TSTP Solution File: NUM856+2 by Leo-III---1.7.15
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.15
% Problem : NUM856+2 : TPTP v8.2.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Jun 24 13:02:49 EDT 2024
% Result : Theorem 79.21s 18.69s
% Output : Refutation 80.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 39
% Number of leaves : 64
% Syntax : Number of formulae : 823 ( 220 unt; 0 typ; 0 def)
% Number of atoms : 2024 (1171 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 6292 (1171 ~; 919 |; 36 &;4082 @)
% ( 4 <=>; 80 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 25 ( 22 usr; 7 con; 0-2 aty)
% Number of variables : 1266 ( 0 ^1236 !; 30 ?;1266 :)
% Comments :
%------------------------------------------------------------------------------
thf(greater_type,type,
greater: $i > $i > $o ).
thf(vmul_type,type,
vmul: $i > $i > $i ).
thf(vd517_type,type,
vd517: $i ).
thf(vd519_type,type,
vd519: $i ).
thf(vd518_type,type,
vd518: $i ).
thf(vd520_type,type,
vd520: $i ).
thf(leq_type,type,
leq: $i > $i > $o ).
thf(vplus_type,type,
vplus: $i > $i > $i ).
thf(vsucc_type,type,
vsucc: $i > $i ).
thf(v1_type,type,
v1: $i ).
thf(less_type,type,
less: $i > $i > $o ).
thf(geq_type,type,
geq: $i > $i > $o ).
thf(vskolem2_type,type,
vskolem2: $i > $i ).
thf(sk1_type,type,
sk1: $i > $i > $i ).
thf(sk2_type,type,
sk2: $i > $i > $i ).
thf(sk3_type,type,
sk3: $i > $i > $i ).
thf(sk4_type,type,
sk4: $i > $i ).
thf(sk5_type,type,
sk5: $i > $i > $i ).
thf(sk6_type,type,
sk6: $i > $i ).
thf(sk7_type,type,
sk7: $i > $i > $i ).
thf(sk8_type,type,
sk8: $i > $i > $i ).
thf(sk9_type,type,
sk9: $i > $i > $i ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( ( vplus @ A @ ( vsucc @ B ) )
= ( vsucc @ ( vplus @ A @ B ) ) )
& ( ( vplus @ A @ v1 )
= ( vsucc @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(conseq(axiom(3)), 3), and(holds(definiens(29), 45, 0), holds(definiens(29), 44, 0)))') ).
thf(64,plain,
! [A: $i,B: $i] :
( ( ( vplus @ A @ ( vsucc @ B ) )
= ( vsucc @ ( vplus @ A @ B ) ) )
& ( ( vplus @ A @ v1 )
= ( vsucc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(65,plain,
( ! [A: $i,B: $i] :
( ( vplus @ A @ ( vsucc @ B ) )
= ( vsucc @ ( vplus @ A @ B ) ) )
& ! [A: $i] :
( ( vplus @ A @ v1 )
= ( vsucc @ A ) ) ),
inference(miniscope,[status(thm)],[64]) ).
thf(66,plain,
! [A: $i] :
( ( vplus @ A @ v1 )
= ( vsucc @ A ) ),
inference(cnf,[status(esa)],[65]) ).
thf(68,plain,
! [A: $i] :
( ( vplus @ A @ v1 )
= ( vsucc @ A ) ),
inference(lifteq,[status(thm)],[66]) ).
thf(69,plain,
! [A: $i] :
( ( vplus @ A @ v1 )
= ( vsucc @ A ) ),
inference(simp,[status(thm)],[68]) ).
thf(39,axiom,
! [A: $i,B: $i] :
( ( ( vmul @ A @ ( vsucc @ B ) )
= ( vplus @ ( vmul @ A @ B ) @ A ) )
& ( ( vmul @ A @ v1 )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(conseq(axiom(3)), 32), and(holds(definiens(249), 399, 0), holds(definiens(249), 398, 0)))') ).
thf(190,plain,
! [A: $i,B: $i] :
( ( ( vmul @ A @ ( vsucc @ B ) )
= ( vplus @ ( vmul @ A @ B ) @ A ) )
& ( ( vmul @ A @ v1 )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(191,plain,
( ! [A: $i,B: $i] :
( ( vmul @ A @ ( vsucc @ B ) )
= ( vplus @ ( vmul @ A @ B ) @ A ) )
& ! [A: $i] :
( ( vmul @ A @ v1 )
= A ) ),
inference(miniscope,[status(thm)],[190]) ).
thf(193,plain,
! [B: $i,A: $i] :
( ( vmul @ A @ ( vsucc @ B ) )
= ( vplus @ ( vmul @ A @ B ) @ A ) ),
inference(cnf,[status(esa)],[191]) ).
thf(196,plain,
! [B: $i,A: $i] :
( ( vplus @ ( vmul @ A @ B ) @ A )
= ( vmul @ A @ ( vsucc @ B ) ) ),
inference(lifteq,[status(thm)],[193]) ).
thf(57,axiom,
! [A: $i,B: $i,C: $i] :
( ( vmul @ A @ ( vplus @ B @ C ) )
= ( vplus @ ( vmul @ A @ B ) @ ( vmul @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(281, 0), 0)') ).
thf(248,plain,
! [A: $i,B: $i,C: $i] :
( ( vmul @ A @ ( vplus @ B @ C ) )
= ( vplus @ ( vmul @ A @ B ) @ ( vmul @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(249,plain,
! [C: $i,B: $i,A: $i] :
( ( vmul @ A @ ( vplus @ B @ C ) )
= ( vplus @ ( vmul @ A @ B ) @ ( vmul @ A @ C ) ) ),
inference(cnf,[status(esa)],[248]) ).
thf(250,plain,
! [C: $i,B: $i,A: $i] :
( ( vplus @ ( vmul @ A @ B ) @ ( vmul @ A @ C ) )
= ( vmul @ A @ ( vplus @ B @ C ) ) ),
inference(lifteq,[status(thm)],[249]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( vplus @ B @ A )
= ( vplus @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(61, 0), 0)') ).
thf(75,plain,
! [A: $i,B: $i] :
( ( vplus @ B @ A )
= ( vplus @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(76,plain,
! [B: $i,A: $i] :
( ( vplus @ B @ A )
= ( vplus @ A @ B ) ),
inference(cnf,[status(esa)],[75]) ).
thf(77,plain,
! [B: $i,A: $i] :
( ( vplus @ B @ A )
= ( vplus @ A @ B ) ),
inference(lifteq,[status(thm)],[76]) ).
thf(35,axiom,
! [A: $i,B: $i] : ( greater @ ( vplus @ A @ B ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(189, 0), 0)') ).
thf(181,plain,
! [A: $i,B: $i] : ( greater @ ( vplus @ A @ B ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(182,plain,
! [B: $i,A: $i] : ( greater @ ( vplus @ A @ B ) @ A ),
inference(cnf,[status(esa)],[181]) ).
thf(1,conjecture,
greater @ ( vmul @ vd517 @ vd519 ) @ ( vmul @ vd518 @ vd520 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','holds(conseq(scope(318)), 525, 0)') ).
thf(2,negated_conjecture,
~ ( greater @ ( vmul @ vd517 @ vd519 ) @ ( vmul @ vd518 @ vd520 ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(61,plain,
~ ( greater @ ( vmul @ vd517 @ vd519 ) @ ( vmul @ vd518 @ vd520 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(477,plain,
! [B: $i,A: $i] :
( ( greater @ ( vplus @ A @ B ) @ A )
!= ( greater @ ( vmul @ vd517 @ vd519 ) @ ( vmul @ vd518 @ vd520 ) ) ),
inference(paramod_ordered,[status(thm)],[182,61]) ).
thf(498,plain,
! [B: $i,A: $i] :
( ( ( vplus @ A @ B )
!= ( vmul @ vd517 @ vd519 ) )
| ( A
!= ( vmul @ vd518 @ vd520 ) ) ),
inference(simp,[status(thm)],[477]) ).
thf(509,plain,
! [A: $i] :
( ( vplus @ ( vmul @ vd518 @ vd520 ) @ A )
!= ( vmul @ vd517 @ vd519 ) ),
inference(simp,[status(thm)],[498]) ).
thf(791,plain,
! [C: $i,B: $i,A: $i] :
( ( ( vplus @ A @ B )
!= ( vmul @ vd517 @ vd519 ) )
| ( ( vplus @ B @ A )
!= ( vplus @ ( vmul @ vd518 @ vd520 ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[77,509]) ).
thf(792,plain,
! [A: $i] :
( ( vplus @ A @ ( vmul @ vd518 @ vd520 ) )
!= ( vmul @ vd517 @ vd519 ) ),
inference(pattern_uni,[status(thm)],[791:[bind(A,$thf( A )),bind(B,$thf( vmul @ vd518 @ vd520 )),bind(C,$thf( A ))]]) ).
thf(23874,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( vmul @ A @ ( vplus @ B @ C ) )
!= ( vmul @ vd517 @ vd519 ) )
| ( ( vplus @ ( vmul @ A @ B ) @ ( vmul @ A @ C ) )
!= ( vplus @ D @ ( vmul @ vd518 @ vd520 ) ) ) ),
inference(paramod_ordered,[status(thm)],[250,792]) ).
thf(23875,plain,
! [A: $i] :
( ( vmul @ vd518 @ ( vplus @ A @ vd520 ) )
!= ( vmul @ vd517 @ vd519 ) ),
inference(pattern_uni,[status(thm)],[23874:[bind(A,$thf( vd518 )),bind(B,$thf( F )),bind(C,$thf( vd520 )),bind(D,$thf( vmul @ vd518 @ F ))]]) ).
thf(24048,plain,
! [A: $i] :
( ( vmul @ vd518 @ ( vplus @ A @ vd520 ) )
!= ( vmul @ vd517 @ vd519 ) ),
inference(simp,[status(thm)],[23875]) ).
thf(24107,plain,
! [C: $i,B: $i,A: $i] :
( ( ( vmul @ vd518 @ ( vmul @ A @ ( vsucc @ B ) ) )
!= ( vmul @ vd517 @ vd519 ) )
| ( ( vplus @ ( vmul @ A @ B ) @ A )
!= ( vplus @ C @ vd520 ) ) ),
inference(paramod_ordered,[status(thm)],[196,24048]) ).
thf(24108,plain,
! [A: $i] :
( ( vmul @ vd518 @ ( vmul @ vd520 @ ( vsucc @ A ) ) )
!= ( vmul @ vd517 @ vd519 ) ),
inference(pattern_uni,[status(thm)],[24107:[bind(A,$thf( vd520 )),bind(B,$thf( E )),bind(C,$thf( vmul @ vd520 @ E ))]]) ).
thf(24195,plain,
! [A: $i] :
( ( vmul @ vd518 @ ( vmul @ vd520 @ ( vsucc @ A ) ) )
!= ( vmul @ vd517 @ vd519 ) ),
inference(simp,[status(thm)],[24108]) ).
thf(13,axiom,
! [A: $i] :
( ( A != v1 )
=> ( A
= ( vsucc @ ( vskolem2 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(20, 0), 0)') ).
thf(97,plain,
! [A: $i] :
( ( A != v1 )
=> ( A
= ( vsucc @ ( vskolem2 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(98,plain,
! [A: $i] :
( ( A = v1 )
| ( A
= ( vsucc @ ( vskolem2 @ A ) ) ) ),
inference(cnf,[status(esa)],[97]) ).
thf(99,plain,
! [A: $i] :
( ( A = v1 )
| ( ( vsucc @ ( vskolem2 @ A ) )
= A ) ),
inference(lifteq,[status(thm)],[98]) ).
thf(31,axiom,
! [A: $i] :
( ( vplus @ v1 @ A )
= ( vsucc @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(43, 0), 0)') ).
thf(168,plain,
! [A: $i] :
( ( vplus @ v1 @ A )
= ( vsucc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(169,plain,
! [A: $i] :
( ( vplus @ v1 @ A )
= ( vsucc @ A ) ),
inference(cnf,[status(esa)],[168]) ).
thf(170,plain,
! [A: $i] :
( ( vplus @ v1 @ A )
= ( vsucc @ A ) ),
inference(lifteq,[status(thm)],[169]) ).
thf(26,axiom,
! [A: $i,B: $i] :
( ( less @ B @ A )
<=> ? [C: $i] :
( A
= ( vplus @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','def(cond(conseq(axiom(3)), 12), 1)') ).
thf(148,plain,
! [A: $i,B: $i] :
( ( ( less @ B @ A )
=> ? [C: $i] :
( A
= ( vplus @ B @ C ) ) )
& ( ? [C: $i] :
( A
= ( vplus @ B @ C ) )
=> ( less @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(149,plain,
( ! [A: $i,B: $i] :
( ( less @ B @ A )
=> ? [C: $i] :
( A
= ( vplus @ B @ C ) ) )
& ! [A: $i,B: $i] :
( ? [C: $i] :
( A
= ( vplus @ B @ C ) )
=> ( less @ B @ A ) ) ),
inference(miniscope,[status(thm)],[148]) ).
thf(150,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( vplus @ B @ C ) )
| ( less @ B @ A ) ),
inference(cnf,[status(esa)],[149]) ).
thf(152,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( vplus @ B @ C ) )
| ( less @ B @ A ) ),
inference(lifteq,[status(thm)],[150]) ).
thf(153,plain,
! [B: $i,A: $i] : ( less @ A @ ( vplus @ A @ B ) ),
inference(simp,[status(thm)],[152]) ).
thf(383,plain,
! [C: $i,B: $i,A: $i] :
( ( less @ B @ ( vsucc @ A ) )
| ( ( vplus @ v1 @ A )
!= ( vplus @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[170,153]) ).
thf(384,plain,
! [A: $i] : ( less @ v1 @ ( vsucc @ A ) ),
inference(pattern_uni,[status(thm)],[383:[bind(A,$thf( A )),bind(B,$thf( v1 )),bind(C,$thf( A ))]]) ).
thf(1439,plain,
! [B: $i,A: $i] :
( ( A = v1 )
| ( less @ v1 @ A )
| ( ( vsucc @ ( vskolem2 @ A ) )
!= ( vsucc @ B ) ) ),
inference(paramod_ordered,[status(thm)],[99,384]) ).
thf(1440,plain,
! [A: $i] :
( ( A = v1 )
| ( less @ v1 @ A ) ),
inference(pattern_uni,[status(thm)],[1439:[bind(A,$thf( C )),bind(B,$thf( vskolem2 @ C ))]]) ).
thf(1522,plain,
! [A: $i] :
( ( A = v1 )
| ( less @ v1 @ A ) ),
inference(simp,[status(thm)],[1440]) ).
thf(56,axiom,
! [A: $i] :
( ( vmul @ v1 @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(253, 0), 0)') ).
thf(245,plain,
! [A: $i] :
( ( vmul @ v1 @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(246,plain,
! [A: $i] :
( ( vmul @ v1 @ A )
= A ),
inference(cnf,[status(esa)],[245]) ).
thf(247,plain,
! [A: $i] :
( ( vmul @ v1 @ A )
= A ),
inference(lifteq,[status(thm)],[246]) ).
thf(283,plain,
! [A: $i] :
( ~ ( greater @ A @ ( vmul @ vd518 @ vd520 ) )
| ( ( vmul @ v1 @ A )
!= ( vmul @ vd517 @ vd519 ) ) ),
inference(paramod_ordered,[status(thm)],[247,61]) ).
thf(289,plain,
! [A: $i] :
( ~ ( greater @ A @ ( vmul @ vd518 @ vd520 ) )
| ( v1 != vd517 )
| ( A != vd519 ) ),
inference(simp,[status(thm)],[283]) ).
thf(291,plain,
( ~ ( greater @ vd519 @ ( vmul @ vd518 @ vd520 ) )
| ( v1 != vd517 ) ),
inference(simp,[status(thm)],[289]) ).
thf(317,plain,
! [A: $i] :
( ~ ( greater @ vd519 @ A )
| ( v1 != vd517 )
| ( ( vmul @ v1 @ A )
!= ( vmul @ vd518 @ vd520 ) ) ),
inference(paramod_ordered,[status(thm)],[247,291]) ).
thf(320,plain,
! [A: $i] :
( ~ ( greater @ vd519 @ A )
| ( v1 != vd517 )
| ( v1 != vd518 )
| ( A != vd520 ) ),
inference(simp,[status(thm)],[317]) ).
thf(323,plain,
( ~ ( greater @ vd519 @ vd520 )
| ( v1 != vd517 )
| ( v1 != vd518 ) ),
inference(simp,[status(thm)],[320]) ).
thf(1976,plain,
! [A: $i] :
( ( less @ v1 @ A )
| ~ ( greater @ vd519 @ vd520 )
| ( A != vd517 )
| ( v1 != vd518 )
| ( v1 != v1 ) ),
inference(paramod_ordered,[status(thm)],[1522,323]) ).
thf(1977,plain,
! [A: $i] :
( ( less @ v1 @ A )
| ~ ( greater @ vd519 @ vd520 )
| ( A != vd517 )
| ( v1 != vd518 ) ),
inference(pattern_uni,[status(thm)],[1976:[]]) ).
thf(2341,plain,
( ( less @ v1 @ vd517 )
| ~ ( greater @ vd519 @ vd520 )
| ( v1 != vd518 ) ),
inference(simp,[status(thm)],[1977]) ).
thf(40,axiom,
( ( ( greater @ vd519 @ vd520 )
& ( geq @ vd517 @ vd518 ) )
| ( ( geq @ vd519 @ vd520 )
& ( greater @ vd517 @ vd518 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','dis(antec(scope(318)))') ).
thf(197,plain,
( ( ( greater @ vd519 @ vd520 )
& ( geq @ vd517 @ vd518 ) )
| ( ( geq @ vd519 @ vd520 )
& ( greater @ vd517 @ vd518 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(199,plain,
( ( greater @ vd519 @ vd520 )
| ( greater @ vd517 @ vd518 ) ),
inference(cnf,[status(esa)],[197]) ).
thf(284,plain,
! [A: $i] :
( ~ ( greater @ ( vmul @ vd517 @ vd519 ) @ A )
| ( ( vmul @ v1 @ A )
!= ( vmul @ vd518 @ vd520 ) ) ),
inference(paramod_ordered,[status(thm)],[247,61]) ).
thf(290,plain,
! [A: $i] :
( ~ ( greater @ ( vmul @ vd517 @ vd519 ) @ A )
| ( v1 != vd518 )
| ( A != vd520 ) ),
inference(simp,[status(thm)],[284]) ).
thf(292,plain,
( ~ ( greater @ ( vmul @ vd517 @ vd519 ) @ vd520 )
| ( v1 != vd518 ) ),
inference(simp,[status(thm)],[290]) ).
thf(327,plain,
( ( greater @ vd517 @ vd518 )
| ( v1 != vd518 )
| ( ( greater @ ( vmul @ vd517 @ vd519 ) @ vd520 )
!= ( greater @ vd519 @ vd520 ) ) ),
inference(paramod_ordered,[status(thm)],[199,292]) ).
thf(330,plain,
( ( greater @ vd517 @ vd518 )
| ( v1 != vd518 )
| ( ( vmul @ vd517 @ vd519 )
!= vd519 )
| ( vd520 != vd520 ) ),
inference(simp,[status(thm)],[327]) ).
thf(333,plain,
( ( greater @ vd517 @ vd518 )
| ( v1 != vd518 )
| ( ( vmul @ vd517 @ vd519 )
!= vd519 ) ),
inference(simp,[status(thm)],[330]) ).
thf(201,plain,
( ( geq @ vd517 @ vd518 )
| ( greater @ vd517 @ vd518 ) ),
inference(cnf,[status(esa)],[197]) ).
thf(14,axiom,
! [A: $i,B: $i] :
( ( geq @ A @ B )
=> ( leq @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(158, 0), 0)') ).
thf(100,plain,
! [A: $i,B: $i] :
( ( geq @ A @ B )
=> ( leq @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(101,plain,
! [B: $i,A: $i] :
( ~ ( geq @ A @ B )
| ( leq @ B @ A ) ),
inference(cnf,[status(esa)],[100]) ).
thf(2396,plain,
! [B: $i,A: $i] :
( ( greater @ vd517 @ vd518 )
| ( leq @ B @ A )
| ( ( geq @ vd517 @ vd518 )
!= ( geq @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[201,101]) ).
thf(2397,plain,
( ( greater @ vd517 @ vd518 )
| ( leq @ vd518 @ vd517 ) ),
inference(pattern_uni,[status(thm)],[2396:[bind(A,$thf( vd517 )),bind(B,$thf( vd518 ))]]) ).
thf(15,axiom,
! [A: $i,B: $i] :
( ( leq @ B @ A )
<=> ( ( less @ B @ A )
| ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','def(cond(conseq(axiom(3)), 17), 1)') ).
thf(102,plain,
! [A: $i,B: $i] :
( ( ( leq @ B @ A )
=> ( ( less @ B @ A )
| ( B = A ) ) )
& ( ( ( less @ B @ A )
| ( B = A ) )
=> ( leq @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(103,plain,
( ! [A: $i,B: $i] :
( ( leq @ B @ A )
=> ( ( less @ B @ A )
| ( B = A ) ) )
& ! [A: $i,B: $i] :
( ( ( less @ B @ A )
| ( B = A ) )
=> ( leq @ B @ A ) ) ),
inference(miniscope,[status(thm)],[102]) ).
thf(106,plain,
! [B: $i,A: $i] :
( ~ ( leq @ B @ A )
| ( less @ B @ A )
| ( B = A ) ),
inference(cnf,[status(esa)],[103]) ).
thf(110,plain,
! [B: $i,A: $i] :
( ( B = A )
| ~ ( leq @ B @ A )
| ( less @ B @ A ) ),
inference(lifteq,[status(thm)],[106]) ).
thf(3346,plain,
! [B: $i,A: $i] :
( ( greater @ vd517 @ vd518 )
| ( B = A )
| ( less @ B @ A )
| ( ( leq @ vd518 @ vd517 )
!= ( leq @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[2397,110]) ).
thf(3347,plain,
( ( greater @ vd517 @ vd518 )
| ( vd518 = vd517 )
| ( less @ vd518 @ vd517 ) ),
inference(pattern_uni,[status(thm)],[3346:[bind(A,$thf( vd517 )),bind(B,$thf( vd518 ))]]) ).
thf(50,axiom,
! [A: $i,B: $i] :
( ( less @ A @ B )
=> ( greater @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(147, 0), 0)') ).
thf(222,plain,
! [A: $i,B: $i] :
( ( less @ A @ B )
=> ( greater @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(223,plain,
! [B: $i,A: $i] :
( ~ ( less @ A @ B )
| ( greater @ B @ A ) ),
inference(cnf,[status(esa)],[222]) ).
thf(18831,plain,
! [B: $i,A: $i] :
( ( greater @ vd517 @ vd518 )
| ( vd518 = vd517 )
| ( greater @ B @ A )
| ( ( less @ vd518 @ vd517 )
!= ( less @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[3347,223]) ).
thf(18832,plain,
( ( greater @ vd517 @ vd518 )
| ( vd518 = vd517 )
| ( greater @ vd517 @ vd518 ) ),
inference(pattern_uni,[status(thm)],[18831:[bind(A,$thf( vd518 )),bind(B,$thf( vd517 ))]]) ).
thf(18839,plain,
( ( greater @ vd517 @ vd518 )
| ( vd518 = vd517 ) ),
inference(simp,[status(thm)],[18832]) ).
thf(393,plain,
( ( greater @ vd517 @ vd518 )
| ( v1 != vd517 )
| ( v1 != vd518 )
| ( ( greater @ vd519 @ vd520 )
!= ( greater @ vd519 @ vd520 ) ) ),
inference(paramod_ordered,[status(thm)],[199,323]) ).
thf(394,plain,
( ( greater @ vd517 @ vd518 )
| ( v1 != vd517 )
| ( v1 != vd518 ) ),
inference(pattern_uni,[status(thm)],[393:[]]) ).
thf(52,axiom,
! [A: $i,B: $i] :
( ( A != B )
| ~ ( greater @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(130), 0), 3)') ).
thf(227,plain,
! [A: $i,B: $i] :
( ( A != B )
| ~ ( greater @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(228,plain,
! [B: $i,A: $i] :
( ( A != B )
| ~ ( greater @ A @ B ) ),
inference(cnf,[status(esa)],[227]) ).
thf(229,plain,
! [B: $i,A: $i] :
( ( A != B )
| ~ ( greater @ A @ B ) ),
inference(lifteq,[status(thm)],[228]) ).
thf(230,plain,
! [A: $i] :
~ ( greater @ A @ A ),
inference(simp,[status(thm)],[229]) ).
thf(521,plain,
! [A: $i] :
( ( v1 != vd517 )
| ( v1 != vd518 )
| ( ( greater @ vd517 @ vd518 )
!= ( greater @ A @ A ) ) ),
inference(paramod_ordered,[status(thm)],[394,230]) ).
