TSTP Solution File: NUM851+1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : NUM851+1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n014.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 11:42:22 EDT 2023
% Result : Theorem 4.17s 2.07s
% Output : Refutation 4.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 67
% Syntax : Number of formulae : 123 ( 38 unt; 13 typ; 0 def)
% Number of atoms : 220 ( 99 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 726 ( 42 ~; 30 |; 24 &; 574 @)
% ( 4 <=>; 52 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 14 ( 14 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 13 usr; 6 con; 0-2 aty)
% Number of variables : 244 ( 0 ^; 226 !; 18 ?; 244 :)
% Comments :
%------------------------------------------------------------------------------
thf(vmul_type,type,
vmul: $i > $i > $i ).
thf(vplus_type,type,
vplus: $i > $i > $i ).
thf(vd471_type,type,
vd471: $i ).
thf(vd473_type,type,
vd473: $i ).
thf(vd469_type,type,
vd469: $i ).
thf(v1_type,type,
v1: $i ).
thf(vsucc_type,type,
vsucc: $i > $i ).
thf(vskolem2_type,type,
vskolem2: $i > $i ).
thf(geq_type,type,
geq: $i > $i > $o ).
thf(leq_type,type,
leq: $i > $i > $o ).
thf(less_type,type,
less: $i > $i > $o ).
thf(greater_type,type,
greater: $i > $i > $o ).
thf(vd470_type,type,
vd470: $i ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( leq @ A @ B )
=> ( geq @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(163, 0), 0)') ).
thf(88,plain,
! [A: $i,B: $i] :
( ( leq @ A @ B )
=> ( geq @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(35,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(170,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)],[35]) ).
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(189,plain,
! [A: $i,B: $i] :
( ( vplus @ ( vsucc @ A ) @ B )
= ( vsucc @ ( vplus @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(14,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(97,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)],[14]) ).
thf(30,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(156,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)],[30]) ).
thf(47,axiom,
! [A: $i] :
( ( vplus @ v1 @ A )
= ( vsucc @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(43, 0), 0)') ).
thf(204,plain,
! [A: $i] :
( ( vplus @ v1 @ A )
= ( vsucc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(5,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(63,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)],[5]) ).
thf(50,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(218,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)],[50]) ).
thf(25,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(139,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)],[25]) ).
thf(1,conjecture,
( ( vmul @ ( vplus @ vd471 @ vd473 ) @ vd469 )
= ( vplus @ ( vmul @ vd471 @ vd469 ) @ ( vmul @ vd473 @ vd469 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(conseq_conjunct2(conseq(302)), 475, 1)') ).
thf(2,negated_conjecture,
( ( vmul @ ( vplus @ vd471 @ vd473 ) @ vd469 )
!= ( vplus @ ( vmul @ vd471 @ vd469 ) @ ( vmul @ vd473 @ vd469 ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(56,plain,
( ( vmul @ ( vplus @ vd471 @ vd473 ) @ vd469 )
!= ( vplus @ ( vmul @ vd471 @ vd469 ) @ ( vmul @ vd473 @ vd469 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(29,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(153,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)],[29]) ).
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(184,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(22,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(125,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)],[22]) ).
thf(37,axiom,
! [A: $i,B: $i] :
( ( vmul @ A @ B )
= ( vmul @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(270, 0), 0)') ).
thf(179,plain,
! [A: $i,B: $i] :
( ( vmul @ A @ B )
= ( vmul @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(49,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(211,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)],[49]) ).
thf(17,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(106,plain,
! [A: $i,B: $i] :
( ~ ( greater @ A @ B )
| ~ ( less @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(54,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(238,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)],[54]) ).
thf(21,axiom,
! [A: $i] :
( ( vsucc @ A )
!= v1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(restrictor(axiom(1)), holds(scope(axiom(1)), 2, 0))') ).
thf(121,plain,
! [A: $i] :
( ( vsucc @ A )
!= v1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( greater @ A @ B )
=> ( less @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(140, 0), 0)') ).
thf(84,plain,
! [A: $i,B: $i] :
( ( greater @ A @ B )
=> ( less @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( geq @ A @ B )
=> ( leq @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(158, 0), 0)') ).
