TSTP Solution File: GRP208-1 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : GRP208-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n005.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 10:16:58 EDT 2022
% Result : Unsatisfiable 3.97s 4.16s
% Output : CNFRefutation 4.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 46
% Number of leaves : 80
% Syntax : Number of formulae : 322 ( 153 unt; 15 typ; 0 def)
% Number of atoms : 2384 (1795 equ; 0 cnn)
% Maximal formula atoms : 16 ( 7 avg)
% Number of connectives : 3393 ( 456 ~; 915 |; 0 &;2022 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 15 usr; 15 con; 0-2 aty)
% Number of variables : 476 ( 0 ^ 476 !; 0 ?; 476 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_identity,type,
identity: $i ).
thf(tp_inverse,type,
inverse: $i > $i ).
thf(tp_multiply,type,
multiply: $i > $i > $i ).
thf(tp_sk_c1,type,
sk_c1: $i ).
thf(tp_sk_c10,type,
sk_c10: $i ).
thf(tp_sk_c11,type,
sk_c11: $i ).
thf(tp_sk_c12,type,
sk_c12: $i ).
thf(tp_sk_c2,type,
sk_c2: $i ).
thf(tp_sk_c3,type,
sk_c3: $i ).
thf(tp_sk_c4,type,
sk_c4: $i ).
thf(tp_sk_c5,type,
sk_c5: $i ).
thf(tp_sk_c6,type,
sk_c6: $i ).
thf(tp_sk_c7,type,
sk_c7: $i ).
thf(tp_sk_c8,type,
sk_c8: $i ).
thf(tp_sk_c9,type,
sk_c9: $i ).
thf(1,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( multiply @ ( multiply @ X @ Y ) @ Z )
= ( multiply @ X @ ( multiply @ Y @ Z ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity) ).
thf(2,axiom,
! [X: $i] :
( ( multiply @ ( inverse @ X ) @ X )
= identity ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_inverse) ).
thf(3,axiom,
! [X: $i] :
( ( multiply @ identity @ X )
= X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_identity) ).
thf(4,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(5,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[4]) ).
thf(6,negated_conjecture,
! [X5: $i,X6: $i,X7: $i,X8: $i,X2: $i,X1: $i,X3: $i,X9: $i,X4: $i,X10: $i] :
( ( ( multiply @ X5 @ X6 )
!= sk_c12 )
| ( ( inverse @ X5 )
!= X6 )
| ( ( multiply @ X6 @ sk_c11 )
!= sk_c12 )
| ( ( multiply @ sk_c12 @ X7 )
!= sk_c11 )
| ( ( multiply @ X8 @ sk_c12 )
!= X7 )
| ( ( inverse @ X8 )
!= sk_c12 )
| ( ( multiply @ X2 @ X1 )
!= sk_c12 )
| ( ( inverse @ X2 )
!= X1 )
| ( ( multiply @ X1 @ sk_c11 )
!= sk_c12 )
| ( ( inverse @ X3 )
!= sk_c12 )
| ( ( multiply @ X3 @ sk_c11 )
!= sk_c12 )
| ( ( multiply @ X9 @ X4 )
!= sk_c11 )
| ( ( inverse @ X9 )
!= X4 )
| ( ( multiply @ X4 @ sk_c12 )
!= sk_c11 )
| ( ( inverse @ X10 )
!= sk_c11 )
| ( ( multiply @ X10 @ sk_c12 )
!= sk_c11 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_61) ).
thf(7,negated_conjecture,
( ( ( inverse @ sk_c3 )
= sk_c12 )
| ( ( multiply @ sk_c10 @ sk_c12 )
= sk_c11 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_60) ).
thf(8,negated_conjecture,
( ( ( inverse @ sk_c3 )
= sk_c12 )
| ( ( inverse @ sk_c10 )
= sk_c11 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_59) ).
thf(9,negated_conjecture,
( ( ( inverse @ sk_c3 )
= sk_c12 )
| ( ( multiply @ sk_c9 @ sk_c12 )
= sk_c11 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_58) ).
thf(10,negated_conjecture,
( ( ( inverse @ sk_c3 )
= sk_c12 )
| ( ( inverse @ sk_c8 )
= sk_c9 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_57) ).
thf(11,negated_conjecture,
( ( ( inverse @ sk_c3 )
= sk_c12 )
| ( ( multiply @ sk_c8 @ sk_c9 )
= sk_c11 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_56) ).
thf(12,negated_conjecture,
( ( ( inverse @ sk_c3 )
= sk_c12 )
| ( ( multiply @ sk_c7 @ sk_c11 )
= sk_c12 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_55) ).
thf(13,negated_conjecture,
( ( ( inverse @ sk_c3 )
= sk_c12 )
| ( ( inverse @ sk_c7 )
= sk_c12 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_54) ).
thf(14,negated_conjecture,
( ( ( inverse @ sk_c3 )
= sk_c12 )
| ( ( multiply @ sk_c6 @ sk_c11 )
= sk_c12 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_53) ).
thf(15,negated_conjecture,
( ( ( inverse @ sk_c3 )
= sk_c12 )
| ( ( inverse @ sk_c5 )
= sk_c6 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_52) ).
thf(16,negated_conjecture,
( ( ( inverse @ sk_c3 )
= sk_c12 )
| ( ( multiply @ sk_c5 @ sk_c6 )
= sk_c12 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_51) ).
thf(17,negated_conjecture,
( ( ( multiply @ sk_c3 @ sk_c12 )
= sk_c4 )
| ( ( multiply @ sk_c10 @ sk_c12 )
= sk_c11 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_50) ).
thf(18,negated_conjecture,
( ( ( multiply @ sk_c3 @ sk_c12 )
= sk_c4 )
| ( ( inverse @ sk_c10 )
= sk_c11 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_49) ).
thf(19,negated_conjecture,
( ( ( multiply @ sk_c3 @ sk_c12 )
= sk_c4 )
| ( ( multiply @ sk_c9 @ sk_c12 )
= sk_c11 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_48) ).
thf(20,negated_conjecture,
( ( ( multiply @ sk_c3 @ sk_c12 )
= sk_c4 )
| ( ( inverse @ sk_c8 )
= sk_c9 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_47) ).
thf(21,negated_conjecture,
( ( ( multiply @ sk_c3 @ sk_c12 )
= sk_c4 )
| ( ( multiply @ sk_c8 @ sk_c9 )
= sk_c11 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_46) ).
thf(22,negated_conjecture,
( ( ( multiply @ sk_c3 @ sk_c12 )
= sk_c4 )
| ( ( multiply @ sk_c7 @ sk_c11 )
= sk_c12 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_45) ).
thf(23,negated_conjecture,
( ( ( multiply @ sk_c3 @ sk_c12 )
= sk_c4 )
| ( ( inverse @ sk_c7 )
= sk_c12 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_44) ).
thf(24,negated_conjecture,
( ( ( multiply @ sk_c3 @ sk_c12 )
= sk_c4 )
| ( ( multiply @ sk_c6 @ sk_c11 )
= sk_c12 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_43) ).
thf(25,negated_conjecture,
( ( ( multiply @ sk_c3 @ sk_c12 )
= sk_c4 )
| ( ( inverse @ sk_c5 )
= sk_c6 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_42) ).
thf(26,negated_conjecture,
( ( ( multiply @ sk_c3 @ sk_c12 )
= sk_c4 )
| ( ( multiply @ sk_c5 @ sk_c6 )
= sk_c12 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_41) ).
thf(27,negated_conjecture,
( ( ( multiply @ sk_c12 @ sk_c4 )
= sk_c11 )
| ( ( multiply @ sk_c10 @ sk_c12 )
= sk_c11 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_40) ).
thf(28,negated_conjecture,
( ( ( multiply @ sk_c12 @ sk_c4 )
= sk_c11 )
| ( ( inverse @ sk_c10 )
= sk_c11 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_39) ).
thf(29,negated_conjecture,
( ( ( multiply @ sk_c12 @ sk_c4 )
= sk_c11 )
| ( ( multiply @ sk_c9 @ sk_c12 )
= sk_c11 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_38) ).
thf(30,negated_conjecture,
( ( ( multiply @ sk_c12 @ sk_c4 )
= sk_c11 )
| ( ( inverse @ sk_c8 )
= sk_c9 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_37) ).
thf(31,negated_conjecture,
( ( ( multiply @ sk_c12 @ sk_c4 )
= sk_c11 )
| ( ( multiply @ sk_c8 @ sk_c9 )
= sk_c11 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_36) ).
thf(32,negated_conjecture,
( ( ( multiply @ sk_c12 @ sk_c4 )
= sk_c11 )
| ( ( multiply @ sk_c7 @ sk_c11 )
= sk_c12 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_35) ).
thf(33,negated_conjecture,
( ( ( multiply @ sk_c12 @ sk_c4 )
= sk_c11 )
| ( ( inverse @ sk_c7 )
= sk_c12 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_34) ).
thf(34,negated_conjecture,
( ( ( multiply @ sk_c12 @ sk_c4 )
= sk_c11 )
| ( ( multiply @ sk_c6 @ sk_c11 )
= sk_c12 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_33) ).
thf(35,negated_conjecture,
( ( ( multiply @ sk_c12 @ sk_c4 )
= sk_c11 )
| ( ( inverse @ sk_c5 )
= sk_c6 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_32) ).
thf(36,negated_conjecture,
( ( ( multiply @ sk_c12 @ sk_c4 )
= sk_c11 )
| ( ( multiply @ sk_c5 @ sk_c6 )
= sk_c12 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_31) ).
thf(37,negated_conjecture,
( ( ( multiply @ sk_c2 @ sk_c11 )
= sk_c12 )
| ( ( multiply @ sk_c10 @ sk_c12 )
= sk_c11 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_30) ).
thf(38,negated_conjecture,
( ( ( multiply @ sk_c2 @ sk_c11 )
= sk_c12 )
| ( ( inverse @ sk_c10 )
= sk_c11 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_29) ).
thf(39,negated_conjecture,
( ( ( multiply @ sk_c2 @ sk_c11 )
= sk_c12 )
| ( ( multiply @ sk_c9 @ sk_c12 )
= sk_c11 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_28) ).
thf(40,negated_conjecture,
( ( ( multiply @ sk_c2 @ sk_c11 )
= sk_c12 )
| ( ( inverse @ sk_c8 )
= sk_c9 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_27) ).
thf(41,negated_conjecture,
( ( ( multiply @ sk_c2 @ sk_c11 )
= sk_c12 )
| ( ( multiply @ sk_c8 @ sk_c9 )
= sk_c11 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_26) ).
thf(42,negated_conjecture,
( ( ( multiply @ sk_c2 @ sk_c11 )
= sk_c12 )
| ( ( multiply @ sk_c7 @ sk_c11 )
= sk_c12 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_25) ).
thf(43,negated_conjecture,
( ( ( multiply @ sk_c2 @ sk_c11 )
= sk_c12 )
| ( ( inverse @ sk_c7 )
= sk_c12 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_24) ).
thf(44,negated_conjecture,
( ( ( multiply @ sk_c2 @ sk_c11 )
= sk_c12 )
| ( ( multiply @ sk_c6 @ sk_c11 )
= sk_c12 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_23) ).
thf(45,negated_conjecture,
( ( ( multiply @ sk_c2 @ sk_c11 )
= sk_c12 )
| ( ( inverse @ sk_c5 )
= sk_c6 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_22) ).
thf(46,negated_conjecture,
( ( ( multiply @ sk_c2 @ sk_c11 )
= sk_c12 )
| ( ( multiply @ sk_c5 @ sk_c6 )
= sk_c12 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_21) ).
thf(47,negated_conjecture,
( ( ( inverse @ sk_c1 )
= sk_c2 )
| ( ( multiply @ sk_c10 @ sk_c12 )
= sk_c11 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_20) ).
thf(48,negated_conjecture,
( ( ( inverse @ sk_c1 )
= sk_c2 )
| ( ( inverse @ sk_c10 )
= sk_c11 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_19) ).
thf(49,negated_conjecture,
( ( ( inverse @ sk_c1 )
= sk_c2 )
| ( ( multiply @ sk_c9 @ sk_c12 )
= sk_c11 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_18) ).
thf(50,negated_conjecture,
( ( ( inverse @ sk_c1 )
= sk_c2 )
| ( ( inverse @ sk_c8 )
= sk_c9 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_17) ).
thf(51,negated_conjecture,
( ( ( inverse @ sk_c1 )
= sk_c2 )
| ( ( multiply @ sk_c8 @ sk_c9 )
= sk_c11 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_16) ).
thf(52,negated_conjecture,
( ( ( inverse @ sk_c1 )
= sk_c2 )
| ( ( multiply @ sk_c7 @ sk_c11 )
= sk_c12 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_15) ).
thf(53,negated_conjecture,
( ( ( inverse @ sk_c1 )
= sk_c2 )
| ( ( inverse @ sk_c7 )
= sk_c12 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_14) ).
thf(54,negated_conjecture,
( ( ( inverse @ sk_c1 )
= sk_c2 )
| ( ( multiply @ sk_c6 @ sk_c11 )
= sk_c12 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_13) ).
thf(55,negated_conjecture,
( ( ( inverse @ sk_c1 )
= sk_c2 )
| ( ( inverse @ sk_c5 )
= sk_c6 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_12) ).
thf(56,negated_conjecture,
( ( ( inverse @ sk_c1 )
= sk_c2 )
| ( ( multiply @ sk_c5 @ sk_c6 )
= sk_c12 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_11) ).
thf(57,negated_conjecture,
( ( ( multiply @ sk_c1 @ sk_c2 )
= sk_c12 )
| ( ( multiply @ sk_c10 @ sk_c12 )
= sk_c11 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_10) ).
thf(58,negated_conjecture,
( ( ( multiply @ sk_c1 @ sk_c2 )
= sk_c12 )
| ( ( inverse @ sk_c10 )
= sk_c11 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_9) ).
thf(59,negated_conjecture,
( ( ( multiply @ sk_c1 @ sk_c2 )
= sk_c12 )
| ( ( multiply @ sk_c9 @ sk_c12 )
= sk_c11 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_8) ).
thf(60,negated_conjecture,
( ( ( multiply @ sk_c1 @ sk_c2 )
= sk_c12 )
| ( ( inverse @ sk_c8 )
= sk_c9 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_7) ).
thf(61,negated_conjecture,
( ( ( multiply @ sk_c1 @ sk_c2 )
= sk_c12 )
| ( ( multiply @ sk_c8 @ sk_c9 )
= sk_c11 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_6) ).
thf(62,negated_conjecture,
( ( ( multiply @ sk_c1 @ sk_c2 )
= sk_c12 )
| ( ( multiply @ sk_c7 @ sk_c11 )
= sk_c12 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_5) ).
thf(63,negated_conjecture,
( ( ( multiply @ sk_c1 @ sk_c2 )
= sk_c12 )
| ( ( inverse @ sk_c7 )
= sk_c12 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_4) ).
thf(64,negated_conjecture,
( ( ( multiply @ sk_c1 @ sk_c2 )
= sk_c12 )
| ( ( multiply @ sk_c6 @ sk_c11 )
= sk_c12 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_3) ).
thf(65,negated_conjecture,
( ( ( multiply @ sk_c1 @ sk_c2 )
= sk_c12 )
| ( ( inverse @ sk_c5 )
= sk_c6 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
thf(66,negated_conjecture,
( ( ( multiply @ sk_c1 @ sk_c2 )
= sk_c12 )
| ( ( multiply @ sk_c5 @ sk_c6 )
= sk_c12 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
thf(67,plain,
$false = $false,
inference(unfold_def,[status(thm)],[5]) ).
