TSTP Solution File: GRP729-1 by LEO-II---1.7.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : GRP729-1 : 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 : n014.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 10:19:47 EDT 2022
% Result : Unsatisfiable 15.50s 15.76s
% Output : CNFRefutation 15.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 37
% Syntax : Number of formulae : 156 ( 143 unt; 13 typ; 0 def)
% Number of atoms : 379 ( 253 equ; 0 cnn)
% Maximal formula atoms : 1 ( 2 avg)
% Number of connectives : 1106 ( 6 ~; 0 |; 0 &;1100 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 18 ( 18 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 13 usr; 7 con; 0-3 aty)
% Number of variables : 422 ( 0 ^ 422 !; 0 ?; 422 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $i ).
thf(tp_asoc,type,
asoc: $i > $i > $i > $i ).
thf(tp_b,type,
b: $i ).
thf(tp_c,type,
c: $i ).
thf(tp_d,type,
d: $i ).
thf(tp_i,type,
i: $i > $i ).
thf(tp_mult,type,
mult: $i > $i > $i ).
thf(tp_op_k,type,
op_k: $i > $i > $i ).
thf(tp_op_l,type,
op_l: $i > $i > $i > $i ).
thf(tp_op_r,type,
op_r: $i > $i > $i > $i ).
thf(tp_op_t,type,
op_t: $i > $i > $i ).
thf(tp_rd,type,
rd: $i > $i > $i ).
thf(tp_unit,type,
unit: $i ).
thf(1,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( asoc @ A @ B @ ( asoc @ C @ D @ E ) )
= unit ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c22) ).
thf(2,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( asoc @ ( asoc @ A @ B @ C ) @ D @ E )
= unit ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c21) ).
thf(3,axiom,
! [A: $i,B: $i,C: $i] :
( ( op_t @ ( op_t @ A @ B ) @ C )
= ( op_t @ ( op_t @ A @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c20) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( op_t @ ( op_l @ A @ B @ C ) @ D )
= ( op_l @ ( op_t @ A @ D ) @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c19) ).
thf(5,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( op_t @ ( op_r @ A @ B @ C ) @ D )
= ( op_r @ ( op_t @ A @ D ) @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c18) ).
thf(6,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( op_l @ ( op_l @ A @ B @ C ) @ D @ E )
= ( op_l @ ( op_l @ A @ D @ E ) @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c17) ).
thf(7,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( op_l @ ( op_r @ A @ B @ C ) @ D @ E )
= ( op_r @ ( op_l @ A @ D @ E ) @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c16) ).
thf(8,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( op_r @ ( op_r @ A @ B @ C ) @ D @ E )
= ( op_r @ ( op_r @ A @ D @ E ) @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c15) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( op_t @ A @ B )
= ( mult @ ( i @ B ) @ ( mult @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c14) ).
thf(10,axiom,
! [A: $i,B: $i,C: $i] :
( ( op_r @ A @ B @ C )
= ( rd @ ( mult @ ( mult @ A @ B ) @ C ) @ ( mult @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c13) ).
thf(11,axiom,
! [A: $i,B: $i,C: $i] :
( ( op_l @ A @ B @ C )
= ( mult @ ( i @ ( mult @ C @ B ) ) @ ( mult @ C @ ( mult @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c12) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( mult @ A @ B )
= ( mult @ ( mult @ B @ A ) @ ( op_k @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c11) ).
thf(13,axiom,
! [A: $i,B: $i,C: $i] :
( ( mult @ ( mult @ A @ B ) @ C )
= ( mult @ ( mult @ A @ ( mult @ B @ C ) ) @ ( asoc @ A @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c10) ).
thf(14,axiom,
! [A: $i,B: $i,C: $i] :
( ( mult @ ( mult @ A @ ( mult @ B @ A ) ) @ C )
= ( mult @ A @ ( mult @ B @ ( mult @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c09) ).
thf(15,axiom,
! [A: $i,B: $i] :
( ( mult @ ( rd @ A @ B ) @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c08) ).
thf(16,axiom,
! [A: $i,B: $i] :
( ( rd @ ( mult @ A @ B ) @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c07) ).
