TSTP Solution File: GEO545+1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : GEO545+1 : TPTP v8.1.2. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 19 11:11:11 EDT 2023
% Result : Theorem 10.76s 3.26s
% Output : Refutation 10.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 127
% Syntax : Number of formulae : 270 ( 33 unt; 32 typ; 0 def)
% Number of atoms : 783 ( 32 equ; 0 cnn)
% Maximal formula atoms : 28 ( 3 avg)
% Number of connectives : 3877 ( 74 ~; 45 |; 297 &;3268 @)
% ( 0 <=>; 193 =>; 0 <=; 0 <~>)
% Maximal formula depth : 53 ( 13 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 56 ( 56 >; 0 *; 0 +; 0 <<)
% Number of symbols : 34 ( 32 usr; 21 con; 0-8 aty)
% Number of variables : 1177 ( 0 ^;1119 !; 58 ?;1177 :)
% Comments :
%------------------------------------------------------------------------------
thf(perp_type,type,
perp: $i > $i > $i > $i > $o ).
thf(midp_type,type,
midp: $i > $i > $i > $o ).
thf(contri_type,type,
contri: $i > $i > $i > $i > $i > $i > $o ).
thf(simtri_type,type,
simtri: $i > $i > $i > $i > $i > $i > $o ).
thf(cong_type,type,
cong: $i > $i > $i > $i > $o ).
thf(eqangle_type,type,
eqangle: $i > $i > $i > $i > $i > $i > $i > $i > $o ).
thf(eqratio_type,type,
eqratio: $i > $i > $i > $i > $i > $i > $i > $i > $o ).
thf(cyclic_type,type,
cyclic: $i > $i > $i > $i > $o ).
thf(coll_type,type,
coll: $i > $i > $i > $o ).
thf(para_type,type,
para: $i > $i > $i > $i > $o ).
thf(circle_type,type,
circle: $i > $i > $i > $i > $o ).
thf(sk1_type,type,
sk1: $i ).
thf(sk2_type,type,
sk2: $i ).
thf(sk3_type,type,
sk3: $i ).
thf(sk4_type,type,
sk4: $i ).
thf(sk5_type,type,
sk5: $i ).
thf(sk6_type,type,
sk6: $i ).
thf(sk7_type,type,
sk7: $i ).
thf(sk8_type,type,
sk8: $i ).
thf(sk9_type,type,
sk9: $i ).
thf(sk10_type,type,
sk10: $i ).
thf(sk11_type,type,
sk11: $i ).
thf(sk12_type,type,
sk12: $i ).
thf(sk13_type,type,
sk13: $i ).
thf(sk14_type,type,
sk14: $i ).
thf(sk15_type,type,
sk15: $i ).
thf(sk16_type,type,
sk16: $i ).
thf(sk17_type,type,
sk17: $i ).
thf(sk18_type,type,
sk18: $i ).
thf(sk19_type,type,
sk19: $i ).
thf(sk20_type,type,
sk20: $i ).
thf(sk36_type,type,
sk36: $i > $i > $i ).
thf(15,axiom,
! [A: $i,B: $i,C: $i] :
( ( coll @ A @ B @ C )
=> ( coll @ B @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD2) ).
thf(152,plain,
! [A: $i,B: $i,C: $i] :
( ( coll @ A @ B @ C )
=> ( coll @ B @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(153,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( coll @ A @ B @ C )
| ( coll @ B @ A @ C ) ),
inference(cnf,[status(esa)],[152]) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( contri @ A @ C @ B @ D @ F @ E )
=> ( contri @ A @ B @ C @ D @ E @ F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD35) ).
thf(129,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( contri @ A @ C @ B @ D @ F @ E )
=> ( contri @ A @ B @ C @ D @ E @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(96,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( perp @ A @ B @ C @ D )
& ( perp @ C @ D @ E @ F ) )
=> ( para @ A @ B @ E @ F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD9) ).
thf(365,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( perp @ A @ B @ C @ D )
& ( perp @ C @ D @ E @ F ) )
=> ( para @ A @ B @ E @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i,L: $i,M: $i,N: $i,O: $i,P: $i,Q: $i,R: $i,S: $i,T: $i] :
( ( ( perp @ A @ B @ C @ D )
& ( perp @ A @ C @ B @ D )
& ( perp @ B @ C @ A @ D )
& ( midp @ I @ A @ B )
& ( perp @ A @ B @ I @ E )
& ( midp @ J @ A @ C )
& ( perp @ A @ C @ J @ E )
& ( midp @ K @ B @ C )
& ( perp @ B @ C @ K @ E )
& ( midp @ L @ A @ B )
& ( perp @ A @ B @ L @ F )
& ( midp @ M @ A @ D )
& ( perp @ A @ D @ M @ F )
& ( midp @ N @ B @ D )
& ( perp @ B @ D @ N @ F )
& ( midp @ O @ A @ D )
& ( perp @ A @ D @ O @ G )
& ( midp @ P @ A @ C )
& ( perp @ A @ C @ P @ G )
& ( midp @ Q @ D @ C )
& ( perp @ D @ C @ Q @ G )
& ( midp @ R @ B @ D )
& ( perp @ B @ D @ R @ H )
& ( midp @ S @ B @ C )
& ( perp @ B @ C @ S @ H )
& ( midp @ T @ D @ C )
& ( perp @ D @ C @ T @ H ) )
=> ( perp @ H @ E @ G @ F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exemplo6GDDFULL012005) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i,L: $i,M: $i,N: $i,O: $i,P: $i,Q: $i,R: $i,S: $i,T: $i] :
( ( ( perp @ A @ B @ C @ D )
& ( perp @ A @ C @ B @ D )
& ( perp @ B @ C @ A @ D )
& ( midp @ I @ A @ B )
& ( perp @ A @ B @ I @ E )
& ( midp @ J @ A @ C )
& ( perp @ A @ C @ J @ E )
& ( midp @ K @ B @ C )
& ( perp @ B @ C @ K @ E )
& ( midp @ L @ A @ B )
& ( perp @ A @ B @ L @ F )
& ( midp @ M @ A @ D )
& ( perp @ A @ D @ M @ F )
& ( midp @ N @ B @ D )
& ( perp @ B @ D @ N @ F )
& ( midp @ O @ A @ D )
& ( perp @ A @ D @ O @ G )
& ( midp @ P @ A @ C )
& ( perp @ A @ C @ P @ G )
& ( midp @ Q @ D @ C )
& ( perp @ D @ C @ Q @ G )
& ( midp @ R @ B @ D )
& ( perp @ B @ D @ R @ H )
& ( midp @ S @ B @ C )
& ( perp @ B @ C @ S @ H )
& ( midp @ T @ D @ C )
& ( perp @ D @ C @ T @ H ) )
=> ( perp @ H @ E @ G @ F ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(97,plain,
~ ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i,L: $i,M: $i,N: $i,O: $i,P: $i,Q: $i,R: $i,S: $i,T: $i] :
( ( ( perp @ A @ B @ C @ D )
& ( perp @ A @ C @ B @ D )
& ( perp @ B @ C @ A @ D )
& ( midp @ I @ A @ B )
& ( perp @ A @ B @ I @ E )
& ( midp @ J @ A @ C )
& ( perp @ A @ C @ J @ E )
& ( midp @ K @ B @ C )
& ( perp @ B @ C @ K @ E )
& ( midp @ L @ A @ B )
& ( perp @ A @ B @ L @ F )
