%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : RNG044+1 : TPTP v9.3.1. Released v4.0.0.
% 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 : n002.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 10:37:34 AM UTC 2026
% Result : Theorem 8.36s 1.69s
% Output : CNFRefutation 8.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 6
% Syntax : Number of formulae : 105 ( 48 unt; 0 typ; 0 def)
% Number of atoms : 856 ( 359 equ; 0 cnn)
% Maximal formula atoms : 7 ( 8 avg)
% Number of connectives : 2173 ( 437 ~; 264 |; 39 &;1421 @)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 13 usr; 8 con; 0-2 aty)
% Number of variables : 210 ( 0 ^; 210 !; 0 ?; 210 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_aNaturalNumber0,type,
aNaturalNumber0: $i > $o ).
thf(tp_aScalar0,type,
aScalar0: $i > $o ).
thf(tp_iLess0,type,
iLess0: $i > $i > $o ).
thf(tp_sdtasdt0,type,
sdtasdt0: $i > $i > $i ).
thf(tp_sdtpldt0,type,
sdtpldt0: $i > $i > $i ).
thf(tp_smndt0,type,
smndt0: $i > $i ).
thf(tp_sz00,type,
sz00: $i ).
thf(tp_sz0z00,type,
sz0z00: $i ).
thf(tp_szszuzczcdt0,type,
szszuzczcdt0: $i > $i ).
thf(tp_xu,type,
xu: $i ).
thf(tp_xv,type,
xv: $i ).
thf(tp_xx,type,
xx: $i ).
thf(tp_xy,type,
xy: $i ).
thf(1,axiom,
! [W0: $i,W1: $i,W2: $i] :
( ( ( aScalar0 @ W0 )
& ( aScalar0 @ W1 )
& ( aScalar0 @ W2 ) )
=> ( ( ( sdtasdt0 @ W0 @ ( sdtpldt0 @ W1 @ W2 ) )
= ( sdtpldt0 @ ( sdtasdt0 @ W0 @ W1 ) @ ( sdtasdt0 @ W0 @ W2 ) ) )
& ( ( sdtasdt0 @ ( sdtpldt0 @ W0 @ W1 ) @ W2 )
= ( sdtpldt0 @ ( sdtasdt0 @ W0 @ W2 ) @ ( sdtasdt0 @ W1 @ W2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDistr) ).
thf(2,axiom,
! [W0: $i,W1: $i,W2: $i] :
( ( ( aScalar0 @ W0 )
& ( aScalar0 @ W1 )
& ( aScalar0 @ W2 ) )
=> ( ( ( sdtpldt0 @ ( sdtpldt0 @ W0 @ W1 ) @ W2 )
= ( sdtpldt0 @ W0 @ ( sdtpldt0 @ W1 @ W2 ) ) )
& ( ( sdtpldt0 @ W0 @ W1 )
= ( sdtpldt0 @ W1 @ W0 ) )
& ( ( sdtasdt0 @ ( sdtasdt0 @ W0 @ W1 ) @ W2 )
= ( sdtasdt0 @ W0 @ ( sdtasdt0 @ W1 @ W2 ) ) )
& ( ( sdtasdt0 @ W0 @ W1 )
= ( sdtasdt0 @ W1 @ W0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mArith) ).
thf(5,axiom,
! [W0: $i,W1: $i] :
( ( ( aScalar0 @ W0 )
& ( aScalar0 @ W1 ) )
=> ( aScalar0 @ ( sdtasdt0 @ W0 @ W1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulSc) ).
thf(6,axiom,
! [W0: $i,W1: $i] :
( ( ( aScalar0 @ W0 )
& ( aScalar0 @ W1 ) )
=> ( aScalar0 @ ( sdtpldt0 @ W0 @ W1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSumSc) ).
thf(16,axiom,
( ( aScalar0 @ xx )
& ( aScalar0 @ xy )
& ( aScalar0 @ xu )
& ( aScalar0 @ xv ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__674) ).
thf(17,conjecture,
( ( sdtasdt0 @ ( sdtpldt0 @ xx @ xy ) @ ( sdtpldt0 @ xu @ xv ) )
= ( sdtpldt0 @ ( sdtpldt0 @ ( sdtasdt0 @ xx @ xu ) @ ( sdtasdt0 @ xx @ xv ) ) @ ( sdtpldt0 @ ( sdtasdt0 @ xy @ xu ) @ ( sdtasdt0 @ xy @ xv ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
thf(18,negated_conjecture,
( ( ( sdtasdt0 @ ( sdtpldt0 @ xx @ xy ) @ ( sdtpldt0 @ xu @ xv ) )
= ( sdtpldt0 @ ( sdtpldt0 @ ( sdtasdt0 @ xx @ xu ) @ ( sdtasdt0 @ xx @ xv ) ) @ ( sdtpldt0 @ ( sdtasdt0 @ xy @ xu ) @ ( sdtasdt0 @ xy @ xv ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[17]) ).
thf(19,plain,
( ( ( sdtasdt0 @ ( sdtpldt0 @ xx @ xy ) @ ( sdtpldt0 @ xu @ xv ) )
= ( sdtpldt0 @ ( sdtpldt0 @ ( sdtasdt0 @ xx @ xu ) @ ( sdtasdt0 @ xx @ xv ) ) @ ( sdtpldt0 @ ( sdtasdt0 @ xy @ xu ) @ ( sdtasdt0 @ xy @ xv ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[18]) ).
thf(20,plain,
( ( ! [W0: $i,W1: $i,W2: $i] :
( ( ( aScalar0 @ W0 )
& ( aScalar0 @ W1 )
& ( aScalar0 @ W2 ) )
=> ( ( ( sdtasdt0 @ W0 @ ( sdtpldt0 @ W1 @ W2 ) )
= ( sdtpldt0 @ ( sdtasdt0 @ W0 @ W1 ) @ ( sdtasdt0 @ W0 @ W2 ) ) )
& ( ( sdtasdt0 @ ( sdtpldt0 @ W0 @ W1 ) @ W2 )
= ( sdtpldt0 @ ( sdtasdt0 @ W0 @ W2 ) @ ( sdtasdt0 @ W1 @ W2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(21,plain,
( ( ! [W0: $i,W1: $i,W2: $i] :
( ( ( aScalar0 @ W0 )
& ( aScalar0 @ W1 )
& ( aScalar0 @ W2 ) )
=> ( ( ( sdtpldt0 @ ( sdtpldt0 @ W0 @ W1 ) @ W2 )
= ( sdtpldt0 @ W0 @ ( sdtpldt0 @ W1 @ W2 ) ) )
& ( ( sdtpldt0 @ W0 @ W1 )
= ( sdtpldt0 @ W1 @ W0 ) )
& ( ( sdtasdt0 @ ( sdtasdt0 @ W0 @ W1 ) @ W2 )
= ( sdtasdt0 @ W0 @ ( sdtasdt0 @ W1 @ W2 ) ) )
& ( ( sdtasdt0 @ W0 @ W1 )
= ( sdtasdt0 @ W1 @ W0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(22,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aScalar0 @ W0 )
& ( aScalar0 @ W1 ) )
=> ( aScalar0 @ ( sdtasdt0 @ W0 @ W1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(23,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aScalar0 @ W0 )
& ( aScalar0 @ W1 ) )
=> ( aScalar0 @ ( sdtpldt0 @ W0 @ W1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(24,plain,
( ( ( aScalar0 @ xx )
& ( aScalar0 @ xy )
& ( aScalar0 @ xu )
& ( aScalar0 @ xv ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(25,plain,
( ( ( sdtasdt0 @ ( sdtpldt0 @ xx @ xy ) @ ( sdtpldt0 @ xu @ xv ) )
!= ( sdtpldt0 @ ( sdtpldt0 @ ( sdtasdt0 @ xx @ xu ) @ ( sdtasdt0 @ xx @ xv ) ) @ ( sdtpldt0 @ ( sdtasdt0 @ xy @ xu ) @ ( sdtasdt0 @ xy @ xv ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[19]) ).
