%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : GEO657+1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n010.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 07:13:47 AM UTC 2026
% Result : Theorem 8.84s 13.34s
% Output : Refutation 9.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 95
% Syntax : Number of formulae : 192 ( 1 unt; 0 typ; 0 def)
% Number of atoms : 585 ( 2 equ; 0 cnn)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 3084 ( 16 ~; 0 |; 202 &;2675 @)
% ( 0 <=>; 191 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 14 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 11 usr; 1 con; 0-8 aty)
% Number of variables : 1064 ( 0 ^;1024 !; 40 ?;1064 :)
% Comments :
%------------------------------------------------------------------------------
thf(coll_decl,type,
coll: $i > $i > $i > $o ).
thf(para_decl,type,
para: $i > $i > $i > $i > $o ).
thf(contri_decl,type,
contri: $i > $i > $i > $i > $i > $i > $o ).
thf(circle_decl,type,
circle: $i > $i > $i > $i > $o ).
thf(eqangle_decl,type,
eqangle: $i > $i > $i > $i > $i > $i > $i > $i > $o ).
thf(perp_decl,type,
perp: $i > $i > $i > $i > $o ).
thf(cyclic_decl,type,
cyclic: $i > $i > $i > $i > $o ).
thf(simtri_decl,type,
simtri: $i > $i > $i > $i > $i > $i > $o ).
thf(eqratio_decl,type,
eqratio: $i > $i > $i > $i > $i > $i > $i > $i > $o ).
thf(cong_decl,type,
cong: $i > $i > $i > $i > $o ).
thf(midp_decl,type,
midp: $i > $i > $i > $o ).
thf(94,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( C @ ( A @ ( E @ coll ) ) )
& ( C @ ( B @ ( E @ ( D @ para ) ) ) )
& ( B @ ( A @ ( D @ midp ) ) ) )
=> ( C @ ( A @ ( E @ midp ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD45) ).
thf(352,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( C @ ( A @ ( E @ coll ) ) )
& ( C @ ( B @ ( E @ ( D @ para ) ) ) )
& ( B @ ( A @ ( D @ midp ) ) ) )
=> ( C @ ( A @ ( E @ midp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(90,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( D @ ( C @ ( E @ midp ) ) )
& ( B @ ( A @ ( E @ midp ) ) ) )
=> ( D @ ( B @ ( C @ ( A @ para ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD63) ).
thf(340,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( D @ ( C @ ( E @ midp ) ) )
& ( B @ ( A @ ( E @ midp ) ) ) )
=> ( D @ ( B @ ( C @ ( A @ para ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(70,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
? [E: $i] :
( ( ( C @ ( A @ ( C @ ( B @ ( C @ ( B @ ( C @ ( D @ eqangle ) ) ) ) ) ) ) )
& ( A @ ( B @ ( B @ ( C @ perp ) ) ) ) )
=> ( ( D @ ( C @ ( E @ coll ) ) )
& ( B @ ( A @ ( E @ coll ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleX1) ).
thf(270,plain,
! [A: $i,B: $i,C: $i,D: $i] :
? [E: $i] :
( ( ( C @ ( A @ ( C @ ( B @ ( C @ ( B @ ( C @ ( D @ eqangle ) ) ) ) ) ) ) )
& ( A @ ( B @ ( B @ ( C @ perp ) ) ) ) )
=> ( ( D @ ( C @ ( E @ coll ) ) )
& ( B @ ( A @ ( E @ coll ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(35,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 @ eqratio ) ) ) ) ) ) ) )
=> ( F @ ( E @ ( H @ ( G @ ( B @ ( A @ ( D @ ( C @ eqratio ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD27) ).
thf(173,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 @ eqratio ) ) ) ) ) ) ) )
=> ( F @ ( E @ ( H @ ( G @ ( B @ ( A @ ( D @ ( C @ eqratio ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(89,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ ( A @ coll ) ) )
& ( C @ ( A @ ( B @ ( A @ cong ) ) ) ) )
=> ( C @ ( B @ ( A @ midp ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD67) ).
thf(338,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ ( A @ coll ) ) )
& ( C @ ( A @ ( B @ ( A @ cong ) ) ) ) )
=> ( C @ ( B @ ( A @ midp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(53,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( E @ ( F @ ( D @ ( B @ ( C @ ( A @ simtri ) ) ) ) ) )
=> ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ simtri ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD31) ).
thf(214,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( E @ ( F @ ( D @ ( B @ ( C @ ( A @ simtri ) ) ) ) ) )
=> ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ simtri ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(8,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
? [E: $i] :
( ( ( D @ ( C @ ( B @ ( A @ cyclic ) ) ) )
& ( B @ ( C @ ( C @ ( A @ perp ) ) ) ) )
=> ( C @ ( B @ ( A @ ( E @ circle ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleX14) ).
thf(115,plain,
! [A: $i,B: $i,C: $i,D: $i] :
? [E: $i] :
( ( ( D @ ( C @ ( B @ ( A @ cyclic ) ) ) )
& ( B @ ( C @ ( C @ ( A @ perp ) ) ) ) )
=> ( C @ ( B @ ( A @ ( E @ circle ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(10,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ simtri ) ) ) ) ) )
=> ( F @ ( E @ ( E @ ( D @ ( C @ ( B @ ( B @ ( A @ eqangle ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD60) ).
thf(120,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ simtri ) ) ) ) ) )
=> ( F @ ( E @ ( E @ ( D @ ( C @ ( B @ ( B @ ( A @ eqangle ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(40,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] :
( ( ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ eqangle ) ) ) ) ) ) ) )
& ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ eqangle ) ) ) ) ) ) ) ) )
=> ( L @ ( K @ ( J @ ( I @ ( D @ ( C @ ( B @ ( A @ eqangle ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD22) ).
thf(185,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] :
( ( ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ eqangle ) ) ) ) ) ) ) )
& ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ eqangle ) ) ) ) ) ) ) ) )
=> ( L @ ( K @ ( J @ ( I @ ( D @ ( C @ ( B @ ( A @ eqangle ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(76,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
? [H: $i] :
( ( ( B @ ( A @ ( D @ coll ) ) )
& ( B @ ( A @ ( C @ coll ) ) )
& ( D @ ( C @ ( F @ midp ) ) )
& ( B @ ( A @ ( E @ midp ) ) ) )
=> ( G @ ( A @ ( H @ midp ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleX7) ).
