TSTP Solution File: GRP194+1 by LEO-II---1.7.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : GRP194+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n017.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 10:16:54 EDT 2022
% Result : Theorem 32.74s 32.94s
% Output : CNFRefutation 32.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 17
% Syntax : Number of formulae : 113 ( 58 unt; 9 typ; 0 def)
% Number of atoms : 648 ( 229 equ; 0 cnn)
% Maximal formula atoms : 4 ( 6 avg)
% Number of connectives : 1428 ( 204 ~; 188 |; 20 &;1002 @)
% ( 2 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 11 ( 11 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 9 usr; 5 con; 0-3 aty)
% Number of variables : 247 ( 0 ^ 245 !; 2 ?; 247 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_f,type,
f: $i ).
thf(tp_f_left_zero,type,
f_left_zero: $i ).
thf(tp_group_member,type,
group_member: $i > $i > $o ).
thf(tp_h,type,
h: $i ).
thf(tp_left_zero,type,
left_zero: $i > $i > $o ).
thf(tp_multiply,type,
multiply: $i > $i > $i > $i ).
thf(tp_phi,type,
phi: $i > $i ).
thf(tp_sK1_Y,type,
sK1_Y: $i > $i > $i ).
thf(tp_sK2_Y,type,
sK2_Y: $i > $i ).
thf(1,axiom,
! [G: $i,X: $i] :
( ( left_zero @ G @ X )
<=> ( ( group_member @ X @ G )
& ! [Y: $i] :
( ( group_member @ Y @ G )
=> ( ( multiply @ G @ X @ Y )
= X ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_zero) ).
thf(2,axiom,
! [X: $i] :
( ( group_member @ X @ h )
=> ? [Y: $i] :
( ( group_member @ Y @ f )
& ( ( phi @ Y )
= X ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',surjective) ).
thf(3,axiom,
! [X: $i,Y: $i] :
( ( ( group_member @ X @ f )
& ( group_member @ Y @ f ) )
=> ( ( multiply @ h @ ( phi @ X ) @ ( phi @ Y ) )
= ( phi @ ( multiply @ f @ X @ Y ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',homomorphism2) ).
thf(4,axiom,
! [X: $i] :
( ( group_member @ X @ f )
=> ( group_member @ ( phi @ X ) @ h ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',homomorphism1) ).
thf(5,axiom,
! [G: $i,X: $i,Y: $i,Z: $i] :
( ( ( group_member @ X @ G )
& ( group_member @ Y @ G )
& ( group_member @ Z @ G ) )
=> ( ( multiply @ G @ ( multiply @ G @ X @ Y ) @ Z )
= ( multiply @ G @ X @ ( multiply @ G @ Y @ Z ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity) ).
thf(6,axiom,
! [G: $i,X: $i,Y: $i] :
( ( ( group_member @ X @ G )
& ( group_member @ Y @ G ) )
=> ( group_member @ ( multiply @ G @ X @ Y ) @ G ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',total_function) ).
thf(7,axiom,
left_zero @ f @ f_left_zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_zero_for_f) ).
thf(8,conjecture,
left_zero @ h @ ( phi @ f_left_zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_left_zero_h) ).
thf(9,negated_conjecture,
( ( left_zero @ h @ ( phi @ f_left_zero ) )
= $false ),
inference(negate_conjecture,[status(cth)],[8]) ).
thf(10,plain,
( ( left_zero @ h @ ( phi @ f_left_zero ) )
= $false ),
inference(unfold_def,[status(thm)],[9]) ).
thf(11,plain,
( ( ! [G: $i,X: $i] :
( ( left_zero @ G @ X )
<=> ( ( group_member @ X @ G )
& ! [Y: $i] :
( ( group_member @ Y @ G )
=> ( ( multiply @ G @ X @ Y )
= X ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(12,plain,
( ( ! [X: $i] :
( ( group_member @ X @ h )
=> ? [Y: $i] :
( ( group_member @ Y @ f )
& ( ( phi @ Y )
= X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(13,plain,
( ( ! [X: $i,Y: $i] :
( ( ( group_member @ X @ f )
& ( group_member @ Y @ f ) )
=> ( ( multiply @ h @ ( phi @ X ) @ ( phi @ Y ) )
= ( phi @ ( multiply @ f @ X @ Y ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(14,plain,
( ( ! [X: $i] :
( ( group_member @ X @ f )
=> ( group_member @ ( phi @ X ) @ h ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(15,plain,
( ( ! [G: $i,X: $i,Y: $i,Z: $i] :
( ( ( group_member @ X @ G )
& ( group_member @ Y @ G )
& ( group_member @ Z @ G ) )
=> ( ( multiply @ G @ ( multiply @ G @ X @ Y ) @ Z )
= ( multiply @ G @ X @ ( multiply @ G @ Y @ Z ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(16,plain,
( ( ! [G: $i,X: $i,Y: $i] :
( ( ( group_member @ X @ G )
& ( group_member @ Y @ G ) )
=> ( group_member @ ( multiply @ G @ X @ Y ) @ G ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(17,plain,
( ( left_zero @ f @ f_left_zero )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(18,plain,
( ( ~ ( left_zero @ h @ ( phi @ f_left_zero ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[10]) ).
