TSTP Solution File: SWV055+1 by Leo-III---1.7.15
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.15
% Problem : SWV055+1 : TPTP v8.2.0. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n025.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 : 300s
% DateTime : Mon Jun 24 17:21:56 EDT 2024
% Result : Theorem 74.25s 18.42s
% Output : Refutation 74.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 90
% Syntax : Number of formulae : 672 ( 303 unt; 0 typ; 0 def)
% Number of atoms : 1953 ( 759 equ; 0 cnn)
% Maximal formula atoms : 20 ( 2 avg)
% Number of connectives : 8375 ( 769 ~; 641 |; 241 &;6579 @)
% ( 5 <=>; 140 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 50 ( 47 usr; 19 con; 0-4 aty)
% Number of variables : 867 ( 0 ^ 865 !; 2 ?; 867 :)
% Comments :
%------------------------------------------------------------------------------
thf(leq_type,type,
leq: $i > $i > $o ).
thf(n0_type,type,
n0: $i ).
thf(pv10_type,type,
pv10: $i ).
thf(minus_type,type,
minus: $i > $i > $i ).
thf(n135300_type,type,
n135300: $i ).
thf(n1_type,type,
n1: $i ).
thf(sum_type,type,
sum: $i > $i > $i > $i ).
thf(n5_type,type,
n5: $i ).
thf(a_select3_type,type,
a_select3: $i > $i > $i > $i ).
thf(q_type,type,
q: $i ).
thf(divide_type,type,
divide: $i > $i > $i ).
thf(sqrt_type,type,
sqrt: $i > $i ).
thf(times_type,type,
times: $i > $i > $i ).
thf(center_type,type,
center: $i ).
thf(a_select2_type,type,
a_select2: $i > $i > $i ).
thf(x_type,type,
x: $i ).
thf(plus_type,type,
plus: $i > $i > $i ).
thf(n3_type,type,
n3: $i ).
thf(succ_type,type,
succ: $i > $i ).
thf(pred_type,type,
pred: $i > $i ).
thf(gt_type,type,
gt: $i > $i > $o ).
thf(tptp_minus_1_type,type,
tptp_minus_1: $i ).
thf(n2_type,type,
n2: $i ).
thf(n4_type,type,
n4: $i ).
thf(lt_type,type,
lt: $i > $i > $o ).
thf(tptp_update2_type,type,
tptp_update2: $i > $i > $i > $i ).
thf(tptp_const_array2_type,type,
tptp_const_array2: $i > $i > $i > $i ).
thf(dim_type,type,
dim: $i > $i > $i ).
thf(tptp_mmul_type,type,
tptp_mmul: $i > $i > $i ).
thf(trans_type,type,
trans: $i > $i ).
thf(tptp_update3_type,type,
tptp_update3: $i > $i > $i > $i > $i ).
thf(tptp_madd_type,type,
tptp_madd: $i > $i > $i ).
thf(geq_type,type,
geq: $i > $i > $o ).
thf(uniform_int_rnd_type,type,
uniform_int_rnd: $i > $i > $i ).
thf(tptp_msub_type,type,
tptp_msub: $i > $i > $i ).
thf(tptp_float_0_0_type,type,
tptp_float_0_0: $i ).
thf(tptp_const_array1_type,type,
tptp_const_array1: $i > $i > $i ).
thf(inv_type,type,
inv: $i > $i ).
thf(sk1_type,type,
sk1: $i ).
thf(sk2_type,type,
sk2: $i ).
thf(sk3_type,type,
sk3: $i ).
thf(sk4_type,type,
sk4: $i ).
thf(sk5_type,type,
sk5: $i > $i > $i > $i > $i ).
thf(sk6_type,type,
sk6: $i > $i > $i > $i ).
thf(sk7_type,type,
sk7: $i > $i > $i > $i ).
thf(sk8_type,type,
sk8: $i > $i > $i ).
thf(sk9_type,type,
sk9: $i > $i > $i ).
thf(1,conjecture,
( ( ( leq @ n0 @ pv10 )
& ( leq @ pv10 @ ( minus @ n135300 @ n1 ) )
& ! [A: $i,B: $i] :
( ( ( leq @ n0 @ A )
& ( leq @ A @ ( minus @ pv10 @ n1 ) ) )
=> ( ( sum @ n0 @ ( minus @ n5 @ n1 ) @ ( a_select3 @ q @ A @ B ) )
= n1 ) ) )
=> ( ( leq @ n0 @ pv10 )
& ( leq @ pv10 @ ( minus @ n135300 @ n1 ) )
& ! [A: $i,B: $i] :
( ( ( leq @ n0 @ A )
& ( leq @ A @ ( minus @ n0 @ n1 ) ) )
=> ( ( a_select3 @ q @ pv10 @ A )
= ( divide @ ( sqrt @ ( times @ ( minus @ ( a_select3 @ center @ A @ n0 ) @ ( a_select2 @ x @ pv10 ) ) @ ( minus @ ( a_select3 @ center @ A @ n0 ) @ ( a_select2 @ x @ pv10 ) ) ) ) @ ( sum @ n0 @ ( minus @ n5 @ n1 ) @ ( sqrt @ ( times @ ( minus @ ( a_select3 @ center @ B @ n0 ) @ ( a_select2 @ x @ pv10 ) ) @ ( minus @ ( a_select3 @ center @ B @ n0 ) @ ( a_select2 @ x @ pv10 ) ) ) ) ) ) ) )
& ! [A: $i,B: $i] :
( ( ( leq @ n0 @ A )
& ( leq @ A @ ( minus @ pv10 @ n1 ) ) )
=> ( ( sum @ n0 @ ( minus @ n5 @ n1 ) @ ( a_select3 @ q @ A @ B ) )
= n1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cl5_nebula_norm_0037) ).
thf(2,negated_conjecture,
~ ( ( ( leq @ n0 @ pv10 )
& ( leq @ pv10 @ ( minus @ n135300 @ n1 ) )
& ! [A: $i,B: $i] :
( ( ( leq @ n0 @ A )
& ( leq @ A @ ( minus @ pv10 @ n1 ) ) )
=> ( ( sum @ n0 @ ( minus @ n5 @ n1 ) @ ( a_select3 @ q @ A @ B ) )
= n1 ) ) )
=> ( ( leq @ n0 @ pv10 )
& ( leq @ pv10 @ ( minus @ n135300 @ n1 ) )
& ! [A: $i,B: $i] :
( ( ( leq @ n0 @ A )
& ( leq @ A @ ( minus @ n0 @ n1 ) ) )
=> ( ( a_select3 @ q @ pv10 @ A )
= ( divide @ ( sqrt @ ( times @ ( minus @ ( a_select3 @ center @ A @ n0 ) @ ( a_select2 @ x @ pv10 ) ) @ ( minus @ ( a_select3 @ center @ A @ n0 ) @ ( a_select2 @ x @ pv10 ) ) ) ) @ ( sum @ n0 @ ( minus @ n5 @ n1 ) @ ( sqrt @ ( times @ ( minus @ ( a_select3 @ center @ B @ n0 ) @ ( a_select2 @ x @ pv10 ) ) @ ( minus @ ( a_select3 @ center @ B @ n0 ) @ ( a_select2 @ x @ pv10 ) ) ) ) ) ) ) )
& ! [A: $i,B: $i] :
( ( ( leq @ n0 @ A )
& ( leq @ A @ ( minus @ pv10 @ n1 ) ) )
=> ( ( sum @ n0 @ ( minus @ n5 @ n1 ) @ ( a_select3 @ q @ A @ B ) )
= n1 ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(92,plain,
~ ( ( ( leq @ n0 @ pv10 )
& ( leq @ pv10 @ ( minus @ n135300 @ n1 ) )
& ! [A: $i,B: $i] :
( ( ( leq @ n0 @ A )
& ( leq @ A @ ( minus @ pv10 @ n1 ) ) )
=> ( ( sum @ n0 @ ( minus @ n5 @ n1 ) @ ( a_select3 @ q @ A @ B ) )
= n1 ) ) )
=> ( ( leq @ n0 @ pv10 )
& ( leq @ pv10 @ ( minus @ n135300 @ n1 ) )
& ! [A: $i,B: $i] :
( ( ( leq @ n0 @ A )
& ( leq @ A @ ( minus @ n0 @ n1 ) ) )
=> ( ( a_select3 @ q @ pv10 @ A )
= ( divide @ ( sqrt @ ( times @ ( minus @ ( a_select3 @ center @ A @ n0 ) @ ( a_select2 @ x @ pv10 ) ) @ ( minus @ ( a_select3 @ center @ A @ n0 ) @ ( a_select2 @ x @ pv10 ) ) ) ) @ ( sum @ n0 @ ( minus @ n5 @ n1 ) @ ( sqrt @ ( times @ ( minus @ ( a_select3 @ center @ B @ n0 ) @ ( a_select2 @ x @ pv10 ) ) @ ( minus @ ( a_select3 @ center @ B @ n0 ) @ ( a_select2 @ x @ pv10 ) ) ) ) ) ) ) )
& ! [A: $i,B: $i] :
( ( ( leq @ n0 @ A )
& ( leq @ A @ ( minus @ pv10 @ n1 ) ) )
=> ( ( sum @ n0 @ ( minus @ n5 @ n1 ) @ ( a_select3 @ q @ A @ B ) )
= n1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(93,plain,
~ ( ( ( leq @ n0 @ pv10 )
& ( leq @ pv10 @ ( minus @ n135300 @ n1 ) )
& ! [A: $i] :
( ( ( leq @ n0 @ A )
& ( leq @ A @ ( minus @ pv10 @ n1 ) ) )
=> ! [B: $i] :
( ( sum @ n0 @ ( minus @ n5 @ n1 ) @ ( a_select3 @ q @ A @ B ) )
= n1 ) ) )
=> ( ( leq @ n0 @ pv10 )
& ( leq @ pv10 @ ( minus @ n135300 @ n1 ) )
& ! [A: $i] :
( ( ( leq @ n0 @ A )
& ( leq @ A @ ( minus @ n0 @ n1 ) ) )
=> ! [B: $i] :
( ( a_select3 @ q @ pv10 @ A )
= ( divide @ ( sqrt @ ( times @ ( minus @ ( a_select3 @ center @ A @ n0 ) @ ( a_select2 @ x @ pv10 ) ) @ ( minus @ ( a_select3 @ center @ A @ n0 ) @ ( a_select2 @ x @ pv10 ) ) ) ) @ ( sum @ n0 @ ( minus @ n5 @ n1 ) @ ( sqrt @ ( times @ ( minus @ ( a_select3 @ center @ B @ n0 ) @ ( a_select2 @ x @ pv10 ) ) @ ( minus @ ( a_select3 @ center @ B @ n0 ) @ ( a_select2 @ x @ pv10 ) ) ) ) ) ) ) )
& ! [A: $i] :
( ( ( leq @ n0 @ A )
& ( leq @ A @ ( minus @ pv10 @ n1 ) ) )
=> ! [B: $i] :
( ( sum @ n0 @ ( minus @ n5 @ n1 ) @ ( a_select3 @ q @ A @ B ) )
= n1 ) ) ) ),
inference(miniscope,[status(thm)],[92]) ).
thf(105,plain,
( ~ ( leq @ n0 @ pv10 )
| ~ ( leq @ pv10 @ ( minus @ n135300 @ n1 ) )
| ( leq @ n0 @ sk1 )
| ( leq @ n0 @ sk3 ) ),
inference(cnf,[status(esa)],[93]) ).
thf(96,plain,
leq @ n0 @ pv10,
inference(cnf,[status(esa)],[93]) ).
thf(95,plain,
leq @ pv10 @ ( minus @ n135300 @ n1 ),
inference(cnf,[status(esa)],[93]) ).
thf(571,plain,
( ~ $true
| ~ $true
| ( leq @ n0 @ sk1 )
| ( leq @ n0 @ sk3 ) ),
inference(rewrite,[status(thm)],[105,96,95]) ).
thf(572,plain,
( ( leq @ n0 @ sk1 )
| ( leq @ n0 @ sk3 ) ),
inference(simp,[status(thm)],[571]) ).
thf(573,plain,
( ( leq @ n0 @ sk1 )
| ( ( leq @ n0 @ sk3 )
!= ( leq @ n0 @ sk1 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[572]) ).
thf(575,plain,
( ( leq @ n0 @ sk1 )
| ( n0 != n0 )
| ( sk3 != sk1 ) ),
inference(simp,[status(thm)],[573]) ).
thf(576,plain,
( ( leq @ n0 @ sk1 )
| ( sk3 != sk1 ) ),
inference(simp,[status(thm)],[575]) ).
thf(102,plain,
( ~ ( leq @ n0 @ pv10 )
| ~ ( leq @ pv10 @ ( minus @ n135300 @ n1 ) )
| ( leq @ sk1 @ ( minus @ n0 @ n1 ) )
| ( leq @ sk3 @ ( minus @ pv10 @ n1 ) ) ),
inference(cnf,[status(esa)],[93]) ).
thf(601,plain,
( ~ $true
| ~ $true
| ( leq @ sk1 @ ( minus @ n0 @ n1 ) )
| ( leq @ sk3 @ ( minus @ pv10 @ n1 ) ) ),
inference(rewrite,[status(thm)],[102,96,95]) ).
thf(602,plain,
( ( leq @ sk1 @ ( minus @ n0 @ n1 ) )
| ( leq @ sk3 @ ( minus @ pv10 @ n1 ) ) ),
inference(simp,[status(thm)],[601]) ).
thf(97,plain,
! [B: $i,A: $i] :
( ~ ( leq @ n0 @ A )
| ~ ( leq @ A @ ( minus @ pv10 @ n1 ) )
| ( ( sum @ n0 @ ( minus @ n5 @ n1 ) @ ( a_select3 @ q @ A @ B ) )
= n1 ) ),
inference(cnf,[status(esa)],[93]) ).
thf(107,plain,
! [B: $i,A: $i] :
( ( ( sum @ n0 @ ( minus @ n5 @ n1 ) @ ( a_select3 @ q @ A @ B ) )
= n1 )
| ~ ( leq @ n0 @ A )
| ~ ( leq @ A @ ( minus @ pv10 @ n1 ) ) ),
inference(lifteq,[status(thm)],[97]) ).
thf(101,plain,
( ~ ( leq @ n0 @ pv10 )
| ~ ( leq @ pv10 @ ( minus @ n135300 @ n1 ) )
| ( leq @ sk1 @ ( minus @ n0 @ n1 ) )
| ( ( sum @ n0 @ ( minus @ n5 @ n1 ) @ ( a_select3 @ q @ sk3 @ sk4 ) )
!= n1 ) ),
inference(cnf,[status(esa)],[93]) ).
thf(106,plain,
( ( ( sum @ n0 @ ( minus @ n5 @ n1 ) @ ( a_select3 @ q @ sk3 @ sk4 ) )
!= n1 )
| ~ ( leq @ n0 @ pv10 )
| ~ ( leq @ pv10 @ ( minus @ n135300 @ n1 ) )
| ( leq @ sk1 @ ( minus @ n0 @ n1 ) ) ),
inference(lifteq,[status(thm)],[101]) ).
thf(1211,plain,
( ( ( sum @ n0 @ ( minus @ n5 @ n1 ) @ ( a_select3 @ q @ sk3 @ sk4 ) )
!= n1 )
| ~ $true
| ~ $true
| ( leq @ sk1 @ ( minus @ n0 @ n1 ) ) ),
inference(rewrite,[status(thm)],[106,96,95]) ).
thf(1212,plain,
( ( ( sum @ n0 @ ( minus @ n5 @ n1 ) @ ( a_select3 @ q @ sk3 @ sk4 ) )
!= n1 )
| ( leq @ sk1 @ ( minus @ n0 @ n1 ) ) ),
inference(simp,[status(thm)],[1211]) ).
thf(1388,plain,
! [B: $i,A: $i] :
( ~ ( leq @ n0 @ A )
| ~ ( leq @ A @ ( minus @ pv10 @ n1 ) )
| ( leq @ sk1 @ ( minus @ n0 @ n1 ) )
| ( ( sum @ n0 @ ( minus @ n5 @ n1 ) @ ( a_select3 @ q @ A @ B ) )
!= ( sum @ n0 @ ( minus @ n5 @ n1 ) @ ( a_select3 @ q @ sk3 @ sk4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[107,1212]) ).
thf(1389,plain,
( ~ ( leq @ n0 @ sk3 )
| ~ ( leq @ sk3 @ ( minus @ pv10 @ n1 ) )
| ( leq @ sk1 @ ( minus @ n0 @ n1 ) ) ),
inference(pattern_uni,[status(thm)],[1388:[bind(A,$thf( sk3 )),bind(B,$thf( sk4 ))]]) ).
thf(1706,plain,
( ( leq @ sk1 @ ( minus @ n0 @ n1 ) )
| ~ ( leq @ n0 @ sk3 )
| ( ( leq @ sk3 @ ( minus @ pv10 @ n1 ) )
!= ( leq @ sk3 @ ( minus @ pv10 @ n1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[602,1389]) ).
thf(1707,plain,
( ( leq @ sk1 @ ( minus @ n0 @ n1 ) )
| ~ ( leq @ n0 @ sk3 ) ),
inference(pattern_uni,[status(thm)],[1706:[]]) ).
thf(1839,plain,
( ( sk3 != sk1 )
| ( leq @ sk1 @ ( minus @ n0 @ n1 ) )
| ( ( leq @ n0 @ sk3 )
!= ( leq @ n0 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[576,1707]) ).
thf(1866,plain,
( ( leq @ sk1 @ ( minus @ n0 @ n1 ) )
| ( sk3 != sk1 )
| ( n0 != n0 )
| ( sk3 != sk1 ) ),
inference(simp,[status(thm)],[1839]) ).
thf(1879,plain,
( ( leq @ sk1 @ ( minus @ n0 @ n1 ) )
| ( sk3 != sk1 ) ),
inference(simp,[status(thm)],[1866]) ).
thf(24,axiom,
( ( succ @ n0 )
= n1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_1) ).
thf(159,plain,
( ( succ @ n0 )
= n1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(160,plain,
( ( succ @ n0 )
= n1 ),
inference(lifteq,[status(thm)],[159]) ).
thf(14,axiom,
! [A: $i] :
( ( pred @ ( succ @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pred_succ) ).
thf(134,plain,
! [A: $i] :
( ( pred @ ( succ @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(135,plain,
! [A: $i] :
( ( pred @ ( succ @ A ) )
= A ),
inference(cnf,[status(esa)],[134]) ).
thf(136,plain,
! [A: $i] :
( ( pred @ ( succ @ A ) )
= A ),
inference(lifteq,[status(thm)],[135]) ).
thf(8397,plain,
! [A: $i] :
( ( ( pred @ n1 )
= A )
| ( ( succ @ n0 )
!= ( succ @ A ) ) ),
inference(paramod_ordered,[status(thm)],[160,136]) ).
thf(8398,plain,
( ( pred @ n1 )
= n0 ),
inference(pattern_uni,[status(thm)],[8397:[bind(A,$thf( n0 ))]]) ).
thf(52,axiom,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i,E: $i] :
( ( ( leq @ n0 @ D )
& ( leq @ D @ C )
& ( leq @ n0 @ E )
& ( leq @ E @ C ) )
=> ( ( a_select3 @ A @ D @ E )
= ( a_select3 @ A @ E @ D ) ) )
& ! [D: $i,E: $i] :
( ( ( leq @ n0 @ D )
& ( leq @ D @ C )
& ( leq @ n0 @ E )
& ( leq @ E @ C ) )
=> ( ( a_select3 @ B @ D @ E )
= ( a_select3 @ B @ E @ D ) ) ) )
=> ! [D: $i,E: $i] :
( ( ( leq @ n0 @ D )
& ( leq @ D @ C )
& ( leq @ n0 @ E )
& ( leq @ E @ C ) )
=> ( ( a_select3 @ ( tptp_msub @ A @ B ) @ D @ E )
= ( a_select3 @ ( tptp_msub @ A @ B ) @ E @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',matrix_symm_sub) ).
thf(347,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i,E: $i] :
( ( ( leq @ n0 @ D )
& ( leq @ D @ C )
& ( leq @ n0 @ E )
& ( leq @ E @ C ) )
=> ( ( a_select3 @ A @ D @ E )
= ( a_select3 @ A @ E @ D ) ) )
& ! [D: $i,E: $i] :
( ( ( leq @ n0 @ D )
& ( leq @ D @ C )
& ( leq @ n0 @ E )
& ( leq @ E @ C ) )
=> ( ( a_select3 @ B @ D @ E )
= ( a_select3 @ B @ E @ D ) ) ) )
=> ! [D: $i,E: $i] :
( ( ( leq @ n0 @ D )
& ( leq @ D @ C )
& ( leq @ n0 @ E )
& ( leq @ E @ C ) )
=> ( ( a_select3 @ ( tptp_msub @ A @ B ) @ D @ E )
= ( a_select3 @ ( tptp_msub @ A @ B ) @ E @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(47,axiom,
! [A: $i] :
( ( plus @ n5 @ A )
= ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',succ_plus_5_l) ).
thf(333,plain,
! [A: $i] :
( ( plus @ n5 @ A )
= ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( gt @ A @ B )
| ( gt @ B @ A )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',totality) ).
thf(129,plain,
! [A: $i,B: $i] :
( ( gt @ A @ B )
| ( gt @ B @ A )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(130,plain,
! [B: $i,A: $i] :
( ( gt @ A @ B )
| ( gt @ B @ A )
| ( A = B ) ),
inference(cnf,[status(esa)],[129]) ).
thf(131,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( gt @ A @ B )
| ( gt @ B @ A ) ),
inference(lifteq,[status(thm)],[130]) ).
thf(76,axiom,
! [A: $i] : ( leq @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_leq) ).
thf(530,plain,
! [A: $i] : ( leq @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(531,plain,
! [A: $i] : ( leq @ A @ A ),
inference(cnf,[status(esa)],[530]) ).
thf(8351,plain,
! [A: $i] :
( ( leq @ sk1 @ ( minus @ n0 @ n1 ) )
| ( ( leq @ A @ A )
!= ( leq @ n0 @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[531,1707]) ).
thf(8374,plain,
! [A: $i] :
( ( leq @ sk1 @ ( minus @ n0 @ n1 ) )
| ( A != n0 )
| ( A != sk3 ) ),
inference(simp,[status(thm)],[8351]) ).
thf(8387,plain,
( ( leq @ sk1 @ ( minus @ n0 @ n1 ) )
| ( sk3 != n0 ) ),
inference(simp,[status(thm)],[8374]) ).
thf(8666,plain,
! [B: $i,A: $i] :
( ( gt @ A @ B )
| ( gt @ B @ A )
| ( leq @ sk1 @ ( minus @ n0 @ n1 ) )
| ( B != n0 )
| ( A != sk3 ) ),
inference(paramod_ordered,[status(thm)],[131,8387]) ).
thf(8667,plain,
! [A: $i] :
( ( gt @ sk3 @ A )
| ( gt @ A @ sk3 )
| ( leq @ sk1 @ ( minus @ n0 @ n1 ) )
| ( A != n0 ) ),
inference(pattern_uni,[status(thm)],[8666:[bind(A,$thf( sk3 ))]]) ).
thf(8701,plain,
( ( gt @ sk3 @ n0 )
| ( gt @ n0 @ sk3 )
| ( leq @ sk1 @ ( minus @ n0 @ n1 ) ) ),
inference(simp,[status(thm)],[8667]) ).
thf(38,axiom,
gt @ n0 @ tptp_minus_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_0_tptp_minus_1) ).
