TSTP Solution File: GEO499+1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : GEO499+1 : TPTP v8.1.2. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 19 11:11:03 EDT 2023
% Result : Theorem 31.12s 6.60s
% Output : Refutation 31.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 140
% Syntax : Number of formulae : 258 ( 37 unt; 24 typ; 0 def)
% Number of atoms : 931 ( 168 equ; 0 cnn)
% Maximal formula atoms : 19 ( 3 avg)
% Number of connectives : 4360 ( 509 ~; 597 |; 100 &;3154 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 29 ( 12 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 92 ( 92 >; 0 *; 0 +; 0 <<)
% Number of symbols : 26 ( 24 usr; 5 con; 0-8 aty)
% Number of variables : 896 ( 0 ^; 896 !; 0 ?; 896 :)
% Comments :
%------------------------------------------------------------------------------
thf(s_t_type,type,
s_t: $i > $i > $i > $o ).
thf(s_type,type,
s: $i > $i > $i ).
thf(s_col_type,type,
s_col: $i > $i > $i > $o ).
thf(s_e_type,type,
s_e: $i > $i > $i > $i > $o ).
thf(s_e3_type,type,
s_e3: $i > $i > $i > $i > $i > $i > $o ).
thf(insert5_type,type,
insert5: $i > $i > $i > $i > $i > $i ).
thf(s_fs_type,type,
s_fs: $i > $i > $i > $i > $i > $i > $i > $i > $o ).
thf(s_m_type,type,
s_m: $i > $i > $i > $o ).
thf(sameside_type,type,
sameside: $i > $i > $i > $o ).
thf(le_type,type,
le: $i > $i > $i > $i > $o ).
thf(alpha_type,type,
alpha: $i ).
thf(beta_type,type,
beta: $i ).
thf(pointOffLine_type,type,
pointOffLine: $i > $i > $i ).
thf(insert_type,type,
insert: $i > $i > $i > $i > $i ).
thf(ext_type,type,
ext: $i > $i > $i > $i > $i ).
thf(gamma_type,type,
gamma: $i ).
thf(s_ifs_type,type,
s_ifs: $i > $i > $i > $i > $i > $i > $i > $i > $o ).
thf(ip_type,type,
ip: $i > $i > $i > $i > $i > $i ).
thf(s_afs_type,type,
s_afs: $i > $i > $i > $i > $i > $i > $i > $i > $o ).
thf(s_kf_type,type,
s_kf: $i > $i > $i > $i > $i > $i > $i > $o ).
thf(crossbar_type,type,
crossbar: $i > $i > $i > $i > $i > $i > $i ).
thf(c63_type,type,
c63: $i > $i > $i > $i ).
thf(xb_type,type,
xb: $i ).
thf(ins_type,type,
ins: $i > $i > $i > $i > $i ).
thf(5,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( A = B )
| ( C = D )
| ~ ( s_col @ A @ B @ E )
| ~ ( s_col @ C @ D @ E )
| ~ ( s_col @ A @ B @ F )
| ~ ( s_col @ C @ D @ F )
| ( E = F )
| ~ ( s_col @ A @ B @ G )
| ( s_col @ C @ D @ G ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz6_21) ).
thf(129,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( A = B )
| ( C = D )
| ~ ( s_col @ A @ B @ E )
| ~ ( s_col @ C @ D @ E )
| ~ ( s_col @ A @ B @ F )
| ~ ( s_col @ C @ D @ F )
| ( E = F )
| ~ ( s_col @ A @ B @ G )
| ( s_col @ C @ D @ G ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(38,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ~ ( s_e @ A @ B @ C @ D )
| ~ ( s_e @ C @ D @ E @ F )
| ( s_e @ A @ B @ E @ F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz2_3) ).
thf(234,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ~ ( s_e @ A @ B @ C @ D )
| ~ ( s_e @ C @ D @ E @ F )
| ( s_e @ A @ B @ E @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(96,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A = B )
| ( A = C )
| ~ ( s_t @ B @ A @ C )
| ~ ( sameside @ D @ A @ C )
| ( s_col @ D @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz6_15c) ).
thf(481,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A = B )
| ( A = C )
| ~ ( s_t @ B @ A @ C )
| ~ ( sameside @ D @ A @ C )
| ( s_col @ D @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(60,axiom,
! [A: $i,B: $i] :
( ~ ( s_t @ A @ B @ A )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aA6) ).
thf(308,plain,
! [A: $i,B: $i] :
( ~ ( s_t @ A @ B @ A )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(91,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ( s_t @ A @ B @ C )
| ~ ( s_t @ D @ E @ C )
| ~ ( s_t @ A @ F @ D )
| ( s_t @ F @ ( crossbar @ A @ B @ C @ D @ E @ F ) @ C ) )
& ( ~ ( s_t @ A @ B @ C )
| ~ ( s_t @ D @ E @ C )
| ~ ( s_t @ A @ F @ D )
| ( s_t @ B @ ( crossbar @ A @ B @ C @ D @ E @ F ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz3_17) ).
thf(449,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ( s_t @ A @ B @ C )
| ~ ( s_t @ D @ E @ C )
| ~ ( s_t @ A @ F @ D )
| ( s_t @ F @ ( crossbar @ A @ B @ C @ D @ E @ F ) @ C ) )
& ( ~ ( s_t @ A @ B @ C )
| ~ ( s_t @ D @ E @ C )
| ~ ( s_t @ A @ F @ D )
| ( s_t @ B @ ( crossbar @ A @ B @ C @ D @ E @ F ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(43,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( s_e @ A @ B @ C @ C )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aA3) ).
thf(247,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( s_e @ A @ B @ C @ C )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(73,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A = B )
| ( A = C )
| ~ ( s_t @ B @ A @ C )
| ~ ( s_col @ D @ A @ B )
| ( D = A )
| ( sameside @ D @ A @ B )
| ( sameside @ D @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz6_15a) ).
thf(379,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A = B )
| ( A = C )
| ~ ( s_t @ B @ A @ C )
| ~ ( s_col @ D @ A @ B )
| ( D = A )
| ( sameside @ D @ A @ B )
| ( sameside @ D @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(104,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( sameside @ A @ B @ C )
| ( le @ B @ A @ B @ C )
| ~ ( s_t @ B @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz6_13b) ).
thf(511,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( sameside @ A @ B @ C )
| ( le @ B @ A @ B @ C )
| ~ ( s_t @ B @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(28,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A = B )
| ( C = A )
| ~ ( s_col @ A @ B @ C )
| ~ ( s_col @ A @ B @ D )
| ( s_col @ A @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz6_16b) ).
thf(202,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A = B )
| ( C = A )
| ~ ( s_col @ A @ B @ C )
| ~ ( s_col @ A @ B @ D )
| ( s_col @ A @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(113,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( le @ A @ B @ C @ D )
| ( s_t @ A @ B @ ( ins @ C @ D @ A @ B ) ) )
& ( ~ ( le @ A @ B @ C @ D )
| ( s_e @ A @ ( ins @ C @ D @ A @ B ) @ C @ D ) )
& ( ~ ( le @ A @ B @ C @ D )
| ( ( ins @ C @ D @ A @ B )
= ( ext @ A @ B @ ( insert @ A @ B @ C @ D ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz5_5a) ).
