd469 @ sk4 ) )
| ( vd480 != vd469 )
| ( A != vd481 ) ),
inference(paramod_ordered,[status(thm)],[337,16460]) ).
thf(20708,plain,
( ( ( vd481 @ vsucc )
!= vd469 )
| ( vd480 != vd469 ) ),
inference(simp,[status(thm)],[20706]) ).
thf(21,axiom,
! [A: $i,B: $i] :
( ~ ( B @ ( A @ less ) )
| ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(130), 0), 1)') ).
thf(136,plain,
! [A: $i,B: $i] :
( ~ ( B @ ( A @ less ) )
| ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(137,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ less ) )
| ( A != B ) ),
inference(cnf,[status(esa)],[136]) ).
thf(138,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ less ) )
| ( A != B ) ),
inference(lifteq,[status(thm)],[137]) ).
thf(139,plain,
! [A: $i] :
~ ( A @ ( A @ less ) ),
inference(simp,[status(thm)],[138]) ).
thf(170,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ less ) )
=> ! [C: $i] : ( C @ ( B @ vplus ) @ ( C @ ( A @ vplus ) @ less ) ) ),
inference(miniscope,[status(thm)],[169]) ).
thf(171,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ vplus ) @ ( C @ ( A @ vplus ) @ less ) )
| ~ ( B @ ( A @ less ) ) ),
inference(cnf,[status(esa)],[170]) ).
thf(522,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ vplus ) )
!= ( D @ ( C @ vplus ) ) )
| ( ( E @ ( A @ ( B @ vplus ) @ vplus ) )
!= C ) ),
inference(paramod_ordered,[status(thm)],[77,81]) ).
thf(523,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( B @ vplus ) @ vplus ) )
!= A ),
inference(pattern_uni,[status(thm)],[522:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(542,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( B @ vplus ) @ vplus ) )
!= A ),
inference(simp,[status(thm)],[523]) ).
thf(34604,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ vplus ) @ ( B @ vplus ) )
!= A ),
inference(rewrite,[status(thm)],[542,95]) ).
thf(19103,plain,
! [B: $i,A: $i] :
( ( B != v1 )
| ( A != vd469 )
| ( A @ ( B @ greater ) )
| ~ ( A @ ( B @ geq ) ) ),
inference(paramod_ordered,[status(thm)],[260,314]) ).
thf(19104,plain,
! [A: $i] :
( ( A != vd469 )
| ( A @ ( v1 @ greater ) )
| ~ ( A @ ( v1 @ geq ) ) ),
inference(pattern_uni,[status(thm)],[19103:[bind(A,$thf( A )),bind(B,$thf( v1 ))]]) ).
thf(19776,plain,
( ( vd469 @ ( v1 @ greater ) )
| ~ ( vd469 @ ( v1 @ geq ) ) ),
inference(simp,[status(thm)],[19104]) ).
thf(16252,plain,
! [B: $i,A: $i] :
( ( ( vd469 @ ( v1 @ less ) )
!= ( B @ ( A @ less ) ) )
| ~ $true
| ~ ( B @ ( A @ greater ) ) ),
inference(paramod_ordered,[status(thm)],[1975,249]) ).
thf(16253,plain,
! [B: $i,A: $i] :
( ( ( vd469 @ ( v1 @ less ) )
!= ( B @ ( A @ less ) ) )
| ~ ( B @ ( A @ greater ) ) ),
inference(simp,[status(thm)],[16252]) ).
thf(16254,plain,
~ ( vd469 @ ( v1 @ greater ) ),
inference(pattern_uni,[status(thm)],[16253:[bind(A,$thf( v1 )),bind(B,$thf( vd469 ))]]) ).
thf(33811,plain,
( $false
| ~ ( vd469 @ ( v1 @ geq ) ) ),
inference(rewrite,[status(thm)],[19776,16254]) ).
thf(33812,plain,
~ ( vd469 @ ( v1 @ geq ) ),
inference(simp,[status(thm)],[33811]) ).
thf(715,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( v1 @ vplus ) )
!= ( C @ ( B @ vplus ) ) )
| ( ( A @ vsucc @ ( B @ sk1 ) )
= C ) ),
inference(paramod_ordered,[status(thm)],[177,708]) ).
thf(716,plain,
! [A: $i] :
( ( A @ vsucc @ ( v1 @ sk1 ) )
= A ),
inference(pattern_uni,[status(thm)],[715:[bind(A,$thf( A )),bind(B,$thf( v1 )),bind(C,$thf( A ))]]) ).
