TSTP Solution File: BOO004-10 by LEO-II---1.7.0
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%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : BOO004-10 : TPTP v8.1.0. Released v7.5.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n024.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 : Thu Jul 14 23:43:28 EDT 2022
% Result : Unsatisfiable 39.41s 39.61s
% Output : CNFRefutation 39.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 37
% Syntax : Number of formulae : 184 ( 173 unt; 11 typ; 0 def)
% Number of atoms : 465 ( 311 equ; 0 cnn)
% Maximal formula atoms : 1 ( 2 avg)
% Number of connectives : 3027 ( 6 ~; 0 |; 0 &;3021 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 19 ( 19 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 11 usr; 6 con; 0-4 aty)
% Number of variables : 740 ( 0 ^ 740 !; 0 ?; 740 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_add,type,
add: $i > $i > $i ).
thf(tp_additive_identity,type,
additive_identity: $i ).
thf(tp_ifeq,type,
ifeq: $i > $i > $i > $i > $i ).
thf(tp_ifeq2,type,
ifeq2: $i > $i > $i > $i > $i ).
thf(tp_inverse,type,
inverse: $i > $i ).
thf(tp_multiplicative_identity,type,
multiplicative_identity: $i ).
thf(tp_multiply,type,
multiply: $i > $i > $i ).
thf(tp_product,type,
product: $i > $i > $i > $i ).
thf(tp_sum,type,
sum: $i > $i > $i > $i ).
thf(tp_true,type,
true: $i ).
thf(tp_x,type,
x: $i ).
thf(1,axiom,
! [X: $i,Y: $i,V: $i,U: $i] :
( ( ifeq2 @ ( product @ X @ Y @ V ) @ true @ ( ifeq2 @ ( product @ X @ Y @ U ) @ true @ U @ V ) @ V )
= V ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplication_is_well_defined) ).
thf(2,axiom,
! [X: $i,Y: $i,V: $i,U: $i] :
( ( ifeq2 @ ( sum @ X @ Y @ V ) @ true @ ( ifeq2 @ ( sum @ X @ Y @ U ) @ true @ U @ V ) @ V )
= V ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',addition_is_well_defined) ).
thf(3,axiom,
! [X: $i] :
( ( product @ X @ ( inverse @ X ) @ additive_identity )
= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_inverse2) ).
thf(4,axiom,
! [X: $i] :
( ( product @ ( inverse @ X ) @ X @ additive_identity )
= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_inverse1) ).
thf(5,axiom,
! [X: $i] :
( ( sum @ X @ ( inverse @ X ) @ multiplicative_identity )
= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_inverse2) ).
thf(6,axiom,
! [X: $i] :
( ( sum @ ( inverse @ X ) @ X @ multiplicative_identity )
= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_inverse1) ).
thf(7,axiom,
! [V1: $i,V2: $i,V4: $i,Y: $i,Z: $i,V3: $i,X: $i] :
( ( ifeq @ ( product @ V1 @ V2 @ V4 ) @ true @ ( ifeq @ ( product @ Y @ Z @ V3 ) @ true @ ( ifeq @ ( sum @ Z @ X @ V2 ) @ true @ ( ifeq @ ( sum @ Y @ X @ V1 ) @ true @ ( sum @ V3 @ X @ V4 ) @ true ) @ true ) @ true ) @ true )
= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity8) ).
thf(8,axiom,
! [Y: $i,Z: $i,V3: $i,X: $i,V4: $i,V2: $i,V1: $i] :
( ( ifeq @ ( product @ Y @ Z @ V3 ) @ true @ ( ifeq @ ( sum @ V3 @ X @ V4 ) @ true @ ( ifeq @ ( sum @ Z @ X @ V2 ) @ true @ ( ifeq @ ( sum @ Y @ X @ V1 ) @ true @ ( product @ V1 @ V2 @ V4 ) @ true ) @ true ) @ true ) @ true )
= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity7) ).
thf(9,axiom,
! [V1: $i,V2: $i,V4: $i,Y: $i,Z: $i,V3: $i,X: $i] :
( ( ifeq @ ( product @ V1 @ V2 @ V4 ) @ true @ ( ifeq @ ( product @ Y @ Z @ V3 ) @ true @ ( ifeq @ ( sum @ X @ Z @ V2 ) @ true @ ( ifeq @ ( sum @ X @ Y @ V1 ) @ true @ ( sum @ X @ V3 @ V4 ) @ true ) @ true ) @ true ) @ true )
= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity6) ).
thf(10,axiom,
! [Y: $i,Z: $i,V3: $i,X: $i,V4: $i,V2: $i,V1: $i] :
( ( ifeq @ ( product @ Y @ Z @ V3 ) @ true @ ( ifeq @ ( sum @ X @ V3 @ V4 ) @ true @ ( ifeq @ ( sum @ X @ Z @ V2 ) @ true @ ( ifeq @ ( sum @ X @ Y @ V1 ) @ true @ ( product @ V1 @ V2 @ V4 ) @ true ) @ true ) @ true ) @ true )
= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity5) ).
thf(11,axiom,
! [Z: $i,X: $i,V2: $i,Y: $i,V1: $i,V4: $i,V3: $i] :
( ( ifeq @ ( product @ Z @ X @ V2 ) @ true @ ( ifeq @ ( product @ Y @ X @ V1 ) @ true @ ( ifeq @ ( sum @ V1 @ V2 @ V4 ) @ true @ ( ifeq @ ( sum @ Y @ Z @ V3 ) @ true @ ( product @ V3 @ X @ V4 ) @ true ) @ true ) @ true ) @ true )
= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity4) ).
thf(12,axiom,
! [V3: $i,X: $i,V4: $i,Z: $i,V2: $i,Y: $i,V1: $i] :
( ( ifeq @ ( product @ V3 @ X @ V4 ) @ true @ ( ifeq @ ( product @ Z @ X @ V2 ) @ true @ ( ifeq @ ( product @ Y @ X @ V1 ) @ true @ ( ifeq @ ( sum @ Y @ Z @ V3 ) @ true @ ( sum @ V1 @ V2 @ V4 ) @ true ) @ true ) @ true ) @ true )
= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity3) ).
thf(13,axiom,
! [X: $i,Z: $i,V2: $i,Y: $i,V1: $i,V4: $i,V3: $i] :
( ( ifeq @ ( product @ X @ Z @ V2 ) @ true @ ( ifeq @ ( product @ X @ Y @ V1 ) @ true @ ( ifeq @ ( sum @ V1 @ V2 @ V4 ) @ true @ ( ifeq @ ( sum @ Y @ Z @ V3 ) @ true @ ( product @ X @ V3 @ V4 ) @ true ) @ true ) @ true ) @ true )
= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity2) ).
thf(14,axiom,
! [X: $i,V3: $i,V4: $i,Z: $i,V2: $i,Y: $i,V1: $i] :
( ( ifeq @ ( product @ X @ V3 @ V4 ) @ true @ ( ifeq @ ( product @ X @ Z @ V2 ) @ true @ ( ifeq @ ( product @ X @ Y @ V1 ) @ true @ ( ifeq @ ( sum @ Y @ Z @ V3 ) @ true @ ( sum @ V1 @ V2 @ V4 ) @ true ) @ true ) @ true ) @ true )
= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity1) ).
thf(15,axiom,
! [X: $i] :
( ( product @ X @ multiplicative_identity @ X )
= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_identity2) ).
thf(16,axiom,
! [X: $i] :
( ( product @ multiplicative_identity @ X @ X )
= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_identity1) ).
thf(17,axiom,
! [X: $i] :
( ( sum @ X @ additive_identity @ X )
= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_identity2) ).
thf(18,axiom,
! [X: $i] :
( ( sum @ additive_identity @ X @ X )
= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_identity1) ).
thf(19,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( ifeq @ ( product @ X @ Y @ Z ) @ true @ ( product @ Y @ X @ Z ) @ true )
= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_multiplication) ).
thf(20,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( ifeq @ ( sum @ X @ Y @ Z ) @ true @ ( sum @ Y @ X @ Z ) @ true )
= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_addition) ).
thf(21,axiom,
! [X: $i,Y: $i] :
( ( product @ X @ Y @ ( multiply @ X @ Y ) )
= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',closure_of_multiplication) ).
thf(22,axiom,
! [X: $i,Y: $i] :
( ( sum @ X @ Y @ ( add @ X @ Y ) )
= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',closure_of_addition) ).
thf(23,axiom,
! [A: $i,B: $i,C: $i] :
( ( ifeq @ A @ A @ B @ C )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom_001) ).
thf(24,axiom,
! [A: $i,B: $i,C: $i] :
( ( ifeq2 @ A @ A @ B @ C )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom) ).
thf(25,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(26,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[25]) ).
thf(27,negated_conjecture,
( sum @ x @ x @ x )
!= true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_both_equalities) ).