thf(550,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( le @ A @ B @ C @ D )
| ( s_t @ A @ B @ ( ins @ C @ D @ A @ B ) ) )
& ( ~ ( le @ A @ B @ C @ D )
| ( s_e @ A @ ( ins @ C @ D @ A @ B ) @ C @ D ) )
& ( ~ ( le @ A @ B @ C @ D )
| ( ( ins @ C @ D @ A @ B )
= ( ext @ A @ B @ ( insert @ A @ B @ C @ D ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(110,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( s_t @ A @ B @ C )
| ~ ( s_e @ A @ C @ D @ E )
| ( s_t @ D @ ( insert @ A @ B @ D @ E ) @ E ) )
& ( ~ ( s_t @ A @ B @ C )
| ~ ( s_e @ A @ C @ D @ E )
| ( s_e3 @ A @ B @ C @ D @ ( insert @ A @ B @ D @ E ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz4_5) ).
thf(538,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( s_t @ A @ B @ C )
| ~ ( s_e @ A @ C @ D @ E )
| ( s_t @ D @ ( insert @ A @ B @ D @ E ) @ E ) )
& ( ~ ( s_t @ A @ B @ C )
| ~ ( s_e @ A @ C @ D @ E )
| ( s_e3 @ A @ B @ C @ D @ ( insert @ A @ B @ D @ E ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(18,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ~ ( s_e @ A @ B @ C @ D )
| ~ ( s_e @ A @ B @ E @ F )
| ( s_e @ C @ D @ E @ F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aA2) ).
thf(174,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ~ ( s_e @ A @ B @ C @ D )
| ~ ( s_e @ A @ B @ E @ F )
| ( s_e @ C @ D @ E @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(22,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( s_col @ A @ B @ C )
| ( s_col @ B @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz4_11d) ).
thf(185,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( s_col @ A @ B @ C )
| ( s_col @ B @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(81,axiom,
! [A: $i,B: $i] :
( ( ( s @ A @ B )
!= B )
| ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz7_10a) ).
thf(417,plain,
! [A: $i,B: $i] :
( ( ( s @ A @ B )
!= B )
| ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(58,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( s_t @ A @ B @ C )
| ~ ( s_t @ B @ D @ C )
| ( s_t @ A @ D @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz3_5b) ).
thf(301,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( s_t @ A @ B @ C )
| ~ ( s_t @ B @ D @ C )
| ( s_t @ A @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(116,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A = B )
| ( A = C )
| ~ ( s_t @ B @ A @ C )
| ( D != A )
| ( s_col @ D @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz6_15d) ).
thf(565,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A = B )
| ( A = C )
| ~ ( s_t @ B @ A @ C )
| ( D != A )
| ( s_col @ D @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(46,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( s_e @ A @ B @ C @ D )
| ( s_e @ B @ A @ D @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz2_14) ).
thf(257,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( s_e @ A @ B @ C @ D )
| ( s_e @ B @ A @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(117,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( s @ A @ B )
!= C )
| ( ( s @ A @ D )
!= C )
| ( B = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz7_8) ).
thf(570,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( s @ A @ B )
!= C )
| ( ( s @ A @ D )
!= C )
| ( B = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A = B )
| ( C = D )
| ~ ( s_col @ C @ D @ A )
| ~ ( s_col @ C @ D @ B )
| ~ ( s_col @ C @ D @ E )
| ( s_col @ A @ B @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz6_18) ).
thf(125,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A = B )
| ( C = D )
| ~ ( s_col @ C @ D @ A )
| ~ ( s_col @ C @ D @ B )
| ~ ( s_col @ C @ D @ E )
| ( s_col @ A @ B @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(26,axiom,
! [A: $i,B: $i,C: $i] :
( ( A = B )
| ~ ( s_col @ A @ B @ C )
| ( s_col @ B @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz6_17b) ).
thf(196,plain,
! [A: $i,B: $i,C: $i] :
( ( A = B )
| ~ ( s_col @ A @ B @ C )
| ( s_col @ B @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( s_m @ A @ B @ A )
| ( B != A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz7_3b) ).
thf(157,plain,
! [A: $i,B: $i] :
( ( s_m @ A @ B @ A )
| ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(10,axiom,
! [A: $i,B: $i] : ( s_col @ A @ A @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz4_12) ).
thf(152,plain,
! [A: $i,B: $i] : ( s_col @ A @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(35,axiom,
! [A: $i,B: $i] : ( s_e @ A @ A @ B @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz2_8) ).
thf(228,plain,
! [A: $i,B: $i] : ( s_e @ A @ A @ B @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(62,axiom,
! [A: $i,B: $i,C: $i] :
( ( sameside @ A @ B @ C )
| ~ ( s_col @ A @ B @ C )
| ( s_t @ A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz6_4b) ).
thf(316,plain,
! [A: $i,B: $i,C: $i] :
( ( sameside @ A @ B @ C )
| ~ ( s_col @ A @ B @ C )
| ( s_t @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(14,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( le @ A @ B @ C @ D )
| ~ ( le @ C @ D @ A @ B )
| ( s_e @ A @ B @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz5_9) ).
thf(164,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( le @ A @ B @ C @ D )
| ~ ( le @ C @ D @ A @ B )
| ( s_e @ A @ B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(20,axiom,
! [A: $i,B: $i] :
( ( A = B )
| ~ ( s_col @ A @ B @ ( pointOffLine @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz6_25) ).
thf(179,plain,
! [A: $i,B: $i] :
( ( A = B )
| ~ ( s_col @ A @ B @ ( pointOffLine @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(64,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ~ ( s_ifs @ A @ B @ C @ D @ E @ F @ G @ H )
| ( s_t @ A @ B @ C ) )
& ( ~ ( s_ifs @ A @ B @ C @ D @ E @ F @ G @ H )
| ( s_t @ E @ F @ G ) )
& ( ~ ( s_ifs @ A @ B @ C @ D @ E @ F @ G @ H )
| ( s_e @ A @ C @ E @ G ) )
& ( ~ ( s_ifs @ A @ B @ C @ D @ E @ F @ G @ H )
| ( s_e @ B @ C @ F @ G ) )
& ( ~ ( s_ifs @ A @ B @ C @ D @ E @ F @ G @ H )
| ( s_e @ A @ D @ E @ H ) )
& ( ~ ( s_ifs @ A @ B @ C @ D @ E @ F @ G @ H )
| ( s_e @ C @ D @ G @ H ) )
& ( ~ ( s_t @ A @ B @ C )
| ~ ( s_t @ E @ F @ G )
| ~ ( s_e @ A @ C @ E @ G )
| ~ ( s_e @ B @ C @ F @ G )
| ~ ( s_e @ A @ D @ E @ H )
| ~ ( s_e @ C @ D @ G @ H )
| ( s_ifs @ A @ B @ C @ D @ E @ F @ G @ H ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d_Defn4_1) ).
