%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : GEO497+1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 07:13:24 AM UTC 2026
% Result : Theorem 7.71s 3.78s
% Output : Refutation 8.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 85
% Syntax : Number of formulae : 172 ( 31 unt; 0 typ; 0 def)
% Number of atoms : 685 ( 96 equ; 0 cnn)
% Maximal formula atoms : 19 ( 3 avg)
% Number of connectives : 3370 ( 382 ~; 428 |; 85 &;2475 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 29 ( 12 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 22 ( 20 usr; 5 con; 0-8 aty)
% Number of variables : 674 ( 0 ^; 674 !; 0 ?; 674 :)
% Comments :
%------------------------------------------------------------------------------
thf(sameside_decl,type,
sameside: $i > $i > $i > $o ).
thf(insert_decl,type,
insert: $i > $i > $i > $i > $i ).
thf(s_e_decl,type,
s_e: $i > $i > $i > $i > $o ).
thf(s_t_decl,type,
s_t: $i > $i > $i > $o ).
thf(ip_decl,type,
ip: $i > $i > $i > $i > $i > $i ).
thf(s_col_decl,type,
s_col: $i > $i > $i > $o ).
thf(ext_decl,type,
ext: $i > $i > $i > $i > $i ).
thf(alpha_decl,type,
alpha: $i ).
thf(gamma_decl,type,
gamma: $i ).
thf(s_e3_decl,type,
s_e3: $i > $i > $i > $i > $i > $i > $o ).
thf(beta_decl,type,
beta: $i ).
thf(le_decl,type,
le: $i > $i > $i > $i > $o ).
thf(crossbar_decl,type,
crossbar: $i > $i > $i > $i > $i > $i > $i ).
thf(insert5_decl,type,
insert5: $i > $i > $i > $i > $i > $i ).
thf(s_ifs_decl,type,
s_ifs: $i > $i > $i > $i > $i > $i > $i > $i > $o ).
thf(s_fs_decl,type,
s_fs: $i > $i > $i > $i > $i > $i > $i > $i > $o ).
thf(xb_decl,type,
xb: $i ).
thf(s_afs_decl,type,
s_afs: $i > $i > $i > $i > $i > $i > $i > $i > $o ).
thf(c63_decl,type,
c63: $i > $i > $i > $i ).
thf(ins_decl,type,
ins: $i > $i > $i > $i > $i ).
thf(31,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( C @ ( A @ ( C @ ( B @ le ) ) ) )
| ~ ( C @ ( A @ ( B @ ( A @ le ) ) ) )
| ( C @ ( B @ ( A @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz5_12b) ).
thf(184,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( C @ ( A @ ( C @ ( B @ le ) ) ) )
| ~ ( C @ ( A @ ( B @ ( A @ le ) ) ) )
| ( C @ ( B @ ( A @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ ( A @ ( B @ ( D @ ( C @ insert ) ) ) @ ( B @ s_e ) ) ) )
| ( C = D )
| ( A = B ) )
& ( ( A @ ( B @ ( A @ ( B @ ( D @ ( C @ insert ) ) ) @ sameside ) ) )
| ( C = D )
| ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz6_11a) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ ( A @ ( B @ ( D @ ( C @ insert ) ) ) @ ( B @ s_e ) ) ) )
| ( C = D )
| ( A = B ) )
& ( ( A @ ( B @ ( A @ ( B @ ( D @ ( C @ insert ) ) ) @ sameside ) ) )
| ( C = D )
| ( A = B ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(87,plain,
~ ! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ ( A @ ( B @ ( D @ ( C @ insert ) ) ) @ ( B @ s_e ) ) ) )
| ( C = D )
| ( A = B ) )
& ( ( A @ ( B @ ( A @ ( B @ ( D @ ( C @ insert ) ) ) @ sameside ) ) )
| ( C = D )
| ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(41,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( B @ ( A @ s_t ) ) )
| ~ ( C @ ( D @ ( B @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz3_5a) ).
thf(217,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( B @ ( A @ s_t ) ) )
| ~ ( C @ ( D @ ( B @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(75,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( E @ ( D @ ( C @ s_e ) ) ) )
| ~ ( F @ ( E @ ( B @ ( A @ s_e ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ s_e ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aA2) ).
thf(379,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( E @ ( D @ ( C @ s_e ) ) ) )
| ~ ( F @ ( E @ ( B @ ( A @ s_e ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ s_e ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(86,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ~ ( D @ ( C @ ( E @ ( A @ s_e ) ) ) )
| ~ ( E @ ( B @ ( A @ s_t ) ) )
| ( D @ ( C @ ( B @ ( A @ le ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz5_5b) ).
thf(440,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ~ ( D @ ( C @ ( E @ ( A @ s_e ) ) ) )
| ~ ( E @ ( B @ ( A @ s_t ) ) )
| ( D @ ( C @ ( B @ ( A @ le ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(52,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ s_e ) ) ) )
| ~ ( B @ ( A @ ( D @ ( C @ le ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ le ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz5_9) ).
thf(284,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ s_e ) ) ) )
| ~ ( B @ ( A @ ( D @ ( C @ le ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ le ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(22,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( A @ s_t ) ) )
| ( D @ ( C @ ( A @ s_t ) ) )
| ~ ( D @ ( B @ ( A @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz5_1) ).
thf(152,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( A @ s_t ) ) )
| ( D @ ( C @ ( A @ s_t ) ) )
| ~ ( D @ ( B @ ( A @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(54,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( H @ ( G @ ( D @ ( C @ s_e ) ) ) )
| ( A = B )
| ~ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s_fs ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz4_16) ).
thf(289,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( H @ ( G @ ( D @ ( C @ s_e ) ) ) )
| ( A = B )
| ~ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s_fs ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(63,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( A @ sameside ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz6_5) ).