thf(26,plain,
( ( ( aScalar0 @ xx )
& ( aScalar0 @ xy )
& ( aScalar0 @ xu )
& ( aScalar0 @ xv ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(27,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aScalar0 @ W0 )
& ( aScalar0 @ W1 ) )
=> ( aScalar0 @ ( sdtpldt0 @ W0 @ W1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(28,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aScalar0 @ W0 )
& ( aScalar0 @ W1 ) )
=> ( aScalar0 @ ( sdtasdt0 @ W0 @ W1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(29,plain,
( ( ! [W0: $i,W1: $i,W2: $i] :
( ( ( aScalar0 @ W0 )
& ( aScalar0 @ W1 )
& ( aScalar0 @ W2 ) )
=> ( ( ( sdtpldt0 @ ( sdtpldt0 @ W0 @ W1 ) @ W2 )
= ( sdtpldt0 @ W0 @ ( sdtpldt0 @ W1 @ W2 ) ) )
& ( ( sdtpldt0 @ W0 @ W1 )
= ( sdtpldt0 @ W1 @ W0 ) )
& ( ( sdtasdt0 @ ( sdtasdt0 @ W0 @ W1 ) @ W2 )
= ( sdtasdt0 @ W0 @ ( sdtasdt0 @ W1 @ W2 ) ) )
& ( ( sdtasdt0 @ W0 @ W1 )
= ( sdtasdt0 @ W1 @ W0 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(30,plain,
( ( ! [W0: $i,W1: $i,W2: $i] :
( ( ( aScalar0 @ W0 )
& ( aScalar0 @ W1 )
& ( aScalar0 @ W2 ) )
=> ( ( ( sdtasdt0 @ W0 @ ( sdtpldt0 @ W1 @ W2 ) )
= ( sdtpldt0 @ ( sdtasdt0 @ W0 @ W1 ) @ ( sdtasdt0 @ W0 @ W2 ) ) )
& ( ( sdtasdt0 @ ( sdtpldt0 @ W0 @ W1 ) @ W2 )
= ( sdtpldt0 @ ( sdtasdt0 @ W0 @ W2 ) @ ( sdtasdt0 @ W1 @ W2 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(31,plain,
( ( ( sdtasdt0 @ ( sdtpldt0 @ xx @ xy ) @ ( sdtpldt0 @ xu @ xv ) )
!= ( sdtpldt0 @ ( sdtpldt0 @ ( sdtasdt0 @ xx @ xu ) @ ( sdtasdt0 @ xx @ xv ) ) @ ( sdtpldt0 @ ( sdtasdt0 @ xy @ xu ) @ ( sdtasdt0 @ xy @ xv ) ) ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(32,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ~ ( ~ ( aScalar0 @ SX0 )
| ~ ( aScalar0 @ SX1 ) )
| ~ ( aScalar0 @ SX2 ) )
| ~ ( ~ ~ ( ~ ~ ( ( ( sdtpldt0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ SX2 )
!= ( sdtpldt0 @ SX0 @ ( sdtpldt0 @ SX1 @ SX2 ) ) )
| ( ( sdtpldt0 @ SX0 @ SX1 )
!= ( sdtpldt0 @ SX1 @ SX0 ) ) )
| ( ( sdtasdt0 @ ( sdtasdt0 @ SX0 @ SX1 ) @ SX2 )
!= ( sdtasdt0 @ SX0 @ ( sdtasdt0 @ SX1 @ SX2 ) ) ) )
| ( ( sdtasdt0 @ SX0 @ SX1 )
!= ( sdtasdt0 @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(33,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ( aScalar0 @ xx )
| ~ ( aScalar0 @ xy ) )
| ~ ( aScalar0 @ xu ) )
| ~ ( aScalar0 @ xv ) ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(34,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( aScalar0 @ SX0 )
| ~ ( aScalar0 @ SX1 ) )
| ( aScalar0 @ ( sdtpldt0 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(35,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ~ ( ~ ( aScalar0 @ SX0 )
| ~ ( aScalar0 @ SX1 ) )
| ~ ( aScalar0 @ SX2 ) )
| ~ ( ( ( sdtasdt0 @ SX0 @ ( sdtpldt0 @ SX1 @ SX2 ) )
!= ( sdtpldt0 @ ( sdtasdt0 @ SX0 @ SX1 ) @ ( sdtasdt0 @ SX0 @ SX2 ) ) )
| ( ( sdtasdt0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ SX2 )
!= ( sdtpldt0 @ ( sdtasdt0 @ SX0 @ SX2 ) @ ( sdtasdt0 @ SX1 @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(36,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( aScalar0 @ SX0 )
| ~ ( aScalar0 @ SX1 ) )
| ( aScalar0 @ ( sdtasdt0 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(37,plain,
( ( ( sdtasdt0 @ ( sdtpldt0 @ xx @ xy ) @ ( sdtpldt0 @ xu @ xv ) )
= ( sdtpldt0 @ ( sdtpldt0 @ ( sdtasdt0 @ xx @ xu ) @ ( sdtasdt0 @ xx @ xv ) ) @ ( sdtpldt0 @ ( sdtasdt0 @ xy @ xu ) @ ( sdtasdt0 @ xy @ xv ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[31]) ).
thf(38,plain,
! [SV1: $i] :
( ( ! [SY10: $i,SY11: $i] :
( ~ ~ ( ~ ~ ( ~ ( aScalar0 @ SV1 )
| ~ ( aScalar0 @ SY10 ) )
| ~ ( aScalar0 @ SY11 ) )
| ~ ( ~ ~ ( ~ ~ ( ( ( sdtpldt0 @ ( sdtpldt0 @ SV1 @ SY10 ) @ SY11 )
!= ( sdtpldt0 @ SV1 @ ( sdtpldt0 @ SY10 @ SY11 ) ) )
| ( ( sdtpldt0 @ SV1 @ SY10 )
!= ( sdtpldt0 @ SY10 @ SV1 ) ) )
| ( ( sdtasdt0 @ ( sdtasdt0 @ SV1 @ SY10 ) @ SY11 )
!= ( sdtasdt0 @ SV1 @ ( sdtasdt0 @ SY10 @ SY11 ) ) ) )
| ( ( sdtasdt0 @ SV1 @ SY10 )
!= ( sdtasdt0 @ SY10 @ SV1 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[32]) ).
thf(39,plain,
( ( ~ ~ ( ~ ~ ( ~ ( aScalar0 @ xx )
| ~ ( aScalar0 @ xy ) )
| ~ ( aScalar0 @ xu ) )
| ~ ( aScalar0 @ xv ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[33]) ).
thf(40,plain,
! [SV2: $i] :
( ( ! [SY12: $i] :
( ~ ~ ( ~ ( aScalar0 @ SV2 )
| ~ ( aScalar0 @ SY12 ) )
| ( aScalar0 @ ( sdtpldt0 @ SV2 @ SY12 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[34]) ).