thf(19,plain,
( ( ! [G: $i,X: $i] :
( ( ( group_member @ ( sK1_Y @ X @ G ) @ G )
& ( ( multiply @ G @ X @ ( sK1_Y @ X @ G ) )
!= X ) )
| ~ ( group_member @ X @ G )
| ( left_zero @ G @ X ) )
& ! [G: $i,X: $i] :
( ~ ( left_zero @ G @ X )
| ! [Y: $i] :
( ~ ( group_member @ Y @ G )
| ( ( multiply @ G @ X @ Y )
= X ) ) )
& ! [G: $i,X: $i] :
( ~ ( left_zero @ G @ X )
| ( group_member @ X @ G ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[11]) ).
thf(20,plain,
( ( ! [X: $i] :
( ~ ( group_member @ X @ h )
| ( ( ( phi @ ( sK2_Y @ X ) )
= X )
& ( group_member @ ( sK2_Y @ X ) @ f ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[12]) ).
thf(21,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( group_member @ X @ f )
| ~ ( group_member @ Y @ f )
| ( ( multiply @ h @ ( phi @ X ) @ ( phi @ Y ) )
= ( phi @ ( multiply @ f @ X @ Y ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[13]) ).
thf(22,plain,
( ( ! [X: $i] :
( ~ ( group_member @ X @ f )
| ( group_member @ ( phi @ X ) @ h ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[14]) ).
thf(23,plain,
( ( ! [G: $i,X: $i,Y: $i,Z: $i] :
( ~ ( group_member @ X @ G )
| ~ ( group_member @ Y @ G )
| ~ ( group_member @ Z @ G )
| ( ( multiply @ G @ ( multiply @ G @ X @ Y ) @ Z )
= ( multiply @ G @ X @ ( multiply @ G @ Y @ Z ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[15]) ).
thf(24,plain,
( ( ! [G: $i,X: $i,Y: $i] :
( ~ ( group_member @ X @ G )
| ~ ( group_member @ Y @ G )
| ( group_member @ ( multiply @ G @ X @ Y ) @ G ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[16]) ).
thf(25,plain,
( ( left_zero @ f @ f_left_zero )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(26,plain,
( ( ! [G: $i,X: $i,Y: $i] :
( ~ ( group_member @ X @ G )
| ~ ( group_member @ Y @ G )
| ( group_member @ ( multiply @ G @ X @ Y ) @ G ) ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(27,plain,
( ( ! [G: $i,X: $i,Y: $i,Z: $i] :
( ~ ( group_member @ X @ G )
| ~ ( group_member @ Y @ G )
| ~ ( group_member @ Z @ G )
| ( ( multiply @ G @ ( multiply @ G @ X @ Y ) @ Z )
= ( multiply @ G @ X @ ( multiply @ G @ Y @ Z ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(28,plain,
( ( ! [X: $i] :
( ~ ( group_member @ X @ f )
| ( group_member @ ( phi @ X ) @ h ) ) )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(29,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( group_member @ X @ f )
| ~ ( group_member @ Y @ f )
| ( ( multiply @ h @ ( phi @ X ) @ ( phi @ Y ) )
= ( phi @ ( multiply @ f @ X @ Y ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(30,plain,
( ( ! [X: $i] :
( ~ ( group_member @ X @ h )
| ( ( ( phi @ ( sK2_Y @ X ) )
= X )
& ( group_member @ ( sK2_Y @ X ) @ f ) ) ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(31,plain,
( ( ! [G: $i,X: $i] :
( ( ( group_member @ ( sK1_Y @ X @ G ) @ G )
& ( ( multiply @ G @ X @ ( sK1_Y @ X @ G ) )
!= X ) )
| ~ ( group_member @ X @ G )
| ( left_zero @ G @ X ) )
& ! [G: $i,X: $i] :
( ~ ( left_zero @ G @ X )
| ! [Y: $i] :
( ~ ( group_member @ Y @ G )
| ( ( multiply @ G @ X @ Y )
= X ) ) )
& ! [G: $i,X: $i] :
( ~ ( left_zero @ G @ X )
| ( group_member @ X @ G ) ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(32,plain,
