TSTP Solution File: GRP767-1 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : GRP767-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sat Jul 16 10:19:55 EDT 2022
% Result : Unsatisfiable 25.98s 26.15s
% Output : CNFRefutation 25.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 33
% Syntax : Number of formulae : 124 ( 113 unt; 11 typ; 0 def)
% Number of atoms : 293 ( 195 equ; 0 cnn)
% Maximal formula atoms : 1 ( 2 avg)
% Number of connectives : 826 ( 6 ~; 0 |; 0 &; 820 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 14 ( 14 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 11 usr; 5 con; 0-3 aty)
% Number of variables : 212 ( 0 ^ 212 !; 0 ?; 212 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_difference,type,
difference: $i > $i > $i ).
thf(tp_eta,type,
eta: $i > $i ).
thf(tp_i,type,
i: $i > $i ).
thf(tp_j,type,
j: $i > $i ).
thf(tp_l,type,
l: $i > $i > $i > $i ).
thf(tp_one,type,
one: $i ).
thf(tp_product,type,
product: $i > $i > $i ).
thf(tp_quotient,type,
quotient: $i > $i > $i ).
thf(tp_t,type,
t: $i > $i > $i ).
thf(tp_x0,type,
x0: $i ).
thf(tp_x1,type,
x1: $i ).
thf(1,axiom,
! [A: $i,B: $i,C: $i] :
( ( t @ ( eta @ A ) @ ( product @ B @ C ) )
= ( product @ ( t @ ( eta @ A ) @ B ) @ ( t @ ( eta @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos20) ).
thf(2,axiom,
! [A: $i,B: $i] :
( ( t @ A @ B )
= ( quotient @ ( product @ A @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos19) ).
thf(3,axiom,
! [A: $i,B: $i,C: $i] :
( ( l @ A @ A @ ( product @ B @ C ) )
= ( product @ ( l @ A @ A @ B ) @ ( l @ A @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos18) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i] :
( ( l @ A @ B @ C )
= ( difference @ ( product @ A @ B ) @ ( product @ A @ ( product @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos17) ).
thf(5,axiom,
! [A: $i,B: $i,C: $i] :
( ( product @ ( eta @ A ) @ ( product @ B @ C ) )
= ( product @ ( product @ ( eta @ A ) @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos16) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( product @ A @ ( product @ B @ ( eta @ A ) ) )
= ( product @ ( product @ A @ B ) @ ( eta @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos15) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( product @ A @ ( product @ ( eta @ A ) @ B ) )
= ( product @ ( j @ ( j @ A ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos14) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( product @ ( i @ ( i @ A ) ) @ B )
= ( product @ ( eta @ A ) @ ( product @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos13) ).
thf(9,axiom,
! [A: $i] :
( ( eta @ A )
= ( product @ ( i @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos12) ).
thf(10,axiom,
! [A: $i] :
( ( product @ ( i @ A ) @ A )
= ( product @ A @ ( j @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos11) ).
thf(11,axiom,
! [A: $i] :
( ( j @ A )
= ( quotient @ one @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos10) ).
thf(12,axiom,
! [A: $i] :
( ( i @ A )
= ( difference @ A @ one ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos09) ).
thf(13,axiom,
! [A: $i,B: $i,C: $i] :
( ( difference @ ( product @ A @ B ) @ ( product @ A @ ( product @ B @ C ) ) )
= ( quotient @ ( quotient @ ( product @ C @ ( product @ A @ B ) ) @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos08) ).
thf(14,axiom,
! [A: $i,B: $i,C: $i] :
( ( difference @ A @ ( product @ ( product @ A @ B ) @ C ) )
= ( quotient @ ( product @ B @ ( product @ C @ A ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos07) ).
thf(15,axiom,
! [A: $i,B: $i] :
( ( product @ ( quotient @ A @ B ) @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos06) ).
thf(16,axiom,
! [A: $i,B: $i] :
( ( quotient @ ( product @ A @ B ) @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos05) ).
