TSTP Solution File: GRP775+1 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : GRP775+1 : 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 : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sat Jul 16 10:19:57 EDT 2022
% Result : Theorem 236.33s 236.72s
% Output : CNFRefutation 236.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 13
% Syntax : Number of formulae : 238 ( 153 unt; 7 typ; 0 def)
% Number of atoms : 1328 ( 613 equ; 0 cnn)
% Maximal formula atoms : 4 ( 5 avg)
% Number of connectives : 2487 ( 448 ~; 369 |; 39 &;1616 @)
% ( 11 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 533 ( 0 ^ 531 !; 2 ?; 533 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_d,type,
d: $i > $i > $o ).
thf(tp_l,type,
l: $i > $i > $o ).
thf(tp_product,type,
product: $i > $i > $i ).
thf(tp_r,type,
r: $i > $i > $o ).
thf(tp_sK1_X7,type,
sK1_X7: $i ).
thf(tp_sK2_SY81,type,
sK2_SY81: $i ).
thf(tp_sK3_X6,type,
sK3_X6: $i > $i > $i ).
thf(1,axiom,
! [X4: $i,X5: $i] :
( ( d @ X4 @ X5 )
<=> ? [X6: $i] :
( ( r @ X4 @ X6 )
& ( l @ X6 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos05) ).
thf(2,axiom,
! [X2: $i,X3: $i] :
( ( r @ X2 @ X3 )
<=> ( ( ( product @ X2 @ X3 )
= X3 )
& ( ( product @ X3 @ X2 )
= X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos04) ).
thf(3,axiom,
! [X0: $i,X1: $i] :
( ( l @ X0 @ X1 )
<=> ( ( ( product @ X0 @ X1 )
= X0 )
& ( ( product @ X1 @ X0 )
= X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos03) ).
thf(4,axiom,
! [A: $i] :
( ( product @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos02) ).
thf(5,axiom,
! [C: $i,B: $i,A: $i] :
( ( product @ ( product @ A @ B ) @ C )
= ( product @ A @ ( product @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos01) ).
thf(6,conjecture,
! [X7: $i,X8: $i] :
( ( d @ X7 @ X8 )
<=> ( ( ( product @ X7 @ ( product @ X8 @ X7 ) )
= X7 )
& ( ( product @ X8 @ ( product @ X7 @ X8 ) )
= X8 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
thf(7,negated_conjecture,
( ( ! [X7: $i,X8: $i] :
( ( d @ X7 @ X8 )
<=> ( ( ( product @ X7 @ ( product @ X8 @ X7 ) )
= X7 )
& ( ( product @ X8 @ ( product @ X7 @ X8 ) )
= X8 ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[6]) ).
thf(8,plain,
( ( ! [X7: $i,X8: $i] :
( ( d @ X7 @ X8 )
<=> ( ( ( product @ X7 @ ( product @ X8 @ X7 ) )
= X7 )
& ( ( product @ X8 @ ( product @ X7 @ X8 ) )
= X8 ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[7]) ).
thf(9,plain,
( ( ! [X4: $i,X5: $i] :
( ( d @ X4 @ X5 )
<=> ? [X6: $i] :
( ( r @ X4 @ X6 )
& ( l @ X6 @ X5 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(10,plain,
( ( ! [X2: $i,X3: $i] :
( ( r @ X2 @ X3 )
<=> ( ( ( product @ X2 @ X3 )
= X3 )
& ( ( product @ X3 @ X2 )
= X2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(11,plain,
( ( ! [X0: $i,X1: $i] :
( ( l @ X0 @ X1 )
<=> ( ( ( product @ X0 @ X1 )
= X0 )
& ( ( product @ X1 @ X0 )
= X1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(12,plain,
( ( ! [A: $i] :
( ( product @ A @ A )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(13,plain,
( ( ! [C: $i,B: $i,A: $i] :
( ( product @ ( product @ A @ B ) @ C )
= ( product @ A @ ( product @ B @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(14,plain,
( ( ! [SY81: $i] :
( ( d @ sK1_X7 @ SY81 )
<=> ( ( ( product @ sK1_X7 @ ( product @ SY81 @ sK1_X7 ) )
= sK1_X7 )
& ( ( product @ SY81 @ ( product @ sK1_X7 @ SY81 ) )
= SY81 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[8]) ).
thf(15,plain,
( ( ( d @ sK1_X7 @ sK2_SY81 )
<=> ( ( ( product @ sK1_X7 @ ( product @ sK2_SY81 @ sK1_X7 ) )
= sK1_X7 )
& ( ( product @ sK2_SY81 @ ( product @ sK1_X7 @ sK2_SY81 ) )
= sK2_SY81 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[14]) ).
thf(16,plain,
( ( ( d @ sK1_X7 @ sK2_SY81 )
=> ( ( ( product @ sK1_X7 @ ( product @ sK2_SY81 @ sK1_X7 ) )
= sK1_X7 )
& ( ( product @ sK2_SY81 @ ( product @ sK1_X7 @ sK2_SY81 ) )
= sK2_SY81 ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[15]) ).
thf(17,plain,
( ( ( ( ( product @ sK1_X7 @ ( product @ sK2_SY81 @ sK1_X7 ) )
= sK1_X7 )
& ( ( product @ sK2_SY81 @ ( product @ sK1_X7 @ sK2_SY81 ) )
= sK2_SY81 ) )
=> ( d @ sK1_X7 @ sK2_SY81 ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[15]) ).
thf(18,plain,
( ( ~ ( ( d @ sK1_X7 @ sK2_SY81 )
=> ( ( ( product @ sK1_X7 @ ( product @ sK2_SY81 @ sK1_X7 ) )
= sK1_X7 )
& ( ( product @ sK2_SY81 @ ( product @ sK1_X7 @ sK2_SY81 ) )
= sK2_SY81 ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[16]) ).
thf(19,plain,
( ( ~ ( ( ( ( product @ sK1_X7 @ ( product @ sK2_SY81 @ sK1_X7 ) )
= sK1_X7 )
& ( ( product @ sK2_SY81 @ ( product @ sK1_X7 @ sK2_SY81 ) )
= sK2_SY81 ) )
=> ( d @ sK1_X7 @ sK2_SY81 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[17]) ).
thf(20,plain,
( ( ( d @ sK1_X7 @ sK2_SY81 )
& ( ( ( product @ sK1_X7 @ ( product @ sK2_SY81 @ sK1_X7 ) )
!= sK1_X7 )
| ( ( product @ sK2_SY81 @ ( product @ sK1_X7 @ sK2_SY81 ) )
!= sK2_SY81 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[18]) ).
thf(21,plain,
( ( ( ( product @ sK1_X7 @ ( product @ sK2_SY81 @ sK1_X7 ) )
= sK1_X7 )
& ( ( product @ sK2_SY81 @ ( product @ sK1_X7 @ sK2_SY81 ) )
= sK2_SY81 )
& ~ ( d @ sK1_X7 @ sK2_SY81 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[19]) ).
thf(22,plain,
( ( ! [X4: $i,X5: $i] :
( ! [X6: $i] :
( ~ ( l @ X6 @ X5 )
| ~ ( r @ X4 @ X6 ) )
| ( d @ X4 @ X5 ) )
& ! [X4: $i,X5: $i] :
( ~ ( d @ X4 @ X5 )
| ( ( l @ ( sK3_X6 @ X5 @ X4 ) @ X5 )
& ( r @ X4 @ ( sK3_X6 @ X5 @ X4 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[9]) ).
thf(23,plain,
( ( ! [X2: $i,X3: $i] :
( ( ( product @ X2 @ X3 )
!= X3 )
| ( ( product @ X3 @ X2 )
!= X2 )
| ( r @ X2 @ X3 ) )
& ! [X2: $i,X3: $i] :
( ~ ( r @ X2 @ X3 )
| ( ( product @ X2 @ X3 )
= X3 ) )
& ! [X2: $i,X3: $i] :
( ~ ( r @ X2 @ X3 )
| ( ( product @ X3 @ X2 )
= X2 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[10]) ).
thf(24,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( product @ X0 @ X1 )
!= X0 )
| ( ( product @ X1 @ X0 )
!= X1 )
| ( l @ X0 @ X1 ) )
& ! [X0: $i,X1: $i] :
( ~ ( l @ X0 @ X1 )
| ( ( product @ X0 @ X1 )
= X0 ) )
& ! [X0: $i,X1: $i] :
( ~ ( l @ X0 @ X1 )
| ( ( product @ X1 @ X0 )
= X1 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[11]) ).