thf(321,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( A @ sameside ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(47,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( E @ ( D @ ( B @ ( A @ s_e ) ) ) )
| ~ ( F @ ( E @ ( C @ ( B @ s_e ) ) ) )
| ~ ( F @ ( D @ ( C @ ( A @ s_e ) ) ) )
| ~ ( F @ ( E @ ( D @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz4_3) ).
thf(253,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( E @ ( D @ ( B @ ( A @ s_e ) ) ) )
| ~ ( F @ ( E @ ( C @ ( B @ s_e ) ) ) )
| ~ ( F @ ( D @ ( C @ ( A @ s_e ) ) ) )
| ~ ( F @ ( E @ ( D @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(20,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( E @ ( D @ s_t ) ) )
| ~ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s_e3 ) ) ) ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz4_6) ).
thf(147,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( E @ ( D @ s_t ) ) )
| ~ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s_e3 ) ) ) ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(14,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( A @ ( D @ ( C @ le ) ) ) )
| ( D @ ( C @ ( B @ ( A @ le ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz5_10) ).
thf(133,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( A @ ( D @ ( C @ le ) ) ) )
| ( D @ ( C @ ( B @ ( A @ le ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(8,axiom,
! [A: $i,B: $i] : ( B @ ( A @ ( A @ s_t ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz3_3) ).
thf(116,plain,
! [A: $i,B: $i] : ( B @ ( A @ ( A @ s_t ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(55,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( H @ ( G @ ( F @ ( E @ le ) ) ) )
| ~ ( H @ ( G @ ( D @ ( C @ s_e ) ) ) )
| ~ ( F @ ( E @ ( B @ ( A @ s_e ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ le ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz5_6) ).
thf(292,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( H @ ( G @ ( F @ ( E @ le ) ) ) )
| ~ ( H @ ( G @ ( D @ ( C @ s_e ) ) ) )
| ~ ( F @ ( E @ ( B @ ( A @ s_e ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ le ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(36,axiom,
! [A: $i,B: $i,C: $i] :
( ( A = B )
| ~ ( C @ ( A @ ( B @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz3_4) ).
thf(201,plain,
! [A: $i,B: $i,C: $i] :
( ( A = B )
| ~ ( C @ ( A @ ( B @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(42,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B = D )
| ~ ( D @ ( C @ ( B @ ( C @ s_e ) ) ) )
| ~ ( D @ ( A @ ( B @ ( A @ s_e ) ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz4_19) ).
thf(220,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B = D )
| ~ ( D @ ( C @ ( B @ ( C @ s_e ) ) ) )
| ~ ( D @ ( A @ ( B @ ( A @ s_e ) ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(69,axiom,
! [A: $i,B: $i,C: $i] :
( ( A = B )
| ~ ( C @ ( C @ ( B @ ( A @ s_e ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aA3) ).
thf(334,plain,
! [A: $i,B: $i,C: $i] :
( ( A = B )
| ~ ( C @ ( C @ ( B @ ( A @ s_e ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(58,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( B @ ( A @ sameside ) ) )
| ~ ( D @ ( B @ ( C @ s_t ) ) )
| ~ ( D @ ( B @ ( A @ s_t ) ) )
| ( D = B )
| ( C = B )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz6_2a) ).
thf(302,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( B @ ( A @ sameside ) ) )
| ~ ( D @ ( B @ ( C @ s_t ) ) )
| ~ ( D @ ( B @ ( A @ s_t ) ) )
| ( D = B )
| ( C = B )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(83,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s_e3 ) ) ) ) ) )
| ~ ( F @ ( E @ ( C @ ( B @ s_e ) ) ) )
| ~ ( F @ ( D @ ( C @ ( A @ s_e ) ) ) )
| ~ ( E @ ( D @ ( B @ ( A @ s_e ) ) ) ) )
& ( ( F @ ( E @ ( C @ ( B @ s_e ) ) ) )
| ~ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s_e3 ) ) ) ) ) ) )
& ( ( F @ ( D @ ( C @ ( A @ s_e ) ) ) )
| ~ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s_e3 ) ) ) ) ) ) )
& ( ( E @ ( D @ ( B @ ( A @ s_e ) ) ) )
| ~ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s_e3 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d_Defn4_4) ).
thf(424,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s_e3 ) ) ) ) ) )
| ~ ( F @ ( E @ ( C @ ( B @ s_e ) ) ) )
| ~ ( F @ ( D @ ( C @ ( A @ s_e ) ) ) )
| ~ ( E @ ( D @ ( B @ ( A @ s_e ) ) ) ) )
& ( ( F @ ( E @ ( C @ ( B @ s_e ) ) ) )
| ~ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s_e3 ) ) ) ) ) ) )
& ( ( F @ ( D @ ( C @ ( A @ s_e ) ) ) )
| ~ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s_e3 ) ) ) ) ) ) )
& ( ( E @ ( D @ ( B @ ( A @ s_e ) ) ) )
| ~ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s_e3 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(33,axiom,
! [A: $i,B: $i] : ( B @ ( A @ ( B @ ( A @ le ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz5_7) ).
thf(192,plain,
! [A: $i,B: $i] : ( B @ ( A @ ( B @ ( A @ le ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(16,axiom,
! [A: $i,B: $i] : ( B @ ( B @ ( A @ s_t ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz3_1) ).
thf(137,plain,
! [A: $i,B: $i] : ( B @ ( B @ ( A @ s_t ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(26,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( A @ s_t ) ) )
| ~ ( C @ ( D @ ( B @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz3_5b) ).
