TSTP Solution File: NUM849+2 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : NUM849+2 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Mon Jul 18 11:56:02 EDT 2022
% Result : Theorem 0.65s 0.82s
% Output : CNFRefutation 0.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 19
% Syntax : Number of formulae : 97 ( 75 unt; 7 typ; 0 def)
% Number of atoms : 304 ( 217 equ; 0 cnn)
% Maximal formula atoms : 2 ( 3 avg)
% Number of connectives : 1134 ( 32 ~; 24 |; 8 &;1058 @)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 133 ( 0 ^ 133 !; 0 ?; 133 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_sK1_Vd454,type,
sK1_Vd454: $i ).
thf(tp_v1,type,
v1: $i ).
thf(tp_vd448,type,
vd448: $i ).
thf(tp_vd449,type,
vd449: $i ).
thf(tp_vmul,type,
vmul: $i > $i > $i ).
thf(tp_vplus,type,
vplus: $i > $i > $i ).
thf(tp_vsucc,type,
vsucc: $i > $i ).
thf(1,axiom,
! [Vd42: $i,Vd43: $i] :
( ( ( vplus @ Vd42 @ ( vsucc @ Vd43 ) )
= ( vsucc @ ( vplus @ Vd42 @ Vd43 ) ) )
& ( ( vplus @ Vd42 @ v1 )
= ( vsucc @ Vd42 ) ) ),
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(2,axiom,
! [Vd78: $i,Vd79: $i] :
( ( vplus @ Vd79 @ Vd78 )
= ( vplus @ Vd78 @ Vd79 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(61, 0), 0)') ).
thf(3,axiom,
! [Vd396: $i,Vd397: $i] :
( ( ( vmul @ Vd396 @ ( vsucc @ Vd397 ) )
= ( vplus @ ( vmul @ Vd396 @ Vd397 ) @ Vd396 ) )
& ( ( vmul @ Vd396 @ v1 )
= Vd396 ) ),
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(4,axiom,
! [Vd408: $i,Vd409: $i] :
( ( vmul @ ( vsucc @ Vd408 ) @ Vd409 )
= ( vplus @ ( vmul @ Vd408 @ Vd409 ) @ Vd409 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(261, 0), 0)') ).
thf(5,axiom,
! [Vd418: $i,Vd419: $i] :
( ( vmul @ Vd418 @ Vd419 )
= ( vmul @ Vd419 @ Vd418 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(270, 0), 0)') ).
thf(6,axiom,
! [Vd432: $i,Vd433: $i,Vd434: $i] :
( ( vmul @ Vd432 @ ( vplus @ Vd433 @ Vd434 ) )
= ( vplus @ ( vmul @ Vd432 @ Vd433 ) @ ( vmul @ Vd432 @ Vd434 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(281, 0), 0)') ).
thf(7,axiom,
( ( vmul @ vd448 @ vd449 )
= ( vmul @ vd448 @ ( vmul @ vd449 @ v1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','holds(293, 450, 1)') ).
thf(8,axiom,
! [Vd451: $i] :
( ( ( vmul @ ( vmul @ vd448 @ vd449 ) @ Vd451 )
= ( vmul @ vd448 @ ( vmul @ vd449 @ Vd451 ) ) )
=> ( ( vmul @ ( vmul @ vd448 @ vd449 ) @ ( vsucc @ Vd451 ) )
= ( vplus @ ( vmul @ ( vmul @ vd448 @ vd449 ) @ Vd451 ) @ ( vmul @ vd448 @ vd449 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(conseq(292), 1), 3)') ).
thf(9,axiom,
! [Vd451: $i] :
( ( ( vmul @ ( vmul @ vd448 @ vd449 ) @ Vd451 )
= ( vmul @ vd448 @ ( vmul @ vd449 @ Vd451 ) ) )
=> ( ( vplus @ ( vmul @ ( vmul @ vd448 @ vd449 ) @ Vd451 ) @ ( vmul @ vd448 @ vd449 ) )
= ( vplus @ ( vmul @ vd448 @ ( vmul @ vd449 @ Vd451 ) ) @ ( vmul @ vd448 @ vd449 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(conseq(292), 1), 2)') ).
