%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : GEO504+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 : n003.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 07:13:25 AM UTC 2026
% Result : Theorem 18.78s 6.49s
% Output : Refutation 20.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 89
% Syntax : Number of formulae : 180 ( 21 unt; 0 typ; 0 def)
% Number of atoms : 743 ( 116 equ; 0 cnn)
% Maximal formula atoms : 30 ( 4 avg)
% Number of connectives : 3636 ( 415 ~; 483 |; 80 &;2658 @)
% ( 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; 1 con; 0-8 aty)
% Number of variables : 731 ( 0 ^; 731 !; 0 ?; 731 :)
% Comments :
%------------------------------------------------------------------------------
thf(s_r_decl,type,
s_r: $i > $i > $i > $o ).
thf(s_kf_decl,type,
s_kf: $i > $i > $i > $i > $i > $i > $i > $o ).
thf(s_t_decl,type,
s_t: $i > $i > $i > $o ).
thf(s_e_decl,type,
s_e: $i > $i > $i > $i > $o ).
thf(s_ifs_decl,type,
s_ifs: $i > $i > $i > $i > $i > $i > $i > $i > $o ).
thf(s_col_decl,type,
s_col: $i > $i > $i > $o ).
thf(s_decl,type,
s: $i > $i > $i ).
thf(s_m_decl,type,
s_m: $i > $i > $i > $o ).
thf(insert_decl,type,
insert: $i > $i > $i > $i > $i ).
thf(s_e3_decl,type,
s_e3: $i > $i > $i > $i > $i > $i > $o ).
thf(insert5_decl,type,
insert5: $i > $i > $i > $i > $i > $i ).
thf(s_fs_decl,type,
s_fs: $i > $i > $i > $i > $i > $i > $i > $i > $o ).
thf(s_afs_decl,type,
s_afs: $i > $i > $i > $i > $i > $i > $i > $i > $o ).
thf(perp_decl,type,
perp: $i > $i > $i > $i > $o ).
thf(perpAt_decl,type,
perpAt: $i > $i > $i > $i > $i > $o ).
thf(il_decl,type,
il: $i > $i > $i > $i > $i ).
thf(pointOffLine_decl,type,
pointOffLine: $i > $i > $i ).
thf(isomidpoint_decl,type,
isomidpoint: $i > $i > $i > $i ).
thf(f811_decl,type,
f811: $i > $i > $i > $i > $i > $i ).
thf(g811_decl,type,
g811: $i > $i > $i > $i > $i > $i ).
thf(26,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B = D )
| ~ ( C @ ( D @ ( A @ s_m ) ) )
| ~ ( C @ ( B @ ( A @ s_m ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz7_17) ).
thf(202,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B = D )
| ~ ( C @ ( D @ ( A @ s_m ) ) )
| ~ ( C @ ( B @ ( A @ s_m ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(24,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(196,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)],[24]) ).
thf(35,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(233,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)],[35]) ).
thf(59,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(339,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)],[59]) ).
thf(41,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(259,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)],[41]) ).
thf(33,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(223,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)],[33]) ).
thf(67,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(363,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)],[67]) ).
thf(70,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( D @ ( C @ ( E @ ( B @ ( A @ perpAt ) ) ) ) )
| ( D @ ( C @ ( B @ ( A @ perp ) ) ) ) )
& ( ( D @ ( C @ ( D @ ( C @ ( B @ ( A @ il ) ) ) @ ( B @ ( A @ perpAt ) ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ perp ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d_Defn8_11b) ).
thf(378,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( D @ ( C @ ( E @ ( B @ ( A @ perpAt ) ) ) ) )
| ( D @ ( C @ ( B @ ( A @ perp ) ) ) ) )
& ( ( D @ ( C @ ( D @ ( C @ ( B @ ( A @ il ) ) ) @ ( B @ ( A @ perpAt ) ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ perp ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(5,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(101,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)],[5]) ).
thf(57,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( A @ s_col ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz6_17a) ).