thf(288,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
? [H: $i] :
( ( ( B @ ( A @ ( D @ coll ) ) )
& ( B @ ( A @ ( C @ coll ) ) )
& ( D @ ( C @ ( F @ midp ) ) )
& ( B @ ( A @ ( E @ midp ) ) ) )
=> ( G @ ( A @ ( H @ midp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(45,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( C @ ( B @ ( E @ midp ) ) )
& ( C @ ( B @ ( A @ ( D @ circle ) ) ) ) )
=> ( E @ ( D @ ( B @ ( D @ ( C @ ( A @ ( B @ ( A @ eqangle ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD50) ).
thf(196,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( C @ ( B @ ( E @ midp ) ) )
& ( C @ ( B @ ( A @ ( D @ circle ) ) ) ) )
=> ( E @ ( D @ ( B @ ( D @ ( C @ ( A @ ( B @ ( A @ eqangle ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(27,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ cyclic ) ) ) )
=> ( D @ ( C @ ( A @ ( B @ cyclic ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD16) ).
thf(157,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ cyclic ) ) ) )
=> ( D @ ( C @ ( A @ ( B @ cyclic ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(42,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( D @ ( E @ ( C @ ( A @ ( B @ simtri ) ) ) ) ) )
=> ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ simtri ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD32) ).
thf(189,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( D @ ( E @ ( C @ ( A @ ( B @ simtri ) ) ) ) ) )
=> ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ simtri ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(74,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E @ ( D @ ( B @ ( D @ ( C @ ( A @ ( B @ ( A @ eqangle ) ) ) ) ) ) ) )
& ( C @ ( B @ ( E @ coll ) ) )
& ( C @ ( B @ ( A @ ( D @ circle ) ) ) ) )
=> ( C @ ( B @ ( E @ midp ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD51) ).
thf(284,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E @ ( D @ ( B @ ( D @ ( C @ ( A @ ( B @ ( A @ eqangle ) ) ) ) ) ) ) )
& ( C @ ( B @ ( E @ coll ) ) )
& ( C @ ( B @ ( A @ ( D @ circle ) ) ) ) )
=> ( C @ ( B @ ( E @ midp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(25,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ cyclic ) ) ) )
=> ( B @ ( D @ ( A @ ( D @ ( B @ ( C @ ( A @ ( C @ eqangle ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD41) ).
thf(152,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ cyclic ) ) ) )
=> ( B @ ( D @ ( A @ ( D @ ( B @ ( C @ ( A @ ( C @ eqangle ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(54,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ coll ) ) )
=> ( C @ ( A @ ( B @ coll ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD2) ).
thf(216,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ coll ) ) )
=> ( C @ ( A @ ( B @ coll ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(61,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
? [F: $i] :
( ( ~ ( C @ ( B @ ( A @ coll ) ) )
& ( E @ ( B @ ( D @ ( A @ ( C @ ( B @ ( C @ ( A @ eqangle ) ) ) ) ) ) ) ) )
=> ( ( F @ ( C @ ( B @ ( D @ cyclic ) ) ) )
& ( F @ ( B @ ( F @ ( A @ ( C @ ( B @ ( C @ ( A @ eqangle ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleX5) ).
thf(238,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
? [F: $i] :
( ( ~ ( C @ ( B @ ( A @ coll ) ) )
& ( E @ ( B @ ( D @ ( A @ ( C @ ( B @ ( C @ ( A @ eqangle ) ) ) ) ) ) ) ) )
=> ( ( F @ ( C @ ( B @ ( D @ cyclic ) ) ) )
& ( F @ ( B @ ( F @ ( A @ ( C @ ( B @ ( C @ ( A @ eqangle ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(92,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( D @ ( C @ ( B @ ( A @ perp ) ) ) )
& ( B @ ( A @ ( D @ ( C @ ( D @ ( C @ ( B @ ( A @ eqangle ) ) ) ) ) ) ) ) )
=> ( D @ ( C @ ( B @ ( A @ para ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD72) ).
thf(348,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( D @ ( C @ ( B @ ( A @ perp ) ) ) )
& ( B @ ( A @ ( D @ ( C @ ( D @ ( C @ ( B @ ( A @ eqangle ) ) ) ) ) ) ) ) )
=> ( D @ ( C @ ( B @ ( A @ para ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(23,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( C @ ( D @ perp ) ) ) )
& ( B @ ( A @ ( C @ midp ) ) ) )
=> ( B @ ( D @ ( A @ ( D @ cong ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD55) ).
thf(147,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( C @ ( D @ perp ) ) ) )
& ( B @ ( A @ ( C @ midp ) ) ) )
=> ( B @ ( D @ ( A @ ( D @ cong ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(72,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( A @ ( B @ ( A @ para ) ) ) )
=> ( C @ ( B @ ( A @ coll ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD66) ).
thf(280,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( A @ ( B @ ( A @ para ) ) ) )
=> ( C @ ( B @ ( A @ coll ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(56,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
? [F: $i] :
( ( ( B @ ( A @ ( E @ midp ) ) )
& ( D @ ( C @ ( B @ ( A @ para ) ) ) )
& ( D @ ( C @ ( B @ ( A @ cyclic ) ) ) ) )
=> ( C @ ( B @ ( A @ ( F @ circle ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleX13) ).
thf(221,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
? [F: $i] :
( ( ( B @ ( A @ ( E @ midp ) ) )
& ( D @ ( C @ ( B @ ( A @ para ) ) ) )
& ( D @ ( C @ ( B @ ( A @ cyclic ) ) ) ) )
=> ( C @ ( B @ ( A @ ( F @ circle ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(78,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( B @ ( A @ coll ) ) )
& ( C @ ( B @ ( A @ coll ) ) ) )
=> ( A @ ( D @ ( C @ coll ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD3) ).
thf(293,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( B @ ( A @ coll ) ) )
& ( C @ ( B @ ( A @ coll ) ) ) )
=> ( A @ ( D @ ( C @ coll ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(16,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 @ eqangle ) ) ) ) ) ) ) )
=> ( D @ ( C @ ( B @ ( A @ ( H @ ( G @ ( F @ ( E @ eqangle ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD20) ).
thf(133,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 @ eqangle ) ) ) ) ) ) ) )
=> ( D @ ( C @ ( B @ ( A @ ( H @ ( G @ ( F @ ( E @ eqangle ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(62,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ coll ) ) )
=> ( B @ ( C @ ( A @ coll ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD1) ).