& ( midp @ M @ A @ D )
& ( perp @ A @ D @ M @ F )
& ( midp @ N @ B @ D )
& ( perp @ B @ D @ N @ F )
& ( midp @ O @ A @ D )
& ( perp @ A @ D @ O @ G )
& ( midp @ P @ A @ C )
& ( perp @ A @ C @ P @ G )
& ( midp @ Q @ D @ C )
& ( perp @ D @ C @ Q @ G )
& ( midp @ R @ B @ D )
& ( perp @ B @ D @ R @ H )
& ( midp @ S @ B @ C )
& ( perp @ B @ C @ S @ H )
& ( midp @ T @ D @ C )
& ( perp @ D @ C @ T @ H ) )
=> ( perp @ H @ E @ G @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(98,plain,
~ ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( perp @ A @ B @ C @ D )
& ( perp @ A @ C @ B @ D )
& ( perp @ B @ C @ A @ D )
& ? [I: $i] :
( ( midp @ I @ A @ B )
& ( perp @ A @ B @ I @ E )
& ? [J: $i] :
( ( midp @ J @ A @ C )
& ( perp @ A @ C @ J @ E )
& ? [K: $i] :
( ( midp @ K @ B @ C )
& ( perp @ B @ C @ K @ E )
& ? [L: $i] :
( ( midp @ L @ A @ B )
& ( perp @ A @ B @ L @ F )
& ? [M: $i] :
( ( midp @ M @ A @ D )
& ( perp @ A @ D @ M @ F )
& ? [N: $i] :
( ( midp @ N @ B @ D )
& ( perp @ B @ D @ N @ F )
& ? [O: $i] :
( ( midp @ O @ A @ D )
& ( perp @ A @ D @ O @ G )
& ? [P: $i] :
( ( midp @ P @ A @ C )
& ( perp @ A @ C @ P @ G )
& ? [Q: $i] :
( ( midp @ Q @ D @ C )
& ( perp @ D @ C @ Q @ G )
& ? [R: $i] :
( ( midp @ R @ B @ D )
& ( perp @ B @ D @ R @ H )
& ? [S: $i] :
( ( midp @ S @ B @ C )
& ( perp @ B @ C @ S @ H )
& ? [T: $i] :
( ( midp @ T @ D @ C )
& ( perp @ D @ C @ T @ H ) ) ) ) ) ) ) ) ) ) ) ) ) )
=> ( perp @ H @ E @ G @ F ) ),
inference(miniscope,[status(thm)],[97]) ).
thf(101,plain,
perp @ sk1 @ sk4 @ sk13 @ sk6,
inference(cnf,[status(esa)],[98]) ).
thf(84,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( circle @ D @ A @ B @ C )
& ( midp @ E @ B @ C ) )
=> ( eqangle @ A @ B @ A @ C @ D @ B @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD50) ).
thf(333,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( circle @ D @ A @ B @ C )
& ( midp @ E @ B @ C ) )
=> ( eqangle @ A @ B @ A @ C @ D @ B @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(53,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( para @ A @ B @ C @ D )
=> ( para @ C @ D @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD5) ).
thf(249,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( para @ A @ B @ C @ D )
=> ( para @ C @ D @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(23,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
? [F: $i] :
( ( ( eqangle @ A @ C @ B @ C @ A @ D @ B @ E )
& ~ ( coll @ A @ B @ C ) )
=> ( ( eqangle @ A @ C @ B @ C @ A @ F @ B @ F )
& ( cyclic @ D @ B @ C @ F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleX5) ).
thf(170,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
? [F: $i] :
( ( ( eqangle @ A @ C @ B @ C @ A @ D @ B @ E )
& ~ ( coll @ A @ B @ C ) )
=> ( ( eqangle @ A @ C @ B @ C @ A @ F @ B @ F )
& ( cyclic @ D @ B @ C @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(115,plain,
midp @ sk16 @ sk1 @ sk3,
inference(cnf,[status(esa)],[98]) ).
thf(120,plain,
perp @ sk1 @ sk4 @ sk15 @ sk7,
inference(cnf,[status(esa)],[98]) ).
thf(52,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( cong @ A @ B @ C @ D )
=> ( cong @ A @ B @ D @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD23) ).
thf(247,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( cong @ A @ B @ C @ D )
=> ( cong @ A @ B @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(24,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( cong @ E @ A @ E @ B )
& ( cong @ E @ A @ E @ C )
& ( cong @ E @ A @ E @ D ) )
=> ( cyclic @ A @ B @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD13) ).
thf(174,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( cong @ E @ A @ E @ B )
& ( cong @ E @ A @ E @ C )
& ( cong @ E @ A @ E @ D ) )
=> ( cyclic @ A @ B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(79,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( eqangle @ A @ B @ C @ D @ E @ F @ G @ H )
& ( perp @ E @ F @ G @ H ) )
=> ( perp @ A @ B @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD74) ).
thf(320,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( eqangle @ A @ B @ C @ D @ E @ F @ G @ H )
& ( perp @ E @ F @ G @ H ) )
=> ( perp @ A @ B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(57,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( eqangle @ C @ A @ A @ B @ A @ B @ C @ B )
& ~ ( coll @ C @ A @ B ) )
=> ( cong @ C @ A @ C @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD47) ).
thf(257,plain,
! [A: $i,B: $i,C: $i] :
( ( ( eqangle @ C @ A @ A @ B @ A @ B @ C @ B )
& ~ ( coll @ C @ A @ B ) )
=> ( cong @ C @ A @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(28,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
? [E: $i] :
( ( ( cong @ C @ A @ C @ B )
& ( eqangle @ A @ C @ C @ D @ C @ D @ C @ B ) )
=> ( ( coll @ B @ A @ E )
& ( coll @ E @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleX2) ).
thf(184,plain,
! [A: $i,B: $i,C: $i,D: $i] :
? [E: $i] :
( ( ( cong @ C @ A @ C @ B )
& ( eqangle @ A @ C @ C @ D @ C @ D @ C @ B ) )
=> ( ( coll @ B @ A @ E )
& ( coll @ E @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(110,plain,
perp @ sk1 @ sk2 @ sk12 @ sk6,
inference(cnf,[status(esa)],[98]) ).
thf(125,plain,
midp @ sk14 @ sk2 @ sk4,
inference(cnf,[status(esa)],[98]) ).
thf(93,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( circle @ D @ A @ B @ C )
& ( coll @ E @ B @ C )
& ( eqangle @ A @ B @ A @ C @ D @ B @ D @ E ) )
=> ( midp @ E @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD51) ).