( ( ~ ( left_zero @ h @ ( phi @ f_left_zero ) ) )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(33,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( group_member @ ( sK1_Y @ SX1 @ SX0 ) @ SX0 )
| ~ ( ( ( multiply @ SX0 @ SX1 @ ( sK1_Y @ SX1 @ SX0 ) )
!= SX1 ) ) )
| ~ ( group_member @ SX1 @ SX0 )
| ( left_zero @ SX0 @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( left_zero @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( group_member @ SX2 @ SX0 )
| ( ( multiply @ SX0 @ SX1 @ SX2 )
= SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( left_zero @ SX0 @ SX1 )
| ( group_member @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(34,plain,
( ( ! [SX0: $i] :
( ~ ( group_member @ SX0 @ h )
| ~ ( ( ( phi @ ( sK2_Y @ SX0 ) )
!= SX0 )
| ~ ( group_member @ ( sK2_Y @ SX0 ) @ f ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(35,plain,
! [SV1: $i] :
( ( ! [SY15: $i,SY16: $i] :
( ~ ( group_member @ SY15 @ SV1 )
| ~ ( group_member @ SY16 @ SV1 )
| ( group_member @ ( multiply @ SV1 @ SY15 @ SY16 ) @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[26]) ).
thf(36,plain,
! [SV2: $i] :
( ( ! [SY17: $i,SY18: $i,SY19: $i] :
( ~ ( group_member @ SY17 @ SV2 )
| ~ ( group_member @ SY18 @ SV2 )
| ~ ( group_member @ SY19 @ SV2 )
| ( ( multiply @ SV2 @ ( multiply @ SV2 @ SY17 @ SY18 ) @ SY19 )
= ( multiply @ SV2 @ SY17 @ ( multiply @ SV2 @ SY18 @ SY19 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[27]) ).
thf(37,plain,
! [SV3: $i] :
( ( ~ ( group_member @ SV3 @ f )
| ( group_member @ ( phi @ SV3 ) @ h ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[28]) ).
thf(38,plain,
! [SV4: $i] :
( ( ! [SY20: $i] :
( ~ ( group_member @ SV4 @ f )
| ~ ( group_member @ SY20 @ f )
| ( ( multiply @ h @ ( phi @ SV4 ) @ ( phi @ SY20 ) )
= ( phi @ ( multiply @ f @ SV4 @ SY20 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[29]) ).
thf(39,plain,
( ( left_zero @ h @ ( phi @ f_left_zero ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[32]) ).
thf(40,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( group_member @ ( sK1_Y @ SX1 @ SX0 ) @ SX0 )
| ~ ( ( ( multiply @ SX0 @ SX1 @ ( sK1_Y @ SX1 @ SX0 ) )
!= SX1 ) ) )
| ~ ( group_member @ SX1 @ SX0 )
| ( left_zero @ SX0 @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( left_zero @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( group_member @ SX2 @ SX0 )
| ( ( multiply @ SX0 @ SX1 @ SX2 )
= SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( left_zero @ SX0 @ SX1 )
| ( group_member @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[33]) ).
thf(41,plain,
! [SV5: $i] :
( ( ~ ( group_member @ SV5 @ h )
| ~ ( ( ( phi @ ( sK2_Y @ SV5 ) )
!= SV5 )
| ~ ( group_member @ ( sK2_Y @ SV5 ) @ f ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[34]) ).
thf(42,plain,
! [SV1: $i,SV6: $i] :
( ( ! [SY21: $i] :
( ~ ( group_member @ SV6 @ SV1 )
| ~ ( group_member @ SY21 @ SV1 )
| ( group_member @ ( multiply @ SV1 @ SV6 @ SY21 ) @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[35]) ).
thf(43,plain,
! [SV2: $i,SV7: $i] :
( ( ! [SY22: $i,SY23: $i] :
( ~ ( group_member @ SV7 @ SV2 )
| ~ ( group_member @ SY22 @ SV2 )
| ~ ( group_member @ SY23 @ SV2 )
| ( ( multiply @ SV2 @ ( multiply @ SV2 @ SV7 @ SY22 ) @ SY23 )
= ( multiply @ SV2 @ SV7 @ ( multiply @ SV2 @ SY22 @ SY23 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[36]) ).
