TSTP Solution File: GEO287+1 by Leo-III---1.7.7
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : GEO287+1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n031.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 11:10:24 EDT 2023
% Result : Theorem 25.50s 7.44s
% Output : Refutation 25.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 190
% Syntax : Number of formulae : 347 ( 10 unt; 35 typ; 0 def)
% Number of atoms : 5683 (2818 equ; 0 cnn)
% Maximal formula atoms : 57 ( 18 avg)
% Number of connectives : 15972 ( 736 ~; 34 |;4911 &;9865 @)
% ( 8 <=>; 418 =>; 0 <=; 0 <~>)
% Maximal formula depth : 47 ( 18 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 78 ( 78 >; 0 *; 0 +; 0 <<)
% Number of symbols : 37 ( 35 usr; 11 con; 0-9 aty)
% Number of variables : 3112 ( 0 ^;1746 !;1366 ?;3112 :)
% Comments :
%------------------------------------------------------------------------------
thf(vf_type,type,
vf: $i > $i > $i ).
thf(vd1157_type,type,
vd1157: $i ).
thf(vd1158_type,type,
vd1158: $i ).
thf(vd1164_type,type,
vd1164: $i ).
thf(vd1165_type,type,
vd1165: $i ).
thf(rintersect_type,type,
rintersect: $i > $i > $o ).
thf(rcircle_type,type,
rcircle: $i > $o ).
thf(ron_type,type,
ron: $i > $i > $o ).
thf(rpoint_type,type,
rpoint: $i > $o ).
thf(rless_type,type,
rless: $i > $i > $o ).
thf(vplus_type,type,
vplus: $i > $i > $i ).
thf(vangle_type,type,
vangle: $i > $i > $i > $i ).
thf(vperp_type,type,
vperp: $i ).
thf(rS_type,type,
rS: $i > $i > $i > $o ).
thf(rline_type,type,
rline: $i > $o ).
thf(rreal_type,type,
rreal: $i > $o ).
thf(vtriangle_type,type,
vtriangle: $i > $i > $i > $i ).
thf(rtriangle_type,type,
rtriangle: $i > $o ).
thf(rR_type,type,
rR: $i > $i > $i > $o ).
thf(vg_type,type,
vg: $i > $i > $i > $i ).
thf(v0_type,type,
v0: $i ).
thf(rcenter_type,type,
rcenter: $i > $i > $o ).
thf(vskolem1052_type,type,
vskolem1052: $i > $i > $i > $i > $i ).
thf(rgeq_type,type,
rgeq: $i > $i > $o ).
thf(rinside_type,type,
rinside: $i > $i > $o ).
thf(vd14_type,type,
vd14: $i ).
thf(vskolem1078_type,type,
vskolem1078: $i > $i > $i > $i > $i ).
thf(vd684_type,type,
vd684: $i ).
thf(rleq_type,type,
rleq: $i > $i > $o ).
thf(vskolem1197_type,type,
vskolem1197: $i > $i > $i > $i > $i > $i > $i ).
thf(vskolem1120_type,type,
vskolem1120: $i > $i > $i > $i > $i > $i > $i > $i > $i ).
thf(vskolem1232_type,type,
vskolem1232: $i > $i > $i > $i > $i > $i > $i > $i > $i > $i ).
thf(vskolem1234_type,type,
vskolem1234: $i > $i > $i > $i > $i > $i > $i > $i > $i > $i ).
thf(vd1163_type,type,
vd1163: $i ).
thf(vd1156_type,type,
vd1156: $i ).
thf(21,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( ron @ B @ D )
& ( rR @ B @ A @ C )
& ( D = E )
& ( rline @ E )
& ? [F: $i] :
( ( C = F )
& ( rpoint @ F ) )
& ? [F: $i] :
( ( B = F )
& ( rpoint @ F ) )
& ? [F: $i] :
( ( A = F )
& ( rpoint @ F ) ) )
=> ~ ( rS @ A @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(109), 0), imp(cond(axiom(109), 0)))') ).
thf(320,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( ron @ B @ D )
& ( rR @ B @ A @ C )
& ( D = E )
& ( rline @ E )
& ? [F: $i] :
( ( C = F )
& ( rpoint @ F ) )
& ? [F: $i] :
( ( B = F )
& ( rpoint @ F ) )
& ? [F: $i] :
( ( A = F )
& ( rpoint @ F ) ) )
=> ~ ( rS @ A @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(14,axiom,
! [A: $i,B: $i] :
( ( ( A != B )
& ? [C: $i] :
( ( B = C )
& ( rpoint @ C ) )
& ? [C: $i] :
( ( A = C )
& ( rpoint @ C ) ) )
=> ? [C: $i] :
( ( ron @ B @ C )
& ( rcenter @ A @ C )
& ( rcircle @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(53), 0), imp(cond(axiom(53), 0)))') ).
thf(270,plain,
! [A: $i,B: $i] :
( ( ( A != B )
& ? [C: $i] :
( ( B = C )
& ( rpoint @ C ) )
& ? [C: $i] :
( ( A = C )
& ( rpoint @ C ) ) )
=> ? [C: $i] :
( ( ron @ B @ C )
& ( rcenter @ A @ C )
& ( rcircle @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(130,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ? [G: $i] :
( ( ron @ F @ G )
& ( ron @ E @ G )
& ( ron @ D @ G )
& ( rline @ G ) )
& ( ( vangle @ B @ A @ C )
= ( vangle @ E @ D @ F ) )
& ( ( vf @ A @ C )
= ( vf @ D @ F ) )
& ( ( vf @ A @ B )
= ( vf @ D @ E ) )
& ? [G: $i] :
( ( F = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( E = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( D = G )
& ( rpoint @ G ) )
& ( B != C )
& ( A != C )
& ( A != B )
& ? [G: $i] :
( ( C = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( B = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( A = G )
& ( rpoint @ G ) ) )
=> ! [G: $i,H: $i,I: $i] :
( ( ( rS @ I @ F @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) )
& ~ ( rR @ E @ G @ D )
& ( ron @ G @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) )
& ( H = E )
& ( ( vf @ A @ C )
= ( vf @ G @ I ) )
& ( ( vf @ B @ C )
= ( vf @ H @ I ) )
& ( ( vf @ A @ B )
= ( vf @ G @ H ) )
& ( ( vangle @ I @ H @ G )
= ( vangle @ C @ B @ A ) )
& ( ( vangle @ G @ I @ H )
= ( vangle @ A @ C @ B ) )
& ( ( vangle @ H @ G @ I )
= ( vangle @ B @ A @ C ) )
& ? [J: $i] :
( ( I = J )
& ( rpoint @ J ) )
& ? [J: $i] :
( ( H = J )
& ( rpoint @ J ) )
& ? [J: $i] :
( ( G = J )
& ( rpoint @ J ) ) )
=> ( ron @ D @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(proof(267), 0), 34)') ).
