TSTP Solution File: GRP665+1 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : GRP665+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n027.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 10:19:25 EDT 2022
% Result : Theorem 5.14s 5.35s
% Output : CNFRefutation 5.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 17
% Syntax : Number of formulae : 124 ( 116 unt; 7 typ; 0 def)
% Number of atoms : 339 ( 229 equ; 0 cnn)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 808 ( 6 ~; 0 |; 10 &; 792 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 203 ( 0 ^ 203 !; 0 ?; 203 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_ld,type,
ld: $i > $i > $i ).
thf(tp_mult,type,
mult: $i > $i > $i ).
thf(tp_op_c,type,
op_c: $i ).
thf(tp_rd,type,
rd: $i > $i > $i ).
thf(tp_sK1_X0,type,
sK1_X0: $i ).
thf(tp_sK2_SY19,type,
sK2_SY19: $i ).
thf(tp_unit,type,
unit: $i ).
thf(1,axiom,
! [A: $i] :
( ( mult @ op_c @ A )
= ( mult @ A @ op_c ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f09) ).
thf(2,axiom,
! [C: $i,B: $i,A: $i] :
( ( mult @ ( mult @ A @ B ) @ C )
= ( mult @ ( mult @ A @ C ) @ ( ld @ C @ ( mult @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f08) ).
thf(3,axiom,
! [C: $i,B: $i,A: $i] :
( ( mult @ A @ ( mult @ B @ C ) )
= ( mult @ ( rd @ ( mult @ A @ B ) @ A ) @ ( mult @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f07) ).
thf(4,axiom,
! [A: $i] :
( ( mult @ unit @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f06) ).
thf(5,axiom,
! [A: $i] :
( ( mult @ A @ unit )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f05) ).
thf(6,axiom,
! [B: $i,A: $i] :
( ( rd @ ( mult @ A @ B ) @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f04) ).
thf(7,axiom,
! [B: $i,A: $i] :
( ( mult @ ( rd @ A @ B ) @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f03) ).
thf(8,axiom,
! [B: $i,A: $i] :
( ( ld @ A @ ( mult @ A @ B ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f02) ).
thf(9,axiom,
! [B: $i,A: $i] :
( ( mult @ A @ ( ld @ A @ B ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f01) ).
thf(10,conjecture,
! [X0: $i,X1: $i] :
( ( ( mult @ op_c @ ( mult @ X0 @ X1 ) )
= ( mult @ ( mult @ op_c @ X0 ) @ X1 ) )
& ( ( mult @ ( mult @ X0 @ op_c ) @ X1 )
= ( mult @ X0 @ ( mult @ op_c @ X1 ) ) )
& ( ( mult @ ( mult @ X0 @ X1 ) @ op_c )
= ( mult @ X0 @ ( mult @ X1 @ op_c ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
thf(11,negated_conjecture,
( ( ! [X0: $i,X1: $i] :
( ( ( mult @ op_c @ ( mult @ X0 @ X1 ) )
= ( mult @ ( mult @ op_c @ X0 ) @ X1 ) )
& ( ( mult @ ( mult @ X0 @ op_c ) @ X1 )
= ( mult @ X0 @ ( mult @ op_c @ X1 ) ) )
& ( ( mult @ ( mult @ X0 @ X1 ) @ op_c )
= ( mult @ X0 @ ( mult @ X1 @ op_c ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[10]) ).
thf(12,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( mult @ op_c @ ( mult @ X0 @ X1 ) )
= ( mult @ ( mult @ op_c @ X0 ) @ X1 ) )
& ( ( mult @ ( mult @ X0 @ op_c ) @ X1 )
= ( mult @ X0 @ ( mult @ op_c @ X1 ) ) )
& ( ( mult @ ( mult @ X0 @ X1 ) @ op_c )
= ( mult @ X0 @ ( mult @ X1 @ op_c ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[11]) ).