thf(243,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ coll ) ) )
=> ( B @ ( C @ ( A @ coll ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(68,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( D @ ( B @ ( E @ coll ) ) )
& ( C @ ( A @ ( E @ coll ) ) )
& ( D @ ( C @ ( B @ ( A @ para ) ) ) ) )
=> ( D @ ( B @ ( B @ ( E @ ( C @ ( A @ ( A @ ( E @ eqratio ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD65) ).
thf(265,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( D @ ( B @ ( E @ coll ) ) )
& ( C @ ( A @ ( E @ coll ) ) )
& ( D @ ( C @ ( B @ ( A @ para ) ) ) ) )
=> ( D @ ( B @ ( B @ ( E @ ( C @ ( A @ ( A @ ( E @ eqratio ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(81,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( F @ ( E @ ( D @ ( C @ para ) ) ) )
& ( D @ ( C @ ( B @ ( A @ para ) ) ) ) )
=> ( F @ ( E @ ( B @ ( A @ para ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD6) ).
thf(302,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( F @ ( E @ ( D @ ( C @ para ) ) ) )
& ( D @ ( C @ ( B @ ( A @ para ) ) ) ) )
=> ( F @ ( E @ ( B @ ( A @ para ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(66,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( D @ ( C @ ( B @ ( A @ para ) ) ) )
=> ( F @ ( E @ ( D @ ( C @ ( F @ ( E @ ( B @ ( A @ eqangle ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD40) ).
thf(260,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( D @ ( C @ ( B @ ( A @ para ) ) ) )
=> ( F @ ( E @ ( D @ ( C @ ( F @ ( E @ ( B @ ( A @ eqangle ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(31,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
( ( ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ simtri ) ) ) ) ) )
& ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ simtri ) ) ) ) ) ) )
=> ( I @ ( H @ ( G @ ( C @ ( B @ ( A @ simtri ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD34) ).
thf(165,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
( ( ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ simtri ) ) ) ) ) )
& ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ simtri ) ) ) ) ) ) )
=> ( I @ ( H @ ( G @ ( C @ ( B @ ( A @ simtri ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(71,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
? [G: $i] :
( ( ( B @ ( A @ ( F @ coll ) ) )
& ( D @ ( B @ ( E @ coll ) ) )
& ( C @ ( A @ ( E @ coll ) ) )
& ( D @ ( C @ ( B @ ( A @ para ) ) ) ) )
=> ( ( D @ ( C @ ( G @ coll ) ) )
& ( G @ ( F @ ( E @ coll ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleX18) ).
thf(275,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
? [G: $i] :
( ( ( B @ ( A @ ( F @ coll ) ) )
& ( D @ ( B @ ( E @ coll ) ) )
& ( C @ ( A @ ( E @ coll ) ) )
& ( D @ ( C @ ( B @ ( A @ para ) ) ) ) )
=> ( ( D @ ( C @ ( G @ coll ) ) )
& ( G @ ( F @ ( E @ coll ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(18,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( D @ ( C @ ( F @ midp ) ) )
& ( B @ ( A @ ( E @ midp ) ) ) )
=> ( D @ ( C @ ( C @ ( F @ ( B @ ( A @ ( A @ ( E @ eqratio ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD70) ).
thf(137,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( D @ ( C @ ( F @ midp ) ) )
& ( B @ ( A @ ( E @ midp ) ) ) )
=> ( D @ ( C @ ( C @ ( F @ ( B @ ( A @ ( A @ ( E @ eqratio ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(64,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( E @ ( D @ ( C @ ( F @ ( E @ ( B @ ( A @ eqangle ) ) ) ) ) ) ) )
=> ( D @ ( C @ ( B @ ( A @ para ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD39) ).
thf(252,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( E @ ( D @ ( C @ ( F @ ( E @ ( B @ ( A @ eqangle ) ) ) ) ) ) ) )
=> ( D @ ( C @ ( B @ ( A @ para ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( C @ ( B @ ( G @ coll ) ) )
& ( D @ ( C @ ( F @ coll ) ) )
& ( E @ ( F @ ( D @ ( A @ para ) ) ) )
& ( E @ ( G @ ( B @ ( A @ para ) ) ) )
& ( C @ ( A @ ( E @ coll ) ) ) )
=> ( F @ ( G @ ( D @ ( B @ para ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exemplo6GDDFULLmoreE02315) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( C @ ( B @ ( G @ coll ) ) )
& ( D @ ( C @ ( F @ coll ) ) )
& ( E @ ( F @ ( D @ ( A @ para ) ) ) )
& ( E @ ( G @ ( B @ ( A @ para ) ) ) )
& ( C @ ( A @ ( E @ coll ) ) ) )
=> ( F @ ( G @ ( D @ ( B @ para ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(97,plain,
~ ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( C @ ( B @ ( G @ coll ) ) )
& ( D @ ( C @ ( F @ coll ) ) )
& ( E @ ( F @ ( D @ ( A @ para ) ) ) )
& ( E @ ( G @ ( B @ ( A @ para ) ) ) )
& ( C @ ( A @ ( E @ coll ) ) ) )
=> ( F @ ( G @ ( D @ ( B @ para ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(86,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
? [G: $i] :
( ( ( D @ ( C @ ( F @ midp ) ) )
& ( B @ ( A @ ( E @ midp ) ) ) )
=> ( ( C @ ( A @ ( F @ ( G @ para ) ) ) )
& ( D @ ( B @ ( E @ ( G @ para ) ) ) )
& ( D @ ( A @ ( G @ midp ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleX6) ).
thf(324,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
? [G: $i] :
( ( ( D @ ( C @ ( F @ midp ) ) )
& ( B @ ( A @ ( E @ midp ) ) ) )
=> ( ( C @ ( A @ ( F @ ( G @ para ) ) ) )
& ( D @ ( B @ ( E @ ( G @ para ) ) ) )
& ( D @ ( A @ ( G @ midp ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(57,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( D @ ( C @ ( B @ ( A @ para ) ) ) )
& ( B @ ( A @ ( D @ ( C @ ( D @ ( C @ ( B @ ( A @ eqangle ) ) ) ) ) ) ) ) )
=> ( D @ ( C @ ( B @ ( A @ perp ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD71) ).
