TSTP Solution File: GRP012+5 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : GRP012+5 : 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 : n023.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 10:15:24 EDT 2022
% Result : Theorem 0.70s 0.92s
% Output : CNFRefutation 0.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 9
% Syntax : Number of formulae : 77 ( 56 unt; 8 typ; 0 def)
% Number of atoms : 428 ( 97 equ; 0 cnn)
% Maximal formula atoms : 16 ( 6 avg)
% Number of connectives : 1041 ( 102 ~; 91 |; 54 &; 774 @)
% ( 0 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 7 con; 0-3 aty)
% Number of variables : 306 ( 0 ^ 301 !; 5 ?; 306 :)
% 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_SY43,type,
sK2_SY43: $i ).
thf(tp_sK3_SY47,type,
sK3_SY47: $i ).
thf(tp_sK4_SY50,type,
sK4_SY50: $i ).
thf(tp_sK5_SY52,type,
sK5_SY52: $i ).
thf(tp_sK6_Z,type,
sK6_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 ) )
=> ! [U: $i,V: $i,W: $i,X: $i] :
( ( ( product @ ( inverse @ U ) @ ( inverse @ V ) @ W )
& ( product @ V @ U @ X ) )
=> ( product @ ( inverse @ W ) @ ( inverse @ X ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_distribution) ).
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 ) )
=> ! [U: $i,V: $i,W: $i,X: $i] :
( ( ( product @ ( inverse @ U ) @ ( inverse @ V ) @ W )
& ( product @ V @ U @ X ) )
=> ( product @ ( inverse @ W ) @ ( inverse @ X ) @ E ) ) ) )
= $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 ) )
=> ! [U: $i,V: $i,W: $i,X: $i] :
( ( ( product @ ( inverse @ U ) @ ( inverse @ V ) @ W )
& ( product @ V @ U @ X ) )
=> ( product @ ( inverse @ W ) @ ( inverse @ X ) @ E ) ) ) )
= $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,SY44: $i,SY45: $i,SY46: $i] :
( ( ( product @ ( inverse @ SY43 ) @ ( inverse @ SY44 ) @ SY45 )
& ( product @ SY44 @ SY43 @ SY46 ) )
=> ( product @ ( inverse @ SY45 ) @ ( inverse @ SY46 ) @ sK1_E ) ) )
= $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,SY44: $i,SY45: $i,SY46: $i] :
( ( ( product @ ( inverse @ SY43 ) @ ( inverse @ SY44 ) @ SY45 )
& ( product @ SY44 @ SY43 @ SY46 ) )
=> ( product @ ( inverse @ SY45 ) @ ( inverse @ SY46 ) @ sK1_E ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[4]) ).
thf(13,plain,
( ( ~ ! [SY43: $i,SY44: $i,SY45: $i,SY46: $i] :
( ( ( product @ ( inverse @ SY43 ) @ ( inverse @ SY44 ) @ SY45 )
& ( product @ SY44 @ SY43 @ SY46 ) )
=> ( product @ ( inverse @ SY45 ) @ ( inverse @ SY46 ) @ sK1_E ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[12]) ).
thf(14,plain,
( ( ( product @ ( inverse @ sK2_SY43 ) @ ( inverse @ sK3_SY47 ) @ sK4_SY50 )
& ( product @ sK3_SY47 @ sK2_SY43 @ sK5_SY52 )
& ~ ( product @ ( inverse @ sK4_SY50 ) @ ( inverse @ sK5_SY52 ) @ sK1_E ) )
= $true ),
inference(extcnf_combined,[status(esa)],[13]) ).
thf(15,plain,
( ( ! [X: $i,Y: $i] : ( product @ X @ Y @ ( sK6_Z @ Y @ X ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[5]) ).
thf(16,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(17,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(18,plain,
( ( ! [SY42: $i] : ( product @ ( inverse @ SY42 ) @ SY42 @ sK1_E ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(19,plain,
( ( ! [SY41: $i] : ( product @ SY41 @ ( inverse @ SY41 ) @ sK1_E ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(20,plain,
( ( ! [SY40: $i] : ( product @ sK1_E @ SY40 @ SY40 ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(21,plain,
( ( ! [SY39: $i] : ( product @ SY39 @ sK1_E @ SY39 ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(22,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)],[17]) ).