thf(10,axiom,
! [Vd451: $i] :
( ( ( vmul @ ( vmul @ vd448 @ vd449 ) @ Vd451 )
= ( vmul @ vd448 @ ( vmul @ vd449 @ Vd451 ) ) )
=> ( ( vplus @ ( vmul @ vd448 @ ( vmul @ vd449 @ Vd451 ) ) @ ( vmul @ vd448 @ vd449 ) )
= ( vmul @ vd448 @ ( vplus @ ( vmul @ vd449 @ Vd451 ) @ vd449 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(conseq(292), 1), 1)') ).
thf(11,axiom,
! [Vd451: $i] :
( ( ( vmul @ ( vmul @ vd448 @ vd449 ) @ Vd451 )
= ( vmul @ vd448 @ ( vmul @ vd449 @ Vd451 ) ) )
=> ( ( vmul @ vd448 @ ( vplus @ ( vmul @ vd449 @ Vd451 ) @ vd449 ) )
= ( vmul @ vd448 @ ( vmul @ vd449 @ ( vsucc @ Vd451 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(conseq(292), 1), 0)') ).
thf(12,conjecture,
! [Vd454: $i] :
( ( ( vmul @ ( vmul @ vd448 @ vd449 ) @ Vd454 )
= ( vmul @ vd448 @ ( vmul @ vd449 @ Vd454 ) ) )
=> ( ( vmul @ ( vmul @ vd448 @ vd449 ) @ ( vsucc @ Vd454 ) )
= ( vmul @ vd448 @ ( vmul @ vd449 @ ( vsucc @ Vd454 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(ind(296), imp(296))') ).
thf(13,negated_conjecture,
( ( ! [Vd454: $i] :
( ( ( vmul @ ( vmul @ vd448 @ vd449 ) @ Vd454 )
= ( vmul @ vd448 @ ( vmul @ vd449 @ Vd454 ) ) )
=> ( ( vmul @ ( vmul @ vd448 @ vd449 ) @ ( vsucc @ Vd454 ) )
= ( vmul @ vd448 @ ( vmul @ vd449 @ ( vsucc @ Vd454 ) ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[12]) ).
thf(14,plain,
( ( ! [Vd454: $i] :
( ( ( vmul @ ( vmul @ vd448 @ vd449 ) @ Vd454 )
= ( vmul @ vd448 @ ( vmul @ vd449 @ Vd454 ) ) )
=> ( ( vmul @ ( vmul @ vd448 @ vd449 ) @ ( vsucc @ Vd454 ) )
= ( vmul @ vd448 @ ( vmul @ vd449 @ ( vsucc @ Vd454 ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[13]) ).
thf(15,plain,
( ( ! [Vd42: $i,Vd43: $i] :
( ( ( vplus @ Vd42 @ ( vsucc @ Vd43 ) )
= ( vsucc @ ( vplus @ Vd42 @ Vd43 ) ) )
& ( ( vplus @ Vd42 @ v1 )
= ( vsucc @ Vd42 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(16,plain,
( ( ! [Vd78: $i,Vd79: $i] :
( ( vplus @ Vd79 @ Vd78 )
= ( vplus @ Vd78 @ Vd79 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(17,plain,
( ( ! [Vd396: $i,Vd397: $i] :
( ( ( vmul @ Vd396 @ ( vsucc @ Vd397 ) )
= ( vplus @ ( vmul @ Vd396 @ Vd397 ) @ Vd396 ) )
& ( ( vmul @ Vd396 @ v1 )
= Vd396 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(18,plain,
( ( ! [Vd408: $i,Vd409: $i] :
( ( vmul @ ( vsucc @ Vd408 ) @ Vd409 )
= ( vplus @ ( vmul @ Vd408 @ Vd409 ) @ Vd409 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(19,plain,
( ( ! [Vd418: $i,Vd419: $i] :
( ( vmul @ Vd418 @ Vd419 )
= ( vmul @ Vd419 @ Vd418 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(20,plain,
( ( ! [Vd432: $i,Vd433: $i,Vd434: $i] :
( ( vmul @ Vd432 @ ( vplus @ Vd433 @ Vd434 ) )
= ( vplus @ ( vmul @ Vd432 @ Vd433 ) @ ( vmul @ Vd432 @ Vd434 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(21,plain,