thf(1322,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ? [G: $i] :
( ( ron @ F @ G )
& ( ron @ E @ G )
& ( ron @ D @ G )
& ( rline @ G ) )
& ( ( vangle @ B @ A @ C )
= ( vangle @ E @ D @ F ) )
& ( ( vf @ A @ C )
= ( vf @ D @ F ) )
& ( ( vf @ A @ B )
= ( vf @ D @ E ) )
& ? [G: $i] :
( ( F = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( E = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( D = G )
& ( rpoint @ G ) )
& ( B != C )
& ( A != C )
& ( A != B )
& ? [G: $i] :
( ( C = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( B = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( A = G )
& ( rpoint @ G ) ) )
=> ! [G: $i,H: $i,I: $i] :
( ( ( rS @ I @ F @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) )
& ~ ( rR @ E @ G @ D )
& ( ron @ G @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) )
& ( H = E )
& ( ( vf @ A @ C )
= ( vf @ G @ I ) )
& ( ( vf @ B @ C )
= ( vf @ H @ I ) )
& ( ( vf @ A @ B )
= ( vf @ G @ H ) )
& ( ( vangle @ I @ H @ G )
= ( vangle @ C @ B @ A ) )
& ( ( vangle @ G @ I @ H )
= ( vangle @ A @ C @ B ) )
& ( ( vangle @ H @ G @ I )
= ( vangle @ B @ A @ C ) )
& ? [J: $i] :
( ( I = J )
& ( rpoint @ J ) )
& ? [J: $i] :
( ( H = J )
& ( rpoint @ J ) )
& ? [J: $i] :
( ( G = J )
& ( rpoint @ J ) ) )
=> ( ron @ D @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(146,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ? [G: $i] :
( ( ron @ F @ G )
& ( ron @ E @ G )
& ( ron @ D @ G )
& ( rline @ G ) )
& ( ( vangle @ B @ A @ C )
= ( vangle @ E @ D @ F ) )
& ( ( vf @ A @ C )
= ( vf @ D @ F ) )
& ( ( vf @ A @ B )
= ( vf @ D @ E ) )
& ? [G: $i] :
( ( F = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( E = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( D = G )
& ( rpoint @ G ) )
& ( B != C )
& ( A != C )
& ( A != B )
& ? [G: $i] :
( ( C = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( B = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( A = G )
& ( rpoint @ G ) ) )
=> ! [G: $i,H: $i,I: $i] :
( ( ( rS @ I @ F @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) )
& ~ ( rR @ E @ G @ D )
& ( ron @ G @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) )
& ( H = E )
& ( ( vf @ A @ C )
= ( vf @ G @ I ) )
& ( ( vf @ B @ C )
= ( vf @ H @ I ) )
& ( ( vf @ A @ B )
= ( vf @ G @ H ) )
& ( ( vangle @ I @ H @ G )
= ( vangle @ C @ B @ A ) )
& ( ( vangle @ G @ I @ H )
= ( vangle @ A @ C @ B ) )
& ( ( vangle @ H @ G @ I )
= ( vangle @ B @ A @ C ) )
& ? [J: $i] :
( ( I = J )
& ( rpoint @ J ) )
& ? [J: $i] :
( ( H = J )
& ( rpoint @ J ) )
& ? [J: $i] :
( ( G = J )
& ( rpoint @ J ) ) )
=> ( ~ ( ron @ I @ ( vskolem1232 @ G @ H @ I @ A @ B @ C @ D @ E @ F ) )
=> ~ ( rS @ E @ I @ ( vskolem1232 @ G @ H @ I @ A @ B @ C @ D @ E @ F ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(proof(267), 0), 20)') ).
thf(1501,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ? [G: $i] :
( ( ron @ F @ G )
& ( ron @ E @ G )
& ( ron @ D @ G )
& ( rline @ G ) )
& ( ( vangle @ B @ A @ C )
= ( vangle @ E @ D @ F ) )
& ( ( vf @ A @ C )
= ( vf @ D @ F ) )
& ( ( vf @ A @ B )
= ( vf @ D @ E ) )
& ? [G: $i] :
( ( F = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( E = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( D = G )
& ( rpoint @ G ) )
& ( B != C )
& ( A != C )
& ( A != B )
& ? [G: $i] :
( ( C = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( B = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( A = G )
& ( rpoint @ G ) ) )
=> ! [G: $i,H: $i,I: $i] :
( ( ( rS @ I @ F @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) )
& ~ ( rR @ E @ G @ D )
& ( ron @ G @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) )
& ( H = E )
& ( ( vf @ A @ C )
= ( vf @ G @ I ) )
& ( ( vf @ B @ C )
= ( vf @ H @ I ) )
& ( ( vf @ A @ B )
= ( vf @ G @ H ) )
& ( ( vangle @ I @ H @ G )
= ( vangle @ C @ B @ A ) )
& ( ( vangle @ G @ I @ H )
= ( vangle @ A @ C @ B ) )
& ( ( vangle @ H @ G @ I )
= ( vangle @ B @ A @ C ) )
& ? [J: $i] :
( ( I = J )
& ( rpoint @ J ) )
& ? [J: $i] :
( ( H = J )
& ( rpoint @ J ) )
& ? [J: $i] :
( ( G = J )
& ( rpoint @ J ) ) )
=> ( ~ ( ron @ I @ ( vskolem1232 @ G @ H @ I @ A @ B @ C @ D @ E @ F ) )
=> ~ ( rS @ E @ I @ ( vskolem1232 @ G @ H @ I @ A @ B @ C @ D @ E @ F ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(118,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ? [G: $i] :
( ( ron @ F @ G )
& ( ron @ E @ G )
& ( ron @ D @ G )
& ( rline @ G ) )
& ( ( vangle @ B @ A @ C )
= ( vangle @ E @ D @ F ) )
& ( ( vf @ A @ C )
= ( vf @ D @ F ) )
& ( ( vf @ A @ B )
= ( vf @ D @ E ) )
& ? [G: $i] :
( ( F = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( E = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( D = G )
& ( rpoint @ G ) )
& ( B != C )
& ( A != C )
& ( A != B )
& ? [G: $i] :
( ( C = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( B = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( A = G )
& ( rpoint @ G ) ) )
=> ! [G: $i,H: $i,I: $i] :
( ( ( rS @ I @ F @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) )
& ~ ( rR @ E @ G @ D )
& ( ron @ G @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) )
& ( H = E )
& ( ( vf @ A @ C )
= ( vf @ G @ I ) )
& ( ( vf @ B @ C )
= ( vf @ H @ I ) )
& ( ( vf @ A @ B )
= ( vf @ G @ H ) )
& ( ( vangle @ I @ H @ G )
= ( vangle @ C @ B @ A ) )
& ( ( vangle @ G @ I @ H )
= ( vangle @ A @ C @ B ) )
& ( ( vangle @ H @ G @ I )
= ( vangle @ B @ A @ C ) )
& ? [J: $i] :
( ( I = J )
& ( rpoint @ J ) )
& ? [J: $i] :
( ( H = J )
& ( rpoint @ J ) )
& ? [J: $i] :
( ( G = J )
& ( rpoint @ J ) ) )
=> ( rS @ F @ I @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(proof(267), 0), 21)') ).
thf(1190,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ? [G: $i] :
( ( ron @ F @ G )
& ( ron @ E @ G )
& ( ron @ D @ G )
& ( rline @ G ) )
& ( ( vangle @ B @ A @ C )
= ( vangle @ E @ D @ F ) )
& ( ( vf @ A @ C )
= ( vf @ D @ F ) )
& ( ( vf @ A @ B )
= ( vf @ D @ E ) )
& ? [G: $i] :
( ( F = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( E = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( D = G )
& ( rpoint @ G ) )
& ( B != C )
& ( A != C )
& ( A != B )
& ? [G: $i] :
( ( C = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( B = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( A = G )
& ( rpoint @ G ) ) )
=> ! [G: $i,H: $i,I: $i] :
( ( ( rS @ I @ F @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) )
& ~ ( rR @ E @ G @ D )
& ( ron @ G @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) )
& ( H = E )
& ( ( vf @ A @ C )
= ( vf @ G @ I ) )
& ( ( vf @ B @ C )
= ( vf @ H @ I ) )
& ( ( vf @ A @ B )
= ( vf @ G @ H ) )
& ( ( vangle @ I @ H @ G )
= ( vangle @ C @ B @ A ) )
& ( ( vangle @ G @ I @ H )
= ( vangle @ A @ C @ B ) )
& ( ( vangle @ H @ G @ I )
= ( vangle @ B @ A @ C ) )
& ? [J: $i] :
( ( I = J )
& ( rpoint @ J ) )
& ? [J: $i] :
( ( H = J )
& ( rpoint @ J ) )
& ? [J: $i] :
( ( G = J )
& ( rpoint @ J ) ) )
=> ( rS @ F @ I @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(96,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( rR @ B @ A @ C )
& ? [D: $i] :
( ( C = D )
& ( rpoint @ D ) )
& ? [D: $i] :
( ( B = D )
& ( rpoint @ D ) )
& ? [D: $i] :
( ( A = D )
& ( rpoint @ D ) ) )
=> ( ~ ( rR @ A @ B @ C )
& ( A != C )
& ( A != B )
& ( rR @ B @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(81), 0), imp(cond(axiom(81), 0)))') ).
thf(909,plain,
! [A: $i,B: $i,C: $i] :
( ( ( rR @ B @ A @ C )
& ? [D: $i] :
( ( C = D )
& ( rpoint @ D ) )
& ? [D: $i] :
( ( B = D )
& ( rpoint @ D ) )
& ? [D: $i] :
( ( A = D )
& ( rpoint @ D ) ) )
=> ( ~ ( rR @ A @ B @ C )
& ( A != C )
& ( A != B )
& ( rR @ B @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(77,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( ron @ C @ G )
& ( ron @ A @ G )
& ( A != E )
& ( A != C )
& ( G = H )
& ( rline @ H )
& ( E = F )
& ( rpoint @ F )
& ( C = D )
& ( rpoint @ D )
& ( A = B )
& ( rpoint @ B ) )
=> ( ( ~ ( rR @ A @ C @ E )
& ( ron @ E @ G ) )
<=> ( ( vangle @ C @ A @ E )
= v0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(188), 0), imp(cond(axiom(188), 0)))') ).