thf(41,plain,
! [SV3: $i] :
( ( ! [SY13: $i,SY14: $i] :
( ~ ~ ( ~ ~ ( ~ ( aScalar0 @ SV3 )
| ~ ( aScalar0 @ SY13 ) )
| ~ ( aScalar0 @ SY14 ) )
| ~ ( ( ( sdtasdt0 @ SV3 @ ( sdtpldt0 @ SY13 @ SY14 ) )
!= ( sdtpldt0 @ ( sdtasdt0 @ SV3 @ SY13 ) @ ( sdtasdt0 @ SV3 @ SY14 ) ) )
| ( ( sdtasdt0 @ ( sdtpldt0 @ SV3 @ SY13 ) @ SY14 )
!= ( sdtpldt0 @ ( sdtasdt0 @ SV3 @ SY14 ) @ ( sdtasdt0 @ SY13 @ SY14 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[35]) ).
thf(42,plain,
! [SV4: $i] :
( ( ! [SY15: $i] :
( ~ ~ ( ~ ( aScalar0 @ SV4 )
| ~ ( aScalar0 @ SY15 ) )
| ( aScalar0 @ ( sdtasdt0 @ SV4 @ SY15 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[36]) ).
thf(43,plain,
! [SV5: $i,SV1: $i] :
( ( ! [SY16: $i] :
( ~ ~ ( ~ ~ ( ~ ( aScalar0 @ SV1 )
| ~ ( aScalar0 @ SV5 ) )
| ~ ( aScalar0 @ SY16 ) )
| ~ ( ~ ~ ( ~ ~ ( ( ( sdtpldt0 @ ( sdtpldt0 @ SV1 @ SV5 ) @ SY16 )
!= ( sdtpldt0 @ SV1 @ ( sdtpldt0 @ SV5 @ SY16 ) ) )
| ( ( sdtpldt0 @ SV1 @ SV5 )
!= ( sdtpldt0 @ SV5 @ SV1 ) ) )
| ( ( sdtasdt0 @ ( sdtasdt0 @ SV1 @ SV5 ) @ SY16 )
!= ( sdtasdt0 @ SV1 @ ( sdtasdt0 @ SV5 @ SY16 ) ) ) )
| ( ( sdtasdt0 @ SV1 @ SV5 )
!= ( sdtasdt0 @ SV5 @ SV1 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[38]) ).
thf(44,plain,
( ( ~ ~ ( ~ ~ ( ~ ( aScalar0 @ xx )
| ~ ( aScalar0 @ xy ) )
| ~ ( aScalar0 @ xu ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[39]) ).
thf(45,plain,
( ( ~ ( aScalar0 @ xv ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[39]) ).
thf(46,plain,
! [SV6: $i,SV2: $i] :
( ( ~ ~ ( ~ ( aScalar0 @ SV2 )
| ~ ( aScalar0 @ SV6 ) )
| ( aScalar0 @ ( sdtpldt0 @ SV2 @ SV6 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[40]) ).
thf(47,plain,
! [SV7: $i,SV3: $i] :
( ( ! [SY17: $i] :
( ~ ~ ( ~ ~ ( ~ ( aScalar0 @ SV3 )
| ~ ( aScalar0 @ SV7 ) )
| ~ ( aScalar0 @ SY17 ) )
| ~ ( ( ( sdtasdt0 @ SV3 @ ( sdtpldt0 @ SV7 @ SY17 ) )
!= ( sdtpldt0 @ ( sdtasdt0 @ SV3 @ SV7 ) @ ( sdtasdt0 @ SV3 @ SY17 ) ) )
| ( ( sdtasdt0 @ ( sdtpldt0 @ SV3 @ SV7 ) @ SY17 )
!= ( sdtpldt0 @ ( sdtasdt0 @ SV3 @ SY17 ) @ ( sdtasdt0 @ SV7 @ SY17 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[41]) ).
thf(48,plain,
! [SV8: $i,SV4: $i] :
( ( ~ ~ ( ~ ( aScalar0 @ SV4 )
| ~ ( aScalar0 @ SV8 ) )
| ( aScalar0 @ ( sdtasdt0 @ SV4 @ SV8 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[42]) ).
thf(49,plain,
! [SV9: $i,SV5: $i,SV1: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( aScalar0 @ SV1 )
| ~ ( aScalar0 @ SV5 ) )
| ~ ( aScalar0 @ SV9 ) )
| ~ ( ~ ~ ( ~ ~ ( ( ( sdtpldt0 @ ( sdtpldt0 @ SV1 @ SV5 ) @ SV9 )
!= ( sdtpldt0 @ SV1 @ ( sdtpldt0 @ SV5 @ SV9 ) ) )
| ( ( sdtpldt0 @ SV1 @ SV5 )
!= ( sdtpldt0 @ SV5 @ SV1 ) ) )
| ( ( sdtasdt0 @ ( sdtasdt0 @ SV1 @ SV5 ) @ SV9 )
!= ( sdtasdt0 @ SV1 @ ( sdtasdt0 @ SV5 @ SV9 ) ) ) )
| ( ( sdtasdt0 @ SV1 @ SV5 )
!= ( sdtasdt0 @ SV5 @ SV1 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[43]) ).
thf(50,plain,
( ( ~ ( ~ ~ ( ~ ( aScalar0 @ xx )
| ~ ( aScalar0 @ xy ) )
| ~ ( aScalar0 @ xu ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[44]) ).
thf(51,plain,
( ( aScalar0 @ xv )
= $true ),
inference(extcnf_not_neg,[status(thm)],[45]) ).
thf(52,plain,
! [SV6: $i,SV2: $i] :
( ( ( ~ ~ ( ~ ( aScalar0 @ SV2 )
| ~ ( aScalar0 @ SV6 ) ) )
= $true )
| ( ( aScalar0 @ ( sdtpldt0 @ SV2 @ SV6 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[46]) ).
thf(53,plain,
! [SV10: $i,SV7: $i,SV3: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( aScalar0 @ SV3 )
| ~ ( aScalar0 @ SV7 ) )
| ~ ( aScalar0 @ SV10 ) )
| ~ ( ( ( sdtasdt0 @ SV3 @ ( sdtpldt0 @ SV7 @ SV10 ) )
!= ( sdtpldt0 @ ( sdtasdt0 @ SV3 @ SV7 ) @ ( sdtasdt0 @ SV3 @ SV10 ) ) )
| ( ( sdtasdt0 @ ( sdtpldt0 @ SV3 @ SV7 ) @ SV10 )
!= ( sdtpldt0 @ ( sdtasdt0 @ SV3 @ SV10 ) @ ( sdtasdt0 @ SV7 @ SV10 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[47]) ).
thf(54,plain,
! [SV8: $i,SV4: $i] :
( ( ( ~ ~ ( ~ ( aScalar0 @ SV4 )
| ~ ( aScalar0 @ SV8 ) ) )
= $true )
| ( ( aScalar0 @ ( sdtasdt0 @ SV4 @ SV8 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[48]) ).