thf(23,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)],[16]) ).
thf(24,plain,
( ( ! [X: $i,Y: $i] : ( product @ X @ Y @ ( sK6_Z @ Y @ X ) ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(25,plain,
( ( ( product @ ( inverse @ sK2_SY43 ) @ ( inverse @ sK3_SY47 ) @ sK4_SY50 )
& ( product @ sK3_SY47 @ sK2_SY43 @ sK5_SY52 )
& ~ ( product @ ( inverse @ sK4_SY50 ) @ ( inverse @ sK5_SY52 ) @ sK1_E ) )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(26,plain,
( ( ~ ( ~ ~ ( ~ ( product @ ( inverse @ sK2_SY43 ) @ ( inverse @ sK3_SY47 ) @ sK4_SY50 )
| ~ ( product @ sK3_SY47 @ sK2_SY43 @ sK5_SY52 ) )
| ~ ~ ( product @ ( inverse @ sK4_SY50 ) @ ( inverse @ sK5_SY52 ) @ sK1_E ) ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(27,plain,
! [SV1: $i] :
( ( product @ ( inverse @ SV1 ) @ SV1 @ sK1_E )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[18]) ).
thf(28,plain,
! [SV2: $i] :
( ( product @ SV2 @ ( inverse @ SV2 ) @ sK1_E )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[19]) ).
thf(29,plain,
! [SV3: $i] :
( ( product @ sK1_E @ SV3 @ SV3 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[20]) ).
thf(30,plain,
! [SV4: $i] :
( ( product @ SV4 @ sK1_E @ SV4 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[21]) ).
thf(31,plain,
! [SV5: $i] :
( ( ! [SY53: $i,SY54: $i,SY55: $i,SY56: $i,SY57: $i] :
( ~ ( product @ SV5 @ SY53 @ SY55 )
| ~ ( product @ SY53 @ SY54 @ SY56 )
| ~ ( product @ SV5 @ SY56 @ SY57 )
| ( product @ SY55 @ SY54 @ SY57 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[22]) ).
thf(32,plain,
! [SV6: $i] :
( ( ! [SY58: $i,SY59: $i,SY60: $i,SY61: $i,SY62: $i] :
( ~ ( product @ SV6 @ SY58 @ SY60 )
| ~ ( product @ SY58 @ SY59 @ SY61 )
| ~ ( product @ SY60 @ SY59 @ SY62 )
| ( product @ SV6 @ SY61 @ SY62 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[23]) ).
thf(33,plain,
! [SV7: $i] :
( ( ! [SY63: $i] : ( product @ SV7 @ SY63 @ ( sK6_Z @ SY63 @ SV7 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[24]) ).
thf(34,plain,
( ( ~ ~ ( ~ ( product @ ( inverse @ sK2_SY43 ) @ ( inverse @ sK3_SY47 ) @ sK4_SY50 )
| ~ ( product @ sK3_SY47 @ sK2_SY43 @ sK5_SY52 ) )
| ~ ~ ( product @ ( inverse @ sK4_SY50 ) @ ( inverse @ sK5_SY52 ) @ sK1_E ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[26]) ).
thf(35,plain,
! [SV8: $i,SV5: $i] :
( ( ! [SY64: $i,SY65: $i,SY66: $i,SY67: $i] :
( ~ ( product @ SV5 @ SV8 @ SY65 )
| ~ ( product @ SV8 @ SY64 @ SY66 )
| ~ ( product @ SV5 @ SY66 @ SY67 )
| ( product @ SY65 @ SY64 @ SY67 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[31]) ).
thf(36,plain,
! [SV9: $i,SV6: $i] :
( ( ! [SY68: $i,SY69: $i,SY70: $i,SY71: $i] :
( ~ ( product @ SV6 @ SV9 @ SY69 )
| ~ ( product @ SV9 @ SY68 @ SY70 )
| ~ ( product @ SY69 @ SY68 @ SY71 )
| ( product @ SV6 @ SY70 @ SY71 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[32]) ).
thf(37,plain,
! [SV10: $i,SV7: $i] :
( ( product @ SV7 @ SV10 @ ( sK6_Z @ SV10 @ SV7 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[33]) ).