thf(44,plain,
! [SV3: $i] :
( ( ( ~ ( group_member @ SV3 @ f ) )
= $true )
| ( ( group_member @ ( phi @ SV3 ) @ h )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[37]) ).
thf(45,plain,
! [SV8: $i,SV4: $i] :
( ( ~ ( group_member @ SV4 @ f )
| ~ ( group_member @ SV8 @ f )
| ( ( multiply @ h @ ( phi @ SV4 ) @ ( phi @ SV8 ) )
= ( phi @ ( multiply @ f @ SV4 @ SV8 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[38]) ).
thf(46,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( group_member @ ( sK1_Y @ SX1 @ SX0 ) @ SX0 )
| ~ ( ( ( multiply @ SX0 @ SX1 @ ( sK1_Y @ SX1 @ SX0 ) )
!= SX1 ) ) )
| ~ ( group_member @ SX1 @ SX0 )
| ( left_zero @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[40]) ).
thf(47,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( left_zero @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( group_member @ SX2 @ SX0 )
| ( ( multiply @ SX0 @ SX1 @ SX2 )
= SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( left_zero @ SX0 @ SX1 )
| ( group_member @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[40]) ).
thf(48,plain,
! [SV5: $i] :
( ( ( ~ ( group_member @ SV5 @ h ) )
= $true )
| ( ( ~ ( ( ( phi @ ( sK2_Y @ SV5 ) )
!= SV5 )
| ~ ( group_member @ ( sK2_Y @ SV5 ) @ f ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[41]) ).
thf(49,plain,
! [SV9: $i,SV1: $i,SV6: $i] :
( ( ~ ( group_member @ SV6 @ SV1 )
| ~ ( group_member @ SV9 @ SV1 )
| ( group_member @ ( multiply @ SV1 @ SV6 @ SV9 ) @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[42]) ).
thf(50,plain,
! [SV10: $i,SV2: $i,SV7: $i] :
( ( ! [SY24: $i] :
( ~ ( group_member @ SV7 @ SV2 )
| ~ ( group_member @ SV10 @ SV2 )
| ~ ( group_member @ SY24 @ SV2 )
| ( ( multiply @ SV2 @ ( multiply @ SV2 @ SV7 @ SV10 ) @ SY24 )
= ( multiply @ SV2 @ SV7 @ ( multiply @ SV2 @ SV10 @ SY24 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[43]) ).
thf(51,plain,
! [SV3: $i] :
( ( ( group_member @ SV3 @ f )
= $false )
| ( ( group_member @ ( phi @ SV3 ) @ h )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[44]) ).
thf(52,plain,
! [SV8: $i,SV4: $i] :
( ( ( ~ ( group_member @ SV4 @ f )
| ~ ( group_member @ SV8 @ f ) )
= $true )
| ( ( ( multiply @ h @ ( phi @ SV4 ) @ ( phi @ SV8 ) )
= ( phi @ ( multiply @ f @ SV4 @ SV8 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[45]) ).
thf(53,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( group_member @ ( sK1_Y @ SX1 @ SX0 ) @ SX0 )
| ~ ( ( ( multiply @ SX0 @ SX1 @ ( sK1_Y @ SX1 @ SX0 ) )
!= SX1 ) ) )
| ~ ( group_member @ SX1 @ SX0 )
| ( left_zero @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[46]) ).
thf(54,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( left_zero @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( group_member @ SX2 @ SX0 )
| ( ( multiply @ SX0 @ SX1 @ SX2 )
= SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( left_zero @ SX0 @ SX1 )
| ( group_member @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[47]) ).
thf(55,plain,
! [SV5: $i] :
( ( ( group_member @ SV5 @ h )
= $false )
| ( ( ~ ( ( ( phi @ ( sK2_Y @ SV5 ) )
!= SV5 )
| ~ ( group_member @ ( sK2_Y @ SV5 ) @ f ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[48]) ).
thf(56,plain,
! [SV9: $i,SV1: $i,SV6: $i] :
( ( ( ~ ( group_member @ SV6 @ SV1 )
| ~ ( group_member @ SV9 @ SV1 ) )
= $true )
| ( ( group_member @ ( multiply @ SV1 @ SV6 @ SV9 ) @ SV1 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[49]) ).