thf(777,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( ron @ C @ G )
& ( ron @ A @ G )
& ( A != E )
& ( A != C )
& ( G = H )
& ( rline @ H )
& ( E = F )
& ( rpoint @ F )
& ( C = D )
& ( rpoint @ D )
& ( A = B )
& ( rpoint @ B ) )
=> ( ( ( ~ ( rR @ A @ C @ E )
& ( ron @ E @ G ) )
=> ( ( vangle @ C @ A @ E )
= v0 ) )
& ( ( ( vangle @ C @ A @ E )
= v0 )
=> ( ~ ( rR @ A @ C @ E )
& ( ron @ E @ G ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(112,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ? [G: $i] :
( ( ron @ F @ G )
& ( ron @ E @ G )
& ( ron @ D @ G )
& ( rline @ G ) )
& ( ( vangle @ B @ A @ C )
= ( vangle @ E @ D @ F ) )
& ( ( vf @ A @ C )
= ( vf @ D @ F ) )
& ( ( vf @ A @ B )
= ( vf @ D @ E ) )
& ? [G: $i] :
( ( F = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( E = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( D = G )
& ( rpoint @ G ) )
& ( B != C )
& ( A != C )
& ( A != B )
& ? [G: $i] :
( ( C = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( B = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( A = G )
& ( rpoint @ G ) ) )
=> ( ron @ E @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(proof(267), 0), 40)') ).
thf(1110,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ? [G: $i] :
( ( ron @ F @ G )
& ( ron @ E @ G )
& ( ron @ D @ G )
& ( rline @ G ) )
& ( ( vangle @ B @ A @ C )
= ( vangle @ E @ D @ F ) )
& ( ( vf @ A @ C )
= ( vf @ D @ F ) )
& ( ( vf @ A @ B )
= ( vf @ D @ E ) )
& ? [G: $i] :
( ( F = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( E = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( D = G )
& ( rpoint @ G ) )
& ( B != C )
& ( A != C )
& ( A != B )
& ? [G: $i] :
( ( C = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( B = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( A = G )
& ( rpoint @ G ) ) )
=> ( ron @ E @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(64,axiom,
! [A: $i,B: $i] :
( ( ( A = B )
& ( rcircle @ B ) )
=> ? [C: $i] :
( ~ ( ron @ C @ A )
& ~ ( rinside @ C @ A )
& ( rpoint @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(49), 0), imp(cond(axiom(49), 0)))') ).
thf(666,plain,
! [A: $i,B: $i] :
( ( ( A = B )
& ( rcircle @ B ) )
=> ? [C: $i] :
( ~ ( ron @ C @ A )
& ~ ( rinside @ C @ A )
& ( rpoint @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(128,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ? [G: $i] :
( ( ron @ F @ G )
& ( ron @ E @ G )
& ( ron @ D @ G )
& ( rline @ G ) )
& ( ( vangle @ B @ A @ C )
= ( vangle @ E @ D @ F ) )
& ( ( vf @ A @ C )
= ( vf @ D @ F ) )
& ( ( vf @ A @ B )
= ( vf @ D @ E ) )
& ? [G: $i] :
( ( F = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( E = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( D = G )
& ( rpoint @ G ) )
& ( B != C )
& ( A != C )
& ( A != B )
& ? [G: $i] :
( ( C = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( B = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( A = G )
& ( rpoint @ G ) ) )
=> ! [G: $i,H: $i,I: $i] :
( ( ( rS @ I @ F @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) )
& ~ ( rR @ E @ G @ D )
& ( ron @ G @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) )
& ( H = E )
& ( ( vf @ A @ C )
= ( vf @ G @ I ) )
& ( ( vf @ B @ C )
= ( vf @ H @ I ) )
& ( ( vf @ A @ B )
= ( vf @ G @ H ) )
& ( ( vangle @ I @ H @ G )
= ( vangle @ C @ B @ A ) )
& ( ( vangle @ G @ I @ H )
= ( vangle @ A @ C @ B ) )
& ( ( vangle @ H @ G @ I )
= ( vangle @ B @ A @ C ) )
& ? [J: $i] :
( ( I = J )
& ( rpoint @ J ) )
& ? [J: $i] :
( ( H = J )
& ( rpoint @ J ) )
& ? [J: $i] :
( ( G = J )
& ( rpoint @ J ) ) )
=> ( ron @ G @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(proof(267), 0), 38)') ).
thf(1295,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ? [G: $i] :
( ( ron @ F @ G )
& ( ron @ E @ G )
& ( ron @ D @ G )
& ( rline @ G ) )
& ( ( vangle @ B @ A @ C )
= ( vangle @ E @ D @ F ) )
& ( ( vf @ A @ C )
= ( vf @ D @ F ) )
& ( ( vf @ A @ B )
= ( vf @ D @ E ) )
& ? [G: $i] :
( ( F = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( E = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( D = G )
& ( rpoint @ G ) )
& ( B != C )
& ( A != C )
& ( A != B )
& ? [G: $i] :
( ( C = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( B = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( A = G )
& ( rpoint @ G ) ) )
=> ! [G: $i,H: $i,I: $i] :
( ( ( rS @ I @ F @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) )
& ~ ( rR @ E @ G @ D )
& ( ron @ G @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) )
& ( H = E )
& ( ( vf @ A @ C )
= ( vf @ G @ I ) )
& ( ( vf @ B @ C )
= ( vf @ H @ I ) )
& ( ( vf @ A @ B )
= ( vf @ G @ H ) )
& ( ( vangle @ I @ H @ G )
= ( vangle @ C @ B @ A ) )
& ( ( vangle @ G @ I @ H )
= ( vangle @ A @ C @ B ) )
& ( ( vangle @ H @ G @ I )
= ( vangle @ B @ A @ C ) )
& ? [J: $i] :
( ( I = J )
& ( rpoint @ J ) )
& ? [J: $i] :
( ( H = J )
& ( rpoint @ J ) )
& ? [J: $i] :
( ( G = J )
& ( rpoint @ J ) ) )
=> ( ron @ G @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( ( rintersect @ A @ B )
& ? [C: $i] :
( ( B = C )
& ( rcircle @ C ) )
& ? [C: $i] :
( ( A = C )
& ( rcircle @ C ) ) )
=> ? [C: $i,D: $i] :
( ( C != D )
& ( ron @ D @ B )
& ( ron @ D @ A )
& ( rpoint @ D )
& ( ron @ C @ B )
& ( ron @ C @ A )
& ( rpoint @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(67), 0), imp(cond(axiom(67), 0)))') ).
thf(170,plain,
! [A: $i,B: $i] :
( ( ( rintersect @ A @ B )
& ? [C: $i] :
( ( B = C )
& ( rcircle @ C ) )
& ? [C: $i] :
( ( A = C )
& ( rcircle @ C ) ) )
=> ? [C: $i,D: $i] :
( ( C != D )
& ( ron @ D @ B )
& ( ron @ D @ A )
& ( rpoint @ D )
& ( ron @ C @ B )
& ( ron @ C @ A )
& ( rpoint @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(74,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( rR @ B @ A @ D )
& ( rR @ B @ A @ C )
& ? [E: $i] :
( ( D = E )
& ( rpoint @ E ) )
& ? [E: $i] :
( ( C = E )
& ( rpoint @ E ) )
& ? [E: $i] :
( ( B = E )
& ( rpoint @ E ) )
& ? [E: $i] :
( ( A = E )
& ( rpoint @ E ) ) )
=> ~ ( rR @ B @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(93), 0), imp(cond(axiom(93), 0)))') ).
thf(762,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( rR @ B @ A @ D )
& ( rR @ B @ A @ C )
& ? [E: $i] :
( ( D = E )
& ( rpoint @ E ) )
& ? [E: $i] :
( ( C = E )
& ( rpoint @ E ) )
& ? [E: $i] :
( ( B = E )
& ( rpoint @ E ) )
& ? [E: $i] :
( ( A = E )
& ( rpoint @ E ) ) )
=> ~ ( rR @ B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(150,axiom,
! [A: $i,B: $i] :
( ( ? [C: $i] :
( ( B = C )
& ( rpoint @ C ) )
& ? [C: $i] :
( ( A = C )
& ( rpoint @ C ) ) )
=> ( ( ( vf @ A @ B )
= v0 )
<=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(162), 0), imp(cond(axiom(162), 0)))') ).