thf(55,plain,
! [SV9: $i,SV5: $i,SV1: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( aScalar0 @ SV1 )
| ~ ( aScalar0 @ SV5 ) )
| ~ ( aScalar0 @ SV9 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ~ ( ( ( sdtpldt0 @ ( sdtpldt0 @ SV1 @ SV5 ) @ SV9 )
!= ( sdtpldt0 @ SV1 @ ( sdtpldt0 @ SV5 @ SV9 ) ) )
| ( ( sdtpldt0 @ SV1 @ SV5 )
!= ( sdtpldt0 @ SV5 @ SV1 ) ) )
| ( ( sdtasdt0 @ ( sdtasdt0 @ SV1 @ SV5 ) @ SV9 )
!= ( sdtasdt0 @ SV1 @ ( sdtasdt0 @ SV5 @ SV9 ) ) ) )
| ( ( sdtasdt0 @ SV1 @ SV5 )
!= ( sdtasdt0 @ SV5 @ SV1 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[49]) ).
thf(56,plain,
( ( ~ ~ ( ~ ( aScalar0 @ xx )
| ~ ( aScalar0 @ xy ) )
| ~ ( aScalar0 @ xu ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[50]) ).
thf(57,plain,
! [SV6: $i,SV2: $i] :
( ( ( ~ ( ~ ( aScalar0 @ SV2 )
| ~ ( aScalar0 @ SV6 ) ) )
= $false )
| ( ( aScalar0 @ ( sdtpldt0 @ SV2 @ SV6 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[52]) ).
thf(58,plain,
! [SV10: $i,SV7: $i,SV3: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( aScalar0 @ SV3 )
| ~ ( aScalar0 @ SV7 ) )
| ~ ( aScalar0 @ SV10 ) ) )
= $true )
| ( ( ~ ( ( ( sdtasdt0 @ SV3 @ ( sdtpldt0 @ SV7 @ SV10 ) )
!= ( sdtpldt0 @ ( sdtasdt0 @ SV3 @ SV7 ) @ ( sdtasdt0 @ SV3 @ SV10 ) ) )
| ( ( sdtasdt0 @ ( sdtpldt0 @ SV3 @ SV7 ) @ SV10 )
!= ( sdtpldt0 @ ( sdtasdt0 @ SV3 @ SV10 ) @ ( sdtasdt0 @ SV7 @ SV10 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[53]) ).
thf(59,plain,
! [SV8: $i,SV4: $i] :
( ( ( ~ ( ~ ( aScalar0 @ SV4 )
| ~ ( aScalar0 @ SV8 ) ) )
= $false )
| ( ( aScalar0 @ ( sdtasdt0 @ SV4 @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[54]) ).
thf(60,plain,
! [SV9: $i,SV5: $i,SV1: $i] :
( ( ( ~ ( ~ ~ ( ~ ( aScalar0 @ SV1 )
| ~ ( aScalar0 @ SV5 ) )
| ~ ( aScalar0 @ SV9 ) ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ~ ( ( ( sdtpldt0 @ ( sdtpldt0 @ SV1 @ SV5 ) @ SV9 )
!= ( sdtpldt0 @ SV1 @ ( sdtpldt0 @ SV5 @ SV9 ) ) )
| ( ( sdtpldt0 @ SV1 @ SV5 )
!= ( sdtpldt0 @ SV5 @ SV1 ) ) )
| ( ( sdtasdt0 @ ( sdtasdt0 @ SV1 @ SV5 ) @ SV9 )
!= ( sdtasdt0 @ SV1 @ ( sdtasdt0 @ SV5 @ SV9 ) ) ) )
| ( ( sdtasdt0 @ SV1 @ SV5 )
!= ( sdtasdt0 @ SV5 @ SV1 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[55]) ).
thf(61,plain,
( ( ~ ~ ( ~ ( aScalar0 @ xx )
| ~ ( aScalar0 @ xy ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[56]) ).
thf(62,plain,
( ( ~ ( aScalar0 @ xu ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[56]) ).
thf(63,plain,
! [SV6: $i,SV2: $i] :
( ( ( ~ ( aScalar0 @ SV2 )
| ~ ( aScalar0 @ SV6 ) )
= $true )
| ( ( aScalar0 @ ( sdtpldt0 @ SV2 @ SV6 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[57]) ).
thf(64,plain,
! [SV10: $i,SV7: $i,SV3: $i] :
( ( ( ~ ( ~ ~ ( ~ ( aScalar0 @ SV3 )
| ~ ( aScalar0 @ SV7 ) )
| ~ ( aScalar0 @ SV10 ) ) )
= $false )
| ( ( ~ ( ( ( sdtasdt0 @ SV3 @ ( sdtpldt0 @ SV7 @ SV10 ) )
!= ( sdtpldt0 @ ( sdtasdt0 @ SV3 @ SV7 ) @ ( sdtasdt0 @ SV3 @ SV10 ) ) )
| ( ( sdtasdt0 @ ( sdtpldt0 @ SV3 @ SV7 ) @ SV10 )
!= ( sdtpldt0 @ ( sdtasdt0 @ SV3 @ SV10 ) @ ( sdtasdt0 @ SV7 @ SV10 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[58]) ).
thf(65,plain,
! [SV8: $i,SV4: $i] :
( ( ( ~ ( aScalar0 @ SV4 )
| ~ ( aScalar0 @ SV8 ) )
= $true )
| ( ( aScalar0 @ ( sdtasdt0 @ SV4 @ SV8 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[59]) ).
thf(66,plain,
! [SV9: $i,SV5: $i,SV1: $i] :
( ( ( ~ ~ ( ~ ( aScalar0 @ SV1 )
| ~ ( aScalar0 @ SV5 ) )
| ~ ( aScalar0 @ SV9 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ~ ( ( ( sdtpldt0 @ ( sdtpldt0 @ SV1 @ SV5 ) @ SV9 )
!= ( sdtpldt0 @ SV1 @ ( sdtpldt0 @ SV5 @ SV9 ) ) )
| ( ( sdtpldt0 @ SV1 @ SV5 )
!= ( sdtpldt0 @ SV5 @ SV1 ) ) )
| ( ( sdtasdt0 @ ( sdtasdt0 @ SV1 @ SV5 ) @ SV9 )
!= ( sdtasdt0 @ SV1 @ ( sdtasdt0 @ SV5 @ SV9 ) ) ) )
| ( ( sdtasdt0 @ SV1 @ SV5 )
!= ( sdtasdt0 @ SV5 @ SV1 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[60]) ).
thf(67,plain,
( ( ~ ( ~ ( aScalar0 @ xx )
| ~ ( aScalar0 @ xy ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[61]) ).
thf(68,plain,
( ( aScalar0 @ xu )
= $true ),
inference(extcnf_not_neg,[status(thm)],[62]) ).
thf(69,plain,
! [SV6: $i,SV2: $i] :
( ( ( ~ ( aScalar0 @ SV2 ) )
= $true )
| ( ( ~ ( aScalar0 @ SV6 ) )
= $true )
| ( ( aScalar0 @ ( sdtpldt0 @ SV2 @ SV6 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[63]) ).
thf(70,plain,
! [SV10: $i,SV7: $i,SV3: $i] :
( ( ( ~ ~ ( ~ ( aScalar0 @ SV3 )
| ~ ( aScalar0 @ SV7 ) )
| ~ ( aScalar0 @ SV10 ) )
= $true )
| ( ( ~ ( ( ( sdtasdt0 @ SV3 @ ( sdtpldt0 @ SV7 @ SV10 ) )
!= ( sdtpldt0 @ ( sdtasdt0 @ SV3 @ SV7 ) @ ( sdtasdt0 @ SV3 @ SV10 ) ) )
| ( ( sdtasdt0 @ ( sdtpldt0 @ SV3 @ SV7 ) @ SV10 )
!= ( sdtpldt0 @ ( sdtasdt0 @ SV3 @ SV10 ) @ ( sdtasdt0 @ SV7 @ SV10 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[64]) ).
