TSTP Solution File: NUM855+1 by Leo-III---1.7.15
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.15
% Problem : NUM855+1 : TPTP v8.2.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n021.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 17.11s 4.22s
% Output : Refutation 17.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 65
% Syntax : Number of formulae : 203 ( 82 unt; 0 typ; 0 def)
% Number of atoms : 385 ( 203 equ; 0 cnn)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 1210 ( 123 ~; 72 |; 28 &; 915 @)
% ( 4 <=>; 68 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 15 usr; 6 con; 0-2 aty)
% Number of variables : 360 ( 0 ^ 340 !; 20 ?; 360 :)
% Comments :
%------------------------------------------------------------------------------
thf(greater_type,type,
greater: $i > $i > $o ).
thf(vmul_type,type,
vmul: $i > $i > $i ).
thf(vd508_type,type,
vd508: $i ).
thf(vd511_type,type,
vd511: $i ).
thf(vd509_type,type,
vd509: $i ).
thf(vd512_type,type,
vd512: $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(sk4_type,type,
sk4: $i > $i ).
thf(sk6_type,type,
sk6: $i > $i ).
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(142,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(58,axiom,
greater @ ( vmul @ vd508 @ vd511 ) @ ( vmul @ vd509 @ vd511 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','holds(conjunct1(315), 514, 0)') ).
thf(248,plain,
greater @ ( vmul @ vd508 @ vd511 ) @ ( vmul @ vd509 @ vd511 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
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(169,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(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(129,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(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(139,plain,
! [A: $i,B: $i] :
( ( vplus @ ( vsucc @ A ) @ B )
= ( vsucc @ ( vplus @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(51,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(227,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)],[51]) ).
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(135,plain,
! [A: $i,B: $i] :
( ( A != B )
| ~ ( less @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(136,plain,
! [B: $i,A: $i] :
( ( A != B )
| ~ ( less @ A @ B ) ),
inference(cnf,[status(esa)],[135]) ).
thf(137,plain,
! [B: $i,A: $i] :
( ( A != B )
| ~ ( less @ A @ B ) ),
inference(lifteq,[status(thm)],[136]) ).
thf(138,plain,
! [A: $i] :
~ ( less @ A @ A ),
inference(simp,[status(thm)],[137]) ).
thf(13,axiom,
! [A: $i] :
( ( A != v1 )
=> ( A
= ( vsucc @ ( vskolem2 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(20, 0), 0)') ).
thf(101,plain,
! [A: $i] :
( ( A != v1 )
=> ( A
= ( vsucc @ ( vskolem2 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(59,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(249,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)],[59]) ).
thf(61,axiom,
! [A: $i] :
( ( vmul @ v1 @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(253, 0), 0)') ).
thf(259,plain,
! [A: $i] :
( ( vmul @ v1 @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(260,plain,
! [A: $i] :
( ( vmul @ v1 @ A )
= A ),
inference(cnf,[status(esa)],[259]) ).
thf(261,plain,
! [A: $i] :
( ( vmul @ v1 @ A )
= A ),
inference(lifteq,[status(thm)],[260]) ).
thf(40,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(198,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)],[40]) ).
thf(199,plain,
( ! [A: $i,B: $i] :
( ( vmul @ A @ ( vsucc @ B ) )
= ( vplus @ ( vmul @ A @ B ) @ A ) )
& ! [A: $i] :
( ( vmul @ A @ v1 )
= A ) ),
inference(miniscope,[status(thm)],[198]) ).
thf(200,plain,
! [A: $i] :
( ( vmul @ A @ v1 )
= A ),
inference(cnf,[status(esa)],[199]) ).
thf(202,plain,
! [A: $i] :
( ( vmul @ A @ v1 )
= A ),
inference(lifteq,[status(thm)],[200]) ).
thf(203,plain,
! [A: $i] :
( ( vmul @ A @ v1 )
= A ),
inference(simp,[status(thm)],[202]) ).
thf(55,axiom,
( ( vmul @ vd509 @ vd511 )
= ( vmul @ vd511 @ vd509 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','holds(conjunct2(315), 515, 0)') ).