thf(1544,plain,
! [A: $i,B: $i] :
( ( ? [C: $i] :
( ( B = C )
& ( rpoint @ C ) )
& ? [C: $i] :
( ( A = C )
& ( rpoint @ C ) ) )
=> ( ( ( ( vf @ A @ B )
= v0 )
=> ( A = B ) )
& ( ( A = B )
=> ( ( vf @ A @ B )
= v0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( ? [C: $i] :
( ( B = C )
& ( rpoint @ C ) )
& ? [C: $i] :
( ( A = C )
& ( rpoint @ C ) ) )
=> ( ( vg @ A @ A @ B )
= v0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(172), 0), imp(cond(axiom(172), 0)))') ).
thf(247,plain,
! [A: $i,B: $i] :
( ( ? [C: $i] :
( ( B = C )
& ( rpoint @ C ) )
& ? [C: $i] :
( ( A = C )
& ( rpoint @ C ) ) )
=> ( ( vg @ A @ A @ B )
= v0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(51,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( rS @ A @ C @ D )
& ( rR @ B @ A @ C )
& ( D = E )
& ( rline @ E )
& ? [F: $i] :
( ( C = F )
& ( rpoint @ F ) )
& ? [F: $i] :
( ( B = F )
& ( rpoint @ F ) )
& ? [F: $i] :
( ( A = F )
& ( rpoint @ F ) ) )
=> ( rS @ A @ B @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(105), 0), imp(cond(axiom(105), 0)))') ).
thf(597,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( rS @ A @ C @ D )
& ( rR @ B @ A @ C )
& ( D = E )
& ( rline @ E )
& ? [F: $i] :
( ( C = F )
& ( rpoint @ F ) )
& ? [F: $i] :
( ( B = F )
& ( rpoint @ F ) )
& ? [F: $i] :
( ( A = F )
& ( rpoint @ F ) ) )
=> ( rS @ A @ B @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(54,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( B != C )
& ( ron @ C @ F )
& ( ron @ B @ F )
& ( rinside @ A @ F )
& ( ron @ C @ D )
& ( ron @ B @ D )
& ( ron @ A @ D )
& ( F = G )
& ( rcircle @ G )
& ( D = E )
& ( rline @ E )
& ? [H: $i] :
( ( C = H )
& ( rpoint @ H ) )
& ? [H: $i] :
( ( B = H )
& ( rpoint @ H ) )
& ? [H: $i] :
( ( A = H )
& ( rpoint @ H ) ) )
=> ( rR @ A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(119), 0), imp(cond(axiom(119), 0)))') ).
thf(614,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( B != C )
& ( ron @ C @ F )
& ( ron @ B @ F )
& ( rinside @ A @ F )
& ( ron @ C @ D )
& ( ron @ B @ D )
& ( ron @ A @ D )
& ( F = G )
& ( rcircle @ G )
& ( D = E )
& ( rline @ E )
& ? [H: $i] :
( ( C = H )
& ( rpoint @ H ) )
& ? [H: $i] :
( ( B = H )
& ( rpoint @ H ) )
& ? [H: $i] :
( ( A = H )
& ( rpoint @ H ) ) )
=> ( rR @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(65,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C = D )
& ( rreal @ D )
& ( A = B )
& ( rreal @ B ) )
=> ? [E: $i] :
( ( ( vplus @ A @ C )
= E )
& ( rreal @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(139), 0), imp(cond(axiom(139), 0)))') ).
thf(677,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C = D )
& ( rreal @ D )
& ( A = B )
& ( rreal @ B ) )
=> ? [E: $i] :
( ( ( vplus @ A @ C )
= E )
& ( rreal @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(108,axiom,
! [A: $i,B: $i] :
( ( ( A != B )
& ? [C: $i] :
( ( B = C )
& ( rpoint @ C ) )
& ? [C: $i] :
( ( A = C )
& ( rpoint @ C ) ) )
=> ! [C: $i,D: $i] :
( ( ( C = D )
& ( C != B )
& ( C != A )
& ( rpoint @ D ) )
=> ( ( vf @ A @ B )
= ( vf @ C @ ( vskolem1078 @ C @ D @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(219), 0), 0)') ).
thf(1078,plain,
! [A: $i,B: $i] :
( ( ( A != B )
& ? [C: $i] :
( ( B = C )
& ( rpoint @ C ) )
& ? [C: $i] :
( ( A = C )
& ( rpoint @ C ) ) )
=> ! [C: $i,D: $i] :
( ( ( C = D )
& ( C != B )
& ( C != A )
& ( rpoint @ D ) )
=> ( ( vf @ A @ B )
= ( vf @ C @ ( vskolem1078 @ C @ D @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(116,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ? [G: $i] :
( ( ron @ F @ G )
& ( ron @ E @ G )
& ( ron @ D @ G )
& ( rline @ G ) )
& ( ( vangle @ B @ A @ C )
= ( vangle @ E @ D @ F ) )
& ( ( vf @ A @ C )
= ( vf @ D @ F ) )
& ( ( vf @ A @ B )
= ( vf @ D @ E ) )
& ? [G: $i] :
( ( F = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( E = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( D = G )
& ( rpoint @ G ) )
& ( B != C )
& ( A != C )
& ( A != B )
& ? [G: $i] :
( ( C = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( B = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( A = G )
& ( rpoint @ G ) ) )
=> ! [G: $i,H: $i,I: $i] :
( ( ( rS @ I @ F @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) )
& ~ ( rR @ E @ G @ D )
& ( ron @ G @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) )
& ( H = E )
& ( ( vf @ A @ C )
= ( vf @ G @ I ) )
& ( ( vf @ B @ C )
= ( vf @ H @ I ) )
& ( ( vf @ A @ B )
= ( vf @ G @ H ) )
& ( ( vangle @ I @ H @ G )
= ( vangle @ C @ B @ A ) )
& ( ( vangle @ G @ I @ H )
= ( vangle @ A @ C @ B ) )
& ( ( vangle @ H @ G @ I )
= ( vangle @ B @ A @ C ) )
& ? [J: $i] :
( ( I = J )
& ( rpoint @ J ) )
& ? [J: $i] :
( ( H = J )
& ( rpoint @ J ) )
& ? [J: $i] :
( ( G = J )
& ( rpoint @ J ) ) )
=> ( ( vf @ G @ I )
= ( vf @ D @ F ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(proof(267), 0), 16)') ).
thf(1164,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ? [G: $i] :
( ( ron @ F @ G )
& ( ron @ E @ G )
& ( ron @ D @ G )
& ( rline @ G ) )
& ( ( vangle @ B @ A @ C )
= ( vangle @ E @ D @ F ) )
& ( ( vf @ A @ C )
= ( vf @ D @ F ) )
& ( ( vf @ A @ B )
= ( vf @ D @ E ) )
& ? [G: $i] :
( ( F = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( E = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( D = G )
& ( rpoint @ G ) )
& ( B != C )
& ( A != C )
& ( A != B )
& ? [G: $i] :
( ( C = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( B = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( A = G )
& ( rpoint @ G ) ) )
=> ! [G: $i,H: $i,I: $i] :
( ( ( rS @ I @ F @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) )
& ~ ( rR @ E @ G @ D )
& ( ron @ G @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) )
& ( H = E )
& ( ( vf @ A @ C )
= ( vf @ G @ I ) )
& ( ( vf @ B @ C )
= ( vf @ H @ I ) )
& ( ( vf @ A @ B )
= ( vf @ G @ H ) )
& ( ( vangle @ I @ H @ G )
= ( vangle @ C @ B @ A ) )
& ( ( vangle @ G @ I @ H )
= ( vangle @ A @ C @ B ) )
& ( ( vangle @ H @ G @ I )
= ( vangle @ B @ A @ C ) )
& ? [J: $i] :
( ( I = J )
& ( rpoint @ J ) )
& ? [J: $i] :
( ( H = J )
& ( rpoint @ J ) )
& ? [J: $i] :
( ( G = J )
& ( rpoint @ J ) ) )
=> ( ( vf @ G @ I )
= ( vf @ D @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(122,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ? [G: $i] :
( ( ron @ F @ G )
& ( ron @ E @ G )
& ( ron @ D @ G )
& ( rline @ G ) )
& ( ( vangle @ B @ A @ C )
= ( vangle @ E @ D @ F ) )
& ( ( vf @ A @ C )
= ( vf @ D @ F ) )
& ( ( vf @ A @ B )
= ( vf @ D @ E ) )
& ? [G: $i] :
( ( F = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( E = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( D = G )
& ( rpoint @ G ) )
& ( B != C )
& ( A != C )
& ( A != B )
& ? [G: $i] :
( ( C = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( B = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( A = G )
& ( rpoint @ G ) ) )
=> ! [G: $i,H: $i,I: $i] :
( ( ( rS @ I @ F @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) )
& ~ ( rR @ E @ G @ D )
& ( ron @ G @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) )
& ( H = E )
& ( ( vf @ A @ C )
= ( vf @ G @ I ) )
& ( ( vf @ B @ C )
= ( vf @ H @ I ) )
& ( ( vf @ A @ B )
= ( vf @ G @ H ) )
& ( ( vangle @ I @ H @ G )
= ( vangle @ C @ B @ A ) )
& ( ( vangle @ G @ I @ H )
= ( vangle @ A @ C @ B ) )
& ( ( vangle @ H @ G @ I )
= ( vangle @ B @ A @ C ) )
& ? [J: $i] :
( ( I = J )
& ( rpoint @ J ) )
& ? [J: $i] :
( ( H = J )
& ( rpoint @ J ) )
& ? [J: $i] :
( ( G = J )
& ( rpoint @ J ) ) )
=> ( rline @ ( vskolem1234 @ G @ H @ I @ A @ B @ C @ D @ E @ F ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(proof(267), 0), 24)') ).