thf(165,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( A @ s_t ) ) )
| ~ ( C @ ( D @ ( B @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(73,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s_afs ) ) ) ) ) ) ) )
| ~ ( H @ ( F @ ( D @ ( B @ s_e ) ) ) )
| ~ ( H @ ( E @ ( D @ ( A @ s_e ) ) ) )
| ~ ( G @ ( F @ ( C @ ( B @ s_e ) ) ) )
| ~ ( F @ ( E @ ( B @ ( A @ s_e ) ) ) )
| ~ ( G @ ( F @ ( E @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) ) )
& ( ( H @ ( F @ ( D @ ( B @ s_e ) ) ) )
| ~ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s_afs ) ) ) ) ) ) ) ) )
& ( ( H @ ( E @ ( D @ ( A @ s_e ) ) ) )
| ~ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s_afs ) ) ) ) ) ) ) ) )
& ( ( G @ ( F @ ( C @ ( B @ s_e ) ) ) )
| ~ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s_afs ) ) ) ) ) ) ) ) )
& ( ( F @ ( E @ ( B @ ( A @ s_e ) ) ) )
| ~ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s_afs ) ) ) ) ) ) ) ) )
& ( ( G @ ( F @ ( E @ s_t ) ) )
| ~ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s_afs ) ) ) ) ) ) ) ) )
& ( ( C @ ( B @ ( A @ s_t ) ) )
| ~ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s_afs ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d_Defn2_10) ).
thf(361,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s_afs ) ) ) ) ) ) ) )
| ~ ( H @ ( F @ ( D @ ( B @ s_e ) ) ) )
| ~ ( H @ ( E @ ( D @ ( A @ s_e ) ) ) )
| ~ ( G @ ( F @ ( C @ ( B @ s_e ) ) ) )
| ~ ( F @ ( E @ ( B @ ( A @ s_e ) ) ) )
| ~ ( G @ ( F @ ( E @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) ) )
& ( ( H @ ( F @ ( D @ ( B @ s_e ) ) ) )
| ~ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s_afs ) ) ) ) ) ) ) ) )
& ( ( H @ ( E @ ( D @ ( A @ s_e ) ) ) )
| ~ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s_afs ) ) ) ) ) ) ) ) )
& ( ( G @ ( F @ ( C @ ( B @ s_e ) ) ) )
| ~ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s_afs ) ) ) ) ) ) ) ) )
& ( ( F @ ( E @ ( B @ ( A @ s_e ) ) ) )
| ~ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s_afs ) ) ) ) ) ) ) ) )
& ( ( G @ ( F @ ( E @ s_t ) ) )
| ~ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s_afs ) ) ) ) ) ) ) ) )
& ( ( C @ ( B @ ( A @ s_t ) ) )
| ~ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s_afs ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(64,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ sameside ) ) )
| ~ ( C @ ( B @ ( A @ sameside ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz6_6) ).
thf(324,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ sameside ) ) )
| ~ ( C @ ( B @ ( A @ sameside ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(43,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ ( D @ ( C @ ( B @ ( A @ insert5 ) ) ) ) @ ( E @ ( D @ ( C @ ( B @ ( A @ s_e3 ) ) ) ) ) )
| ~ ( E @ ( D @ ( B @ ( A @ s_e ) ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz4_14) ).
thf(224,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ ( D @ ( C @ ( B @ ( A @ insert5 ) ) ) ) @ ( E @ ( D @ ( C @ ( B @ ( A @ s_e3 ) ) ) ) ) )
| ~ ( E @ ( D @ ( B @ ( A @ s_e ) ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(62,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C = D )
| ~ ( D @ ( B @ ( C @ ( B @ s_e ) ) ) )
| ~ ( D @ ( A @ ( C @ ( A @ s_e ) ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz4_18) ).
thf(317,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C = D )
| ~ ( D @ ( B @ ( C @ ( B @ s_e ) ) ) )
| ~ ( D @ ( A @ ( C @ ( A @ s_e ) ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(23,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( D @ ( A @ s_t ) ) )
| ( D @ ( B @ ( A @ s_t ) ) )
| ~ ( C @ ( D @ ( A @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz5_3) ).
thf(156,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( D @ ( A @ s_t ) ) )
| ( D @ ( B @ ( A @ s_t ) ) )
| ~ ( C @ ( D @ ( A @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(11,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( B @ ( A @ s_t ) ) )
| ~ ( D @ ( C @ ( A @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz3_6b) ).
thf(124,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( B @ ( A @ s_t ) ) )
| ~ ( D @ ( C @ ( A @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(40,axiom,
( ~ ( beta @ ( alpha @ ( gamma @ s_t ) ) )
& ~ ( alpha @ ( gamma @ ( beta @ s_t ) ) )
& ~ ( gamma @ ( beta @ ( alpha @ s_t ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aA8) ).
thf(212,plain,
( ~ ( beta @ ( alpha @ ( gamma @ s_t ) ) )
& ~ ( alpha @ ( gamma @ ( beta @ s_t ) ) )
& ~ ( gamma @ ( beta @ ( alpha @ s_t ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(48,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( C @ ( B @ ( A @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ sameside ) ) ) )
& ( ( C @ ( B @ ( A @ s_col ) ) )
| ~ ( C @ ( B @ ( A @ sameside ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz6_4a) ).
thf(256,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( C @ ( B @ ( A @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ sameside ) ) ) )
& ( ( C @ ( B @ ( A @ s_col ) ) )
| ~ ( C @ ( B @ ( A @ sameside ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(5,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( A @ s_col ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz4_11e) ).
thf(109,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( A @ s_col ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(66,axiom,
! [A: $i,B: $i] : ( B @ ( A @ ( B @ ( A @ s_e ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz2_1) ).