thf(531,plain,
! [A: $i] :
( ( v1 != vd517 )
| ( v1 != vd518 )
| ( vd517 != A )
| ( vd518 != A ) ),
inference(simp,[status(thm)],[521]) ).
thf(535,plain,
( ( v1 != vd517 )
| ( v1 != vd518 )
| ( vd518 != vd517 ) ),
inference(simp,[status(thm)],[531]) ).
thf(1966,plain,
! [A: $i] :
( ( less @ v1 @ A )
| ( A != vd517 )
| ( v1 != vd518 )
| ( vd518 != vd517 )
| ( v1 != v1 ) ),
inference(paramod_ordered,[status(thm)],[1522,535]) ).
thf(1967,plain,
! [A: $i] :
( ( less @ v1 @ A )
| ( A != vd517 )
| ( v1 != vd518 )
| ( vd518 != vd517 ) ),
inference(pattern_uni,[status(thm)],[1966:[]]) ).
thf(2339,plain,
( ( less @ v1 @ vd517 )
| ( v1 != vd518 )
| ( vd518 != vd517 ) ),
inference(simp,[status(thm)],[1967]) ).
thf(2370,plain,
! [A: $i] :
( ( less @ v1 @ A )
| ( less @ v1 @ vd517 )
| ( A != vd518 )
| ( vd518 != vd517 )
| ( v1 != v1 ) ),
inference(paramod_ordered,[status(thm)],[1522,2339]) ).
thf(2371,plain,
! [A: $i] :
( ( less @ v1 @ A )
| ( less @ v1 @ vd517 )
| ( A != vd518 )
| ( vd518 != vd517 ) ),
inference(pattern_uni,[status(thm)],[2370:[]]) ).
thf(2376,plain,
( ( less @ v1 @ vd518 )
| ( less @ v1 @ vd517 )
| ( vd518 != vd517 ) ),
inference(simp,[status(thm)],[2371]) ).
thf(16991,plain,
( ( less @ v1 @ vd517 )
| ( vd518 != vd517 )
| ( ( less @ v1 @ vd518 )
!= ( less @ v1 @ vd517 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[2376]) ).
thf(17005,plain,
( ( less @ v1 @ vd517 )
| ( vd518 != vd517 )
| ( v1 != v1 )
| ( vd518 != vd517 ) ),
inference(simp,[status(thm)],[16991]) ).
thf(17020,plain,
( ( less @ v1 @ vd517 )
| ( vd518 != vd517 ) ),
inference(simp,[status(thm)],[17005]) ).
thf(21,axiom,
! [A: $i,B: $i] :
( ( A != B )
| ~ ( less @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(130), 0), 1)') ).
thf(131,plain,
! [A: $i,B: $i] :
( ( A != B )
| ~ ( less @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(132,plain,
! [B: $i,A: $i] :
( ( A != B )
| ~ ( less @ A @ B ) ),
inference(cnf,[status(esa)],[131]) ).
thf(133,plain,
! [B: $i,A: $i] :
( ( A != B )
| ~ ( less @ A @ B ) ),
inference(lifteq,[status(thm)],[132]) ).
thf(134,plain,
! [A: $i] :
~ ( less @ A @ A ),
inference(simp,[status(thm)],[133]) ).
thf(17054,plain,
! [A: $i] :
( ( vd518 != vd517 )
| ( ( less @ v1 @ vd517 )
!= ( less @ A @ A ) ) ),
inference(paramod_ordered,[status(thm)],[17020,134]) ).
thf(17096,plain,
! [A: $i] :
( ( vd518 != vd517 )
| ( v1 != A )
| ( vd517 != A ) ),
inference(simp,[status(thm)],[17054]) ).
thf(17103,plain,
( ( vd518 != vd517 )
| ( v1 != vd517 ) ),
inference(simp,[status(thm)],[17096]) ).
thf(19364,plain,
( ( greater @ vd517 @ vd518 )
| ( v1 != vd517 )
| ( vd518 != vd518 ) ),
inference(paramod_ordered,[status(thm)],[18839,17103]) ).
thf(19365,plain,
( ( greater @ vd517 @ vd518 )
| ( v1 != vd517 ) ),
inference(pattern_uni,[status(thm)],[19364:[]]) ).
thf(198,plain,
( ( greater @ vd519 @ vd520 )
| ( geq @ vd519 @ vd520 ) ),
inference(cnf,[status(esa)],[197]) ).
thf(2402,plain,
! [B: $i,A: $i] :
( ( greater @ vd519 @ vd520 )
| ( leq @ B @ A )
| ( ( geq @ vd519 @ vd520 )
!= ( geq @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[198,101]) ).
thf(2403,plain,
( ( greater @ vd519 @ vd520 )
| ( leq @ vd520 @ vd519 ) ),
inference(pattern_uni,[status(thm)],[2402:[bind(A,$thf( vd519 )),bind(B,$thf( vd520 ))]]) ).
thf(2734,plain,
! [B: $i,A: $i] :
( ( greater @ vd519 @ vd520 )
| ( B = A )
| ( less @ B @ A )
| ( ( leq @ vd520 @ vd519 )
!= ( leq @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[2403,110]) ).
thf(2735,plain,
( ( greater @ vd519 @ vd520 )
| ( vd520 = vd519 )
| ( less @ vd520 @ vd519 ) ),
inference(pattern_uni,[status(thm)],[2734:[bind(A,$thf( vd519 )),bind(B,$thf( vd520 ))]]) ).
thf(18755,plain,
! [B: $i,A: $i] :
( ( greater @ vd519 @ vd520 )
| ( vd520 = vd519 )
| ( greater @ B @ A )
| ( ( less @ vd520 @ vd519 )
!= ( less @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[2735,223]) ).
thf(18756,plain,
( ( greater @ vd519 @ vd520 )
| ( vd520 = vd519 )
| ( greater @ vd519 @ vd520 ) ),
inference(pattern_uni,[status(thm)],[18755:[bind(A,$thf( vd520 )),bind(B,$thf( vd519 ))]]) ).
thf(18842,plain,
( ( greater @ vd519 @ vd520 )
| ( vd520 = vd519 ) ),
inference(simp,[status(thm)],[18756]) ).
thf(36,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( greater @ C @ D )
& ( greater @ A @ B ) )
=> ( greater @ ( vmul @ A @ C ) @ ( vmul @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(312, 0), 0)') ).
thf(183,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( greater @ C @ D )
& ( greater @ A @ B ) )
=> ( greater @ ( vmul @ A @ C ) @ ( vmul @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(184,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( greater @ C @ D )
| ~ ( greater @ A @ B )
| ( greater @ ( vmul @ A @ C ) @ ( vmul @ B @ D ) ) ),
inference(cnf,[status(esa)],[183]) ).
thf(9736,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( greater @ C @ D )
| ~ ( greater @ A @ B )
| ( ( greater @ ( vmul @ A @ C ) @ ( vmul @ B @ D ) )
!= ( greater @ ( vmul @ vd517 @ vd519 ) @ ( vmul @ vd518 @ vd520 ) ) ) ),
inference(paramod_ordered,[status(thm)],[184,61]) ).
thf(9737,plain,
( ~ ( greater @ vd519 @ vd520 )
| ~ ( greater @ vd517 @ vd518 ) ),
inference(pattern_uni,[status(thm)],[9736:[bind(A,$thf( vd517 )),bind(B,$thf( vd518 )),bind(C,$thf( vd519 )),bind(D,$thf( vd520 ))]]) ).
thf(20478,plain,
( ( vd520 = vd519 )
| ~ ( greater @ vd517 @ vd518 )
| ( ( greater @ vd519 @ vd520 )
!= ( greater @ vd519 @ vd520 ) ) ),
inference(paramod_ordered,[status(thm)],[18842,9737]) ).
thf(20479,plain,
( ( vd520 = vd519 )
| ~ ( greater @ vd517 @ vd518 ) ),
inference(pattern_uni,[status(thm)],[20478:[]]) ).
thf(22520,plain,
( ( v1 != vd517 )
| ( vd520 = vd519 )
| ( ( greater @ vd517 @ vd518 )
!= ( greater @ vd517 @ vd518 ) ) ),
inference(paramod_ordered,[status(thm)],[19365,20479]) ).
thf(22521,plain,
( ( v1 != vd517 )
| ( vd520 = vd519 ) ),
inference(pattern_uni,[status(thm)],[22520:[]]) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( A != B )
=> ! [C: $i] :
( ( vplus @ C @ A )
!= ( vplus @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(81, 0), 0)') ).
thf(84,plain,
! [A: $i,B: $i] :
( ( A != B )
=> ! [C: $i] :
( ( vplus @ C @ A )
!= ( vplus @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(85,plain,
! [A: $i,B: $i] :
( ( A != B )
=> ~ ? [C: $i] :
( ( vplus @ C @ A )
= ( vplus @ C @ B ) ) ),
inference(miniscope,[status(thm)],[84]) ).
thf(86,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ( ( vplus @ C @ A )
!= ( vplus @ C @ B ) ) ),
inference(cnf,[status(esa)],[85]) ).
thf(87,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ( ( vplus @ C @ A )
!= ( vplus @ C @ B ) ) ),
inference(lifteq,[status(thm)],[86]) ).
thf(88,plain,
! [B: $i,A: $i] :
( ( sk1 @ A @ ( vplus @ A @ B ) )
= B ),
introduced(tautology,[new_symbols(inverse(vplus),[sk1])]) ).
thf(23,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( geq @ C @ D )
& ( geq @ A @ B ) )
=> ( geq @ ( vplus @ A @ C ) @ ( vplus @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(223, 0), 0)') ).
thf(138,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( geq @ C @ D )
& ( geq @ A @ B ) )
=> ( geq @ ( vplus @ A @ C ) @ ( vplus @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(67,plain,
! [B: $i,A: $i] :
( ( vplus @ A @ ( vsucc @ B ) )
= ( vsucc @ ( vplus @ A @ B ) ) ),
inference(cnf,[status(esa)],[65]) ).
thf(70,plain,
! [B: $i,A: $i] :
( ( vplus @ A @ ( vsucc @ B ) )
= ( vsucc @ ( vplus @ A @ B ) ) ),
inference(lifteq,[status(thm)],[67]) ).
thf(789,plain,
! [C: $i,B: $i,A: $i] :
( ( ( vsucc @ ( vplus @ A @ B ) )
!= ( vmul @ vd517 @ vd519 ) )
| ( ( vplus @ A @ ( vsucc @ B ) )
!= ( vplus @ ( vmul @ vd518 @ vd520 ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[70,509]) ).
thf(790,plain,
! [A: $i] :
( ( vsucc @ ( vplus @ ( vmul @ vd518 @ vd520 ) @ A ) )
!= ( vmul @ vd517 @ vd519 ) ),
inference(pattern_uni,[status(thm)],[789:[bind(A,$thf( vmul @ vd518 @ vd520 )),bind(B,$thf( F )),bind(C,$thf( vsucc @ F ))]]) ).
thf(799,plain,
! [A: $i] :
( ( vsucc @ ( vplus @ ( vmul @ vd518 @ vd520 ) @ A ) )
!= ( vmul @ vd517 @ vd519 ) ),
inference(simp,[status(thm)],[790]) ).
thf(1307,plain,
! [C: $i,B: $i,A: $i] :
( ( ( vsucc @ ( vplus @ A @ B ) )
!= ( vmul @ vd517 @ vd519 ) )
| ( ( vplus @ B @ A )
!= ( vplus @ ( vmul @ vd518 @ vd520 ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[77,799]) ).
thf(1308,plain,
! [A: $i] :
( ( vsucc @ ( vplus @ A @ ( vmul @ vd518 @ vd520 ) ) )
!= ( vmul @ vd517 @ vd519 ) ),
inference(pattern_uni,[status(thm)],[1307:[bind(A,$thf( A )),bind(B,$thf( vmul @ vd518 @ vd520 )),bind(C,$thf( A ))]]) ).
thf(23947,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( vsucc @ ( vmul @ A @ ( vplus @ B @ C ) ) )
!= ( vmul @ vd517 @ vd519 ) )
| ( ( vplus @ ( vmul @ A @ B ) @ ( vmul @ A @ C ) )
!= ( vplus @ D @ ( vmul @ vd518 @ vd520 ) ) ) ),
inference(paramod_ordered,[status(thm)],[250,1308]) ).
thf(23948,plain,
! [A: $i] :
( ( vsucc @ ( vmul @ vd518 @ ( vplus @ A @ vd520 ) ) )
!= ( vmul @ vd517 @ vd519 ) ),
inference(pattern_uni,[status(thm)],[23947:[bind(A,$thf( vd518 )),bind(B,$thf( F )),bind(C,$thf( vd520 )),bind(D,$thf( vmul @ vd518 @ F ))]]) ).
thf(23996,plain,
! [A: $i] :
( ( vsucc @ ( vmul @ vd518 @ ( vplus @ A @ vd520 ) ) )
!= ( vmul @ vd517 @ vd519 ) ),
inference(simp,[status(thm)],[23948]) ).
thf(473,plain,
! [C: $i,B: $i,A: $i] :
( ( greater @ ( vsucc @ A ) @ B )
| ( ( vplus @ A @ v1 )
!= ( vplus @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[69,182]) ).
thf(474,plain,
! [A: $i] : ( greater @ ( vsucc @ A ) @ A ),
inference(pattern_uni,[status(thm)],[473:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( v1 ))]]) ).
thf(192,plain,
! [A: $i] :
( ( vmul @ A @ v1 )
= A ),
inference(cnf,[status(esa)],[191]) ).
thf(194,plain,
! [A: $i] :
( ( vmul @ A @ v1 )
= A ),
inference(lifteq,[status(thm)],[192]) ).
thf(195,plain,
! [A: $i] :
( ( vmul @ A @ v1 )
= A ),
inference(simp,[status(thm)],[194]) ).
thf(277,plain,
! [A: $i] :
( ~ ( greater @ A @ ( vmul @ vd518 @ vd520 ) )
| ( ( vmul @ A @ v1 )
!= ( vmul @ vd517 @ vd519 ) ) ),
inference(paramod_ordered,[status(thm)],[195,61]) ).
thf(279,plain,
! [A: $i] :
( ~ ( greater @ A @ ( vmul @ vd518 @ vd520 ) )
| ( A != vd517 )
| ( v1 != vd519 ) ),
inference(simp,[status(thm)],[277]) ).
thf(281,plain,
( ~ ( greater @ vd517 @ ( vmul @ vd518 @ vd520 ) )
| ( v1 != vd519 ) ),
inference(simp,[status(thm)],[279]) ).
thf(597,plain,
! [A: $i] :
( ( v1 != vd519 )
| ( ( greater @ ( vsucc @ A ) @ A )
!= ( greater @ vd517 @ ( vmul @ vd518 @ vd520 ) ) ) ),
inference(paramod_ordered,[status(thm)],[474,281]) ).
thf(602,plain,
! [A: $i] :
( ( v1 != vd519 )
| ( ( vsucc @ A )
!= vd517 )
| ( A
!= ( vmul @ vd518 @ vd520 ) ) ),
inference(simp,[status(thm)],[597]) ).
thf(616,plain,
( ( v1 != vd519 )
| ( ( vsucc @ ( vmul @ vd518 @ vd520 ) )
!= vd517 ) ),
inference(simp,[status(thm)],[602]) ).
thf(1949,plain,
! [A: $i] :
( ( less @ v1 @ A )
| ( A != vd519 )
| ( ( vsucc @ ( vmul @ vd518 @ vd520 ) )
!= vd517 )
| ( v1 != v1 ) ),
inference(paramod_ordered,[status(thm)],[1522,616]) ).
thf(1950,plain,
! [A: $i] :
( ( less @ v1 @ A )
| ( A != vd519 )
| ( ( vsucc @ ( vmul @ vd518 @ vd520 ) )
!= vd517 ) ),
inference(pattern_uni,[status(thm)],[1949:[]]) ).
thf(2336,plain,
( ( less @ v1 @ vd519 )
| ( ( vsucc @ ( vmul @ vd518 @ vd520 ) )
!= vd517 ) ),
inference(simp,[status(thm)],[1950]) ).
thf(47,axiom,
! [A: $i,B: $i] :
( ~ ( greater @ A @ B )
| ~ ( less @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(130), 0), 2)') ).
thf(216,plain,
! [A: $i,B: $i] :
( ~ ( greater @ A @ B )
| ~ ( less @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(217,plain,
! [B: $i,A: $i] :
( ~ ( greater @ A @ B )
| ~ ( less @ A @ B ) ),
inference(cnf,[status(esa)],[216]) ).
thf(20539,plain,
! [B: $i,A: $i] :
( ( v1 != vd517 )
| ~ ( less @ A @ B )
| ( ( greater @ vd517 @ vd518 )
!= ( greater @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[19365,217]) ).
thf(20540,plain,
( ( v1 != vd517 )
| ~ ( less @ vd517 @ vd518 ) ),
inference(pattern_uni,[status(thm)],[20539:[bind(A,$thf( vd517 )),bind(B,$thf( vd518 ))]]) ).
thf(21890,plain,
! [A: $i] :
( ( A = v1 )
| ( v1 != vd517 )
| ( ( less @ v1 @ A )
!= ( less @ vd517 @ vd518 ) ) ),
inference(paramod_ordered,[status(thm)],[1522,20540]) ).
thf(21985,plain,
! [A: $i] :
( ( A = v1 )
| ( v1 != vd517 )
| ( v1 != vd517 )
| ( A != vd518 ) ),
inference(simp,[status(thm)],[21890]) ).
thf(22037,plain,
( ( v1 = vd518 )
| ( v1 != vd517 ) ),
inference(simp,[status(thm)],[21985]) ).
thf(22409,plain,
! [A: $i] :
( ( less @ v1 @ A )
| ( v1 = vd518 )
| ( A != vd517 )
| ( v1 != v1 ) ),
inference(paramod_ordered,[status(thm)],[1522,22037]) ).
thf(22410,plain,
! [A: $i] :
( ( less @ v1 @ A )
| ( v1 = vd518 )
| ( A != vd517 ) ),
inference(pattern_uni,[status(thm)],[22409:[]]) ).
thf(22421,plain,
( ( less @ v1 @ vd517 )
| ( v1 = vd518 ) ),
inference(simp,[status(thm)],[22410]) ).
thf(24399,plain,
! [B: $i,A: $i] :
( ( v1 = vd518 )
| ~ ( greater @ A @ B )
| ( ( less @ v1 @ vd517 )
!= ( less @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[22421,217]) ).
thf(24400,plain,
( ( v1 = vd518 )
| ~ ( greater @ v1 @ vd517 ) ),
inference(pattern_uni,[status(thm)],[24399:[bind(A,$thf( v1 )),bind(B,$thf( vd517 ))]]) ).
thf(1921,plain,
! [A: $i] :
( ( less @ v1 @ A )
| ~ ( greater @ vd517 @ ( vmul @ vd518 @ vd520 ) )
| ( A != vd519 )
| ( v1 != v1 ) ),
inference(paramod_ordered,[status(thm)],[1522,281]) ).
thf(1922,plain,
! [A: $i] :
( ( less @ v1 @ A )
| ~ ( greater @ vd517 @ ( vmul @ vd518 @ vd520 ) )
| ( A != vd519 ) ),
inference(pattern_uni,[status(thm)],[1921:[]]) ).
thf(2331,plain,
( ( less @ v1 @ vd519 )
| ~ ( greater @ vd517 @ ( vmul @ vd518 @ vd520 ) ) ),
inference(simp,[status(thm)],[1922]) ).
thf(51,axiom,
! [A: $i,B: $i] :
( ( vmul @ ( vsucc @ A ) @ B )
= ( vplus @ ( vmul @ A @ B ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(261, 0), 0)') ).
thf(224,plain,
! [A: $i,B: $i] :
( ( vmul @ ( vsucc @ A ) @ B )
= ( vplus @ ( vmul @ A @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(225,plain,
! [B: $i,A: $i] :
( ( vmul @ ( vsucc @ A ) @ B )
= ( vplus @ ( vmul @ A @ B ) @ B ) ),
inference(cnf,[status(esa)],[224]) ).
thf(226,plain,
! [B: $i,A: $i] :
( ( vplus @ ( vmul @ A @ B ) @ B )
= ( vmul @ ( vsucc @ A ) @ B ) ),
inference(lifteq,[status(thm)],[225]) ).
thf(19686,plain,
! [C: $i,B: $i,A: $i] :
( ( ( vmul @ ( vsucc @ A ) @ B )
!= ( vmul @ vd517 @ vd519 ) )
| ( ( vplus @ ( vmul @ A @ B ) @ B )
!= ( vplus @ ( vmul @ vd518 @ vd520 ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[226,509]) ).
thf(19687,plain,
( ( vmul @ ( vsucc @ vd518 ) @ vd520 )
!= ( vmul @ vd517 @ vd519 ) ),
inference(pattern_uni,[status(thm)],[19686:[bind(A,$thf( vd518 )),bind(B,$thf( vd520 )),bind(C,$thf( vd520 ))]]) ).
thf(17,axiom,
! [A: $i,B: $i,C: $i] :
( ( A = B )
=> ( ( vplus @ A @ C )
= ( vplus @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(193), 0), 1)') ).
thf(115,plain,
! [A: $i,B: $i,C: $i] :
( ( A = B )
=> ( ( vplus @ A @ C )
= ( vplus @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(151,plain,
! [B: $i,A: $i] :
( ~ ( less @ B @ A )
| ( A
= ( vplus @ B @ ( sk7 @ B @ A ) ) ) ),
inference(cnf,[status(esa)],[149]) ).
thf(154,plain,
! [B: $i,A: $i] :
( ( ( vplus @ B @ ( sk7 @ B @ A ) )
= A )
| ~ ( less @ B @ A ) ),
inference(lifteq,[status(thm)],[151]) ).
thf(7051,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( less @ B @ A )
| ( A
!= ( vmul @ vd517 @ vd519 ) )
| ( ( vplus @ B @ ( sk7 @ B @ A ) )
!= ( vplus @ ( vmul @ vd518 @ vd520 ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[154,509]) ).
thf(7052,plain,
! [A: $i] :
( ~ ( less @ ( vmul @ vd518 @ vd520 ) @ A )
| ( A
!= ( vmul @ vd517 @ vd519 ) ) ),
inference(pattern_uni,[status(thm)],[7051:[bind(A,$thf( G )),bind(B,$thf( vmul @ vd518 @ vd520 )),bind(C,$thf( sk7 @ ( vmul @ vd518 @ vd520 ) @ G ))]]) ).
thf(7127,plain,
~ ( less @ ( vmul @ vd518 @ vd520 ) @ ( vmul @ vd517 @ vd519 ) ),
inference(simp,[status(thm)],[7052]) ).
thf(7198,plain,
! [A: $i] :
( ~ ( less @ A @ ( vmul @ vd517 @ vd519 ) )
| ( ( vmul @ v1 @ A )
!= ( vmul @ vd518 @ vd520 ) ) ),
inference(paramod_ordered,[status(thm)],[247,7127]) ).
thf(7264,plain,
! [A: $i] :
( ~ ( less @ A @ ( vmul @ vd517 @ vd519 ) )
| ( v1 != vd518 )
| ( A != vd520 ) ),
inference(simp,[status(thm)],[7198]) ).
thf(7295,plain,
( ~ ( less @ vd520 @ ( vmul @ vd517 @ vd519 ) )
| ( v1 != vd518 ) ),
inference(simp,[status(thm)],[7264]) ).
thf(7417,plain,
! [A: $i] :
( ~ ( less @ vd520 @ A )
| ( v1 != vd518 )
| ( ( vmul @ v1 @ A )
!= ( vmul @ vd517 @ vd519 ) ) ),
inference(paramod_ordered,[status(thm)],[247,7295]) ).
thf(7485,plain,
! [A: $i] :
( ~ ( less @ vd520 @ A )
| ( v1 != vd518 )
| ( v1 != vd517 )
| ( A != vd519 ) ),
inference(simp,[status(thm)],[7417]) ).
thf(7516,plain,
( ~ ( less @ vd520 @ vd519 )
| ( v1 != vd518 )
| ( v1 != vd517 ) ),
inference(simp,[status(thm)],[7485]) ).
thf(41,axiom,
! [A: $i,B: $i] :
( ( greater @ A @ B )
=> ( geq @ A @ ( vplus @ B @ v1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(234, 0), 0)') ).
thf(202,plain,
! [A: $i,B: $i] :
( ( greater @ A @ B )
=> ( geq @ A @ ( vplus @ B @ v1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(203,plain,
! [B: $i,A: $i] :
( ~ ( greater @ A @ B )
| ( geq @ A @ ( vplus @ B @ v1 ) ) ),
inference(cnf,[status(esa)],[202]) ).
