TSTP Solution File: GRP001+6 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : GRP001+6 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n015.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 10:15:18 EDT 2022
% Result : Theorem 0.20s 0.56s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 8
% Syntax : Number of formulae : 74 ( 54 unt; 7 typ; 0 def)
% Number of atoms : 413 ( 95 equ; 0 cnn)
% Maximal formula atoms : 16 ( 6 avg)
% Number of connectives : 927 ( 86 ~; 86 |; 46 &; 685 @)
% ( 0 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 6 con; 0-3 aty)
% Number of variables : 307 ( 0 ^ 302 !; 5 ?; 307 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_inverse,type,
inverse: $i > $i ).
thf(tp_product,type,
product: $i > $i > $i > $o ).
thf(tp_sK1_E,type,
sK1_E: $i ).
thf(tp_sK2_U,type,
sK2_U: $i ).
thf(tp_sK3_SY47,type,
sK3_SY47: $i ).
thf(tp_sK4_SY49,type,
sK4_SY49: $i ).
thf(tp_sK5_Z,type,
sK5_Z: $i > $i > $i ).
thf(1,conjecture,
! [E: $i] :
( ( ! [X: $i,Y: $i] :
? [Z: $i] : ( product @ X @ Y @ Z )
& ! [X: $i,Y: $i,Z: $i,U: $i,V: $i,W: $i] :
( ( ( product @ X @ Y @ U )
& ( product @ Y @ Z @ V )
& ( product @ U @ Z @ W ) )
=> ( product @ X @ V @ W ) )
& ! [X: $i,Y: $i,Z: $i,U: $i,V: $i,W: $i] :
( ( ( product @ X @ Y @ U )
& ( product @ Y @ Z @ V )
& ( product @ X @ V @ W ) )
=> ( product @ U @ Z @ W ) )
& ! [X: $i] : ( product @ X @ E @ X )
& ! [X: $i] : ( product @ E @ X @ X )
& ! [X: $i] : ( product @ X @ ( inverse @ X ) @ E )
& ! [X: $i] : ( product @ ( inverse @ X ) @ X @ E ) )
=> ( ! [X: $i] : ( product @ X @ X @ E )
=> ! [U: $i,V: $i,W: $i] :
( ( product @ U @ V @ W )
=> ( product @ V @ U @ W ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity) ).
thf(2,negated_conjecture,
( ( ! [E: $i] :
( ( ! [X: $i,Y: $i] :
? [Z: $i] : ( product @ X @ Y @ Z )
& ! [X: $i,Y: $i,Z: $i,U: $i,V: $i,W: $i] :
( ( ( product @ X @ Y @ U )
& ( product @ Y @ Z @ V )
& ( product @ U @ Z @ W ) )
=> ( product @ X @ V @ W ) )
& ! [X: $i,Y: $i,Z: $i,U: $i,V: $i,W: $i] :
( ( ( product @ X @ Y @ U )
& ( product @ Y @ Z @ V )
& ( product @ X @ V @ W ) )
=> ( product @ U @ Z @ W ) )
& ! [X: $i] : ( product @ X @ E @ X )
& ! [X: $i] : ( product @ E @ X @ X )
& ! [X: $i] : ( product @ X @ ( inverse @ X ) @ E )
& ! [X: $i] : ( product @ ( inverse @ X ) @ X @ E ) )
=> ( ! [X: $i] : ( product @ X @ X @ E )
=> ! [U: $i,V: $i,W: $i] :
( ( product @ U @ V @ W )
=> ( product @ V @ U @ W ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [E: $i] :
( ( ! [X: $i,Y: $i] :
? [Z: $i] : ( product @ X @ Y @ Z )
& ! [X: $i,Y: $i,Z: $i,U: $i,V: $i,W: $i] :
( ( ( product @ X @ Y @ U )
& ( product @ Y @ Z @ V )
& ( product @ U @ Z @ W ) )
=> ( product @ X @ V @ W ) )
& ! [X: $i,Y: $i,Z: $i,U: $i,V: $i,W: $i] :
( ( ( product @ X @ Y @ U )
& ( product @ Y @ Z @ V )
& ( product @ X @ V @ W ) )
=> ( product @ U @ Z @ W ) )