thf(328,plain,
! [A: $i,B: $i] : ( B @ ( A @ ( B @ ( A @ s_e ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(50,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s_fs ) ) ) ) ) ) ) )
| ~ ( H @ ( F @ ( D @ ( B @ s_e ) ) ) )
| ~ ( H @ ( E @ ( D @ ( A @ s_e ) ) ) )
| ~ ( G @ ( F @ ( E @ ( C @ ( B @ ( A @ s_e3 ) ) ) ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) ) )
& ( ( H @ ( F @ ( D @ ( B @ s_e ) ) ) )
| ~ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s_fs ) ) ) ) ) ) ) ) )
& ( ( H @ ( E @ ( D @ ( A @ s_e ) ) ) )
| ~ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s_fs ) ) ) ) ) ) ) ) )
& ( ( G @ ( F @ ( E @ ( C @ ( B @ ( A @ s_e3 ) ) ) ) ) )
| ~ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s_fs ) ) ) ) ) ) ) ) )
& ( ( C @ ( B @ ( A @ s_col ) ) )
| ~ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s_fs ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d_Defn4_15) ).
thf(266,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s_fs ) ) ) ) ) ) ) )
| ~ ( H @ ( F @ ( D @ ( B @ s_e ) ) ) )
| ~ ( H @ ( E @ ( D @ ( A @ s_e ) ) ) )
| ~ ( G @ ( F @ ( E @ ( C @ ( B @ ( A @ s_e3 ) ) ) ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) ) )
& ( ( H @ ( F @ ( D @ ( B @ s_e ) ) ) )
| ~ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s_fs ) ) ) ) ) ) ) ) )
& ( ( H @ ( E @ ( D @ ( A @ s_e ) ) ) )
| ~ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s_fs ) ) ) ) ) ) ) ) )
& ( ( G @ ( F @ ( E @ ( C @ ( B @ ( A @ s_e3 ) ) ) ) ) )
| ~ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s_fs ) ) ) ) ) ) ) ) )
& ( ( C @ ( B @ ( A @ s_col ) ) )
| ~ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s_fs ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(61,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E @ ( E @ ( D @ ( B @ ( A @ insert ) ) ) @ ( D @ ( C @ ( B @ ( A @ s_e3 ) ) ) ) ) )
| ~ ( E @ ( D @ ( C @ ( A @ s_e ) ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) ) )
& ( ( E @ ( E @ ( D @ ( B @ ( A @ insert ) ) ) @ ( D @ s_t ) ) )
| ~ ( E @ ( D @ ( C @ ( A @ s_e ) ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz4_5) ).
thf(311,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E @ ( E @ ( D @ ( B @ ( A @ insert ) ) ) @ ( D @ ( C @ ( B @ ( A @ s_e3 ) ) ) ) ) )
| ~ ( E @ ( D @ ( C @ ( A @ s_e ) ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) ) )
& ( ( E @ ( E @ ( D @ ( B @ ( A @ insert ) ) ) @ ( D @ s_t ) ) )
| ~ ( E @ ( D @ ( C @ ( A @ s_e ) ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(57,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( H @ ( F @ ( G @ ( E @ s_e ) ) ) )
| ( A = B )
| ~ ( F @ ( D @ ( C @ s_t ) ) )
| ~ ( E @ ( B @ ( A @ s_t ) ) )
| ~ ( H @ ( D @ ( G @ ( B @ s_e ) ) ) )
| ~ ( H @ ( C @ ( G @ ( A @ s_e ) ) ) )
| ~ ( F @ ( D @ ( E @ ( B @ s_e ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ s_e ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aA5) ).
thf(298,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( H @ ( F @ ( G @ ( E @ s_e ) ) ) )
| ( A = B )
| ~ ( F @ ( D @ ( C @ s_t ) ) )
| ~ ( E @ ( B @ ( A @ s_t ) ) )
| ~ ( H @ ( D @ ( G @ ( B @ s_e ) ) ) )
| ~ ( H @ ( C @ ( G @ ( A @ s_e ) ) ) )
| ~ ( F @ ( D @ ( E @ ( B @ s_e ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ s_e ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(29,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( A @ ( C @ ( B @ le ) ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz5_12a2) ).
thf(180,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( A @ ( C @ ( B @ le ) ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(53,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( D @ ( C @ ( A @ s_e ) ) ) )
| ~ ( E @ ( D @ ( C @ ( B @ s_e ) ) ) )
| ~ ( F @ ( E @ ( B @ ( A @ s_e ) ) ) )
| ~ ( F @ ( E @ ( D @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz2_15) ).
thf(286,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( D @ ( C @ ( A @ s_e ) ) ) )
| ~ ( E @ ( D @ ( C @ ( B @ s_e ) ) ) )
| ~ ( F @ ( E @ ( B @ ( A @ s_e ) ) ) )
| ~ ( F @ ( E @ ( D @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(9,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( B @ ( A @ s_t ) ) )
| ( B = C )
| ~ ( D @ ( C @ ( B @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz3_7b) ).
thf(118,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( B @ ( A @ s_t ) ) )
| ( B = C )
| ~ ( D @ ( C @ ( B @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(37,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( E @ ( B @ ( A @ le ) ) ) )
| ~ ( F @ ( E @ ( D @ ( C @ le ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ le ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz5_8) ).
thf(204,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( E @ ( B @ ( A @ le ) ) ) )
| ~ ( F @ ( E @ ( D @ ( C @ le ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ le ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(81,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( H @ ( F @ ( D @ ( B @ s_e ) ) ) )
| ~ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s_ifs ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz4_2) ).
thf(413,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( H @ ( F @ ( D @ ( B @ s_e ) ) ) )
| ~ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s_ifs ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(76,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( C @ ( B @ ( A @ sameside ) ) )
| ( D @ ( B @ ( C @ s_t ) ) )
| ~ ( D @ ( B @ ( A @ s_t ) ) )
| ( D = B )
| ( C = B )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz6_2b) ).
thf(382,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( C @ ( B @ ( A @ sameside ) ) )
| ( D @ ( B @ ( C @ s_t ) ) )
| ~ ( D @ ( B @ ( A @ s_t ) ) )
| ( D = B )
| ( C = B )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(24,axiom,
! [A: $i,B: $i] :
( A
!= ( gamma @ ( alpha @ ( A @ ( B @ ext ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz3_14b) ).
