TSTP Solution File: NUM845+1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : NUM845+1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n013.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 : Fri May 19 11:42:19 EDT 2023
% Result : Theorem 4.60s 2.12s
% Output : Refutation 4.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 68
% Syntax : Number of formulae : 128 ( 27 unt; 10 typ; 0 def)
% Number of atoms : 247 ( 128 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 1042 ( 42 ~; 30 |; 24 &; 871 @)
% ( 4 <=>; 71 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 14 ( 14 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 10 usr; 3 con; 0-2 aty)
% Number of variables : 243 ( 0 ^; 225 !; 18 ?; 243 :)
% Comments :
%------------------------------------------------------------------------------
thf(vmul_type,type,
vmul: $i > $i > $i ).
thf(vsucc_type,type,
vsucc: $i > $i ).
thf(vd411_type,type,
vd411: $i ).
thf(vplus_type,type,
vplus: $i > $i > $i ).
thf(greater_type,type,
greater: $i > $i > $o ).
thf(less_type,type,
less: $i > $i > $o ).
thf(leq_type,type,
leq: $i > $i > $o ).
thf(geq_type,type,
geq: $i > $i > $o ).
thf(v1_type,type,
v1: $i ).
thf(vskolem2_type,type,
vskolem2: $i > $i ).
thf(18,axiom,
! [A: $i,B: $i] :
( ( A != B )
| ~ ? [C: $i] :
( A
= ( vplus @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(88), 0), 3)') ).
thf(120,plain,
! [A: $i,B: $i] :
( ( A != B )
| ~ ? [C: $i] :
( A
= ( vplus @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(28,axiom,
! [A: $i] :
( ( ( vmul @ ( vsucc @ vd411 ) @ A )
= ( vplus @ ( vmul @ vd411 @ A ) @ A ) )
=> ( ( vplus @ ( vmul @ vd411 @ A ) @ ( vplus @ vd411 @ ( vsucc @ A ) ) )
= ( vplus @ ( vplus @ ( vmul @ vd411 @ A ) @ vd411 ) @ ( vsucc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(conseq(263), 1), 1)') ).
thf(153,plain,
! [A: $i] :
( ( ( vmul @ ( vsucc @ vd411 ) @ A )
= ( vplus @ ( vmul @ vd411 @ A ) @ A ) )
=> ( ( vplus @ ( vmul @ vd411 @ A ) @ ( vplus @ vd411 @ ( vsucc @ A ) ) )
= ( vplus @ ( vplus @ ( vmul @ vd411 @ A ) @ vd411 ) @ ( vsucc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(36,axiom,
! [A: $i,B: $i,C: $i] :
( ( A = B )
=> ( ( vplus @ A @ C )
= ( vplus @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(193), 0), 1)') ).
thf(185,plain,
! [A: $i,B: $i,C: $i] :
( ( A = B )
=> ( ( vplus @ A @ C )
= ( vplus @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(27,axiom,
! [A: $i,B: $i] :
( ( A != B )
| ~ ? [C: $i] :
( B
= ( vplus @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(88), 0), 1)') ).
thf(149,plain,
! [A: $i,B: $i] :
( ( A != B )
| ~ ? [C: $i] :
( B
= ( vplus @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(41,axiom,
! [A: $i,B: $i] :
( ( vplus @ ( vsucc @ A ) @ B )
= ( vsucc @ ( vplus @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(52, 0), 0)') ).
thf(204,plain,
! [A: $i,B: $i] :
( ( vplus @ ( vsucc @ A ) @ B )
= ( vsucc @ ( vplus @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(58,axiom,
! [A: $i] :
( ( ( vmul @ ( vsucc @ vd411 ) @ A )
= ( vplus @ ( vmul @ vd411 @ A ) @ A ) )
=> ( ( vplus @ ( vmul @ ( vsucc @ vd411 ) @ A ) @ ( vsucc @ vd411 ) )
= ( vplus @ ( vplus @ ( vmul @ vd411 @ A ) @ A ) @ ( vsucc @ vd411 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(conseq(263), 1), 6)') ).