thf(28,plain,
$false = $false,
inference(unfold_def,[status(thm)],[26]) ).
thf(29,plain,
( ( ! [X: $i,Y: $i,V: $i,U: $i] :
( ( ifeq2 @ ( product @ X @ Y @ V ) @ true @ ( ifeq2 @ ( product @ X @ Y @ U ) @ true @ U @ V ) @ V )
= V ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(30,plain,
( ( ! [X: $i,Y: $i,V: $i,U: $i] :
( ( ifeq2 @ ( sum @ X @ Y @ V ) @ true @ ( ifeq2 @ ( sum @ X @ Y @ U ) @ true @ U @ V ) @ V )
= V ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(31,plain,
( ( ! [X: $i] :
( ( product @ X @ ( inverse @ X ) @ additive_identity )
= true ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(32,plain,
( ( ! [X: $i] :
( ( product @ ( inverse @ X ) @ X @ additive_identity )
= true ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(33,plain,
( ( ! [X: $i] :
( ( sum @ X @ ( inverse @ X ) @ multiplicative_identity )
= true ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(34,plain,
( ( ! [X: $i] :
( ( sum @ ( inverse @ X ) @ X @ multiplicative_identity )
= true ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(35,plain,
( ( ! [V1: $i,V2: $i,V4: $i,Y: $i,Z: $i,V3: $i,X: $i] :
( ( ifeq @ ( product @ V1 @ V2 @ V4 ) @ true @ ( ifeq @ ( product @ Y @ Z @ V3 ) @ true @ ( ifeq @ ( sum @ Z @ X @ V2 ) @ true @ ( ifeq @ ( sum @ Y @ X @ V1 ) @ true @ ( sum @ V3 @ X @ V4 ) @ true ) @ true ) @ true ) @ true )
= true ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(36,plain,
( ( ! [Y: $i,Z: $i,V3: $i,X: $i,V4: $i,V2: $i,V1: $i] :
( ( ifeq @ ( product @ Y @ Z @ V3 ) @ true @ ( ifeq @ ( sum @ V3 @ X @ V4 ) @ true @ ( ifeq @ ( sum @ Z @ X @ V2 ) @ true @ ( ifeq @ ( sum @ Y @ X @ V1 ) @ true @ ( product @ V1 @ V2 @ V4 ) @ true ) @ true ) @ true ) @ true )
= true ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(37,plain,
( ( ! [V1: $i,V2: $i,V4: $i,Y: $i,Z: $i,V3: $i,X: $i] :
( ( ifeq @ ( product @ V1 @ V2 @ V4 ) @ true @ ( ifeq @ ( product @ Y @ Z @ V3 ) @ true @ ( ifeq @ ( sum @ X @ Z @ V2 ) @ true @ ( ifeq @ ( sum @ X @ Y @ V1 ) @ true @ ( sum @ X @ V3 @ V4 ) @ true ) @ true ) @ true ) @ true )
= true ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(38,plain,
( ( ! [Y: $i,Z: $i,V3: $i,X: $i,V4: $i,V2: $i,V1: $i] :
( ( ifeq @ ( product @ Y @ Z @ V3 ) @ true @ ( ifeq @ ( sum @ X @ V3 @ V4 ) @ true @ ( ifeq @ ( sum @ X @ Z @ V2 ) @ true @ ( ifeq @ ( sum @ X @ Y @ V1 ) @ true @ ( product @ V1 @ V2 @ V4 ) @ true ) @ true ) @ true ) @ true )
= true ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(39,plain,
( ( ! [Z: $i,X: $i,V2: $i,Y: $i,V1: $i,V4: $i,V3: $i] :
( ( ifeq @ ( product @ Z @ X @ V2 ) @ true @ ( ifeq @ ( product @ Y @ X @ V1 ) @ true @ ( ifeq @ ( sum @ V1 @ V2 @ V4 ) @ true @ ( ifeq @ ( sum @ Y @ Z @ V3 ) @ true @ ( product @ V3 @ X @ V4 ) @ true ) @ true ) @ true ) @ true )
= true ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(40,plain,
( ( ! [V3: $i,X: $i,V4: $i,Z: $i,V2: $i,Y: $i,V1: $i] :
( ( ifeq @ ( product @ V3 @ X @ V4 ) @ true @ ( ifeq @ ( product @ Z @ X @ V2 ) @ true @ ( ifeq @ ( product @ Y @ X @ V1 ) @ true @ ( ifeq @ ( sum @ Y @ Z @ V3 ) @ true @ ( sum @ V1 @ V2 @ V4 ) @ true ) @ true ) @ true ) @ true )
= true ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(41,plain,
( ( ! [X: $i,Z: $i,V2: $i,Y: $i,V1: $i,V4: $i,V3: $i] :
( ( ifeq @ ( product @ X @ Z @ V2 ) @ true @ ( ifeq @ ( product @ X @ Y @ V1 ) @ true @ ( ifeq @ ( sum @ V1 @ V2 @ V4 ) @ true @ ( ifeq @ ( sum @ Y @ Z @ V3 ) @ true @ ( product @ X @ V3 @ V4 ) @ true ) @ true ) @ true ) @ true )
= true ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(42,plain,
( ( ! [X: $i,V3: $i,V4: $i,Z: $i,V2: $i,Y: $i,V1: $i] :
( ( ifeq @ ( product @ X @ V3 @ V4 ) @ true @ ( ifeq @ ( product @ X @ Z @ V2 ) @ true @ ( ifeq @ ( product @ X @ Y @ V1 ) @ true @ ( ifeq @ ( sum @ Y @ Z @ V3 ) @ true @ ( sum @ V1 @ V2 @ V4 ) @ true ) @ true ) @ true ) @ true )
= true ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(43,plain,
( ( ! [X: $i] :
( ( product @ X @ multiplicative_identity @ X )
= true ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(44,plain,
( ( ! [X: $i] :
( ( product @ multiplicative_identity @ X @ X )
= true ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(45,plain,
( ( ! [X: $i] :
( ( sum @ X @ additive_identity @ X )
= true ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(46,plain,
( ( ! [X: $i] :
( ( sum @ additive_identity @ X @ X )
= true ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(47,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( ifeq @ ( product @ X @ Y @ Z ) @ true @ ( product @ Y @ X @ Z ) @ true )
= true ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(48,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( ifeq @ ( sum @ X @ Y @ Z ) @ true @ ( sum @ Y @ X @ Z ) @ true )
= true ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(49,plain,
( ( ! [X: $i,Y: $i] :
( ( product @ X @ Y @ ( multiply @ X @ Y ) )
= true ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(50,plain,
( ( ! [X: $i,Y: $i] :
( ( sum @ X @ Y @ ( add @ X @ Y ) )
= true ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(51,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ifeq @ A @ A @ B @ C )
= B ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(52,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ifeq2 @ A @ A @ B @ C )
= B ) )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(53,plain,
( ( ( ( sum @ x @ x @ x )
!= true ) )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(54,plain,
( ( ~ $false )
= $true ),
inference(polarity_switch,[status(thm)],[28]) ).
thf(55,plain,
( ( ( ( sum @ x @ x @ x )
!= true ) )
= $true ),
inference(extcnf_combined,[status(esa)],[53]) ).
thf(56,plain,
( ( ( ( sum @ x @ x @ x )
!= true ) )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(57,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ifeq2 @ A @ A @ B @ C )
= B ) )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(58,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ifeq @ A @ A @ B @ C )
= B ) )
= $true ),
inference(copy,[status(thm)],[51]) ).