thf(25,plain,
( ( ! [C: $i,B: $i,A: $i] :
( ( product @ ( product @ A @ B ) @ C )
= ( product @ A @ ( product @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(26,plain,
( ( ! [A: $i] :
( ( product @ A @ A )
= A ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(27,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( product @ X0 @ X1 )
!= X0 )
| ( ( product @ X1 @ X0 )
!= X1 )
| ( l @ X0 @ X1 ) )
& ! [X0: $i,X1: $i] :
( ~ ( l @ X0 @ X1 )
| ( ( product @ X0 @ X1 )
= X0 ) )
& ! [X0: $i,X1: $i] :
( ~ ( l @ X0 @ X1 )
| ( ( product @ X1 @ X0 )
= X1 ) ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(28,plain,
( ( ! [X2: $i,X3: $i] :
( ( ( product @ X2 @ X3 )
!= X3 )
| ( ( product @ X3 @ X2 )
!= X2 )
| ( r @ X2 @ X3 ) )
& ! [X2: $i,X3: $i] :
( ~ ( r @ X2 @ X3 )
| ( ( product @ X2 @ X3 )
= X3 ) )
& ! [X2: $i,X3: $i] :
( ~ ( r @ X2 @ X3 )
| ( ( product @ X3 @ X2 )
= X2 ) ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(29,plain,
( ( ! [X4: $i,X5: $i] :
( ! [X6: $i] :
( ~ ( l @ X6 @ X5 )
| ~ ( r @ X4 @ X6 ) )
| ( d @ X4 @ X5 ) )
& ! [X4: $i,X5: $i] :
( ~ ( d @ X4 @ X5 )
| ( ( l @ ( sK3_X6 @ X5 @ X4 ) @ X5 )
& ( r @ X4 @ ( sK3_X6 @ X5 @ X4 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(30,plain,
( ( ( d @ sK1_X7 @ sK2_SY81 )
& ( ( ( product @ sK1_X7 @ ( product @ sK2_SY81 @ sK1_X7 ) )
!= sK1_X7 )
| ( ( product @ sK2_SY81 @ ( product @ sK1_X7 @ sK2_SY81 ) )
!= sK2_SY81 ) ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(31,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( l @ SX2 @ SX1 )
| ~ ( r @ SX0 @ SX2 ) )
| ( d @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( d @ SX0 @ SX1 )
| ~ ( ~ ( l @ ( sK3_X6 @ SX1 @ SX0 ) @ SX1 )
| ~ ( r @ SX0 @ ( sK3_X6 @ SX1 @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(32,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( ( product @ SX0 @ SX1 )
!= SX0 )
| ( ( product @ SX1 @ SX0 )
!= SX1 )
| ( l @ SX0 @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( l @ SX0 @ SX1 )
| ( ( product @ SX0 @ SX1 )
= SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( l @ SX0 @ SX1 )
| ( ( product @ SX1 @ SX0 )
= SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(33,plain,
( ( ~ ( ~ ( d @ sK1_X7 @ sK2_SY81 )
| ~ ( ( ( product @ sK1_X7 @ ( product @ sK2_SY81 @ sK1_X7 ) )
!= sK1_X7 )
| ( ( product @ sK2_SY81 @ ( product @ sK1_X7 @ sK2_SY81 ) )
!= sK2_SY81 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(34,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( ( product @ SX0 @ SX1 )
!= SX1 )
| ( ( product @ SX1 @ SX0 )
!= SX0 )
| ( r @ SX0 @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( r @ SX0 @ SX1 )
| ( ( product @ SX0 @ SX1 )
= SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( r @ SX0 @ SX1 )
| ( ( product @ SX1 @ SX0 )
= SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(35,plain,
! [SV1: $i] :
( ( ! [SY82: $i,SY83: $i] :
( ( product @ ( product @ SY83 @ SY82 ) @ SV1 )
= ( product @ SY83 @ ( product @ SY82 @ SV1 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[25]) ).
thf(36,plain,
! [SV2: $i] :
( ( ( product @ SV2 @ SV2 )
= SV2 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[26]) ).
thf(37,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( l @ SX2 @ SX1 )
| ~ ( r @ SX0 @ SX2 ) )
| ( d @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( d @ SX0 @ SX1 )
| ~ ( ~ ( l @ ( sK3_X6 @ SX1 @ SX0 ) @ SX1 )
| ~ ( r @ SX0 @ ( sK3_X6 @ SX1 @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[31]) ).
thf(38,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( product @ SX0 @ SX1 )
!= SX0 )
| ( ( product @ SX1 @ SX0 )
!= SX1 )
| ( l @ SX0 @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( l @ SX0 @ SX1 )
| ( ( product @ SX0 @ SX1 )
= SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( l @ SX0 @ SX1 )
| ( ( product @ SX1 @ SX0 )
= SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[32]) ).
thf(39,plain,
( ( ~ ( d @ sK1_X7 @ sK2_SY81 )
| ~ ( ( ( product @ sK1_X7 @ ( product @ sK2_SY81 @ sK1_X7 ) )
!= sK1_X7 )
| ( ( product @ sK2_SY81 @ ( product @ sK1_X7 @ sK2_SY81 ) )
!= sK2_SY81 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[33]) ).
thf(40,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( product @ SX0 @ SX1 )
!= SX1 )
| ( ( product @ SX1 @ SX0 )
!= SX0 )
| ( r @ SX0 @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( r @ SX0 @ SX1 )
| ( ( product @ SX0 @ SX1 )
= SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( r @ SX0 @ SX1 )
| ( ( product @ SX1 @ SX0 )
= SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[34]) ).
thf(41,plain,
! [SV1: $i,SV3: $i] :
( ( ! [SY84: $i] :
( ( product @ ( product @ SY84 @ SV3 ) @ SV1 )
= ( product @ SY84 @ ( product @ SV3 @ SV1 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[35]) ).
thf(42,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( l @ SX2 @ SX1 )
| ~ ( r @ SX0 @ SX2 ) )
| ( d @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[37]) ).
thf(43,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( d @ SX0 @ SX1 )
| ~ ( ~ ( l @ ( sK3_X6 @ SX1 @ SX0 ) @ SX1 )
| ~ ( r @ SX0 @ ( sK3_X6 @ SX1 @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[37]) ).
thf(44,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( product @ SX0 @ SX1 )
!= SX0 )
| ( ( product @ SX1 @ SX0 )
!= SX1 )
| ( l @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[38]) ).
thf(45,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( l @ SX0 @ SX1 )
| ( ( product @ SX0 @ SX1 )
= SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( l @ SX0 @ SX1 )
| ( ( product @ SX1 @ SX0 )
= SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[38]) ).
thf(46,plain,
( ( ~ ( d @ sK1_X7 @ sK2_SY81 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[39]) ).
thf(47,plain,
( ( ~ ( ( ( product @ sK1_X7 @ ( product @ sK2_SY81 @ sK1_X7 ) )
!= sK1_X7 )
| ( ( product @ sK2_SY81 @ ( product @ sK1_X7 @ sK2_SY81 ) )
!= sK2_SY81 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[39]) ).
thf(48,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( product @ SX0 @ SX1 )
!= SX1 )
| ( ( product @ SX1 @ SX0 )
!= SX0 )
| ( r @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[40]) ).
thf(49,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( r @ SX0 @ SX1 )
| ( ( product @ SX0 @ SX1 )
= SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( r @ SX0 @ SX1 )
| ( ( product @ SX1 @ SX0 )
= SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[40]) ).
thf(50,plain,
! [SV1: $i,SV3: $i,SV4: $i] :
( ( ( product @ ( product @ SV4 @ SV3 ) @ SV1 )
= ( product @ SV4 @ ( product @ SV3 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[41]) ).
thf(51,plain,
( ( ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( l @ SX2 @ SX1 )
| ~ ( r @ SX0 @ SX2 ) )
| ( d @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[42]) ).
thf(52,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( d @ SX0 @ SX1 )
| ~ ( ~ ( l @ ( sK3_X6 @ SX1 @ SX0 ) @ SX1 )
| ~ ( r @ SX0 @ ( sK3_X6 @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[43]) ).