thf(258,plain,
! [A: $i] :
( ( ( vmul @ ( vsucc @ vd411 ) @ A )
= ( vplus @ ( vmul @ vd411 @ A ) @ A ) )
=> ( ( vplus @ ( vmul @ ( vsucc @ vd411 ) @ A ) @ ( vsucc @ vd411 ) )
= ( vplus @ ( vplus @ ( vmul @ vd411 @ A ) @ A ) @ ( vsucc @ vd411 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(37,axiom,
! [A: $i,B: $i] :
( ( A != B )
=> ( ( vsucc @ A )
!= ( vsucc @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(6, 0), 0)') ).
thf(190,plain,
! [A: $i,B: $i] :
( ( A != B )
=> ( ( vsucc @ A )
!= ( vsucc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( A != B )
| ~ ( less @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(130), 0), 1)') ).
thf(94,plain,
! [A: $i,B: $i] :
( ( A != B )
| ~ ( less @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( leq @ A @ B )
=> ( geq @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(163, 0), 0)') ).
thf(69,plain,
! [A: $i,B: $i] :
( ( leq @ A @ B )
=> ( geq @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(23,axiom,
! [A: $i,B: $i] :
( ( A = B )
| ? [C: $i] :
( A
= ( vplus @ B @ C ) )
| ? [C: $i] :
( B
= ( vplus @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(88), 0), 0)') ).
thf(138,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)],[23]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( geq @ A @ B )
=> ( leq @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(158, 0), 0)') ).
thf(78,plain,
! [A: $i,B: $i] :
( ( geq @ A @ B )
=> ( leq @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(59,axiom,
! [A: $i] :
( ( vplus @ v1 @ A )
= ( vsucc @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(43, 0), 0)') ).
thf(261,plain,
! [A: $i] :
( ( vplus @ v1 @ A )
= ( vsucc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(46,axiom,
! [A: $i] :
( ( vsucc @ A )
!= v1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(restrictor(axiom(1)), holds(scope(axiom(1)), 2, 0))') ).
thf(216,plain,
! [A: $i] :
( ( vsucc @ A )
!= v1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(34,axiom,
! [A: $i,B: $i] :
( ( greater @ A @ B )
=> ( geq @ A @ ( vplus @ B @ v1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(234, 0), 0)') ).
thf(179,plain,
! [A: $i,B: $i] :
( ( greater @ A @ B )
=> ( geq @ A @ ( vplus @ B @ v1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(56,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/sandbox2/benchmark/theBenchmark.p','ass(cond(209, 0), 0)') ).
thf(253,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)],[56]) ).
thf(53,axiom,
! [A: $i,B: $i] :
( ( greater @ B @ A )
<=> ? [C: $i] :
( B
= ( vplus @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','def(cond(conseq(axiom(3)), 11), 1)') ).
thf(238,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(26,axiom,
! [A: $i,B: $i] : ( greater @ ( vplus @ A @ B ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(189, 0), 0)') ).
thf(147,plain,
! [A: $i,B: $i] : ( greater @ ( vplus @ A @ B ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(22,axiom,
! [A: $i,B: $i] :
( ( A != B )
=> ! [C: $i] :
( ( vplus @ C @ A )
!= ( vplus @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(81, 0), 0)') ).
thf(133,plain,
! [A: $i,B: $i] :
( ( A != B )
=> ! [C: $i] :
( ( vplus @ C @ A )
!= ( vplus @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(51,axiom,
( ( vmul @ ( vsucc @ vd411 ) @ v1 )
= ( vsucc @ vd411 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(264, 412, 0)') ).
thf(233,plain,
( ( vmul @ ( vsucc @ vd411 ) @ v1 )
= ( vsucc @ vd411 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(55,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( vplus @ A @ C )
= ( vplus @ B @ C ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(202), 0), 1)') ).
thf(248,plain,
! [A: $i,B: $i,C: $i] :
( ( ( vplus @ A @ C )
= ( vplus @ B @ C ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(1,conjecture,
! [A: $i] :
( ( ( vmul @ ( vsucc @ vd411 ) @ A )
= ( vplus @ ( vmul @ vd411 @ A ) @ A ) )
=> ( ( vmul @ ( vsucc @ vd411 ) @ ( vsucc @ A ) )
= ( vplus @ ( vmul @ vd411 @ ( vsucc @ A ) ) @ ( vsucc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(ind(267), imp(267))') ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( ( vmul @ ( vsucc @ vd411 ) @ A )
= ( vplus @ ( vmul @ vd411 @ A ) @ A ) )
=> ( ( vmul @ ( vsucc @ vd411 ) @ ( vsucc @ A ) )
= ( vplus @ ( vmul @ vd411 @ ( vsucc @ A ) ) @ ( vsucc @ A ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(60,plain,
~ ! [A: $i] :
( ( ( vmul @ ( vsucc @ vd411 ) @ A )
= ( vplus @ ( vmul @ vd411 @ A ) @ A ) )
=> ( ( vmul @ ( vsucc @ vd411 ) @ ( vsucc @ A ) )
= ( vplus @ ( vmul @ vd411 @ ( vsucc @ A ) ) @ ( vsucc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(47,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/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(216), 0), 0)') ).