thf(59,plain,
( ( ! [X: $i,Y: $i] :
( ( sum @ X @ Y @ ( add @ X @ Y ) )
= true ) )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(60,plain,
( ( ! [X: $i,Y: $i] :
( ( product @ X @ Y @ ( multiply @ X @ Y ) )
= true ) )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(61,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( ifeq @ ( sum @ X @ Y @ Z ) @ true @ ( sum @ Y @ X @ Z ) @ true )
= true ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(62,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( ifeq @ ( product @ X @ Y @ Z ) @ true @ ( product @ Y @ X @ Z ) @ true )
= true ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(63,plain,
( ( ! [X: $i] :
( ( sum @ additive_identity @ X @ X )
= true ) )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(64,plain,
( ( ! [X: $i] :
( ( sum @ X @ additive_identity @ X )
= true ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(65,plain,
( ( ! [X: $i] :
( ( product @ multiplicative_identity @ X @ X )
= true ) )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(66,plain,
( ( ! [X: $i] :
( ( product @ X @ multiplicative_identity @ X )
= true ) )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(67,plain,
( ( ! [X: $i,V3: $i,V4: $i,Z: $i,V2: $i,Y: $i,V1: $i] :
( ( ifeq @ ( product @ X @ V3 @ V4 ) @ true @ ( ifeq @ ( product @ X @ Z @ V2 ) @ true @ ( ifeq @ ( product @ X @ Y @ V1 ) @ true @ ( ifeq @ ( sum @ Y @ Z @ V3 ) @ true @ ( sum @ V1 @ V2 @ V4 ) @ true ) @ true ) @ true ) @ true )
= true ) )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(68,plain,
( ( ! [X: $i,Z: $i,V2: $i,Y: $i,V1: $i,V4: $i,V3: $i] :
( ( ifeq @ ( product @ X @ Z @ V2 ) @ true @ ( ifeq @ ( product @ X @ Y @ V1 ) @ true @ ( ifeq @ ( sum @ V1 @ V2 @ V4 ) @ true @ ( ifeq @ ( sum @ Y @ Z @ V3 ) @ true @ ( product @ X @ V3 @ V4 ) @ true ) @ true ) @ true ) @ true )
= true ) )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(69,plain,
( ( ! [V3: $i,X: $i,V4: $i,Z: $i,V2: $i,Y: $i,V1: $i] :
( ( ifeq @ ( product @ V3 @ X @ V4 ) @ true @ ( ifeq @ ( product @ Z @ X @ V2 ) @ true @ ( ifeq @ ( product @ Y @ X @ V1 ) @ true @ ( ifeq @ ( sum @ Y @ Z @ V3 ) @ true @ ( sum @ V1 @ V2 @ V4 ) @ true ) @ true ) @ true ) @ true )
= true ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(70,plain,
( ( ! [Z: $i,X: $i,V2: $i,Y: $i,V1: $i,V4: $i,V3: $i] :
( ( ifeq @ ( product @ Z @ X @ V2 ) @ true @ ( ifeq @ ( product @ Y @ X @ V1 ) @ true @ ( ifeq @ ( sum @ V1 @ V2 @ V4 ) @ true @ ( ifeq @ ( sum @ Y @ Z @ V3 ) @ true @ ( product @ V3 @ X @ V4 ) @ true ) @ true ) @ true ) @ true )
= true ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(71,plain,
( ( ! [Y: $i,Z: $i,V3: $i,X: $i,V4: $i,V2: $i,V1: $i] :
( ( ifeq @ ( product @ Y @ Z @ V3 ) @ true @ ( ifeq @ ( sum @ X @ V3 @ V4 ) @ true @ ( ifeq @ ( sum @ X @ Z @ V2 ) @ true @ ( ifeq @ ( sum @ X @ Y @ V1 ) @ true @ ( product @ V1 @ V2 @ V4 ) @ true ) @ true ) @ true ) @ true )
= true ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(72,plain,
( ( ! [V1: $i,V2: $i,V4: $i,Y: $i,Z: $i,V3: $i,X: $i] :
( ( ifeq @ ( product @ V1 @ V2 @ V4 ) @ true @ ( ifeq @ ( product @ Y @ Z @ V3 ) @ true @ ( ifeq @ ( sum @ X @ Z @ V2 ) @ true @ ( ifeq @ ( sum @ X @ Y @ V1 ) @ true @ ( sum @ X @ V3 @ V4 ) @ true ) @ true ) @ true ) @ true )
= true ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(73,plain,
( ( ! [Y: $i,Z: $i,V3: $i,X: $i,V4: $i,V2: $i,V1: $i] :
( ( ifeq @ ( product @ Y @ Z @ V3 ) @ true @ ( ifeq @ ( sum @ V3 @ X @ V4 ) @ true @ ( ifeq @ ( sum @ Z @ X @ V2 ) @ true @ ( ifeq @ ( sum @ Y @ X @ V1 ) @ true @ ( product @ V1 @ V2 @ V4 ) @ true ) @ true ) @ true ) @ true )
= true ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(74,plain,
( ( ! [V1: $i,V2: $i,V4: $i,Y: $i,Z: $i,V3: $i,X: $i] :
( ( ifeq @ ( product @ V1 @ V2 @ V4 ) @ true @ ( ifeq @ ( product @ Y @ Z @ V3 ) @ true @ ( ifeq @ ( sum @ Z @ X @ V2 ) @ true @ ( ifeq @ ( sum @ Y @ X @ V1 ) @ true @ ( sum @ V3 @ X @ V4 ) @ true ) @ true ) @ true ) @ true )
= true ) )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(75,plain,
( ( ! [X: $i] :
( ( sum @ ( inverse @ X ) @ X @ multiplicative_identity )
= true ) )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(76,plain,
( ( ! [X: $i] :
( ( sum @ X @ ( inverse @ X ) @ multiplicative_identity )
= true ) )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(77,plain,
( ( ! [X: $i] :
( ( product @ ( inverse @ X ) @ X @ additive_identity )
= true ) )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(78,plain,
( ( ! [X: $i] :
( ( product @ X @ ( inverse @ X ) @ additive_identity )
= true ) )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(79,plain,
( ( ! [X: $i,Y: $i,V: $i,U: $i] :
( ( ifeq2 @ ( sum @ X @ Y @ V ) @ true @ ( ifeq2 @ ( sum @ X @ Y @ U ) @ true @ U @ V ) @ V )
= V ) )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(80,plain,
( ( ! [X: $i,Y: $i,V: $i,U: $i] :
( ( ifeq2 @ ( product @ X @ Y @ V ) @ true @ ( ifeq2 @ ( product @ X @ Y @ U ) @ true @ U @ V ) @ V )
= V ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(81,plain,
( ( ~ $false )
= $true ),
inference(copy,[status(thm)],[54]) ).
thf(82,plain,
( ( ( sum @ x @ x @ x )
= true )
= $false ),
inference(extcnf_not_pos,[status(thm)],[56]) ).
thf(83,plain,
! [SV1: $i] :
( ( ! [SY88: $i,SY89: $i] :
( ( ifeq2 @ SV1 @ SV1 @ SY88 @ SY89 )
= SY88 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[57]) ).
thf(84,plain,
! [SV2: $i] :
( ( ! [SY90: $i,SY91: $i] :
( ( ifeq @ SV2 @ SV2 @ SY90 @ SY91 )
= SY90 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[58]) ).
thf(85,plain,
! [SV3: $i] :
( ( ! [SY92: $i] :
( ( sum @ SV3 @ SY92 @ ( add @ SV3 @ SY92 ) )
= true ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[59]) ).
thf(86,plain,
! [SV4: $i] :
( ( ! [SY93: $i] :
( ( product @ SV4 @ SY93 @ ( multiply @ SV4 @ SY93 ) )
= true ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[60]) ).
thf(87,plain,
! [SV5: $i] :
( ( ! [SY94: $i,SY95: $i] :
( ( ifeq @ ( sum @ SV5 @ SY94 @ SY95 ) @ true @ ( sum @ SY94 @ SV5 @ SY95 ) @ true )
= true ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[61]) ).
thf(88,plain,
! [SV6: $i] :
( ( ! [SY96: $i,SY97: $i] :
( ( ifeq @ ( product @ SV6 @ SY96 @ SY97 ) @ true @ ( product @ SY96 @ SV6 @ SY97 ) @ true )
= true ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[62]) ).
thf(89,plain,
! [SV7: $i] :
( ( ( sum @ additive_identity @ SV7 @ SV7 )
= true )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[63]) ).
thf(90,plain,
! [SV8: $i] :
( ( ( sum @ SV8 @ additive_identity @ SV8 )
= true )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[64]) ).
thf(91,plain,
! [SV9: $i] :
( ( ( product @ multiplicative_identity @ SV9 @ SV9 )
= true )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[65]) ).
thf(92,plain,
! [SV10: $i] :
( ( ( product @ SV10 @ multiplicative_identity @ SV10 )
= true )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[66]) ).
thf(93,plain,
! [SV11: $i] :
( ( ! [SY98: $i,SY99: $i,SY100: $i,SY101: $i,SY102: $i,SY103: $i] :
( ( ifeq @ ( product @ SV11 @ SY98 @ SY99 ) @ true @ ( ifeq @ ( product @ SV11 @ SY100 @ SY101 ) @ true @ ( ifeq @ ( product @ SV11 @ SY102 @ SY103 ) @ true @ ( ifeq @ ( sum @ SY102 @ SY100 @ SY98 ) @ true @ ( sum @ SY103 @ SY101 @ SY99 ) @ true ) @ true ) @ true ) @ true )
= true ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[67]) ).
thf(94,plain,
! [SV12: $i] :
( ( ! [SY104: $i,SY105: $i,SY106: $i,SY107: $i,SY108: $i,SY109: $i] :
( ( ifeq @ ( product @ SV12 @ SY104 @ SY105 ) @ true @ ( ifeq @ ( product @ SV12 @ SY106 @ SY107 ) @ true @ ( ifeq @ ( sum @ SY107 @ SY105 @ SY108 ) @ true @ ( ifeq @ ( sum @ SY106 @ SY104 @ SY109 ) @ true @ ( product @ SV12 @ SY109 @ SY108 ) @ true ) @ true ) @ true ) @ true )
= true ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[68]) ).