thf(68,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( multiply @ ( multiply @ X @ Y ) @ Z )
= ( multiply @ X @ ( multiply @ Y @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(69,plain,
( ( ! [X: $i] :
( ( multiply @ ( inverse @ X ) @ X )
= identity ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(70,plain,
( ( ! [X: $i] :
( ( multiply @ identity @ X )
= X ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(71,plain,
( ( ! [X5: $i,X6: $i,X7: $i,X8: $i,X2: $i,X1: $i,X3: $i,X9: $i,X4: $i,X10: $i] :
( ( ( multiply @ X5 @ X6 )
!= sk_c12 )
| ( ( inverse @ X5 )
!= X6 )
| ( ( multiply @ X6 @ sk_c11 )
!= sk_c12 )
| ( ( multiply @ sk_c12 @ X7 )
!= sk_c11 )
| ( ( multiply @ X8 @ sk_c12 )
!= X7 )
| ( ( inverse @ X8 )
!= sk_c12 )
| ( ( multiply @ X2 @ X1 )
!= sk_c12 )
| ( ( inverse @ X2 )
!= X1 )
| ( ( multiply @ X1 @ sk_c11 )
!= sk_c12 )
| ( ( inverse @ X3 )
!= sk_c12 )
| ( ( multiply @ X3 @ sk_c11 )
!= sk_c12 )
| ( ( multiply @ X9 @ X4 )
!= sk_c11 )
| ( ( inverse @ X9 )
!= X4 )
| ( ( multiply @ X4 @ sk_c12 )
!= sk_c11 )
| ( ( inverse @ X10 )
!= sk_c11 )
| ( ( multiply @ X10 @ sk_c12 )
!= sk_c11 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(72,plain,
( ( ( ( inverse @ sk_c3 )
= sk_c12 )
| ( ( multiply @ sk_c10 @ sk_c12 )
= sk_c11 ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(73,plain,
( ( ( ( inverse @ sk_c3 )
= sk_c12 )
| ( ( inverse @ sk_c10 )
= sk_c11 ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(74,plain,
( ( ( ( inverse @ sk_c3 )
= sk_c12 )
| ( ( multiply @ sk_c9 @ sk_c12 )
= sk_c11 ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(75,plain,
( ( ( ( inverse @ sk_c3 )
= sk_c12 )
| ( ( inverse @ sk_c8 )
= sk_c9 ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(76,plain,
( ( ( ( inverse @ sk_c3 )
= sk_c12 )
| ( ( multiply @ sk_c8 @ sk_c9 )
= sk_c11 ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(77,plain,
( ( ( ( inverse @ sk_c3 )
= sk_c12 )
| ( ( multiply @ sk_c7 @ sk_c11 )
= sk_c12 ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(78,plain,
( ( ( ( inverse @ sk_c3 )
= sk_c12 )
| ( ( inverse @ sk_c7 )
= sk_c12 ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(79,plain,
( ( ( ( inverse @ sk_c3 )
= sk_c12 )
| ( ( multiply @ sk_c6 @ sk_c11 )
= sk_c12 ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(80,plain,
( ( ( ( inverse @ sk_c3 )
= sk_c12 )
| ( ( inverse @ sk_c5 )
= sk_c6 ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(81,plain,
( ( ( ( inverse @ sk_c3 )
= sk_c12 )
| ( ( multiply @ sk_c5 @ sk_c6 )
= sk_c12 ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(82,plain,
( ( ( ( multiply @ sk_c3 @ sk_c12 )
= sk_c4 )
| ( ( multiply @ sk_c10 @ sk_c12 )
= sk_c11 ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(83,plain,
( ( ( ( multiply @ sk_c3 @ sk_c12 )
= sk_c4 )
| ( ( inverse @ sk_c10 )
= sk_c11 ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(84,plain,
( ( ( ( multiply @ sk_c3 @ sk_c12 )
= sk_c4 )
| ( ( multiply @ sk_c9 @ sk_c12 )
= sk_c11 ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(85,plain,
( ( ( ( multiply @ sk_c3 @ sk_c12 )
= sk_c4 )
| ( ( inverse @ sk_c8 )
= sk_c9 ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(86,plain,
( ( ( ( multiply @ sk_c3 @ sk_c12 )
= sk_c4 )
| ( ( multiply @ sk_c8 @ sk_c9 )
= sk_c11 ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(87,plain,
( ( ( ( multiply @ sk_c3 @ sk_c12 )
= sk_c4 )
| ( ( multiply @ sk_c7 @ sk_c11 )
= sk_c12 ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(88,plain,
( ( ( ( multiply @ sk_c3 @ sk_c12 )
= sk_c4 )
| ( ( inverse @ sk_c7 )
= sk_c12 ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(89,plain,
( ( ( ( multiply @ sk_c3 @ sk_c12 )
= sk_c4 )
| ( ( multiply @ sk_c6 @ sk_c11 )
= sk_c12 ) )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(90,plain,
( ( ( ( multiply @ sk_c3 @ sk_c12 )
= sk_c4 )
| ( ( inverse @ sk_c5 )
= sk_c6 ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(91,plain,
( ( ( ( multiply @ sk_c3 @ sk_c12 )
= sk_c4 )
| ( ( multiply @ sk_c5 @ sk_c6 )
= sk_c12 ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(92,plain,
( ( ( ( multiply @ sk_c12 @ sk_c4 )
= sk_c11 )
| ( ( multiply @ sk_c10 @ sk_c12 )
= sk_c11 ) )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(93,plain,
( ( ( ( multiply @ sk_c12 @ sk_c4 )
= sk_c11 )
| ( ( inverse @ sk_c10 )
= sk_c11 ) )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(94,plain,
( ( ( ( multiply @ sk_c12 @ sk_c4 )
= sk_c11 )
| ( ( multiply @ sk_c9 @ sk_c12 )
= sk_c11 ) )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(95,plain,
( ( ( ( multiply @ sk_c12 @ sk_c4 )
= sk_c11 )
| ( ( inverse @ sk_c8 )
= sk_c9 ) )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(96,plain,
( ( ( ( multiply @ sk_c12 @ sk_c4 )
= sk_c11 )
| ( ( multiply @ sk_c8 @ sk_c9 )
= sk_c11 ) )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(97,plain,
( ( ( ( multiply @ sk_c12 @ sk_c4 )
= sk_c11 )
| ( ( multiply @ sk_c7 @ sk_c11 )
= sk_c12 ) )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(98,plain,
( ( ( ( multiply @ sk_c12 @ sk_c4 )
= sk_c11 )
| ( ( inverse @ sk_c7 )
= sk_c12 ) )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(99,plain,
( ( ( ( multiply @ sk_c12 @ sk_c4 )
= sk_c11 )
| ( ( multiply @ sk_c6 @ sk_c11 )
= sk_c12 ) )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(100,plain,
( ( ( ( multiply @ sk_c12 @ sk_c4 )
= sk_c11 )
| ( ( inverse @ sk_c5 )
= sk_c6 ) )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(101,plain,
( ( ( ( multiply @ sk_c12 @ sk_c4 )
= sk_c11 )
| ( ( multiply @ sk_c5 @ sk_c6 )
= sk_c12 ) )
= $true ),
inference(unfold_def,[status(thm)],[36]) ).
thf(102,plain,
( ( ( ( multiply @ sk_c2 @ sk_c11 )
= sk_c12 )
| ( ( multiply @ sk_c10 @ sk_c12 )
= sk_c11 ) )
= $true ),
inference(unfold_def,[status(thm)],[37]) ).
thf(103,plain,
( ( ( ( multiply @ sk_c2 @ sk_c11 )
= sk_c12 )
| ( ( inverse @ sk_c10 )
= sk_c11 ) )
= $true ),
inference(unfold_def,[status(thm)],[38]) ).
thf(104,plain,
( ( ( ( multiply @ sk_c2 @ sk_c11 )
= sk_c12 )
| ( ( multiply @ sk_c9 @ sk_c12 )
= sk_c11 ) )
= $true ),
inference(unfold_def,[status(thm)],[39]) ).
thf(105,plain,
( ( ( ( multiply @ sk_c2 @ sk_c11 )
= sk_c12 )
| ( ( inverse @ sk_c8 )
= sk_c9 ) )
= $true ),
inference(unfold_def,[status(thm)],[40]) ).
thf(106,plain,
( ( ( ( multiply @ sk_c2 @ sk_c11 )
= sk_c12 )
| ( ( multiply @ sk_c8 @ sk_c9 )
= sk_c11 ) )
= $true ),
inference(unfold_def,[status(thm)],[41]) ).
thf(107,plain,
( ( ( ( multiply @ sk_c2 @ sk_c11 )
= sk_c12 )
| ( ( multiply @ sk_c7 @ sk_c11 )
= sk_c12 ) )
= $true ),
inference(unfold_def,[status(thm)],[42]) ).
thf(108,plain,
( ( ( ( multiply @ sk_c2 @ sk_c11 )
= sk_c12 )
| ( ( inverse @ sk_c7 )
= sk_c12 ) )
= $true ),
inference(unfold_def,[status(thm)],[43]) ).
thf(109,plain,
( ( ( ( multiply @ sk_c2 @ sk_c11 )
= sk_c12 )
| ( ( multiply @ sk_c6 @ sk_c11 )
= sk_c12 ) )
= $true ),
inference(unfold_def,[status(thm)],[44]) ).
thf(110,plain,
( ( ( ( multiply @ sk_c2 @ sk_c11 )
= sk_c12 )
| ( ( inverse @ sk_c5 )
= sk_c6 ) )
= $true ),
inference(unfold_def,[status(thm)],[45]) ).
thf(111,plain,
( ( ( ( multiply @ sk_c2 @ sk_c11 )
= sk_c12 )
| ( ( multiply @ sk_c5 @ sk_c6 )
= sk_c12 ) )
= $true ),
inference(unfold_def,[status(thm)],[46]) ).
thf(112,plain,
( ( ( ( inverse @ sk_c1 )
= sk_c2 )
| ( ( multiply @ sk_c10 @ sk_c12 )
= sk_c11 ) )
= $true ),
inference(unfold_def,[status(thm)],[47]) ).
thf(113,plain,
( ( ( ( inverse @ sk_c1 )
= sk_c2 )
| ( ( inverse @ sk_c10 )
= sk_c11 ) )
= $true ),
inference(unfold_def,[status(thm)],[48]) ).
thf(114,plain,
( ( ( ( inverse @ sk_c1 )
= sk_c2 )
| ( ( multiply @ sk_c9 @ sk_c12 )
= sk_c11 ) )
= $true ),
inference(unfold_def,[status(thm)],[49]) ).
thf(115,plain,
( ( ( ( inverse @ sk_c1 )
= sk_c2 )
| ( ( inverse @ sk_c8 )
= sk_c9 ) )
= $true ),
inference(unfold_def,[status(thm)],[50]) ).
thf(116,plain,
( ( ( ( inverse @ sk_c1 )
= sk_c2 )
| ( ( multiply @ sk_c8 @ sk_c9 )
= sk_c11 ) )
= $true ),
inference(unfold_def,[status(thm)],[51]) ).
thf(117,plain,
( ( ( ( inverse @ sk_c1 )
= sk_c2 )
| ( ( multiply @ sk_c7 @ sk_c11 )
= sk_c12 ) )
= $true ),
inference(unfold_def,[status(thm)],[52]) ).
thf(118,plain,
( ( ( ( inverse @ sk_c1 )
= sk_c2 )
| ( ( inverse @ sk_c7 )
= sk_c12 ) )
= $true ),
inference(unfold_def,[status(thm)],[53]) ).
thf(119,plain,
( ( ( ( inverse @ sk_c1 )
= sk_c2 )
| ( ( multiply @ sk_c6 @ sk_c11 )
= sk_c12 ) )
= $true ),
inference(unfold_def,[status(thm)],[54]) ).
thf(120,plain,
( ( ( ( inverse @ sk_c1 )
= sk_c2 )
| ( ( inverse @ sk_c5 )
= sk_c6 ) )
= $true ),
inference(unfold_def,[status(thm)],[55]) ).
thf(121,plain,
( ( ( ( inverse @ sk_c1 )
= sk_c2 )
| ( ( multiply @ sk_c5 @ sk_c6 )
= sk_c12 ) )
= $true ),
inference(unfold_def,[status(thm)],[56]) ).
thf(122,plain,
( ( ( ( multiply @ sk_c1 @ sk_c2 )
= sk_c12 )
| ( ( multiply @ sk_c10 @ sk_c12 )
= sk_c11 ) )
= $true ),
inference(unfold_def,[status(thm)],[57]) ).
thf(123,plain,
( ( ( ( multiply @ sk_c1 @ sk_c2 )
= sk_c12 )
| ( ( inverse @ sk_c10 )
= sk_c11 ) )
= $true ),
inference(unfold_def,[status(thm)],[58]) ).
thf(124,plain,
( ( ( ( multiply @ sk_c1 @ sk_c2 )
= sk_c12 )
| ( ( multiply @ sk_c9 @ sk_c12 )
= sk_c11 ) )
= $true ),
inference(unfold_def,[status(thm)],[59]) ).
thf(125,plain,
( ( ( ( multiply @ sk_c1 @ sk_c2 )
= sk_c12 )
| ( ( inverse @ sk_c8 )
= sk_c9 ) )
= $true ),
inference(unfold_def,[status(thm)],[60]) ).
thf(126,plain,
( ( ( ( multiply @ sk_c1 @ sk_c2 )
= sk_c12 )
| ( ( multiply @ sk_c8 @ sk_c9 )
= sk_c11 ) )
= $true ),
inference(unfold_def,[status(thm)],[61]) ).
thf(127,plain,
( ( ( ( multiply @ sk_c1 @ sk_c2 )
= sk_c12 )
| ( ( multiply @ sk_c7 @ sk_c11 )
= sk_c12 ) )
= $true ),
inference(unfold_def,[status(thm)],[62]) ).
thf(128,plain,
( ( ( ( multiply @ sk_c1 @ sk_c2 )
= sk_c12 )
| ( ( inverse @ sk_c7 )
= sk_c12 ) )
= $true ),
inference(unfold_def,[status(thm)],[63]) ).
thf(129,plain,
( ( ( ( multiply @ sk_c1 @ sk_c2 )
= sk_c12 )
| ( ( multiply @ sk_c6 @ sk_c11 )
= sk_c12 ) )
= $true ),
inference(unfold_def,[status(thm)],[64]) ).
thf(130,plain,
( ( ( ( multiply @ sk_c1 @ sk_c2 )
= sk_c12 )
| ( ( inverse @ sk_c5 )
= sk_c6 ) )
= $true ),
inference(unfold_def,[status(thm)],[65]) ).
thf(131,plain,
( ( ( ( multiply @ sk_c1 @ sk_c2 )
= sk_c12 )
| ( ( multiply @ sk_c5 @ sk_c6 )
= sk_c12 ) )
= $true ),
inference(unfold_def,[status(thm)],[66]) ).
thf(132,plain,
( ( ~ $false )
= $true ),
inference(polarity_switch,[status(thm)],[67]) ).
thf(133,plain,
( ( ! [X5: $i,X6: $i,X7: $i,X8: $i,X2: $i,X1: $i,X3: $i,X9: $i] :
( ( ( multiply @ X5 @ X6 )
!= sk_c12 )
| ( ( inverse @ X5 )
!= X6 )
| ( ( multiply @ X6 @ sk_c11 )
!= sk_c12 )
| ( ( multiply @ sk_c12 @ X7 )
!= sk_c11 )
| ( ( multiply @ X8 @ sk_c12 )
!= X7 )
| ( ( inverse @ X8 )
!= sk_c12 )
| ( ( multiply @ X2 @ X1 )
!= sk_c12 )
| ( ( inverse @ X2 )
!= X1 )
| ( ( multiply @ X1 @ sk_c11 )
!= sk_c12 )
| ( ( inverse @ X3 )
!= sk_c12 )
| ( ( multiply @ X3 @ sk_c11 )
!= sk_c12 )
| ! [X4: $i] :
( ( ( multiply @ X9 @ X4 )
!= sk_c11 )
| ( ( inverse @ X9 )
!= X4 )
| ( ( multiply @ X4 @ sk_c12 )
!= sk_c11 )
| ! [X10: $i] :
( ( ( inverse @ X10 )
!= sk_c11 )
| ( ( multiply @ X10 @ sk_c12 )
!= sk_c11 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[71]) ).
