TSTP Solution File: NUM845+2 by Leo-III-SAT---1.7.12
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.12
% Problem : NUM845+2 : TPTP v8.2.0. 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 : Tue May 21 01:36:33 EDT 2024
% Result : Theorem 40.42s 7.02s
% Output : Refutation 40.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 13
% Syntax : Number of formulae : 81 ( 41 unt; 6 typ; 0 def)
% Number of atoms : 111 ( 110 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 1028 ( 33 ~; 23 |; 6 &; 959 @)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 79 ( 0 ^ 79 !; 0 ?; 79 :)
% 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(v1_type,type,
v1: $i ).
thf(sk1_type,type,
sk1: $i ).
thf(13,axiom,
! [A: $i,B: $i] :
( ( vplus @ B @ A )
= ( vplus @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(61, 0), 0)') ).
thf(55,plain,
! [A: $i,B: $i] :
( ( vplus @ B @ A )
= ( vplus @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(56,plain,
! [B: $i,A: $i] :
( ( vplus @ B @ A )
= ( vplus @ A @ B ) ),
inference(cnf,[status(esa)],[55]) ).
thf(57,plain,
! [B: $i,A: $i] :
( ( vplus @ B @ A )
= ( vplus @ A @ B ) ),
inference(lifteq,[status(thm)],[56]) ).
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/sandbox/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(17,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(19,plain,
( ( vmul @ ( vsucc @ vd411 ) @ sk1 )
= ( vplus @ ( vmul @ vd411 @ sk1 ) @ sk1 ) ),
inference(cnf,[status(esa)],[17]) ).
thf(21,plain,
( ( vplus @ ( vmul @ vd411 @ sk1 ) @ sk1 )
= ( vmul @ ( vsucc @ vd411 ) @ sk1 ) ),
inference(lifteq,[status(thm)],[19]) ).
thf(3,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/sandbox/benchmark/theBenchmark.p','ass(cond(conseq(263), 1), 0)') ).
thf(22,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)],[3]) ).
thf(23,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(cnf,[status(esa)],[22]) ).
thf(24,plain,
! [A: $i] :
( ( ( vplus @ ( vmul @ vd411 @ A ) @ A )
!= ( vmul @ ( vsucc @ vd411 ) @ A ) )
| ( ( vplus @ ( vplus @ ( vmul @ vd411 @ A ) @ vd411 ) @ ( vsucc @ A ) )
= ( vplus @ ( vmul @ vd411 @ ( vsucc @ A ) ) @ ( vsucc @ A ) ) ) ),
inference(lifteq,[status(thm)],[23]) ).
thf(158,plain,
! [A: $i] :
( ( ( vmul @ ( vsucc @ vd411 ) @ sk1 )
!= ( vmul @ ( vsucc @ vd411 ) @ A ) )
| ( ( vplus @ ( vplus @ ( vmul @ vd411 @ A ) @ vd411 ) @ ( vsucc @ A ) )
= ( vplus @ ( vmul @ vd411 @ ( vsucc @ A ) ) @ ( vsucc @ A ) ) )
| ( ( vplus @ ( vmul @ vd411 @ sk1 ) @ sk1 )
!= ( vplus @ ( vmul @ vd411 @ A ) @ A ) ) ),
inference(paramod_ordered,[status(thm)],[21,24]) ).
thf(159,plain,
( ( ( vmul @ ( vsucc @ vd411 ) @ sk1 )
!= ( vmul @ ( vsucc @ vd411 ) @ sk1 ) )
| ( ( vplus @ ( vplus @ ( vmul @ vd411 @ sk1 ) @ vd411 ) @ ( vsucc @ sk1 ) )
= ( vplus @ ( vmul @ vd411 @ ( vsucc @ sk1 ) ) @ ( vsucc @ sk1 ) ) ) ),
inference(pattern_uni,[status(thm)],[158:[bind(A,$thf( sk1 ))]]) ).
thf(200,plain,
( ( vplus @ ( vplus @ ( vmul @ vd411 @ sk1 ) @ vd411 ) @ ( vsucc @ sk1 ) )
= ( vplus @ ( vmul @ vd411 @ ( vsucc @ sk1 ) ) @ ( vsucc @ sk1 ) ) ),
inference(simp,[status(thm)],[159]) ).