thf(159,plain,
! [A: $i,B: $i] :
( A
!= ( gamma @ ( alpha @ ( A @ ( B @ ext ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(79,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( B @ ( A @ sameside ) ) )
| ~ ( D @ ( B @ ( C @ sameside ) ) )
| ~ ( C @ ( B @ ( A @ sameside ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz6_7) ).
thf(406,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( B @ ( A @ sameside ) ) )
| ~ ( D @ ( B @ ( C @ sameside ) ) )
| ~ ( C @ ( B @ ( A @ sameside ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(7,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ s_t ) ) )
| ~ ( D @ ( C @ ( A @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz3_6a) ).
thf(113,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ s_t ) ) )
| ~ ( D @ ( C @ ( A @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(74,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( A @ ( B @ s_e ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ s_e ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz2_14) ).
thf(377,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( A @ ( B @ s_e ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ s_e ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(84,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( D @ ( C @ ( A @ s_e ) ) ) )
| ~ ( F @ ( E @ ( C @ ( B @ s_e ) ) ) )
| ~ ( E @ ( D @ ( B @ ( A @ s_e ) ) ) )
| ~ ( F @ ( E @ ( D @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz2_11) ).
thf(434,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( D @ ( C @ ( A @ s_e ) ) ) )
| ~ ( F @ ( E @ ( C @ ( B @ s_e ) ) ) )
| ~ ( E @ ( D @ ( B @ ( A @ s_e ) ) ) )
| ~ ( F @ ( E @ ( D @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( A @ ( E @ ( D @ ( C @ ( B @ ( A @ ip ) ) ) ) @ ( E @ s_t ) ) )
| ~ ( C @ ( E @ ( D @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) ) )
& ( ( D @ ( E @ ( D @ ( C @ ( B @ ( A @ ip ) ) ) ) @ ( B @ s_t ) ) )
| ~ ( C @ ( E @ ( D @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aA7) ).
thf(103,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( A @ ( E @ ( D @ ( C @ ( B @ ( A @ ip ) ) ) ) @ ( E @ s_t ) ) )
| ~ ( C @ ( E @ ( D @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) ) )
& ( ( D @ ( E @ ( D @ ( C @ ( B @ ( A @ ip ) ) ) ) @ ( B @ s_t ) ) )
| ~ ( C @ ( E @ ( D @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(46,axiom,
! [A: $i,B: $i] : ( A @ ( B @ ( B @ ( A @ s_e ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aA1) ).
thf(251,plain,
! [A: $i,B: $i] : ( A @ ( B @ ( B @ ( A @ s_e ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(35,axiom,
beta != gamma,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz3_13b) ).
thf(198,plain,
beta != gamma,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(67,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( B @ ( A @ s_e ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ s_e ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz2_5) ).
thf(330,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( B @ ( A @ s_e ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ s_e ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(13,axiom,
alpha != beta,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz3_13a) ).
thf(130,plain,
alpha != beta,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(51,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( D @ ( C @ ( B @ ( A @ ext ) ) ) @ ( B @ s_e ) ) ) )
& ( D @ ( C @ ( B @ ( A @ ext ) ) ) @ ( B @ ( A @ s_t ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aA4) ).
thf(278,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( D @ ( C @ ( B @ ( A @ ext ) ) ) @ ( B @ s_e ) ) ) )
& ( D @ ( C @ ( B @ ( A @ ext ) ) ) @ ( B @ ( A @ s_t ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(59,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ insert ) ) ) )
= ( B @ ( A @ ( C @ ( gamma @ ( alpha @ ( C @ ( D @ ext ) ) ) @ ext ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d_insert) ).
thf(306,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ insert ) ) ) )
= ( B @ ( A @ ( C @ ( gamma @ ( alpha @ ( C @ ( D @ ext ) ) ) @ ext ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(15,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ ( B @ s_col ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz4_11a) ).
thf(135,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ ( B @ s_col ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(71,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ ( A @ sameside ) ) )
| ( C = B )
| ( A = B )
| ~ ( A @ ( C @ ( B @ s_t ) ) ) )
& ( ( C @ ( B @ ( A @ sameside ) ) )
| ( xb = B )
| ( A = B )
| ~ ( C @ ( A @ ( B @ s_t ) ) ) )
& ( ( A @ ( C @ ( B @ s_t ) ) )
| ( C @ ( A @ ( B @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ sameside ) ) ) )
& ( ( C != B )
| ~ ( C @ ( B @ ( A @ sameside ) ) ) )
& ( ( A != B )
| ~ ( C @ ( B @ ( A @ sameside ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d_Defn6_1) ).
thf(342,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ ( A @ sameside ) ) )
| ( C = B )
| ( A = B )
| ~ ( A @ ( C @ ( B @ s_t ) ) ) )
& ( ( C @ ( B @ ( A @ sameside ) ) )
| ( xb = B )
| ( A = B )
| ~ ( C @ ( A @ ( B @ s_t ) ) ) )
& ( ( A @ ( C @ ( B @ s_t ) ) )
| ( C @ ( A @ ( B @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ sameside ) ) ) )
& ( ( C != B )
| ~ ( C @ ( B @ ( A @ sameside ) ) ) )
& ( ( A != B )
| ~ ( C @ ( B @ ( A @ sameside ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(34,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( B @ s_t ) ) )
| ( D @ ( C @ ( B @ s_t ) ) )
| ~ ( D @ ( B @ ( A @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz5_2) ).
thf(194,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( B @ s_t ) ) )
| ( D @ ( C @ ( B @ s_t ) ) )
| ~ ( D @ ( B @ ( A @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(19,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ s_col ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz4_11c) ).
thf(145,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ s_col ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(56,axiom,
! [A: $i,B: $i,C: $i] :
( ( C = B )
| ~ ( B @ ( A @ ( C @ ( A @ s_e ) ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aNarbouxLemma1) ).