thf(134,plain,
( ( ( ( multiply @ sk_c1 @ sk_c2 )
= sk_c12 )
| ( ( multiply @ sk_c5 @ sk_c6 )
= sk_c12 ) )
= $true ),
inference(copy,[status(thm)],[131]) ).
thf(135,plain,
( ( ( ( multiply @ sk_c1 @ sk_c2 )
= sk_c12 )
| ( ( inverse @ sk_c5 )
= sk_c6 ) )
= $true ),
inference(copy,[status(thm)],[130]) ).
thf(136,plain,
( ( ( ( multiply @ sk_c1 @ sk_c2 )
= sk_c12 )
| ( ( multiply @ sk_c6 @ sk_c11 )
= sk_c12 ) )
= $true ),
inference(copy,[status(thm)],[129]) ).
thf(137,plain,
( ( ( ( multiply @ sk_c1 @ sk_c2 )
= sk_c12 )
| ( ( inverse @ sk_c7 )
= sk_c12 ) )
= $true ),
inference(copy,[status(thm)],[128]) ).
thf(138,plain,
( ( ( ( multiply @ sk_c1 @ sk_c2 )
= sk_c12 )
| ( ( multiply @ sk_c7 @ sk_c11 )
= sk_c12 ) )
= $true ),
inference(copy,[status(thm)],[127]) ).
thf(139,plain,
( ( ( ( multiply @ sk_c1 @ sk_c2 )
= sk_c12 )
| ( ( multiply @ sk_c8 @ sk_c9 )
= sk_c11 ) )
= $true ),
inference(copy,[status(thm)],[126]) ).
thf(140,plain,
( ( ( ( multiply @ sk_c1 @ sk_c2 )
= sk_c12 )
| ( ( inverse @ sk_c8 )
= sk_c9 ) )
= $true ),
inference(copy,[status(thm)],[125]) ).
thf(141,plain,
( ( ( ( multiply @ sk_c1 @ sk_c2 )
= sk_c12 )
| ( ( multiply @ sk_c9 @ sk_c12 )
= sk_c11 ) )
= $true ),
inference(copy,[status(thm)],[124]) ).
thf(142,plain,
( ( ( ( multiply @ sk_c1 @ sk_c2 )
= sk_c12 )
| ( ( inverse @ sk_c10 )
= sk_c11 ) )
= $true ),
inference(copy,[status(thm)],[123]) ).
thf(143,plain,
( ( ( ( multiply @ sk_c1 @ sk_c2 )
= sk_c12 )
| ( ( multiply @ sk_c10 @ sk_c12 )
= sk_c11 ) )
= $true ),
inference(copy,[status(thm)],[122]) ).
thf(144,plain,
( ( ( ( inverse @ sk_c1 )
= sk_c2 )
| ( ( multiply @ sk_c5 @ sk_c6 )
= sk_c12 ) )
= $true ),
inference(copy,[status(thm)],[121]) ).
thf(145,plain,
( ( ( ( inverse @ sk_c1 )
= sk_c2 )
| ( ( inverse @ sk_c5 )
= sk_c6 ) )
= $true ),
inference(copy,[status(thm)],[120]) ).
thf(146,plain,
( ( ( ( inverse @ sk_c1 )
= sk_c2 )
| ( ( multiply @ sk_c6 @ sk_c11 )
= sk_c12 ) )
= $true ),
inference(copy,[status(thm)],[119]) ).
thf(147,plain,
( ( ( ( inverse @ sk_c1 )
= sk_c2 )
| ( ( inverse @ sk_c7 )
= sk_c12 ) )
= $true ),
inference(copy,[status(thm)],[118]) ).
thf(148,plain,
( ( ( ( inverse @ sk_c1 )
= sk_c2 )
| ( ( multiply @ sk_c7 @ sk_c11 )
= sk_c12 ) )
= $true ),
inference(copy,[status(thm)],[117]) ).
thf(149,plain,
( ( ( ( inverse @ sk_c1 )
= sk_c2 )
| ( ( multiply @ sk_c8 @ sk_c9 )
= sk_c11 ) )
= $true ),
inference(copy,[status(thm)],[116]) ).
thf(150,plain,
( ( ( ( inverse @ sk_c1 )
= sk_c2 )
| ( ( inverse @ sk_c8 )
= sk_c9 ) )
= $true ),
inference(copy,[status(thm)],[115]) ).
thf(151,plain,
( ( ( ( inverse @ sk_c1 )
= sk_c2 )
| ( ( multiply @ sk_c9 @ sk_c12 )
= sk_c11 ) )
= $true ),
inference(copy,[status(thm)],[114]) ).
thf(152,plain,
( ( ( ( inverse @ sk_c1 )
= sk_c2 )
| ( ( inverse @ sk_c10 )
= sk_c11 ) )
= $true ),
inference(copy,[status(thm)],[113]) ).
thf(153,plain,
( ( ( ( inverse @ sk_c1 )
= sk_c2 )
| ( ( multiply @ sk_c10 @ sk_c12 )
= sk_c11 ) )
= $true ),
inference(copy,[status(thm)],[112]) ).
thf(154,plain,
( ( ( ( multiply @ sk_c2 @ sk_c11 )
= sk_c12 )
| ( ( multiply @ sk_c5 @ sk_c6 )
= sk_c12 ) )
= $true ),
inference(copy,[status(thm)],[111]) ).
thf(155,plain,
( ( ( ( multiply @ sk_c2 @ sk_c11 )
= sk_c12 )
| ( ( inverse @ sk_c5 )
= sk_c6 ) )
= $true ),
inference(copy,[status(thm)],[110]) ).
thf(156,plain,
( ( ( ( multiply @ sk_c2 @ sk_c11 )
= sk_c12 )
| ( ( multiply @ sk_c6 @ sk_c11 )
= sk_c12 ) )
= $true ),
inference(copy,[status(thm)],[109]) ).
thf(157,plain,
( ( ( ( multiply @ sk_c2 @ sk_c11 )
= sk_c12 )
| ( ( inverse @ sk_c7 )
= sk_c12 ) )
= $true ),
inference(copy,[status(thm)],[108]) ).
thf(158,plain,
( ( ( ( multiply @ sk_c2 @ sk_c11 )
= sk_c12 )
| ( ( multiply @ sk_c7 @ sk_c11 )
= sk_c12 ) )
= $true ),
inference(copy,[status(thm)],[107]) ).
thf(159,plain,
( ( ( ( multiply @ sk_c2 @ sk_c11 )
= sk_c12 )
| ( ( multiply @ sk_c8 @ sk_c9 )
= sk_c11 ) )
= $true ),
inference(copy,[status(thm)],[106]) ).
thf(160,plain,
( ( ( ( multiply @ sk_c2 @ sk_c11 )
= sk_c12 )
| ( ( inverse @ sk_c8 )
= sk_c9 ) )
= $true ),
inference(copy,[status(thm)],[105]) ).
thf(161,plain,
( ( ( ( multiply @ sk_c2 @ sk_c11 )
= sk_c12 )
| ( ( multiply @ sk_c9 @ sk_c12 )
= sk_c11 ) )
= $true ),
inference(copy,[status(thm)],[104]) ).
thf(162,plain,
( ( ( ( multiply @ sk_c2 @ sk_c11 )
= sk_c12 )
| ( ( inverse @ sk_c10 )
= sk_c11 ) )
= $true ),
inference(copy,[status(thm)],[103]) ).
thf(163,plain,
( ( ( ( multiply @ sk_c2 @ sk_c11 )
= sk_c12 )
| ( ( multiply @ sk_c10 @ sk_c12 )
= sk_c11 ) )
= $true ),
inference(copy,[status(thm)],[102]) ).
thf(164,plain,
( ( ( ( multiply @ sk_c12 @ sk_c4 )
= sk_c11 )
| ( ( multiply @ sk_c5 @ sk_c6 )
= sk_c12 ) )
= $true ),
inference(copy,[status(thm)],[101]) ).
thf(165,plain,
( ( ( ( multiply @ sk_c12 @ sk_c4 )
= sk_c11 )
| ( ( inverse @ sk_c5 )
= sk_c6 ) )
= $true ),
inference(copy,[status(thm)],[100]) ).
thf(166,plain,
( ( ( ( multiply @ sk_c12 @ sk_c4 )
= sk_c11 )
| ( ( multiply @ sk_c6 @ sk_c11 )
= sk_c12 ) )
= $true ),
inference(copy,[status(thm)],[99]) ).
thf(167,plain,
( ( ( ( multiply @ sk_c12 @ sk_c4 )
= sk_c11 )
| ( ( inverse @ sk_c7 )
= sk_c12 ) )
= $true ),
inference(copy,[status(thm)],[98]) ).
thf(168,plain,
( ( ( ( multiply @ sk_c12 @ sk_c4 )
= sk_c11 )
| ( ( multiply @ sk_c7 @ sk_c11 )
= sk_c12 ) )
= $true ),
inference(copy,[status(thm)],[97]) ).
thf(169,plain,
( ( ( ( multiply @ sk_c12 @ sk_c4 )
= sk_c11 )
| ( ( multiply @ sk_c8 @ sk_c9 )
= sk_c11 ) )
= $true ),
inference(copy,[status(thm)],[96]) ).
thf(170,plain,
( ( ( ( multiply @ sk_c12 @ sk_c4 )
= sk_c11 )
| ( ( inverse @ sk_c8 )
= sk_c9 ) )
= $true ),
inference(copy,[status(thm)],[95]) ).
thf(171,plain,
( ( ( ( multiply @ sk_c12 @ sk_c4 )
= sk_c11 )
| ( ( multiply @ sk_c9 @ sk_c12 )
= sk_c11 ) )
= $true ),
inference(copy,[status(thm)],[94]) ).
thf(172,plain,
( ( ( ( multiply @ sk_c12 @ sk_c4 )
= sk_c11 )
| ( ( inverse @ sk_c10 )
= sk_c11 ) )
= $true ),
inference(copy,[status(thm)],[93]) ).
thf(173,plain,
( ( ( ( multiply @ sk_c12 @ sk_c4 )
= sk_c11 )
| ( ( multiply @ sk_c10 @ sk_c12 )
= sk_c11 ) )
= $true ),
inference(copy,[status(thm)],[92]) ).
thf(174,plain,
( ( ( ( multiply @ sk_c3 @ sk_c12 )
= sk_c4 )
| ( ( multiply @ sk_c5 @ sk_c6 )
= sk_c12 ) )
= $true ),
inference(copy,[status(thm)],[91]) ).
thf(175,plain,
( ( ( ( multiply @ sk_c3 @ sk_c12 )
= sk_c4 )
| ( ( inverse @ sk_c5 )
= sk_c6 ) )
= $true ),
inference(copy,[status(thm)],[90]) ).
thf(176,plain,
( ( ( ( multiply @ sk_c3 @ sk_c12 )
= sk_c4 )
| ( ( multiply @ sk_c6 @ sk_c11 )
= sk_c12 ) )
= $true ),
inference(copy,[status(thm)],[89]) ).
thf(177,plain,
( ( ( ( multiply @ sk_c3 @ sk_c12 )
= sk_c4 )
| ( ( inverse @ sk_c7 )
= sk_c12 ) )
= $true ),
inference(copy,[status(thm)],[88]) ).
thf(178,plain,
( ( ( ( multiply @ sk_c3 @ sk_c12 )
= sk_c4 )
| ( ( multiply @ sk_c7 @ sk_c11 )
= sk_c12 ) )
= $true ),
inference(copy,[status(thm)],[87]) ).
thf(179,plain,
( ( ( ( multiply @ sk_c3 @ sk_c12 )
= sk_c4 )
| ( ( multiply @ sk_c8 @ sk_c9 )
= sk_c11 ) )
= $true ),
inference(copy,[status(thm)],[86]) ).
thf(180,plain,
( ( ( ( multiply @ sk_c3 @ sk_c12 )
= sk_c4 )
| ( ( inverse @ sk_c8 )
= sk_c9 ) )
= $true ),
inference(copy,[status(thm)],[85]) ).
thf(181,plain,
( ( ( ( multiply @ sk_c3 @ sk_c12 )
= sk_c4 )
| ( ( multiply @ sk_c9 @ sk_c12 )
= sk_c11 ) )
= $true ),
inference(copy,[status(thm)],[84]) ).
thf(182,plain,
( ( ( ( multiply @ sk_c3 @ sk_c12 )
= sk_c4 )
| ( ( inverse @ sk_c10 )
= sk_c11 ) )
= $true ),
inference(copy,[status(thm)],[83]) ).
thf(183,plain,
( ( ( ( multiply @ sk_c3 @ sk_c12 )
= sk_c4 )
| ( ( multiply @ sk_c10 @ sk_c12 )
= sk_c11 ) )
= $true ),
inference(copy,[status(thm)],[82]) ).
thf(184,plain,
( ( ( ( inverse @ sk_c3 )
= sk_c12 )
| ( ( multiply @ sk_c5 @ sk_c6 )
= sk_c12 ) )
= $true ),
inference(copy,[status(thm)],[81]) ).
thf(185,plain,
( ( ( ( inverse @ sk_c3 )
= sk_c12 )
| ( ( inverse @ sk_c5 )
= sk_c6 ) )
= $true ),
inference(copy,[status(thm)],[80]) ).
thf(186,plain,
( ( ( ( inverse @ sk_c3 )
= sk_c12 )
| ( ( multiply @ sk_c6 @ sk_c11 )
= sk_c12 ) )
= $true ),
inference(copy,[status(thm)],[79]) ).
thf(187,plain,
( ( ( ( inverse @ sk_c3 )
= sk_c12 )
| ( ( inverse @ sk_c7 )
= sk_c12 ) )
= $true ),
inference(copy,[status(thm)],[78]) ).
thf(188,plain,
( ( ( ( inverse @ sk_c3 )
= sk_c12 )
| ( ( multiply @ sk_c7 @ sk_c11 )
= sk_c12 ) )
= $true ),
inference(copy,[status(thm)],[77]) ).
thf(189,plain,
( ( ( ( inverse @ sk_c3 )
= sk_c12 )
| ( ( multiply @ sk_c8 @ sk_c9 )
= sk_c11 ) )
= $true ),
inference(copy,[status(thm)],[76]) ).
thf(190,plain,
( ( ( ( inverse @ sk_c3 )
= sk_c12 )
| ( ( inverse @ sk_c8 )
= sk_c9 ) )
= $true ),
inference(copy,[status(thm)],[75]) ).
thf(191,plain,
( ( ( ( inverse @ sk_c3 )
= sk_c12 )
| ( ( multiply @ sk_c9 @ sk_c12 )
= sk_c11 ) )
= $true ),
inference(copy,[status(thm)],[74]) ).
thf(192,plain,
( ( ( ( inverse @ sk_c3 )
= sk_c12 )
| ( ( inverse @ sk_c10 )
= sk_c11 ) )
= $true ),
inference(copy,[status(thm)],[73]) ).
thf(193,plain,
( ( ( ( inverse @ sk_c3 )
= sk_c12 )
| ( ( multiply @ sk_c10 @ sk_c12 )
= sk_c11 ) )
= $true ),
inference(copy,[status(thm)],[72]) ).
thf(194,plain,
( ( ! [X5: $i,X6: $i,X7: $i,X8: $i,X2: $i,X1: $i,X3: $i,X9: $i] :
( ( ( multiply @ X5 @ X6 )
!= sk_c12 )
| ( ( inverse @ X5 )
!= X6 )
| ( ( multiply @ X6 @ sk_c11 )
!= sk_c12 )
| ( ( multiply @ sk_c12 @ X7 )
!= sk_c11 )
| ( ( multiply @ X8 @ sk_c12 )
!= X7 )
| ( ( inverse @ X8 )
!= sk_c12 )
| ( ( multiply @ X2 @ X1 )
!= sk_c12 )
| ( ( inverse @ X2 )
!= X1 )
| ( ( multiply @ X1 @ sk_c11 )
!= sk_c12 )
| ( ( inverse @ X3 )
!= sk_c12 )
| ( ( multiply @ X3 @ sk_c11 )
!= sk_c12 )
| ! [X4: $i] :
( ( ( multiply @ X9 @ X4 )
!= sk_c11 )
| ( ( inverse @ X9 )
!= X4 )
| ( ( multiply @ X4 @ sk_c12 )
!= sk_c11 )
| ! [X10: $i] :
( ( ( inverse @ X10 )
!= sk_c11 )
| ( ( multiply @ X10 @ sk_c12 )
!= sk_c11 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[133]) ).