thf(14381,plain,
! [B: $i,A: $i] :
( ~ ( greater @ A @ B )
| ( geq @ A @ ( vsucc @ B ) ) ),
inference(rewrite,[status(thm)],[203,69]) ).
thf(14408,plain,
! [B: $i,A: $i] :
( ( greater @ vd517 @ vd518 )
| ( geq @ A @ ( vsucc @ B ) )
| ( ( greater @ vd519 @ vd520 )
!= ( greater @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[199,14381]) ).
thf(14409,plain,
( ( greater @ vd517 @ vd518 )
| ( geq @ vd519 @ ( vsucc @ vd520 ) ) ),
inference(pattern_uni,[status(thm)],[14408:[bind(A,$thf( vd519 )),bind(B,$thf( vd520 ))]]) ).
thf(3,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( leq @ B @ C )
& ( leq @ A @ B ) )
=> ( leq @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(184, 0), 0)') ).
thf(62,plain,
! [A: $i,B: $i,C: $i] :
( ( ( leq @ B @ C )
& ( leq @ A @ B ) )
=> ( leq @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(63,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( leq @ B @ C )
| ~ ( leq @ A @ B )
| ( leq @ A @ C ) ),
inference(cnf,[status(esa)],[62]) ).
thf(272,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( leq @ B @ C )
| ~ ( leq @ A @ B )
| ~ ( leq @ E @ F )
| ( leq @ D @ F )
| ( ( leq @ A @ C )
!= ( leq @ D @ E ) ) ),
inference(paramod_ordered,[status(thm)],[63,63]) ).
thf(273,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( leq @ B @ C )
| ~ ( leq @ A @ B )
| ~ ( leq @ C @ D )
| ( leq @ A @ D ) ),
inference(pattern_uni,[status(thm)],[272:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( A )),bind(E,$thf( C ))]]) ).
thf(276,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( leq @ B @ C )
| ~ ( leq @ A @ B )
| ~ ( leq @ C @ D )
| ( leq @ A @ D ) ),
inference(simp,[status(thm)],[273]) ).
thf(18,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( vplus @ A @ C )
= ( vplus @ B @ C ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(202), 0), 1)') ).
thf(120,plain,
! [A: $i,B: $i,C: $i] :
( ( ( vplus @ A @ C )
= ( vplus @ B @ C ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(19371,plain,
( ( vd518 = vd517 )
| ~ ( greater @ vd519 @ vd520 )
| ( ( greater @ vd517 @ vd518 )
!= ( greater @ vd517 @ vd518 ) ) ),
inference(paramod_ordered,[status(thm)],[18839,9737]) ).
thf(19372,plain,
( ( vd518 = vd517 )
| ~ ( greater @ vd519 @ vd520 ) ),
inference(pattern_uni,[status(thm)],[19371:[]]) ).
thf(18817,plain,
! [B: $i,A: $i] :
( ( vd518 != vd517 )
| ( greater @ B @ A )
| ( ( less @ v1 @ vd517 )
!= ( less @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[17020,223]) ).
thf(18818,plain,
( ( vd518 != vd517 )
| ( greater @ vd517 @ v1 ) ),
inference(pattern_uni,[status(thm)],[18817:[bind(A,$thf( v1 )),bind(B,$thf( vd517 ))]]) ).
thf(19431,plain,
! [B: $i,A: $i] :
( ( vd518 != vd517 )
| ~ ( less @ A @ B )
| ( ( greater @ vd517 @ v1 )
!= ( greater @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[18818,217]) ).
thf(19432,plain,
( ( vd518 != vd517 )
| ~ ( less @ vd517 @ v1 ) ),
inference(pattern_uni,[status(thm)],[19431:[bind(A,$thf( vd517 )),bind(B,$thf( v1 ))]]) ).
thf(20884,plain,
( ~ ( greater @ vd519 @ vd520 )
| ~ ( less @ vd517 @ v1 )
| ( vd518 != vd518 ) ),
inference(paramod_ordered,[status(thm)],[19372,19432]) ).
thf(20885,plain,
( ~ ( greater @ vd519 @ vd520 )
| ~ ( less @ vd517 @ v1 ) ),
inference(pattern_uni,[status(thm)],[20884:[]]) ).
thf(55,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( vmul @ A @ B )
= ( vmul @ C @ B ) )
=> ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(conjunct1(conjunct2(307)), 0), 0)') ).
thf(241,plain,
! [A: $i,B: $i,C: $i] :
( ( ( vmul @ A @ B )
= ( vmul @ C @ B ) )
=> ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(242,plain,
! [C: $i,B: $i,A: $i] :
( ( ( vmul @ A @ B )
!= ( vmul @ C @ B ) )
| ( A = C ) ),
inference(cnf,[status(esa)],[241]) ).
thf(243,plain,
! [C: $i,B: $i,A: $i] :
( ( ( vmul @ A @ B )
!= ( vmul @ C @ B ) )
| ( A = C ) ),
inference(lifteq,[status(thm)],[242]) ).
thf(244,plain,
! [B: $i,A: $i] :
( ( sk9 @ A @ ( vmul @ B @ A ) )
= B ),
introduced(tautology,[new_symbols(inverse(vmul),[sk9])]) ).
thf(23143,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk9 @ B @ A )
= C )
| ( ( vmul @ v1 @ A )
!= ( vmul @ C @ B ) ) ),
inference(paramod_ordered,[status(thm)],[247,244]) ).
thf(23144,plain,
! [A: $i] :
( ( sk9 @ A @ A )
= v1 ),
inference(pattern_uni,[status(thm)],[23143:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( v1 ))]]) ).
thf(37,axiom,
! [A: $i,B: $i] :
( ( A = B )
| ( greater @ A @ B )
| ( less @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(130), 0), 0)') ).
thf(185,plain,
! [A: $i,B: $i] :
( ( A = B )
| ( greater @ A @ B )
| ( less @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( A != B )
| ~ ? [C: $i] :
( A
= ( vplus @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(88), 0), 3)') ).
thf(71,plain,
! [A: $i,B: $i] :
( ( A != B )
| ~ ? [C: $i] :
( A
= ( vplus @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(72,plain,
! [C: $i,B: $i,A: $i] :
( ( A != B )
| ( A
!= ( vplus @ B @ C ) ) ),
inference(cnf,[status(esa)],[71]) ).
thf(73,plain,
! [C: $i,B: $i,A: $i] :
( ( A != B )
| ( A
!= ( vplus @ B @ C ) ) ),
inference(lifteq,[status(thm)],[72]) ).
thf(74,plain,
! [B: $i,A: $i] :
( ( vplus @ A @ B )
!= A ),
inference(simp,[status(thm)],[73]) ).
thf(366,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( vsucc @ ( vplus @ A @ B ) )
!= C )
| ( ( vplus @ A @ ( vsucc @ B ) )
!= ( vplus @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[70,74]) ).
thf(367,plain,
! [B: $i,A: $i] :
( ( vsucc @ ( vplus @ A @ B ) )
!= A ),
inference(pattern_uni,[status(thm)],[366:[bind(A,$thf( A )),bind(B,$thf( E )),bind(C,$thf( A )),bind(D,$thf( vsucc @ E ))]]) ).
thf(375,plain,
! [B: $i,A: $i] :
( ( vsucc @ ( vplus @ A @ B ) )
!= A ),
inference(simp,[status(thm)],[367]) ).
thf(1893,plain,
! [C: $i,B: $i,A: $i] :
( ( less @ v1 @ A )
| ( ( vsucc @ v1 )
!= B )
| ( A
!= ( vplus @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[1522,375]) ).
thf(1894,plain,
! [B: $i,A: $i] :
( ( less @ v1 @ ( vplus @ A @ B ) )
| ( ( vsucc @ v1 )
!= A ) ),
inference(pattern_uni,[status(thm)],[1893:[bind(A,$thf( vplus @ D @ E )),bind(B,$thf( D )),bind(C,$thf( E ))]]) ).
thf(2324,plain,
! [A: $i] : ( less @ v1 @ ( vplus @ ( vsucc @ v1 ) @ A ) ),
inference(simp,[status(thm)],[1894]) ).
thf(4218,plain,
! [B: $i,A: $i] :
( ( less @ v1 @ ( vplus @ ( vsucc @ v1 ) @ A ) )
!= ( less @ B @ B ) ),
inference(paramod_ordered,[status(thm)],[2324,134]) ).
thf(4231,plain,
! [B: $i,A: $i] :
( ( v1 != B )
| ( ( vplus @ ( vsucc @ v1 ) @ A )
!= B ) ),
inference(simp,[status(thm)],[4218]) ).
thf(4236,plain,
! [A: $i] :
( ( vplus @ ( vsucc @ v1 ) @ A )
!= v1 ),
inference(simp,[status(thm)],[4231]) ).
thf(4416,plain,
! [C: $i,B: $i,A: $i] :
( ( ( vsucc @ ( vplus @ A @ B ) )
!= v1 )
| ( ( vplus @ A @ ( vsucc @ B ) )
!= ( vplus @ ( vsucc @ v1 ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[70,4236]) ).
thf(4417,plain,
! [A: $i] :
( ( vsucc @ ( vplus @ ( vsucc @ v1 ) @ A ) )
!= v1 ),
inference(pattern_uni,[status(thm)],[4416:[bind(A,$thf( vsucc @ v1 )),bind(B,$thf( E )),bind(C,$thf( vsucc @ E ))]]) ).
thf(4431,plain,
! [A: $i] :
( ( vsucc @ ( vplus @ ( vsucc @ v1 ) @ A ) )
!= v1 ),
inference(simp,[status(thm)],[4417]) ).
thf(5454,plain,
! [C: $i,B: $i,A: $i] :
( ( ( vsucc @ ( vplus @ A @ B ) )
!= v1 )
| ( ( vplus @ B @ A )
!= ( vplus @ ( vsucc @ v1 ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[77,4431]) ).
thf(5455,plain,
! [A: $i] :
( ( vsucc @ ( vplus @ A @ ( vsucc @ v1 ) ) )
!= v1 ),
inference(pattern_uni,[status(thm)],[5454:[bind(A,$thf( A )),bind(B,$thf( vsucc @ v1 )),bind(C,$thf( A ))]]) ).
thf(5750,plain,
! [A: $i] :
( ( vsucc @ ( vsucc @ ( vplus @ A @ v1 ) ) )
!= v1 ),
inference(rewrite,[status(thm)],[5455,70]) ).
thf(11,axiom,
! [A: $i,B: $i,C: $i] :
( ( vplus @ ( vplus @ A @ B ) @ C )
= ( vplus @ A @ ( vplus @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(33, 0), 0)') ).
thf(92,plain,
! [A: $i,B: $i,C: $i] :
( ( vplus @ ( vplus @ A @ B ) @ C )
= ( vplus @ A @ ( vplus @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(93,plain,
! [C: $i,B: $i,A: $i] :
( ( vplus @ ( vplus @ A @ B ) @ C )
= ( vplus @ A @ ( vplus @ B @ C ) ) ),
inference(cnf,[status(esa)],[92]) ).
thf(94,plain,
! [C: $i,B: $i,A: $i] :
( ( vplus @ ( vplus @ A @ B ) @ C )
= ( vplus @ A @ ( vplus @ B @ C ) ) ),
inference(lifteq,[status(thm)],[93]) ).
thf(4418,plain,
! [C: $i,B: $i,A: $i] :
( ( ( vplus @ A @ B )
!= v1 )
| ( ( vplus @ B @ A )
!= ( vplus @ ( vsucc @ v1 ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[77,4236]) ).
thf(4419,plain,
! [A: $i] :
( ( vplus @ A @ ( vsucc @ v1 ) )
!= v1 ),
inference(pattern_uni,[status(thm)],[4418:[bind(A,$thf( A )),bind(B,$thf( vsucc @ v1 )),bind(C,$thf( A ))]]) ).
thf(4474,plain,
! [A: $i] :
( ( vsucc @ ( vplus @ A @ v1 ) )
!= v1 ),
inference(rewrite,[status(thm)],[4419,70]) ).
thf(4507,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( vsucc @ ( vplus @ A @ ( vplus @ B @ C ) ) )
!= v1 )
| ( ( vplus @ ( vplus @ A @ B ) @ C )
!= ( vplus @ D @ v1 ) ) ),
inference(paramod_ordered,[status(thm)],[94,4474]) ).
thf(4508,plain,
! [B: $i,A: $i] :
( ( vsucc @ ( vplus @ A @ ( vplus @ B @ v1 ) ) )
!= v1 ),
inference(pattern_uni,[status(thm)],[4507:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( v1 )),bind(D,$thf( vplus @ E @ F ))]]) ).
thf(4522,plain,
! [B: $i,A: $i] :
( ( vsucc @ ( vplus @ A @ ( vplus @ B @ v1 ) ) )
!= v1 ),
inference(simp,[status(thm)],[4508]) ).
thf(13519,plain,
! [B: $i,A: $i] :
( ( vsucc @ ( vplus @ A @ ( vsucc @ B ) ) )
!= v1 ),
inference(rewrite,[status(thm)],[4522,69]) ).
thf(13823,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( vsucc @ ( vmul @ A @ ( vsucc @ B ) ) )
!= v1 )
| ( ( vplus @ ( vmul @ A @ B ) @ A )
!= ( vplus @ C @ ( vsucc @ D ) ) ) ),
inference(paramod_ordered,[status(thm)],[196,13519]) ).
thf(13824,plain,
! [B: $i,A: $i] :
( ( vsucc @ ( vmul @ ( vsucc @ B ) @ ( vsucc @ A ) ) )
!= v1 ),
inference(pattern_uni,[status(thm)],[13823:[bind(A,$thf( vsucc @ G )),bind(B,$thf( F )),bind(C,$thf( vmul @ ( vsucc @ G ) @ F )),bind(D,$thf( G ))]]) ).
thf(13923,plain,
! [B: $i,A: $i] :
( ( vsucc @ ( vmul @ ( vsucc @ B ) @ ( vsucc @ A ) ) )
!= v1 ),
inference(simp,[status(thm)],[13824]) ).
thf(49,axiom,
! [A: $i,B: $i] :
( ( greater @ A @ B )
=> ( less @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(140, 0), 0)') ).
thf(220,plain,
! [A: $i,B: $i] :
( ( greater @ A @ B )
=> ( less @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(221,plain,
! [B: $i,A: $i] :
( ~ ( greater @ A @ B )
| ( less @ B @ A ) ),
inference(cnf,[status(esa)],[220]) ).
thf(21910,plain,
! [B: $i,A: $i] :
( ~ ( greater @ A @ B )
| ( v1 != vd517 )
| ( ( less @ B @ A )
!= ( less @ vd517 @ vd518 ) ) ),
inference(paramod_ordered,[status(thm)],[221,20540]) ).
thf(21911,plain,
( ~ ( greater @ vd518 @ vd517 )
| ( v1 != vd517 ) ),
inference(pattern_uni,[status(thm)],[21910:[bind(A,$thf( vd518 )),bind(B,$thf( vd517 ))]]) ).
thf(19182,plain,
! [B: $i,A: $i] :
( ( vd518 = vd517 )
| ( less @ B @ A )
| ( ( greater @ vd517 @ vd518 )
!= ( greater @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[18839,221]) ).
thf(19183,plain,
( ( vd518 = vd517 )
| ( less @ vd518 @ vd517 ) ),
inference(pattern_uni,[status(thm)],[19182:[bind(A,$thf( vd517 )),bind(B,$thf( vd518 ))]]) ).
thf(104,plain,
! [B: $i,A: $i] :
( ~ ( less @ B @ A )
| ( leq @ B @ A ) ),
inference(cnf,[status(esa)],[103]) ).
thf(107,plain,
! [B: $i,A: $i] :
( ~ ( less @ B @ A )
| ( leq @ B @ A ) ),
inference(simp,[status(thm)],[104]) ).
thf(22345,plain,
! [B: $i,A: $i] :
( ( vd518 = vd517 )
| ( leq @ B @ A )
| ( ( less @ vd518 @ vd517 )
!= ( less @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[19183,107]) ).
thf(22346,plain,
( ( vd518 = vd517 )
| ( leq @ vd518 @ vd517 ) ),
inference(pattern_uni,[status(thm)],[22345:[bind(A,$thf( vd517 )),bind(B,$thf( vd518 ))]]) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( leq @ A @ B )
=> ( geq @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(163, 0), 0)') ).
thf(95,plain,
! [A: $i,B: $i] :
( ( leq @ A @ B )
=> ( geq @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(96,plain,
! [B: $i,A: $i] :
( ~ ( leq @ A @ B )
| ( geq @ B @ A ) ),
inference(cnf,[status(esa)],[95]) ).
thf(23464,plain,
! [B: $i,A: $i] :
( ( vd518 = vd517 )
| ( geq @ B @ A )
| ( ( leq @ vd518 @ vd517 )
!= ( leq @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[22346,96]) ).
thf(23465,plain,
( ( vd518 = vd517 )
| ( geq @ vd517 @ vd518 ) ),
inference(pattern_uni,[status(thm)],[23464:[bind(A,$thf( vd518 )),bind(B,$thf( vd517 ))]]) ).
thf(382,plain,
! [C: $i,B: $i,A: $i] :
( ( less @ A @ ( vplus @ A @ B ) )
!= ( less @ C @ C ) ),
inference(paramod_ordered,[status(thm)],[153,134]) ).
thf(387,plain,
! [C: $i,B: $i,A: $i] :
( ( A != C )
| ( ( vplus @ A @ B )
!= C ) ),
inference(simp,[status(thm)],[382]) ).
thf(389,plain,
! [B: $i,A: $i] :
( ( vplus @ B @ A )
!= B ),
inference(simp,[status(thm)],[387]) ).
thf(278,plain,
! [A: $i] :
( ~ ( greater @ ( vmul @ vd517 @ vd519 ) @ A )
| ( ( vmul @ A @ v1 )
!= ( vmul @ vd518 @ vd520 ) ) ),
inference(paramod_ordered,[status(thm)],[195,61]) ).
thf(280,plain,
! [A: $i] :
( ~ ( greater @ ( vmul @ vd517 @ vd519 ) @ A )
| ( A != vd518 )
| ( v1 != vd520 ) ),
inference(simp,[status(thm)],[278]) ).
thf(282,plain,
( ~ ( greater @ ( vmul @ vd517 @ vd519 ) @ vd518 )
| ( v1 != vd520 ) ),
inference(simp,[status(thm)],[280]) ).
thf(601,plain,
! [A: $i] :
( ( v1 != vd520 )
| ( ( greater @ ( vsucc @ A ) @ A )
!= ( greater @ ( vmul @ vd517 @ vd519 ) @ vd518 ) ) ),
inference(paramod_ordered,[status(thm)],[474,282]) ).
thf(605,plain,
! [A: $i] :
( ( v1 != vd520 )
| ( ( vsucc @ A )
!= ( vmul @ vd517 @ vd519 ) )
| ( A != vd518 ) ),
inference(simp,[status(thm)],[601]) ).
thf(619,plain,
( ( v1 != vd520 )
| ( ( vmul @ vd517 @ vd519 )
!= ( vsucc @ vd518 ) ) ),
inference(simp,[status(thm)],[605]) ).
thf(19,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( less @ B @ C )
& ( less @ A @ B ) )
=> ( less @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(168, 0), 0)') ).
thf(125,plain,
! [A: $i,B: $i,C: $i] :
( ( ( less @ B @ C )
& ( less @ A @ B ) )
=> ( less @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(27,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( ( less @ B @ C )
& ( leq @ A @ B ) )
| ( ( leq @ B @ C )
& ( less @ A @ B ) ) )
=> ( less @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(177), 0), 0)') ).
thf(155,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( less @ B @ C )
& ( leq @ A @ B ) )
| ( ( leq @ B @ C )
& ( less @ A @ B ) ) )
=> ( less @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(157,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( leq @ B @ C )
| ~ ( less @ A @ B )
| ( less @ A @ C ) ),
inference(cnf,[status(esa)],[155]) ).
thf(23124,plain,
! [A: $i] :
( ( less @ v1 @ A )
| ( A != vd517 )
| ( vd520 = vd519 )
| ( v1 != v1 ) ),
inference(paramod_ordered,[status(thm)],[1522,22521]) ).
thf(23125,plain,
! [A: $i] :
( ( less @ v1 @ A )
| ( A != vd517 )
| ( vd520 = vd519 ) ),
inference(pattern_uni,[status(thm)],[23124:[]]) ).
thf(23134,plain,
( ( less @ v1 @ vd517 )
| ( vd520 = vd519 ) ),
inference(simp,[status(thm)],[23125]) ).
thf(1300,plain,
! [B: $i,A: $i] :
( ( ( vsucc @ ( vsucc @ A ) )
!= ( vmul @ vd517 @ vd519 ) )
| ( ( vplus @ A @ v1 )
!= ( vplus @ ( vmul @ vd518 @ vd520 ) @ B ) ) ),
inference(paramod_ordered,[status(thm)],[69,799]) ).
thf(1301,plain,
( ( vsucc @ ( vsucc @ ( vmul @ vd518 @ vd520 ) ) )
!= ( vmul @ vd517 @ vd519 ) ),
inference(pattern_uni,[status(thm)],[1300:[bind(A,$thf( vmul @ vd518 @ vd520 )),bind(B,$thf( v1 ))]]) ).
thf(1341,plain,
! [A: $i] :
( ( A
!= ( vsucc @ ( vsucc @ ( vmul @ vd518 @ vd520 ) ) ) )
| ( ( vmul @ A @ v1 )
!= ( vmul @ vd517 @ vd519 ) ) ),
inference(paramod_ordered,[status(thm)],[195,1301]) ).
thf(1347,plain,
( ( ( vsucc @ ( vsucc @ ( vmul @ vd518 @ vd520 ) ) )
!= vd517 )
| ( v1 != vd519 ) ),
inference(simp,[status(thm)],[1341]) ).
thf(1358,plain,
! [A: $i] :
( ( ( vsucc @ ( vsucc @ A ) )
!= vd517 )
| ( v1 != vd519 )
| ( ( vmul @ v1 @ A )
!= ( vmul @ vd518 @ vd520 ) ) ),
inference(paramod_ordered,[status(thm)],[247,1347]) ).
thf(1360,plain,
! [A: $i] :
( ( ( vsucc @ ( vsucc @ A ) )
!= vd517 )
| ( v1 != vd519 )
| ( v1 != vd518 )
| ( A != vd520 ) ),
inference(simp,[status(thm)],[1358]) ).
thf(1362,plain,
( ( ( vsucc @ ( vsucc @ vd520 ) )
!= vd517 )
| ( v1 != vd519 )
| ( v1 != vd518 ) ),
inference(simp,[status(thm)],[1360]) ).
thf(13862,plain,
! [C: $i,B: $i,A: $i] :
( ( ( vmul @ A @ ( vsucc @ B ) )
!= ( vmul @ vd517 @ vd519 ) )
| ( ( vplus @ ( vmul @ A @ B ) @ A )
!= ( vplus @ ( vmul @ vd518 @ vd520 ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[196,509]) ).
thf(13863,plain,
( ( vmul @ vd518 @ ( vsucc @ vd520 ) )
!= ( vmul @ vd517 @ vd519 ) ),
inference(pattern_uni,[status(thm)],[13862:[bind(A,$thf( vd518 )),bind(B,$thf( vd520 )),bind(C,$thf( vd518 ))]]) ).
thf(14033,plain,
! [A: $i] :
( ( A = v1 )
| ( ( vmul @ vd518 @ A )
!= ( vmul @ vd517 @ vd519 ) )
| ( ( vsucc @ ( vskolem2 @ A ) )
!= ( vsucc @ vd520 ) ) ),
inference(paramod_ordered,[status(thm)],[99,13863]) ).
thf(14043,plain,
! [A: $i] :
( ( A = v1 )
| ( vd518 != vd517 )
| ( A != vd519 )
| ( ( vskolem2 @ A )
!= vd520 ) ),
inference(simp,[status(thm)],[14033]) ).
thf(14051,plain,
( ( v1 = vd519 )
| ( vd518 != vd517 )
| ( ( vskolem2 @ vd519 )
!= vd520 ) ),
inference(simp,[status(thm)],[14043]) ).
thf(38,axiom,
! [A: $i,B: $i,C: $i] :
( ( greater @ B @ C )
=> ( greater @ ( vmul @ B @ A ) @ ( vmul @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(299, 0), 2)') ).
thf(188,plain,
! [A: $i,B: $i,C: $i] :
( ( greater @ B @ C )
=> ( greater @ ( vmul @ B @ A ) @ ( vmul @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(189,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( greater @ B @ C )
| ( greater @ ( vmul @ B @ A ) @ ( vmul @ C @ A ) ) ),
inference(cnf,[status(esa)],[188]) ).
thf(7037,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( less @ B @ A )
| ( ( vsucc @ A )
!= C )
| ( ( vplus @ B @ ( sk7 @ B @ A ) )
!= ( vplus @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[154,375]) ).
