%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : NUM849+1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 10:35:23 AM UTC 2026
% Result : Theorem 0.51s 0.28s
% Output : CNFRefutation 0.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 16
% Syntax : Number of formulae : 101 ( 80 unt; 0 typ; 0 def)
% Number of atoms : 347 ( 247 equ; 0 cnn)
% Maximal formula atoms : 2 ( 3 avg)
% Number of connectives : 1066 ( 49 ~; 28 |; 0 &; 967 @)
% ( 0 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 12 usr; 6 con; 0-2 aty)
% Number of variables : 131 ( 0 ^; 131 !; 0 ?; 131 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_geq,type,
geq: $i > $i > $o ).
thf(tp_greater,type,
greater: $i > $i > $o ).
thf(tp_leq,type,
leq: $i > $i > $o ).
thf(tp_less,type,
less: $i > $i > $o ).
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_vskolem2,type,
vskolem2: $i > $i ).
thf(tp_vsucc,type,
vsucc: $i > $i ).
thf(1,axiom,
! [Vd1: $i] :
( ( vsucc @ Vd1 )
!= v1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(restrictor(axiom(1)), holds(scope(axiom(1)), 2, 0))') ).
thf(2,axiom,
! [Vd3: $i,Vd4: $i] :
( ( ( vsucc @ Vd3 )
= ( vsucc @ Vd4 ) )
=> ( Vd3 = Vd4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(antec(axiom(3)), imp(antec(axiom(3))))') ).
thf(3,axiom,
! [Vd7: $i,Vd8: $i] :
( ( Vd7 != Vd8 )
=> ( ( vsucc @ Vd7 )
!= ( vsucc @ Vd8 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(6, 0), 0)') ).
thf(4,axiom,
! [Vd16: $i] :
( ( vsucc @ Vd16 )
!= Vd16 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(12, 0), 0)') ).
thf(9,axiom,
! [Vd68: $i,Vd69: $i] :
( ( vplus @ ( vsucc @ Vd68 ) @ Vd69 )
= ( vsucc @ ( vplus @ Vd68 @ Vd69 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(52, 0), 0)') ).
thf(46,axiom,
! [Vd400: $i] :
( ( vmul @ v1 @ Vd400 )
= Vd400 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(253, 0), 0)') ).
thf(47,axiom,
! [Vd408: $i,Vd409: $i] :
( ( vmul @ ( vsucc @ Vd408 ) @ Vd409 )
= ( vplus @ ( vmul @ Vd408 @ Vd409 ) @ Vd409 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(261, 0), 0)') ).
thf(48,axiom,
! [Vd418: $i,Vd419: $i] :
( ( vmul @ Vd418 @ Vd419 )
= ( vmul @ Vd419 @ Vd418 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(270, 0), 0)') ).
thf(49,axiom,
! [Vd432: $i,Vd433: $i,Vd434: $i] :
( ( vmul @ Vd432 @ ( vplus @ Vd433 @ Vd434 ) )
= ( vplus @ ( vmul @ Vd432 @ Vd433 ) @ ( vmul @ Vd432 @ Vd434 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(281, 0), 0)') ).
thf(50,axiom,
( ( vmul @ ( vmul @ vd448 @ vd449 ) @ v1 )
= ( vmul @ vd448 @ vd449 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(293, 450, 0)') ).
thf(51,axiom,
( ( vmul @ vd448 @ vd449 )
= ( vmul @ vd448 @ ( vmul @ vd449 @ v1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(293, 450, 1)') ).
thf(52,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/sandbox2/benchmark/theBenchmark.p','ass(cond(conseq(292), 1), 3)') ).
thf(53,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/sandbox2/benchmark/theBenchmark.p','ass(cond(conseq(292), 1), 2)') ).
thf(54,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/sandbox2/benchmark/theBenchmark.p','ass(cond(conseq(292), 1), 1)') ).