thf(195,plain,
( ( ! [X: $i] :
( ( multiply @ identity @ X )
= X ) )
= $true ),
inference(copy,[status(thm)],[70]) ).
thf(196,plain,
( ( ! [X: $i] :
( ( multiply @ ( inverse @ X ) @ X )
= identity ) )
= $true ),
inference(copy,[status(thm)],[69]) ).
thf(197,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( multiply @ ( multiply @ X @ Y ) @ Z )
= ( multiply @ X @ ( multiply @ Y @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[68]) ).
thf(198,plain,
( ( ~ $false )
= $true ),
inference(copy,[status(thm)],[132]) ).
thf(199,plain,
( ( ( ( multiply @ sk_c1 @ sk_c2 )
= sk_c12 )
= $true )
| ( ( ( multiply @ sk_c5 @ sk_c6 )
= sk_c12 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[134]) ).
thf(200,plain,
( ( ( ( multiply @ sk_c1 @ sk_c2 )
= sk_c12 )
= $true )
| ( ( ( inverse @ sk_c5 )
= sk_c6 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[135]) ).
thf(201,plain,
( ( ( ( multiply @ sk_c1 @ sk_c2 )
= sk_c12 )
= $true )
| ( ( ( multiply @ sk_c6 @ sk_c11 )
= sk_c12 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[136]) ).
thf(202,plain,
( ( ( ( multiply @ sk_c1 @ sk_c2 )
= sk_c12 )
= $true )
| ( ( ( inverse @ sk_c7 )
= sk_c12 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[137]) ).
thf(203,plain,
( ( ( ( multiply @ sk_c1 @ sk_c2 )
= sk_c12 )
= $true )
| ( ( ( multiply @ sk_c7 @ sk_c11 )
= sk_c12 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[138]) ).
thf(204,plain,
( ( ( ( multiply @ sk_c1 @ sk_c2 )
= sk_c12 )
= $true )
| ( ( ( multiply @ sk_c8 @ sk_c9 )
= sk_c11 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[139]) ).
thf(205,plain,
( ( ( ( multiply @ sk_c1 @ sk_c2 )
= sk_c12 )
= $true )
| ( ( ( inverse @ sk_c8 )
= sk_c9 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[140]) ).
thf(206,plain,
( ( ( ( multiply @ sk_c1 @ sk_c2 )
= sk_c12 )
= $true )
| ( ( ( multiply @ sk_c9 @ sk_c12 )
= sk_c11 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[141]) ).
thf(207,plain,
( ( ( ( multiply @ sk_c1 @ sk_c2 )
= sk_c12 )
= $true )
| ( ( ( inverse @ sk_c10 )
= sk_c11 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[142]) ).
thf(208,plain,
( ( ( ( multiply @ sk_c1 @ sk_c2 )
= sk_c12 )
= $true )
| ( ( ( multiply @ sk_c10 @ sk_c12 )
= sk_c11 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[143]) ).
thf(209,plain,
( ( ( ( inverse @ sk_c1 )
= sk_c2 )
= $true )
| ( ( ( multiply @ sk_c5 @ sk_c6 )
= sk_c12 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[144]) ).
thf(210,plain,
( ( ( ( inverse @ sk_c1 )
= sk_c2 )
= $true )
| ( ( ( inverse @ sk_c5 )
= sk_c6 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[145]) ).
thf(211,plain,
( ( ( ( inverse @ sk_c1 )
= sk_c2 )
= $true )
| ( ( ( multiply @ sk_c6 @ sk_c11 )
= sk_c12 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[146]) ).
thf(212,plain,
( ( ( ( inverse @ sk_c1 )
= sk_c2 )
= $true )
| ( ( ( inverse @ sk_c7 )
= sk_c12 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[147]) ).
thf(213,plain,
( ( ( ( inverse @ sk_c1 )
= sk_c2 )
= $true )
| ( ( ( multiply @ sk_c7 @ sk_c11 )
= sk_c12 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[148]) ).
thf(214,plain,
( ( ( ( inverse @ sk_c1 )
= sk_c2 )
= $true )
| ( ( ( multiply @ sk_c8 @ sk_c9 )
= sk_c11 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[149]) ).
thf(215,plain,
( ( ( ( inverse @ sk_c1 )
= sk_c2 )
= $true )
| ( ( ( inverse @ sk_c8 )
= sk_c9 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[150]) ).
thf(216,plain,
( ( ( ( inverse @ sk_c1 )
= sk_c2 )
= $true )
| ( ( ( multiply @ sk_c9 @ sk_c12 )
= sk_c11 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[151]) ).
thf(217,plain,
( ( ( ( inverse @ sk_c1 )
= sk_c2 )
= $true )
| ( ( ( inverse @ sk_c10 )
= sk_c11 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[152]) ).
thf(218,plain,
( ( ( ( inverse @ sk_c1 )
= sk_c2 )
= $true )
| ( ( ( multiply @ sk_c10 @ sk_c12 )
= sk_c11 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[153]) ).
thf(219,plain,
( ( ( ( multiply @ sk_c2 @ sk_c11 )
= sk_c12 )
= $true )
| ( ( ( multiply @ sk_c5 @ sk_c6 )
= sk_c12 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[154]) ).
thf(220,plain,
( ( ( ( multiply @ sk_c2 @ sk_c11 )
= sk_c12 )
= $true )
| ( ( ( inverse @ sk_c5 )
= sk_c6 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[155]) ).
thf(221,plain,
( ( ( ( multiply @ sk_c2 @ sk_c11 )
= sk_c12 )
= $true )
| ( ( ( multiply @ sk_c6 @ sk_c11 )
= sk_c12 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[156]) ).
thf(222,plain,
( ( ( ( multiply @ sk_c2 @ sk_c11 )
= sk_c12 )
= $true )
| ( ( ( inverse @ sk_c7 )
= sk_c12 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[157]) ).
thf(223,plain,
( ( ( ( multiply @ sk_c2 @ sk_c11 )
= sk_c12 )
= $true )
| ( ( ( multiply @ sk_c7 @ sk_c11 )
= sk_c12 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[158]) ).
thf(224,plain,
( ( ( ( multiply @ sk_c2 @ sk_c11 )
= sk_c12 )
= $true )
| ( ( ( multiply @ sk_c8 @ sk_c9 )
= sk_c11 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[159]) ).
thf(225,plain,
( ( ( ( multiply @ sk_c2 @ sk_c11 )
= sk_c12 )
= $true )
| ( ( ( inverse @ sk_c8 )
= sk_c9 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[160]) ).
thf(226,plain,
( ( ( ( multiply @ sk_c2 @ sk_c11 )
= sk_c12 )
= $true )
| ( ( ( multiply @ sk_c9 @ sk_c12 )
= sk_c11 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[161]) ).
thf(227,plain,
( ( ( ( multiply @ sk_c2 @ sk_c11 )
= sk_c12 )
= $true )
| ( ( ( inverse @ sk_c10 )
= sk_c11 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[162]) ).
thf(228,plain,
( ( ( ( multiply @ sk_c2 @ sk_c11 )
= sk_c12 )
= $true )
| ( ( ( multiply @ sk_c10 @ sk_c12 )
= sk_c11 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[163]) ).
thf(229,plain,
( ( ( ( multiply @ sk_c12 @ sk_c4 )
= sk_c11 )
= $true )
| ( ( ( multiply @ sk_c5 @ sk_c6 )
= sk_c12 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[164]) ).
thf(230,plain,
( ( ( ( multiply @ sk_c12 @ sk_c4 )
= sk_c11 )
= $true )
| ( ( ( inverse @ sk_c5 )
= sk_c6 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[165]) ).
thf(231,plain,
( ( ( ( multiply @ sk_c12 @ sk_c4 )
= sk_c11 )
= $true )
| ( ( ( multiply @ sk_c6 @ sk_c11 )
= sk_c12 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[166]) ).
thf(232,plain,
( ( ( ( multiply @ sk_c12 @ sk_c4 )
= sk_c11 )
= $true )
| ( ( ( inverse @ sk_c7 )
= sk_c12 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[167]) ).
thf(233,plain,
( ( ( ( multiply @ sk_c12 @ sk_c4 )
= sk_c11 )
= $true )
| ( ( ( multiply @ sk_c7 @ sk_c11 )
= sk_c12 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[168]) ).
thf(234,plain,
( ( ( ( multiply @ sk_c12 @ sk_c4 )
= sk_c11 )
= $true )
| ( ( ( multiply @ sk_c8 @ sk_c9 )
= sk_c11 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[169]) ).
thf(235,plain,
( ( ( ( multiply @ sk_c12 @ sk_c4 )
= sk_c11 )
= $true )
| ( ( ( inverse @ sk_c8 )
= sk_c9 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[170]) ).
thf(236,plain,
( ( ( ( multiply @ sk_c12 @ sk_c4 )
= sk_c11 )
= $true )
| ( ( ( multiply @ sk_c9 @ sk_c12 )
= sk_c11 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[171]) ).
thf(237,plain,
( ( ( ( multiply @ sk_c12 @ sk_c4 )
= sk_c11 )
= $true )
| ( ( ( inverse @ sk_c10 )
= sk_c11 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[172]) ).
thf(238,plain,
( ( ( ( multiply @ sk_c12 @ sk_c4 )
= sk_c11 )
= $true )
| ( ( ( multiply @ sk_c10 @ sk_c12 )
= sk_c11 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[173]) ).
thf(239,plain,
( ( ( ( multiply @ sk_c3 @ sk_c12 )
= sk_c4 )
= $true )
| ( ( ( multiply @ sk_c5 @ sk_c6 )
= sk_c12 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[174]) ).
thf(240,plain,
( ( ( ( multiply @ sk_c3 @ sk_c12 )
= sk_c4 )
= $true )
| ( ( ( inverse @ sk_c5 )
= sk_c6 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[175]) ).
thf(241,plain,
( ( ( ( multiply @ sk_c3 @ sk_c12 )
= sk_c4 )
= $true )
| ( ( ( multiply @ sk_c6 @ sk_c11 )
= sk_c12 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[176]) ).
thf(242,plain,
( ( ( ( multiply @ sk_c3 @ sk_c12 )
= sk_c4 )
= $true )
| ( ( ( inverse @ sk_c7 )
= sk_c12 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[177]) ).
thf(243,plain,
( ( ( ( multiply @ sk_c3 @ sk_c12 )
= sk_c4 )
= $true )
| ( ( ( multiply @ sk_c7 @ sk_c11 )
= sk_c12 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[178]) ).
thf(244,plain,
( ( ( ( multiply @ sk_c3 @ sk_c12 )
= sk_c4 )
= $true )
| ( ( ( multiply @ sk_c8 @ sk_c9 )
= sk_c11 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[179]) ).
thf(245,plain,
( ( ( ( multiply @ sk_c3 @ sk_c12 )
= sk_c4 )
= $true )
| ( ( ( inverse @ sk_c8 )
= sk_c9 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[180]) ).
thf(246,plain,
( ( ( ( multiply @ sk_c3 @ sk_c12 )
= sk_c4 )
= $true )
| ( ( ( multiply @ sk_c9 @ sk_c12 )
= sk_c11 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[181]) ).
thf(247,plain,
( ( ( ( multiply @ sk_c3 @ sk_c12 )
= sk_c4 )
= $true )
| ( ( ( inverse @ sk_c10 )
= sk_c11 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[182]) ).
thf(248,plain,
( ( ( ( multiply @ sk_c3 @ sk_c12 )
= sk_c4 )
= $true )
| ( ( ( multiply @ sk_c10 @ sk_c12 )
= sk_c11 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[183]) ).
thf(249,plain,
( ( ( ( inverse @ sk_c3 )
= sk_c12 )
= $true )
| ( ( ( multiply @ sk_c5 @ sk_c6 )
= sk_c12 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[184]) ).
thf(250,plain,
( ( ( ( inverse @ sk_c3 )
= sk_c12 )
= $true )
| ( ( ( inverse @ sk_c5 )
= sk_c6 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[185]) ).
thf(251,plain,
( ( ( ( inverse @ sk_c3 )
= sk_c12 )
= $true )
| ( ( ( multiply @ sk_c6 @ sk_c11 )
= sk_c12 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[186]) ).
thf(252,plain,
( ( ( ( inverse @ sk_c3 )
= sk_c12 )
= $true )
| ( ( ( inverse @ sk_c7 )
= sk_c12 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[187]) ).
thf(253,plain,
( ( ( ( inverse @ sk_c3 )
= sk_c12 )
= $true )
| ( ( ( multiply @ sk_c7 @ sk_c11 )
= sk_c12 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[188]) ).
thf(254,plain,
( ( ( ( inverse @ sk_c3 )
= sk_c12 )
= $true )
| ( ( ( multiply @ sk_c8 @ sk_c9 )
= sk_c11 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[189]) ).
thf(255,plain,
( ( ( ( inverse @ sk_c3 )
= sk_c12 )
= $true )
| ( ( ( inverse @ sk_c8 )
= sk_c9 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[190]) ).
thf(256,plain,
( ( ( ( inverse @ sk_c3 )
= sk_c12 )
= $true )
| ( ( ( multiply @ sk_c9 @ sk_c12 )
= sk_c11 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[191]) ).
thf(257,plain,
( ( ( ( inverse @ sk_c3 )
= sk_c12 )
= $true )
| ( ( ( inverse @ sk_c10 )
= sk_c11 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[192]) ).
thf(258,plain,
( ( ( ( inverse @ sk_c3 )
= sk_c12 )
= $true )
| ( ( ( multiply @ sk_c10 @ sk_c12 )
= sk_c11 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[193]) ).
thf(259,plain,
! [SV1: $i] :
( ( ! [SY15: $i,SY16: $i,SY17: $i,SY18: $i,SY19: $i,SY20: $i,SY21: $i] :
( ( ( multiply @ SV1 @ SY15 )
!= sk_c12 )
| ( ( inverse @ SV1 )
!= SY15 )
| ( ( multiply @ SY15 @ sk_c11 )
!= sk_c12 )
| ( ( multiply @ sk_c12 @ SY16 )
!= sk_c11 )
| ( ( multiply @ SY17 @ sk_c12 )
!= SY16 )
| ( ( inverse @ SY17 )
!= sk_c12 )
| ( ( multiply @ SY18 @ SY19 )
!= sk_c12 )
| ( ( inverse @ SY18 )
!= SY19 )
| ( ( multiply @ SY19 @ sk_c11 )
!= sk_c12 )
| ( ( inverse @ SY20 )
!= sk_c12 )
| ( ( multiply @ SY20 @ sk_c11 )
!= sk_c12 )
| ! [X4: $i] :
( ( ( multiply @ SY21 @ X4 )
!= sk_c11 )
| ( ( inverse @ SY21 )
!= X4 )
| ( ( multiply @ X4 @ sk_c12 )
!= sk_c11 )
| ! [X10: $i] :
( ( ( inverse @ X10 )
!= sk_c11 )
| ( ( multiply @ X10 @ sk_c12 )
!= sk_c11 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[194]) ).
thf(260,plain,
! [SV2: $i] :
( ( ( multiply @ identity @ SV2 )
= SV2 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[195]) ).
thf(261,plain,
! [SV3: $i] :
( ( ( multiply @ ( inverse @ SV3 ) @ SV3 )
= identity )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[196]) ).
thf(262,plain,
! [SV4: $i] :
( ( ! [SY24: $i,SY25: $i] :
( ( multiply @ ( multiply @ SV4 @ SY24 ) @ SY25 )
= ( multiply @ SV4 @ ( multiply @ SY24 @ SY25 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[197]) ).