( ( ( vmul @ vd448 @ vd449 )
= ( vmul @ vd448 @ ( vmul @ vd449 @ v1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(22,plain,
( ( ! [Vd451: $i] :
( ( ( vmul @ ( vmul @ vd448 @ vd449 ) @ Vd451 )
= ( vmul @ vd448 @ ( vmul @ vd449 @ Vd451 ) ) )
=> ( ( vmul @ ( vmul @ vd448 @ vd449 ) @ ( vsucc @ Vd451 ) )
= ( vplus @ ( vmul @ ( vmul @ vd448 @ vd449 ) @ Vd451 ) @ ( vmul @ vd448 @ vd449 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(23,plain,
( ( ! [Vd451: $i] :
( ( ( vmul @ ( vmul @ vd448 @ vd449 ) @ Vd451 )
= ( vmul @ vd448 @ ( vmul @ vd449 @ Vd451 ) ) )
=> ( ( vplus @ ( vmul @ ( vmul @ vd448 @ vd449 ) @ Vd451 ) @ ( vmul @ vd448 @ vd449 ) )
= ( vplus @ ( vmul @ vd448 @ ( vmul @ vd449 @ Vd451 ) ) @ ( vmul @ vd448 @ vd449 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(24,plain,
( ( ! [Vd451: $i] :
( ( ( vmul @ ( vmul @ vd448 @ vd449 ) @ Vd451 )
= ( vmul @ vd448 @ ( vmul @ vd449 @ Vd451 ) ) )
=> ( ( vplus @ ( vmul @ vd448 @ ( vmul @ vd449 @ Vd451 ) ) @ ( vmul @ vd448 @ vd449 ) )
= ( vmul @ vd448 @ ( vplus @ ( vmul @ vd449 @ Vd451 ) @ vd449 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(25,plain,
( ( ! [Vd451: $i] :
( ( ( vmul @ ( vmul @ vd448 @ vd449 ) @ Vd451 )
= ( vmul @ vd448 @ ( vmul @ vd449 @ Vd451 ) ) )
=> ( ( vmul @ vd448 @ ( vplus @ ( vmul @ vd449 @ Vd451 ) @ vd449 ) )
= ( vmul @ vd448 @ ( vmul @ vd449 @ ( vsucc @ Vd451 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(26,plain,
( ( ( ( vmul @ ( vmul @ vd448 @ vd449 ) @ sK1_Vd454 )
= ( vmul @ vd448 @ ( vmul @ vd449 @ sK1_Vd454 ) ) )
=> ( ( vmul @ ( vmul @ vd448 @ vd449 ) @ ( vsucc @ sK1_Vd454 ) )
= ( vmul @ vd448 @ ( vmul @ vd449 @ ( vsucc @ sK1_Vd454 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[14]) ).
thf(27,plain,
( ( ( vmul @ ( vmul @ vd448 @ vd449 ) @ sK1_Vd454 )
= ( vmul @ vd448 @ ( vmul @ vd449 @ sK1_Vd454 ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[26]) ).
thf(28,plain,
( ( ( vmul @ ( vmul @ vd448 @ vd449 ) @ ( vsucc @ sK1_Vd454 ) )
= ( vmul @ vd448 @ ( vmul @ vd449 @ ( vsucc @ sK1_Vd454 ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[26]) ).
thf(29,plain,
( ( ( ( vmul @ ( vmul @ vd448 @ vd449 ) @ ( vsucc @ sK1_Vd454 ) )
!= ( vmul @ vd448 @ ( vmul @ vd449 @ ( vsucc @ sK1_Vd454 ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[28]) ).
thf(30,plain,
( ( ! [Vd42: $i,Vd43: $i] :
( ( vplus @ Vd42 @ ( vsucc @ Vd43 ) )
= ( vsucc @ ( vplus @ Vd42 @ Vd43 ) ) )
& ! [Vd42: $i] :
( ( vplus @ Vd42 @ v1 )
= ( vsucc @ Vd42 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[15]) ).
thf(31,plain,
( ( ! [Vd396: $i,Vd397: $i] :
( ( vmul @ Vd396 @ ( vsucc @ Vd397 ) )
= ( vplus @ ( vmul @ Vd396 @ Vd397 ) @ Vd396 ) )
& ! [Vd396: $i] :
( ( vmul @ Vd396 @ v1 )
= Vd396 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[17]) ).