& ! [X: $i] : ( product @ X @ E @ X )
& ! [X: $i] : ( product @ E @ X @ X )
& ! [X: $i] : ( product @ X @ ( inverse @ X ) @ E )
& ! [X: $i] : ( product @ ( inverse @ X ) @ X @ E ) )
=> ( ! [X: $i] : ( product @ X @ X @ E )
=> ! [U: $i,V: $i,W: $i] :
( ( product @ U @ V @ W )
=> ( product @ V @ U @ W ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ( ! [X: $i,Y: $i] :
? [Z: $i] : ( product @ X @ Y @ Z )
& ! [X: $i,Y: $i,Z: $i,U: $i,V: $i,W: $i] :
( ( ( product @ X @ Y @ U )
& ( product @ Y @ Z @ V )
& ( product @ U @ Z @ W ) )
=> ( product @ X @ V @ W ) )
& ! [X: $i,Y: $i,Z: $i,U: $i,V: $i,W: $i] :
( ( ( product @ X @ Y @ U )
& ( product @ Y @ Z @ V )
& ( product @ X @ V @ W ) )
=> ( product @ U @ Z @ W ) )
& ! [SY39: $i] : ( product @ SY39 @ sK1_E @ SY39 )
& ! [SY40: $i] : ( product @ sK1_E @ SY40 @ SY40 )
& ! [SY41: $i] : ( product @ SY41 @ ( inverse @ SY41 ) @ sK1_E )
& ! [SY42: $i] : ( product @ ( inverse @ SY42 ) @ SY42 @ sK1_E ) )
=> ( ! [SY43: $i] : ( product @ SY43 @ SY43 @ sK1_E )
=> ! [U: $i,V: $i,W: $i] :
( ( product @ U @ V @ W )
=> ( product @ V @ U @ W ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[3]) ).
thf(5,plain,
( ( ! [X: $i,Y: $i] :
? [Z: $i] : ( product @ X @ Y @ Z ) )
= $true ),
inference(standard_cnf,[status(thm)],[4]) ).
thf(6,plain,
( ( ! [X: $i,Y: $i,Z: $i,U: $i,V: $i,W: $i] :
( ( ( product @ X @ Y @ U )
& ( product @ Y @ Z @ V )
& ( product @ U @ Z @ W ) )
=> ( product @ X @ V @ W ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[4]) ).
thf(7,plain,
( ( ! [X: $i,Y: $i,Z: $i,U: $i,V: $i,W: $i] :
( ( ( product @ X @ Y @ U )
& ( product @ Y @ Z @ V )
& ( product @ X @ V @ W ) )
=> ( product @ U @ Z @ W ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[4]) ).
thf(8,plain,
( ( ! [SY39: $i] : ( product @ SY39 @ sK1_E @ SY39 ) )
= $true ),
inference(standard_cnf,[status(thm)],[4]) ).
thf(9,plain,
( ( ! [SY40: $i] : ( product @ sK1_E @ SY40 @ SY40 ) )
= $true ),
inference(standard_cnf,[status(thm)],[4]) ).
thf(10,plain,
( ( ! [SY41: $i] : ( product @ SY41 @ ( inverse @ SY41 ) @ sK1_E ) )
= $true ),
inference(standard_cnf,[status(thm)],[4]) ).
thf(11,plain,
( ( ! [SY42: $i] : ( product @ ( inverse @ SY42 ) @ SY42 @ sK1_E ) )
= $true ),
inference(standard_cnf,[status(thm)],[4]) ).
thf(12,plain,
( ( ! [SY43: $i] : ( product @ SY43 @ SY43 @ sK1_E ) )
= $true ),
inference(standard_cnf,[status(thm)],[4]) ).
thf(13,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( product @ U @ V @ W )
=> ( product @ V @ U @ W ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[4]) ).
thf(14,plain,
( ( ~ ! [U: $i,V: $i,W: $i] :
( ( product @ U @ V @ W )
=> ( product @ V @ U @ W ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[13]) ).
thf(15,plain,
( ( ( product @ sK2_U @ sK3_SY47 @ sK4_SY49 )
& ~ ( product @ sK3_SY47 @ sK2_U @ sK4_SY49 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[14]) ).