thf(71,plain,
! [SV8: $i,SV4: $i] :
( ( ( ~ ( aScalar0 @ SV4 ) )
= $true )
| ( ( ~ ( aScalar0 @ SV8 ) )
= $true )
| ( ( aScalar0 @ ( sdtasdt0 @ SV4 @ SV8 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[65]) ).
thf(72,plain,
! [SV9: $i,SV5: $i,SV1: $i] :
( ( ( ~ ~ ( ~ ( aScalar0 @ SV1 )
| ~ ( aScalar0 @ SV5 ) ) )
= $true )
| ( ( ~ ( aScalar0 @ SV9 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ~ ( ( ( sdtpldt0 @ ( sdtpldt0 @ SV1 @ SV5 ) @ SV9 )
!= ( sdtpldt0 @ SV1 @ ( sdtpldt0 @ SV5 @ SV9 ) ) )
| ( ( sdtpldt0 @ SV1 @ SV5 )
!= ( sdtpldt0 @ SV5 @ SV1 ) ) )
| ( ( sdtasdt0 @ ( sdtasdt0 @ SV1 @ SV5 ) @ SV9 )
!= ( sdtasdt0 @ SV1 @ ( sdtasdt0 @ SV5 @ SV9 ) ) ) )
| ( ( sdtasdt0 @ SV1 @ SV5 )
!= ( sdtasdt0 @ SV5 @ SV1 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[66]) ).
thf(73,plain,
( ( ~ ( aScalar0 @ xx )
| ~ ( aScalar0 @ xy ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[67]) ).
thf(74,plain,
! [SV6: $i,SV2: $i] :
( ( ( aScalar0 @ SV2 )
= $false )
| ( ( ~ ( aScalar0 @ SV6 ) )
= $true )
| ( ( aScalar0 @ ( sdtpldt0 @ SV2 @ SV6 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[69]) ).
thf(75,plain,
! [SV10: $i,SV7: $i,SV3: $i] :
( ( ( ~ ~ ( ~ ( aScalar0 @ SV3 )
| ~ ( aScalar0 @ SV7 ) ) )
= $true )
| ( ( ~ ( aScalar0 @ SV10 ) )
= $true )
| ( ( ~ ( ( ( sdtasdt0 @ SV3 @ ( sdtpldt0 @ SV7 @ SV10 ) )
!= ( sdtpldt0 @ ( sdtasdt0 @ SV3 @ SV7 ) @ ( sdtasdt0 @ SV3 @ SV10 ) ) )
| ( ( sdtasdt0 @ ( sdtpldt0 @ SV3 @ SV7 ) @ SV10 )
!= ( sdtpldt0 @ ( sdtasdt0 @ SV3 @ SV10 ) @ ( sdtasdt0 @ SV7 @ SV10 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[70]) ).
thf(76,plain,
! [SV8: $i,SV4: $i] :
( ( ( aScalar0 @ SV4 )
= $false )
| ( ( ~ ( aScalar0 @ SV8 ) )
= $true )
| ( ( aScalar0 @ ( sdtasdt0 @ SV4 @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[71]) ).
thf(77,plain,
! [SV9: $i,SV5: $i,SV1: $i] :
( ( ( ~ ( ~ ( aScalar0 @ SV1 )
| ~ ( aScalar0 @ SV5 ) ) )
= $false )
| ( ( ~ ( aScalar0 @ SV9 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ~ ( ( ( sdtpldt0 @ ( sdtpldt0 @ SV1 @ SV5 ) @ SV9 )
!= ( sdtpldt0 @ SV1 @ ( sdtpldt0 @ SV5 @ SV9 ) ) )
| ( ( sdtpldt0 @ SV1 @ SV5 )
!= ( sdtpldt0 @ SV5 @ SV1 ) ) )
| ( ( sdtasdt0 @ ( sdtasdt0 @ SV1 @ SV5 ) @ SV9 )
!= ( sdtasdt0 @ SV1 @ ( sdtasdt0 @ SV5 @ SV9 ) ) ) )
| ( ( sdtasdt0 @ SV1 @ SV5 )
!= ( sdtasdt0 @ SV5 @ SV1 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[72]) ).
thf(78,plain,
( ( ~ ( aScalar0 @ xx ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[73]) ).
thf(79,plain,
( ( ~ ( aScalar0 @ xy ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[73]) ).
thf(80,plain,
! [SV2: $i,SV6: $i] :
( ( ( aScalar0 @ SV6 )
= $false )
| ( ( aScalar0 @ SV2 )
= $false )
| ( ( aScalar0 @ ( sdtpldt0 @ SV2 @ SV6 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[74]) ).
thf(81,plain,
! [SV10: $i,SV7: $i,SV3: $i] :
( ( ( ~ ( ~ ( aScalar0 @ SV3 )
| ~ ( aScalar0 @ SV7 ) ) )
= $false )
| ( ( ~ ( aScalar0 @ SV10 ) )
= $true )
| ( ( ~ ( ( ( sdtasdt0 @ SV3 @ ( sdtpldt0 @ SV7 @ SV10 ) )
!= ( sdtpldt0 @ ( sdtasdt0 @ SV3 @ SV7 ) @ ( sdtasdt0 @ SV3 @ SV10 ) ) )
| ( ( sdtasdt0 @ ( sdtpldt0 @ SV3 @ SV7 ) @ SV10 )
!= ( sdtpldt0 @ ( sdtasdt0 @ SV3 @ SV10 ) @ ( sdtasdt0 @ SV7 @ SV10 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[75]) ).
thf(82,plain,
! [SV4: $i,SV8: $i] :
( ( ( aScalar0 @ SV8 )
= $false )
| ( ( aScalar0 @ SV4 )
= $false )
| ( ( aScalar0 @ ( sdtasdt0 @ SV4 @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[76]) ).
thf(83,plain,
! [SV9: $i,SV5: $i,SV1: $i] :
( ( ( ~ ( aScalar0 @ SV1 )
| ~ ( aScalar0 @ SV5 ) )
= $true )
| ( ( ~ ( aScalar0 @ SV9 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ~ ( ( ( sdtpldt0 @ ( sdtpldt0 @ SV1 @ SV5 ) @ SV9 )
!= ( sdtpldt0 @ SV1 @ ( sdtpldt0 @ SV5 @ SV9 ) ) )
| ( ( sdtpldt0 @ SV1 @ SV5 )
!= ( sdtpldt0 @ SV5 @ SV1 ) ) )
| ( ( sdtasdt0 @ ( sdtasdt0 @ SV1 @ SV5 ) @ SV9 )
!= ( sdtasdt0 @ SV1 @ ( sdtasdt0 @ SV5 @ SV9 ) ) ) )
| ( ( sdtasdt0 @ SV1 @ SV5 )
!= ( sdtasdt0 @ SV5 @ SV1 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[77]) ).
thf(84,plain,
( ( aScalar0 @ xx )
= $true ),
inference(extcnf_not_neg,[status(thm)],[78]) ).
thf(85,plain,
( ( aScalar0 @ xy )
= $true ),
inference(extcnf_not_neg,[status(thm)],[79]) ).