thf(224,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( D @ ( C @ ( B @ ( A @ para ) ) ) )
& ( B @ ( A @ ( D @ ( C @ ( D @ ( C @ ( B @ ( A @ eqangle ) ) ) ) ) ) ) ) )
=> ( D @ ( C @ ( B @ ( A @ perp ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(84,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ midp ) ) )
=> ( C @ ( B @ ( A @ coll ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD69) ).
thf(317,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ midp ) ) )
=> ( C @ ( B @ ( A @ coll ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(96,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( B @ ( A @ ( C @ coll ) ) )
& ( B @ ( C @ ( B @ ( A @ ( B @ ( A @ ( A @ ( C @ eqangle ) ) ) ) ) ) ) ) )
=> ( B @ ( C @ ( A @ ( C @ cong ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD47) ).
thf(356,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( B @ ( A @ ( C @ coll ) ) )
& ( B @ ( C @ ( B @ ( A @ ( B @ ( A @ ( A @ ( C @ eqangle ) ) ) ) ) ) ) ) )
=> ( B @ ( C @ ( A @ ( C @ cong ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(33,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E @ ( A @ ( A @ ( D @ perp ) ) ) )
& ( C @ ( B @ ( A @ ( D @ circle ) ) ) ) )
=> ( B @ ( C @ ( A @ ( C @ ( B @ ( A @ ( E @ ( A @ eqangle ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD48) ).
thf(169,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E @ ( A @ ( A @ ( D @ perp ) ) ) )
& ( C @ ( B @ ( A @ ( D @ circle ) ) ) ) )
=> ( B @ ( C @ ( A @ ( C @ ( B @ ( A @ ( E @ ( A @ eqangle ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(20,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ midp ) ) )
=> ( B @ ( A @ ( C @ midp ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD11) ).
thf(141,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ midp ) ) )
=> ( B @ ( A @ ( C @ midp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(5,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( C @ ( B @ ( A @ ( F @ ( E @ ( D @ contri ) ) ) ) ) )
=> ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ contri ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD37) ).
thf(109,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( C @ ( B @ ( A @ ( F @ ( E @ ( D @ contri ) ) ) ) ) )
=> ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ contri ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(12,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ ( B @ ( A @ cyclic ) ) ) )
& ( D @ ( B @ ( D @ ( A @ cong ) ) ) )
& ( C @ ( B @ ( C @ ( A @ cong ) ) ) ) )
=> ( D @ ( A @ ( A @ ( C @ perp ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD57) ).
thf(124,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ ( B @ ( A @ cyclic ) ) ) )
& ( D @ ( B @ ( D @ ( A @ cong ) ) ) )
& ( C @ ( B @ ( C @ ( A @ cong ) ) ) ) )
=> ( D @ ( A @ ( A @ ( C @ perp ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(44,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
? [F: $i] :
( ( ( D @ ( B @ ( E @ midp ) ) )
& ( D @ ( C @ ( A @ ( C @ perp ) ) ) )
& ( C @ ( A @ ( B @ ( A @ perp ) ) ) ) )
=> ( C @ ( A @ ( F @ midp ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleX16) ).
thf(193,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
? [F: $i] :
( ( ( D @ ( B @ ( E @ midp ) ) )
& ( D @ ( C @ ( A @ ( C @ perp ) ) ) )
& ( C @ ( A @ ( B @ ( A @ perp ) ) ) ) )
=> ( C @ ( A @ ( F @ midp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(52,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 @ eqangle ) ) ) ) ) ) ) )
=> ( H @ ( G @ ( D @ ( C @ ( F @ ( E @ ( B @ ( A @ eqangle ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD21) ).
thf(212,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 @ eqangle ) ) ) ) ) ) ) )
=> ( H @ ( G @ ( D @ ( C @ ( F @ ( E @ ( B @ ( A @ eqangle ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(3,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( D @ ( E @ ( C @ ( A @ ( B @ contri ) ) ) ) ) )
=> ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ contri ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD36) ).
thf(105,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( D @ ( E @ ( C @ ( A @ ( B @ contri ) ) ) ) ) )
=> ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ contri ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(49,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ contri ) ) ) ) ) )
=> ( E @ ( D @ ( B @ ( A @ cong ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD62) ).
thf(205,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ contri ) ) ) ) ) )
=> ( E @ ( D @ ( B @ ( A @ cong ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(14,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( H @ ( G @ ( F @ ( E @ cong ) ) ) )
& ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ eqratio ) ) ) ) ) ) ) ) )
=> ( D @ ( C @ ( B @ ( A @ cong ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD75) ).
thf(128,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( H @ ( G @ ( F @ ( E @ cong ) ) ) )
& ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ eqratio ) ) ) ) ) ) ) ) )
=> ( D @ ( C @ ( B @ ( A @ cong ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(91,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
? [E: $i] :
( ( ( B @ ( C @ ( D @ ( C @ ( D @ ( C @ ( C @ ( A @ eqangle ) ) ) ) ) ) ) )
& ( B @ ( C @ ( A @ ( C @ cong ) ) ) ) )
=> ( ( D @ ( C @ ( E @ coll ) ) )
& ( E @ ( A @ ( B @ coll ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleX2) ).
thf(343,plain,
! [A: $i,B: $i,C: $i,D: $i] :
? [E: $i] :
( ( ( B @ ( C @ ( D @ ( C @ ( D @ ( C @ ( C @ ( A @ eqangle ) ) ) ) ) ) ) )
& ( B @ ( C @ ( A @ ( C @ cong ) ) ) ) )
=> ( ( D @ ( C @ ( E @ coll ) ) )
& ( E @ ( A @ ( B @ coll ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(29,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ cong ) ) ) )
=> ( C @ ( D @ ( B @ ( A @ cong ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD23) ).
thf(161,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ cong ) ) ) )
=> ( C @ ( D @ ( B @ ( A @ cong ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(24,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
? [E: $i] :
( ( C @ ( B @ ( A @ ( D @ circle ) ) ) )
=> ( D @ ( A @ ( A @ ( E @ perp ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleX11) ).
thf(149,plain,
! [A: $i,B: $i,C: $i,D: $i] :
? [E: $i] :
( ( C @ ( B @ ( A @ ( D @ circle ) ) ) )
=> ( D @ ( A @ ( A @ ( E @ perp ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(43,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 @ eqratio ) ) ) ) ) ) ) )
=> ( H @ ( G @ ( D @ ( C @ ( F @ ( E @ ( B @ ( A @ eqratio ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD29) ).