thf(241,plain,
( ( vmul @ vd509 @ vd511 )
= ( vmul @ vd511 @ vd509 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(242,plain,
( ( vmul @ vd509 @ vd511 )
= ( vmul @ vd511 @ vd509 ) ),
inference(lifteq,[status(thm)],[241]) ).
thf(349,plain,
greater @ ( vmul @ vd508 @ vd511 ) @ ( vmul @ vd511 @ vd509 ),
inference(rewrite,[status(thm)],[248,242]) ).
thf(1,conjecture,
greater @ ( vmul @ vd508 @ vd511 ) @ ( vmul @ vd509 @ vd512 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','holds(conseq_conjunct2(315), 516, 0)') ).
thf(2,negated_conjecture,
~ ( greater @ ( vmul @ vd508 @ vd511 ) @ ( vmul @ vd509 @ vd512 ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(65,plain,
~ ( greater @ ( vmul @ vd508 @ vd511 ) @ ( vmul @ vd509 @ vd512 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(350,plain,
( ( greater @ ( vmul @ vd508 @ vd511 ) @ ( vmul @ vd509 @ vd512 ) )
!= ( greater @ ( vmul @ vd508 @ vd511 ) @ ( vmul @ vd511 @ vd509 ) ) ),
inference(paramod_ordered,[status(thm)],[349,65]) ).
thf(357,plain,
( ( ( vmul @ vd508 @ vd511 )
!= ( vmul @ vd508 @ vd511 ) )
| ( ( vmul @ vd509 @ vd512 )
!= ( vmul @ vd511 @ vd509 ) ) ),
inference(simp,[status(thm)],[350]) ).
thf(361,plain,
( ( vmul @ vd509 @ vd512 )
!= ( vmul @ vd511 @ vd509 ) ),
inference(simp,[status(thm)],[357]) ).
thf(406,plain,
! [A: $i] :
( ( A
!= ( vmul @ vd511 @ vd509 ) )
| ( ( vmul @ A @ v1 )
!= ( vmul @ vd509 @ vd512 ) ) ),
inference(paramod_ordered,[status(thm)],[203,361]) ).
thf(419,plain,
( ( ( vmul @ vd511 @ vd509 )
!= vd509 )
| ( v1 != vd512 ) ),
inference(simp,[status(thm)],[406]) ).
thf(479,plain,
! [A: $i] :
( ( A != vd509 )
| ( v1 != vd512 )
| ( ( vmul @ v1 @ A )
!= ( vmul @ vd511 @ vd509 ) ) ),
inference(paramod_ordered,[status(thm)],[261,419]) ).
thf(499,plain,
( ( v1 != vd512 )
| ( v1 != vd511 )
| ( vd509 != vd509 ) ),
inference(simp,[status(thm)],[479]) ).
thf(518,plain,
( ( v1 != vd512 )
| ( v1 != vd511 ) ),
inference(simp,[status(thm)],[499]) ).
thf(228,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)],[227]) ).
thf(230,plain,
! [B: $i,A: $i] :
( ( B != A )
| ( geq @ B @ A ) ),
inference(cnf,[status(esa)],[228]) ).
thf(233,plain,
! [B: $i,A: $i] :
( ( B != A )
| ( geq @ B @ A ) ),
inference(lifteq,[status(thm)],[230]) ).
thf(234,plain,
! [A: $i] : ( geq @ A @ A ),
inference(simp,[status(thm)],[233]) ).
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(88,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(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(115,plain,
! [A: $i,B: $i] :
( ( ( vsucc @ A )
= ( vsucc @ B ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
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(217,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(57,axiom,
greater @ vd511 @ vd512,
file('/export/starexec/sandbox/benchmark/theBenchmark.p','holds(conjunct2(314), 513, 0)') ).
thf(247,plain,
greater @ vd511 @ vd512,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
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(185,plain,
! [A: $i,B: $i] : ( greater @ ( vplus @ A @ B ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(52,axiom,
greater @ ( vmul @ vd511 @ vd509 ) @ ( vmul @ vd512 @ vd509 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','holds(conjunct2(315), 515, 1)') ).
thf(236,plain,
greater @ ( vmul @ vd511 @ vd509 ) @ ( vmul @ vd512 @ vd509 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(38,axiom,
( ( vmul @ vd512 @ vd509 )
= ( vmul @ vd509 @ vd512 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','holds(conjunct2(315), 515, 2)') ).
thf(192,plain,
( ( vmul @ vd512 @ vd509 )
= ( vmul @ vd509 @ vd512 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(193,plain,
( ( vmul @ vd512 @ vd509 )
= ( vmul @ vd509 @ vd512 ) ),
inference(lifteq,[status(thm)],[192]) ).
thf(320,plain,
greater @ ( vmul @ vd511 @ vd509 ) @ ( vmul @ vd509 @ vd512 ),
inference(rewrite,[status(thm)],[236,193]) ).