thf(86,plain,
! [SV10: $i,SV7: $i,SV3: $i] :
( ( ( ~ ( aScalar0 @ SV3 )
| ~ ( aScalar0 @ SV7 ) )
= $true )
| ( ( ~ ( aScalar0 @ SV10 ) )
= $true )
| ( ( ~ ( ( ( sdtasdt0 @ SV3 @ ( sdtpldt0 @ SV7 @ SV10 ) )
!= ( sdtpldt0 @ ( sdtasdt0 @ SV3 @ SV7 ) @ ( sdtasdt0 @ SV3 @ SV10 ) ) )
| ( ( sdtasdt0 @ ( sdtpldt0 @ SV3 @ SV7 ) @ SV10 )
!= ( sdtpldt0 @ ( sdtasdt0 @ SV3 @ SV10 ) @ ( sdtasdt0 @ SV7 @ SV10 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[81]) ).
thf(87,plain,
! [SV9: $i,SV5: $i,SV1: $i] :
( ( ( ~ ( aScalar0 @ SV1 ) )
= $true )
| ( ( ~ ( aScalar0 @ SV5 ) )
= $true )
| ( ( ~ ( aScalar0 @ SV9 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ~ ( ( ( sdtpldt0 @ ( sdtpldt0 @ SV1 @ SV5 ) @ SV9 )
!= ( sdtpldt0 @ SV1 @ ( sdtpldt0 @ SV5 @ SV9 ) ) )
| ( ( sdtpldt0 @ SV1 @ SV5 )
!= ( sdtpldt0 @ SV5 @ SV1 ) ) )
| ( ( sdtasdt0 @ ( sdtasdt0 @ SV1 @ SV5 ) @ SV9 )
!= ( sdtasdt0 @ SV1 @ ( sdtasdt0 @ SV5 @ SV9 ) ) ) )
| ( ( sdtasdt0 @ SV1 @ SV5 )
!= ( sdtasdt0 @ SV5 @ SV1 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[83]) ).
thf(88,plain,
! [SV10: $i,SV7: $i,SV3: $i] :
( ( ( ~ ( aScalar0 @ SV3 ) )
= $true )
| ( ( ~ ( aScalar0 @ SV7 ) )
= $true )
| ( ( ~ ( aScalar0 @ SV10 ) )
= $true )
| ( ( ~ ( ( ( sdtasdt0 @ SV3 @ ( sdtpldt0 @ SV7 @ SV10 ) )
!= ( sdtpldt0 @ ( sdtasdt0 @ SV3 @ SV7 ) @ ( sdtasdt0 @ SV3 @ SV10 ) ) )
| ( ( sdtasdt0 @ ( sdtpldt0 @ SV3 @ SV7 ) @ SV10 )
!= ( sdtpldt0 @ ( sdtasdt0 @ SV3 @ SV10 ) @ ( sdtasdt0 @ SV7 @ SV10 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[86]) ).
thf(89,plain,
! [SV9: $i,SV5: $i,SV1: $i] :
( ( ( aScalar0 @ SV1 )
= $false )
| ( ( ~ ( aScalar0 @ SV5 ) )
= $true )
| ( ( ~ ( aScalar0 @ SV9 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ~ ( ( ( sdtpldt0 @ ( sdtpldt0 @ SV1 @ SV5 ) @ SV9 )
!= ( sdtpldt0 @ SV1 @ ( sdtpldt0 @ SV5 @ SV9 ) ) )
| ( ( sdtpldt0 @ SV1 @ SV5 )
!= ( sdtpldt0 @ SV5 @ SV1 ) ) )
| ( ( sdtasdt0 @ ( sdtasdt0 @ SV1 @ SV5 ) @ SV9 )
!= ( sdtasdt0 @ SV1 @ ( sdtasdt0 @ SV5 @ SV9 ) ) ) )
| ( ( sdtasdt0 @ SV1 @ SV5 )
!= ( sdtasdt0 @ SV5 @ SV1 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[87]) ).
thf(90,plain,
! [SV10: $i,SV7: $i,SV3: $i] :
( ( ( aScalar0 @ SV3 )
= $false )
| ( ( ~ ( aScalar0 @ SV7 ) )
= $true )
| ( ( ~ ( aScalar0 @ SV10 ) )
= $true )
| ( ( ~ ( ( ( sdtasdt0 @ SV3 @ ( sdtpldt0 @ SV7 @ SV10 ) )
!= ( sdtpldt0 @ ( sdtasdt0 @ SV3 @ SV7 ) @ ( sdtasdt0 @ SV3 @ SV10 ) ) )
| ( ( sdtasdt0 @ ( sdtpldt0 @ SV3 @ SV7 ) @ SV10 )
!= ( sdtpldt0 @ ( sdtasdt0 @ SV3 @ SV10 ) @ ( sdtasdt0 @ SV7 @ SV10 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[88]) ).
thf(91,plain,
! [SV9: $i,SV1: $i,SV5: $i] :
( ( ( aScalar0 @ SV5 )
= $false )
| ( ( aScalar0 @ SV1 )
= $false )
| ( ( ~ ( aScalar0 @ SV9 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ~ ( ( ( sdtpldt0 @ ( sdtpldt0 @ SV1 @ SV5 ) @ SV9 )
!= ( sdtpldt0 @ SV1 @ ( sdtpldt0 @ SV5 @ SV9 ) ) )
| ( ( sdtpldt0 @ SV1 @ SV5 )
!= ( sdtpldt0 @ SV5 @ SV1 ) ) )
| ( ( sdtasdt0 @ ( sdtasdt0 @ SV1 @ SV5 ) @ SV9 )
!= ( sdtasdt0 @ SV1 @ ( sdtasdt0 @ SV5 @ SV9 ) ) ) )
| ( ( sdtasdt0 @ SV1 @ SV5 )
!= ( sdtasdt0 @ SV5 @ SV1 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[89]) ).
thf(92,plain,
! [SV10: $i,SV3: $i,SV7: $i] :
( ( ( aScalar0 @ SV7 )
= $false )
| ( ( aScalar0 @ SV3 )
= $false )
| ( ( ~ ( aScalar0 @ SV10 ) )
= $true )
| ( ( ~ ( ( ( sdtasdt0 @ SV3 @ ( sdtpldt0 @ SV7 @ SV10 ) )
!= ( sdtpldt0 @ ( sdtasdt0 @ SV3 @ SV7 ) @ ( sdtasdt0 @ SV3 @ SV10 ) ) )
| ( ( sdtasdt0 @ ( sdtpldt0 @ SV3 @ SV7 ) @ SV10 )
!= ( sdtpldt0 @ ( sdtasdt0 @ SV3 @ SV10 ) @ ( sdtasdt0 @ SV7 @ SV10 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[90]) ).
thf(93,plain,
! [SV5: $i,SV1: $i,SV9: $i] :
( ( ( aScalar0 @ SV9 )
= $false )
| ( ( aScalar0 @ SV1 )
= $false )
| ( ( aScalar0 @ SV5 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ~ ( ( ( sdtpldt0 @ ( sdtpldt0 @ SV1 @ SV5 ) @ SV9 )
!= ( sdtpldt0 @ SV1 @ ( sdtpldt0 @ SV5 @ SV9 ) ) )
| ( ( sdtpldt0 @ SV1 @ SV5 )
!= ( sdtpldt0 @ SV5 @ SV1 ) ) )
| ( ( sdtasdt0 @ ( sdtasdt0 @ SV1 @ SV5 ) @ SV9 )
!= ( sdtasdt0 @ SV1 @ ( sdtasdt0 @ SV5 @ SV9 ) ) ) )
| ( ( sdtasdt0 @ SV1 @ SV5 )
!= ( sdtasdt0 @ SV5 @ SV1 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[91]) ).