thf(228,plain,
gt @ n0 @ tptp_minus_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(20,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( gt @ A @ B )
& ( gt @ B @ C ) )
=> ( gt @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity_gt) ).
thf(152,plain,
! [A: $i,B: $i,C: $i] :
( ( ( gt @ A @ B )
& ( gt @ B @ C ) )
=> ( gt @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(153,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( gt @ A @ B )
| ~ ( gt @ B @ C )
| ( gt @ A @ C ) ),
inference(cnf,[status(esa)],[152]) ).
thf(16,axiom,
! [A: $i] :
~ ( gt @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',irreflexivity_gt) ).
thf(140,plain,
! [A: $i] :
~ ( gt @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(141,plain,
~ ? [A: $i] : ( gt @ A @ A ),
inference(miniscope,[status(thm)],[140]) ).
thf(142,plain,
! [A: $i] :
~ ( gt @ A @ A ),
inference(cnf,[status(esa)],[141]) ).
thf(9918,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( gt @ A @ B )
| ~ ( gt @ B @ C )
| ( ( gt @ A @ C )
!= ( gt @ D @ D ) ) ),
inference(paramod_ordered,[status(thm)],[153,142]) ).
thf(9919,plain,
! [B: $i,A: $i] :
( ~ ( gt @ B @ A )
| ~ ( gt @ A @ B ) ),
inference(pattern_uni,[status(thm)],[9918:[bind(A,$thf( C )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( C ))]]) ).
thf(10060,plain,
! [B: $i,A: $i] :
( ~ ( gt @ B @ A )
| ~ ( gt @ A @ B ) ),
inference(simp,[status(thm)],[9919]) ).
thf(11429,plain,
! [B: $i,A: $i] :
( ~ ( gt @ A @ B )
| ( ( gt @ n0 @ tptp_minus_1 )
!= ( gt @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[228,10060]) ).
thf(11430,plain,
~ ( gt @ tptp_minus_1 @ n0 ),
inference(pattern_uni,[status(thm)],[11429:[bind(A,$thf( tptp_minus_1 )),bind(B,$thf( n0 ))]]) ).
thf(13505,plain,
( ( gt @ n0 @ sk3 )
| ( leq @ sk1 @ ( minus @ n0 @ n1 ) )
| ( ( gt @ sk3 @ n0 )
!= ( gt @ tptp_minus_1 @ n0 ) ) ),
inference(paramod_ordered,[status(thm)],[8701,11430]) ).
thf(13556,plain,
( ( gt @ n0 @ sk3 )
| ( leq @ sk1 @ ( minus @ n0 @ n1 ) )
| ( sk3 != tptp_minus_1 )
| ( n0 != n0 ) ),
inference(simp,[status(thm)],[13505]) ).
thf(13569,plain,
( ( gt @ n0 @ sk3 )
| ( leq @ sk1 @ ( minus @ n0 @ n1 ) )
| ( sk3 != tptp_minus_1 ) ),
inference(simp,[status(thm)],[13556]) ).
thf(75,axiom,
gt @ n2 @ n0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_2_0) ).
thf(529,plain,
gt @ n2 @ n0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(11445,plain,
! [B: $i,A: $i] :
( ~ ( gt @ A @ B )
| ( ( gt @ n2 @ n0 )
!= ( gt @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[529,10060]) ).
thf(11446,plain,
~ ( gt @ n0 @ n2 ),
inference(pattern_uni,[status(thm)],[11445:[bind(A,$thf( n0 )),bind(B,$thf( n2 ))]]) ).
thf(14886,plain,
( ( leq @ sk1 @ ( minus @ n0 @ n1 ) )
| ( sk3 != tptp_minus_1 )
| ( ( gt @ n0 @ sk3 )
!= ( gt @ n0 @ n2 ) ) ),
inference(paramod_ordered,[status(thm)],[13569,11446]) ).
thf(14916,plain,
( ( leq @ sk1 @ ( minus @ n0 @ n1 ) )
| ( sk3 != tptp_minus_1 )
| ( n0 != n0 )
| ( sk3 != n2 ) ),
inference(simp,[status(thm)],[14886]) ).
thf(14944,plain,
( ( leq @ sk1 @ ( minus @ n0 @ n1 ) )
| ( sk3 != tptp_minus_1 )
| ( sk3 != n2 ) ),
inference(simp,[status(thm)],[14916]) ).
thf(90,axiom,
gt @ n135300 @ n4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_135300_4) ).
thf(556,plain,
gt @ n135300 @ n4,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(11393,plain,
! [B: $i,A: $i] :
( ~ ( gt @ A @ B )
| ( ( gt @ n135300 @ n4 )
!= ( gt @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[556,10060]) ).
thf(11394,plain,
~ ( gt @ n4 @ n135300 ),
inference(pattern_uni,[status(thm)],[11393:[bind(A,$thf( n4 )),bind(B,$thf( n135300 ))]]) ).
thf(89,axiom,
gt @ n5 @ n1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_5_1) ).
thf(555,plain,
gt @ n5 @ n1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(57,axiom,
gt @ n5 @ n2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_5_2) ).
thf(408,plain,
gt @ n5 @ n2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(27,axiom,
gt @ n135300 @ n3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_135300_3) ).
thf(166,plain,
gt @ n135300 @ n3,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(18,axiom,
! [A: $i,B: $i] :
( ( lt @ A @ B )
<=> ( gt @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lt_gt) ).
thf(146,plain,
! [A: $i,B: $i] :
( ( ( lt @ A @ B )
=> ( gt @ B @ A ) )
& ( ( gt @ B @ A )
=> ( lt @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(147,plain,
( ! [A: $i,B: $i] :
( ( lt @ A @ B )
=> ( gt @ B @ A ) )
& ! [A: $i,B: $i] :
( ( gt @ B @ A )
=> ( lt @ A @ B ) ) ),
inference(miniscope,[status(thm)],[146]) ).
thf(148,plain,
! [B: $i,A: $i] :
( ~ ( gt @ B @ A )
| ( lt @ A @ B ) ),
inference(cnf,[status(esa)],[147]) ).
thf(150,plain,
! [B: $i,A: $i] :
( ~ ( gt @ B @ A )
| ( lt @ A @ B ) ),
inference(simp,[status(thm)],[148]) ).
thf(9790,plain,
! [B: $i,A: $i] :
( ( lt @ A @ B )
| ( ( gt @ n135300 @ n3 )
!= ( gt @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[166,150]) ).
thf(9791,plain,
lt @ n3 @ n135300,
inference(pattern_uni,[status(thm)],[9790:[bind(A,$thf( n3 )),bind(B,$thf( n135300 ))]]) ).
thf(37,axiom,
! [A: $i,B: $i] :
( ! [C: $i,D: $i] :
( ( ( leq @ n0 @ C )
& ( leq @ C @ B )
& ( leq @ n0 @ D )
& ( leq @ D @ B ) )
=> ( ( a_select3 @ A @ C @ D )
= ( a_select3 @ A @ D @ C ) ) )
=> ! [C: $i,D: $i] :
( ( ( leq @ n0 @ C )
& ( leq @ C @ B )
& ( leq @ n0 @ D )
& ( leq @ D @ B ) )
=> ( ( a_select3 @ ( trans @ A ) @ C @ D )
= ( a_select3 @ ( trans @ A ) @ D @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',matrix_symm_trans) ).
thf(217,plain,
! [A: $i,B: $i] :
( ! [C: $i,D: $i] :
( ( ( leq @ n0 @ C )
& ( leq @ C @ B )
& ( leq @ n0 @ D )
& ( leq @ D @ B ) )
=> ( ( a_select3 @ A @ C @ D )
= ( a_select3 @ A @ D @ C ) ) )
=> ! [C: $i,D: $i] :
( ( ( leq @ n0 @ C )
& ( leq @ C @ B )
& ( leq @ n0 @ D )
& ( leq @ D @ B ) )
=> ( ( a_select3 @ ( trans @ A ) @ C @ D )
= ( a_select3 @ ( trans @ A ) @ D @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(2657,plain,
! [A: $i] :
( ( gt @ n5 @ n1 )
!= ( gt @ A @ A ) ),
inference(paramod_ordered,[status(thm)],[555,142]) ).
thf(2658,plain,
! [A: $i] :
( ( n5 != A )
| ( n1 != A ) ),
inference(simp,[status(thm)],[2657]) ).
thf(2659,plain,
n5 != n1,
inference(simp,[status(thm)],[2658]) ).
thf(91,axiom,
( ( succ @ ( succ @ n0 ) )
= n2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_2) ).
thf(557,plain,
( ( succ @ ( succ @ n0 ) )
= n2 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(558,plain,
( ( succ @ ( succ @ n0 ) )
= n2 ),
inference(lifteq,[status(thm)],[557]) ).
thf(2766,plain,
( ( succ @ n1 )
= n2 ),
inference(rewrite,[status(thm)],[558,160]) ).
thf(8401,plain,
! [A: $i] :
( ( ( pred @ n2 )
= A )
| ( ( succ @ n1 )
!= ( succ @ A ) ) ),
inference(paramod_ordered,[status(thm)],[2766,136]) ).
thf(8402,plain,
( ( pred @ n2 )
= n1 ),
inference(pattern_uni,[status(thm)],[8401:[bind(A,$thf( n1 ))]]) ).
thf(9768,plain,
! [B: $i,A: $i] :
( ( lt @ A @ B )
| ( ( gt @ n0 @ tptp_minus_1 )
!= ( gt @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[228,150]) ).
thf(9769,plain,
lt @ tptp_minus_1 @ n0,
inference(pattern_uni,[status(thm)],[9768:[bind(A,$thf( tptp_minus_1 )),bind(B,$thf( n0 ))]]) ).
thf(31,axiom,
! [A: $i] :
( ( sum @ n0 @ tptp_minus_1 @ A )
= n0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_plus_base) ).
thf(180,plain,
! [A: $i] :
( ( sum @ n0 @ tptp_minus_1 @ A )
= n0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(181,plain,
! [A: $i] :
( ( sum @ n0 @ tptp_minus_1 @ A )
= n0 ),
inference(cnf,[status(esa)],[180]) ).
thf(182,plain,
! [A: $i] :
( ( sum @ n0 @ tptp_minus_1 @ A )
= n0 ),
inference(lifteq,[status(thm)],[181]) ).
thf(104,plain,
( ~ ( leq @ n0 @ pv10 )
| ~ ( leq @ pv10 @ ( minus @ n135300 @ n1 ) )
| ( ( a_select3 @ q @ pv10 @ sk1 )
!= ( divide @ ( sqrt @ ( times @ ( minus @ ( a_select3 @ center @ sk1 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) @ ( minus @ ( a_select3 @ center @ sk1 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) ) ) @ ( sum @ n0 @ ( minus @ n5 @ n1 ) @ ( sqrt @ ( times @ ( minus @ ( a_select3 @ center @ sk2 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) @ ( minus @ ( a_select3 @ center @ sk2 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) ) ) ) ) )
| ( ( sum @ n0 @ ( minus @ n5 @ n1 ) @ ( a_select3 @ q @ sk3 @ sk4 ) )
!= n1 ) ),
inference(cnf,[status(esa)],[93]) ).
thf(111,plain,
( ( ( a_select3 @ q @ pv10 @ sk1 )
!= ( divide @ ( sqrt @ ( times @ ( minus @ ( a_select3 @ center @ sk1 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) @ ( minus @ ( a_select3 @ center @ sk1 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) ) ) @ ( sum @ n0 @ ( minus @ n5 @ n1 ) @ ( sqrt @ ( times @ ( minus @ ( a_select3 @ center @ sk2 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) @ ( minus @ ( a_select3 @ center @ sk2 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) ) ) ) ) )
| ( ( sum @ n0 @ ( minus @ n5 @ n1 ) @ ( a_select3 @ q @ sk3 @ sk4 ) )
!= n1 )
| ~ ( leq @ n0 @ pv10 )
| ~ ( leq @ pv10 @ ( minus @ n135300 @ n1 ) ) ),
inference(lifteq,[status(thm)],[104]) ).
thf(585,plain,
( ( ( a_select3 @ q @ pv10 @ sk1 )
!= ( divide @ ( sqrt @ ( times @ ( minus @ ( a_select3 @ center @ sk1 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) @ ( minus @ ( a_select3 @ center @ sk1 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) ) ) @ ( sum @ n0 @ ( minus @ n5 @ n1 ) @ ( sqrt @ ( times @ ( minus @ ( a_select3 @ center @ sk2 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) @ ( minus @ ( a_select3 @ center @ sk2 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) ) ) ) ) )
| ( ( sum @ n0 @ ( minus @ n5 @ n1 ) @ ( a_select3 @ q @ sk3 @ sk4 ) )
!= n1 )
| ~ $true
| ~ $true ),
inference(rewrite,[status(thm)],[111,96,95]) ).
thf(586,plain,
( ( ( a_select3 @ q @ pv10 @ sk1 )
!= ( divide @ ( sqrt @ ( times @ ( minus @ ( a_select3 @ center @ sk1 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) @ ( minus @ ( a_select3 @ center @ sk1 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) ) ) @ ( sum @ n0 @ ( minus @ n5 @ n1 ) @ ( sqrt @ ( times @ ( minus @ ( a_select3 @ center @ sk2 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) @ ( minus @ ( a_select3 @ center @ sk2 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) ) ) ) ) )
| ( ( sum @ n0 @ ( minus @ n5 @ n1 ) @ ( a_select3 @ q @ sk3 @ sk4 ) )
!= n1 ) ),
inference(simp,[status(thm)],[585]) ).
thf(1405,plain,
! [B: $i,A: $i] :
( ~ ( leq @ n0 @ A )
| ~ ( leq @ A @ ( minus @ pv10 @ n1 ) )
| ( ( a_select3 @ q @ pv10 @ sk1 )
!= ( divide @ ( sqrt @ ( times @ ( minus @ ( a_select3 @ center @ sk1 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) @ ( minus @ ( a_select3 @ center @ sk1 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) ) ) @ ( sum @ n0 @ ( minus @ n5 @ n1 ) @ ( sqrt @ ( times @ ( minus @ ( a_select3 @ center @ sk2 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) @ ( minus @ ( a_select3 @ center @ sk2 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) ) ) ) ) )
| ( ( sum @ n0 @ ( minus @ n5 @ n1 ) @ ( a_select3 @ q @ A @ B ) )
!= ( sum @ n0 @ ( minus @ n5 @ n1 ) @ ( a_select3 @ q @ sk3 @ sk4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[107,586]) ).
thf(1406,plain,
( ~ ( leq @ n0 @ sk3 )
| ~ ( leq @ sk3 @ ( minus @ pv10 @ n1 ) )
| ( ( a_select3 @ q @ pv10 @ sk1 )
!= ( divide @ ( sqrt @ ( times @ ( minus @ ( a_select3 @ center @ sk1 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) @ ( minus @ ( a_select3 @ center @ sk1 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) ) ) @ ( sum @ n0 @ ( minus @ n5 @ n1 ) @ ( sqrt @ ( times @ ( minus @ ( a_select3 @ center @ sk2 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) @ ( minus @ ( a_select3 @ center @ sk2 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[1405:[bind(A,$thf( sk3 )),bind(B,$thf( sk4 ))]]) ).
thf(1473,plain,
( ~ ( leq @ sk3 @ ( minus @ pv10 @ n1 ) )
| ( ( a_select3 @ q @ pv10 @ sk1 )
!= ( divide @ ( sqrt @ ( times @ ( minus @ ( a_select3 @ center @ sk1 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) @ ( minus @ ( a_select3 @ center @ sk1 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) ) ) @ ( sum @ n0 @ ( minus @ n5 @ n1 ) @ ( sqrt @ ( times @ ( minus @ ( a_select3 @ center @ sk2 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) @ ( minus @ ( a_select3 @ center @ sk2 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) ) ) ) ) )
| ( ( leq @ n0 @ sk3 )
!= ( leq @ n0 @ pv10 ) ) ),
inference(paramod_ordered,[status(thm)],[96,1406]) ).
thf(1546,plain,
( ~ ( leq @ sk3 @ ( minus @ pv10 @ n1 ) )
| ( ( a_select3 @ q @ pv10 @ sk1 )
!= ( divide @ ( sqrt @ ( times @ ( minus @ ( a_select3 @ center @ sk1 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) @ ( minus @ ( a_select3 @ center @ sk1 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) ) ) @ ( sum @ n0 @ ( minus @ n5 @ n1 ) @ ( sqrt @ ( times @ ( minus @ ( a_select3 @ center @ sk2 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) @ ( minus @ ( a_select3 @ center @ sk2 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) ) ) ) ) )
| ( n0 != n0 )
| ( sk3 != pv10 ) ),
inference(simp,[status(thm)],[1473]) ).
thf(1555,plain,
( ~ ( leq @ sk3 @ ( minus @ pv10 @ n1 ) )
| ( ( a_select3 @ q @ pv10 @ sk1 )
!= ( divide @ ( sqrt @ ( times @ ( minus @ ( a_select3 @ center @ sk1 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) @ ( minus @ ( a_select3 @ center @ sk1 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) ) ) @ ( sum @ n0 @ ( minus @ n5 @ n1 ) @ ( sqrt @ ( times @ ( minus @ ( a_select3 @ center @ sk2 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) @ ( minus @ ( a_select3 @ center @ sk2 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) ) ) ) ) )
| ( sk3 != pv10 ) ),
inference(simp,[status(thm)],[1546]) ).
thf(8270,plain,
! [A: $i] :
( ~ ( leq @ sk3 @ ( minus @ pv10 @ n1 ) )
| ( ( divide @ ( sqrt @ ( times @ ( minus @ ( a_select3 @ center @ sk1 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) @ ( minus @ ( a_select3 @ center @ sk1 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) ) ) @ n0 )
!= ( a_select3 @ q @ pv10 @ sk1 ) )
| ( sk3 != pv10 )
| ( ( sum @ n0 @ tptp_minus_1 @ A )
!= ( sum @ n0 @ ( minus @ n5 @ n1 ) @ ( sqrt @ ( times @ ( minus @ ( a_select3 @ center @ sk2 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) @ ( minus @ ( a_select3 @ center @ sk2 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[182,1555]) ).
thf(8297,plain,
! [A: $i] :
( ~ ( leq @ sk3 @ ( minus @ pv10 @ n1 ) )
| ( ( divide @ ( sqrt @ ( times @ ( minus @ ( a_select3 @ center @ sk1 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) @ ( minus @ ( a_select3 @ center @ sk1 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) ) ) @ n0 )
!= ( a_select3 @ q @ pv10 @ sk1 ) )
| ( sk3 != pv10 )
| ( n0 != n0 )
| ( ( minus @ n5 @ n1 )
!= tptp_minus_1 )
| ( A
!= ( sqrt @ ( times @ ( minus @ ( a_select3 @ center @ sk2 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) @ ( minus @ ( a_select3 @ center @ sk2 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) ) ) ) ),
inference(simp,[status(thm)],[8270]) ).
thf(8325,plain,
( ~ ( leq @ sk3 @ ( minus @ pv10 @ n1 ) )
| ( ( divide @ ( sqrt @ ( times @ ( minus @ ( a_select3 @ center @ sk1 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) @ ( minus @ ( a_select3 @ center @ sk1 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) ) ) @ n0 )
!= ( a_select3 @ q @ pv10 @ sk1 ) )
| ( sk3 != pv10 )
| ( ( minus @ n5 @ n1 )
!= tptp_minus_1 ) ),
inference(simp,[status(thm)],[8297]) ).
thf(9141,plain,
! [A: $i] :
( ( ( divide @ ( sqrt @ ( times @ ( minus @ ( a_select3 @ center @ sk1 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) @ ( minus @ ( a_select3 @ center @ sk1 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) ) ) @ n0 )
!= ( a_select3 @ q @ pv10 @ sk1 ) )
| ( sk3 != pv10 )
| ( ( minus @ n5 @ n1 )
!= tptp_minus_1 )
| ( ( leq @ A @ A )
!= ( leq @ sk3 @ ( minus @ pv10 @ n1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[531,8325]) ).
thf(9298,plain,
! [A: $i] :
( ( ( divide @ ( sqrt @ ( times @ ( minus @ ( a_select3 @ center @ sk1 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) @ ( minus @ ( a_select3 @ center @ sk1 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) ) ) @ n0 )
!= ( a_select3 @ q @ pv10 @ sk1 ) )
| ( sk3 != pv10 )
| ( ( minus @ n5 @ n1 )
!= tptp_minus_1 )
| ( A != sk3 )
| ( A
!= ( minus @ pv10 @ n1 ) ) ),
inference(simp,[status(thm)],[9141]) ).
thf(9337,plain,
( ( ( divide @ ( sqrt @ ( times @ ( minus @ ( a_select3 @ center @ sk1 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) @ ( minus @ ( a_select3 @ center @ sk1 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) ) ) @ n0 )
!= ( a_select3 @ q @ pv10 @ sk1 ) )
| ( sk3 != pv10 )
| ( ( minus @ n5 @ n1 )
!= tptp_minus_1 )
| ( ( minus @ pv10 @ n1 )
!= sk3 ) ),
inference(simp,[status(thm)],[9298]) ).
thf(6,axiom,
gt @ n3 @ tptp_minus_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_3_tptp_minus_1) ).
thf(120,plain,
gt @ n3 @ tptp_minus_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(70,axiom,
gt @ n1 @ tptp_minus_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_1_tptp_minus_1) ).
thf(511,plain,
gt @ n1 @ tptp_minus_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(9758,plain,
! [B: $i,A: $i] :
( ( lt @ A @ B )
| ( ( gt @ n3 @ tptp_minus_1 )
!= ( gt @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[120,150]) ).
thf(9759,plain,
lt @ tptp_minus_1 @ n3,
inference(pattern_uni,[status(thm)],[9758:[bind(A,$thf( tptp_minus_1 )),bind(B,$thf( n3 ))]]) ).
thf(4,axiom,
! [A: $i] :
( ( succ @ ( pred @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',succ_pred) ).
thf(115,plain,
! [A: $i] :
( ( succ @ ( pred @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(62,axiom,
! [A: $i,B: $i] :
( ( leq @ n0 @ A )
=> ( leq @ ( uniform_int_rnd @ B @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',uniform_int_rand_ranges_hi) ).
thf(472,plain,
! [A: $i,B: $i] :
( ( leq @ n0 @ A )
=> ( leq @ ( uniform_int_rnd @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(5,axiom,
! [A: $i] : ( gt @ ( succ @ A ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_succ) ).
thf(118,plain,
! [A: $i] : ( gt @ ( succ @ A ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(119,plain,
! [A: $i] : ( gt @ ( succ @ A ) @ A ),
inference(cnf,[status(esa)],[118]) ).
thf(3107,plain,
! [B: $i,A: $i] :
( ( gt @ ( succ @ A ) @ A )
!= ( gt @ B @ B ) ),
inference(paramod_ordered,[status(thm)],[119,142]) ).
thf(3120,plain,
! [B: $i,A: $i] :
( ( ( succ @ A )
!= B )
| ( A != B ) ),
inference(simp,[status(thm)],[3107]) ).
thf(3121,plain,
! [A: $i] :
( ( succ @ A )
!= A ),
inference(simp,[status(thm)],[3120]) ).
thf(45,axiom,
gt @ n135300 @ tptp_minus_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_135300_tptp_minus_1) ).
thf(331,plain,
gt @ n135300 @ tptp_minus_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(9800,plain,
! [B: $i,A: $i] :
( ( lt @ A @ B )
| ( ( gt @ n135300 @ tptp_minus_1 )
!= ( gt @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[331,150]) ).