thf(17,axiom,
! [A: $i,B: $i] :
( ( difference @ A @ ( product @ A @ B ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos04) ).
thf(18,axiom,
! [A: $i,B: $i] :
( ( product @ A @ ( difference @ A @ B ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos03) ).
thf(19,axiom,
! [A: $i] :
( ( product @ one @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos02) ).
thf(20,axiom,
! [A: $i] :
( ( product @ A @ one )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos01) ).
thf(21,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(22,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[21]) ).
thf(23,negated_conjecture,
( product @ ( j @ ( j @ x0 ) ) @ ( j @ ( product @ x1 @ x0 ) ) )
!= ( j @ x1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
thf(24,plain,
$false = $false,
inference(unfold_def,[status(thm)],[22]) ).
thf(25,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( t @ ( eta @ A ) @ ( product @ B @ C ) )
= ( product @ ( t @ ( eta @ A ) @ B ) @ ( t @ ( eta @ A ) @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(26,plain,
( ( ! [A: $i,B: $i] :
( ( t @ A @ B )
= ( quotient @ ( product @ A @ B ) @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(27,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( l @ A @ A @ ( product @ B @ C ) )
= ( product @ ( l @ A @ A @ B ) @ ( l @ A @ A @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(28,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( l @ A @ B @ C )
= ( difference @ ( product @ A @ B ) @ ( product @ A @ ( product @ B @ C ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(29,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( product @ ( eta @ A ) @ ( product @ B @ C ) )
= ( product @ ( product @ ( eta @ A ) @ B ) @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(30,plain,
( ( ! [A: $i,B: $i] :
( ( product @ A @ ( product @ B @ ( eta @ A ) ) )
= ( product @ ( product @ A @ B ) @ ( eta @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(31,plain,
( ( ! [A: $i,B: $i] :
( ( product @ A @ ( product @ ( eta @ A ) @ B ) )
= ( product @ ( j @ ( j @ A ) ) @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(32,plain,
( ( ! [A: $i,B: $i] :
( ( product @ ( i @ ( i @ A ) ) @ B )
= ( product @ ( eta @ A ) @ ( product @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(33,plain,
( ( ! [A: $i] :
( ( eta @ A )
= ( product @ ( i @ A ) @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(34,plain,
( ( ! [A: $i] :
( ( product @ ( i @ A ) @ A )
= ( product @ A @ ( j @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(35,plain,
( ( ! [A: $i] :
( ( j @ A )
= ( quotient @ one @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(36,plain,
( ( ! [A: $i] :
( ( i @ A )
= ( difference @ A @ one ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(37,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( difference @ ( product @ A @ B ) @ ( product @ A @ ( product @ B @ C ) ) )
= ( quotient @ ( quotient @ ( product @ C @ ( product @ A @ B ) ) @ B ) @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(38,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( difference @ A @ ( product @ ( product @ A @ B ) @ C ) )
= ( quotient @ ( product @ B @ ( product @ C @ A ) ) @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(39,plain,
( ( ! [A: $i,B: $i] :
( ( product @ ( quotient @ A @ B ) @ B )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(40,plain,
( ( ! [A: $i,B: $i] :
( ( quotient @ ( product @ A @ B ) @ B )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(41,plain,
( ( ! [A: $i,B: $i] :
( ( difference @ A @ ( product @ A @ B ) )
= B ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(42,plain,
( ( ! [A: $i,B: $i] :
( ( product @ A @ ( difference @ A @ B ) )
= B ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(43,plain,
( ( ! [A: $i] :
( ( product @ one @ A )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(44,plain,
( ( ! [A: $i] :
( ( product @ A @ one )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(45,plain,
( ( ( ( product @ ( j @ ( j @ x0 ) ) @ ( j @ ( product @ x1 @ x0 ) ) )
!= ( j @ x1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(46,plain,
( ( ~ $false )
= $true ),
inference(polarity_switch,[status(thm)],[24]) ).
