TSTP Solution File: GRP347-1 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : GRP347-1 : 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 : n029.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 10:17:39 EDT 2022
% Result : Unsatisfiable 36.42s 36.61s
% Output : CNFRefutation 36.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 45
% Syntax : Number of formulae : 181 ( 87 unt; 10 typ; 0 def)
% Number of atoms : 1183 ( 874 equ; 0 cnn)
% Maximal formula atoms : 11 ( 6 avg)
% Number of connectives : 1537 ( 194 ~; 410 |; 0 &; 933 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 10 usr; 10 con; 0-2 aty)
% Number of variables : 142 ( 0 ^ 142 !; 0 ?; 142 :)
% 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_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(1,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( multiply @ ( multiply @ X @ Y ) @ Z )
= ( multiply @ X @ ( multiply @ Y @ Z ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity) ).
thf(2,axiom,
! [X: $i] :
( ( multiply @ ( inverse @ X ) @ X )
= identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_inverse) ).
thf(3,axiom,
! [X: $i] :
( ( multiply @ identity @ X )
= X ),
file('/export/starexec/sandbox2/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,
! [X3: $i,X4: $i,X1: $i,X2: $i] :
( ( ( multiply @ sk_c6 @ sk_c7 )
!= sk_c5 )
| ( ( inverse @ X3 )
!= sk_c7 )
| ( ( multiply @ X3 @ sk_c6 )
!= sk_c7 )
| ( ( inverse @ X4 )
!= sk_c6 )
| ( ( multiply @ X4 @ sk_c5 )
!= sk_c6 )
| ( ( multiply @ sk_c6 @ sk_c5 )
!= sk_c7 )
| ( ( inverse @ sk_c6 )
!= sk_c5 )
| ( ( multiply @ X1 @ sk_c6 )
!= sk_c7 )
| ( ( inverse @ X1 )
!= sk_c6 )
| ( ( multiply @ X2 @ sk_c7 )
!= sk_c5 )
| ( ( inverse @ X2 )
!= sk_c7 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_31) ).
thf(7,negated_conjecture,
( ( ( multiply @ sk_c2 @ sk_c5 )
= sk_c6 )
| ( ( inverse @ sk_c4 )
= sk_c7 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_30) ).
thf(8,negated_conjecture,
( ( ( multiply @ sk_c2 @ sk_c5 )
= sk_c6 )
| ( ( multiply @ sk_c4 @ sk_c7 )
= sk_c5 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_29) ).
thf(9,negated_conjecture,
( ( ( multiply @ sk_c2 @ sk_c5 )
= sk_c6 )
| ( ( inverse @ sk_c3 )
= sk_c6 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_28) ).
thf(10,negated_conjecture,
( ( ( multiply @ sk_c2 @ sk_c5 )
= sk_c6 )
| ( ( multiply @ sk_c3 @ sk_c6 )
= sk_c7 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_27) ).
thf(11,negated_conjecture,
( ( ( multiply @ sk_c2 @ sk_c5 )
= sk_c6 )
| ( ( inverse @ sk_c6 )
= sk_c5 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_26) ).
thf(12,negated_conjecture,
( ( ( multiply @ sk_c2 @ sk_c5 )
= sk_c6 )
| ( ( multiply @ sk_c6 @ sk_c5 )
= sk_c7 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_25) ).
thf(13,negated_conjecture,
( ( ( inverse @ sk_c2 )
= sk_c6 )
| ( ( inverse @ sk_c4 )
= sk_c7 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_24) ).
thf(14,negated_conjecture,
( ( ( inverse @ sk_c2 )
= sk_c6 )
| ( ( multiply @ sk_c4 @ sk_c7 )
= sk_c5 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_23) ).
thf(15,negated_conjecture,
( ( ( inverse @ sk_c2 )
= sk_c6 )
| ( ( inverse @ sk_c3 )
= sk_c6 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_22) ).
thf(16,negated_conjecture,
( ( ( inverse @ sk_c2 )
= sk_c6 )
| ( ( multiply @ sk_c3 @ sk_c6 )
= sk_c7 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_21) ).
thf(17,negated_conjecture,
( ( ( inverse @ sk_c2 )
= sk_c6 )
| ( ( inverse @ sk_c6 )
= sk_c5 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_20) ).
thf(18,negated_conjecture,
( ( ( inverse @ sk_c2 )
= sk_c6 )
| ( ( multiply @ sk_c6 @ sk_c5 )
= sk_c7 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_19) ).
thf(19,negated_conjecture,
( ( ( multiply @ sk_c1 @ sk_c6 )
= sk_c7 )
| ( ( inverse @ sk_c4 )
= sk_c7 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_18) ).
thf(20,negated_conjecture,
( ( ( multiply @ sk_c1 @ sk_c6 )
= sk_c7 )
| ( ( multiply @ sk_c4 @ sk_c7 )
= sk_c5 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_17) ).
thf(21,negated_conjecture,
( ( ( multiply @ sk_c1 @ sk_c6 )
= sk_c7 )
| ( ( inverse @ sk_c3 )
= sk_c6 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_16) ).
thf(22,negated_conjecture,
( ( ( multiply @ sk_c1 @ sk_c6 )
= sk_c7 )
| ( ( multiply @ sk_c3 @ sk_c6 )
= sk_c7 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_15) ).
thf(23,negated_conjecture,
( ( ( multiply @ sk_c1 @ sk_c6 )
= sk_c7 )
| ( ( inverse @ sk_c6 )
= sk_c5 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_14) ).
thf(24,negated_conjecture,
( ( ( multiply @ sk_c1 @ sk_c6 )
= sk_c7 )
| ( ( multiply @ sk_c6 @ sk_c5 )
= sk_c7 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_13) ).
thf(25,negated_conjecture,
( ( ( inverse @ sk_c1 )
= sk_c7 )
| ( ( inverse @ sk_c4 )
= sk_c7 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_12) ).
thf(26,negated_conjecture,
( ( ( inverse @ sk_c1 )
= sk_c7 )
| ( ( multiply @ sk_c4 @ sk_c7 )
= sk_c5 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_11) ).
thf(27,negated_conjecture,
( ( ( inverse @ sk_c1 )
= sk_c7 )
| ( ( inverse @ sk_c3 )
= sk_c6 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_10) ).
thf(28,negated_conjecture,
( ( ( inverse @ sk_c1 )
= sk_c7 )
| ( ( multiply @ sk_c3 @ sk_c6 )
= sk_c7 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_9) ).
thf(29,negated_conjecture,
( ( ( inverse @ sk_c1 )
= sk_c7 )
| ( ( inverse @ sk_c6 )
= sk_c5 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_8) ).
thf(30,negated_conjecture,
( ( ( inverse @ sk_c1 )
= sk_c7 )
| ( ( multiply @ sk_c6 @ sk_c5 )
= sk_c7 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_7) ).
thf(31,negated_conjecture,
( ( ( multiply @ sk_c6 @ sk_c7 )
= sk_c5 )
| ( ( inverse @ sk_c4 )
= sk_c7 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_6) ).
thf(32,negated_conjecture,
( ( ( multiply @ sk_c6 @ sk_c7 )
= sk_c5 )
| ( ( multiply @ sk_c4 @ sk_c7 )
= sk_c5 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_5) ).
thf(33,negated_conjecture,
( ( ( multiply @ sk_c6 @ sk_c7 )
= sk_c5 )
| ( ( inverse @ sk_c3 )
= sk_c6 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_4) ).
