%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : GRP001+6 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 10:20:00 AM UTC 2026
% Result : Theorem 0.26s 0.29s
% Output : CNFRefutation 0.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 1
% Syntax : Number of formulae : 78 ( 57 unt; 0 typ; 0 def)
% Number of atoms : 496 ( 118 equ; 0 cnn)
% Maximal formula atoms : 16 ( 6 avg)
% Number of connectives : 1161 ( 187 ~; 107 |; 48 &; 792 @)
% ( 0 <=>; 27 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 6 con; 0-3 aty)
% Number of variables : 378 ( 0 ^; 372 !; 6 ?; 378 :)
% 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_SX0,type,
sK2_SX0: $i ).
thf(tp_sK3_SY67,type,
sK3_SY67: $i ).
thf(tp_sK4_SY76,type,
sK4_SY76: $i ).
thf(tp_sK5_SY69,type,
sK5_SY69: $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/sandbox/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,
( ( ! [SY43: $i] : ( product @ SY43 @ SY43 @ sK1_E ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(16,plain,
( ( ! [SY42: $i] : ( product @ ( inverse @ SY42 ) @ SY42 @ sK1_E ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(17,plain,
( ( ! [SY41: $i] : ( product @ SY41 @ ( inverse @ SY41 ) @ sK1_E ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(18,plain,
( ( ! [SY40: $i] : ( product @ sK1_E @ SY40 @ SY40 ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(19,plain,
( ( ! [SY39: $i] : ( product @ SY39 @ sK1_E @ SY39 ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(20,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)],[7]) ).
thf(21,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)],[6]) ).
thf(22,plain,
( ( ! [X: $i,Y: $i] :
? [Z: $i] : ( product @ X @ Y @ Z ) )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(23,plain,
( ( ~ ! [U: $i,V: $i,W: $i] :
( ( product @ U @ V @ W )
=> ( product @ V @ U @ W ) ) )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(24,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ~ ~ ( ~ ~ ( ~ ( product @ SX0 @ SX1 @ SX3 )
| ~ ( product @ SX1 @ SX2 @ SX4 ) )
| ~ ( product @ SX0 @ SX4 @ SX5 ) )
| ( product @ SX3 @ SX2 @ SX5 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(25,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ~ ~ ( ~ ~ ( ~ ( product @ SX0 @ SX1 @ SX3 )
| ~ ( product @ SX1 @ SX2 @ SX4 ) )
| ~ ( product @ SX3 @ SX2 @ SX5 ) )
| ( product @ SX0 @ SX4 @ SX5 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(26,plain,
( ( ~ ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( product @ SX0 @ SX1 @ SX2 )
| ( product @ SX1 @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(27,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ! [SX2: $i] :
~ ( product @ SX0 @ SX1 @ SX2 ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(28,plain,
! [SV1: $i] :
( ( product @ SV1 @ SV1 @ sK1_E )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[15]) ).
thf(29,plain,
! [SV2: $i] :
( ( product @ ( inverse @ SV2 ) @ SV2 @ sK1_E )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[16]) ).
thf(30,plain,
! [SV3: $i] :
( ( product @ SV3 @ ( inverse @ SV3 ) @ sK1_E )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[17]) ).
thf(31,plain,
! [SV4: $i] :
( ( product @ sK1_E @ SV4 @ SV4 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[18]) ).
thf(32,plain,
! [SV5: $i] :
( ( product @ SV5 @ sK1_E @ SV5 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[19]) ).
thf(33,plain,
! [SV6: $i] :
( ( ! [SY47: $i,SY48: $i,SY49: $i,SY50: $i,SY51: $i] :
( ~ ~ ( ~ ~ ( ~ ( product @ SV6 @ SY47 @ SY49 )
| ~ ( product @ SY47 @ SY48 @ SY50 ) )
| ~ ( product @ SV6 @ SY50 @ SY51 ) )
| ( product @ SY49 @ SY48 @ SY51 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[24]) ).
thf(34,plain,
! [SV7: $i] :
( ( ! [SY52: $i,SY53: $i,SY54: $i,SY55: $i,SY56: $i] :
( ~ ~ ( ~ ~ ( ~ ( product @ SV7 @ SY52 @ SY54 )
| ~ ( product @ SY52 @ SY53 @ SY55 ) )
| ~ ( product @ SY54 @ SY53 @ SY56 ) )
| ( product @ SV7 @ SY55 @ SY56 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[25]) ).
thf(35,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( product @ SX0 @ SX1 @ SX2 )
| ( product @ SX1 @ SX0 @ SX2 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[26]) ).
thf(36,plain,
! [SV8: $i] :
( ( ! [SY57: $i] :
~ ! [SY58: $i] :
~ ( product @ SV8 @ SY57 @ SY58 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[27]) ).