thf(32,plain,
( ( ! [Vd451: $i] :
( ( ( vmul @ ( vmul @ vd448 @ vd449 ) @ Vd451 )
!= ( vmul @ vd448 @ ( vmul @ vd449 @ Vd451 ) ) )
| ( ( vmul @ ( vmul @ vd448 @ vd449 ) @ ( vsucc @ Vd451 ) )
= ( vplus @ ( vmul @ ( vmul @ vd448 @ vd449 ) @ Vd451 ) @ ( vmul @ vd448 @ vd449 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[22]) ).
thf(33,plain,
( ( ! [Vd451: $i] :
( ( ( vmul @ ( vmul @ vd448 @ vd449 ) @ Vd451 )
!= ( vmul @ vd448 @ ( vmul @ vd449 @ Vd451 ) ) )
| ( ( vplus @ ( vmul @ ( vmul @ vd448 @ vd449 ) @ Vd451 ) @ ( vmul @ vd448 @ vd449 ) )
= ( vplus @ ( vmul @ vd448 @ ( vmul @ vd449 @ Vd451 ) ) @ ( vmul @ vd448 @ vd449 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[23]) ).
thf(34,plain,
( ( ! [Vd451: $i] :
( ( ( vmul @ ( vmul @ vd448 @ vd449 ) @ Vd451 )
!= ( vmul @ vd448 @ ( vmul @ vd449 @ Vd451 ) ) )
| ( ( vplus @ ( vmul @ vd448 @ ( vmul @ vd449 @ Vd451 ) ) @ ( vmul @ vd448 @ vd449 ) )
= ( vmul @ vd448 @ ( vplus @ ( vmul @ vd449 @ Vd451 ) @ vd449 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[24]) ).
thf(35,plain,
( ( ! [Vd451: $i] :
( ( ( vmul @ ( vmul @ vd448 @ vd449 ) @ Vd451 )
!= ( vmul @ vd448 @ ( vmul @ vd449 @ Vd451 ) ) )
| ( ( vmul @ vd448 @ ( vplus @ ( vmul @ vd449 @ Vd451 ) @ vd449 ) )
= ( vmul @ vd448 @ ( vmul @ vd449 @ ( vsucc @ Vd451 ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[25]) ).
thf(36,plain,
( ( ! [Vd451: $i] :
( ( ( vmul @ ( vmul @ vd448 @ vd449 ) @ Vd451 )
!= ( vmul @ vd448 @ ( vmul @ vd449 @ Vd451 ) ) )
| ( ( vmul @ vd448 @ ( vplus @ ( vmul @ vd449 @ Vd451 ) @ vd449 ) )
= ( vmul @ vd448 @ ( vmul @ vd449 @ ( vsucc @ Vd451 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(37,plain,
( ( ! [Vd451: $i] :
( ( ( vmul @ ( vmul @ vd448 @ vd449 ) @ Vd451 )
!= ( vmul @ vd448 @ ( vmul @ vd449 @ Vd451 ) ) )
| ( ( vplus @ ( vmul @ vd448 @ ( vmul @ vd449 @ Vd451 ) ) @ ( vmul @ vd448 @ vd449 ) )
= ( vmul @ vd448 @ ( vplus @ ( vmul @ vd449 @ Vd451 ) @ vd449 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(38,plain,
( ( ! [Vd451: $i] :
( ( ( vmul @ ( vmul @ vd448 @ vd449 ) @ Vd451 )
!= ( vmul @ vd448 @ ( vmul @ vd449 @ Vd451 ) ) )
| ( ( vplus @ ( vmul @ ( vmul @ vd448 @ vd449 ) @ Vd451 ) @ ( vmul @ vd448 @ vd449 ) )
= ( vplus @ ( vmul @ vd448 @ ( vmul @ vd449 @ Vd451 ) ) @ ( vmul @ vd448 @ vd449 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(39,plain,
( ( ! [Vd451: $i] :
( ( ( vmul @ ( vmul @ vd448 @ vd449 ) @ Vd451 )
!= ( vmul @ vd448 @ ( vmul @ vd449 @ Vd451 ) ) )
| ( ( vmul @ ( vmul @ vd448 @ vd449 ) @ ( vsucc @ Vd451 ) )
= ( vplus @ ( vmul @ ( vmul @ vd448 @ vd449 ) @ Vd451 ) @ ( vmul @ vd448 @ vd449 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(40,plain,
( ( ( vmul @ vd448 @ vd449 )