thf(16,plain,
( ( ! [X: $i,Y: $i] : ( product @ X @ Y @ ( sK5_Z @ Y @ X ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[5]) ).
thf(17,plain,
( ( ! [X: $i,Y: $i,Z: $i,U: $i,V: $i,W: $i] :
( ~ ( product @ X @ Y @ U )
| ~ ( product @ Y @ Z @ V )
| ~ ( product @ U @ Z @ W )
| ( product @ X @ V @ W ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[6]) ).
thf(18,plain,
( ( ! [X: $i,Y: $i,Z: $i,U: $i,V: $i,W: $i] :
( ~ ( product @ X @ Y @ U )
| ~ ( product @ Y @ Z @ V )
| ~ ( product @ X @ V @ W )
| ( product @ U @ Z @ W ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[7]) ).
thf(19,plain,
( ( ! [SY43: $i] : ( product @ SY43 @ SY43 @ sK1_E ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(20,plain,
( ( ! [SY42: $i] : ( product @ ( inverse @ SY42 ) @ SY42 @ sK1_E ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(21,plain,
( ( ! [SY41: $i] : ( product @ SY41 @ ( inverse @ SY41 ) @ sK1_E ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(22,plain,
( ( ! [SY40: $i] : ( product @ sK1_E @ SY40 @ SY40 ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(23,plain,
( ( ! [SY39: $i] : ( product @ SY39 @ sK1_E @ SY39 ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(24,plain,
( ( ! [X: $i,Y: $i,Z: $i,U: $i,V: $i,W: $i] :
( ~ ( product @ X @ Y @ U )
| ~ ( product @ Y @ Z @ V )
| ~ ( product @ X @ V @ W )
| ( product @ U @ Z @ W ) ) )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(25,plain,
( ( ! [X: $i,Y: $i,Z: $i,U: $i,V: $i,W: $i] :
( ~ ( product @ X @ Y @ U )
| ~ ( product @ Y @ Z @ V )
| ~ ( product @ U @ Z @ W )
| ( product @ X @ V @ W ) ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(26,plain,
( ( ! [X: $i,Y: $i] : ( product @ X @ Y @ ( sK5_Z @ Y @ X ) ) )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(27,plain,
( ( ( product @ sK2_U @ sK3_SY47 @ sK4_SY49 )
& ~ ( product @ sK3_SY47 @ sK2_U @ sK4_SY49 ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(28,plain,
( ( ~ ( ~ ( product @ sK2_U @ sK3_SY47 @ sK4_SY49 )
| ~ ~ ( product @ sK3_SY47 @ sK2_U @ sK4_SY49 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(29,plain,
! [SV1: $i] :
( ( product @ SV1 @ SV1 @ sK1_E )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[19]) ).
thf(30,plain,
! [SV2: $i] :
( ( product @ ( inverse @ SV2 ) @ SV2 @ sK1_E )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[20]) ).
thf(31,plain,
! [SV3: $i] :
( ( product @ SV3 @ ( inverse @ SV3 ) @ sK1_E )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[21]) ).
thf(32,plain,
! [SV4: $i] :
( ( product @ sK1_E @ SV4 @ SV4 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[22]) ).
thf(33,plain,
! [SV5: $i] :
( ( product @ SV5 @ sK1_E @ SV5 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[23]) ).
thf(34,plain,
! [SV6: $i] :
( ( ! [SY50: $i,SY51: $i,SY52: $i,SY53: $i,SY54: $i] :
( ~ ( product @ SV6 @ SY50 @ SY52 )
| ~ ( product @ SY50 @ SY51 @ SY53 )
| ~ ( product @ SV6 @ SY53 @ SY54 )
| ( product @ SY52 @ SY51 @ SY54 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[24]) ).
thf(35,plain,
! [SV7: $i] :
( ( ! [SY55: $i,SY56: $i,SY57: $i,SY58: $i,SY59: $i] :
( ~ ( product @ SV7 @ SY55 @ SY57 )
| ~ ( product @ SY55 @ SY56 @ SY58 )
| ~ ( product @ SY57 @ SY56 @ SY59 )
| ( product @ SV7 @ SY58 @ SY59 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[25]) ).