thf(8659,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ vmul ) )
!= ( vd469 @ ( vd480 @ vmul ) ) )
| ~ ( A @ ( B @ vmul ) @ ( vd469 @ ( vd481 @ vmul ) @ greater ) ) ),
inference(paramod_ordered,[status(thm)],[223,60]) ).
thf(8660,plain,
~ ( vd480 @ ( vd469 @ vmul ) @ ( vd469 @ ( vd481 @ vmul ) @ greater ) ),
inference(pattern_uni,[status(thm)],[8659:[bind(A,$thf( vd480 )),bind(B,$thf( vd469 ))]]) ).
thf(409,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ vplus ) )
!= ( D @ ( C @ vplus ) ) )
| ( ( A @ ( B @ vplus ) )
!= C ) ),
inference(paramod_ordered,[status(thm)],[77,74]) ).
thf(410,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ vplus ) )
!= A ),
inference(pattern_uni,[status(thm)],[409:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(20395,plain,
! [A: $i] :
( ( ( A @ vsucc @ ( A @ less ) )
!= ( vd480 @ ( vd481 @ vskolem9 ) @ ( vd481 @ less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[388,16227]) ).
thf(20396,plain,
! [A: $i] :
( ( A @ vsucc @ ( A @ less ) )
!= ( vd480 @ ( vd481 @ vskolem9 ) @ ( vd481 @ less ) ) ),
inference(simp,[status(thm)],[20395]) ).
thf(20464,plain,
! [A: $i] :
( ( ( A @ vsucc )
!= ( vd480 @ ( vd481 @ vskolem9 ) ) )
| ( A != vd481 ) ),
inference(simp,[status(thm)],[20396]) ).
thf(20492,plain,
( ( vd480 @ ( vd481 @ vskolem9 ) )
!= ( vd481 @ vsucc ) ),
inference(simp,[status(thm)],[20464]) ).
thf(181,plain,
~ ? [A: $i] :
( ( A @ vsucc )
= v1 ),
inference(miniscope,[status(thm)],[180]) ).
thf(182,plain,
! [A: $i] :
( ( A @ vsucc )
!= v1 ),
inference(cnf,[status(esa)],[181]) ).
thf(183,plain,
! [A: $i] :
( ( A @ vsucc )
!= v1 ),
inference(lifteq,[status(thm)],[182]) ).
thf(16501,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ vplus ) @ ( A @ less ) )
!= ( v1 @ ( vd469 @ less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[160,16251]) ).
thf(16502,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ vplus ) @ ( A @ less ) )
!= ( v1 @ ( vd469 @ less ) ) ),
inference(simp,[status(thm)],[16501]) ).
thf(16575,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ vplus ) )
!= v1 )
| ( A != vd469 ) ),
inference(simp,[status(thm)],[16502]) ).
thf(16590,plain,
! [A: $i] :
( ( A @ ( vd469 @ vplus ) )
!= v1 ),
inference(simp,[status(thm)],[16575]) ).
thf(33984,plain,
! [A: $i] :
( ( ( A @ vskolem2 @ vsucc )
!= ( vd480 @ vsucc ) )
| ( ( vd469 @ ( A @ vmul ) )
!= ( vd469 @ ( vd481 @ vmul ) ) )
| ( A = v1 ) ),
inference(paramod_ordered,[status(thm)],[100,11045]) ).
thf(33992,plain,
! [A: $i] :
( ( ( A @ vskolem2 )
!= vd480 )
| ( vd469 != vd469 )
| ( A != vd481 )
| ( A = v1 ) ),
inference(simp,[status(thm)],[33984]) ).
thf(34026,plain,
( ( ( vd481 @ vskolem2 )
!= vd480 )
| ( v1 = vd481 ) ),
inference(simp,[status(thm)],[33992]) ).
thf(16324,plain,
! [B: $i,A: $i] :
( ( ( vd481 @ ( vd480 @ less ) )
!= ( B @ ( A @ less ) ) )
| ~ $true
| ~ ( B @ ( A @ greater ) ) ),
inference(paramod_ordered,[status(thm)],[250,249]) ).
thf(16325,plain,
! [B: $i,A: $i] :
( ( ( vd481 @ ( vd480 @ less ) )
!= ( B @ ( A @ less ) ) )
| ~ ( B @ ( A @ greater ) ) ),
inference(simp,[status(thm)],[16324]) ).