thf(1233,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ? [G: $i] :
( ( ron @ F @ G )
& ( ron @ E @ G )
& ( ron @ D @ G )
& ( rline @ G ) )
& ( ( vangle @ B @ A @ C )
= ( vangle @ E @ D @ F ) )
& ( ( vf @ A @ C )
= ( vf @ D @ F ) )
& ( ( vf @ A @ B )
= ( vf @ D @ E ) )
& ? [G: $i] :
( ( F = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( E = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( D = G )
& ( rpoint @ G ) )
& ( B != C )
& ( A != C )
& ( A != B )
& ? [G: $i] :
( ( C = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( B = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( A = G )
& ( rpoint @ G ) ) )
=> ! [G: $i,H: $i,I: $i] :
( ( ( rS @ I @ F @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) )
& ~ ( rR @ E @ G @ D )
& ( ron @ G @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) )
& ( H = E )
& ( ( vf @ A @ C )
= ( vf @ G @ I ) )
& ( ( vf @ B @ C )
= ( vf @ H @ I ) )
& ( ( vf @ A @ B )
= ( vf @ G @ H ) )
& ( ( vangle @ I @ H @ G )
= ( vangle @ C @ B @ A ) )
& ( ( vangle @ G @ I @ H )
= ( vangle @ A @ C @ B ) )
& ( ( vangle @ H @ G @ I )
= ( vangle @ B @ A @ C ) )
& ? [J: $i] :
( ( I = J )
& ( rpoint @ J ) )
& ? [J: $i] :
( ( H = J )
& ( rpoint @ J ) )
& ? [J: $i] :
( ( G = J )
& ( rpoint @ J ) ) )
=> ( rline @ ( vskolem1234 @ G @ H @ I @ A @ B @ C @ D @ E @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(124,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( ( vangle @ C @ A @ B )
= ( vangle @ F @ D @ E ) )
& ( ( vangle @ B @ C @ A )
= ( vangle @ E @ F @ D ) )
& ( ( vangle @ A @ B @ C )
= ( vangle @ D @ E @ F ) )
& ( ( vf @ C @ A )
= ( vf @ F @ D ) )
& ( ( vf @ B @ C )
= ( vf @ E @ F ) )
& ( ( vf @ A @ B )
= ( vf @ D @ E ) )
& ? [G: $i] :
( ( F = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( E = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( D = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( C = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( B = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( A = G )
& ( rpoint @ G ) ) )
=> ( ( vg @ A @ B @ C )
= ( vg @ D @ E @ F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(178), 0), imp(cond(axiom(178), 0)))') ).
thf(1260,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( ( vangle @ C @ A @ B )
= ( vangle @ F @ D @ E ) )
& ( ( vangle @ B @ C @ A )
= ( vangle @ E @ F @ D ) )
& ( ( vangle @ A @ B @ C )
= ( vangle @ D @ E @ F ) )
& ( ( vf @ C @ A )
= ( vf @ F @ D ) )
& ( ( vf @ B @ C )
= ( vf @ E @ F ) )
& ( ( vf @ A @ B )
= ( vf @ D @ E ) )
& ? [G: $i] :
( ( F = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( E = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( D = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( C = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( B = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( A = G )
& ( rpoint @ G ) ) )
=> ( ( vg @ A @ B @ C )
= ( vg @ D @ E @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(72,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ron @ B @ D )
& ( rinside @ A @ D )
& ( rinside @ B @ C )
& ( ron @ A @ C )
& ? [E: $i] :
( ( B = E )
& ( rpoint @ E ) )
& ? [E: $i] :
( ( A = E )
& ( rpoint @ E ) ) )
=> ( rintersect @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(135), 0), imp(cond(axiom(135), 0)))') ).
thf(747,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ron @ B @ D )
& ( rinside @ A @ D )
& ( rinside @ B @ C )
& ( ron @ A @ C )
& ? [E: $i] :
( ( B = E )
& ( rpoint @ E ) )
& ? [E: $i] :
( ( A = E )
& ( rpoint @ E ) ) )
=> ( rintersect @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(125,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ? [G: $i] :
( ( ron @ F @ G )
& ( ron @ E @ G )
& ( ron @ D @ G )
& ( rline @ G ) )
& ( ( vangle @ B @ A @ C )
= ( vangle @ E @ D @ F ) )
& ( ( vf @ A @ C )
= ( vf @ D @ F ) )
& ( ( vf @ A @ B )
= ( vf @ D @ E ) )
& ? [G: $i] :
( ( F = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( E = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( D = G )
& ( rpoint @ G ) )
& ( B != C )
& ( A != C )
& ( A != B )
& ? [G: $i] :
( ( C = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( B = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( A = G )
& ( rpoint @ G ) ) )
=> ! [G: $i,H: $i,I: $i] :
( ( ( rS @ I @ F @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) )
& ~ ( rR @ E @ G @ D )
& ( ron @ G @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) )
& ( H = E )
& ( ( vf @ A @ C )
= ( vf @ G @ I ) )
& ( ( vf @ B @ C )
= ( vf @ H @ I ) )
& ( ( vf @ A @ B )
= ( vf @ G @ H ) )
& ( ( vangle @ I @ H @ G )
= ( vangle @ C @ B @ A ) )
& ( ( vangle @ G @ I @ H )
= ( vangle @ A @ C @ B ) )
& ( ( vangle @ H @ G @ I )
= ( vangle @ B @ A @ C ) )
& ? [J: $i] :
( ( I = J )
& ( rpoint @ J ) )
& ? [J: $i] :
( ( H = J )
& ( rpoint @ J ) )
& ? [J: $i] :
( ( G = J )
& ( rpoint @ J ) ) )
=> ( G = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(proof(267), 0), 29)') ).
thf(1264,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ? [G: $i] :
( ( ron @ F @ G )
& ( ron @ E @ G )
& ( ron @ D @ G )
& ( rline @ G ) )
& ( ( vangle @ B @ A @ C )
= ( vangle @ E @ D @ F ) )
& ( ( vf @ A @ C )
= ( vf @ D @ F ) )
& ( ( vf @ A @ B )
= ( vf @ D @ E ) )
& ? [G: $i] :
( ( F = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( E = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( D = G )
& ( rpoint @ G ) )
& ( B != C )
& ( A != C )
& ( A != B )
& ? [G: $i] :
( ( C = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( B = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( A = G )
& ( rpoint @ G ) ) )
=> ! [G: $i,H: $i,I: $i] :
( ( ( rS @ I @ F @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) )
& ~ ( rR @ E @ G @ D )
& ( ron @ G @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) )
& ( H = E )
& ( ( vf @ A @ C )
= ( vf @ G @ I ) )
& ( ( vf @ B @ C )
= ( vf @ H @ I ) )
& ( ( vf @ A @ B )
= ( vf @ G @ H ) )
& ( ( vangle @ I @ H @ G )
= ( vangle @ C @ B @ A ) )
& ( ( vangle @ G @ I @ H )
= ( vangle @ A @ C @ B ) )
& ( ( vangle @ H @ G @ I )
= ( vangle @ B @ A @ C ) )
& ? [J: $i] :
( ( I = J )
& ( rpoint @ J ) )
& ? [J: $i] :
( ( H = J )
& ( rpoint @ J ) )
& ? [J: $i] :
( ( G = J )
& ( rpoint @ J ) ) )
=> ( G = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(55,axiom,
! [A: $i,B: $i] :
( ( ( A = B )
& ( rcircle @ B ) )
=> ? [C: $i] :
( ( ron @ C @ A )
& ( rpoint @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(41), 0), imp(cond(axiom(41), 0)))') ).