thf(34,negated_conjecture,
( ( ( multiply @ sk_c6 @ sk_c7 )
= sk_c5 )
| ( ( multiply @ sk_c3 @ sk_c6 )
= sk_c7 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_3) ).
thf(35,negated_conjecture,
( ( ( multiply @ sk_c6 @ sk_c7 )
= sk_c5 )
| ( ( inverse @ sk_c6 )
= sk_c5 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_2) ).
thf(36,negated_conjecture,
( ( ( multiply @ sk_c6 @ sk_c7 )
= sk_c5 )
| ( ( multiply @ sk_c6 @ sk_c5 )
= sk_c7 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_1) ).
thf(37,plain,
$false = $false,
inference(unfold_def,[status(thm)],[5]) ).
thf(38,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(39,plain,
( ( ! [X: $i] :
( ( multiply @ ( inverse @ X ) @ X )
= identity ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(40,plain,
( ( ! [X: $i] :
( ( multiply @ identity @ X )
= X ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(41,plain,
( ( ! [X3: $i,X4: $i,X1: $i,X2: $i] :
( ( ( multiply @ sk_c6 @ sk_c7 )
!= sk_c5 )
| ( ( inverse @ X3 )
!= sk_c7 )
| ( ( multiply @ X3 @ sk_c6 )
!= sk_c7 )
| ( ( inverse @ X4 )
!= sk_c6 )
| ( ( multiply @ X4 @ sk_c5 )
!= sk_c6 )
| ( ( multiply @ sk_c6 @ sk_c5 )
!= sk_c7 )
| ( ( inverse @ sk_c6 )
!= sk_c5 )
| ( ( multiply @ X1 @ sk_c6 )
!= sk_c7 )
| ( ( inverse @ X1 )
!= sk_c6 )
| ( ( multiply @ X2 @ sk_c7 )
!= sk_c5 )
| ( ( inverse @ X2 )
!= sk_c7 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(42,plain,
( ( ( ( multiply @ sk_c2 @ sk_c5 )
= sk_c6 )
| ( ( inverse @ sk_c4 )
= sk_c7 ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(43,plain,
( ( ( ( multiply @ sk_c2 @ sk_c5 )
= sk_c6 )
| ( ( multiply @ sk_c4 @ sk_c7 )
= sk_c5 ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(44,plain,
( ( ( ( multiply @ sk_c2 @ sk_c5 )
= sk_c6 )
| ( ( inverse @ sk_c3 )
= sk_c6 ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(45,plain,
( ( ( ( multiply @ sk_c2 @ sk_c5 )
= sk_c6 )
| ( ( multiply @ sk_c3 @ sk_c6 )
= sk_c7 ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(46,plain,
( ( ( ( multiply @ sk_c2 @ sk_c5 )
= sk_c6 )
| ( ( inverse @ sk_c6 )
= sk_c5 ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(47,plain,
( ( ( ( multiply @ sk_c2 @ sk_c5 )
= sk_c6 )
| ( ( multiply @ sk_c6 @ sk_c5 )
= sk_c7 ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(48,plain,
( ( ( ( inverse @ sk_c2 )
= sk_c6 )
| ( ( inverse @ sk_c4 )
= sk_c7 ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(49,plain,
( ( ( ( inverse @ sk_c2 )
= sk_c6 )
| ( ( multiply @ sk_c4 @ sk_c7 )
= sk_c5 ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(50,plain,
( ( ( ( inverse @ sk_c2 )
= sk_c6 )
| ( ( inverse @ sk_c3 )
= sk_c6 ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(51,plain,
( ( ( ( inverse @ sk_c2 )
= sk_c6 )
| ( ( multiply @ sk_c3 @ sk_c6 )
= sk_c7 ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(52,plain,
( ( ( ( inverse @ sk_c2 )
= sk_c6 )
| ( ( inverse @ sk_c6 )
= sk_c5 ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(53,plain,
( ( ( ( inverse @ sk_c2 )
= sk_c6 )
| ( ( multiply @ sk_c6 @ sk_c5 )
= sk_c7 ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(54,plain,
( ( ( ( multiply @ sk_c1 @ sk_c6 )
= sk_c7 )
| ( ( inverse @ sk_c4 )
= sk_c7 ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(55,plain,
( ( ( ( multiply @ sk_c1 @ sk_c6 )
= sk_c7 )
| ( ( multiply @ sk_c4 @ sk_c7 )
= sk_c5 ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(56,plain,
( ( ( ( multiply @ sk_c1 @ sk_c6 )
= sk_c7 )
| ( ( inverse @ sk_c3 )
= sk_c6 ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(57,plain,
( ( ( ( multiply @ sk_c1 @ sk_c6 )
= sk_c7 )
| ( ( multiply @ sk_c3 @ sk_c6 )
= sk_c7 ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(58,plain,
( ( ( ( multiply @ sk_c1 @ sk_c6 )
= sk_c7 )
| ( ( inverse @ sk_c6 )
= sk_c5 ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(59,plain,
( ( ( ( multiply @ sk_c1 @ sk_c6 )
= sk_c7 )
| ( ( multiply @ sk_c6 @ sk_c5 )
= sk_c7 ) )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(60,plain,
( ( ( ( inverse @ sk_c1 )
= sk_c7 )
| ( ( inverse @ sk_c4 )
= sk_c7 ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(61,plain,
( ( ( ( inverse @ sk_c1 )
= sk_c7 )
| ( ( multiply @ sk_c4 @ sk_c7 )
= sk_c5 ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(62,plain,
( ( ( ( inverse @ sk_c1 )
= sk_c7 )
| ( ( inverse @ sk_c3 )
= sk_c6 ) )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(63,plain,
( ( ( ( inverse @ sk_c1 )
= sk_c7 )
| ( ( multiply @ sk_c3 @ sk_c6 )
= sk_c7 ) )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(64,plain,
( ( ( ( inverse @ sk_c1 )
= sk_c7 )
| ( ( inverse @ sk_c6 )
= sk_c5 ) )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(65,plain,
( ( ( ( inverse @ sk_c1 )
= sk_c7 )
| ( ( multiply @ sk_c6 @ sk_c5 )
= sk_c7 ) )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(66,plain,
( ( ( ( multiply @ sk_c6 @ sk_c7 )
= sk_c5 )
| ( ( inverse @ sk_c4 )
= sk_c7 ) )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(67,plain,
( ( ( ( multiply @ sk_c6 @ sk_c7 )
= sk_c5 )
| ( ( multiply @ sk_c4 @ sk_c7 )
= sk_c5 ) )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(68,plain,
( ( ( ( multiply @ sk_c6 @ sk_c7 )
= sk_c5 )
| ( ( inverse @ sk_c3 )
= sk_c6 ) )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(69,plain,
( ( ( ( multiply @ sk_c6 @ sk_c7 )
= sk_c5 )
| ( ( multiply @ sk_c3 @ sk_c6 )
= sk_c7 ) )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(70,plain,
( ( ( ( multiply @ sk_c6 @ sk_c7 )
= sk_c5 )
| ( ( inverse @ sk_c6 )
= sk_c5 ) )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(71,plain,
( ( ( ( multiply @ sk_c6 @ sk_c7 )
= sk_c5 )
| ( ( multiply @ sk_c6 @ sk_c5 )
= sk_c7 ) )
= $true ),
inference(unfold_def,[status(thm)],[36]) ).
thf(72,plain,
( ( ~ $false )
= $true ),
inference(polarity_switch,[status(thm)],[37]) ).