thf(191,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 @ eqratio ) ) ) ) ) ) ) )
=> ( H @ ( G @ ( D @ ( C @ ( F @ ( E @ ( B @ ( A @ eqratio ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(75,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( D @ ( C @ coll ) ) )
& ( B @ ( D @ ( A @ ( D @ ( B @ ( C @ ( A @ ( C @ eqangle ) ) ) ) ) ) ) ) )
=> ( D @ ( C @ ( B @ ( A @ cyclic ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD42b) ).
thf(286,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( D @ ( C @ coll ) ) )
& ( B @ ( D @ ( A @ ( D @ ( B @ ( C @ ( A @ ( C @ eqangle ) ) ) ) ) ) ) ) )
=> ( D @ ( C @ ( B @ ( A @ cyclic ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(77,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( F @ ( E @ ( D @ ( C @ perp ) ) ) )
& ( D @ ( C @ ( B @ ( A @ para ) ) ) ) )
=> ( F @ ( E @ ( B @ ( A @ perp ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD10) ).
thf(291,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( F @ ( E @ ( D @ ( C @ perp ) ) ) )
& ( D @ ( C @ ( B @ ( A @ para ) ) ) ) )
=> ( F @ ( E @ ( B @ ( A @ perp ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(9,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ perp ) ) ) )
=> ( C @ ( D @ ( B @ ( A @ perp ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD7) ).
thf(118,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ perp ) ) ) )
=> ( C @ ( D @ ( B @ ( A @ perp ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(60,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( C @ ( B @ ( D @ ( A @ para ) ) ) )
& ( D @ ( B @ ( C @ ( A @ para ) ) ) )
& ( B @ ( A @ ( E @ midp ) ) ) )
=> ( D @ ( C @ ( E @ midp ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD64) ).
thf(236,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( C @ ( B @ ( D @ ( A @ para ) ) ) )
& ( D @ ( B @ ( C @ ( A @ para ) ) ) )
& ( B @ ( A @ ( E @ midp ) ) ) )
=> ( D @ ( C @ ( E @ midp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(38,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ cyclic ) ) ) )
=> ( D @ ( B @ ( C @ ( A @ cyclic ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD15) ).
thf(181,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ cyclic ) ) ) )
=> ( D @ ( B @ ( C @ ( A @ cyclic ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(93,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ para ) ) ) )
=> ( C @ ( D @ ( B @ ( A @ para ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD4) ).
thf(350,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ para ) ) ) )
=> ( C @ ( D @ ( B @ ( A @ para ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(28,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 @ eqratio ) ) ) ) ) ) ) )
=> ( D @ ( C @ ( B @ ( A @ ( H @ ( G @ ( F @ ( E @ eqratio ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD28) ).
thf(159,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 @ eqratio ) ) ) ) ) ) ) )
=> ( D @ ( C @ ( B @ ( A @ ( H @ ( G @ ( F @ ( E @ eqratio ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(41,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( E @ ( D @ ( B @ ( A @ cong ) ) ) )
& ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ simtri ) ) ) ) ) ) )
=> ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ contri ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD61) ).
thf(187,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( E @ ( D @ ( B @ ( A @ cong ) ) ) )
& ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ simtri ) ) ) ) ) ) )
=> ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ contri ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(7,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( B @ ( C @ ( A @ ( C @ ( B @ ( A @ ( E @ ( A @ eqangle ) ) ) ) ) ) ) )
& ( C @ ( B @ ( A @ ( D @ circle ) ) ) ) )
=> ( E @ ( A @ ( A @ ( D @ perp ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD49) ).
thf(113,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( B @ ( C @ ( A @ ( C @ ( B @ ( A @ ( E @ ( A @ eqangle ) ) ) ) ) ) ) )
& ( C @ ( B @ ( A @ ( D @ circle ) ) ) ) )
=> ( E @ ( A @ ( A @ ( D @ perp ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(63,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
? [E: $i,F: $i] :
( ( ( C @ ( A @ ( D @ ( B @ perp ) ) ) )
& ( C @ ( B @ ( D @ ( A @ perp ) ) ) ) )
=> ( ( A @ ( C @ ( F @ ( B @ perp ) ) ) )
& ( A @ ( C @ ( F @ coll ) ) )
& ( B @ ( C @ ( E @ ( A @ perp ) ) ) )
& ( B @ ( C @ ( E @ coll ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleX10) ).
thf(245,plain,
! [A: $i,B: $i,C: $i,D: $i] :
? [E: $i,F: $i] :
( ( ( C @ ( A @ ( D @ ( B @ perp ) ) ) )
& ( C @ ( B @ ( D @ ( A @ perp ) ) ) ) )
=> ( ( A @ ( C @ ( F @ ( B @ perp ) ) ) )
& ( A @ ( C @ ( F @ coll ) ) )
& ( B @ ( C @ ( E @ ( A @ perp ) ) ) )
& ( B @ ( C @ ( E @ coll ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(50,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ cong ) ) ) )
=> ( B @ ( A @ ( D @ ( C @ cong ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD24) ).
thf(208,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ cong ) ) ) )
=> ( B @ ( A @ ( D @ ( C @ cong ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(46,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( A @ ( D @ midp ) ) )
& ( C @ ( B @ ( B @ ( A @ perp ) ) ) ) )
=> ( D @ ( B @ ( D @ ( A @ cong ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD52) ).
thf(198,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( A @ ( D @ midp ) ) )
& ( C @ ( B @ ( B @ ( A @ perp ) ) ) ) )
=> ( D @ ( B @ ( D @ ( A @ cong ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(87,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( A @ ( D @ ( C @ coll ) ) )
& ( B @ ( D @ ( A @ ( D @ ( B @ ( C @ ( A @ ( C @ eqangle ) ) ) ) ) ) ) ) )
=> ( D @ ( C @ ( B @ ( A @ cyclic ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD42a) ).
thf(330,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( A @ ( D @ ( C @ coll ) ) )
& ( B @ ( D @ ( A @ ( D @ ( B @ ( C @ ( A @ ( C @ eqangle ) ) ) ) ) ) ) ) )
=> ( D @ ( C @ ( B @ ( A @ cyclic ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(17,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ simtri ) ) ) ) ) )
=> ( F @ ( D @ ( E @ ( D @ ( C @ ( A @ ( B @ ( A @ eqratio ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD59) ).