thf(57,plain,
! [SV11: $i,SV10: $i,SV2: $i,SV7: $i] :
( ( ~ ( group_member @ SV7 @ SV2 )
| ~ ( group_member @ SV10 @ SV2 )
| ~ ( group_member @ SV11 @ SV2 )
| ( ( multiply @ SV2 @ ( multiply @ SV2 @ SV7 @ SV10 ) @ SV11 )
= ( multiply @ SV2 @ SV7 @ ( multiply @ SV2 @ SV10 @ SV11 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[50]) ).
thf(58,plain,
! [SV8: $i,SV4: $i] :
( ( ( ~ ( group_member @ SV4 @ f ) )
= $true )
| ( ( ~ ( group_member @ SV8 @ f ) )
= $true )
| ( ( ( multiply @ h @ ( phi @ SV4 ) @ ( phi @ SV8 ) )
= ( phi @ ( multiply @ f @ SV4 @ SV8 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[52]) ).
thf(59,plain,
! [SV12: $i] :
( ( ! [SY25: $i] :
( ~ ( ~ ( group_member @ ( sK1_Y @ SY25 @ SV12 ) @ SV12 )
| ~ ( ( ( multiply @ SV12 @ SY25 @ ( sK1_Y @ SY25 @ SV12 ) )
!= SY25 ) ) )
| ~ ( group_member @ SY25 @ SV12 )
| ( left_zero @ SV12 @ SY25 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[53]) ).
thf(60,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( left_zero @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( group_member @ SX2 @ SX0 )
| ( ( multiply @ SX0 @ SX1 @ SX2 )
= SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( left_zero @ SX0 @ SX1 )
| ( group_member @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[54]) ).
thf(61,plain,
! [SV5: $i] :
( ( ( ( ( phi @ ( sK2_Y @ SV5 ) )
!= SV5 )
| ~ ( group_member @ ( sK2_Y @ SV5 ) @ f ) )
= $false )
| ( ( group_member @ SV5 @ h )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[55]) ).
thf(62,plain,
! [SV9: $i,SV1: $i,SV6: $i] :
( ( ( ~ ( group_member @ SV6 @ SV1 ) )
= $true )
| ( ( ~ ( group_member @ SV9 @ SV1 ) )
= $true )
| ( ( group_member @ ( multiply @ SV1 @ SV6 @ SV9 ) @ SV1 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[56]) ).
thf(63,plain,
! [SV11: $i,SV10: $i,SV2: $i,SV7: $i] :
( ( ( ~ ( group_member @ SV7 @ SV2 )
| ~ ( group_member @ SV10 @ SV2 )
| ~ ( group_member @ SV11 @ SV2 ) )
= $true )
| ( ( ( multiply @ SV2 @ ( multiply @ SV2 @ SV7 @ SV10 ) @ SV11 )
= ( multiply @ SV2 @ SV7 @ ( multiply @ SV2 @ SV10 @ SV11 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[57]) ).
thf(64,plain,
! [SV8: $i,SV4: $i] :
( ( ( group_member @ SV4 @ f )
= $false )
| ( ( ~ ( group_member @ SV8 @ f ) )
= $true )
| ( ( ( multiply @ h @ ( phi @ SV4 ) @ ( phi @ SV8 ) )
= ( phi @ ( multiply @ f @ SV4 @ SV8 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[58]) ).
thf(65,plain,
! [SV12: $i,SV13: $i] :
( ( ~ ( ~ ( group_member @ ( sK1_Y @ SV13 @ SV12 ) @ SV12 )
| ~ ( ( ( multiply @ SV12 @ SV13 @ ( sK1_Y @ SV13 @ SV12 ) )
!= SV13 ) ) )
| ~ ( group_member @ SV13 @ SV12 )
| ( left_zero @ SV12 @ SV13 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[59]) ).
thf(66,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( left_zero @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( group_member @ SX2 @ SX0 )
| ( ( multiply @ SX0 @ SX1 @ SX2 )
= SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[60]) ).
thf(67,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( left_zero @ SX0 @ SX1 )
| ( group_member @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[60]) ).
thf(68,plain,
! [SV5: $i] :
( ( ( ( ( phi @ ( sK2_Y @ SV5 ) )
!= SV5 ) )
= $false )
| ( ( group_member @ SV5 @ h )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[61]) ).
thf(69,plain,
! [SV5: $i] :
( ( ( ~ ( group_member @ ( sK2_Y @ SV5 ) @ f ) )
= $false )
| ( ( group_member @ SV5 @ h )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[61]) ).
