TSTP Solution File: GRP005-1 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : GRP005-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n026.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 10:15:20 EDT 2022
% Result : Unsatisfiable 0.22s 0.43s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 15
% Syntax : Number of formulae : 81 ( 49 unt; 5 typ; 0 def)
% Number of atoms : 431 ( 110 equ; 0 cnn)
% Maximal formula atoms : 4 ( 5 avg)
% Number of connectives : 777 ( 104 ~; 135 |; 0 &; 538 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 4 con; 0-3 aty)
% Number of variables : 247 ( 0 ^ 247 !; 0 ?; 247 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $i ).
thf(tp_an_element,type,
an_element: $i > $o ).
thf(tp_identity,type,
identity: $i ).
thf(tp_inverse,type,
inverse: $i > $i ).
thf(tp_product,type,
product: $i > $i > $i > $o ).
thf(1,axiom,
! [X: $i,Y: $i,U: $i,Z: $i,V: $i,W: $i] :
( ~ ( product @ X @ Y @ U )
| ~ ( product @ Y @ Z @ V )
| ~ ( product @ X @ V @ W )
| ( product @ U @ Z @ W ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity2) ).
thf(2,axiom,
! [X: $i,Y: $i,U: $i,Z: $i,V: $i,W: $i] :
( ~ ( product @ X @ Y @ U )
| ~ ( product @ Y @ Z @ V )
| ~ ( product @ U @ Z @ W )
| ( product @ X @ V @ W ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity1) ).
thf(3,axiom,
! [X: $i,Y: $i,Z: $i] :
( ~ ( an_element @ X )
| ~ ( an_element @ Y )
| ~ ( product @ X @ ( inverse @ Y ) @ Z )
| ( an_element @ Z ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',condition) ).
thf(4,axiom,
an_element @ a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_of_set) ).
thf(5,axiom,
! [X: $i] : ( product @ ( inverse @ X ) @ X @ identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_inverse) ).
thf(6,axiom,
! [X: $i] : ( product @ X @ ( inverse @ X ) @ identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_inverse) ).
thf(7,axiom,
! [X: $i] : ( product @ X @ identity @ X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_identity) ).
thf(8,axiom,
! [X: $i] : ( product @ identity @ X @ X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_identity) ).
thf(9,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(10,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[9]) ).
thf(11,negated_conjecture,
~ ( an_element @ identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_identity_is_an_element) ).
thf(12,plain,
$false = $false,
inference(unfold_def,[status(thm)],[10]) ).
thf(13,plain,
( ( ! [X: $i,Y: $i,U: $i,Z: $i,V: $i,W: $i] :
( ~ ( product @ X @ Y @ U )
| ~ ( product @ Y @ Z @ V )
| ~ ( product @ X @ V @ W )
| ( product @ U @ Z @ W ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(14,plain,
( ( ! [X: $i,Y: $i,U: $i,Z: $i,V: $i,W: $i] :
( ~ ( product @ X @ Y @ U )
| ~ ( product @ Y @ Z @ V )
| ~ ( product @ U @ Z @ W )
| ( product @ X @ V @ W ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(15,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( an_element @ X )
| ~ ( an_element @ Y )
| ~ ( product @ X @ ( inverse @ Y ) @ Z )
| ( an_element @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(16,plain,
( ( an_element @ a )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(17,plain,
( ( ! [X: $i] : ( product @ ( inverse @ X ) @ X @ identity ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(18,plain,
( ( ! [X: $i] : ( product @ X @ ( inverse @ X ) @ identity ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(19,plain,
( ( ! [X: $i] : ( product @ X @ identity @ X ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(20,plain,
( ( ! [X: $i] : ( product @ identity @ X @ X ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(21,plain,
( ( ~ ( an_element @ identity ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(22,plain,
( ( ~ $false )
= $true ),
inference(polarity_switch,[status(thm)],[12]) ).
thf(23,plain,
( ( ! [X: $i,Y: $i,U: $i,Z: $i] :
( ~ ( product @ X @ Y @ U )
| ! [V: $i] :
( ~ ( product @ Y @ Z @ V )
| ! [W: $i] :
( ~ ( product @ X @ V @ W )
| ( product @ U @ Z @ W ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[13]) ).
thf(24,plain,
( ( ! [X: $i,Y: $i,U: $i,Z: $i] :
( ~ ( product @ X @ Y @ U )
| ! [V: $i] :
( ~ ( product @ Y @ Z @ V )
| ! [W: $i] :
( ~ ( product @ U @ Z @ W )
| ( product @ X @ V @ W ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[14]) ).