thf(321,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ~ ( s_ifs @ A @ B @ C @ D @ E @ F @ G @ H )
| ( s_t @ A @ B @ C ) )
& ( ~ ( s_ifs @ A @ B @ C @ D @ E @ F @ G @ H )
| ( s_t @ E @ F @ G ) )
& ( ~ ( s_ifs @ A @ B @ C @ D @ E @ F @ G @ H )
| ( s_e @ A @ C @ E @ G ) )
& ( ~ ( s_ifs @ A @ B @ C @ D @ E @ F @ G @ H )
| ( s_e @ B @ C @ F @ G ) )
& ( ~ ( s_ifs @ A @ B @ C @ D @ E @ F @ G @ H )
| ( s_e @ A @ D @ E @ H ) )
& ( ~ ( s_ifs @ A @ B @ C @ D @ E @ F @ G @ H )
| ( s_e @ C @ D @ G @ H ) )
& ( ~ ( s_t @ A @ B @ C )
| ~ ( s_t @ E @ F @ G )
| ~ ( s_e @ A @ C @ E @ G )
| ~ ( s_e @ B @ C @ F @ G )
| ~ ( s_e @ A @ D @ E @ H )
| ~ ( s_e @ C @ D @ G @ H )
| ( s_ifs @ A @ B @ C @ D @ E @ F @ G @ H ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(97,axiom,
! [A: $i,B: $i] : ( s_m @ A @ B @ ( s @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz7_4a) ).
thf(485,plain,
! [A: $i,B: $i] : ( s_m @ A @ B @ ( s @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(67,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( sameside @ A @ B @ C )
| ( s_col @ A @ B @ C ) )
& ( ~ ( sameside @ A @ B @ C )
| ~ ( s_t @ A @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz6_4a) ).
thf(348,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( sameside @ A @ B @ C )
| ( s_col @ A @ B @ C ) )
& ( ~ ( sameside @ A @ B @ C )
| ~ ( s_t @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(68,axiom,
! [A: $i,B: $i] : ( s_t @ A @ B @ ( ext @ A @ B @ alpha @ gamma ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz3_14a) ).
thf(353,plain,
! [A: $i,B: $i] : ( s_t @ A @ B @ ( ext @ A @ B @ alpha @ gamma ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(78,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ~ ( s_kf @ A @ B @ C @ D @ E @ F @ G )
| ( s_t @ A @ D @ G ) )
& ( ~ ( s_kf @ A @ B @ C @ D @ E @ F @ G )
| ( s_t @ C @ D @ E ) )
& ( ~ ( s_kf @ A @ B @ C @ D @ E @ F @ G )
| ( s_e @ D @ A @ D @ C ) )
& ( ~ ( s_kf @ A @ B @ C @ D @ E @ F @ G )
| ( s_e @ D @ G @ D @ E ) )
& ( ~ ( s_kf @ A @ B @ C @ D @ E @ F @ G )
| ( s_m @ A @ B @ C ) )
& ( ~ ( s_kf @ A @ B @ C @ D @ E @ F @ G )
| ( s_m @ G @ F @ E ) )
& ( ~ ( s_t @ A @ D @ G )
| ~ ( s_t @ C @ D @ E )
| ~ ( s_e @ D @ A @ D @ C )
| ~ ( s_e @ D @ G @ D @ E )
| ~ ( s_m @ A @ B @ C )
| ~ ( s_m @ G @ F @ E )
| ( s_kf @ A @ B @ C @ D @ E @ F @ G ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d_Defn7_23) ).
thf(397,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ~ ( s_kf @ A @ B @ C @ D @ E @ F @ G )
| ( s_t @ A @ D @ G ) )
& ( ~ ( s_kf @ A @ B @ C @ D @ E @ F @ G )
| ( s_t @ C @ D @ E ) )
& ( ~ ( s_kf @ A @ B @ C @ D @ E @ F @ G )
| ( s_e @ D @ A @ D @ C ) )
& ( ~ ( s_kf @ A @ B @ C @ D @ E @ F @ G )
| ( s_e @ D @ G @ D @ E ) )
& ( ~ ( s_kf @ A @ B @ C @ D @ E @ F @ G )
| ( s_m @ A @ B @ C ) )
& ( ~ ( s_kf @ A @ B @ C @ D @ E @ F @ G )
| ( s_m @ G @ F @ E ) )
& ( ~ ( s_t @ A @ D @ G )
| ~ ( s_t @ C @ D @ E )
| ~ ( s_e @ D @ A @ D @ C )
| ~ ( s_e @ D @ G @ D @ E )
| ~ ( s_m @ A @ B @ C )
| ~ ( s_m @ G @ F @ E )
| ( s_kf @ A @ B @ C @ D @ E @ F @ G ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(53,axiom,
! [A: $i,B: $i] : ( s_col @ A @ B @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz4_12b) ).
thf(280,plain,
! [A: $i,B: $i] : ( s_col @ A @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(6,axiom,
! [A: $i,B: $i] : ( s_e @ A @ B @ B @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aA1) ).
thf(133,plain,
! [A: $i,B: $i] : ( s_e @ A @ B @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(41,axiom,
! [A: $i,B: $i,C: $i] : ( le @ A @ A @ B @ C ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz5_11) ).
thf(243,plain,
! [A: $i,B: $i,C: $i] : ( le @ A @ A @ B @ C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(29,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A = B )
| ~ ( s_col @ A @ B @ C )
| ~ ( s_e @ A @ C @ A @ D )
| ~ ( s_e @ B @ C @ B @ D )
| ( C = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz4_18) ).
thf(206,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A = B )
| ~ ( s_col @ A @ B @ C )
| ~ ( s_e @ A @ C @ A @ D )
| ~ ( s_e @ B @ C @ B @ D )
| ( C = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(32,axiom,
! [A: $i,B: $i] :
( ( A = B )
| ( sameside @ A @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz6_5) ).
thf(220,plain,
! [A: $i,B: $i] :
( ( A = B )
| ( sameside @ A @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(108,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( s_t @ A @ B @ C )
| ( s_t @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz3_2) ).
thf(534,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( s_t @ A @ B @ C )
| ( s_t @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(115,axiom,
! [A: $i,B: $i] :
( ( ( s @ A @ B )
= B )
| ( B != A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz7_10b) ).
thf(561,plain,
! [A: $i,B: $i] :
( ( ( s @ A @ B )
= B )
| ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(57,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( s @ A @ B )
!= ( s @ A @ C ) )
| ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz7_9) ).
thf(297,plain,
! [A: $i,B: $i,C: $i] :
( ( ( s @ A @ B )
!= ( s @ A @ C ) )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(8,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A = B )
| ~ ( s_col @ A @ B @ C )
| ~ ( s_e @ A @ D @ A @ E )
| ~ ( s_e @ B @ D @ B @ E )
| ( s_e @ C @ D @ C @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz4_17) ).
thf(137,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A = B )
| ~ ( s_col @ A @ B @ C )
| ~ ( s_e @ A @ D @ A @ E )
| ~ ( s_e @ B @ D @ B @ E )
| ( s_e @ C @ D @ C @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(16,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( le @ A @ B @ C @ D )
| ( le @ C @ D @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz5_10) ).
thf(169,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( le @ A @ B @ C @ D )
| ( le @ C @ D @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(9,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ~ ( s_fs @ A @ B @ C @ D @ E @ F @ G @ H )
| ( s_col @ A @ B @ C ) )
& ( ~ ( s_fs @ A @ B @ C @ D @ E @ F @ G @ H )
| ( s_e3 @ A @ B @ C @ E @ F @ G ) )
& ( ~ ( s_fs @ A @ B @ C @ D @ E @ F @ G @ H )
| ( s_e @ A @ D @ E @ H ) )
& ( ~ ( s_fs @ A @ B @ C @ D @ E @ F @ G @ H )
| ( s_e @ B @ D @ F @ H ) )
& ( ~ ( s_col @ A @ B @ C )
| ~ ( s_e3 @ A @ B @ C @ E @ F @ G )
| ~ ( s_e @ A @ D @ E @ H )
| ~ ( s_e @ B @ D @ F @ H )
| ( s_fs @ A @ B @ C @ D @ E @ F @ G @ H ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d_Defn4_15) ).