thf(55,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/sandbox2/benchmark/theBenchmark.p','ass(cond(conseq(292), 1), 0)') ).
thf(56,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/sandbox2/benchmark/theBenchmark.p','qu(ind(296), imp(296))') ).
thf(57,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)],[56]) ).
thf(58,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)],[57]) ).
thf(59,plain,
( ( ! [Vd1: $i] :
( ( vsucc @ Vd1 )
!= v1 ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(60,plain,
( ( ! [Vd3: $i,Vd4: $i] :
( ( ( vsucc @ Vd3 )
= ( vsucc @ Vd4 ) )
=> ( Vd3 = Vd4 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(61,plain,
( ( ! [Vd7: $i,Vd8: $i] :
( ( Vd7 != Vd8 )
=> ( ( vsucc @ Vd7 )
!= ( vsucc @ Vd8 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(62,plain,
( ( ! [Vd16: $i] :
( ( vsucc @ Vd16 )
!= Vd16 ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(63,plain,
( ( ! [Vd68: $i,Vd69: $i] :
( ( vplus @ ( vsucc @ Vd68 ) @ Vd69 )
= ( vsucc @ ( vplus @ Vd68 @ Vd69 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(64,plain,
( ( ! [Vd400: $i] :
( ( vmul @ v1 @ Vd400 )
= Vd400 ) )
= $true ),
inference(unfold_def,[status(thm)],[46]) ).
thf(65,plain,
( ( ! [Vd408: $i,Vd409: $i] :
( ( vmul @ ( vsucc @ Vd408 ) @ Vd409 )
= ( vplus @ ( vmul @ Vd408 @ Vd409 ) @ Vd409 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[47]) ).
thf(66,plain,
( ( ! [Vd418: $i,Vd419: $i] :
( ( vmul @ Vd418 @ Vd419 )
= ( vmul @ Vd419 @ Vd418 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[48]) ).
thf(67,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)],[49]) ).
thf(68,plain,
( ( ( vmul @ ( vmul @ vd448 @ vd449 ) @ v1 )
= ( vmul @ vd448 @ vd449 ) )
= $true ),
inference(unfold_def,[status(thm)],[50]) ).
thf(69,plain,
( ( ( vmul @ vd448 @ vd449 )
= ( vmul @ vd448 @ ( vmul @ vd449 @ v1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[51]) ).
thf(70,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)],[52]) ).
thf(71,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)],[53]) ).
thf(72,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)],[54]) ).
thf(73,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)],[55]) ).
thf(74,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)],[58]) ).
thf(75,plain,
( ( ( vmul @ ( vmul @ vd448 @ vd449 ) @ sK1_Vd454 )
= ( vmul @ vd448 @ ( vmul @ vd449 @ sK1_Vd454 ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[74]) ).
thf(76,plain,
( ( ( vmul @ ( vmul @ vd448 @ vd449 ) @ ( vsucc @ sK1_Vd454 ) )
= ( vmul @ vd448 @ ( vmul @ vd449 @ ( vsucc @ sK1_Vd454 ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[74]) ).
thf(77,plain,
( ( ( vmul @ ( vmul @ vd448 @ vd449 ) @ ( vsucc @ sK1_Vd454 ) )
!= ( vmul @ vd448 @ ( vmul @ vd449 @ ( vsucc @ sK1_Vd454 ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[76]) ).
thf(78,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)],[73]) ).
thf(79,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)],[72]) ).
thf(80,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)],[71]) ).
thf(81,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)],[70]) ).
thf(82,plain,
( ( ( vmul @ vd448 @ vd449 )
= ( vmul @ vd448 @ ( vmul @ vd449 @ v1 ) ) )
= $true ),
inference(copy,[status(thm)],[69]) ).
thf(83,plain,
( ( ( vmul @ ( vmul @ vd448 @ vd449 ) @ v1 )
= ( vmul @ vd448 @ vd449 ) )
= $true ),
inference(copy,[status(thm)],[68]) ).