thf(13,plain,
( ( ! [A: $i] :
( ( mult @ op_c @ A )
= ( mult @ A @ op_c ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(14,plain,
( ( ! [C: $i,B: $i,A: $i] :
( ( mult @ ( mult @ A @ B ) @ C )
= ( mult @ ( mult @ A @ C ) @ ( ld @ C @ ( mult @ B @ C ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(15,plain,
( ( ! [C: $i,B: $i,A: $i] :
( ( mult @ A @ ( mult @ B @ C ) )
= ( mult @ ( rd @ ( mult @ A @ B ) @ A ) @ ( mult @ A @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(16,plain,
( ( ! [A: $i] :
( ( mult @ unit @ A )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(17,plain,
( ( ! [A: $i] :
( ( mult @ A @ unit )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(18,plain,
( ( ! [B: $i,A: $i] :
( ( rd @ ( mult @ A @ B ) @ B )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(19,plain,
( ( ! [B: $i,A: $i] :
( ( mult @ ( rd @ A @ B ) @ B )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(20,plain,
( ( ! [B: $i,A: $i] :
( ( ld @ A @ ( mult @ A @ B ) )
= B ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(21,plain,
( ( ! [B: $i,A: $i] :
( ( mult @ A @ ( ld @ A @ B ) )
= B ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(22,plain,
( ( ! [SY19: $i] :
( ( ( mult @ op_c @ ( mult @ sK1_X0 @ SY19 ) )
= ( mult @ ( mult @ op_c @ sK1_X0 ) @ SY19 ) )
& ( ( mult @ ( mult @ sK1_X0 @ op_c ) @ SY19 )
= ( mult @ sK1_X0 @ ( mult @ op_c @ SY19 ) ) )
& ( ( mult @ ( mult @ sK1_X0 @ SY19 ) @ op_c )
= ( mult @ sK1_X0 @ ( mult @ SY19 @ op_c ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[12]) ).
thf(23,plain,
( ( ( ( mult @ op_c @ ( mult @ sK1_X0 @ sK2_SY19 ) )
= ( mult @ ( mult @ op_c @ sK1_X0 ) @ sK2_SY19 ) )
& ( ( mult @ ( mult @ sK1_X0 @ op_c ) @ sK2_SY19 )
= ( mult @ sK1_X0 @ ( mult @ op_c @ sK2_SY19 ) ) )
& ( ( mult @ ( mult @ sK1_X0 @ sK2_SY19 ) @ op_c )
= ( mult @ sK1_X0 @ ( mult @ sK2_SY19 @ op_c ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[22]) ).
thf(24,plain,
( ( ( mult @ op_c @ ( mult @ sK1_X0 @ sK2_SY19 ) )
= ( mult @ ( mult @ op_c @ sK1_X0 ) @ sK2_SY19 ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[23]) ).
thf(25,plain,
( ( ( mult @ ( mult @ sK1_X0 @ op_c ) @ sK2_SY19 )
= ( mult @ sK1_X0 @ ( mult @ op_c @ sK2_SY19 ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[23]) ).
thf(26,plain,
( ( ( mult @ ( mult @ sK1_X0 @ sK2_SY19 ) @ op_c )
= ( mult @ sK1_X0 @ ( mult @ sK2_SY19 @ op_c ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[23]) ).
thf(27,plain,
( ( ( ( mult @ op_c @ ( mult @ sK1_X0 @ sK2_SY19 ) )
!= ( mult @ ( mult @ op_c @ sK1_X0 ) @ sK2_SY19 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[24]) ).
thf(28,plain,
( ( ( ( mult @ ( mult @ sK1_X0 @ op_c ) @ sK2_SY19 )
!= ( mult @ sK1_X0 @ ( mult @ op_c @ sK2_SY19 ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[25]) ).
thf(29,plain,
( ( ( ( mult @ ( mult @ sK1_X0 @ sK2_SY19 ) @ op_c )
!= ( mult @ sK1_X0 @ ( mult @ sK2_SY19 @ op_c ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[26]) ).
thf(30,plain,
( ( ! [B: $i,A: $i] :
( ( mult @ A @ ( ld @ A @ B ) )
= B ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(31,plain,
( ( ! [B: $i,A: $i] :
( ( ld @ A @ ( mult @ A @ B ) )
= B ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(32,plain,
( ( ! [B: $i,A: $i] :
( ( mult @ ( rd @ A @ B ) @ B )
= A ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(33,plain,
( ( ! [B: $i,A: $i] :
( ( rd @ ( mult @ A @ B ) @ B )
= A ) )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(34,plain,
( ( ! [A: $i] :
( ( mult @ A @ unit )
= A ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(35,plain,
( ( ! [A: $i] :
( ( mult @ unit @ A )
= A ) )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(36,plain,
( ( ! [C: $i,B: $i,A: $i] :
( ( mult @ A @ ( mult @ B @ C ) )
= ( mult @ ( rd @ ( mult @ A @ B ) @ A ) @ ( mult @ A @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(37,plain,
( ( ! [C: $i,B: $i,A: $i] :
( ( mult @ ( mult @ A @ B ) @ C )
= ( mult @ ( mult @ A @ C ) @ ( ld @ C @ ( mult @ B @ C ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(38,plain,
( ( ! [A: $i] :
( ( mult @ op_c @ A )
= ( mult @ A @ op_c ) ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(39,plain,
( ( ( ( mult @ op_c @ ( mult @ sK1_X0 @ sK2_SY19 ) )
!= ( mult @ ( mult @ op_c @ sK1_X0 ) @ sK2_SY19 ) ) )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(40,plain,
! [SV1: $i] :
( ( ! [SY20: $i] :
( ( mult @ SY20 @ ( ld @ SY20 @ SV1 ) )
= SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[30]) ).