thf(141,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ~ ( s_fs @ A @ B @ C @ D @ E @ F @ G @ H )
| ( s_col @ A @ B @ C ) )
& ( ~ ( s_fs @ A @ B @ C @ D @ E @ F @ G @ H )
| ( s_e3 @ A @ B @ C @ E @ F @ G ) )
& ( ~ ( s_fs @ A @ B @ C @ D @ E @ F @ G @ H )
| ( s_e @ A @ D @ E @ H ) )
& ( ~ ( s_fs @ A @ B @ C @ D @ E @ F @ G @ H )
| ( s_e @ B @ D @ F @ H ) )
& ( ~ ( s_col @ A @ B @ C )
| ~ ( s_e3 @ A @ B @ C @ E @ F @ G )
| ~ ( s_e @ A @ D @ E @ H )
| ~ ( s_e @ B @ D @ F @ H )
| ( s_fs @ A @ B @ C @ D @ E @ F @ G @ H ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(82,axiom,
! [A: $i,B: $i] :
( ( s @ A @ ( s @ A @ B ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz7_7) ).
thf(420,plain,
! [A: $i,B: $i] :
( ( s @ A @ ( s @ A @ B ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(34,axiom,
alpha != gamma,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz3_13c) ).
thf(225,plain,
alpha != gamma,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(25,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( sameside @ A @ B @ C )
| ~ ( sameside @ C @ B @ D )
| ( sameside @ A @ B @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz6_7) ).
thf(193,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( sameside @ A @ B @ C )
| ~ ( sameside @ C @ B @ D )
| ( sameside @ A @ B @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(112,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ~ ( s_t @ A @ B @ C )
| ~ ( s_e3 @ A @ B @ C @ D @ E @ F )
| ( s_t @ D @ E @ F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz4_6) ).
thf(547,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ~ ( s_t @ A @ B @ C )
| ~ ( s_e3 @ A @ B @ C @ D @ E @ F )
| ( s_t @ D @ E @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(39,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( s_m @ A @ B @ C )
| ( s_m @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz7_2) ).
thf(237,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( s_m @ A @ B @ C )
| ( s_m @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(50,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ~ ( s_ifs @ A @ B @ C @ D @ E @ F @ G @ H )
| ( s_e @ B @ D @ F @ H ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz4_2) ).
thf(266,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ~ ( s_ifs @ A @ B @ C @ D @ E @ F @ G @ H )
| ( s_e @ B @ D @ F @ H ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(71,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ~ ( s_afs @ A @ B @ C @ D @ E @ F @ G @ H )
| ( s_t @ A @ B @ C ) )
& ( ~ ( s_afs @ A @ B @ C @ D @ E @ F @ G @ H )
| ( s_t @ E @ F @ G ) )
& ( ~ ( s_afs @ A @ B @ C @ D @ E @ F @ G @ H )
| ( s_e @ A @ B @ E @ F ) )
& ( ~ ( s_afs @ A @ B @ C @ D @ E @ F @ G @ H )
| ( s_e @ B @ C @ F @ G ) )
& ( ~ ( s_afs @ A @ B @ C @ D @ E @ F @ G @ H )
| ( s_e @ A @ D @ E @ H ) )
& ( ~ ( s_afs @ A @ B @ C @ D @ E @ F @ G @ H )
| ( s_e @ B @ D @ F @ H ) )
& ( ~ ( s_t @ A @ B @ C )
| ~ ( s_t @ E @ F @ G )
| ~ ( s_e @ A @ B @ E @ F )
| ~ ( s_e @ B @ C @ F @ G )
| ~ ( s_e @ A @ D @ E @ H )
| ~ ( s_e @ B @ D @ F @ H )
| ( s_afs @ A @ B @ C @ D @ E @ F @ G @ H ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d_Defn2_10) ).
thf(360,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ~ ( s_afs @ A @ B @ C @ D @ E @ F @ G @ H )
| ( s_t @ A @ B @ C ) )
& ( ~ ( s_afs @ A @ B @ C @ D @ E @ F @ G @ H )
| ( s_t @ E @ F @ G ) )
& ( ~ ( s_afs @ A @ B @ C @ D @ E @ F @ G @ H )
| ( s_e @ A @ B @ E @ F ) )
& ( ~ ( s_afs @ A @ B @ C @ D @ E @ F @ G @ H )
| ( s_e @ B @ C @ F @ G ) )
& ( ~ ( s_afs @ A @ B @ C @ D @ E @ F @ G @ H )
| ( s_e @ A @ D @ E @ H ) )
& ( ~ ( s_afs @ A @ B @ C @ D @ E @ F @ G @ H )
| ( s_e @ B @ D @ F @ H ) )
& ( ~ ( s_t @ A @ B @ C )
| ~ ( s_t @ E @ F @ G )
| ~ ( s_e @ A @ B @ E @ F )
| ~ ( s_e @ B @ C @ F @ G )
| ~ ( s_e @ A @ D @ E @ H )
| ~ ( s_e @ B @ D @ F @ H )
| ( s_afs @ A @ B @ C @ D @ E @ F @ G @ H ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(103,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( le @ A @ B @ C @ D )
| ~ ( s_t @ A @ B @ E )
| ~ ( s_e @ A @ E @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz5_5b) ).
thf(508,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( le @ A @ B @ C @ D )
| ~ ( s_t @ A @ B @ E )
| ~ ( s_e @ A @ E @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(61,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( s_t @ A @ B @ C )
| ~ ( s_t @ D @ E @ C )
| ( s_t @ B @ ( ip @ A @ B @ C @ D @ E ) @ D ) )
& ( ~ ( s_t @ A @ B @ C )
| ~ ( s_t @ D @ E @ C )
| ( s_t @ E @ ( ip @ A @ B @ C @ D @ E ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aA7) ).
thf(311,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( s_t @ A @ B @ C )
| ~ ( s_t @ D @ E @ C )
| ( s_t @ B @ ( ip @ A @ B @ C @ D @ E ) @ D ) )
& ( ~ ( s_t @ A @ B @ C )
| ~ ( s_t @ D @ E @ C )
| ( s_t @ E @ ( ip @ A @ B @ C @ D @ E ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(114,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( s_t @ A @ B @ C )
| ~ ( s_t @ B @ A @ C )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz3_4) ).
thf(558,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( s_t @ A @ B @ C )
| ~ ( s_t @ B @ A @ C )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(79,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( s_col @ A @ B @ C )
| ~ ( s_t @ A @ B @ C )
| ( le @ B @ C @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz5_12a2) ).
thf(412,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( s_col @ A @ B @ C )
| ~ ( s_t @ A @ B @ C )
| ( le @ B @ C @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(15,axiom,
alpha != beta,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz3_13a) ).
thf(166,plain,
alpha != beta,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(49,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( s_col @ A @ B @ C )
| ( s_col @ C @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz4_11b) ).