thf(95,plain,
! [SV13: $i] :
( ( ! [SY110: $i,SY111: $i,SY112: $i,SY113: $i,SY114: $i,SY115: $i] :
( ( ifeq @ ( product @ SV13 @ SY110 @ SY111 ) @ true @ ( ifeq @ ( product @ SY112 @ SY110 @ SY113 ) @ true @ ( ifeq @ ( product @ SY114 @ SY110 @ SY115 ) @ true @ ( ifeq @ ( sum @ SY114 @ SY112 @ SV13 ) @ true @ ( sum @ SY115 @ SY113 @ SY111 ) @ true ) @ true ) @ true ) @ true )
= true ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[69]) ).
thf(96,plain,
! [SV14: $i] :
( ( ! [SY116: $i,SY117: $i,SY118: $i,SY119: $i,SY120: $i,SY121: $i] :
( ( ifeq @ ( product @ SV14 @ SY116 @ SY117 ) @ true @ ( ifeq @ ( product @ SY118 @ SY116 @ SY119 ) @ true @ ( ifeq @ ( sum @ SY119 @ SY117 @ SY120 ) @ true @ ( ifeq @ ( sum @ SY118 @ SV14 @ SY121 ) @ true @ ( product @ SY121 @ SY116 @ SY120 ) @ true ) @ true ) @ true ) @ true )
= true ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[70]) ).
thf(97,plain,
! [SV15: $i] :
( ( ! [SY122: $i,SY123: $i,SY124: $i,SY125: $i,SY126: $i,SY127: $i] :
( ( ifeq @ ( product @ SV15 @ SY122 @ SY123 ) @ true @ ( ifeq @ ( sum @ SY124 @ SY123 @ SY125 ) @ true @ ( ifeq @ ( sum @ SY124 @ SY122 @ SY126 ) @ true @ ( ifeq @ ( sum @ SY124 @ SV15 @ SY127 ) @ true @ ( product @ SY127 @ SY126 @ SY125 ) @ true ) @ true ) @ true ) @ true )
= true ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(98,plain,
! [SV16: $i] :
( ( ! [SY128: $i,SY129: $i,SY130: $i,SY131: $i,SY132: $i,SY133: $i] :
( ( ifeq @ ( product @ SV16 @ SY128 @ SY129 ) @ true @ ( ifeq @ ( product @ SY130 @ SY131 @ SY132 ) @ true @ ( ifeq @ ( sum @ SY133 @ SY131 @ SY128 ) @ true @ ( ifeq @ ( sum @ SY133 @ SY130 @ SV16 ) @ true @ ( sum @ SY133 @ SY132 @ SY129 ) @ true ) @ true ) @ true ) @ true )
= true ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[72]) ).
thf(99,plain,
! [SV17: $i] :
( ( ! [SY134: $i,SY135: $i,SY136: $i,SY137: $i,SY138: $i,SY139: $i] :
( ( ifeq @ ( product @ SV17 @ SY134 @ SY135 ) @ true @ ( ifeq @ ( sum @ SY135 @ SY136 @ SY137 ) @ true @ ( ifeq @ ( sum @ SY134 @ SY136 @ SY138 ) @ true @ ( ifeq @ ( sum @ SV17 @ SY136 @ SY139 ) @ true @ ( product @ SY139 @ SY138 @ SY137 ) @ true ) @ true ) @ true ) @ true )
= true ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[73]) ).
thf(100,plain,
! [SV18: $i] :
( ( ! [SY140: $i,SY141: $i,SY142: $i,SY143: $i,SY144: $i,SY145: $i] :
( ( ifeq @ ( product @ SV18 @ SY140 @ SY141 ) @ true @ ( ifeq @ ( product @ SY142 @ SY143 @ SY144 ) @ true @ ( ifeq @ ( sum @ SY143 @ SY145 @ SY140 ) @ true @ ( ifeq @ ( sum @ SY142 @ SY145 @ SV18 ) @ true @ ( sum @ SY144 @ SY145 @ SY141 ) @ true ) @ true ) @ true ) @ true )
= true ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[74]) ).
thf(101,plain,
! [SV19: $i] :
( ( ( sum @ ( inverse @ SV19 ) @ SV19 @ multiplicative_identity )
= true )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[75]) ).
thf(102,plain,
! [SV20: $i] :
( ( ( sum @ SV20 @ ( inverse @ SV20 ) @ multiplicative_identity )
= true )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[76]) ).
thf(103,plain,
! [SV21: $i] :
( ( ( product @ ( inverse @ SV21 ) @ SV21 @ additive_identity )
= true )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[77]) ).
thf(104,plain,
! [SV22: $i] :
( ( ( product @ SV22 @ ( inverse @ SV22 ) @ additive_identity )
= true )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[78]) ).
thf(105,plain,
! [SV23: $i] :
( ( ! [SY146: $i,SY147: $i,SY148: $i] :
( ( ifeq2 @ ( sum @ SV23 @ SY146 @ SY147 ) @ true @ ( ifeq2 @ ( sum @ SV23 @ SY146 @ SY148 ) @ true @ SY148 @ SY147 ) @ SY147 )
= SY147 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[79]) ).
thf(106,plain,
! [SV24: $i] :
( ( ! [SY149: $i,SY150: $i,SY151: $i] :
( ( ifeq2 @ ( product @ SV24 @ SY149 @ SY150 ) @ true @ ( ifeq2 @ ( product @ SV24 @ SY149 @ SY151 ) @ true @ SY151 @ SY150 ) @ SY150 )
= SY150 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[80]) ).
thf(107,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[81]) ).
thf(108,plain,
! [SV25: $i,SV1: $i] :
( ( ! [SY152: $i] :
( ( ifeq2 @ SV1 @ SV1 @ SV25 @ SY152 )
= SV25 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[83]) ).
thf(109,plain,
! [SV26: $i,SV2: $i] :
( ( ! [SY153: $i] :
( ( ifeq @ SV2 @ SV2 @ SV26 @ SY153 )
= SV26 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).
thf(110,plain,
! [SV27: $i,SV3: $i] :
( ( ( sum @ SV3 @ SV27 @ ( add @ SV3 @ SV27 ) )
= true )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(111,plain,
! [SV28: $i,SV4: $i] :
( ( ( product @ SV4 @ SV28 @ ( multiply @ SV4 @ SV28 ) )
= true )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[86]) ).
thf(112,plain,
! [SV29: $i,SV5: $i] :
( ( ! [SY154: $i] :
( ( ifeq @ ( sum @ SV5 @ SV29 @ SY154 ) @ true @ ( sum @ SV29 @ SV5 @ SY154 ) @ true )
= true ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).
thf(113,plain,
! [SV30: $i,SV6: $i] :
( ( ! [SY155: $i] :
( ( ifeq @ ( product @ SV6 @ SV30 @ SY155 ) @ true @ ( product @ SV30 @ SV6 @ SY155 ) @ true )
= true ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(114,plain,
! [SV31: $i,SV11: $i] :
( ( ! [SY156: $i,SY157: $i,SY158: $i,SY159: $i,SY160: $i] :
( ( ifeq @ ( product @ SV11 @ SV31 @ SY156 ) @ true @ ( ifeq @ ( product @ SV11 @ SY157 @ SY158 ) @ true @ ( ifeq @ ( product @ SV11 @ SY159 @ SY160 ) @ true @ ( ifeq @ ( sum @ SY159 @ SY157 @ SV31 ) @ true @ ( sum @ SY160 @ SY158 @ SY156 ) @ true ) @ true ) @ true ) @ true )
= true ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[93]) ).
thf(115,plain,
! [SV32: $i,SV12: $i] :
( ( ! [SY161: $i,SY162: $i,SY163: $i,SY164: $i,SY165: $i] :
( ( ifeq @ ( product @ SV12 @ SV32 @ SY161 ) @ true @ ( ifeq @ ( product @ SV12 @ SY162 @ SY163 ) @ true @ ( ifeq @ ( sum @ SY163 @ SY161 @ SY164 ) @ true @ ( ifeq @ ( sum @ SY162 @ SV32 @ SY165 ) @ true @ ( product @ SV12 @ SY165 @ SY164 ) @ true ) @ true ) @ true ) @ true )
= true ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[94]) ).
thf(116,plain,
! [SV33: $i,SV13: $i] :
( ( ! [SY166: $i,SY167: $i,SY168: $i,SY169: $i,SY170: $i] :
( ( ifeq @ ( product @ SV13 @ SV33 @ SY166 ) @ true @ ( ifeq @ ( product @ SY167 @ SV33 @ SY168 ) @ true @ ( ifeq @ ( product @ SY169 @ SV33 @ SY170 ) @ true @ ( ifeq @ ( sum @ SY169 @ SY167 @ SV13 ) @ true @ ( sum @ SY170 @ SY168 @ SY166 ) @ true ) @ true ) @ true ) @ true )
= true ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[95]) ).