thf(94,plain,
! [SV7: $i,SV3: $i,SV10: $i] :
( ( ( aScalar0 @ SV10 )
= $false )
| ( ( aScalar0 @ SV3 )
= $false )
| ( ( aScalar0 @ SV7 )
= $false )
| ( ( ~ ( ( ( sdtasdt0 @ SV3 @ ( sdtpldt0 @ SV7 @ SV10 ) )
!= ( sdtpldt0 @ ( sdtasdt0 @ SV3 @ SV7 ) @ ( sdtasdt0 @ SV3 @ SV10 ) ) )
| ( ( sdtasdt0 @ ( sdtpldt0 @ SV3 @ SV7 ) @ SV10 )
!= ( sdtpldt0 @ ( sdtasdt0 @ SV3 @ SV10 ) @ ( sdtasdt0 @ SV7 @ SV10 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[92]) ).
thf(95,plain,
! [SV9: $i,SV5: $i,SV1: $i] :
( ( ( ~ ~ ( ~ ~ ( ( ( sdtpldt0 @ ( sdtpldt0 @ SV1 @ SV5 ) @ SV9 )
!= ( sdtpldt0 @ SV1 @ ( sdtpldt0 @ SV5 @ SV9 ) ) )
| ( ( sdtpldt0 @ SV1 @ SV5 )
!= ( sdtpldt0 @ SV5 @ SV1 ) ) )
| ( ( sdtasdt0 @ ( sdtasdt0 @ SV1 @ SV5 ) @ SV9 )
!= ( sdtasdt0 @ SV1 @ ( sdtasdt0 @ SV5 @ SV9 ) ) ) )
| ( ( sdtasdt0 @ SV1 @ SV5 )
!= ( sdtasdt0 @ SV5 @ SV1 ) ) )
= $false )
| ( ( aScalar0 @ SV5 )
= $false )
| ( ( aScalar0 @ SV1 )
= $false )
| ( ( aScalar0 @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[93]) ).
thf(96,plain,
! [SV10: $i,SV7: $i,SV3: $i] :
( ( ( ( ( sdtasdt0 @ SV3 @ ( sdtpldt0 @ SV7 @ SV10 ) )
!= ( sdtpldt0 @ ( sdtasdt0 @ SV3 @ SV7 ) @ ( sdtasdt0 @ SV3 @ SV10 ) ) )
| ( ( sdtasdt0 @ ( sdtpldt0 @ SV3 @ SV7 ) @ SV10 )
!= ( sdtpldt0 @ ( sdtasdt0 @ SV3 @ SV10 ) @ ( sdtasdt0 @ SV7 @ SV10 ) ) ) )
= $false )
| ( ( aScalar0 @ SV7 )
= $false )
| ( ( aScalar0 @ SV3 )
= $false )
| ( ( aScalar0 @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[94]) ).
thf(97,plain,
! [SV9: $i,SV5: $i,SV1: $i] :
( ( ( ~ ~ ( ~ ~ ( ( ( sdtpldt0 @ ( sdtpldt0 @ SV1 @ SV5 ) @ SV9 )
!= ( sdtpldt0 @ SV1 @ ( sdtpldt0 @ SV5 @ SV9 ) ) )
| ( ( sdtpldt0 @ SV1 @ SV5 )
!= ( sdtpldt0 @ SV5 @ SV1 ) ) )
| ( ( sdtasdt0 @ ( sdtasdt0 @ SV1 @ SV5 ) @ SV9 )
!= ( sdtasdt0 @ SV1 @ ( sdtasdt0 @ SV5 @ SV9 ) ) ) ) )
= $false )
| ( ( aScalar0 @ SV5 )
= $false )
| ( ( aScalar0 @ SV1 )
= $false )
| ( ( aScalar0 @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[95]) ).
thf(98,plain,
! [SV9: $i,SV5: $i,SV1: $i] :
( ( ( ( sdtasdt0 @ SV1 @ SV5 )
!= ( sdtasdt0 @ SV5 @ SV1 ) )
= $false )
| ( ( aScalar0 @ SV5 )
= $false )
| ( ( aScalar0 @ SV1 )
= $false )
| ( ( aScalar0 @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[95]) ).
thf(99,plain,
! [SV10: $i,SV7: $i,SV3: $i] :
( ( ( ( sdtasdt0 @ SV3 @ ( sdtpldt0 @ SV7 @ SV10 ) )
!= ( sdtpldt0 @ ( sdtasdt0 @ SV3 @ SV7 ) @ ( sdtasdt0 @ SV3 @ SV10 ) ) )
= $false )
| ( ( aScalar0 @ SV7 )
= $false )
| ( ( aScalar0 @ SV3 )
= $false )
| ( ( aScalar0 @ SV10 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[96]) ).
thf(100,plain,
! [SV10: $i,SV7: $i,SV3: $i] :
( ( ( ( sdtasdt0 @ ( sdtpldt0 @ SV3 @ SV7 ) @ SV10 )
!= ( sdtpldt0 @ ( sdtasdt0 @ SV3 @ SV10 ) @ ( sdtasdt0 @ SV7 @ SV10 ) ) )
= $false )
| ( ( aScalar0 @ SV7 )
= $false )
| ( ( aScalar0 @ SV3 )
= $false )
| ( ( aScalar0 @ SV10 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[96]) ).
thf(101,plain,
! [SV9: $i,SV5: $i,SV1: $i] :
( ( ( ~ ( ~ ~ ( ( ( sdtpldt0 @ ( sdtpldt0 @ SV1 @ SV5 ) @ SV9 )
!= ( sdtpldt0 @ SV1 @ ( sdtpldt0 @ SV5 @ SV9 ) ) )
| ( ( sdtpldt0 @ SV1 @ SV5 )
!= ( sdtpldt0 @ SV5 @ SV1 ) ) )
| ( ( sdtasdt0 @ ( sdtasdt0 @ SV1 @ SV5 ) @ SV9 )
!= ( sdtasdt0 @ SV1 @ ( sdtasdt0 @ SV5 @ SV9 ) ) ) ) )
= $true )
| ( ( aScalar0 @ SV5 )
= $false )
| ( ( aScalar0 @ SV1 )
= $false )
| ( ( aScalar0 @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[97]) ).
thf(102,plain,
! [SV9: $i,SV5: $i,SV1: $i] :
( ( ( ( sdtasdt0 @ SV1 @ SV5 )
= ( sdtasdt0 @ SV5 @ SV1 ) )
= $true )
| ( ( aScalar0 @ SV5 )
= $false )
| ( ( aScalar0 @ SV1 )
= $false )
| ( ( aScalar0 @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[98]) ).
thf(103,plain,
! [SV10: $i,SV7: $i,SV3: $i] :
( ( ( ( sdtasdt0 @ SV3 @ ( sdtpldt0 @ SV7 @ SV10 ) )
= ( sdtpldt0 @ ( sdtasdt0 @ SV3 @ SV7 ) @ ( sdtasdt0 @ SV3 @ SV10 ) ) )
= $true )
| ( ( aScalar0 @ SV7 )
= $false )
| ( ( aScalar0 @ SV3 )
= $false )
| ( ( aScalar0 @ SV10 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[99]) ).