thf(36,plain,
! [SV8: $i] :
( ( ! [SY60: $i] : ( product @ SV8 @ SY60 @ ( sK5_Z @ SY60 @ SV8 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[26]) ).
thf(37,plain,
( ( ~ ( product @ sK2_U @ sK3_SY47 @ sK4_SY49 )
| ~ ~ ( product @ sK3_SY47 @ sK2_U @ sK4_SY49 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[28]) ).
thf(38,plain,
! [SV9: $i,SV6: $i] :
( ( ! [SY61: $i,SY62: $i,SY63: $i,SY64: $i] :
( ~ ( product @ SV6 @ SV9 @ SY62 )
| ~ ( product @ SV9 @ SY61 @ SY63 )
| ~ ( product @ SV6 @ SY63 @ SY64 )
| ( product @ SY62 @ SY61 @ SY64 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[34]) ).
thf(39,plain,
! [SV10: $i,SV7: $i] :
( ( ! [SY65: $i,SY66: $i,SY67: $i,SY68: $i] :
( ~ ( product @ SV7 @ SV10 @ SY66 )
| ~ ( product @ SV10 @ SY65 @ SY67 )
| ~ ( product @ SY66 @ SY65 @ SY68 )
| ( product @ SV7 @ SY67 @ SY68 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[35]) ).
thf(40,plain,
! [SV11: $i,SV8: $i] :
( ( product @ SV8 @ SV11 @ ( sK5_Z @ SV11 @ SV8 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[36]) ).
thf(41,plain,
( ( ~ ( product @ sK2_U @ sK3_SY47 @ sK4_SY49 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[37]) ).
thf(42,plain,
( ( ~ ~ ( product @ sK3_SY47 @ sK2_U @ sK4_SY49 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[37]) ).
thf(43,plain,
! [SV12: $i,SV9: $i,SV6: $i] :
( ( ! [SY69: $i,SY70: $i,SY71: $i] :
( ~ ( product @ SV6 @ SV9 @ SY69 )
| ~ ( product @ SV9 @ SV12 @ SY70 )
| ~ ( product @ SV6 @ SY70 @ SY71 )
| ( product @ SY69 @ SV12 @ SY71 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[38]) ).
thf(44,plain,
! [SV13: $i,SV10: $i,SV7: $i] :
( ( ! [SY72: $i,SY73: $i,SY74: $i] :
( ~ ( product @ SV7 @ SV10 @ SY72 )
| ~ ( product @ SV10 @ SV13 @ SY73 )
| ~ ( product @ SY72 @ SV13 @ SY74 )
| ( product @ SV7 @ SY73 @ SY74 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[39]) ).
thf(45,plain,
( ( product @ sK2_U @ sK3_SY47 @ sK4_SY49 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[41]) ).
thf(46,plain,
( ( ~ ( product @ sK3_SY47 @ sK2_U @ sK4_SY49 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[42]) ).
thf(47,plain,
! [SV12: $i,SV14: $i,SV9: $i,SV6: $i] :
( ( ! [SY75: $i,SY76: $i] :
( ~ ( product @ SV6 @ SV9 @ SV14 )
| ~ ( product @ SV9 @ SV12 @ SY75 )
| ~ ( product @ SV6 @ SY75 @ SY76 )
| ( product @ SV14 @ SV12 @ SY76 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[43]) ).
thf(48,plain,
! [SV13: $i,SV15: $i,SV10: $i,SV7: $i] :
( ( ! [SY77: $i,SY78: $i] :
( ~ ( product @ SV7 @ SV10 @ SV15 )
| ~ ( product @ SV10 @ SV13 @ SY77 )
| ~ ( product @ SV15 @ SV13 @ SY78 )
| ( product @ SV7 @ SY77 @ SY78 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[44]) ).
thf(49,plain,
( ( product @ sK3_SY47 @ sK2_U @ sK4_SY49 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[46]) ).
thf(50,plain,
! [SV16: $i,SV12: $i,SV14: $i,SV9: $i,SV6: $i] :
( ( ! [SY79: $i] :
( ~ ( product @ SV6 @ SV9 @ SV14 )
| ~ ( product @ SV9 @ SV12 @ SV16 )
| ~ ( product @ SV6 @ SV16 @ SY79 )
| ( product @ SV14 @ SV12 @ SY79 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[47]) ).