thf(38,plain,
( ( ~ ~ ( ~ ( product @ ( inverse @ sK2_SY43 ) @ ( inverse @ sK3_SY47 ) @ sK4_SY50 )
| ~ ( product @ sK3_SY47 @ sK2_SY43 @ sK5_SY52 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[34]) ).
thf(39,plain,
( ( ~ ~ ( product @ ( inverse @ sK4_SY50 ) @ ( inverse @ sK5_SY52 ) @ sK1_E ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[34]) ).
thf(40,plain,
! [SV11: $i,SV8: $i,SV5: $i] :
( ( ! [SY72: $i,SY73: $i,SY74: $i] :
( ~ ( product @ SV5 @ SV8 @ SY72 )
| ~ ( product @ SV8 @ SV11 @ SY73 )
| ~ ( product @ SV5 @ SY73 @ SY74 )
| ( product @ SY72 @ SV11 @ SY74 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[35]) ).
thf(41,plain,
! [SV12: $i,SV9: $i,SV6: $i] :
( ( ! [SY75: $i,SY76: $i,SY77: $i] :
( ~ ( product @ SV6 @ SV9 @ SY75 )
| ~ ( product @ SV9 @ SV12 @ SY76 )
| ~ ( product @ SY75 @ SV12 @ SY77 )
| ( product @ SV6 @ SY76 @ SY77 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[36]) ).
thf(42,plain,
( ( ~ ( ~ ( product @ ( inverse @ sK2_SY43 ) @ ( inverse @ sK3_SY47 ) @ sK4_SY50 )
| ~ ( product @ sK3_SY47 @ sK2_SY43 @ sK5_SY52 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[38]) ).
thf(43,plain,
( ( ~ ( product @ ( inverse @ sK4_SY50 ) @ ( inverse @ sK5_SY52 ) @ sK1_E ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[39]) ).
thf(44,plain,
! [SV11: $i,SV13: $i,SV8: $i,SV5: $i] :
( ( ! [SY78: $i,SY79: $i] :
( ~ ( product @ SV5 @ SV8 @ SV13 )
| ~ ( product @ SV8 @ SV11 @ SY78 )
| ~ ( product @ SV5 @ SY78 @ SY79 )
| ( product @ SV13 @ SV11 @ SY79 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[40]) ).
thf(45,plain,
! [SV12: $i,SV14: $i,SV9: $i,SV6: $i] :
( ( ! [SY80: $i,SY81: $i] :
( ~ ( product @ SV6 @ SV9 @ SV14 )
| ~ ( product @ SV9 @ SV12 @ SY80 )
| ~ ( product @ SV14 @ SV12 @ SY81 )
| ( product @ SV6 @ SY80 @ SY81 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[41]) ).
thf(46,plain,
( ( ~ ( product @ ( inverse @ sK2_SY43 ) @ ( inverse @ sK3_SY47 ) @ sK4_SY50 )
| ~ ( product @ sK3_SY47 @ sK2_SY43 @ sK5_SY52 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[42]) ).
thf(47,plain,
( ( product @ ( inverse @ sK4_SY50 ) @ ( inverse @ sK5_SY52 ) @ sK1_E )
= $false ),
inference(extcnf_not_pos,[status(thm)],[43]) ).
thf(48,plain,
! [SV15: $i,SV11: $i,SV13: $i,SV8: $i,SV5: $i] :
( ( ! [SY82: $i] :
( ~ ( product @ SV5 @ SV8 @ SV13 )
| ~ ( product @ SV8 @ SV11 @ SV15 )
| ~ ( product @ SV5 @ SV15 @ SY82 )
| ( product @ SV13 @ SV11 @ SY82 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[44]) ).
thf(49,plain,
! [SV16: $i,SV12: $i,SV14: $i,SV9: $i,SV6: $i] :
( ( ! [SY83: $i] :
( ~ ( product @ SV6 @ SV9 @ SV14 )
| ~ ( product @ SV9 @ SV12 @ SV16 )
| ~ ( product @ SV14 @ SV12 @ SY83 )
| ( product @ SV6 @ SV16 @ SY83 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[45]) ).