thf(220,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)],[47]) ).
thf(11,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( less @ B @ C )
& ( less @ A @ B ) )
=> ( less @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(168, 0), 0)') ).
thf(92,plain,
! [A: $i,B: $i,C: $i] :
( ( ( less @ B @ C )
& ( less @ A @ B ) )
=> ( less @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(39,axiom,
! [A: $i,B: $i,C: $i] :
( ( greater @ ( vplus @ A @ C ) @ ( vplus @ B @ C ) )
=> ( greater @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(202), 0), 2)') ).
thf(197,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)],[39]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( greater @ A @ B )
=> ( less @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(140, 0), 0)') ).
thf(65,plain,
! [A: $i,B: $i] :
( ( greater @ A @ B )
=> ( less @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(29,axiom,
! [A: $i] :
( ( A != v1 )
=> ( A
= ( vsucc @ ( vskolem2 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(20, 0), 0)') ).
thf(156,plain,
! [A: $i] :
( ( A != v1 )
=> ( A
= ( vsucc @ ( vskolem2 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(32,axiom,
! [A: $i] :
( ( ( vmul @ ( vsucc @ vd411 ) @ A )
= ( vplus @ ( vmul @ vd411 @ A ) @ A ) )
=> ( ( vmul @ ( vsucc @ vd411 ) @ ( vsucc @ A ) )
= ( vplus @ ( vmul @ ( vsucc @ vd411 ) @ A ) @ ( vsucc @ vd411 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(conseq(263), 1), 7)') ).
thf(169,plain,
! [A: $i] :
( ( ( vmul @ ( vsucc @ vd411 ) @ A )
= ( vplus @ ( vmul @ vd411 @ A ) @ A ) )
=> ( ( vmul @ ( vsucc @ vd411 ) @ ( vsucc @ A ) )
= ( vplus @ ( vmul @ ( vsucc @ vd411 ) @ A ) @ ( vsucc @ vd411 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(24,axiom,
! [A: $i,B: $i,C: $i] :
( ( vplus @ ( vplus @ A @ B ) @ C )
= ( vplus @ A @ ( vplus @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(33, 0), 0)') ).
thf(141,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)],[24]) ).
thf(15,axiom,
! [A: $i] : ( geq @ A @ v1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(228, 0), 0)') ).
thf(109,plain,
! [A: $i] : ( geq @ A @ v1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(19,axiom,
! [A: $i,B: $i] :
( ( vplus @ B @ A )
= ( vplus @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(61, 0), 0)') ).
thf(124,plain,
! [A: $i,B: $i] :
( ( vplus @ B @ A )
= ( vplus @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(44,axiom,
( ( vsucc @ vd411 )
= ( vsucc @ ( vmul @ vd411 @ v1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(264, 412, 1)') ).
thf(212,plain,
( ( vsucc @ vd411 )
= ( vsucc @ ( vmul @ vd411 @ v1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( A != B )
| ~ ( greater @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(130), 0), 3)') ).
thf(71,plain,
! [A: $i,B: $i] :
( ( A != B )
| ~ ( greater @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(25,axiom,
! [A: $i] :
( ( ( vmul @ ( vsucc @ vd411 ) @ A )
= ( vplus @ ( vmul @ vd411 @ A ) @ A ) )
=> ( ( vplus @ ( vmul @ vd411 @ A ) @ ( vplus @ A @ ( vsucc @ vd411 ) ) )
= ( vplus @ ( vmul @ vd411 @ A ) @ ( vplus @ ( vsucc @ vd411 ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(conseq(263), 1), 4)') ).