thf(25,plain,
( ( ! [X: $i] :
( ~ ( an_element @ X )
| ! [Y: $i] :
( ~ ( an_element @ Y )
| ! [Z: $i] :
( ~ ( product @ X @ ( inverse @ Y ) @ Z )
| ( an_element @ Z ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[15]) ).
thf(26,plain,
( ( ~ ( an_element @ identity ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(27,plain,
( ( ! [X: $i] : ( product @ identity @ X @ X ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(28,plain,
( ( ! [X: $i] : ( product @ X @ identity @ X ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(29,plain,
( ( ! [X: $i] : ( product @ X @ ( inverse @ X ) @ identity ) )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(30,plain,
( ( ! [X: $i] : ( product @ ( inverse @ X ) @ X @ identity ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(31,plain,
( ( an_element @ a )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(32,plain,
( ( ! [X: $i] :
( ~ ( an_element @ X )
| ! [Y: $i] :
( ~ ( an_element @ Y )
| ! [Z: $i] :
( ~ ( product @ X @ ( inverse @ Y ) @ Z )
| ( an_element @ Z ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(33,plain,
( ( ! [X: $i,Y: $i,U: $i,Z: $i] :
( ~ ( product @ X @ Y @ U )
| ! [V: $i] :
( ~ ( product @ Y @ Z @ V )
| ! [W: $i] :
( ~ ( product @ U @ Z @ W )
| ( product @ X @ V @ W ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(34,plain,
( ( ! [X: $i,Y: $i,U: $i,Z: $i] :
( ~ ( product @ X @ Y @ U )
| ! [V: $i] :
( ~ ( product @ Y @ Z @ V )
| ! [W: $i] :
( ~ ( product @ X @ V @ W )
| ( product @ U @ Z @ W ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(35,plain,
( ( ~ $false )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(36,plain,
( ( an_element @ identity )
= $false ),
inference(extcnf_not_pos,[status(thm)],[26]) ).
thf(37,plain,
! [SV1: $i] :
( ( product @ identity @ SV1 @ SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[27]) ).
thf(38,plain,
! [SV2: $i] :
( ( product @ SV2 @ identity @ SV2 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[28]) ).
thf(39,plain,
! [SV3: $i] :
( ( product @ SV3 @ ( inverse @ SV3 ) @ identity )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[29]) ).
thf(40,plain,
! [SV4: $i] :
( ( product @ ( inverse @ SV4 ) @ SV4 @ identity )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[30]) ).
thf(41,plain,
! [SV5: $i] :
( ( ~ ( an_element @ SV5 )
| ! [SY19: $i] :
( ~ ( an_element @ SY19 )
| ! [SY20: $i] :
( ~ ( product @ SV5 @ ( inverse @ SY19 ) @ SY20 )
| ( an_element @ SY20 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[32]) ).
thf(42,plain,
! [SV6: $i] :
( ( ! [SY21: $i,SY22: $i,SY23: $i] :
( ~ ( product @ SV6 @ SY21 @ SY22 )
| ! [SY24: $i] :
( ~ ( product @ SY21 @ SY23 @ SY24 )
| ! [SY25: $i] :
( ~ ( product @ SY22 @ SY23 @ SY25 )
| ( product @ SV6 @ SY24 @ SY25 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[33]) ).
thf(43,plain,
! [SV7: $i] :
( ( ! [SY26: $i,SY27: $i,SY28: $i] :
( ~ ( product @ SV7 @ SY26 @ SY27 )
| ! [SY29: $i] :
( ~ ( product @ SY26 @ SY28 @ SY29 )
| ! [SY30: $i] :
( ~ ( product @ SV7 @ SY29 @ SY30 )
| ( product @ SY27 @ SY28 @ SY30 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[34]) ).
thf(44,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[35]) ).
thf(45,plain,
! [SV5: $i] :
( ( ( ~ ( an_element @ SV5 ) )
= $true )
| ( ( ! [SY19: $i] :
( ~ ( an_element @ SY19 )
| ! [SY20: $i] :
( ~ ( product @ SV5 @ ( inverse @ SY19 ) @ SY20 )
| ( an_element @ SY20 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[41]) ).
thf(46,plain,
! [SV8: $i,SV6: $i] :
( ( ! [SY31: $i,SY32: $i] :
( ~ ( product @ SV6 @ SV8 @ SY31 )
| ! [SY33: $i] :
( ~ ( product @ SV8 @ SY32 @ SY33 )
| ! [SY25: $i] :
( ~ ( product @ SY31 @ SY32 @ SY25 )
| ( product @ SV6 @ SY33 @ SY25 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[42]) ).