thf(50,plain,
( ( ~ ( product @ ( inverse @ sK2_SY43 ) @ ( inverse @ sK3_SY47 ) @ sK4_SY50 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[46]) ).
thf(51,plain,
( ( ~ ( product @ sK3_SY47 @ sK2_SY43 @ sK5_SY52 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[46]) ).
thf(52,plain,
! [SV17: $i,SV15: $i,SV11: $i,SV13: $i,SV8: $i,SV5: $i] :
( ( ~ ( product @ SV5 @ SV8 @ SV13 )
| ~ ( product @ SV8 @ SV11 @ SV15 )
| ~ ( product @ SV5 @ SV15 @ SV17 )
| ( product @ SV13 @ SV11 @ SV17 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[48]) ).
thf(53,plain,
! [SV18: $i,SV16: $i,SV12: $i,SV14: $i,SV9: $i,SV6: $i] :
( ( ~ ( product @ SV6 @ SV9 @ SV14 )
| ~ ( product @ SV9 @ SV12 @ SV16 )
| ~ ( product @ SV14 @ SV12 @ SV18 )
| ( product @ SV6 @ SV16 @ SV18 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[49]) ).
thf(54,plain,
( ( product @ ( inverse @ sK2_SY43 ) @ ( inverse @ sK3_SY47 ) @ sK4_SY50 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[50]) ).
thf(55,plain,
( ( product @ sK3_SY47 @ sK2_SY43 @ sK5_SY52 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[51]) ).
thf(56,plain,
! [SV17: $i,SV15: $i,SV11: $i,SV13: $i,SV8: $i,SV5: $i] :
( ( ( ~ ( product @ SV5 @ SV8 @ SV13 )
| ~ ( product @ SV8 @ SV11 @ SV15 )
| ~ ( product @ SV5 @ SV15 @ SV17 ) )
= $true )
| ( ( product @ SV13 @ SV11 @ SV17 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[52]) ).
thf(57,plain,
! [SV18: $i,SV16: $i,SV12: $i,SV14: $i,SV9: $i,SV6: $i] :
( ( ( ~ ( product @ SV6 @ SV9 @ SV14 )
| ~ ( product @ SV9 @ SV12 @ SV16 )
| ~ ( product @ SV14 @ SV12 @ SV18 ) )
= $true )
| ( ( product @ SV6 @ SV16 @ SV18 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[53]) ).
thf(58,plain,
! [SV17: $i,SV15: $i,SV11: $i,SV13: $i,SV8: $i,SV5: $i] :
( ( ( ~ ( product @ SV5 @ SV8 @ SV13 )
| ~ ( product @ SV8 @ SV11 @ SV15 ) )
= $true )
| ( ( ~ ( product @ SV5 @ SV15 @ SV17 ) )
= $true )
| ( ( product @ SV13 @ SV11 @ SV17 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[56]) ).
thf(59,plain,
! [SV18: $i,SV16: $i,SV12: $i,SV14: $i,SV9: $i,SV6: $i] :
( ( ( ~ ( product @ SV6 @ SV9 @ SV14 )
| ~ ( product @ SV9 @ SV12 @ SV16 ) )
= $true )
| ( ( ~ ( product @ SV14 @ SV12 @ SV18 ) )
= $true )
| ( ( product @ SV6 @ SV16 @ SV18 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[57]) ).
thf(60,plain,
! [SV17: $i,SV15: $i,SV11: $i,SV13: $i,SV8: $i,SV5: $i] :
( ( ( ~ ( product @ SV5 @ SV8 @ SV13 ) )
= $true )
| ( ( ~ ( product @ SV8 @ SV11 @ SV15 ) )
= $true )
| ( ( ~ ( product @ SV5 @ SV15 @ SV17 ) )
= $true )
| ( ( product @ SV13 @ SV11 @ SV17 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[58]) ).
thf(61,plain,
! [SV18: $i,SV16: $i,SV12: $i,SV14: $i,SV9: $i,SV6: $i] :
( ( ( ~ ( product @ SV6 @ SV9 @ SV14 ) )
= $true )
| ( ( ~ ( product @ SV9 @ SV12 @ SV16 ) )
= $true )
| ( ( ~ ( product @ SV14 @ SV12 @ SV18 ) )
= $true )
| ( ( product @ SV6 @ SV16 @ SV18 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[59]) ).