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(93,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(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(152,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(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(75,plain,
! [A: $i,B: $i] :
( ( A != B )
| ~ ? [C: $i] :
( A
= ( vplus @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(76,plain,
! [C: $i,B: $i,A: $i] :
( ( A != B )
| ( A
!= ( vplus @ B @ C ) ) ),
inference(cnf,[status(esa)],[75]) ).
thf(77,plain,
! [C: $i,B: $i,A: $i] :
( ( A != B )
| ( A
!= ( vplus @ B @ C ) ) ),
inference(lifteq,[status(thm)],[76]) ).
thf(78,plain,
! [B: $i,A: $i] :
( ( vplus @ A @ B )
!= A ),
inference(simp,[status(thm)],[77]) ).
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(106,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(54,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(238,plain,
! [A: $i,B: $i] :
( ( vmul @ ( vsucc @ A ) @ B )
= ( vplus @ ( vmul @ A @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
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(221,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(56,axiom,
! [A: $i,B: $i] :
( ( A != B )
| ~ ( greater @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(130), 0), 3)') ).
thf(243,plain,
! [A: $i,B: $i] :
( ( A != B )
| ~ ( greater @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(63,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(265,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)],[63]) ).
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(68,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(69,plain,
( ! [A: $i,B: $i] :
( ( vplus @ A @ ( vsucc @ B ) )
= ( vsucc @ ( vplus @ A @ B ) ) )
& ! [A: $i] :
( ( vplus @ A @ v1 )
= ( vsucc @ A ) ) ),
inference(miniscope,[status(thm)],[68]) ).
thf(71,plain,
! [B: $i,A: $i] :
( ( vplus @ A @ ( vsucc @ B ) )
= ( vsucc @ ( vplus @ A @ B ) ) ),
inference(cnf,[status(esa)],[69]) ).
thf(74,plain,
! [B: $i,A: $i] :
( ( vplus @ A @ ( vsucc @ B ) )
= ( vsucc @ ( vplus @ A @ B ) ) ),
inference(lifteq,[status(thm)],[71]) ).
thf(28,axiom,
! [A: $i] :
( ( vsucc @ A )
!= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(12, 0), 0)') ).
thf(162,plain,
! [A: $i] :
( ( vsucc @ A )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(163,plain,
~ ? [A: $i] :
( ( vsucc @ A )
= A ),
inference(miniscope,[status(thm)],[162]) ).
thf(164,plain,
! [A: $i] :
( ( vsucc @ A )
!= A ),
inference(cnf,[status(esa)],[163]) ).
thf(165,plain,
! [A: $i] :
( ( vsucc @ A )
!= A ),
inference(lifteq,[status(thm)],[164]) ).
thf(321,plain,
( ( greater @ ( vmul @ vd511 @ vd509 ) @ ( vmul @ vd509 @ vd512 ) )
!= ( greater @ ( vmul @ vd508 @ vd511 ) @ ( vmul @ vd509 @ vd512 ) ) ),
inference(paramod_ordered,[status(thm)],[320,65]) ).
thf(327,plain,
( ( ( vmul @ vd511 @ vd509 )
!= ( vmul @ vd508 @ vd511 ) )
| ( ( vmul @ vd509 @ vd512 )
!= ( vmul @ vd509 @ vd512 ) ) ),
inference(simp,[status(thm)],[321]) ).
thf(332,plain,
( ( vmul @ vd511 @ vd509 )
!= ( vmul @ vd508 @ vd511 ) ),
inference(simp,[status(thm)],[327]) ).