thf(70,plain,
! [SV9: $i,SV1: $i,SV6: $i] :
( ( ( group_member @ SV6 @ SV1 )
= $false )
| ( ( ~ ( group_member @ SV9 @ SV1 ) )
= $true )
| ( ( group_member @ ( multiply @ SV1 @ SV6 @ SV9 ) @ SV1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[62]) ).
thf(71,plain,
! [SV11: $i,SV10: $i,SV2: $i,SV7: $i] :
( ( ( ~ ( group_member @ SV7 @ SV2 )
| ~ ( group_member @ SV10 @ SV2 ) )
= $true )
| ( ( ~ ( group_member @ SV11 @ SV2 ) )
= $true )
| ( ( ( multiply @ SV2 @ ( multiply @ SV2 @ SV7 @ SV10 ) @ SV11 )
= ( multiply @ SV2 @ SV7 @ ( multiply @ SV2 @ SV10 @ SV11 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[63]) ).
thf(72,plain,
! [SV4: $i,SV8: $i] :
( ( ( group_member @ SV8 @ f )
= $false )
| ( ( group_member @ SV4 @ f )
= $false )
| ( ( ( multiply @ h @ ( phi @ SV4 ) @ ( phi @ SV8 ) )
= ( phi @ ( multiply @ f @ SV4 @ SV8 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[64]) ).
thf(73,plain,
! [SV12: $i,SV13: $i] :
( ( ( ~ ( ~ ( group_member @ ( sK1_Y @ SV13 @ SV12 ) @ SV12 )
| ~ ( ( ( multiply @ SV12 @ SV13 @ ( sK1_Y @ SV13 @ SV12 ) )
!= SV13 ) ) )
| ~ ( group_member @ SV13 @ SV12 ) )
= $true )
| ( ( left_zero @ SV12 @ SV13 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[65]) ).
thf(74,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( left_zero @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( group_member @ SX2 @ SX0 )
| ( ( multiply @ SX0 @ SX1 @ SX2 )
= SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[66]) ).
thf(75,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( left_zero @ SX0 @ SX1 )
| ( group_member @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[67]) ).
thf(76,plain,
! [SV5: $i] :
( ( ( ( phi @ ( sK2_Y @ SV5 ) )
= SV5 )
= $true )
| ( ( group_member @ SV5 @ h )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[68]) ).
thf(77,plain,
! [SV5: $i] :
( ( ( group_member @ ( sK2_Y @ SV5 ) @ f )
= $true )
| ( ( group_member @ SV5 @ h )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[69]) ).
thf(78,plain,
! [SV6: $i,SV1: $i,SV9: $i] :
( ( ( group_member @ SV9 @ SV1 )
= $false )
| ( ( group_member @ SV6 @ SV1 )
= $false )
| ( ( group_member @ ( multiply @ SV1 @ SV6 @ SV9 ) @ SV1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[70]) ).
thf(79,plain,
! [SV11: $i,SV10: $i,SV2: $i,SV7: $i] :
( ( ( ~ ( group_member @ SV7 @ SV2 ) )
= $true )
| ( ( ~ ( group_member @ SV10 @ SV2 ) )
= $true )
| ( ( ~ ( group_member @ SV11 @ SV2 ) )
= $true )
| ( ( ( multiply @ SV2 @ ( multiply @ SV2 @ SV7 @ SV10 ) @ SV11 )
= ( multiply @ SV2 @ SV7 @ ( multiply @ SV2 @ SV10 @ SV11 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[71]) ).
thf(80,plain,
! [SV12: $i,SV13: $i] :
( ( ( ~ ( ~ ( group_member @ ( sK1_Y @ SV13 @ SV12 ) @ SV12 )
| ~ ( ( ( multiply @ SV12 @ SV13 @ ( sK1_Y @ SV13 @ SV12 ) )
!= SV13 ) ) ) )
= $true )
| ( ( ~ ( group_member @ SV13 @ SV12 ) )
= $true )
| ( ( left_zero @ SV12 @ SV13 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[73]) ).
thf(81,plain,
! [SV14: $i] :
( ( ! [SY26: $i] :
( ~ ( left_zero @ SV14 @ SY26 )
| ! [SY27: $i] :
( ~ ( group_member @ SY27 @ SV14 )
| ( ( multiply @ SV14 @ SY26 @ SY27 )
= SY26 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[74]) ).