thf(37,plain,
! [SV9: $i,SV6: $i] :
( ( ! [SY59: $i,SY60: $i,SY61: $i,SY62: $i] :
( ~ ~ ( ~ ~ ( ~ ( product @ SV6 @ SV9 @ SY60 )
| ~ ( product @ SV9 @ SY59 @ SY61 ) )
| ~ ( product @ SV6 @ SY61 @ SY62 ) )
| ( product @ SY60 @ SY59 @ SY62 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[33]) ).
thf(38,plain,
! [SV10: $i,SV7: $i] :
( ( ! [SY63: $i,SY64: $i,SY65: $i,SY66: $i] :
( ~ ~ ( ~ ~ ( ~ ( product @ SV7 @ SV10 @ SY64 )
| ~ ( product @ SV10 @ SY63 @ SY65 ) )
| ~ ( product @ SY64 @ SY63 @ SY66 ) )
| ( product @ SV7 @ SY65 @ SY66 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[34]) ).
thf(39,plain,
( ( ! [SY67: $i,SY68: $i] :
( ~ ( product @ sK2_SX0 @ SY67 @ SY68 )
| ( product @ SY67 @ sK2_SX0 @ SY68 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[35]) ).
thf(40,plain,
! [SV11: $i,SV8: $i] :
( ( ~ ! [SY69: $i] :
~ ( product @ SV8 @ SV11 @ SY69 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[36]) ).
thf(41,plain,
! [SV12: $i,SV9: $i,SV6: $i] :
( ( ! [SY70: $i,SY71: $i,SY72: $i] :
( ~ ~ ( ~ ~ ( ~ ( product @ SV6 @ SV9 @ SY70 )
| ~ ( product @ SV9 @ SV12 @ SY71 ) )
| ~ ( product @ SV6 @ SY71 @ SY72 ) )
| ( product @ SY70 @ SV12 @ SY72 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[37]) ).
thf(42,plain,
! [SV13: $i,SV10: $i,SV7: $i] :
( ( ! [SY73: $i,SY74: $i,SY75: $i] :
( ~ ~ ( ~ ~ ( ~ ( product @ SV7 @ SV10 @ SY73 )
| ~ ( product @ SV10 @ SV13 @ SY74 ) )
| ~ ( product @ SY73 @ SV13 @ SY75 ) )
| ( product @ SV7 @ SY74 @ SY75 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[38]) ).
thf(43,plain,
( ( ! [SY76: $i] :
( ~ ( product @ sK2_SX0 @ sK3_SY67 @ SY76 )
| ( product @ sK3_SY67 @ sK2_SX0 @ SY76 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[39]) ).
thf(44,plain,
! [SV11: $i,SV8: $i] :
( ( ! [SY69: $i] :
~ ( product @ SV8 @ SV11 @ SY69 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[40]) ).
thf(45,plain,
! [SV12: $i,SV14: $i,SV9: $i,SV6: $i] :
( ( ! [SY77: $i,SY78: $i] :
( ~ ~ ( ~ ~ ( ~ ( product @ SV6 @ SV9 @ SV14 )
| ~ ( product @ SV9 @ SV12 @ SY77 ) )
| ~ ( product @ SV6 @ SY77 @ SY78 ) )
| ( product @ SV14 @ SV12 @ SY78 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[41]) ).
thf(46,plain,
! [SV13: $i,SV15: $i,SV10: $i,SV7: $i] :
( ( ! [SY79: $i,SY80: $i] :
( ~ ~ ( ~ ~ ( ~ ( product @ SV7 @ SV10 @ SV15 )
| ~ ( product @ SV10 @ SV13 @ SY79 ) )
| ~ ( product @ SV15 @ SV13 @ SY80 ) )
| ( product @ SV7 @ SY79 @ SY80 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[42]) ).
thf(47,plain,
( ( ~ ( product @ sK2_SX0 @ sK3_SY67 @ sK4_SY76 )
| ( product @ sK3_SY67 @ sK2_SX0 @ sK4_SY76 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[43]) ).
thf(48,plain,
! [SV11: $i,SV8: $i] :
( ( ~ ( product @ SV8 @ SV11 @ ( sK5_SY69 @ SV11 @ SV8 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[44]) ).
thf(49,plain,
! [SV16: $i,SV12: $i,SV14: $i,SV9: $i,SV6: $i] :
( ( ! [SY81: $i] :
( ~ ~ ( ~ ~ ( ~ ( product @ SV6 @ SV9 @ SV14 )
| ~ ( product @ SV9 @ SV12 @ SV16 ) )
| ~ ( product @ SV6 @ SV16 @ SY81 ) )
| ( product @ SV14 @ SV12 @ SY81 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[45]) ).