thf(47,plain,
! [SV9: $i,SV7: $i] :
( ( ! [SY35: $i,SY36: $i] :
( ~ ( product @ SV7 @ SV9 @ SY35 )
| ! [SY37: $i] :
( ~ ( product @ SV9 @ SY36 @ SY37 )
| ! [SY30: $i] :
( ~ ( product @ SV7 @ SY37 @ SY30 )
| ( product @ SY35 @ SY36 @ SY30 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[43]) ).
thf(48,plain,
! [SV5: $i] :
( ( ( an_element @ SV5 )
= $false )
| ( ( ! [SY19: $i] :
( ~ ( an_element @ SY19 )
| ! [SY20: $i] :
( ~ ( product @ SV5 @ ( inverse @ SY19 ) @ SY20 )
| ( an_element @ SY20 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[45]) ).
thf(49,plain,
! [SV10: $i,SV8: $i,SV6: $i] :
( ( ! [SY39: $i] :
( ~ ( product @ SV6 @ SV8 @ SV10 )
| ! [SY40: $i] :
( ~ ( product @ SV8 @ SY39 @ SY40 )
| ! [SY41: $i] :
( ~ ( product @ SV10 @ SY39 @ SY41 )
| ( product @ SV6 @ SY40 @ SY41 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[46]) ).
thf(50,plain,
! [SV11: $i,SV9: $i,SV7: $i] :
( ( ! [SY42: $i] :
( ~ ( product @ SV7 @ SV9 @ SV11 )
| ! [SY43: $i] :
( ~ ( product @ SV9 @ SY42 @ SY43 )
| ! [SY44: $i] :
( ~ ( product @ SV7 @ SY43 @ SY44 )
| ( product @ SV11 @ SY42 @ SY44 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[47]) ).
thf(51,plain,
! [SV5: $i,SV12: $i] :
( ( ( ~ ( an_element @ SV12 )
| ! [SY45: $i] :
( ~ ( product @ SV5 @ ( inverse @ SV12 ) @ SY45 )
| ( an_element @ SY45 ) ) )
= $true )
| ( ( an_element @ SV5 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[48]) ).
thf(52,plain,
! [SV13: $i,SV10: $i,SV8: $i,SV6: $i] :
( ( ~ ( product @ SV6 @ SV8 @ SV10 )
| ! [SY46: $i] :
( ~ ( product @ SV8 @ SV13 @ SY46 )
| ! [SY47: $i] :
( ~ ( product @ SV10 @ SV13 @ SY47 )
| ( product @ SV6 @ SY46 @ SY47 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[49]) ).
thf(53,plain,
! [SV14: $i,SV11: $i,SV9: $i,SV7: $i] :
( ( ~ ( product @ SV7 @ SV9 @ SV11 )
| ! [SY48: $i] :
( ~ ( product @ SV9 @ SV14 @ SY48 )
| ! [SY49: $i] :
( ~ ( product @ SV7 @ SY48 @ SY49 )
| ( product @ SV11 @ SV14 @ SY49 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[50]) ).
thf(54,plain,
! [SV5: $i,SV12: $i] :
( ( ( ~ ( an_element @ SV12 ) )
= $true )
| ( ( ! [SY45: $i] :
( ~ ( product @ SV5 @ ( inverse @ SV12 ) @ SY45 )
| ( an_element @ SY45 ) ) )
= $true )
| ( ( an_element @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[51]) ).
thf(55,plain,
! [SV13: $i,SV10: $i,SV8: $i,SV6: $i] :
( ( ( ~ ( product @ SV6 @ SV8 @ SV10 ) )
= $true )
| ( ( ! [SY46: $i] :
( ~ ( product @ SV8 @ SV13 @ SY46 )
| ! [SY47: $i] :
( ~ ( product @ SV10 @ SV13 @ SY47 )
| ( product @ SV6 @ SY46 @ SY47 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[52]) ).
thf(56,plain,
! [SV14: $i,SV11: $i,SV9: $i,SV7: $i] :
( ( ( ~ ( product @ SV7 @ SV9 @ SV11 ) )
= $true )
| ( ( ! [SY48: $i] :
( ~ ( product @ SV9 @ SV14 @ SY48 )
| ! [SY49: $i] :
( ~ ( product @ SV7 @ SY48 @ SY49 )
| ( product @ SV11 @ SV14 @ SY49 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[53]) ).
