%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : NUM849+2 : 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 : n026.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 10:35:24 AM UTC 2026
% Result : Theorem 0.39s 0.36s
% Output : CNFRefutation 0.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of formulae : 59 ( 46 unt; 0 typ; 0 def)
% Number of atoms : 205 ( 146 equ; 0 cnn)
% Maximal formula atoms : 2 ( 3 avg)
% Number of connectives : 909 ( 14 ~; 16 |; 0 &; 863 @)
% ( 0 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 69 ( 0 ^; 69 !; 0 ?; 69 :)
% 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(4,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(5,axiom,
! [Vd418: $i,Vd419: $i] :
( ( vmul @ Vd418 @ Vd419 )
= ( vmul @ Vd419 @ Vd418 ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p','ass(cond(281, 0), 0)') ).
thf(7,axiom,
( ( vmul @ vd448 @ vd449 )
= ( vmul @ vd448 @ ( vmul @ vd449 @ v1 ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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,
( ( ! [Vd408: $i,Vd409: $i] :
( ( vmul @ ( vsucc @ Vd408 ) @ Vd409 )
= ( vplus @ ( vmul @ Vd408 @ Vd409 ) @ Vd409 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(16,plain,
( ( ! [Vd418: $i,Vd419: $i] :
( ( vmul @ Vd418 @ Vd419 )
= ( vmul @ Vd419 @ Vd418 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(17,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(18,plain,
( ( ( vmul @ vd448 @ vd449 )
= ( vmul @ vd448 @ ( vmul @ vd449 @ v1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(19,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(20,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(21,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(22,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(23,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(24,plain,
( ( ( vmul @ ( vmul @ vd448 @ vd449 ) @ sK1_Vd454 )
= ( vmul @ vd448 @ ( vmul @ vd449 @ sK1_Vd454 ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[23]) ).
thf(25,plain,
( ( ( vmul @ ( vmul @ vd448 @ vd449 ) @ ( vsucc @ sK1_Vd454 ) )
= ( vmul @ vd448 @ ( vmul @ vd449 @ ( vsucc @ sK1_Vd454 ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[23]) ).
thf(26,plain,
( ( ( vmul @ ( vmul @ vd448 @ vd449 ) @ ( vsucc @ sK1_Vd454 ) )
!= ( vmul @ vd448 @ ( vmul @ vd449 @ ( vsucc @ sK1_Vd454 ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[25]) ).
thf(27,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)],[22]) ).
thf(28,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)],[21]) ).
thf(29,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)],[20]) ).
thf(30,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)],[19]) ).
thf(31,plain,
( ( ( vmul @ vd448 @ vd449 )
= ( vmul @ vd448 @ ( vmul @ vd449 @ v1 ) ) )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(32,plain,
( ( ! [Vd432: $i,Vd433: $i,Vd434: $i] :
( ( vmul @ Vd432 @ ( vplus @ Vd433 @ Vd434 ) )
= ( vplus @ ( vmul @ Vd432 @ Vd433 ) @ ( vmul @ Vd432 @ Vd434 ) ) ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(33,plain,
( ( ! [Vd418: $i,Vd419: $i] :
( ( vmul @ Vd418 @ Vd419 )
= ( vmul @ Vd419 @ Vd418 ) ) )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(34,plain,
( ( ! [Vd408: $i,Vd409: $i] :
( ( vmul @ ( vsucc @ Vd408 ) @ Vd409 )
= ( vplus @ ( vmul @ Vd408 @ Vd409 ) @ Vd409 ) ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(35,plain,
( ( ( vmul @ ( vmul @ vd448 @ vd449 ) @ sK1_Vd454 )
= ( vmul @ vd448 @ ( vmul @ vd449 @ sK1_Vd454 ) ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(36,plain,
( ( ( vmul @ ( vmul @ vd448 @ vd449 ) @ ( vsucc @ sK1_Vd454 ) )
!= ( vmul @ vd448 @ ( vmul @ vd449 @ ( vsucc @ sK1_Vd454 ) ) ) )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(37,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)],[29]) ).
thf(38,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)],[28]) ).
thf(39,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)],[27]) ).
thf(40,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)],[30]) ).
thf(41,plain,
! [SV1: $i] :
( ( ! [SY12: $i,SY13: $i] :
( ( vmul @ SV1 @ ( vplus @ SY12 @ SY13 ) )
= ( vplus @ ( vmul @ SV1 @ SY12 ) @ ( vmul @ SV1 @ SY13 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[32]) ).
thf(42,plain,
! [SV2: $i] :
( ( ! [SY14: $i] :
( ( vmul @ SV2 @ SY14 )
= ( vmul @ SY14 @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[33]) ).