thf(41,plain,
! [SV2: $i] :
( ( ! [SY21: $i] :
( ( ld @ SY21 @ ( mult @ SY21 @ SV2 ) )
= SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[31]) ).
thf(42,plain,
! [SV3: $i] :
( ( ! [SY22: $i] :
( ( mult @ ( rd @ SY22 @ SV3 ) @ SV3 )
= SY22 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[32]) ).
thf(43,plain,
! [SV4: $i] :
( ( ! [SY23: $i] :
( ( rd @ ( mult @ SY23 @ SV4 ) @ SV4 )
= SY23 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[33]) ).
thf(44,plain,
! [SV5: $i] :
( ( ( mult @ SV5 @ unit )
= SV5 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[34]) ).
thf(45,plain,
! [SV6: $i] :
( ( ( mult @ unit @ SV6 )
= SV6 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[35]) ).
thf(46,plain,
! [SV7: $i] :
( ( ! [SY24: $i,SY25: $i] :
( ( mult @ SY25 @ ( mult @ SY24 @ SV7 ) )
= ( mult @ ( rd @ ( mult @ SY25 @ SY24 ) @ SY25 ) @ ( mult @ SY25 @ SV7 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[36]) ).
thf(47,plain,
! [SV8: $i] :
( ( ! [SY26: $i,SY27: $i] :
( ( mult @ ( mult @ SY27 @ SY26 ) @ SV8 )
= ( mult @ ( mult @ SY27 @ SV8 ) @ ( ld @ SV8 @ ( mult @ SY26 @ SV8 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[37]) ).
thf(48,plain,
! [SV9: $i] :
( ( ( mult @ op_c @ SV9 )
= ( mult @ SV9 @ op_c ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[38]) ).
thf(49,plain,
( ( ( mult @ op_c @ ( mult @ sK1_X0 @ sK2_SY19 ) )
= ( mult @ ( mult @ op_c @ sK1_X0 ) @ sK2_SY19 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[39]) ).
thf(50,plain,
! [SV1: $i,SV10: $i] :
( ( ( mult @ SV10 @ ( ld @ SV10 @ SV1 ) )
= SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[40]) ).
thf(51,plain,
! [SV2: $i,SV11: $i] :
( ( ( ld @ SV11 @ ( mult @ SV11 @ SV2 ) )
= SV2 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[41]) ).
thf(52,plain,
! [SV3: $i,SV12: $i] :
( ( ( mult @ ( rd @ SV12 @ SV3 ) @ SV3 )
= SV12 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[42]) ).
thf(53,plain,
! [SV4: $i,SV13: $i] :
( ( ( rd @ ( mult @ SV13 @ SV4 ) @ SV4 )
= SV13 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[43]) ).
thf(54,plain,
! [SV7: $i,SV14: $i] :
( ( ! [SY28: $i] :
( ( mult @ SY28 @ ( mult @ SV14 @ SV7 ) )
= ( mult @ ( rd @ ( mult @ SY28 @ SV14 ) @ SY28 ) @ ( mult @ SY28 @ SV7 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[46]) ).
thf(55,plain,
! [SV8: $i,SV15: $i] :
( ( ! [SY29: $i] :
( ( mult @ ( mult @ SY29 @ SV15 ) @ SV8 )
= ( mult @ ( mult @ SY29 @ SV8 ) @ ( ld @ SV8 @ ( mult @ SV15 @ SV8 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[47]) ).
thf(56,plain,
! [SV7: $i,SV14: $i,SV16: $i] :
( ( ( mult @ SV16 @ ( mult @ SV14 @ SV7 ) )
= ( mult @ ( rd @ ( mult @ SV16 @ SV14 ) @ SV16 ) @ ( mult @ SV16 @ SV7 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[54]) ).