thf(144,plain,
! [A: $i] :
( ( ( vmul @ ( vsucc @ vd411 ) @ A )
= ( vplus @ ( vmul @ vd411 @ A ) @ A ) )
=> ( ( vplus @ ( vmul @ vd411 @ A ) @ ( vplus @ A @ ( vsucc @ vd411 ) ) )
= ( vplus @ ( vmul @ vd411 @ A ) @ ( vplus @ ( vsucc @ vd411 ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(35,axiom,
! [A: $i,B: $i] :
( ( ( vsucc @ A )
= ( vsucc @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(antec(axiom(3)), imp(antec(axiom(3))))') ).
thf(181,plain,
! [A: $i,B: $i] :
( ( ( vsucc @ A )
= ( vsucc @ B ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(30,axiom,
! [A: $i] :
( ( ( vmul @ ( vsucc @ vd411 ) @ A )
= ( vplus @ ( vmul @ vd411 @ A ) @ A ) )
=> ( ( vplus @ ( vmul @ vd411 @ A ) @ ( vsucc @ ( vplus @ vd411 @ A ) ) )
= ( vplus @ ( vmul @ vd411 @ A ) @ ( vplus @ vd411 @ ( vsucc @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(conseq(263), 1), 2)') ).
thf(159,plain,
! [A: $i] :
( ( ( vmul @ ( vsucc @ vd411 ) @ A )
= ( vplus @ ( vmul @ vd411 @ A ) @ A ) )
=> ( ( vplus @ ( vmul @ vd411 @ A ) @ ( vsucc @ ( vplus @ vd411 @ A ) ) )
= ( vplus @ ( vmul @ vd411 @ A ) @ ( vplus @ vd411 @ ( vsucc @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(33,axiom,
! [A: $i,B: $i] :
( ( ( vmul @ A @ ( vsucc @ B ) )
= ( vplus @ ( vmul @ A @ B ) @ A ) )
& ( ( vmul @ A @ v1 )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(conseq(axiom(3)), 32), and(holds(definiens(249), 399, 0), holds(definiens(249), 398, 0)))') ).
thf(172,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)],[33]) ).
thf(17,axiom,
! [A: $i,B: $i] :
( ( ( vplus @ A @ ( vsucc @ B ) )
= ( vsucc @ ( vplus @ A @ B ) ) )
& ( ( vplus @ A @ v1 )
= ( vsucc @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(conseq(axiom(3)), 3), and(holds(definiens(29), 45, 0), holds(definiens(29), 44, 0)))') ).
thf(113,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)],[17]) ).
thf(50,axiom,
! [A: $i] :
( ( ( vmul @ ( vsucc @ vd411 ) @ A )
= ( vplus @ ( vmul @ vd411 @ A ) @ A ) )
=> ( ( vplus @ ( vplus @ ( vmul @ vd411 @ A ) @ vd411 ) @ ( vsucc @ A ) )
= ( vplus @ ( vmul @ vd411 @ ( vsucc @ A ) ) @ ( vsucc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(conseq(263), 1), 0)') ).
thf(230,plain,
! [A: $i] :
( ( ( vmul @ ( vsucc @ vd411 ) @ A )
= ( vplus @ ( vmul @ vd411 @ A ) @ A ) )
=> ( ( vplus @ ( vplus @ ( vmul @ vd411 @ A ) @ vd411 ) @ ( vsucc @ A ) )
= ( vplus @ ( vmul @ vd411 @ ( vsucc @ A ) ) @ ( vsucc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(54,axiom,
! [A: $i,B: $i,C: $i] :
( ( greater @ A @ B )
=> ( greater @ ( vplus @ A @ C ) @ ( vplus @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(193), 0), 2)') ).
thf(245,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(13,axiom,
! [A: $i,B: $i] :
( ~ ( greater @ A @ B )
| ~ ( less @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(130), 0), 2)') ).
thf(98,plain,
! [A: $i,B: $i] :
( ~ ( greater @ A @ B )
| ~ ( less @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(48,axiom,
! [A: $i,B: $i] :
( B
!= ( vplus @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(73, 0), 0)') ).
thf(223,plain,
! [A: $i,B: $i] :
( B
!= ( vplus @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(9,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/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(177), 0), 0)') ).
thf(80,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)],[9]) ).
thf(31,axiom,
! [A: $i,B: $i] :
( ( less @ B @ A )
<=> ? [C: $i] :
( A
= ( vplus @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','def(cond(conseq(axiom(3)), 12), 1)') ).
thf(162,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)],[31]) ).
thf(57,axiom,
! [A: $i,B: $i,C: $i] :
( ( less @ A @ B )
=> ( less @ ( vplus @ A @ C ) @ ( vplus @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(193), 0), 0)') ).