thf(61,plain,
! [A: $i,B: $i] :
( ( geq @ A @ B )
=> ( leq @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(23,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(132,plain,
! [A: $i,B: $i] :
( ( A != B )
| ~ ? [C: $i] :
( A
= ( vplus @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(19,axiom,
! [A: $i] : ( geq @ A @ v1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(228, 0), 0)') ).
thf(117,plain,
! [A: $i] : ( geq @ A @ v1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(46,axiom,
! [A: $i,B: $i,C: $i] :
( ( vmul @ ( vmul @ A @ B ) @ C )
= ( vmul @ A @ ( vmul @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(290, 0), 0)') ).
thf(201,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)],[46]) ).
thf(16,axiom,
! [A: $i] :
( ( vsucc @ A )
!= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(12, 0), 0)') ).
thf(102,plain,
! [A: $i] :
( ( vsucc @ A )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(42,axiom,
greater @ vd470 @ vd471,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(antec(302), 472, 0)') ).
thf(192,plain,
greater @ vd470 @ vd471,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(33,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(165,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)],[33]) ).
thf(51,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(225,plain,
! [A: $i,B: $i,C: $i] :
( ( A = B )
=> ( ( vplus @ A @ C )
= ( vplus @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(43,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(193,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)],[43]) ).
thf(28,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(148,plain,
! [A: $i,B: $i] :
( ( A != B )
=> ! [C: $i] :
( ( vplus @ C @ A )
!= ( vplus @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(32,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(161,plain,
! [A: $i,B: $i] :
( ( A != B )
| ~ ? [C: $i] :
( B
= ( vplus @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( less @ A @ B )
=> ( greater @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(147, 0), 0)') ).
thf(86,plain,
! [A: $i,B: $i] :
( ( less @ A @ B )
=> ( greater @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(31,axiom,
! [A: $i,B: $i] : ( greater @ ( vplus @ A @ B ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(189, 0), 0)') ).
thf(159,plain,
! [A: $i,B: $i] : ( greater @ ( vplus @ A @ B ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(40,axiom,
( vd470
= ( vplus @ vd471 @ vd473 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(conseq_conjunct1(conseq(302)), 474, 0)') ).
thf(187,plain,
( vd470
= ( vplus @ vd471 @ vd473 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(52,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(230,plain,
! [A: $i,B: $i,C: $i] :
( ( ( vplus @ A @ C )
= ( vplus @ B @ C ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( A != B )
=> ( ( vsucc @ A )
!= ( vsucc @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(6, 0), 0)') ).
thf(76,plain,
! [A: $i,B: $i] :
( ( A != B )
=> ( ( vsucc @ A )
!= ( vsucc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(45,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(198,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)],[45]) ).
thf(18,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(108,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)],[18]) ).
thf(55,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(241,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)],[55]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( A != B )
| ~ ( less @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(130), 0), 1)') ).
thf(80,plain,
! [A: $i,B: $i] :
( ( A != B )
| ~ ( less @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(36,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(177,plain,
! [A: $i,B: $i] :
( ( greater @ A @ B )
=> ( geq @ A @ ( vplus @ B @ v1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(38,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(182,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)],[38]) ).
thf(6,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(72,plain,
! [A: $i,B: $i] :
( ( ( vsucc @ A )
= ( vsucc @ B ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(26,axiom,
! [A: $i,B: $i] :
( ( vmul @ ( vsucc @ A ) @ B )
= ( vplus @ ( vmul @ A @ B ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(261, 0), 0)') ).
thf(143,plain,
! [A: $i,B: $i] :
( ( vmul @ ( vsucc @ A ) @ B )
= ( vplus @ ( vmul @ A @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(53,axiom,
! [A: $i] :
( ( vmul @ v1 @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(253, 0), 0)') ).
thf(235,plain,
! [A: $i] :
( ( vmul @ v1 @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(48,axiom,
! [A: $i,B: $i] :
( B
!= ( vplus @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(73, 0), 0)') ).
thf(207,plain,
! [A: $i,B: $i] :
( B
!= ( vplus @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(20,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(119,plain,
! [A: $i,B: $i,C: $i] :
( ( ( leq @ B @ C )
& ( leq @ A @ B ) )
=> ( leq @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(3,axiom,
! [A: $i] :
( ( A != v1 )
=> ( A
= ( vsucc @ ( vskolem2 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(20, 0), 0)') ).