thf(47,plain,
( ( ( ( product @ ( j @ ( j @ x0 ) ) @ ( j @ ( product @ x1 @ x0 ) ) )
!= ( j @ x1 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[45]) ).
thf(48,plain,
( ( ( ( product @ ( j @ ( j @ x0 ) ) @ ( j @ ( product @ x1 @ x0 ) ) )
!= ( j @ x1 ) ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(49,plain,
( ( ! [A: $i] :
( ( product @ A @ one )
= A ) )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(50,plain,
( ( ! [A: $i] :
( ( product @ one @ A )
= A ) )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(51,plain,
( ( ! [A: $i,B: $i] :
( ( product @ A @ ( difference @ A @ B ) )
= B ) )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(52,plain,
( ( ! [A: $i,B: $i] :
( ( difference @ A @ ( product @ A @ B ) )
= B ) )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(53,plain,
( ( ! [A: $i,B: $i] :
( ( quotient @ ( product @ A @ B ) @ B )
= A ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(54,plain,
( ( ! [A: $i,B: $i] :
( ( product @ ( quotient @ A @ B ) @ B )
= A ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(55,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( difference @ A @ ( product @ ( product @ A @ B ) @ C ) )
= ( quotient @ ( product @ B @ ( product @ C @ A ) ) @ A ) ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(56,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( difference @ ( product @ A @ B ) @ ( product @ A @ ( product @ B @ C ) ) )
= ( quotient @ ( quotient @ ( product @ C @ ( product @ A @ B ) ) @ B ) @ A ) ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(57,plain,
( ( ! [A: $i] :
( ( i @ A )
= ( difference @ A @ one ) ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(58,plain,
( ( ! [A: $i] :
( ( j @ A )
= ( quotient @ one @ A ) ) )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(59,plain,
( ( ! [A: $i] :
( ( product @ ( i @ A ) @ A )
= ( product @ A @ ( j @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(60,plain,
( ( ! [A: $i] :
( ( eta @ A )
= ( product @ ( i @ A ) @ A ) ) )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(61,plain,
( ( ! [A: $i,B: $i] :
( ( product @ ( i @ ( i @ A ) ) @ B )
= ( product @ ( eta @ A ) @ ( product @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(62,plain,
( ( ! [A: $i,B: $i] :
( ( product @ A @ ( product @ ( eta @ A ) @ B ) )
= ( product @ ( j @ ( j @ A ) ) @ B ) ) )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(63,plain,
( ( ! [A: $i,B: $i] :
( ( product @ A @ ( product @ B @ ( eta @ A ) ) )
= ( product @ ( product @ A @ B ) @ ( eta @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(64,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( product @ ( eta @ A ) @ ( product @ B @ C ) )
= ( product @ ( product @ ( eta @ A ) @ B ) @ C ) ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(65,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( l @ A @ B @ C )
= ( difference @ ( product @ A @ B ) @ ( product @ A @ ( product @ B @ C ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[28]) ).
thf(66,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( l @ A @ A @ ( product @ B @ C ) )
= ( product @ ( l @ A @ A @ B ) @ ( l @ A @ A @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(67,plain,
( ( ! [A: $i,B: $i] :
( ( t @ A @ B )
= ( quotient @ ( product @ A @ B ) @ A ) ) )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(68,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( t @ ( eta @ A ) @ ( product @ B @ C ) )
= ( product @ ( t @ ( eta @ A ) @ B ) @ ( t @ ( eta @ A ) @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(69,plain,
( ( ~ $false )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(70,plain,
( ( ( product @ ( j @ ( j @ x0 ) ) @ ( j @ ( product @ x1 @ x0 ) ) )
= ( j @ x1 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[48]) ).
thf(71,plain,
! [SV1: $i] :
( ( ( product @ SV1 @ one )
= SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[49]) ).
thf(72,plain,
! [SV2: $i] :
( ( ( product @ one @ SV2 )
= SV2 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[50]) ).