thf(264,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( s_col @ A @ B @ C )
| ( s_col @ C @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(13,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ~ ( sameside @ A @ B @ C )
| ~ ( sameside @ D @ E @ F )
| ~ ( s_e @ B @ A @ E @ D )
| ~ ( s_e @ B @ C @ E @ F )
| ( s_e @ A @ C @ D @ F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz6_28) ).
thf(161,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ~ ( sameside @ A @ B @ C )
| ~ ( sameside @ D @ E @ F )
| ~ ( s_e @ B @ A @ E @ D )
| ~ ( s_e @ B @ C @ E @ F )
| ( s_e @ A @ C @ D @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(72,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A = B )
| ~ ( s_t @ C @ A @ B )
| ~ ( s_t @ D @ A @ B )
| ( s_t @ D @ C @ B )
| ( s_t @ C @ D @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz6_16a) ).
thf(375,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A = B )
| ~ ( s_t @ C @ A @ B )
| ~ ( s_t @ D @ A @ B )
| ( s_t @ D @ C @ B )
| ( s_t @ C @ D @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(105,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( s_t @ A @ B @ C )
| ~ ( s_t @ B @ D @ C )
| ( s_t @ A @ B @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz3_5a) ).
thf(513,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( s_t @ A @ B @ C )
| ~ ( s_t @ B @ D @ C )
| ( s_t @ A @ B @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(85,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( s_col @ A @ B @ C )
| ( s_t @ A @ B @ C )
| ~ ( le @ A @ B @ A @ C )
| ~ ( le @ B @ C @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz5_12b) ).
thf(430,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( s_col @ A @ B @ C )
| ( s_t @ A @ B @ C )
| ~ ( le @ A @ B @ A @ C )
| ~ ( le @ B @ C @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(83,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A = B )
| ( C = B )
| ( D = B )
| ~ ( s_t @ A @ B @ D )
| ( s_t @ C @ B @ D )
| ~ ( sameside @ A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz6_2b) ).
thf(423,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A = B )
| ( C = B )
| ( D = B )
| ~ ( s_t @ A @ B @ D )
| ( s_t @ C @ B @ D )
| ~ ( sameside @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(24,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( s_col @ A @ B @ C )
| ( s_col @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz4_11c) ).
thf(191,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( s_col @ A @ B @ C )
| ( s_col @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(55,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( s_e @ A @ B @ C @ C )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz2_13) ).
thf(286,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( s_e @ A @ B @ C @ C )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i,D: $i] :
( ( s_t @ A @ B @ C )
| ~ ( s_t @ ( s @ D @ A ) @ ( s @ D @ B ) @ ( s @ D @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz7_15b) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i,D: $i] :
( ( s_t @ A @ B @ C )
| ~ ( s_t @ ( s @ D @ A ) @ ( s @ D @ B ) @ ( s @ D @ C ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(118,plain,
~ ! [A: $i,B: $i,C: $i,D: $i] :
( ( s_t @ A @ B @ C )
| ~ ( s_t @ ( s @ D @ A ) @ ( s @ D @ B ) @ ( s @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(47,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ~ ( le @ A @ B @ C @ D )
| ~ ( s_e @ A @ B @ E @ F )
| ~ ( s_e @ C @ D @ G @ H )
| ( le @ E @ F @ G @ H ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz5_6) ).
thf(259,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ~ ( le @ A @ B @ C @ D )
| ~ ( s_e @ A @ B @ E @ F )
| ~ ( s_e @ C @ D @ G @ H )
| ( le @ E @ F @ G @ H ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(90,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A = B )
| ( C = B )
| ( D = B )
| ~ ( s_t @ A @ B @ D )
| ~ ( s_t @ C @ B @ D )
| ( sameside @ A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz6_2a) ).
thf(445,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A = B )
| ( C = B )
| ( D = B )
| ~ ( s_t @ A @ B @ D )
| ~ ( s_t @ C @ B @ D )
| ( sameside @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(100,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A = B )
| ~ ( s_t @ A @ B @ C )
| ~ ( s_t @ A @ B @ D )
| ( s_t @ A @ C @ D )
| ( s_t @ A @ D @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz5_1) ).
thf(498,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A = B )
| ~ ( s_t @ A @ B @ C )
| ~ ( s_t @ A @ B @ D )
| ( s_t @ A @ C @ D )
| ( s_t @ A @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(23,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A = B )
| ( C = D )
| ~ ( sameside @ E @ B @ A )
| ~ ( s_e @ B @ E @ C @ D )
| ~ ( sameside @ F @ B @ A )
| ~ ( s_e @ B @ F @ C @ D )
| ( E = F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz6_11b) ).
thf(187,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A = B )
| ( C = D )
| ~ ( sameside @ E @ B @ A )
| ~ ( s_e @ B @ E @ C @ D )
| ~ ( sameside @ F @ B @ A )
| ~ ( s_e @ B @ F @ C @ D )
| ( E = F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(36,axiom,
! [A: $i,B: $i] : ( s_e @ A @ B @ A @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz2_1) ).
thf(230,plain,
! [A: $i,B: $i] : ( s_e @ A @ B @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(42,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( s_e @ A @ B @ C @ D )
| ( s_e @ B @ A @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz2_4) ).
thf(245,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( s_e @ A @ B @ C @ D )
| ( s_e @ B @ A @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(63,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( s_m @ A @ B @ C )
| ( C
= ( s @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz7_6) ).
thf(318,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( s_m @ A @ B @ C )
| ( C
= ( s @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(87,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( s_t @ A @ B @ C )
| ~ ( s_t @ B @ C @ D )
| ( B = C )
| ( s_t @ A @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz3_7a) ).
thf(434,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( s_t @ A @ B @ C )
| ~ ( s_t @ B @ C @ D )
| ( B = C )
| ( s_t @ A @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(95,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A = B )
| ~ ( s_t @ A @ B @ C )
| ~ ( s_t @ A @ B @ D )
| ( s_t @ B @ C @ D )
| ( s_t @ B @ D @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz5_2) ).
thf(477,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A = B )
| ~ ( s_t @ A @ B @ C )
| ~ ( s_t @ A @ B @ D )
| ( s_t @ B @ C @ D )
| ( s_t @ B @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(75,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( s_t @ A @ B @ C )
| ~ ( s_t @ A @ C @ D )
| ( s_t @ A @ B @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz3_6b) ).
thf(387,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( s_t @ A @ B @ C )
| ~ ( s_t @ A @ C @ D )
| ( s_t @ A @ B @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(66,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ~ ( s_t @ A @ B @ C )
| ~ ( s_t @ D @ E @ F )
| ~ ( s_e @ A @ C @ D @ F )
| ~ ( s_e @ B @ C @ E @ F )
| ( s_e @ A @ B @ D @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz4_3) ).
thf(345,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ~ ( s_t @ A @ B @ C )
| ~ ( s_t @ D @ E @ F )
| ~ ( s_e @ A @ C @ D @ F )
| ~ ( s_e @ B @ C @ E @ F )
| ( s_e @ A @ B @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(31,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A = B )
| ( C = D )
| ( sameside @ ( insert @ C @ D @ B @ A ) @ B @ A ) )
& ( ( A = B )
| ( C = D )
| ( s_e @ B @ ( insert @ C @ D @ B @ A ) @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz6_11a) ).