thf(84,plain,
( ( ! [Vd432: $i,Vd433: $i,Vd434: $i] :
( ( vmul @ Vd432 @ ( vplus @ Vd433 @ Vd434 ) )
= ( vplus @ ( vmul @ Vd432 @ Vd433 ) @ ( vmul @ Vd432 @ Vd434 ) ) ) )
= $true ),
inference(copy,[status(thm)],[67]) ).
thf(85,plain,
( ( ! [Vd418: $i,Vd419: $i] :
( ( vmul @ Vd418 @ Vd419 )
= ( vmul @ Vd419 @ Vd418 ) ) )
= $true ),
inference(copy,[status(thm)],[66]) ).
thf(86,plain,
( ( ! [Vd408: $i,Vd409: $i] :
( ( vmul @ ( vsucc @ Vd408 ) @ Vd409 )
= ( vplus @ ( vmul @ Vd408 @ Vd409 ) @ Vd409 ) ) )
= $true ),
inference(copy,[status(thm)],[65]) ).
thf(87,plain,
( ( ! [Vd400: $i] :
( ( vmul @ v1 @ Vd400 )
= Vd400 ) )
= $true ),
inference(copy,[status(thm)],[64]) ).
thf(88,plain,
( ( ! [Vd68: $i,Vd69: $i] :
( ( vplus @ ( vsucc @ Vd68 ) @ Vd69 )
= ( vsucc @ ( vplus @ Vd68 @ Vd69 ) ) ) )
= $true ),
inference(copy,[status(thm)],[63]) ).
thf(89,plain,
( ( ! [Vd16: $i] :
( ( vsucc @ Vd16 )
!= Vd16 ) )
= $true ),
inference(copy,[status(thm)],[62]) ).
thf(90,plain,
( ( ! [Vd7: $i,Vd8: $i] :
( ( Vd7 != Vd8 )
=> ( ( vsucc @ Vd7 )
!= ( vsucc @ Vd8 ) ) ) )
= $true ),
inference(copy,[status(thm)],[61]) ).
thf(91,plain,
( ( ! [Vd3: $i,Vd4: $i] :
( ( ( vsucc @ Vd3 )
= ( vsucc @ Vd4 ) )
=> ( Vd3 = Vd4 ) ) )
= $true ),
inference(copy,[status(thm)],[60]) ).
thf(92,plain,
( ( ! [Vd1: $i] :
( ( vsucc @ Vd1 )
!= v1 ) )
= $true ),
inference(copy,[status(thm)],[59]) ).
thf(93,plain,
( ( ( vmul @ ( vmul @ vd448 @ vd449 ) @ sK1_Vd454 )
= ( vmul @ vd448 @ ( vmul @ vd449 @ sK1_Vd454 ) ) )
= $true ),
inference(copy,[status(thm)],[75]) ).
thf(94,plain,
( ( ( vmul @ ( vmul @ vd448 @ vd449 ) @ ( vsucc @ sK1_Vd454 ) )
!= ( vmul @ vd448 @ ( vmul @ vd449 @ ( vsucc @ sK1_Vd454 ) ) ) )
= $true ),
inference(copy,[status(thm)],[77]) ).
thf(95,plain,
( ( ! [SX0: $i] :
( ( vsucc @ SX0 )
!= v1 ) )
= $true ),
inference(unfold_def,[status(thm)],[92]) ).
thf(96,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( vsucc @ SX0 )
!= ( vsucc @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[91]) ).
thf(97,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ( SX0 != SX1 ) )
| ( ( vsucc @ SX0 )
!= ( vsucc @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[90]) ).