thf(255,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)],[57]) ).
thf(43,axiom,
! [A: $i,B: $i,C: $i] :
( ( less @ ( vplus @ A @ C ) @ ( vplus @ B @ C ) )
=> ( less @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(202), 0), 0)') ).
thf(209,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)],[43]) ).
thf(38,axiom,
! [A: $i] :
( ( vmul @ v1 @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(253, 0), 0)') ).
thf(194,plain,
! [A: $i] :
( ( vmul @ v1 @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( less @ A @ B )
=> ( greater @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(147, 0), 0)') ).
thf(67,plain,
! [A: $i,B: $i] :
( ( less @ A @ B )
=> ( greater @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(20,axiom,
! [A: $i,B: $i] :
( ~ ? [C: $i] :
( A
= ( vplus @ B @ C ) )
| ~ ? [C: $i] :
( B
= ( vplus @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(88), 0), 2)') ).
thf(127,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)],[20]) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( A = B )
| ( greater @ A @ B )
| ( less @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(130), 0), 0)') ).
thf(75,plain,
! [A: $i,B: $i] :
( ( A = B )
| ( greater @ A @ B )
| ( less @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(52,axiom,
! [A: $i] :
( ( ( vmul @ ( vsucc @ vd411 ) @ A )
= ( vplus @ ( vmul @ vd411 @ A ) @ A ) )
=> ( ( vplus @ ( vmul @ vd411 @ A ) @ ( vplus @ ( vsucc @ vd411 ) @ A ) )
= ( vplus @ ( vmul @ vd411 @ A ) @ ( vsucc @ ( vplus @ vd411 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(conseq(263), 1), 3)') ).
thf(235,plain,
! [A: $i] :
( ( ( vmul @ ( vsucc @ vd411 ) @ A )
= ( vplus @ ( vmul @ vd411 @ A ) @ A ) )
=> ( ( vplus @ ( vmul @ vd411 @ A ) @ ( vplus @ ( vsucc @ vd411 ) @ A ) )
= ( vplus @ ( vmul @ vd411 @ A ) @ ( vsucc @ ( vplus @ vd411 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(42,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/sandbox2/benchmark/theBenchmark.p','ass(cond(223, 0), 0)') ).
thf(207,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)],[42]) ).
thf(45,axiom,
( ( vsucc @ ( vmul @ vd411 @ v1 ) )
= ( vplus @ ( vmul @ vd411 @ v1 ) @ v1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(264, 412, 2)') ).
thf(214,plain,
( ( vsucc @ ( vmul @ vd411 @ v1 ) )
= ( vplus @ ( vmul @ vd411 @ v1 ) @ v1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(21,axiom,
! [A: $i,B: $i] :
( ( less @ A @ ( vplus @ B @ v1 ) )
=> ( leq @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(241, 0), 0)') ).
thf(131,plain,
! [A: $i,B: $i] :
( ( less @ A @ ( vplus @ B @ v1 ) )
=> ( leq @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(40,axiom,
! [A: $i] :
( ( vsucc @ A )
!= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(12, 0), 0)') ).
thf(200,plain,
! [A: $i] :
( ( vsucc @ A )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(16,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( leq @ B @ C )
& ( leq @ A @ B ) )
=> ( leq @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(184, 0), 0)') ).
thf(111,plain,
! [A: $i,B: $i,C: $i] :
( ( ( leq @ B @ C )
& ( leq @ A @ B ) )
=> ( leq @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(49,axiom,
! [A: $i] :
( ( ( vmul @ ( vsucc @ vd411 ) @ A )
= ( vplus @ ( vmul @ vd411 @ A ) @ A ) )
=> ( ( vplus @ ( vplus @ ( vmul @ vd411 @ A ) @ A ) @ ( vsucc @ vd411 ) )
= ( vplus @ ( vmul @ vd411 @ A ) @ ( vplus @ A @ ( vsucc @ vd411 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(conseq(263), 1), 5)') ).
thf(227,plain,
! [A: $i] :
( ( ( vmul @ ( vsucc @ vd411 ) @ A )
= ( vplus @ ( vmul @ vd411 @ A ) @ A ) )
=> ( ( vplus @ ( vplus @ ( vmul @ vd411 @ A ) @ A ) @ ( vsucc @ vd411 ) )
= ( vplus @ ( vmul @ vd411 @ A ) @ ( vplus @ A @ ( vsucc @ vd411 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( leq @ B @ A )
<=> ( ( less @ B @ A )
| ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','def(cond(conseq(axiom(3)), 17), 1)') ).