thf(357,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( circle @ D @ A @ B @ C )
& ( coll @ E @ B @ C )
& ( eqangle @ A @ B @ A @ C @ D @ B @ D @ E ) )
=> ( midp @ E @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(17,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( cong @ D @ A @ D @ B )
& ( cong @ D @ A @ D @ C ) )
=> ( circle @ D @ A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD12) ).
thf(157,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( cong @ D @ A @ D @ B )
& ( cong @ D @ A @ D @ C ) )
=> ( circle @ D @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(81,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
? [H: $i] :
( ( ( midp @ E @ A @ B )
& ( midp @ F @ C @ D )
& ( coll @ C @ A @ B )
& ( coll @ D @ A @ B ) )
=> ( midp @ H @ A @ G ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleX7) ).
thf(325,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
? [H: $i] :
( ( ( midp @ E @ A @ B )
& ( midp @ F @ C @ D )
& ( coll @ C @ A @ B )
& ( coll @ D @ A @ B ) )
=> ( midp @ H @ A @ G ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(78,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
? [E: $i] :
( ( ( perp @ C @ B @ B @ A )
& ( eqangle @ D @ C @ B @ C @ B @ C @ A @ C ) )
=> ( ( coll @ E @ A @ B )
& ( coll @ E @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleX1) ).
thf(316,plain,
! [A: $i,B: $i,C: $i,D: $i] :
? [E: $i] :
( ( ( perp @ C @ B @ B @ A )
& ( eqangle @ D @ C @ B @ C @ B @ C @ A @ C ) )
=> ( ( coll @ E @ A @ B )
& ( coll @ E @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(59,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( midp @ D @ A @ B )
& ( midp @ E @ A @ C ) )
=> ( para @ D @ E @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD44) ).
thf(261,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( midp @ D @ A @ B )
& ( midp @ E @ A @ C ) )
=> ( para @ D @ E @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(41,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( para @ A @ B @ C @ D )
=> ( para @ A @ B @ D @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD4) ).
thf(216,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( para @ A @ B @ C @ D )
=> ( para @ A @ B @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(20,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( eqangle @ A @ B @ C @ D @ E @ F @ G @ H )
=> ( eqangle @ E @ F @ G @ H @ A @ B @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD20) ).
thf(164,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( eqangle @ A @ B @ C @ D @ E @ F @ G @ H )
=> ( eqangle @ E @ F @ G @ H @ A @ B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(26,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( eqangle @ A @ B @ E @ F @ C @ D @ E @ F )
=> ( para @ A @ B @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD39) ).
thf(179,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( eqangle @ A @ B @ E @ F @ C @ D @ E @ F )
=> ( para @ A @ B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(107,plain,
~ ( perp @ sk8 @ sk5 @ sk7 @ sk6 ),
inference(cnf,[status(esa)],[98]) ).
thf(621,plain,
( ( perp @ sk8 @ sk5 @ sk7 @ sk6 )
!= ( perp @ sk1 @ sk2 @ sk12 @ sk6 ) ),
inference(paramod_ordered,[status(thm)],[110,107]) ).
thf(622,plain,
( ( sk8 != sk1 )
| ( sk5 != sk2 )
| ( sk12 != sk7 )
| ( sk6 != sk6 ) ),
inference(simp,[status(thm)],[621]) ).
thf(623,plain,
( ( sk8 != sk1 )
| ( sk5 != sk2 )
| ( sk12 != sk7 ) ),
inference(simp,[status(thm)],[622]) ).
thf(55,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i,L: $i] :
( ( ( eqangle @ A @ B @ C @ D @ E @ F @ G @ H )
& ( eqangle @ E @ F @ G @ H @ I @ J @ K @ L ) )
=> ( eqangle @ A @ B @ C @ D @ I @ J @ K @ L ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD22) ).
thf(253,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i,L: $i] :
( ( ( eqangle @ A @ B @ C @ D @ E @ F @ G @ H )
& ( eqangle @ E @ F @ G @ H @ I @ J @ K @ L ) )
=> ( eqangle @ A @ B @ C @ D @ I @ J @ K @ L ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(106,plain,
midp @ sk10 @ sk1 @ sk3,
inference(cnf,[status(esa)],[98]) ).
thf(48,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( contri @ A @ B @ C @ D @ E @ F )
=> ( cong @ A @ B @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD62) ).
thf(238,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( contri @ A @ B @ C @ D @ E @ F )
=> ( cong @ A @ B @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(121,plain,
perp @ sk2 @ sk3 @ sk19 @ sk8,
inference(cnf,[status(esa)],[98]) ).
thf(89,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( cong @ A @ B @ A @ C )
& ( coll @ A @ B @ C ) )
=> ( midp @ A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD67) ).
thf(348,plain,
! [A: $i,B: $i,C: $i] :
( ( ( cong @ A @ B @ A @ C )
& ( coll @ A @ B @ C ) )
=> ( midp @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(91,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( circle @ D @ A @ B @ C )
& ( perp @ D @ A @ A @ E ) )
=> ( eqangle @ A @ E @ A @ B @ C @ A @ C @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD48) ).
thf(353,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( circle @ D @ A @ B @ C )
& ( perp @ D @ A @ A @ E ) )
=> ( eqangle @ A @ E @ A @ B @ C @ A @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(13,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( eqratio @ A @ B @ C @ D @ E @ F @ G @ H )
=> ( eqratio @ B @ A @ C @ D @ E @ F @ G @ H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD26) ).
thf(147,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( eqratio @ A @ B @ C @ D @ E @ F @ G @ H )
=> ( eqratio @ B @ A @ C @ D @ E @ F @ G @ H ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(6,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
( ( ( contri @ A @ B @ C @ D @ E @ F )
& ( contri @ D @ E @ F @ G @ H @ I ) )
=> ( contri @ A @ B @ C @ G @ H @ I ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD38) ).
thf(133,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
( ( ( contri @ A @ B @ C @ D @ E @ F )
& ( contri @ D @ E @ F @ G @ H @ I ) )
=> ( contri @ A @ B @ C @ G @ H @ I ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(37,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( cong @ A @ B @ C @ D )
& ( cong @ C @ D @ E @ F ) )
=> ( cong @ A @ B @ E @ F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD25) ).
thf(206,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( cong @ A @ B @ C @ D )
& ( cong @ C @ D @ E @ F ) )
=> ( cong @ A @ B @ E @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(116,plain,
perp @ sk2 @ sk3 @ sk1 @ sk4,
inference(cnf,[status(esa)],[98]) ).
thf(50,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( simtri @ A @ B @ C @ D @ E @ F )
=> ( eqratio @ A @ B @ A @ C @ D @ E @ D @ F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD59) ).
thf(243,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( simtri @ A @ B @ C @ D @ E @ F )
=> ( eqratio @ A @ B @ A @ C @ D @ E @ D @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(70,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( perp @ A @ B @ C @ D )
=> ( perp @ C @ D @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD8) ).
thf(292,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( perp @ A @ B @ C @ D )
=> ( perp @ C @ D @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(117,plain,
perp @ sk1 @ sk3 @ sk10 @ sk5,
inference(cnf,[status(esa)],[98]) ).