thf(297,plain,
! [B: $i,A: $i] :
( ( ( vplus @ ( vplus @ A @ B ) @ ( vsucc @ sk1 ) )
= ( vplus @ ( vmul @ vd411 @ ( vsucc @ sk1 ) ) @ ( vsucc @ sk1 ) ) )
| ( ( vplus @ B @ A )
!= ( vplus @ ( vmul @ vd411 @ sk1 ) @ vd411 ) ) ),
inference(paramod_ordered,[status(thm)],[57,200]) ).
thf(298,plain,
( ( vplus @ ( vplus @ vd411 @ ( vmul @ vd411 @ sk1 ) ) @ ( vsucc @ sk1 ) )
= ( vplus @ ( vmul @ vd411 @ ( vsucc @ sk1 ) ) @ ( vsucc @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[297:[bind(A,$thf( vd411 )),bind(B,$thf( vmul @ vd411 @ sk1 ))]]) ).
thf(599,plain,
! [B: $i,A: $i] :
( ( ( vplus @ ( vmul @ vd411 @ ( vsucc @ sk1 ) ) @ ( vsucc @ sk1 ) )
= ( vplus @ B @ A ) )
| ( ( vplus @ ( vplus @ vd411 @ ( vmul @ vd411 @ sk1 ) ) @ ( vsucc @ sk1 ) )
!= ( vplus @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[298,57]) ).
thf(600,plain,
( ( vplus @ ( vmul @ vd411 @ ( vsucc @ sk1 ) ) @ ( vsucc @ sk1 ) )
= ( vplus @ ( vsucc @ sk1 ) @ ( vplus @ vd411 @ ( vmul @ vd411 @ sk1 ) ) ) ),
inference(pattern_uni,[status(thm)],[599:[bind(A,$thf( vplus @ vd411 @ ( vmul @ vd411 @ sk1 ) )),bind(B,$thf( vsucc @ sk1 ))]]) ).
thf(299,plain,
! [B: $i,A: $i] :
( ( ( vplus @ A @ B )
= ( vplus @ ( vmul @ vd411 @ ( vsucc @ sk1 ) ) @ ( vsucc @ sk1 ) ) )
| ( ( vplus @ B @ A )
!= ( vplus @ ( vplus @ ( vmul @ vd411 @ sk1 ) @ vd411 ) @ ( vsucc @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[57,200]) ).
thf(300,plain,
( ( vplus @ ( vmul @ vd411 @ ( vsucc @ sk1 ) ) @ ( vsucc @ sk1 ) )
= ( vplus @ ( vsucc @ sk1 ) @ ( vplus @ ( vmul @ vd411 @ sk1 ) @ vd411 ) ) ),
inference(pattern_uni,[status(thm)],[299:[bind(A,$thf( vsucc @ sk1 )),bind(B,$thf( vplus @ ( vmul @ vd411 @ sk1 ) @ vd411 ))]]) ).
thf(716,plain,
! [B: $i,A: $i] :
( ( ( vplus @ ( vsucc @ sk1 ) @ ( vplus @ ( vmul @ vd411 @ sk1 ) @ vd411 ) )
= ( vplus @ A @ B ) )
| ( ( vplus @ ( vmul @ vd411 @ ( vsucc @ sk1 ) ) @ ( vsucc @ sk1 ) )
!= ( vplus @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[300,57]) ).
thf(717,plain,
( ( vplus @ ( vsucc @ sk1 ) @ ( vplus @ ( vmul @ vd411 @ sk1 ) @ vd411 ) )
= ( vplus @ ( vsucc @ sk1 ) @ ( vmul @ vd411 @ ( vsucc @ sk1 ) ) ) ),
inference(pattern_uni,[status(thm)],[716:[bind(A,$thf( vsucc @ sk1 )),bind(B,$thf( vmul @ vd411 @ ( vsucc @ sk1 ) ))]]) ).
thf(597,plain,
! [B: $i,A: $i] :
( ( ( vplus @ ( vmul @ vd411 @ ( vsucc @ sk1 ) ) @ ( vsucc @ sk1 ) )
= ( vplus @ A @ B ) )
| ( ( vplus @ ( vplus @ vd411 @ ( vmul @ vd411 @ sk1 ) ) @ ( vsucc @ sk1 ) )
!= ( vplus @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[298,57]) ).