thf(263,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[198]) ).
thf(264,plain,
! [SV5: $i,SV1: $i] :
( ( ! [SY26: $i,SY27: $i,SY28: $i,SY29: $i,SY30: $i,SY31: $i] :
( ( ( multiply @ SV1 @ SV5 )
!= sk_c12 )
| ( ( inverse @ SV1 )
!= SV5 )
| ( ( multiply @ SV5 @ sk_c11 )
!= sk_c12 )
| ( ( multiply @ sk_c12 @ SY26 )
!= sk_c11 )
| ( ( multiply @ SY27 @ sk_c12 )
!= SY26 )
| ( ( inverse @ SY27 )
!= sk_c12 )
| ( ( multiply @ SY28 @ SY29 )
!= sk_c12 )
| ( ( inverse @ SY28 )
!= SY29 )
| ( ( multiply @ SY29 @ sk_c11 )
!= sk_c12 )
| ( ( inverse @ SY30 )
!= sk_c12 )
| ( ( multiply @ SY30 @ sk_c11 )
!= sk_c12 )
| ! [X4: $i] :
( ( ( multiply @ SY31 @ X4 )
!= sk_c11 )
| ( ( inverse @ SY31 )
!= X4 )
| ( ( multiply @ X4 @ sk_c12 )
!= sk_c11 )
| ! [X10: $i] :
( ( ( inverse @ X10 )
!= sk_c11 )
| ( ( multiply @ X10 @ sk_c12 )
!= sk_c11 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[259]) ).
thf(265,plain,
! [SV6: $i,SV4: $i] :
( ( ! [SY34: $i] :
( ( multiply @ ( multiply @ SV4 @ SV6 ) @ SY34 )
= ( multiply @ SV4 @ ( multiply @ SV6 @ SY34 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[262]) ).
thf(266,plain,
! [SV7: $i,SV5: $i,SV1: $i] :
( ( ! [SY35: $i,SY36: $i,SY37: $i,SY38: $i,SY39: $i] :
( ( ( multiply @ SV1 @ SV5 )
!= sk_c12 )
| ( ( inverse @ SV1 )
!= SV5 )
| ( ( multiply @ SV5 @ sk_c11 )
!= sk_c12 )
| ( ( multiply @ sk_c12 @ SV7 )
!= sk_c11 )
| ( ( multiply @ SY35 @ sk_c12 )
!= SV7 )
| ( ( inverse @ SY35 )
!= sk_c12 )
| ( ( multiply @ SY36 @ SY37 )
!= sk_c12 )
| ( ( inverse @ SY36 )
!= SY37 )
| ( ( multiply @ SY37 @ sk_c11 )
!= sk_c12 )
| ( ( inverse @ SY38 )
!= sk_c12 )
| ( ( multiply @ SY38 @ sk_c11 )
!= sk_c12 )
| ! [X4: $i] :
( ( ( multiply @ SY39 @ X4 )
!= sk_c11 )
| ( ( inverse @ SY39 )
!= X4 )
| ( ( multiply @ X4 @ sk_c12 )
!= sk_c11 )
| ! [X10: $i] :
( ( ( inverse @ X10 )
!= sk_c11 )
| ( ( multiply @ X10 @ sk_c12 )
!= sk_c11 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[264]) ).
thf(267,plain,
! [SV8: $i,SV6: $i,SV4: $i] :
( ( ( multiply @ ( multiply @ SV4 @ SV6 ) @ SV8 )
= ( multiply @ SV4 @ ( multiply @ SV6 @ SV8 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[265]) ).
thf(268,plain,
! [SV9: $i,SV7: $i,SV5: $i,SV1: $i] :
( ( ! [SY42: $i,SY43: $i,SY44: $i,SY45: $i] :
( ( ( multiply @ SV1 @ SV5 )
!= sk_c12 )
| ( ( inverse @ SV1 )
!= SV5 )
| ( ( multiply @ SV5 @ sk_c11 )
!= sk_c12 )
| ( ( multiply @ sk_c12 @ SV7 )
!= sk_c11 )
| ( ( multiply @ SV9 @ sk_c12 )
!= SV7 )
| ( ( inverse @ SV9 )
!= sk_c12 )
| ( ( multiply @ SY42 @ SY43 )
!= sk_c12 )
| ( ( inverse @ SY42 )
!= SY43 )
| ( ( multiply @ SY43 @ sk_c11 )
!= sk_c12 )
| ( ( inverse @ SY44 )
!= sk_c12 )
| ( ( multiply @ SY44 @ sk_c11 )
!= sk_c12 )
| ! [X4: $i] :
( ( ( multiply @ SY45 @ X4 )
!= sk_c11 )
| ( ( inverse @ SY45 )
!= X4 )
| ( ( multiply @ X4 @ sk_c12 )
!= sk_c11 )
| ! [X10: $i] :
( ( ( inverse @ X10 )
!= sk_c11 )
| ( ( multiply @ X10 @ sk_c12 )
!= sk_c11 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[266]) ).
thf(269,plain,
! [SV10: $i,SV9: $i,SV7: $i,SV5: $i,SV1: $i] :
( ( ! [SY48: $i,SY49: $i,SY50: $i] :
( ( ( multiply @ SV1 @ SV5 )
!= sk_c12 )
| ( ( inverse @ SV1 )
!= SV5 )
| ( ( multiply @ SV5 @ sk_c11 )
!= sk_c12 )
| ( ( multiply @ sk_c12 @ SV7 )
!= sk_c11 )
| ( ( multiply @ SV9 @ sk_c12 )
!= SV7 )
| ( ( inverse @ SV9 )
!= sk_c12 )
| ( ( multiply @ SV10 @ SY48 )
!= sk_c12 )
| ( ( inverse @ SV10 )
!= SY48 )
| ( ( multiply @ SY48 @ sk_c11 )
!= sk_c12 )
| ( ( inverse @ SY49 )
!= sk_c12 )
| ( ( multiply @ SY49 @ sk_c11 )
!= sk_c12 )
| ! [X4: $i] :
( ( ( multiply @ SY50 @ X4 )
!= sk_c11 )
| ( ( inverse @ SY50 )
!= X4 )
| ( ( multiply @ X4 @ sk_c12 )
!= sk_c11 )
| ! [X10: $i] :
( ( ( inverse @ X10 )
!= sk_c11 )
| ( ( multiply @ X10 @ sk_c12 )
!= sk_c11 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[268]) ).
thf(270,plain,
! [SV11: $i,SV10: $i,SV9: $i,SV7: $i,SV5: $i,SV1: $i] :
( ( ! [SY53: $i,SY54: $i] :
( ( ( multiply @ SV1 @ SV5 )
!= sk_c12 )
| ( ( inverse @ SV1 )
!= SV5 )
| ( ( multiply @ SV5 @ sk_c11 )
!= sk_c12 )
| ( ( multiply @ sk_c12 @ SV7 )
!= sk_c11 )
| ( ( multiply @ SV9 @ sk_c12 )
!= SV7 )
| ( ( inverse @ SV9 )
!= sk_c12 )
| ( ( multiply @ SV10 @ SV11 )
!= sk_c12 )
| ( ( inverse @ SV10 )
!= SV11 )
| ( ( multiply @ SV11 @ sk_c11 )
!= sk_c12 )
| ( ( inverse @ SY53 )
!= sk_c12 )
| ( ( multiply @ SY53 @ sk_c11 )
!= sk_c12 )
| ! [X4: $i] :
( ( ( multiply @ SY54 @ X4 )
!= sk_c11 )
| ( ( inverse @ SY54 )
!= X4 )
| ( ( multiply @ X4 @ sk_c12 )
!= sk_c11 )
| ! [X10: $i] :
( ( ( inverse @ X10 )
!= sk_c11 )
| ( ( multiply @ X10 @ sk_c12 )
!= sk_c11 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[269]) ).
thf(271,plain,
! [SV12: $i,SV11: $i,SV10: $i,SV9: $i,SV7: $i,SV5: $i,SV1: $i] :
( ( ! [SY57: $i] :
( ( ( multiply @ SV1 @ SV5 )
!= sk_c12 )
| ( ( inverse @ SV1 )
!= SV5 )
| ( ( multiply @ SV5 @ sk_c11 )
!= sk_c12 )
| ( ( multiply @ sk_c12 @ SV7 )
!= sk_c11 )
| ( ( multiply @ SV9 @ sk_c12 )
!= SV7 )
| ( ( inverse @ SV9 )
!= sk_c12 )
| ( ( multiply @ SV10 @ SV11 )
!= sk_c12 )
| ( ( inverse @ SV10 )
!= SV11 )
| ( ( multiply @ SV11 @ sk_c11 )
!= sk_c12 )
| ( ( inverse @ SV12 )
!= sk_c12 )
| ( ( multiply @ SV12 @ sk_c11 )
!= sk_c12 )
| ! [X4: $i] :
( ( ( multiply @ SY57 @ X4 )
!= sk_c11 )
| ( ( inverse @ SY57 )
!= X4 )
| ( ( multiply @ X4 @ sk_c12 )
!= sk_c11 )
| ! [X10: $i] :
( ( ( inverse @ X10 )
!= sk_c11 )
| ( ( multiply @ X10 @ sk_c12 )
!= sk_c11 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[270]) ).
thf(272,plain,
! [SV13: $i,SV12: $i,SV11: $i,SV10: $i,SV9: $i,SV7: $i,SV5: $i,SV1: $i] :
( ( ( ( multiply @ SV1 @ SV5 )
!= sk_c12 )
| ( ( inverse @ SV1 )
!= SV5 )
| ( ( multiply @ SV5 @ sk_c11 )
!= sk_c12 )
| ( ( multiply @ sk_c12 @ SV7 )
!= sk_c11 )
| ( ( multiply @ SV9 @ sk_c12 )
!= SV7 )
| ( ( inverse @ SV9 )
!= sk_c12 )
| ( ( multiply @ SV10 @ SV11 )
!= sk_c12 )
| ( ( inverse @ SV10 )
!= SV11 )
| ( ( multiply @ SV11 @ sk_c11 )
!= sk_c12 )
| ( ( inverse @ SV12 )
!= sk_c12 )
| ( ( multiply @ SV12 @ sk_c11 )
!= sk_c12 )
| ! [SY60: $i] :
( ( ( multiply @ SV13 @ SY60 )
!= sk_c11 )
| ( ( inverse @ SV13 )
!= SY60 )
| ( ( multiply @ SY60 @ sk_c12 )
!= sk_c11 )
| ! [X10: $i] :
( ( ( inverse @ X10 )
!= sk_c11 )
| ( ( multiply @ X10 @ sk_c12 )
!= sk_c11 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[271]) ).
thf(273,plain,
! [SV13: $i,SV12: $i,SV11: $i,SV10: $i,SV9: $i,SV7: $i,SV5: $i,SV1: $i] :
( ( ( ( ( multiply @ SV1 @ SV5 )
!= sk_c12 ) )
= $true )
| ( ( ( ( inverse @ SV1 )
!= SV5 )
| ( ( multiply @ SV5 @ sk_c11 )
!= sk_c12 )
| ( ( multiply @ sk_c12 @ SV7 )
!= sk_c11 )
| ( ( multiply @ SV9 @ sk_c12 )
!= SV7 )
| ( ( inverse @ SV9 )
!= sk_c12 )
| ( ( multiply @ SV10 @ SV11 )
!= sk_c12 )
| ( ( inverse @ SV10 )
!= SV11 )
| ( ( multiply @ SV11 @ sk_c11 )
!= sk_c12 )
| ( ( inverse @ SV12 )
!= sk_c12 )
| ( ( multiply @ SV12 @ sk_c11 )
!= sk_c12 )
| ! [SY60: $i] :
( ( ( multiply @ SV13 @ SY60 )
!= sk_c11 )
| ( ( inverse @ SV13 )
!= SY60 )
| ( ( multiply @ SY60 @ sk_c12 )
!= sk_c11 )
| ! [X10: $i] :
( ( ( inverse @ X10 )
!= sk_c11 )
| ( ( multiply @ X10 @ sk_c12 )
!= sk_c11 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[272]) ).
thf(274,plain,
! [SV13: $i,SV12: $i,SV11: $i,SV10: $i,SV9: $i,SV7: $i,SV5: $i,SV1: $i] :
( ( ( ( multiply @ SV1 @ SV5 )
= sk_c12 )
= $false )
| ( ( ( ( inverse @ SV1 )
!= SV5 )
| ( ( multiply @ SV5 @ sk_c11 )
!= sk_c12 )
| ( ( multiply @ sk_c12 @ SV7 )
!= sk_c11 )
| ( ( multiply @ SV9 @ sk_c12 )
!= SV7 )
| ( ( inverse @ SV9 )
!= sk_c12 )
| ( ( multiply @ SV10 @ SV11 )
!= sk_c12 )
| ( ( inverse @ SV10 )
!= SV11 )
| ( ( multiply @ SV11 @ sk_c11 )
!= sk_c12 )
| ( ( inverse @ SV12 )
!= sk_c12 )
| ( ( multiply @ SV12 @ sk_c11 )
!= sk_c12 )
| ! [SY60: $i] :
( ( ( multiply @ SV13 @ SY60 )
!= sk_c11 )
| ( ( inverse @ SV13 )
!= SY60 )
| ( ( multiply @ SY60 @ sk_c12 )
!= sk_c11 )
| ! [X10: $i] :
( ( ( inverse @ X10 )
!= sk_c11 )
| ( ( multiply @ X10 @ sk_c12 )
!= sk_c11 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[273]) ).
thf(275,plain,
! [SV13: $i,SV12: $i,SV11: $i,SV10: $i,SV9: $i,SV7: $i,SV5: $i,SV1: $i] :
( ( ( ( ( inverse @ SV1 )
!= SV5 ) )
= $true )
| ( ( ( ( multiply @ SV5 @ sk_c11 )
!= sk_c12 )
| ( ( multiply @ sk_c12 @ SV7 )
!= sk_c11 )
| ( ( multiply @ SV9 @ sk_c12 )
!= SV7 )
| ( ( inverse @ SV9 )
!= sk_c12 )
| ( ( multiply @ SV10 @ SV11 )
!= sk_c12 )
| ( ( inverse @ SV10 )
!= SV11 )
| ( ( multiply @ SV11 @ sk_c11 )
!= sk_c12 )
| ( ( inverse @ SV12 )
!= sk_c12 )
| ( ( multiply @ SV12 @ sk_c11 )
!= sk_c12 )
| ! [SY60: $i] :
( ( ( multiply @ SV13 @ SY60 )
!= sk_c11 )
| ( ( inverse @ SV13 )
!= SY60 )
| ( ( multiply @ SY60 @ sk_c12 )
!= sk_c11 )
| ! [X10: $i] :
( ( ( inverse @ X10 )
!= sk_c11 )
| ( ( multiply @ X10 @ sk_c12 )
!= sk_c11 ) ) ) )
= $true )
| ( ( ( multiply @ SV1 @ SV5 )
= sk_c12 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[274]) ).
thf(276,plain,
! [SV13: $i,SV12: $i,SV11: $i,SV10: $i,SV9: $i,SV7: $i,SV5: $i,SV1: $i] :
( ( ( ( inverse @ SV1 )
= SV5 )
= $false )
| ( ( ( ( multiply @ SV5 @ sk_c11 )
!= sk_c12 )
| ( ( multiply @ sk_c12 @ SV7 )
!= sk_c11 )
| ( ( multiply @ SV9 @ sk_c12 )
!= SV7 )
| ( ( inverse @ SV9 )
!= sk_c12 )
| ( ( multiply @ SV10 @ SV11 )
!= sk_c12 )
| ( ( inverse @ SV10 )
!= SV11 )
| ( ( multiply @ SV11 @ sk_c11 )
!= sk_c12 )
| ( ( inverse @ SV12 )
!= sk_c12 )
| ( ( multiply @ SV12 @ sk_c11 )
!= sk_c12 )
| ! [SY60: $i] :
( ( ( multiply @ SV13 @ SY60 )
!= sk_c11 )
| ( ( inverse @ SV13 )
!= SY60 )
| ( ( multiply @ SY60 @ sk_c12 )
!= sk_c11 )
| ! [X10: $i] :
( ( ( inverse @ X10 )
!= sk_c11 )
| ( ( multiply @ X10 @ sk_c12 )
!= sk_c11 ) ) ) )
= $true )
| ( ( ( multiply @ SV1 @ SV5 )
= sk_c12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[275]) ).