thf(17,axiom,
! [A: $i,B: $i] :
( ( mult @ ( i @ A ) @ ( mult @ A @ B ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c06) ).
thf(18,axiom,
! [A: $i,B: $i] :
( ( i @ ( mult @ A @ B ) )
= ( mult @ ( i @ A ) @ ( i @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c05) ).
thf(19,axiom,
! [A: $i] :
( ( mult @ ( i @ A ) @ A )
= unit ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c04) ).
thf(20,axiom,
! [A: $i] :
( ( mult @ A @ ( i @ A ) )
= unit ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c03) ).
thf(21,axiom,
! [A: $i] :
( ( mult @ A @ unit )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c02) ).
thf(22,axiom,
! [A: $i] :
( ( mult @ unit @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c01) ).
thf(23,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(24,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[23]) ).
thf(25,negated_conjecture,
( asoc @ a @ b @ ( op_k @ c @ d ) )
!= unit,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
thf(26,plain,
$false = $false,
inference(unfold_def,[status(thm)],[24]) ).
thf(27,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( asoc @ A @ B @ ( asoc @ C @ D @ E ) )
= unit ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(28,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( asoc @ ( asoc @ A @ B @ C ) @ D @ E )
= unit ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(29,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( op_t @ ( op_t @ A @ B ) @ C )
= ( op_t @ ( op_t @ A @ C ) @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(30,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( op_t @ ( op_l @ A @ B @ C ) @ D )
= ( op_l @ ( op_t @ A @ D ) @ B @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(31,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( op_t @ ( op_r @ A @ B @ C ) @ D )
= ( op_r @ ( op_t @ A @ D ) @ B @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(32,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( op_l @ ( op_l @ A @ B @ C ) @ D @ E )
= ( op_l @ ( op_l @ A @ D @ E ) @ B @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(33,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( op_l @ ( op_r @ A @ B @ C ) @ D @ E )
= ( op_r @ ( op_l @ A @ D @ E ) @ B @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(34,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( op_r @ ( op_r @ A @ B @ C ) @ D @ E )
= ( op_r @ ( op_r @ A @ D @ E ) @ B @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(35,plain,
( ( ! [A: $i,B: $i] :
( ( op_t @ A @ B )
= ( mult @ ( i @ B ) @ ( mult @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(36,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( op_r @ A @ B @ C )
= ( rd @ ( mult @ ( mult @ A @ B ) @ C ) @ ( mult @ B @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(37,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( op_l @ A @ B @ C )
= ( mult @ ( i @ ( mult @ C @ B ) ) @ ( mult @ C @ ( mult @ B @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(38,plain,
( ( ! [A: $i,B: $i] :
( ( mult @ A @ B )
= ( mult @ ( mult @ B @ A ) @ ( op_k @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(39,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( mult @ ( mult @ A @ B ) @ C )
= ( mult @ ( mult @ A @ ( mult @ B @ C ) ) @ ( asoc @ A @ B @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(40,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( mult @ ( mult @ A @ ( mult @ B @ A ) ) @ C )
= ( mult @ A @ ( mult @ B @ ( mult @ A @ C ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(41,plain,
( ( ! [A: $i,B: $i] :
( ( mult @ ( rd @ A @ B ) @ B )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(42,plain,
( ( ! [A: $i,B: $i] :
( ( rd @ ( mult @ A @ B ) @ B )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(43,plain,
( ( ! [A: $i,B: $i] :
( ( mult @ ( i @ A ) @ ( mult @ A @ B ) )
= B ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(44,plain,
( ( ! [A: $i,B: $i] :
( ( i @ ( mult @ A @ B ) )
= ( mult @ ( i @ A ) @ ( i @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(45,plain,
( ( ! [A: $i] :
( ( mult @ ( i @ A ) @ A )
= unit ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(46,plain,
( ( ! [A: $i] :
( ( mult @ A @ ( i @ A ) )
= unit ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(47,plain,
( ( ! [A: $i] :
( ( mult @ A @ unit )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(48,plain,
( ( ! [A: $i] :
( ( mult @ unit @ A )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(49,plain,
( ( ( ( asoc @ a @ b @ ( op_k @ c @ d ) )
!= unit ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(50,plain,
( ( ~ $false )
= $true ),
inference(polarity_switch,[status(thm)],[26]) ).