thf(53,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( product @ SX0 @ SX1 )
!= SX0 )
| ( ( product @ SX1 @ SX0 )
!= SX1 )
| ( l @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[44]) ).
thf(54,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( l @ SX0 @ SX1 )
| ( ( product @ SX0 @ SX1 )
= SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( l @ SX0 @ SX1 )
| ( ( product @ SX1 @ SX0 )
= SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[45]) ).
thf(55,plain,
( ( d @ sK1_X7 @ sK2_SY81 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[46]) ).
thf(56,plain,
( ( ( ( product @ sK1_X7 @ ( product @ sK2_SY81 @ sK1_X7 ) )
!= sK1_X7 )
| ( ( product @ sK2_SY81 @ ( product @ sK1_X7 @ sK2_SY81 ) )
!= sK2_SY81 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[47]) ).
thf(57,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( product @ SX0 @ SX1 )
!= SX1 )
| ( ( product @ SX1 @ SX0 )
!= SX0 )
| ( r @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[48]) ).
thf(58,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( r @ SX0 @ SX1 )
| ( ( product @ SX0 @ SX1 )
= SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( r @ SX0 @ SX1 )
| ( ( product @ SX1 @ SX0 )
= SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[49]) ).
thf(59,plain,
! [SV5: $i] :
( ( ! [SY85: $i] :
( ! [SY86: $i] :
( ~ ( l @ SY86 @ SY85 )
| ~ ( r @ SV5 @ SY86 ) )
| ( d @ SV5 @ SY85 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[51]) ).
thf(60,plain,
! [SV6: $i] :
( ( ! [SY87: $i] :
( ~ ( d @ SV6 @ SY87 )
| ~ ( ~ ( l @ ( sK3_X6 @ SY87 @ SV6 ) @ SY87 )
| ~ ( r @ SV6 @ ( sK3_X6 @ SY87 @ SV6 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[52]) ).
thf(61,plain,
! [SV7: $i] :
( ( ! [SY88: $i] :
( ( ( product @ SV7 @ SY88 )
!= SV7 )
| ( ( product @ SY88 @ SV7 )
!= SY88 )
| ( l @ SV7 @ SY88 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[53]) ).
thf(62,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( l @ SX0 @ SX1 )
| ( ( product @ SX0 @ SX1 )
= SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( l @ SX0 @ SX1 )
| ( ( product @ SX1 @ SX0 )
= SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[54]) ).
thf(63,plain,
( ( ( ( ( product @ sK1_X7 @ ( product @ sK2_SY81 @ sK1_X7 ) )
!= sK1_X7 ) )
= $true )
| ( ( ( ( product @ sK2_SY81 @ ( product @ sK1_X7 @ sK2_SY81 ) )
!= sK2_SY81 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[56]) ).
thf(64,plain,
! [SV8: $i] :
( ( ! [SY89: $i] :
( ( ( product @ SV8 @ SY89 )
!= SY89 )
| ( ( product @ SY89 @ SV8 )
!= SV8 )
| ( r @ SV8 @ SY89 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[57]) ).
thf(65,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( r @ SX0 @ SX1 )
| ( ( product @ SX0 @ SX1 )
= SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( r @ SX0 @ SX1 )
| ( ( product @ SX1 @ SX0 )
= SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[58]) ).
thf(66,plain,
! [SV5: $i,SV9: $i] :
( ( ! [SY90: $i] :
( ~ ( l @ SY90 @ SV9 )
| ~ ( r @ SV5 @ SY90 ) )
| ( d @ SV5 @ SV9 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[59]) ).
thf(67,plain,
! [SV10: $i,SV6: $i] :
( ( ~ ( d @ SV6 @ SV10 )
| ~ ( ~ ( l @ ( sK3_X6 @ SV10 @ SV6 ) @ SV10 )
| ~ ( r @ SV6 @ ( sK3_X6 @ SV10 @ SV6 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[60]) ).
thf(68,plain,
! [SV11: $i,SV7: $i] :
( ( ( ( product @ SV7 @ SV11 )
!= SV7 )
| ( ( product @ SV11 @ SV7 )
!= SV11 )
| ( l @ SV7 @ SV11 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[61]) ).
thf(69,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( l @ SX0 @ SX1 )
| ( ( product @ SX0 @ SX1 )
= SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[62]) ).
thf(70,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( l @ SX0 @ SX1 )
| ( ( product @ SX1 @ SX0 )
= SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[62]) ).
thf(71,plain,
( ( ( ( product @ sK1_X7 @ ( product @ sK2_SY81 @ sK1_X7 ) )
= sK1_X7 )
= $false )
| ( ( ( ( product @ sK2_SY81 @ ( product @ sK1_X7 @ sK2_SY81 ) )
!= sK2_SY81 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[63]) ).
thf(72,plain,
! [SV12: $i,SV8: $i] :
( ( ( ( product @ SV8 @ SV12 )
!= SV12 )
| ( ( product @ SV12 @ SV8 )
!= SV8 )
| ( r @ SV8 @ SV12 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[64]) ).
thf(73,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( r @ SX0 @ SX1 )
| ( ( product @ SX0 @ SX1 )
= SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[65]) ).
thf(74,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( r @ SX0 @ SX1 )
| ( ( product @ SX1 @ SX0 )
= SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[65]) ).
thf(75,plain,
! [SV5: $i,SV9: $i] :
( ( ( ! [SY90: $i] :
( ~ ( l @ SY90 @ SV9 )
| ~ ( r @ SV5 @ SY90 ) ) )
= $true )
| ( ( d @ SV5 @ SV9 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[66]) ).
thf(76,plain,
! [SV10: $i,SV6: $i] :
( ( ( ~ ( d @ SV6 @ SV10 ) )
= $true )
| ( ( ~ ( ~ ( l @ ( sK3_X6 @ SV10 @ SV6 ) @ SV10 )
| ~ ( r @ SV6 @ ( sK3_X6 @ SV10 @ SV6 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[67]) ).
thf(77,plain,
! [SV11: $i,SV7: $i] :
( ( ( ( ( product @ SV7 @ SV11 )
!= SV7 )
| ( ( product @ SV11 @ SV7 )
!= SV11 ) )
= $true )
| ( ( l @ SV7 @ SV11 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[68]) ).
thf(78,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( l @ SX0 @ SX1 )
| ( ( product @ SX0 @ SX1 )
= SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[69]) ).
thf(79,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( l @ SX0 @ SX1 )
| ( ( product @ SX1 @ SX0 )
= SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[70]) ).
thf(80,plain,
( ( ( ( product @ sK2_SY81 @ ( product @ sK1_X7 @ sK2_SY81 ) )
= sK2_SY81 )
= $false )
| ( ( ( product @ sK1_X7 @ ( product @ sK2_SY81 @ sK1_X7 ) )
= sK1_X7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[71]) ).
thf(81,plain,
! [SV12: $i,SV8: $i] :
( ( ( ( ( product @ SV8 @ SV12 )
!= SV12 )
| ( ( product @ SV12 @ SV8 )
!= SV8 ) )
= $true )
| ( ( r @ SV8 @ SV12 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[72]) ).
thf(82,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( r @ SX0 @ SX1 )
| ( ( product @ SX0 @ SX1 )
= SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[73]) ).
thf(83,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( r @ SX0 @ SX1 )
| ( ( product @ SX1 @ SX0 )
= SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[74]) ).
thf(84,plain,
! [SV5: $i,SV9: $i,SV13: $i] :
( ( ( ~ ( l @ SV13 @ SV9 )
| ~ ( r @ SV5 @ SV13 ) )
= $true )
| ( ( d @ SV5 @ SV9 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[75]) ).
thf(85,plain,
! [SV10: $i,SV6: $i] :
( ( ( d @ SV6 @ SV10 )
= $false )
| ( ( ~ ( ~ ( l @ ( sK3_X6 @ SV10 @ SV6 ) @ SV10 )
| ~ ( r @ SV6 @ ( sK3_X6 @ SV10 @ SV6 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[76]) ).
thf(86,plain,
! [SV11: $i,SV7: $i] :
( ( ( ( ( product @ SV7 @ SV11 )
!= SV7 ) )
= $true )
| ( ( ( ( product @ SV11 @ SV7 )
!= SV11 ) )
= $true )
| ( ( l @ SV7 @ SV11 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[77]) ).