thf(9801,plain,
lt @ tptp_minus_1 @ n135300,
inference(pattern_uni,[status(thm)],[9800:[bind(A,$thf( tptp_minus_1 )),bind(B,$thf( n135300 ))]]) ).
thf(103,plain,
( ~ ( leq @ n0 @ pv10 )
| ~ ( leq @ pv10 @ ( minus @ n135300 @ n1 ) )
| ( leq @ sk1 @ ( minus @ n0 @ n1 ) )
| ( leq @ n0 @ sk3 ) ),
inference(cnf,[status(esa)],[93]) ).
thf(929,plain,
( ~ $true
| ~ $true
| ( leq @ sk1 @ ( minus @ n0 @ n1 ) )
| ( leq @ n0 @ sk3 ) ),
inference(rewrite,[status(thm)],[103,96,95]) ).
thf(930,plain,
( ( leq @ sk1 @ ( minus @ n0 @ n1 ) )
| ( leq @ n0 @ sk3 ) ),
inference(simp,[status(thm)],[929]) ).
thf(42,axiom,
gt @ n135300 @ n0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_135300_0) ).
thf(322,plain,
gt @ n135300 @ n0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(13694,plain,
! [B: $i,A: $i] :
( ( leq @ sk1 @ ( minus @ n0 @ n1 ) )
| ( sk3 != tptp_minus_1 )
| ~ ( gt @ A @ B )
| ( ( gt @ n0 @ sk3 )
!= ( gt @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[13569,10060]) ).
thf(13695,plain,
( ( leq @ sk1 @ ( minus @ n0 @ n1 ) )
| ( sk3 != tptp_minus_1 )
| ~ ( gt @ sk3 @ n0 ) ),
inference(pattern_uni,[status(thm)],[13694:[bind(A,$thf( sk3 )),bind(B,$thf( n0 ))]]) ).
thf(16573,plain,
( ( leq @ sk1 @ ( minus @ n0 @ n1 ) )
| ( sk3 != tptp_minus_1 )
| ( ( gt @ sk3 @ n0 )
!= ( gt @ n135300 @ n0 ) ) ),
inference(paramod_ordered,[status(thm)],[322,13695]) ).
thf(16595,plain,
( ( leq @ sk1 @ ( minus @ n0 @ n1 ) )
| ( sk3 != tptp_minus_1 )
| ( sk3 != n135300 )
| ( n0 != n0 ) ),
inference(simp,[status(thm)],[16573]) ).
thf(16613,plain,
( ( leq @ sk1 @ ( minus @ n0 @ n1 ) )
| ( sk3 != tptp_minus_1 )
| ( sk3 != n135300 ) ),
inference(simp,[status(thm)],[16595]) ).
thf(36,axiom,
gt @ n5 @ n3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_5_3) ).
thf(216,plain,
gt @ n5 @ n3,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(1194,plain,
! [A: $i] :
( ( gt @ n5 @ n3 )
!= ( gt @ A @ A ) ),
inference(paramod_ordered,[status(thm)],[216,142]) ).
thf(1195,plain,
! [A: $i] :
( ( n5 != A )
| ( n3 != A ) ),
inference(simp,[status(thm)],[1194]) ).
thf(1196,plain,
n3 != n5,
inference(simp,[status(thm)],[1195]) ).
thf(25,axiom,
( ( succ @ ( succ @ ( succ @ ( succ @ n0 ) ) ) )
= n4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_4) ).
thf(161,plain,
( ( succ @ ( succ @ ( succ @ ( succ @ n0 ) ) ) )
= n4 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(162,plain,
( ( succ @ ( succ @ ( succ @ ( succ @ n0 ) ) ) )
= n4 ),
inference(lifteq,[status(thm)],[161]) ).
thf(2972,plain,
( ( succ @ ( succ @ ( succ @ n1 ) ) )
= n4 ),
inference(rewrite,[status(thm)],[162,160]) ).
thf(83,axiom,
gt @ n1 @ n0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_1_0) ).
thf(545,plain,
gt @ n1 @ n0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(2489,plain,
! [A: $i] :
( ( gt @ n1 @ n0 )
!= ( gt @ A @ A ) ),
inference(paramod_ordered,[status(thm)],[545,142]) ).
thf(2490,plain,
! [A: $i] :
( ( n1 != A )
| ( n0 != A ) ),
inference(simp,[status(thm)],[2489]) ).
thf(2491,plain,
n1 != n0,
inference(simp,[status(thm)],[2490]) ).
thf(60,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( leq @ B @ A )
& ( leq @ A @ C ) )
=> ( ( a_select2 @ ( tptp_const_array1 @ ( dim @ B @ C ) @ D ) @ A )
= D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',const_array1_select) ).
thf(417,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( leq @ B @ A )
& ( leq @ A @ C ) )
=> ( ( a_select2 @ ( tptp_const_array1 @ ( dim @ B @ C ) @ D ) @ A )
= D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(1501,plain,
( ( sk3 != sk1 )
| ~ ( leq @ sk3 @ ( minus @ pv10 @ n1 ) )
| ( ( a_select3 @ q @ pv10 @ sk1 )
!= ( divide @ ( sqrt @ ( times @ ( minus @ ( a_select3 @ center @ sk1 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) @ ( minus @ ( a_select3 @ center @ sk1 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) ) ) @ ( sum @ n0 @ ( minus @ n5 @ n1 ) @ ( sqrt @ ( times @ ( minus @ ( a_select3 @ center @ sk2 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) @ ( minus @ ( a_select3 @ center @ sk2 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) ) ) ) ) )
| ( ( leq @ n0 @ sk3 )
!= ( leq @ n0 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[576,1406]) ).
thf(1503,plain,
( ( sk3 != sk1 )
| ~ ( leq @ sk3 @ ( minus @ pv10 @ n1 ) )
| ( ( a_select3 @ q @ pv10 @ sk1 )
!= ( divide @ ( sqrt @ ( times @ ( minus @ ( a_select3 @ center @ sk1 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) @ ( minus @ ( a_select3 @ center @ sk1 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) ) ) @ ( sum @ n0 @ ( minus @ n5 @ n1 ) @ ( sqrt @ ( times @ ( minus @ ( a_select3 @ center @ sk2 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) @ ( minus @ ( a_select3 @ center @ sk2 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) ) ) ) ) )
| ( n0 != n0 )
| ( sk3 != sk1 ) ),
inference(simp,[status(thm)],[1501]) ).
thf(1556,plain,
( ( sk3 != sk1 )
| ~ ( leq @ sk3 @ ( minus @ pv10 @ n1 ) )
| ( ( a_select3 @ q @ pv10 @ sk1 )
!= ( divide @ ( sqrt @ ( times @ ( minus @ ( a_select3 @ center @ sk1 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) @ ( minus @ ( a_select3 @ center @ sk1 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) ) ) @ ( sum @ n0 @ ( minus @ n5 @ n1 ) @ ( sqrt @ ( times @ ( minus @ ( a_select3 @ center @ sk2 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) @ ( minus @ ( a_select3 @ center @ sk2 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) ) ) ) ) ) ),
inference(simp,[status(thm)],[1503]) ).
thf(1998,plain,
( ( sk3 != sk1 )
| ( ( a_select3 @ q @ pv10 @ sk1 )
!= ( divide @ ( sqrt @ ( times @ ( minus @ ( a_select3 @ center @ sk1 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) @ ( minus @ ( a_select3 @ center @ sk1 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) ) ) @ ( sum @ n0 @ ( minus @ n5 @ n1 ) @ ( sqrt @ ( times @ ( minus @ ( a_select3 @ center @ sk2 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) @ ( minus @ ( a_select3 @ center @ sk2 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) ) ) ) ) )
| ( ( leq @ sk3 @ ( minus @ pv10 @ n1 ) )
!= ( leq @ n0 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[576,1556]) ).
thf(2010,plain,
( ( sk3 != sk1 )
| ( ( a_select3 @ q @ pv10 @ sk1 )
!= ( divide @ ( sqrt @ ( times @ ( minus @ ( a_select3 @ center @ sk1 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) @ ( minus @ ( a_select3 @ center @ sk1 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) ) ) @ ( sum @ n0 @ ( minus @ n5 @ n1 ) @ ( sqrt @ ( times @ ( minus @ ( a_select3 @ center @ sk2 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) @ ( minus @ ( a_select3 @ center @ sk2 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) ) ) ) ) )
| ( sk3 != n0 )
| ( ( minus @ pv10 @ n1 )
!= sk1 ) ),
inference(simp,[status(thm)],[1998]) ).
thf(11401,plain,
! [B: $i,A: $i] :
( ~ ( gt @ A @ B )
| ( ( gt @ n5 @ n2 )
!= ( gt @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[408,10060]) ).
thf(11402,plain,
~ ( gt @ n2 @ n5 ),
inference(pattern_uni,[status(thm)],[11401:[bind(A,$thf( n2 )),bind(B,$thf( n5 ))]]) ).
thf(12202,plain,
! [A: $i] :
( ( gt @ ( succ @ A ) @ A )
!= ( gt @ n2 @ n5 ) ),
inference(paramod_ordered,[status(thm)],[119,11402]) ).
thf(12245,plain,
! [A: $i] :
( ( ( succ @ A )
!= n2 )
| ( A != n5 ) ),
inference(simp,[status(thm)],[12202]) ).
thf(12257,plain,
( ( succ @ n5 )
!= n2 ),
inference(simp,[status(thm)],[12245]) ).
thf(559,plain,
! [A: $i] :
( ( gt @ n3 @ tptp_minus_1 )
!= ( gt @ A @ A ) ),
inference(paramod_ordered,[status(thm)],[120,142]) ).
thf(562,plain,
! [A: $i] :
( ( n3 != A )
| ( tptp_minus_1 != A ) ),
inference(simp,[status(thm)],[559]) ).
thf(565,plain,
tptp_minus_1 != n3,
inference(simp,[status(thm)],[562]) ).
thf(29,axiom,
gt @ n4 @ n1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_4_1) ).
thf(174,plain,
gt @ n4 @ n1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(55,axiom,
gt @ n3 @ n0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_3_0) ).
thf(404,plain,
gt @ n3 @ n0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(22,axiom,
gt @ n3 @ n1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_3_1) ).
thf(157,plain,
gt @ n3 @ n1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(11425,plain,
! [B: $i,A: $i] :
( ~ ( gt @ A @ B )
| ( ( gt @ n3 @ n1 )
!= ( gt @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[157,10060]) ).
thf(11426,plain,
~ ( gt @ n1 @ n3 ),
inference(pattern_uni,[status(thm)],[11425:[bind(A,$thf( n1 )),bind(B,$thf( n3 ))]]) ).
thf(12,axiom,
gt @ n4 @ n2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_4_2) ).
thf(132,plain,
gt @ n4 @ n2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(568,plain,
! [A: $i] :
( ( gt @ n4 @ n2 )
!= ( gt @ A @ A ) ),
inference(paramod_ordered,[status(thm)],[132,142]) ).
thf(569,plain,
! [A: $i] :
( ( n4 != A )
| ( n2 != A ) ),
inference(simp,[status(thm)],[568]) ).
thf(570,plain,
n4 != n2,
inference(simp,[status(thm)],[569]) ).
thf(2733,plain,
! [A: $i] :
( ( gt @ n135300 @ n4 )
!= ( gt @ A @ A ) ),
inference(paramod_ordered,[status(thm)],[556,142]) ).
thf(2734,plain,
! [A: $i] :
( ( n135300 != A )
| ( n4 != A ) ),
inference(simp,[status(thm)],[2733]) ).
thf(2735,plain,
n4 != n135300,
inference(simp,[status(thm)],[2734]) ).
thf(67,axiom,
! [A: $i] :
( ( plus @ A @ n1 )
= ( succ @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',succ_plus_1_r) ).
thf(504,plain,
! [A: $i] :
( ( plus @ A @ n1 )
= ( succ @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(1311,plain,
! [A: $i] :
( ( gt @ n135300 @ tptp_minus_1 )
!= ( gt @ A @ A ) ),
inference(paramod_ordered,[status(thm)],[331,142]) ).
thf(1312,plain,
! [A: $i] :
( ( n135300 != A )
| ( tptp_minus_1 != A ) ),
inference(simp,[status(thm)],[1311]) ).
thf(1313,plain,
tptp_minus_1 != n135300,
inference(simp,[status(thm)],[1312]) ).
thf(81,axiom,
gt @ n5 @ n4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_5_4) ).
thf(541,plain,
gt @ n5 @ n4,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(2486,plain,
! [A: $i] :
( ( gt @ n5 @ n4 )
!= ( gt @ A @ A ) ),
inference(paramod_ordered,[status(thm)],[541,142]) ).
thf(2487,plain,
! [A: $i] :
( ( n5 != A )
| ( n4 != A ) ),
inference(simp,[status(thm)],[2486]) ).
thf(2488,plain,
n4 != n5,
inference(simp,[status(thm)],[2487]) ).
thf(23,axiom,
gt @ n135300 @ n2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_135300_2) ).
thf(158,plain,
gt @ n135300 @ n2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(9804,plain,
! [B: $i,A: $i] :
( ( lt @ A @ B )
| ( ( gt @ n135300 @ n2 )
!= ( gt @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[158,150]) ).
thf(9805,plain,
lt @ n2 @ n135300,
inference(pattern_uni,[status(thm)],[9804:[bind(A,$thf( n2 )),bind(B,$thf( n135300 ))]]) ).
thf(33,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i,F: $i] :
( ( ( leq @ n0 @ E )
& ( leq @ E @ D )
& ( leq @ n0 @ F )
& ( leq @ F @ D ) )
=> ( ( a_select3 @ B @ E @ F )
= ( a_select3 @ B @ F @ E ) ) )
=> ! [E: $i,F: $i] :
( ( ( leq @ n0 @ E )
& ( leq @ E @ C )
& ( leq @ n0 @ F )
& ( leq @ F @ C ) )
=> ( ( a_select3 @ ( tptp_mmul @ A @ ( tptp_mmul @ B @ ( trans @ A ) ) ) @ E @ F )
= ( a_select3 @ ( tptp_mmul @ A @ ( tptp_mmul @ B @ ( trans @ A ) ) ) @ F @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',matrix_symm_aba2) ).
thf(187,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i,F: $i] :
( ( ( leq @ n0 @ E )
& ( leq @ E @ D )
& ( leq @ n0 @ F )
& ( leq @ F @ D ) )
=> ( ( a_select3 @ B @ E @ F )
= ( a_select3 @ B @ F @ E ) ) )
=> ! [E: $i,F: $i] :
( ( ( leq @ n0 @ E )
& ( leq @ E @ C )
& ( leq @ n0 @ F )
& ( leq @ F @ C ) )
=> ( ( a_select3 @ ( tptp_mmul @ A @ ( tptp_mmul @ B @ ( trans @ A ) ) ) @ E @ F )
= ( a_select3 @ ( tptp_mmul @ A @ ( tptp_mmul @ B @ ( trans @ A ) ) ) @ F @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(188,plain,
! [A: $i,B: $i] :
( ? [C: $i] :
! [D: $i,E: $i] :
( ( ( leq @ n0 @ D )
& ( leq @ D @ C )
& ( leq @ n0 @ E )
& ( leq @ E @ C ) )
=> ( ( a_select3 @ B @ D @ E )
= ( a_select3 @ B @ E @ D ) ) )
=> ! [C: $i,D: $i,E: $i] :
( ( ( leq @ n0 @ D )
& ( leq @ D @ C )
& ( leq @ n0 @ E )
& ( leq @ E @ C ) )
=> ( ( a_select3 @ ( tptp_mmul @ A @ ( tptp_mmul @ B @ ( trans @ A ) ) ) @ D @ E )
= ( a_select3 @ ( tptp_mmul @ A @ ( tptp_mmul @ B @ ( trans @ A ) ) ) @ E @ D ) ) ) ),
inference(miniscope,[status(thm)],[187]) ).
thf(193,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( leq @ n0 @ ( sk6 @ C @ B @ A ) )
| ~ ( leq @ n0 @ E )
| ~ ( leq @ E @ D )
| ~ ( leq @ n0 @ F )
| ~ ( leq @ F @ D )
| ( ( a_select3 @ ( tptp_mmul @ A @ ( tptp_mmul @ B @ ( trans @ A ) ) ) @ E @ F )
= ( a_select3 @ ( tptp_mmul @ A @ ( tptp_mmul @ B @ ( trans @ A ) ) ) @ F @ E ) ) ),
inference(cnf,[status(esa)],[188]) ).
thf(196,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( a_select3 @ ( tptp_mmul @ A @ ( tptp_mmul @ B @ ( trans @ A ) ) ) @ E @ F )
= ( a_select3 @ ( tptp_mmul @ A @ ( tptp_mmul @ B @ ( trans @ A ) ) ) @ F @ E ) )
| ( leq @ n0 @ ( sk6 @ C @ B @ A ) )
| ~ ( leq @ n0 @ E )
| ~ ( leq @ E @ D )
| ~ ( leq @ n0 @ F )
| ~ ( leq @ F @ D ) ),
inference(lifteq,[status(thm)],[193]) ).
thf(73,axiom,
gt @ n5 @ tptp_minus_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_5_tptp_minus_1) ).
thf(526,plain,
gt @ n5 @ tptp_minus_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(11457,plain,
! [B: $i,A: $i] :
( ~ ( gt @ A @ B )
| ( ( gt @ n5 @ tptp_minus_1 )
!= ( gt @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[526,10060]) ).
thf(11458,plain,
~ ( gt @ tptp_minus_1 @ n5 ),
inference(pattern_uni,[status(thm)],[11457:[bind(A,$thf( tptp_minus_1 )),bind(B,$thf( n5 ))]]) ).
thf(51,axiom,
! [A: $i,B: $i] :
( ( leq @ n0 @ A )
=> ( leq @ n0 @ ( uniform_int_rnd @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',uniform_int_rand_ranges_lo) ).
thf(344,plain,
! [A: $i,B: $i] :
( ( leq @ n0 @ A )
=> ( leq @ n0 @ ( uniform_int_rnd @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(11473,plain,
! [B: $i,A: $i] :
( ~ ( gt @ A @ B )
| ( ( gt @ n135300 @ n3 )
!= ( gt @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[166,10060]) ).
thf(11474,plain,
~ ( gt @ n3 @ n135300 ),
inference(pattern_uni,[status(thm)],[11473:[bind(A,$thf( n3 )),bind(B,$thf( n135300 ))]]) ).
thf(19420,plain,
! [A: $i] :
( ( gt @ ( succ @ A ) @ A )
!= ( gt @ n3 @ n135300 ) ),
inference(paramod_ordered,[status(thm)],[119,11474]) ).
thf(19466,plain,
! [A: $i] :
( ( ( succ @ A )
!= n3 )
| ( A != n135300 ) ),
inference(simp,[status(thm)],[19420]) ).
thf(19472,plain,
( ( succ @ n135300 )
!= n3 ),
inference(simp,[status(thm)],[19466]) ).
thf(82,axiom,
! [A: $i] :
( ( ( leq @ n0 @ A )
& ( leq @ A @ n4 ) )
=> ( ( A = n0 )
| ( A = n1 )
| ( A = n2 )
| ( A = n3 )
| ( A = n4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',finite_domain_4) ).
thf(542,plain,
! [A: $i] :
( ( ( leq @ n0 @ A )
& ( leq @ A @ n4 ) )
=> ( ( A = n0 )
| ( A = n1 )
| ( A = n2 )
| ( A = n3 )
| ( A = n4 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(1601,plain,
( ( ( a_select3 @ q @ pv10 @ sk1 )
!= ( divide @ ( sqrt @ ( times @ ( minus @ ( a_select3 @ center @ sk1 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) @ ( minus @ ( a_select3 @ center @ sk1 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) ) ) @ ( sum @ n0 @ ( minus @ n5 @ n1 ) @ ( sqrt @ ( times @ ( minus @ ( a_select3 @ center @ sk2 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) @ ( minus @ ( a_select3 @ center @ sk2 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) ) ) ) ) )
| ( sk3 != pv10 )
| ( ( leq @ pv10 @ ( minus @ n135300 @ n1 ) )
!= ( leq @ sk3 @ ( minus @ pv10 @ n1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[95,1555]) ).
thf(1604,plain,
( ( ( a_select3 @ q @ pv10 @ sk1 )
!= ( divide @ ( sqrt @ ( times @ ( minus @ ( a_select3 @ center @ sk1 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) @ ( minus @ ( a_select3 @ center @ sk1 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) ) ) @ ( sum @ n0 @ ( minus @ n5 @ n1 ) @ ( sqrt @ ( times @ ( minus @ ( a_select3 @ center @ sk2 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) @ ( minus @ ( a_select3 @ center @ sk2 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) ) ) ) ) )
| ( sk3 != pv10 )
| ( sk3 != pv10 )
| ( ( minus @ n135300 @ n1 )
!= ( minus @ pv10 @ n1 ) ) ),
inference(simp,[status(thm)],[1601]) ).
thf(1641,plain,
( ( ( a_select3 @ q @ pv10 @ sk1 )
!= ( divide @ ( sqrt @ ( times @ ( minus @ ( a_select3 @ center @ sk1 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) @ ( minus @ ( a_select3 @ center @ sk1 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) ) ) @ ( sum @ n0 @ ( minus @ n5 @ n1 ) @ ( sqrt @ ( times @ ( minus @ ( a_select3 @ center @ sk2 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) @ ( minus @ ( a_select3 @ center @ sk2 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) ) ) ) ) )
| ( sk3 != pv10 )
| ( ( minus @ n135300 @ n1 )
!= ( minus @ pv10 @ n1 ) ) ),
inference(simp,[status(thm)],[1604]) ).
thf(1230,plain,
! [A: $i] :
( ( gt @ n135300 @ n0 )
!= ( gt @ A @ A ) ),
inference(paramod_ordered,[status(thm)],[322,142]) ).
thf(1231,plain,
! [A: $i] :
( ( n135300 != A )
| ( n0 != A ) ),
inference(simp,[status(thm)],[1230]) ).
thf(1232,plain,
n135300 != n0,
inference(simp,[status(thm)],[1231]) ).
thf(17,axiom,
! [A: $i] :
( ( plus @ A @ n4 )
= ( succ @ ( succ @ ( succ @ ( succ @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',succ_plus_4_r) ).
thf(143,plain,
! [A: $i] :
( ( plus @ A @ n4 )
= ( succ @ ( succ @ ( succ @ ( succ @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(144,plain,
! [A: $i] :
( ( plus @ A @ n4 )
= ( succ @ ( succ @ ( succ @ ( succ @ A ) ) ) ) ),
inference(cnf,[status(esa)],[143]) ).
thf(145,plain,
! [A: $i] :
( ( plus @ A @ n4 )
= ( succ @ ( succ @ ( succ @ ( succ @ A ) ) ) ) ),
inference(lifteq,[status(thm)],[144]) ).
thf(15,axiom,
! [A: $i] :
( ( plus @ n2 @ A )
= ( succ @ ( succ @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',succ_plus_2_l) ).
thf(137,plain,
! [A: $i] :
( ( plus @ n2 @ A )
= ( succ @ ( succ @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(138,plain,
! [A: $i] :
( ( plus @ n2 @ A )
= ( succ @ ( succ @ A ) ) ),
inference(cnf,[status(esa)],[137]) ).
thf(139,plain,
! [A: $i] :
( ( plus @ n2 @ A )
= ( succ @ ( succ @ A ) ) ),
inference(lifteq,[status(thm)],[138]) ).