thf(277,plain,
! [SV1: $i,SV13: $i,SV12: $i,SV11: $i,SV10: $i,SV9: $i,SV7: $i,SV5: $i] :
( ( ( ( ( multiply @ SV5 @ sk_c11 )
!= sk_c12 ) )
= $true )
| ( ( ( ( multiply @ sk_c12 @ SV7 )
!= sk_c11 )
| ( ( multiply @ SV9 @ sk_c12 )
!= SV7 )
| ( ( inverse @ SV9 )
!= sk_c12 )
| ( ( multiply @ SV10 @ SV11 )
!= sk_c12 )
| ( ( inverse @ SV10 )
!= SV11 )
| ( ( multiply @ SV11 @ sk_c11 )
!= sk_c12 )
| ( ( inverse @ SV12 )
!= sk_c12 )
| ( ( multiply @ SV12 @ sk_c11 )
!= sk_c12 )
| ! [SY60: $i] :
( ( ( multiply @ SV13 @ SY60 )
!= sk_c11 )
| ( ( inverse @ SV13 )
!= SY60 )
| ( ( multiply @ SY60 @ sk_c12 )
!= sk_c11 )
| ! [X10: $i] :
( ( ( inverse @ X10 )
!= sk_c11 )
| ( ( multiply @ X10 @ sk_c12 )
!= sk_c11 ) ) ) )
= $true )
| ( ( ( inverse @ SV1 )
= SV5 )
= $false )
| ( ( ( multiply @ SV1 @ SV5 )
= sk_c12 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[276]) ).
thf(278,plain,
! [SV1: $i,SV13: $i,SV12: $i,SV11: $i,SV10: $i,SV9: $i,SV7: $i,SV5: $i] :
( ( ( ( multiply @ SV5 @ sk_c11 )
= sk_c12 )
= $false )
| ( ( ( ( multiply @ sk_c12 @ SV7 )
!= sk_c11 )
| ( ( multiply @ SV9 @ sk_c12 )
!= SV7 )
| ( ( inverse @ SV9 )
!= sk_c12 )
| ( ( multiply @ SV10 @ SV11 )
!= sk_c12 )
| ( ( inverse @ SV10 )
!= SV11 )
| ( ( multiply @ SV11 @ sk_c11 )
!= sk_c12 )
| ( ( inverse @ SV12 )
!= sk_c12 )
| ( ( multiply @ SV12 @ sk_c11 )
!= sk_c12 )
| ! [SY60: $i] :
( ( ( multiply @ SV13 @ SY60 )
!= sk_c11 )
| ( ( inverse @ SV13 )
!= SY60 )
| ( ( multiply @ SY60 @ sk_c12 )
!= sk_c11 )
| ! [X10: $i] :
( ( ( inverse @ X10 )
!= sk_c11 )
| ( ( multiply @ X10 @ sk_c12 )
!= sk_c11 ) ) ) )
= $true )
| ( ( ( inverse @ SV1 )
= SV5 )
= $false )
| ( ( ( multiply @ SV1 @ SV5 )
= sk_c12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[277]) ).
thf(279,plain,
! [SV1: $i,SV5: $i,SV13: $i,SV12: $i,SV11: $i,SV10: $i,SV9: $i,SV7: $i] :
( ( ( ( ( multiply @ sk_c12 @ SV7 )
!= sk_c11 ) )
= $true )
| ( ( ( ( multiply @ SV9 @ sk_c12 )
!= SV7 )
| ( ( inverse @ SV9 )
!= sk_c12 )
| ( ( multiply @ SV10 @ SV11 )
!= sk_c12 )
| ( ( inverse @ SV10 )
!= SV11 )
| ( ( multiply @ SV11 @ sk_c11 )
!= sk_c12 )
| ( ( inverse @ SV12 )
!= sk_c12 )
| ( ( multiply @ SV12 @ sk_c11 )
!= sk_c12 )
| ! [SY60: $i] :
( ( ( multiply @ SV13 @ SY60 )
!= sk_c11 )
| ( ( inverse @ SV13 )
!= SY60 )
| ( ( multiply @ SY60 @ sk_c12 )
!= sk_c11 )
| ! [X10: $i] :
( ( ( inverse @ X10 )
!= sk_c11 )
| ( ( multiply @ X10 @ sk_c12 )
!= sk_c11 ) ) ) )
= $true )
| ( ( ( multiply @ SV5 @ sk_c11 )
= sk_c12 )
= $false )
| ( ( ( inverse @ SV1 )
= SV5 )
= $false )
| ( ( ( multiply @ SV1 @ SV5 )
= sk_c12 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[278]) ).
thf(280,plain,
! [SV1: $i,SV5: $i,SV13: $i,SV12: $i,SV11: $i,SV10: $i,SV9: $i,SV7: $i] :
( ( ( ( multiply @ sk_c12 @ SV7 )
= sk_c11 )
= $false )
| ( ( ( ( multiply @ SV9 @ sk_c12 )
!= SV7 )
| ( ( inverse @ SV9 )
!= sk_c12 )
| ( ( multiply @ SV10 @ SV11 )
!= sk_c12 )
| ( ( inverse @ SV10 )
!= SV11 )
| ( ( multiply @ SV11 @ sk_c11 )
!= sk_c12 )
| ( ( inverse @ SV12 )
!= sk_c12 )
| ( ( multiply @ SV12 @ sk_c11 )
!= sk_c12 )
| ! [SY60: $i] :
( ( ( multiply @ SV13 @ SY60 )
!= sk_c11 )
| ( ( inverse @ SV13 )
!= SY60 )
| ( ( multiply @ SY60 @ sk_c12 )
!= sk_c11 )
| ! [X10: $i] :
( ( ( inverse @ X10 )
!= sk_c11 )
| ( ( multiply @ X10 @ sk_c12 )
!= sk_c11 ) ) ) )
= $true )
| ( ( ( multiply @ SV5 @ sk_c11 )
= sk_c12 )
= $false )
| ( ( ( inverse @ SV1 )
= SV5 )
= $false )
| ( ( ( multiply @ SV1 @ SV5 )
= sk_c12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[279]) ).
thf(281,plain,
! [SV1: $i,SV5: $i,SV13: $i,SV12: $i,SV11: $i,SV10: $i,SV7: $i,SV9: $i] :
( ( ( ( ( multiply @ SV9 @ sk_c12 )
!= SV7 ) )
= $true )
| ( ( ( ( inverse @ SV9 )
!= sk_c12 )
| ( ( multiply @ SV10 @ SV11 )
!= sk_c12 )
| ( ( inverse @ SV10 )
!= SV11 )
| ( ( multiply @ SV11 @ sk_c11 )
!= sk_c12 )
| ( ( inverse @ SV12 )
!= sk_c12 )
| ( ( multiply @ SV12 @ sk_c11 )
!= sk_c12 )
| ! [SY60: $i] :
( ( ( multiply @ SV13 @ SY60 )
!= sk_c11 )
| ( ( inverse @ SV13 )
!= SY60 )
| ( ( multiply @ SY60 @ sk_c12 )
!= sk_c11 )
| ! [X10: $i] :
( ( ( inverse @ X10 )
!= sk_c11 )
| ( ( multiply @ X10 @ sk_c12 )
!= sk_c11 ) ) ) )
= $true )
| ( ( ( multiply @ sk_c12 @ SV7 )
= sk_c11 )
= $false )
| ( ( ( multiply @ SV5 @ sk_c11 )
= sk_c12 )
= $false )
| ( ( ( inverse @ SV1 )
= SV5 )
= $false )
| ( ( ( multiply @ SV1 @ SV5 )
= sk_c12 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[280]) ).
thf(282,plain,
! [SV1: $i,SV5: $i,SV13: $i,SV12: $i,SV11: $i,SV10: $i,SV7: $i,SV9: $i] :
( ( ( ( multiply @ SV9 @ sk_c12 )
= SV7 )
= $false )
| ( ( ( ( inverse @ SV9 )
!= sk_c12 )
| ( ( multiply @ SV10 @ SV11 )
!= sk_c12 )
| ( ( inverse @ SV10 )
!= SV11 )
| ( ( multiply @ SV11 @ sk_c11 )
!= sk_c12 )
| ( ( inverse @ SV12 )
!= sk_c12 )
| ( ( multiply @ SV12 @ sk_c11 )
!= sk_c12 )
| ! [SY60: $i] :
( ( ( multiply @ SV13 @ SY60 )
!= sk_c11 )
| ( ( inverse @ SV13 )
!= SY60 )
| ( ( multiply @ SY60 @ sk_c12 )
!= sk_c11 )
| ! [X10: $i] :
( ( ( inverse @ X10 )
!= sk_c11 )
| ( ( multiply @ X10 @ sk_c12 )
!= sk_c11 ) ) ) )
= $true )
| ( ( ( multiply @ sk_c12 @ SV7 )
= sk_c11 )
= $false )
| ( ( ( multiply @ SV5 @ sk_c11 )
= sk_c12 )
= $false )
| ( ( ( inverse @ SV1 )
= SV5 )
= $false )
| ( ( ( multiply @ SV1 @ SV5 )
= sk_c12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[281]) ).
thf(283,plain,
! [SV1: $i,SV5: $i,SV7: $i,SV13: $i,SV12: $i,SV11: $i,SV10: $i,SV9: $i] :
( ( ( ( ( inverse @ SV9 )
!= sk_c12 ) )
= $true )
| ( ( ( ( multiply @ SV10 @ SV11 )
!= sk_c12 )
| ( ( inverse @ SV10 )
!= SV11 )
| ( ( multiply @ SV11 @ sk_c11 )
!= sk_c12 )
| ( ( inverse @ SV12 )
!= sk_c12 )
| ( ( multiply @ SV12 @ sk_c11 )
!= sk_c12 )
| ! [SY60: $i] :
( ( ( multiply @ SV13 @ SY60 )
!= sk_c11 )
| ( ( inverse @ SV13 )
!= SY60 )
| ( ( multiply @ SY60 @ sk_c12 )
!= sk_c11 )
| ! [X10: $i] :
( ( ( inverse @ X10 )
!= sk_c11 )
| ( ( multiply @ X10 @ sk_c12 )
!= sk_c11 ) ) ) )
= $true )
| ( ( ( multiply @ SV9 @ sk_c12 )
= SV7 )
= $false )
| ( ( ( multiply @ sk_c12 @ SV7 )
= sk_c11 )
= $false )
| ( ( ( multiply @ SV5 @ sk_c11 )
= sk_c12 )
= $false )
| ( ( ( inverse @ SV1 )
= SV5 )
= $false )
| ( ( ( multiply @ SV1 @ SV5 )
= sk_c12 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[282]) ).
thf(284,plain,
! [SV1: $i,SV5: $i,SV7: $i,SV13: $i,SV12: $i,SV11: $i,SV10: $i,SV9: $i] :
( ( ( ( inverse @ SV9 )
= sk_c12 )
= $false )
| ( ( ( ( multiply @ SV10 @ SV11 )
!= sk_c12 )
| ( ( inverse @ SV10 )
!= SV11 )
| ( ( multiply @ SV11 @ sk_c11 )
!= sk_c12 )
| ( ( inverse @ SV12 )
!= sk_c12 )
| ( ( multiply @ SV12 @ sk_c11 )
!= sk_c12 )
| ! [SY60: $i] :
( ( ( multiply @ SV13 @ SY60 )
!= sk_c11 )
| ( ( inverse @ SV13 )
!= SY60 )
| ( ( multiply @ SY60 @ sk_c12 )
!= sk_c11 )
| ! [X10: $i] :
( ( ( inverse @ X10 )
!= sk_c11 )
| ( ( multiply @ X10 @ sk_c12 )
!= sk_c11 ) ) ) )
= $true )
| ( ( ( multiply @ SV9 @ sk_c12 )
= SV7 )
= $false )
| ( ( ( multiply @ sk_c12 @ SV7 )
= sk_c11 )
= $false )
| ( ( ( multiply @ SV5 @ sk_c11 )
= sk_c12 )
= $false )
| ( ( ( inverse @ SV1 )
= SV5 )
= $false )
| ( ( ( multiply @ SV1 @ SV5 )
= sk_c12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[283]) ).
thf(285,plain,
! [SV1: $i,SV5: $i,SV7: $i,SV9: $i,SV13: $i,SV12: $i,SV11: $i,SV10: $i] :
( ( ( ( ( multiply @ SV10 @ SV11 )
!= sk_c12 ) )
= $true )
| ( ( ( ( inverse @ SV10 )
!= SV11 )
| ( ( multiply @ SV11 @ sk_c11 )
!= sk_c12 )
| ( ( inverse @ SV12 )
!= sk_c12 )
| ( ( multiply @ SV12 @ sk_c11 )
!= sk_c12 )
| ! [SY60: $i] :
( ( ( multiply @ SV13 @ SY60 )
!= sk_c11 )
| ( ( inverse @ SV13 )
!= SY60 )
| ( ( multiply @ SY60 @ sk_c12 )
!= sk_c11 )
| ! [X10: $i] :
( ( ( inverse @ X10 )
!= sk_c11 )
| ( ( multiply @ X10 @ sk_c12 )
!= sk_c11 ) ) ) )
= $true )
| ( ( ( inverse @ SV9 )
= sk_c12 )
= $false )
| ( ( ( multiply @ SV9 @ sk_c12 )
= SV7 )
= $false )
| ( ( ( multiply @ sk_c12 @ SV7 )
= sk_c11 )
= $false )
| ( ( ( multiply @ SV5 @ sk_c11 )
= sk_c12 )
= $false )
| ( ( ( inverse @ SV1 )
= SV5 )
= $false )
| ( ( ( multiply @ SV1 @ SV5 )
= sk_c12 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[284]) ).
thf(286,plain,
! [SV1: $i,SV5: $i,SV7: $i,SV9: $i,SV13: $i,SV12: $i,SV11: $i,SV10: $i] :
( ( ( ( multiply @ SV10 @ SV11 )
= sk_c12 )
= $false )
| ( ( ( ( inverse @ SV10 )
!= SV11 )
| ( ( multiply @ SV11 @ sk_c11 )
!= sk_c12 )
| ( ( inverse @ SV12 )
!= sk_c12 )
| ( ( multiply @ SV12 @ sk_c11 )
!= sk_c12 )
| ! [SY60: $i] :
( ( ( multiply @ SV13 @ SY60 )
!= sk_c11 )
| ( ( inverse @ SV13 )
!= SY60 )
| ( ( multiply @ SY60 @ sk_c12 )
!= sk_c11 )
| ! [X10: $i] :
( ( ( inverse @ X10 )
!= sk_c11 )
| ( ( multiply @ X10 @ sk_c12 )
!= sk_c11 ) ) ) )
= $true )
| ( ( ( inverse @ SV9 )
= sk_c12 )
= $false )
| ( ( ( multiply @ SV9 @ sk_c12 )
= SV7 )
= $false )
| ( ( ( multiply @ sk_c12 @ SV7 )
= sk_c11 )
= $false )
| ( ( ( multiply @ SV5 @ sk_c11 )
= sk_c12 )
= $false )
| ( ( ( inverse @ SV1 )
= SV5 )
= $false )
| ( ( ( multiply @ SV1 @ SV5 )
= sk_c12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[285]) ).