thf(73,plain,
! [SV3: $i] :
( ( ! [SY40: $i] :
( ( product @ SV3 @ ( difference @ SV3 @ SY40 ) )
= SY40 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[51]) ).
thf(74,plain,
! [SV4: $i] :
( ( ! [SY41: $i] :
( ( difference @ SV4 @ ( product @ SV4 @ SY41 ) )
= SY41 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[52]) ).
thf(75,plain,
! [SV5: $i] :
( ( ! [SY42: $i] :
( ( quotient @ ( product @ SV5 @ SY42 ) @ SY42 )
= SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[53]) ).
thf(76,plain,
! [SV6: $i] :
( ( ! [SY43: $i] :
( ( product @ ( quotient @ SV6 @ SY43 ) @ SY43 )
= SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[54]) ).
thf(77,plain,
! [SV7: $i] :
( ( ! [SY44: $i,SY45: $i] :
( ( difference @ SV7 @ ( product @ ( product @ SV7 @ SY44 ) @ SY45 ) )
= ( quotient @ ( product @ SY44 @ ( product @ SY45 @ SV7 ) ) @ SV7 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[55]) ).
thf(78,plain,
! [SV8: $i] :
( ( ! [SY46: $i,SY47: $i] :
( ( difference @ ( product @ SV8 @ SY46 ) @ ( product @ SV8 @ ( product @ SY46 @ SY47 ) ) )
= ( quotient @ ( quotient @ ( product @ SY47 @ ( product @ SV8 @ SY46 ) ) @ SY46 ) @ SV8 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[56]) ).
thf(79,plain,
! [SV9: $i] :
( ( ( i @ SV9 )
= ( difference @ SV9 @ one ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[57]) ).
thf(80,plain,
! [SV10: $i] :
( ( ( j @ SV10 )
= ( quotient @ one @ SV10 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[58]) ).
thf(81,plain,
! [SV11: $i] :
( ( ( product @ ( i @ SV11 ) @ SV11 )
= ( product @ SV11 @ ( j @ SV11 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[59]) ).
thf(82,plain,
! [SV12: $i] :
( ( ( eta @ SV12 )
= ( product @ ( i @ SV12 ) @ SV12 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[60]) ).
thf(83,plain,
! [SV13: $i] :
( ( ! [SY48: $i] :
( ( product @ ( i @ ( i @ SV13 ) ) @ SY48 )
= ( product @ ( eta @ SV13 ) @ ( product @ SV13 @ SY48 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[61]) ).
thf(84,plain,
! [SV14: $i] :
( ( ! [SY49: $i] :
( ( product @ SV14 @ ( product @ ( eta @ SV14 ) @ SY49 ) )
= ( product @ ( j @ ( j @ SV14 ) ) @ SY49 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[62]) ).
thf(85,plain,
! [SV15: $i] :
( ( ! [SY50: $i] :
( ( product @ SV15 @ ( product @ SY50 @ ( eta @ SV15 ) ) )
= ( product @ ( product @ SV15 @ SY50 ) @ ( eta @ SV15 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[63]) ).
thf(86,plain,
! [SV16: $i] :
( ( ! [SY51: $i,SY52: $i] :
( ( product @ ( eta @ SV16 ) @ ( product @ SY51 @ SY52 ) )
= ( product @ ( product @ ( eta @ SV16 ) @ SY51 ) @ SY52 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[64]) ).
thf(87,plain,
! [SV17: $i] :
( ( ! [SY53: $i,SY54: $i] :
( ( l @ SV17 @ SY53 @ SY54 )
= ( difference @ ( product @ SV17 @ SY53 ) @ ( product @ SV17 @ ( product @ SY53 @ SY54 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[65]) ).
thf(88,plain,
! [SV18: $i] :
( ( ! [SY55: $i,SY56: $i] :
( ( l @ SV18 @ SV18 @ ( product @ SY55 @ SY56 ) )
= ( product @ ( l @ SV18 @ SV18 @ SY55 ) @ ( l @ SV18 @ SV18 @ SY56 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[66]) ).