thf(598,plain,
( ( vplus @ ( vmul @ vd411 @ ( vsucc @ sk1 ) ) @ ( vsucc @ sk1 ) )
= ( vplus @ ( vsucc @ sk1 ) @ ( vplus @ vd411 @ ( vmul @ vd411 @ sk1 ) ) ) ),
inference(pattern_uni,[status(thm)],[597:[bind(A,$thf( vsucc @ sk1 )),bind(B,$thf( vplus @ vd411 @ ( vmul @ vd411 @ sk1 ) ))]]) ).
thf(1420,plain,
( ( vplus @ ( vsucc @ sk1 ) @ ( vplus @ ( vmul @ vd411 @ sk1 ) @ vd411 ) )
= ( vplus @ ( vsucc @ sk1 ) @ ( vplus @ vd411 @ ( vmul @ vd411 @ sk1 ) ) ) ),
inference(rewrite,[status(thm)],[598,300]) ).
thf(2038,plain,
( ( vplus @ ( vsucc @ sk1 ) @ ( vplus @ vd411 @ ( vmul @ vd411 @ sk1 ) ) )
= ( vplus @ ( vsucc @ sk1 ) @ ( vmul @ vd411 @ ( vsucc @ sk1 ) ) ) ),
inference(rewrite,[status(thm)],[717,1420]) ).
thf(2040,plain,
( ( vplus @ ( vmul @ vd411 @ ( vsucc @ sk1 ) ) @ ( vsucc @ sk1 ) )
= ( vplus @ ( vsucc @ sk1 ) @ ( vmul @ vd411 @ ( vsucc @ sk1 ) ) ) ),
inference(rewrite,[status(thm)],[600,2038]) ).
thf(16,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)],[16]) ).
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(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(5209,plain,
( ( vsucc @ ( vplus @ ( vmul @ vd411 @ ( vsucc @ sk1 ) ) @ sk1 ) )
= ( vplus @ ( vsucc @ sk1 ) @ ( vmul @ vd411 @ ( vsucc @ sk1 ) ) ) ),
inference(rewrite,[status(thm)],[2040,70]) ).
thf(18,plain,
( ( vmul @ ( vsucc @ vd411 ) @ ( vsucc @ sk1 ) )
!= ( vplus @ ( vmul @ vd411 @ ( vsucc @ sk1 ) ) @ ( vsucc @ sk1 ) ) ),
inference(cnf,[status(esa)],[17]) ).
thf(20,plain,
( ( vplus @ ( vmul @ vd411 @ ( vsucc @ sk1 ) ) @ ( vsucc @ sk1 ) )
!= ( vmul @ ( vsucc @ vd411 ) @ ( vsucc @ sk1 ) ) ),
inference(lifteq,[status(thm)],[18]) ).
thf(309,plain,
! [B: $i,A: $i] :
( ( ( vplus @ A @ B )
!= ( vmul @ ( vsucc @ vd411 ) @ ( vsucc @ sk1 ) ) )
| ( ( vplus @ B @ A )
!= ( vplus @ ( vmul @ vd411 @ ( vsucc @ sk1 ) ) @ ( vsucc @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[57,20]) ).
thf(310,plain,
( ( vplus @ ( vsucc @ sk1 ) @ ( vmul @ vd411 @ ( vsucc @ sk1 ) ) )
!= ( vmul @ ( vsucc @ vd411 ) @ ( vsucc @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[309:[bind(A,$thf( vsucc @ sk1 )),bind(B,$thf( vmul @ vd411 @ ( vsucc @ sk1 ) ))]]) ).
thf(8527,plain,
( ( ( vsucc @ ( vplus @ ( vmul @ vd411 @ ( vsucc @ sk1 ) ) @ sk1 ) )
!= ( vmul @ ( vsucc @ vd411 ) @ ( vsucc @ sk1 ) ) )
| ( ( vplus @ ( vsucc @ sk1 ) @ ( vmul @ vd411 @ ( vsucc @ sk1 ) ) )
!= ( vplus @ ( vsucc @ sk1 ) @ ( vmul @ vd411 @ ( vsucc @ sk1 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[5209,310]) ).