= ( vmul @ vd448 @ ( vmul @ vd449 @ v1 ) ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(41,plain,
( ( ! [Vd432: $i,Vd433: $i,Vd434: $i] :
( ( vmul @ Vd432 @ ( vplus @ Vd433 @ Vd434 ) )
= ( vplus @ ( vmul @ Vd432 @ Vd433 ) @ ( vmul @ Vd432 @ Vd434 ) ) ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(42,plain,
( ( ! [Vd418: $i,Vd419: $i] :
( ( vmul @ Vd418 @ Vd419 )
= ( vmul @ Vd419 @ Vd418 ) ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(43,plain,
( ( ! [Vd408: $i,Vd409: $i] :
( ( vmul @ ( vsucc @ Vd408 ) @ Vd409 )
= ( vplus @ ( vmul @ Vd408 @ Vd409 ) @ Vd409 ) ) )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(44,plain,
( ( ! [Vd396: $i,Vd397: $i] :
( ( vmul @ Vd396 @ ( vsucc @ Vd397 ) )
= ( vplus @ ( vmul @ Vd396 @ Vd397 ) @ Vd396 ) )
& ! [Vd396: $i] :
( ( vmul @ Vd396 @ v1 )
= Vd396 ) )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(45,plain,
( ( ! [Vd78: $i,Vd79: $i] :
( ( vplus @ Vd79 @ Vd78 )
= ( vplus @ Vd78 @ Vd79 ) ) )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(46,plain,
( ( ! [Vd42: $i,Vd43: $i] :
( ( vplus @ Vd42 @ ( vsucc @ Vd43 ) )
= ( vsucc @ ( vplus @ Vd42 @ Vd43 ) ) )
& ! [Vd42: $i] :
( ( vplus @ Vd42 @ v1 )
= ( vsucc @ Vd42 ) ) )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(47,plain,
( ( ( vmul @ ( vmul @ vd448 @ vd449 ) @ sK1_Vd454 )
= ( vmul @ vd448 @ ( vmul @ vd449 @ sK1_Vd454 ) ) )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(48,plain,
( ( ( ( vmul @ ( vmul @ vd448 @ vd449 ) @ ( vsucc @ sK1_Vd454 ) )
!= ( vmul @ vd448 @ ( vmul @ vd449 @ ( vsucc @ sK1_Vd454 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(49,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( vplus @ SX0 @ ( vsucc @ SX1 ) )
= ( vsucc @ ( vplus @ SX0 @ SX1 ) ) )
| ~ ! [SX0: $i] :
( ( vplus @ SX0 @ v1 )
= ( vsucc @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[46]) ).
thf(50,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( vmul @ SX0 @ ( vsucc @ SX1 ) )
= ( vplus @ ( vmul @ SX0 @ SX1 ) @ SX0 ) )
| ~ ! [SX0: $i] :
( ( vmul @ SX0 @ v1 )
= SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[44]) ).
thf(51,plain,
! [SV1: $i] :
( ( ( ( vmul @ ( vmul @ vd448 @ vd449 ) @ SV1 )
!= ( vmul @ vd448 @ ( vmul @ vd449 @ SV1 ) ) )
| ( ( vmul @ vd448 @ ( vplus @ ( vmul @ vd449 @ SV1 ) @ vd449 ) )
= ( vmul @ vd448 @ ( vmul @ vd449 @ ( vsucc @ SV1 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[36]) ).
thf(52,plain,
! [SV2: $i] :
( ( ( ( vmul @ ( vmul @ vd448 @ vd449 ) @ SV2 )
!= ( vmul @ vd448 @ ( vmul @ vd449 @ SV2 ) ) )
| ( ( vplus @ ( vmul @ vd448 @ ( vmul @ vd449 @ SV2 ) ) @ ( vmul @ vd448 @ vd449 ) )
= ( vmul @ vd448 @ ( vplus @ ( vmul @ vd449 @ SV2 ) @ vd449 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[37]) ).