thf(63,axiom,
! [A: $i,B: $i,C: $i] :
( ( midp @ A @ B @ C )
=> ( coll @ A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD69) ).
thf(270,plain,
! [A: $i,B: $i,C: $i] :
( ( midp @ A @ B @ C )
=> ( coll @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(35,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( eqratio @ A @ B @ C @ D @ E @ F @ G @ H )
=> ( eqratio @ C @ D @ A @ B @ G @ H @ E @ F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD27) ).
thf(201,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( eqratio @ A @ B @ C @ D @ E @ F @ G @ H )
=> ( eqratio @ C @ D @ A @ B @ G @ H @ E @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(43,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( eqratio @ A @ B @ C @ D @ E @ F @ G @ H )
=> ( eqratio @ A @ B @ E @ F @ C @ D @ G @ H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD29) ).
thf(220,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( eqratio @ A @ B @ C @ D @ E @ F @ G @ H )
=> ( eqratio @ A @ B @ E @ F @ C @ D @ G @ H ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(102,plain,
midp @ sk9 @ sk1 @ sk2,
inference(cnf,[status(esa)],[98]) ).
thf(65,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( eqangle @ A @ B @ C @ D @ C @ D @ A @ B )
& ~ ( para @ A @ B @ C @ D ) )
=> ( perp @ A @ B @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD71) ).
thf(275,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( eqangle @ A @ B @ C @ D @ C @ D @ A @ B )
& ~ ( para @ A @ B @ C @ D ) )
=> ( perp @ A @ B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(8,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
( ( ( simtri @ A @ B @ C @ D @ E @ F )
& ( simtri @ D @ E @ F @ G @ H @ I ) )
=> ( simtri @ A @ B @ C @ G @ H @ I ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD34) ).
thf(137,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
( ( ( simtri @ A @ B @ C @ D @ E @ F )
& ( simtri @ D @ E @ F @ G @ H @ I ) )
=> ( simtri @ A @ B @ C @ G @ H @ I ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(33,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( eqangle @ A @ B @ B @ C @ D @ E @ E @ F )
& ( eqangle @ A @ C @ B @ C @ D @ F @ E @ F )
& ~ ( coll @ A @ B @ C ) )
=> ( simtri @ A @ B @ C @ D @ E @ F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD58) ).
thf(197,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( eqangle @ A @ B @ B @ C @ D @ E @ E @ F )
& ( eqangle @ A @ C @ B @ C @ D @ F @ E @ F )
& ~ ( coll @ A @ B @ C ) )
=> ( simtri @ A @ B @ C @ D @ E @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(95,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
? [H: $i] :
( ( ( midp @ G @ A @ B )
& ( para @ A @ D @ F @ G )
& ( para @ A @ D @ B @ E )
& ( coll @ D @ E @ F ) )
=> ( ( coll @ H @ A @ E )
& ( coll @ H @ G @ F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleX8) ).
thf(361,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
? [G: $i] :
( ( ( midp @ F @ A @ B )
& ( para @ A @ C @ E @ F )
& ( para @ A @ C @ B @ D )
& ( coll @ C @ D @ E ) )
=> ( ( coll @ G @ A @ D )
& ( coll @ G @ F @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(68,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
? [F: $i] :
( ( ( cong @ E @ C @ E @ D )
& ( perp @ A @ B @ B @ E ) )
=> ( ( cong @ E @ C @ E @ F )
& ( para @ F @ C @ A @ B )
& ( cong @ B @ C @ B @ F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleX9) ).
thf(285,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
? [F: $i] :
( ( ( cong @ E @ C @ E @ D )
& ( perp @ A @ B @ B @ E ) )
=> ( ( cong @ E @ C @ E @ F )
& ( para @ F @ C @ A @ B )
& ( cong @ B @ C @ B @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(45,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( para @ A @ B @ C @ D )
& ( para @ C @ D @ E @ F ) )
=> ( para @ A @ B @ E @ F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD6) ).
thf(224,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( para @ A @ B @ C @ D )
& ( para @ C @ D @ E @ F ) )
=> ( para @ A @ B @ E @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(29,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( cong @ A @ B @ C @ D )
=> ( cong @ C @ D @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD24) ).
thf(188,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( cong @ A @ B @ C @ D )
=> ( cong @ C @ D @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(10,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( simtri @ A @ C @ B @ D @ F @ E )
=> ( simtri @ A @ B @ C @ D @ E @ F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD31) ).
thf(141,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( simtri @ A @ C @ B @ D @ F @ E )
=> ( simtri @ A @ B @ C @ D @ E @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(124,plain,
perp @ sk1 @ sk2 @ sk3 @ sk4,
inference(cnf,[status(esa)],[98]) ).
thf(31,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( eqangle @ A @ B @ C @ D @ E @ F @ G @ H )
=> ( eqangle @ C @ D @ A @ B @ G @ H @ E @ F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD19) ).
thf(193,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( eqangle @ A @ B @ C @ D @ E @ F @ G @ H )
=> ( eqangle @ C @ D @ A @ B @ G @ H @ E @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(39,axiom,
! [A: $i,B: $i,C: $i] :
( ( para @ A @ B @ A @ C )
=> ( coll @ A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD66) ).
thf(212,plain,
! [A: $i,B: $i,C: $i] :
( ( para @ A @ B @ A @ C )
=> ( coll @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(109,plain,
midp @ sk17 @ sk4 @ sk3,
inference(cnf,[status(esa)],[98]) ).
thf(82,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( para @ A @ B @ C @ D )
& ( perp @ C @ D @ E @ F ) )
=> ( perp @ A @ B @ E @ F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD10) ).
thf(328,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( para @ A @ B @ C @ D )
& ( perp @ C @ D @ E @ F ) )
=> ( perp @ A @ B @ E @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(105,plain,
perp @ sk2 @ sk3 @ sk11 @ sk5,
inference(cnf,[status(esa)],[98]) ).
thf(61,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( perp @ A @ B @ C @ D )
=> ( perp @ A @ B @ D @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD7) ).
thf(266,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( perp @ A @ B @ C @ D )
=> ( perp @ A @ B @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(73,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( midp @ E @ A @ B )
& ( para @ A @ C @ B @ D )
& ( para @ A @ D @ B @ C ) )
=> ( midp @ E @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD64) ).
thf(298,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( midp @ E @ A @ B )
& ( para @ A @ C @ B @ D )
& ( para @ A @ D @ B @ C ) )
=> ( midp @ E @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(21,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( cyclic @ A @ B @ C @ D )
=> ( eqangle @ C @ A @ C @ B @ D @ A @ D @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD41) ).
thf(166,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( cyclic @ A @ B @ C @ D )
=> ( eqangle @ C @ A @ C @ B @ D @ A @ D @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(72,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( midp @ C @ A @ B )
& ( perp @ D @ C @ A @ B ) )
=> ( cong @ D @ A @ D @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD55) ).