thf(117,plain,
! [SV34: $i,SV14: $i] :
( ( ! [SY171: $i,SY172: $i,SY173: $i,SY174: $i,SY175: $i] :
( ( ifeq @ ( product @ SV14 @ SV34 @ SY171 ) @ true @ ( ifeq @ ( product @ SY172 @ SV34 @ SY173 ) @ true @ ( ifeq @ ( sum @ SY173 @ SY171 @ SY174 ) @ true @ ( ifeq @ ( sum @ SY172 @ SV14 @ SY175 ) @ true @ ( product @ SY175 @ SV34 @ SY174 ) @ true ) @ true ) @ true ) @ true )
= true ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[96]) ).
thf(118,plain,
! [SV35: $i,SV15: $i] :
( ( ! [SY176: $i,SY177: $i,SY178: $i,SY179: $i,SY180: $i] :
( ( ifeq @ ( product @ SV15 @ SV35 @ SY176 ) @ true @ ( ifeq @ ( sum @ SY177 @ SY176 @ SY178 ) @ true @ ( ifeq @ ( sum @ SY177 @ SV35 @ SY179 ) @ true @ ( ifeq @ ( sum @ SY177 @ SV15 @ SY180 ) @ true @ ( product @ SY180 @ SY179 @ SY178 ) @ true ) @ true ) @ true ) @ true )
= true ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[97]) ).
thf(119,plain,
! [SV36: $i,SV16: $i] :
( ( ! [SY181: $i,SY182: $i,SY183: $i,SY184: $i,SY185: $i] :
( ( ifeq @ ( product @ SV16 @ SV36 @ SY181 ) @ true @ ( ifeq @ ( product @ SY182 @ SY183 @ SY184 ) @ true @ ( ifeq @ ( sum @ SY185 @ SY183 @ SV36 ) @ true @ ( ifeq @ ( sum @ SY185 @ SY182 @ SV16 ) @ true @ ( sum @ SY185 @ SY184 @ SY181 ) @ true ) @ true ) @ true ) @ true )
= true ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[98]) ).
thf(120,plain,
! [SV37: $i,SV17: $i] :
( ( ! [SY186: $i,SY187: $i,SY188: $i,SY189: $i,SY190: $i] :
( ( ifeq @ ( product @ SV17 @ SV37 @ SY186 ) @ true @ ( ifeq @ ( sum @ SY186 @ SY187 @ SY188 ) @ true @ ( ifeq @ ( sum @ SV37 @ SY187 @ SY189 ) @ true @ ( ifeq @ ( sum @ SV17 @ SY187 @ SY190 ) @ true @ ( product @ SY190 @ SY189 @ SY188 ) @ true ) @ true ) @ true ) @ true )
= true ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[99]) ).
thf(121,plain,
! [SV38: $i,SV18: $i] :
( ( ! [SY191: $i,SY192: $i,SY193: $i,SY194: $i,SY195: $i] :
( ( ifeq @ ( product @ SV18 @ SV38 @ SY191 ) @ true @ ( ifeq @ ( product @ SY192 @ SY193 @ SY194 ) @ true @ ( ifeq @ ( sum @ SY193 @ SY195 @ SV38 ) @ true @ ( ifeq @ ( sum @ SY192 @ SY195 @ SV18 ) @ true @ ( sum @ SY194 @ SY195 @ SY191 ) @ true ) @ true ) @ true ) @ true )
= true ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[100]) ).
thf(122,plain,
! [SV39: $i,SV23: $i] :
( ( ! [SY196: $i,SY197: $i] :
( ( ifeq2 @ ( sum @ SV23 @ SV39 @ SY196 ) @ true @ ( ifeq2 @ ( sum @ SV23 @ SV39 @ SY197 ) @ true @ SY197 @ SY196 ) @ SY196 )
= SY196 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[105]) ).
thf(123,plain,
! [SV40: $i,SV24: $i] :
( ( ! [SY198: $i,SY199: $i] :
( ( ifeq2 @ ( product @ SV24 @ SV40 @ SY198 ) @ true @ ( ifeq2 @ ( product @ SV24 @ SV40 @ SY199 ) @ true @ SY199 @ SY198 ) @ SY198 )
= SY198 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[106]) ).
thf(124,plain,
! [SV41: $i,SV25: $i,SV1: $i] :
( ( ( ifeq2 @ SV1 @ SV1 @ SV25 @ SV41 )
= SV25 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[108]) ).
thf(125,plain,
! [SV42: $i,SV26: $i,SV2: $i] :
( ( ( ifeq @ SV2 @ SV2 @ SV26 @ SV42 )
= SV26 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[109]) ).
thf(126,plain,
! [SV43: $i,SV29: $i,SV5: $i] :
( ( ( ifeq @ ( sum @ SV5 @ SV29 @ SV43 ) @ true @ ( sum @ SV29 @ SV5 @ SV43 ) @ true )
= true )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[112]) ).
thf(127,plain,
! [SV44: $i,SV30: $i,SV6: $i] :
( ( ( ifeq @ ( product @ SV6 @ SV30 @ SV44 ) @ true @ ( product @ SV30 @ SV6 @ SV44 ) @ true )
= true )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[113]) ).
thf(128,plain,
! [SV45: $i,SV31: $i,SV11: $i] :
( ( ! [SY200: $i,SY201: $i,SY202: $i,SY203: $i] :
( ( ifeq @ ( product @ SV11 @ SV31 @ SV45 ) @ true @ ( ifeq @ ( product @ SV11 @ SY200 @ SY201 ) @ true @ ( ifeq @ ( product @ SV11 @ SY202 @ SY203 ) @ true @ ( ifeq @ ( sum @ SY202 @ SY200 @ SV31 ) @ true @ ( sum @ SY203 @ SY201 @ SV45 ) @ true ) @ true ) @ true ) @ true )
= true ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[114]) ).
thf(129,plain,
! [SV46: $i,SV32: $i,SV12: $i] :
( ( ! [SY204: $i,SY205: $i,SY206: $i,SY207: $i] :
( ( ifeq @ ( product @ SV12 @ SV32 @ SV46 ) @ true @ ( ifeq @ ( product @ SV12 @ SY204 @ SY205 ) @ true @ ( ifeq @ ( sum @ SY205 @ SV46 @ SY206 ) @ true @ ( ifeq @ ( sum @ SY204 @ SV32 @ SY207 ) @ true @ ( product @ SV12 @ SY207 @ SY206 ) @ true ) @ true ) @ true ) @ true )
= true ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[115]) ).
thf(130,plain,
! [SV47: $i,SV33: $i,SV13: $i] :
( ( ! [SY208: $i,SY209: $i,SY210: $i,SY211: $i] :
( ( ifeq @ ( product @ SV13 @ SV33 @ SV47 ) @ true @ ( ifeq @ ( product @ SY208 @ SV33 @ SY209 ) @ true @ ( ifeq @ ( product @ SY210 @ SV33 @ SY211 ) @ true @ ( ifeq @ ( sum @ SY210 @ SY208 @ SV13 ) @ true @ ( sum @ SY211 @ SY209 @ SV47 ) @ true ) @ true ) @ true ) @ true )
= true ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[116]) ).
thf(131,plain,
! [SV48: $i,SV34: $i,SV14: $i] :
( ( ! [SY212: $i,SY213: $i,SY214: $i,SY215: $i] :
( ( ifeq @ ( product @ SV14 @ SV34 @ SV48 ) @ true @ ( ifeq @ ( product @ SY212 @ SV34 @ SY213 ) @ true @ ( ifeq @ ( sum @ SY213 @ SV48 @ SY214 ) @ true @ ( ifeq @ ( sum @ SY212 @ SV14 @ SY215 ) @ true @ ( product @ SY215 @ SV34 @ SY214 ) @ true ) @ true ) @ true ) @ true )
= true ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[117]) ).
thf(132,plain,
! [SV49: $i,SV35: $i,SV15: $i] :
( ( ! [SY216: $i,SY217: $i,SY218: $i,SY219: $i] :
( ( ifeq @ ( product @ SV15 @ SV35 @ SV49 ) @ true @ ( ifeq @ ( sum @ SY216 @ SV49 @ SY217 ) @ true @ ( ifeq @ ( sum @ SY216 @ SV35 @ SY218 ) @ true @ ( ifeq @ ( sum @ SY216 @ SV15 @ SY219 ) @ true @ ( product @ SY219 @ SY218 @ SY217 ) @ true ) @ true ) @ true ) @ true )
= true ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[118]) ).