thf(9092,plain,
! [B: $i,A: $i] :
( ( ( succ @ ( succ @ ( succ @ ( succ @ A ) ) ) )
= ( succ @ ( succ @ B ) ) )
| ( ( plus @ A @ n4 )
!= ( plus @ n2 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[145,139]) ).
thf(9093,plain,
( ( succ @ ( succ @ ( succ @ ( succ @ n2 ) ) ) )
= ( succ @ ( succ @ n4 ) ) ),
inference(pattern_uni,[status(thm)],[9092:[bind(A,$thf( n2 )),bind(B,$thf( n4 ))]]) ).
thf(65,axiom,
( ( succ @ ( succ @ ( succ @ n0 ) ) )
= n3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_3) ).
thf(491,plain,
( ( succ @ ( succ @ ( succ @ n0 ) ) )
= n3 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(492,plain,
( ( succ @ ( succ @ ( succ @ n0 ) ) )
= n3 ),
inference(lifteq,[status(thm)],[491]) ).
thf(2779,plain,
( ( succ @ ( succ @ n1 ) )
= n3 ),
inference(rewrite,[status(thm)],[492,160]) ).
thf(2782,plain,
( ( ( succ @ n2 )
= n3 )
| ( ( succ @ n1 )
!= ( succ @ n1 ) ) ),
inference(paramod_ordered,[status(thm)],[2766,2779]) ).
thf(2783,plain,
( ( succ @ n2 )
= n3 ),
inference(pattern_uni,[status(thm)],[2782:[]]) ).
thf(84,axiom,
( ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ n0 ) ) ) ) )
= n5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_5) ).
thf(546,plain,
( ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ n0 ) ) ) ) )
= n5 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(547,plain,
( ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ n0 ) ) ) ) )
= n5 ),
inference(lifteq,[status(thm)],[546]) ).
thf(3234,plain,
( ( succ @ ( succ @ ( succ @ ( succ @ n1 ) ) ) )
= n5 ),
inference(rewrite,[status(thm)],[547,160]) ).
thf(3246,plain,
( ( ( succ @ n4 )
= n5 )
| ( ( succ @ ( succ @ ( succ @ n1 ) ) )
!= ( succ @ ( succ @ ( succ @ n1 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[2972,3234]) ).
thf(3247,plain,
( ( succ @ n4 )
= n5 ),
inference(pattern_uni,[status(thm)],[3246:[]]) ).
thf(9580,plain,
( ( succ @ ( succ @ ( succ @ n3 ) ) )
= ( succ @ n5 ) ),
inference(rewrite,[status(thm)],[9093,2783,3247]) ).
thf(11509,plain,
! [B: $i,A: $i] :
( ~ ( gt @ A @ B )
| ( ( gt @ n135300 @ n2 )
!= ( gt @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[158,10060]) ).
thf(11510,plain,
~ ( gt @ n2 @ n135300 ),
inference(pattern_uni,[status(thm)],[11509:[bind(A,$thf( n2 )),bind(B,$thf( n135300 ))]]) ).
thf(61,axiom,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i,E: $i] :
( ( ( leq @ n0 @ D )
& ( leq @ D @ C )
& ( leq @ n0 @ E )
& ( leq @ E @ C ) )
=> ( ( a_select3 @ A @ D @ E )
= ( a_select3 @ A @ E @ D ) ) )
& ! [D: $i,E: $i] :
( ( ( leq @ n0 @ D )
& ( leq @ D @ C )
& ( leq @ n0 @ E )
& ( leq @ E @ C ) )
=> ( ( a_select3 @ B @ D @ E )
= ( a_select3 @ B @ E @ D ) ) ) )
=> ! [D: $i,E: $i] :
( ( ( leq @ n0 @ D )
& ( leq @ D @ C )
& ( leq @ n0 @ E )
& ( leq @ E @ C ) )
=> ( ( a_select3 @ ( tptp_madd @ A @ B ) @ D @ E )
= ( a_select3 @ ( tptp_madd @ A @ B ) @ E @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',matrix_symm_add) ).
thf(421,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i,E: $i] :
( ( ( leq @ n0 @ D )
& ( leq @ D @ C )
& ( leq @ n0 @ E )
& ( leq @ E @ C ) )
=> ( ( a_select3 @ A @ D @ E )
= ( a_select3 @ A @ E @ D ) ) )
& ! [D: $i,E: $i] :
( ( ( leq @ n0 @ D )
& ( leq @ D @ C )
& ( leq @ n0 @ E )
& ( leq @ E @ C ) )
=> ( ( a_select3 @ B @ D @ E )
= ( a_select3 @ B @ E @ D ) ) ) )
=> ! [D: $i,E: $i] :
( ( ( leq @ n0 @ D )
& ( leq @ D @ C )
& ( leq @ n0 @ E )
& ( leq @ E @ C ) )
=> ( ( a_select3 @ ( tptp_madd @ A @ B ) @ D @ E )
= ( a_select3 @ ( tptp_madd @ A @ B ) @ E @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(63,axiom,
! [A: $i,B: $i,C: $i] :
( ! [D: $i,E: $i] :
( ( ( leq @ n0 @ D )
& ( leq @ D @ C )
& ( leq @ n0 @ E )
& ( leq @ E @ C ) )
=> ( ( a_select3 @ B @ D @ E )
= ( a_select3 @ B @ E @ D ) ) )
=> ! [D: $i,E: $i] :
( ( ( leq @ n0 @ D )
& ( leq @ D @ C )
& ( leq @ n0 @ E )
& ( leq @ E @ C ) )
=> ( ( a_select3 @ ( tptp_mmul @ A @ ( tptp_mmul @ B @ ( trans @ A ) ) ) @ D @ E )
= ( a_select3 @ ( tptp_mmul @ A @ ( tptp_mmul @ B @ ( trans @ A ) ) ) @ E @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',matrix_symm_aba1) ).
thf(475,plain,
! [A: $i,B: $i,C: $i] :
( ! [D: $i,E: $i] :
( ( ( leq @ n0 @ D )
& ( leq @ D @ C )
& ( leq @ n0 @ E )
& ( leq @ E @ C ) )
=> ( ( a_select3 @ B @ D @ E )
= ( a_select3 @ B @ E @ D ) ) )
=> ! [D: $i,E: $i] :
( ( ( leq @ n0 @ D )
& ( leq @ D @ C )
& ( leq @ n0 @ E )
& ( leq @ E @ C ) )
=> ( ( a_select3 @ ( tptp_mmul @ A @ ( tptp_mmul @ B @ ( trans @ A ) ) ) @ D @ E )
= ( a_select3 @ ( tptp_mmul @ A @ ( tptp_mmul @ B @ ( trans @ A ) ) ) @ E @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(30,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( A != B )
& ( ( a_select2 @ C @ B )
= D ) )
=> ( ( a_select2 @ ( tptp_update2 @ C @ A @ E ) @ B )
= D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sel2_update_2) ).
thf(175,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( A != B )
& ( ( a_select2 @ C @ B )
= D ) )
=> ( ( a_select2 @ ( tptp_update2 @ C @ A @ E ) @ B )
= D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(176,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A != B )
& ( ( a_select2 @ C @ B )
= D ) )
=> ! [E: $i] :
( ( a_select2 @ ( tptp_update2 @ C @ A @ E ) @ B )
= D ) ),
inference(miniscope,[status(thm)],[175]) ).
thf(177,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ( ( a_select2 @ C @ B )
!= D )
| ( ( a_select2 @ ( tptp_update2 @ C @ A @ E ) @ B )
= D ) ),
inference(cnf,[status(esa)],[176]) ).
thf(178,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ( ( a_select2 @ C @ B )
!= D )
| ( ( a_select2 @ ( tptp_update2 @ C @ A @ E ) @ B )
= D ) ),
inference(lifteq,[status(thm)],[177]) ).
thf(179,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ( ( a_select2 @ ( tptp_update2 @ C @ A @ D ) @ B )
= ( a_select2 @ C @ B ) ) ),
inference(simp,[status(thm)],[178]) ).
thf(35,axiom,
! [A: $i,B: $i] :
( ( leq @ ( succ @ A ) @ ( succ @ B ) )
<=> ( leq @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',leq_succ_succ) ).
thf(211,plain,
! [A: $i,B: $i] :
( ( ( leq @ ( succ @ A ) @ ( succ @ B ) )
=> ( leq @ A @ B ) )
& ( ( leq @ A @ B )
=> ( leq @ ( succ @ A ) @ ( succ @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(46,axiom,
gt @ n5 @ n0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_5_0) ).
thf(332,plain,
gt @ n5 @ n0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(9810,plain,
! [B: $i,A: $i] :
( ( lt @ A @ B )
| ( ( gt @ n5 @ n0 )
!= ( gt @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[332,150]) ).
thf(9811,plain,
lt @ n0 @ n5,
inference(pattern_uni,[status(thm)],[9810:[bind(A,$thf( n0 )),bind(B,$thf( n5 ))]]) ).
thf(1838,plain,
( ( leq @ sk1 @ ( minus @ n0 @ n1 ) )
| ( ( leq @ pv10 @ ( minus @ n135300 @ n1 ) )
!= ( leq @ n0 @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[95,1707]) ).
thf(1858,plain,
( ( leq @ sk1 @ ( minus @ n0 @ n1 ) )
| ( pv10 != n0 )
| ( ( minus @ n135300 @ n1 )
!= sk3 ) ),
inference(simp,[status(thm)],[1838]) ).
thf(7,axiom,
! [A: $i] :
( ( plus @ A @ n2 )
= ( succ @ ( succ @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',succ_plus_2_r) ).
thf(121,plain,
! [A: $i] :
( ( plus @ A @ n2 )
= ( succ @ ( succ @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(11397,plain,
! [B: $i,A: $i] :
( ~ ( gt @ A @ B )
| ( ( gt @ n5 @ n1 )
!= ( gt @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[555,10060]) ).
thf(11398,plain,
~ ( gt @ n1 @ n5 ),
inference(pattern_uni,[status(thm)],[11397:[bind(A,$thf( n1 )),bind(B,$thf( n5 ))]]) ).
thf(88,axiom,
gt @ n135300 @ n5,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_135300_5) ).
thf(554,plain,
gt @ n135300 @ n5,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(9780,plain,
! [B: $i,A: $i] :
( ( lt @ A @ B )
| ( ( gt @ n135300 @ n5 )
!= ( gt @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[554,150]) ).
thf(9781,plain,
lt @ n5 @ n135300,
inference(pattern_uni,[status(thm)],[9780:[bind(A,$thf( n5 )),bind(B,$thf( n135300 ))]]) ).
thf(86,axiom,
gt @ n2 @ n1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_2_1) ).
thf(551,plain,
gt @ n2 @ n1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(9778,plain,
! [B: $i,A: $i] :
( ( lt @ A @ B )
| ( ( gt @ n2 @ n1 )
!= ( gt @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[551,150]) ).
thf(9779,plain,
lt @ n1 @ n2,
inference(pattern_uni,[status(thm)],[9778:[bind(A,$thf( n1 )),bind(B,$thf( n2 ))]]) ).
thf(98,plain,
( ~ ( leq @ n0 @ pv10 )
| ~ ( leq @ pv10 @ ( minus @ n135300 @ n1 ) )
| ( ( a_select3 @ q @ pv10 @ sk1 )
!= ( divide @ ( sqrt @ ( times @ ( minus @ ( a_select3 @ center @ sk1 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) @ ( minus @ ( a_select3 @ center @ sk1 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) ) ) @ ( sum @ n0 @ ( minus @ n5 @ n1 ) @ ( sqrt @ ( times @ ( minus @ ( a_select3 @ center @ sk2 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) @ ( minus @ ( a_select3 @ center @ sk2 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) ) ) ) ) )
| ( leq @ n0 @ sk3 ) ),
inference(cnf,[status(esa)],[93]) ).
thf(108,plain,
( ( ( a_select3 @ q @ pv10 @ sk1 )
!= ( divide @ ( sqrt @ ( times @ ( minus @ ( a_select3 @ center @ sk1 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) @ ( minus @ ( a_select3 @ center @ sk1 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) ) ) @ ( sum @ n0 @ ( minus @ n5 @ n1 ) @ ( sqrt @ ( times @ ( minus @ ( a_select3 @ center @ sk2 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) @ ( minus @ ( a_select3 @ center @ sk2 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) ) ) ) ) )
| ~ ( leq @ n0 @ pv10 )
| ~ ( leq @ pv10 @ ( minus @ n135300 @ n1 ) )
| ( leq @ n0 @ sk3 ) ),
inference(lifteq,[status(thm)],[98]) ).
thf(1895,plain,
( ( ( a_select3 @ q @ pv10 @ sk1 )
!= ( divide @ ( sqrt @ ( times @ ( minus @ ( a_select3 @ center @ sk1 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) @ ( minus @ ( a_select3 @ center @ sk1 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) ) ) @ ( sum @ n0 @ ( minus @ n5 @ n1 ) @ ( sqrt @ ( times @ ( minus @ ( a_select3 @ center @ sk2 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) @ ( minus @ ( a_select3 @ center @ sk2 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) ) ) ) ) )
| ~ $true
| ~ $true
| ( leq @ n0 @ sk3 ) ),
inference(rewrite,[status(thm)],[108,96,95]) ).
thf(1896,plain,
( ( ( a_select3 @ q @ pv10 @ sk1 )
!= ( divide @ ( sqrt @ ( times @ ( minus @ ( a_select3 @ center @ sk1 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) @ ( minus @ ( a_select3 @ center @ sk1 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) ) ) @ ( sum @ n0 @ ( minus @ n5 @ n1 ) @ ( sqrt @ ( times @ ( minus @ ( a_select3 @ center @ sk2 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) @ ( minus @ ( a_select3 @ center @ sk2 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) ) ) ) ) )
| ( leq @ n0 @ sk3 ) ),
inference(simp,[status(thm)],[1895]) ).
thf(2991,plain,
( ( ( succ @ n3 )
= n4 )
| ( ( succ @ ( succ @ n1 ) )
!= ( succ @ ( succ @ n1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[2779,2972]) ).
thf(2992,plain,
( ( succ @ n3 )
= n4 ),
inference(pattern_uni,[status(thm)],[2991:[]]) ).
thf(8405,plain,
! [A: $i] :
( ( ( pred @ n4 )
= A )
| ( ( succ @ n3 )
!= ( succ @ A ) ) ),
inference(paramod_ordered,[status(thm)],[2992,136]) ).
thf(8406,plain,
( ( pred @ n4 )
= n3 ),
inference(pattern_uni,[status(thm)],[8405:[bind(A,$thf( n3 ))]]) ).
thf(2102,plain,
( ( sk3 != sk1 )
| ( ( a_select3 @ q @ pv10 @ sk1 )
!= ( divide @ ( sqrt @ ( times @ ( minus @ ( a_select3 @ center @ sk1 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) @ ( minus @ ( a_select3 @ center @ sk1 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) ) ) @ ( sum @ n0 @ ( minus @ n5 @ n1 ) @ ( sqrt @ ( times @ ( minus @ ( a_select3 @ center @ sk2 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) @ ( minus @ ( a_select3 @ center @ sk2 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) ) ) ) ) )
| ( ( leq @ sk1 @ ( minus @ n0 @ n1 ) )
!= ( leq @ sk3 @ ( minus @ pv10 @ n1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[1879,1556]) ).
thf(2115,plain,
( ( sk3 != sk1 )
| ( ( a_select3 @ q @ pv10 @ sk1 )
!= ( divide @ ( sqrt @ ( times @ ( minus @ ( a_select3 @ center @ sk1 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) @ ( minus @ ( a_select3 @ center @ sk1 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) ) ) @ ( sum @ n0 @ ( minus @ n5 @ n1 ) @ ( sqrt @ ( times @ ( minus @ ( a_select3 @ center @ sk2 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) @ ( minus @ ( a_select3 @ center @ sk2 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) ) ) ) ) )
| ( sk3 != sk1 )
| ( ( minus @ pv10 @ n1 )
!= ( minus @ n0 @ n1 ) ) ),
inference(simp,[status(thm)],[2102]) ).
thf(2137,plain,
( ( sk3 != sk1 )
| ( ( a_select3 @ q @ pv10 @ sk1 )
!= ( divide @ ( sqrt @ ( times @ ( minus @ ( a_select3 @ center @ sk1 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) @ ( minus @ ( a_select3 @ center @ sk1 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) ) ) @ ( sum @ n0 @ ( minus @ n5 @ n1 ) @ ( sqrt @ ( times @ ( minus @ ( a_select3 @ center @ sk2 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) @ ( minus @ ( a_select3 @ center @ sk2 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) ) ) ) ) )
| ( ( minus @ pv10 @ n1 )
!= ( minus @ n0 @ n1 ) ) ),
inference(simp,[status(thm)],[2115]) ).
thf(13,axiom,
gt @ n4 @ n3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_4_3) ).
thf(133,plain,
gt @ n4 @ n3,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(78,axiom,
gt @ n4 @ n0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_4_0) ).
thf(535,plain,
gt @ n4 @ n0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(11489,plain,
! [B: $i,A: $i] :
( ~ ( gt @ A @ B )
| ( ( gt @ n4 @ n0 )
!= ( gt @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[535,10060]) ).
thf(11490,plain,
~ ( gt @ n0 @ n4 ),
inference(pattern_uni,[status(thm)],[11489:[bind(A,$thf( n0 )),bind(B,$thf( n4 ))]]) ).
thf(3474,plain,
( ( sk3 != sk1 )
| ( ( a_select3 @ q @ pv10 @ sk1 )
!= ( divide @ ( sqrt @ ( times @ ( minus @ ( a_select3 @ center @ sk1 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) @ ( minus @ ( a_select3 @ center @ sk1 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) ) ) @ ( sum @ n0 @ ( minus @ n5 @ n1 ) @ ( sqrt @ ( times @ ( minus @ ( a_select3 @ center @ sk2 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) @ ( minus @ ( a_select3 @ center @ sk2 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) ) ) ) ) )
| ( pv10 != n0 )
| ( n1 != n1 ) ),
inference(simp,[status(thm)],[2137]) ).
thf(3559,plain,
( ( sk3 != sk1 )
| ( ( a_select3 @ q @ pv10 @ sk1 )
!= ( divide @ ( sqrt @ ( times @ ( minus @ ( a_select3 @ center @ sk1 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) @ ( minus @ ( a_select3 @ center @ sk1 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) ) ) @ ( sum @ n0 @ ( minus @ n5 @ n1 ) @ ( sqrt @ ( times @ ( minus @ ( a_select3 @ center @ sk2 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) @ ( minus @ ( a_select3 @ center @ sk2 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) ) ) ) ) )
| ( pv10 != n0 ) ),
inference(simp,[status(thm)],[3474]) ).
thf(68,axiom,
! [A: $i,B: $i] :
( ( leq @ A @ B )
=> ( leq @ A @ ( succ @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',leq_succ) ).
thf(507,plain,
! [A: $i,B: $i] :
( ( leq @ A @ B )
=> ( leq @ A @ ( succ @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(34,axiom,
! [A: $i,B: $i] :
( ! [C: $i,D: $i] :
( ( ( leq @ n0 @ C )
& ( leq @ C @ B )
& ( leq @ n0 @ D )
& ( leq @ D @ B ) )
=> ( ( a_select3 @ A @ C @ D )
= ( a_select3 @ A @ D @ C ) ) )
=> ! [C: $i,D: $i,E: $i,F: $i] :
( ( ( leq @ n0 @ C )
& ( leq @ C @ B )
& ( leq @ n0 @ D )
& ( leq @ D @ B )
& ( leq @ n0 @ E )
& ( leq @ E @ B ) )
=> ( ( a_select3 @ ( tptp_update3 @ A @ E @ E @ F ) @ C @ D )
= ( a_select3 @ ( tptp_update3 @ A @ E @ E @ F ) @ D @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',matrix_symm_update_diagonal) ).
thf(199,plain,
! [A: $i,B: $i] :
( ! [C: $i,D: $i] :
( ( ( leq @ n0 @ C )
& ( leq @ C @ B )
& ( leq @ n0 @ D )
& ( leq @ D @ B ) )
=> ( ( a_select3 @ A @ C @ D )
= ( a_select3 @ A @ D @ C ) ) )
=> ! [C: $i,D: $i,E: $i,F: $i] :
( ( ( leq @ n0 @ C )
& ( leq @ C @ B )
& ( leq @ n0 @ D )
& ( leq @ D @ B )
& ( leq @ n0 @ E )
& ( leq @ E @ B ) )
=> ( ( a_select3 @ ( tptp_update3 @ A @ E @ E @ F ) @ C @ D )
= ( a_select3 @ ( tptp_update3 @ A @ E @ E @ F ) @ D @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(200,plain,
! [A: $i,B: $i] :
( ! [C: $i,D: $i] :
( ( ( leq @ n0 @ C )
& ( leq @ C @ B )
& ( leq @ n0 @ D )
& ( leq @ D @ B ) )
=> ( ( a_select3 @ A @ C @ D )
= ( a_select3 @ A @ D @ C ) ) )
=> ! [C: $i,D: $i,E: $i] :
( ( ( leq @ n0 @ C )
& ( leq @ C @ B )
& ( leq @ n0 @ D )
& ( leq @ D @ B )
& ( leq @ n0 @ E )
& ( leq @ E @ B ) )
=> ! [F: $i] :
( ( a_select3 @ ( tptp_update3 @ A @ E @ E @ F ) @ C @ D )
= ( a_select3 @ ( tptp_update3 @ A @ E @ E @ F ) @ D @ C ) ) ) ),
inference(miniscope,[status(thm)],[199]) ).
thf(202,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( leq @ n0 @ ( sk9 @ B @ A ) )
| ~ ( leq @ n0 @ C )
| ~ ( leq @ C @ B )
| ~ ( leq @ n0 @ D )
| ~ ( leq @ D @ B )
| ~ ( leq @ n0 @ E )
| ~ ( leq @ E @ B )
| ( ( a_select3 @ ( tptp_update3 @ A @ E @ E @ F ) @ C @ D )
= ( a_select3 @ ( tptp_update3 @ A @ E @ E @ F ) @ D @ C ) ) ),
inference(cnf,[status(esa)],[200]) ).
thf(206,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( a_select3 @ ( tptp_update3 @ A @ E @ E @ F ) @ C @ D )
= ( a_select3 @ ( tptp_update3 @ A @ E @ E @ F ) @ D @ C ) )
| ( leq @ n0 @ ( sk9 @ B @ A ) )
| ~ ( leq @ n0 @ C )
| ~ ( leq @ C @ B )
| ~ ( leq @ n0 @ D )
| ~ ( leq @ D @ B )
| ~ ( leq @ n0 @ E )
| ~ ( leq @ E @ B ) ),
inference(lifteq,[status(thm)],[202]) ).
thf(1973,plain,
! [A: $i] :
( ( gt @ n5 @ n2 )
!= ( gt @ A @ A ) ),
inference(paramod_ordered,[status(thm)],[408,142]) ).
thf(1974,plain,
! [A: $i] :
( ( n5 != A )
| ( n2 != A ) ),
inference(simp,[status(thm)],[1973]) ).
thf(1975,plain,
n2 != n5,
inference(simp,[status(thm)],[1974]) ).
thf(74,axiom,
! [A: $i,B: $i] :
( ( leq @ ( succ @ A ) @ B )
=> ( gt @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',leq_succ_gt) ).