thf(43,plain,
! [SV3: $i] :
( ( ! [SY15: $i] :
( ( vmul @ ( vsucc @ SV3 ) @ SY15 )
= ( vplus @ ( vmul @ SV3 @ SY15 ) @ SY15 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[34]) ).
thf(44,plain,
( ( ( vmul @ ( vmul @ vd448 @ vd449 ) @ ( vsucc @ sK1_Vd454 ) )
= ( vmul @ vd448 @ ( vmul @ vd449 @ ( vsucc @ sK1_Vd454 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[36]) ).
thf(45,plain,
! [SV4: $i] :
( ( ( ( vmul @ ( vmul @ vd448 @ vd449 ) @ SV4 )
!= ( vmul @ vd448 @ ( vmul @ vd449 @ SV4 ) ) )
| ( ( vplus @ ( vmul @ ( vmul @ vd448 @ vd449 ) @ SV4 ) @ ( vmul @ vd448 @ vd449 ) )
= ( vplus @ ( vmul @ vd448 @ ( vmul @ vd449 @ SV4 ) ) @ ( vmul @ vd448 @ vd449 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[37]) ).
thf(46,plain,
! [SV5: $i] :
( ( ( ( vmul @ ( vmul @ vd448 @ vd449 ) @ SV5 )
!= ( vmul @ vd448 @ ( vmul @ vd449 @ SV5 ) ) )
| ( ( vplus @ ( vmul @ vd448 @ ( vmul @ vd449 @ SV5 ) ) @ ( vmul @ vd448 @ vd449 ) )
= ( vmul @ vd448 @ ( vplus @ ( vmul @ vd449 @ SV5 ) @ vd449 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[38]) ).
thf(47,plain,
! [SV6: $i] :
( ( ( ( vmul @ ( vmul @ vd448 @ vd449 ) @ SV6 )
!= ( vmul @ vd448 @ ( vmul @ vd449 @ SV6 ) ) )
| ( ( vmul @ vd448 @ ( vplus @ ( vmul @ vd449 @ SV6 ) @ vd449 ) )
= ( vmul @ vd448 @ ( vmul @ vd449 @ ( vsucc @ SV6 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[39]) ).
thf(48,plain,
! [SV7: $i] :
( ( ( ( vmul @ ( vmul @ vd448 @ vd449 ) @ SV7 )
!= ( vmul @ vd448 @ ( vmul @ vd449 @ SV7 ) ) )
| ( ( vmul @ ( vmul @ vd448 @ vd449 ) @ ( vsucc @ SV7 ) )
= ( vplus @ ( vmul @ ( vmul @ vd448 @ vd449 ) @ SV7 ) @ ( vmul @ vd448 @ vd449 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[40]) ).
thf(49,plain,
! [SV8: $i,SV1: $i] :
( ( ! [SY16: $i] :
( ( vmul @ SV1 @ ( vplus @ SV8 @ SY16 ) )
= ( vplus @ ( vmul @ SV1 @ SV8 ) @ ( vmul @ SV1 @ SY16 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[41]) ).
thf(50,plain,
! [SV9: $i,SV2: $i] :
( ( ( vmul @ SV2 @ SV9 )
= ( vmul @ SV9 @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[42]) ).
thf(51,plain,
! [SV10: $i,SV3: $i] :
( ( ( vmul @ ( vsucc @ SV3 ) @ SV10 )
= ( vplus @ ( vmul @ SV3 @ SV10 ) @ SV10 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[43]) ).
thf(52,plain,
! [SV4: $i] :
( ( ( ( vmul @ ( vmul @ vd448 @ vd449 ) @ SV4 )
!= ( vmul @ vd448 @ ( vmul @ vd449 @ SV4 ) ) )
= $true )
| ( ( ( vplus @ ( vmul @ ( vmul @ vd448 @ vd449 ) @ SV4 ) @ ( vmul @ vd448 @ vd449 ) )
= ( vplus @ ( vmul @ vd448 @ ( vmul @ vd449 @ SV4 ) ) @ ( vmul @ vd448 @ vd449 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[45]) ).
thf(53,plain,
! [SV5: $i] :
( ( ( ( vmul @ ( vmul @ vd448 @ vd449 ) @ SV5 )
!= ( vmul @ vd448 @ ( vmul @ vd449 @ SV5 ) ) )
= $true )
| ( ( ( vplus @ ( vmul @ vd448 @ ( vmul @ vd449 @ SV5 ) ) @ ( vmul @ vd448 @ vd449 ) )
= ( vmul @ vd448 @ ( vplus @ ( vmul @ vd449 @ SV5 ) @ vd449 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[46]) ).
thf(54,plain,
! [SV6: $i] :
( ( ( ( vmul @ ( vmul @ vd448 @ vd449 ) @ SV6 )
!= ( vmul @ vd448 @ ( vmul @ vd449 @ SV6 ) ) )
= $true )
| ( ( ( vmul @ vd448 @ ( vplus @ ( vmul @ vd449 @ SV6 ) @ vd449 ) )
= ( vmul @ vd448 @ ( vmul @ vd449 @ ( vsucc @ SV6 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[47]) ).