thf(333,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( A @ s_col ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(71,axiom,
! [A: $i,B: $i] : ( A @ ( B @ s ) @ ( B @ ( A @ s_m ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz7_4a) ).
thf(384,plain,
! [A: $i,B: $i] : ( A @ ( B @ s ) @ ( B @ ( A @ s_m ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(12,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( D @ ( C @ s_t ) ) )
| ( B @ ( C @ ( D @ s_t ) ) )
| ~ ( B @ ( A @ ( D @ s_t ) ) )
| ~ ( B @ ( A @ ( C @ s_t ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz6_16a) ).
thf(142,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( D @ ( C @ s_t ) ) )
| ( B @ ( C @ ( D @ s_t ) ) )
| ~ ( B @ ( A @ ( D @ s_t ) ) )
| ~ ( B @ ( A @ ( C @ s_t ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(15,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(153,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)],[15]) ).
thf(21,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(185,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)],[21]) ).
thf(82,axiom,
! [A: $i,B: $i] :
( ~ ( B @ ( A @ pointOffLine ) @ ( B @ ( A @ s_col ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz6_25) ).
thf(417,plain,
! [A: $i,B: $i] :
( ~ ( B @ ( A @ pointOffLine ) @ ( B @ ( A @ s_col ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(47,axiom,
! [A: $i,B: $i,C: $i] :
( ( A = C )
| ( ( B @ ( A @ s ) )
!= ( B @ ( C @ s ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz7_18) ).
thf(289,plain,
! [A: $i,B: $i,C: $i] :
( ( A = C )
| ( ( B @ ( A @ s ) )
!= ( B @ ( C @ s ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(51,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ~ ( D @ ( E @ s ) @ ( C @ ( E @ s ) @ ( B @ ( E @ s ) @ ( A @ ( E @ s ) @ s_e ) ) ) )
| ( D @ ( C @ ( B @ ( A @ s_e ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz7_16b) ).
thf(316,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ~ ( D @ ( E @ s ) @ ( C @ ( E @ s ) @ ( B @ ( E @ s ) @ ( A @ ( E @ s ) @ s_e ) ) ) )
| ( D @ ( C @ ( B @ ( A @ s_e ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(31,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ s ) @ ( B @ ( D @ s ) @ ( A @ ( D @ s ) @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz7_15a) ).
thf(216,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ s ) @ ( B @ ( D @ s ) @ ( A @ ( D @ s ) @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(19,axiom,
! [A: $i,B: $i] : ( B @ ( B @ ( A @ s_t ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz3_1) ).
thf(179,plain,
! [A: $i,B: $i] : ( B @ ( B @ ( A @ s_t ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(53,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(321,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)],[53]) ).
thf(29,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(211,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)],[29]) ).
thf(7,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(121,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)],[7]) ).
thf(76,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B = D )
| ( ( D @ ( A @ s ) )
!= C )
| ( ( B @ ( A @ s ) )
!= C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz7_8) ).
thf(396,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B = D )
| ( ( D @ ( A @ s ) )
!= C )
| ( ( B @ ( A @ s ) )
!= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(27,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ s_m ) ) )
| ~ ( C @ ( B @ ( A @ s_m ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz7_2) ).
thf(206,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ s_m ) ) )
| ~ ( C @ ( B @ ( A @ s_m ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(63,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(349,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)],[63]) ).
thf(17,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(160,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)],[17]) ).
thf(75,axiom,
! [A: $i,B: $i,C: $i] :
( ( A = B )
| ~ ( C @ ( C @ ( B @ ( A @ s_e ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aA3) ).
thf(392,plain,
! [A: $i,B: $i,C: $i] :
( ( A = B )
| ~ ( C @ ( C @ ( B @ ( A @ s_e ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(85,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(424,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)],[85]) ).
thf(23,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C = D )
| ~ ( D @ ( B @ ( A @ s_m ) ) )
| ~ ( C @ ( B @ ( A @ s_m ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz7_4b) ).
thf(192,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C = D )
| ~ ( D @ ( B @ ( A @ s_m ) ) )
| ~ ( C @ ( B @ ( A @ s_m ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(45,axiom,
! [A: $i,B: $i] : ( A @ ( B @ ( B @ ( A @ s_e ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aA1) ).
thf(275,plain,
! [A: $i,B: $i] : ( A @ ( B @ ( B @ ( A @ s_e ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(10,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(137,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)],[10]) ).