thf(51,plain,
( ( ( ( asoc @ a @ b @ ( op_k @ c @ d ) )
!= unit ) )
= $true ),
inference(extcnf_combined,[status(esa)],[49]) ).
thf(52,plain,
( ( ( ( asoc @ a @ b @ ( op_k @ c @ d ) )
!= unit ) )
= $true ),
inference(copy,[status(thm)],[51]) ).
thf(53,plain,
( ( ! [A: $i] :
( ( mult @ unit @ A )
= A ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(54,plain,
( ( ! [A: $i] :
( ( mult @ A @ unit )
= A ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(55,plain,
( ( ! [A: $i] :
( ( mult @ A @ ( i @ A ) )
= unit ) )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(56,plain,
( ( ! [A: $i] :
( ( mult @ ( i @ A ) @ A )
= unit ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(57,plain,
( ( ! [A: $i,B: $i] :
( ( i @ ( mult @ A @ B ) )
= ( mult @ ( i @ A ) @ ( i @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(58,plain,
( ( ! [A: $i,B: $i] :
( ( mult @ ( i @ A ) @ ( mult @ A @ B ) )
= B ) )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(59,plain,
( ( ! [A: $i,B: $i] :
( ( rd @ ( mult @ A @ B ) @ B )
= A ) )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(60,plain,
( ( ! [A: $i,B: $i] :
( ( mult @ ( rd @ A @ B ) @ B )
= A ) )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(61,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( mult @ ( mult @ A @ ( mult @ B @ A ) ) @ C )
= ( mult @ A @ ( mult @ B @ ( mult @ A @ C ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(62,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( mult @ ( mult @ A @ B ) @ C )
= ( mult @ ( mult @ A @ ( mult @ B @ C ) ) @ ( asoc @ A @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(63,plain,
( ( ! [A: $i,B: $i] :
( ( mult @ A @ B )
= ( mult @ ( mult @ B @ A ) @ ( op_k @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(64,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( op_l @ A @ B @ C )
= ( mult @ ( i @ ( mult @ C @ B ) ) @ ( mult @ C @ ( mult @ B @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(65,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( op_r @ A @ B @ C )
= ( rd @ ( mult @ ( mult @ A @ B ) @ C ) @ ( mult @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(66,plain,
( ( ! [A: $i,B: $i] :
( ( op_t @ A @ B )
= ( mult @ ( i @ B ) @ ( mult @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(67,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( op_r @ ( op_r @ A @ B @ C ) @ D @ E )
= ( op_r @ ( op_r @ A @ D @ E ) @ B @ C ) ) )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(68,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( op_l @ ( op_r @ A @ B @ C ) @ D @ E )
= ( op_r @ ( op_l @ A @ D @ E ) @ B @ C ) ) )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(69,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( op_l @ ( op_l @ A @ B @ C ) @ D @ E )
= ( op_l @ ( op_l @ A @ D @ E ) @ B @ C ) ) )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(70,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( op_t @ ( op_r @ A @ B @ C ) @ D )
= ( op_r @ ( op_t @ A @ D ) @ B @ C ) ) )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(71,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( op_t @ ( op_l @ A @ B @ C ) @ D )
= ( op_l @ ( op_t @ A @ D ) @ B @ C ) ) )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(72,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( op_t @ ( op_t @ A @ B ) @ C )
= ( op_t @ ( op_t @ A @ C ) @ B ) ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(73,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( asoc @ ( asoc @ A @ B @ C ) @ D @ E )
= unit ) )
= $true ),
inference(copy,[status(thm)],[28]) ).
thf(74,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( asoc @ A @ B @ ( asoc @ C @ D @ E ) )
= unit ) )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(75,plain,
( ( ~ $false )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(76,plain,
( ( ( asoc @ a @ b @ ( op_k @ c @ d ) )
= unit )
= $false ),
inference(extcnf_not_pos,[status(thm)],[52]) ).
thf(77,plain,
! [SV1: $i] :
( ( ( mult @ unit @ SV1 )
= SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[53]) ).