thf(296,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( midp @ C @ A @ B )
& ( perp @ D @ C @ A @ B ) )
=> ( cong @ D @ A @ D @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(14,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( cyclic @ A @ B @ C @ D )
& ( cyclic @ A @ B @ C @ E )
& ( cyclic @ A @ B @ C @ F )
& ( eqangle @ C @ A @ C @ B @ F @ D @ F @ E ) )
=> ( cong @ A @ B @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD43) ).
thf(149,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( cyclic @ A @ B @ C @ D )
& ( cyclic @ A @ B @ C @ E )
& ( cyclic @ A @ B @ C @ F )
& ( eqangle @ C @ A @ C @ B @ F @ D @ F @ E ) )
=> ( cong @ A @ B @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(118,plain,
perp @ sk1 @ sk3 @ sk2 @ sk4,
inference(cnf,[status(esa)],[98]) ).
thf(67,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
? [E: $i] :
( ( ( perp @ C @ D @ A @ B )
& ( eqangle @ A @ C @ C @ D @ C @ D @ C @ B ) )
=> ( ( coll @ B @ A @ E )
& ( coll @ E @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleX3) ).
thf(281,plain,
! [A: $i,B: $i,C: $i,D: $i] :
? [E: $i] :
( ( ( perp @ C @ D @ A @ B )
& ( eqangle @ A @ C @ C @ D @ C @ D @ C @ B ) )
=> ( ( coll @ B @ A @ E )
& ( coll @ E @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(58,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( circle @ D @ A @ B @ C )
& ( eqangle @ A @ E @ A @ B @ C @ A @ C @ B ) )
=> ( perp @ D @ A @ A @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD49) ).
thf(259,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( circle @ D @ A @ B @ C )
& ( eqangle @ A @ E @ A @ B @ C @ A @ C @ B ) )
=> ( perp @ D @ A @ A @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(77,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( circle @ D @ A @ B @ C )
& ( coll @ D @ A @ C ) )
=> ( perp @ A @ B @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD53) ).
thf(313,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( circle @ D @ A @ B @ C )
& ( coll @ D @ A @ C ) )
=> ( perp @ A @ B @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(85,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( perp @ A @ B @ B @ C )
& ( midp @ D @ A @ C ) )
=> ( cong @ A @ D @ B @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD52) ).
thf(335,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( perp @ A @ B @ B @ C )
& ( midp @ D @ A @ C ) )
=> ( cong @ A @ D @ B @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(47,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( cyclic @ A @ B @ C @ D )
& ( cyclic @ A @ B @ C @ E ) )
=> ( cyclic @ B @ C @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD17) ).
thf(236,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( cyclic @ A @ B @ C @ D )
& ( cyclic @ A @ B @ C @ E ) )
=> ( cyclic @ B @ C @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(90,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( midp @ E @ A @ B )
& ( midp @ E @ C @ D ) )
=> ( para @ A @ C @ B @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD63) ).
thf(350,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( midp @ E @ A @ B )
& ( midp @ E @ C @ D ) )
=> ( para @ A @ C @ B @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(18,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( eqratio @ A @ B @ C @ D @ E @ F @ G @ H )
& ( cong @ E @ F @ G @ H ) )
=> ( cong @ A @ B @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD75) ).
thf(159,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( eqratio @ A @ B @ C @ D @ E @ F @ G @ H )
& ( cong @ E @ F @ G @ H ) )
=> ( cong @ A @ B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(113,plain,
perp @ sk1 @ sk2 @ sk9 @ sk5,
inference(cnf,[status(esa)],[98]) ).
thf(51,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( eqangle @ A @ B @ C @ D @ E @ F @ G @ H )
=> ( eqangle @ B @ A @ C @ D @ E @ F @ G @ H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD18) ).
thf(245,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( eqangle @ A @ B @ C @ D @ E @ F @ G @ H )
=> ( eqangle @ B @ A @ C @ D @ E @ F @ G @ H ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(38,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
? [G: $i] :
( ( ( para @ A @ B @ C @ D )
& ( coll @ E @ A @ C )
& ( coll @ E @ B @ D )
& ( coll @ F @ A @ B ) )
=> ( ( coll @ E @ F @ G )
& ( coll @ G @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleX18) ).
thf(208,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
? [G: $i] :
( ( ( para @ A @ B @ C @ D )
& ( coll @ E @ A @ C )
& ( coll @ E @ B @ D )
& ( coll @ F @ A @ B ) )
=> ( ( coll @ E @ F @ G )
& ( coll @ G @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(614,plain,
( ( perp @ sk8 @ sk5 @ sk7 @ sk6 )
!= ( perp @ sk1 @ sk4 @ sk13 @ sk6 ) ),
inference(paramod_ordered,[status(thm)],[101,107]) ).
thf(615,plain,
( ( sk8 != sk1 )
| ( sk5 != sk4 )
| ( sk13 != sk7 )
| ( sk6 != sk6 ) ),
inference(simp,[status(thm)],[614]) ).
thf(616,plain,
( ( sk8 != sk1 )
| ( sk5 != sk4 )
| ( sk13 != sk7 ) ),
inference(simp,[status(thm)],[615]) ).
thf(75,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
? [E: $i,F: $i] :
( ( ( perp @ A @ D @ B @ C )
& ( perp @ B @ D @ A @ C ) )
=> ( ( coll @ E @ C @ B )
& ( perp @ A @ E @ C @ B )
& ( coll @ F @ C @ A )
& ( perp @ B @ F @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleX10) ).
thf(303,plain,
! [A: $i,B: $i,C: $i,D: $i] :
? [E: $i,F: $i] :
( ( ( perp @ A @ D @ B @ C )
& ( perp @ B @ D @ A @ C ) )
=> ( ( coll @ E @ C @ B )
& ( perp @ A @ E @ C @ B )
& ( coll @ F @ C @ A )
& ( perp @ B @ F @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(103,plain,
midp @ sk12 @ sk1 @ sk2,
inference(cnf,[status(esa)],[98]) ).
thf(80,axiom,
! [A: $i,B: $i,C: $i] :
( ( midp @ A @ B @ C )
=> ( cong @ A @ B @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD68) ).
thf(323,plain,
! [A: $i,B: $i,C: $i] :
( ( midp @ A @ B @ C )
=> ( cong @ A @ B @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(54,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( cyclic @ A @ B @ C @ D )
=> ( cyclic @ A @ C @ B @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD15) ).
thf(251,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( cyclic @ A @ B @ C @ D )
=> ( cyclic @ A @ C @ B @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(108,plain,
perp @ sk4 @ sk3 @ sk17 @ sk7,
inference(cnf,[status(esa)],[98]) ).
thf(83,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
? [F: $i] :
( ( ( perp @ A @ B @ A @ C )
& ( perp @ C @ A @ C @ D )
& ( midp @ E @ B @ D ) )
=> ( midp @ F @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleX16) ).
thf(330,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
? [F: $i] :
( ( ( perp @ A @ B @ A @ C )
& ( perp @ C @ A @ C @ D )
& ( midp @ E @ B @ D ) )
=> ( midp @ F @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(7,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( simtri @ D @ E @ F @ A @ B @ C )
=> ( simtri @ A @ B @ C @ D @ E @ F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD33) ).