thf(57,plain,
! [SV5: $i,SV12: $i] :
( ( ( an_element @ SV12 )
= $false )
| ( ( ! [SY45: $i] :
( ~ ( product @ SV5 @ ( inverse @ SV12 ) @ SY45 )
| ( an_element @ SY45 ) ) )
= $true )
| ( ( an_element @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[54]) ).
thf(58,plain,
! [SV13: $i,SV10: $i,SV8: $i,SV6: $i] :
( ( ( product @ SV6 @ SV8 @ SV10 )
= $false )
| ( ( ! [SY46: $i] :
( ~ ( product @ SV8 @ SV13 @ SY46 )
| ! [SY47: $i] :
( ~ ( product @ SV10 @ SV13 @ SY47 )
| ( product @ SV6 @ SY46 @ SY47 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[55]) ).
thf(59,plain,
! [SV14: $i,SV11: $i,SV9: $i,SV7: $i] :
( ( ( product @ SV7 @ SV9 @ SV11 )
= $false )
| ( ( ! [SY48: $i] :
( ~ ( product @ SV9 @ SV14 @ SY48 )
| ! [SY49: $i] :
( ~ ( product @ SV7 @ SY48 @ SY49 )
| ( product @ SV11 @ SV14 @ SY49 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[56]) ).
thf(60,plain,
! [SV15: $i,SV12: $i,SV5: $i] :
( ( ( ~ ( product @ SV5 @ ( inverse @ SV12 ) @ SV15 )
| ( an_element @ SV15 ) )
= $true )
| ( ( an_element @ SV12 )
= $false )
| ( ( an_element @ SV5 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[57]) ).
thf(61,plain,
! [SV6: $i,SV10: $i,SV16: $i,SV13: $i,SV8: $i] :
( ( ( ~ ( product @ SV8 @ SV13 @ SV16 )
| ! [SY50: $i] :
( ~ ( product @ SV10 @ SV13 @ SY50 )
| ( product @ SV6 @ SV16 @ SY50 ) ) )
= $true )
| ( ( product @ SV6 @ SV8 @ SV10 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[58]) ).
thf(62,plain,
! [SV11: $i,SV7: $i,SV17: $i,SV14: $i,SV9: $i] :
( ( ( ~ ( product @ SV9 @ SV14 @ SV17 )
| ! [SY51: $i] :
( ~ ( product @ SV7 @ SV17 @ SY51 )
| ( product @ SV11 @ SV14 @ SY51 ) ) )
= $true )
| ( ( product @ SV7 @ SV9 @ SV11 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[59]) ).
thf(63,plain,
! [SV15: $i,SV12: $i,SV5: $i] :
( ( ( ~ ( product @ SV5 @ ( inverse @ SV12 ) @ SV15 ) )
= $true )
| ( ( an_element @ SV15 )
= $true )
| ( ( an_element @ SV12 )
= $false )
| ( ( an_element @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[60]) ).
thf(64,plain,
! [SV6: $i,SV10: $i,SV16: $i,SV13: $i,SV8: $i] :
( ( ( ~ ( product @ SV8 @ SV13 @ SV16 ) )
= $true )
| ( ( ! [SY50: $i] :
( ~ ( product @ SV10 @ SV13 @ SY50 )
| ( product @ SV6 @ SV16 @ SY50 ) ) )
= $true )
| ( ( product @ SV6 @ SV8 @ SV10 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[61]) ).
thf(65,plain,
! [SV11: $i,SV7: $i,SV17: $i,SV14: $i,SV9: $i] :
( ( ( ~ ( product @ SV9 @ SV14 @ SV17 ) )
= $true )
| ( ( ! [SY51: $i] :
( ~ ( product @ SV7 @ SV17 @ SY51 )
| ( product @ SV11 @ SV14 @ SY51 ) ) )
= $true )
| ( ( product @ SV7 @ SV9 @ SV11 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[62]) ).
thf(66,plain,
! [SV15: $i,SV12: $i,SV5: $i] :
( ( ( product @ SV5 @ ( inverse @ SV12 ) @ SV15 )
= $false )
| ( ( an_element @ SV15 )
= $true )
| ( ( an_element @ SV12 )
= $false )
| ( ( an_element @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[63]) ).
thf(67,plain,
! [SV6: $i,SV10: $i,SV16: $i,SV13: $i,SV8: $i] :
( ( ( product @ SV8 @ SV13 @ SV16 )
= $false )
| ( ( ! [SY50: $i] :
( ~ ( product @ SV10 @ SV13 @ SY50 )
| ( product @ SV6 @ SV16 @ SY50 ) ) )
= $true )
| ( ( product @ SV6 @ SV8 @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[64]) ).