thf(53,plain,
! [SV3: $i] :
( ( ( ( vmul @ ( vmul @ vd448 @ vd449 ) @ SV3 )
!= ( vmul @ vd448 @ ( vmul @ vd449 @ SV3 ) ) )
| ( ( vplus @ ( vmul @ ( vmul @ vd448 @ vd449 ) @ SV3 ) @ ( vmul @ vd448 @ vd449 ) )
= ( vplus @ ( vmul @ vd448 @ ( vmul @ vd449 @ SV3 ) ) @ ( vmul @ vd448 @ vd449 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[38]) ).
thf(54,plain,
! [SV4: $i] :
( ( ( ( vmul @ ( vmul @ vd448 @ vd449 ) @ SV4 )
!= ( vmul @ vd448 @ ( vmul @ vd449 @ SV4 ) ) )
| ( ( vmul @ ( vmul @ vd448 @ vd449 ) @ ( vsucc @ SV4 ) )
= ( vplus @ ( vmul @ ( vmul @ vd448 @ vd449 ) @ SV4 ) @ ( vmul @ vd448 @ vd449 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[39]) ).
thf(55,plain,
! [SV5: $i] :
( ( ! [SY18: $i,SY19: $i] :
( ( vmul @ SV5 @ ( vplus @ SY18 @ SY19 ) )
= ( vplus @ ( vmul @ SV5 @ SY18 ) @ ( vmul @ SV5 @ SY19 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[41]) ).
thf(56,plain,
! [SV6: $i] :
( ( ! [SY20: $i] :
( ( vmul @ SV6 @ SY20 )
= ( vmul @ SY20 @ SV6 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[42]) ).
thf(57,plain,
! [SV7: $i] :
( ( ! [SY21: $i] :
( ( vmul @ ( vsucc @ SV7 ) @ SY21 )
= ( vplus @ ( vmul @ SV7 @ SY21 ) @ SY21 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[43]) ).
thf(58,plain,
! [SV8: $i] :
( ( ! [SY22: $i] :
( ( vplus @ SY22 @ SV8 )
= ( vplus @ SV8 @ SY22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[45]) ).
thf(59,plain,
( ( ( vmul @ ( vmul @ vd448 @ vd449 ) @ ( vsucc @ sK1_Vd454 ) )
= ( vmul @ vd448 @ ( vmul @ vd449 @ ( vsucc @ sK1_Vd454 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[48]) ).
thf(60,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( vplus @ SX0 @ ( vsucc @ SX1 ) )
= ( vsucc @ ( vplus @ SX0 @ SX1 ) ) )
| ~ ! [SX0: $i] :
( ( vplus @ SX0 @ v1 )
= ( vsucc @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[49]) ).
thf(61,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( vmul @ SX0 @ ( vsucc @ SX1 ) )
= ( vplus @ ( vmul @ SX0 @ SX1 ) @ SX0 ) )
| ~ ! [SX0: $i] :
( ( vmul @ SX0 @ v1 )
= SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[50]) ).
thf(62,plain,
! [SV1: $i] :
( ( ( ( ( vmul @ ( vmul @ vd448 @ vd449 ) @ SV1 )
!= ( vmul @ vd448 @ ( vmul @ vd449 @ SV1 ) ) ) )
= $true )
| ( ( ( vmul @ vd448 @ ( vplus @ ( vmul @ vd449 @ SV1 ) @ vd449 ) )
= ( vmul @ vd448 @ ( vmul @ vd449 @ ( vsucc @ SV1 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[51]) ).
thf(63,plain,
! [SV2: $i] :
( ( ( ( ( vmul @ ( vmul @ vd448 @ vd449 ) @ SV2 )
!= ( vmul @ vd448 @ ( vmul @ vd449 @ SV2 ) ) ) )
= $true )
| ( ( ( vplus @ ( vmul @ vd448 @ ( vmul @ vd449 @ SV2 ) ) @ ( vmul @ vd448 @ vd449 ) )
= ( vmul @ vd448 @ ( vplus @ ( vmul @ vd449 @ SV2 ) @ vd449 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[52]) ).