thf(78,plain,
! [SV2: $i] :
( ( ( mult @ SV2 @ unit )
= SV2 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[54]) ).
thf(79,plain,
! [SV3: $i] :
( ( ( mult @ SV3 @ ( i @ SV3 ) )
= unit )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[55]) ).
thf(80,plain,
! [SV4: $i] :
( ( ( mult @ ( i @ SV4 ) @ SV4 )
= unit )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[56]) ).
thf(81,plain,
! [SV5: $i] :
( ( ! [SY64: $i] :
( ( i @ ( mult @ SV5 @ SY64 ) )
= ( mult @ ( i @ SV5 ) @ ( i @ SY64 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[57]) ).
thf(82,plain,
! [SV6: $i] :
( ( ! [SY65: $i] :
( ( mult @ ( i @ SV6 ) @ ( mult @ SV6 @ SY65 ) )
= SY65 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[58]) ).
thf(83,plain,
! [SV7: $i] :
( ( ! [SY66: $i] :
( ( rd @ ( mult @ SV7 @ SY66 ) @ SY66 )
= SV7 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[59]) ).
thf(84,plain,
! [SV8: $i] :
( ( ! [SY67: $i] :
( ( mult @ ( rd @ SV8 @ SY67 ) @ SY67 )
= SV8 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[60]) ).
thf(85,plain,
! [SV9: $i] :
( ( ! [SY68: $i,SY69: $i] :
( ( mult @ ( mult @ SV9 @ ( mult @ SY68 @ SV9 ) ) @ SY69 )
= ( mult @ SV9 @ ( mult @ SY68 @ ( mult @ SV9 @ SY69 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[61]) ).
thf(86,plain,
! [SV10: $i] :
( ( ! [SY70: $i,SY71: $i] :
( ( mult @ ( mult @ SV10 @ SY70 ) @ SY71 )
= ( mult @ ( mult @ SV10 @ ( mult @ SY70 @ SY71 ) ) @ ( asoc @ SV10 @ SY70 @ SY71 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[62]) ).
thf(87,plain,
! [SV11: $i] :
( ( ! [SY72: $i] :
( ( mult @ SV11 @ SY72 )
= ( mult @ ( mult @ SY72 @ SV11 ) @ ( op_k @ SV11 @ SY72 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[63]) ).
thf(88,plain,
! [SV12: $i] :
( ( ! [SY73: $i,SY74: $i] :
( ( op_l @ SV12 @ SY73 @ SY74 )
= ( mult @ ( i @ ( mult @ SY74 @ SY73 ) ) @ ( mult @ SY74 @ ( mult @ SY73 @ SV12 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[64]) ).
thf(89,plain,
! [SV13: $i] :
( ( ! [SY75: $i,SY76: $i] :
( ( op_r @ SV13 @ SY75 @ SY76 )
= ( rd @ ( mult @ ( mult @ SV13 @ SY75 ) @ SY76 ) @ ( mult @ SY75 @ SY76 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[65]) ).
thf(90,plain,
! [SV14: $i] :
( ( ! [SY77: $i] :
( ( op_t @ SV14 @ SY77 )
= ( mult @ ( i @ SY77 ) @ ( mult @ SV14 @ SY77 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[66]) ).
thf(91,plain,
! [SV15: $i] :
( ( ! [SY78: $i,SY79: $i,SY80: $i,SY81: $i] :
( ( op_r @ ( op_r @ SV15 @ SY78 @ SY79 ) @ SY80 @ SY81 )
= ( op_r @ ( op_r @ SV15 @ SY80 @ SY81 ) @ SY78 @ SY79 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[67]) ).
thf(92,plain,
! [SV16: $i] :
( ( ! [SY82: $i,SY83: $i,SY84: $i,SY85: $i] :
( ( op_l @ ( op_r @ SV16 @ SY82 @ SY83 ) @ SY84 @ SY85 )
= ( op_r @ ( op_l @ SV16 @ SY84 @ SY85 ) @ SY82 @ SY83 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[68]) ).
thf(93,plain,
! [SV17: $i] :
( ( ! [SY86: $i,SY87: $i,SY88: $i,SY89: $i] :
( ( op_l @ ( op_l @ SV17 @ SY86 @ SY87 ) @ SY88 @ SY89 )
= ( op_l @ ( op_l @ SV17 @ SY88 @ SY89 ) @ SY86 @ SY87 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[69]) ).