thf(8528,plain,
( ( vsucc @ ( vplus @ ( vmul @ vd411 @ ( vsucc @ sk1 ) ) @ sk1 ) )
!= ( vmul @ ( vsucc @ vd411 ) @ ( vsucc @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[8527:[]]) ).
thf(9074,plain,
! [B: $i,A: $i] :
( ( ( vsucc @ ( vplus @ A @ B ) )
!= ( vmul @ ( vsucc @ vd411 ) @ ( vsucc @ sk1 ) ) )
| ( ( vplus @ B @ A )
!= ( vplus @ ( vmul @ vd411 @ ( vsucc @ sk1 ) ) @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[57,8528]) ).
thf(9075,plain,
( ( vsucc @ ( vplus @ sk1 @ ( vmul @ vd411 @ ( vsucc @ sk1 ) ) ) )
!= ( vmul @ ( vsucc @ vd411 ) @ ( vsucc @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[9074:[bind(A,$thf( sk1 )),bind(B,$thf( vmul @ vd411 @ ( vsucc @ sk1 ) ))]]) ).
thf(12,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(48,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)],[12]) ).
thf(49,plain,
( ! [A: $i,B: $i] :
( ( vmul @ A @ ( vsucc @ B ) )
= ( vplus @ ( vmul @ A @ B ) @ A ) )
& ! [A: $i] :
( ( vmul @ A @ v1 )
= A ) ),
inference(miniscope,[status(thm)],[48]) ).
thf(51,plain,
! [B: $i,A: $i] :
( ( vmul @ A @ ( vsucc @ B ) )
= ( vplus @ ( vmul @ A @ B ) @ A ) ),
inference(cnf,[status(esa)],[49]) ).
thf(54,plain,
! [B: $i,A: $i] :
( ( vplus @ ( vmul @ A @ B ) @ A )
= ( vmul @ A @ ( vsucc @ B ) ) ),
inference(lifteq,[status(thm)],[51]) ).
thf(9,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/sandbox/benchmark/theBenchmark.p','ass(cond(conseq(263), 1), 6)') ).
thf(40,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)],[9]) ).
thf(41,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(cnf,[status(esa)],[40]) ).
thf(42,plain,
! [A: $i] :
( ( ( vplus @ ( vmul @ vd411 @ A ) @ A )
!= ( vmul @ ( vsucc @ vd411 ) @ A ) )
| ( ( vplus @ ( vplus @ ( vmul @ vd411 @ A ) @ A ) @ ( vsucc @ vd411 ) )
= ( vplus @ ( vmul @ ( vsucc @ vd411 ) @ A ) @ ( vsucc @ vd411 ) ) ) ),
inference(lifteq,[status(thm)],[41]) ).
thf(2867,plain,
! [A: $i] :
( ( ( vmul @ ( vsucc @ vd411 ) @ sk1 )
!= ( vmul @ ( vsucc @ vd411 ) @ A ) )
| ( ( vplus @ ( vplus @ ( vmul @ vd411 @ A ) @ A ) @ ( vsucc @ vd411 ) )
= ( vplus @ ( vmul @ ( vsucc @ vd411 ) @ A ) @ ( vsucc @ vd411 ) ) )
| ( ( vplus @ ( vmul @ vd411 @ sk1 ) @ sk1 )
!= ( vplus @ ( vmul @ vd411 @ A ) @ A ) ) ),
inference(paramod_ordered,[status(thm)],[21,42]) ).
thf(2868,plain,
( ( ( vmul @ ( vsucc @ vd411 ) @ sk1 )
!= ( vmul @ ( vsucc @ vd411 ) @ sk1 ) )
| ( ( vplus @ ( vplus @ ( vmul @ vd411 @ sk1 ) @ sk1 ) @ ( vsucc @ vd411 ) )
= ( vplus @ ( vmul @ ( vsucc @ vd411 ) @ sk1 ) @ ( vsucc @ vd411 ) ) ) ),
inference(pattern_uni,[status(thm)],[2867:[bind(A,$thf( sk1 ))]]) ).
thf(3008,plain,
( ( vplus @ ( vplus @ ( vmul @ vd411 @ sk1 ) @ sk1 ) @ ( vsucc @ vd411 ) )
= ( vplus @ ( vmul @ ( vsucc @ vd411 ) @ sk1 ) @ ( vsucc @ vd411 ) ) ),
inference(simp,[status(thm)],[2868]) ).