thf(104,plain,
! [SV10: $i,SV7: $i,SV3: $i] :
( ( ( ( sdtasdt0 @ ( sdtpldt0 @ SV3 @ SV7 ) @ SV10 )
= ( sdtpldt0 @ ( sdtasdt0 @ SV3 @ SV10 ) @ ( sdtasdt0 @ SV7 @ SV10 ) ) )
= $true )
| ( ( aScalar0 @ SV7 )
= $false )
| ( ( aScalar0 @ SV3 )
= $false )
| ( ( aScalar0 @ SV10 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[100]) ).
thf(105,plain,
! [SV9: $i,SV5: $i,SV1: $i] :
( ( ( ~ ~ ( ( ( sdtpldt0 @ ( sdtpldt0 @ SV1 @ SV5 ) @ SV9 )
!= ( sdtpldt0 @ SV1 @ ( sdtpldt0 @ SV5 @ SV9 ) ) )
| ( ( sdtpldt0 @ SV1 @ SV5 )
!= ( sdtpldt0 @ SV5 @ SV1 ) ) )
| ( ( sdtasdt0 @ ( sdtasdt0 @ SV1 @ SV5 ) @ SV9 )
!= ( sdtasdt0 @ SV1 @ ( sdtasdt0 @ SV5 @ SV9 ) ) ) )
= $false )
| ( ( aScalar0 @ SV5 )
= $false )
| ( ( aScalar0 @ SV1 )
= $false )
| ( ( aScalar0 @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[101]) ).
thf(106,plain,
! [SV9: $i,SV5: $i,SV1: $i] :
( ( ( ~ ~ ( ( ( sdtpldt0 @ ( sdtpldt0 @ SV1 @ SV5 ) @ SV9 )
!= ( sdtpldt0 @ SV1 @ ( sdtpldt0 @ SV5 @ SV9 ) ) )
| ( ( sdtpldt0 @ SV1 @ SV5 )
!= ( sdtpldt0 @ SV5 @ SV1 ) ) ) )
= $false )
| ( ( aScalar0 @ SV5 )
= $false )
| ( ( aScalar0 @ SV1 )
= $false )
| ( ( aScalar0 @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[105]) ).
thf(107,plain,
! [SV9: $i,SV5: $i,SV1: $i] :
( ( ( ( sdtasdt0 @ ( sdtasdt0 @ SV1 @ SV5 ) @ SV9 )
!= ( sdtasdt0 @ SV1 @ ( sdtasdt0 @ SV5 @ SV9 ) ) )
= $false )
| ( ( aScalar0 @ SV5 )
= $false )
| ( ( aScalar0 @ SV1 )
= $false )
| ( ( aScalar0 @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[105]) ).
thf(108,plain,
! [SV9: $i,SV5: $i,SV1: $i] :
( ( ( ~ ( ( ( sdtpldt0 @ ( sdtpldt0 @ SV1 @ SV5 ) @ SV9 )
!= ( sdtpldt0 @ SV1 @ ( sdtpldt0 @ SV5 @ SV9 ) ) )
| ( ( sdtpldt0 @ SV1 @ SV5 )
!= ( sdtpldt0 @ SV5 @ SV1 ) ) ) )
= $true )
| ( ( aScalar0 @ SV5 )
= $false )
| ( ( aScalar0 @ SV1 )
= $false )
| ( ( aScalar0 @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[106]) ).
thf(109,plain,
! [SV9: $i,SV5: $i,SV1: $i] :
( ( ( ( sdtasdt0 @ ( sdtasdt0 @ SV1 @ SV5 ) @ SV9 )
= ( sdtasdt0 @ SV1 @ ( sdtasdt0 @ SV5 @ SV9 ) ) )
= $true )
| ( ( aScalar0 @ SV5 )
= $false )
| ( ( aScalar0 @ SV1 )
= $false )
| ( ( aScalar0 @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[107]) ).
thf(110,plain,
! [SV9: $i,SV5: $i,SV1: $i] :
( ( ( ( ( sdtpldt0 @ ( sdtpldt0 @ SV1 @ SV5 ) @ SV9 )
!= ( sdtpldt0 @ SV1 @ ( sdtpldt0 @ SV5 @ SV9 ) ) )
| ( ( sdtpldt0 @ SV1 @ SV5 )
!= ( sdtpldt0 @ SV5 @ SV1 ) ) )
= $false )
| ( ( aScalar0 @ SV5 )
= $false )
| ( ( aScalar0 @ SV1 )
= $false )
| ( ( aScalar0 @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[108]) ).
thf(111,plain,
! [SV9: $i,SV5: $i,SV1: $i] :
( ( ( ( sdtpldt0 @ ( sdtpldt0 @ SV1 @ SV5 ) @ SV9 )
!= ( sdtpldt0 @ SV1 @ ( sdtpldt0 @ SV5 @ SV9 ) ) )
= $false )
| ( ( aScalar0 @ SV5 )
= $false )
| ( ( aScalar0 @ SV1 )
= $false )
| ( ( aScalar0 @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[110]) ).
thf(112,plain,
! [SV9: $i,SV5: $i,SV1: $i] :
( ( ( ( sdtpldt0 @ SV1 @ SV5 )
!= ( sdtpldt0 @ SV5 @ SV1 ) )
= $false )
| ( ( aScalar0 @ SV5 )
= $false )
| ( ( aScalar0 @ SV1 )
= $false )
| ( ( aScalar0 @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[110]) ).
thf(113,plain,
! [SV9: $i,SV5: $i,SV1: $i] :
( ( ( ( sdtpldt0 @ ( sdtpldt0 @ SV1 @ SV5 ) @ SV9 )
= ( sdtpldt0 @ SV1 @ ( sdtpldt0 @ SV5 @ SV9 ) ) )
= $true )
| ( ( aScalar0 @ SV5 )
= $false )
| ( ( aScalar0 @ SV1 )
= $false )
| ( ( aScalar0 @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[111]) ).
thf(114,plain,
! [SV9: $i,SV5: $i,SV1: $i] :
( ( ( ( sdtpldt0 @ SV1 @ SV5 )
= ( sdtpldt0 @ SV5 @ SV1 ) )
= $true )
| ( ( aScalar0 @ SV5 )
= $false )
| ( ( aScalar0 @ SV1 )
= $false )
| ( ( aScalar0 @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[112]) ).
thf(115,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[37,114,113,109,104,103,102,85,84,82,80,68,51]) ).
thf(116,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[115]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG044+1 : TPTP v9.3.1. Released v4.0.0.
% 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
% 0.09/0.18 % Computer : n002.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Oct 6 14:13:57 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.36/1.69
% 8.36/1.69 No.of.Axioms: 5
% 8.36/1.69
% 8.36/1.69 Length.of.Defs: 0
% 8.36/1.69
% 8.36/1.69 Contains.Choice.Funs: false
% 8.36/1.69 ...
% 8.36/1.69
% 8.36/1.69 ********************************
% 8.36/1.69 * All subproblems solved! *
% 8.36/1.69 ********************************
% 8.36/1.69 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:5,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:115,loop_count:0,foatp_calls:1,translation:fof_full)
% 8.36/1.69
% 8.36/1.69 %**** Beginning of derivation protocol ****
% 8.36/1.69 % SZS output start CNFRefutation
% See solution above
% 8.36/1.69
% 8.36/1.69 %**** End of derivation protocol ****
% 8.36/1.69 %**** no. of clauses in derivation: 105 ****
% 8.36/1.69 %**** clause counter: 115 ****
% 8.36/1.69
% 8.36/1.69 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:5,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:115,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------