thf(7038,plain,
! [B: $i,A: $i] :
( ~ ( less @ A @ B )
| ( ( vsucc @ B )
!= A ) ),
inference(pattern_uni,[status(thm)],[7037:[bind(A,$thf( F )),bind(B,$thf( E )),bind(C,$thf( E )),bind(D,$thf( sk7 @ E @ F ))]]) ).
thf(7183,plain,
! [A: $i] :
~ ( less @ ( vsucc @ A ) @ A ),
inference(simp,[status(thm)],[7038]) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ~ ? [C: $i] :
( A
= ( vplus @ B @ C ) )
| ~ ? [C: $i] :
( B
= ( vplus @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(88), 0), 2)') ).
thf(78,plain,
! [A: $i,B: $i] :
( ~ ? [C: $i] :
( A
= ( vplus @ B @ C ) )
| ~ ? [C: $i] :
( B
= ( vplus @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(29,axiom,
! [A: $i,B: $i,C: $i] :
( ( less @ A @ B )
=> ( less @ ( vplus @ A @ C ) @ ( vplus @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(193), 0), 0)') ).
thf(162,plain,
! [A: $i,B: $i,C: $i] :
( ( less @ A @ B )
=> ( less @ ( vplus @ A @ C ) @ ( vplus @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(163,plain,
! [A: $i,B: $i] :
( ( less @ A @ B )
=> ! [C: $i] : ( less @ ( vplus @ A @ C ) @ ( vplus @ B @ C ) ) ),
inference(miniscope,[status(thm)],[162]) ).
thf(164,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( less @ A @ B )
| ( less @ ( vplus @ A @ C ) @ ( vplus @ B @ C ) ) ),
inference(cnf,[status(esa)],[163]) ).
thf(23165,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk9 @ B @ A )
= C )
| ( ( vmul @ A @ v1 )
!= ( vmul @ C @ B ) ) ),
inference(paramod_ordered,[status(thm)],[195,244]) ).
thf(23166,plain,
! [A: $i] :
( ( sk9 @ v1 @ A )
= A ),
inference(pattern_uni,[status(thm)],[23165:[bind(A,$thf( A )),bind(B,$thf( v1 )),bind(C,$thf( A ))]]) ).
thf(45,axiom,
! [A: $i,B: $i,C: $i] :
( ( greater @ ( vplus @ A @ C ) @ ( vplus @ B @ C ) )
=> ( greater @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(202), 0), 2)') ).
thf(211,plain,
! [A: $i,B: $i,C: $i] :
( ( greater @ ( vplus @ A @ C ) @ ( vplus @ B @ C ) )
=> ( greater @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(484,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( greater @ ( vplus @ B @ A ) @ C )
| ( ( vplus @ A @ B )
!= ( vplus @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[77,182]) ).
thf(485,plain,
! [B: $i,A: $i] : ( greater @ ( vplus @ B @ A ) @ A ),
inference(pattern_uni,[status(thm)],[484:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(54,axiom,
! [A: $i,B: $i,C: $i] :
( ( greater @ A @ B )
=> ( greater @ ( vplus @ A @ C ) @ ( vplus @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(193), 0), 2)') ).
thf(238,plain,
! [A: $i,B: $i,C: $i] :
( ( greater @ A @ B )
=> ( greater @ ( vplus @ A @ C ) @ ( vplus @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(294,plain,
! [A: $i] :
( ~ ( greater @ vd517 @ A )
| ( v1 != vd519 )
| ( ( vmul @ A @ v1 )
!= ( vmul @ vd518 @ vd520 ) ) ),
inference(paramod_ordered,[status(thm)],[195,281]) ).
thf(296,plain,
! [A: $i] :
( ~ ( greater @ vd517 @ A )
| ( v1 != vd519 )
| ( A != vd518 )
| ( v1 != vd520 ) ),
inference(simp,[status(thm)],[294]) ).
thf(298,plain,
( ~ ( greater @ vd517 @ vd518 )
| ( v1 != vd519 )
| ( v1 != vd520 ) ),
inference(simp,[status(thm)],[296]) ).
thf(20578,plain,
( ( v1 != vd517 )
| ( v1 != vd519 )
| ( v1 != vd520 )
| ( ( greater @ vd517 @ vd518 )
!= ( greater @ vd517 @ vd518 ) ) ),
inference(paramod_ordered,[status(thm)],[19365,298]) ).
thf(20579,plain,
( ( v1 != vd517 )
| ( v1 != vd519 )
| ( v1 != vd520 ) ),
inference(pattern_uni,[status(thm)],[20578:[]]) ).
thf(25,axiom,
! [A: $i,B: $i] :
( B
!= ( vplus @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(73, 0), 0)') ).
thf(144,plain,
! [A: $i,B: $i] :
( B
!= ( vplus @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(145,plain,
~ ? [A: $i,B: $i] :
( B
= ( vplus @ A @ B ) ),
inference(miniscope,[status(thm)],[144]) ).
thf(146,plain,
! [B: $i,A: $i] :
( B
!= ( vplus @ A @ B ) ),
inference(cnf,[status(esa)],[145]) ).
thf(147,plain,
! [B: $i,A: $i] :
( ( vplus @ A @ B )
!= B ),
inference(lifteq,[status(thm)],[146]) ).
thf(13864,plain,
! [C: $i,B: $i,A: $i] :
( ( ( vsucc @ ( vmul @ A @ ( vsucc @ B ) ) )
!= ( vmul @ vd517 @ vd519 ) )
| ( ( vplus @ ( vmul @ A @ B ) @ A )
!= ( vplus @ ( vmul @ vd518 @ vd520 ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[196,799]) ).
thf(13865,plain,
( ( vsucc @ ( vmul @ vd518 @ ( vsucc @ vd520 ) ) )
!= ( vmul @ vd517 @ vd519 ) ),
inference(pattern_uni,[status(thm)],[13864:[bind(A,$thf( vd518 )),bind(B,$thf( vd520 )),bind(C,$thf( vd518 ))]]) ).
thf(17205,plain,
! [B: $i,A: $i] :
( ( vd518 != vd517 )
| ~ ( greater @ A @ B )
| ( ( less @ v1 @ vd517 )
!= ( less @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[17020,217]) ).
thf(17206,plain,
( ( vd518 != vd517 )
| ~ ( greater @ v1 @ vd517 ) ),
inference(pattern_uni,[status(thm)],[17205:[bind(A,$thf( v1 )),bind(B,$thf( vd517 ))]]) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( A = B )
| ? [C: $i] :
( A
= ( vplus @ B @ C ) )
| ? [C: $i] :
( B
= ( vplus @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(88), 0), 0)') ).
thf(89,plain,
! [A: $i,B: $i] :
( ( A = B )
| ? [C: $i] :
( A
= ( vplus @ B @ C ) )
| ? [C: $i] :
( B
= ( vplus @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(60,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( greater @ C @ D )
& ( geq @ A @ B ) )
| ( ( geq @ C @ D )
& ( greater @ A @ B ) ) )
=> ( greater @ ( vplus @ A @ C ) @ ( vplus @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(216), 0), 0)') ).
thf(263,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( greater @ C @ D )
& ( geq @ A @ B ) )
| ( ( geq @ C @ D )
& ( greater @ A @ B ) ) )
=> ( greater @ ( vplus @ A @ C ) @ ( vplus @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(265,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( geq @ C @ D )
| ~ ( greater @ A @ B )
| ( greater @ ( vplus @ A @ C ) @ ( vplus @ B @ D ) ) ),
inference(cnf,[status(esa)],[263]) ).
thf(79,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
!= ( vplus @ B @ C ) )
| ( B
!= ( vplus @ A @ D ) ) ),
inference(cnf,[status(esa)],[78]) ).
thf(80,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
!= ( vplus @ B @ C ) )
| ( B
!= ( vplus @ A @ D ) ) ),
inference(lifteq,[status(thm)],[79]) ).
thf(81,plain,
! [C: $i,B: $i,A: $i] :
( ( vplus @ ( vplus @ A @ B ) @ C )
!= A ),
inference(simp,[status(thm)],[80]) ).
thf(543,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( vplus @ ( vsucc @ A ) @ D )
!= B )
| ( ( vplus @ v1 @ A )
!= ( vplus @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[170,81]) ).
thf(544,plain,
! [B: $i,A: $i] :
( ( vplus @ ( vsucc @ A ) @ B )
!= v1 ),
inference(pattern_uni,[status(thm)],[543:[bind(A,$thf( A )),bind(B,$thf( v1 )),bind(C,$thf( A ))]]) ).
thf(560,plain,
! [B: $i,A: $i] :
( ( vplus @ ( vsucc @ A ) @ B )
!= v1 ),
inference(simp,[status(thm)],[544]) ).
thf(660,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( vplus @ A @ B )
!= v1 )
| ( ( vplus @ B @ A )
!= ( vplus @ ( vsucc @ C ) @ D ) ) ),
inference(paramod_ordered,[status(thm)],[77,560]) ).
thf(661,plain,
! [B: $i,A: $i] :
( ( vplus @ A @ ( vsucc @ B ) )
!= v1 ),
inference(pattern_uni,[status(thm)],[660:[bind(A,$thf( A )),bind(B,$thf( vsucc @ E )),bind(C,$thf( E )),bind(D,$thf( A ))]]) ).
thf(667,plain,
! [B: $i,A: $i] :
( ( vplus @ A @ ( vsucc @ B ) )
!= v1 ),
inference(simp,[status(thm)],[661]) ).
thf(733,plain,
! [B: $i,A: $i] :
( ( vsucc @ ( vplus @ A @ B ) )
!= v1 ),
inference(rewrite,[status(thm)],[667,70]) ).
thf(19674,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( vsucc @ ( vmul @ ( vsucc @ A ) @ B ) )
!= v1 )
| ( ( vplus @ ( vmul @ A @ B ) @ B )
!= ( vplus @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[226,733]) ).
thf(19675,plain,
! [B: $i,A: $i] :
( ( vsucc @ ( vmul @ ( vsucc @ A ) @ B ) )
!= v1 ),
inference(pattern_uni,[status(thm)],[19674:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( vmul @ E @ F )),bind(D,$thf( F ))]]) ).
thf(19812,plain,
! [B: $i,A: $i] :
( ( vsucc @ ( vmul @ ( vsucc @ A ) @ B ) )
!= v1 ),
inference(simp,[status(thm)],[19675]) ).
thf(23897,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( vmul @ A @ ( vplus @ B @ C ) )
!= ( vmul @ vd517 @ vd519 ) )
| ( ( vplus @ ( vmul @ A @ B ) @ ( vmul @ A @ C ) )
!= ( vplus @ ( vmul @ vd518 @ vd520 ) @ D ) ) ),
inference(paramod_ordered,[status(thm)],[250,509]) ).
thf(23898,plain,
! [A: $i] :
( ( vmul @ vd518 @ ( vplus @ vd520 @ A ) )
!= ( vmul @ vd517 @ vd519 ) ),
inference(pattern_uni,[status(thm)],[23897:[bind(A,$thf( vd518 )),bind(B,$thf( vd520 )),bind(C,$thf( F )),bind(D,$thf( vmul @ vd518 @ F ))]]) ).
thf(24059,plain,
! [A: $i] :
( ( vmul @ vd518 @ ( vplus @ vd520 @ A ) )
!= ( vmul @ vd517 @ vd519 ) ),
inference(simp,[status(thm)],[23898]) ).
thf(24264,plain,
! [C: $i,B: $i,A: $i] :
( ( ( vmul @ vd518 @ ( vsucc @ ( vplus @ A @ B ) ) )
!= ( vmul @ vd517 @ vd519 ) )
| ( ( vplus @ A @ ( vsucc @ B ) )
!= ( vplus @ vd520 @ C ) ) ),
inference(paramod_ordered,[status(thm)],[70,24059]) ).
thf(24265,plain,
! [A: $i] :
( ( vmul @ vd518 @ ( vsucc @ ( vplus @ vd520 @ A ) ) )
!= ( vmul @ vd517 @ vd519 ) ),
inference(pattern_uni,[status(thm)],[24264:[bind(A,$thf( vd520 )),bind(B,$thf( D )),bind(C,$thf( vsucc @ D ))]]) ).
thf(24352,plain,
! [A: $i] :
( ( vmul @ vd518 @ ( vsucc @ ( vplus @ vd520 @ A ) ) )
!= ( vmul @ vd517 @ vd519 ) ),
inference(simp,[status(thm)],[24265]) ).
thf(22,axiom,
! [A: $i,B: $i] :
( ( vplus @ ( vsucc @ A ) @ B )
= ( vsucc @ ( vplus @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(52, 0), 0)') ).
thf(135,plain,
! [A: $i,B: $i] :
( ( vplus @ ( vsucc @ A ) @ B )
= ( vsucc @ ( vplus @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(136,plain,
! [B: $i,A: $i] :
( ( vplus @ ( vsucc @ A ) @ B )
= ( vsucc @ ( vplus @ A @ B ) ) ),
inference(cnf,[status(esa)],[135]) ).
thf(137,plain,
! [B: $i,A: $i] :
( ( vplus @ ( vsucc @ A ) @ B )
= ( vsucc @ ( vplus @ A @ B ) ) ),
inference(lifteq,[status(thm)],[136]) ).
thf(738,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( vsucc @ ( vsucc @ ( vplus @ A @ B ) ) )
!= v1 )
| ( ( vplus @ A @ ( vsucc @ B ) )
!= ( vplus @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[70,733]) ).
thf(739,plain,
! [B: $i,A: $i] :
( ( vsucc @ ( vsucc @ ( vplus @ A @ B ) ) )
!= v1 ),
inference(pattern_uni,[status(thm)],[738:[bind(A,$thf( A )),bind(B,$thf( E )),bind(C,$thf( A )),bind(D,$thf( vsucc @ E ))]]) ).
thf(744,plain,
! [B: $i,A: $i] :
( ( vsucc @ ( vsucc @ ( vplus @ A @ B ) ) )
!= v1 ),
inference(simp,[status(thm)],[739]) ).
thf(6171,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( vsucc @ ( vsucc @ ( vsucc @ ( vplus @ A @ B ) ) ) )
!= v1 )
| ( ( vplus @ ( vsucc @ A ) @ B )
!= ( vplus @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[137,744]) ).
thf(6172,plain,
! [B: $i,A: $i] :
( ( vsucc @ ( vsucc @ ( vsucc @ ( vplus @ B @ A ) ) ) )
!= v1 ),
inference(pattern_uni,[status(thm)],[6171:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( vsucc @ E )),bind(D,$thf( B ))]]) ).
thf(6210,plain,
! [B: $i,A: $i] :
( ( vsucc @ ( vsucc @ ( vsucc @ ( vplus @ B @ A ) ) ) )
!= v1 ),
inference(simp,[status(thm)],[6172]) ).
thf(42,axiom,
! [A: $i,B: $i] :
( ( vmul @ A @ B )
= ( vmul @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(270, 0), 0)') ).
thf(204,plain,
! [A: $i,B: $i] :
( ( vmul @ A @ B )
= ( vmul @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(205,plain,
! [B: $i,A: $i] :
( ( vmul @ A @ B )
= ( vmul @ B @ A ) ),
inference(cnf,[status(esa)],[204]) ).
thf(206,plain,
! [B: $i,A: $i] :
( ( vmul @ A @ B )
= ( vmul @ B @ A ) ),
inference(lifteq,[status(thm)],[205]) ).
thf(1073,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( vsucc @ ( vsucc @ ( vplus @ B @ A ) ) )
!= v1 )
| ( ( vplus @ A @ B )
!= ( vplus @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[77,744]) ).
thf(1074,plain,
! [B: $i,A: $i] :
( ( vsucc @ ( vsucc @ ( vplus @ B @ A ) ) )
!= v1 ),
inference(pattern_uni,[status(thm)],[1073:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(515,plain,
( ( v1 != vd517 )
| ( v1 != vd518 )
| ( ( greater @ ( vmul @ vd517 @ vd519 ) @ vd520 )
!= ( greater @ vd517 @ vd518 ) ) ),
inference(paramod_ordered,[status(thm)],[394,292]) ).
thf(529,plain,
( ( v1 != vd517 )
| ( v1 != vd518 )
| ( ( vmul @ vd517 @ vd519 )
!= vd517 )
| ( vd520 != vd518 ) ),
inference(simp,[status(thm)],[515]) ).
thf(380,plain,
! [C: $i,B: $i,A: $i] :
( ( less @ B @ ( vsucc @ A ) )
| ( ( vplus @ A @ v1 )
!= ( vplus @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[69,153]) ).
thf(381,plain,
! [A: $i] : ( less @ A @ ( vsucc @ A ) ),
inference(pattern_uni,[status(thm)],[380:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( v1 ))]]) ).
thf(17147,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( greater @ B @ C )
| ( ( less @ A @ ( vsucc @ A ) )
!= ( less @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[381,217]) ).
thf(17148,plain,
! [A: $i] :
~ ( greater @ A @ ( vsucc @ A ) ),
inference(pattern_uni,[status(thm)],[17147:[bind(A,$thf( D )),bind(B,$thf( D )),bind(C,$thf( vsucc @ D ))]]) ).
thf(17245,plain,
! [A: $i] :
~ ( greater @ A @ ( vsucc @ A ) ),
inference(simp,[status(thm)],[17148]) ).
thf(20573,plain,
! [A: $i] :
( ( v1 != vd517 )
| ( ( greater @ vd517 @ vd518 )
!= ( greater @ A @ ( vsucc @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[19365,17245]) ).
thf(20630,plain,
! [A: $i] :
( ( v1 != vd517 )
| ( vd517 != A )
| ( ( vsucc @ A )
!= vd518 ) ),
inference(simp,[status(thm)],[20573]) ).
thf(20652,plain,
( ( v1 != vd517 )
| ( ( vsucc @ vd517 )
!= vd518 ) ),
inference(simp,[status(thm)],[20630]) ).
thf(760,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk1 @ B @ ( vsucc @ A ) )
= C )
| ( ( vplus @ v1 @ A )
!= ( vplus @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[170,88]) ).
thf(761,plain,
! [A: $i] :
( ( sk1 @ v1 @ ( vsucc @ A ) )
= A ),
inference(pattern_uni,[status(thm)],[760:[bind(A,$thf( A )),bind(B,$thf( v1 )),bind(C,$thf( A ))]]) ).
thf(520,plain,
( ( v1 != vd517 )
| ( v1 != vd518 )
| ( v1 != vd519 )
| ( ( greater @ vd517 @ ( vmul @ vd518 @ vd520 ) )
!= ( greater @ vd517 @ vd518 ) ) ),
inference(paramod_ordered,[status(thm)],[394,281]) ).
thf(530,plain,
( ( v1 != vd517 )
| ( v1 != vd518 )
| ( v1 != vd519 )
| ( vd517 != vd517 )
| ( ( vmul @ vd518 @ vd520 )
!= vd518 ) ),
inference(simp,[status(thm)],[520]) ).
thf(534,plain,
( ( v1 != vd517 )
| ( v1 != vd518 )
| ( v1 != vd519 )
| ( ( vmul @ vd518 @ vd520 )
!= vd518 ) ),
inference(simp,[status(thm)],[530]) ).
thf(1780,plain,
! [A: $i] :
( ( less @ v1 @ A )
| ( A != vd520 )
| ( ( vmul @ vd517 @ vd519 )
!= ( vsucc @ vd518 ) )
| ( v1 != v1 ) ),
inference(paramod_ordered,[status(thm)],[1522,619]) ).
thf(1781,plain,
! [A: $i] :
( ( less @ v1 @ A )
| ( A != vd520 )
| ( ( vmul @ vd517 @ vd519 )
!= ( vsucc @ vd518 ) ) ),
inference(pattern_uni,[status(thm)],[1780:[]]) ).
thf(2296,plain,
( ( less @ v1 @ vd520 )
| ( ( vmul @ vd517 @ vd519 )
!= ( vsucc @ vd518 ) ) ),
inference(simp,[status(thm)],[1781]) ).
thf(293,plain,
! [A: $i] :
( ~ ( greater @ vd517 @ A )
| ( v1 != vd519 )
| ( ( vmul @ v1 @ A )
!= ( vmul @ vd518 @ vd520 ) ) ),
inference(paramod_ordered,[status(thm)],[247,281]) ).
thf(295,plain,
! [A: $i] :
( ~ ( greater @ vd517 @ A )
| ( v1 != vd519 )
| ( v1 != vd518 )
| ( A != vd520 ) ),
inference(simp,[status(thm)],[293]) ).
thf(297,plain,
( ~ ( greater @ vd517 @ vd520 )
| ( v1 != vd519 )
| ( v1 != vd518 ) ),
inference(simp,[status(thm)],[295]) ).
thf(1827,plain,
! [A: $i] :
( ( less @ v1 @ A )
| ~ ( greater @ vd517 @ vd520 )
| ( A != vd519 )
| ( v1 != vd518 )
| ( v1 != v1 ) ),
inference(paramod_ordered,[status(thm)],[1522,297]) ).
thf(1828,plain,
! [A: $i] :
( ( less @ v1 @ A )
| ~ ( greater @ vd517 @ vd520 )
| ( A != vd519 )
| ( v1 != vd518 ) ),
inference(pattern_uni,[status(thm)],[1827:[]]) ).
thf(2307,plain,
( ( less @ v1 @ vd519 )
| ~ ( greater @ vd517 @ vd520 )
| ( v1 != vd518 ) ),
inference(simp,[status(thm)],[1828]) ).
thf(59,axiom,
! [A: $i,B: $i,C: $i] :
( ( vmul @ ( vmul @ A @ B ) @ C )
= ( vmul @ A @ ( vmul @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(290, 0), 0)') ).
thf(260,plain,
! [A: $i,B: $i,C: $i] :
( ( vmul @ ( vmul @ A @ B ) @ C )
= ( vmul @ A @ ( vmul @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(30,axiom,
! [A: $i,B: $i,C: $i] :
( ( less @ ( vplus @ A @ C ) @ ( vplus @ B @ C ) )
=> ( less @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(202), 0), 0)') ).
thf(165,plain,
! [A: $i,B: $i,C: $i] :
( ( less @ ( vplus @ A @ C ) @ ( vplus @ B @ C ) )
=> ( less @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(2047,plain,
! [A: $i] :
( ( less @ v1 @ A )
| ( greater @ vd517 @ vd518 )
| ( v1 != vd517 )
| ( A != vd518 )
| ( v1 != v1 ) ),
inference(paramod_ordered,[status(thm)],[1522,394]) ).
thf(2048,plain,
! [A: $i] :
( ( less @ v1 @ A )
| ( greater @ vd517 @ vd518 )
| ( v1 != vd517 )
| ( A != vd518 ) ),
inference(pattern_uni,[status(thm)],[2047:[]]) ).
thf(2213,plain,
( ( less @ v1 @ vd518 )
| ( greater @ vd517 @ vd518 )
| ( v1 != vd517 ) ),
inference(simp,[status(thm)],[2048]) ).
thf(4264,plain,
! [A: $i] :
( ( less @ v1 @ A )
| ( less @ v1 @ vd518 )
| ( greater @ vd517 @ vd518 )
| ( A != vd517 )
| ( v1 != v1 ) ),
inference(paramod_ordered,[status(thm)],[1522,2213]) ).
thf(4265,plain,
! [A: $i] :
( ( less @ v1 @ A )
| ( less @ v1 @ vd518 )
| ( greater @ vd517 @ vd518 )
| ( A != vd517 ) ),
inference(pattern_uni,[status(thm)],[4264:[]]) ).
thf(4284,plain,
( ( less @ v1 @ vd517 )
| ( less @ v1 @ vd518 )
| ( greater @ vd517 @ vd518 ) ),
inference(simp,[status(thm)],[4265]) ).
thf(2469,plain,
! [C: $i,B: $i,A: $i] :
( ( leq @ C @ B )
| ( ( less @ A @ ( vsucc @ A ) )
!= ( less @ C @ B ) ) ),
inference(paramod_ordered,[status(thm)],[381,107]) ).
thf(2470,plain,
! [A: $i] : ( leq @ A @ ( vsucc @ A ) ),
inference(pattern_uni,[status(thm)],[2469:[bind(A,$thf( D )),bind(B,$thf( vsucc @ D )),bind(C,$thf( D ))]]) ).
thf(2477,plain,
! [A: $i] : ( leq @ A @ ( vsucc @ A ) ),
inference(simp,[status(thm)],[2470]) ).
thf(7197,plain,
! [A: $i] :
( ~ ( less @ ( vmul @ vd518 @ vd520 ) @ A )
| ( ( vmul @ v1 @ A )
!= ( vmul @ vd517 @ vd519 ) ) ),
inference(paramod_ordered,[status(thm)],[247,7127]) ).