thf(98,plain,
( ( ! [SX0: $i] :
( ( ( vmul @ ( vmul @ vd448 @ vd449 ) @ SX0 )
!= ( vmul @ vd448 @ ( vmul @ vd449 @ SX0 ) ) )
| ( ( vmul @ ( vmul @ vd448 @ vd449 ) @ ( vsucc @ SX0 ) )
= ( vplus @ ( vmul @ ( vmul @ vd448 @ vd449 ) @ SX0 ) @ ( vmul @ vd448 @ vd449 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[81]) ).
thf(99,plain,
( ( ! [SX0: $i] :
( ( ( vmul @ ( vmul @ vd448 @ vd449 ) @ SX0 )
!= ( vmul @ vd448 @ ( vmul @ vd449 @ SX0 ) ) )
| ( ( vmul @ vd448 @ ( vplus @ ( vmul @ vd449 @ SX0 ) @ vd449 ) )
= ( vmul @ vd448 @ ( vmul @ vd449 @ ( vsucc @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[78]) ).
thf(100,plain,
( ( ! [SX0: $i] :
( ( ( vmul @ ( vmul @ vd448 @ vd449 ) @ SX0 )
!= ( vmul @ vd448 @ ( vmul @ vd449 @ SX0 ) ) )
| ( ( vplus @ ( vmul @ vd448 @ ( vmul @ vd449 @ SX0 ) ) @ ( vmul @ vd448 @ vd449 ) )
= ( vmul @ vd448 @ ( vplus @ ( vmul @ vd449 @ SX0 ) @ vd449 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[79]) ).
thf(101,plain,
( ( ! [SX0: $i] :
( ( vsucc @ SX0 )
!= SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[89]) ).
thf(102,plain,
( ( ! [SX0: $i] :
( ( ( vmul @ ( vmul @ vd448 @ vd449 ) @ SX0 )
!= ( vmul @ vd448 @ ( vmul @ vd449 @ SX0 ) ) )
| ( ( vplus @ ( vmul @ ( vmul @ vd448 @ vd449 ) @ SX0 ) @ ( vmul @ vd448 @ vd449 ) )
= ( vplus @ ( vmul @ vd448 @ ( vmul @ vd449 @ SX0 ) ) @ ( vmul @ vd448 @ vd449 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[80]) ).
thf(103,plain,
! [SV1: $i] :
( ( ! [SY21: $i,SY22: $i] :
( ( vmul @ SV1 @ ( vplus @ SY21 @ SY22 ) )
= ( vplus @ ( vmul @ SV1 @ SY21 ) @ ( vmul @ SV1 @ SY22 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).
thf(104,plain,
! [SV2: $i] :
( ( ! [SY23: $i] :
( ( vmul @ SV2 @ SY23 )
= ( vmul @ SY23 @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(105,plain,
! [SV3: $i] :
( ( ! [SY24: $i] :
( ( vmul @ ( vsucc @ SV3 ) @ SY24 )
= ( vplus @ ( vmul @ SV3 @ SY24 ) @ SY24 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[86]) ).
thf(106,plain,
! [SV4: $i] :
( ( ( vmul @ v1 @ SV4 )
= SV4 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).
thf(107,plain,
! [SV5: $i] :
( ( ! [SY25: $i] :
( ( vplus @ ( vsucc @ SV5 ) @ SY25 )
= ( vsucc @ ( vplus @ SV5 @ SY25 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(108,plain,
( ( ( vmul @ ( vmul @ vd448 @ vd449 ) @ ( vsucc @ sK1_Vd454 ) )
= ( vmul @ vd448 @ ( vmul @ vd449 @ ( vsucc @ sK1_Vd454 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[94]) ).
thf(109,plain,
! [SV6: $i] :
( ( ( vsucc @ SV6 )
!= v1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[95]) ).
thf(110,plain,
! [SV7: $i] :
( ( ! [SY26: $i] :
( ( ( vsucc @ SV7 )
!= ( vsucc @ SY26 ) )
| ( SV7 = SY26 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[96]) ).