thf(94,plain,
! [SV18: $i] :
( ( ! [SY90: $i,SY91: $i,SY92: $i] :
( ( op_t @ ( op_r @ SV18 @ SY90 @ SY91 ) @ SY92 )
= ( op_r @ ( op_t @ SV18 @ SY92 ) @ SY90 @ SY91 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[70]) ).
thf(95,plain,
! [SV19: $i] :
( ( ! [SY93: $i,SY94: $i,SY95: $i] :
( ( op_t @ ( op_l @ SV19 @ SY93 @ SY94 ) @ SY95 )
= ( op_l @ ( op_t @ SV19 @ SY95 ) @ SY93 @ SY94 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(96,plain,
! [SV20: $i] :
( ( ! [SY96: $i,SY97: $i] :
( ( op_t @ ( op_t @ SV20 @ SY96 ) @ SY97 )
= ( op_t @ ( op_t @ SV20 @ SY97 ) @ SY96 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[72]) ).
thf(97,plain,
! [SV21: $i] :
( ( ! [SY98: $i,SY99: $i,SY100: $i,SY101: $i] :
( ( asoc @ ( asoc @ SV21 @ SY98 @ SY99 ) @ SY100 @ SY101 )
= unit ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[73]) ).
thf(98,plain,
! [SV22: $i] :
( ( ! [SY102: $i,SY103: $i,SY104: $i,SY105: $i] :
( ( asoc @ SV22 @ SY102 @ ( asoc @ SY103 @ SY104 @ SY105 ) )
= unit ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[74]) ).
thf(99,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[75]) ).
thf(100,plain,
! [SV23: $i,SV5: $i] :
( ( ( i @ ( mult @ SV5 @ SV23 ) )
= ( mult @ ( i @ SV5 ) @ ( i @ SV23 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[81]) ).
thf(101,plain,
! [SV24: $i,SV6: $i] :
( ( ( mult @ ( i @ SV6 ) @ ( mult @ SV6 @ SV24 ) )
= SV24 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[82]) ).
thf(102,plain,
! [SV25: $i,SV7: $i] :
( ( ( rd @ ( mult @ SV7 @ SV25 ) @ SV25 )
= SV7 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[83]) ).
thf(103,plain,
! [SV26: $i,SV8: $i] :
( ( ( mult @ ( rd @ SV8 @ SV26 ) @ SV26 )
= SV8 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).
thf(104,plain,
! [SV27: $i,SV9: $i] :
( ( ! [SY106: $i] :
( ( mult @ ( mult @ SV9 @ ( mult @ SV27 @ SV9 ) ) @ SY106 )
= ( mult @ SV9 @ ( mult @ SV27 @ ( mult @ SV9 @ SY106 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(105,plain,
! [SV28: $i,SV10: $i] :
( ( ! [SY107: $i] :
( ( mult @ ( mult @ SV10 @ SV28 ) @ SY107 )
= ( mult @ ( mult @ SV10 @ ( mult @ SV28 @ SY107 ) ) @ ( asoc @ SV10 @ SV28 @ SY107 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[86]) ).
thf(106,plain,
! [SV29: $i,SV11: $i] :
( ( ( mult @ SV11 @ SV29 )
= ( mult @ ( mult @ SV29 @ SV11 ) @ ( op_k @ SV11 @ SV29 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).
thf(107,plain,
! [SV30: $i,SV12: $i] :
( ( ! [SY108: $i] :
( ( op_l @ SV12 @ SV30 @ SY108 )
= ( mult @ ( i @ ( mult @ SY108 @ SV30 ) ) @ ( mult @ SY108 @ ( mult @ SV30 @ SV12 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(108,plain,
! [SV31: $i,SV13: $i] :
( ( ! [SY109: $i] :
( ( op_r @ SV13 @ SV31 @ SY109 )
= ( rd @ ( mult @ ( mult @ SV13 @ SV31 ) @ SY109 ) @ ( mult @ SV31 @ SY109 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[89]) ).