thf(527,plain,
! [A: $i,B: $i] :
( ( leq @ ( succ @ A ) @ B )
=> ( gt @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(9625,plain,
! [A: $i] :
( ( gt @ ( succ @ n5 ) @ A )
| ( ( succ @ ( succ @ ( succ @ n3 ) ) )
!= ( succ @ A ) ) ),
inference(paramod_ordered,[status(thm)],[9580,119]) ).
thf(9626,plain,
gt @ ( succ @ n5 ) @ ( succ @ ( succ @ n3 ) ),
inference(pattern_uni,[status(thm)],[9625:[bind(A,$thf( succ @ ( succ @ n3 ) ))]]) ).
thf(3238,plain,
( ( ( succ @ ( succ @ ( succ @ n2 ) ) )
= n5 )
| ( ( succ @ n1 )
!= ( succ @ n1 ) ) ),
inference(paramod_ordered,[status(thm)],[2766,3234]) ).
thf(3239,plain,
( ( succ @ ( succ @ ( succ @ n2 ) ) )
= n5 ),
inference(pattern_uni,[status(thm)],[3238:[]]) ).
thf(3383,plain,
( ( succ @ ( succ @ n3 ) )
= n5 ),
inference(rewrite,[status(thm)],[3239,2783]) ).
thf(11343,plain,
gt @ ( succ @ n5 ) @ n5,
inference(rewrite,[status(thm)],[9626,3383]) ).
thf(11356,plain,
! [B: $i,A: $i] :
( ( lt @ A @ B )
| ( ( gt @ ( succ @ n5 ) @ n5 )
!= ( gt @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[11343,150]) ).
thf(11357,plain,
lt @ n5 @ ( succ @ n5 ),
inference(pattern_uni,[status(thm)],[11356:[bind(A,$thf( n5 )),bind(B,$thf( succ @ n5 ))]]) ).
thf(116,plain,
! [A: $i] :
( ( succ @ ( pred @ A ) )
= A ),
inference(cnf,[status(esa)],[115]) ).
thf(117,plain,
! [A: $i] :
( ( succ @ ( pred @ A ) )
= A ),
inference(lifteq,[status(thm)],[116]) ).
thf(71,axiom,
! [A: $i] :
( ( ( leq @ n0 @ A )
& ( leq @ A @ n2 ) )
=> ( ( A = n0 )
| ( A = n1 )
| ( A = n2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',finite_domain_2) ).
thf(512,plain,
! [A: $i] :
( ( ( leq @ n0 @ A )
& ( leq @ A @ n2 ) )
=> ( ( A = n0 )
| ( A = n1 )
| ( A = n2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(1798,plain,
( ( leq @ sk1 @ ( minus @ n0 @ n1 ) )
| ( ( leq @ n0 @ sk3 )
!= ( leq @ n0 @ pv10 ) ) ),
inference(paramod_ordered,[status(thm)],[96,1707]) ).
thf(1848,plain,
( ( leq @ sk1 @ ( minus @ n0 @ n1 ) )
| ( n0 != n0 )
| ( sk3 != pv10 ) ),
inference(simp,[status(thm)],[1798]) ).
thf(1893,plain,
( ( leq @ sk1 @ ( minus @ n0 @ n1 ) )
| ( sk3 != pv10 ) ),
inference(simp,[status(thm)],[1848]) ).
thf(6741,plain,
! [B: $i,A: $i] :
( ( gt @ A @ B )
| ( gt @ B @ A )
| ( leq @ sk1 @ ( minus @ n0 @ n1 ) )
| ( B != pv10 )
| ( A != sk3 ) ),
inference(paramod_ordered,[status(thm)],[131,1893]) ).
thf(6742,plain,
! [A: $i] :
( ( gt @ sk3 @ A )
| ( gt @ A @ sk3 )
| ( leq @ sk1 @ ( minus @ n0 @ n1 ) )
| ( A != pv10 ) ),
inference(pattern_uni,[status(thm)],[6741:[bind(A,$thf( sk3 ))]]) ).
thf(7995,plain,
( ( gt @ sk3 @ pv10 )
| ( gt @ pv10 @ sk3 )
| ( leq @ sk1 @ ( minus @ n0 @ n1 ) ) ),
inference(simp,[status(thm)],[6742]) ).
thf(9796,plain,
! [B: $i,A: $i] :
( ( gt @ pv10 @ sk3 )
| ( leq @ sk1 @ ( minus @ n0 @ n1 ) )
| ( lt @ A @ B )
| ( ( gt @ sk3 @ pv10 )
!= ( gt @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7995,150]) ).
thf(9797,plain,
( ( gt @ pv10 @ sk3 )
| ( leq @ sk1 @ ( minus @ n0 @ n1 ) )
| ( lt @ pv10 @ sk3 ) ),
inference(pattern_uni,[status(thm)],[9796:[bind(A,$thf( pv10 )),bind(B,$thf( sk3 ))]]) ).
thf(9784,plain,
! [B: $i,A: $i] :
( ( lt @ A @ B )
| ( ( gt @ n5 @ n4 )
!= ( gt @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[541,150]) ).
thf(9785,plain,
lt @ n4 @ n5,
inference(pattern_uni,[status(thm)],[9784:[bind(A,$thf( n4 )),bind(B,$thf( n5 ))]]) ).
thf(11409,plain,
! [B: $i,A: $i] :
( ~ ( gt @ A @ B )
| ( ( gt @ n1 @ tptp_minus_1 )
!= ( gt @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[511,10060]) ).
thf(11410,plain,
~ ( gt @ tptp_minus_1 @ n1 ),
inference(pattern_uni,[status(thm)],[11409:[bind(A,$thf( tptp_minus_1 )),bind(B,$thf( n1 ))]]) ).
thf(3761,plain,
! [B: $i,A: $i] :
( ( gt @ A @ B )
| ( gt @ B @ A )
| ( leq @ sk1 @ ( minus @ n0 @ n1 ) )
| ( B != sk1 )
| ( A != sk3 ) ),
inference(paramod_ordered,[status(thm)],[131,1879]) ).
thf(3762,plain,
! [A: $i] :
( ( gt @ sk3 @ A )
| ( gt @ A @ sk3 )
| ( leq @ sk1 @ ( minus @ n0 @ n1 ) )
| ( A != sk1 ) ),
inference(pattern_uni,[status(thm)],[3761:[bind(A,$thf( sk3 ))]]) ).
thf(8156,plain,
( ( gt @ sk3 @ sk1 )
| ( gt @ sk1 @ sk3 )
| ( leq @ sk1 @ ( minus @ n0 @ n1 ) ) ),
inference(simp,[status(thm)],[3762]) ).
thf(9880,plain,
! [B: $i,A: $i] :
( ( gt @ sk1 @ sk3 )
| ( leq @ sk1 @ ( minus @ n0 @ n1 ) )
| ( lt @ A @ B )
| ( ( gt @ sk3 @ sk1 )
!= ( gt @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[8156,150]) ).
thf(9881,plain,
( ( gt @ sk1 @ sk3 )
| ( leq @ sk1 @ ( minus @ n0 @ n1 ) )
| ( lt @ sk1 @ sk3 ) ),
inference(pattern_uni,[status(thm)],[9880:[bind(A,$thf( sk1 )),bind(B,$thf( sk3 ))]]) ).
thf(54,axiom,
! [A: $i] :
( tptp_float_0_0
= ( sum @ n0 @ tptp_minus_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_plus_base_float) ).
thf(401,plain,
! [A: $i] :
( tptp_float_0_0
= ( sum @ n0 @ tptp_minus_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(402,plain,
! [A: $i] :
( tptp_float_0_0
= ( sum @ n0 @ tptp_minus_1 @ A ) ),
inference(cnf,[status(esa)],[401]) ).
thf(403,plain,
! [A: $i] :
( ( sum @ n0 @ tptp_minus_1 @ A )
= tptp_float_0_0 ),
inference(lifteq,[status(thm)],[402]) ).
thf(8343,plain,
tptp_float_0_0 = n0,
inference(rewrite,[status(thm)],[403,182]) ).
thf(9752,plain,
! [B: $i,A: $i] :
( ( lt @ A @ B )
| ( ( gt @ n135300 @ n4 )
!= ( gt @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[556,150]) ).
thf(9753,plain,
lt @ n4 @ n135300,
inference(pattern_uni,[status(thm)],[9752:[bind(A,$thf( n4 )),bind(B,$thf( n135300 ))]]) ).
thf(9816,plain,
! [B: $i,A: $i] :
( ( lt @ A @ B )
| ( ( gt @ n135300 @ n0 )
!= ( gt @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[322,150]) ).
thf(9817,plain,
lt @ n0 @ n135300,
inference(pattern_uni,[status(thm)],[9816:[bind(A,$thf( n0 )),bind(B,$thf( n135300 ))]]) ).
thf(50,axiom,
gt @ n135300 @ n1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_135300_1) ).
thf(343,plain,
gt @ n135300 @ n1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(1674,plain,
! [A: $i] :
( ( gt @ n135300 @ n1 )
!= ( gt @ A @ A ) ),
inference(paramod_ordered,[status(thm)],[343,142]) ).
thf(1675,plain,
! [A: $i] :
( ( n135300 != A )
| ( n1 != A ) ),
inference(simp,[status(thm)],[1674]) ).
thf(1676,plain,
n1 != n135300,
inference(simp,[status(thm)],[1675]) ).
thf(8269,plain,
! [A: $i] :
( ( sk3 != sk1 )
| ( ( divide @ ( sqrt @ ( times @ ( minus @ ( a_select3 @ center @ sk1 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) @ ( minus @ ( a_select3 @ center @ sk1 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) ) ) @ n0 )
!= ( a_select3 @ q @ pv10 @ sk1 ) )
| ( pv10 != n0 )
| ( ( sum @ n0 @ tptp_minus_1 @ A )
!= ( sum @ n0 @ ( minus @ n5 @ n1 ) @ ( sqrt @ ( times @ ( minus @ ( a_select3 @ center @ sk2 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) @ ( minus @ ( a_select3 @ center @ sk2 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[182,3559]) ).
thf(8306,plain,
! [A: $i] :
( ( sk3 != sk1 )
| ( ( divide @ ( sqrt @ ( times @ ( minus @ ( a_select3 @ center @ sk1 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) @ ( minus @ ( a_select3 @ center @ sk1 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) ) ) @ n0 )
!= ( a_select3 @ q @ pv10 @ sk1 ) )
| ( pv10 != n0 )
| ( n0 != n0 )
| ( ( minus @ n5 @ n1 )
!= tptp_minus_1 )
| ( A
!= ( sqrt @ ( times @ ( minus @ ( a_select3 @ center @ sk2 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) @ ( minus @ ( a_select3 @ center @ sk2 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) ) ) ) ),
inference(simp,[status(thm)],[8269]) ).
thf(8334,plain,
( ( sk3 != sk1 )
| ( ( divide @ ( sqrt @ ( times @ ( minus @ ( a_select3 @ center @ sk1 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) @ ( minus @ ( a_select3 @ center @ sk1 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) ) ) @ n0 )
!= ( a_select3 @ q @ pv10 @ sk1 ) )
| ( pv10 != n0 )
| ( ( minus @ n5 @ n1 )
!= tptp_minus_1 ) ),
inference(simp,[status(thm)],[8306]) ).
thf(26,axiom,
! [A: $i,B: $i,C: $i] :
( ( a_select2 @ ( tptp_update2 @ A @ B @ C ) @ B )
= C ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sel2_update_1) ).
thf(163,plain,
! [A: $i,B: $i,C: $i] :
( ( a_select2 @ ( tptp_update2 @ A @ B @ C ) @ B )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(164,plain,
! [C: $i,B: $i,A: $i] :
( ( a_select2 @ ( tptp_update2 @ A @ B @ C ) @ B )
= C ),
inference(cnf,[status(esa)],[163]) ).
thf(165,plain,
! [C: $i,B: $i,A: $i] :
( ( a_select2 @ ( tptp_update2 @ A @ B @ C ) @ B )
= C ),
inference(lifteq,[status(thm)],[164]) ).
thf(16546,plain,
( ( leq @ sk1 @ ( minus @ n0 @ n1 ) )
| ( sk3 != tptp_minus_1 )
| ( ( gt @ sk3 @ n0 )
!= ( gt @ n4 @ n0 ) ) ),
inference(paramod_ordered,[status(thm)],[535,13695]) ).
thf(16604,plain,
( ( leq @ sk1 @ ( minus @ n0 @ n1 ) )
| ( sk3 != tptp_minus_1 )
| ( sk3 != n4 )
| ( n0 != n0 ) ),
inference(simp,[status(thm)],[16546]) ).
thf(16616,plain,
( ( leq @ sk1 @ ( minus @ n0 @ n1 ) )
| ( sk3 != tptp_minus_1 )
| ( sk3 != n4 ) ),
inference(simp,[status(thm)],[16604]) ).
thf(2394,plain,
! [A: $i] :
( ( gt @ n4 @ n0 )
!= ( gt @ A @ A ) ),
inference(paramod_ordered,[status(thm)],[535,142]) ).
thf(2395,plain,
! [A: $i] :
( ( n4 != A )
| ( n0 != A ) ),
inference(simp,[status(thm)],[2394]) ).
thf(2396,plain,
n4 != n0,
inference(simp,[status(thm)],[2395]) ).
thf(191,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( leq @ ( sk7 @ C @ B @ A ) @ C )
| ~ ( leq @ n0 @ E )
| ~ ( leq @ E @ D )
| ~ ( leq @ n0 @ F )
| ~ ( leq @ F @ D )
| ( ( a_select3 @ ( tptp_mmul @ A @ ( tptp_mmul @ B @ ( trans @ A ) ) ) @ E @ F )
= ( a_select3 @ ( tptp_mmul @ A @ ( tptp_mmul @ B @ ( trans @ A ) ) ) @ F @ E ) ) ),
inference(cnf,[status(esa)],[188]) ).
thf(197,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( a_select3 @ ( tptp_mmul @ A @ ( tptp_mmul @ B @ ( trans @ A ) ) ) @ E @ F )
= ( a_select3 @ ( tptp_mmul @ A @ ( tptp_mmul @ B @ ( trans @ A ) ) ) @ F @ E ) )
| ( leq @ ( sk7 @ C @ B @ A ) @ C )
| ~ ( leq @ n0 @ E )
| ~ ( leq @ E @ D )
| ~ ( leq @ n0 @ F )
| ~ ( leq @ F @ D ) ),
inference(lifteq,[status(thm)],[191]) ).
thf(66,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ! [G: $i,H: $i] :
( ( ( leq @ n0 @ G )
& ( leq @ n0 @ H )
& ( leq @ G @ C )
& ( leq @ H @ D ) )
=> ( ( a_select3 @ E @ G @ H )
= F ) )
& ( leq @ n0 @ A )
& ( leq @ A @ C )
& ( leq @ n0 @ B )
& ( leq @ B @ D ) )
=> ( ( a_select3 @ ( tptp_update3 @ E @ C @ D @ F ) @ A @ B )
= F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sel3_update_3) ).
thf(493,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ! [G: $i,H: $i] :
( ( ( leq @ n0 @ G )
& ( leq @ n0 @ H )
& ( leq @ G @ C )
& ( leq @ H @ D ) )
=> ( ( a_select3 @ E @ G @ H )
= F ) )
& ( leq @ n0 @ A )
& ( leq @ A @ C )
& ( leq @ n0 @ B )
& ( leq @ B @ D ) )
=> ( ( a_select3 @ ( tptp_update3 @ E @ C @ D @ F ) @ A @ B )
= F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(2651,plain,
! [A: $i] :
( ( gt @ n2 @ n1 )
!= ( gt @ A @ A ) ),
inference(paramod_ordered,[status(thm)],[551,142]) ).
thf(2652,plain,
! [A: $i] :
( ( n2 != A )
| ( n1 != A ) ),
inference(simp,[status(thm)],[2651]) ).
thf(2653,plain,
n2 != n1,
inference(simp,[status(thm)],[2652]) ).
thf(39,axiom,
! [A: $i] :
( ( minus @ A @ n1 )
= ( pred @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pred_minus_1) ).
thf(229,plain,
! [A: $i] :
( ( minus @ A @ n1 )
= ( pred @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(10,axiom,
gt @ n2 @ tptp_minus_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_2_tptp_minus_1) ).
thf(128,plain,
gt @ n2 @ tptp_minus_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(560,plain,
! [A: $i] :
( ( gt @ n2 @ tptp_minus_1 )
!= ( gt @ A @ A ) ),
inference(paramod_ordered,[status(thm)],[128,142]) ).
thf(563,plain,
! [A: $i] :
( ( n2 != A )
| ( tptp_minus_1 != A ) ),
inference(simp,[status(thm)],[560]) ).
thf(566,plain,
n2 != tptp_minus_1,
inference(simp,[status(thm)],[563]) ).
thf(21,axiom,
! [A: $i] :
( ( plus @ n4 @ A )
= ( succ @ ( succ @ ( succ @ ( succ @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',succ_plus_4_l) ).
thf(154,plain,
! [A: $i] :
( ( plus @ n4 @ A )
= ( succ @ ( succ @ ( succ @ ( succ @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(155,plain,
! [A: $i] :
( ( plus @ n4 @ A )
= ( succ @ ( succ @ ( succ @ ( succ @ A ) ) ) ) ),
inference(cnf,[status(esa)],[154]) ).
thf(156,plain,
! [A: $i] :
( ( plus @ n4 @ A )
= ( succ @ ( succ @ ( succ @ ( succ @ A ) ) ) ) ),
inference(lifteq,[status(thm)],[155]) ).
thf(8413,plain,
! [A: $i] :
( ( ( pred @ n3 )
= A )
| ( ( succ @ n2 )
!= ( succ @ A ) ) ),
inference(paramod_ordered,[status(thm)],[2783,136]) ).
thf(8414,plain,
( ( pred @ n3 )
= n2 ),
inference(pattern_uni,[status(thm)],[8413:[bind(A,$thf( n2 ))]]) ).
thf(9772,plain,
! [B: $i,A: $i] :
( ( lt @ A @ B )
| ( ( gt @ n4 @ n2 )
!= ( gt @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[132,150]) ).
thf(9773,plain,
lt @ n2 @ n4,
inference(pattern_uni,[status(thm)],[9772:[bind(A,$thf( n2 )),bind(B,$thf( n4 ))]]) ).
thf(608,plain,
! [A: $i] :
( ( gt @ n3 @ n1 )
!= ( gt @ A @ A ) ),
inference(paramod_ordered,[status(thm)],[157,142]) ).
thf(609,plain,
! [A: $i] :
( ( n3 != A )
| ( n1 != A ) ),
inference(simp,[status(thm)],[608]) ).
thf(610,plain,
n3 != n1,
inference(simp,[status(thm)],[609]) ).
thf(44,axiom,
! [A: $i,B: $i] :
( ( ( leq @ A @ B )
& ( A != B ) )
=> ( gt @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',leq_gt2) ).
thf(328,plain,
! [A: $i,B: $i] :
( ( ( leq @ A @ B )
& ( A != B ) )
=> ( gt @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(8,axiom,
! [A: $i] :
( ( plus @ A @ n3 )
= ( succ @ ( succ @ ( succ @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',succ_plus_3_r) ).
thf(124,plain,
! [A: $i] :
( ( plus @ A @ n3 )
= ( succ @ ( succ @ ( succ @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(11441,plain,
! [B: $i,A: $i] :
( ~ ( gt @ A @ B )
| ( ( gt @ n4 @ n3 )
!= ( gt @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[133,10060]) ).
thf(11442,plain,
~ ( gt @ n3 @ n4 ),
inference(pattern_uni,[status(thm)],[11441:[bind(A,$thf( n3 )),bind(B,$thf( n4 ))]]) ).
thf(2315,plain,
! [A: $i] :
( ( gt @ n5 @ tptp_minus_1 )
!= ( gt @ A @ A ) ),
inference(paramod_ordered,[status(thm)],[526,142]) ).
thf(2316,plain,
! [A: $i] :
( ( n5 != A )
| ( tptp_minus_1 != A ) ),
inference(simp,[status(thm)],[2315]) ).
thf(2317,plain,
tptp_minus_1 != n5,
inference(simp,[status(thm)],[2316]) ).
thf(72,axiom,
! [A: $i,B: $i] :
( ! [C: $i,D: $i] :
( ( ( leq @ n0 @ C )
& ( leq @ C @ B )
& ( leq @ n0 @ D )
& ( leq @ D @ B ) )
=> ( ( a_select3 @ A @ C @ D )
= ( a_select3 @ A @ D @ C ) ) )
=> ! [C: $i,D: $i] :
( ( ( leq @ n0 @ C )
& ( leq @ C @ B )
& ( leq @ n0 @ D )
& ( leq @ D @ B ) )
=> ( ( a_select3 @ ( inv @ A ) @ C @ D )
= ( a_select3 @ ( inv @ A ) @ D @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',matrix_symm_inv) ).
thf(515,plain,
! [A: $i,B: $i] :
( ! [C: $i,D: $i] :
( ( ( leq @ n0 @ C )
& ( leq @ C @ B )
& ( leq @ n0 @ D )
& ( leq @ D @ B ) )
=> ( ( a_select3 @ A @ C @ D )
= ( a_select3 @ A @ D @ C ) ) )
=> ! [C: $i,D: $i] :
( ( ( leq @ n0 @ C )
& ( leq @ C @ B )
& ( leq @ n0 @ D )
& ( leq @ D @ B ) )
=> ( ( a_select3 @ ( inv @ A ) @ C @ D )
= ( a_select3 @ ( inv @ A ) @ D @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(2492,plain,
( ( ( a_select3 @ q @ pv10 @ sk1 )
!= ( divide @ ( sqrt @ ( times @ ( minus @ ( a_select3 @ center @ sk1 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) @ ( minus @ ( a_select3 @ center @ sk1 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) ) ) @ ( sum @ n0 @ ( minus @ n5 @ n1 ) @ ( sqrt @ ( times @ ( minus @ ( a_select3 @ center @ sk2 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) @ ( minus @ ( a_select3 @ center @ sk2 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) ) ) ) ) )
| ( sk3 != pv10 )
| ( n135300 != pv10 )
| ( n1 != n1 ) ),
inference(simp,[status(thm)],[1641]) ).
thf(2594,plain,
( ( ( a_select3 @ q @ pv10 @ sk1 )
!= ( divide @ ( sqrt @ ( times @ ( minus @ ( a_select3 @ center @ sk1 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) @ ( minus @ ( a_select3 @ center @ sk1 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) ) ) @ ( sum @ n0 @ ( minus @ n5 @ n1 ) @ ( sqrt @ ( times @ ( minus @ ( a_select3 @ center @ sk2 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) @ ( minus @ ( a_select3 @ center @ sk2 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) ) ) ) ) )
| ( sk3 != pv10 )
| ( n135300 != pv10 ) ),
inference(simp,[status(thm)],[2492]) ).
thf(8275,plain,
! [A: $i] :
( ( ( divide @ ( sqrt @ ( times @ ( minus @ ( a_select3 @ center @ sk1 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) @ ( minus @ ( a_select3 @ center @ sk1 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) ) ) @ n0 )
!= ( a_select3 @ q @ pv10 @ sk1 ) )
| ( sk3 != pv10 )
| ( n135300 != pv10 )
| ( ( sum @ n0 @ tptp_minus_1 @ A )
!= ( sum @ n0 @ ( minus @ n5 @ n1 ) @ ( sqrt @ ( times @ ( minus @ ( a_select3 @ center @ sk2 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) @ ( minus @ ( a_select3 @ center @ sk2 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[182,2594]) ).