thf(15,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(61,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)],[15]) ).
thf(62,plain,
! [C: $i,B: $i,A: $i] :
( ( vplus @ ( vplus @ A @ B ) @ C )
= ( vplus @ A @ ( vplus @ B @ C ) ) ),
inference(cnf,[status(esa)],[61]) ).
thf(63,plain,
! [C: $i,B: $i,A: $i] :
( ( vplus @ ( vplus @ A @ B ) @ C )
= ( vplus @ A @ ( vplus @ B @ C ) ) ),
inference(lifteq,[status(thm)],[62]) ).
thf(4993,plain,
( ( vplus @ ( vmul @ vd411 @ sk1 ) @ ( vplus @ sk1 @ ( vsucc @ vd411 ) ) )
= ( vmul @ ( vsucc @ vd411 ) @ ( vsucc @ sk1 ) ) ),
inference(rewrite,[status(thm)],[3008,54,63]) ).
thf(5013,plain,
! [B: $i,A: $i] :
( ( ( vplus @ A @ B )
= ( vmul @ ( vsucc @ vd411 ) @ ( vsucc @ sk1 ) ) )
| ( ( vplus @ ( vmul @ vd411 @ sk1 ) @ ( vplus @ sk1 @ ( vsucc @ vd411 ) ) )
!= ( vplus @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4993,57]) ).
thf(5014,plain,
( ( vplus @ ( vplus @ sk1 @ ( vsucc @ vd411 ) ) @ ( vmul @ vd411 @ sk1 ) )
= ( vmul @ ( vsucc @ vd411 ) @ ( vsucc @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[5013:[bind(A,$thf( vplus @ sk1 @ ( vsucc @ vd411 ) )),bind(B,$thf( vmul @ vd411 @ sk1 ))]]) ).
thf(5305,plain,
( ( vplus @ sk1 @ ( vplus @ ( vsucc @ vd411 ) @ ( vmul @ vd411 @ sk1 ) ) )
= ( vmul @ ( vsucc @ vd411 ) @ ( vsucc @ sk1 ) ) ),
inference(rewrite,[status(thm)],[5014,63]) ).
thf(5325,plain,
! [B: $i,A: $i] :
( ( ( vplus @ A @ B )
= ( vmul @ ( vsucc @ vd411 ) @ ( vsucc @ sk1 ) ) )
| ( ( vplus @ sk1 @ ( vplus @ ( vsucc @ vd411 ) @ ( vmul @ vd411 @ sk1 ) ) )
!= ( vplus @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[5305,57]) ).
thf(5326,plain,
( ( vplus @ ( vplus @ ( vsucc @ vd411 ) @ ( vmul @ vd411 @ sk1 ) ) @ sk1 )
= ( vmul @ ( vsucc @ vd411 ) @ ( vsucc @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[5325:[bind(A,$thf( vplus @ ( vsucc @ vd411 ) @ ( vmul @ vd411 @ sk1 ) )),bind(B,$thf( sk1 ))]]) ).
thf(5814,plain,
( ( vplus @ ( vsucc @ vd411 ) @ ( vplus @ ( vmul @ vd411 @ sk1 ) @ sk1 ) )
= ( vmul @ ( vsucc @ vd411 ) @ ( vsucc @ sk1 ) ) ),
inference(rewrite,[status(thm)],[5326,63]) ).
thf(5839,plain,
! [B: $i,A: $i] :
( ( ( vplus @ A @ B )
= ( vmul @ ( vsucc @ vd411 ) @ ( vsucc @ sk1 ) ) )
| ( ( vplus @ ( vsucc @ vd411 ) @ ( vplus @ ( vmul @ vd411 @ sk1 ) @ sk1 ) )
!= ( vplus @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[5814,57]) ).
thf(5840,plain,
( ( vplus @ ( vplus @ ( vmul @ vd411 @ sk1 ) @ sk1 ) @ ( vsucc @ vd411 ) )
= ( vmul @ ( vsucc @ vd411 ) @ ( vsucc @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[5839:[bind(A,$thf( vplus @ ( vmul @ vd411 @ sk1 ) @ sk1 )),bind(B,$thf( vsucc @ vd411 ))]]) ).