thf(7271,plain,
! [A: $i] :
( ~ ( less @ ( vmul @ vd518 @ vd520 ) @ A )
| ( v1 != vd517 )
| ( A != vd519 ) ),
inference(simp,[status(thm)],[7197]) ).
thf(7297,plain,
( ~ ( less @ ( vmul @ vd518 @ vd520 ) @ vd519 )
| ( v1 != vd517 ) ),
inference(simp,[status(thm)],[7271]) ).
thf(7583,plain,
! [A: $i] :
( ~ ( less @ A @ vd519 )
| ( v1 != vd517 )
| ( ( vmul @ A @ v1 )
!= ( vmul @ vd518 @ vd520 ) ) ),
inference(paramod_ordered,[status(thm)],[195,7297]) ).
thf(7606,plain,
! [A: $i] :
( ~ ( less @ A @ vd519 )
| ( v1 != vd517 )
| ( A != vd518 )
| ( v1 != vd520 ) ),
inference(simp,[status(thm)],[7583]) ).
thf(7625,plain,
( ~ ( less @ vd518 @ vd519 )
| ( v1 != vd517 )
| ( v1 != vd520 ) ),
inference(simp,[status(thm)],[7606]) ).
thf(186,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( greater @ A @ B )
| ( less @ A @ B ) ),
inference(cnf,[status(esa)],[185]) ).
thf(187,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( greater @ A @ B )
| ( less @ A @ B ) ),
inference(lifteq,[status(thm)],[186]) ).
thf(17060,plain,
! [B: $i,A: $i] :
( ( greater @ A @ B )
| ( less @ A @ B )
| ( less @ v1 @ vd517 )
| ( B != vd517 )
| ( A != vd518 ) ),
inference(paramod_ordered,[status(thm)],[187,17020]) ).
thf(17061,plain,
! [A: $i] :
( ( greater @ vd518 @ A )
| ( less @ vd518 @ A )
| ( less @ v1 @ vd517 )
| ( A != vd517 ) ),
inference(pattern_uni,[status(thm)],[17060:[bind(A,$thf( vd518 ))]]) ).
thf(17114,plain,
( ( greater @ vd518 @ vd517 )
| ( less @ vd518 @ vd517 )
| ( less @ v1 @ vd517 ) ),
inference(simp,[status(thm)],[17061]) ).
thf(19647,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( vsucc @ ( vmul @ ( vsucc @ A ) @ B ) )
!= v1 )
| ( ( vplus @ ( vmul @ A @ B ) @ B )
!= ( vplus @ C @ ( vsucc @ D ) ) ) ),
inference(paramod_ordered,[status(thm)],[226,13519]) ).
thf(19648,plain,
! [B: $i,A: $i] :
( ( vsucc @ ( vmul @ ( vsucc @ A ) @ ( vsucc @ B ) ) )
!= v1 ),
inference(pattern_uni,[status(thm)],[19647:[bind(A,$thf( E )),bind(B,$thf( vsucc @ G )),bind(C,$thf( vmul @ E @ ( vsucc @ G ) )),bind(D,$thf( G ))]]) ).
thf(19800,plain,
! [B: $i,A: $i] :
( ( vsucc @ ( vmul @ ( vsucc @ A ) @ ( vsucc @ B ) ) )
!= v1 ),
inference(simp,[status(thm)],[19648]) ).
thf(2209,plain,
! [C: $i,B: $i,A: $i] :
( ( less @ v1 @ A )
| ( A
!= ( vplus @ ( vsucc @ B ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[1522,560]) ).
thf(2210,plain,
! [B: $i,A: $i] : ( less @ v1 @ ( vplus @ ( vsucc @ B ) @ A ) ),
inference(pattern_uni,[status(thm)],[2209:[bind(A,$thf( vplus @ ( vsucc @ F ) @ E )),bind(B,$thf( F )),bind(C,$thf( E ))]]) ).
thf(2271,plain,
! [B: $i,A: $i] : ( less @ v1 @ ( vplus @ ( vsucc @ B ) @ A ) ),
inference(simp,[status(thm)],[2210]) ).
thf(8920,plain,
! [B: $i,A: $i] : ( less @ v1 @ ( vsucc @ ( vplus @ B @ A ) ) ),
inference(rewrite,[status(thm)],[2271,137]) ).
thf(475,plain,
! [C: $i,B: $i,A: $i] :
( ( greater @ ( vsucc @ A ) @ B )
| ( ( vplus @ v1 @ A )
!= ( vplus @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[170,182]) ).
thf(476,plain,
! [A: $i] : ( greater @ ( vsucc @ A ) @ v1 ),
inference(pattern_uni,[status(thm)],[475:[bind(A,$thf( A )),bind(B,$thf( v1 )),bind(C,$thf( A ))]]) ).
thf(17161,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( less @ B @ C )
| ( ( greater @ ( vsucc @ A ) @ v1 )
!= ( greater @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[476,217]) ).
thf(17162,plain,
! [A: $i] :
~ ( less @ ( vsucc @ A ) @ v1 ),
inference(pattern_uni,[status(thm)],[17161:[bind(A,$thf( D )),bind(B,$thf( vsucc @ D )),bind(C,$thf( v1 ))]]) ).
thf(17232,plain,
! [A: $i] :
~ ( less @ ( vsucc @ A ) @ v1 ),
inference(simp,[status(thm)],[17162]) ).
thf(156,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( less @ B @ C )
| ~ ( leq @ A @ B )
| ( less @ A @ C ) ),
inference(cnf,[status(esa)],[155]) ).
thf(7467,plain,
! [A: $i] :
( ~ ( less @ vd520 @ A )
| ( v1 != vd518 )
| ( ( vmul @ A @ v1 )
!= ( vmul @ vd517 @ vd519 ) ) ),
inference(paramod_ordered,[status(thm)],[195,7295]) ).
thf(7478,plain,
! [A: $i] :
( ~ ( less @ vd520 @ A )
| ( v1 != vd518 )
| ( A != vd517 )
| ( v1 != vd519 ) ),
inference(simp,[status(thm)],[7467]) ).
thf(7513,plain,
( ~ ( less @ vd520 @ vd517 )
| ( v1 != vd518 )
| ( v1 != vd519 ) ),
inference(simp,[status(thm)],[7478]) ).
thf(13843,plain,
! [C: $i,B: $i,A: $i] :
( ( ( vmul @ A @ ( vsucc @ B ) )
!= ( vmul @ vd517 @ vd519 ) )
| ( ( vplus @ ( vmul @ A @ B ) @ A )
!= ( vplus @ C @ ( vmul @ vd518 @ vd520 ) ) ) ),
inference(paramod_ordered,[status(thm)],[196,792]) ).
thf(13844,plain,
! [A: $i] :
( ( vmul @ ( vmul @ vd518 @ vd520 ) @ ( vsucc @ A ) )
!= ( vmul @ vd517 @ vd519 ) ),
inference(pattern_uni,[status(thm)],[13843:[bind(A,$thf( vmul @ vd518 @ vd520 )),bind(B,$thf( E )),bind(C,$thf( vmul @ ( vmul @ vd518 @ vd520 ) @ E ))]]) ).
thf(13932,plain,
! [A: $i] :
( ( vmul @ ( vmul @ vd518 @ vd520 ) @ ( vsucc @ A ) )
!= ( vmul @ vd517 @ vd519 ) ),
inference(simp,[status(thm)],[13844]) ).
thf(15424,plain,
! [C: $i,B: $i,A: $i] :
( ( ( vmul @ B @ A )
!= ( vmul @ vd517 @ vd519 ) )
| ( ( vmul @ A @ B )
!= ( vmul @ ( vmul @ vd518 @ vd520 ) @ ( vsucc @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[206,13932]) ).
thf(15425,plain,
! [A: $i] :
( ( vmul @ ( vsucc @ A ) @ ( vmul @ vd518 @ vd520 ) )
!= ( vmul @ vd517 @ vd519 ) ),
inference(pattern_uni,[status(thm)],[15424:[bind(A,$thf( vmul @ vd518 @ vd520 )),bind(B,$thf( vsucc @ F )),bind(C,$thf( F ))]]) ).
thf(15466,plain,
! [A: $i] :
( ( vmul @ ( vsucc @ A ) @ ( vmul @ vd518 @ vd520 ) )
!= ( vmul @ vd517 @ vd519 ) ),
inference(simp,[status(thm)],[15425]) ).
thf(121,plain,
! [A: $i,B: $i] :
( ? [C: $i] :
( ( vplus @ A @ C )
= ( vplus @ B @ C ) )
=> ( A = B ) ),
inference(miniscope,[status(thm)],[120]) ).
thf(122,plain,
! [C: $i,B: $i,A: $i] :
( ( ( vplus @ A @ C )
!= ( vplus @ B @ C ) )
| ( A = B ) ),
inference(cnf,[status(esa)],[121]) ).
thf(123,plain,
! [C: $i,B: $i,A: $i] :
( ( ( vplus @ A @ C )
!= ( vplus @ B @ C ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[122]) ).
thf(124,plain,
! [B: $i,A: $i] :
( ( sk5 @ A @ ( vplus @ B @ A ) )
= B ),
introduced(tautology,[new_symbols(inverse(vplus),[sk5])]) ).
thf(524,plain,
( ( v1 != vd517 )
| ( v1 != vd518 )
| ( v1 != vd520 )
| ( ( greater @ ( vmul @ vd517 @ vd519 ) @ vd518 )
!= ( greater @ vd517 @ vd518 ) ) ),
inference(paramod_ordered,[status(thm)],[394,282]) ).
thf(533,plain,
( ( v1 != vd517 )
| ( v1 != vd518 )
| ( v1 != vd520 )
| ( ( vmul @ vd517 @ vd519 )
!= vd517 )
| ( vd518 != vd518 ) ),
inference(simp,[status(thm)],[524]) ).
thf(537,plain,
( ( v1 != vd517 )
| ( v1 != vd518 )
| ( v1 != vd520 )
| ( ( vmul @ vd517 @ vd519 )
!= vd517 ) ),
inference(simp,[status(thm)],[533]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( less @ A @ ( vplus @ B @ v1 ) )
=> ( leq @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(241, 0), 0)') ).
thf(82,plain,
! [A: $i,B: $i] :
( ( less @ A @ ( vplus @ B @ v1 ) )
=> ( leq @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(83,plain,
! [B: $i,A: $i] :
( ~ ( less @ A @ ( vplus @ B @ v1 ) )
| ( leq @ A @ B ) ),
inference(cnf,[status(esa)],[82]) ).
thf(640,plain,
! [B: $i,A: $i] :
( ~ ( less @ A @ ( vsucc @ B ) )
| ( leq @ A @ B ) ),
inference(rewrite,[status(thm)],[83,69]) ).
thf(641,plain,
! [C: $i,B: $i,A: $i] :
( ( leq @ B @ C )
| ( ( less @ v1 @ ( vsucc @ A ) )
!= ( less @ B @ ( vsucc @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[384,640]) ).
thf(642,plain,
! [A: $i] : ( leq @ v1 @ A ),
inference(pattern_uni,[status(thm)],[641:[bind(A,$thf( A )),bind(B,$thf( v1 )),bind(C,$thf( A ))]]) ).
thf(17129,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( greater @ B @ C )
| ( ( less @ v1 @ ( vsucc @ A ) )
!= ( less @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[384,217]) ).
thf(17130,plain,
! [A: $i] :
~ ( greater @ v1 @ ( vsucc @ A ) ),
inference(pattern_uni,[status(thm)],[17129:[bind(A,$thf( D )),bind(B,$thf( v1 )),bind(C,$thf( vsucc @ D ))]]) ).
thf(17239,plain,
! [A: $i] :
~ ( greater @ v1 @ ( vsucc @ A ) ),
inference(simp,[status(thm)],[17130]) ).
thf(105,plain,
! [B: $i,A: $i] :
( ( B != A )
| ( leq @ B @ A ) ),
inference(cnf,[status(esa)],[103]) ).
thf(108,plain,
! [B: $i,A: $i] :
( ( B != A )
| ( leq @ B @ A ) ),
inference(lifteq,[status(thm)],[105]) ).
thf(109,plain,
! [A: $i] : ( leq @ A @ A ),
inference(simp,[status(thm)],[108]) ).
thf(58,axiom,
! [A: $i,B: $i] :
( ( geq @ B @ A )
<=> ( ( greater @ B @ A )
| ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','def(cond(conseq(axiom(3)), 16), 1)') ).
thf(251,plain,
! [A: $i,B: $i] :
( ( ( geq @ B @ A )
=> ( ( greater @ B @ A )
| ( B = A ) ) )
& ( ( ( greater @ B @ A )
| ( B = A ) )
=> ( geq @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(252,plain,
( ! [A: $i,B: $i] :
( ( geq @ B @ A )
=> ( ( greater @ B @ A )
| ( B = A ) ) )
& ! [A: $i,B: $i] :
( ( ( greater @ B @ A )
| ( B = A ) )
=> ( geq @ B @ A ) ) ),
inference(miniscope,[status(thm)],[251]) ).
thf(253,plain,
! [B: $i,A: $i] :
( ~ ( greater @ B @ A )
| ( geq @ B @ A ) ),
inference(cnf,[status(esa)],[252]) ).
thf(256,plain,
! [B: $i,A: $i] :
( ~ ( greater @ B @ A )
| ( geq @ B @ A ) ),
inference(simp,[status(thm)],[253]) ).
thf(24149,plain,
! [C: $i,B: $i,A: $i] :
( ( ( vmul @ vd518 @ ( vmul @ ( vsucc @ A ) @ B ) )
!= ( vmul @ vd517 @ vd519 ) )
| ( ( vplus @ ( vmul @ A @ B ) @ B )
!= ( vplus @ C @ vd520 ) ) ),
inference(paramod_ordered,[status(thm)],[226,24048]) ).
thf(24150,plain,
! [A: $i] :
( ( vmul @ vd518 @ ( vmul @ ( vsucc @ A ) @ vd520 ) )
!= ( vmul @ vd517 @ vd519 ) ),
inference(pattern_uni,[status(thm)],[24149:[bind(A,$thf( D )),bind(B,$thf( vd520 )),bind(C,$thf( vmul @ D @ vd520 ))]]) ).
thf(24206,plain,
! [A: $i] :
( ( vmul @ vd518 @ ( vmul @ ( vsucc @ A ) @ vd520 ) )
!= ( vmul @ vd517 @ vd519 ) ),
inference(simp,[status(thm)],[24150]) ).
thf(25628,plain,
! [B: $i,A: $i] :
( ( vd520 = vd519 )
| ~ ( greater @ A @ B )
| ( ( less @ v1 @ vd517 )
!= ( less @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[23134,217]) ).
thf(25629,plain,
( ( vd520 = vd519 )
| ~ ( greater @ v1 @ vd517 ) ),
inference(pattern_uni,[status(thm)],[25628:[bind(A,$thf( v1 )),bind(B,$thf( vd517 ))]]) ).
thf(24782,plain,
! [B: $i,A: $i] :
( ( v1 != vd517 )
| ( geq @ B @ A )
| ( ( greater @ vd517 @ vd518 )
!= ( greater @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[19365,256]) ).
thf(24783,plain,
( ( v1 != vd517 )
| ( geq @ vd517 @ vd518 ) ),
inference(pattern_uni,[status(thm)],[24782:[bind(A,$thf( vd518 )),bind(B,$thf( vd517 ))]]) ).
thf(658,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( vsucc @ ( vplus @ A @ B ) )
!= v1 )
| ( ( vplus @ A @ ( vsucc @ B ) )
!= ( vplus @ ( vsucc @ C ) @ D ) ) ),
inference(paramod_ordered,[status(thm)],[70,560]) ).
thf(659,plain,
! [B: $i,A: $i] :
( ( vsucc @ ( vplus @ ( vsucc @ A ) @ B ) )
!= v1 ),
inference(pattern_uni,[status(thm)],[658:[bind(A,$thf( vsucc @ E )),bind(B,$thf( F )),bind(C,$thf( E )),bind(D,$thf( vsucc @ F ))]]) ).
thf(666,plain,
! [B: $i,A: $i] :
( ( vsucc @ ( vplus @ ( vsucc @ A ) @ B ) )
!= v1 ),
inference(simp,[status(thm)],[659]) ).
thf(1044,plain,
! [C: $i,B: $i,A: $i] :
( ( ( vsucc @ ( vsucc @ A ) )
!= v1 )
| ( ( vplus @ A @ v1 )
!= ( vplus @ ( vsucc @ B ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[69,666]) ).
thf(1045,plain,
! [A: $i] :
( ( vsucc @ ( vsucc @ ( vsucc @ A ) ) )
!= v1 ),
inference(pattern_uni,[status(thm)],[1044:[bind(A,$thf( vsucc @ D )),bind(B,$thf( D )),bind(C,$thf( v1 ))]]) ).
thf(1060,plain,
! [A: $i] :
( ( vsucc @ ( vsucc @ ( vsucc @ A ) ) )
!= v1 ),
inference(simp,[status(thm)],[1045]) ).
thf(33,axiom,
! [A: $i] :
( ( vsucc @ A )
!= v1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(restrictor(axiom(1)), holds(scope(axiom(1)), 2, 0))') ).
thf(173,plain,
! [A: $i] :
( ( vsucc @ A )
!= v1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(23909,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( vsucc @ ( vmul @ A @ ( vplus @ B @ C ) ) )
!= ( vmul @ vd517 @ vd519 ) )
| ( ( vplus @ ( vmul @ A @ B ) @ ( vmul @ A @ C ) )
!= ( vplus @ ( vmul @ vd518 @ vd520 ) @ D ) ) ),
inference(paramod_ordered,[status(thm)],[250,799]) ).
thf(23910,plain,
! [A: $i] :
( ( vsucc @ ( vmul @ vd518 @ ( vplus @ vd520 @ A ) ) )
!= ( vmul @ vd517 @ vd519 ) ),
inference(pattern_uni,[status(thm)],[23909:[bind(A,$thf( vd518 )),bind(B,$thf( vd520 )),bind(C,$thf( F )),bind(D,$thf( vmul @ vd518 @ F ))]]) ).
thf(24065,plain,
! [A: $i] :
( ( vsucc @ ( vmul @ vd518 @ ( vplus @ vd520 @ A ) ) )
!= ( vmul @ vd517 @ vd519 ) ),
inference(simp,[status(thm)],[23910]) ).
thf(24116,plain,
! [C: $i,B: $i,A: $i] :
( ( ( vmul @ vd518 @ ( vsucc @ ( vplus @ A @ B ) ) )
!= ( vmul @ vd517 @ vd519 ) )
| ( ( vplus @ ( vsucc @ A ) @ B )
!= ( vplus @ C @ vd520 ) ) ),
inference(paramod_ordered,[status(thm)],[137,24048]) ).
thf(24117,plain,
! [A: $i] :
( ( vmul @ vd518 @ ( vsucc @ ( vplus @ A @ vd520 ) ) )
!= ( vmul @ vd517 @ vd519 ) ),
inference(pattern_uni,[status(thm)],[24116:[bind(A,$thf( D )),bind(B,$thf( vd520 )),bind(C,$thf( vsucc @ D ))]]) ).
thf(24196,plain,
! [A: $i] :
( ( vmul @ vd518 @ ( vsucc @ ( vplus @ A @ vd520 ) ) )
!= ( vmul @ vd517 @ vd519 ) ),
inference(simp,[status(thm)],[24117]) ).
thf(30434,plain,
! [B: $i,A: $i] :
( ( ( vmul @ vd518 @ ( vsucc @ ( vsucc @ A ) ) )
!= ( vmul @ vd517 @ vd519 ) )
| ( ( vplus @ v1 @ A )
!= ( vplus @ B @ vd520 ) ) ),
inference(paramod_ordered,[status(thm)],[170,24196]) ).
thf(30435,plain,
( ( vmul @ vd518 @ ( vsucc @ ( vsucc @ vd520 ) ) )
!= ( vmul @ vd517 @ vd519 ) ),
inference(pattern_uni,[status(thm)],[30434:[bind(A,$thf( vd520 )),bind(B,$thf( v1 ))]]) ).
thf(13850,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( vsucc @ ( vmul @ A @ ( vsucc @ B ) ) )
!= v1 )
| ( ( vplus @ ( vmul @ A @ B ) @ A )
!= ( vplus @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[196,733]) ).
thf(13851,plain,
! [B: $i,A: $i] :
( ( vsucc @ ( vmul @ A @ ( vsucc @ B ) ) )
!= v1 ),
inference(pattern_uni,[status(thm)],[13850:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( vmul @ E @ F )),bind(D,$thf( E ))]]) ).
thf(13935,plain,
! [B: $i,A: $i] :
( ( vsucc @ ( vmul @ A @ ( vsucc @ B ) ) )
!= v1 ),
inference(simp,[status(thm)],[13851]) ).
thf(14852,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( vsucc @ ( vmul @ B @ A ) )
!= v1 )
| ( ( vmul @ A @ B )
!= ( vmul @ C @ ( vsucc @ D ) ) ) ),
inference(paramod_ordered,[status(thm)],[206,13935]) ).
thf(14853,plain,
! [B: $i,A: $i] :
( ( vsucc @ ( vmul @ ( vsucc @ B ) @ A ) )
!= v1 ),
inference(pattern_uni,[status(thm)],[14852:[bind(A,$thf( A )),bind(B,$thf( vsucc @ E )),bind(C,$thf( A )),bind(D,$thf( E ))]]) ).
thf(14875,plain,
! [B: $i,A: $i] :
( ( vsucc @ ( vmul @ ( vsucc @ B ) @ A ) )
!= v1 ),
inference(simp,[status(thm)],[14853]) ).
thf(20729,plain,
( ( vd520 = vd519 )
| ( vd518 = vd517 )
| ( ( greater @ vd519 @ vd520 )
!= ( greater @ vd519 @ vd520 ) ) ),
inference(paramod_ordered,[status(thm)],[18842,19372]) ).
thf(20730,plain,
( ( vd520 = vd519 )
| ( vd518 = vd517 ) ),
inference(pattern_uni,[status(thm)],[20729:[]]) ).
thf(53,axiom,
! [A: $i,B: $i] :
( ( greater @ B @ A )
<=> ? [C: $i] :
( B
= ( vplus @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','def(cond(conseq(axiom(3)), 11), 1)') ).
thf(231,plain,
! [A: $i,B: $i] :
( ( ( greater @ B @ A )
=> ? [C: $i] :
( B
= ( vplus @ A @ C ) ) )
& ( ? [C: $i] :
( B
= ( vplus @ A @ C ) )
=> ( greater @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(232,plain,
( ! [A: $i,B: $i] :
( ( greater @ B @ A )
=> ? [C: $i] :
( B
= ( vplus @ A @ C ) ) )
& ! [A: $i,B: $i] :
( ? [C: $i] :
( B
= ( vplus @ A @ C ) )
=> ( greater @ B @ A ) ) ),
inference(miniscope,[status(thm)],[231]) ).
thf(234,plain,
! [B: $i,A: $i] :
( ~ ( greater @ B @ A )
| ( B
= ( vplus @ A @ ( sk8 @ B @ A ) ) ) ),
inference(cnf,[status(esa)],[232]) ).
thf(237,plain,
! [B: $i,A: $i] :
( ( ( vplus @ A @ ( sk8 @ B @ A ) )
= B )
| ~ ( greater @ B @ A ) ),
inference(lifteq,[status(thm)],[234]) ).
thf(20619,plain,
( ( v1 != vd517 )
| ~ ( greater @ vd519 @ vd520 )
| ( ( greater @ vd517 @ vd518 )
!= ( greater @ vd517 @ vd518 ) ) ),
inference(paramod_ordered,[status(thm)],[19365,9737]) ).
thf(20620,plain,
( ( v1 != vd517 )
| ~ ( greater @ vd519 @ vd520 ) ),
inference(pattern_uni,[status(thm)],[20619:[]]) ).
thf(9945,plain,
! [A: $i] :
( ~ ( greater @ vd517 @ vd518 )
| ( ( greater @ ( vsucc @ A ) @ A )
!= ( greater @ vd519 @ vd520 ) ) ),
inference(paramod_ordered,[status(thm)],[474,9737]) ).
thf(9952,plain,
! [A: $i] :
( ~ ( greater @ vd517 @ vd518 )
| ( ( vsucc @ A )
!= vd519 )
| ( A != vd520 ) ),
inference(simp,[status(thm)],[9945]) ).
thf(9972,plain,
( ~ ( greater @ vd517 @ vd518 )
| ( ( vsucc @ vd520 )
!= vd519 ) ),
inference(simp,[status(thm)],[9952]) ).
thf(20613,plain,
( ( v1 != vd517 )
| ( ( vsucc @ vd520 )
!= vd519 )
| ( ( greater @ vd517 @ vd518 )
!= ( greater @ vd517 @ vd518 ) ) ),
inference(paramod_ordered,[status(thm)],[19365,9972]) ).