thf(8298,plain,
! [A: $i] :
( ( ( divide @ ( sqrt @ ( times @ ( minus @ ( a_select3 @ center @ sk1 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) @ ( minus @ ( a_select3 @ center @ sk1 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) ) ) @ n0 )
!= ( a_select3 @ q @ pv10 @ sk1 ) )
| ( sk3 != pv10 )
| ( n135300 != pv10 )
| ( n0 != n0 )
| ( ( minus @ n5 @ n1 )
!= tptp_minus_1 )
| ( A
!= ( sqrt @ ( times @ ( minus @ ( a_select3 @ center @ sk2 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) @ ( minus @ ( a_select3 @ center @ sk2 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) ) ) ) ),
inference(simp,[status(thm)],[8275]) ).
thf(8326,plain,
( ( ( divide @ ( sqrt @ ( times @ ( minus @ ( a_select3 @ center @ sk1 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) @ ( minus @ ( a_select3 @ center @ sk1 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) ) ) @ n0 )
!= ( a_select3 @ q @ pv10 @ sk1 ) )
| ( sk3 != pv10 )
| ( n135300 != pv10 )
| ( ( minus @ n5 @ n1 )
!= tptp_minus_1 ) ),
inference(simp,[status(thm)],[8298]) ).
thf(9760,plain,
! [B: $i,A: $i] :
( ( lt @ A @ B )
| ( ( gt @ n1 @ tptp_minus_1 )
!= ( gt @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[511,150]) ).
thf(9761,plain,
lt @ tptp_minus_1 @ n1,
inference(pattern_uni,[status(thm)],[9760:[bind(A,$thf( tptp_minus_1 )),bind(B,$thf( n1 ))]]) ).
thf(28,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ! [E: $i] :
( ( ( leq @ n0 @ E )
& ( leq @ E @ B ) )
=> ( ( a_select2 @ C @ E )
= D ) )
& ( leq @ n0 @ A )
& ( leq @ A @ B ) )
=> ( ( a_select2 @ ( tptp_update2 @ C @ B @ D ) @ A )
= D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sel2_update_3) ).
thf(167,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ! [E: $i] :
( ( ( leq @ n0 @ E )
& ( leq @ E @ B ) )
=> ( ( a_select2 @ C @ E )
= D ) )
& ( leq @ n0 @ A )
& ( leq @ A @ B ) )
=> ( ( a_select2 @ ( tptp_update2 @ C @ B @ D ) @ A )
= D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(170,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( leq @ n0 @ ( sk5 @ D @ C @ B @ A ) )
| ~ ( leq @ n0 @ A )
| ~ ( leq @ A @ B )
| ( ( a_select2 @ ( tptp_update2 @ C @ B @ D ) @ A )
= D ) ),
inference(cnf,[status(esa)],[167]) ).
thf(173,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( a_select2 @ ( tptp_update2 @ C @ B @ D ) @ A )
= D )
| ( leq @ n0 @ ( sk5 @ D @ C @ B @ A ) )
| ~ ( leq @ n0 @ A )
| ~ ( leq @ A @ B ) ),
inference(lifteq,[status(thm)],[170]) ).
thf(53,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( a_select3 @ ( tptp_update3 @ A @ B @ C @ D ) @ B @ C )
= D ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sel3_update_1) ).
thf(398,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( a_select3 @ ( tptp_update3 @ A @ B @ C @ D ) @ B @ C )
= D ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(1464,plain,
! [A: $i] :
( ( gt @ n5 @ n0 )
!= ( gt @ A @ A ) ),
inference(paramod_ordered,[status(thm)],[332,142]) ).
thf(1465,plain,
! [A: $i] :
( ( n5 != A )
| ( n0 != A ) ),
inference(simp,[status(thm)],[1464]) ).
thf(1466,plain,
n5 != n0,
inference(simp,[status(thm)],[1465]) ).
thf(59,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( A != C )
& ( B = D )
& ( ( a_select3 @ E @ C @ D )
= F ) )
=> ( ( a_select3 @ ( tptp_update3 @ E @ A @ B @ G ) @ C @ D )
= F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sel3_update_2) ).
thf(412,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( A != C )
& ( B = D )
& ( ( a_select3 @ E @ C @ D )
= F ) )
=> ( ( a_select3 @ ( tptp_update3 @ E @ A @ B @ G ) @ C @ D )
= F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(9,axiom,
gt @ n3 @ n2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_3_2) ).
thf(127,plain,
gt @ n3 @ n2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(11505,plain,
! [B: $i,A: $i] :
( ~ ( gt @ A @ B )
| ( ( gt @ n3 @ n2 )
!= ( gt @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[127,10060]) ).
thf(11506,plain,
~ ( gt @ n2 @ n3 ),
inference(pattern_uni,[status(thm)],[11505:[bind(A,$thf( n2 )),bind(B,$thf( n3 ))]]) ).
thf(9764,plain,
! [B: $i,A: $i] :
( ( lt @ A @ B )
| ( ( gt @ n3 @ n0 )
!= ( gt @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[404,150]) ).
thf(9765,plain,
lt @ n0 @ n3,
inference(pattern_uni,[status(thm)],[9764:[bind(A,$thf( n0 )),bind(B,$thf( n3 ))]]) ).
thf(149,plain,
! [B: $i,A: $i] :
( ~ ( lt @ A @ B )
| ( gt @ B @ A ) ),
inference(cnf,[status(esa)],[147]) ).
thf(16556,plain,
( ( leq @ sk1 @ ( minus @ n0 @ n1 ) )
| ( sk3 != tptp_minus_1 )
| ( ( gt @ sk3 @ n0 )
!= ( gt @ n5 @ n0 ) ) ),
inference(paramod_ordered,[status(thm)],[332,13695]) ).
thf(16590,plain,
( ( leq @ sk1 @ ( minus @ n0 @ n1 ) )
| ( sk3 != tptp_minus_1 )
| ( sk3 != n5 )
| ( n0 != n0 ) ),
inference(simp,[status(thm)],[16556]) ).
thf(16612,plain,
( ( leq @ sk1 @ ( minus @ n0 @ n1 ) )
| ( sk3 != tptp_minus_1 )
| ( sk3 != n5 ) ),
inference(simp,[status(thm)],[16590]) ).
thf(16433,plain,
( ( gt @ ( succ @ n5 ) @ n5 )
!= ( gt @ tptp_minus_1 @ n5 ) ),
inference(paramod_ordered,[status(thm)],[11343,11458]) ).
thf(16461,plain,
( ( ( succ @ n5 )
!= tptp_minus_1 )
| ( n5 != n5 ) ),
inference(simp,[status(thm)],[16433]) ).
thf(16496,plain,
( ( succ @ n5 )
!= tptp_minus_1 ),
inference(simp,[status(thm)],[16461]) ).
thf(582,plain,
! [A: $i] :
( ( gt @ n4 @ n3 )
!= ( gt @ A @ A ) ),
inference(paramod_ordered,[status(thm)],[133,142]) ).
thf(583,plain,
! [A: $i] :
( ( n4 != A )
| ( n3 != A ) ),
inference(simp,[status(thm)],[582]) ).
thf(584,plain,
n4 != n3,
inference(simp,[status(thm)],[583]) ).
thf(11433,plain,
! [B: $i,A: $i] :
( ~ ( gt @ A @ B )
| ( ( gt @ n5 @ n3 )
!= ( gt @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[216,10060]) ).
thf(11434,plain,
~ ( gt @ n3 @ n5 ),
inference(pattern_uni,[status(thm)],[11433:[bind(A,$thf( n3 )),bind(B,$thf( n5 ))]]) ).
thf(94,plain,
( ~ ( leq @ n0 @ pv10 )
| ~ ( leq @ pv10 @ ( minus @ n135300 @ n1 ) )
| ( leq @ n0 @ sk1 )
| ( leq @ sk3 @ ( minus @ pv10 @ n1 ) ) ),
inference(cnf,[status(esa)],[93]) ).
thf(577,plain,
( ~ $true
| ~ $true
| ( leq @ n0 @ sk1 )
| ( leq @ sk3 @ ( minus @ pv10 @ n1 ) ) ),
inference(rewrite,[status(thm)],[94,96,95]) ).
thf(578,plain,
( ( leq @ n0 @ sk1 )
| ( leq @ sk3 @ ( minus @ pv10 @ n1 ) ) ),
inference(simp,[status(thm)],[577]) ).
thf(99,plain,
( ~ ( leq @ n0 @ pv10 )
| ~ ( leq @ pv10 @ ( minus @ n135300 @ n1 ) )
| ( leq @ n0 @ sk1 )
| ( ( sum @ n0 @ ( minus @ n5 @ n1 ) @ ( a_select3 @ q @ sk3 @ sk4 ) )
!= n1 ) ),
inference(cnf,[status(esa)],[93]) ).
thf(110,plain,
( ( ( sum @ n0 @ ( minus @ n5 @ n1 ) @ ( a_select3 @ q @ sk3 @ sk4 ) )
!= n1 )
| ~ ( leq @ n0 @ pv10 )
| ~ ( leq @ pv10 @ ( minus @ n135300 @ n1 ) )
| ( leq @ n0 @ sk1 ) ),
inference(lifteq,[status(thm)],[99]) ).
thf(2468,plain,
( ( ( sum @ n0 @ ( minus @ n5 @ n1 ) @ ( a_select3 @ q @ sk3 @ sk4 ) )
!= n1 )
| ~ $true
| ~ $true
| ( leq @ n0 @ sk1 ) ),
inference(rewrite,[status(thm)],[110,96,95]) ).
thf(2469,plain,
( ( ( sum @ n0 @ ( minus @ n5 @ n1 ) @ ( a_select3 @ q @ sk3 @ sk4 ) )
!= n1 )
| ( leq @ n0 @ sk1 ) ),
inference(simp,[status(thm)],[2468]) ).
thf(2470,plain,
! [B: $i,A: $i] :
( ~ ( leq @ n0 @ A )
| ~ ( leq @ A @ ( minus @ pv10 @ n1 ) )
| ( leq @ n0 @ sk1 )
| ( ( sum @ n0 @ ( minus @ n5 @ n1 ) @ ( a_select3 @ q @ A @ B ) )
!= ( sum @ n0 @ ( minus @ n5 @ n1 ) @ ( a_select3 @ q @ sk3 @ sk4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[107,2469]) ).
thf(2471,plain,
( ~ ( leq @ n0 @ sk3 )
| ~ ( leq @ sk3 @ ( minus @ pv10 @ n1 ) )
| ( leq @ n0 @ sk1 ) ),
inference(pattern_uni,[status(thm)],[2470:[bind(A,$thf( sk3 )),bind(B,$thf( sk4 ))]]) ).
thf(3037,plain,
( ( leq @ n0 @ sk1 )
| ~ ( leq @ n0 @ sk3 )
| ( ( leq @ sk3 @ ( minus @ pv10 @ n1 ) )
!= ( leq @ sk3 @ ( minus @ pv10 @ n1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[578,2471]) ).
thf(3038,plain,
( ( leq @ n0 @ sk1 )
| ~ ( leq @ n0 @ sk3 ) ),
inference(pattern_uni,[status(thm)],[3037:[]]) ).
thf(3085,plain,
( ( leq @ n0 @ sk1 )
| ( ( leq @ n0 @ sk3 )
!= ( leq @ n0 @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[572,3038]) ).
thf(3086,plain,
leq @ n0 @ sk1,
inference(pattern_uni,[status(thm)],[3085:[]]) ).
thf(11465,plain,
! [B: $i,A: $i] :
( ~ ( gt @ A @ B )
| ( ( gt @ n2 @ tptp_minus_1 )
!= ( gt @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[128,10060]) ).
thf(11466,plain,
~ ( gt @ tptp_minus_1 @ n2 ),
inference(pattern_uni,[status(thm)],[11465:[bind(A,$thf( tptp_minus_1 )),bind(B,$thf( n2 ))]]) ).
thf(11501,plain,
! [B: $i,A: $i] :
( ~ ( gt @ A @ B )
| ( ( gt @ n135300 @ tptp_minus_1 )
!= ( gt @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[331,10060]) ).
thf(11502,plain,
~ ( gt @ tptp_minus_1 @ n135300 ),
inference(pattern_uni,[status(thm)],[11501:[bind(A,$thf( tptp_minus_1 )),bind(B,$thf( n135300 ))]]) ).
thf(9802,plain,
! [B: $i,A: $i] :
( ( lt @ A @ B )
| ( ( gt @ n3 @ n2 )
!= ( gt @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[127,150]) ).
thf(9803,plain,
lt @ n2 @ n3,
inference(pattern_uni,[status(thm)],[9802:[bind(A,$thf( n2 )),bind(B,$thf( n3 ))]]) ).
thf(169,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( leq @ ( sk5 @ D @ C @ B @ A ) @ B )
| ~ ( leq @ n0 @ A )
| ~ ( leq @ A @ B )
| ( ( a_select2 @ ( tptp_update2 @ C @ B @ D ) @ A )
= D ) ),
inference(cnf,[status(esa)],[167]) ).
thf(172,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( a_select2 @ ( tptp_update2 @ C @ B @ D ) @ A )
= D )
| ( leq @ ( sk5 @ D @ C @ B @ A ) @ B )
| ~ ( leq @ n0 @ A )
| ~ ( leq @ A @ B ) ),
inference(lifteq,[status(thm)],[169]) ).
thf(9770,plain,
! [B: $i,A: $i] :
( ( lt @ A @ B )
| ( ( gt @ n5 @ n3 )
!= ( gt @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[216,150]) ).
thf(9771,plain,
lt @ n3 @ n5,
inference(pattern_uni,[status(thm)],[9770:[bind(A,$thf( n3 )),bind(B,$thf( n5 ))]]) ).
thf(561,plain,
! [A: $i] :
( ( gt @ n3 @ n2 )
!= ( gt @ A @ A ) ),
inference(paramod_ordered,[status(thm)],[127,142]) ).
thf(564,plain,
! [A: $i] :
( ( n3 != A )
| ( n2 != A ) ),
inference(simp,[status(thm)],[561]) ).
thf(567,plain,
n2 != n3,
inference(simp,[status(thm)],[564]) ).
thf(69,axiom,
! [A: $i,B: $i] :
( ( leq @ ( minus @ A @ B ) @ A )
=> ( leq @ n0 @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',leq_minus) ).
thf(509,plain,
! [A: $i,B: $i] :
( ( leq @ ( minus @ A @ B ) @ A )
=> ( leq @ n0 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(11437,plain,
! [B: $i,A: $i] :
( ~ ( gt @ A @ B )
| ( ( gt @ n4 @ n2 )
!= ( gt @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[132,10060]) ).
thf(11438,plain,
~ ( gt @ n2 @ n4 ),
inference(pattern_uni,[status(thm)],[11437:[bind(A,$thf( n2 )),bind(B,$thf( n4 ))]]) ).
thf(9788,plain,
! [B: $i,A: $i] :
( ( lt @ A @ B )
| ( ( gt @ n135300 @ n1 )
!= ( gt @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[343,150]) ).
thf(9789,plain,
lt @ n1 @ n135300,
inference(pattern_uni,[status(thm)],[9788:[bind(A,$thf( n1 )),bind(B,$thf( n135300 ))]]) ).
thf(205,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( a_select3 @ A @ ( sk8 @ B @ A ) @ ( sk9 @ B @ A ) )
!= ( a_select3 @ A @ ( sk9 @ B @ A ) @ ( sk8 @ B @ A ) ) )
| ~ ( leq @ n0 @ C )
| ~ ( leq @ C @ B )
| ~ ( leq @ n0 @ D )
| ~ ( leq @ D @ B )
| ~ ( leq @ n0 @ E )
| ~ ( leq @ E @ B )
| ( ( a_select3 @ ( tptp_update3 @ A @ E @ E @ F ) @ C @ D )
= ( a_select3 @ ( tptp_update3 @ A @ E @ E @ F ) @ D @ C ) ) ),
inference(cnf,[status(esa)],[200]) ).
thf(208,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( a_select3 @ A @ ( sk9 @ B @ A ) @ ( sk8 @ B @ A ) )
!= ( a_select3 @ A @ ( sk8 @ B @ A ) @ ( sk9 @ B @ A ) ) )
| ( ( a_select3 @ ( tptp_update3 @ A @ E @ E @ F ) @ C @ D )
= ( a_select3 @ ( tptp_update3 @ A @ E @ E @ F ) @ D @ C ) )
| ~ ( leq @ n0 @ C )
| ~ ( leq @ C @ B )
| ~ ( leq @ n0 @ D )
| ~ ( leq @ D @ B )
| ~ ( leq @ n0 @ E )
| ~ ( leq @ E @ B ) ),
inference(lifteq,[status(thm)],[205]) ).
thf(11405,plain,
! [B: $i,A: $i] :
( ~ ( gt @ A @ B )
| ( ( gt @ n3 @ tptp_minus_1 )
!= ( gt @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[120,10060]) ).
thf(11406,plain,
~ ( gt @ tptp_minus_1 @ n3 ),
inference(pattern_uni,[status(thm)],[11405:[bind(A,$thf( tptp_minus_1 )),bind(B,$thf( n3 ))]]) ).
thf(11453,plain,
! [B: $i,A: $i] :
( ~ ( gt @ A @ B )
| ( ( gt @ n135300 @ n5 )
!= ( gt @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[554,10060]) ).
thf(11454,plain,
~ ( gt @ n5 @ n135300 ),
inference(pattern_uni,[status(thm)],[11453:[bind(A,$thf( n5 )),bind(B,$thf( n135300 ))]]) ).
thf(16350,plain,
! [A: $i] :
( ( gt @ ( succ @ A ) @ A )
!= ( gt @ n5 @ n135300 ) ),
inference(paramod_ordered,[status(thm)],[119,11454]) ).
thf(16392,plain,
! [A: $i] :
( ( ( succ @ A )
!= n5 )
| ( A != n135300 ) ),
inference(simp,[status(thm)],[16350]) ).
thf(16404,plain,
( ( succ @ n135300 )
!= n5 ),
inference(simp,[status(thm)],[16392]) ).
thf(9756,plain,
! [B: $i,A: $i] :
( ( lt @ A @ B )
| ( ( gt @ n5 @ n2 )
!= ( gt @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[408,150]) ).
thf(9757,plain,
lt @ n2 @ n5,
inference(pattern_uni,[status(thm)],[9756:[bind(A,$thf( n2 )),bind(B,$thf( n5 ))]]) ).
thf(11469,plain,
! [B: $i,A: $i] :
( ~ ( gt @ A @ B )
| ( ( gt @ n135300 @ n1 )
!= ( gt @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[343,10060]) ).
thf(11470,plain,
~ ( gt @ n1 @ n135300 ),
inference(pattern_uni,[status(thm)],[11469:[bind(A,$thf( n1 )),bind(B,$thf( n135300 ))]]) ).
thf(87,axiom,
! [A: $i,B: $i] :
( ( gt @ B @ A )
=> ( leq @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',leq_gt1) ).
thf(552,plain,
! [A: $i,B: $i] :
( ( gt @ B @ A )
=> ( leq @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(43,axiom,
! [A: $i,B: $i] :
( ( geq @ A @ B )
<=> ( leq @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',leq_geq) ).
thf(323,plain,
! [A: $i,B: $i] :
( ( ( geq @ A @ B )
=> ( leq @ B @ A ) )
& ( ( leq @ B @ A )
=> ( geq @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(942,plain,
( ( leq @ n0 @ sk3 )
| ( ( leq @ sk1 @ ( minus @ n0 @ n1 ) )
!= ( leq @ n0 @ sk3 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[930]) ).
thf(943,plain,
( ( leq @ n0 @ sk3 )
| ( ( leq @ sk1 @ ( minus @ n0 @ n1 ) )
!= ( leq @ n0 @ sk3 ) ) ),
inference(simp,[status(thm)],[942]) ).
thf(190,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( a_select3 @ B @ ( sk6 @ C @ B @ A ) @ ( sk7 @ C @ B @ A ) )
!= ( a_select3 @ B @ ( sk7 @ C @ B @ A ) @ ( sk6 @ C @ B @ A ) ) )
| ~ ( leq @ n0 @ E )
| ~ ( leq @ E @ D )
| ~ ( leq @ n0 @ F )
| ~ ( leq @ F @ D )
| ( ( a_select3 @ ( tptp_mmul @ A @ ( tptp_mmul @ B @ ( trans @ A ) ) ) @ E @ F )
= ( a_select3 @ ( tptp_mmul @ A @ ( tptp_mmul @ B @ ( trans @ A ) ) ) @ F @ E ) ) ),
inference(cnf,[status(esa)],[188]) ).
thf(198,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( a_select3 @ B @ ( sk7 @ C @ B @ A ) @ ( sk6 @ C @ B @ A ) )
!= ( a_select3 @ B @ ( sk6 @ C @ B @ A ) @ ( sk7 @ C @ B @ A ) ) )
| ( ( a_select3 @ ( tptp_mmul @ A @ ( tptp_mmul @ B @ ( trans @ A ) ) ) @ E @ F )
= ( a_select3 @ ( tptp_mmul @ A @ ( tptp_mmul @ B @ ( trans @ A ) ) ) @ F @ E ) )
| ~ ( leq @ n0 @ E )
| ~ ( leq @ E @ D )
| ~ ( leq @ n0 @ F )
| ~ ( leq @ F @ D ) ),
inference(lifteq,[status(thm)],[190]) ).
thf(2073,plain,
! [A: $i] :
( ( gt @ n1 @ tptp_minus_1 )
!= ( gt @ A @ A ) ),
inference(paramod_ordered,[status(thm)],[511,142]) ).
thf(2074,plain,
! [A: $i] :
( ( n1 != A )
| ( tptp_minus_1 != A ) ),
inference(simp,[status(thm)],[2073]) ).
thf(2075,plain,
tptp_minus_1 != n1,
inference(simp,[status(thm)],[2074]) ).
thf(19,axiom,
gt @ n4 @ tptp_minus_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_4_tptp_minus_1) ).
thf(151,plain,
gt @ n4 @ tptp_minus_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(587,plain,
! [A: $i] :
( ( gt @ n4 @ tptp_minus_1 )
!= ( gt @ A @ A ) ),
inference(paramod_ordered,[status(thm)],[151,142]) ).
thf(588,plain,
! [A: $i] :
( ( n4 != A )
| ( tptp_minus_1 != A ) ),
inference(simp,[status(thm)],[587]) ).
thf(589,plain,
n4 != tptp_minus_1,
inference(simp,[status(thm)],[588]) ).
thf(85,axiom,
! [A: $i] :
( ( ( leq @ n0 @ A )
& ( leq @ A @ n5 ) )
=> ( ( A = n0 )
| ( A = n1 )
| ( A = n2 )
| ( A = n3 )
| ( A = n4 )
| ( A = n5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',finite_domain_5) ).
thf(548,plain,
! [A: $i] :
( ( ( leq @ n0 @ A )
& ( leq @ A @ n5 ) )
=> ( ( A = n0 )
| ( A = n1 )
| ( A = n2 )
| ( A = n3 )
| ( A = n4 )
| ( A = n5 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(22059,plain,
! [A: $i] :
( ( gt @ ( succ @ A ) @ A )
!= ( gt @ tptp_minus_1 @ n135300 ) ),
inference(paramod_ordered,[status(thm)],[119,11502]) ).
thf(22096,plain,
! [A: $i] :
( ( ( succ @ A )
!= tptp_minus_1 )
| ( A != n135300 ) ),
inference(simp,[status(thm)],[22059]) ).