thf(82,plain,
! [SV15: $i] :
( ( ! [SY28: $i] :
( ~ ( left_zero @ SV15 @ SY28 )
| ( group_member @ SY28 @ SV15 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[75]) ).
thf(83,plain,
! [SV11: $i,SV10: $i,SV2: $i,SV7: $i] :
( ( ( group_member @ SV7 @ SV2 )
= $false )
| ( ( ~ ( group_member @ SV10 @ SV2 ) )
= $true )
| ( ( ~ ( group_member @ SV11 @ SV2 ) )
= $true )
| ( ( ( multiply @ SV2 @ ( multiply @ SV2 @ SV7 @ SV10 ) @ SV11 )
= ( multiply @ SV2 @ SV7 @ ( multiply @ SV2 @ SV10 @ SV11 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[79]) ).
thf(84,plain,
! [SV12: $i,SV13: $i] :
( ( ( ~ ( group_member @ ( sK1_Y @ SV13 @ SV12 ) @ SV12 )
| ~ ( ( ( multiply @ SV12 @ SV13 @ ( sK1_Y @ SV13 @ SV12 ) )
!= SV13 ) ) )
= $false )
| ( ( ~ ( group_member @ SV13 @ SV12 ) )
= $true )
| ( ( left_zero @ SV12 @ SV13 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[80]) ).
thf(85,plain,
! [SV16: $i,SV14: $i] :
( ( ~ ( left_zero @ SV14 @ SV16 )
| ! [SY29: $i] :
( ~ ( group_member @ SY29 @ SV14 )
| ( ( multiply @ SV14 @ SV16 @ SY29 )
= SV16 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[81]) ).
thf(86,plain,
! [SV17: $i,SV15: $i] :
( ( ~ ( left_zero @ SV15 @ SV17 )
| ( group_member @ SV17 @ SV15 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[82]) ).
thf(87,plain,
! [SV11: $i,SV7: $i,SV2: $i,SV10: $i] :
( ( ( group_member @ SV10 @ SV2 )
= $false )
| ( ( group_member @ SV7 @ SV2 )
= $false )
| ( ( ~ ( group_member @ SV11 @ SV2 ) )
= $true )
| ( ( ( multiply @ SV2 @ ( multiply @ SV2 @ SV7 @ SV10 ) @ SV11 )
= ( multiply @ SV2 @ SV7 @ ( multiply @ SV2 @ SV10 @ SV11 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[83]) ).
thf(88,plain,
! [SV12: $i,SV13: $i] :
( ( ( ~ ( group_member @ ( sK1_Y @ SV13 @ SV12 ) @ SV12 ) )
= $false )
| ( ( ~ ( group_member @ SV13 @ SV12 ) )
= $true )
| ( ( left_zero @ SV12 @ SV13 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[84]) ).
thf(89,plain,
! [SV13: $i,SV12: $i] :
( ( ( ~ ( ( ( multiply @ SV12 @ SV13 @ ( sK1_Y @ SV13 @ SV12 ) )
!= SV13 ) ) )
= $false )
| ( ( ~ ( group_member @ SV13 @ SV12 ) )
= $true )
| ( ( left_zero @ SV12 @ SV13 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[84]) ).
thf(90,plain,
! [SV16: $i,SV14: $i] :
( ( ( ~ ( left_zero @ SV14 @ SV16 ) )
= $true )
| ( ( ! [SY29: $i] :
( ~ ( group_member @ SY29 @ SV14 )
| ( ( multiply @ SV14 @ SV16 @ SY29 )
= SV16 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[85]) ).
thf(91,plain,
! [SV17: $i,SV15: $i] :
( ( ( ~ ( left_zero @ SV15 @ SV17 ) )
= $true )
| ( ( group_member @ SV17 @ SV15 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[86]) ).
thf(92,plain,
! [SV10: $i,SV7: $i,SV2: $i,SV11: $i] :
( ( ( group_member @ SV11 @ SV2 )
= $false )
| ( ( group_member @ SV7 @ SV2 )
= $false )
| ( ( group_member @ SV10 @ SV2 )
= $false )
| ( ( ( multiply @ SV2 @ ( multiply @ SV2 @ SV7 @ SV10 ) @ SV11 )
= ( multiply @ SV2 @ SV7 @ ( multiply @ SV2 @ SV10 @ SV11 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[87]) ).
thf(93,plain,
! [SV12: $i,SV13: $i] :
( ( ( group_member @ ( sK1_Y @ SV13 @ SV12 ) @ SV12 )
= $true )
| ( ( ~ ( group_member @ SV13 @ SV12 ) )
= $true )
| ( ( left_zero @ SV12 @ SV13 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[88]) ).