thf(51,plain,
! [SV17: $i,SV13: $i,SV15: $i,SV10: $i,SV7: $i] :
( ( ! [SY80: $i] :
( ~ ( product @ SV7 @ SV10 @ SV15 )
| ~ ( product @ SV10 @ SV13 @ SV17 )
| ~ ( product @ SV15 @ SV13 @ SY80 )
| ( product @ SV7 @ SV17 @ SY80 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[48]) ).
thf(52,plain,
! [SV18: $i,SV16: $i,SV12: $i,SV14: $i,SV9: $i,SV6: $i] :
( ( ~ ( product @ SV6 @ SV9 @ SV14 )
| ~ ( product @ SV9 @ SV12 @ SV16 )
| ~ ( product @ SV6 @ SV16 @ SV18 )
| ( product @ SV14 @ SV12 @ SV18 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[50]) ).
thf(53,plain,
! [SV19: $i,SV17: $i,SV13: $i,SV15: $i,SV10: $i,SV7: $i] :
( ( ~ ( product @ SV7 @ SV10 @ SV15 )
| ~ ( product @ SV10 @ SV13 @ SV17 )
| ~ ( product @ SV15 @ SV13 @ SV19 )
| ( product @ SV7 @ SV17 @ SV19 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[51]) ).
thf(54,plain,
! [SV18: $i,SV16: $i,SV12: $i,SV14: $i,SV9: $i,SV6: $i] :
( ( ( ~ ( product @ SV6 @ SV9 @ SV14 )
| ~ ( product @ SV9 @ SV12 @ SV16 )
| ~ ( product @ SV6 @ SV16 @ SV18 ) )
= $true )
| ( ( product @ SV14 @ SV12 @ SV18 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[52]) ).
thf(55,plain,
! [SV19: $i,SV17: $i,SV13: $i,SV15: $i,SV10: $i,SV7: $i] :
( ( ( ~ ( product @ SV7 @ SV10 @ SV15 )
| ~ ( product @ SV10 @ SV13 @ SV17 )
| ~ ( product @ SV15 @ SV13 @ SV19 ) )
= $true )
| ( ( product @ SV7 @ SV17 @ SV19 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[53]) ).
thf(56,plain,
! [SV18: $i,SV16: $i,SV12: $i,SV14: $i,SV9: $i,SV6: $i] :
( ( ( ~ ( product @ SV6 @ SV9 @ SV14 )
| ~ ( product @ SV9 @ SV12 @ SV16 ) )
= $true )
| ( ( ~ ( product @ SV6 @ SV16 @ SV18 ) )
= $true )
| ( ( product @ SV14 @ SV12 @ SV18 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[54]) ).
thf(57,plain,
! [SV19: $i,SV17: $i,SV13: $i,SV15: $i,SV10: $i,SV7: $i] :
( ( ( ~ ( product @ SV7 @ SV10 @ SV15 )
| ~ ( product @ SV10 @ SV13 @ SV17 ) )
= $true )
| ( ( ~ ( product @ SV15 @ SV13 @ SV19 ) )
= $true )
| ( ( product @ SV7 @ SV17 @ SV19 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[55]) ).
thf(58,plain,
! [SV18: $i,SV16: $i,SV12: $i,SV14: $i,SV9: $i,SV6: $i] :
( ( ( ~ ( product @ SV6 @ SV9 @ SV14 ) )
= $true )
| ( ( ~ ( product @ SV9 @ SV12 @ SV16 ) )
= $true )
| ( ( ~ ( product @ SV6 @ SV16 @ SV18 ) )
= $true )
| ( ( product @ SV14 @ SV12 @ SV18 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[56]) ).
thf(59,plain,
! [SV19: $i,SV17: $i,SV13: $i,SV15: $i,SV10: $i,SV7: $i] :
( ( ( ~ ( product @ SV7 @ SV10 @ SV15 ) )
= $true )
| ( ( ~ ( product @ SV10 @ SV13 @ SV17 ) )
= $true )
| ( ( ~ ( product @ SV15 @ SV13 @ SV19 ) )
= $true )
| ( ( product @ SV7 @ SV17 @ SV19 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[57]) ).