thf(213,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A = B )
| ( C = D )
| ( sameside @ ( insert @ C @ D @ B @ A ) @ B @ A ) )
& ( ( A = B )
| ( C = D )
| ( s_e @ B @ ( insert @ C @ D @ B @ A ) @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(44,axiom,
! [A: $i,B: $i] :
( ~ ( s_m @ A @ B @ A )
| ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz7_3a) ).
thf(251,plain,
! [A: $i,B: $i] :
( ~ ( s_m @ A @ B @ A )
| ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(94,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( sameside @ A @ B @ C )
| ( A != B ) )
& ( ~ ( sameside @ A @ B @ C )
| ( C != B ) )
& ( ~ ( sameside @ A @ B @ C )
| ( ( c63 @ A @ B @ C )
!= B ) )
& ( ~ ( sameside @ A @ B @ C )
| ( s_t @ A @ B @ ( c63 @ A @ B @ C ) ) )
& ( ~ ( sameside @ A @ B @ C )
| ( s_t @ C @ B @ ( c63 @ A @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz6_3a) ).
thf(462,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( sameside @ A @ B @ C )
| ( A != B ) )
& ( ~ ( sameside @ A @ B @ C )
| ( C != B ) )
& ( ~ ( sameside @ A @ B @ C )
| ( ( c63 @ A @ B @ C )
!= B ) )
& ( ~ ( sameside @ A @ B @ C )
| ( s_t @ A @ B @ ( c63 @ A @ B @ C ) ) )
& ( ~ ( sameside @ A @ B @ C )
| ( s_t @ C @ B @ ( c63 @ A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(33,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( sameside @ A @ B @ C )
| ( sameside @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz6_6) ).
thf(223,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( sameside @ A @ B @ C )
| ( sameside @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(7,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( s_col @ A @ B @ C )
| ( s_col @ A @ C @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz4_11e) ).
thf(135,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( s_col @ A @ B @ C )
| ( s_col @ A @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(102,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( s_t @ A @ B @ C )
| ~ ( s_t @ A @ D @ C )
| ( s_t @ A @ B @ D )
| ( s_t @ A @ D @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz5_3) ).
thf(505,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( s_t @ A @ B @ C )
| ~ ( s_t @ A @ D @ C )
| ( s_t @ A @ B @ D )
| ( s_t @ A @ D @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(88,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( s_t @ A @ B @ C )
| ~ ( s_e @ A @ C @ A @ B )
| ( C = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aNarbouxLemma1) ).
thf(438,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( s_t @ A @ B @ C )
| ~ ( s_e @ A @ C @ A @ B )
| ( C = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(98,axiom,
( ~ ( s_t @ alpha @ beta @ gamma )
& ~ ( s_t @ beta @ gamma @ alpha )
& ~ ( s_t @ gamma @ alpha @ beta ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aA8) ).
thf(487,plain,
( ~ ( s_t @ alpha @ beta @ gamma )
& ~ ( s_t @ beta @ gamma @ alpha )
& ~ ( s_t @ gamma @ alpha @ beta ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(106,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( sameside @ A @ B @ C )
| ( A != B ) )
& ( ~ ( sameside @ A @ B @ C )
| ( C != B ) )
& ( ~ ( sameside @ A @ B @ C )
| ( s_t @ B @ A @ C )
| ( s_t @ B @ C @ A ) )
& ( ~ ( s_t @ B @ A @ C )
| ( A = B )
| ( xb = B )
| ( sameside @ A @ B @ C ) )
& ( ~ ( s_t @ B @ C @ A )
| ( A = B )
| ( C = B )
| ( sameside @ A @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d_Defn6_1) ).
thf(516,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( sameside @ A @ B @ C )
| ( A != B ) )
& ( ~ ( sameside @ A @ B @ C )
| ( C != B ) )
& ( ~ ( sameside @ A @ B @ C )
| ( s_t @ B @ A @ C )
| ( s_t @ B @ C @ A ) )
& ( ~ ( s_t @ B @ A @ C )
| ( A = B )
| ( xb = B )
| ( sameside @ A @ B @ C ) )
& ( ~ ( s_t @ B @ C @ A )
| ( A = B )
| ( C = B )
| ( sameside @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(69,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( s_t @ A @ B @ C )
| ~ ( s_t @ A @ C @ D )
| ( s_t @ B @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz3_6a) ).
thf(355,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( s_t @ A @ B @ C )
| ~ ( s_t @ A @ C @ D )
| ( s_t @ B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(93,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A = B )
| ( A = C )
| ~ ( s_t @ B @ A @ C )
| ~ ( sameside @ D @ A @ B )
| ( s_col @ D @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz6_15b) ).
thf(458,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A = B )
| ( A = C )
| ~ ( s_t @ B @ A @ C )
| ~ ( sameside @ D @ A @ B )
| ( s_col @ D @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(54,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( s_m @ A @ B @ C )
| ~ ( s_m @ A @ B @ D )
| ( C = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz7_4b) ).
thf(282,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( s_m @ A @ B @ C )
| ~ ( s_m @ A @ B @ D )
| ( C = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(80,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ~ ( s_t @ A @ B @ C )
| ~ ( s_t @ D @ E @ F )
| ~ ( s_e @ A @ B @ E @ F )
| ~ ( s_e @ B @ C @ D @ E )
| ( s_e @ A @ C @ D @ F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz2_15) ).
thf(414,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ~ ( s_t @ A @ B @ C )
| ~ ( s_t @ D @ E @ F )
| ~ ( s_e @ A @ B @ E @ F )
| ~ ( s_e @ B @ C @ D @ E )
| ( s_e @ A @ C @ D @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(89,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ~ ( s_e @ A @ B @ C @ D )
| ~ ( s_e @ B @ E @ D @ F )
| ~ ( s_e @ A @ G @ C @ H )
| ~ ( s_e @ B @ G @ D @ H )
| ~ ( s_t @ A @ B @ E )
| ~ ( s_t @ C @ D @ F )
| ( A = B )
| ( s_e @ E @ G @ F @ H ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aA5) ).
thf(441,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ~ ( s_e @ A @ B @ C @ D )
| ~ ( s_e @ B @ E @ D @ F )
| ~ ( s_e @ A @ G @ C @ H )
| ~ ( s_e @ B @ G @ D @ H )
| ~ ( s_t @ A @ B @ E )
| ~ ( s_t @ C @ D @ F )
| ( A = B )
| ( s_e @ E @ G @ F @ H ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(101,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ~ ( s_t @ A @ B @ C )
| ~ ( s_t @ D @ E @ F )
| ~ ( s_e @ A @ B @ D @ E )
| ~ ( s_e @ B @ C @ E @ F )
| ( s_e @ A @ C @ D @ F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz2_11) ).
thf(502,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ~ ( s_t @ A @ B @ C )
| ~ ( s_t @ D @ E @ F )
| ~ ( s_e @ A @ B @ D @ E )
| ~ ( s_e @ B @ C @ E @ F )
| ( s_e @ A @ C @ D @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(19,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( s_col @ A @ B @ C )
| ( s_col @ B @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz4_11a) ).
thf(177,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( s_col @ A @ B @ C )
| ( s_col @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(21,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( insert @ A @ B @ C @ D )
= ( ext @ ( ext @ D @ C @ alpha @ gamma ) @ C @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d_insert) ).