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(229,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(39,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(252,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)],[39]) ).
thf(89,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( C @ ( B @ s ) @ ( A @ ( C @ ( A @ s_e ) ) ) )
| ( C @ ( B @ ( A @ s_r ) ) ) )
& ( ( C @ ( B @ s ) @ ( A @ ( C @ ( A @ s_e ) ) ) )
| ~ ( C @ ( B @ ( A @ s_r ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d_Defn8_1) ).
thf(435,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( C @ ( B @ s ) @ ( A @ ( C @ ( A @ s_e ) ) ) )
| ( C @ ( B @ ( A @ s_r ) ) ) )
& ( ( C @ ( B @ s ) @ ( A @ ( C @ ( A @ s_e ) ) ) )
| ~ ( C @ ( B @ ( A @ s_r ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(54,axiom,
! [A: $i,B: $i] :
( ( B = A )
| ( ( B @ ( A @ s ) )
!= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz7_10a) ).
thf(324,plain,
! [A: $i,B: $i] :
( ( B = A )
| ( ( B @ ( A @ s ) )
!= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(16,axiom,
! [A: $i,B: $i] :
( ( B != A )
| ( A @ ( B @ ( A @ s_m ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz7_3b) ).
thf(156,plain,
! [A: $i,B: $i] :
( ( B != A )
| ( A @ ( B @ ( A @ s_m ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(77,axiom,
! [A: $i,B: $i,C: $i] : ( B @ ( C @ s ) @ ( A @ ( C @ s ) @ ( B @ ( A @ s_e ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz7_13) ).
thf(403,plain,
! [A: $i,B: $i,C: $i] : ( B @ ( C @ s ) @ ( A @ ( C @ s ) @ ( B @ ( A @ s_e ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
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(188,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(73,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(388,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)],[73]) ).
thf(83,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( A @ ( C @ ( B @ isomidpoint ) ) @ ( B @ s_m ) ) )
| ~ ( C @ ( A @ ( B @ ( A @ s_e ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz7_25) ).
thf(420,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( A @ ( C @ ( B @ isomidpoint ) ) @ ( B @ s_m ) ) )
| ~ ( C @ ( A @ ( B @ ( A @ s_e ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(9,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( C @ ( D @ s ) @ ( B @ ( D @ s ) @ ( A @ ( D @ s ) @ s_t ) ) )
| ( C @ ( B @ ( A @ s_t ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz7_15b) ).
thf(134,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( C @ ( D @ s ) @ ( B @ ( D @ s ) @ ( A @ ( D @ s ) @ s_t ) ) )
| ( C @ ( B @ ( A @ s_t ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(61,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(343,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)],[61]) ).
thf(43,axiom,
! [A: $i,B: $i,C: $i] :
( ( B = C )
| ( ( B @ ( A @ s ) )
!= ( C @ ( A @ s ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz7_9) ).
thf(266,plain,
! [A: $i,B: $i,C: $i] :
( ( B = C )
| ( ( B @ ( A @ s ) )
!= ( C @ ( A @ s ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(6,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(105,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)],[6]) ).
thf(38,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ ( A @ s_m ) ) )
| ~ ( C @ ( B @ ( A @ ( B @ s_e ) ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) ) )
& ( ( C @ ( B @ ( A @ ( B @ s_e ) ) ) )
| ~ ( C @ ( B @ ( A @ s_m ) ) ) )
& ( ( C @ ( B @ ( A @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_m ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d_Defn7_1) ).
thf(244,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ ( A @ s_m ) ) )
| ~ ( C @ ( B @ ( A @ ( B @ s_e ) ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) ) )
& ( ( C @ ( B @ ( A @ ( B @ s_e ) ) ) )
| ~ ( C @ ( B @ ( A @ s_m ) ) ) )
& ( ( C @ ( B @ ( A @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_m ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(80,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(412,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)],[80]) ).