thf(295,plain,
! [A: $i,B: $i,C: $i] :
( ( C = B )
| ~ ( B @ ( A @ ( C @ ( A @ s_e ) ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(21,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ s_col ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz4_11b) ).
thf(150,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ s_col ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(80,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( D @ ( B @ ( C @ s_t ) ) )
| ~ ( D @ ( B @ ( A @ s_t ) ) )
| ( D = B )
| ( C = B )
| ( A = B )
| ( C @ ( B @ ( A @ sameside ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz6_3b) ).
thf(409,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( D @ ( B @ ( C @ s_t ) ) )
| ~ ( D @ ( B @ ( A @ s_t ) ) )
| ( D = B )
| ( C = B )
| ( A = B )
| ( C @ ( B @ ( A @ sameside ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(30,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz3_2) ).
thf(182,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(12,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( E @ ( D @ s_col ) ) )
| ~ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s_e3 ) ) ) ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz4_13) ).
thf(127,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( E @ ( D @ s_col ) ) )
| ~ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s_e3 ) ) ) ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(70,axiom,
! [A: $i,B: $i,C: $i] :
( ( A = B )
| ~ ( C @ ( C @ ( B @ ( A @ s_e ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz2_13) ).
thf(338,plain,
! [A: $i,B: $i,C: $i] :
( ( A = B )
| ~ ( C @ ( C @ ( B @ ( A @ s_e ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(72,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) )
| ( C @ ( B @ ( A @ sameside ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz6_4b) ).
thf(359,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) )
| ( C @ ( B @ ( A @ sameside ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(77,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C
= ( E @ ( D @ ( B @ ( A @ ext ) ) ) ) )
| ~ ( E @ ( D @ ( C @ ( B @ s_e ) ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz2_12) ).
thf(386,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C
= ( E @ ( D @ ( B @ ( A @ ext ) ) ) ) )
| ~ ( E @ ( D @ ( C @ ( B @ s_e ) ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(18,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( A @ ( B @ s_col ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz4_11d) ).
thf(143,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( A @ ( B @ s_col ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(78,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ ( A @ c63 ) ) @ ( B @ ( C @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ sameside ) ) ) )
& ( ( C @ ( B @ ( A @ c63 ) ) @ ( B @ ( A @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ sameside ) ) ) )
& ( ( ( C @ ( B @ ( A @ c63 ) ) )
!= B )
| ~ ( C @ ( B @ ( A @ sameside ) ) ) )
& ( ( C != B )
| ~ ( C @ ( B @ ( A @ sameside ) ) ) )
& ( ( A != B )
| ~ ( C @ ( B @ ( A @ sameside ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz6_3a) ).
thf(390,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ ( A @ c63 ) ) @ ( B @ ( C @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ sameside ) ) ) )
& ( ( C @ ( B @ ( A @ c63 ) ) @ ( B @ ( A @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ sameside ) ) ) )
& ( ( ( C @ ( B @ ( A @ c63 ) ) )
!= B )
| ~ ( C @ ( B @ ( A @ sameside ) ) ) )
& ( ( C != B )
| ~ ( C @ ( B @ ( A @ sameside ) ) ) )
& ( ( A != B )
| ~ ( C @ ( B @ ( A @ sameside ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(32,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( E @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ crossbar ) ) ) ) ) @ ( B @ s_t ) ) )
| ~ ( D @ ( F @ ( A @ s_t ) ) )
| ~ ( C @ ( E @ ( D @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) ) )
& ( ( C @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ crossbar ) ) ) ) ) @ ( F @ s_t ) ) )
| ~ ( D @ ( F @ ( A @ s_t ) ) )
| ~ ( C @ ( E @ ( D @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz3_17) ).
thf(186,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( E @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ crossbar ) ) ) ) ) @ ( B @ s_t ) ) )
| ~ ( D @ ( F @ ( A @ s_t ) ) )
| ~ ( C @ ( E @ ( D @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) ) )
& ( ( C @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ crossbar ) ) ) ) ) @ ( F @ s_t ) ) )
| ~ ( D @ ( F @ ( A @ s_t ) ) )
| ~ ( C @ ( E @ ( D @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(17,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( A @ s_t ) ) )
| ( B = C )
| ~ ( D @ ( C @ ( B @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz3_7a) ).
thf(139,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( A @ s_t ) ) )
| ( B = C )
| ~ ( D @ ( C @ ( B @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(45,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s_ifs ) ) ) ) ) ) ) )
| ~ ( H @ ( G @ ( D @ ( C @ s_e ) ) ) )
| ~ ( H @ ( E @ ( D @ ( A @ s_e ) ) ) )
| ~ ( G @ ( F @ ( C @ ( B @ s_e ) ) ) )
| ~ ( G @ ( E @ ( C @ ( A @ s_e ) ) ) )
| ~ ( G @ ( F @ ( E @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) ) )
& ( ( H @ ( G @ ( D @ ( C @ s_e ) ) ) )
| ~ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s_ifs ) ) ) ) ) ) ) ) )
& ( ( H @ ( E @ ( D @ ( A @ s_e ) ) ) )
| ~ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s_ifs ) ) ) ) ) ) ) ) )
& ( ( G @ ( F @ ( C @ ( B @ s_e ) ) ) )
| ~ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s_ifs ) ) ) ) ) ) ) ) )
& ( ( G @ ( E @ ( C @ ( A @ s_e ) ) ) )
| ~ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s_ifs ) ) ) ) ) ) ) ) )
& ( ( G @ ( F @ ( E @ s_t ) ) )
| ~ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s_ifs ) ) ) ) ) ) ) ) )
& ( ( C @ ( B @ ( A @ s_t ) ) )
| ~ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s_ifs ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d_Defn4_1) ).