thf(111,plain,
! [SV8: $i] :
( ( ! [SY27: $i] :
( ~ ( ( SV8 != SY27 ) )
| ( ( vsucc @ SV8 )
!= ( vsucc @ SY27 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[97]) ).
thf(112,plain,
! [SV9: $i] :
( ( ( ( vmul @ ( vmul @ vd448 @ vd449 ) @ SV9 )
!= ( vmul @ vd448 @ ( vmul @ vd449 @ SV9 ) ) )
| ( ( vmul @ ( vmul @ vd448 @ vd449 ) @ ( vsucc @ SV9 ) )
= ( vplus @ ( vmul @ ( vmul @ vd448 @ vd449 ) @ SV9 ) @ ( vmul @ vd448 @ vd449 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[98]) ).
thf(113,plain,
! [SV10: $i] :
( ( ( ( vmul @ ( vmul @ vd448 @ vd449 ) @ SV10 )
!= ( vmul @ vd448 @ ( vmul @ vd449 @ SV10 ) ) )
| ( ( vmul @ vd448 @ ( vplus @ ( vmul @ vd449 @ SV10 ) @ vd449 ) )
= ( vmul @ vd448 @ ( vmul @ vd449 @ ( vsucc @ SV10 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[99]) ).
thf(114,plain,
! [SV11: $i] :
( ( ( ( vmul @ ( vmul @ vd448 @ vd449 ) @ SV11 )
!= ( vmul @ vd448 @ ( vmul @ vd449 @ SV11 ) ) )
| ( ( vplus @ ( vmul @ vd448 @ ( vmul @ vd449 @ SV11 ) ) @ ( vmul @ vd448 @ vd449 ) )
= ( vmul @ vd448 @ ( vplus @ ( vmul @ vd449 @ SV11 ) @ vd449 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[100]) ).
thf(115,plain,
! [SV12: $i] :
( ( ( vsucc @ SV12 )
!= SV12 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[101]) ).
thf(116,plain,
! [SV13: $i] :
( ( ( ( vmul @ ( vmul @ vd448 @ vd449 ) @ SV13 )
!= ( vmul @ vd448 @ ( vmul @ vd449 @ SV13 ) ) )
| ( ( vplus @ ( vmul @ ( vmul @ vd448 @ vd449 ) @ SV13 ) @ ( vmul @ vd448 @ vd449 ) )
= ( vplus @ ( vmul @ vd448 @ ( vmul @ vd449 @ SV13 ) ) @ ( vmul @ vd448 @ vd449 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[102]) ).
thf(117,plain,
! [SV14: $i,SV1: $i] :
( ( ! [SY28: $i] :
( ( vmul @ SV1 @ ( vplus @ SV14 @ SY28 ) )
= ( vplus @ ( vmul @ SV1 @ SV14 ) @ ( vmul @ SV1 @ SY28 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[103]) ).
thf(118,plain,
! [SV15: $i,SV2: $i] :
( ( ( vmul @ SV2 @ SV15 )
= ( vmul @ SV15 @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[104]) ).
thf(119,plain,
! [SV16: $i,SV3: $i] :
( ( ( vmul @ ( vsucc @ SV3 ) @ SV16 )
= ( vplus @ ( vmul @ SV3 @ SV16 ) @ SV16 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[105]) ).
thf(120,plain,
! [SV17: $i,SV5: $i] :
( ( ( vplus @ ( vsucc @ SV5 ) @ SV17 )
= ( vsucc @ ( vplus @ SV5 @ SV17 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[107]) ).
thf(121,plain,
! [SV6: $i] :
( ( ( vsucc @ SV6 )
= v1 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[109]) ).
thf(122,plain,
! [SV18: $i,SV7: $i] :
( ( ( ( vsucc @ SV7 )
!= ( vsucc @ SV18 ) )
| ( SV7 = SV18 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[110]) ).