thf(87,plain,
! [SV14: $i] :
( ( ! [SY91: $i] :
( ~ ( l @ SV14 @ SY91 )
| ( ( product @ SV14 @ SY91 )
= SV14 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[78]) ).
thf(88,plain,
! [SV15: $i] :
( ( ! [SY92: $i] :
( ~ ( l @ SV15 @ SY92 )
| ( ( product @ SY92 @ SV15 )
= SY92 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[79]) ).
thf(89,plain,
! [SV12: $i,SV8: $i] :
( ( ( ( ( product @ SV8 @ SV12 )
!= SV12 ) )
= $true )
| ( ( ( ( product @ SV12 @ SV8 )
!= SV8 ) )
= $true )
| ( ( r @ SV8 @ SV12 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[81]) ).
thf(90,plain,
! [SV16: $i] :
( ( ! [SY93: $i] :
( ~ ( r @ SV16 @ SY93 )
| ( ( product @ SV16 @ SY93 )
= SY93 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[82]) ).
thf(91,plain,
! [SV17: $i] :
( ( ! [SY94: $i] :
( ~ ( r @ SV17 @ SY94 )
| ( ( product @ SY94 @ SV17 )
= SV17 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[83]) ).
thf(92,plain,
! [SV5: $i,SV9: $i,SV13: $i] :
( ( ( ~ ( l @ SV13 @ SV9 ) )
= $true )
| ( ( ~ ( r @ SV5 @ SV13 ) )
= $true )
| ( ( d @ SV5 @ SV9 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[84]) ).
thf(93,plain,
! [SV6: $i,SV10: $i] :
( ( ( ~ ( l @ ( sK3_X6 @ SV10 @ SV6 ) @ SV10 )
| ~ ( r @ SV6 @ ( sK3_X6 @ SV10 @ SV6 ) ) )
= $false )
| ( ( d @ SV6 @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[85]) ).
thf(94,plain,
! [SV11: $i,SV7: $i] :
( ( ( ( product @ SV7 @ SV11 )
= SV7 )
= $false )
| ( ( ( ( product @ SV11 @ SV7 )
!= SV11 ) )
= $true )
| ( ( l @ SV7 @ SV11 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[86]) ).
thf(95,plain,
! [SV18: $i,SV14: $i] :
( ( ~ ( l @ SV14 @ SV18 )
| ( ( product @ SV14 @ SV18 )
= SV14 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).
thf(96,plain,
! [SV19: $i,SV15: $i] :
( ( ~ ( l @ SV15 @ SV19 )
| ( ( product @ SV19 @ SV15 )
= SV19 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(97,plain,
! [SV12: $i,SV8: $i] :
( ( ( ( product @ SV8 @ SV12 )
= SV12 )
= $false )
| ( ( ( ( product @ SV12 @ SV8 )
!= SV8 ) )
= $true )
| ( ( r @ SV8 @ SV12 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[89]) ).
thf(98,plain,
! [SV20: $i,SV16: $i] :
( ( ~ ( r @ SV16 @ SV20 )
| ( ( product @ SV16 @ SV20 )
= SV20 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[90]) ).
thf(99,plain,
! [SV21: $i,SV17: $i] :
( ( ~ ( r @ SV17 @ SV21 )
| ( ( product @ SV21 @ SV17 )
= SV17 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[91]) ).
thf(100,plain,
! [SV5: $i,SV9: $i,SV13: $i] :
( ( ( l @ SV13 @ SV9 )
= $false )
| ( ( ~ ( r @ SV5 @ SV13 ) )
= $true )
| ( ( d @ SV5 @ SV9 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[92]) ).
thf(101,plain,
! [SV6: $i,SV10: $i] :
( ( ( ~ ( l @ ( sK3_X6 @ SV10 @ SV6 ) @ SV10 ) )
= $false )
| ( ( d @ SV6 @ SV10 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[93]) ).
thf(102,plain,
! [SV10: $i,SV6: $i] :
( ( ( ~ ( r @ SV6 @ ( sK3_X6 @ SV10 @ SV6 ) ) )
= $false )
| ( ( d @ SV6 @ SV10 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[93]) ).
thf(103,plain,
! [SV7: $i,SV11: $i] :
( ( ( ( product @ SV11 @ SV7 )
= SV11 )
= $false )
| ( ( ( product @ SV7 @ SV11 )
= SV7 )
= $false )
| ( ( l @ SV7 @ SV11 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[94]) ).
thf(104,plain,
! [SV18: $i,SV14: $i] :
( ( ( ~ ( l @ SV14 @ SV18 ) )
= $true )
| ( ( ( product @ SV14 @ SV18 )
= SV14 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[95]) ).
thf(105,plain,
! [SV19: $i,SV15: $i] :
( ( ( ~ ( l @ SV15 @ SV19 ) )
= $true )
| ( ( ( product @ SV19 @ SV15 )
= SV19 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[96]) ).
thf(106,plain,
! [SV8: $i,SV12: $i] :
( ( ( ( product @ SV12 @ SV8 )
= SV8 )
= $false )
| ( ( ( product @ SV8 @ SV12 )
= SV12 )
= $false )
| ( ( r @ SV8 @ SV12 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[97]) ).
thf(107,plain,
! [SV20: $i,SV16: $i] :
( ( ( ~ ( r @ SV16 @ SV20 ) )
= $true )
| ( ( ( product @ SV16 @ SV20 )
= SV20 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[98]) ).
thf(108,plain,
! [SV21: $i,SV17: $i] :
( ( ( ~ ( r @ SV17 @ SV21 ) )
= $true )
| ( ( ( product @ SV21 @ SV17 )
= SV17 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[99]) ).
thf(109,plain,
! [SV9: $i,SV13: $i,SV5: $i] :
( ( ( r @ SV5 @ SV13 )
= $false )
| ( ( l @ SV13 @ SV9 )
= $false )
| ( ( d @ SV5 @ SV9 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[100]) ).
thf(110,plain,
! [SV6: $i,SV10: $i] :
( ( ( l @ ( sK3_X6 @ SV10 @ SV6 ) @ SV10 )
= $true )
| ( ( d @ SV6 @ SV10 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[101]) ).
thf(111,plain,
! [SV10: $i,SV6: $i] :
( ( ( r @ SV6 @ ( sK3_X6 @ SV10 @ SV6 ) )
= $true )
| ( ( d @ SV6 @ SV10 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[102]) ).
thf(112,plain,
! [SV18: $i,SV14: $i] :
( ( ( l @ SV14 @ SV18 )
= $false )
| ( ( ( product @ SV14 @ SV18 )
= SV14 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[104]) ).
thf(113,plain,
! [SV19: $i,SV15: $i] :
( ( ( l @ SV15 @ SV19 )
= $false )
| ( ( ( product @ SV19 @ SV15 )
= SV19 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[105]) ).
thf(114,plain,
! [SV20: $i,SV16: $i] :
( ( ( r @ SV16 @ SV20 )
= $false )
| ( ( ( product @ SV16 @ SV20 )
= SV20 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[107]) ).
thf(115,plain,
! [SV21: $i,SV17: $i] :
( ( ( r @ SV17 @ SV21 )
= $false )
| ( ( ( product @ SV21 @ SV17 )
= SV17 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[108]) ).
thf(127,plain,
! [SV22: $i] :
( ( ( product @ SV22 @ SV22 )
= SV22 )
= $true ),
inference(rename,[status(thm)],[36]) ).
thf(128,plain,
! [SV23: $i,SV24: $i,SV25: $i] :
( ( ( product @ ( product @ SV25 @ SV24 ) @ SV23 )
= ( product @ SV25 @ ( product @ SV24 @ SV23 ) ) )
= $true ),
inference(rename,[status(thm)],[50]) ).
thf(136,plain,
! [SV26: $i,SV27: $i] :
( ( ( ( product @ SV27 @ SV26 )
= SV27 )
= $false )
| ( ( ( product @ SV26 @ SV27 )
= SV26 )
= $false )
| ( ( l @ SV26 @ SV27 )
= $true ) ),
inference(rename,[status(thm)],[103]) ).