thf(619,plain,
! [A: $i,B: $i] :
( ( ( A = B )
& ( rcircle @ B ) )
=> ? [C: $i] :
( ( ron @ C @ A )
& ( rpoint @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(73,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ron @ C @ A )
& ( C = D )
& ( rpoint @ D )
& ( A = B )
& ( rcircle @ B ) )
=> ? [E: $i] :
( ( E != C )
& ( ron @ E @ A )
& ( rpoint @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(43), 0), imp(cond(axiom(43), 0)))') ).
thf(751,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ron @ C @ A )
& ( C = D )
& ( rpoint @ D )
& ( A = B )
& ( rcircle @ B ) )
=> ? [E: $i] :
( ( E != C )
& ( ron @ E @ A )
& ( rpoint @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(25,axiom,
! [A: $i,B: $i] :
( ( ( A != B )
& ? [C: $i] :
( ( B = C )
& ( rpoint @ C ) )
& ? [C: $i] :
( ( A = C )
& ( rpoint @ C ) ) )
=> ? [C: $i] :
( ( ron @ B @ C )
& ( ron @ A @ C )
& ( rline @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(51), 0), imp(cond(axiom(51), 0)))') ).
thf(344,plain,
! [A: $i,B: $i] :
( ( ( A != B )
& ? [C: $i] :
( ( B = C )
& ( rpoint @ C ) )
& ? [C: $i] :
( ( A = C )
& ( rpoint @ C ) ) )
=> ? [C: $i] :
( ( ron @ B @ C )
& ( ron @ A @ C )
& ( rline @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(153,axiom,
( ~ ? [A: $i] :
( ( ron @ vd1165 @ A )
& ( ron @ vd1164 @ A )
& ( ron @ vd1163 @ A )
& ( rline @ A ) )
& ( ( vangle @ vd1157 @ vd1156 @ vd1158 )
= ( vangle @ vd1164 @ vd1163 @ vd1165 ) )
& ( ( vf @ vd1156 @ vd1158 )
= ( vf @ vd1163 @ vd1165 ) )
& ( ( vf @ vd1156 @ vd1157 )
= ( vf @ vd1163 @ vd1164 ) )
& ? [A: $i] :
( ( vd1165 = A )
& ( rpoint @ A ) )
& ? [A: $i] :
( ( vd1164 = A )
& ( rpoint @ A ) )
& ? [A: $i] :
( ( vd1163 = A )
& ( rpoint @ A ) )
& ( vd1157 != vd1158 )
& ( vd1156 != vd1158 )
& ( vd1156 != vd1157 )
& ? [A: $i] :
( ( vd1158 = A )
& ( rpoint @ A ) )
& ? [A: $i] :
( ( vd1157 = A )
& ( rpoint @ A ) )
& ? [A: $i] :
( ( vd1156 = A )
& ( rpoint @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','and(neg(neg(conjunct2(conjunct2(conjunct2(plural(comma_conjunct2(265))))))), and(holds(conjunct1(conjunct2(conjunct2(plural(comma_conjunct2(265))))), 1172, 0), and(holds(conjunct1(conjunct2(plural(comma_conjunct2(265)))), 1171, 0), and(holds(conjunct1(plural(comma_conjunct2(265))), 1170, 0), and(qe(s3(plural(comma_conjunct2(265)))), and(qe(s2(plural(comma_conjunct2(265)))), and(qe(s1(plural(comma_conjunct2(265)))), and(pred(comma_conjunct1(265), 9), and(pred(comma_conjunct1(265), 8), and(pred(comma_conjunct1(265), 7), and(qe(s3(plural(265))), and(qe(s2(plural(265))), qe(s1(plural(265)))))))))))))))') ).
thf(1577,plain,
( ~ ? [A: $i] :
( ( ron @ vd1165 @ A )
& ( ron @ vd1164 @ A )
& ( ron @ vd1163 @ A )
& ( rline @ A ) )
& ( ( vangle @ vd1157 @ vd1156 @ vd1158 )
= ( vangle @ vd1164 @ vd1163 @ vd1165 ) )
& ( ( vf @ vd1156 @ vd1158 )
= ( vf @ vd1163 @ vd1165 ) )
& ( ( vf @ vd1156 @ vd1157 )
= ( vf @ vd1163 @ vd1164 ) )
& ? [A: $i] :
( ( vd1165 = A )
& ( rpoint @ A ) )
& ? [A: $i] :
( ( vd1164 = A )
& ( rpoint @ A ) )
& ? [A: $i] :
( ( vd1163 = A )
& ( rpoint @ A ) )
& ( vd1157 != vd1158 )
& ( vd1156 != vd1158 )
& ( vd1156 != vd1157 )
& ? [A: $i] :
( ( vd1158 = A )
& ( rpoint @ A ) )
& ? [A: $i] :
( ( vd1157 = A )
& ( rpoint @ A ) )
& ? [A: $i] :
( ( vd1156 = A )
& ( rpoint @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(1,conjecture,
( ( vf @ vd1157 @ vd1158 )
= ( vf @ vd1164 @ vd1165 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(conjunct1(266), 1175, 0)') ).
thf(2,negated_conjecture,
( ( vf @ vd1157 @ vd1158 )
!= ( vf @ vd1164 @ vd1165 ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(157,plain,
( ( vf @ vd1157 @ vd1158 )
!= ( vf @ vd1164 @ vd1165 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(47,axiom,
! [A: $i,B: $i] :
( ( ( A != B )
& ? [C: $i] :
( ( B = C )
& ( rpoint @ C ) )
& ? [C: $i] :
( ( A = C )
& ( rpoint @ C ) ) )
=> ! [C: $i,D: $i] :
( ( ( C = D )
& ( C != B )
& ( C != A )
& ( rpoint @ D ) )
=> ( rpoint @ ( vskolem1078 @ C @ D @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(219), 0), 1)') ).
thf(559,plain,
! [A: $i,B: $i] :
( ( ( A != B )
& ? [C: $i] :
( ( B = C )
& ( rpoint @ C ) )
& ? [C: $i] :
( ( A = C )
& ( rpoint @ C ) ) )
=> ! [C: $i,D: $i] :
( ( ( C = D )
& ( C != B )
& ( C != A )
& ( rpoint @ D ) )
=> ( rpoint @ ( vskolem1078 @ C @ D @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(147,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ? [G: $i] :
( ( ron @ F @ G )
& ( ron @ E @ G )
& ( ron @ D @ G )
& ( rline @ G ) )
& ( ( vangle @ B @ A @ C )
= ( vangle @ E @ D @ F ) )
& ( ( vf @ A @ C )
= ( vf @ D @ F ) )
& ( ( vf @ A @ B )
= ( vf @ D @ E ) )
& ? [G: $i] :
( ( F = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( E = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( D = G )
& ( rpoint @ G ) )
& ( B != C )
& ( A != C )
& ( A != B )
& ? [G: $i] :
( ( C = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( B = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( A = G )
& ( rpoint @ G ) ) )
=> ! [G: $i,H: $i,I: $i] :
( ( ( rS @ I @ F @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) )
& ~ ( rR @ E @ G @ D )
& ( ron @ G @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) )
& ( H = E )
& ( ( vf @ A @ C )
= ( vf @ G @ I ) )
& ( ( vf @ B @ C )
= ( vf @ H @ I ) )
& ( ( vf @ A @ B )
= ( vf @ G @ H ) )
& ( ( vangle @ I @ H @ G )
= ( vangle @ C @ B @ A ) )
& ( ( vangle @ G @ I @ H )
= ( vangle @ A @ C @ B ) )
& ( ( vangle @ H @ G @ I )
= ( vangle @ B @ A @ C ) )
& ? [J: $i] :
( ( I = J )
& ( rpoint @ J ) )
& ? [J: $i] :
( ( H = J )
& ( rpoint @ J ) )
& ? [J: $i] :
( ( G = J )
& ( rpoint @ J ) ) )
=> ( ron @ F @ ( vskolem1232 @ G @ H @ I @ A @ B @ C @ D @ E @ F ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(proof(267), 0), 13)') ).