thf(20614,plain,
( ( v1 != vd517 )
| ( ( vsucc @ vd520 )
!= vd519 ) ),
inference(pattern_uni,[status(thm)],[20613:[]]) ).
thf(299,plain,
! [A: $i] :
( ~ ( greater @ A @ vd518 )
| ( v1 != vd520 )
| ( ( vmul @ v1 @ A )
!= ( vmul @ vd517 @ vd519 ) ) ),
inference(paramod_ordered,[status(thm)],[247,282]) ).
thf(301,plain,
! [A: $i] :
( ~ ( greater @ A @ vd518 )
| ( v1 != vd520 )
| ( v1 != vd517 )
| ( A != vd519 ) ),
inference(simp,[status(thm)],[299]) ).
thf(303,plain,
( ~ ( greater @ vd519 @ vd518 )
| ( v1 != vd520 )
| ( v1 != vd517 ) ),
inference(simp,[status(thm)],[301]) ).
thf(1959,plain,
! [A: $i] :
( ( less @ v1 @ A )
| ~ ( greater @ vd519 @ vd518 )
| ( v1 != vd520 )
| ( A != vd517 )
| ( v1 != v1 ) ),
inference(paramod_ordered,[status(thm)],[1522,303]) ).
thf(1960,plain,
! [A: $i] :
( ( less @ v1 @ A )
| ~ ( greater @ vd519 @ vd518 )
| ( v1 != vd520 )
| ( A != vd517 ) ),
inference(pattern_uni,[status(thm)],[1959:[]]) ).
thf(2338,plain,
( ( less @ v1 @ vd517 )
| ~ ( greater @ vd519 @ vd518 )
| ( v1 != vd520 ) ),
inference(simp,[status(thm)],[1960]) ).
thf(14572,plain,
! [B: $i,A: $i] :
( ( greater @ vd517 @ vd518 )
| ( leq @ B @ A )
| ( ( geq @ vd519 @ ( vsucc @ vd520 ) )
!= ( geq @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[14409,101]) ).
thf(14573,plain,
( ( greater @ vd517 @ vd518 )
| ( leq @ ( vsucc @ vd520 ) @ vd519 ) ),
inference(pattern_uni,[status(thm)],[14572:[bind(A,$thf( vd519 )),bind(B,$thf( vsucc @ vd520 ))]]) ).
thf(411,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( less @ C @ ( vplus @ A @ B ) )
| ( ( vplus @ B @ A )
!= ( vplus @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[77,153]) ).
thf(412,plain,
! [B: $i,A: $i] : ( less @ B @ ( vplus @ A @ B ) ),
inference(pattern_uni,[status(thm)],[411:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A ))]]) ).
thf(13989,plain,
( ( vd518 != vd517 )
| ( ( vsucc @ vd520 )
!= vd519 ) ),
inference(simp,[status(thm)],[13863]) ).
thf(5452,plain,
! [C: $i,B: $i,A: $i] :
( ( ( vsucc @ ( vsucc @ ( vplus @ A @ B ) ) )
!= v1 )
| ( ( vplus @ A @ ( vsucc @ B ) )
!= ( vplus @ ( vsucc @ v1 ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[70,4431]) ).
thf(5453,plain,
! [A: $i] :
( ( vsucc @ ( vsucc @ ( vplus @ ( vsucc @ v1 ) @ A ) ) )
!= v1 ),
inference(pattern_uni,[status(thm)],[5452:[bind(A,$thf( vsucc @ v1 )),bind(B,$thf( E )),bind(C,$thf( vsucc @ E ))]]) ).
thf(5474,plain,
! [A: $i] :
( ( vsucc @ ( vsucc @ ( vplus @ ( vsucc @ v1 ) @ A ) ) )
!= v1 ),
inference(simp,[status(thm)],[5453]) ).
thf(6699,plain,
! [A: $i] :
( ( vsucc @ ( vsucc @ ( vsucc @ ( vplus @ v1 @ A ) ) ) )
!= v1 ),
inference(rewrite,[status(thm)],[5474,137]) ).
thf(264,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( greater @ C @ D )
| ~ ( geq @ A @ B )
| ( greater @ ( vplus @ A @ C ) @ ( vplus @ B @ D ) ) ),
inference(cnf,[status(esa)],[263]) ).
thf(593,plain,
! [A: $i] :
( ( v1 != vd518 )
| ( ( greater @ ( vsucc @ A ) @ A )
!= ( greater @ ( vmul @ vd517 @ vd519 ) @ vd520 ) ) ),
inference(paramod_ordered,[status(thm)],[474,292]) ).
thf(604,plain,
! [A: $i] :
( ( v1 != vd518 )
| ( ( vsucc @ A )
!= ( vmul @ vd517 @ vd519 ) )
| ( A != vd520 ) ),
inference(simp,[status(thm)],[593]) ).
thf(618,plain,
( ( v1 != vd518 )
| ( ( vmul @ vd517 @ vd519 )
!= ( vsucc @ vd520 ) ) ),
inference(simp,[status(thm)],[604]) ).
thf(200,plain,
( ( geq @ vd517 @ vd518 )
| ( geq @ vd519 @ vd520 ) ),
inference(cnf,[status(esa)],[197]) ).
thf(2406,plain,
! [B: $i,A: $i] :
( ( geq @ vd517 @ vd518 )
| ( leq @ B @ A )
| ( ( geq @ vd519 @ vd520 )
!= ( geq @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[200,101]) ).
thf(2407,plain,
( ( geq @ vd517 @ vd518 )
| ( leq @ vd520 @ vd519 ) ),
inference(pattern_uni,[status(thm)],[2406:[bind(A,$thf( vd519 )),bind(B,$thf( vd520 ))]]) ).
thf(4528,plain,
! [B: $i,A: $i] :
( ( leq @ vd520 @ vd519 )
| ( leq @ B @ A )
| ( ( geq @ vd517 @ vd518 )
!= ( geq @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[2407,101]) ).
thf(4529,plain,
( ( leq @ vd520 @ vd519 )
| ( leq @ vd518 @ vd517 ) ),
inference(pattern_uni,[status(thm)],[4528:[bind(A,$thf( vd517 )),bind(B,$thf( vd518 ))]]) ).
thf(4918,plain,
! [B: $i,A: $i] :
( ( leq @ vd518 @ vd517 )
| ( geq @ B @ A )
| ( ( leq @ vd520 @ vd519 )
!= ( leq @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[4529,96]) ).
thf(4919,plain,
( ( leq @ vd518 @ vd517 )
| ( geq @ vd519 @ vd520 ) ),
inference(pattern_uni,[status(thm)],[4918:[bind(A,$thf( vd520 )),bind(B,$thf( vd519 ))]]) ).
thf(28,axiom,
! [A: $i] :
( ( vsucc @ A )
!= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(12, 0), 0)') ).
thf(158,plain,
! [A: $i] :
( ( vsucc @ A )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(159,plain,
~ ? [A: $i] :
( ( vsucc @ A )
= A ),
inference(miniscope,[status(thm)],[158]) ).
thf(160,plain,
! [A: $i] :
( ( vsucc @ A )
!= A ),
inference(cnf,[status(esa)],[159]) ).
thf(161,plain,
! [A: $i] :
( ( vsucc @ A )
!= A ),
inference(lifteq,[status(thm)],[160]) ).
thf(174,plain,
~ ? [A: $i] :
( ( vsucc @ A )
= v1 ),
inference(miniscope,[status(thm)],[173]) ).
thf(175,plain,
! [A: $i] :
( ( vsucc @ A )
!= v1 ),
inference(cnf,[status(esa)],[174]) ).
thf(176,plain,
! [A: $i] :
( ( vsucc @ A )
!= v1 ),
inference(lifteq,[status(thm)],[175]) ).
thf(596,plain,
! [A: $i] :
( ( v1 != vd517 )
| ( ( greater @ ( vsucc @ A ) @ A )
!= ( greater @ vd519 @ ( vmul @ vd518 @ vd520 ) ) ) ),
inference(paramod_ordered,[status(thm)],[474,291]) ).
thf(608,plain,
! [A: $i] :
( ( v1 != vd517 )
| ( ( vsucc @ A )
!= vd519 )
| ( A
!= ( vmul @ vd518 @ vd520 ) ) ),
inference(simp,[status(thm)],[596]) ).
thf(612,plain,
( ( v1 != vd517 )
| ( ( vsucc @ ( vmul @ vd518 @ vd520 ) )
!= vd519 ) ),
inference(simp,[status(thm)],[608]) ).
thf(2104,plain,
! [A: $i] :
( ( less @ v1 @ A )
| ( A != vd517 )
| ( ( vsucc @ ( vmul @ vd518 @ vd520 ) )
!= vd519 )
| ( v1 != v1 ) ),
inference(paramod_ordered,[status(thm)],[1522,612]) ).
thf(2105,plain,
! [A: $i] :
( ( less @ v1 @ A )
| ( A != vd517 )
| ( ( vsucc @ ( vmul @ vd518 @ vd520 ) )
!= vd519 ) ),
inference(pattern_uni,[status(thm)],[2104:[]]) ).
thf(2225,plain,
( ( less @ v1 @ vd517 )
| ( ( vsucc @ ( vmul @ vd518 @ vd520 ) )
!= vd519 ) ),
inference(simp,[status(thm)],[2105]) ).
thf(742,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( vsucc @ ( vplus @ B @ A ) )
!= v1 )
| ( ( vplus @ A @ B )
!= ( vplus @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[77,733]) ).
thf(743,plain,
! [B: $i,A: $i] :
( ( vsucc @ ( vplus @ B @ A ) )
!= v1 ),
inference(pattern_uni,[status(thm)],[742:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(255,plain,
! [B: $i,A: $i] :
( ~ ( geq @ B @ A )
| ( greater @ B @ A )
| ( B = A ) ),
inference(cnf,[status(esa)],[252]) ).
thf(259,plain,
! [B: $i,A: $i] :
( ( B = A )
| ~ ( geq @ B @ A )
| ( greater @ B @ A ) ),
inference(lifteq,[status(thm)],[255]) ).
thf(17066,plain,
! [B: $i,A: $i] :
( ( greater @ A @ B )
| ( less @ A @ B )
| ( less @ v1 @ vd517 )
| ( A != vd517 )
| ( B != vd518 ) ),
inference(paramod_ordered,[status(thm)],[187,17020]) ).
thf(17067,plain,
! [A: $i] :
( ( greater @ A @ vd518 )
| ( less @ A @ vd518 )
| ( less @ v1 @ vd517 )
| ( A != vd517 ) ),
inference(pattern_uni,[status(thm)],[17066:[bind(A,$thf( A )),bind(B,$thf( vd518 ))]]) ).
thf(17115,plain,
( ( greater @ vd517 @ vd518 )
| ( less @ vd517 @ vd518 )
| ( less @ v1 @ vd517 ) ),
inference(simp,[status(thm)],[17067]) ).
thf(9946,plain,
! [A: $i] :
( ~ ( greater @ vd519 @ vd520 )
| ( ( greater @ ( vsucc @ A ) @ A )
!= ( greater @ vd517 @ vd518 ) ) ),
inference(paramod_ordered,[status(thm)],[474,9737]) ).
thf(9950,plain,
! [A: $i] :
( ~ ( greater @ vd519 @ vd520 )
| ( ( vsucc @ A )
!= vd517 )
| ( A != vd518 ) ),
inference(simp,[status(thm)],[9946]) ).
thf(9970,plain,
( ~ ( greater @ vd519 @ vd520 )
| ( ( vsucc @ vd518 )
!= vd517 ) ),
inference(simp,[status(thm)],[9950]) ).
thf(10010,plain,
( ( greater @ vd517 @ vd518 )
| ( ( vsucc @ vd518 )
!= vd517 )
| ( ( greater @ vd519 @ vd520 )
!= ( greater @ vd519 @ vd520 ) ) ),
inference(paramod_ordered,[status(thm)],[199,9970]) ).
thf(10011,plain,
( ( greater @ vd517 @ vd518 )
| ( ( vsucc @ vd518 )
!= vd517 ) ),
inference(pattern_uni,[status(thm)],[10010:[]]) ).
thf(10135,plain,
! [A: $i] :
( ( ( vsucc @ vd518 )
!= vd517 )
| ( ( greater @ vd517 @ vd518 )
!= ( greater @ A @ A ) ) ),
inference(paramod_ordered,[status(thm)],[10011,230]) ).
thf(10172,plain,
! [A: $i] :
( ( ( vsucc @ vd518 )
!= vd517 )
| ( vd517 != A )
| ( vd518 != A ) ),
inference(simp,[status(thm)],[10135]) ).
thf(10189,plain,
( ( ( vsucc @ vd518 )
!= vd517 )
| ( vd518 != vd517 ) ),
inference(simp,[status(thm)],[10172]) ).
thf(13313,plain,
! [A: $i] :
( ( A = v1 )
| ( A != vd517 )
| ( vd518 != vd517 )
| ( ( vsucc @ ( vskolem2 @ A ) )
!= ( vsucc @ vd518 ) ) ),
inference(paramod_ordered,[status(thm)],[99,10189]) ).
thf(13319,plain,
( ( v1 = vd517 )
| ( vd518 != vd517 )
| ( ( vskolem2 @ vd517 )
!= vd518 ) ),
inference(simp,[status(thm)],[13313]) ).
thf(5032,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk5 @ B @ ( vsucc @ A ) )
= C )
| ( ( vplus @ A @ v1 )
!= ( vplus @ C @ B ) ) ),
inference(paramod_ordered,[status(thm)],[69,124]) ).
thf(5033,plain,
! [A: $i] :
( ( sk5 @ v1 @ ( vsucc @ A ) )
= A ),
inference(pattern_uni,[status(thm)],[5032:[bind(A,$thf( A )),bind(B,$thf( v1 )),bind(C,$thf( A ))]]) ).
thf(1829,plain,
! [A: $i] :
( ( less @ v1 @ A )
| ~ ( greater @ vd517 @ vd520 )
| ( v1 != vd519 )
| ( A != vd518 )
| ( v1 != v1 ) ),
inference(paramod_ordered,[status(thm)],[1522,297]) ).
thf(1830,plain,
! [A: $i] :
( ( less @ v1 @ A )
| ~ ( greater @ vd517 @ vd520 )
| ( v1 != vd519 )
| ( A != vd518 ) ),
inference(pattern_uni,[status(thm)],[1829:[]]) ).
thf(2308,plain,
( ( less @ v1 @ vd518 )
| ~ ( greater @ vd517 @ vd520 )
| ( v1 != vd519 ) ),
inference(simp,[status(thm)],[1830]) ).
thf(7254,plain,
! [A: $i] :
( ~ ( less @ ( vmul @ vd518 @ vd520 ) @ A )
| ( ( vmul @ A @ v1 )
!= ( vmul @ vd517 @ vd519 ) ) ),
inference(paramod_ordered,[status(thm)],[195,7127]) ).
thf(7272,plain,
! [A: $i] :
( ~ ( less @ ( vmul @ vd518 @ vd520 ) @ A )
| ( A != vd517 )
| ( v1 != vd519 ) ),
inference(simp,[status(thm)],[7254]) ).
thf(7298,plain,
( ~ ( less @ ( vmul @ vd518 @ vd520 ) @ vd517 )
| ( v1 != vd519 ) ),
inference(simp,[status(thm)],[7272]) ).
thf(7699,plain,
! [A: $i] :
( ~ ( less @ A @ vd517 )
| ( v1 != vd519 )
| ( ( vmul @ A @ v1 )
!= ( vmul @ vd518 @ vd520 ) ) ),
inference(paramod_ordered,[status(thm)],[195,7298]) ).
thf(7721,plain,
! [A: $i] :
( ~ ( less @ A @ vd517 )
| ( v1 != vd519 )
| ( A != vd518 )
| ( v1 != vd520 ) ),
inference(simp,[status(thm)],[7699]) ).
thf(7741,plain,
( ~ ( less @ vd518 @ vd517 )
| ( v1 != vd519 )
| ( v1 != vd520 ) ),
inference(simp,[status(thm)],[7721]) ).
thf(25785,plain,
! [B: $i,A: $i] :
( ( vd520 = vd519 )
| ( greater @ B @ A )
| ( ( less @ v1 @ vd517 )
!= ( less @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[23134,223]) ).
thf(25786,plain,
( ( vd520 = vd519 )
| ( greater @ vd517 @ v1 ) ),
inference(pattern_uni,[status(thm)],[25785:[bind(A,$thf( v1 )),bind(B,$thf( vd517 ))]]) ).
thf(35546,plain,
( ( vd520 = vd519 )
| ( ( greater @ vd517 @ v1 )
!= ( greater @ vd517 @ vd518 ) ) ),
inference(paramod_ordered,[status(thm)],[25786,20479]) ).
thf(35689,plain,
( ( vd520 = vd519 )
| ( vd517 != vd517 )
| ( v1 != vd518 ) ),
inference(simp,[status(thm)],[35546]) ).
thf(35718,plain,
( ( vd520 = vd519 )
| ( v1 != vd518 ) ),
inference(simp,[status(thm)],[35689]) ).
thf(20723,plain,
( ~ ( greater @ vd519 @ vd520 )
| ~ ( greater @ v1 @ vd517 )
| ( vd518 != vd518 ) ),
inference(paramod_ordered,[status(thm)],[19372,17206]) ).
thf(20724,plain,
( ~ ( greater @ vd519 @ vd520 )
| ~ ( greater @ v1 @ vd517 ) ),
inference(pattern_uni,[status(thm)],[20723:[]]) ).
thf(1865,plain,
! [A: $i] :
( ( less @ v1 @ A )
| ~ ( greater @ vd517 @ vd518 )
| ( v1 != vd519 )
| ( A != vd520 )
| ( v1 != v1 ) ),
inference(paramod_ordered,[status(thm)],[1522,298]) ).
thf(1866,plain,
! [A: $i] :
( ( less @ v1 @ A )
| ~ ( greater @ vd517 @ vd518 )
| ( v1 != vd519 )
| ( A != vd520 ) ),
inference(pattern_uni,[status(thm)],[1865:[]]) ).
thf(2319,plain,
( ( less @ v1 @ vd520 )
| ~ ( greater @ vd517 @ vd518 )
| ( v1 != vd519 ) ),
inference(simp,[status(thm)],[1866]) ).
thf(1339,plain,
! [A: $i] :
( ( A
!= ( vsucc @ ( vsucc @ ( vmul @ vd518 @ vd520 ) ) ) )
| ( ( vmul @ v1 @ A )
!= ( vmul @ vd517 @ vd519 ) ) ),
inference(paramod_ordered,[status(thm)],[247,1301]) ).
thf(1344,plain,
( ( v1 != vd517 )
| ( ( vsucc @ ( vsucc @ ( vmul @ vd518 @ vd520 ) ) )
!= vd519 ) ),
inference(simp,[status(thm)],[1339]) ).
thf(1352,plain,
! [A: $i] :
( ( v1 != vd517 )
| ( ( vsucc @ ( vsucc @ A ) )
!= vd519 )
| ( ( vmul @ v1 @ A )
!= ( vmul @ vd518 @ vd520 ) ) ),
inference(paramod_ordered,[status(thm)],[247,1344]) ).
thf(1354,plain,
! [A: $i] :
( ( v1 != vd517 )
| ( ( vsucc @ ( vsucc @ A ) )
!= vd519 )
| ( v1 != vd518 )
| ( A != vd520 ) ),
inference(simp,[status(thm)],[1352]) ).
thf(1356,plain,
( ( v1 != vd517 )
| ( ( vsucc @ ( vsucc @ vd520 ) )
!= vd519 )
| ( v1 != vd518 ) ),
inference(simp,[status(thm)],[1354]) ).
thf(2045,plain,
! [A: $i] :
( ( less @ v1 @ A )
| ( greater @ vd517 @ vd518 )
| ( A != vd517 )
| ( v1 != vd518 )
| ( v1 != v1 ) ),
inference(paramod_ordered,[status(thm)],[1522,394]) ).
thf(2046,plain,
! [A: $i] :
( ( less @ v1 @ A )
| ( greater @ vd517 @ vd518 )
| ( A != vd517 )
| ( v1 != vd518 ) ),
inference(pattern_uni,[status(thm)],[2045:[]]) ).
thf(2361,plain,
( ( less @ v1 @ vd517 )
| ( greater @ vd517 @ vd518 )
| ( v1 != vd518 ) ),
inference(simp,[status(thm)],[2046]) ).
thf(32,axiom,
! [A: $i] : ( geq @ A @ v1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(228, 0), 0)') ).
thf(171,plain,
! [A: $i] : ( geq @ A @ v1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(172,plain,
! [A: $i] : ( geq @ A @ v1 ),
inference(cnf,[status(esa)],[171]) ).
thf(16,axiom,
! [A: $i,B: $i] :
( ( ( vsucc @ A )
= ( vsucc @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(antec(axiom(3)), imp(antec(axiom(3))))') ).
thf(111,plain,
! [A: $i,B: $i] :
( ( ( vsucc @ A )
= ( vsucc @ B ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(112,plain,
! [B: $i,A: $i] :
( ( ( vsucc @ A )
!= ( vsucc @ B ) )
| ( A = B ) ),
inference(cnf,[status(esa)],[111]) ).
thf(113,plain,
! [B: $i,A: $i] :
( ( ( vsucc @ A )
!= ( vsucc @ B ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[112]) ).
thf(48,axiom,
! [A: $i,B: $i,C: $i] :
( ( less @ B @ C )
=> ( less @ ( vmul @ B @ A ) @ ( vmul @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(299, 0), 0)') ).
thf(218,plain,
! [A: $i,B: $i,C: $i] :
( ( less @ B @ C )
=> ( less @ ( vmul @ B @ A ) @ ( vmul @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(219,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( less @ B @ C )
| ( less @ ( vmul @ B @ A ) @ ( vmul @ C @ A ) ) ),
inference(cnf,[status(esa)],[218]) ).
thf(1338,plain,
! [A: $i] :
( ( ( vsucc @ ( vsucc @ A ) )
!= ( vmul @ vd517 @ vd519 ) )
| ( ( vmul @ v1 @ A )
!= ( vmul @ vd518 @ vd520 ) ) ),
inference(paramod_ordered,[status(thm)],[247,1301]) ).
thf(1342,plain,
! [A: $i] :
( ( ( vsucc @ ( vsucc @ A ) )
!= ( vmul @ vd517 @ vd519 ) )
| ( v1 != vd518 )
| ( A != vd520 ) ),
inference(simp,[status(thm)],[1338]) ).
thf(1349,plain,
( ( ( vmul @ vd517 @ vd519 )
!= ( vsucc @ ( vsucc @ vd520 ) ) )
| ( v1 != vd518 ) ),
inference(simp,[status(thm)],[1342]) ).
thf(599,plain,
! [A: $i] :
( ( v1 != vd520 )
| ( v1 != vd517 )
| ( ( greater @ ( vsucc @ A ) @ A )
!= ( greater @ vd519 @ vd518 ) ) ),
inference(paramod_ordered,[status(thm)],[474,303]) ).
thf(606,plain,
! [A: $i] :
( ( v1 != vd520 )
| ( v1 != vd517 )
| ( ( vsucc @ A )
!= vd519 )
| ( A != vd518 ) ),
inference(simp,[status(thm)],[599]) ).
thf(620,plain,
( ( v1 != vd520 )
| ( v1 != vd517 )
| ( ( vsucc @ vd518 )
!= vd519 ) ),
inference(simp,[status(thm)],[606]) ).
thf(2166,plain,
! [A: $i] :
( ( less @ v1 @ A )
| ( A != vd520 )
| ( v1 != vd517 )
| ( ( vsucc @ vd518 )
!= vd519 )
| ( v1 != v1 ) ),
inference(paramod_ordered,[status(thm)],[1522,620]) ).
thf(2167,plain,
! [A: $i] :
( ( less @ v1 @ A )
| ( A != vd520 )
| ( v1 != vd517 )
| ( ( vsucc @ vd518 )
!= vd519 ) ),
inference(pattern_uni,[status(thm)],[2166:[]]) ).
thf(2246,plain,
( ( less @ v1 @ vd520 )
| ( v1 != vd517 )
| ( ( vsucc @ vd518 )
!= vd519 ) ),
inference(simp,[status(thm)],[2167]) ).
thf(19827,plain,
( ( ( vsucc @ vd518 )
!= vd517 )
| ( vd520 != vd519 ) ),
inference(simp,[status(thm)],[19687]) ).
thf(22458,plain,
( ~ ( greater @ vd517 @ vd518 )
| ( ( vsucc @ vd518 )
!= vd517 )
| ( vd520 != vd520 ) ),
inference(paramod_ordered,[status(thm)],[20479,19827]) ).