thf(22110,plain,
( ( succ @ n135300 )
!= tptp_minus_1 ),
inference(simp,[status(thm)],[22096]) ).
thf(9776,plain,
! [B: $i,A: $i] :
( ( lt @ A @ B )
| ( ( gt @ n2 @ n0 )
!= ( gt @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[529,150]) ).
thf(9777,plain,
lt @ n0 @ n2,
inference(pattern_uni,[status(thm)],[9776:[bind(A,$thf( n0 )),bind(B,$thf( n2 ))]]) ).
thf(204,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( leq @ n0 @ ( sk8 @ B @ A ) )
| ~ ( leq @ n0 @ C )
| ~ ( leq @ C @ B )
| ~ ( leq @ n0 @ D )
| ~ ( leq @ D @ B )
| ~ ( leq @ n0 @ E )
| ~ ( leq @ E @ B )
| ( ( a_select3 @ ( tptp_update3 @ A @ E @ E @ F ) @ C @ D )
= ( a_select3 @ ( tptp_update3 @ A @ E @ E @ F ) @ D @ C ) ) ),
inference(cnf,[status(esa)],[200]) ).
thf(209,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( a_select3 @ ( tptp_update3 @ A @ E @ E @ F ) @ C @ D )
= ( a_select3 @ ( tptp_update3 @ A @ E @ E @ F ) @ D @ C ) )
| ( leq @ n0 @ ( sk8 @ B @ A ) )
| ~ ( leq @ n0 @ C )
| ~ ( leq @ C @ B )
| ~ ( leq @ n0 @ D )
| ~ ( leq @ D @ B )
| ~ ( leq @ n0 @ E )
| ~ ( leq @ E @ B ) ),
inference(lifteq,[status(thm)],[204]) ).
thf(3,axiom,
! [A: $i] :
( ( plus @ n3 @ A )
= ( succ @ ( succ @ ( succ @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',succ_plus_3_l) ).
thf(112,plain,
! [A: $i] :
( ( plus @ n3 @ A )
= ( succ @ ( succ @ ( succ @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(122,plain,
! [A: $i] :
( ( plus @ A @ n2 )
= ( succ @ ( succ @ A ) ) ),
inference(cnf,[status(esa)],[121]) ).
thf(123,plain,
! [A: $i] :
( ( plus @ A @ n2 )
= ( succ @ ( succ @ A ) ) ),
inference(lifteq,[status(thm)],[122]) ).
thf(9782,plain,
! [B: $i,A: $i] :
( ( lt @ A @ B )
| ( ( gt @ n5 @ tptp_minus_1 )
!= ( gt @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[526,150]) ).
thf(9783,plain,
lt @ tptp_minus_1 @ n5,
inference(pattern_uni,[status(thm)],[9782:[bind(A,$thf( tptp_minus_1 )),bind(B,$thf( n5 ))]]) ).
thf(966,plain,
! [A: $i] :
( ( gt @ n135300 @ n3 )
!= ( gt @ A @ A ) ),
inference(paramod_ordered,[status(thm)],[166,142]) ).
thf(967,plain,
! [A: $i] :
( ( n135300 != A )
| ( n3 != A ) ),
inference(simp,[status(thm)],[966]) ).
thf(968,plain,
n3 != n135300,
inference(simp,[status(thm)],[967]) ).
thf(11572,plain,
! [A: $i] :
( ( gt @ ( succ @ A ) @ A )
!= ( gt @ n4 @ n135300 ) ),
inference(paramod_ordered,[status(thm)],[119,11394]) ).
thf(11614,plain,
! [A: $i] :
( ( ( succ @ A )
!= n4 )
| ( A != n135300 ) ),
inference(simp,[status(thm)],[11572]) ).
thf(11626,plain,
( ( succ @ n135300 )
!= n4 ),
inference(simp,[status(thm)],[11614]) ).
thf(944,plain,
( ( leq @ n0 @ sk3 )
| ( sk1 != n0 )
| ( ( minus @ n0 @ n1 )
!= sk3 ) ),
inference(simp,[status(thm)],[942]) ).
thf(189,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( leq @ ( sk6 @ C @ B @ A ) @ C )
| ~ ( leq @ n0 @ E )
| ~ ( leq @ E @ D )
| ~ ( leq @ n0 @ F )
| ~ ( leq @ F @ D )
| ( ( a_select3 @ ( tptp_mmul @ A @ ( tptp_mmul @ B @ ( trans @ A ) ) ) @ E @ F )
= ( a_select3 @ ( tptp_mmul @ A @ ( tptp_mmul @ B @ ( trans @ A ) ) ) @ F @ E ) ) ),
inference(cnf,[status(esa)],[188]) ).
thf(194,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( a_select3 @ ( tptp_mmul @ A @ ( tptp_mmul @ B @ ( trans @ A ) ) ) @ E @ F )
= ( a_select3 @ ( tptp_mmul @ A @ ( tptp_mmul @ B @ ( trans @ A ) ) ) @ F @ E ) )
| ( leq @ ( sk6 @ C @ B @ A ) @ C )
| ~ ( leq @ n0 @ E )
| ~ ( leq @ E @ D )
| ~ ( leq @ n0 @ F )
| ~ ( leq @ F @ D ) ),
inference(lifteq,[status(thm)],[189]) ).
thf(58,axiom,
! [A: $i] :
( ( plus @ A @ n5 )
= ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',succ_plus_5_r) ).
thf(409,plain,
! [A: $i] :
( ( plus @ A @ n5 )
= ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(969,plain,
! [A: $i] :
( ( gt @ n4 @ n1 )
!= ( gt @ A @ A ) ),
inference(paramod_ordered,[status(thm)],[174,142]) ).
thf(970,plain,
! [A: $i] :
( ( n4 != A )
| ( n1 != A ) ),
inference(simp,[status(thm)],[969]) ).
thf(971,plain,
n4 != n1,
inference(simp,[status(thm)],[970]) ).
thf(2654,plain,
! [A: $i] :
( ( gt @ n135300 @ n5 )
!= ( gt @ A @ A ) ),
inference(paramod_ordered,[status(thm)],[554,142]) ).
thf(2655,plain,
! [A: $i] :
( ( n135300 != A )
| ( n5 != A ) ),
inference(simp,[status(thm)],[2654]) ).
thf(2656,plain,
n5 != n135300,
inference(simp,[status(thm)],[2655]) ).
thf(1582,plain,
( ( ( a_select3 @ q @ pv10 @ sk1 )
!= ( divide @ ( sqrt @ ( times @ ( minus @ ( a_select3 @ center @ sk1 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) @ ( minus @ ( a_select3 @ center @ sk1 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) ) ) @ ( sum @ n0 @ ( minus @ n5 @ n1 ) @ ( sqrt @ ( times @ ( minus @ ( a_select3 @ center @ sk2 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) @ ( minus @ ( a_select3 @ center @ sk2 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) ) ) ) ) )
| ( sk3 != pv10 )
| ( ( leq @ sk3 @ ( minus @ pv10 @ n1 ) )
!= ( leq @ n0 @ pv10 ) ) ),
inference(paramod_ordered,[status(thm)],[96,1555]) ).
thf(1637,plain,
( ( ( a_select3 @ q @ pv10 @ sk1 )
!= ( divide @ ( sqrt @ ( times @ ( minus @ ( a_select3 @ center @ sk1 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) @ ( minus @ ( a_select3 @ center @ sk1 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) ) ) @ ( sum @ n0 @ ( minus @ n5 @ n1 ) @ ( sqrt @ ( times @ ( minus @ ( a_select3 @ center @ sk2 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) @ ( minus @ ( a_select3 @ center @ sk2 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) ) ) ) ) )
| ( sk3 != pv10 )
| ( sk3 != n0 )
| ( ( minus @ pv10 @ n1 )
!= pv10 ) ),
inference(simp,[status(thm)],[1582]) ).
thf(9808,plain,
! [B: $i,A: $i] :
( ( lt @ A @ B )
| ( ( gt @ n4 @ tptp_minus_1 )
!= ( gt @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[151,150]) ).
thf(9809,plain,
lt @ tptp_minus_1 @ n4,
inference(pattern_uni,[status(thm)],[9808:[bind(A,$thf( tptp_minus_1 )),bind(B,$thf( n4 ))]]) ).
thf(49,axiom,
! [A: $i,B: $i] :
( ( leq @ A @ ( pred @ B ) )
<=> ( gt @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',leq_gt_pred) ).
thf(338,plain,
! [A: $i,B: $i] :
( ( ( leq @ A @ ( pred @ B ) )
=> ( gt @ B @ A ) )
& ( ( gt @ B @ A )
=> ( leq @ A @ ( pred @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(12105,plain,
( ( gt @ ( succ @ n5 ) @ n5 )
!= ( gt @ n1 @ n5 ) ),
inference(paramod_ordered,[status(thm)],[11343,11398]) ).
thf(12129,plain,
( ( ( succ @ n5 )
!= n1 )
| ( n5 != n5 ) ),
inference(simp,[status(thm)],[12105]) ).
thf(12163,plain,
( ( succ @ n5 )
!= n1 ),
inference(simp,[status(thm)],[12129]) ).
thf(48,axiom,
( ( succ @ tptp_minus_1 )
= n0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',succ_tptp_minus_1) ).
thf(336,plain,
( ( succ @ tptp_minus_1 )
= n0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(611,plain,
! [A: $i] :
( ( gt @ n135300 @ n2 )
!= ( gt @ A @ A ) ),
inference(paramod_ordered,[status(thm)],[158,142]) ).
thf(612,plain,
! [A: $i] :
( ( n135300 != A )
| ( n2 != A ) ),
inference(simp,[status(thm)],[611]) ).
thf(613,plain,
n2 != n135300,
inference(simp,[status(thm)],[612]) ).
thf(3212,plain,
! [B: $i,A: $i] :
( ( A != B )
| ( ( succ @ ( pred @ A ) )
!= ( succ @ B ) ) ),
inference(paramod_ordered,[status(thm)],[117,3121]) ).
thf(3213,plain,
! [A: $i] :
( ( pred @ A )
!= A ),
inference(pattern_uni,[status(thm)],[3212:[bind(A,$thf( C )),bind(B,$thf( pred @ C ))]]) ).
thf(3224,plain,
! [A: $i] :
( ( pred @ A )
!= A ),
inference(simp,[status(thm)],[3213]) ).
thf(9774,plain,
! [B: $i,A: $i] :
( ( lt @ A @ B )
| ( ( gt @ n4 @ n3 )
!= ( gt @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[133,150]) ).
thf(9775,plain,
lt @ n3 @ n4,
inference(pattern_uni,[status(thm)],[9774:[bind(A,$thf( n3 )),bind(B,$thf( n4 ))]]) ).
thf(11517,plain,
! [B: $i,A: $i] :
( ~ ( gt @ A @ B )
| ( ( gt @ n4 @ tptp_minus_1 )
!= ( gt @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[151,10060]) ).
thf(11518,plain,
~ ( gt @ tptp_minus_1 @ n4 ),
inference(pattern_uni,[status(thm)],[11517:[bind(A,$thf( tptp_minus_1 )),bind(B,$thf( n4 ))]]) ).
thf(1970,plain,
! [A: $i] :
( ( gt @ n3 @ n0 )
!= ( gt @ A @ A ) ),
inference(paramod_ordered,[status(thm)],[404,142]) ).
thf(1971,plain,
! [A: $i] :
( ( n3 != A )
| ( n0 != A ) ),
inference(simp,[status(thm)],[1970]) ).
thf(1972,plain,
n3 != n0,
inference(simp,[status(thm)],[1971]) ).
thf(2318,plain,
! [A: $i] :
( ( gt @ n2 @ n0 )
!= ( gt @ A @ A ) ),
inference(paramod_ordered,[status(thm)],[529,142]) ).
thf(2319,plain,
! [A: $i] :
( ( n2 != A )
| ( n0 != A ) ),
inference(simp,[status(thm)],[2318]) ).
thf(2320,plain,
n2 != n0,
inference(simp,[status(thm)],[2319]) ).
thf(11449,plain,
! [B: $i,A: $i] :
( ~ ( gt @ A @ B )
| ( ( gt @ n2 @ n1 )
!= ( gt @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[551,10060]) ).
thf(11450,plain,
~ ( gt @ n1 @ n2 ),
inference(pattern_uni,[status(thm)],[11449:[bind(A,$thf( n1 )),bind(B,$thf( n2 ))]]) ).
thf(80,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( leq @ A @ B )
& ( leq @ B @ C ) )
=> ( leq @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity_leq) ).
thf(539,plain,
! [A: $i,B: $i,C: $i] :
( ( ( leq @ A @ B )
& ( leq @ B @ C ) )
=> ( leq @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(10525,plain,
! [B: $i,A: $i] :
( ( gt @ n0 @ sk3 )
| ( leq @ sk1 @ ( minus @ n0 @ n1 ) )
| ( lt @ A @ B )
| ( ( gt @ sk3 @ n0 )
!= ( gt @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[8701,150]) ).
thf(10526,plain,
( ( gt @ n0 @ sk3 )
| ( leq @ sk1 @ ( minus @ n0 @ n1 ) )
| ( lt @ n0 @ sk3 ) ),
inference(pattern_uni,[status(thm)],[10525:[bind(A,$thf( n0 )),bind(B,$thf( sk3 ))]]) ).
thf(9754,plain,
! [B: $i,A: $i] :
( ( lt @ A @ B )
| ( ( gt @ n5 @ n1 )
!= ( gt @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[555,150]) ).
thf(9755,plain,
lt @ n1 @ n5,
inference(pattern_uni,[status(thm)],[9754:[bind(A,$thf( n1 )),bind(B,$thf( n5 ))]]) ).
thf(11481,plain,
! [B: $i,A: $i] :
( ~ ( gt @ A @ B )
| ( ( gt @ n1 @ n0 )
!= ( gt @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[545,10060]) ).
thf(11482,plain,
~ ( gt @ n0 @ n1 ),
inference(pattern_uni,[status(thm)],[11481:[bind(A,$thf( n0 )),bind(B,$thf( n1 ))]]) ).
thf(32,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( leq @ B @ A )
& ( leq @ A @ C )
& ( leq @ E @ D )
& ( leq @ D @ F ) )
=> ( ( a_select3 @ ( tptp_const_array2 @ ( dim @ B @ C ) @ ( dim @ E @ F ) @ G ) @ A @ D )
= G ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',const_array2_select) ).
thf(183,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( leq @ B @ A )
& ( leq @ A @ C )
& ( leq @ E @ D )
& ( leq @ D @ F ) )
=> ( ( a_select3 @ ( tptp_const_array2 @ ( dim @ B @ C ) @ ( dim @ E @ F ) @ G ) @ A @ D )
= G ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(184,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( leq @ B @ A )
& ( leq @ A @ C )
& ( leq @ E @ D )
& ( leq @ D @ F ) )
=> ! [G: $i] :
( ( a_select3 @ ( tptp_const_array2 @ ( dim @ B @ C ) @ ( dim @ E @ F ) @ G ) @ A @ D )
= G ) ),
inference(miniscope,[status(thm)],[183]) ).
thf(185,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( leq @ B @ A )
| ~ ( leq @ A @ C )
| ~ ( leq @ E @ D )
| ~ ( leq @ D @ F )
| ( ( a_select3 @ ( tptp_const_array2 @ ( dim @ B @ C ) @ ( dim @ E @ F ) @ G ) @ A @ D )
= G ) ),
inference(cnf,[status(esa)],[184]) ).
thf(186,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( a_select3 @ ( tptp_const_array2 @ ( dim @ B @ C ) @ ( dim @ E @ F ) @ G ) @ A @ D )
= G )
| ~ ( leq @ B @ A )
| ~ ( leq @ A @ C )
| ~ ( leq @ E @ D )
| ~ ( leq @ D @ F ) ),
inference(lifteq,[status(thm)],[185]) ).
thf(113,plain,
! [A: $i] :
( ( plus @ n3 @ A )
= ( succ @ ( succ @ ( succ @ A ) ) ) ),
inference(cnf,[status(esa)],[112]) ).
thf(114,plain,
! [A: $i] :
( ( plus @ n3 @ A )
= ( succ @ ( succ @ ( succ @ A ) ) ) ),
inference(lifteq,[status(thm)],[113]) ).
thf(168,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( a_select2 @ C @ ( sk5 @ D @ C @ B @ A ) )
!= D )
| ~ ( leq @ n0 @ A )
| ~ ( leq @ A @ B )
| ( ( a_select2 @ ( tptp_update2 @ C @ B @ D ) @ A )
= D ) ),
inference(cnf,[status(esa)],[167]) ).
thf(171,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( a_select2 @ C @ ( sk5 @ D @ C @ B @ A ) )
!= D )
| ( ( a_select2 @ ( tptp_update2 @ C @ B @ D ) @ A )
= D )
| ~ ( leq @ n0 @ A )
| ~ ( leq @ A @ B ) ),
inference(lifteq,[status(thm)],[168]) ).
thf(41,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ! [I: $i,J: $i] :
( ( ( leq @ n0 @ I )
& ( leq @ I @ H )
& ( leq @ n0 @ J )
& ( leq @ J @ H ) )
=> ( ( a_select3 @ D @ I @ J )
= ( a_select3 @ D @ J @ I ) ) )
& ! [I: $i,J: $i] :
( ( ( leq @ n0 @ I )
& ( leq @ I @ G )
& ( leq @ n0 @ J )
& ( leq @ J @ G ) )
=> ( ( a_select3 @ A @ I @ J )
= ( a_select3 @ A @ J @ I ) ) )
& ! [I: $i,J: $i] :
( ( ( leq @ n0 @ I )
& ( leq @ I @ G )
& ( leq @ n0 @ J )
& ( leq @ J @ G ) )
=> ( ( a_select3 @ F @ I @ J )
= ( a_select3 @ F @ J @ I ) ) ) )
=> ! [I: $i,J: $i] :
( ( ( leq @ n0 @ I )
& ( leq @ I @ G )
& ( leq @ n0 @ J )
& ( leq @ J @ G ) )
=> ( ( a_select3 @ ( tptp_madd @ A @ ( tptp_mmul @ B @ ( tptp_mmul @ ( tptp_madd @ ( tptp_mmul @ C @ ( tptp_mmul @ D @ ( trans @ C ) ) ) @ ( tptp_mmul @ E @ ( tptp_mmul @ F @ ( trans @ E ) ) ) ) @ ( trans @ B ) ) ) ) @ I @ J )
= ( a_select3 @ ( tptp_madd @ A @ ( tptp_mmul @ B @ ( tptp_mmul @ ( tptp_madd @ ( tptp_mmul @ C @ ( tptp_mmul @ D @ ( trans @ C ) ) ) @ ( tptp_mmul @ E @ ( tptp_mmul @ F @ ( trans @ E ) ) ) ) @ ( trans @ B ) ) ) ) @ J @ I ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',matrix_symm_joseph_update) ).
thf(235,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ! [I: $i,J: $i] :
( ( ( leq @ n0 @ I )
& ( leq @ I @ H )
& ( leq @ n0 @ J )
& ( leq @ J @ H ) )
=> ( ( a_select3 @ D @ I @ J )
= ( a_select3 @ D @ J @ I ) ) )
& ! [I: $i,J: $i] :
( ( ( leq @ n0 @ I )
& ( leq @ I @ G )
& ( leq @ n0 @ J )
& ( leq @ J @ G ) )
=> ( ( a_select3 @ A @ I @ J )
= ( a_select3 @ A @ J @ I ) ) )
& ! [I: $i,J: $i] :
( ( ( leq @ n0 @ I )
& ( leq @ I @ G )
& ( leq @ n0 @ J )
& ( leq @ J @ G ) )
=> ( ( a_select3 @ F @ I @ J )
= ( a_select3 @ F @ J @ I ) ) ) )
=> ! [I: $i,J: $i] :
( ( ( leq @ n0 @ I )
& ( leq @ I @ G )
& ( leq @ n0 @ J )
& ( leq @ J @ G ) )
=> ( ( a_select3 @ ( tptp_madd @ A @ ( tptp_mmul @ B @ ( tptp_mmul @ ( tptp_madd @ ( tptp_mmul @ C @ ( tptp_mmul @ D @ ( trans @ C ) ) ) @ ( tptp_mmul @ E @ ( tptp_mmul @ F @ ( trans @ E ) ) ) ) @ ( trans @ B ) ) ) ) @ I @ J )
= ( a_select3 @ ( tptp_madd @ A @ ( tptp_mmul @ B @ ( tptp_mmul @ ( tptp_madd @ ( tptp_mmul @ C @ ( tptp_mmul @ D @ ( trans @ C ) ) ) @ ( tptp_mmul @ E @ ( tptp_mmul @ F @ ( trans @ E ) ) ) ) @ ( trans @ B ) ) ) ) @ J @ I ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(201,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( leq @ ( sk8 @ B @ A ) @ B )
| ~ ( leq @ n0 @ C )
| ~ ( leq @ C @ B )
| ~ ( leq @ n0 @ D )
| ~ ( leq @ D @ B )
| ~ ( leq @ n0 @ E )
| ~ ( leq @ E @ B )
| ( ( a_select3 @ ( tptp_update3 @ A @ E @ E @ F ) @ C @ D )
= ( a_select3 @ ( tptp_update3 @ A @ E @ E @ F ) @ D @ C ) ) ),
inference(cnf,[status(esa)],[200]) ).
thf(207,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( a_select3 @ ( tptp_update3 @ A @ E @ E @ F ) @ C @ D )
= ( a_select3 @ ( tptp_update3 @ A @ E @ E @ F ) @ D @ C ) )
| ( leq @ ( sk8 @ B @ A ) @ B )
| ~ ( leq @ n0 @ C )
| ~ ( leq @ C @ B )
| ~ ( leq @ n0 @ D )
| ~ ( leq @ D @ B )
| ~ ( leq @ n0 @ E )
| ~ ( leq @ E @ B ) ),
inference(lifteq,[status(thm)],[201]) ).
thf(9798,plain,
! [B: $i,A: $i] :
( ( lt @ A @ B )
| ( ( gt @ n4 @ n0 )
!= ( gt @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[535,150]) ).
thf(9799,plain,
lt @ n0 @ n4,
inference(pattern_uni,[status(thm)],[9798:[bind(A,$thf( n0 )),bind(B,$thf( n4 ))]]) ).
thf(212,plain,
( ! [A: $i,B: $i] :
( ( leq @ ( succ @ A ) @ ( succ @ B ) )
=> ( leq @ A @ B ) )
& ! [A: $i,B: $i] :
( ( leq @ A @ B )
=> ( leq @ ( succ @ A ) @ ( succ @ B ) ) ) ),
inference(miniscope,[status(thm)],[211]) ).
thf(214,plain,
! [B: $i,A: $i] :
( ~ ( leq @ ( succ @ A ) @ ( succ @ B ) )
| ( leq @ A @ B ) ),
inference(cnf,[status(esa)],[212]) ).
thf(11421,plain,
! [B: $i,A: $i] :
( ~ ( gt @ A @ B )
| ( ( gt @ n3 @ n0 )
!= ( gt @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[404,10060]) ).
thf(11422,plain,
~ ( gt @ n0 @ n3 ),
inference(pattern_uni,[status(thm)],[11421:[bind(A,$thf( n0 )),bind(B,$thf( n3 ))]]) ).
thf(13680,plain,
( ( leq @ sk1 @ ( minus @ n0 @ n1 ) )
| ( sk3 != tptp_minus_1 )
| ( ( gt @ n0 @ sk3 )
!= ( gt @ n0 @ n3 ) ) ),
inference(paramod_ordered,[status(thm)],[13569,11422]) ).