thf(64,plain,
! [SV3: $i] :
( ( ( ( ( vmul @ ( vmul @ vd448 @ vd449 ) @ SV3 )
!= ( vmul @ vd448 @ ( vmul @ vd449 @ SV3 ) ) ) )
= $true )
| ( ( ( vplus @ ( vmul @ ( vmul @ vd448 @ vd449 ) @ SV3 ) @ ( vmul @ vd448 @ vd449 ) )
= ( vplus @ ( vmul @ vd448 @ ( vmul @ vd449 @ SV3 ) ) @ ( vmul @ vd448 @ vd449 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[53]) ).
thf(65,plain,
! [SV4: $i] :
( ( ( ( ( vmul @ ( vmul @ vd448 @ vd449 ) @ SV4 )
!= ( vmul @ vd448 @ ( vmul @ vd449 @ SV4 ) ) ) )
= $true )
| ( ( ( vmul @ ( vmul @ vd448 @ vd449 ) @ ( vsucc @ SV4 ) )
= ( vplus @ ( vmul @ ( vmul @ vd448 @ vd449 ) @ SV4 ) @ ( vmul @ vd448 @ vd449 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[54]) ).
thf(66,plain,
! [SV9: $i,SV5: $i] :
( ( ! [SY23: $i] :
( ( vmul @ SV5 @ ( vplus @ SV9 @ SY23 ) )
= ( vplus @ ( vmul @ SV5 @ SV9 ) @ ( vmul @ SV5 @ SY23 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[55]) ).
thf(67,plain,
! [SV10: $i,SV6: $i] :
( ( ( vmul @ SV6 @ SV10 )
= ( vmul @ SV10 @ SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[56]) ).
thf(68,plain,
! [SV11: $i,SV7: $i] :
( ( ( vmul @ ( vsucc @ SV7 ) @ SV11 )
= ( vplus @ ( vmul @ SV7 @ SV11 ) @ SV11 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[57]) ).
thf(69,plain,
! [SV8: $i,SV12: $i] :
( ( ( vplus @ SV12 @ SV8 )
= ( vplus @ SV8 @ SV12 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[58]) ).
thf(70,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( vplus @ SX0 @ ( vsucc @ SX1 ) )
= ( vsucc @ ( vplus @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[60]) ).
thf(71,plain,
( ( ~ ! [SX0: $i] :
( ( vplus @ SX0 @ v1 )
= ( vsucc @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[60]) ).
thf(72,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( vmul @ SX0 @ ( vsucc @ SX1 ) )
= ( vplus @ ( vmul @ SX0 @ SX1 ) @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[61]) ).
thf(73,plain,
( ( ~ ! [SX0: $i] :
( ( vmul @ SX0 @ v1 )
= SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[61]) ).
thf(74,plain,
! [SV1: $i] :
( ( ( ( vmul @ ( vmul @ vd448 @ vd449 ) @ SV1 )
= ( vmul @ vd448 @ ( vmul @ vd449 @ SV1 ) ) )
= $false )
| ( ( ( vmul @ vd448 @ ( vplus @ ( vmul @ vd449 @ SV1 ) @ vd449 ) )
= ( vmul @ vd448 @ ( vmul @ vd449 @ ( vsucc @ SV1 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[62]) ).
thf(75,plain,
! [SV2: $i] :
( ( ( ( vmul @ ( vmul @ vd448 @ vd449 ) @ SV2 )
= ( vmul @ vd448 @ ( vmul @ vd449 @ SV2 ) ) )
= $false )
| ( ( ( vplus @ ( vmul @ vd448 @ ( vmul @ vd449 @ SV2 ) ) @ ( vmul @ vd448 @ vd449 ) )
= ( vmul @ vd448 @ ( vplus @ ( vmul @ vd449 @ SV2 ) @ vd449 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[63]) ).
thf(76,plain,
! [SV3: $i] :
( ( ( ( vmul @ ( vmul @ vd448 @ vd449 ) @ SV3 )
= ( vmul @ vd448 @ ( vmul @ vd449 @ SV3 ) ) )
= $false )
| ( ( ( vplus @ ( vmul @ ( vmul @ vd448 @ vd449 ) @ SV3 ) @ ( vmul @ vd448 @ vd449 ) )
= ( vplus @ ( vmul @ vd448 @ ( vmul @ vd449 @ SV3 ) ) @ ( vmul @ vd448 @ vd449 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[64]) ).