thf(149,plain,
! [SV28: $i,SV29: $i] :
( ( ( ( product @ SV29 @ SV28 )
= SV28 )
= $false )
| ( ( ( product @ SV28 @ SV29 )
= SV29 )
= $false )
| ( ( r @ SV28 @ SV29 )
= $true ) ),
inference(rename,[status(thm)],[106]) ).
thf(166,plain,
! [SV30: $i,SV31: $i,SV32: $i] :
( ( ( r @ SV32 @ SV31 )
= $false )
| ( ( l @ SV31 @ SV30 )
= $false )
| ( ( d @ SV32 @ SV30 )
= $true ) ),
inference(rename,[status(thm)],[109]) ).
thf(187,plain,
! [SV33: $i,SV34: $i] :
( ( ( l @ ( sK3_X6 @ SV34 @ SV33 ) @ SV34 )
= $true )
| ( ( d @ SV33 @ SV34 )
= $false ) ),
inference(rename,[status(thm)],[110]) ).
thf(190,plain,
! [SV33: $i,SV34: $i,SV30: $i,SV31: $i,SV32: $i] :
( ( ( ( d @ SV33 @ SV34 )
= ( d @ SV32 @ SV30 ) )
= $false )
| ( ( l @ ( sK3_X6 @ SV34 @ SV33 ) @ SV34 )
= $true )
| ( ( r @ SV32 @ SV31 )
= $false )
| ( ( l @ SV31 @ SV30 )
= $false ) ),
inference(res,[status(thm)],[187,166]) ).
thf(191,plain,
! [SV33: $i,SV34: $i,SV30: $i,SV31: $i,SV32: $i] :
( ( ( ( l @ ( sK3_X6 @ SV34 @ SV33 ) @ SV34 )
= ( l @ SV31 @ SV30 ) )
= $false )
| ( ( d @ SV33 @ SV34 )
= $false )
| ( ( r @ SV32 @ SV31 )
= $false )
| ( ( d @ SV32 @ SV30 )
= $true ) ),
inference(res,[status(thm)],[187,166]) ).
thf(203,plain,
! [SV33: $i,SV34: $i] :
( ( ( ( d @ SV33 @ SV34 )
= ( d @ sK1_X7 @ sK2_SY81 ) )
= $false )
| ( ( l @ ( sK3_X6 @ SV34 @ SV33 ) @ SV34 )
= $true ) ),
inference(res,[status(thm)],[187,55]) ).
thf(204,plain,
( ( l @ ( sK3_X6 @ sK2_SY81 @ sK1_X7 ) @ sK2_SY81 )
= $true ),
inference(extuni,[status(esa)],[203:[bind(SV34,$thf( sK2_SY81 )),bind(SV33,$thf( sK1_X7 ))]]) ).
thf(205,plain,
! [SV33: $i,SV30: $i,SV32: $i] :
( ( ( d @ SV32 @ SV30 )
= $true )
| ( ( r @ SV32 @ ( sK3_X6 @ SV30 @ SV33 ) )
= $false )
| ( ( d @ SV33 @ SV30 )
= $false ) ),
inference(extuni,[status(esa)],[191:[bind(SV34,$thf( SV30 )),bind(SV31,$thf( sK3_X6 @ SV30 @ SV33 ))]]) ).
thf(206,plain,
! [SV32: $i,SV30: $i,SV31: $i] :
( ( ( l @ SV31 @ SV30 )
= $false )
| ( ( r @ SV32 @ SV31 )
= $false )
| ( ( l @ ( sK3_X6 @ SV30 @ SV32 ) @ SV30 )
= $true ) ),
inference(extuni,[status(esa)],[190:[bind(SV34,$thf( SV30 )),bind(SV33,$thf( SV32 ))]]) ).
thf(207,plain,
! [SV35: $i,SV36: $i] :
( ( ( r @ SV36 @ ( sK3_X6 @ SV35 @ SV36 ) )
= $true )
| ( ( d @ SV36 @ SV35 )
= $false ) ),
inference(rename,[status(thm)],[111]) ).
thf(212,plain,
! [SV35: $i,SV36: $i,SV30: $i,SV31: $i,SV32: $i] :
( ( ( ( d @ SV36 @ SV35 )
= ( d @ SV32 @ SV30 ) )
= $false )
| ( ( r @ SV36 @ ( sK3_X6 @ SV35 @ SV36 ) )
= $true )
| ( ( r @ SV32 @ SV31 )
= $false )
| ( ( l @ SV31 @ SV30 )
= $false ) ),
inference(res,[status(thm)],[207,166]) ).
thf(214,plain,
! [SV35: $i,SV36: $i,SV30: $i,SV31: $i,SV32: $i] :
( ( ( ( r @ SV36 @ ( sK3_X6 @ SV35 @ SV36 ) )
= ( r @ SV32 @ SV31 ) )
= $false )
| ( ( d @ SV36 @ SV35 )
= $false )
| ( ( l @ SV31 @ SV30 )
= $false )
| ( ( d @ SV32 @ SV30 )
= $true ) ),
inference(res,[status(thm)],[207,166]) ).
thf(225,plain,
! [SV35: $i,SV36: $i] :
( ( ( ( d @ SV36 @ SV35 )
= ( d @ sK1_X7 @ sK2_SY81 ) )
= $false )
| ( ( r @ SV36 @ ( sK3_X6 @ SV35 @ SV36 ) )
= $true ) ),
inference(res,[status(thm)],[207,55]) ).
thf(226,plain,
( ( r @ sK1_X7 @ ( sK3_X6 @ sK2_SY81 @ sK1_X7 ) )
= $true ),
inference(extuni,[status(esa)],[225:[bind(SV35,$thf( sK2_SY81 )),bind(SV36,$thf( sK1_X7 ))]]) ).
thf(227,plain,
! [SV35: $i,SV30: $i,SV32: $i] :
( ( ( d @ SV32 @ SV30 )
= $true )
| ( ( l @ ( sK3_X6 @ SV35 @ SV32 ) @ SV30 )
= $false )
| ( ( d @ SV32 @ SV35 )
= $false ) ),
inference(extuni,[status(esa)],[214:[bind(SV31,$thf( sK3_X6 @ SV35 @ SV32 )),bind(SV36,$thf( SV32 ))]]) ).
thf(228,plain,
! [SV32: $i,SV30: $i,SV31: $i] :
( ( ( l @ SV31 @ SV30 )
= $false )
| ( ( r @ SV32 @ SV31 )
= $false )
| ( ( r @ SV32 @ ( sK3_X6 @ SV30 @ SV32 ) )
= $true ) ),
inference(extuni,[status(esa)],[212:[bind(SV35,$thf( SV30 )),bind(SV36,$thf( SV32 ))]]) ).
thf(229,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[55,228,227,226,207,206,205,204,187,166,149,136,128,127,115,114,113,112,80]) ).
thf(230,plain,
( ( ! [C: $i,B: $i,A: $i] :
( ( product @ ( product @ A @ B ) @ C )
= ( product @ A @ ( product @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(231,plain,
( ( ! [A: $i] :
( ( product @ A @ A )
= A ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(232,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( product @ X0 @ X1 )
!= X0 )
| ( ( product @ X1 @ X0 )
!= X1 )
| ( l @ X0 @ X1 ) )
& ! [X0: $i,X1: $i] :
( ~ ( l @ X0 @ X1 )
| ( ( product @ X0 @ X1 )
= X0 ) )
& ! [X0: $i,X1: $i] :
( ~ ( l @ X0 @ X1 )
| ( ( product @ X1 @ X0 )
= X1 ) ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(233,plain,
( ( ! [X2: $i,X3: $i] :
( ( ( product @ X2 @ X3 )
!= X3 )
| ( ( product @ X3 @ X2 )
!= X2 )
| ( r @ X2 @ X3 ) )
& ! [X2: $i,X3: $i] :
( ~ ( r @ X2 @ X3 )
| ( ( product @ X2 @ X3 )
= X3 ) )
& ! [X2: $i,X3: $i] :
( ~ ( r @ X2 @ X3 )
| ( ( product @ X3 @ X2 )
= X2 ) ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(234,plain,
( ( ! [X4: $i,X5: $i] :
( ! [X6: $i] :
( ~ ( l @ X6 @ X5 )
| ~ ( r @ X4 @ X6 ) )
| ( d @ X4 @ X5 ) )
& ! [X4: $i,X5: $i] :
( ~ ( d @ X4 @ X5 )
| ( ( l @ ( sK3_X6 @ X5 @ X4 ) @ X5 )
& ( r @ X4 @ ( sK3_X6 @ X5 @ X4 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(235,plain,
( ( ( ( product @ sK1_X7 @ ( product @ sK2_SY81 @ sK1_X7 ) )
= sK1_X7 )
& ( ( product @ sK2_SY81 @ ( product @ sK1_X7 @ sK2_SY81 ) )
= sK2_SY81 )
& ~ ( d @ sK1_X7 @ sK2_SY81 ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(236,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( ( product @ SX0 @ SX1 )
!= SX0 )
| ( ( product @ SX1 @ SX0 )
!= SX1 )
| ( l @ SX0 @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( l @ SX0 @ SX1 )
| ( ( product @ SX0 @ SX1 )
= SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( l @ SX0 @ SX1 )
| ( ( product @ SX1 @ SX0 )
= SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[232]) ).