thf(73,plain,
( ( ! [X3: $i,X4: $i] :
( ( ( multiply @ sk_c6 @ sk_c7 )
!= sk_c5 )
| ( ( inverse @ X3 )
!= sk_c7 )
| ( ( multiply @ X3 @ sk_c6 )
!= sk_c7 )
| ( ( inverse @ X4 )
!= sk_c6 )
| ( ( multiply @ X4 @ sk_c5 )
!= sk_c6 )
| ( ( multiply @ sk_c6 @ sk_c5 )
!= sk_c7 )
| ( ( inverse @ sk_c6 )
!= sk_c5 )
| ! [X1: $i] :
( ( ( multiply @ X1 @ sk_c6 )
!= sk_c7 )
| ( ( inverse @ X1 )
!= sk_c6 )
| ! [X2: $i] :
( ( ( multiply @ X2 @ sk_c7 )
!= sk_c5 )
| ( ( inverse @ X2 )
!= sk_c7 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[41]) ).
thf(74,plain,
( ( ( ( multiply @ sk_c6 @ sk_c7 )
= sk_c5 )
| ( ( multiply @ sk_c6 @ sk_c5 )
= sk_c7 ) )
= $true ),
inference(copy,[status(thm)],[71]) ).
thf(75,plain,
( ( ( ( multiply @ sk_c6 @ sk_c7 )
= sk_c5 )
| ( ( inverse @ sk_c6 )
= sk_c5 ) )
= $true ),
inference(copy,[status(thm)],[70]) ).
thf(76,plain,
( ( ( ( multiply @ sk_c6 @ sk_c7 )
= sk_c5 )
| ( ( multiply @ sk_c3 @ sk_c6 )
= sk_c7 ) )
= $true ),
inference(copy,[status(thm)],[69]) ).
thf(77,plain,
( ( ( ( multiply @ sk_c6 @ sk_c7 )
= sk_c5 )
| ( ( inverse @ sk_c3 )
= sk_c6 ) )
= $true ),
inference(copy,[status(thm)],[68]) ).
thf(78,plain,
( ( ( ( multiply @ sk_c6 @ sk_c7 )
= sk_c5 )
| ( ( multiply @ sk_c4 @ sk_c7 )
= sk_c5 ) )
= $true ),
inference(copy,[status(thm)],[67]) ).
thf(79,plain,
( ( ( ( multiply @ sk_c6 @ sk_c7 )
= sk_c5 )
| ( ( inverse @ sk_c4 )
= sk_c7 ) )
= $true ),
inference(copy,[status(thm)],[66]) ).
thf(80,plain,
( ( ( ( inverse @ sk_c1 )
= sk_c7 )
| ( ( multiply @ sk_c6 @ sk_c5 )
= sk_c7 ) )
= $true ),
inference(copy,[status(thm)],[65]) ).
thf(81,plain,
( ( ( ( inverse @ sk_c1 )
= sk_c7 )
| ( ( inverse @ sk_c6 )
= sk_c5 ) )
= $true ),
inference(copy,[status(thm)],[64]) ).
thf(82,plain,
( ( ( ( inverse @ sk_c1 )
= sk_c7 )
| ( ( multiply @ sk_c3 @ sk_c6 )
= sk_c7 ) )
= $true ),
inference(copy,[status(thm)],[63]) ).
thf(83,plain,
( ( ( ( inverse @ sk_c1 )
= sk_c7 )
| ( ( inverse @ sk_c3 )
= sk_c6 ) )
= $true ),
inference(copy,[status(thm)],[62]) ).
thf(84,plain,
( ( ( ( inverse @ sk_c1 )
= sk_c7 )
| ( ( multiply @ sk_c4 @ sk_c7 )
= sk_c5 ) )
= $true ),
inference(copy,[status(thm)],[61]) ).
thf(85,plain,
( ( ( ( inverse @ sk_c1 )
= sk_c7 )
| ( ( inverse @ sk_c4 )
= sk_c7 ) )
= $true ),
inference(copy,[status(thm)],[60]) ).
thf(86,plain,
( ( ( ( multiply @ sk_c1 @ sk_c6 )
= sk_c7 )
| ( ( multiply @ sk_c6 @ sk_c5 )
= sk_c7 ) )
= $true ),
inference(copy,[status(thm)],[59]) ).
thf(87,plain,
( ( ( ( multiply @ sk_c1 @ sk_c6 )
= sk_c7 )
| ( ( inverse @ sk_c6 )
= sk_c5 ) )
= $true ),
inference(copy,[status(thm)],[58]) ).
thf(88,plain,
( ( ( ( multiply @ sk_c1 @ sk_c6 )
= sk_c7 )
| ( ( multiply @ sk_c3 @ sk_c6 )
= sk_c7 ) )
= $true ),
inference(copy,[status(thm)],[57]) ).
thf(89,plain,
( ( ( ( multiply @ sk_c1 @ sk_c6 )
= sk_c7 )
| ( ( inverse @ sk_c3 )
= sk_c6 ) )
= $true ),
inference(copy,[status(thm)],[56]) ).
thf(90,plain,
( ( ( ( multiply @ sk_c1 @ sk_c6 )
= sk_c7 )
| ( ( multiply @ sk_c4 @ sk_c7 )
= sk_c5 ) )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(91,plain,
( ( ( ( multiply @ sk_c1 @ sk_c6 )
= sk_c7 )
| ( ( inverse @ sk_c4 )
= sk_c7 ) )
= $true ),
inference(copy,[status(thm)],[54]) ).
thf(92,plain,
( ( ( ( inverse @ sk_c2 )
= sk_c6 )
| ( ( multiply @ sk_c6 @ sk_c5 )
= sk_c7 ) )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(93,plain,
( ( ( ( inverse @ sk_c2 )
= sk_c6 )
| ( ( inverse @ sk_c6 )
= sk_c5 ) )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(94,plain,
( ( ( ( inverse @ sk_c2 )
= sk_c6 )
| ( ( multiply @ sk_c3 @ sk_c6 )
= sk_c7 ) )
= $true ),
inference(copy,[status(thm)],[51]) ).
thf(95,plain,
( ( ( ( inverse @ sk_c2 )
= sk_c6 )
| ( ( inverse @ sk_c3 )
= sk_c6 ) )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(96,plain,
( ( ( ( inverse @ sk_c2 )
= sk_c6 )
| ( ( multiply @ sk_c4 @ sk_c7 )
= sk_c5 ) )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(97,plain,
( ( ( ( inverse @ sk_c2 )
= sk_c6 )
| ( ( inverse @ sk_c4 )
= sk_c7 ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(98,plain,
( ( ( ( multiply @ sk_c2 @ sk_c5 )
= sk_c6 )
| ( ( multiply @ sk_c6 @ sk_c5 )
= sk_c7 ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(99,plain,
( ( ( ( multiply @ sk_c2 @ sk_c5 )
= sk_c6 )
| ( ( inverse @ sk_c6 )
= sk_c5 ) )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(100,plain,
( ( ( ( multiply @ sk_c2 @ sk_c5 )
= sk_c6 )
| ( ( multiply @ sk_c3 @ sk_c6 )
= sk_c7 ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(101,plain,
( ( ( ( multiply @ sk_c2 @ sk_c5 )
= sk_c6 )
| ( ( inverse @ sk_c3 )
= sk_c6 ) )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(102,plain,
( ( ( ( multiply @ sk_c2 @ sk_c5 )
= sk_c6 )
| ( ( multiply @ sk_c4 @ sk_c7 )
= sk_c5 ) )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(103,plain,
( ( ( ( multiply @ sk_c2 @ sk_c5 )
= sk_c6 )
| ( ( inverse @ sk_c4 )
= sk_c7 ) )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(104,plain,
( ( ! [X3: $i,X4: $i] :
( ( ( multiply @ sk_c6 @ sk_c7 )
!= sk_c5 )
| ( ( inverse @ X3 )
!= sk_c7 )
| ( ( multiply @ X3 @ sk_c6 )
!= sk_c7 )
| ( ( inverse @ X4 )
!= sk_c6 )
| ( ( multiply @ X4 @ sk_c5 )
!= sk_c6 )
| ( ( multiply @ sk_c6 @ sk_c5 )
!= sk_c7 )
| ( ( inverse @ sk_c6 )
!= sk_c5 )
| ! [X1: $i] :
( ( ( multiply @ X1 @ sk_c6 )
!= sk_c7 )
| ( ( inverse @ X1 )
!= sk_c6 )
| ! [X2: $i] :
( ( ( multiply @ X2 @ sk_c7 )
!= sk_c5 )
| ( ( inverse @ X2 )
!= sk_c7 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[73]) ).