thf(22459,plain,
( ~ ( greater @ vd517 @ vd518 )
| ( ( vsucc @ vd518 )
!= vd517 ) ),
inference(pattern_uni,[status(thm)],[22458:[]]) ).
thf(34649,plain,
( ( ( vsucc @ vd518 )
!= vd517 )
| ( ( greater @ vd517 @ vd518 )
!= ( greater @ vd517 @ vd518 ) ) ),
inference(paramod_ordered,[status(thm)],[10011,22459]) ).
thf(34650,plain,
( ( vsucc @ vd518 )
!= vd517 ),
inference(pattern_uni,[status(thm)],[34649:[]]) ).
thf(270,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( leq @ B @ C )
| ~ ( leq @ A @ B )
| ~ ( leq @ D @ E )
| ( leq @ D @ F )
| ( ( leq @ A @ C )
!= ( leq @ E @ F ) ) ),
inference(paramod_ordered,[status(thm)],[63,63]) ).
thf(271,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( leq @ B @ C )
| ~ ( leq @ A @ B )
| ~ ( leq @ D @ A )
| ( leq @ D @ C ) ),
inference(pattern_uni,[status(thm)],[270:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( A )),bind(F,$thf( C ))]]) ).
thf(43,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( greater @ C @ D )
& ( greater @ A @ B ) )
=> ( greater @ ( vplus @ A @ C ) @ ( vplus @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(209, 0), 0)') ).
thf(207,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( greater @ C @ D )
& ( greater @ A @ B ) )
=> ( greater @ ( vplus @ A @ C ) @ ( vplus @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(208,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( greater @ C @ D )
| ~ ( greater @ A @ B )
| ( greater @ ( vplus @ A @ C ) @ ( vplus @ B @ D ) ) ),
inference(cnf,[status(esa)],[207]) ).
thf(9947,plain,
( ~ ( greater @ vd517 @ vd518 )
| ( ( greater @ vd519 @ vd520 )
!= ( greater @ vd517 @ vd518 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[9737]) ).
thf(9964,plain,
( ~ ( greater @ vd517 @ vd518 )
| ( vd519 != vd517 )
| ( vd520 != vd518 ) ),
inference(simp,[status(thm)],[9947]) ).
thf(13649,plain,
( ( greater @ vd517 @ vd518 )
| ( vd519 != vd517 )
| ( vd520 != vd518 )
| ( ( greater @ vd519 @ vd520 )
!= ( greater @ vd517 @ vd518 ) ) ),
inference(paramod_ordered,[status(thm)],[199,9964]) ).
thf(13659,plain,
( ( greater @ vd517 @ vd518 )
| ( vd519 != vd517 )
| ( vd520 != vd518 )
| ( vd519 != vd517 )
| ( vd520 != vd518 ) ),
inference(simp,[status(thm)],[13649]) ).
thf(13672,plain,
( ( greater @ vd517 @ vd518 )
| ( vd519 != vd517 )
| ( vd520 != vd518 ) ),
inference(simp,[status(thm)],[13659]) ).
thf(14261,plain,
( ( vd519 != vd517 )
| ( vd520 != vd518 )
| ( ( greater @ vd517 @ vd518 )
!= ( greater @ vd517 @ vd518 ) ) ),
inference(paramod_ordered,[status(thm)],[13672,9964]) ).
thf(14262,plain,
( ( vd519 != vd517 )
| ( vd520 != vd518 ) ),
inference(pattern_uni,[status(thm)],[14261:[]]) ).
thf(24,axiom,
! [A: $i,B: $i] :
( ( A != B )
| ~ ? [C: $i] :
( B
= ( vplus @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(88), 0), 1)') ).
thf(140,plain,
! [A: $i,B: $i] :
( ( A != B )
| ~ ? [C: $i] :
( B
= ( vplus @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(482,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( greater @ ( vplus @ A @ B ) @ C )
| ( ( vplus @ B @ A )
!= ( vplus @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[77,182]) ).
thf(483,plain,
! [B: $i,A: $i] : ( greater @ ( vplus @ A @ B ) @ B ),
inference(pattern_uni,[status(thm)],[482:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A ))]]) ).
thf(5034,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk5 @ B @ ( vsucc @ A ) )
= C )
| ( ( vplus @ v1 @ A )
!= ( vplus @ C @ B ) ) ),
inference(paramod_ordered,[status(thm)],[170,124]) ).
thf(5035,plain,
! [A: $i] :
( ( sk5 @ A @ ( vsucc @ A ) )
= v1 ),
inference(pattern_uni,[status(thm)],[5034:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( v1 ))]]) ).
thf(19855,plain,
! [B: $i,A: $i] :
( ( ( vmul @ B @ A )
!= ( vmul @ vd517 @ vd519 ) )
| ( ( vmul @ A @ B )
!= ( vmul @ ( vsucc @ vd518 ) @ vd520 ) ) ),
inference(paramod_ordered,[status(thm)],[206,19687]) ).
thf(19856,plain,
( ( vmul @ vd520 @ ( vsucc @ vd518 ) )
!= ( vmul @ vd517 @ vd519 ) ),
inference(pattern_uni,[status(thm)],[19855:[bind(A,$thf( vsucc @ vd518 )),bind(B,$thf( vd520 ))]]) ).
thf(19898,plain,
( ( vd520 != vd517 )
| ( ( vsucc @ vd518 )
!= vd519 ) ),
inference(simp,[status(thm)],[19856]) ).
thf(212,plain,
! [A: $i,B: $i] :
( ? [C: $i] : ( greater @ ( vplus @ A @ C ) @ ( vplus @ B @ C ) )
=> ( greater @ A @ B ) ),
inference(miniscope,[status(thm)],[211]) ).
thf(213,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( greater @ ( vplus @ A @ C ) @ ( vplus @ B @ C ) )
| ( greater @ A @ B ) ),
inference(cnf,[status(esa)],[212]) ).
thf(594,plain,
! [A: $i] :
( ( v1 != vd519 )
| ( v1 != vd518 )
| ( ( greater @ ( vsucc @ A ) @ A )
!= ( greater @ vd517 @ vd520 ) ) ),
inference(paramod_ordered,[status(thm)],[474,297]) ).
thf(607,plain,
! [A: $i] :
( ( v1 != vd519 )
| ( v1 != vd518 )
| ( ( vsucc @ A )
!= vd517 )
| ( A != vd520 ) ),
inference(simp,[status(thm)],[594]) ).
thf(621,plain,
( ( v1 != vd519 )
| ( v1 != vd518 )
| ( ( vsucc @ vd520 )
!= vd517 ) ),
inference(simp,[status(thm)],[607]) ).
thf(90,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( A
= ( vplus @ B @ ( sk2 @ B @ A ) ) )
| ( B
= ( vplus @ A @ ( sk3 @ B @ A ) ) ) ),
inference(cnf,[status(esa)],[89]) ).
thf(91,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( vplus @ B @ ( sk2 @ B @ A ) )
= A )
| ( ( vplus @ A @ ( sk3 @ B @ A ) )
= B ) ),
inference(lifteq,[status(thm)],[90]) ).
thf(239,plain,
! [A: $i,B: $i] :
( ( greater @ A @ B )
=> ! [C: $i] : ( greater @ ( vplus @ A @ C ) @ ( vplus @ B @ C ) ) ),
inference(miniscope,[status(thm)],[238]) ).
thf(240,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( greater @ A @ B )
| ( greater @ ( vplus @ A @ C ) @ ( vplus @ B @ C ) ) ),
inference(cnf,[status(esa)],[239]) ).
thf(6737,plain,
! [C: $i,B: $i,A: $i] :
( ( ( vsucc @ ( vsucc @ ( vsucc @ ( vsucc @ ( vplus @ A @ B ) ) ) ) )
!= v1 )
| ( ( vplus @ A @ ( vsucc @ B ) )
!= ( vplus @ v1 @ C ) ) ),
inference(paramod_ordered,[status(thm)],[70,6699]) ).
thf(6738,plain,
! [A: $i] :
( ( vsucc @ ( vsucc @ ( vsucc @ ( vsucc @ ( vplus @ v1 @ A ) ) ) ) )
!= v1 ),
inference(pattern_uni,[status(thm)],[6737:[bind(A,$thf( v1 )),bind(B,$thf( D )),bind(C,$thf( vsucc @ D ))]]) ).
thf(6763,plain,
! [A: $i] :
( ( vsucc @ ( vsucc @ ( vsucc @ ( vsucc @ ( vplus @ v1 @ A ) ) ) ) )
!= v1 ),
inference(simp,[status(thm)],[6738]) ).
thf(8423,plain,
! [A: $i] :
( ( vsucc @ ( vsucc @ ( vsucc @ ( vsucc @ ( vsucc @ A ) ) ) ) )
!= v1 ),
inference(rewrite,[status(thm)],[6763,170]) ).
thf(20,axiom,
! [A: $i,B: $i] :
( ( A != B )
=> ( ( vsucc @ A )
!= ( vsucc @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(6, 0), 0)') ).
thf(127,plain,
! [A: $i,B: $i] :
( ( A != B )
=> ( ( vsucc @ A )
!= ( vsucc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(128,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( vsucc @ A )
!= ( vsucc @ B ) ) ),
inference(cnf,[status(esa)],[127]) ).
thf(129,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( vsucc @ A )
!= ( vsucc @ B ) ) ),
inference(lifteq,[status(thm)],[128]) ).
thf(130,plain,
! [A: $i] :
( ( sk6 @ ( vsucc @ A ) )
= A ),
introduced(tautology,[new_symbols(inverse(vsucc),[sk6])]) ).
thf(20604,plain,
( ( v1 != vd517 )
| ( v1 != vd520 )
| ( ( greater @ vd519 @ vd518 )
!= ( greater @ vd517 @ vd518 ) ) ),
inference(paramod_ordered,[status(thm)],[19365,303]) ).
thf(20643,plain,
( ( v1 != vd517 )
| ( v1 != vd520 )
| ( vd519 != vd517 )
| ( vd518 != vd518 ) ),
inference(simp,[status(thm)],[20604]) ).
thf(20660,plain,
( ( v1 != vd517 )
| ( v1 != vd520 )
| ( vd519 != vd517 ) ),
inference(simp,[status(thm)],[20643]) ).
thf(166,plain,
! [A: $i,B: $i] :
( ? [C: $i] : ( less @ ( vplus @ A @ C ) @ ( vplus @ B @ C ) )
=> ( less @ A @ B ) ),
inference(miniscope,[status(thm)],[165]) ).
thf(167,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( less @ ( vplus @ A @ C ) @ ( vplus @ B @ C ) )
| ( less @ A @ B ) ),
inference(cnf,[status(esa)],[166]) ).
thf(5423,plain,
! [B: $i,A: $i] :
( ( ( vsucc @ ( vsucc @ A ) )
!= v1 )
| ( ( vplus @ A @ v1 )
!= ( vplus @ ( vsucc @ v1 ) @ B ) ) ),
inference(paramod_ordered,[status(thm)],[69,4431]) ).
thf(5424,plain,
( ( vsucc @ ( vsucc @ ( vsucc @ v1 ) ) )
!= v1 ),
inference(pattern_uni,[status(thm)],[5423:[bind(A,$thf( vsucc @ v1 )),bind(B,$thf( v1 ))]]) ).
thf(4393,plain,
! [B: $i,A: $i] :
( ( ( vsucc @ A )
!= v1 )
| ( ( vplus @ A @ v1 )
!= ( vplus @ ( vsucc @ v1 ) @ B ) ) ),
inference(paramod_ordered,[status(thm)],[69,4236]) ).
thf(4394,plain,
( ( vsucc @ ( vsucc @ v1 ) )
!= v1 ),
inference(pattern_uni,[status(thm)],[4393:[bind(A,$thf( vsucc @ v1 )),bind(B,$thf( v1 ))]]) ).
thf(6661,plain,
! [C: $i,B: $i,A: $i] :
( ( geq @ C @ B )
| ( ( leq @ A @ ( vsucc @ A ) )
!= ( leq @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[2477,96]) ).
thf(6662,plain,
! [A: $i] : ( geq @ ( vsucc @ A ) @ A ),
inference(pattern_uni,[status(thm)],[6661:[bind(A,$thf( D )),bind(B,$thf( D )),bind(C,$thf( vsucc @ D ))]]) ).
thf(6672,plain,
! [A: $i] : ( geq @ ( vsucc @ A ) @ A ),
inference(simp,[status(thm)],[6662]) ).
thf(1863,plain,
! [A: $i] :
( ( less @ v1 @ A )
| ~ ( greater @ vd517 @ vd518 )
| ( A != vd519 )
| ( v1 != vd520 )
| ( v1 != v1 ) ),
inference(paramod_ordered,[status(thm)],[1522,298]) ).
thf(1864,plain,
! [A: $i] :
( ( less @ v1 @ A )
| ~ ( greater @ vd517 @ vd518 )
| ( A != vd519 )
| ( v1 != vd520 ) ),
inference(pattern_uni,[status(thm)],[1863:[]]) ).
thf(2318,plain,
( ( less @ v1 @ vd519 )
| ~ ( greater @ vd517 @ vd518 )
| ( v1 != vd520 ) ),
inference(simp,[status(thm)],[1864]) ).
thf(44,axiom,
! [A: $i,B: $i,C: $i] :
( ( less @ ( vmul @ A @ B ) @ ( vmul @ C @ B ) )
=> ( less @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(conjunct2(conjunct2(307)), 0), 0)') ).
thf(209,plain,
! [A: $i,B: $i,C: $i] :
( ( less @ ( vmul @ A @ B ) @ ( vmul @ C @ B ) )
=> ( less @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(1069,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( vsucc @ ( vsucc @ ( vsucc @ ( vplus @ A @ B ) ) ) )
!= v1 )
| ( ( vplus @ A @ ( vsucc @ B ) )
!= ( vplus @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[70,744]) ).
thf(1070,plain,
! [B: $i,A: $i] :
( ( vsucc @ ( vsucc @ ( vsucc @ ( vplus @ A @ B ) ) ) )
!= v1 ),
inference(pattern_uni,[status(thm)],[1069:[bind(A,$thf( A )),bind(B,$thf( E )),bind(C,$thf( A )),bind(D,$thf( vsucc @ E ))]]) ).
thf(1081,plain,
! [B: $i,A: $i] :
( ( vsucc @ ( vsucc @ ( vsucc @ ( vplus @ A @ B ) ) ) )
!= v1 ),
inference(simp,[status(thm)],[1070]) ).
thf(14396,plain,
! [C: $i,B: $i,A: $i] :
( ( geq @ B @ ( vsucc @ C ) )
| ( ( greater @ ( vsucc @ A ) @ v1 )
!= ( greater @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[476,14381]) ).
thf(14397,plain,
! [A: $i] : ( geq @ ( vsucc @ A ) @ ( vsucc @ v1 ) ),
inference(pattern_uni,[status(thm)],[14396:[bind(A,$thf( D )),bind(B,$thf( vsucc @ D )),bind(C,$thf( v1 ))]]) ).
thf(14438,plain,
! [A: $i] : ( geq @ ( vsucc @ A ) @ ( vsucc @ v1 ) ),
inference(simp,[status(thm)],[14397]) ).
thf(19716,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( vsucc @ ( vsucc @ ( vmul @ ( vsucc @ A ) @ B ) ) )
!= v1 )
| ( ( vplus @ ( vmul @ A @ B ) @ B )
!= ( vplus @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[226,744]) ).
thf(19717,plain,
! [B: $i,A: $i] :
( ( vsucc @ ( vsucc @ ( vmul @ ( vsucc @ A ) @ B ) ) )
!= v1 ),
inference(pattern_uni,[status(thm)],[19716:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( vmul @ E @ F )),bind(D,$thf( F ))]]) ).
thf(19757,plain,
! [B: $i,A: $i] :
( ( vsucc @ ( vsucc @ ( vmul @ ( vsucc @ A ) @ B ) ) )
!= v1 ),
inference(simp,[status(thm)],[19717]) ).
thf(19694,plain,
! [C: $i,B: $i,A: $i] :
( ( ( vsucc @ ( vmul @ ( vsucc @ A ) @ B ) )
!= ( vmul @ vd517 @ vd519 ) )
| ( ( vplus @ ( vmul @ A @ B ) @ B )
!= ( vplus @ ( vmul @ vd518 @ vd520 ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[226,799]) ).
thf(19695,plain,
( ( vsucc @ ( vmul @ ( vsucc @ vd518 ) @ vd520 ) )
!= ( vmul @ vd517 @ vd519 ) ),
inference(pattern_uni,[status(thm)],[19694:[bind(A,$thf( vd518 )),bind(B,$thf( vd520 )),bind(C,$thf( vd520 ))]]) ).
thf(24776,plain,
! [B: $i,A: $i] :
( ( vd520 = vd519 )
| ( geq @ B @ A )
| ( ( greater @ vd519 @ vd520 )
!= ( greater @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[18842,256]) ).
thf(24777,plain,
( ( vd520 = vd519 )
| ( geq @ vd519 @ vd520 ) ),
inference(pattern_uni,[status(thm)],[24776:[bind(A,$thf( vd520 )),bind(B,$thf( vd519 ))]]) ).
thf(14439,plain,
! [C: $i,B: $i,A: $i] :
( ( leq @ C @ B )
| ( ( geq @ ( vsucc @ A ) @ ( vsucc @ v1 ) )
!= ( geq @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[14438,101]) ).
thf(14440,plain,
! [A: $i] : ( leq @ ( vsucc @ v1 ) @ ( vsucc @ A ) ),
inference(pattern_uni,[status(thm)],[14439:[bind(A,$thf( D )),bind(B,$thf( vsucc @ D )),bind(C,$thf( vsucc @ v1 ))]]) ).
thf(14485,plain,
! [A: $i] : ( leq @ ( vsucc @ v1 ) @ ( vsucc @ A ) ),
inference(simp,[status(thm)],[14440]) ).
thf(13884,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( vsucc @ ( vsucc @ ( vmul @ A @ ( vsucc @ B ) ) ) )
!= v1 )
| ( ( vplus @ ( vmul @ A @ B ) @ A )
!= ( vplus @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[196,744]) ).
thf(13885,plain,
! [B: $i,A: $i] :
( ( vsucc @ ( vsucc @ ( vmul @ A @ ( vsucc @ B ) ) ) )
!= v1 ),
inference(pattern_uni,[status(thm)],[13884:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( vmul @ E @ F )),bind(D,$thf( E ))]]) ).
thf(13948,plain,
! [B: $i,A: $i] :
( ( vsucc @ ( vsucc @ ( vmul @ A @ ( vsucc @ B ) ) ) )
!= v1 ),
inference(simp,[status(thm)],[13885]) ).
thf(23612,plain,
( ( leq @ vd518 @ vd517 )
| ( v1 != vd517 )
| ( vd518 != vd518 ) ),
inference(paramod_ordered,[status(thm)],[22346,17103]) ).
thf(23613,plain,
( ( leq @ vd518 @ vd517 )
| ( v1 != vd517 ) ),
inference(pattern_uni,[status(thm)],[23612:[]]) ).
thf(2025,plain,
! [A: $i] :
( ( less @ v1 @ A )
| ( v1 != vd519 )
| ( A != vd518 )
| ( ( vsucc @ vd520 )
!= vd517 )
| ( v1 != v1 ) ),
inference(paramod_ordered,[status(thm)],[1522,621]) ).
thf(2026,plain,
! [A: $i] :
( ( less @ v1 @ A )
| ( v1 != vd519 )
| ( A != vd518 )
| ( ( vsucc @ vd520 )
!= vd517 ) ),
inference(pattern_uni,[status(thm)],[2025:[]]) ).
thf(2354,plain,
( ( less @ v1 @ vd518 )
| ( v1 != vd519 )
| ( ( vsucc @ vd520 )
!= vd517 ) ),
inference(simp,[status(thm)],[2026]) ).
thf(34,axiom,
! [A: $i,B: $i,C: $i] :
( ( B = C )
=> ( ( vmul @ B @ A )
= ( vmul @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(299, 0), 1)') ).
thf(177,plain,
! [A: $i,B: $i,C: $i] :
( ( B = C )
=> ( ( vmul @ B @ A )
= ( vmul @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(462,plain,
! [C: $i,B: $i,A: $i] :
( ( ( vsucc @ ( vsucc @ A ) )
!= B )
| ( ( vplus @ A @ v1 )
!= ( vplus @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[69,375]) ).
thf(463,plain,
! [A: $i] :
( ( vsucc @ ( vsucc @ A ) )
!= A ),
inference(pattern_uni,[status(thm)],[462:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( v1 ))]]) ).
thf(1957,plain,
! [A: $i] :
( ( less @ v1 @ A )
| ~ ( greater @ vd519 @ vd518 )
| ( A != vd520 )
| ( v1 != vd517 )
| ( v1 != v1 ) ),
inference(paramod_ordered,[status(thm)],[1522,303]) ).
thf(1958,plain,
! [A: $i] :
( ( less @ v1 @ A )
| ~ ( greater @ vd519 @ vd518 )
| ( A != vd520 )
| ( v1 != vd517 ) ),
inference(pattern_uni,[status(thm)],[1957:[]]) ).
thf(2337,plain,
( ( less @ v1 @ vd520 )
| ~ ( greater @ vd519 @ vd518 )
| ( v1 != vd517 ) ),
inference(simp,[status(thm)],[1958]) ).
thf(2168,plain,
! [A: $i] :
( ( less @ v1 @ A )
| ( v1 != vd520 )
| ( A != vd517 )
| ( ( vsucc @ vd518 )
!= vd519 )
| ( v1 != v1 ) ),
inference(paramod_ordered,[status(thm)],[1522,620]) ).
thf(2169,plain,
! [A: $i] :
( ( less @ v1 @ A )
| ( v1 != vd520 )
| ( A != vd517 )
| ( ( vsucc @ vd518 )
!= vd519 ) ),
inference(pattern_uni,[status(thm)],[2168:[]]) ).
thf(2247,plain,
( ( less @ v1 @ vd517 )
| ( v1 != vd520 )
| ( ( vsucc @ vd518 )
!= vd519 ) ),
inference(simp,[status(thm)],[2169]) ).
thf(6700,plain,
! [B: $i,A: $i] :
( ( ( vsucc @ ( vsucc @ ( vsucc @ ( vsucc @ A ) ) ) )
!= v1 )
| ( ( vplus @ A @ v1 )
!= ( vplus @ v1 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[69,6699]) ).
thf(6701,plain,
( ( vsucc @ ( vsucc @ ( vsucc @ ( vsucc @ v1 ) ) ) )
!= v1 ),
inference(pattern_uni,[status(thm)],[6700:[bind(A,$thf( v1 )),bind(B,$thf( v1 ))]]) ).
thf(592,plain,
! [A: $i] :
( ( greater @ ( vsucc @ A ) @ A )
!= ( greater @ ( vmul @ vd517 @ vd519 ) @ ( vmul @ vd518 @ vd520 ) ) ),
inference(paramod_ordered,[status(thm)],[474,61]) ).
thf(609,plain,
! [A: $i] :
( ( ( vsucc @ A )
!= ( vmul @ vd517 @ vd519 ) )
| ( A
!= ( vmul @ vd518 @ vd520 ) ) ),
inference(simp,[status(thm)],[592]) ).
thf(613,plain,
( ( vsucc @ ( vmul @ vd518 @ vd520 ) )
!= ( vmul @ vd517 @ vd519 ) ),
inference(simp,[status(thm)],[609]) ).
thf(20313,plain,
! [B: $i,A: $i] :
( ( vd520 = vd519 )
| ( less @ B @ A )
| ( ( greater @ vd519 @ vd520 )
!= ( greater @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[18842,221]) ).
thf(20314,plain,
( ( vd520 = vd519 )
| ( less @ vd520 @ vd519 ) ),
inference(pattern_uni,[status(thm)],[20313:[bind(A,$thf( vd519 )),bind(B,$thf( vd520 ))]]) ).
thf(23069,plain,
! [B: $i,A: $i] :
( ( vd520 = vd519 )
| ( leq @ B @ A )
| ( ( less @ vd520 @ vd519 )
!= ( less @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[20314,107]) ).
thf(23070,plain,
( ( vd520 = vd519 )
| ( leq @ vd520 @ vd519 ) ),
inference(pattern_uni,[status(thm)],[23069:[bind(A,$thf( vd519 )),bind(B,$thf( vd520 ))]]) ).
thf(18876,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( vsucc @ ( vsucc @ ( vmul @ B @ A ) ) )
!= v1 )
| ( ( vmul @ A @ B )
!= ( vmul @ C @ ( vsucc @ D ) ) ) ),
inference(paramod_ordered,[status(thm)],[206,13948]) ).
thf(18877,plain,
! [B: $i,A: $i] :
( ( vsucc @ ( vsucc @ ( vmul @ ( vsucc @ B ) @ A ) ) )
!= v1 ),
inference(pattern_uni,[status(thm)],[18876:[bind(A,$thf( A )),bind(B,$thf( vsucc @ E )),bind(C,$thf( A )),bind(D,$thf( E ))]]) ).