thf(57,plain,
! [SV8: $i,SV15: $i,SV17: $i] :
( ( ( mult @ ( mult @ SV17 @ SV15 ) @ SV8 )
= ( mult @ ( mult @ SV17 @ SV8 ) @ ( ld @ SV8 @ ( mult @ SV15 @ SV8 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[55]) ).
thf(58,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[44,57,56,53,52,51,50,49,48,45]) ).
thf(59,plain,
( ( ! [B: $i,A: $i] :
( ( mult @ A @ ( ld @ A @ B ) )
= B ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(60,plain,
( ( ! [B: $i,A: $i] :
( ( ld @ A @ ( mult @ A @ B ) )
= B ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(61,plain,
( ( ! [B: $i,A: $i] :
( ( mult @ ( rd @ A @ B ) @ B )
= A ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(62,plain,
( ( ! [B: $i,A: $i] :
( ( rd @ ( mult @ A @ B ) @ B )
= A ) )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(63,plain,
( ( ! [A: $i] :
( ( mult @ A @ unit )
= A ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(64,plain,
( ( ! [A: $i] :
( ( mult @ unit @ A )
= A ) )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(65,plain,
( ( ! [C: $i,B: $i,A: $i] :
( ( mult @ A @ ( mult @ B @ C ) )
= ( mult @ ( rd @ ( mult @ A @ B ) @ A ) @ ( mult @ A @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(66,plain,
( ( ! [C: $i,B: $i,A: $i] :
( ( mult @ ( mult @ A @ B ) @ C )
= ( mult @ ( mult @ A @ C ) @ ( ld @ C @ ( mult @ B @ C ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(67,plain,
( ( ! [A: $i] :
( ( mult @ op_c @ A )
= ( mult @ A @ op_c ) ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(68,plain,
( ( ( ( mult @ ( mult @ sK1_X0 @ op_c ) @ sK2_SY19 )
!= ( mult @ sK1_X0 @ ( mult @ op_c @ sK2_SY19 ) ) ) )
= $true ),
inference(copy,[status(thm)],[28]) ).
thf(69,plain,
! [SV18: $i] :
( ( ! [SY30: $i] :
( ( mult @ SY30 @ ( ld @ SY30 @ SV18 ) )
= SV18 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[59]) ).
thf(70,plain,
! [SV19: $i] :
( ( ! [SY31: $i] :
( ( ld @ SY31 @ ( mult @ SY31 @ SV19 ) )
= SV19 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[60]) ).
thf(71,plain,
! [SV20: $i] :
( ( ! [SY32: $i] :
( ( mult @ ( rd @ SY32 @ SV20 ) @ SV20 )
= SY32 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[61]) ).
thf(72,plain,
! [SV21: $i] :
( ( ! [SY33: $i] :
( ( rd @ ( mult @ SY33 @ SV21 ) @ SV21 )
= SY33 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[62]) ).
thf(73,plain,
! [SV22: $i] :
( ( ( mult @ SV22 @ unit )
= SV22 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[63]) ).
thf(74,plain,
! [SV23: $i] :
( ( ( mult @ unit @ SV23 )
= SV23 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[64]) ).
thf(75,plain,
! [SV24: $i] :
( ( ! [SY34: $i,SY35: $i] :
( ( mult @ SY35 @ ( mult @ SY34 @ SV24 ) )
= ( mult @ ( rd @ ( mult @ SY35 @ SY34 ) @ SY35 ) @ ( mult @ SY35 @ SV24 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[65]) ).
thf(76,plain,
! [SV25: $i] :
( ( ! [SY36: $i,SY37: $i] :
( ( mult @ ( mult @ SY37 @ SY36 ) @ SV25 )
= ( mult @ ( mult @ SY37 @ SV25 ) @ ( ld @ SV25 @ ( mult @ SY36 @ SV25 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[66]) ).
thf(77,plain,
! [SV26: $i] :
( ( ( mult @ op_c @ SV26 )
= ( mult @ SV26 @ op_c ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[67]) ).
thf(78,plain,
( ( ( mult @ ( mult @ sK1_X0 @ op_c ) @ sK2_SY19 )
= ( mult @ sK1_X0 @ ( mult @ op_c @ sK2_SY19 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[68]) ).
thf(79,plain,
! [SV18: $i,SV27: $i] :
( ( ( mult @ SV27 @ ( ld @ SV27 @ SV18 ) )
= SV18 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[69]) ).
thf(80,plain,
! [SV19: $i,SV28: $i] :
( ( ( ld @ SV28 @ ( mult @ SV28 @ SV19 ) )
= SV19 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[70]) ).