thf(133,plain,
! [SV50: $i,SV36: $i,SV16: $i] :
( ( ! [SY220: $i,SY221: $i,SY222: $i,SY223: $i] :
( ( ifeq @ ( product @ SV16 @ SV36 @ SV50 ) @ true @ ( ifeq @ ( product @ SY220 @ SY221 @ SY222 ) @ true @ ( ifeq @ ( sum @ SY223 @ SY221 @ SV36 ) @ true @ ( ifeq @ ( sum @ SY223 @ SY220 @ SV16 ) @ true @ ( sum @ SY223 @ SY222 @ SV50 ) @ true ) @ true ) @ true ) @ true )
= true ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[119]) ).
thf(134,plain,
! [SV51: $i,SV37: $i,SV17: $i] :
( ( ! [SY224: $i,SY225: $i,SY226: $i,SY227: $i] :
( ( ifeq @ ( product @ SV17 @ SV37 @ SV51 ) @ true @ ( ifeq @ ( sum @ SV51 @ SY224 @ SY225 ) @ true @ ( ifeq @ ( sum @ SV37 @ SY224 @ SY226 ) @ true @ ( ifeq @ ( sum @ SV17 @ SY224 @ SY227 ) @ true @ ( product @ SY227 @ SY226 @ SY225 ) @ true ) @ true ) @ true ) @ true )
= true ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[120]) ).
thf(135,plain,
! [SV52: $i,SV38: $i,SV18: $i] :
( ( ! [SY228: $i,SY229: $i,SY230: $i,SY231: $i] :
( ( ifeq @ ( product @ SV18 @ SV38 @ SV52 ) @ true @ ( ifeq @ ( product @ SY228 @ SY229 @ SY230 ) @ true @ ( ifeq @ ( sum @ SY229 @ SY231 @ SV38 ) @ true @ ( ifeq @ ( sum @ SY228 @ SY231 @ SV18 ) @ true @ ( sum @ SY230 @ SY231 @ SV52 ) @ true ) @ true ) @ true ) @ true )
= true ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[121]) ).
thf(136,plain,
! [SV53: $i,SV39: $i,SV23: $i] :
( ( ! [SY232: $i] :
( ( ifeq2 @ ( sum @ SV23 @ SV39 @ SV53 ) @ true @ ( ifeq2 @ ( sum @ SV23 @ SV39 @ SY232 ) @ true @ SY232 @ SV53 ) @ SV53 )
= SV53 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[122]) ).
thf(137,plain,
! [SV54: $i,SV40: $i,SV24: $i] :
( ( ! [SY233: $i] :
( ( ifeq2 @ ( product @ SV24 @ SV40 @ SV54 ) @ true @ ( ifeq2 @ ( product @ SV24 @ SV40 @ SY233 ) @ true @ SY233 @ SV54 ) @ SV54 )
= SV54 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[123]) ).
thf(138,plain,
! [SV55: $i,SV45: $i,SV31: $i,SV11: $i] :
( ( ! [SY234: $i,SY235: $i,SY236: $i] :
( ( ifeq @ ( product @ SV11 @ SV31 @ SV45 ) @ true @ ( ifeq @ ( product @ SV11 @ SV55 @ SY234 ) @ true @ ( ifeq @ ( product @ SV11 @ SY235 @ SY236 ) @ true @ ( ifeq @ ( sum @ SY235 @ SV55 @ SV31 ) @ true @ ( sum @ SY236 @ SY234 @ SV45 ) @ true ) @ true ) @ true ) @ true )
= true ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[128]) ).
thf(139,plain,
! [SV56: $i,SV46: $i,SV32: $i,SV12: $i] :
( ( ! [SY237: $i,SY238: $i,SY239: $i] :
( ( ifeq @ ( product @ SV12 @ SV32 @ SV46 ) @ true @ ( ifeq @ ( product @ SV12 @ SV56 @ SY237 ) @ true @ ( ifeq @ ( sum @ SY237 @ SV46 @ SY238 ) @ true @ ( ifeq @ ( sum @ SV56 @ SV32 @ SY239 ) @ true @ ( product @ SV12 @ SY239 @ SY238 ) @ true ) @ true ) @ true ) @ true )
= true ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[129]) ).
thf(140,plain,
! [SV57: $i,SV47: $i,SV33: $i,SV13: $i] :
( ( ! [SY240: $i,SY241: $i,SY242: $i] :
( ( ifeq @ ( product @ SV13 @ SV33 @ SV47 ) @ true @ ( ifeq @ ( product @ SV57 @ SV33 @ SY240 ) @ true @ ( ifeq @ ( product @ SY241 @ SV33 @ SY242 ) @ true @ ( ifeq @ ( sum @ SY241 @ SV57 @ SV13 ) @ true @ ( sum @ SY242 @ SY240 @ SV47 ) @ true ) @ true ) @ true ) @ true )
= true ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[130]) ).
thf(141,plain,
! [SV58: $i,SV48: $i,SV34: $i,SV14: $i] :
( ( ! [SY243: $i,SY244: $i,SY245: $i] :
( ( ifeq @ ( product @ SV14 @ SV34 @ SV48 ) @ true @ ( ifeq @ ( product @ SV58 @ SV34 @ SY243 ) @ true @ ( ifeq @ ( sum @ SY243 @ SV48 @ SY244 ) @ true @ ( ifeq @ ( sum @ SV58 @ SV14 @ SY245 ) @ true @ ( product @ SY245 @ SV34 @ SY244 ) @ true ) @ true ) @ true ) @ true )
= true ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[131]) ).
thf(142,plain,
! [SV59: $i,SV49: $i,SV35: $i,SV15: $i] :
( ( ! [SY246: $i,SY247: $i,SY248: $i] :
( ( ifeq @ ( product @ SV15 @ SV35 @ SV49 ) @ true @ ( ifeq @ ( sum @ SV59 @ SV49 @ SY246 ) @ true @ ( ifeq @ ( sum @ SV59 @ SV35 @ SY247 ) @ true @ ( ifeq @ ( sum @ SV59 @ SV15 @ SY248 ) @ true @ ( product @ SY248 @ SY247 @ SY246 ) @ true ) @ true ) @ true ) @ true )
= true ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[132]) ).
thf(143,plain,
! [SV60: $i,SV50: $i,SV36: $i,SV16: $i] :
( ( ! [SY249: $i,SY250: $i,SY251: $i] :
( ( ifeq @ ( product @ SV16 @ SV36 @ SV50 ) @ true @ ( ifeq @ ( product @ SV60 @ SY249 @ SY250 ) @ true @ ( ifeq @ ( sum @ SY251 @ SY249 @ SV36 ) @ true @ ( ifeq @ ( sum @ SY251 @ SV60 @ SV16 ) @ true @ ( sum @ SY251 @ SY250 @ SV50 ) @ true ) @ true ) @ true ) @ true )
= true ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[133]) ).
thf(144,plain,
! [SV61: $i,SV51: $i,SV37: $i,SV17: $i] :
( ( ! [SY252: $i,SY253: $i,SY254: $i] :
( ( ifeq @ ( product @ SV17 @ SV37 @ SV51 ) @ true @ ( ifeq @ ( sum @ SV51 @ SV61 @ SY252 ) @ true @ ( ifeq @ ( sum @ SV37 @ SV61 @ SY253 ) @ true @ ( ifeq @ ( sum @ SV17 @ SV61 @ SY254 ) @ true @ ( product @ SY254 @ SY253 @ SY252 ) @ true ) @ true ) @ true ) @ true )
= true ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[134]) ).
thf(145,plain,
! [SV62: $i,SV52: $i,SV38: $i,SV18: $i] :
( ( ! [SY255: $i,SY256: $i,SY257: $i] :
( ( ifeq @ ( product @ SV18 @ SV38 @ SV52 ) @ true @ ( ifeq @ ( product @ SV62 @ SY255 @ SY256 ) @ true @ ( ifeq @ ( sum @ SY255 @ SY257 @ SV38 ) @ true @ ( ifeq @ ( sum @ SV62 @ SY257 @ SV18 ) @ true @ ( sum @ SY256 @ SY257 @ SV52 ) @ true ) @ true ) @ true ) @ true )
= true ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[135]) ).
thf(146,plain,
! [SV63: $i,SV53: $i,SV39: $i,SV23: $i] :
( ( ( ifeq2 @ ( sum @ SV23 @ SV39 @ SV53 ) @ true @ ( ifeq2 @ ( sum @ SV23 @ SV39 @ SV63 ) @ true @ SV63 @ SV53 ) @ SV53 )
= SV53 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[136]) ).
thf(147,plain,
! [SV64: $i,SV54: $i,SV40: $i,SV24: $i] :
( ( ( ifeq2 @ ( product @ SV24 @ SV40 @ SV54 ) @ true @ ( ifeq2 @ ( product @ SV24 @ SV40 @ SV64 ) @ true @ SV64 @ SV54 ) @ SV54 )
= SV54 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[137]) ).