thf(16326,plain,
~ ( vd481 @ ( vd480 @ greater ) ),
inference(pattern_uni,[status(thm)],[16325:[bind(A,$thf( vd480 )),bind(B,$thf( vd481 ))]]) ).
thf(8265,plain,
! [B: $i,A: $i] :
( ( ( vd481 @ ( vd480 @ sk7 ) @ ( vd481 @ greater ) )
!= ( B @ ( A @ greater ) ) )
| ( B @ vsucc @ ( A @ geq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7308,8252]) ).
thf(8266,plain,
! [B: $i,A: $i] :
( ( ( vd481 @ ( vd480 @ sk7 ) @ ( vd481 @ greater ) )
!= ( B @ ( A @ greater ) ) )
| ( B @ vsucc @ ( A @ geq ) ) ),
inference(simp,[status(thm)],[8265]) ).
thf(8267,plain,
vd481 @ ( vd480 @ sk7 ) @ vsucc @ ( vd481 @ geq ),
inference(pattern_uni,[status(thm)],[8266:[bind(A,$thf( vd481 )),bind(B,$thf( vd481 @ ( vd480 @ sk7 ) ))]]) ).
thf(13790,plain,
vd481 @ ( vd480 @ sk1 ) @ vsucc @ ( vd481 @ geq ),
inference(rewrite,[status(thm)],[8267,7425]) ).
thf(13812,plain,
! [B: $i,A: $i] :
( ( ( vd481 @ ( vd480 @ sk1 ) @ vsucc @ ( vd481 @ geq ) )
!= ( B @ ( A @ geq ) ) )
| ( A @ ( B @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[13790,102]) ).
thf(13813,plain,
! [B: $i,A: $i] :
( ( ( vd481 @ ( vd480 @ sk1 ) @ vsucc @ ( vd481 @ geq ) )
!= ( B @ ( A @ geq ) ) )
| ( A @ ( B @ leq ) ) ),
inference(simp,[status(thm)],[13812]) ).
thf(13814,plain,
vd481 @ ( vd481 @ ( vd480 @ sk1 ) @ vsucc @ leq ),
inference(pattern_uni,[status(thm)],[13813:[bind(A,$thf( vd481 )),bind(B,$thf( vd481 @ ( vd480 @ sk1 ) @ vsucc ))]]) ).
thf(28545,plain,
vd481 @ ( vd480 @ ( vd481 @ vskolem9 ) @ vsucc @ leq ),
inference(rewrite,[status(thm)],[13814,15611]) ).
thf(1619,plain,
! [A: $i] :
( ( v1 != v1 )
| ( ( vd469 @ ( vd480 @ vmul ) @ vsucc )
!= vd469 )
| ( A != vd481 )
| ( A @ ( v1 @ less ) ) ),
inference(paramod_ordered,[status(thm)],[1448,570]) ).
thf(1620,plain,
! [A: $i] :
( ( ( vd469 @ ( vd480 @ vmul ) @ vsucc )
!= vd469 )
| ( A != vd481 )
| ( A @ ( v1 @ less ) ) ),
inference(pattern_uni,[status(thm)],[1619:[]]) ).
thf(1989,plain,
( ( ( vd469 @ ( vd480 @ vmul ) @ vsucc )
!= vd469 )
| ( vd481 @ ( v1 @ less ) ) ),
inference(simp,[status(thm)],[1620]) ).
thf(385,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ vplus ) @ ( A @ less ) )
!= ( C @ ( C @ less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[160,139]) ).
thf(386,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ vplus ) @ ( A @ less ) )
!= ( C @ ( C @ less ) ) ),
inference(simp,[status(thm)],[385]) ).
thf(393,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ vplus ) )
!= C )
| ( A != C ) ),
inference(simp,[status(thm)],[386]) ).
thf(395,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ vplus ) )
!= B ),
inference(simp,[status(thm)],[393]) ).
thf(36392,plain,
! [B: $i,A: $i] :
( ( ( v1 @ vsucc @ ( vd469 @ ( vd469 @ vmul ) @ geq ) )
!= ( B @ ( A @ geq ) ) )
| ( A @ ( B @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[35908,102]) ).
thf(36393,plain,
! [B: $i,A: $i] :
( ( ( v1 @ vsucc @ ( vd469 @ ( vd469 @ vmul ) @ geq ) )
!= ( B @ ( A @ geq ) ) )
| ( A @ ( B @ leq ) ) ),
inference(simp,[status(thm)],[36392]) ).