thf(123,plain,
! [SV19: $i,SV8: $i] :
( ( ~ ( ( SV8 != SV19 ) )
| ( ( vsucc @ SV8 )
!= ( vsucc @ SV19 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[111]) ).
thf(124,plain,
! [SV9: $i] :
( ( ( ( vmul @ ( vmul @ vd448 @ vd449 ) @ SV9 )
!= ( vmul @ vd448 @ ( vmul @ vd449 @ SV9 ) ) )
= $true )
| ( ( ( vmul @ ( vmul @ vd448 @ vd449 ) @ ( vsucc @ SV9 ) )
= ( vplus @ ( vmul @ ( vmul @ vd448 @ vd449 ) @ SV9 ) @ ( vmul @ vd448 @ vd449 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[112]) ).
thf(125,plain,
! [SV10: $i] :
( ( ( ( vmul @ ( vmul @ vd448 @ vd449 ) @ SV10 )
!= ( vmul @ vd448 @ ( vmul @ vd449 @ SV10 ) ) )
= $true )
| ( ( ( vmul @ vd448 @ ( vplus @ ( vmul @ vd449 @ SV10 ) @ vd449 ) )
= ( vmul @ vd448 @ ( vmul @ vd449 @ ( vsucc @ SV10 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[113]) ).
thf(126,plain,
! [SV11: $i] :
( ( ( ( vmul @ ( vmul @ vd448 @ vd449 ) @ SV11 )
!= ( vmul @ vd448 @ ( vmul @ vd449 @ SV11 ) ) )
= $true )
| ( ( ( vplus @ ( vmul @ vd448 @ ( vmul @ vd449 @ SV11 ) ) @ ( vmul @ vd448 @ vd449 ) )
= ( vmul @ vd448 @ ( vplus @ ( vmul @ vd449 @ SV11 ) @ vd449 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[114]) ).
thf(127,plain,
! [SV12: $i] :
( ( ( vsucc @ SV12 )
= SV12 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[115]) ).
thf(128,plain,
! [SV13: $i] :
( ( ( ( vmul @ ( vmul @ vd448 @ vd449 ) @ SV13 )
!= ( vmul @ vd448 @ ( vmul @ vd449 @ SV13 ) ) )
= $true )
| ( ( ( vplus @ ( vmul @ ( vmul @ vd448 @ vd449 ) @ SV13 ) @ ( vmul @ vd448 @ vd449 ) )
= ( vplus @ ( vmul @ vd448 @ ( vmul @ vd449 @ SV13 ) ) @ ( vmul @ vd448 @ vd449 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[116]) ).
thf(129,plain,
! [SV20: $i,SV14: $i,SV1: $i] :
( ( ( vmul @ SV1 @ ( vplus @ SV14 @ SV20 ) )
= ( vplus @ ( vmul @ SV1 @ SV14 ) @ ( vmul @ SV1 @ SV20 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[117]) ).
thf(130,plain,
! [SV18: $i,SV7: $i] :
( ( ( ( vsucc @ SV7 )
!= ( vsucc @ SV18 ) )
= $true )
| ( ( SV7 = SV18 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[122]) ).
thf(131,plain,
! [SV19: $i,SV8: $i] :
( ( ( ~ ( ( SV8 != SV19 ) ) )
= $true )
| ( ( ( vsucc @ SV8 )
!= ( vsucc @ SV19 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[123]) ).
thf(132,plain,
! [SV9: $i] :
( ( ( ( vmul @ ( vmul @ vd448 @ vd449 ) @ SV9 )
= ( vmul @ vd448 @ ( vmul @ vd449 @ SV9 ) ) )
= $false )
| ( ( ( vmul @ ( vmul @ vd448 @ vd449 ) @ ( vsucc @ SV9 ) )
= ( vplus @ ( vmul @ ( vmul @ vd448 @ vd449 ) @ SV9 ) @ ( vmul @ vd448 @ vd449 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[124]) ).