thf(287,plain,
! [SV1: $i,SV5: $i,SV7: $i,SV9: $i,SV13: $i,SV12: $i,SV11: $i,SV10: $i] :
( ( ( ( ( inverse @ SV10 )
!= SV11 ) )
= $true )
| ( ( ( ( multiply @ SV11 @ sk_c11 )
!= sk_c12 )
| ( ( inverse @ SV12 )
!= sk_c12 )
| ( ( multiply @ SV12 @ sk_c11 )
!= sk_c12 )
| ! [SY60: $i] :
( ( ( multiply @ SV13 @ SY60 )
!= sk_c11 )
| ( ( inverse @ SV13 )
!= SY60 )
| ( ( multiply @ SY60 @ sk_c12 )
!= sk_c11 )
| ! [X10: $i] :
( ( ( inverse @ X10 )
!= sk_c11 )
| ( ( multiply @ X10 @ sk_c12 )
!= sk_c11 ) ) ) )
= $true )
| ( ( ( multiply @ SV10 @ SV11 )
= sk_c12 )
= $false )
| ( ( ( inverse @ SV9 )
= sk_c12 )
= $false )
| ( ( ( multiply @ SV9 @ sk_c12 )
= SV7 )
= $false )
| ( ( ( multiply @ sk_c12 @ SV7 )
= sk_c11 )
= $false )
| ( ( ( multiply @ SV5 @ sk_c11 )
= sk_c12 )
= $false )
| ( ( ( inverse @ SV1 )
= SV5 )
= $false )
| ( ( ( multiply @ SV1 @ SV5 )
= sk_c12 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[286]) ).
thf(288,plain,
! [SV1: $i,SV5: $i,SV7: $i,SV9: $i,SV13: $i,SV12: $i,SV11: $i,SV10: $i] :
( ( ( ( inverse @ SV10 )
= SV11 )
= $false )
| ( ( ( ( multiply @ SV11 @ sk_c11 )
!= sk_c12 )
| ( ( inverse @ SV12 )
!= sk_c12 )
| ( ( multiply @ SV12 @ sk_c11 )
!= sk_c12 )
| ! [SY60: $i] :
( ( ( multiply @ SV13 @ SY60 )
!= sk_c11 )
| ( ( inverse @ SV13 )
!= SY60 )
| ( ( multiply @ SY60 @ sk_c12 )
!= sk_c11 )
| ! [X10: $i] :
( ( ( inverse @ X10 )
!= sk_c11 )
| ( ( multiply @ X10 @ sk_c12 )
!= sk_c11 ) ) ) )
= $true )
| ( ( ( multiply @ SV10 @ SV11 )
= sk_c12 )
= $false )
| ( ( ( inverse @ SV9 )
= sk_c12 )
= $false )
| ( ( ( multiply @ SV9 @ sk_c12 )
= SV7 )
= $false )
| ( ( ( multiply @ sk_c12 @ SV7 )
= sk_c11 )
= $false )
| ( ( ( multiply @ SV5 @ sk_c11 )
= sk_c12 )
= $false )
| ( ( ( inverse @ SV1 )
= SV5 )
= $false )
| ( ( ( multiply @ SV1 @ SV5 )
= sk_c12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[287]) ).
thf(289,plain,
! [SV1: $i,SV5: $i,SV7: $i,SV9: $i,SV10: $i,SV13: $i,SV12: $i,SV11: $i] :
( ( ( ( ( multiply @ SV11 @ sk_c11 )
!= sk_c12 ) )
= $true )
| ( ( ( ( inverse @ SV12 )
!= sk_c12 )
| ( ( multiply @ SV12 @ sk_c11 )
!= sk_c12 )
| ! [SY60: $i] :
( ( ( multiply @ SV13 @ SY60 )
!= sk_c11 )
| ( ( inverse @ SV13 )
!= SY60 )
| ( ( multiply @ SY60 @ sk_c12 )
!= sk_c11 )
| ! [X10: $i] :
( ( ( inverse @ X10 )
!= sk_c11 )
| ( ( multiply @ X10 @ sk_c12 )
!= sk_c11 ) ) ) )
= $true )
| ( ( ( inverse @ SV10 )
= SV11 )
= $false )
| ( ( ( multiply @ SV10 @ SV11 )
= sk_c12 )
= $false )
| ( ( ( inverse @ SV9 )
= sk_c12 )
= $false )
| ( ( ( multiply @ SV9 @ sk_c12 )
= SV7 )
= $false )
| ( ( ( multiply @ sk_c12 @ SV7 )
= sk_c11 )
= $false )
| ( ( ( multiply @ SV5 @ sk_c11 )
= sk_c12 )
= $false )
| ( ( ( inverse @ SV1 )
= SV5 )
= $false )
| ( ( ( multiply @ SV1 @ SV5 )
= sk_c12 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[288]) ).
thf(290,plain,
! [SV1: $i,SV5: $i,SV7: $i,SV9: $i,SV10: $i,SV13: $i,SV12: $i,SV11: $i] :
( ( ( ( multiply @ SV11 @ sk_c11 )
= sk_c12 )
= $false )
| ( ( ( ( inverse @ SV12 )
!= sk_c12 )
| ( ( multiply @ SV12 @ sk_c11 )
!= sk_c12 )
| ! [SY60: $i] :
( ( ( multiply @ SV13 @ SY60 )
!= sk_c11 )
| ( ( inverse @ SV13 )
!= SY60 )
| ( ( multiply @ SY60 @ sk_c12 )
!= sk_c11 )
| ! [X10: $i] :
( ( ( inverse @ X10 )
!= sk_c11 )
| ( ( multiply @ X10 @ sk_c12 )
!= sk_c11 ) ) ) )
= $true )
| ( ( ( inverse @ SV10 )
= SV11 )
= $false )
| ( ( ( multiply @ SV10 @ SV11 )
= sk_c12 )
= $false )
| ( ( ( inverse @ SV9 )
= sk_c12 )
= $false )
| ( ( ( multiply @ SV9 @ sk_c12 )
= SV7 )
= $false )
| ( ( ( multiply @ sk_c12 @ SV7 )
= sk_c11 )
= $false )
| ( ( ( multiply @ SV5 @ sk_c11 )
= sk_c12 )
= $false )
| ( ( ( inverse @ SV1 )
= SV5 )
= $false )
| ( ( ( multiply @ SV1 @ SV5 )
= sk_c12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[289]) ).
thf(291,plain,
! [SV1: $i,SV5: $i,SV7: $i,SV9: $i,SV10: $i,SV11: $i,SV13: $i,SV12: $i] :
( ( ( ( ( inverse @ SV12 )
!= sk_c12 ) )
= $true )
| ( ( ( ( multiply @ SV12 @ sk_c11 )
!= sk_c12 )
| ! [SY60: $i] :
( ( ( multiply @ SV13 @ SY60 )
!= sk_c11 )
| ( ( inverse @ SV13 )
!= SY60 )
| ( ( multiply @ SY60 @ sk_c12 )
!= sk_c11 )
| ! [X10: $i] :
( ( ( inverse @ X10 )
!= sk_c11 )
| ( ( multiply @ X10 @ sk_c12 )
!= sk_c11 ) ) ) )
= $true )
| ( ( ( multiply @ SV11 @ sk_c11 )
= sk_c12 )
= $false )
| ( ( ( inverse @ SV10 )
= SV11 )
= $false )
| ( ( ( multiply @ SV10 @ SV11 )
= sk_c12 )
= $false )
| ( ( ( inverse @ SV9 )
= sk_c12 )
= $false )
| ( ( ( multiply @ SV9 @ sk_c12 )
= SV7 )
= $false )
| ( ( ( multiply @ sk_c12 @ SV7 )
= sk_c11 )
= $false )
| ( ( ( multiply @ SV5 @ sk_c11 )
= sk_c12 )
= $false )
| ( ( ( inverse @ SV1 )
= SV5 )
= $false )
| ( ( ( multiply @ SV1 @ SV5 )
= sk_c12 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[290]) ).
thf(292,plain,
! [SV1: $i,SV5: $i,SV7: $i,SV9: $i,SV10: $i,SV11: $i,SV13: $i,SV12: $i] :
( ( ( ( inverse @ SV12 )
= sk_c12 )
= $false )
| ( ( ( ( multiply @ SV12 @ sk_c11 )
!= sk_c12 )
| ! [SY60: $i] :
( ( ( multiply @ SV13 @ SY60 )
!= sk_c11 )
| ( ( inverse @ SV13 )
!= SY60 )
| ( ( multiply @ SY60 @ sk_c12 )
!= sk_c11 )
| ! [X10: $i] :
( ( ( inverse @ X10 )
!= sk_c11 )
| ( ( multiply @ X10 @ sk_c12 )
!= sk_c11 ) ) ) )
= $true )
| ( ( ( multiply @ SV11 @ sk_c11 )
= sk_c12 )
= $false )
| ( ( ( inverse @ SV10 )
= SV11 )
= $false )
| ( ( ( multiply @ SV10 @ SV11 )
= sk_c12 )
= $false )
| ( ( ( inverse @ SV9 )
= sk_c12 )
= $false )
| ( ( ( multiply @ SV9 @ sk_c12 )
= SV7 )
= $false )
| ( ( ( multiply @ sk_c12 @ SV7 )
= sk_c11 )
= $false )
| ( ( ( multiply @ SV5 @ sk_c11 )
= sk_c12 )
= $false )
| ( ( ( inverse @ SV1 )
= SV5 )
= $false )
| ( ( ( multiply @ SV1 @ SV5 )
= sk_c12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[291]) ).
thf(293,plain,
! [SV1: $i,SV5: $i,SV7: $i,SV9: $i,SV10: $i,SV11: $i,SV13: $i,SV12: $i] :
( ( ( ( ( multiply @ SV12 @ sk_c11 )
!= sk_c12 ) )
= $true )
| ( ( ! [SY60: $i] :
( ( ( multiply @ SV13 @ SY60 )
!= sk_c11 )
| ( ( inverse @ SV13 )
!= SY60 )
| ( ( multiply @ SY60 @ sk_c12 )
!= sk_c11 )
| ! [X10: $i] :
( ( ( inverse @ X10 )
!= sk_c11 )
| ( ( multiply @ X10 @ sk_c12 )
!= sk_c11 ) ) ) )
= $true )
| ( ( ( inverse @ SV12 )
= sk_c12 )
= $false )
| ( ( ( multiply @ SV11 @ sk_c11 )
= sk_c12 )
= $false )
| ( ( ( inverse @ SV10 )
= SV11 )
= $false )
| ( ( ( multiply @ SV10 @ SV11 )
= sk_c12 )
= $false )
| ( ( ( inverse @ SV9 )
= sk_c12 )
= $false )
| ( ( ( multiply @ SV9 @ sk_c12 )
= SV7 )
= $false )
| ( ( ( multiply @ sk_c12 @ SV7 )
= sk_c11 )
= $false )
| ( ( ( multiply @ SV5 @ sk_c11 )
= sk_c12 )
= $false )
| ( ( ( inverse @ SV1 )
= SV5 )
= $false )
| ( ( ( multiply @ SV1 @ SV5 )
= sk_c12 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[292]) ).
thf(294,plain,
! [SV1: $i,SV5: $i,SV7: $i,SV9: $i,SV10: $i,SV11: $i,SV13: $i,SV12: $i] :
( ( ( ( multiply @ SV12 @ sk_c11 )
= sk_c12 )
= $false )
| ( ( ! [SY60: $i] :
( ( ( multiply @ SV13 @ SY60 )
!= sk_c11 )
| ( ( inverse @ SV13 )
!= SY60 )
| ( ( multiply @ SY60 @ sk_c12 )
!= sk_c11 )
| ! [X10: $i] :
( ( ( inverse @ X10 )
!= sk_c11 )
| ( ( multiply @ X10 @ sk_c12 )
!= sk_c11 ) ) ) )
= $true )
| ( ( ( inverse @ SV12 )
= sk_c12 )
= $false )
| ( ( ( multiply @ SV11 @ sk_c11 )
= sk_c12 )
= $false )
| ( ( ( inverse @ SV10 )
= SV11 )
= $false )
| ( ( ( multiply @ SV10 @ SV11 )
= sk_c12 )
= $false )
| ( ( ( inverse @ SV9 )
= sk_c12 )
= $false )
| ( ( ( multiply @ SV9 @ sk_c12 )
= SV7 )
= $false )
| ( ( ( multiply @ sk_c12 @ SV7 )
= sk_c11 )
= $false )
| ( ( ( multiply @ SV5 @ sk_c11 )
= sk_c12 )
= $false )
| ( ( ( inverse @ SV1 )
= SV5 )
= $false )
| ( ( ( multiply @ SV1 @ SV5 )
= sk_c12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[293]) ).
thf(295,plain,
! [SV1: $i,SV5: $i,SV7: $i,SV9: $i,SV10: $i,SV11: $i,SV12: $i,SV14: $i,SV13: $i] :
( ( ( ( ( multiply @ SV13 @ SV14 )
!= sk_c11 )
| ( ( inverse @ SV13 )
!= SV14 )
| ( ( multiply @ SV14 @ sk_c12 )
!= sk_c11 )
| ! [X10: $i] :
( ( ( inverse @ X10 )
!= sk_c11 )
| ( ( multiply @ X10 @ sk_c12 )
!= sk_c11 ) ) )
= $true )
| ( ( ( multiply @ SV12 @ sk_c11 )
= sk_c12 )
= $false )
| ( ( ( inverse @ SV12 )
= sk_c12 )
= $false )
| ( ( ( multiply @ SV11 @ sk_c11 )
= sk_c12 )
= $false )
| ( ( ( inverse @ SV10 )
= SV11 )
= $false )
| ( ( ( multiply @ SV10 @ SV11 )
= sk_c12 )
= $false )
| ( ( ( inverse @ SV9 )
= sk_c12 )
= $false )
| ( ( ( multiply @ SV9 @ sk_c12 )
= SV7 )
= $false )
| ( ( ( multiply @ sk_c12 @ SV7 )
= sk_c11 )
= $false )
| ( ( ( multiply @ SV5 @ sk_c11 )
= sk_c12 )
= $false )
| ( ( ( inverse @ SV1 )
= SV5 )
= $false )
| ( ( ( multiply @ SV1 @ SV5 )
= sk_c12 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[294]) ).
thf(296,plain,
! [SV1: $i,SV5: $i,SV7: $i,SV9: $i,SV10: $i,SV11: $i,SV12: $i,SV14: $i,SV13: $i] :
( ( ( ( ( multiply @ SV13 @ SV14 )
!= sk_c11 ) )
= $true )
| ( ( ( ( inverse @ SV13 )
!= SV14 )
| ( ( multiply @ SV14 @ sk_c12 )
!= sk_c11 )
| ! [X10: $i] :
( ( ( inverse @ X10 )
!= sk_c11 )
| ( ( multiply @ X10 @ sk_c12 )
!= sk_c11 ) ) )
= $true )
| ( ( ( multiply @ SV12 @ sk_c11 )
= sk_c12 )
= $false )
| ( ( ( inverse @ SV12 )
= sk_c12 )
= $false )
| ( ( ( multiply @ SV11 @ sk_c11 )
= sk_c12 )
= $false )
| ( ( ( inverse @ SV10 )
= SV11 )
= $false )
| ( ( ( multiply @ SV10 @ SV11 )
= sk_c12 )
= $false )
| ( ( ( inverse @ SV9 )
= sk_c12 )
= $false )
| ( ( ( multiply @ SV9 @ sk_c12 )
= SV7 )
= $false )
| ( ( ( multiply @ sk_c12 @ SV7 )
= sk_c11 )
= $false )
| ( ( ( multiply @ SV5 @ sk_c11 )
= sk_c12 )
= $false )
| ( ( ( inverse @ SV1 )
= SV5 )
= $false )
| ( ( ( multiply @ SV1 @ SV5 )
= sk_c12 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[295]) ).