thf(89,plain,
! [SV19: $i] :
( ( ! [SY57: $i] :
( ( t @ SV19 @ SY57 )
= ( quotient @ ( product @ SV19 @ SY57 ) @ SV19 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[67]) ).
thf(90,plain,
! [SV20: $i] :
( ( ! [SY58: $i,SY59: $i] :
( ( t @ ( eta @ SV20 ) @ ( product @ SY58 @ SY59 ) )
= ( product @ ( t @ ( eta @ SV20 ) @ SY58 ) @ ( t @ ( eta @ SV20 ) @ SY59 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[68]) ).
thf(91,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[69]) ).
thf(92,plain,
! [SV21: $i,SV3: $i] :
( ( ( product @ SV3 @ ( difference @ SV3 @ SV21 ) )
= SV21 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[73]) ).
thf(93,plain,
! [SV22: $i,SV4: $i] :
( ( ( difference @ SV4 @ ( product @ SV4 @ SV22 ) )
= SV22 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[74]) ).
thf(94,plain,
! [SV23: $i,SV5: $i] :
( ( ( quotient @ ( product @ SV5 @ SV23 ) @ SV23 )
= SV5 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[75]) ).
thf(95,plain,
! [SV24: $i,SV6: $i] :
( ( ( product @ ( quotient @ SV6 @ SV24 ) @ SV24 )
= SV6 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[76]) ).
thf(96,plain,
! [SV25: $i,SV7: $i] :
( ( ! [SY60: $i] :
( ( difference @ SV7 @ ( product @ ( product @ SV7 @ SV25 ) @ SY60 ) )
= ( quotient @ ( product @ SV25 @ ( product @ SY60 @ SV7 ) ) @ SV7 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[77]) ).
thf(97,plain,
! [SV26: $i,SV8: $i] :
( ( ! [SY61: $i] :
( ( difference @ ( product @ SV8 @ SV26 ) @ ( product @ SV8 @ ( product @ SV26 @ SY61 ) ) )
= ( quotient @ ( quotient @ ( product @ SY61 @ ( product @ SV8 @ SV26 ) ) @ SV26 ) @ SV8 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[78]) ).
thf(98,plain,
! [SV27: $i,SV13: $i] :
( ( ( product @ ( i @ ( i @ SV13 ) ) @ SV27 )
= ( product @ ( eta @ SV13 ) @ ( product @ SV13 @ SV27 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[83]) ).
thf(99,plain,
! [SV28: $i,SV14: $i] :
( ( ( product @ SV14 @ ( product @ ( eta @ SV14 ) @ SV28 ) )
= ( product @ ( j @ ( j @ SV14 ) ) @ SV28 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).
thf(100,plain,
! [SV29: $i,SV15: $i] :
( ( ( product @ SV15 @ ( product @ SV29 @ ( eta @ SV15 ) ) )
= ( product @ ( product @ SV15 @ SV29 ) @ ( eta @ SV15 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(101,plain,
! [SV30: $i,SV16: $i] :
( ( ! [SY62: $i] :
( ( product @ ( eta @ SV16 ) @ ( product @ SV30 @ SY62 ) )
= ( product @ ( product @ ( eta @ SV16 ) @ SV30 ) @ SY62 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[86]) ).
thf(102,plain,
! [SV31: $i,SV17: $i] :
( ( ! [SY63: $i] :
( ( l @ SV17 @ SV31 @ SY63 )
= ( difference @ ( product @ SV17 @ SV31 ) @ ( product @ SV17 @ ( product @ SV31 @ SY63 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).
thf(103,plain,
! [SV32: $i,SV18: $i] :
( ( ! [SY64: $i] :
( ( l @ SV18 @ SV18 @ ( product @ SV32 @ SY64 ) )
= ( product @ ( l @ SV18 @ SV18 @ SV32 ) @ ( l @ SV18 @ SV18 @ SY64 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(104,plain,
! [SV33: $i,SV19: $i] :
( ( ( t @ SV19 @ SV33 )
= ( quotient @ ( product @ SV19 @ SV33 ) @ SV19 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[89]) ).