thf(109,plain,
! [SV32: $i,SV14: $i] :
( ( ( op_t @ SV14 @ SV32 )
= ( mult @ ( i @ SV32 ) @ ( mult @ SV14 @ SV32 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[90]) ).
thf(110,plain,
! [SV33: $i,SV15: $i] :
( ( ! [SY110: $i,SY111: $i,SY112: $i] :
( ( op_r @ ( op_r @ SV15 @ SV33 @ SY110 ) @ SY111 @ SY112 )
= ( op_r @ ( op_r @ SV15 @ SY111 @ SY112 ) @ SV33 @ SY110 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[91]) ).
thf(111,plain,
! [SV34: $i,SV16: $i] :
( ( ! [SY113: $i,SY114: $i,SY115: $i] :
( ( op_l @ ( op_r @ SV16 @ SV34 @ SY113 ) @ SY114 @ SY115 )
= ( op_r @ ( op_l @ SV16 @ SY114 @ SY115 ) @ SV34 @ SY113 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[92]) ).
thf(112,plain,
! [SV35: $i,SV17: $i] :
( ( ! [SY116: $i,SY117: $i,SY118: $i] :
( ( op_l @ ( op_l @ SV17 @ SV35 @ SY116 ) @ SY117 @ SY118 )
= ( op_l @ ( op_l @ SV17 @ SY117 @ SY118 ) @ SV35 @ SY116 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[93]) ).
thf(113,plain,
! [SV36: $i,SV18: $i] :
( ( ! [SY119: $i,SY120: $i] :
( ( op_t @ ( op_r @ SV18 @ SV36 @ SY119 ) @ SY120 )
= ( op_r @ ( op_t @ SV18 @ SY120 ) @ SV36 @ SY119 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[94]) ).
thf(114,plain,
! [SV37: $i,SV19: $i] :
( ( ! [SY121: $i,SY122: $i] :
( ( op_t @ ( op_l @ SV19 @ SV37 @ SY121 ) @ SY122 )
= ( op_l @ ( op_t @ SV19 @ SY122 ) @ SV37 @ SY121 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[95]) ).
thf(115,plain,
! [SV38: $i,SV20: $i] :
( ( ! [SY123: $i] :
( ( op_t @ ( op_t @ SV20 @ SV38 ) @ SY123 )
= ( op_t @ ( op_t @ SV20 @ SY123 ) @ SV38 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[96]) ).
thf(116,plain,
! [SV39: $i,SV21: $i] :
( ( ! [SY124: $i,SY125: $i,SY126: $i] :
( ( asoc @ ( asoc @ SV21 @ SV39 @ SY124 ) @ SY125 @ SY126 )
= unit ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[97]) ).
thf(117,plain,
! [SV40: $i,SV22: $i] :
( ( ! [SY127: $i,SY128: $i,SY129: $i] :
( ( asoc @ SV22 @ SV40 @ ( asoc @ SY127 @ SY128 @ SY129 ) )
= unit ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[98]) ).
thf(118,plain,
! [SV41: $i,SV27: $i,SV9: $i] :
( ( ( mult @ ( mult @ SV9 @ ( mult @ SV27 @ SV9 ) ) @ SV41 )
= ( mult @ SV9 @ ( mult @ SV27 @ ( mult @ SV9 @ SV41 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[104]) ).
thf(119,plain,
! [SV42: $i,SV28: $i,SV10: $i] :
( ( ( mult @ ( mult @ SV10 @ SV28 ) @ SV42 )
= ( mult @ ( mult @ SV10 @ ( mult @ SV28 @ SV42 ) ) @ ( asoc @ SV10 @ SV28 @ SV42 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[105]) ).
thf(120,plain,
! [SV43: $i,SV30: $i,SV12: $i] :
( ( ( op_l @ SV12 @ SV30 @ SV43 )
= ( mult @ ( i @ ( mult @ SV43 @ SV30 ) ) @ ( mult @ SV43 @ ( mult @ SV30 @ SV12 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[107]) ).
thf(121,plain,
! [SV44: $i,SV31: $i,SV13: $i] :
( ( ( op_r @ SV13 @ SV31 @ SV44 )
= ( rd @ ( mult @ ( mult @ SV13 @ SV31 ) @ SV44 ) @ ( mult @ SV31 @ SV44 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[108]) ).