thf(58,plain,
! [A: $i] :
( ( A != v1 )
=> ( A
= ( vsucc @ ( vskolem2 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(34,axiom,
( ( vmul @ vd470 @ vd469 )
= ( vmul @ ( vplus @ vd471 @ vd473 ) @ vd469 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(conseq_conjunct2(conseq(302)), 475, 0)') ).
thf(168,plain,
( ( vmul @ vd470 @ vd469 )
= ( vmul @ ( vplus @ vd471 @ vd473 ) @ vd469 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(27,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(146,plain,
! [A: $i,B: $i] :
( ( less @ A @ ( vplus @ B @ v1 ) )
=> ( leq @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(24,axiom,
! [A: $i,B: $i] :
( ( vplus @ B @ A )
= ( vplus @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(61, 0), 0)') ).
thf(136,plain,
! [A: $i,B: $i] :
( ( vplus @ B @ A )
= ( vplus @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(44,axiom,
! [A: $i,B: $i,C: $i] :
( ( vmul @ A @ ( vplus @ B @ C ) )
= ( vplus @ ( vmul @ A @ B ) @ ( vmul @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(281, 0), 0)') ).
thf(195,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)],[44]) ).
thf(13,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(94,plain,
! [A: $i,B: $i] :
( ( A = B )
| ( greater @ A @ B )
| ( less @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( A != B )
| ~ ( greater @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(130), 0), 3)') ).
thf(90,plain,
! [A: $i,B: $i] :
( ( A != B )
| ~ ( greater @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(15,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(100,plain,
! [A: $i,B: $i,C: $i] :
( ( ( less @ B @ C )
& ( less @ A @ B ) )
=> ( less @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(244,plain,
$false,
inference(e,[status(thm)],[88,170,189,97,156,204,63,218,139,56,153,184,125,179,211,106,238,121,84,61,132,117,201,102,192,165,225,193,148,161,86,159,187,230,76,198,108,241,80,177,182,72,143,235,207,119,58,168,146,136,195,94,90,100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM851+1 : TPTP v8.1.2. Released v4.1.0.
% 0.14/0.16 % Command : run_Leo-III %s %d
% 0.16/0.37 % Computer : n014.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Thu May 18 17:42:43 EDT 2023
% 0.16/0.37 % CPUTime :
% 0.95/0.86 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.24/1.00 % [INFO] Parsing done (132ms).
% 1.24/1.01 % [INFO] Running in sequential loop mode.
% 1.75/1.22 % [INFO] eprover registered as external prover.
% 1.75/1.22 % [INFO] cvc4 registered as external prover.
% 1.75/1.23 % [INFO] Scanning for conjecture ...
% 1.91/1.29 % [INFO] Found a conjecture and 53 axioms. Running axiom selection ...
% 2.08/1.34 % [INFO] Axiom selection finished. Selected 53 axioms (removed 0 axioms).
% 2.26/1.40 % [INFO] Problem is first-order (TPTP FOF).
% 2.26/1.41 % [INFO] Type checking passed.
% 2.26/1.41 % [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 ...
% 4.17/2.06 % External prover 'e' found a proof!
% 4.17/2.06 % [INFO] Killing All external provers ...
% 4.17/2.06 % Time passed: 1524ms (effective reasoning time: 1055ms)
% 4.17/2.06 % 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)>
% 4.17/2.07 % Axioms used in derivation (53): ass(cond(223, 0), 0), ass(cond(6, 0), 0), def(cond(conseq(axiom(3)), 11), 1), def(cond(conseq(axiom(3)), 16), 1), ass(cond(228, 0), 0), ass(cond(12, 0), 0), ass(cond(140, 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(163, 0), 0), 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), 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), 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(antec(302), 472, 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), holds(conseq_conjunct1(conseq(302)), 474, 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(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), holds(conseq_conjunct2(conseq(302)), 475, 0), ass(cond(241, 0), 0), ass(cond(goal(130), 0), 2), ass(cond(goal(202), 0), 0), ass(cond(168, 0), 0), ass(cond(43, 0), 0)
% 4.17/2.07 % No. of inferences in proof: 110
% 4.17/2.07 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1524 ms resp. 1055 ms w/o parsing
% 4.76/2.13 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.76/2.13 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------