thf(62,plain,
! [SV17: $i,SV15: $i,SV11: $i,SV13: $i,SV8: $i,SV5: $i] :
( ( ( product @ SV5 @ SV8 @ SV13 )
= $false )
| ( ( ~ ( product @ SV8 @ SV11 @ SV15 ) )
= $true )
| ( ( ~ ( product @ SV5 @ SV15 @ SV17 ) )
= $true )
| ( ( product @ SV13 @ SV11 @ SV17 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[60]) ).
thf(63,plain,
! [SV18: $i,SV16: $i,SV12: $i,SV14: $i,SV9: $i,SV6: $i] :
( ( ( product @ SV6 @ SV9 @ SV14 )
= $false )
| ( ( ~ ( product @ SV9 @ SV12 @ SV16 ) )
= $true )
| ( ( ~ ( product @ SV14 @ SV12 @ SV18 ) )
= $true )
| ( ( product @ SV6 @ SV16 @ SV18 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[61]) ).
thf(64,plain,
! [SV17: $i,SV13: $i,SV5: $i,SV15: $i,SV11: $i,SV8: $i] :
( ( ( product @ SV8 @ SV11 @ SV15 )
= $false )
| ( ( product @ SV5 @ SV8 @ SV13 )
= $false )
| ( ( ~ ( product @ SV5 @ SV15 @ SV17 ) )
= $true )
| ( ( product @ SV13 @ SV11 @ SV17 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[62]) ).
thf(65,plain,
! [SV18: $i,SV14: $i,SV6: $i,SV16: $i,SV12: $i,SV9: $i] :
( ( ( product @ SV9 @ SV12 @ SV16 )
= $false )
| ( ( product @ SV6 @ SV9 @ SV14 )
= $false )
| ( ( ~ ( product @ SV14 @ SV12 @ SV18 ) )
= $true )
| ( ( product @ SV6 @ SV16 @ SV18 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[63]) ).
thf(66,plain,
! [SV11: $i,SV13: $i,SV8: $i,SV17: $i,SV15: $i,SV5: $i] :
( ( ( product @ SV5 @ SV15 @ SV17 )
= $false )
| ( ( product @ SV5 @ SV8 @ SV13 )
= $false )
| ( ( product @ SV8 @ SV11 @ SV15 )
= $false )
| ( ( product @ SV13 @ SV11 @ SV17 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[64]) ).
thf(67,plain,
! [SV16: $i,SV9: $i,SV6: $i,SV18: $i,SV12: $i,SV14: $i] :
( ( ( product @ SV14 @ SV12 @ SV18 )
= $false )
| ( ( product @ SV6 @ SV9 @ SV14 )
= $false )
| ( ( product @ SV9 @ SV12 @ SV16 )
= $false )
| ( ( product @ SV6 @ SV16 @ SV18 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[65]) ).
thf(68,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[27,67,66,55,54,47,37,30,29,28]) ).
thf(69,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[68]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : GRP012+5 : TPTP v8.1.0. Released v3.1.0.
% 0.04/0.14 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.14/0.36 % Computer : n023.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 600
% 0.14/0.36 % DateTime : Tue Jun 14 14:07:35 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.21/0.38
% 0.21/0.38 No.of.Axioms: 0
% 0.21/0.38
% 0.21/0.38 Length.of.Defs: 0
% 0.21/0.38
% 0.21/0.38 Contains.Choice.Funs: false
% 0.21/0.39 (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)....
% 0.70/0.92
% 0.70/0.92 ********************************
% 0.70/0.92 * All subproblems solved! *
% 0.70/0.92 ********************************
% 0.70/0.92 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:7,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:68,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.70/0.92
% 0.70/0.92 %**** Beginning of derivation protocol ****
% 0.70/0.92 % SZS output start CNFRefutation
% See solution above
% 0.70/0.92
% 0.70/0.92 %**** End of derivation protocol ****
% 0.70/0.92 %**** no. of clauses in derivation: 69 ****
% 0.70/0.92 %**** clause counter: 68 ****
% 0.70/0.92
% 0.70/0.92 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:7,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:68,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------