thf(105,plain,
( ( ! [X: $i] :
( ( multiply @ identity @ X )
= X ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(106,plain,
( ( ! [X: $i] :
( ( multiply @ ( inverse @ X ) @ X )
= identity ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(107,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( multiply @ ( multiply @ X @ Y ) @ Z )
= ( multiply @ X @ ( multiply @ Y @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(108,plain,
( ( ~ $false )
= $true ),
inference(copy,[status(thm)],[72]) ).
thf(109,plain,
( ( ( ( multiply @ sk_c6 @ sk_c7 )
= sk_c5 )
= $true )
| ( ( ( multiply @ sk_c6 @ sk_c5 )
= sk_c7 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[74]) ).
thf(110,plain,
( ( ( ( multiply @ sk_c6 @ sk_c7 )
= sk_c5 )
= $true )
| ( ( ( inverse @ sk_c6 )
= sk_c5 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[75]) ).
thf(111,plain,
( ( ( ( multiply @ sk_c6 @ sk_c7 )
= sk_c5 )
= $true )
| ( ( ( multiply @ sk_c3 @ sk_c6 )
= sk_c7 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[76]) ).
thf(112,plain,
( ( ( ( multiply @ sk_c6 @ sk_c7 )
= sk_c5 )
= $true )
| ( ( ( inverse @ sk_c3 )
= sk_c6 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[77]) ).
thf(113,plain,
( ( ( ( multiply @ sk_c6 @ sk_c7 )
= sk_c5 )
= $true )
| ( ( ( multiply @ sk_c4 @ sk_c7 )
= sk_c5 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[78]) ).
thf(114,plain,
( ( ( ( multiply @ sk_c6 @ sk_c7 )
= sk_c5 )
= $true )
| ( ( ( inverse @ sk_c4 )
= sk_c7 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[79]) ).
thf(115,plain,
( ( ( ( inverse @ sk_c1 )
= sk_c7 )
= $true )
| ( ( ( multiply @ sk_c6 @ sk_c5 )
= sk_c7 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[80]) ).
thf(116,plain,
( ( ( ( inverse @ sk_c1 )
= sk_c7 )
= $true )
| ( ( ( inverse @ sk_c6 )
= sk_c5 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[81]) ).
thf(117,plain,
( ( ( ( inverse @ sk_c1 )
= sk_c7 )
= $true )
| ( ( ( multiply @ sk_c3 @ sk_c6 )
= sk_c7 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[82]) ).
thf(118,plain,
( ( ( ( inverse @ sk_c1 )
= sk_c7 )
= $true )
| ( ( ( inverse @ sk_c3 )
= sk_c6 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[83]) ).
thf(119,plain,
( ( ( ( inverse @ sk_c1 )
= sk_c7 )
= $true )
| ( ( ( multiply @ sk_c4 @ sk_c7 )
= sk_c5 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[84]) ).
thf(120,plain,
( ( ( ( inverse @ sk_c1 )
= sk_c7 )
= $true )
| ( ( ( inverse @ sk_c4 )
= sk_c7 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[85]) ).
thf(121,plain,
( ( ( ( multiply @ sk_c1 @ sk_c6 )
= sk_c7 )
= $true )
| ( ( ( multiply @ sk_c6 @ sk_c5 )
= sk_c7 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[86]) ).
thf(122,plain,
( ( ( ( multiply @ sk_c1 @ sk_c6 )
= sk_c7 )
= $true )
| ( ( ( inverse @ sk_c6 )
= sk_c5 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[87]) ).
thf(123,plain,
( ( ( ( multiply @ sk_c1 @ sk_c6 )
= sk_c7 )
= $true )
| ( ( ( multiply @ sk_c3 @ sk_c6 )
= sk_c7 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[88]) ).
thf(124,plain,
( ( ( ( multiply @ sk_c1 @ sk_c6 )
= sk_c7 )
= $true )
| ( ( ( inverse @ sk_c3 )
= sk_c6 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[89]) ).
thf(125,plain,
( ( ( ( multiply @ sk_c1 @ sk_c6 )
= sk_c7 )
= $true )
| ( ( ( multiply @ sk_c4 @ sk_c7 )
= sk_c5 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[90]) ).
thf(126,plain,
( ( ( ( multiply @ sk_c1 @ sk_c6 )
= sk_c7 )
= $true )
| ( ( ( inverse @ sk_c4 )
= sk_c7 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[91]) ).
thf(127,plain,
( ( ( ( inverse @ sk_c2 )
= sk_c6 )
= $true )
| ( ( ( multiply @ sk_c6 @ sk_c5 )
= sk_c7 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[92]) ).
thf(128,plain,
( ( ( ( inverse @ sk_c2 )
= sk_c6 )
= $true )
| ( ( ( inverse @ sk_c6 )
= sk_c5 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[93]) ).
thf(129,plain,
( ( ( ( inverse @ sk_c2 )
= sk_c6 )
= $true )
| ( ( ( multiply @ sk_c3 @ sk_c6 )
= sk_c7 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[94]) ).
thf(130,plain,
( ( ( ( inverse @ sk_c2 )
= sk_c6 )
= $true )
| ( ( ( inverse @ sk_c3 )
= sk_c6 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[95]) ).
thf(131,plain,
( ( ( ( inverse @ sk_c2 )
= sk_c6 )
= $true )
| ( ( ( multiply @ sk_c4 @ sk_c7 )
= sk_c5 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[96]) ).
thf(132,plain,
( ( ( ( inverse @ sk_c2 )
= sk_c6 )
= $true )
| ( ( ( inverse @ sk_c4 )
= sk_c7 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[97]) ).
thf(133,plain,
( ( ( ( multiply @ sk_c2 @ sk_c5 )
= sk_c6 )
= $true )
| ( ( ( multiply @ sk_c6 @ sk_c5 )
= sk_c7 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[98]) ).
thf(134,plain,
( ( ( ( multiply @ sk_c2 @ sk_c5 )
= sk_c6 )
= $true )
| ( ( ( inverse @ sk_c6 )
= sk_c5 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[99]) ).
thf(135,plain,
( ( ( ( multiply @ sk_c2 @ sk_c5 )
= sk_c6 )
= $true )
| ( ( ( multiply @ sk_c3 @ sk_c6 )
= sk_c7 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[100]) ).
thf(136,plain,
( ( ( ( multiply @ sk_c2 @ sk_c5 )
= sk_c6 )
= $true )
| ( ( ( inverse @ sk_c3 )
= sk_c6 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[101]) ).