thf(135,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ simtri ) ) ) ) ) )
=> ( F @ ( D @ ( E @ ( D @ ( C @ ( A @ ( B @ ( A @ eqratio ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(58,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
? [E: $i] :
( ( ( B @ ( C @ ( A @ ( C @ cong ) ) ) )
& ( B @ ( A @ ( D @ ( C @ perp ) ) ) ) )
=> ( ( D @ ( C @ ( E @ coll ) ) )
& ( E @ ( A @ ( B @ coll ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleX4) ).
thf(226,plain,
! [A: $i,B: $i,C: $i,D: $i] :
? [E: $i] :
( ( ( B @ ( C @ ( A @ ( C @ cong ) ) ) )
& ( B @ ( A @ ( D @ ( C @ perp ) ) ) ) )
=> ( ( D @ ( C @ ( E @ coll ) ) )
& ( E @ ( A @ ( B @ coll ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(69,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( A @ ( D @ coll ) ) )
& ( C @ ( B @ ( A @ ( D @ circle ) ) ) ) )
=> ( C @ ( B @ ( B @ ( A @ perp ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD53) ).
thf(267,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( A @ ( D @ coll ) ) )
& ( C @ ( B @ ( A @ ( D @ circle ) ) ) ) )
=> ( C @ ( B @ ( B @ ( A @ perp ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(32,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 @ eqangle ) ) ) ) ) ) ) )
=> ( F @ ( E @ ( H @ ( G @ ( B @ ( A @ ( D @ ( C @ eqangle ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD19) ).
thf(167,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 @ eqangle ) ) ) ) ) ) ) )
=> ( F @ ( E @ ( H @ ( G @ ( B @ ( A @ ( D @ ( C @ eqangle ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(65,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
? [F: $i] :
( ( ( E @ ( D @ ( B @ coll ) ) )
& ( B @ ( C @ ( C @ ( A @ perp ) ) ) ) )
=> ( ( E @ ( D @ ( A @ ( F @ perp ) ) ) )
& ( E @ ( D @ ( F @ coll ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleX15) ).
thf(255,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
? [F: $i] :
( ( ( E @ ( D @ ( B @ coll ) ) )
& ( B @ ( C @ ( C @ ( A @ perp ) ) ) ) )
=> ( ( E @ ( D @ ( A @ ( F @ perp ) ) ) )
& ( E @ ( D @ ( F @ coll ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(22,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( B @ ( D @ ( A @ cong ) ) ) )
& ( C @ ( B @ ( C @ ( A @ cong ) ) ) ) )
=> ( D @ ( C @ ( B @ ( A @ perp ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD56) ).
thf(145,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( B @ ( D @ ( A @ cong ) ) ) )
& ( C @ ( B @ ( C @ ( A @ cong ) ) ) ) )
=> ( D @ ( C @ ( B @ ( A @ perp ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(79,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
? [H: $i] :
( ( ( F @ ( E @ ( D @ coll ) ) )
& ( E @ ( B @ ( D @ ( A @ para ) ) ) )
& ( G @ ( F @ ( D @ ( A @ para ) ) ) )
& ( B @ ( A @ ( G @ midp ) ) ) )
=> ( ( F @ ( G @ ( H @ coll ) ) )
& ( E @ ( A @ ( H @ coll ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleX8) ).
thf(295,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
? [G: $i] :
( ( ( E @ ( D @ ( C @ coll ) ) )
& ( D @ ( B @ ( C @ ( A @ para ) ) ) )
& ( F @ ( E @ ( C @ ( A @ para ) ) ) )
& ( B @ ( A @ ( F @ midp ) ) ) )
=> ( ( E @ ( F @ ( G @ coll ) ) )
& ( D @ ( A @ ( G @ coll ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(73,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ para ) ) ) )
=> ( B @ ( A @ ( D @ ( C @ para ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD5) ).
thf(282,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ para ) ) ) )
=> ( B @ ( A @ ( D @ ( C @ para ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(67,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ( C @ ( B @ ( A @ coll ) ) )
& ( F @ ( E @ ( F @ ( D @ ( C @ ( B @ ( C @ ( A @ eqangle ) ) ) ) ) ) ) )
& ( F @ ( E @ ( E @ ( D @ ( C @ ( B @ ( B @ ( A @ eqangle ) ) ) ) ) ) ) ) )
=> ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ simtri ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD58) ).
thf(263,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ( C @ ( B @ ( A @ coll ) ) )
& ( F @ ( E @ ( F @ ( D @ ( C @ ( B @ ( C @ ( A @ eqangle ) ) ) ) ) ) ) )
& ( F @ ( E @ ( E @ ( D @ ( C @ ( B @ ( B @ ( A @ eqangle ) ) ) ) ) ) ) ) )
=> ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ simtri ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(26,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( D @ ( E @ ( A @ ( E @ cong ) ) ) )
& ( C @ ( E @ ( A @ ( E @ cong ) ) ) )
& ( B @ ( E @ ( A @ ( E @ cong ) ) ) ) )
=> ( D @ ( C @ ( B @ ( A @ cyclic ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD13) ).
thf(154,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( D @ ( E @ ( A @ ( E @ cong ) ) ) )
& ( C @ ( E @ ( A @ ( E @ cong ) ) ) )
& ( B @ ( E @ ( A @ ( E @ cong ) ) ) ) )
=> ( D @ ( C @ ( B @ ( A @ cyclic ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
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] :
( ( ( H @ ( G @ ( F @ ( E @ ( L @ ( K @ ( J @ ( I @ eqratio ) ) ) ) ) ) ) )
& ( L @ ( K @ ( J @ ( I @ ( D @ ( C @ ( B @ ( A @ eqratio ) ) ) ) ) ) ) ) )
=> ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ eqratio ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD30) ).
thf(175,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] :
( ( ( H @ ( G @ ( F @ ( E @ ( L @ ( K @ ( J @ ( I @ eqratio ) ) ) ) ) ) ) )
& ( L @ ( K @ ( J @ ( I @ ( D @ ( C @ ( B @ ( A @ eqratio ) ) ) ) ) ) ) ) )
=> ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ eqratio ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(21,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 @ eqangle ) ) ) ) ) ) ) )
=> ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( A @ ( B @ eqangle ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD18) ).
thf(143,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 @ eqangle ) ) ) ) ) ) ) )
=> ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( A @ ( B @ eqangle ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(59,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
? [E: $i] :
( ( ( B @ ( C @ ( D @ ( C @ ( D @ ( C @ ( C @ ( A @ eqangle ) ) ) ) ) ) ) )
& ( B @ ( A @ ( D @ ( C @ perp ) ) ) ) )
=> ( ( D @ ( C @ ( E @ coll ) ) )
& ( E @ ( A @ ( B @ coll ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleX3) ).