thf(237,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( l @ SX2 @ SX1 )
| ~ ( r @ SX0 @ SX2 ) )
| ( d @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( d @ SX0 @ SX1 )
| ~ ( ~ ( l @ ( sK3_X6 @ SX1 @ SX0 ) @ SX1 )
| ~ ( r @ SX0 @ ( sK3_X6 @ SX1 @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[234]) ).
thf(238,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( ( product @ SX0 @ SX1 )
!= SX1 )
| ( ( product @ SX1 @ SX0 )
!= SX0 )
| ( r @ SX0 @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( r @ SX0 @ SX1 )
| ( ( product @ SX0 @ SX1 )
= SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( r @ SX0 @ SX1 )
| ( ( product @ SX1 @ SX0 )
= SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[233]) ).
thf(239,plain,
( ( ~ ( ~ ~ ( ( ( product @ sK1_X7 @ ( product @ sK2_SY81 @ sK1_X7 ) )
!= sK1_X7 )
| ( ( product @ sK2_SY81 @ ( product @ sK1_X7 @ sK2_SY81 ) )
!= sK2_SY81 ) )
| ~ ~ ( d @ sK1_X7 @ sK2_SY81 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[235]) ).
thf(240,plain,
! [SV37: $i] :
( ( ! [SY95: $i,SY96: $i] :
( ( product @ ( product @ SY96 @ SY95 ) @ SV37 )
= ( product @ SY96 @ ( product @ SY95 @ SV37 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[230]) ).
thf(241,plain,
! [SV38: $i] :
( ( ( product @ SV38 @ SV38 )
= SV38 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[231]) ).
thf(242,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( product @ SX0 @ SX1 )
!= SX0 )
| ( ( product @ SX1 @ SX0 )
!= SX1 )
| ( l @ SX0 @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( l @ SX0 @ SX1 )
| ( ( product @ SX0 @ SX1 )
= SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( l @ SX0 @ SX1 )
| ( ( product @ SX1 @ SX0 )
= SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[236]) ).
thf(243,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( l @ SX2 @ SX1 )
| ~ ( r @ SX0 @ SX2 ) )
| ( d @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( d @ SX0 @ SX1 )
| ~ ( ~ ( l @ ( sK3_X6 @ SX1 @ SX0 ) @ SX1 )
| ~ ( r @ SX0 @ ( sK3_X6 @ SX1 @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[237]) ).
thf(244,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( product @ SX0 @ SX1 )
!= SX1 )
| ( ( product @ SX1 @ SX0 )
!= SX0 )
| ( r @ SX0 @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( r @ SX0 @ SX1 )
| ( ( product @ SX0 @ SX1 )
= SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( r @ SX0 @ SX1 )
| ( ( product @ SX1 @ SX0 )
= SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[238]) ).
thf(245,plain,
( ( ~ ~ ( ( ( product @ sK1_X7 @ ( product @ sK2_SY81 @ sK1_X7 ) )
!= sK1_X7 )
| ( ( product @ sK2_SY81 @ ( product @ sK1_X7 @ sK2_SY81 ) )
!= sK2_SY81 ) )
| ~ ~ ( d @ sK1_X7 @ sK2_SY81 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[239]) ).
thf(246,plain,
! [SV37: $i,SV39: $i] :
( ( ! [SY97: $i] :
( ( product @ ( product @ SY97 @ SV39 ) @ SV37 )
= ( product @ SY97 @ ( product @ SV39 @ SV37 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[240]) ).
thf(247,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( product @ SX0 @ SX1 )
!= SX0 )
| ( ( product @ SX1 @ SX0 )
!= SX1 )
| ( l @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[242]) ).
thf(248,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( l @ SX0 @ SX1 )
| ( ( product @ SX0 @ SX1 )
= SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( l @ SX0 @ SX1 )
| ( ( product @ SX1 @ SX0 )
= SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[242]) ).
thf(249,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( l @ SX2 @ SX1 )
| ~ ( r @ SX0 @ SX2 ) )
| ( d @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[243]) ).
thf(250,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( d @ SX0 @ SX1 )
| ~ ( ~ ( l @ ( sK3_X6 @ SX1 @ SX0 ) @ SX1 )
| ~ ( r @ SX0 @ ( sK3_X6 @ SX1 @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[243]) ).
thf(251,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( product @ SX0 @ SX1 )
!= SX1 )
| ( ( product @ SX1 @ SX0 )
!= SX0 )
| ( r @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[244]) ).
thf(252,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( r @ SX0 @ SX1 )
| ( ( product @ SX0 @ SX1 )
= SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( r @ SX0 @ SX1 )
| ( ( product @ SX1 @ SX0 )
= SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[244]) ).
thf(253,plain,
( ( ~ ~ ( ( ( product @ sK1_X7 @ ( product @ sK2_SY81 @ sK1_X7 ) )
!= sK1_X7 )
| ( ( product @ sK2_SY81 @ ( product @ sK1_X7 @ sK2_SY81 ) )
!= sK2_SY81 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[245]) ).
thf(254,plain,
( ( ~ ~ ( d @ sK1_X7 @ sK2_SY81 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[245]) ).
thf(255,plain,
! [SV37: $i,SV39: $i,SV40: $i] :
( ( ( product @ ( product @ SV40 @ SV39 ) @ SV37 )
= ( product @ SV40 @ ( product @ SV39 @ SV37 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[246]) ).
thf(256,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( product @ SX0 @ SX1 )
!= SX0 )
| ( ( product @ SX1 @ SX0 )
!= SX1 )
| ( l @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[247]) ).
thf(257,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( l @ SX0 @ SX1 )
| ( ( product @ SX0 @ SX1 )
= SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( l @ SX0 @ SX1 )
| ( ( product @ SX1 @ SX0 )
= SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[248]) ).
thf(258,plain,
( ( ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( l @ SX2 @ SX1 )
| ~ ( r @ SX0 @ SX2 ) )
| ( d @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[249]) ).
thf(259,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( d @ SX0 @ SX1 )
| ~ ( ~ ( l @ ( sK3_X6 @ SX1 @ SX0 ) @ SX1 )
| ~ ( r @ SX0 @ ( sK3_X6 @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[250]) ).
thf(260,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( product @ SX0 @ SX1 )
!= SX1 )
| ( ( product @ SX1 @ SX0 )
!= SX0 )
| ( r @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[251]) ).
thf(261,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( r @ SX0 @ SX1 )
| ( ( product @ SX0 @ SX1 )
= SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( r @ SX0 @ SX1 )
| ( ( product @ SX1 @ SX0 )
= SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[252]) ).
thf(262,plain,
( ( ~ ( ( ( product @ sK1_X7 @ ( product @ sK2_SY81 @ sK1_X7 ) )
!= sK1_X7 )
| ( ( product @ sK2_SY81 @ ( product @ sK1_X7 @ sK2_SY81 ) )
!= sK2_SY81 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[253]) ).
thf(263,plain,
( ( ~ ( d @ sK1_X7 @ sK2_SY81 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[254]) ).
thf(264,plain,
! [SV41: $i] :
( ( ! [SY98: $i] :
( ( ( product @ SV41 @ SY98 )
!= SV41 )
| ( ( product @ SY98 @ SV41 )
!= SY98 )
| ( l @ SV41 @ SY98 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[256]) ).