thf(137,plain,
( ( ( ( multiply @ sk_c2 @ sk_c5 )
= sk_c6 )
= $true )
| ( ( ( multiply @ sk_c4 @ sk_c7 )
= sk_c5 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[102]) ).
thf(138,plain,
( ( ( ( multiply @ sk_c2 @ sk_c5 )
= sk_c6 )
= $true )
| ( ( ( inverse @ sk_c4 )
= sk_c7 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[103]) ).
thf(139,plain,
! [SV1: $i] :
( ( ! [SY9: $i] :
( ( ( multiply @ sk_c6 @ sk_c7 )
!= sk_c5 )
| ( ( inverse @ SV1 )
!= sk_c7 )
| ( ( multiply @ SV1 @ sk_c6 )
!= sk_c7 )
| ( ( inverse @ SY9 )
!= sk_c6 )
| ( ( multiply @ SY9 @ sk_c5 )
!= sk_c6 )
| ( ( multiply @ sk_c6 @ sk_c5 )
!= sk_c7 )
| ( ( inverse @ sk_c6 )
!= sk_c5 )
| ! [X1: $i] :
( ( ( multiply @ X1 @ sk_c6 )
!= sk_c7 )
| ( ( inverse @ X1 )
!= sk_c6 )
| ! [X2: $i] :
( ( ( multiply @ X2 @ sk_c7 )
!= sk_c5 )
| ( ( inverse @ X2 )
!= sk_c7 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[104]) ).
thf(140,plain,
! [SV2: $i] :
( ( ( multiply @ identity @ SV2 )
= SV2 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[105]) ).
thf(141,plain,
! [SV3: $i] :
( ( ( multiply @ ( inverse @ SV3 ) @ SV3 )
= identity )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[106]) ).
thf(142,plain,
! [SV4: $i] :
( ( ! [SY12: $i,SY13: $i] :
( ( multiply @ ( multiply @ SV4 @ SY12 ) @ SY13 )
= ( multiply @ SV4 @ ( multiply @ SY12 @ SY13 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[107]) ).
thf(143,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[108]) ).
thf(144,plain,
! [SV5: $i,SV1: $i] :
( ( ( ( multiply @ sk_c6 @ sk_c7 )
!= sk_c5 )
| ( ( inverse @ SV1 )
!= sk_c7 )
| ( ( multiply @ SV1 @ sk_c6 )
!= sk_c7 )
| ( ( inverse @ SV5 )
!= sk_c6 )
| ( ( multiply @ SV5 @ sk_c5 )
!= sk_c6 )
| ( ( multiply @ sk_c6 @ sk_c5 )
!= sk_c7 )
| ( ( inverse @ sk_c6 )
!= sk_c5 )
| ! [X1: $i] :
( ( ( multiply @ X1 @ sk_c6 )
!= sk_c7 )
| ( ( inverse @ X1 )
!= sk_c6 )
| ! [X2: $i] :
( ( ( multiply @ X2 @ sk_c7 )
!= sk_c5 )
| ( ( inverse @ X2 )
!= sk_c7 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[139]) ).
thf(145,plain,
! [SV6: $i,SV4: $i] :
( ( ! [SY16: $i] :
( ( multiply @ ( multiply @ SV4 @ SV6 ) @ SY16 )
= ( multiply @ SV4 @ ( multiply @ SV6 @ SY16 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[142]) ).
thf(146,plain,
! [SV5: $i,SV1: $i] :
( ( ( ( ( multiply @ sk_c6 @ sk_c7 )
!= sk_c5 ) )
= $true )
| ( ( ( ( inverse @ SV1 )
!= sk_c7 )
| ( ( multiply @ SV1 @ sk_c6 )
!= sk_c7 )
| ( ( inverse @ SV5 )
!= sk_c6 )
| ( ( multiply @ SV5 @ sk_c5 )
!= sk_c6 )
| ( ( multiply @ sk_c6 @ sk_c5 )
!= sk_c7 )
| ( ( inverse @ sk_c6 )
!= sk_c5 )
| ! [X1: $i] :
( ( ( multiply @ X1 @ sk_c6 )
!= sk_c7 )
| ( ( inverse @ X1 )
!= sk_c6 )
| ! [X2: $i] :
( ( ( multiply @ X2 @ sk_c7 )
!= sk_c5 )
| ( ( inverse @ X2 )
!= sk_c7 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[144]) ).
thf(147,plain,
! [SV7: $i,SV6: $i,SV4: $i] :
( ( ( multiply @ ( multiply @ SV4 @ SV6 ) @ SV7 )
= ( multiply @ SV4 @ ( multiply @ SV6 @ SV7 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[145]) ).
thf(148,plain,
! [SV5: $i,SV1: $i] :
( ( ( ( multiply @ sk_c6 @ sk_c7 )
= sk_c5 )
= $false )
| ( ( ( ( inverse @ SV1 )
!= sk_c7 )
| ( ( multiply @ SV1 @ sk_c6 )
!= sk_c7 )
| ( ( inverse @ SV5 )
!= sk_c6 )
| ( ( multiply @ SV5 @ sk_c5 )
!= sk_c6 )
| ( ( multiply @ sk_c6 @ sk_c5 )
!= sk_c7 )
| ( ( inverse @ sk_c6 )
!= sk_c5 )
| ! [X1: $i] :
( ( ( multiply @ X1 @ sk_c6 )
!= sk_c7 )
| ( ( inverse @ X1 )
!= sk_c6 )
| ! [X2: $i] :
( ( ( multiply @ X2 @ sk_c7 )
!= sk_c5 )
| ( ( inverse @ X2 )
!= sk_c7 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[146]) ).
thf(149,plain,
! [SV5: $i,SV1: $i] :
( ( ( ( ( inverse @ SV1 )
!= sk_c7 ) )
= $true )
| ( ( ( ( multiply @ SV1 @ sk_c6 )
!= sk_c7 )
| ( ( inverse @ SV5 )
!= sk_c6 )
| ( ( multiply @ SV5 @ sk_c5 )
!= sk_c6 )
| ( ( multiply @ sk_c6 @ sk_c5 )
!= sk_c7 )
| ( ( inverse @ sk_c6 )
!= sk_c5 )
| ! [X1: $i] :
( ( ( multiply @ X1 @ sk_c6 )
!= sk_c7 )
| ( ( inverse @ X1 )
!= sk_c6 )
| ! [X2: $i] :
( ( ( multiply @ X2 @ sk_c7 )
!= sk_c5 )
| ( ( inverse @ X2 )
!= sk_c7 ) ) ) )
= $true )
| ( ( ( multiply @ sk_c6 @ sk_c7 )
= sk_c5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[148]) ).
thf(150,plain,
! [SV5: $i,SV1: $i] :
( ( ( ( inverse @ SV1 )
= sk_c7 )
= $false )
| ( ( ( ( multiply @ SV1 @ sk_c6 )
!= sk_c7 )
| ( ( inverse @ SV5 )
!= sk_c6 )
| ( ( multiply @ SV5 @ sk_c5 )
!= sk_c6 )
| ( ( multiply @ sk_c6 @ sk_c5 )
!= sk_c7 )
| ( ( inverse @ sk_c6 )
!= sk_c5 )
| ! [X1: $i] :
( ( ( multiply @ X1 @ sk_c6 )
!= sk_c7 )
| ( ( inverse @ X1 )
!= sk_c6 )
| ! [X2: $i] :
( ( ( multiply @ X2 @ sk_c7 )
!= sk_c5 )
| ( ( inverse @ X2 )
!= sk_c7 ) ) ) )
= $true )
| ( ( ( multiply @ sk_c6 @ sk_c7 )
= sk_c5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[149]) ).