thf(81,plain,
! [SV20: $i,SV29: $i] :
( ( ( mult @ ( rd @ SV29 @ SV20 ) @ SV20 )
= SV29 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(82,plain,
! [SV21: $i,SV30: $i] :
( ( ( rd @ ( mult @ SV30 @ SV21 ) @ SV21 )
= SV30 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[72]) ).
thf(83,plain,
! [SV24: $i,SV31: $i] :
( ( ! [SY38: $i] :
( ( mult @ SY38 @ ( mult @ SV31 @ SV24 ) )
= ( mult @ ( rd @ ( mult @ SY38 @ SV31 ) @ SY38 ) @ ( mult @ SY38 @ SV24 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[75]) ).
thf(84,plain,
! [SV25: $i,SV32: $i] :
( ( ! [SY39: $i] :
( ( mult @ ( mult @ SY39 @ SV32 ) @ SV25 )
= ( mult @ ( mult @ SY39 @ SV25 ) @ ( ld @ SV25 @ ( mult @ SV32 @ SV25 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[76]) ).
thf(85,plain,
! [SV24: $i,SV31: $i,SV33: $i] :
( ( ( mult @ SV33 @ ( mult @ SV31 @ SV24 ) )
= ( mult @ ( rd @ ( mult @ SV33 @ SV31 ) @ SV33 ) @ ( mult @ SV33 @ SV24 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[83]) ).
thf(86,plain,
! [SV25: $i,SV32: $i,SV34: $i] :
( ( ( mult @ ( mult @ SV34 @ SV32 ) @ SV25 )
= ( mult @ ( mult @ SV34 @ SV25 ) @ ( ld @ SV25 @ ( mult @ SV32 @ SV25 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).
thf(87,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[73,86,85,82,81,80,79,78,77,74]) ).
thf(88,plain,
( ( ! [B: $i,A: $i] :
( ( mult @ A @ ( ld @ A @ B ) )
= B ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(89,plain,
( ( ! [B: $i,A: $i] :
( ( ld @ A @ ( mult @ A @ B ) )
= B ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(90,plain,
( ( ! [B: $i,A: $i] :
( ( mult @ ( rd @ A @ B ) @ B )
= A ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(91,plain,
( ( ! [B: $i,A: $i] :
( ( rd @ ( mult @ A @ B ) @ B )
= A ) )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(92,plain,
( ( ! [A: $i] :
( ( mult @ A @ unit )
= A ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(93,plain,
( ( ! [A: $i] :
( ( mult @ unit @ A )
= A ) )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(94,plain,
( ( ! [C: $i,B: $i,A: $i] :
( ( mult @ A @ ( mult @ B @ C ) )
= ( mult @ ( rd @ ( mult @ A @ B ) @ A ) @ ( mult @ A @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(95,plain,
( ( ! [C: $i,B: $i,A: $i] :
( ( mult @ ( mult @ A @ B ) @ C )
= ( mult @ ( mult @ A @ C ) @ ( ld @ C @ ( mult @ B @ C ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(96,plain,
( ( ! [A: $i] :
( ( mult @ op_c @ A )
= ( mult @ A @ op_c ) ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(97,plain,
( ( ( ( mult @ ( mult @ sK1_X0 @ sK2_SY19 ) @ op_c )
!= ( mult @ sK1_X0 @ ( mult @ sK2_SY19 @ op_c ) ) ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(98,plain,
! [SV35: $i] :
( ( ! [SY40: $i] :
( ( mult @ SY40 @ ( ld @ SY40 @ SV35 ) )
= SV35 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(99,plain,
! [SV36: $i] :
( ( ! [SY41: $i] :
( ( ld @ SY41 @ ( mult @ SY41 @ SV36 ) )
= SV36 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[89]) ).
thf(100,plain,
! [SV37: $i] :
( ( ! [SY42: $i] :
( ( mult @ ( rd @ SY42 @ SV37 ) @ SV37 )
= SY42 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[90]) ).
thf(101,plain,
! [SV38: $i] :
( ( ! [SY43: $i] :
( ( rd @ ( mult @ SY43 @ SV38 ) @ SV38 )
= SY43 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[91]) ).
thf(102,plain,
! [SV39: $i] :
( ( ( mult @ SV39 @ unit )
= SV39 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[92]) ).
thf(103,plain,
! [SV40: $i] :
( ( ( mult @ unit @ SV40 )
= SV40 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[93]) ).