thf(297,plain,
! [SV1: $i,SV5: $i,SV7: $i,SV9: $i,SV10: $i,SV11: $i,SV12: $i,SV14: $i,SV13: $i] :
( ( ( ( multiply @ SV13 @ SV14 )
= sk_c11 )
= $false )
| ( ( ( ( inverse @ SV13 )
!= SV14 )
| ( ( multiply @ SV14 @ sk_c12 )
!= sk_c11 )
| ! [X10: $i] :
( ( ( inverse @ X10 )
!= sk_c11 )
| ( ( multiply @ X10 @ sk_c12 )
!= sk_c11 ) ) )
= $true )
| ( ( ( multiply @ SV12 @ sk_c11 )
= sk_c12 )
= $false )
| ( ( ( inverse @ SV12 )
= sk_c12 )
= $false )
| ( ( ( multiply @ SV11 @ sk_c11 )
= sk_c12 )
= $false )
| ( ( ( inverse @ SV10 )
= SV11 )
= $false )
| ( ( ( multiply @ SV10 @ SV11 )
= sk_c12 )
= $false )
| ( ( ( inverse @ SV9 )
= sk_c12 )
= $false )
| ( ( ( multiply @ SV9 @ sk_c12 )
= SV7 )
= $false )
| ( ( ( multiply @ sk_c12 @ SV7 )
= sk_c11 )
= $false )
| ( ( ( multiply @ SV5 @ sk_c11 )
= sk_c12 )
= $false )
| ( ( ( inverse @ SV1 )
= SV5 )
= $false )
| ( ( ( multiply @ SV1 @ SV5 )
= sk_c12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[296]) ).
thf(298,plain,
! [SV1: $i,SV5: $i,SV7: $i,SV9: $i,SV10: $i,SV11: $i,SV12: $i,SV14: $i,SV13: $i] :
( ( ( ( ( inverse @ SV13 )
!= SV14 ) )
= $true )
| ( ( ( ( multiply @ SV14 @ sk_c12 )
!= sk_c11 )
| ! [X10: $i] :
( ( ( inverse @ X10 )
!= sk_c11 )
| ( ( multiply @ X10 @ sk_c12 )
!= sk_c11 ) ) )
= $true )
| ( ( ( multiply @ SV13 @ SV14 )
= sk_c11 )
= $false )
| ( ( ( multiply @ SV12 @ sk_c11 )
= sk_c12 )
= $false )
| ( ( ( inverse @ SV12 )
= sk_c12 )
= $false )
| ( ( ( multiply @ SV11 @ sk_c11 )
= sk_c12 )
= $false )
| ( ( ( inverse @ SV10 )
= SV11 )
= $false )
| ( ( ( multiply @ SV10 @ SV11 )
= sk_c12 )
= $false )
| ( ( ( inverse @ SV9 )
= sk_c12 )
= $false )
| ( ( ( multiply @ SV9 @ sk_c12 )
= SV7 )
= $false )
| ( ( ( multiply @ sk_c12 @ SV7 )
= sk_c11 )
= $false )
| ( ( ( multiply @ SV5 @ sk_c11 )
= sk_c12 )
= $false )
| ( ( ( inverse @ SV1 )
= SV5 )
= $false )
| ( ( ( multiply @ SV1 @ SV5 )
= sk_c12 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[297]) ).
thf(299,plain,
! [SV1: $i,SV5: $i,SV7: $i,SV9: $i,SV10: $i,SV11: $i,SV12: $i,SV14: $i,SV13: $i] :
( ( ( ( inverse @ SV13 )
= SV14 )
= $false )
| ( ( ( ( multiply @ SV14 @ sk_c12 )
!= sk_c11 )
| ! [X10: $i] :
( ( ( inverse @ X10 )
!= sk_c11 )
| ( ( multiply @ X10 @ sk_c12 )
!= sk_c11 ) ) )
= $true )
| ( ( ( multiply @ SV13 @ SV14 )
= sk_c11 )
= $false )
| ( ( ( multiply @ SV12 @ sk_c11 )
= sk_c12 )
= $false )
| ( ( ( inverse @ SV12 )
= sk_c12 )
= $false )
| ( ( ( multiply @ SV11 @ sk_c11 )
= sk_c12 )
= $false )
| ( ( ( inverse @ SV10 )
= SV11 )
= $false )
| ( ( ( multiply @ SV10 @ SV11 )
= sk_c12 )
= $false )
| ( ( ( inverse @ SV9 )
= sk_c12 )
= $false )
| ( ( ( multiply @ SV9 @ sk_c12 )
= SV7 )
= $false )
| ( ( ( multiply @ sk_c12 @ SV7 )
= sk_c11 )
= $false )
| ( ( ( multiply @ SV5 @ sk_c11 )
= sk_c12 )
= $false )
| ( ( ( inverse @ SV1 )
= SV5 )
= $false )
| ( ( ( multiply @ SV1 @ SV5 )
= sk_c12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[298]) ).
thf(300,plain,
! [SV1: $i,SV5: $i,SV7: $i,SV9: $i,SV10: $i,SV11: $i,SV12: $i,SV13: $i,SV14: $i] :
( ( ( ( ( multiply @ SV14 @ sk_c12 )
!= sk_c11 ) )
= $true )
| ( ( ! [X10: $i] :
( ( ( inverse @ X10 )
!= sk_c11 )
| ( ( multiply @ X10 @ sk_c12 )
!= sk_c11 ) ) )
= $true )
| ( ( ( inverse @ SV13 )
= SV14 )
= $false )
| ( ( ( multiply @ SV13 @ SV14 )
= sk_c11 )
= $false )
| ( ( ( multiply @ SV12 @ sk_c11 )
= sk_c12 )
= $false )
| ( ( ( inverse @ SV12 )
= sk_c12 )
= $false )
| ( ( ( multiply @ SV11 @ sk_c11 )
= sk_c12 )
= $false )
| ( ( ( inverse @ SV10 )
= SV11 )
= $false )
| ( ( ( multiply @ SV10 @ SV11 )
= sk_c12 )
= $false )
| ( ( ( inverse @ SV9 )
= sk_c12 )
= $false )
| ( ( ( multiply @ SV9 @ sk_c12 )
= SV7 )
= $false )
| ( ( ( multiply @ sk_c12 @ SV7 )
= sk_c11 )
= $false )
| ( ( ( multiply @ SV5 @ sk_c11 )
= sk_c12 )
= $false )
| ( ( ( inverse @ SV1 )
= SV5 )
= $false )
| ( ( ( multiply @ SV1 @ SV5 )
= sk_c12 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[299]) ).
thf(301,plain,
! [SV1: $i,SV5: $i,SV7: $i,SV9: $i,SV10: $i,SV11: $i,SV12: $i,SV13: $i,SV14: $i] :
( ( ( ( multiply @ SV14 @ sk_c12 )
= sk_c11 )
= $false )
| ( ( ! [X10: $i] :
( ( ( inverse @ X10 )
!= sk_c11 )
| ( ( multiply @ X10 @ sk_c12 )
!= sk_c11 ) ) )
= $true )
| ( ( ( inverse @ SV13 )
= SV14 )
= $false )
| ( ( ( multiply @ SV13 @ SV14 )
= sk_c11 )
= $false )
| ( ( ( multiply @ SV12 @ sk_c11 )
= sk_c12 )
= $false )
| ( ( ( inverse @ SV12 )
= sk_c12 )
= $false )
| ( ( ( multiply @ SV11 @ sk_c11 )
= sk_c12 )
= $false )
| ( ( ( inverse @ SV10 )
= SV11 )
= $false )
| ( ( ( multiply @ SV10 @ SV11 )
= sk_c12 )
= $false )
| ( ( ( inverse @ SV9 )
= sk_c12 )
= $false )
| ( ( ( multiply @ SV9 @ sk_c12 )
= SV7 )
= $false )
| ( ( ( multiply @ sk_c12 @ SV7 )
= sk_c11 )
= $false )
| ( ( ( multiply @ SV5 @ sk_c11 )
= sk_c12 )
= $false )
| ( ( ( inverse @ SV1 )
= SV5 )
= $false )
| ( ( ( multiply @ SV1 @ SV5 )
= sk_c12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[300]) ).
thf(302,plain,
! [SV1: $i,SV5: $i,SV7: $i,SV9: $i,SV10: $i,SV11: $i,SV12: $i,SV13: $i,SV14: $i,SV15: $i] :
( ( ( ( ( inverse @ SV15 )
!= sk_c11 )
| ( ( multiply @ SV15 @ sk_c12 )
!= sk_c11 ) )
= $true )
| ( ( ( multiply @ SV14 @ sk_c12 )
= sk_c11 )
= $false )
| ( ( ( inverse @ SV13 )
= SV14 )
= $false )
| ( ( ( multiply @ SV13 @ SV14 )
= sk_c11 )
= $false )
| ( ( ( multiply @ SV12 @ sk_c11 )
= sk_c12 )
= $false )
| ( ( ( inverse @ SV12 )
= sk_c12 )
= $false )
| ( ( ( multiply @ SV11 @ sk_c11 )
= sk_c12 )
= $false )
| ( ( ( inverse @ SV10 )
= SV11 )
= $false )
| ( ( ( multiply @ SV10 @ SV11 )
= sk_c12 )
= $false )
| ( ( ( inverse @ SV9 )
= sk_c12 )
= $false )
| ( ( ( multiply @ SV9 @ sk_c12 )
= SV7 )
= $false )
| ( ( ( multiply @ sk_c12 @ SV7 )
= sk_c11 )
= $false )
| ( ( ( multiply @ SV5 @ sk_c11 )
= sk_c12 )
= $false )
| ( ( ( inverse @ SV1 )
= SV5 )
= $false )
| ( ( ( multiply @ SV1 @ SV5 )
= sk_c12 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[301]) ).
thf(303,plain,
! [SV1: $i,SV5: $i,SV7: $i,SV9: $i,SV10: $i,SV11: $i,SV12: $i,SV13: $i,SV14: $i,SV15: $i] :
( ( ( ( ( inverse @ SV15 )
!= sk_c11 ) )
= $true )
| ( ( ( ( multiply @ SV15 @ sk_c12 )
!= sk_c11 ) )
= $true )
| ( ( ( multiply @ SV14 @ sk_c12 )
= sk_c11 )
= $false )
| ( ( ( inverse @ SV13 )
= SV14 )
= $false )
| ( ( ( multiply @ SV13 @ SV14 )
= sk_c11 )
= $false )
| ( ( ( multiply @ SV12 @ sk_c11 )
= sk_c12 )
= $false )
| ( ( ( inverse @ SV12 )
= sk_c12 )
= $false )
| ( ( ( multiply @ SV11 @ sk_c11 )
= sk_c12 )
= $false )
| ( ( ( inverse @ SV10 )
= SV11 )
= $false )
| ( ( ( multiply @ SV10 @ SV11 )
= sk_c12 )
= $false )
| ( ( ( inverse @ SV9 )
= sk_c12 )
= $false )
| ( ( ( multiply @ SV9 @ sk_c12 )
= SV7 )
= $false )
| ( ( ( multiply @ sk_c12 @ SV7 )
= sk_c11 )
= $false )
| ( ( ( multiply @ SV5 @ sk_c11 )
= sk_c12 )
= $false )
| ( ( ( inverse @ SV1 )
= SV5 )
= $false )
| ( ( ( multiply @ SV1 @ SV5 )
= sk_c12 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[302]) ).
thf(304,plain,
! [SV1: $i,SV5: $i,SV7: $i,SV9: $i,SV10: $i,SV11: $i,SV12: $i,SV13: $i,SV14: $i,SV15: $i] :
( ( ( ( inverse @ SV15 )
= sk_c11 )
= $false )
| ( ( ( ( multiply @ SV15 @ sk_c12 )
!= sk_c11 ) )
= $true )
| ( ( ( multiply @ SV14 @ sk_c12 )
= sk_c11 )
= $false )
| ( ( ( inverse @ SV13 )
= SV14 )
= $false )
| ( ( ( multiply @ SV13 @ SV14 )
= sk_c11 )
= $false )
| ( ( ( multiply @ SV12 @ sk_c11 )
= sk_c12 )
= $false )
| ( ( ( inverse @ SV12 )
= sk_c12 )
= $false )
| ( ( ( multiply @ SV11 @ sk_c11 )
= sk_c12 )
= $false )
| ( ( ( inverse @ SV10 )
= SV11 )
= $false )
| ( ( ( multiply @ SV10 @ SV11 )
= sk_c12 )
= $false )
| ( ( ( inverse @ SV9 )
= sk_c12 )
= $false )
| ( ( ( multiply @ SV9 @ sk_c12 )
= SV7 )
= $false )
| ( ( ( multiply @ sk_c12 @ SV7 )
= sk_c11 )
= $false )
| ( ( ( multiply @ SV5 @ sk_c11 )
= sk_c12 )
= $false )
| ( ( ( inverse @ SV1 )
= SV5 )
= $false )
| ( ( ( multiply @ SV1 @ SV5 )
= sk_c12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[303]) ).
thf(305,plain,
! [SV1: $i,SV5: $i,SV7: $i,SV9: $i,SV10: $i,SV11: $i,SV12: $i,SV13: $i,SV14: $i,SV15: $i] :
( ( ( ( multiply @ SV15 @ sk_c12 )
= sk_c11 )
= $false )
| ( ( ( inverse @ SV15 )
= sk_c11 )
= $false )
| ( ( ( multiply @ SV14 @ sk_c12 )
= sk_c11 )
= $false )
| ( ( ( inverse @ SV13 )
= SV14 )
= $false )
| ( ( ( multiply @ SV13 @ SV14 )
= sk_c11 )
= $false )
| ( ( ( multiply @ SV12 @ sk_c11 )
= sk_c12 )
= $false )
| ( ( ( inverse @ SV12 )
= sk_c12 )
= $false )
| ( ( ( multiply @ SV11 @ sk_c11 )
= sk_c12 )
= $false )
| ( ( ( inverse @ SV10 )
= SV11 )
= $false )
| ( ( ( multiply @ SV10 @ SV11 )
= sk_c12 )
= $false )
| ( ( ( inverse @ SV9 )
= sk_c12 )
= $false )
| ( ( ( multiply @ SV9 @ sk_c12 )
= SV7 )
= $false )
| ( ( ( multiply @ sk_c12 @ SV7 )
= sk_c11 )
= $false )
| ( ( ( multiply @ SV5 @ sk_c11 )
= sk_c12 )
= $false )
| ( ( ( inverse @ SV1 )
= SV5 )
= $false )
| ( ( ( multiply @ SV1 @ SV5 )
= sk_c12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[304]) ).
thf(306,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[199,305,267,263,261,260,258,257,256,255,254,253,252,251,250,249,248,247,246,245,244,243,242,241,240,239,238,237,236,235,234,233,232,231,230,229,228,227,226,225,224,223,222,221,220,219,218,217,216,215,214,213,212,211,210,209,208,207,206,205,204,203,202,201,200]) ).
thf(307,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[306]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : GRP208-1 : TPTP v8.1.0. Released v2.5.0.
% 0.13/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.35 % Computer : n005.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Mon Jun 13 17:31:09 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.39
% 0.13/0.39 No.of.Axioms: 64
% 0.13/0.39
% 0.13/0.39 Length.of.Defs: 0
% 0.13/0.39
% 0.13/0.39 Contains.Choice.Funs: false
% 0.13/0.42 (rf:0,axioms:64,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:66,loop_count:0,foatp_calls:0,translation:fof_full)................
% 3.97/4.16
% 3.97/4.16 ********************************
% 3.97/4.16 * All subproblems solved! *
% 3.97/4.16 ********************************
% 3.97/4.16 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:64,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:306,loop_count:0,foatp_calls:1,translation:fof_full)
% 4.00/4.21
% 4.00/4.21 %**** Beginning of derivation protocol ****
% 4.00/4.21 % SZS output start CNFRefutation
% See solution above
% 4.00/4.21
% 4.00/4.21 %**** End of derivation protocol ****
% 4.00/4.21 %**** no. of clauses in derivation: 307 ****
% 4.00/4.21 %**** clause counter: 306 ****
% 4.00/4.21
% 4.00/4.21 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:64,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:306,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------