thf(235,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s_ifs ) ) ) ) ) ) ) )
| ~ ( H @ ( G @ ( D @ ( C @ s_e ) ) ) )
| ~ ( H @ ( E @ ( D @ ( A @ s_e ) ) ) )
| ~ ( G @ ( F @ ( C @ ( B @ s_e ) ) ) )
| ~ ( G @ ( E @ ( C @ ( A @ s_e ) ) ) )
| ~ ( G @ ( F @ ( E @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) ) )
& ( ( H @ ( G @ ( D @ ( C @ s_e ) ) ) )
| ~ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s_ifs ) ) ) ) ) ) ) ) )
& ( ( H @ ( E @ ( D @ ( A @ s_e ) ) ) )
| ~ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s_ifs ) ) ) ) ) ) ) ) )
& ( ( G @ ( F @ ( C @ ( B @ s_e ) ) ) )
| ~ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s_ifs ) ) ) ) ) ) ) ) )
& ( ( G @ ( E @ ( C @ ( A @ s_e ) ) ) )
| ~ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s_ifs ) ) ) ) ) ) ) ) )
& ( ( G @ ( F @ ( E @ s_t ) ) )
| ~ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s_ifs ) ) ) ) ) ) ) ) )
& ( ( C @ ( B @ ( A @ s_t ) ) )
| ~ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s_ifs ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(38,axiom,
alpha != gamma,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz3_13c) ).
thf(207,plain,
alpha != gamma,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(27,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( B @ ( A @ ( C @ s_t ) ) )
| ( C @ ( B @ ( A @ s_col ) ) ) )
& ( ~ ( A @ ( C @ ( B @ s_t ) ) )
| ( C @ ( B @ ( A @ s_col ) ) ) )
& ( ~ ( C @ ( B @ ( A @ s_t ) ) )
| ( C @ ( B @ ( A @ s_col ) ) ) )
& ( ( B @ ( A @ ( C @ s_t ) ) )
| ( A @ ( C @ ( B @ s_t ) ) )
| ( C @ ( B @ ( A @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d_Defn4_10) ).
thf(168,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( B @ ( A @ ( C @ s_t ) ) )
| ( C @ ( B @ ( A @ s_col ) ) ) )
& ( ~ ( A @ ( C @ ( B @ s_t ) ) )
| ( C @ ( B @ ( A @ s_col ) ) ) )
& ( ~ ( C @ ( B @ ( A @ s_t ) ) )
| ( C @ ( B @ ( A @ s_col ) ) ) )
& ( ( B @ ( A @ ( C @ s_t ) ) )
| ( A @ ( C @ ( B @ s_t ) ) )
| ( C @ ( B @ ( A @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(49,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ ( C @ ( D @ ( C @ s_e ) ) ) )
| ~ ( E @ ( B @ ( D @ ( B @ s_e ) ) ) )
| ~ ( E @ ( A @ ( D @ ( A @ s_e ) ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz4_17) ).
thf(262,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ ( C @ ( D @ ( C @ s_e ) ) ) )
| ~ ( E @ ( B @ ( D @ ( B @ s_e ) ) ) )
| ~ ( E @ ( A @ ( D @ ( A @ s_e ) ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(39,axiom,
! [A: $i,B: $i] : ( A @ ( B @ ( A @ s_col ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz4_12b) ).
thf(210,plain,
! [A: $i,B: $i] : ( A @ ( B @ ( A @ s_col ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(65,axiom,
! [A: $i,B: $i] : ( B @ ( B @ ( A @ ( A @ s_e ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz2_8) ).
thf(326,plain,
! [A: $i,B: $i] : ( B @ ( B @ ( A @ ( A @ s_e ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(85,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( E @ ( B @ ( A @ s_e ) ) ) )
| ~ ( F @ ( E @ ( D @ ( C @ s_e ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ s_e ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz2_3) ).
thf(437,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( E @ ( B @ ( A @ s_e ) ) ) )
| ~ ( F @ ( E @ ( D @ ( C @ s_e ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ s_e ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(82,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( B @ ( A @ ( D @ ( C @ ins ) ) ) )
= ( D @ ( D @ ( C @ ( B @ ( A @ insert ) ) ) @ ( B @ ( A @ ext ) ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ le ) ) ) ) )
& ( ( D @ ( C @ ( B @ ( A @ ( D @ ( C @ ins ) ) ) @ ( A @ s_e ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ le ) ) ) ) )
& ( ( B @ ( A @ ( D @ ( C @ ins ) ) ) @ ( B @ ( A @ s_t ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ le ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz5_5a) ).
thf(415,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( B @ ( A @ ( D @ ( C @ ins ) ) ) )
= ( D @ ( D @ ( C @ ( B @ ( A @ insert ) ) ) @ ( B @ ( A @ ext ) ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ le ) ) ) ) )
& ( ( D @ ( C @ ( B @ ( A @ ( D @ ( C @ ins ) ) ) @ ( A @ s_e ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ le ) ) ) ) )
& ( ( B @ ( A @ ( D @ ( C @ ins ) ) ) @ ( B @ ( A @ s_t ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ le ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(68,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( A @ ( B @ s_e ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ s_e ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz2_4) ).
thf(332,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( A @ ( B @ s_e ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ s_e ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(25,axiom,
! [A: $i,B: $i,C: $i] : ( C @ ( B @ ( A @ ( A @ le ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz5_11) ).
thf(163,plain,
! [A: $i,B: $i,C: $i] : ( C @ ( B @ ( A @ ( A @ le ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(28,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( A @ ( B @ ( A @ le ) ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz5_12a1) ).
thf(178,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( A @ ( B @ ( A @ le ) ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(6,axiom,
! [A: $i,B: $i] : ( gamma @ ( alpha @ ( B @ ( A @ ext ) ) ) @ ( B @ ( A @ s_t ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz3_14a) ).