thf(87,axiom,
! [A: $i,B: $i] : ( A @ ( B @ ( A @ s_col ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz4_12b) ).
thf(430,plain,
! [A: $i,B: $i] : ( A @ ( B @ ( A @ s_col ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
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(296,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(14,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(149,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)],[14]) ).
thf(69,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ s_m ) ) )
| ( A = C )
| ~ ( C @ ( B @ ( A @ ( B @ s_e ) ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz7_20) ).
thf(375,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ s_m ) ) )
| ( A = C )
| ~ ( C @ ( B @ ( A @ ( B @ s_e ) ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
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(236,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(20,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(181,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)],[20]) ).
thf(32,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(219,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)],[32]) ).
thf(4,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(98,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)],[4]) ).
thf(44,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( G @ ( D @ ( C @ s_col ) ) )
| ~ ( G @ ( B @ ( A @ s_col ) ) )
| ( E = F )
| ~ ( F @ ( D @ ( C @ s_col ) ) )
| ~ ( F @ ( B @ ( A @ s_col ) ) )
| ~ ( E @ ( D @ ( C @ s_col ) ) )
| ~ ( E @ ( B @ ( A @ s_col ) ) )
| ( C = D )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz6_21) ).
thf(271,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( G @ ( D @ ( C @ s_col ) ) )
| ~ ( G @ ( B @ ( A @ s_col ) ) )
| ( E = F )
| ~ ( F @ ( D @ ( C @ s_col ) ) )
| ~ ( F @ ( B @ ( A @ s_col ) ) )
| ~ ( E @ ( D @ ( C @ s_col ) ) )
| ~ ( E @ ( B @ ( A @ s_col ) ) )
| ( C = D )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(28,axiom,
! [A: $i,B: $i] :
( ( A = B )
| ~ ( A @ ( B @ ( A @ s_t ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aA6) ).
thf(208,plain,
! [A: $i,B: $i] :
( ( A = B )
| ~ ( A @ ( B @ ( A @ s_t ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(62,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( A @ ( B @ s_col ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz6_17b) ).
thf(345,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( A @ ( B @ s_col ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(11,axiom,
! [A: $i,B: $i] : ( B @ ( A @ ( A @ s_t ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz3_3) ).
thf(140,plain,
! [A: $i,B: $i] : ( B @ ( A @ ( A @ s_t ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(30,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( G @ ( B @ ( F @ s_t ) ) )
| ~ ( E @ ( G @ ( C @ s_m ) ) )
| ~ ( D @ ( F @ ( A @ s_m ) ) )
| ~ ( E @ ( B @ ( C @ ( B @ s_e ) ) ) )
| ~ ( D @ ( B @ ( A @ ( B @ s_e ) ) ) )
| ~ ( E @ ( B @ ( D @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz7_22) ).
thf(213,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( G @ ( B @ ( F @ s_t ) ) )
| ~ ( E @ ( G @ ( C @ s_m ) ) )
| ~ ( D @ ( F @ ( A @ s_m ) ) )
| ~ ( E @ ( B @ ( C @ ( B @ s_e ) ) ) )
| ~ ( D @ ( B @ ( A @ ( B @ s_e ) ) ) )
| ~ ( E @ ( B @ ( D @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ s_r ) ) )
| ~ ( C @ ( B @ ( A @ s_r ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz8_2) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ s_r ) ) )
| ~ ( C @ ( B @ ( A @ s_r ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(91,plain,
~ ! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ s_r ) ) )
| ~ ( C @ ( B @ ( A @ s_r ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(56,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(330,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)],[56]) ).
thf(86,axiom,
! [A: $i,B: $i] :
( ( B != A )
| ( ( B @ ( A @ s ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz7_10b) ).
thf(426,plain,
! [A: $i,B: $i] :
( ( B != A )
| ( ( B @ ( A @ s ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(40,axiom,
! [A: $i,B: $i,C: $i] :
( ( A = B )
| ( ( C @ ( B @ s ) @ ( A @ s ) )
!= ( C @ ( A @ s ) @ ( B @ s ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz7_19) ).