thf(50,plain,
! [SV17: $i,SV13: $i,SV15: $i,SV10: $i,SV7: $i] :
( ( ! [SY82: $i] :
( ~ ~ ( ~ ~ ( ~ ( product @ SV7 @ SV10 @ SV15 )
| ~ ( product @ SV10 @ SV13 @ SV17 ) )
| ~ ( product @ SV15 @ SV13 @ SY82 ) )
| ( product @ SV7 @ SV17 @ SY82 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[46]) ).
thf(51,plain,
( ( ~ ( product @ sK2_SX0 @ sK3_SY67 @ sK4_SY76 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[47]) ).
thf(52,plain,
( ( product @ sK3_SY67 @ sK2_SX0 @ sK4_SY76 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[47]) ).
thf(53,plain,
! [SV11: $i,SV8: $i] :
( ( product @ SV8 @ SV11 @ ( sK5_SY69 @ SV11 @ SV8 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[48]) ).
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 ) )
| ( product @ SV14 @ SV12 @ SV18 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[49]) ).
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 ) )
| ( product @ SV7 @ SV17 @ SV19 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[50]) ).
thf(56,plain,
( ( product @ sK2_SX0 @ sK3_SY67 @ sK4_SY76 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[51]) ).
thf(57,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)],[54]) ).
thf(58,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)],[55]) ).
thf(59,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 ) ) )
= $false )
| ( ( product @ SV14 @ SV12 @ SV18 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[57]) ).
thf(60,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 ) ) )
= $false )
| ( ( product @ SV7 @ SV17 @ SV19 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[58]) ).
thf(61,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_not_neg,[status(thm)],[59]) ).
thf(62,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_not_neg,[status(thm)],[60]) ).
thf(63,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)],[61]) ).
thf(64,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)],[62]) ).
thf(65,plain,
! [SV18: $i,SV16: $i,SV12: $i,SV14: $i,SV9: $i,SV6: $i] :
( ( ( ~ ( ~ ( product @ SV6 @ SV9 @ SV14 )
| ~ ( product @ SV9 @ SV12 @ SV16 ) ) )
= $false )
| ( ( ~ ( product @ SV6 @ SV16 @ SV18 ) )
= $true )
| ( ( product @ SV14 @ SV12 @ SV18 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[63]) ).
thf(66,plain,
! [SV19: $i,SV17: $i,SV13: $i,SV15: $i,SV10: $i,SV7: $i] :
( ( ( ~ ( ~ ( product @ SV7 @ SV10 @ SV15 )
| ~ ( product @ SV10 @ SV13 @ SV17 ) ) )
= $false )
| ( ( ~ ( product @ SV15 @ SV13 @ SV19 ) )
= $true )
| ( ( product @ SV7 @ SV17 @ SV19 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[64]) ).
thf(67,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_not_neg,[status(thm)],[65]) ).
thf(68,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_not_neg,[status(thm)],[66]) ).
thf(69,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)],[67]) ).
thf(70,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)],[68]) ).
thf(71,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)],[69]) ).
thf(72,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)],[70]) ).
thf(73,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)],[71]) ).
thf(74,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)],[72]) ).
thf(75,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)],[73]) ).
thf(76,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)],[74]) ).
thf(77,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[28,76,75,56,53,52,32,31,30,29]) ).
thf(78,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[77]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP001+6 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.20 % Computer : n014.cluster.edu
% 0.07/0.20 % Model : x86_64 x86_64
% 0.07/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.20 % Memory : 8046.5625MB
% 0.07/0.20 % OS : Linux 6.8.0-71-generic
% 0.07/0.20 % CPULimit : 300
% 0.07/0.20 % WCLimit : 300
% 0.07/0.20 % DateTime : Tue Oct 6 10:30:56 UTC 2026
% 0.07/0.21 % CPUTime :
% 0.07/0.21 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.26/0.29
% 0.26/0.29 No.of.Axioms: 0
% 0.26/0.29
% 0.26/0.29 Length.of.Defs: 0
% 0.26/0.29
% 0.26/0.29 Contains.Choice.Funs: false
% 0.26/0.29 ...
% 0.26/0.29
% 0.26/0.29 ********************************
% 0.26/0.29 * All subproblems solved! *
% 0.26/0.29 ********************************
% 0.26/0.29 % SZS status Theorem for /export/starexec/sandbox/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:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:77,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.26/0.29
% 0.26/0.29 %**** Beginning of derivation protocol ****
% 0.26/0.29 % SZS output start CNFRefutation
% See solution above
% 0.26/0.29
% 0.26/0.29 %**** End of derivation protocol ****
% 0.26/0.29 %**** no. of clauses in derivation: 78 ****
% 0.26/0.29 %**** clause counter: 77 ****
% 0.26/0.29
% 0.26/0.29 % SZS status Theorem for /export/starexec/sandbox/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:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:77,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------