thf(111,plain,
! [A: $i,B: $i] : ( gamma @ ( alpha @ ( B @ ( A @ ext ) ) ) @ ( B @ ( A @ s_t ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(44,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( D @ ( C @ ( B @ ( A @ le ) ) ) )
| ~ ( E @ ( C @ ( B @ ( A @ s_e ) ) ) )
| ~ ( D @ ( E @ ( C @ s_t ) ) ) )
& ( ( D @ ( C @ ( B @ ( A @ insert ) ) ) @ ( C @ ( B @ ( A @ s_e ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ le ) ) ) ) )
& ( ( D @ ( D @ ( C @ ( B @ ( A @ insert ) ) ) @ ( C @ s_t ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ le ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d_Defn5_4) ).
thf(227,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( D @ ( C @ ( B @ ( A @ le ) ) ) )
| ~ ( E @ ( C @ ( B @ ( A @ s_e ) ) ) )
| ~ ( D @ ( E @ ( C @ s_t ) ) ) )
& ( ( D @ ( C @ ( B @ ( A @ insert ) ) ) @ ( C @ ( B @ ( A @ s_e ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ le ) ) ) ) )
& ( ( D @ ( D @ ( C @ ( B @ ( A @ insert ) ) ) @ ( C @ s_t ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ le ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(10,axiom,
! [A: $i,B: $i] : ( B @ ( A @ ( A @ s_col ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz4_12) ).
thf(122,plain,
! [A: $i,B: $i] : ( B @ ( A @ ( A @ s_col ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(60,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( A @ ( D @ ( C @ s_e ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ s_e ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz2_2) ).
thf(309,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( A @ ( D @ ( C @ s_e ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ s_e ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( A = B )
| ~ ( A @ ( B @ ( A @ s_t ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aA6) ).
thf(100,plain,
! [A: $i,B: $i] :
( ( A = B )
| ~ ( A @ ( B @ ( A @ s_t ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(467,plain,
$false,
inference(e,[status(thm)],[184,87,217,379,440,284,152,289,321,253,147,133,116,292,201,220,334,302,424,192,137,165,361,324,224,317,156,124,212,256,109,328,266,311,298,180,286,118,204,413,382,159,406,113,377,434,103,251,198,330,130,278,306,135,342,194,145,295,150,409,182,127,338,359,386,143,390,186,139,235,207,168,262,210,326,437,415,332,163,178,111,227,122,309,100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO497+1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.12/0.40 % Computer : n015.cluster.edu
% 0.12/0.40 % Model : x86_64 x86_64
% 0.12/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.40 % Memory : 8046.5625MB
% 0.12/0.40 % OS : Linux 6.8.0-71-generic
% 0.12/0.40 % CPULimit : 300
% 0.12/0.40 % WCLimit : 300
% 0.12/0.40 % DateTime : Fri Sep 25 13:39:42 UTC 2026
% 0.12/0.41 % CPUTime :
% 0.12/0.41 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.84/0.99 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.35/1.27 % [INFO] Parsing done (278ms).
% 1.35/1.29 % [INFO] Running in sequential loop mode.
% 2.21/1.67 % [INFO] eprover registered as external prover.
% 2.21/1.68 % [INFO] Scanning for conjecture ...
% 2.58/1.80 % [INFO] Found a conjecture (or negated_conjecture) and 84 axioms. Running axiom selection ...
% 2.58/1.89 % [INFO] Axiom selection finished. Selected 84 axioms (removed 0 axioms).
% 3.07/2.04 % [INFO] Problem is first-order (TPTP FOF).
% 3.07/2.07 % [INFO] Type checking passed.
% 3.07/2.07 % [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 ...
% 7.71/3.78 % External prover 'e' found a proof!
% 7.71/3.78 % [INFO] Killing All external provers ...
% 7.71/3.78 % Time passed: 3226ms (effective reasoning time: 2482ms)
% 7.71/3.78 % 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)>
% 7.71/3.78 % Axioms used in derivation (84): aSatz4_5, aSatz5_2, aSatz6_2b, aSatz3_5a, aNarbouxLemma1, aSatz4_3, aSatz4_12b, aA7, aSatz5_9, aSatz3_4, aSatz6_5, aSatz2_13, aSatz3_14b, aSatz2_3, d_Defn5_4, aSatz4_11d, aSatz5_6, aSatz6_2a, d_Defn4_4, aSatz3_1, aSatz3_13c, aSatz6_3a, aSatz6_4b, aA1, aSatz4_16, d_insert, aSatz6_3b, aA5, aSatz5_12a1, d_Defn6_1, aSatz3_13a, aSatz6_6, d_Defn4_15, aSatz2_12, aSatz3_3, aSatz3_5b, aSatz3_17, aSatz4_11c, d_Defn4_10, aSatz5_1, aSatz5_12b, aSatz3_13b, aSatz4_19, aSatz4_14, aSatz2_1, d_Defn4_1, aA2, aSatz4_11b, aSatz2_5, aSatz3_6b, aA3, aSatz3_2, aSatz5_12a2, aA6, aSatz3_6a, aSatz5_11, aSatz4_18, aSatz2_2, aSatz5_5a, aSatz2_15, aSatz4_11a, aSatz2_4, aSatz3_14a, aA4, aSatz5_8, aSatz3_7a, aSatz4_6, aSatz5_7, aSatz4_13, aSatz2_11, aSatz2_14, aSatz4_11e, aSatz5_10, d_Defn2_10, aSatz5_5b, aSatz4_12, aSatz4_17, aSatz5_3, aSatz2_8, aSatz4_2, aSatz6_4a, aA8, aSatz3_7b, aSatz6_7
% 7.71/3.78 % No. of inferences in proof: 172
% 7.71/3.78 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 3226 ms resp. 2482 ms w/o parsing
% 8.52/3.91 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 8.52/3.91 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------