thf(255,plain,
! [A: $i,B: $i,C: $i] :
( ( A = B )
| ( ( C @ ( B @ s ) @ ( A @ s ) )
!= ( C @ ( A @ s ) @ ( B @ s ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(65,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(355,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)],[65]) ).
thf(55,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ s ) @ ( A @ s ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz7_7) ).
thf(327,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ s ) @ ( A @ s ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(79,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( A @ ( B @ s ) ) )
| ~ ( C @ ( B @ ( A @ s_m ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz7_6) ).
thf(409,plain,
! [A: $i,B: $i,C: $i] :
( ( C
= ( A @ ( B @ s ) ) )
| ~ ( C @ ( B @ ( A @ s_m ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(81,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D @ ( E @ s ) @ ( C @ ( E @ s ) @ ( B @ ( E @ s ) @ ( A @ ( E @ s ) @ s_e ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ s_e ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz7_16a) ).
thf(414,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D @ ( E @ s ) @ ( C @ ( E @ s ) @ ( B @ ( E @ s ) @ ( A @ ( E @ s ) @ s_e ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ s_e ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(3,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( F @ ( D @ ( B @ s_t ) ) )
| ~ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s_kf ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz7_22b) ).
thf(95,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( F @ ( D @ ( B @ s_t ) ) )
| ~ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s_kf ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(25,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(199,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)],[25]) ).
thf(90,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ~ ( C @ ( E @ ( D @ ( B @ ( A @ g811 ) ) ) ) @ ( C @ ( C @ ( E @ ( D @ ( B @ ( A @ f811 ) ) ) ) @ s_r ) ) )
| ~ ( C @ ( E @ ( D @ s_col ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) )
| ( D = E )
| ( A = B )
| ( E @ ( D @ ( C @ ( B @ ( A @ perpAt ) ) ) ) ) )
& ( ( C @ ( E @ ( D @ ( B @ ( A @ g811 ) ) ) ) @ ( E @ ( D @ s_col ) ) )
| ~ ( C @ ( E @ ( D @ s_col ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) )
| ( D = E )
| ( A = B )
| ( E @ ( D @ ( C @ ( B @ ( A @ perpAt ) ) ) ) ) )
& ( ( C @ ( E @ ( D @ ( B @ ( A @ f811 ) ) ) ) @ ( B @ ( A @ s_col ) ) )
| ~ ( C @ ( E @ ( D @ s_col ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) )
| ( D = E )
| ( A = B )
| ( E @ ( D @ ( C @ ( B @ ( A @ perpAt ) ) ) ) ) )
& ( ( G @ ( C @ ( F @ s_r ) ) )
| ~ ( G @ ( E @ ( D @ s_col ) ) )
| ~ ( F @ ( B @ ( A @ s_col ) ) )
| ~ ( E @ ( D @ ( C @ ( B @ ( A @ perpAt ) ) ) ) ) )
& ( ( D != E )
| ~ ( E @ ( D @ ( C @ ( B @ ( A @ perpAt ) ) ) ) ) )
& ( ( A != B )
| ~ ( E @ ( D @ ( C @ ( B @ ( A @ perpAt ) ) ) ) ) )
& ( ( C @ ( E @ ( D @ s_col ) ) )
| ~ ( E @ ( D @ ( C @ ( B @ ( A @ perpAt ) ) ) ) ) )
& ( ( C @ ( B @ ( A @ s_col ) ) )
| ~ ( E @ ( D @ ( C @ ( B @ ( A @ perpAt ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d_Defn8_11a) ).