thf(135,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( simtri @ D @ E @ F @ A @ B @ C )
=> ( simtri @ A @ B @ C @ D @ E @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(46,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
? [G: $i,H: $i] :
( ( ( circle @ E @ A @ B @ C )
& ( cong @ E @ A @ E @ D )
& ( cong @ F @ A @ F @ B )
& ( E != F ) )
=> ( ( coll @ G @ A @ C )
& ( cong @ G @ F @ F @ A )
& ( coll @ H @ B @ D )
& ( cong @ H @ F @ F @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleX12) ).
thf(226,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
? [G: $i,H: $i] :
( ( ( circle @ E @ A @ B @ C )
& ( cong @ E @ A @ E @ D )
& ( cong @ F @ A @ F @ B )
& ( E != F ) )
=> ( ( coll @ G @ A @ C )
& ( cong @ G @ F @ F @ A )
& ( coll @ H @ B @ D )
& ( cong @ H @ F @ F @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(49,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( eqangle @ C @ A @ C @ B @ D @ A @ D @ B )
& ~ ( coll @ C @ D @ A ) )
=> ( cyclic @ A @ B @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD42a) ).
thf(241,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( eqangle @ C @ A @ C @ B @ D @ A @ D @ B )
& ~ ( coll @ C @ D @ A ) )
=> ( cyclic @ A @ B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(19,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( cyclic @ A @ B @ C @ D )
=> ( cyclic @ A @ B @ D @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD14) ).
thf(162,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( cyclic @ A @ B @ C @ D )
=> ( cyclic @ A @ B @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(56,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( eqangle @ C @ A @ C @ B @ D @ A @ D @ B )
& ( coll @ C @ D @ B ) )
=> ( cyclic @ A @ B @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD42b) ).
thf(255,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( eqangle @ C @ A @ C @ B @ D @ A @ D @ B )
& ( coll @ C @ D @ B ) )
=> ( cyclic @ A @ B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(112,plain,
midp @ sk20 @ sk4 @ sk3,
inference(cnf,[status(esa)],[98]) ).
thf(123,plain,
perp @ sk2 @ sk4 @ sk14 @ sk6,
inference(cnf,[status(esa)],[98]) ).
thf(92,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( eqangle @ A @ B @ C @ D @ C @ D @ A @ B )
& ~ ( perp @ A @ B @ C @ D ) )
=> ( para @ A @ B @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD72) ).
thf(355,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( eqangle @ A @ B @ C @ D @ C @ D @ A @ B )
& ~ ( perp @ A @ B @ C @ D ) )
=> ( para @ A @ B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(12,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( simtri @ A @ B @ C @ D @ E @ F )
=> ( eqangle @ A @ B @ B @ C @ D @ E @ E @ F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD60) ).
thf(145,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( simtri @ A @ B @ C @ D @ E @ F )
=> ( eqangle @ A @ B @ B @ C @ D @ E @ E @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(638,plain,
( ( perp @ sk8 @ sk5 @ sk7 @ sk6 )
!= ( perp @ sk2 @ sk4 @ sk14 @ sk6 ) ),
inference(paramod_ordered,[status(thm)],[123,107]) ).
thf(639,plain,
( ( sk8 != sk2 )
| ( sk5 != sk4 )
| ( sk14 != sk7 )
| ( sk6 != sk6 ) ),
inference(simp,[status(thm)],[638]) ).
thf(640,plain,
( ( sk8 != sk2 )
| ( sk5 != sk4 )
| ( sk14 != sk7 ) ),
inference(simp,[status(thm)],[639]) ).
thf(326,plain,
! [A: $i] :
( ? [B: $i] :
( ? [C: $i] : ( midp @ C @ A @ B )
& ? [C: $i,D: $i] :
( ? [E: $i] : ( midp @ E @ C @ D )
& ( coll @ C @ A @ B )
& ( coll @ D @ A @ B ) ) )
=> ! [B: $i] :
? [C: $i] : ( midp @ C @ A @ B ) ),
inference(miniscope,[status(thm)],[325]) ).
thf(327,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( midp @ C @ A @ B )
| ~ ( midp @ F @ D @ E )
| ~ ( coll @ D @ A @ B )
| ~ ( coll @ E @ A @ B )
| ( midp @ ( sk36 @ G @ A ) @ A @ G ) ),
inference(cnf,[status(esa)],[326]) ).
thf(60,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
? [E: $i] :
( ( ( perp @ A @ C @ C @ B )
& ( cyclic @ A @ B @ C @ D ) )
=> ( circle @ E @ A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleX14) ).
thf(263,plain,
! [A: $i,B: $i,C: $i,D: $i] :
? [E: $i] :
( ( ( perp @ A @ C @ C @ B )
& ( cyclic @ A @ B @ C @ D ) )
=> ( circle @ E @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(34,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( para @ A @ B @ C @ D )
& ( coll @ E @ A @ C )
& ( coll @ E @ B @ D ) )
=> ( eqratio @ E @ A @ A @ C @ E @ B @ B @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD65) ).
thf(199,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( para @ A @ B @ C @ D )
& ( coll @ E @ A @ C )
& ( coll @ E @ B @ D ) )
=> ( eqratio @ E @ A @ A @ C @ E @ B @ B @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(3,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( contri @ B @ A @ C @ E @ D @ F )
=> ( contri @ A @ B @ C @ D @ E @ F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD36) ).
thf(127,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( contri @ B @ A @ C @ E @ D @ F )
=> ( contri @ A @ B @ C @ D @ E @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(94,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( midp @ D @ A @ B )
& ( para @ D @ E @ B @ C )
& ( coll @ E @ A @ C ) )
=> ( midp @ E @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD45) ).
thf(359,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( midp @ D @ A @ B )
& ( para @ D @ E @ B @ C )
& ( coll @ E @ A @ C ) )
=> ( midp @ E @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(25,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( cyclic @ A @ B @ C @ D )
=> ( cyclic @ B @ A @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD16) ).
thf(177,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( cyclic @ A @ B @ C @ D )
=> ( cyclic @ B @ A @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(27,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( eqratio @ A @ B @ C @ D @ E @ F @ G @ H )
=> ( eqratio @ E @ F @ G @ H @ A @ B @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD28) ).
thf(182,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( eqratio @ A @ B @ C @ D @ E @ F @ G @ H )
=> ( eqratio @ E @ F @ G @ H @ A @ B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(16,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( eqangle @ A @ B @ C @ D @ E @ F @ G @ H )
& ( para @ E @ F @ G @ H ) )
=> ( para @ A @ B @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD73) ).
thf(154,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( eqangle @ A @ B @ C @ D @ E @ F @ G @ H )
& ( para @ E @ F @ G @ H ) )
=> ( para @ A @ B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(11,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( simtri @ B @ A @ C @ E @ D @ F )
=> ( simtri @ A @ B @ C @ D @ E @ F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD32) ).
thf(143,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( simtri @ B @ A @ C @ E @ D @ F )
=> ( simtri @ A @ B @ C @ D @ E @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(99,plain,
perp @ sk4 @ sk3 @ sk20 @ sk8,
inference(cnf,[status(esa)],[98]) ).