thf(94,plain,
! [SV13: $i,SV12: $i] :
( ( ( ( ( multiply @ SV12 @ SV13 @ ( sK1_Y @ SV13 @ SV12 ) )
!= SV13 ) )
= $true )
| ( ( ~ ( group_member @ SV13 @ SV12 ) )
= $true )
| ( ( left_zero @ SV12 @ SV13 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[89]) ).
thf(95,plain,
! [SV16: $i,SV14: $i] :
( ( ( left_zero @ SV14 @ SV16 )
= $false )
| ( ( ! [SY29: $i] :
( ~ ( group_member @ SY29 @ SV14 )
| ( ( multiply @ SV14 @ SV16 @ SY29 )
= SV16 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[90]) ).
thf(96,plain,
! [SV17: $i,SV15: $i] :
( ( ( left_zero @ SV15 @ SV17 )
= $false )
| ( ( group_member @ SV17 @ SV15 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[91]) ).
thf(97,plain,
! [SV12: $i,SV13: $i] :
( ( ( group_member @ SV13 @ SV12 )
= $false )
| ( ( group_member @ ( sK1_Y @ SV13 @ SV12 ) @ SV12 )
= $true )
| ( ( left_zero @ SV12 @ SV13 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[93]) ).
thf(98,plain,
! [SV13: $i,SV12: $i] :
( ( ( ( multiply @ SV12 @ SV13 @ ( sK1_Y @ SV13 @ SV12 ) )
= SV13 )
= $false )
| ( ( ~ ( group_member @ SV13 @ SV12 ) )
= $true )
| ( ( left_zero @ SV12 @ SV13 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[94]) ).
thf(99,plain,
! [SV16: $i,SV14: $i,SV18: $i] :
( ( ( ~ ( group_member @ SV18 @ SV14 )
| ( ( multiply @ SV14 @ SV16 @ SV18 )
= SV16 ) )
= $true )
| ( ( left_zero @ SV14 @ SV16 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[95]) ).
thf(100,plain,
! [SV12: $i,SV13: $i] :
( ( ( group_member @ SV13 @ SV12 )
= $false )
| ( ( ( multiply @ SV12 @ SV13 @ ( sK1_Y @ SV13 @ SV12 ) )
= SV13 )
= $false )
| ( ( left_zero @ SV12 @ SV13 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[98]) ).
thf(101,plain,
! [SV16: $i,SV14: $i,SV18: $i] :
( ( ( ~ ( group_member @ SV18 @ SV14 ) )
= $true )
| ( ( ( multiply @ SV14 @ SV16 @ SV18 )
= SV16 )
= $true )
| ( ( left_zero @ SV14 @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[99]) ).
thf(102,plain,
! [SV16: $i,SV14: $i,SV18: $i] :
( ( ( group_member @ SV18 @ SV14 )
= $false )
| ( ( ( multiply @ SV14 @ SV16 @ SV18 )
= SV16 )
= $true )
| ( ( left_zero @ SV14 @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[101]) ).
thf(103,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[25,102,100,97,96,92,78,77,76,72,51,39]) ).
thf(104,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[103]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP194+1 : TPTP v8.1.0. Released v2.0.0.
% 0.11/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.35 % Computer : n017.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Mon Jun 13 11:32:08 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.36
% 0.13/0.36 No.of.Axioms: 7
% 0.13/0.36
% 0.13/0.36 Length.of.Defs: 0
% 0.13/0.36
% 0.13/0.36 Contains.Choice.Funs: false
% 0.13/0.36 (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:600,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:9,loop_count:0,foatp_calls:0,translation:fof_full).....
% 32.74/32.94
% 32.74/32.94 ********************************
% 32.74/32.94 * All subproblems solved! *
% 32.74/32.94 ********************************
% 32.74/32.94 % 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:103,loop_count:0,foatp_calls:1,translation:fof_full)
% 32.74/32.94
% 32.74/32.94 %**** Beginning of derivation protocol ****
% 32.74/32.94 % SZS output start CNFRefutation
% See solution above
% 32.74/32.94
% 32.74/32.94 %**** End of derivation protocol ****
% 32.74/32.94 %**** no. of clauses in derivation: 104 ****
% 32.74/32.94 %**** clause counter: 103 ****
% 32.74/32.94
% 32.74/32.94 % 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:103,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------