thf(151,plain,
! [SV5: $i,SV1: $i] :
( ( ( ( ( multiply @ SV1 @ sk_c6 )
!= sk_c7 ) )
= $true )
| ( ( ( ( inverse @ SV5 )
!= sk_c6 )
| ( ( multiply @ SV5 @ sk_c5 )
!= sk_c6 )
| ( ( multiply @ sk_c6 @ sk_c5 )
!= sk_c7 )
| ( ( inverse @ sk_c6 )
!= sk_c5 )
| ! [X1: $i] :
( ( ( multiply @ X1 @ sk_c6 )
!= sk_c7 )
| ( ( inverse @ X1 )
!= sk_c6 )
| ! [X2: $i] :
( ( ( multiply @ X2 @ sk_c7 )
!= sk_c5 )
| ( ( inverse @ X2 )
!= sk_c7 ) ) ) )
= $true )
| ( ( ( inverse @ SV1 )
= sk_c7 )
= $false )
| ( ( ( multiply @ sk_c6 @ sk_c7 )
= sk_c5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[150]) ).
thf(152,plain,
! [SV5: $i,SV1: $i] :
( ( ( ( multiply @ SV1 @ sk_c6 )
= sk_c7 )
= $false )
| ( ( ( ( inverse @ SV5 )
!= sk_c6 )
| ( ( multiply @ SV5 @ sk_c5 )
!= sk_c6 )
| ( ( multiply @ sk_c6 @ sk_c5 )
!= sk_c7 )
| ( ( inverse @ sk_c6 )
!= sk_c5 )
| ! [X1: $i] :
( ( ( multiply @ X1 @ sk_c6 )
!= sk_c7 )
| ( ( inverse @ X1 )
!= sk_c6 )
| ! [X2: $i] :
( ( ( multiply @ X2 @ sk_c7 )
!= sk_c5 )
| ( ( inverse @ X2 )
!= sk_c7 ) ) ) )
= $true )
| ( ( ( inverse @ SV1 )
= sk_c7 )
= $false )
| ( ( ( multiply @ sk_c6 @ sk_c7 )
= sk_c5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[151]) ).
thf(153,plain,
! [SV1: $i,SV5: $i] :
( ( ( ( ( inverse @ SV5 )
!= sk_c6 ) )
= $true )
| ( ( ( ( multiply @ SV5 @ sk_c5 )
!= sk_c6 )
| ( ( multiply @ sk_c6 @ sk_c5 )
!= sk_c7 )
| ( ( inverse @ sk_c6 )
!= sk_c5 )
| ! [X1: $i] :
( ( ( multiply @ X1 @ sk_c6 )
!= sk_c7 )
| ( ( inverse @ X1 )
!= sk_c6 )
| ! [X2: $i] :
( ( ( multiply @ X2 @ sk_c7 )
!= sk_c5 )
| ( ( inverse @ X2 )
!= sk_c7 ) ) ) )
= $true )
| ( ( ( multiply @ SV1 @ sk_c6 )
= sk_c7 )
= $false )
| ( ( ( inverse @ SV1 )
= sk_c7 )
= $false )
| ( ( ( multiply @ sk_c6 @ sk_c7 )
= sk_c5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[152]) ).
thf(154,plain,
! [SV1: $i,SV5: $i] :
( ( ( ( inverse @ SV5 )
= sk_c6 )
= $false )
| ( ( ( ( multiply @ SV5 @ sk_c5 )
!= sk_c6 )
| ( ( multiply @ sk_c6 @ sk_c5 )
!= sk_c7 )
| ( ( inverse @ sk_c6 )
!= sk_c5 )
| ! [X1: $i] :
( ( ( multiply @ X1 @ sk_c6 )
!= sk_c7 )
| ( ( inverse @ X1 )
!= sk_c6 )
| ! [X2: $i] :
( ( ( multiply @ X2 @ sk_c7 )
!= sk_c5 )
| ( ( inverse @ X2 )
!= sk_c7 ) ) ) )
= $true )
| ( ( ( multiply @ SV1 @ sk_c6 )
= sk_c7 )
= $false )
| ( ( ( inverse @ SV1 )
= sk_c7 )
= $false )
| ( ( ( multiply @ sk_c6 @ sk_c7 )
= sk_c5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[153]) ).
thf(155,plain,
! [SV1: $i,SV5: $i] :
( ( ( ( ( multiply @ SV5 @ sk_c5 )
!= sk_c6 ) )
= $true )
| ( ( ( ( multiply @ sk_c6 @ sk_c5 )
!= sk_c7 )
| ( ( inverse @ sk_c6 )
!= sk_c5 )
| ! [X1: $i] :
( ( ( multiply @ X1 @ sk_c6 )
!= sk_c7 )
| ( ( inverse @ X1 )
!= sk_c6 )
| ! [X2: $i] :
( ( ( multiply @ X2 @ sk_c7 )
!= sk_c5 )
| ( ( inverse @ X2 )
!= sk_c7 ) ) ) )
= $true )
| ( ( ( inverse @ SV5 )
= sk_c6 )
= $false )
| ( ( ( multiply @ SV1 @ sk_c6 )
= sk_c7 )
= $false )
| ( ( ( inverse @ SV1 )
= sk_c7 )
= $false )
| ( ( ( multiply @ sk_c6 @ sk_c7 )
= sk_c5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[154]) ).
thf(156,plain,
! [SV1: $i,SV5: $i] :
( ( ( ( multiply @ SV5 @ sk_c5 )
= sk_c6 )
= $false )
| ( ( ( ( multiply @ sk_c6 @ sk_c5 )
!= sk_c7 )
| ( ( inverse @ sk_c6 )
!= sk_c5 )
| ! [X1: $i] :
( ( ( multiply @ X1 @ sk_c6 )
!= sk_c7 )
| ( ( inverse @ X1 )
!= sk_c6 )
| ! [X2: $i] :
( ( ( multiply @ X2 @ sk_c7 )
!= sk_c5 )
| ( ( inverse @ X2 )
!= sk_c7 ) ) ) )
= $true )
| ( ( ( inverse @ SV5 )
= sk_c6 )
= $false )
| ( ( ( multiply @ SV1 @ sk_c6 )
= sk_c7 )
= $false )
| ( ( ( inverse @ SV1 )
= sk_c7 )
= $false )
| ( ( ( multiply @ sk_c6 @ sk_c7 )
= sk_c5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[155]) ).
thf(157,plain,
! [SV1: $i,SV5: $i] :
( ( ( ( ( multiply @ sk_c6 @ sk_c5 )
!= sk_c7 ) )
= $true )
| ( ( ( ( inverse @ sk_c6 )
!= sk_c5 )
| ! [X1: $i] :
( ( ( multiply @ X1 @ sk_c6 )
!= sk_c7 )
| ( ( inverse @ X1 )
!= sk_c6 )
| ! [X2: $i] :
( ( ( multiply @ X2 @ sk_c7 )
!= sk_c5 )
| ( ( inverse @ X2 )
!= sk_c7 ) ) ) )
= $true )
| ( ( ( multiply @ SV5 @ sk_c5 )
= sk_c6 )
= $false )
| ( ( ( inverse @ SV5 )
= sk_c6 )
= $false )
| ( ( ( multiply @ SV1 @ sk_c6 )
= sk_c7 )
= $false )
| ( ( ( inverse @ SV1 )
= sk_c7 )
= $false )
| ( ( ( multiply @ sk_c6 @ sk_c7 )
= sk_c5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[156]) ).