thf(83,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)],[10]) ).
thf(14,axiom,
! [A: $i,B: $i] :
( ( geq @ B @ A )
<=> ( ( greater @ B @ A )
| ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','def(cond(conseq(axiom(3)), 16), 1)') ).
thf(100,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)],[14]) ).
thf(264,plain,
$false,
inference(e,[status(thm)],[120,153,185,149,204,258,190,94,69,138,78,261,216,179,253,238,147,133,233,248,60,220,92,197,65,156,169,141,109,124,212,71,144,181,159,172,113,230,245,98,223,80,162,255,209,194,67,127,75,235,207,214,131,200,111,227,83,100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : NUM845+1 : TPTP v8.1.2. Released v4.1.0.
% 0.06/0.15 % Command : run_Leo-III %s %d
% 0.14/0.36 % Computer : n013.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Thu May 18 16:33:36 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.92/0.90 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.22/1.05 % [INFO] Parsing done (155ms).
% 1.46/1.06 % [INFO] Running in sequential loop mode.
% 1.81/1.26 % [INFO] eprover registered as external prover.
% 1.81/1.27 % [INFO] cvc4 registered as external prover.
% 1.81/1.27 % [INFO] Scanning for conjecture ...
% 1.93/1.33 % [INFO] Found a conjecture and 57 axioms. Running axiom selection ...
% 2.20/1.38 % [INFO] Axiom selection finished. Selected 57 axioms (removed 0 axioms).
% 2.45/1.45 % [INFO] Problem is first-order (TPTP FOF).
% 2.52/1.46 % [INFO] Type checking passed.
% 2.52/1.46 % [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 ...
% 4.60/2.12 % External prover 'e' found a proof!
% 4.60/2.12 % [INFO] Killing All external provers ...
% 4.60/2.12 % Time passed: 1579ms (effective reasoning time: 1054ms)
% 4.60/2.12 % 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)>
% 4.60/2.12 % Axioms used in derivation (57): ass(cond(223, 0), 0), ass(cond(6, 0), 0), ass(cond(conseq(263), 1), 6), def(cond(conseq(axiom(3)), 11), 1), def(cond(conseq(axiom(3)), 16), 1), ass(cond(228, 0), 0), ass(cond(goal(202), 0), 2), ass(cond(241, 0), 0), def(cond(conseq(axiom(3)), 12), 1), ass(cond(81, 0), 0), ass(cond(goal(193), 0), 0), ass(cond(goal(130), 0), 1), ass(cond(conseq(263), 1), 4), ass(cond(163, 0), 0), ass(cond(conseq(263), 1), 7), ass(cond(goal(177), 0), 0), ass(cond(goal(193), 0), 2), ass(cond(goal(88), 0), 1), ass(cond(goal(130), 0), 0), ass(cond(goal(130), 0), 3), ass(cond(goal(193), 0), 1), ass(cond(189, 0), 0), ass(cond(conseq(263), 1), 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(conseq(263), 1), 1), 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(264, 412, 1), ass(cond(20, 0), 0), ass(cond(goal(202), 0), 1), ass(cond(goal(216), 0), 0), ass(cond(253, 0), 0), qu(antec(axiom(3)), imp(antec(axiom(3)))), ass(cond(209, 0), 0), ass(cond(52, 0), 0), ass(cond(158, 0), 0), ass(cond(conseq(263), 1), 2), ass(cond(234, 0), 0), ass(cond(33, 0), 0), qu(restrictor(axiom(1)), holds(scope(axiom(1)), 2, 0)), ass(cond(61, 0), 0), ass(cond(goal(130), 0), 2), holds(264, 412, 2), ass(cond(goal(202), 0), 0), holds(264, 412, 0), ass(cond(12, 0), 0), ass(cond(conseq(263), 1), 3), ass(cond(168, 0), 0), ass(cond(43, 0), 0), ass(cond(conseq(263), 1), 5), ass(cond(140, 0), 0)
% 4.60/2.12 % No. of inferences in proof: 118
% 4.60/2.12 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1579 ms resp. 1054 ms w/o parsing
% 4.81/2.19 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.81/2.19 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------