thf(55,plain,
! [SV7: $i] :
( ( ( ( vmul @ ( vmul @ vd448 @ vd449 ) @ SV7 )
!= ( vmul @ vd448 @ ( vmul @ vd449 @ SV7 ) ) )
= $true )
| ( ( ( vmul @ ( vmul @ vd448 @ vd449 ) @ ( vsucc @ SV7 ) )
= ( vplus @ ( vmul @ ( vmul @ vd448 @ vd449 ) @ SV7 ) @ ( vmul @ vd448 @ vd449 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[48]) ).
thf(56,plain,
! [SV11: $i,SV8: $i,SV1: $i] :
( ( ( vmul @ SV1 @ ( vplus @ SV8 @ SV11 ) )
= ( vplus @ ( vmul @ SV1 @ SV8 ) @ ( vmul @ SV1 @ SV11 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[49]) ).
thf(57,plain,
! [SV4: $i] :
( ( ( ( vmul @ ( vmul @ vd448 @ vd449 ) @ SV4 )
= ( vmul @ vd448 @ ( vmul @ vd449 @ SV4 ) ) )
= $false )
| ( ( ( vplus @ ( vmul @ ( vmul @ vd448 @ vd449 ) @ SV4 ) @ ( vmul @ vd448 @ vd449 ) )
= ( vplus @ ( vmul @ vd448 @ ( vmul @ vd449 @ SV4 ) ) @ ( vmul @ vd448 @ vd449 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[52]) ).
thf(58,plain,
! [SV5: $i] :
( ( ( ( vmul @ ( vmul @ vd448 @ vd449 ) @ SV5 )
= ( vmul @ vd448 @ ( vmul @ vd449 @ SV5 ) ) )
= $false )
| ( ( ( vplus @ ( vmul @ vd448 @ ( vmul @ vd449 @ SV5 ) ) @ ( vmul @ vd448 @ vd449 ) )
= ( vmul @ vd448 @ ( vplus @ ( vmul @ vd449 @ SV5 ) @ vd449 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[53]) ).
thf(59,plain,
! [SV6: $i] :
( ( ( ( vmul @ ( vmul @ vd448 @ vd449 ) @ SV6 )
= ( vmul @ vd448 @ ( vmul @ vd449 @ SV6 ) ) )
= $false )
| ( ( ( vmul @ vd448 @ ( vplus @ ( vmul @ vd449 @ SV6 ) @ vd449 ) )
= ( vmul @ vd448 @ ( vmul @ vd449 @ ( vsucc @ SV6 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[54]) ).
thf(60,plain,
! [SV7: $i] :
( ( ( ( vmul @ ( vmul @ vd448 @ vd449 ) @ SV7 )
= ( vmul @ vd448 @ ( vmul @ vd449 @ SV7 ) ) )
= $false )
| ( ( ( vmul @ ( vmul @ vd448 @ vd449 ) @ ( vsucc @ SV7 ) )
= ( vplus @ ( vmul @ ( vmul @ vd448 @ vd449 ) @ SV7 ) @ ( vmul @ vd448 @ vd449 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[55]) ).
thf(61,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[31,60,59,58,57,56,51,50,44,35]) ).
thf(62,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[61]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM849+2 : 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
% 0.08/0.20 % Computer : n026.cluster.edu
% 0.08/0.20 % Model : x86_64 x86_64
% 0.08/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.20 % Memory : 8046.5625MB
% 0.08/0.20 % OS : Linux 6.8.0-71-generic
% 0.08/0.20 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.20 % DateTime : Tue Oct 6 13:44:02 UTC 2026
% 0.08/0.21 % CPUTime :
% 0.08/0.21 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.39/0.36
% 0.39/0.36 No.of.Axioms: 8
% 0.39/0.36
% 0.39/0.36 Length.of.Defs: 0
% 0.39/0.36
% 0.39/0.36 Contains.Choice.Funs: false
% 0.39/0.36 ..
% 0.39/0.36
% 0.39/0.36 ********************************
% 0.39/0.36 * All subproblems solved! *
% 0.39/0.36 ********************************
% 0.39/0.36 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:9,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:61,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.39/0.36
% 0.39/0.36 %**** Beginning of derivation protocol ****
% 0.39/0.36 % SZS output start CNFRefutation
% See solution above
% 0.39/0.36
% 0.39/0.36 %**** End of derivation protocol ****
% 0.39/0.36 %**** no. of clauses in derivation: 59 ****
% 0.39/0.36 %**** clause counter: 61 ****
% 0.39/0.36
% 0.39/0.36 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:9,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:61,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------