thf(158,plain,
! [SV1: $i,SV5: $i] :
( ( ( ( multiply @ sk_c6 @ sk_c5 )
= sk_c7 )
= $false )
| ( ( ( ( inverse @ sk_c6 )
!= sk_c5 )
| ! [X1: $i] :
( ( ( multiply @ X1 @ sk_c6 )
!= sk_c7 )
| ( ( inverse @ X1 )
!= sk_c6 )
| ! [X2: $i] :
( ( ( multiply @ X2 @ sk_c7 )
!= sk_c5 )
| ( ( inverse @ X2 )
!= sk_c7 ) ) ) )
= $true )
| ( ( ( multiply @ SV5 @ sk_c5 )
= sk_c6 )
= $false )
| ( ( ( inverse @ SV5 )
= sk_c6 )
= $false )
| ( ( ( multiply @ SV1 @ sk_c6 )
= sk_c7 )
= $false )
| ( ( ( inverse @ SV1 )
= sk_c7 )
= $false )
| ( ( ( multiply @ sk_c6 @ sk_c7 )
= sk_c5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[157]) ).
thf(159,plain,
! [SV1: $i,SV5: $i] :
( ( ( ( ( inverse @ sk_c6 )
!= sk_c5 ) )
= $true )
| ( ( ! [X1: $i] :
( ( ( multiply @ X1 @ sk_c6 )
!= sk_c7 )
| ( ( inverse @ X1 )
!= sk_c6 )
| ! [X2: $i] :
( ( ( multiply @ X2 @ sk_c7 )
!= sk_c5 )
| ( ( inverse @ X2 )
!= sk_c7 ) ) ) )
= $true )
| ( ( ( multiply @ sk_c6 @ sk_c5 )
= sk_c7 )
= $false )
| ( ( ( multiply @ SV5 @ sk_c5 )
= sk_c6 )
= $false )
| ( ( ( inverse @ SV5 )
= sk_c6 )
= $false )
| ( ( ( multiply @ SV1 @ sk_c6 )
= sk_c7 )
= $false )
| ( ( ( inverse @ SV1 )
= sk_c7 )
= $false )
| ( ( ( multiply @ sk_c6 @ sk_c7 )
= sk_c5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[158]) ).
thf(160,plain,
! [SV1: $i,SV5: $i] :
( ( ( ( inverse @ sk_c6 )
= sk_c5 )
= $false )
| ( ( ! [X1: $i] :
( ( ( multiply @ X1 @ sk_c6 )
!= sk_c7 )
| ( ( inverse @ X1 )
!= sk_c6 )
| ! [X2: $i] :
( ( ( multiply @ X2 @ sk_c7 )
!= sk_c5 )
| ( ( inverse @ X2 )
!= sk_c7 ) ) ) )
= $true )
| ( ( ( multiply @ sk_c6 @ sk_c5 )
= sk_c7 )
= $false )
| ( ( ( multiply @ SV5 @ sk_c5 )
= sk_c6 )
= $false )
| ( ( ( inverse @ SV5 )
= sk_c6 )
= $false )
| ( ( ( multiply @ SV1 @ sk_c6 )
= sk_c7 )
= $false )
| ( ( ( inverse @ SV1 )
= sk_c7 )
= $false )
| ( ( ( multiply @ sk_c6 @ sk_c7 )
= sk_c5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[159]) ).
thf(161,plain,
! [SV1: $i,SV5: $i,SV8: $i] :
( ( ( ( ( multiply @ SV8 @ sk_c6 )
!= sk_c7 )
| ( ( inverse @ SV8 )
!= sk_c6 )
| ! [X2: $i] :
( ( ( multiply @ X2 @ sk_c7 )
!= sk_c5 )
| ( ( inverse @ X2 )
!= sk_c7 ) ) )
= $true )
| ( ( ( inverse @ sk_c6 )
= sk_c5 )
= $false )
| ( ( ( multiply @ sk_c6 @ sk_c5 )
= sk_c7 )
= $false )
| ( ( ( multiply @ SV5 @ sk_c5 )
= sk_c6 )
= $false )
| ( ( ( inverse @ SV5 )
= sk_c6 )
= $false )
| ( ( ( multiply @ SV1 @ sk_c6 )
= sk_c7 )
= $false )
| ( ( ( inverse @ SV1 )
= sk_c7 )
= $false )
| ( ( ( multiply @ sk_c6 @ sk_c7 )
= sk_c5 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[160]) ).
thf(162,plain,
! [SV1: $i,SV5: $i,SV8: $i] :
( ( ( ( ( multiply @ SV8 @ sk_c6 )
!= sk_c7 ) )
= $true )
| ( ( ( ( inverse @ SV8 )
!= sk_c6 )
| ! [X2: $i] :
( ( ( multiply @ X2 @ sk_c7 )
!= sk_c5 )
| ( ( inverse @ X2 )
!= sk_c7 ) ) )
= $true )
| ( ( ( inverse @ sk_c6 )
= sk_c5 )
= $false )
| ( ( ( multiply @ sk_c6 @ sk_c5 )
= sk_c7 )
= $false )
| ( ( ( multiply @ SV5 @ sk_c5 )
= sk_c6 )
= $false )
| ( ( ( inverse @ SV5 )
= sk_c6 )
= $false )
| ( ( ( multiply @ SV1 @ sk_c6 )
= sk_c7 )
= $false )
| ( ( ( inverse @ SV1 )
= sk_c7 )
= $false )
| ( ( ( multiply @ sk_c6 @ sk_c7 )
= sk_c5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[161]) ).
thf(163,plain,
! [SV1: $i,SV5: $i,SV8: $i] :
( ( ( ( multiply @ SV8 @ sk_c6 )
= sk_c7 )
= $false )
| ( ( ( ( inverse @ SV8 )
!= sk_c6 )
| ! [X2: $i] :
( ( ( multiply @ X2 @ sk_c7 )
!= sk_c5 )
| ( ( inverse @ X2 )
!= sk_c7 ) ) )
= $true )
| ( ( ( inverse @ sk_c6 )
= sk_c5 )
= $false )
| ( ( ( multiply @ sk_c6 @ sk_c5 )
= sk_c7 )
= $false )
| ( ( ( multiply @ SV5 @ sk_c5 )
= sk_c6 )
= $false )
| ( ( ( inverse @ SV5 )
= sk_c6 )
= $false )
| ( ( ( multiply @ SV1 @ sk_c6 )
= sk_c7 )
= $false )
| ( ( ( inverse @ SV1 )
= sk_c7 )
= $false )
| ( ( ( multiply @ sk_c6 @ sk_c7 )
= sk_c5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[162]) ).
thf(164,plain,
! [SV1: $i,SV5: $i,SV8: $i] :
( ( ( ( ( inverse @ SV8 )
!= sk_c6 ) )
= $true )
| ( ( ! [X2: $i] :
( ( ( multiply @ X2 @ sk_c7 )
!= sk_c5 )
| ( ( inverse @ X2 )
!= sk_c7 ) ) )
= $true )
| ( ( ( multiply @ SV8 @ sk_c6 )
= sk_c7 )
= $false )
| ( ( ( inverse @ sk_c6 )
= sk_c5 )
= $false )
| ( ( ( multiply @ sk_c6 @ sk_c5 )
= sk_c7 )
= $false )
| ( ( ( multiply @ SV5 @ sk_c5 )
= sk_c6 )
= $false )
| ( ( ( inverse @ SV5 )
= sk_c6 )
= $false )
| ( ( ( multiply @ SV1 @ sk_c6 )
= sk_c7 )
= $false )
| ( ( ( inverse @ SV1 )
= sk_c7 )
= $false )
| ( ( ( multiply @ sk_c6 @ sk_c7 )
= sk_c5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[163]) ).