thf(1514,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ? [G: $i] :
( ( ron @ F @ G )
& ( ron @ E @ G )
& ( ron @ D @ G )
& ( rline @ G ) )
& ( ( vangle @ B @ A @ C )
= ( vangle @ E @ D @ F ) )
& ( ( vf @ A @ C )
= ( vf @ D @ F ) )
& ( ( vf @ A @ B )
= ( vf @ D @ E ) )
& ? [G: $i] :
( ( F = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( E = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( D = G )
& ( rpoint @ G ) )
& ( B != C )
& ( A != C )
& ( A != B )
& ? [G: $i] :
( ( C = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( B = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( A = G )
& ( rpoint @ G ) ) )
=> ! [G: $i,H: $i,I: $i] :
( ( ( rS @ I @ F @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) )
& ~ ( rR @ E @ G @ D )
& ( ron @ G @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) )
& ( H = E )
& ( ( vf @ A @ C )
= ( vf @ G @ I ) )
& ( ( vf @ B @ C )
= ( vf @ H @ I ) )
& ( ( vf @ A @ B )
= ( vf @ G @ H ) )
& ( ( vangle @ I @ H @ G )
= ( vangle @ C @ B @ A ) )
& ( ( vangle @ G @ I @ H )
= ( vangle @ A @ C @ B ) )
& ( ( vangle @ H @ G @ I )
= ( vangle @ B @ A @ C ) )
& ? [J: $i] :
( ( I = J )
& ( rpoint @ J ) )
& ? [J: $i] :
( ( H = J )
& ( rpoint @ J ) )
& ? [J: $i] :
( ( G = J )
& ( rpoint @ J ) ) )
=> ( ron @ F @ ( vskolem1232 @ G @ H @ I @ A @ B @ C @ D @ E @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(34,axiom,
! [A: $i,B: $i,C: $i] :
( ( ? [D: $i] :
( ( C = D )
& ( rpoint @ D ) )
& ? [D: $i] :
( ( B = D )
& ( rpoint @ D ) )
& ? [D: $i] :
( ( A = D )
& ( rpoint @ D ) ) )
=> ? [D: $i] :
( ( D != C )
& ( D != B )
& ( D != A )
& ( rpoint @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(11), 0), imp(cond(axiom(11), 0)))') ).
thf(421,plain,
! [A: $i,B: $i,C: $i] :
( ( ? [D: $i] :
( ( C = D )
& ( rpoint @ D ) )
& ? [D: $i] :
( ( B = D )
& ( rpoint @ D ) )
& ? [D: $i] :
( ( A = D )
& ( rpoint @ D ) ) )
=> ? [D: $i] :
( ( D != C )
& ( D != B )
& ( D != A )
& ( rpoint @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(154,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ? [G: $i] :
( ( ron @ F @ G )
& ( ron @ E @ G )
& ( ron @ D @ G )
& ( rline @ G ) )
& ( ( vangle @ B @ A @ C )
= ( vangle @ E @ D @ F ) )
& ( ( vf @ A @ C )
= ( vf @ D @ F ) )
& ( ( vf @ A @ B )
= ( vf @ D @ E ) )
& ? [G: $i] :
( ( F = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( E = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( D = G )
& ( rpoint @ G ) )
& ( B != C )
& ( A != C )
& ( A != B )
& ? [G: $i] :
( ( C = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( B = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( A = G )
& ( rpoint @ G ) ) )
=> ! [G: $i,H: $i,I: $i] :
( ( ( rS @ I @ F @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) )
& ~ ( rR @ E @ G @ D )
& ( ron @ G @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) )
& ( H = E )
& ( ( vf @ A @ C )
= ( vf @ G @ I ) )
& ( ( vf @ B @ C )
= ( vf @ H @ I ) )
& ( ( vf @ A @ B )
= ( vf @ G @ H ) )
& ( ( vangle @ I @ H @ G )
= ( vangle @ C @ B @ A ) )
& ( ( vangle @ G @ I @ H )
= ( vangle @ A @ C @ B ) )
& ( ( vangle @ H @ G @ I )
= ( vangle @ B @ A @ C ) )
& ? [J: $i] :
( ( I = J )
& ( rpoint @ J ) )
& ? [J: $i] :
( ( H = J )
& ( rpoint @ J ) )
& ? [J: $i] :
( ( G = J )
& ( rpoint @ J ) ) )
=> ( ron @ I @ ( vskolem1234 @ G @ H @ I @ A @ B @ C @ D @ E @ F ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(proof(267), 0), 22)') ).
thf(1609,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ? [G: $i] :
( ( ron @ F @ G )
& ( ron @ E @ G )
& ( ron @ D @ G )
& ( rline @ G ) )
& ( ( vangle @ B @ A @ C )
= ( vangle @ E @ D @ F ) )
& ( ( vf @ A @ C )
= ( vf @ D @ F ) )
& ( ( vf @ A @ B )
= ( vf @ D @ E ) )
& ? [G: $i] :
( ( F = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( E = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( D = G )
& ( rpoint @ G ) )
& ( B != C )
& ( A != C )
& ( A != B )
& ? [G: $i] :
( ( C = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( B = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( A = G )
& ( rpoint @ G ) ) )
=> ! [G: $i,H: $i,I: $i] :
( ( ( rS @ I @ F @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) )
& ~ ( rR @ E @ G @ D )
& ( ron @ G @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) )
& ( H = E )
& ( ( vf @ A @ C )
= ( vf @ G @ I ) )
& ( ( vf @ B @ C )
= ( vf @ H @ I ) )
& ( ( vf @ A @ B )
= ( vf @ G @ H ) )
& ( ( vangle @ I @ H @ G )
= ( vangle @ C @ B @ A ) )
& ( ( vangle @ G @ I @ H )
= ( vangle @ A @ C @ B ) )
& ( ( vangle @ H @ G @ I )
= ( vangle @ B @ A @ C ) )
& ? [J: $i] :
( ( I = J )
& ( rpoint @ J ) )
& ? [J: $i] :
( ( H = J )
& ( rpoint @ J ) )
& ? [J: $i] :
( ( G = J )
& ( rpoint @ J ) ) )
=> ( ron @ I @ ( vskolem1234 @ G @ H @ I @ A @ B @ C @ D @ E @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(33,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( ron @ B @ D )
& ( ron @ B @ E )
& ~ ( rS @ A @ C @ D )
& ( ron @ C @ E )
& ( ron @ A @ E )
& ( D != E )
& ? [F: $i] :
( ( E = F )
& ( rline @ F ) )
& ? [F: $i] :
( ( D = F )
& ( rline @ F ) )
& ( B != C )
& ( A != C )
& ( A != B )
& ? [F: $i] :
( ( C = F )
& ( rpoint @ F ) )
& ? [F: $i] :
( ( B = F )
& ( rpoint @ F ) )
& ? [F: $i] :
( ( A = F )
& ( rpoint @ F ) ) )
=> ( rR @ B @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(111), 0), imp(cond(axiom(111), 0)))') ).
thf(416,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( ron @ B @ D )
& ( ron @ B @ E )
& ~ ( rS @ A @ C @ D )
& ( ron @ C @ E )
& ( ron @ A @ E )
& ( D != E )
& ? [F: $i] :
( ( E = F )
& ( rline @ F ) )
& ? [F: $i] :
( ( D = F )
& ( rline @ F ) )
& ( B != C )
& ( A != C )
& ( A != B )
& ? [F: $i] :
( ( C = F )
& ( rpoint @ F ) )
& ? [F: $i] :
( ( B = F )
& ( rpoint @ F ) )
& ? [F: $i] :
( ( A = F )
& ( rpoint @ F ) ) )
=> ( rR @ B @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(22,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( rR @ D @ A @ B )
& ( rR @ B @ A @ C )
& ? [E: $i] :
( ( D = E )
& ( rpoint @ E ) )
& ? [E: $i] :
( ( C = E )
& ( rpoint @ E ) )
& ? [E: $i] :
( ( B = E )
& ( rpoint @ E ) )
& ? [E: $i] :
( ( A = E )
& ( rpoint @ E ) ) )
=> ( rR @ D @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(87), 0), imp(cond(axiom(87), 0)))') ).