thf(265,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( l @ SX0 @ SX1 )
| ( ( product @ SX0 @ SX1 )
= SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( l @ SX0 @ SX1 )
| ( ( product @ SX1 @ SX0 )
= SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[257]) ).
thf(266,plain,
! [SV42: $i] :
( ( ! [SY99: $i] :
( ! [SY100: $i] :
( ~ ( l @ SY100 @ SY99 )
| ~ ( r @ SV42 @ SY100 ) )
| ( d @ SV42 @ SY99 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[258]) ).
thf(267,plain,
! [SV43: $i] :
( ( ! [SY101: $i] :
( ~ ( d @ SV43 @ SY101 )
| ~ ( ~ ( l @ ( sK3_X6 @ SY101 @ SV43 ) @ SY101 )
| ~ ( r @ SV43 @ ( sK3_X6 @ SY101 @ SV43 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[259]) ).
thf(268,plain,
! [SV44: $i] :
( ( ! [SY102: $i] :
( ( ( product @ SV44 @ SY102 )
!= SY102 )
| ( ( product @ SY102 @ SV44 )
!= SV44 )
| ( r @ SV44 @ SY102 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[260]) ).
thf(269,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( r @ SX0 @ SX1 )
| ( ( product @ SX0 @ SX1 )
= SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( r @ SX0 @ SX1 )
| ( ( product @ SX1 @ SX0 )
= SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[261]) ).
thf(270,plain,
( ( ( ( product @ sK1_X7 @ ( product @ sK2_SY81 @ sK1_X7 ) )
!= sK1_X7 )
| ( ( product @ sK2_SY81 @ ( product @ sK1_X7 @ sK2_SY81 ) )
!= sK2_SY81 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[262]) ).
thf(271,plain,
( ( d @ sK1_X7 @ sK2_SY81 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[263]) ).
thf(272,plain,
! [SV45: $i,SV41: $i] :
( ( ( ( product @ SV41 @ SV45 )
!= SV41 )
| ( ( product @ SV45 @ SV41 )
!= SV45 )
| ( l @ SV41 @ SV45 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[264]) ).
thf(273,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( l @ SX0 @ SX1 )
| ( ( product @ SX0 @ SX1 )
= SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[265]) ).
thf(274,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( l @ SX0 @ SX1 )
| ( ( product @ SX1 @ SX0 )
= SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[265]) ).
thf(275,plain,
! [SV42: $i,SV46: $i] :
( ( ! [SY103: $i] :
( ~ ( l @ SY103 @ SV46 )
| ~ ( r @ SV42 @ SY103 ) )
| ( d @ SV42 @ SV46 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[266]) ).
thf(276,plain,
! [SV47: $i,SV43: $i] :
( ( ~ ( d @ SV43 @ SV47 )
| ~ ( ~ ( l @ ( sK3_X6 @ SV47 @ SV43 ) @ SV47 )
| ~ ( r @ SV43 @ ( sK3_X6 @ SV47 @ SV43 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[267]) ).
thf(277,plain,
! [SV48: $i,SV44: $i] :
( ( ( ( product @ SV44 @ SV48 )
!= SV48 )
| ( ( product @ SV48 @ SV44 )
!= SV44 )
| ( r @ SV44 @ SV48 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[268]) ).
thf(278,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( r @ SX0 @ SX1 )
| ( ( product @ SX0 @ SX1 )
= SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[269]) ).
thf(279,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( r @ SX0 @ SX1 )
| ( ( product @ SX1 @ SX0 )
= SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[269]) ).
thf(280,plain,
( ( ( ( product @ sK1_X7 @ ( product @ sK2_SY81 @ sK1_X7 ) )
!= sK1_X7 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[270]) ).
thf(281,plain,
( ( ( ( product @ sK2_SY81 @ ( product @ sK1_X7 @ sK2_SY81 ) )
!= sK2_SY81 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[270]) ).
thf(282,plain,
! [SV45: $i,SV41: $i] :
( ( ( ( ( product @ SV41 @ SV45 )
!= SV41 )
| ( ( product @ SV45 @ SV41 )
!= SV45 ) )
= $true )
| ( ( l @ SV41 @ SV45 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[272]) ).
thf(283,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( l @ SX0 @ SX1 )
| ( ( product @ SX0 @ SX1 )
= SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[273]) ).
thf(284,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( l @ SX0 @ SX1 )
| ( ( product @ SX1 @ SX0 )
= SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[274]) ).
thf(285,plain,
! [SV42: $i,SV46: $i] :
( ( ( ! [SY103: $i] :
( ~ ( l @ SY103 @ SV46 )
| ~ ( r @ SV42 @ SY103 ) ) )
= $true )
| ( ( d @ SV42 @ SV46 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[275]) ).
thf(286,plain,
! [SV47: $i,SV43: $i] :
( ( ( ~ ( d @ SV43 @ SV47 ) )
= $true )
| ( ( ~ ( ~ ( l @ ( sK3_X6 @ SV47 @ SV43 ) @ SV47 )
| ~ ( r @ SV43 @ ( sK3_X6 @ SV47 @ SV43 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[276]) ).
thf(287,plain,
! [SV48: $i,SV44: $i] :
( ( ( ( ( product @ SV44 @ SV48 )
!= SV48 )
| ( ( product @ SV48 @ SV44 )
!= SV44 ) )
= $true )
| ( ( r @ SV44 @ SV48 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[277]) ).
thf(288,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( r @ SX0 @ SX1 )
| ( ( product @ SX0 @ SX1 )
= SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[278]) ).
thf(289,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( r @ SX0 @ SX1 )
| ( ( product @ SX1 @ SX0 )
= SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[279]) ).
thf(290,plain,
( ( ( product @ sK1_X7 @ ( product @ sK2_SY81 @ sK1_X7 ) )
= sK1_X7 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[280]) ).
thf(291,plain,
( ( ( product @ sK2_SY81 @ ( product @ sK1_X7 @ sK2_SY81 ) )
= sK2_SY81 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[281]) ).
thf(292,plain,
! [SV45: $i,SV41: $i] :
( ( ( ( ( product @ SV41 @ SV45 )
!= SV41 ) )
= $true )
| ( ( ( ( product @ SV45 @ SV41 )
!= SV45 ) )
= $true )
| ( ( l @ SV41 @ SV45 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[282]) ).
thf(293,plain,
! [SV49: $i] :
( ( ! [SY104: $i] :
( ~ ( l @ SV49 @ SY104 )
| ( ( product @ SV49 @ SY104 )
= SV49 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[283]) ).
thf(294,plain,
! [SV50: $i] :
( ( ! [SY105: $i] :
( ~ ( l @ SV50 @ SY105 )
| ( ( product @ SY105 @ SV50 )
= SY105 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[284]) ).
thf(295,plain,
! [SV42: $i,SV46: $i,SV51: $i] :
( ( ( ~ ( l @ SV51 @ SV46 )
| ~ ( r @ SV42 @ SV51 ) )
= $true )
| ( ( d @ SV42 @ SV46 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[285]) ).
thf(296,plain,
! [SV47: $i,SV43: $i] :
( ( ( d @ SV43 @ SV47 )
= $false )
| ( ( ~ ( ~ ( l @ ( sK3_X6 @ SV47 @ SV43 ) @ SV47 )
| ~ ( r @ SV43 @ ( sK3_X6 @ SV47 @ SV43 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[286]) ).
thf(297,plain,
! [SV48: $i,SV44: $i] :
( ( ( ( ( product @ SV44 @ SV48 )
!= SV48 ) )
= $true )
| ( ( ( ( product @ SV48 @ SV44 )
!= SV44 ) )
= $true )
| ( ( r @ SV44 @ SV48 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[287]) ).
thf(298,plain,
! [SV52: $i] :
( ( ! [SY106: $i] :
( ~ ( r @ SV52 @ SY106 )
| ( ( product @ SV52 @ SY106 )
= SY106 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[288]) ).
thf(299,plain,
! [SV53: $i] :
( ( ! [SY107: $i] :
( ~ ( r @ SV53 @ SY107 )
| ( ( product @ SY107 @ SV53 )
= SV53 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[289]) ).
thf(300,plain,
! [SV45: $i,SV41: $i] :
( ( ( ( product @ SV41 @ SV45 )
= SV41 )
= $false )
| ( ( ( ( product @ SV45 @ SV41 )
!= SV45 ) )
= $true )
| ( ( l @ SV41 @ SV45 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[292]) ).