thf(36394,plain,
vd469 @ ( vd469 @ vmul ) @ ( v1 @ vsucc @ leq ),
inference(pattern_uni,[status(thm)],[36393:[bind(A,$thf( vd469 @ ( vd469 @ vmul ) )),bind(B,$thf( v1 @ vsucc ))]]) ).
thf(15443,plain,
! [B: $i,A: $i] :
( ( ( vd480 @ ( vd481 @ vskolem9 ) @ ( vd480 @ vplus ) )
!= ( B @ ( A @ vplus ) ) )
| ( ( vd481 @ ( B @ sk5 ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[9644,3959]) ).
thf(15444,plain,
( ( vd481 @ ( vd480 @ ( vd481 @ vskolem9 ) @ sk5 ) )
= vd480 ),
inference(pattern_uni,[status(thm)],[15443:[bind(A,$thf( vd480 )),bind(B,$thf( vd480 @ ( vd481 @ vskolem9 ) ))]]) ).
thf(9660,plain,
! [B: $i,A: $i] :
( ( ( v1 @ ( vd469 @ greater ) )
!= ( B @ ( A @ greater ) ) )
| ~ $true
| ( ( B @ ( A @ vskolem9 ) @ ( B @ vplus ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[5169,228]) ).
thf(9661,plain,
! [B: $i,A: $i] :
( ( ( v1 @ ( vd469 @ greater ) )
!= ( B @ ( A @ greater ) ) )
| ( ( B @ ( A @ vskolem9 ) @ ( B @ vplus ) )
= A ) ),
inference(simp,[status(thm)],[9660]) ).
thf(9662,plain,
( ( v1 @ ( vd469 @ vskolem9 ) @ ( v1 @ vplus ) )
= vd469 ),
inference(pattern_uni,[status(thm)],[9661:[bind(A,$thf( vd469 )),bind(B,$thf( v1 ))]]) ).
thf(21296,plain,
( ( v1 @ ( vd469 @ vskolem9 ) @ vsucc )
= vd469 ),
inference(rewrite,[status(thm)],[9662,177]) ).
thf(21412,plain,
! [A: $i] :
( ( ( v1 @ ( vd469 @ vskolem9 ) @ vsucc )
!= ( A @ vsucc ) )
| ( ( vd469 @ sk6 )
= A ) ),
inference(paramod_ordered,[status(thm)],[21296,338]) ).
thf(21413,plain,
( ( v1 @ ( vd469 @ vskolem9 ) )
= ( vd469 @ sk6 ) ),
inference(pattern_uni,[status(thm)],[21412:[bind(A,$thf( v1 @ ( vd469 @ vskolem9 ) ))]]) ).
thf(23350,plain,
( ( v1 @ ( vd469 @ vskolem9 ) )
= ( vd469 @ sk4 ) ),
inference(rewrite,[status(thm)],[21413,5879]) ).
thf(163,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ less ) )
| ~ ( B @ ( A @ leq ) )
| ~ ( C @ ( B @ less ) ) ),
inference(cnfConj,[status(thm)],[162]) ).
thf(274,plain,
! [A: $i] :
( ( ( vd481 @ ( vd480 @ less ) )
!= ( A @ ( A @ less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[250,139]) ).
thf(275,plain,
! [A: $i] :
( ( vd481 @ ( vd480 @ less ) )
!= ( A @ ( A @ less ) ) ),
inference(simp,[status(thm)],[274]) ).
thf(276,plain,
! [A: $i] :
( ( vd481 != A )
| ( vd480 != A ) ),
inference(simp,[status(thm)],[275]) ).
thf(277,plain,
vd480 != vd481,
inference(simp,[status(thm)],[276]) ).
thf(529,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ vsucc @ ( A @ vplus ) )
!= ( D @ ( C @ vplus ) ) )
| ( ( E @ ( B @ ( A @ vplus ) @ vsucc @ vplus ) )
!= C ) ),
inference(paramod_ordered,[status(thm)],[68,81]) ).
thf(530,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( A @ vplus ) @ vsucc @ vplus ) )
!= A ),
inference(pattern_uni,[status(thm)],[529:[bind(A,$thf( A )),bind(B,$thf( F )),bind(C,$thf( A )),bind(D,$thf( F @ vsucc ))]]) ).
thf(535,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( A @ vplus ) @ vsucc @ vplus ) )
!= A ),
inference(simp,[status(thm)],[530]) ).