thf(182,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( insert @ A @ B @ C @ D )
= ( ext @ ( ext @ D @ C @ alpha @ gamma ) @ C @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(65,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( s_col @ A @ B @ C )
| ( s_t @ A @ B @ C )
| ( s_t @ B @ C @ A )
| ( s_t @ C @ A @ B ) )
& ( ( s_col @ A @ B @ C )
| ~ ( s_t @ A @ B @ C ) )
& ( ( s_col @ A @ B @ C )
| ~ ( s_t @ B @ C @ A ) )
& ( ( s_col @ A @ B @ C )
| ~ ( s_t @ C @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d_Defn4_10) ).
thf(336,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( s_col @ A @ B @ C )
| ( s_t @ A @ B @ C )
| ( s_t @ B @ C @ A )
| ( s_t @ C @ A @ B ) )
& ( ( s_col @ A @ B @ C )
| ~ ( s_t @ A @ B @ C ) )
& ( ( s_col @ A @ B @ C )
| ~ ( s_t @ B @ C @ A ) )
& ( ( s_col @ A @ B @ C )
| ~ ( s_t @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(11,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ~ ( s_col @ A @ B @ C )
| ~ ( s_e3 @ A @ B @ C @ D @ E @ F )
| ( s_col @ D @ E @ F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz4_13) ).
thf(154,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ~ ( s_col @ A @ B @ C )
| ~ ( s_e3 @ A @ B @ C @ D @ E @ F )
| ( s_col @ D @ E @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(59,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( s_t @ A @ B @ C )
| ~ ( s_e @ A @ B @ A @ D )
| ~ ( s_e @ C @ B @ C @ D )
| ( B = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz4_19) ).
thf(304,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( s_t @ A @ B @ C )
| ~ ( s_e @ A @ B @ A @ D )
| ~ ( s_e @ C @ B @ C @ D )
| ( B = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(76,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( s_t @ A @ B @ ( ext @ A @ B @ C @ D ) )
& ( s_e @ B @ ( ext @ A @ B @ C @ D ) @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aA4) ).
thf(390,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( s_t @ A @ B @ ( ext @ A @ B @ C @ D ) )
& ( s_e @ B @ ( ext @ A @ B @ C @ D ) @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(17,axiom,
! [A: $i,B: $i] :
( ( A = B )
| ( s_col @ A @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz6_17a) ).
thf(171,plain,
! [A: $i,B: $i] :
( ( A = B )
| ( s_col @ A @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(56,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( le @ A @ B @ C @ D )
| ( s_t @ C @ ( insert @ A @ B @ C @ D ) @ D ) )
& ( ~ ( le @ A @ B @ C @ D )
| ( s_e @ A @ B @ C @ ( insert @ A @ B @ C @ D ) ) )
& ( ~ ( s_t @ C @ E @ D )
| ~ ( s_e @ A @ B @ C @ E )
| ( le @ A @ B @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d_Defn5_4) ).
thf(290,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( le @ A @ B @ C @ D )
| ( s_t @ C @ ( insert @ A @ B @ C @ D ) @ D ) )
& ( ~ ( le @ A @ B @ C @ D )
| ( s_e @ A @ B @ C @ ( insert @ A @ B @ C @ D ) ) )
& ( ~ ( s_t @ C @ E @ D )
| ~ ( s_e @ A @ B @ C @ E )
| ( le @ A @ B @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(74,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( s_t @ A @ B @ C )
| ~ ( s_t @ B @ C @ D )
| ( B = C )
| ( s_t @ A @ B @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz3_7b) ).
thf(383,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( s_t @ A @ B @ C )
| ~ ( s_t @ B @ C @ D )
| ( B = C )
| ( s_t @ A @ B @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(109,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( sameside @ A @ B @ C )
| ~ ( le @ B @ A @ B @ C )
| ( s_t @ B @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz6_13a) ).
thf(536,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( sameside @ A @ B @ C )
| ~ ( le @ B @ A @ B @ C )
| ( s_t @ B @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(86,axiom,
! [A: $i,B: $i] : ( s_t @ A @ B @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz3_1) ).
thf(432,plain,
! [A: $i,B: $i] : ( s_t @ A @ B @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(48,axiom,
! [A: $i,B: $i] : ( le @ A @ B @ A @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz5_7) ).
thf(262,plain,
! [A: $i,B: $i] : ( le @ A @ B @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(30,axiom,
beta != gamma,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz3_13b) ).
thf(210,plain,
beta != gamma,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(40,axiom,
! [A: $i,B: $i] :
( A
!= ( ext @ B @ A @ alpha @ gamma ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz3_14b) ).
thf(239,plain,
! [A: $i,B: $i] :
( A
!= ( ext @ B @ A @ alpha @ gamma ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(51,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ( s_e3 @ A @ B @ C @ D @ E @ F )
| ( s_e @ A @ B @ D @ E ) )
& ( ~ ( s_e3 @ A @ B @ C @ D @ E @ F )
| ( s_e @ A @ C @ D @ F ) )
& ( ~ ( s_e3 @ A @ B @ C @ D @ E @ F )
| ( s_e @ B @ C @ E @ F ) )
& ( ~ ( s_e @ A @ B @ D @ E )
| ~ ( s_e @ A @ C @ D @ F )
| ~ ( s_e @ B @ C @ E @ F )
| ( s_e3 @ A @ B @ C @ D @ E @ F ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d_Defn4_4) ).
thf(268,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ( s_e3 @ A @ B @ C @ D @ E @ F )
| ( s_e @ A @ B @ D @ E ) )
& ( ~ ( s_e3 @ A @ B @ C @ D @ E @ F )
| ( s_e @ A @ C @ D @ F ) )
& ( ~ ( s_e3 @ A @ B @ C @ D @ E @ F )
| ( s_e @ B @ C @ E @ F ) )
& ( ~ ( s_e @ A @ B @ D @ E )
| ~ ( s_e @ A @ C @ D @ F )
| ~ ( s_e @ B @ C @ E @ F )
| ( s_e3 @ A @ B @ C @ D @ E @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(70,axiom,
! [A: $i,B: $i] : ( s_t @ A @ A @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz3_3) ).
thf(358,plain,
! [A: $i,B: $i] : ( s_t @ A @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(107,axiom,
! [A: $i,B: $i,C: $i] : ( s_e @ A @ B @ ( s @ C @ A ) @ ( s @ C @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz7_13) ).
thf(532,plain,
! [A: $i,B: $i,C: $i] : ( s_e @ A @ B @ ( s @ C @ A ) @ ( s @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(77,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( s_col @ A @ B @ C )
| ~ ( s_t @ A @ B @ C )
| ( le @ A @ B @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz5_12a1) ).
thf(395,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( s_col @ A @ B @ C )
| ~ ( s_t @ A @ B @ C )
| ( le @ A @ B @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(84,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( s_t @ A @ B @ C )
| ( s_t @ ( s @ D @ A ) @ ( s @ D @ B ) @ ( s @ D @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz7_15a) ).
thf(427,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( s_t @ A @ B @ C )
| ( s_t @ ( s @ D @ A ) @ ( s @ D @ B ) @ ( s @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(27,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( s_e @ A @ B @ C @ D )
| ( s_e @ C @ D @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz2_2) ).
thf(200,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( s_e @ A @ B @ C @ D )
| ( s_e @ C @ D @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(52,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ~ ( le @ A @ B @ C @ D )
| ~ ( le @ C @ D @ E @ F )
| ( le @ A @ B @ E @ F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz5_8) ).