thf(104,plain,
! [SV41: $i] :
( ( ! [SY44: $i,SY45: $i] :
( ( mult @ SY45 @ ( mult @ SY44 @ SV41 ) )
= ( mult @ ( rd @ ( mult @ SY45 @ SY44 ) @ SY45 ) @ ( mult @ SY45 @ SV41 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[94]) ).
thf(105,plain,
! [SV42: $i] :
( ( ! [SY46: $i,SY47: $i] :
( ( mult @ ( mult @ SY47 @ SY46 ) @ SV42 )
= ( mult @ ( mult @ SY47 @ SV42 ) @ ( ld @ SV42 @ ( mult @ SY46 @ SV42 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[95]) ).
thf(106,plain,
! [SV43: $i] :
( ( ( mult @ op_c @ SV43 )
= ( mult @ SV43 @ op_c ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[96]) ).
thf(107,plain,
( ( ( mult @ ( mult @ sK1_X0 @ sK2_SY19 ) @ op_c )
= ( mult @ sK1_X0 @ ( mult @ sK2_SY19 @ op_c ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[97]) ).
thf(108,plain,
! [SV35: $i,SV44: $i] :
( ( ( mult @ SV44 @ ( ld @ SV44 @ SV35 ) )
= SV35 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[98]) ).
thf(109,plain,
! [SV36: $i,SV45: $i] :
( ( ( ld @ SV45 @ ( mult @ SV45 @ SV36 ) )
= SV36 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[99]) ).
thf(110,plain,
! [SV37: $i,SV46: $i] :
( ( ( mult @ ( rd @ SV46 @ SV37 ) @ SV37 )
= SV46 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[100]) ).
thf(111,plain,
! [SV38: $i,SV47: $i] :
( ( ( rd @ ( mult @ SV47 @ SV38 ) @ SV38 )
= SV47 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[101]) ).
thf(112,plain,
! [SV41: $i,SV48: $i] :
( ( ! [SY48: $i] :
( ( mult @ SY48 @ ( mult @ SV48 @ SV41 ) )
= ( mult @ ( rd @ ( mult @ SY48 @ SV48 ) @ SY48 ) @ ( mult @ SY48 @ SV41 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[104]) ).
thf(113,plain,
! [SV42: $i,SV49: $i] :
( ( ! [SY49: $i] :
( ( mult @ ( mult @ SY49 @ SV49 ) @ SV42 )
= ( mult @ ( mult @ SY49 @ SV42 ) @ ( ld @ SV42 @ ( mult @ SV49 @ SV42 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[105]) ).
thf(114,plain,
! [SV41: $i,SV48: $i,SV50: $i] :
( ( ( mult @ SV50 @ ( mult @ SV48 @ SV41 ) )
= ( mult @ ( rd @ ( mult @ SV50 @ SV48 ) @ SV50 ) @ ( mult @ SV50 @ SV41 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[112]) ).
thf(115,plain,
! [SV42: $i,SV49: $i,SV51: $i] :
( ( ( mult @ ( mult @ SV51 @ SV49 ) @ SV42 )
= ( mult @ ( mult @ SV51 @ SV42 ) @ ( ld @ SV42 @ ( mult @ SV49 @ SV42 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[113]) ).
thf(116,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[102,115,114,111,110,109,108,107,106,103]) ).
thf(117,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[116,58,87]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : GRP665+1 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.12 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.33 % Computer : n027.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 : Tue Jun 14 01:09:02 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34
% 0.12/0.34 No.of.Axioms: 9
% 0.12/0.34
% 0.12/0.34 Length.of.Defs: 0
% 0.12/0.34
% 0.12/0.34 Contains.Choice.Funs: false
% 0.12/0.35 (rf:0,axioms:9,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:600,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:11,loop_count:0,foatp_calls:0,translation:fof_full).....
% 5.14/5.35
% 5.14/5.35 ********************************
% 5.14/5.35 * All subproblems solved! *
% 5.14/5.35 ********************************
% 5.14/5.35 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:9,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:72,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:116,loop_count:0,foatp_calls:1,translation:fof_full)
% 5.14/5.35
% 5.14/5.35 %**** Beginning of derivation protocol ****
% 5.14/5.35 % SZS output start CNFRefutation
% See solution above
% 5.14/5.35
% 5.14/5.35 %**** End of derivation protocol ****
% 5.14/5.35 %**** no. of clauses in derivation: 117 ****
% 5.14/5.35 %**** clause counter: 116 ****
% 5.14/5.35
% 5.14/5.35 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:9,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:72,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:116,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------