thf(31662,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( A @ vplus ) @ vplus ) @ vsucc )
!= A ),
inference(rewrite,[status(thm)],[535,142]) ).
thf(7309,plain,
! [B: $i,A: $i] :
( ( ( vd481 @ ( vd480 @ sk7 ) @ ( vd480 @ vplus ) )
!= ( B @ ( A @ vplus ) ) )
| ( ( vd481 @ vsucc )
!= v1 ) ),
inference(paramod_ordered,[status(thm)],[5038,683]) ).
thf(7310,plain,
( ( vd481 @ vsucc )
!= v1 ),
inference(pattern_uni,[status(thm)],[7309:[bind(A,$thf( vd480 )),bind(B,$thf( vd481 @ ( vd480 @ sk7 ) ))]]) ).
thf(5862,plain,
! [A: $i] :
( ( ( vd469 @ sk6 @ vsucc )
!= ( A @ vsucc ) )
| ( ( vd469 @ ( v1 @ sk1 ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[5679,716]) ).
thf(5863,plain,
( ( vd469 @ ( v1 @ sk1 ) )
= ( vd469 @ sk6 ) ),
inference(pattern_uni,[status(thm)],[5862:[bind(A,$thf( vd469 @ sk6 ))]]) ).
thf(7056,plain,
( ( vd469 @ ( v1 @ sk1 ) )
= ( vd469 @ sk4 ) ),
inference(rewrite,[status(thm)],[5863,5879]) ).
thf(431,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ vplus ) )
!= ( D @ vsucc @ ( C @ vplus ) ) )
| ( ( B @ ( A @ vplus ) )
= ( D @ ( C @ vplus ) @ vsucc ) ) ),
inference(paramod_ordered,[status(thm)],[77,68]) ).
thf(432,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ vsucc @ vplus ) )
= ( B @ ( A @ vplus ) @ vsucc ) ),
inference(pattern_uni,[status(thm)],[431:[bind(A,$thf( E @ vsucc )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( E ))]]) ).
thf(441,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ vsucc @ vplus ) )
= ( B @ ( A @ vplus ) @ vsucc ) ),
inference(simp,[status(thm)],[432]) ).
thf(27247,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ vplus ) @ vsucc )
= ( B @ ( A @ vplus ) @ vsucc ) ),
inference(rewrite,[status(thm)],[441,142]) ).
thf(38287,plain,
$false,
inference(e,[status(thm)],[30927,15440,249,33245,481,101,34114,26549,115,25607,683,217,5242,3959,247,269,7368,32274,5120,9644,142,797,8342,30112,153,5192,15611,16236,174,16351,6182,8603,28550,25611,16251,184,504,1330,751,16480,35510,196,28106,570,29540,17234,110,22161,6905,2049,93,325,152,228,78,8252,261,164,179,26938,238,6964,30870,84,16463,253,7413,15458,221,5101,32619,5321,5169,74,1975,8261,61,292,233,248,60,8655,270,28551,33972,220,102,16227,29650,16460,260,70,192,16016,29531,598,160,26983,2032,165,6178,92,22864,31011,493,224,229,5879,97,329,1291,710,15739,16833,188,388,169,22122,554,25544,212,96,109,328,35908,225,77,3622,25101,8258,9348,1530,4068,35363,129,6450,16473,8307,28831,22250,503,9372,26079,244,266,8422,5209,17235,7046,26528,25366,3523,34036,149,375,412,16464,264,35268,15025,161,180,689,694,191,16302,286,118,25870,204,6949,3519,34033,71,382,572,787,144,16823,2055,236,23751,187,172,113,6179,6217,22036,230,34588,245,98,103,16338,140,483,251,26404,769,198,330,130,27117,16474,5248,2064,394,226,28533,16305,223,608,6180,267,241,22152,35689,13985,3981,112,8067,123,16457,145,1049,63,95,5721,8350,263,11045,8725,199,177,1038,502,16461,338,11198,1285,7009,29764,30513,25596,8317,175,314,143,27106,3961,571,35895,31022,16350,16121,539,15525,218,1448,17237,250,231,17391,87,1326,16586,23691,158,20708,390,186,139,26730,171,75,34604,235,207,29211,33812,82,716,214,26721,8660,410,20492,183,273,16590,34026,29528,168,16326,15540,35392,1056,635,16254,3506,26808,28545,239,242,126,1989,136,395,740,36394,15444,23350,163,68,62,178,277,501,131,31662,90,254,337,22238,7310,7056,215,491,27247,100,708,232]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUM852+1 : TPTP v9.3.1. Released v4.1.0.