thf(441,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ~ ( C @ ( E @ ( D @ ( B @ ( A @ g811 ) ) ) ) @ ( C @ ( C @ ( E @ ( D @ ( B @ ( A @ f811 ) ) ) ) @ s_r ) ) )
| ~ ( C @ ( E @ ( D @ s_col ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) )
| ( D = E )
| ( A = B )
| ( E @ ( D @ ( C @ ( B @ ( A @ perpAt ) ) ) ) ) )
& ( ( C @ ( E @ ( D @ ( B @ ( A @ g811 ) ) ) ) @ ( E @ ( D @ s_col ) ) )
| ~ ( C @ ( E @ ( D @ s_col ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) )
| ( D = E )
| ( A = B )
| ( E @ ( D @ ( C @ ( B @ ( A @ perpAt ) ) ) ) ) )
& ( ( C @ ( E @ ( D @ ( B @ ( A @ f811 ) ) ) ) @ ( B @ ( A @ s_col ) ) )
| ~ ( C @ ( E @ ( D @ s_col ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) )
| ( D = E )
| ( A = B )
| ( E @ ( D @ ( C @ ( B @ ( A @ perpAt ) ) ) ) ) )
& ( ( G @ ( C @ ( F @ s_r ) ) )
| ~ ( G @ ( E @ ( D @ s_col ) ) )
| ~ ( F @ ( B @ ( A @ s_col ) ) )
| ~ ( E @ ( D @ ( C @ ( B @ ( A @ perpAt ) ) ) ) ) )
& ( ( D != E )
| ~ ( E @ ( D @ ( C @ ( B @ ( A @ perpAt ) ) ) ) ) )
& ( ( A != B )
| ~ ( E @ ( D @ ( C @ ( B @ ( A @ perpAt ) ) ) ) ) )
& ( ( C @ ( E @ ( D @ s_col ) ) )
| ~ ( E @ ( D @ ( C @ ( B @ ( A @ perpAt ) ) ) ) ) )
& ( ( C @ ( B @ ( A @ s_col ) ) )
| ~ ( E @ ( D @ ( C @ ( B @ ( A @ perpAt ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(66,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( E @ ( A @ s_m ) ) )
| ~ ( D @ ( E @ ( B @ s_col ) ) )
| ~ ( C @ ( E @ ( A @ s_col ) ) )
| ~ ( A @ ( D @ ( C @ ( B @ s_e ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ s_e ) ) ) )
| ( B = D )
| ( C @ ( B @ ( A @ s_col ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz7_21) ).
thf(359,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( E @ ( A @ s_m ) ) )
| ~ ( D @ ( E @ ( B @ s_col ) ) )
| ~ ( C @ ( E @ ( A @ s_col ) ) )
| ~ ( A @ ( D @ ( C @ ( B @ s_e ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ s_e ) ) ) )
| ( B = D )
| ( C @ ( B @ ( A @ s_col ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(58,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(336,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)],[58]) ).
thf(72,axiom,
! [A: $i,B: $i] : ( B @ ( A @ ( B @ ( A @ s_e ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz2_1) ).
thf(386,plain,
! [A: $i,B: $i] : ( B @ ( A @ ( B @ ( A @ s_e ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(52,axiom,
! [A: $i,B: $i] : ( B @ ( A @ ( A @ s_col ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz4_12) ).
thf(319,plain,
! [A: $i,B: $i] : ( B @ ( A @ ( A @ s_col ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(64,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( A @ s_col ) ) )
| ~ ( D @ ( B @ ( A @ s_col ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) )
| ( C = A )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz6_16b) ).
thf(351,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( A @ s_col ) ) )
| ~ ( D @ ( B @ ( A @ s_col ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) )
| ( C = A )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(74,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(390,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)],[74]) ).
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_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(300,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)],[50]) ).
thf(88,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(432,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)],[88]) ).
thf(42,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ ( B @ ( A @ s_col ) ) )
| ~ ( E @ ( D @ ( C @ s_col ) ) )
| ~ ( B @ ( D @ ( C @ s_col ) ) )
| ~ ( A @ ( D @ ( C @ s_col ) ) )
| ( C = D )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz6_18) ).
thf(262,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ ( B @ ( A @ s_col ) ) )
| ~ ( E @ ( D @ ( C @ s_col ) ) )
| ~ ( B @ ( D @ ( C @ s_col ) ) )
| ~ ( A @ ( D @ ( C @ s_col ) ) )
| ( C = D )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(13,axiom,
! [A: $i,B: $i] :
( ( B = A )
| ~ ( A @ ( B @ ( A @ s_m ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz7_3a) ).