thf(165,plain,
! [SV1: $i,SV5: $i,SV8: $i] :
( ( ( ( inverse @ SV8 )
= sk_c6 )
= $false )
| ( ( ! [X2: $i] :
( ( ( multiply @ X2 @ sk_c7 )
!= sk_c5 )
| ( ( inverse @ X2 )
!= sk_c7 ) ) )
= $true )
| ( ( ( multiply @ SV8 @ sk_c6 )
= sk_c7 )
= $false )
| ( ( ( inverse @ sk_c6 )
= sk_c5 )
= $false )
| ( ( ( multiply @ sk_c6 @ sk_c5 )
= sk_c7 )
= $false )
| ( ( ( multiply @ SV5 @ sk_c5 )
= sk_c6 )
= $false )
| ( ( ( inverse @ SV5 )
= sk_c6 )
= $false )
| ( ( ( multiply @ SV1 @ sk_c6 )
= sk_c7 )
= $false )
| ( ( ( inverse @ SV1 )
= sk_c7 )
= $false )
| ( ( ( multiply @ sk_c6 @ sk_c7 )
= sk_c5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[164]) ).
thf(166,plain,
! [SV1: $i,SV5: $i,SV8: $i,SV9: $i] :
( ( ( ( ( multiply @ SV9 @ sk_c7 )
!= sk_c5 )
| ( ( inverse @ SV9 )
!= sk_c7 ) )
= $true )
| ( ( ( inverse @ SV8 )
= sk_c6 )
= $false )
| ( ( ( multiply @ SV8 @ sk_c6 )
= sk_c7 )
= $false )
| ( ( ( inverse @ sk_c6 )
= sk_c5 )
= $false )
| ( ( ( multiply @ sk_c6 @ sk_c5 )
= sk_c7 )
= $false )
| ( ( ( multiply @ SV5 @ sk_c5 )
= sk_c6 )
= $false )
| ( ( ( inverse @ SV5 )
= sk_c6 )
= $false )
| ( ( ( multiply @ SV1 @ sk_c6 )
= sk_c7 )
= $false )
| ( ( ( inverse @ SV1 )
= sk_c7 )
= $false )
| ( ( ( multiply @ sk_c6 @ sk_c7 )
= sk_c5 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[165]) ).
thf(167,plain,
! [SV1: $i,SV5: $i,SV8: $i,SV9: $i] :
( ( ( ( ( multiply @ SV9 @ sk_c7 )
!= sk_c5 ) )
= $true )
| ( ( ( ( inverse @ SV9 )
!= sk_c7 ) )
= $true )
| ( ( ( inverse @ SV8 )
= sk_c6 )
= $false )
| ( ( ( multiply @ SV8 @ sk_c6 )
= sk_c7 )
= $false )
| ( ( ( inverse @ sk_c6 )
= sk_c5 )
= $false )
| ( ( ( multiply @ sk_c6 @ sk_c5 )
= sk_c7 )
= $false )
| ( ( ( multiply @ SV5 @ sk_c5 )
= sk_c6 )
= $false )
| ( ( ( inverse @ SV5 )
= sk_c6 )
= $false )
| ( ( ( multiply @ SV1 @ sk_c6 )
= sk_c7 )
= $false )
| ( ( ( inverse @ SV1 )
= sk_c7 )
= $false )
| ( ( ( multiply @ sk_c6 @ sk_c7 )
= sk_c5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[166]) ).
thf(168,plain,
! [SV1: $i,SV5: $i,SV8: $i,SV9: $i] :
( ( ( ( multiply @ SV9 @ sk_c7 )
= sk_c5 )
= $false )
| ( ( ( ( inverse @ SV9 )
!= sk_c7 ) )
= $true )
| ( ( ( inverse @ SV8 )
= sk_c6 )
= $false )
| ( ( ( multiply @ SV8 @ sk_c6 )
= sk_c7 )
= $false )
| ( ( ( inverse @ sk_c6 )
= sk_c5 )
= $false )
| ( ( ( multiply @ sk_c6 @ sk_c5 )
= sk_c7 )
= $false )
| ( ( ( multiply @ SV5 @ sk_c5 )
= sk_c6 )
= $false )
| ( ( ( inverse @ SV5 )
= sk_c6 )
= $false )
| ( ( ( multiply @ SV1 @ sk_c6 )
= sk_c7 )
= $false )
| ( ( ( inverse @ SV1 )
= sk_c7 )
= $false )
| ( ( ( multiply @ sk_c6 @ sk_c7 )
= sk_c5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[167]) ).
thf(169,plain,
! [SV1: $i,SV5: $i,SV8: $i,SV9: $i] :
( ( ( ( inverse @ SV9 )
= sk_c7 )
= $false )
| ( ( ( multiply @ SV9 @ sk_c7 )
= sk_c5 )
= $false )
| ( ( ( inverse @ SV8 )
= sk_c6 )
= $false )
| ( ( ( multiply @ SV8 @ sk_c6 )
= sk_c7 )
= $false )
| ( ( ( inverse @ sk_c6 )
= sk_c5 )
= $false )
| ( ( ( multiply @ sk_c6 @ sk_c5 )
= sk_c7 )
= $false )
| ( ( ( multiply @ SV5 @ sk_c5 )
= sk_c6 )
= $false )
| ( ( ( inverse @ SV5 )
= sk_c6 )
= $false )
| ( ( ( multiply @ SV1 @ sk_c6 )
= sk_c7 )
= $false )
| ( ( ( inverse @ SV1 )
= sk_c7 )
= $false )
| ( ( ( multiply @ sk_c6 @ sk_c7 )
= sk_c5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[168]) ).
thf(170,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[109,169,147,143,141,140,138,137,136,135,134,133,132,131,130,129,128,127,126,125,124,123,122,121,120,119,118,117,116,115,114,113,112,111,110]) ).
thf(171,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[170]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP347-1 : TPTP v8.1.0. Released v2.5.0.
% 0.07/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.34 % Computer : n029.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jun 13 08:12:10 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.36
% 0.13/0.36 No.of.Axioms: 34
% 0.13/0.36
% 0.13/0.36 Length.of.Defs: 0
% 0.13/0.36
% 0.13/0.36 Contains.Choice.Funs: false
% 0.13/0.37 (rf:0,axioms:34,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:36,loop_count:0,foatp_calls:0,translation:fof_full).......
% 36.42/36.61
% 36.42/36.61 ********************************
% 36.42/36.61 * All subproblems solved! *
% 36.42/36.61 ********************************
% 36.42/36.61 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:34,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:170,loop_count:0,foatp_calls:1,translation:fof_full)
% 36.42/36.62
% 36.42/36.62 %**** Beginning of derivation protocol ****
% 36.42/36.62 % SZS output start CNFRefutation
% See solution above
% 36.42/36.62
% 36.42/36.62 %**** End of derivation protocol ****
% 36.42/36.62 %**** no. of clauses in derivation: 171 ****
% 36.42/36.62 %**** clause counter: 170 ****
% 36.42/36.62
% 36.42/36.62 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:34,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:170,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------