% 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
% 0.23/0.49 % Computer : n003.cluster.edu
% 0.23/0.49 % Model : x86_64 x86_64
% 0.23/0.49 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.23/0.49 % Memory : 8046.5625MB
% 0.23/0.49 % OS : Linux 6.8.0-71-generic
% 0.23/0.49 % CPULimit : 300
% 0.23/0.49 % WCLimit : 300
% 0.23/0.49 % DateTime : Sat Sep 26 04:14:53 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
% 1.25/1.25 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.84/1.55 % [INFO] Parsing done (296ms).
% 1.84/1.57 % [INFO] Running in sequential loop mode.
% 3.05/2.16 % [INFO] eprover registered as external prover.
% 3.05/2.17 % [INFO] Scanning for conjecture ...
% 3.31/2.32 % [INFO] Found a conjecture (or negated_conjecture) and 57 axioms. Running axiom selection ...
% 3.49/2.44 % [INFO] Axiom selection finished. Selected 57 axioms (removed 0 axioms).
% 3.71/2.58 % [INFO] Problem is first-order (TPTP FOF).
% 3.93/2.60 % [INFO] Type checking passed.
% 3.93/2.61 % [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 ...
% 96.65/19.66 % External prover 'e' found a proof!
% 96.65/19.66 % [INFO] Killing All external provers ...
% 96.65/19.66 % Time passed: 18972ms (effective reasoning time: 18084ms)
% 96.65/19.66 % 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)>
% 96.65/19.67 % Axioms used in derivation (57): ass(cond(223, 0), 0), ass(cond(6, 0), 0), def(cond(conseq(axiom(3)), 11), 1), def(cond(conseq(axiom(3)), 16), 1), ass(cond(228, 0), 0), ass(cond(20, 0), 0), ass(cond(241, 0), 0), ass(cond(12, 0), 0), ass(cond(140, 0), 0), def(cond(conseq(axiom(3)), 12), 1), ass(cond(goal(193), 0), 0), ass(cond(goal(130), 0), 1), ass(cond(163, 0), 0), ass(cond(302, 0), 3), ass(cond(goal(177), 0), 0), ass(cond(goal(193), 0), 2), ass(cond(goal(88), 0), 1), ass(cond(goal(130), 0), 0), ass(cond(goal(130), 0), 3), ass(cond(goal(193), 0), 1), ass(cond(189, 0), 0), holds(antec(304), 482, 0), qu(cond(conseq(axiom(3)), 32), and(holds(definiens(249), 399, 0), holds(definiens(249), 398, 0))), ass(cond(goal(88), 0), 3), ass(cond(goal(202), 0), 2), ass(cond(270, 0), 0), holds(conseq_conjunct1(conseq(304)), 483, 0), ass(cond(184, 0), 0), ass(cond(302, 0), 2), ass(cond(goal(88), 0), 2), ass(cond(147, 0), 0), qu(cond(conseq(axiom(3)), 3), and(holds(definiens(29), 45, 0), holds(definiens(29), 44, 0))), ass(cond(73, 0), 0), ass(cond(goal(88), 0), 0), def(cond(conseq(axiom(3)), 17), 1), ass(cond(goal(202), 0), 1), ass(cond(goal(216), 0), 0), ass(cond(281, 0), 0), qu(antec(axiom(3)), imp(antec(axiom(3)))), ass(cond(253, 0), 0), ass(cond(302, 0), 1), ass(cond(209, 0), 0), ass(cond(261, 0), 0), ass(cond(52, 0), 0), ass(cond(158, 0), 0), ass(cond(234, 0), 0), ass(cond(33, 0), 0), ass(cond(290, 0), 0), ass(cond(303, 0), 0), qu(restrictor(axiom(1)), holds(scope(axiom(1)), 2, 0)), ass(cond(61, 0), 0), ass(cond(goal(130), 0), 2), ass(cond(goal(202), 0), 0), ass(cond(168, 0), 0), ass(cond(43, 0), 0), ass(cond(302, 0), 0), ass(cond(81, 0), 0)
% 96.65/19.67 % No. of inferences in proof: 946
% 96.65/19.67 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 18972 ms resp. 18084 ms w/o parsing
% 83.43/19.93 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 83.43/19.94 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------