thf(60,plain,
! [SV18: $i,SV16: $i,SV12: $i,SV14: $i,SV9: $i,SV6: $i] :
( ( ( product @ SV6 @ SV9 @ SV14 )
= $false )
| ( ( ~ ( product @ SV9 @ SV12 @ SV16 ) )
= $true )
| ( ( ~ ( product @ SV6 @ SV16 @ SV18 ) )
= $true )
| ( ( product @ SV14 @ SV12 @ SV18 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[58]) ).
thf(61,plain,
! [SV19: $i,SV17: $i,SV13: $i,SV15: $i,SV10: $i,SV7: $i] :
( ( ( product @ SV7 @ SV10 @ SV15 )
= $false )
| ( ( ~ ( product @ SV10 @ SV13 @ SV17 ) )
= $true )
| ( ( ~ ( product @ SV15 @ SV13 @ SV19 ) )
= $true )
| ( ( product @ SV7 @ SV17 @ SV19 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[59]) ).
thf(62,plain,
! [SV18: $i,SV14: $i,SV6: $i,SV16: $i,SV12: $i,SV9: $i] :
( ( ( product @ SV9 @ SV12 @ SV16 )
= $false )
| ( ( product @ SV6 @ SV9 @ SV14 )
= $false )
| ( ( ~ ( product @ SV6 @ SV16 @ SV18 ) )
= $true )
| ( ( product @ SV14 @ SV12 @ SV18 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[60]) ).
thf(63,plain,
! [SV19: $i,SV15: $i,SV7: $i,SV17: $i,SV13: $i,SV10: $i] :
( ( ( product @ SV10 @ SV13 @ SV17 )
= $false )
| ( ( product @ SV7 @ SV10 @ SV15 )
= $false )
| ( ( ~ ( product @ SV15 @ SV13 @ SV19 ) )
= $true )
| ( ( product @ SV7 @ SV17 @ SV19 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[61]) ).
thf(64,plain,
! [SV12: $i,SV14: $i,SV9: $i,SV18: $i,SV16: $i,SV6: $i] :
( ( ( product @ SV6 @ SV16 @ SV18 )
= $false )
| ( ( product @ SV6 @ SV9 @ SV14 )
= $false )
| ( ( product @ SV9 @ SV12 @ SV16 )
= $false )
| ( ( product @ SV14 @ SV12 @ SV18 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[62]) ).
thf(65,plain,
! [SV17: $i,SV10: $i,SV7: $i,SV19: $i,SV13: $i,SV15: $i] :
( ( ( product @ SV15 @ SV13 @ SV19 )
= $false )
| ( ( product @ SV7 @ SV10 @ SV15 )
= $false )
| ( ( product @ SV10 @ SV13 @ SV17 )
= $false )
| ( ( product @ SV7 @ SV17 @ SV19 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[63]) ).
thf(66,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[29,65,64,49,45,40,33,32,31,30]) ).
thf(67,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[66]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : GRP001+6 : TPTP v8.1.0. Released v3.1.0.
% 0.11/0.12 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.33 % Computer : n015.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon Jun 13 14:53:08 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.35
% 0.12/0.35 No.of.Axioms: 0
% 0.12/0.35
% 0.12/0.35 Length.of.Defs: 0
% 0.12/0.35
% 0.12/0.35 Contains.Choice.Funs: false
% 0.12/0.36 (rf:0,axioms:0,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:2,loop_count:0,foatp_calls:0,translation:fof_full)....
% 0.20/0.56
% 0.20/0.56 ********************************
% 0.20/0.56 * All subproblems solved! *
% 0.20/0.56 ********************************
% 0.20/0.56 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:8,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:66,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.20/0.56
% 0.20/0.56 %**** Beginning of derivation protocol ****
% 0.20/0.56 % SZS output start CNFRefutation
% See solution above
% 0.20/0.56
% 0.20/0.56 %**** End of derivation protocol ****
% 0.20/0.56 %**** no. of clauses in derivation: 67 ****
% 0.20/0.56 %**** clause counter: 66 ****
% 0.20/0.56
% 0.20/0.56 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:8,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:66,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------