thf(18926,plain,
! [B: $i,A: $i] :
( ( vsucc @ ( vsucc @ ( vmul @ ( vsucc @ B ) @ A ) ) )
!= v1 ),
inference(simp,[status(thm)],[18877]) ).
thf(20763,plain,
( ~ ( greater @ vd519 @ vd520 )
| ( ( vsucc @ vd520 )
!= vd519 )
| ( vd518 != vd518 ) ),
inference(paramod_ordered,[status(thm)],[19372,13989]) ).
thf(20764,plain,
( ~ ( greater @ vd519 @ vd520 )
| ( ( vsucc @ vd520 )
!= vd519 ) ),
inference(pattern_uni,[status(thm)],[20763:[]]) ).
thf(758,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk1 @ B @ ( vsucc @ A ) )
= C )
| ( ( vplus @ A @ v1 )
!= ( vplus @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[69,88]) ).
thf(759,plain,
! [A: $i] :
( ( sk1 @ A @ ( vsucc @ A ) )
= v1 ),
inference(pattern_uni,[status(thm)],[758:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( v1 ))]]) ).
thf(464,plain,
! [C: $i,B: $i,A: $i] :
( ( ( vsucc @ ( vsucc @ A ) )
!= B )
| ( ( vplus @ v1 @ A )
!= ( vplus @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[170,375]) ).
thf(465,plain,
! [A: $i] :
( ( vsucc @ ( vsucc @ A ) )
!= v1 ),
inference(pattern_uni,[status(thm)],[464:[bind(A,$thf( A )),bind(B,$thf( v1 )),bind(C,$thf( A ))]]) ).
thf(254,plain,
! [B: $i,A: $i] :
( ( B != A )
| ( geq @ B @ A ) ),
inference(cnf,[status(esa)],[252]) ).
thf(257,plain,
! [B: $i,A: $i] :
( ( B != A )
| ( geq @ B @ A ) ),
inference(lifteq,[status(thm)],[254]) ).
thf(258,plain,
! [A: $i] : ( geq @ A @ A ),
inference(simp,[status(thm)],[257]) ).
thf(114,plain,
! [A: $i] :
( ( sk4 @ ( vsucc @ A ) )
= A ),
introduced(tautology,[new_symbols(inverse(vsucc),[sk4])]) ).
thf(139,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( geq @ C @ D )
| ~ ( geq @ A @ B )
| ( geq @ ( vplus @ A @ C ) @ ( vplus @ B @ D ) ) ),
inference(cnf,[status(esa)],[138]) ).
thf(19345,plain,
( ( vd518 = vd517 )
| ( ( vsucc @ vd520 )
!= vd519 )
| ( ( greater @ vd517 @ vd518 )
!= ( greater @ vd517 @ vd518 ) ) ),
inference(paramod_ordered,[status(thm)],[18839,9972]) ).
thf(19346,plain,
( ( vd518 = vd517 )
| ( ( vsucc @ vd520 )
!= vd519 ) ),
inference(pattern_uni,[status(thm)],[19345:[]]) ).
thf(20017,plain,
! [B: $i,A: $i] :
( ( ( vsucc @ ( vmul @ B @ A ) )
!= ( vmul @ vd517 @ vd519 ) )
| ( ( vmul @ A @ B )
!= ( vmul @ ( vsucc @ vd518 ) @ vd520 ) ) ),
inference(paramod_ordered,[status(thm)],[206,19695]) ).
thf(20018,plain,
( ( vsucc @ ( vmul @ vd520 @ ( vsucc @ vd518 ) ) )
!= ( vmul @ vd517 @ vd519 ) ),
inference(pattern_uni,[status(thm)],[20017:[bind(A,$thf( vsucc @ vd518 )),bind(B,$thf( vd520 ))]]) ).
thf(1912,plain,
! [A: $i] :
( ( less @ v1 @ A )
| ~ ( greater @ vd519 @ ( vmul @ vd518 @ vd520 ) )
| ( A != vd517 )
| ( v1 != v1 ) ),
inference(paramod_ordered,[status(thm)],[1522,291]) ).
thf(1913,plain,
! [A: $i] :
( ( less @ v1 @ A )
| ~ ( greater @ vd519 @ ( vmul @ vd518 @ vd520 ) )
| ( A != vd517 ) ),
inference(pattern_uni,[status(thm)],[1912:[]]) ).
thf(2330,plain,
( ( less @ v1 @ vd517 )
| ~ ( greater @ vd519 @ ( vmul @ vd518 @ vd520 ) ) ),
inference(simp,[status(thm)],[1913]) ).
thf(46,axiom,
! [A: $i,B: $i,C: $i] :
( ( greater @ ( vmul @ A @ B ) @ ( vmul @ C @ B ) )
=> ( greater @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(conjunct1(307), 0), 0)') ).
thf(214,plain,
! [A: $i,B: $i,C: $i] :
( ( greater @ ( vmul @ A @ B ) @ ( vmul @ C @ B ) )
=> ( greater @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(18262,plain,
! [B: $i,A: $i] :
( ( greater @ vd517 @ vd518 )
| ( less @ B @ A )
| ( ( greater @ vd519 @ vd520 )
!= ( greater @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[199,221]) ).
thf(18263,plain,
( ( greater @ vd517 @ vd518 )
| ( less @ vd520 @ vd519 ) ),
inference(pattern_uni,[status(thm)],[18262:[bind(A,$thf( vd519 )),bind(B,$thf( vd520 ))]]) ).
thf(516,plain,
( ( v1 != vd517 )
| ( v1 != vd518 )
| ( v1 != vd519 )
| ( ( greater @ vd517 @ vd520 )
!= ( greater @ vd517 @ vd518 ) ) ),
inference(paramod_ordered,[status(thm)],[394,297]) ).
thf(532,plain,
( ( v1 != vd517 )
| ( v1 != vd518 )
| ( v1 != vd519 )
| ( vd517 != vd517 )
| ( vd520 != vd518 ) ),
inference(simp,[status(thm)],[516]) ).
thf(536,plain,
( ( v1 != vd517 )
| ( v1 != vd518 )
| ( v1 != vd519 )
| ( vd520 != vd518 ) ),
inference(simp,[status(thm)],[532]) ).
thf(2070,plain,
! [A: $i] :
( ( less @ v1 @ A )
| ~ ( greater @ ( vmul @ vd517 @ vd519 ) @ vd518 )
| ( A != vd520 )
| ( v1 != v1 ) ),
inference(paramod_ordered,[status(thm)],[1522,282]) ).
thf(2071,plain,
! [A: $i] :
( ( less @ v1 @ A )
| ~ ( greater @ ( vmul @ vd517 @ vd519 ) @ vd518 )
| ( A != vd520 ) ),
inference(pattern_uni,[status(thm)],[2070:[]]) ).
thf(2218,plain,
( ( less @ v1 @ vd520 )
| ~ ( greater @ ( vmul @ vd517 @ vd519 ) @ vd518 ) ),
inference(simp,[status(thm)],[2071]) ).
thf(1340,plain,
! [A: $i] :
( ( ( vsucc @ ( vsucc @ A ) )
!= ( vmul @ vd517 @ vd519 ) )
| ( ( vmul @ A @ v1 )
!= ( vmul @ vd518 @ vd520 ) ) ),
inference(paramod_ordered,[status(thm)],[195,1301]) ).
thf(1345,plain,
! [A: $i] :
( ( ( vsucc @ ( vsucc @ A ) )
!= ( vmul @ vd517 @ vd519 ) )
| ( A != vd518 )
| ( v1 != vd520 ) ),
inference(simp,[status(thm)],[1340]) ).
thf(1348,plain,
( ( ( vmul @ vd517 @ vd519 )
!= ( vsucc @ ( vsucc @ vd518 ) ) )
| ( v1 != vd520 ) ),
inference(simp,[status(thm)],[1345]) ).
thf(1807,plain,
! [A: $i] :
( ( less @ v1 @ A )
| ~ ( greater @ ( vmul @ vd517 @ vd519 ) @ vd520 )
| ( A != vd518 )
| ( v1 != v1 ) ),
inference(paramod_ordered,[status(thm)],[1522,292]) ).
thf(1808,plain,
! [A: $i] :
( ( less @ v1 @ A )
| ~ ( greater @ ( vmul @ vd517 @ vd519 ) @ vd520 )
| ( A != vd518 ) ),
inference(pattern_uni,[status(thm)],[1807:[]]) ).
thf(2302,plain,
( ( less @ v1 @ vd518 )
| ~ ( greater @ ( vmul @ vd517 @ vd519 ) @ vd520 ) ),
inference(simp,[status(thm)],[1808]) ).
thf(20566,plain,
! [B: $i,A: $i] :
( ( v1 != vd517 )
| ( less @ B @ A )
| ( ( greater @ vd517 @ vd518 )
!= ( greater @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[19365,221]) ).
thf(20567,plain,
( ( v1 != vd517 )
| ( less @ vd518 @ vd517 ) ),
inference(pattern_uni,[status(thm)],[20566:[bind(A,$thf( vd517 )),bind(B,$thf( vd518 ))]]) ).
thf(421,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( vplus @ B @ A )
!= C )
| ( ( vplus @ A @ B )
!= ( vplus @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[77,74]) ).
thf(422,plain,
! [B: $i,A: $i] :
( ( vplus @ B @ A )
!= A ),
inference(pattern_uni,[status(thm)],[421:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(600,plain,
! [A: $i] :
( ( v1 != vd517 )
| ( v1 != vd518 )
| ( ( greater @ ( vsucc @ A ) @ A )
!= ( greater @ vd519 @ vd520 ) ) ),
inference(paramod_ordered,[status(thm)],[474,323]) ).
thf(610,plain,
! [A: $i] :
( ( v1 != vd517 )
| ( v1 != vd518 )
| ( ( vsucc @ A )
!= vd519 )
| ( A != vd520 ) ),
inference(simp,[status(thm)],[600]) ).
thf(614,plain,
( ( v1 != vd517 )
| ( v1 != vd518 )
| ( ( vsucc @ vd520 )
!= vd519 ) ),
inference(simp,[status(thm)],[610]) ).
thf(1747,plain,
! [A: $i] :
( ( less @ v1 @ A )
| ( A != vd517 )
| ( v1 != vd518 )
| ( ( vsucc @ vd520 )
!= vd519 )
| ( v1 != v1 ) ),
inference(paramod_ordered,[status(thm)],[1522,614]) ).
thf(1748,plain,
! [A: $i] :
( ( less @ v1 @ A )
| ( A != vd517 )
| ( v1 != vd518 )
| ( ( vsucc @ vd520 )
!= vd519 ) ),
inference(pattern_uni,[status(thm)],[1747:[]]) ).
thf(2287,plain,
( ( less @ v1 @ vd517 )
| ( v1 != vd518 )
| ( ( vsucc @ vd520 )
!= vd519 ) ),
inference(simp,[status(thm)],[1748]) ).
thf(834,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( greater @ ( vplus @ B @ A ) @ D )
| ( ( vplus @ A @ B )
!= ( vplus @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[77,483]) ).
thf(835,plain,
! [B: $i,A: $i] : ( greater @ ( vplus @ B @ A ) @ B ),
inference(pattern_uni,[status(thm)],[834:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(261,plain,
! [C: $i,B: $i,A: $i] :
( ( vmul @ ( vmul @ A @ B ) @ C )
= ( vmul @ A @ ( vmul @ B @ C ) ) ),
inference(cnf,[status(esa)],[260]) ).
thf(262,plain,
! [C: $i,B: $i,A: $i] :
( ( vmul @ ( vmul @ A @ B ) @ C )
= ( vmul @ A @ ( vmul @ B @ C ) ) ),
inference(lifteq,[status(thm)],[261]) ).
thf(210,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( less @ ( vmul @ A @ B ) @ ( vmul @ C @ B ) )
| ( less @ A @ C ) ),
inference(cnf,[status(esa)],[209]) ).
thf(1359,plain,
! [A: $i] :
( ( ( vsucc @ ( vsucc @ A ) )
!= vd517 )
| ( v1 != vd519 )
| ( ( vmul @ A @ v1 )
!= ( vmul @ vd518 @ vd520 ) ) ),
inference(paramod_ordered,[status(thm)],[195,1347]) ).
thf(1361,plain,
! [A: $i] :
( ( ( vsucc @ ( vsucc @ A ) )
!= vd517 )
| ( v1 != vd519 )
| ( A != vd518 )
| ( v1 != vd520 ) ),
inference(simp,[status(thm)],[1359]) ).
thf(1363,plain,
( ( ( vsucc @ ( vsucc @ vd518 ) )
!= vd517 )
| ( v1 != vd519 )
| ( v1 != vd520 ) ),
inference(simp,[status(thm)],[1361]) ).
thf(126,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( less @ B @ C )
| ~ ( less @ A @ B )
| ( less @ A @ C ) ),
inference(cnf,[status(esa)],[125]) ).
thf(2023,plain,
! [A: $i] :
( ( less @ v1 @ A )
| ( A != vd519 )
| ( v1 != vd518 )
| ( ( vsucc @ vd520 )
!= vd517 )
| ( v1 != v1 ) ),
inference(paramod_ordered,[status(thm)],[1522,621]) ).
thf(2024,plain,
! [A: $i] :
( ( less @ v1 @ A )
| ( A != vd519 )
| ( v1 != vd518 )
| ( ( vsucc @ vd520 )
!= vd517 ) ),
inference(pattern_uni,[status(thm)],[2023:[]]) ).
thf(2353,plain,
( ( less @ v1 @ vd519 )
| ( v1 != vd518 )
| ( ( vsucc @ vd520 )
!= vd517 ) ),
inference(simp,[status(thm)],[2024]) ).
thf(519,plain,
( ( v1 != vd517 )
| ( v1 != vd518 )
| ( ( greater @ vd519 @ ( vmul @ vd518 @ vd520 ) )
!= ( greater @ vd517 @ vd518 ) ) ),
inference(paramod_ordered,[status(thm)],[394,291]) ).
thf(528,plain,
( ( v1 != vd517 )
| ( v1 != vd518 )
| ( vd519 != vd517 )
| ( ( vmul @ vd518 @ vd520 )
!= vd518 ) ),
inference(simp,[status(thm)],[519]) ).
thf(1353,plain,
! [A: $i] :
( ( v1 != vd517 )
| ( ( vsucc @ ( vsucc @ A ) )
!= vd519 )
| ( ( vmul @ A @ v1 )
!= ( vmul @ vd518 @ vd520 ) ) ),
inference(paramod_ordered,[status(thm)],[195,1344]) ).
thf(1355,plain,
! [A: $i] :
( ( v1 != vd517 )
| ( ( vsucc @ ( vsucc @ A ) )
!= vd519 )
| ( A != vd518 )
| ( v1 != vd520 ) ),
inference(simp,[status(thm)],[1353]) ).
thf(1357,plain,
( ( v1 != vd517 )
| ( ( vsucc @ ( vsucc @ vd518 ) )
!= vd519 )
| ( v1 != vd520 ) ),
inference(simp,[status(thm)],[1355]) ).
thf(9065,plain,
( ( greater @ vd517 @ vd518 )
| ( less @ vd518 @ vd517 )
| ( less @ v1 @ vd517 )
| ( vd518 != vd518 ) ),
inference(paramod_ordered,[status(thm)],[3347,4284]) ).
thf(9066,plain,
( ( greater @ vd517 @ vd518 )
| ( less @ vd518 @ vd517 )
| ( less @ v1 @ vd517 ) ),
inference(pattern_uni,[status(thm)],[9065:[]]) ).
thf(7255,plain,
! [A: $i] :
( ~ ( less @ A @ ( vmul @ vd517 @ vd519 ) )
| ( ( vmul @ A @ v1 )
!= ( vmul @ vd518 @ vd520 ) ) ),
inference(paramod_ordered,[status(thm)],[195,7127]) ).
thf(7274,plain,
! [A: $i] :
( ~ ( less @ A @ ( vmul @ vd517 @ vd519 ) )
| ( A != vd518 )
| ( v1 != vd520 ) ),
inference(simp,[status(thm)],[7255]) ).
thf(7299,plain,
( ~ ( less @ vd518 @ ( vmul @ vd517 @ vd519 ) )
| ( v1 != vd520 ) ),
inference(simp,[status(thm)],[7274]) ).
thf(215,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( greater @ ( vmul @ A @ B ) @ ( vmul @ C @ B ) )
| ( greater @ A @ C ) ),
inference(cnf,[status(esa)],[214]) ).
thf(24621,plain,
! [B: $i,A: $i] :
( ( v1 = vd518 )
| ( greater @ B @ A )
| ( ( less @ v1 @ vd517 )
!= ( less @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[22421,223]) ).
thf(24622,plain,
( ( v1 = vd518 )
| ( greater @ vd517 @ v1 ) ),
inference(pattern_uni,[status(thm)],[24621:[bind(A,$thf( v1 )),bind(B,$thf( vd517 ))]]) ).
thf(1047,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( vsucc @ ( vsucc @ ( vplus @ A @ B ) ) )
!= v1 )
| ( ( vplus @ A @ ( vsucc @ B ) )
!= ( vplus @ ( vsucc @ C ) @ D ) ) ),
inference(paramod_ordered,[status(thm)],[70,666]) ).
thf(1048,plain,
! [B: $i,A: $i] :
( ( vsucc @ ( vsucc @ ( vplus @ ( vsucc @ A ) @ B ) ) )
!= v1 ),
inference(pattern_uni,[status(thm)],[1047:[bind(A,$thf( vsucc @ E )),bind(B,$thf( F )),bind(C,$thf( E )),bind(D,$thf( vsucc @ F ))]]) ).
thf(1061,plain,
! [B: $i,A: $i] :
( ( vsucc @ ( vsucc @ ( vplus @ ( vsucc @ A ) @ B ) ) )
!= v1 ),
inference(simp,[status(thm)],[1048]) ).
thf(1584,plain,
! [C: $i,B: $i,A: $i] :
( ( ( vsucc @ ( vsucc @ ( vsucc @ A ) ) )
!= v1 )
| ( ( vplus @ A @ v1 )
!= ( vplus @ ( vsucc @ B ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[69,1061]) ).
thf(1585,plain,
! [A: $i] :
( ( vsucc @ ( vsucc @ ( vsucc @ ( vsucc @ A ) ) ) )
!= v1 ),
inference(pattern_uni,[status(thm)],[1584:[bind(A,$thf( vsucc @ D )),bind(B,$thf( D )),bind(C,$thf( v1 ))]]) ).
thf(1606,plain,
! [A: $i] :
( ( vsucc @ ( vsucc @ ( vsucc @ ( vsucc @ A ) ) ) )
!= v1 ),
inference(simp,[status(thm)],[1585]) ).
thf(1875,plain,
! [A: $i] :
( ( less @ v1 @ A )
| ( A != vd518 )
| ( ( vmul @ vd517 @ vd519 )
!= ( vsucc @ vd520 ) )
| ( v1 != v1 ) ),
inference(paramod_ordered,[status(thm)],[1522,618]) ).
thf(1876,plain,
! [A: $i] :
( ( less @ v1 @ A )
| ( A != vd518 )
| ( ( vmul @ vd517 @ vd519 )
!= ( vsucc @ vd520 ) ) ),
inference(pattern_uni,[status(thm)],[1875:[]]) ).
thf(2321,plain,
( ( less @ v1 @ vd518 )
| ( ( vmul @ vd517 @ vd519 )
!= ( vsucc @ vd520 ) ) ),
inference(simp,[status(thm)],[1876]) ).
thf(468,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( vsucc @ ( vplus @ A @ B ) )
!= C )
| ( ( vplus @ B @ A )
!= ( vplus @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[77,375]) ).
thf(469,plain,
! [B: $i,A: $i] :
( ( vsucc @ ( vplus @ A @ B ) )
!= B ),
inference(pattern_uni,[status(thm)],[468:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A ))]]) ).
thf(41336,plain,
$false,
inference(e,[status(thm)],[69,24195,2341,333,22521,88,138,23996,101,2336,24400,2331,19687,170,115,1522,7516,202,14409,217,276,120,247,384,153,20885,23144,185,5750,13923,21911,23465,389,184,110,619,125,196,157,23134,1347,1362,14051,2403,189,7183,78,164,13863,23166,211,485,238,84,20579,216,147,13865,17206,61,221,18842,89,22421,243,265,19812,74,24352,6210,206,1074,292,248,529,20652,201,761,381,220,102,534,13519,2296,2307,260,24059,165,22346,297,70,4284,137,92,17245,2477,97,7625,17114,19800,224,8920,197,17232,156,188,7513,15466,14381,124,77,537,476,642,17239,96,109,256,24206,25629,24783,1060,173,24065,30435,14875,134,20730,237,244,792,20620,20614,2338,14573,298,412,13989,6699,148,264,64,1301,618,4919,161,19365,375,733,176,2225,743,291,18839,259,281,204,17115,71,13319,5033,2308,144,181,7741,35718,13935,20724,2319,1356,2361,187,172,113,219,1349,2246,230,245,509,20479,34650,616,303,271,208,19372,14262,140,483,1344,155,198,7297,5035,19898,799,213,621,91,240,251,8423,130,20660,223,135,226,241,167,5424,4394,6672,2318,7298,4529,209,1081,14438,123,19757,162,19695,63,640,2397,24777,282,14485,95,2407,263,25786,13948,199,23613,127,24196,7127,2354,177,182,463,2337,2247,6701,744,613,154,23070,612,18926,99,20764,87,759,218,250,465,231,258,20540,114,139,24048,19346,20018,158,18818,17020,20314,171,75,9972,207,2330,1308,82,214,18263,536,2218,1348,2302,20567,19432,190,183,422,2287,620,168,835,262,210,107,1363,474,94,126,22037,195,4474,2353,17103,19183,528,1357,9737,131,200,62,9066,7299,111,19856,215,24622,100,227,1606,2321,469,222,7295]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM856+2 : TPTP v8.2.0. Released v4.1.0.
% 0.07/0.12 % Command : run_Leo-III %s %d THM
% 0.11/0.33 % Computer : n026.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Sat Jun 22 20:22:55 EDT 2024
% 0.11/0.33 % CPUTime :
% 1.16/1.07 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.64/1.29 % [INFO] Parsing done (220ms).
% 1.64/1.31 % [INFO] Running in sequential loop mode.
% 2.34/1.71 % [INFO] eprover registered as external prover.
% 2.34/1.72 % [INFO] Scanning for conjecture ...
% 2.60/1.83 % [INFO] Found a conjecture (or negated_conjecture) and 58 axioms. Running axiom selection ...
% 2.67/1.92 % [INFO] Axiom selection finished. Selected 58 axioms (removed 0 axioms).
% 3.02/2.03 % [INFO] Problem is first-order (TPTP FOF).
% 3.18/2.04 % [INFO] Type checking passed.
% 3.18/2.05 % [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 ...
% 79.21/18.68 % External prover 'e' found a proof!
% 79.21/18.68 % [INFO] Killing All external provers ...
% 79.21/18.68 % Time passed: 18155ms (effective reasoning time: 17368ms)
% 79.21/18.68 % 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)>
% 79.21/18.69 % Axioms used in derivation (58): ass(cond(223, 0), 0), ass(cond(6, 0), 0), def(cond(conseq(axiom(3)), 16), 1), ass(cond(228, 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(81, 0), 0), ass(cond(conjunct2(conjunct2(307)), 0), 0), ass(cond(goal(193), 0), 0), ass(cond(goal(130), 0), 1), ass(cond(163, 0), 0), ass(cond(goal(177), 0), 0), ass(cond(goal(193), 0), 2), def(cond(conseq(axiom(3)), 11), 1), ass(cond(312, 0), 0), ass(cond(299, 0), 0), ass(cond(299, 0), 2), ass(cond(299, 0), 1), 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), 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), ass(cond(184, 0), 0), ass(cond(goal(88), 0), 2), dis(antec(scope(318))), 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(conjunct1(307), 0), 0), ass(cond(20, 0), 0), ass(cond(goal(202), 0), 1), ass(cond(goal(216), 0), 0), ass(cond(281, 0), 0), ass(cond(253, 0), 0), qu(antec(axiom(3)), imp(antec(axiom(3)))), ass(cond(209, 0), 0), ass(cond(261, 0), 0), ass(cond(52, 0), 0), ass(cond(conjunct1(conjunct2(307)), 0), 0), ass(cond(158, 0), 0), ass(cond(234, 0), 0), ass(cond(33, 0), 0), ass(cond(290, 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)
% 79.21/18.69 % No. of inferences in proof: 823
% 79.21/18.69 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 18155 ms resp. 17368 ms w/o parsing
% 80.12/18.91 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 80.12/18.92 % [INFO] Killing All external provers ...
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