thf(301,plain,
! [SV54: $i,SV49: $i] :
( ( ~ ( l @ SV49 @ SV54 )
| ( ( product @ SV49 @ SV54 )
= SV49 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[293]) ).
thf(302,plain,
! [SV55: $i,SV50: $i] :
( ( ~ ( l @ SV50 @ SV55 )
| ( ( product @ SV55 @ SV50 )
= SV55 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[294]) ).
thf(303,plain,
! [SV42: $i,SV46: $i,SV51: $i] :
( ( ( ~ ( l @ SV51 @ SV46 ) )
= $true )
| ( ( ~ ( r @ SV42 @ SV51 ) )
= $true )
| ( ( d @ SV42 @ SV46 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[295]) ).
thf(304,plain,
! [SV43: $i,SV47: $i] :
( ( ( ~ ( l @ ( sK3_X6 @ SV47 @ SV43 ) @ SV47 )
| ~ ( r @ SV43 @ ( sK3_X6 @ SV47 @ SV43 ) ) )
= $false )
| ( ( d @ SV43 @ SV47 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[296]) ).
thf(305,plain,
! [SV48: $i,SV44: $i] :
( ( ( ( product @ SV44 @ SV48 )
= SV48 )
= $false )
| ( ( ( ( product @ SV48 @ SV44 )
!= SV44 ) )
= $true )
| ( ( r @ SV44 @ SV48 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[297]) ).
thf(306,plain,
! [SV56: $i,SV52: $i] :
( ( ~ ( r @ SV52 @ SV56 )
| ( ( product @ SV52 @ SV56 )
= SV56 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[298]) ).
thf(307,plain,
! [SV57: $i,SV53: $i] :
( ( ~ ( r @ SV53 @ SV57 )
| ( ( product @ SV57 @ SV53 )
= SV53 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[299]) ).
thf(308,plain,
! [SV41: $i,SV45: $i] :
( ( ( ( product @ SV45 @ SV41 )
= SV45 )
= $false )
| ( ( ( product @ SV41 @ SV45 )
= SV41 )
= $false )
| ( ( l @ SV41 @ SV45 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[300]) ).
thf(309,plain,
! [SV54: $i,SV49: $i] :
( ( ( ~ ( l @ SV49 @ SV54 ) )
= $true )
| ( ( ( product @ SV49 @ SV54 )
= SV49 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[301]) ).
thf(310,plain,
! [SV55: $i,SV50: $i] :
( ( ( ~ ( l @ SV50 @ SV55 ) )
= $true )
| ( ( ( product @ SV55 @ SV50 )
= SV55 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[302]) ).
thf(311,plain,
! [SV42: $i,SV46: $i,SV51: $i] :
( ( ( l @ SV51 @ SV46 )
= $false )
| ( ( ~ ( r @ SV42 @ SV51 ) )
= $true )
| ( ( d @ SV42 @ SV46 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[303]) ).
thf(312,plain,
! [SV43: $i,SV47: $i] :
( ( ( ~ ( l @ ( sK3_X6 @ SV47 @ SV43 ) @ SV47 ) )
= $false )
| ( ( d @ SV43 @ SV47 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[304]) ).
thf(313,plain,
! [SV47: $i,SV43: $i] :
( ( ( ~ ( r @ SV43 @ ( sK3_X6 @ SV47 @ SV43 ) ) )
= $false )
| ( ( d @ SV43 @ SV47 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[304]) ).
thf(314,plain,
! [SV44: $i,SV48: $i] :
( ( ( ( product @ SV48 @ SV44 )
= SV44 )
= $false )
| ( ( ( product @ SV44 @ SV48 )
= SV48 )
= $false )
| ( ( r @ SV44 @ SV48 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[305]) ).
thf(315,plain,
! [SV56: $i,SV52: $i] :
( ( ( ~ ( r @ SV52 @ SV56 ) )
= $true )
| ( ( ( product @ SV52 @ SV56 )
= SV56 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[306]) ).
thf(316,plain,
! [SV57: $i,SV53: $i] :
( ( ( ~ ( r @ SV53 @ SV57 ) )
= $true )
| ( ( ( product @ SV57 @ SV53 )
= SV53 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[307]) ).
thf(317,plain,
! [SV54: $i,SV49: $i] :
( ( ( l @ SV49 @ SV54 )
= $false )
| ( ( ( product @ SV49 @ SV54 )
= SV49 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[309]) ).
thf(318,plain,
! [SV55: $i,SV50: $i] :
( ( ( l @ SV50 @ SV55 )
= $false )
| ( ( ( product @ SV55 @ SV50 )
= SV55 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[310]) ).
thf(319,plain,
! [SV46: $i,SV51: $i,SV42: $i] :
( ( ( r @ SV42 @ SV51 )
= $false )
| ( ( l @ SV51 @ SV46 )
= $false )
| ( ( d @ SV42 @ SV46 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[311]) ).
thf(320,plain,
! [SV43: $i,SV47: $i] :
( ( ( l @ ( sK3_X6 @ SV47 @ SV43 ) @ SV47 )
= $true )
| ( ( d @ SV43 @ SV47 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[312]) ).
thf(321,plain,
! [SV47: $i,SV43: $i] :
( ( ( r @ SV43 @ ( sK3_X6 @ SV47 @ SV43 ) )
= $true )
| ( ( d @ SV43 @ SV47 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[313]) ).
thf(322,plain,
! [SV56: $i,SV52: $i] :
( ( ( r @ SV52 @ SV56 )
= $false )
| ( ( ( product @ SV52 @ SV56 )
= SV56 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[315]) ).
thf(323,plain,
! [SV57: $i,SV53: $i] :
( ( ( r @ SV53 @ SV57 )
= $false )
| ( ( ( product @ SV57 @ SV53 )
= SV53 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[316]) ).
thf(324,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[241,323,322,321,320,319,318,317,314,308,291,290,271,255]) ).
thf(325,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[324,229]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP775+1 : TPTP v8.1.0. Released v4.1.0.
% 0.12/0.12 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.33 % Computer : n014.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Tue Jun 14 13:28:06 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.34
% 0.19/0.34 No.of.Axioms: 5
% 0.19/0.34
% 0.19/0.34 Length.of.Defs: 0
% 0.19/0.34
% 0.19/0.34 Contains.Choice.Funs: false
% 0.19/0.35 (rf:0,axioms:5,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:7,loop_count:0,foatp_calls:0,translation:fof_full).......eprover: CPU time limit exceeded, terminating
% 74.25/74.55 ..
% 74.99/75.25 (rf:0,axioms:5,ps:2,u:1,ude:false,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:7,loop_count:0,foatp_calls:0,translation:fof_full)......eprover: CPU time limit exceeded, terminating
% 150.05/150.35 .
% 150.05/150.35 (rf:0,axioms:5,ps:3,u:8,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:false,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:7,loop_count:0,foatp_calls:0,translation:fof_full).......eprover: CPU time limit exceeded, terminating
% 224.26/224.51 ...
% 224.95/225.21 (rf:2,axioms:5,ps:1,u:3,ude:true,rLeibEQ:false,rAndEQ:false,use_choice:false,use_extuni:false,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:7,loop_count:0,foatp_calls:0,translation:fof_full).............
% 236.33/236.72
% 236.33/236.72 ********************************
% 236.33/236.72 * All subproblems solved! *
% 236.33/236.72 ********************************
% 236.33/236.72 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:2,axioms:5,ps:1,u:3,ude:true,rLeibEQ:false,rAndEQ:false,use_choice:false,use_extuni:false,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:63,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:324,loop_count:0,foatp_calls:1,translation:fof_full)
% 236.33/236.74
% 236.33/236.74 %**** Beginning of derivation protocol ****
% 236.33/236.74 % SZS output start CNFRefutation
% See solution above
% 236.33/236.74
% 236.33/236.74 %**** End of derivation protocol ****
% 236.33/236.74 %**** no. of clauses in derivation: 231 ****
% 236.33/236.74 %**** clause counter: 324 ****
% 236.33/236.74
% 236.33/236.74 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:2,axioms:5,ps:1,u:3,ude:true,rLeibEQ:false,rAndEQ:false,use_choice:false,use_extuni:false,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:63,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:324,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------