thf(6227,plain,
( ( vsucc @ ( vplus @ ( vplus @ ( vmul @ vd411 @ sk1 ) @ sk1 ) @ vd411 ) )
= ( vmul @ ( vsucc @ vd411 ) @ ( vsucc @ sk1 ) ) ),
inference(rewrite,[status(thm)],[5840,70]) ).
thf(6288,plain,
! [B: $i,A: $i] :
( ( ( vsucc @ ( vplus @ ( vplus @ A @ B ) @ vd411 ) )
= ( vmul @ ( vsucc @ vd411 ) @ ( vsucc @ sk1 ) ) )
| ( ( vplus @ B @ A )
!= ( vplus @ ( vmul @ vd411 @ sk1 ) @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[57,6227]) ).
thf(6289,plain,
( ( vsucc @ ( vplus @ ( vplus @ sk1 @ ( vmul @ vd411 @ sk1 ) ) @ vd411 ) )
= ( vmul @ ( vsucc @ vd411 ) @ ( vsucc @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[6288:[bind(A,$thf( sk1 )),bind(B,$thf( vmul @ vd411 @ sk1 ))]]) ).
thf(7232,plain,
( ( vsucc @ ( vplus @ sk1 @ ( vplus @ ( vmul @ vd411 @ sk1 ) @ vd411 ) ) )
= ( vmul @ ( vsucc @ vd411 ) @ ( vsucc @ sk1 ) ) ),
inference(rewrite,[status(thm)],[6289,63]) ).
thf(7363,plain,
! [B: $i,A: $i] :
( ( ( vsucc @ ( vplus @ sk1 @ ( vmul @ A @ ( vsucc @ B ) ) ) )
= ( vmul @ ( vsucc @ vd411 ) @ ( vsucc @ sk1 ) ) )
| ( ( vplus @ ( vmul @ A @ B ) @ A )
!= ( vplus @ ( vmul @ vd411 @ sk1 ) @ vd411 ) ) ),
inference(paramod_ordered,[status(thm)],[54,7232]) ).
thf(7364,plain,
( ( vsucc @ ( vplus @ sk1 @ ( vmul @ vd411 @ ( vsucc @ sk1 ) ) ) )
= ( vmul @ ( vsucc @ vd411 ) @ ( vsucc @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[7363:[bind(A,$thf( vd411 )),bind(B,$thf( sk1 ))]]) ).
thf(9266,plain,
$false,
inference(simplifyReflect,[status(thm)],[9075,7364]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : NUM845+2 : TPTP v8.2.0. Released v4.1.0.
% 0.06/0.15 % Command : run_Leo-III %s %d
% 0.15/0.37 % Computer : n014.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Mon May 20 06:19:24 EDT 2024
% 0.15/0.37 % CPUTime :
% 0.88/0.84 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.21/0.97 % [INFO] Parsing done (126ms).
% 1.21/0.98 % [INFO] Running in sequential loop mode.
% 1.72/1.20 % [INFO] nitpick registered as external prover.
% 1.72/1.20 % [INFO] Scanning for conjecture ...
% 1.85/1.26 % [INFO] Found a conjecture (or negated_conjecture) and 14 axioms. Running axiom selection ...
% 1.85/1.29 % [INFO] Axiom selection finished. Selected 14 axioms (removed 0 axioms).
% 2.04/1.33 % [INFO] Problem is first-order (TPTP FOF).
% 2.04/1.33 % [INFO] Type checking passed.
% 2.04/1.33 % [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 ...
% 40.42/7.01 % [INFO] Killing All external provers ...
% 40.42/7.01 % Time passed: 6504ms (effective reasoning time: 6031ms)
% 40.42/7.01 % 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)>
% 40.42/7.02 % Axioms used in derivation (6): ass(cond(conseq(263), 1), 6), qu(cond(conseq(axiom(3)), 3), and(holds(definiens(29), 45, 0), holds(definiens(29), 44, 0))), ass(cond(33, 0), 0), ass(cond(61, 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)))
% 40.42/7.02 % No. of inferences in proof: 75
% 40.42/7.02 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 6504 ms resp. 6031 ms w/o parsing
% 40.42/7.09 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 40.42/7.09 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------