thf(148,plain,
! [SV65: $i,SV55: $i,SV45: $i,SV31: $i,SV11: $i] :
( ( ! [SY258: $i,SY259: $i] :
( ( ifeq @ ( product @ SV11 @ SV31 @ SV45 ) @ true @ ( ifeq @ ( product @ SV11 @ SV55 @ SV65 ) @ true @ ( ifeq @ ( product @ SV11 @ SY258 @ SY259 ) @ true @ ( ifeq @ ( sum @ SY258 @ SV55 @ SV31 ) @ true @ ( sum @ SY259 @ SV65 @ SV45 ) @ true ) @ true ) @ true ) @ true )
= true ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[138]) ).
thf(149,plain,
! [SV66: $i,SV56: $i,SV46: $i,SV32: $i,SV12: $i] :
( ( ! [SY260: $i,SY261: $i] :
( ( ifeq @ ( product @ SV12 @ SV32 @ SV46 ) @ true @ ( ifeq @ ( product @ SV12 @ SV56 @ SV66 ) @ true @ ( ifeq @ ( sum @ SV66 @ SV46 @ SY260 ) @ true @ ( ifeq @ ( sum @ SV56 @ SV32 @ SY261 ) @ true @ ( product @ SV12 @ SY261 @ SY260 ) @ true ) @ true ) @ true ) @ true )
= true ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[139]) ).
thf(150,plain,
! [SV67: $i,SV57: $i,SV47: $i,SV33: $i,SV13: $i] :
( ( ! [SY262: $i,SY263: $i] :
( ( ifeq @ ( product @ SV13 @ SV33 @ SV47 ) @ true @ ( ifeq @ ( product @ SV57 @ SV33 @ SV67 ) @ true @ ( ifeq @ ( product @ SY262 @ SV33 @ SY263 ) @ true @ ( ifeq @ ( sum @ SY262 @ SV57 @ SV13 ) @ true @ ( sum @ SY263 @ SV67 @ SV47 ) @ true ) @ true ) @ true ) @ true )
= true ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[140]) ).
thf(151,plain,
! [SV68: $i,SV58: $i,SV48: $i,SV34: $i,SV14: $i] :
( ( ! [SY264: $i,SY265: $i] :
( ( ifeq @ ( product @ SV14 @ SV34 @ SV48 ) @ true @ ( ifeq @ ( product @ SV58 @ SV34 @ SV68 ) @ true @ ( ifeq @ ( sum @ SV68 @ SV48 @ SY264 ) @ true @ ( ifeq @ ( sum @ SV58 @ SV14 @ SY265 ) @ true @ ( product @ SY265 @ SV34 @ SY264 ) @ true ) @ true ) @ true ) @ true )
= true ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[141]) ).
thf(152,plain,
! [SV69: $i,SV59: $i,SV49: $i,SV35: $i,SV15: $i] :
( ( ! [SY266: $i,SY267: $i] :
( ( ifeq @ ( product @ SV15 @ SV35 @ SV49 ) @ true @ ( ifeq @ ( sum @ SV59 @ SV49 @ SV69 ) @ true @ ( ifeq @ ( sum @ SV59 @ SV35 @ SY266 ) @ true @ ( ifeq @ ( sum @ SV59 @ SV15 @ SY267 ) @ true @ ( product @ SY267 @ SY266 @ SV69 ) @ true ) @ true ) @ true ) @ true )
= true ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[142]) ).
thf(153,plain,
! [SV70: $i,SV60: $i,SV50: $i,SV36: $i,SV16: $i] :
( ( ! [SY268: $i,SY269: $i] :
( ( ifeq @ ( product @ SV16 @ SV36 @ SV50 ) @ true @ ( ifeq @ ( product @ SV60 @ SV70 @ SY268 ) @ true @ ( ifeq @ ( sum @ SY269 @ SV70 @ SV36 ) @ true @ ( ifeq @ ( sum @ SY269 @ SV60 @ SV16 ) @ true @ ( sum @ SY269 @ SY268 @ SV50 ) @ true ) @ true ) @ true ) @ true )
= true ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[143]) ).
thf(154,plain,
! [SV71: $i,SV61: $i,SV51: $i,SV37: $i,SV17: $i] :
( ( ! [SY270: $i,SY271: $i] :
( ( ifeq @ ( product @ SV17 @ SV37 @ SV51 ) @ true @ ( ifeq @ ( sum @ SV51 @ SV61 @ SV71 ) @ true @ ( ifeq @ ( sum @ SV37 @ SV61 @ SY270 ) @ true @ ( ifeq @ ( sum @ SV17 @ SV61 @ SY271 ) @ true @ ( product @ SY271 @ SY270 @ SV71 ) @ true ) @ true ) @ true ) @ true )
= true ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[144]) ).
thf(155,plain,
! [SV72: $i,SV62: $i,SV52: $i,SV38: $i,SV18: $i] :
( ( ! [SY272: $i,SY273: $i] :
( ( ifeq @ ( product @ SV18 @ SV38 @ SV52 ) @ true @ ( ifeq @ ( product @ SV62 @ SV72 @ SY272 ) @ true @ ( ifeq @ ( sum @ SV72 @ SY273 @ SV38 ) @ true @ ( ifeq @ ( sum @ SV62 @ SY273 @ SV18 ) @ true @ ( sum @ SY272 @ SY273 @ SV52 ) @ true ) @ true ) @ true ) @ true )
= true ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[145]) ).
thf(156,plain,
! [SV73: $i,SV65: $i,SV55: $i,SV45: $i,SV31: $i,SV11: $i] :
( ( ! [SY274: $i] :
( ( ifeq @ ( product @ SV11 @ SV31 @ SV45 ) @ true @ ( ifeq @ ( product @ SV11 @ SV55 @ SV65 ) @ true @ ( ifeq @ ( product @ SV11 @ SV73 @ SY274 ) @ true @ ( ifeq @ ( sum @ SV73 @ SV55 @ SV31 ) @ true @ ( sum @ SY274 @ SV65 @ SV45 ) @ true ) @ true ) @ true ) @ true )
= true ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[148]) ).
thf(157,plain,
! [SV74: $i,SV66: $i,SV56: $i,SV46: $i,SV32: $i,SV12: $i] :
( ( ! [SY275: $i] :
( ( ifeq @ ( product @ SV12 @ SV32 @ SV46 ) @ true @ ( ifeq @ ( product @ SV12 @ SV56 @ SV66 ) @ true @ ( ifeq @ ( sum @ SV66 @ SV46 @ SV74 ) @ true @ ( ifeq @ ( sum @ SV56 @ SV32 @ SY275 ) @ true @ ( product @ SV12 @ SY275 @ SV74 ) @ true ) @ true ) @ true ) @ true )
= true ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[149]) ).
thf(158,plain,
! [SV75: $i,SV67: $i,SV57: $i,SV47: $i,SV33: $i,SV13: $i] :
( ( ! [SY276: $i] :
( ( ifeq @ ( product @ SV13 @ SV33 @ SV47 ) @ true @ ( ifeq @ ( product @ SV57 @ SV33 @ SV67 ) @ true @ ( ifeq @ ( product @ SV75 @ SV33 @ SY276 ) @ true @ ( ifeq @ ( sum @ SV75 @ SV57 @ SV13 ) @ true @ ( sum @ SY276 @ SV67 @ SV47 ) @ true ) @ true ) @ true ) @ true )
= true ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[150]) ).
thf(159,plain,
! [SV76: $i,SV68: $i,SV58: $i,SV48: $i,SV34: $i,SV14: $i] :
( ( ! [SY277: $i] :
( ( ifeq @ ( product @ SV14 @ SV34 @ SV48 ) @ true @ ( ifeq @ ( product @ SV58 @ SV34 @ SV68 ) @ true @ ( ifeq @ ( sum @ SV68 @ SV48 @ SV76 ) @ true @ ( ifeq @ ( sum @ SV58 @ SV14 @ SY277 ) @ true @ ( product @ SY277 @ SV34 @ SV76 ) @ true ) @ true ) @ true ) @ true )
= true ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[151]) ).
thf(160,plain,
! [SV77: $i,SV69: $i,SV59: $i,SV49: $i,SV35: $i,SV15: $i] :
( ( ! [SY278: $i] :
( ( ifeq @ ( product @ SV15 @ SV35 @ SV49 ) @ true @ ( ifeq @ ( sum @ SV59 @ SV49 @ SV69 ) @ true @ ( ifeq @ ( sum @ SV59 @ SV35 @ SV77 ) @ true @ ( ifeq @ ( sum @ SV59 @ SV15 @ SY278 ) @ true @ ( product @ SY278 @ SV77 @ SV69 ) @ true ) @ true ) @ true ) @ true )
= true ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[152]) ).