thf(105,plain,
! [SV34: $i,SV20: $i] :
( ( ! [SY65: $i] :
( ( t @ ( eta @ SV20 ) @ ( product @ SV34 @ SY65 ) )
= ( product @ ( t @ ( eta @ SV20 ) @ SV34 ) @ ( t @ ( eta @ SV20 ) @ SY65 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[90]) ).
thf(106,plain,
! [SV35: $i,SV25: $i,SV7: $i] :
( ( ( difference @ SV7 @ ( product @ ( product @ SV7 @ SV25 ) @ SV35 ) )
= ( quotient @ ( product @ SV25 @ ( product @ SV35 @ SV7 ) ) @ SV7 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[96]) ).
thf(107,plain,
! [SV36: $i,SV26: $i,SV8: $i] :
( ( ( difference @ ( product @ SV8 @ SV26 ) @ ( product @ SV8 @ ( product @ SV26 @ SV36 ) ) )
= ( quotient @ ( quotient @ ( product @ SV36 @ ( product @ SV8 @ SV26 ) ) @ SV26 ) @ SV8 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[97]) ).
thf(108,plain,
! [SV37: $i,SV30: $i,SV16: $i] :
( ( ( product @ ( eta @ SV16 ) @ ( product @ SV30 @ SV37 ) )
= ( product @ ( product @ ( eta @ SV16 ) @ SV30 ) @ SV37 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[101]) ).
thf(109,plain,
! [SV38: $i,SV31: $i,SV17: $i] :
( ( ( l @ SV17 @ SV31 @ SV38 )
= ( difference @ ( product @ SV17 @ SV31 ) @ ( product @ SV17 @ ( product @ SV31 @ SV38 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[102]) ).
thf(110,plain,
! [SV39: $i,SV32: $i,SV18: $i] :
( ( ( l @ SV18 @ SV18 @ ( product @ SV32 @ SV39 ) )
= ( product @ ( l @ SV18 @ SV18 @ SV32 ) @ ( l @ SV18 @ SV18 @ SV39 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[103]) ).
thf(111,plain,
! [SV40: $i,SV34: $i,SV20: $i] :
( ( ( t @ ( eta @ SV20 ) @ ( product @ SV34 @ SV40 ) )
= ( product @ ( t @ ( eta @ SV20 ) @ SV34 ) @ ( t @ ( eta @ SV20 ) @ SV40 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[105]) ).
thf(112,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[70,111,110,109,108,107,106,104,100,99,98,95,94,93,92,91,82,81,80,79,72,71]) ).
thf(113,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[112]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : GRP767-1 : TPTP v8.1.0. Released v4.1.0.
% 0.03/0.14 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.14/0.35 % Computer : n018.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Mon Jun 13 20:40:58 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.21/0.37
% 0.21/0.37 No.of.Axioms: 21
% 0.21/0.37
% 0.21/0.37 Length.of.Defs: 0
% 0.21/0.37
% 0.21/0.37 Contains.Choice.Funs: false
% 0.21/0.38 .
% 0.21/0.38 (rf:0,axioms:21,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:23,loop_count:0,foatp_calls:0,translation:fof_full)......
% 25.98/26.15
% 25.98/26.15 ********************************
% 25.98/26.15 * All subproblems solved! *
% 25.98/26.15 ********************************
% 25.98/26.15 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:21,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:112,loop_count:0,foatp_calls:1,translation:fof_full)
% 25.98/26.15
% 25.98/26.15 %**** Beginning of derivation protocol ****
% 25.98/26.15 % SZS output start CNFRefutation
% See solution above
% 25.98/26.15
% 25.98/26.15 %**** End of derivation protocol ****
% 25.98/26.15 %**** no. of clauses in derivation: 113 ****
% 25.98/26.15 %**** clause counter: 112 ****
% 25.98/26.15
% 25.98/26.15 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:21,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:112,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------