thf(77,plain,
! [SV4: $i] :
( ( ( ( vmul @ ( vmul @ vd448 @ vd449 ) @ SV4 )
= ( vmul @ vd448 @ ( vmul @ vd449 @ SV4 ) ) )
= $false )
| ( ( ( vmul @ ( vmul @ vd448 @ vd449 ) @ ( vsucc @ SV4 ) )
= ( vplus @ ( vmul @ ( vmul @ vd448 @ vd449 ) @ SV4 ) @ ( vmul @ vd448 @ vd449 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[65]) ).
thf(78,plain,
! [SV13: $i,SV9: $i,SV5: $i] :
( ( ( vmul @ SV5 @ ( vplus @ SV9 @ SV13 ) )
= ( vplus @ ( vmul @ SV5 @ SV9 ) @ ( vmul @ SV5 @ SV13 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[66]) ).
thf(79,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( vplus @ SX0 @ ( vsucc @ SX1 ) )
= ( vsucc @ ( vplus @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[70]) ).
thf(80,plain,
( ( ! [SX0: $i] :
( ( vplus @ SX0 @ v1 )
= ( vsucc @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[71]) ).
thf(81,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( vmul @ SX0 @ ( vsucc @ SX1 ) )
= ( vplus @ ( vmul @ SX0 @ SX1 ) @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[72]) ).
thf(82,plain,
( ( ! [SX0: $i] :
( ( vmul @ SX0 @ v1 )
= SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[73]) ).
thf(83,plain,
! [SV14: $i] :
( ( ! [SY24: $i] :
( ( vplus @ SV14 @ ( vsucc @ SY24 ) )
= ( vsucc @ ( vplus @ SV14 @ SY24 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[79]) ).
thf(84,plain,
! [SV15: $i] :
( ( ( vplus @ SV15 @ v1 )
= ( vsucc @ SV15 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[80]) ).
thf(85,plain,
! [SV16: $i] :
( ( ! [SY25: $i] :
( ( vmul @ SV16 @ ( vsucc @ SY25 ) )
= ( vplus @ ( vmul @ SV16 @ SY25 ) @ SV16 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[81]) ).
thf(86,plain,
! [SV17: $i] :
( ( ( vmul @ SV17 @ v1 )
= SV17 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[82]) ).
thf(87,plain,
! [SV18: $i,SV14: $i] :
( ( ( vplus @ SV14 @ ( vsucc @ SV18 ) )
= ( vsucc @ ( vplus @ SV14 @ SV18 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[83]) ).
thf(88,plain,
! [SV19: $i,SV16: $i] :
( ( ( vmul @ SV16 @ ( vsucc @ SV19 ) )
= ( vplus @ ( vmul @ SV16 @ SV19 ) @ SV16 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(89,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[40,88,87,86,84,78,77,76,75,74,69,68,67,59,47]) ).
thf(90,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[89]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : NUM849+2 : TPTP v8.1.0. Released v4.1.0.
% 0.07/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.15/0.35 % Computer : n026.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 600
% 0.15/0.35 % DateTime : Thu Jul 7 22:34:39 EDT 2022
% 0.15/0.35 % CPUTime :
% 0.15/0.36
% 0.15/0.36 No.of.Axioms: 11
% 0.15/0.36
% 0.15/0.36 Length.of.Defs: 0
% 0.15/0.36
% 0.15/0.36 Contains.Choice.Funs: false
% 0.15/0.37 (rf:0,axioms:11,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:600,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:13,loop_count:0,foatp_calls:0,translation:fof_full).....
% 0.65/0.82
% 0.65/0.82 ********************************
% 0.65/0.82 * All subproblems solved! *
% 0.65/0.82 ********************************
% 0.65/0.82 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:12,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:89,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.65/0.82
% 0.65/0.82 %**** Beginning of derivation protocol ****
% 0.65/0.82 % SZS output start CNFRefutation
% See solution above
% 0.65/0.82
% 0.65/0.82 %**** End of derivation protocol ****
% 0.65/0.82 %**** no. of clauses in derivation: 90 ****
% 0.65/0.82 %**** clause counter: 89 ****
% 0.65/0.82
% 0.65/0.82 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:12,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:89,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------