thf(231,plain,
! [A: $i,B: $i,C: $i,D: $i] :
? [E: $i] :
( ( ( B @ ( C @ ( D @ ( C @ ( D @ ( C @ ( C @ ( A @ eqangle ) ) ) ) ) ) ) )
& ( B @ ( A @ ( D @ ( C @ perp ) ) ) ) )
=> ( ( D @ ( C @ ( E @ coll ) ) )
& ( E @ ( A @ ( B @ coll ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(48,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E @ ( C @ ( B @ ( A @ cyclic ) ) ) )
& ( D @ ( C @ ( B @ ( A @ cyclic ) ) ) ) )
=> ( E @ ( D @ ( C @ ( B @ cyclic ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD17) ).
thf(203,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E @ ( C @ ( B @ ( A @ cyclic ) ) ) )
& ( D @ ( C @ ( B @ ( A @ cyclic ) ) ) ) )
=> ( E @ ( D @ ( C @ ( B @ cyclic ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(55,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( H @ ( G @ ( F @ ( E @ para ) ) ) )
& ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ eqangle ) ) ) ) ) ) ) ) )
=> ( D @ ( C @ ( B @ ( A @ para ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD73) ).
thf(218,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( H @ ( G @ ( F @ ( E @ para ) ) ) )
& ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ eqangle ) ) ) ) ) ) ) ) )
=> ( D @ ( C @ ( B @ ( A @ para ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(85,axiom,
! [A: $i,B: $i,C: $i] :
? [D: $i] :
( ( ( B @ ( C @ ( C @ ( A @ perp ) ) ) )
& ( B @ ( C @ ( A @ ( C @ cong ) ) ) ) )
=> ( ( D @ ( C @ ( A @ ( C @ cong ) ) ) )
& ( D @ ( C @ ( A @ coll ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleX17) ).
thf(319,plain,
! [A: $i,B: $i,C: $i] :
? [D: $i] :
( ( ( B @ ( C @ ( C @ ( A @ perp ) ) ) )
& ( B @ ( C @ ( A @ ( C @ cong ) ) ) ) )
=> ( ( D @ ( C @ ( A @ ( C @ cong ) ) ) )
& ( D @ ( C @ ( A @ coll ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(82,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
? [G: $i,H: $i] :
( ( ( E != F )
& ( B @ ( F @ ( A @ ( F @ cong ) ) ) )
& ( D @ ( E @ ( A @ ( E @ cong ) ) ) )
& ( C @ ( B @ ( A @ ( E @ circle ) ) ) ) )
=> ( ( A @ ( F @ ( F @ ( H @ cong ) ) ) )
& ( D @ ( B @ ( H @ coll ) ) )
& ( A @ ( F @ ( F @ ( G @ cong ) ) ) )
& ( C @ ( A @ ( G @ coll ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleX12) ).
thf(304,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
? [G: $i,H: $i] :
( ( ( E != F )
& ( B @ ( F @ ( A @ ( F @ cong ) ) ) )
& ( D @ ( E @ ( A @ ( E @ cong ) ) ) )
& ( C @ ( B @ ( A @ ( E @ circle ) ) ) ) )
=> ( ( A @ ( F @ ( F @ ( H @ cong ) ) ) )
& ( D @ ( B @ ( H @ coll ) ) )
& ( A @ ( F @ ( F @ ( G @ cong ) ) ) )
& ( C @ ( A @ ( G @ coll ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(34,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( A @ ( C @ cong ) ) ) )
=> ( B @ ( C @ ( B @ ( A @ ( B @ ( A @ ( A @ ( C @ eqangle ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD46) ).
thf(171,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( A @ ( C @ cong ) ) ) )
=> ( B @ ( C @ ( B @ ( A @ ( B @ ( A @ ( A @ ( C @ eqangle ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(19,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ perp ) ) ) )
=> ( B @ ( A @ ( D @ ( C @ perp ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD8) ).
thf(139,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ perp ) ) ) )
=> ( B @ ( A @ ( D @ ( C @ perp ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(80,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ ( B @ ( A @ para ) ) ) )
& ( D @ ( C @ ( B @ ( A @ cyclic ) ) ) ) )
=> ( B @ ( C @ ( D @ ( C @ ( D @ ( C @ ( D @ ( A @ eqangle ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD54) ).
thf(300,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ ( B @ ( A @ para ) ) ) )
& ( D @ ( C @ ( B @ ( A @ cyclic ) ) ) ) )
=> ( B @ ( C @ ( D @ ( C @ ( D @ ( C @ ( D @ ( A @ eqangle ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(83,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( C @ ( A @ ( E @ midp ) ) )
& ( B @ ( A @ ( D @ midp ) ) ) )
=> ( C @ ( B @ ( E @ ( D @ para ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD44) ).
thf(315,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( C @ ( A @ ( E @ midp ) ) )
& ( B @ ( A @ ( D @ midp ) ) ) )
=> ( C @ ( B @ ( E @ ( D @ para ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(39,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ midp ) ) )
=> ( C @ ( A @ ( B @ ( A @ cong ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD68) ).
thf(183,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ midp ) ) )
=> ( C @ ( A @ ( B @ ( A @ cong ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(51,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( F @ ( E @ ( D @ ( C @ cong ) ) ) )
& ( D @ ( C @ ( B @ ( A @ cong ) ) ) ) )
=> ( F @ ( E @ ( B @ ( A @ cong ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD25) ).
thf(210,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( F @ ( E @ ( D @ ( C @ cong ) ) ) )
& ( D @ ( C @ ( B @ ( A @ cong ) ) ) ) )
=> ( F @ ( E @ ( B @ ( A @ cong ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( E @ ( F @ ( D @ ( B @ ( C @ ( A @ contri ) ) ) ) ) )
=> ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ contri ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD35) ).
thf(107,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( E @ ( F @ ( D @ ( B @ ( C @ ( A @ contri ) ) ) ) ) )
=> ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ contri ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(13,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( D @ ( A @ ( D @ cong ) ) ) )
& ( B @ ( D @ ( A @ ( D @ cong ) ) ) ) )
=> ( C @ ( B @ ( A @ ( D @ circle ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD12) ).