thf(146,plain,
! [A: $i,B: $i] :
( ( B = A )
| ~ ( A @ ( B @ ( A @ s_m ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(78,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(405,plain,
! [A: $i,B: $i,C: $i] :
( ( A = B )
| ~ ( C @ ( C @ ( B @ ( A @ s_e ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(84,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(422,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)],[84]) ).
thf(68,axiom,
! [A: $i,B: $i] : ( B @ ( B @ ( A @ ( A @ s_e ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz2_8) ).
thf(373,plain,
! [A: $i,B: $i] : ( B @ ( B @ ( A @ ( A @ s_e ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(37,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( A @ ( D @ s_col ) ) )
| ( D != A )
| ~ ( C @ ( A @ ( B @ s_t ) ) )
| ( A = C )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz6_15d) ).
thf(239,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( A @ ( D @ s_col ) ) )
| ( D != A )
| ~ ( C @ ( A @ ( B @ s_t ) ) )
| ( A = C )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(48,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(294,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)],[48]) ).
thf(60,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(341,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)],[60]) ).
thf(8,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(131,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)],[8]) ).
thf(18,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s_kf ) ) ) ) ) ) )
| ~ ( E @ ( F @ ( G @ s_m ) ) )
| ~ ( C @ ( B @ ( A @ s_m ) ) )
| ~ ( E @ ( D @ ( G @ ( D @ s_e ) ) ) )
| ~ ( C @ ( D @ ( A @ ( D @ s_e ) ) ) )
| ~ ( E @ ( D @ ( C @ s_t ) ) )
| ~ ( G @ ( D @ ( A @ s_t ) ) ) )
& ( ( E @ ( F @ ( G @ s_m ) ) )
| ~ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s_kf ) ) ) ) ) ) ) )
& ( ( C @ ( B @ ( A @ s_m ) ) )
| ~ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s_kf ) ) ) ) ) ) ) )
& ( ( E @ ( D @ ( G @ ( D @ s_e ) ) ) )
| ~ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s_kf ) ) ) ) ) ) ) )
& ( ( C @ ( D @ ( A @ ( D @ s_e ) ) ) )
| ~ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s_kf ) ) ) ) ) ) ) )
& ( ( E @ ( D @ ( C @ s_t ) ) )
| ~ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s_kf ) ) ) ) ) ) ) )
& ( ( G @ ( D @ ( A @ s_t ) ) )
| ~ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s_kf ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d_Defn7_23) ).
thf(163,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s_kf ) ) ) ) ) ) )
| ~ ( E @ ( F @ ( G @ s_m ) ) )
| ~ ( C @ ( B @ ( A @ s_m ) ) )
| ~ ( E @ ( D @ ( G @ ( D @ s_e ) ) ) )
| ~ ( C @ ( D @ ( A @ ( D @ s_e ) ) ) )
| ~ ( E @ ( D @ ( C @ s_t ) ) )
| ~ ( G @ ( D @ ( A @ s_t ) ) ) )
& ( ( E @ ( F @ ( G @ s_m ) ) )
| ~ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s_kf ) ) ) ) ) ) ) )
& ( ( C @ ( B @ ( A @ s_m ) ) )
| ~ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s_kf ) ) ) ) ) ) ) )
& ( ( E @ ( D @ ( G @ ( D @ s_e ) ) ) )
| ~ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s_kf ) ) ) ) ) ) ) )
& ( ( C @ ( D @ ( A @ ( D @ s_e ) ) ) )
| ~ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s_kf ) ) ) ) ) ) ) )
& ( ( E @ ( D @ ( C @ s_t ) ) )
| ~ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s_kf ) ) ) ) ) ) ) )
& ( ( G @ ( D @ ( A @ s_t ) ) )
| ~ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s_kf ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(46,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(277,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)],[46]) ).