thf(277,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ~ ( le @ A @ B @ C @ D )
| ~ ( le @ C @ D @ E @ F )
| ( le @ A @ B @ E @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(45,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ~ ( s_fs @ A @ B @ C @ D @ E @ F @ G @ H )
| ( A = B )
| ( s_e @ C @ D @ G @ H ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz4_16) ).
thf(254,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ~ ( s_fs @ A @ B @ C @ D @ E @ F @ G @ H )
| ( A = B )
| ( s_e @ C @ D @ G @ H ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(3,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ~ ( s_col @ A @ B @ C )
| ~ ( s_e @ A @ B @ D @ E )
| ( s_e3 @ A @ B @ C @ D @ E @ ( insert5 @ A @ B @ C @ D @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz4_14) ).
thf(122,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ~ ( s_col @ A @ B @ C )
| ~ ( s_e @ A @ B @ D @ E )
| ( s_e3 @ A @ B @ C @ D @ E @ ( insert5 @ A @ B @ C @ D @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(111,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( sameside @ A @ B @ C )
| ( A = B )
| ( C = B )
| ( D = B )
| ~ ( s_t @ A @ B @ D )
| ~ ( s_t @ C @ B @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz6_3b) ).
thf(543,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( sameside @ A @ B @ C )
| ( A = B )
| ( C = B )
| ( D = B )
| ~ ( s_t @ A @ B @ D )
| ~ ( s_t @ C @ B @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(99,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( s_m @ A @ B @ C )
| ( s_t @ A @ B @ C ) )
& ( ~ ( s_m @ A @ B @ C )
| ( s_e @ B @ A @ B @ C ) )
& ( ~ ( s_t @ A @ B @ C )
| ~ ( s_e @ B @ A @ B @ C )
| ( s_m @ A @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d_Defn7_1) ).
thf(491,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( s_m @ A @ B @ C )
| ( s_t @ A @ B @ C ) )
& ( ~ ( s_m @ A @ B @ C )
| ( s_e @ B @ A @ B @ C ) )
& ( ~ ( s_t @ A @ B @ C )
| ~ ( s_e @ B @ A @ B @ C )
| ( s_m @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(92,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A = B )
| ~ ( s_t @ A @ B @ C )
| ~ ( s_e @ B @ C @ D @ E )
| ( C
= ( ext @ A @ B @ D @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz2_12) ).
thf(454,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A = B )
| ~ ( s_t @ A @ B @ C )
| ~ ( s_e @ B @ C @ D @ E )
| ( C
= ( ext @ A @ B @ D @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(37,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( s_e @ A @ B @ C @ D )
| ( s_e @ A @ B @ D @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz2_5) ).
thf(232,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( s_e @ A @ B @ C @ D )
| ( s_e @ A @ B @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(11735,plain,
$false,
inference(e,[status(thm)],[129,234,481,308,449,247,379,511,202,550,538,174,185,417,301,565,257,570,125,196,157,152,228,316,164,179,321,485,348,353,397,280,133,243,206,220,534,561,297,137,169,141,420,225,193,547,237,266,360,508,311,558,412,166,264,161,375,513,430,423,191,286,118,259,445,498,187,230,245,318,434,477,387,345,213,251,462,223,135,505,438,487,516,355,458,282,414,441,502,177,182,336,154,304,390,171,290,383,536,432,262,210,239,268,358,532,395,427,200,277,254,122,543,491,454,232]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : GEO499+1 : TPTP v8.1.2. Released v7.0.0.
% 0.10/0.15 % Command : run_Leo-III %s %d
% 0.14/0.36 % Computer : n017.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Fri May 19 03:53:32 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.85/0.83 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.53/1.02 % [INFO] Parsing done (186ms).
% 1.53/1.02 % [INFO] Running in sequential loop mode.
% 1.93/1.22 % [INFO] eprover registered as external prover.
% 1.93/1.22 % [INFO] cvc4 registered as external prover.
% 1.93/1.22 % [INFO] Scanning for conjecture ...
% 2.01/1.29 % [INFO] Found a conjecture and 115 axioms. Running axiom selection ...
% 2.28/1.35 % [INFO] Axiom selection finished. Selected 115 axioms (removed 0 axioms).
% 2.71/1.48 % [INFO] Problem is first-order (TPTP FOF).
% 2.71/1.50 % [INFO] Type checking passed.
% 2.71/1.50 % [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 ...
% 31.12/6.60 % External prover 'e' found a proof!
% 31.12/6.60 % [INFO] Killing All external provers ...
% 31.12/6.60 % Time passed: 6086ms (effective reasoning time: 5571ms)
% 31.12/6.60 % 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)>
% 31.12/6.60 % Axioms used in derivation (115): aSatz6_2b, aSatz3_5a, aSatz6_21, aSatz5_9, aSatz3_4, aSatz6_5, aSatz2_13, aSatz7_10b, aSatz3_14b, aSatz7_2, aSatz2_3, aSatz6_16b, aSatz4_5, d_Defn5_4, aSatz4_11d, aSatz5_6, aSatz6_2a, d_Defn4_4, aSatz3_1, aSatz3_13c, aSatz6_3a, aSatz5_2, d_Defn7_23, aSatz6_15d, aSatz6_4b, aA1, aSatz4_16, aSatz6_13a, d_insert, aSatz6_3b, aA5, aSatz7_10a, aSatz5_12a1, d_Defn6_1, aSatz6_6, d_Defn4_15, aSatz7_3b, aSatz2_12, aSatz3_3, aSatz3_13a, aSatz6_18, aSatz3_5b, aSatz3_17, aSatz7_7, aSatz4_11c, d_Defn4_10, aSatz5_1, aSatz5_12b, aSatz3_13b, aSatz4_19, aSatz6_15a, aSatz4_14, aSatz6_15c, aSatz2_1, aSatz6_11b, aSatz6_25, d_Defn4_1, aA2, aSatz7_4a, aSatz4_11b, aSatz2_5, aSatz3_6b, aA3, aSatz3_2, aA6, aSatz3_6a, aSatz7_15a, aSatz5_12a2, aNarbouxLemma1, aSatz6_17a, aSatz4_3, aSatz7_6, d_Defn7_1, aSatz5_11, aSatz4_18, aSatz2_2, aSatz5_5a, aSatz6_28, aSatz4_12b, aSatz2_15, aSatz4_11a, aSatz6_11a, aA7, aSatz6_15b, aSatz2_4, aSatz7_9, aSatz3_14a, aA4, aSatz5_8, aSatz6_16a, aSatz3_7a, aSatz6_17b, aSatz4_6, aSatz7_4b, aSatz5_7, aSatz4_13, aSatz2_11, aSatz7_13, aSatz2_14, aSatz4_11e, aSatz5_10, d_Defn2_10, aSatz5_5b, aSatz4_12, aSatz4_17, aSatz5_3, aSatz6_13b, aSatz7_8, aSatz2_8, aSatz4_2, aSatz6_4a, aA8, aSatz3_7b, aSatz7_3a, aSatz6_7
% 31.12/6.60 % No. of inferences in proof: 234
% 31.12/6.60 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 6086 ms resp. 5571 ms w/o parsing
% 31.31/6.69 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 31.31/6.69 % [INFO] Killing All external provers ...
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