thf(411,plain,
! [A: $i] :
( ( A
!= ( vmul @ vd508 @ vd511 ) )
| ( ( vmul @ A @ v1 )
!= ( vmul @ vd511 @ vd509 ) ) ),
inference(paramod_ordered,[status(thm)],[203,332]) ).
thf(430,plain,
( ( ( vmul @ vd508 @ vd511 )
!= vd511 )
| ( v1 != vd509 ) ),
inference(simp,[status(thm)],[411]) ).
thf(476,plain,
! [A: $i] :
( ( A != vd511 )
| ( v1 != vd509 )
| ( ( vmul @ v1 @ A )
!= ( vmul @ vd508 @ vd511 ) ) ),
inference(paramod_ordered,[status(thm)],[261,430]) ).
thf(508,plain,
( ( v1 != vd509 )
| ( v1 != vd508 )
| ( vd511 != vd511 ) ),
inference(simp,[status(thm)],[476]) ).
thf(522,plain,
( ( v1 != vd509 )
| ( v1 != vd508 ) ),
inference(simp,[status(thm)],[508]) ).
thf(60,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(256,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)],[60]) ).
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(212,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(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(96,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(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(124,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(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(225,plain,
! [A: $i,B: $i] :
( ( less @ A @ B )
=> ( greater @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
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(131,plain,
! [A: $i,B: $i] :
( ( A != B )
=> ( ( vsucc @ A )
!= ( vsucc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(132,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( vsucc @ A )
!= ( vsucc @ B ) ) ),
inference(cnf,[status(esa)],[131]) ).
thf(133,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( vsucc @ A )
!= ( vsucc @ B ) ) ),
inference(lifteq,[status(thm)],[132]) ).
thf(134,plain,
! [A: $i] :
( ( sk6 @ ( vsucc @ A ) )
= A ),
introduced(tautology,[new_symbols(inverse(vsucc),[sk6])]) ).
thf(70,plain,
! [A: $i] :
( ( vplus @ A @ v1 )
= ( vsucc @ A ) ),
inference(cnf,[status(esa)],[69]) ).
thf(72,plain,
! [A: $i] :
( ( vplus @ A @ v1 )
= ( vsucc @ A ) ),
inference(lifteq,[status(thm)],[70]) ).
thf(73,plain,
! [A: $i] :
( ( vplus @ A @ v1 )
= ( vsucc @ A ) ),
inference(simp,[status(thm)],[72]) ).
thf(53,axiom,
greater @ vd508 @ vd509,
file('/export/starexec/sandbox/benchmark/theBenchmark.p','holds(conjunct1(314), 510, 0)') ).
thf(237,plain,
greater @ vd508 @ vd509,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
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(205,plain,
! [A: $i,B: $i] :
( ( greater @ A @ B )
=> ( geq @ A @ ( vplus @ B @ v1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
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(166,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(25,axiom,
! [A: $i,B: $i] :
( B
!= ( vplus @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(73, 0), 0)') ).
thf(148,plain,
! [A: $i,B: $i] :
( B
!= ( vplus @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
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(177,plain,
! [A: $i] :
( ( vsucc @ A )
!= v1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(178,plain,
~ ? [A: $i] :
( ( vsucc @ A )
= v1 ),
inference(miniscope,[status(thm)],[177]) ).
thf(179,plain,
! [A: $i] :
( ( vsucc @ A )
!= v1 ),
inference(cnf,[status(esa)],[178]) ).
thf(180,plain,
! [A: $i] :
( ( vsucc @ A )
!= v1 ),
inference(lifteq,[status(thm)],[179]) ).
thf(32,axiom,
! [A: $i] : ( geq @ A @ v1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(228, 0), 0)') ).
thf(175,plain,
! [A: $i] : ( geq @ A @ v1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(176,plain,
! [A: $i] : ( geq @ A @ v1 ),
inference(cnf,[status(esa)],[175]) ).
thf(116,plain,
! [B: $i,A: $i] :
( ( ( vsucc @ A )
!= ( vsucc @ B ) )
| ( A = B ) ),
inference(cnf,[status(esa)],[115]) ).
thf(117,plain,
! [B: $i,A: $i] :
( ( ( vsucc @ A )
!= ( vsucc @ B ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[116]) ).
thf(118,plain,
! [A: $i] :
( ( sk4 @ ( vsucc @ A ) )
= A ),
introduced(tautology,[new_symbols(inverse(vsucc),[sk4])]) ).