thf(13707,plain,
( ( leq @ sk1 @ ( minus @ n0 @ n1 ) )
| ( sk3 != tptp_minus_1 )
| ( n0 != n0 )
| ( sk3 != n3 ) ),
inference(simp,[status(thm)],[13680]) ).
thf(13711,plain,
( ( leq @ sk1 @ ( minus @ n0 @ n1 ) )
| ( sk3 != tptp_minus_1 )
| ( sk3 != n3 ) ),
inference(simp,[status(thm)],[13707]) ).
thf(1977,plain,
( ( sk3 != sk1 )
| ( ( a_select3 @ q @ pv10 @ sk1 )
!= ( divide @ ( sqrt @ ( times @ ( minus @ ( a_select3 @ center @ sk1 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) @ ( minus @ ( a_select3 @ center @ sk1 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) ) ) @ ( sum @ n0 @ ( minus @ n5 @ n1 ) @ ( sqrt @ ( times @ ( minus @ ( a_select3 @ center @ sk2 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) @ ( minus @ ( a_select3 @ center @ sk2 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) ) ) ) ) )
| ( ( leq @ sk3 @ ( minus @ pv10 @ n1 ) )
!= ( leq @ n0 @ pv10 ) ) ),
inference(paramod_ordered,[status(thm)],[96,1556]) ).
thf(2036,plain,
( ( sk3 != sk1 )
| ( ( a_select3 @ q @ pv10 @ sk1 )
!= ( divide @ ( sqrt @ ( times @ ( minus @ ( a_select3 @ center @ sk1 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) @ ( minus @ ( a_select3 @ center @ sk1 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) ) ) @ ( sum @ n0 @ ( minus @ n5 @ n1 ) @ ( sqrt @ ( times @ ( minus @ ( a_select3 @ center @ sk2 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) @ ( minus @ ( a_select3 @ center @ sk2 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) ) ) ) ) )
| ( sk3 != n0 )
| ( ( minus @ pv10 @ n1 )
!= pv10 ) ),
inference(simp,[status(thm)],[1977]) ).
thf(9786,plain,
! [B: $i,A: $i] :
( ( lt @ A @ B )
| ( ( gt @ n2 @ tptp_minus_1 )
!= ( gt @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[128,150]) ).
thf(9787,plain,
lt @ tptp_minus_1 @ n2,
inference(pattern_uni,[status(thm)],[9786:[bind(A,$thf( tptp_minus_1 )),bind(B,$thf( n2 ))]]) ).
thf(11417,plain,
! [B: $i,A: $i] :
( ~ ( gt @ A @ B )
| ( ( gt @ n4 @ n1 )
!= ( gt @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[174,10060]) ).
thf(11418,plain,
~ ( gt @ n1 @ n4 ),
inference(pattern_uni,[status(thm)],[11417:[bind(A,$thf( n1 )),bind(B,$thf( n4 ))]]) ).
thf(79,axiom,
! [A: $i] :
( ( ( leq @ n0 @ A )
& ( leq @ A @ n3 ) )
=> ( ( A = n0 )
| ( A = n1 )
| ( A = n2 )
| ( A = n3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',finite_domain_3) ).
thf(536,plain,
! [A: $i] :
( ( ( leq @ n0 @ A )
& ( leq @ A @ n3 ) )
=> ( ( A = n0 )
| ( A = n1 )
| ( A = n2 )
| ( A = n3 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(9581,plain,
! [A: $i] :
( ( ( succ @ n5 )
!= A )
| ( ( succ @ ( succ @ ( succ @ n3 ) ) )
!= ( succ @ A ) ) ),
inference(paramod_ordered,[status(thm)],[9580,3121]) ).
thf(9582,plain,
( ( succ @ ( succ @ n3 ) )
!= ( succ @ n5 ) ),
inference(pattern_uni,[status(thm)],[9581:[bind(A,$thf( succ @ ( succ @ n3 ) ))]]) ).
thf(9711,plain,
( ( succ @ n5 )
!= n5 ),
inference(rewrite,[status(thm)],[9582,3383]) ).
thf(56,axiom,
! [A: $i] :
( ( ( leq @ n0 @ A )
& ( leq @ A @ n1 ) )
=> ( ( A = n0 )
| ( A = n1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',finite_domain_1) ).
thf(405,plain,
! [A: $i] :
( ( ( leq @ n0 @ A )
& ( leq @ A @ n1 ) )
=> ( ( A = n0 )
| ( A = n1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(16544,plain,
( ( leq @ sk1 @ ( minus @ n0 @ n1 ) )
| ( sk3 != tptp_minus_1 )
| ( ( gt @ sk3 @ n0 )
!= ( gt @ n1 @ n0 ) ) ),
inference(paramod_ordered,[status(thm)],[545,13695]) ).
thf(16588,plain,
( ( leq @ sk1 @ ( minus @ n0 @ n1 ) )
| ( sk3 != tptp_minus_1 )
| ( sk3 != n1 )
| ( n0 != n0 ) ),
inference(simp,[status(thm)],[16544]) ).
thf(16610,plain,
( ( leq @ sk1 @ ( minus @ n0 @ n1 ) )
| ( sk3 != tptp_minus_1 )
| ( sk3 != n1 ) ),
inference(simp,[status(thm)],[16588]) ).
thf(1227,plain,
! [A: $i] :
( ( gt @ n0 @ tptp_minus_1 )
!= ( gt @ A @ A ) ),
inference(paramod_ordered,[status(thm)],[228,142]) ).
thf(1228,plain,
! [A: $i] :
( ( n0 != A )
| ( tptp_minus_1 != A ) ),
inference(simp,[status(thm)],[1227]) ).
thf(1229,plain,
tptp_minus_1 != n0,
inference(simp,[status(thm)],[1228]) ).
thf(9766,plain,
! [B: $i,A: $i] :
( ( lt @ A @ B )
| ( ( gt @ n3 @ n1 )
!= ( gt @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[157,150]) ).
thf(9767,plain,
lt @ n1 @ n3,
inference(pattern_uni,[status(thm)],[9766:[bind(A,$thf( n1 )),bind(B,$thf( n3 ))]]) ).
thf(13603,plain,
! [A: $i] :
( ( gt @ ( succ @ A ) @ A )
!= ( gt @ n3 @ n5 ) ),
inference(paramod_ordered,[status(thm)],[119,11434]) ).
thf(13635,plain,
! [A: $i] :
( ( ( succ @ A )
!= n3 )
| ( A != n5 ) ),
inference(simp,[status(thm)],[13603]) ).
thf(13652,plain,
( ( succ @ n5 )
!= n3 ),
inference(simp,[status(thm)],[13635]) ).
thf(203,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( leq @ ( sk9 @ B @ A ) @ B )
| ~ ( leq @ n0 @ C )
| ~ ( leq @ C @ B )
| ~ ( leq @ n0 @ D )
| ~ ( leq @ D @ B )
| ~ ( leq @ n0 @ E )
| ~ ( leq @ E @ B )
| ( ( a_select3 @ ( tptp_update3 @ A @ E @ E @ F ) @ C @ D )
= ( a_select3 @ ( tptp_update3 @ A @ E @ E @ F ) @ D @ C ) ) ),
inference(cnf,[status(esa)],[200]) ).
thf(210,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( a_select3 @ ( tptp_update3 @ A @ E @ E @ F ) @ C @ D )
= ( a_select3 @ ( tptp_update3 @ A @ E @ E @ F ) @ D @ C ) )
| ( leq @ ( sk9 @ B @ A ) @ B )
| ~ ( leq @ n0 @ C )
| ~ ( leq @ C @ B )
| ~ ( leq @ n0 @ D )
| ~ ( leq @ D @ B )
| ~ ( leq @ n0 @ E )
| ~ ( leq @ E @ B ) ),
inference(lifteq,[status(thm)],[203]) ).
thf(8399,plain,
! [A: $i] :
( ( ( pred @ n5 )
= A )
| ( ( succ @ n4 )
!= ( succ @ A ) ) ),
inference(paramod_ordered,[status(thm)],[3247,136]) ).
thf(8400,plain,
( ( pred @ n5 )
= n4 ),
inference(pattern_uni,[status(thm)],[8399:[bind(A,$thf( n4 ))]]) ).
thf(192,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( leq @ n0 @ ( sk7 @ C @ B @ A ) )
| ~ ( leq @ n0 @ E )
| ~ ( leq @ E @ D )
| ~ ( leq @ n0 @ F )
| ~ ( leq @ F @ D )
| ( ( a_select3 @ ( tptp_mmul @ A @ ( tptp_mmul @ B @ ( trans @ A ) ) ) @ E @ F )
= ( a_select3 @ ( tptp_mmul @ A @ ( tptp_mmul @ B @ ( trans @ A ) ) ) @ F @ E ) ) ),
inference(cnf,[status(esa)],[188]) ).
thf(195,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( a_select3 @ ( tptp_mmul @ A @ ( tptp_mmul @ B @ ( trans @ A ) ) ) @ E @ F )
= ( a_select3 @ ( tptp_mmul @ A @ ( tptp_mmul @ B @ ( trans @ A ) ) ) @ F @ E ) )
| ( leq @ n0 @ ( sk7 @ C @ B @ A ) )
| ~ ( leq @ n0 @ E )
| ~ ( leq @ E @ D )
| ~ ( leq @ n0 @ F )
| ~ ( leq @ F @ D ) ),
inference(lifteq,[status(thm)],[192]) ).
thf(337,plain,
( ( succ @ tptp_minus_1 )
= n0 ),
inference(lifteq,[status(thm)],[336]) ).
thf(8423,plain,
! [A: $i] :
( ( ( pred @ n0 )
= A )
| ( ( succ @ tptp_minus_1 )
!= ( succ @ A ) ) ),
inference(paramod_ordered,[status(thm)],[337,136]) ).
thf(8424,plain,
( ( pred @ n0 )
= tptp_minus_1 ),
inference(pattern_uni,[status(thm)],[8423:[bind(A,$thf( tptp_minus_1 ))]]) ).
thf(11521,plain,
! [B: $i,A: $i] :
( ~ ( gt @ A @ B )
| ( ( gt @ n5 @ n0 )
!= ( gt @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[332,10060]) ).
thf(11522,plain,
~ ( gt @ n0 @ n5 ),
inference(pattern_uni,[status(thm)],[11521:[bind(A,$thf( n0 )),bind(B,$thf( n5 ))]]) ).
thf(11461,plain,
! [B: $i,A: $i] :
( ~ ( gt @ A @ B )
| ( ( gt @ n5 @ n4 )
!= ( gt @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[541,10060]) ).
thf(11462,plain,
~ ( gt @ n4 @ n5 ),
inference(pattern_uni,[status(thm)],[11461:[bind(A,$thf( n4 )),bind(B,$thf( n5 ))]]) ).
thf(17702,plain,
( ( gt @ ( succ @ n5 ) @ n5 )
!= ( gt @ n4 @ n5 ) ),
inference(paramod_ordered,[status(thm)],[11343,11462]) ).
thf(17746,plain,
( ( ( succ @ n5 )
!= n4 )
| ( n5 != n5 ) ),
inference(simp,[status(thm)],[17702]) ).
thf(17765,plain,
( ( succ @ n5 )
!= n4 ),
inference(simp,[status(thm)],[17746]) ).
thf(9794,plain,
! [B: $i,A: $i] :
( ( lt @ A @ B )
| ( ( gt @ n1 @ n0 )
!= ( gt @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[545,150]) ).
thf(9795,plain,
lt @ n0 @ n1,
inference(pattern_uni,[status(thm)],[9794:[bind(A,$thf( n0 )),bind(B,$thf( n1 ))]]) ).
thf(125,plain,
! [A: $i] :
( ( plus @ A @ n3 )
= ( succ @ ( succ @ ( succ @ A ) ) ) ),
inference(cnf,[status(esa)],[124]) ).
thf(126,plain,
! [A: $i] :
( ( plus @ A @ n3 )
= ( succ @ ( succ @ ( succ @ A ) ) ) ),
inference(lifteq,[status(thm)],[125]) ).
thf(77,axiom,
! [A: $i] :
( ( plus @ n1 @ A )
= ( succ @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',succ_plus_1_l) ).
thf(532,plain,
! [A: $i] :
( ( plus @ n1 @ A )
= ( succ @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(100,plain,
( ~ ( leq @ n0 @ pv10 )
| ~ ( leq @ pv10 @ ( minus @ n135300 @ n1 ) )
| ( ( a_select3 @ q @ pv10 @ sk1 )
!= ( divide @ ( sqrt @ ( times @ ( minus @ ( a_select3 @ center @ sk1 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) @ ( minus @ ( a_select3 @ center @ sk1 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) ) ) @ ( sum @ n0 @ ( minus @ n5 @ n1 ) @ ( sqrt @ ( times @ ( minus @ ( a_select3 @ center @ sk2 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) @ ( minus @ ( a_select3 @ center @ sk2 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) ) ) ) ) )
| ( leq @ sk3 @ ( minus @ pv10 @ n1 ) ) ),
inference(cnf,[status(esa)],[93]) ).
thf(109,plain,
( ( ( a_select3 @ q @ pv10 @ sk1 )
!= ( divide @ ( sqrt @ ( times @ ( minus @ ( a_select3 @ center @ sk1 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) @ ( minus @ ( a_select3 @ center @ sk1 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) ) ) @ ( sum @ n0 @ ( minus @ n5 @ n1 ) @ ( sqrt @ ( times @ ( minus @ ( a_select3 @ center @ sk2 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) @ ( minus @ ( a_select3 @ center @ sk2 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) ) ) ) ) )
| ~ ( leq @ n0 @ pv10 )
| ~ ( leq @ pv10 @ ( minus @ n135300 @ n1 ) )
| ( leq @ sk3 @ ( minus @ pv10 @ n1 ) ) ),
inference(lifteq,[status(thm)],[100]) ).
thf(2240,plain,
( ( ( a_select3 @ q @ pv10 @ sk1 )
!= ( divide @ ( sqrt @ ( times @ ( minus @ ( a_select3 @ center @ sk1 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) @ ( minus @ ( a_select3 @ center @ sk1 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) ) ) @ ( sum @ n0 @ ( minus @ n5 @ n1 ) @ ( sqrt @ ( times @ ( minus @ ( a_select3 @ center @ sk2 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) @ ( minus @ ( a_select3 @ center @ sk2 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) ) ) ) ) )
| ~ $true
| ~ $true
| ( leq @ sk3 @ ( minus @ pv10 @ n1 ) ) ),
inference(rewrite,[status(thm)],[109,96,95]) ).
thf(2241,plain,
( ( ( a_select3 @ q @ pv10 @ sk1 )
!= ( divide @ ( sqrt @ ( times @ ( minus @ ( a_select3 @ center @ sk1 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) @ ( minus @ ( a_select3 @ center @ sk1 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) ) ) @ ( sum @ n0 @ ( minus @ n5 @ n1 ) @ ( sqrt @ ( times @ ( minus @ ( a_select3 @ center @ sk2 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) @ ( minus @ ( a_select3 @ center @ sk2 @ n0 ) @ ( a_select2 @ x @ pv10 ) ) ) ) ) ) )
| ( leq @ sk3 @ ( minus @ pv10 @ n1 ) ) ),
inference(simp,[status(thm)],[2240]) ).
thf(9762,plain,
! [B: $i,A: $i] :
( ( lt @ A @ B )
| ( ( gt @ n4 @ n1 )
!= ( gt @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[174,150]) ).
thf(9763,plain,
lt @ n1 @ n4,
inference(pattern_uni,[status(thm)],[9762:[bind(A,$thf( n1 )),bind(B,$thf( n4 ))]]) ).
thf(17898,plain,
! [A: $i] :
( ( gt @ ( succ @ A ) @ A )
!= ( gt @ n1 @ n135300 ) ),
inference(paramod_ordered,[status(thm)],[119,11470]) ).
thf(17918,plain,
! [A: $i] :
( ( ( succ @ A )
!= n1 )
| ( A != n135300 ) ),
inference(simp,[status(thm)],[17898]) ).
thf(17954,plain,
( ( succ @ n135300 )
!= n1 ),
inference(simp,[status(thm)],[17918]) ).
thf(13677,plain,
! [B: $i,A: $i] :
( ( leq @ sk1 @ ( minus @ n0 @ n1 ) )
| ( sk3 != tptp_minus_1 )
| ( lt @ A @ B )
| ( ( gt @ n0 @ sk3 )
!= ( gt @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[13569,150]) ).
thf(13678,plain,
( ( leq @ sk1 @ ( minus @ n0 @ n1 ) )
| ( sk3 != tptp_minus_1 )
| ( lt @ sk3 @ n0 ) ),
inference(pattern_uni,[status(thm)],[13677:[bind(A,$thf( sk3 )),bind(B,$thf( n0 ))]]) ).
thf(64,axiom,
! [A: $i,B: $i] :
( ( leq @ A @ B )
<=> ( gt @ ( succ @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',leq_succ_gt_equiv) ).
thf(486,plain,
! [A: $i,B: $i] :
( ( ( leq @ A @ B )
=> ( gt @ ( succ @ B ) @ A ) )
& ( ( gt @ ( succ @ B ) @ A )
=> ( leq @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(11533,plain,
! [B: $i,A: $i] :
( ~ ( gt @ A @ B )
| ( ( gt @ n135300 @ n0 )
!= ( gt @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[322,10060]) ).
thf(11534,plain,
~ ( gt @ n0 @ n135300 ),
inference(pattern_uni,[status(thm)],[11533:[bind(A,$thf( n0 )),bind(B,$thf( n135300 ))]]) ).
thf(213,plain,
! [B: $i,A: $i] :
( ~ ( leq @ A @ B )
| ( leq @ ( succ @ A ) @ ( succ @ B ) ) ),
inference(cnf,[status(esa)],[212]) ).
thf(215,plain,
! [B: $i,A: $i] :
( ~ ( leq @ A @ B )
| ( leq @ ( succ @ A ) @ ( succ @ B ) ) ),
inference(simp,[status(thm)],[213]) ).
thf(40,axiom,
! [A: $i] :
( ( ( leq @ n0 @ A )
& ( leq @ A @ n0 ) )
=> ( A = n0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',finite_domain_0) ).
thf(232,plain,
! [A: $i] :
( ( ( leq @ n0 @ A )
& ( leq @ A @ n0 ) )
=> ( A = n0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(33677,plain,
$false,
inference(e,[status(thm)],[1879,8398,347,333,14944,11394,555,408,9791,217,2659,8402,9769,9337,120,511,9759,1406,115,472,3121,9801,153,930,142,16613,1196,2972,2491,8325,417,2010,12257,565,174,404,11426,570,2735,504,1313,2488,9805,196,11458,344,19472,542,157,152,228,1641,1232,9580,11510,421,216,475,179,211,9811,1858,121,11398,11446,9781,9779,602,1896,8406,132,2137,133,11490,3559,507,206,1975,527,11357,117,512,529,546,9797,9785,11410,9881,8343,9753,9817,1676,160,8334,137,165,16616,2396,92,197,1555,493,551,2653,229,566,156,8414,9773,610,328,124,554,526,11442,2317,96,515,8326,9761,11474,173,129,3247,2766,134,541,398,1466,530,586,128,343,412,11506,9765,166,161,11343,149,16612,16496,180,584,11434,3234,3086,13569,118,545,1707,11466,11502,9803,8387,159,7995,187,172,9771,567,509,11438,9789,208,11406,16404,9757,11470,552,323,140,1556,943,198,535,8156,2075,167,11402,589,548,22110,9777,209,112,123,9783,968,11626,531,944,194,145,557,150,8701,409,971,95,2656,199,1637,182,331,9809,127,338,12163,336,2992,613,154,3224,175,143,9775,11518,1972,2320,556,11450,539,10526,9755,2594,11482,3383,158,186,114,401,171,139,119,235,207,1212,9799,214,13711,11454,1893,2036,9787,11418,2779,536,151,9711,405,16610,146,1229,9767,13695,183,13652,210,107,8400,195,8424,11522,17765,9795,2783,126,136,11422,532,2241,332,9763,131,11462,163,11430,17954,13678,10060,322,486,337,11534,215,491,232]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWV055+1 : TPTP v8.2.0. Bugfixed v3.3.0.
% 0.03/0.12 % Command : run_Leo-III %s %d THM
% 0.12/0.33 % Computer : n025.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 : 300
% 0.12/0.33 % DateTime : Thu Jun 20 17:31:10 EDT 2024
% 0.12/0.34 % CPUTime :
% 0.96/0.86 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.22/1.00 % [INFO] Parsing done (133ms).
% 1.22/1.00 % [INFO] Running in sequential loop mode.
% 1.80/1.20 % [INFO] eprover registered as external prover.
% 1.80/1.20 % [INFO] Scanning for conjecture ...
% 2.02/1.29 % [INFO] Found a conjecture (or negated_conjecture) and 91 axioms. Running axiom selection ...
% 2.30/1.35 % [INFO] Axiom selection finished. Selected 89 axioms (removed 2 axioms).
% 2.51/1.43 % [INFO] Problem is first-order (TPTP FOF).
% 2.51/1.44 % [INFO] Type checking passed.
% 2.51/1.44 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 74.25/18.42 % External prover 'e' found a proof!
% 74.25/18.42 % [INFO] Killing All external provers ...
% 74.25/18.42 % Time passed: 17889ms (effective reasoning time: 17411ms)
% 74.25/18.42 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 74.25/18.42 % Axioms used in derivation (89): sel3_update_2, gt_135300_0, gt_0_tptp_minus_1, gt_3_1, leq_minus, sel2_update_2, succ_plus_5_l, lt_gt, gt_5_tptp_minus_1, succ_plus_3_r, gt_4_3, transitivity_gt, matrix_symm_inv, matrix_symm_trans, finite_domain_1, gt_5_0, const_array2_select, gt_2_tptp_minus_1, gt_135300_1, sel3_update_3, leq_geq, gt_1_0, leq_gt2, gt_5_4, gt_135300_5, succ_plus_1_l, gt_3_2, matrix_symm_add, leq_succ_gt, finite_domain_5, pred_minus_1, successor_3, gt_3_tptp_minus_1, matrix_symm_update_diagonal, sel2_update_1, gt_4_2, matrix_symm_sub, gt_135300_4, gt_5_3, successor_4, gt_succ, succ_plus_4_l, reflexivity_leq, successor_2, leq_gt1, gt_1_tptp_minus_1, finite_domain_2, matrix_symm_aba1, finite_domain_4, matrix_symm_aba2, succ_tptp_minus_1, succ_plus_5_r, gt_135300_3, leq_succ_succ, sum_plus_base_float, succ_plus_2_l, gt_4_1, gt_2_0, gt_5_2, const_array1_select, leq_gt_pred, matrix_symm_joseph_update, succ_pred, totality, transitivity_leq, finite_domain_3, uniform_int_rand_ranges_lo, sel3_update_1, successor_1, gt_135300_tptp_minus_1, sum_plus_base, irreflexivity_gt, successor_5, gt_3_0, sel2_update_3, pred_succ, gt_135300_2, succ_plus_1_r, succ_plus_3_l, gt_4_tptp_minus_1, succ_plus_4_r, gt_4_0, succ_plus_2_r, leq_succ_gt_equiv, gt_5_1, uniform_int_rand_ranges_hi, gt_2_1, finite_domain_0, leq_succ
% 74.25/18.42 % No. of inferences in proof: 672
% 74.25/18.42 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 17889 ms resp. 17411 ms w/o parsing
% 74.75/18.55 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 74.75/18.56 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------