thf(161,plain,
! [SV78: $i,SV70: $i,SV60: $i,SV50: $i,SV36: $i,SV16: $i] :
( ( ! [SY279: $i] :
( ( ifeq @ ( product @ SV16 @ SV36 @ SV50 ) @ true @ ( ifeq @ ( product @ SV60 @ SV70 @ SV78 ) @ true @ ( ifeq @ ( sum @ SY279 @ SV70 @ SV36 ) @ true @ ( ifeq @ ( sum @ SY279 @ SV60 @ SV16 ) @ true @ ( sum @ SY279 @ SV78 @ SV50 ) @ true ) @ true ) @ true ) @ true )
= true ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[153]) ).
thf(162,plain,
! [SV79: $i,SV71: $i,SV61: $i,SV51: $i,SV37: $i,SV17: $i] :
( ( ! [SY280: $i] :
( ( ifeq @ ( product @ SV17 @ SV37 @ SV51 ) @ true @ ( ifeq @ ( sum @ SV51 @ SV61 @ SV71 ) @ true @ ( ifeq @ ( sum @ SV37 @ SV61 @ SV79 ) @ true @ ( ifeq @ ( sum @ SV17 @ SV61 @ SY280 ) @ true @ ( product @ SY280 @ SV79 @ SV71 ) @ true ) @ true ) @ true ) @ true )
= true ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[154]) ).
thf(163,plain,
! [SV80: $i,SV72: $i,SV62: $i,SV52: $i,SV38: $i,SV18: $i] :
( ( ! [SY281: $i] :
( ( ifeq @ ( product @ SV18 @ SV38 @ SV52 ) @ true @ ( ifeq @ ( product @ SV62 @ SV72 @ SV80 ) @ true @ ( ifeq @ ( sum @ SV72 @ SY281 @ SV38 ) @ true @ ( ifeq @ ( sum @ SV62 @ SY281 @ SV18 ) @ true @ ( sum @ SV80 @ SY281 @ SV52 ) @ true ) @ true ) @ true ) @ true )
= true ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[155]) ).
thf(164,plain,
! [SV81: $i,SV73: $i,SV65: $i,SV55: $i,SV45: $i,SV31: $i,SV11: $i] :
( ( ( ifeq @ ( product @ SV11 @ SV31 @ SV45 ) @ true @ ( ifeq @ ( product @ SV11 @ SV55 @ SV65 ) @ true @ ( ifeq @ ( product @ SV11 @ SV73 @ SV81 ) @ true @ ( ifeq @ ( sum @ SV73 @ SV55 @ SV31 ) @ true @ ( sum @ SV81 @ SV65 @ SV45 ) @ true ) @ true ) @ true ) @ true )
= true )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[156]) ).
thf(165,plain,
! [SV82: $i,SV74: $i,SV66: $i,SV56: $i,SV46: $i,SV32: $i,SV12: $i] :
( ( ( ifeq @ ( product @ SV12 @ SV32 @ SV46 ) @ true @ ( ifeq @ ( product @ SV12 @ SV56 @ SV66 ) @ true @ ( ifeq @ ( sum @ SV66 @ SV46 @ SV74 ) @ true @ ( ifeq @ ( sum @ SV56 @ SV32 @ SV82 ) @ true @ ( product @ SV12 @ SV82 @ SV74 ) @ true ) @ true ) @ true ) @ true )
= true )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[157]) ).
thf(166,plain,
! [SV83: $i,SV75: $i,SV67: $i,SV57: $i,SV47: $i,SV33: $i,SV13: $i] :
( ( ( ifeq @ ( product @ SV13 @ SV33 @ SV47 ) @ true @ ( ifeq @ ( product @ SV57 @ SV33 @ SV67 ) @ true @ ( ifeq @ ( product @ SV75 @ SV33 @ SV83 ) @ true @ ( ifeq @ ( sum @ SV75 @ SV57 @ SV13 ) @ true @ ( sum @ SV83 @ SV67 @ SV47 ) @ true ) @ true ) @ true ) @ true )
= true )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[158]) ).
thf(167,plain,
! [SV84: $i,SV76: $i,SV68: $i,SV58: $i,SV48: $i,SV34: $i,SV14: $i] :
( ( ( ifeq @ ( product @ SV14 @ SV34 @ SV48 ) @ true @ ( ifeq @ ( product @ SV58 @ SV34 @ SV68 ) @ true @ ( ifeq @ ( sum @ SV68 @ SV48 @ SV76 ) @ true @ ( ifeq @ ( sum @ SV58 @ SV14 @ SV84 ) @ true @ ( product @ SV84 @ SV34 @ SV76 ) @ true ) @ true ) @ true ) @ true )
= true )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[159]) ).
thf(168,plain,
! [SV85: $i,SV77: $i,SV69: $i,SV59: $i,SV49: $i,SV35: $i,SV15: $i] :
( ( ( ifeq @ ( product @ SV15 @ SV35 @ SV49 ) @ true @ ( ifeq @ ( sum @ SV59 @ SV49 @ SV69 ) @ true @ ( ifeq @ ( sum @ SV59 @ SV35 @ SV77 ) @ true @ ( ifeq @ ( sum @ SV59 @ SV15 @ SV85 ) @ true @ ( product @ SV85 @ SV77 @ SV69 ) @ true ) @ true ) @ true ) @ true )
= true )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[160]) ).
thf(169,plain,
! [SV86: $i,SV78: $i,SV70: $i,SV60: $i,SV50: $i,SV36: $i,SV16: $i] :
( ( ( ifeq @ ( product @ SV16 @ SV36 @ SV50 ) @ true @ ( ifeq @ ( product @ SV60 @ SV70 @ SV78 ) @ true @ ( ifeq @ ( sum @ SV86 @ SV70 @ SV36 ) @ true @ ( ifeq @ ( sum @ SV86 @ SV60 @ SV16 ) @ true @ ( sum @ SV86 @ SV78 @ SV50 ) @ true ) @ true ) @ true ) @ true )
= true )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[161]) ).
thf(170,plain,
! [SV87: $i,SV79: $i,SV71: $i,SV61: $i,SV51: $i,SV37: $i,SV17: $i] :
( ( ( ifeq @ ( product @ SV17 @ SV37 @ SV51 ) @ true @ ( ifeq @ ( sum @ SV51 @ SV61 @ SV71 ) @ true @ ( ifeq @ ( sum @ SV37 @ SV61 @ SV79 ) @ true @ ( ifeq @ ( sum @ SV17 @ SV61 @ SV87 ) @ true @ ( product @ SV87 @ SV79 @ SV71 ) @ true ) @ true ) @ true ) @ true )
= true )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[162]) ).
thf(171,plain,
! [SV88: $i,SV80: $i,SV72: $i,SV62: $i,SV52: $i,SV38: $i,SV18: $i] :
( ( ( ifeq @ ( product @ SV18 @ SV38 @ SV52 ) @ true @ ( ifeq @ ( product @ SV62 @ SV72 @ SV80 ) @ true @ ( ifeq @ ( sum @ SV72 @ SV88 @ SV38 ) @ true @ ( ifeq @ ( sum @ SV62 @ SV88 @ SV18 ) @ true @ ( sum @ SV80 @ SV88 @ SV52 ) @ true ) @ true ) @ true ) @ true )
= true )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[163]) ).
thf(172,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[82,171,170,169,168,167,166,165,164,147,146,127,126,125,124,111,110,107,104,103,102,101,92,91,90,89]) ).
thf(173,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[172]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : BOO004-10 : TPTP v8.1.0. Released v7.5.0.
% 0.11/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.34 % Computer : n024.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 : Wed Jun 1 23:23:06 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.41
% 0.13/0.41 No.of.Axioms: 25
% 0.13/0.41
% 0.13/0.41 Length.of.Defs: 0
% 0.13/0.41
% 0.13/0.41 Contains.Choice.Funs: false
% 0.20/0.43 .
% 0.20/0.48 (rf:0,axioms:25,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:27,loop_count:0,foatp_calls:0,translation:fof_full)..............
% 39.41/39.61
% 39.41/39.61 ********************************
% 39.41/39.61 * All subproblems solved! *
% 39.41/39.61 ********************************
% 39.41/39.61 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:25,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:172,loop_count:0,foatp_calls:1,translation:fof_full)
% 39.41/39.63
% 39.41/39.63 %**** Beginning of derivation protocol ****
% 39.41/39.63 % SZS output start CNFRefutation
% See solution above
% 39.41/39.63
% 39.41/39.63 %**** End of derivation protocol ****
% 39.41/39.63 %**** no. of clauses in derivation: 173 ****
% 39.41/39.63 %**** clause counter: 172 ****
% 39.41/39.63
% 39.41/39.63 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:25,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:172,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------