thf(122,plain,
! [SV45: $i,SV33: $i,SV15: $i] :
( ( ! [SY130: $i,SY131: $i] :
( ( op_r @ ( op_r @ SV15 @ SV33 @ SV45 ) @ SY130 @ SY131 )
= ( op_r @ ( op_r @ SV15 @ SY130 @ SY131 ) @ SV33 @ SV45 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[110]) ).
thf(123,plain,
! [SV46: $i,SV34: $i,SV16: $i] :
( ( ! [SY132: $i,SY133: $i] :
( ( op_l @ ( op_r @ SV16 @ SV34 @ SV46 ) @ SY132 @ SY133 )
= ( op_r @ ( op_l @ SV16 @ SY132 @ SY133 ) @ SV34 @ SV46 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[111]) ).
thf(124,plain,
! [SV47: $i,SV35: $i,SV17: $i] :
( ( ! [SY134: $i,SY135: $i] :
( ( op_l @ ( op_l @ SV17 @ SV35 @ SV47 ) @ SY134 @ SY135 )
= ( op_l @ ( op_l @ SV17 @ SY134 @ SY135 ) @ SV35 @ SV47 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[112]) ).
thf(125,plain,
! [SV48: $i,SV36: $i,SV18: $i] :
( ( ! [SY136: $i] :
( ( op_t @ ( op_r @ SV18 @ SV36 @ SV48 ) @ SY136 )
= ( op_r @ ( op_t @ SV18 @ SY136 ) @ SV36 @ SV48 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[113]) ).
thf(126,plain,
! [SV49: $i,SV37: $i,SV19: $i] :
( ( ! [SY137: $i] :
( ( op_t @ ( op_l @ SV19 @ SV37 @ SV49 ) @ SY137 )
= ( op_l @ ( op_t @ SV19 @ SY137 ) @ SV37 @ SV49 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[114]) ).
thf(127,plain,
! [SV50: $i,SV38: $i,SV20: $i] :
( ( ( op_t @ ( op_t @ SV20 @ SV38 ) @ SV50 )
= ( op_t @ ( op_t @ SV20 @ SV50 ) @ SV38 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[115]) ).
thf(128,plain,
! [SV51: $i,SV39: $i,SV21: $i] :
( ( ! [SY138: $i,SY139: $i] :
( ( asoc @ ( asoc @ SV21 @ SV39 @ SV51 ) @ SY138 @ SY139 )
= unit ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[116]) ).
thf(129,plain,
! [SV52: $i,SV40: $i,SV22: $i] :
( ( ! [SY140: $i,SY141: $i] :
( ( asoc @ SV22 @ SV40 @ ( asoc @ SV52 @ SY140 @ SY141 ) )
= unit ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[117]) ).
thf(130,plain,
! [SV53: $i,SV45: $i,SV33: $i,SV15: $i] :
( ( ! [SY142: $i] :
( ( op_r @ ( op_r @ SV15 @ SV33 @ SV45 ) @ SV53 @ SY142 )
= ( op_r @ ( op_r @ SV15 @ SV53 @ SY142 ) @ SV33 @ SV45 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[122]) ).
thf(131,plain,
! [SV54: $i,SV46: $i,SV34: $i,SV16: $i] :
( ( ! [SY143: $i] :
( ( op_l @ ( op_r @ SV16 @ SV34 @ SV46 ) @ SV54 @ SY143 )
= ( op_r @ ( op_l @ SV16 @ SV54 @ SY143 ) @ SV34 @ SV46 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[123]) ).
thf(132,plain,
! [SV55: $i,SV47: $i,SV35: $i,SV17: $i] :
( ( ! [SY144: $i] :
( ( op_l @ ( op_l @ SV17 @ SV35 @ SV47 ) @ SV55 @ SY144 )
= ( op_l @ ( op_l @ SV17 @ SV55 @ SY144 ) @ SV35 @ SV47 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[124]) ).