thf(126,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( D @ ( A @ ( D @ cong ) ) ) )
& ( B @ ( D @ ( A @ ( D @ cong ) ) ) ) )
=> ( C @ ( B @ ( A @ ( D @ circle ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(88,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
? [F: $i] :
( ( ( E @ ( B @ ( B @ ( A @ perp ) ) ) )
& ( D @ ( E @ ( C @ ( E @ cong ) ) ) ) )
=> ( ( F @ ( B @ ( C @ ( B @ cong ) ) ) )
& ( B @ ( A @ ( C @ ( F @ para ) ) ) )
& ( F @ ( E @ ( C @ ( E @ cong ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleX9) ).
thf(332,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
? [F: $i] :
( ( ( E @ ( B @ ( B @ ( A @ perp ) ) ) )
& ( D @ ( E @ ( C @ ( E @ cong ) ) ) ) )
=> ( ( F @ ( B @ ( C @ ( B @ cong ) ) ) )
& ( B @ ( A @ ( C @ ( F @ para ) ) ) )
& ( F @ ( E @ ( C @ ( E @ cong ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(15,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ cyclic ) ) ) )
=> ( C @ ( D @ ( B @ ( A @ cyclic ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD14) ).
thf(131,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ cyclic ) ) ) )
=> ( C @ ( D @ ( B @ ( A @ cyclic ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(37,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( H @ ( G @ ( F @ ( E @ perp ) ) ) )
& ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ eqangle ) ) ) ) ) ) ) ) )
=> ( D @ ( C @ ( B @ ( A @ perp ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD74) ).
thf(178,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( H @ ( G @ ( F @ ( E @ perp ) ) ) )
& ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ eqangle ) ) ) ) ) ) ) ) )
=> ( D @ ( C @ ( B @ ( A @ perp ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(30,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( C @ ( B @ ( A @ ( F @ ( E @ ( D @ simtri ) ) ) ) ) )
=> ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ simtri ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD33) ).
thf(163,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( C @ ( B @ ( A @ ( F @ ( E @ ( D @ simtri ) ) ) ) ) )
=> ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ simtri ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(47,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( E @ ( F @ ( D @ ( F @ ( B @ ( C @ ( A @ ( C @ eqangle ) ) ) ) ) ) ) )
& ( F @ ( C @ ( B @ ( A @ cyclic ) ) ) )
& ( E @ ( C @ ( B @ ( A @ cyclic ) ) ) )
& ( D @ ( C @ ( B @ ( A @ cyclic ) ) ) ) )
=> ( E @ ( D @ ( B @ ( A @ cong ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD43) ).
thf(200,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( E @ ( F @ ( D @ ( F @ ( B @ ( C @ ( A @ ( C @ eqangle ) ) ) ) ) ) ) )
& ( F @ ( C @ ( B @ ( A @ cyclic ) ) ) )
& ( E @ ( C @ ( B @ ( A @ cyclic ) ) ) )
& ( D @ ( C @ ( B @ ( A @ cyclic ) ) ) ) )
=> ( E @ ( D @ ( B @ ( A @ cong ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(6,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
( ( ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ contri ) ) ) ) ) )
& ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ contri ) ) ) ) ) ) )
=> ( I @ ( H @ ( G @ ( C @ ( B @ ( A @ contri ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD38) ).
thf(111,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
( ( ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ contri ) ) ) ) ) )
& ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ contri ) ) ) ) ) ) )
=> ( I @ ( H @ ( G @ ( C @ ( B @ ( A @ contri ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(11,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 @ eqratio ) ) ) ) ) ) ) )
=> ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( A @ ( B @ eqratio ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD26) ).
thf(122,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 @ eqratio ) ) ) ) ) ) ) )
=> ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( A @ ( B @ eqratio ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(95,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( F @ ( E @ ( D @ ( C @ perp ) ) ) )
& ( D @ ( C @ ( B @ ( A @ perp ) ) ) ) )
=> ( F @ ( E @ ( B @ ( A @ para ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD9) ).
thf(354,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( F @ ( E @ ( D @ ( C @ perp ) ) ) )
& ( D @ ( C @ ( B @ ( A @ perp ) ) ) ) )
=> ( F @ ( E @ ( B @ ( A @ para ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(390,plain,
$false,
inference(e,[status(thm)],[352,340,270,173,338,214,115,120,185,288,196,157,189,284,152,216,238,348,147,280,221,293,133,243,265,302,260,165,275,137,252,97,324,224,317,356,169,141,109,124,193,212,105,205,128,343,161,149,191,286,291,118,236,181,350,159,187,113,245,208,198,330,135,226,267,167,255,145,295,282,263,154,175,143,231,203,218,319,304,171,139,300,315,183,210,107,126,332,131,178,163,200,111,122,354]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GEO657+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.12 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.24/10.50 % Computer : n010.cluster.edu
% 0.24/10.50 % Model : x86_64 x86_64
% 0.24/10.50 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.24/10.50 % Memory : 8046.5625MB
% 0.24/10.50 % OS : Linux 6.8.0-71-generic
% 0.24/10.50 % CPULimit : 300
% 0.24/10.50 % WCLimit : 300
% 0.24/10.50 % DateTime : Fri Sep 25 13:47:39 UTC 2026
% 0.24/10.50 % CPUTime :
% 0.24/10.50 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 1.02/11.06 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.49/11.24 % [INFO] Parsing done (181ms).
% 1.49/11.25 % [INFO] Running in sequential loop mode.
% 1.99/11.45 % [INFO] eprover registered as external prover.
% 1.99/11.45 % [INFO] Scanning for conjecture ...
% 2.27/11.51 % [INFO] Found a conjecture (or negated_conjecture) and 94 axioms. Running axiom selection ...
% 2.27/11.56 % [INFO] Axiom selection finished. Selected 94 axioms (removed 0 axioms).
% 2.57/11.67 % [INFO] Problem is first-order (TPTP FOF).
% 2.57/11.69 % [INFO] Type checking passed.
% 2.57/11.69 % [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 ...
% 8.84/13.33 % External prover 'e' found a proof!
% 8.84/13.33 % [INFO] Killing All external provers ...
% 8.84/13.33 % Time passed: 2679ms (effective reasoning time: 2076ms)
% 8.84/13.33 % 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)>
% 8.84/13.34 % 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
% 8.84/13.34 % No. of inferences in proof: 192
% 8.84/13.34 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2679 ms resp. 2076 ms w/o parsing
% 9.19/13.48 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 9.19/13.48 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------