thf(674,plain,
$false,
inference(e,[status(thm)],[202,196,233,339,259,223,363,378,101,333,384,142,153,185,417,289,316,216,179,321,211,121,396,206,349,160,392,424,192,275,137,229,252,435,324,156,403,188,388,420,134,343,266,105,244,412,430,296,149,375,236,181,219,98,271,208,345,140,213,91,330,426,255,355,327,409,414,95,199,441,359,336,386,319,351,390,300,432,262,146,405,422,373,239,294,341,131,163,277]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GEO504+1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.12 % 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
% 0.25/0.65 % Computer : n003.cluster.edu
% 0.25/0.65 % Model : x86_64 x86_64
% 0.25/0.65 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.25/0.65 % Memory : 8046.5625MB
% 0.25/0.65 % OS : Linux 6.8.0-71-generic
% 0.25/0.65 % CPULimit : 300
% 0.25/0.65 % WCLimit : 300
% 0.25/0.65 % DateTime : Fri Sep 25 13:38:38 UTC 2026
% 0.25/0.65 % CPUTime :
% 0.25/0.65 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
% 1.21/1.20 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 2.62/1.61 % [INFO] Parsing done (406ms).
% 2.62/1.64 % [INFO] Running in sequential loop mode.
% 3.99/2.30 % [INFO] eprover registered as external prover.
% 3.99/2.31 % [INFO] Scanning for conjecture ...
% 4.20/2.47 % [INFO] Found a conjecture (or negated_conjecture) and 130 axioms. Running axiom selection ...
% 4.37/2.58 % [INFO] Axiom selection finished. Selected 88 axioms (removed 42 axioms).
% 5.10/2.89 % [INFO] Problem is first-order (TPTP FOF).
% 5.32/2.93 % [INFO] Type checking passed.
% 5.32/2.94 % [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 ...
% 18.78/6.48 % External prover 'e' found a proof!
% 18.78/6.48 % [INFO] Killing All external provers ...
% 18.78/6.48 % Time passed: 5682ms (effective reasoning time: 4836ms)
% 18.78/6.49 % 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)>
% 18.78/6.49 % Axioms used in derivation (88): aSatz4_11d, aSatz4_16, aSatz3_5a, aSatz6_21, aSatz3_4, aSatz7_19, aSatz2_13, aSatz7_10b, aSatz7_2, aSatz2_3, aSatz6_16b, aSatz4_5, d_Defn4_4, aSatz3_1, aSatz5_2, d_Defn7_23, aSatz6_15d, aA1, aA5, aSatz7_10a, aSatz7_15b, aSatz6_18, d_Defn4_15, aSatz7_3b, aSatz3_3, aSatz3_5b, aSatz7_7, aSatz4_11c, d_Defn4_10, aSatz5_1, aSatz4_19, aSatz4_14, aSatz2_1, aSatz7_18, aSatz6_25, aSatz7_25, d_Defn4_1, aA2, aSatz7_4a, aSatz4_11b, aSatz2_5, aSatz3_6b, aA3, aSatz3_2, aSatz7_15a, aA6, aSatz3_6a, aNarbouxLemma1, aSatz6_17a, aSatz7_22b, d_Defn8_11b, aSatz4_3, aSatz7_6, d_Defn7_1, aSatz4_18, aSatz2_2, aSatz7_20, aSatz7_22, aSatz7_21, aSatz4_12b, aSatz2_15, aSatz4_11a, aSatz2_4, aSatz7_16a, d_Defn8_1, aSatz7_9, d_Defn8_11a, aSatz6_16a, aSatz3_7a, aSatz7_17, aSatz6_17b, aSatz4_6, aSatz7_4b, aSatz4_13, aSatz2_11, aSatz7_13, aSatz2_14, d_Defn2_10, aSatz4_11e, aSatz4_12, aSatz4_17, aSatz5_3, aSatz7_8, aSatz7_16b, aSatz2_8, aSatz4_2, aSatz3_7b, aSatz7_3a
% 18.78/6.49 % No. of inferences in proof: 180
% 18.78/6.49 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 5682 ms resp. 4836 ms w/o parsing
% 20.12/6.72 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 20.12/6.72 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------