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(144,plain,
! [A: $i,B: $i] :
( ( A != B )
| ~ ? [C: $i] :
( B
= ( vplus @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
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(181,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(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(86,plain,
! [A: $i,B: $i] :
( ( less @ A @ ( vplus @ B @ v1 ) )
=> ( leq @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
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(159,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(36,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(187,plain,
! [A: $i,B: $i] :
( ( A = B )
| ( greater @ A @ B )
| ( less @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(31,axiom,
! [A: $i] :
( ( vplus @ v1 @ A )
= ( vsucc @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(43, 0), 0)') ).
thf(172,plain,
! [A: $i] :
( ( vplus @ v1 @ A )
= ( vsucc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(107,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)],[106]) ).
thf(109,plain,
! [B: $i,A: $i] :
( ( B != A )
| ( leq @ B @ A ) ),
inference(cnf,[status(esa)],[107]) ).
thf(112,plain,
! [B: $i,A: $i] :
( ( B != A )
| ( leq @ B @ A ) ),
inference(lifteq,[status(thm)],[109]) ).
thf(113,plain,
! [A: $i] : ( leq @ A @ A ),
inference(simp,[status(thm)],[112]) ).
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(219,plain,
! [A: $i,B: $i] :
( ~ ( greater @ A @ B )
| ~ ( less @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(272,plain,
( ( greater @ ( vmul @ vd508 @ vd511 ) @ ( vmul @ vd509 @ vd512 ) )
!= ( greater @ vd508 @ vd509 ) ),
inference(paramod_ordered,[status(thm)],[237,65]) ).
thf(274,plain,
( ( ( vmul @ vd508 @ vd511 )
!= vd508 )
| ( ( vmul @ vd509 @ vd512 )
!= vd509 ) ),
inference(simp,[status(thm)],[272]) ).
thf(370,plain,
( ( vmul @ vd509 @ vd512 )
!= ( vmul @ vd509 @ vd511 ) ),
inference(paramod_ordered,[status(thm)],[242,361]) ).
thf(374,plain,
( ( vd509 != vd509 )
| ( vd512 != vd511 ) ),
inference(simp,[status(thm)],[370]) ).
thf(377,plain,
vd512 != vd511,
inference(simp,[status(thm)],[374]) ).
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(66,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(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(223,plain,
! [A: $i,B: $i] :
( ( greater @ A @ B )
=> ( less @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(39,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(194,plain,
! [A: $i,B: $i,C: $i] :
( ( ( vmul @ A @ B )
= ( vmul @ C @ B ) )
=> ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(67,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( leq @ B @ C )
| ~ ( leq @ A @ B )
| ( leq @ A @ C ) ),
inference(cnf,[status(esa)],[66]) ).
thf(336,plain,
( ( vd511 != vd508 )
| ( vd509 != vd511 ) ),
inference(simp,[status(thm)],[332]) ).
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(99,plain,
! [A: $i,B: $i] :
( ( leq @ A @ B )
=> ( geq @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
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(104,plain,
! [A: $i,B: $i] :
( ( geq @ A @ B )
=> ( leq @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(368,plain,
( ( vd509 != vd511 )
| ( vd512 != vd509 ) ),
inference(simp,[status(thm)],[361]) ).
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(119,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(244,plain,
! [B: $i,A: $i] :
( ( A != B )
| ~ ( greater @ A @ B ) ),
inference(cnf,[status(esa)],[243]) ).
thf(245,plain,
! [B: $i,A: $i] :
( ( A != B )
| ~ ( greater @ A @ B ) ),
inference(lifteq,[status(thm)],[244]) ).
thf(246,plain,
! [A: $i] :
~ ( greater @ A @ A ),
inference(simp,[status(thm)],[245]) ).