thf(133,plain,
! [SV10: $i] :
( ( ( ( vmul @ ( vmul @ vd448 @ vd449 ) @ SV10 )
= ( vmul @ vd448 @ ( vmul @ vd449 @ SV10 ) ) )
= $false )
| ( ( ( vmul @ vd448 @ ( vplus @ ( vmul @ vd449 @ SV10 ) @ vd449 ) )
= ( vmul @ vd448 @ ( vmul @ vd449 @ ( vsucc @ SV10 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[125]) ).
thf(134,plain,
! [SV11: $i] :
( ( ( ( vmul @ ( vmul @ vd448 @ vd449 ) @ SV11 )
= ( vmul @ vd448 @ ( vmul @ vd449 @ SV11 ) ) )
= $false )
| ( ( ( vplus @ ( vmul @ vd448 @ ( vmul @ vd449 @ SV11 ) ) @ ( vmul @ vd448 @ vd449 ) )
= ( vmul @ vd448 @ ( vplus @ ( vmul @ vd449 @ SV11 ) @ vd449 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[126]) ).
thf(135,plain,
! [SV13: $i] :
( ( ( ( vmul @ ( vmul @ vd448 @ vd449 ) @ SV13 )
= ( vmul @ vd448 @ ( vmul @ vd449 @ SV13 ) ) )
= $false )
| ( ( ( vplus @ ( vmul @ ( vmul @ vd448 @ vd449 ) @ SV13 ) @ ( vmul @ vd448 @ vd449 ) )
= ( vplus @ ( vmul @ vd448 @ ( vmul @ vd449 @ SV13 ) ) @ ( vmul @ vd448 @ vd449 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[128]) ).
thf(136,plain,
! [SV18: $i,SV7: $i] :
( ( ( ( vsucc @ SV7 )
= ( vsucc @ SV18 ) )
= $false )
| ( ( SV7 = SV18 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[130]) ).
thf(137,plain,
! [SV19: $i,SV8: $i] :
( ( ( SV8 != SV19 )
= $false )
| ( ( ( vsucc @ SV8 )
!= ( vsucc @ SV19 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[131]) ).
thf(138,plain,
! [SV19: $i,SV8: $i] :
( ( ( SV8 = SV19 )
= $true )
| ( ( ( vsucc @ SV8 )
!= ( vsucc @ SV19 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[137]) ).
thf(139,plain,
! [SV19: $i,SV8: $i] :
( ( ( ( vsucc @ SV8 )
= ( vsucc @ SV19 ) )
= $false )
| ( ( SV8 = SV19 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[138]) ).
thf(140,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[82,139,136,135,134,133,132,129,127,121,120,119,118,108,106,93,83]) ).
thf(141,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[140]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM849+1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.17 % Computer : n001.cluster.edu
% 0.08/0.17 % Model : x86_64 x86_64
% 0.08/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.17 % Memory : 8046.5625MB
% 0.08/0.17 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Oct 6 13:48:40 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.51/0.28
% 0.51/0.28 No.of.Axioms: 15
% 0.51/0.28
% 0.51/0.28 Length.of.Defs: 0
% 0.51/0.28
% 0.51/0.28 Contains.Choice.Funs: false
% 0.51/0.28 ...
% 0.51/0.28
% 0.51/0.28 ********************************
% 0.51/0.28 * All subproblems solved! *
% 0.51/0.28 ********************************
% 0.51/0.28 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:16,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:140,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.51/0.28
% 0.51/0.28 %**** Beginning of derivation protocol ****
% 0.51/0.28 % SZS output start CNFRefutation
% See solution above
% 0.51/0.28
% 0.51/0.28 %**** End of derivation protocol ****
% 0.51/0.28 %**** no. of clauses in derivation: 101 ****
% 0.51/0.28 %**** clause counter: 140 ****
% 0.51/0.28
% 0.51/0.28 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:16,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:140,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------