thf(36,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i,L: $i] :
( ( ( eqratio @ A @ B @ C @ D @ I @ J @ K @ L )
& ( eqratio @ I @ J @ K @ L @ E @ F @ G @ H ) )
=> ( eqratio @ A @ B @ C @ D @ E @ F @ G @ H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD30) ).
thf(203,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i,L: $i] :
( ( ( eqratio @ A @ B @ C @ D @ I @ J @ K @ L )
& ( eqratio @ I @ J @ K @ L @ E @ F @ G @ H ) )
=> ( eqratio @ A @ B @ C @ D @ E @ F @ G @ H ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(42,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( coll @ A @ B @ C )
& ( coll @ A @ B @ D ) )
=> ( coll @ C @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD3) ).
thf(218,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( coll @ A @ B @ C )
& ( coll @ A @ B @ D ) )
=> ( coll @ C @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(104,plain,
midp @ sk11 @ sk2 @ sk3,
inference(cnf,[status(esa)],[98]) ).
thf(114,plain,
midp @ sk19 @ sk2 @ sk3,
inference(cnf,[status(esa)],[98]) ).
thf(379,plain,
! [N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( midp @ C @ A @ B )
| ~ ( midp @ F @ D @ E )
| ~ ( coll @ D @ A @ B )
| ~ ( coll @ E @ A @ B )
| ~ ( midp @ M @ K @ L )
| ~ ( coll @ K @ H @ I )
| ~ ( coll @ L @ H @ I )
| ( midp @ ( sk36 @ N @ H ) @ H @ N )
| ( ( midp @ ( sk36 @ G @ A ) @ A @ G )
!= ( midp @ J @ H @ I ) ) ),
inference(paramod_ordered,[status(thm)],[327,327]) ).
thf(380,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( midp @ B @ K @ A )
| ~ ( midp @ E @ C @ D )
| ~ ( coll @ C @ K @ A )
| ~ ( coll @ D @ K @ A )
| ~ ( midp @ H @ F @ G )
| ~ ( coll @ F @ K @ J )
| ~ ( coll @ G @ K @ J )
| ( midp @ ( sk36 @ I @ K ) @ K @ I ) ),
inference(pattern_uni,[status(thm)],[379:[bind(A,$thf( P )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( E )),bind(F,$thf( F )),bind(G,$thf( O )),bind(H,$thf( P )),bind(I,$thf( O )),bind(J,$thf( sk36 @ O @ P ))]]) ).
thf(401,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( midp @ B @ K @ A )
| ~ ( midp @ E @ C @ D )
| ~ ( coll @ C @ K @ A )
| ~ ( coll @ D @ K @ A )
| ~ ( midp @ H @ F @ G )
| ~ ( coll @ F @ K @ J )
| ~ ( coll @ G @ K @ J )
| ( midp @ ( sk36 @ I @ K ) @ K @ I ) ),
inference(simp,[status(thm)],[380]) ).
thf(9,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( simtri @ A @ B @ C @ D @ E @ F )
& ( cong @ A @ B @ D @ E ) )
=> ( contri @ A @ B @ C @ D @ E @ F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD61) ).
thf(139,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( simtri @ A @ B @ C @ D @ E @ F )
& ( cong @ A @ B @ D @ E ) )
=> ( contri @ A @ B @ C @ D @ E @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(64,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
? [F: $i] :
( ( ( cyclic @ A @ B @ C @ D )
& ( para @ A @ B @ C @ D )
& ( midp @ E @ A @ B ) )
=> ( circle @ F @ A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleX13) ).
thf(272,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
? [F: $i] :
( ( ( cyclic @ A @ B @ C @ D )
& ( para @ A @ B @ C @ D )
& ( midp @ E @ A @ B ) )
=> ( circle @ F @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(88,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( cong @ A @ C @ B @ C )
& ( cong @ A @ D @ B @ D ) )
=> ( perp @ A @ B @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD56) ).
thf(346,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( cong @ A @ C @ B @ C )
& ( cong @ A @ D @ B @ D ) )
=> ( perp @ A @ B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(40,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( eqangle @ A @ B @ C @ D @ E @ F @ G @ H )
=> ( eqangle @ A @ B @ E @ F @ C @ D @ G @ H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD21) ).
thf(214,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( eqangle @ A @ B @ C @ D @ E @ F @ G @ H )
=> ( eqangle @ A @ B @ E @ F @ C @ D @ G @ H ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(69,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( midp @ E @ A @ B )
& ( midp @ F @ C @ D ) )
=> ( eqratio @ E @ A @ A @ B @ F @ C @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD70) ).
thf(290,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( midp @ E @ A @ B )
& ( midp @ F @ C @ D ) )
=> ( eqratio @ E @ A @ A @ B @ F @ C @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(119,plain,
perp @ sk2 @ sk4 @ sk18 @ sk8,
inference(cnf,[status(esa)],[98]) ).
thf(74,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
? [E: $i] :
( ( circle @ D @ A @ B @ C )
=> ( perp @ E @ A @ A @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleX11) ).
thf(300,plain,
! [A: $i,B: $i,C: $i,D: $i] :
? [E: $i] :
( ( circle @ D @ A @ B @ C )
=> ( perp @ E @ A @ A @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(22,axiom,
! [A: $i,B: $i,C: $i] :
( ( coll @ A @ B @ C )
=> ( coll @ A @ C @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD1) ).
thf(168,plain,
! [A: $i,B: $i,C: $i] :
( ( coll @ A @ B @ C )
=> ( coll @ A @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(30,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( para @ A @ B @ C @ D )
=> ( eqangle @ A @ B @ E @ F @ C @ D @ E @ F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD40) ).
thf(190,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( para @ A @ B @ C @ D )
=> ( eqangle @ A @ B @ E @ F @ C @ D @ E @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(421,plain,
( ( perp @ sk8 @ sk5 @ sk7 @ sk6 )
!= ( perp @ sk4 @ sk3 @ sk20 @ sk8 ) ),
inference(paramod_ordered,[status(thm)],[99,107]) ).
thf(422,plain,
( ( sk8 != sk4 )
| ( sk5 != sk3 )
| ( sk20 != sk7 )
| ( sk8 != sk6 ) ),
inference(simp,[status(thm)],[421]) ).
thf(87,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
? [G: $i] :
( ( ( midp @ E @ A @ B )
& ( midp @ F @ C @ D ) )
=> ( ( midp @ G @ A @ D )
& ( para @ G @ E @ B @ D )
& ( para @ G @ F @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleX6) ).
thf(341,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
? [G: $i] :
( ( ( midp @ E @ A @ B )
& ( midp @ F @ C @ D ) )
=> ( ( midp @ G @ A @ D )
& ( para @ G @ E @ B @ D )
& ( para @ G @ F @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(62,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( cong @ A @ C @ B @ C )
& ( cong @ A @ D @ B @ D )
& ( cyclic @ A @ B @ C @ D ) )
=> ( perp @ C @ A @ A @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD57) ).