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(207,plain,
! [A: $i,B: $i] :
( ( vmul @ A @ B )
= ( vmul @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
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(82,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(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(214,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(62,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(262,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)],[62]) ).
thf(37,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(190,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)],[37]) ).
thf(271,plain,
( ( greater @ ( vmul @ vd508 @ vd511 ) @ ( vmul @ vd509 @ vd512 ) )
!= ( greater @ vd511 @ vd512 ) ),
inference(paramod_ordered,[status(thm)],[247,65]) ).
thf(273,plain,
( ( ( vmul @ vd508 @ vd511 )
!= vd511 )
| ( ( vmul @ vd509 @ vd512 )
!= vd512 ) ),
inference(simp,[status(thm)],[271]) ).
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(210,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(64,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(268,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)],[64]) ).
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(79,plain,
! [A: $i,B: $i] :
( ( vplus @ B @ A )
= ( vplus @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(387,plain,
! [A: $i] :
( ( greater @ vd508 @ vd509 )
!= ( greater @ A @ A ) ),
inference(paramod_ordered,[status(thm)],[237,246]) ).
thf(391,plain,
! [A: $i] :
( ( vd508 != A )
| ( vd509 != A ) ),
inference(simp,[status(thm)],[387]) ).
thf(395,plain,
vd509 != vd508,
inference(simp,[status(thm)],[391]) ).
thf(5318,plain,
$false,
inference(e,[status(thm)],[142,248,169,129,139,227,138,101,249,518,234,88,115,217,247,185,320,93,152,78,261,106,238,221,243,265,74,349,192,165,522,361,65,256,193,212,96,124,225,134,73,237,205,430,166,148,180,176,118,259,144,236,181,86,159,187,172,113,219,274,419,377,66,198,223,135,241,162,194,67,177,336,175,99,203,104,368,75,119,246,207,82,214,262,190,273,210,242,268,79,395,332,131,68]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM855+1 : TPTP v8.2.0. Released v4.1.0.
% 0.03/0.12 % Command : run_Leo-III %s %d THM
% 0.12/0.33 % Computer : n021.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sun Jun 23 01:07:10 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.99/0.91 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.35/1.06 % [INFO] Parsing done (145ms).
% 1.35/1.07 % [INFO] Running in sequential loop mode.
% 1.86/1.28 % [INFO] eprover registered as external prover.
% 1.86/1.28 % [INFO] Scanning for conjecture ...
% 2.08/1.34 % [INFO] Found a conjecture (or negated_conjecture) and 62 axioms. Running axiom selection ...
% 2.22/1.39 % [INFO] Axiom selection finished. Selected 62 axioms (removed 0 axioms).
% 2.22/1.46 % [INFO] Problem is first-order (TPTP FOF).
% 2.58/1.46 % [INFO] Type checking passed.
% 2.58/1.47 % [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 ...
% 17.11/4.22 % External prover 'e' found a proof!
% 17.11/4.22 % [INFO] Killing All external provers ...
% 17.11/4.22 % Time passed: 3692ms (effective reasoning time: 3150ms)
% 17.11/4.22 % 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)>
% 17.11/4.22 % Axioms used in derivation (62): ass(cond(223, 0), 0), ass(cond(6, 0), 0), def(cond(conseq(axiom(3)), 11), 1), def(cond(conseq(axiom(3)), 16), 1), holds(conjunct1(315), 514, 0), ass(cond(241, 0), 0), ass(cond(12, 0), 0), ass(cond(140, 0), 0), 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), 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), holds(conjunct1(314), 510, 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(228, 0), 0), holds(conjunct2(315), 515, 2), ass(cond(goal(202), 0), 2), ass(cond(270, 0), 0), ass(cond(184, 0), 0), ass(cond(goal(88), 0), 2), ass(cond(147, 0), 0), qu(cond(conseq(axiom(3)), 3), and(holds(definiens(29), 45, 0), holds(definiens(29), 44, 0))), ass(cond(73, 0), 0), ass(cond(goal(88), 0), 0), def(cond(conseq(axiom(3)), 17), 1), holds(conjunct2(314), 513, 0), 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), holds(conjunct2(315), 515, 1), 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), def(cond(conseq(axiom(3)), 12), 1), holds(conjunct2(315), 515, 0)
% 17.11/4.22 % No. of inferences in proof: 203
% 17.11/4.22 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 3692 ms resp. 3150 ms w/o parsing
% 17.19/4.28 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 17.19/4.28 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------