thf(133,plain,
! [SV56: $i,SV48: $i,SV36: $i,SV18: $i] :
( ( ( op_t @ ( op_r @ SV18 @ SV36 @ SV48 ) @ SV56 )
= ( op_r @ ( op_t @ SV18 @ SV56 ) @ SV36 @ SV48 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[125]) ).
thf(134,plain,
! [SV57: $i,SV49: $i,SV37: $i,SV19: $i] :
( ( ( op_t @ ( op_l @ SV19 @ SV37 @ SV49 ) @ SV57 )
= ( op_l @ ( op_t @ SV19 @ SV57 ) @ SV37 @ SV49 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[126]) ).
thf(135,plain,
! [SV58: $i,SV51: $i,SV39: $i,SV21: $i] :
( ( ! [SY145: $i] :
( ( asoc @ ( asoc @ SV21 @ SV39 @ SV51 ) @ SV58 @ SY145 )
= unit ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[128]) ).
thf(136,plain,
! [SV59: $i,SV52: $i,SV40: $i,SV22: $i] :
( ( ! [SY146: $i] :
( ( asoc @ SV22 @ SV40 @ ( asoc @ SV52 @ SV59 @ SY146 ) )
= unit ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[129]) ).
thf(137,plain,
! [SV60: $i,SV53: $i,SV45: $i,SV33: $i,SV15: $i] :
( ( ( op_r @ ( op_r @ SV15 @ SV33 @ SV45 ) @ SV53 @ SV60 )
= ( op_r @ ( op_r @ SV15 @ SV53 @ SV60 ) @ SV33 @ SV45 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[130]) ).
thf(138,plain,
! [SV61: $i,SV54: $i,SV46: $i,SV34: $i,SV16: $i] :
( ( ( op_l @ ( op_r @ SV16 @ SV34 @ SV46 ) @ SV54 @ SV61 )
= ( op_r @ ( op_l @ SV16 @ SV54 @ SV61 ) @ SV34 @ SV46 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[131]) ).
thf(139,plain,
! [SV62: $i,SV55: $i,SV47: $i,SV35: $i,SV17: $i] :
( ( ( op_l @ ( op_l @ SV17 @ SV35 @ SV47 ) @ SV55 @ SV62 )
= ( op_l @ ( op_l @ SV17 @ SV55 @ SV62 ) @ SV35 @ SV47 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[132]) ).
thf(140,plain,
! [SV63: $i,SV58: $i,SV51: $i,SV39: $i,SV21: $i] :
( ( ( asoc @ ( asoc @ SV21 @ SV39 @ SV51 ) @ SV58 @ SV63 )
= unit )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[135]) ).
thf(141,plain,
! [SV64: $i,SV59: $i,SV52: $i,SV40: $i,SV22: $i] :
( ( ( asoc @ SV22 @ SV40 @ ( asoc @ SV52 @ SV59 @ SV64 ) )
= unit )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[136]) ).
thf(142,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[76,141,140,139,138,137,134,133,127,121,120,119,118,109,106,103,102,101,100,99,80,79,78,77]) ).
thf(143,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[142]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GRP729-1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.14/0.35 % Computer : n014.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Mon Jun 13 07:25:22 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.37
% 0.14/0.37 No.of.Axioms: 23
% 0.14/0.37
% 0.14/0.37 Length.of.Defs: 0
% 0.14/0.37
% 0.14/0.37 Contains.Choice.Funs: false
% 0.14/0.38 .
% 0.14/0.39 (rf:0,axioms:23,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:25,loop_count:0,foatp_calls:0,translation:fof_full)........
% 15.50/15.76
% 15.50/15.76 ********************************
% 15.50/15.76 * All subproblems solved! *
% 15.50/15.76 ********************************
% 15.50/15.76 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:23,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:142,loop_count:0,foatp_calls:1,translation:fof_full)
% 15.50/15.76
% 15.50/15.76 %**** Beginning of derivation protocol ****
% 15.50/15.76 % SZS output start CNFRefutation
% See solution above
% 15.50/15.76
% 15.50/15.76 %**** End of derivation protocol ****
% 15.50/15.76 %**** no. of clauses in derivation: 143 ****
% 15.50/15.76 %**** clause counter: 142 ****
% 15.50/15.76
% 15.50/15.76 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:23,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:142,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------