thf(68,plain,
! [SV11: $i,SV7: $i,SV17: $i,SV14: $i,SV9: $i] :
( ( ( product @ SV9 @ SV14 @ SV17 )
= $false )
| ( ( ! [SY51: $i] :
( ~ ( product @ SV7 @ SV17 @ SY51 )
| ( product @ SV11 @ SV14 @ SY51 ) ) )
= $true )
| ( ( product @ SV7 @ SV9 @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[65]) ).
thf(69,plain,
! [SV8: $i,SV16: $i,SV6: $i,SV18: $i,SV13: $i,SV10: $i] :
( ( ( ~ ( product @ SV10 @ SV13 @ SV18 )
| ( product @ SV6 @ SV16 @ SV18 ) )
= $true )
| ( ( product @ SV8 @ SV13 @ SV16 )
= $false )
| ( ( product @ SV6 @ SV8 @ SV10 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[67]) ).
thf(70,plain,
! [SV9: $i,SV14: $i,SV11: $i,SV19: $i,SV17: $i,SV7: $i] :
( ( ( ~ ( product @ SV7 @ SV17 @ SV19 )
| ( product @ SV11 @ SV14 @ SV19 ) )
= $true )
| ( ( product @ SV9 @ SV14 @ SV17 )
= $false )
| ( ( product @ SV7 @ SV9 @ SV11 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[68]) ).
thf(71,plain,
! [SV8: $i,SV16: $i,SV6: $i,SV18: $i,SV13: $i,SV10: $i] :
( ( ( ~ ( product @ SV10 @ SV13 @ SV18 ) )
= $true )
| ( ( product @ SV6 @ SV16 @ SV18 )
= $true )
| ( ( product @ SV8 @ SV13 @ SV16 )
= $false )
| ( ( product @ SV6 @ SV8 @ SV10 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[69]) ).
thf(72,plain,
! [SV9: $i,SV14: $i,SV11: $i,SV19: $i,SV17: $i,SV7: $i] :
( ( ( ~ ( product @ SV7 @ SV17 @ SV19 ) )
= $true )
| ( ( product @ SV11 @ SV14 @ SV19 )
= $true )
| ( ( product @ SV9 @ SV14 @ SV17 )
= $false )
| ( ( product @ SV7 @ SV9 @ SV11 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[70]) ).
thf(73,plain,
! [SV8: $i,SV16: $i,SV6: $i,SV18: $i,SV13: $i,SV10: $i] :
( ( ( product @ SV10 @ SV13 @ SV18 )
= $false )
| ( ( product @ SV6 @ SV16 @ SV18 )
= $true )
| ( ( product @ SV8 @ SV13 @ SV16 )
= $false )
| ( ( product @ SV6 @ SV8 @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[71]) ).
thf(74,plain,
! [SV9: $i,SV14: $i,SV11: $i,SV19: $i,SV17: $i,SV7: $i] :
( ( ( product @ SV7 @ SV17 @ SV19 )
= $false )
| ( ( product @ SV11 @ SV14 @ SV19 )
= $true )
| ( ( product @ SV9 @ SV14 @ SV17 )
= $false )
| ( ( product @ SV7 @ SV9 @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[72]) ).
thf(75,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[31,74,73,66,44,40,39,38,37,36]) ).
thf(76,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[75]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GRP005-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.14 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.15/0.35 % Computer : n026.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 600
% 0.15/0.36 % DateTime : Mon Jun 13 11:57:35 EDT 2022
% 0.15/0.36 % CPUTime :
% 0.15/0.37
% 0.15/0.37 No.of.Axioms: 9
% 0.15/0.37
% 0.15/0.37 Length.of.Defs: 0
% 0.15/0.37
% 0.15/0.37 Contains.Choice.Funs: false
% 0.15/0.37 (rf:0,axioms:9,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:11,loop_count:0,foatp_calls:0,translation:fof_full)....
% 0.22/0.43
% 0.22/0.43 ********************************
% 0.22/0.43 * All subproblems solved! *
% 0.22/0.43 ********************************
% 0.22/0.43 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:9,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:75,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.22/0.43
% 0.22/0.43 %**** Beginning of derivation protocol ****
% 0.22/0.43 % SZS output start CNFRefutation
% See solution above
% 0.22/0.43
% 0.22/0.43 %**** End of derivation protocol ****
% 0.22/0.43 %**** no. of clauses in derivation: 76 ****
% 0.22/0.43 %**** clause counter: 75 ****
% 0.22/0.43
% 0.22/0.43 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:9,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:75,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------