thf(268,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( cong @ A @ C @ B @ C )
& ( cong @ A @ D @ B @ D )
& ( cyclic @ A @ B @ C @ D ) )
=> ( perp @ C @ A @ A @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(32,axiom,
! [A: $i,B: $i,C: $i] :
( ( cong @ C @ A @ C @ B )
=> ( eqangle @ C @ A @ A @ B @ A @ B @ C @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD46) ).
thf(195,plain,
! [A: $i,B: $i,C: $i] :
( ( cong @ C @ A @ C @ B )
=> ( eqangle @ C @ A @ A @ B @ A @ B @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(71,axiom,
! [A: $i,B: $i,C: $i] :
( ( midp @ C @ B @ A )
=> ( midp @ C @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD11) ).
thf(294,plain,
! [A: $i,B: $i,C: $i] :
( ( midp @ C @ B @ A )
=> ( midp @ C @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(126,plain,
midp @ sk15 @ sk1 @ sk4,
inference(cnf,[status(esa)],[98]) ).
thf(5,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( contri @ D @ E @ F @ A @ B @ C )
=> ( contri @ A @ B @ C @ D @ E @ F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD37) ).
thf(131,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( contri @ D @ E @ F @ A @ B @ C )
=> ( contri @ A @ B @ C @ D @ E @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(66,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
? [E: $i] :
( ( ( perp @ C @ D @ A @ B )
& ( cong @ C @ A @ C @ B ) )
=> ( ( coll @ B @ A @ E )
& ( coll @ E @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleX4) ).
thf(277,plain,
! [A: $i,B: $i,C: $i,D: $i] :
? [E: $i] :
( ( ( perp @ C @ D @ A @ B )
& ( cong @ C @ A @ C @ B ) )
=> ( ( coll @ B @ A @ E )
& ( coll @ E @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(111,plain,
midp @ sk18 @ sk2 @ sk4,
inference(cnf,[status(esa)],[98]) ).
thf(76,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
? [F: $i] :
( ( ( perp @ A @ C @ C @ B )
& ( coll @ B @ D @ E ) )
=> ( ( coll @ F @ D @ E )
& ( perp @ F @ A @ D @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleX15) ).
thf(309,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
? [F: $i] :
( ( ( perp @ A @ C @ C @ B )
& ( coll @ B @ D @ E ) )
=> ( ( coll @ F @ D @ E )
& ( perp @ F @ A @ D @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(44,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( cyclic @ A @ B @ C @ D )
& ( para @ A @ B @ C @ D ) )
=> ( eqangle @ A @ D @ C @ D @ C @ D @ C @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD54) ).
thf(222,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( cyclic @ A @ B @ C @ D )
& ( para @ A @ B @ C @ D ) )
=> ( eqangle @ A @ D @ C @ D @ C @ D @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(100,plain,
perp @ sk1 @ sk3 @ sk16 @ sk7,
inference(cnf,[status(esa)],[98]) ).
thf(86,axiom,
! [A: $i,B: $i,C: $i] :
? [D: $i] :
( ( ( cong @ C @ A @ C @ B )
& ( perp @ A @ C @ C @ B ) )
=> ( ( coll @ A @ C @ D )
& ( cong @ C @ A @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleX17) ).
thf(337,plain,
! [A: $i,B: $i,C: $i] :
? [D: $i] :
( ( ( cong @ C @ A @ C @ B )
& ( perp @ A @ C @ C @ B ) )
=> ( ( coll @ A @ C @ D )
& ( cong @ C @ A @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(122,plain,
midp @ sk13 @ sk1 @ sk4,
inference(cnf,[status(esa)],[98]) ).
thf(901,plain,
$false,
inference(e,[status(thm)],[153,129,365,101,333,249,170,115,120,247,174,320,257,184,110,125,357,157,325,152,316,261,216,164,179,623,253,106,238,121,348,353,147,133,206,116,243,292,117,270,201,220,102,275,137,197,361,97,285,224,188,141,124,193,212,109,328,105,266,298,166,296,149,118,281,259,313,335,236,350,159,113,245,208,616,303,103,323,251,108,330,135,226,241,162,255,112,123,355,145,640,327,263,199,127,359,177,182,154,143,99,203,218,104,114,401,139,272,346,214,290,119,300,168,190,422,107,341,268,195,294,126,131,277,111,309,222,100,337,122]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GEO545+1 : TPTP v8.1.2. Released v7.5.0.
% 0.11/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n002.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Fri May 19 04:30:50 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.90/0.83 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.24/1.00 % [INFO] Parsing done (166ms).
% 1.24/1.00 % [INFO] Running in sequential loop mode.
% 1.89/1.20 % [INFO] eprover registered as external prover.
% 1.89/1.20 % [INFO] cvc4 registered as external prover.
% 1.89/1.21 % [INFO] Scanning for conjecture ...
% 2.05/1.30 % [INFO] Found a conjecture and 94 axioms. Running axiom selection ...
% 2.27/1.36 % [INFO] Axiom selection finished. Selected 94 axioms (removed 0 axioms).
% 2.51/1.45 % [INFO] Problem is first-order (TPTP FOF).
% 2.77/1.47 % [INFO] Type checking passed.
% 2.77/1.47 % [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 ...
% 10.76/3.25 % External prover 'e' found a proof!
% 10.76/3.25 % [INFO] Killing All external provers ...
% 10.76/3.25 % Time passed: 2744ms (effective reasoning time: 2247ms)
% 10.76/3.25 % 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)>
% 10.76/3.26 % Axioms used in derivation (94): ruleD34, ruleD66, ruleD52, ruleX16, ruleD61, ruleD23, ruleD56, ruleD9, ruleD18, ruleD62, ruleD8, ruleD39, ruleD21, ruleD45, ruleX18, ruleX7, ruleD68, ruleD11, ruleD49, ruleD44, ruleD51, ruleD33, ruleX2, ruleD73, ruleD14, ruleX12, ruleD55, ruleD24, ruleD29, ruleD40, ruleD4, ruleX6, ruleD42a, ruleD41, ruleX17, ruleD59, ruleD20, ruleD19, ruleD74, ruleD26, ruleD38, ruleD7, ruleD48, ruleD67, ruleD10, ruleD25, ruleX3, ruleD63, ruleX13, ruleX10, ruleD15, ruleD30, ruleD70, ruleD60, ruleD58, ruleD75, ruleD3, ruleD47, ruleD36, ruleX4, ruleD6, ruleD16, ruleD37, ruleD53, ruleD27, ruleX5, ruleX14, ruleD2, ruleD12, ruleX9, ruleD42b, ruleD64, ruleD31, ruleD71, ruleD35, ruleX8, ruleX11, ruleX1, ruleD57, ruleD17, ruleD46, ruleD22, ruleD5, ruleD32, ruleD13, ruleD72, ruleD1, ruleD28, ruleD43, ruleD50, ruleD65, ruleD54, ruleX15, ruleD69
% 10.76/3.26 % No. of inferences in proof: 238
% 10.76/3.26 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2744 ms resp. 2247 ms w/o parsing
% 10.76/3.33 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 10.76/3.33 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------