thf(325,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( rR @ D @ A @ B )
& ( rR @ B @ A @ C )
& ? [E: $i] :
( ( D = E )
& ( rpoint @ E ) )
& ? [E: $i] :
( ( C = E )
& ( rpoint @ E ) )
& ? [E: $i] :
( ( B = E )
& ( rpoint @ E ) )
& ? [E: $i] :
( ( A = E )
& ( rpoint @ E ) ) )
=> ( rR @ D @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(36,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( ron @ E @ A )
& ( ron @ D @ A )
& ( ron @ C @ A )
& ? [F: $i] :
( ( E = F )
& ( rpoint @ F ) )
& ? [F: $i] :
( ( D = F )
& ( rpoint @ F ) )
& ? [F: $i] :
( ( C = F )
& ( rpoint @ F ) )
& ( A = B )
& ( rline @ B ) )
=> ? [F: $i] :
( ( F != D )
& ( F != C )
& ( ron @ F @ A )
& ( rpoint @ F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(21), 0), imp(cond(axiom(21), 0)))') ).
thf(448,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( ron @ E @ A )
& ( ron @ D @ A )
& ( ron @ C @ A )
& ? [F: $i] :
( ( E = F )
& ( rpoint @ F ) )
& ? [F: $i] :
( ( D = F )
& ( rpoint @ F ) )
& ? [F: $i] :
( ( C = F )
& ( rpoint @ F ) )
& ( A = B )
& ( rline @ B ) )
=> ? [F: $i] :
( ( F != D )
& ( F != C )
& ( ron @ F @ A )
& ( rpoint @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( ( A = B )
& ( rreal @ B ) )
=> ( ( vplus @ A @ v0 )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(141), 0), imp(cond(axiom(141), 0)))') ).
thf(261,plain,
! [A: $i,B: $i] :
( ( ( A = B )
& ( rreal @ B ) )
=> ( ( vplus @ A @ v0 )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(83,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C = D )
& ( rreal @ D )
& ( A = B )
& ( rreal @ B ) )
=> ( ( rless @ A @ C )
| ( A = C )
| ( rless @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(145), 0), imp(cond(axiom(145), 0)))') ).
thf(821,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C = D )
& ( rreal @ D )
& ( A = B )
& ( rreal @ B ) )
=> ( ( rless @ A @ C )
| ( A = C )
| ( rless @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(114,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ? [G: $i] :
( ( ron @ F @ G )
& ( ron @ E @ G )
& ( ron @ D @ G )
& ( rline @ G ) )
& ( ( vangle @ B @ A @ C )
= ( vangle @ E @ D @ F ) )
& ( ( vf @ A @ C )
= ( vf @ D @ F ) )
& ( ( vf @ A @ B )
= ( vf @ D @ E ) )
& ? [G: $i] :
( ( F = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( E = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( D = G )
& ( rpoint @ G ) )
& ( B != C )
& ( A != C )
& ( A != B )
& ? [G: $i] :
( ( C = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( B = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( A = G )
& ( rpoint @ G ) ) )
=> ! [G: $i,H: $i,I: $i] :
( ( ( rS @ I @ F @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) )
& ~ ( rR @ E @ G @ D )
& ( ron @ G @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) )
& ( H = E )
& ( ( vf @ A @ C )
= ( vf @ G @ I ) )
& ( ( vf @ B @ C )
= ( vf @ H @ I ) )
& ( ( vf @ A @ B )
= ( vf @ G @ H ) )
& ( ( vangle @ I @ H @ G )
= ( vangle @ C @ B @ A ) )
& ( ( vangle @ G @ I @ H )
= ( vangle @ A @ C @ B ) )
& ( ( vangle @ H @ G @ I )
= ( vangle @ B @ A @ C ) )
& ? [J: $i] :
( ( I = J )
& ( rpoint @ J ) )
& ? [J: $i] :
( ( H = J )
& ( rpoint @ J ) )
& ? [J: $i] :
( ( G = J )
& ( rpoint @ J ) ) )
=> ( ( vangle @ D @ F @ E )
= ( vangle @ A @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(proof(267), 0), 3)') ).
thf(1136,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ? [G: $i] :
( ( ron @ F @ G )
& ( ron @ E @ G )
& ( ron @ D @ G )
& ( rline @ G ) )
& ( ( vangle @ B @ A @ C )
= ( vangle @ E @ D @ F ) )
& ( ( vf @ A @ C )
= ( vf @ D @ F ) )
& ( ( vf @ A @ B )
= ( vf @ D @ E ) )
& ? [G: $i] :
( ( F = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( E = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( D = G )
& ( rpoint @ G ) )
& ( B != C )
& ( A != C )
& ( A != B )
& ? [G: $i] :
( ( C = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( B = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( A = G )
& ( rpoint @ G ) ) )
=> ! [G: $i,H: $i,I: $i] :
( ( ( rS @ I @ F @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) )
& ~ ( rR @ E @ G @ D )
& ( ron @ G @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) )
& ( H = E )
& ( ( vf @ A @ C )
= ( vf @ G @ I ) )
& ( ( vf @ B @ C )
= ( vf @ H @ I ) )
& ( ( vf @ A @ B )
= ( vf @ G @ H ) )
& ( ( vangle @ I @ H @ G )
= ( vangle @ C @ B @ A ) )
& ( ( vangle @ G @ I @ H )
= ( vangle @ A @ C @ B ) )
& ( ( vangle @ H @ G @ I )
= ( vangle @ B @ A @ C ) )
& ? [J: $i] :
( ( I = J )
& ( rpoint @ J ) )
& ? [J: $i] :
( ( H = J )
& ( rpoint @ J ) )
& ? [J: $i] :
( ( G = J )
& ( rpoint @ J ) ) )
=> ( ( vangle @ D @ F @ E )
= ( vangle @ A @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(85,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( rR @ C @ A @ B )
& ~ ( rinside @ C @ D )
& ( ( ron @ A @ D )
| ( rinside @ A @ D ) )
& ( D = E )
& ( rcircle @ E )
& ? [F: $i] :
( ( C = F )
& ( rpoint @ F ) )
& ? [F: $i] :
( ( B = F )
& ( rpoint @ F ) )
& ? [F: $i] :
( ( A = F )
& ( rpoint @ F ) ) )
=> ( ~ ( ron @ B @ D )
& ~ ( ron @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(123), 0), imp(cond(axiom(123), 0)))') ).
thf(834,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( rR @ C @ A @ B )
& ~ ( rinside @ C @ D )
& ( ( ron @ A @ D )
| ( rinside @ A @ D ) )
& ( D = E )
& ( rcircle @ E )
& ? [F: $i] :
( ( C = F )
& ( rpoint @ F ) )
& ? [F: $i] :
( ( B = F )
& ( rpoint @ F ) )
& ? [F: $i] :
( ( A = F )
& ( rpoint @ F ) ) )
=> ~ ( ron @ B @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(31,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( C = D )
& ( E = F )
& ( ron @ B @ E )
& ( ron @ A @ E )
& ( rline @ F )
& ~ ( rS @ A @ B @ C )
& ( rline @ D )
& ? [G: $i] :
( ( B = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( A = G )
& ( rpoint @ G ) ) )
=> ( rintersect @ C @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(127), 0), imp(cond(axiom(127), 0)))') ).
thf(397,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( C = D )
& ( E = F )
& ( ron @ B @ E )
& ( ron @ A @ E )
& ( rline @ F )
& ~ ( rS @ A @ B @ C )
& ( rline @ D )
& ? [G: $i] :
( ( B = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( A = G )
& ( rpoint @ G ) ) )
=> ( rintersect @ C @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(15,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( ron @ F @ G )
& ( ron @ E @ G )
& ( G = H )
& ( rline @ H )
& ( rcenter @ F @ B )
& ( rcenter @ E @ A )
& ( C != D )
& ( ron @ D @ B )
& ( ron @ D @ A )
& ( ron @ C @ B )
& ( ron @ C @ A )
& ? [I: $i] :
( ( D = I )
& ( rpoint @ I ) )
& ? [I: $i] :
( ( C = I )
& ( rpoint @ I ) )
& ( rintersect @ A @ B )
& ( A != B )
& ? [I: $i] :
( ( B = I )
& ( rcircle @ I ) )
& ? [I: $i] :
( ( A = I )
& ( rcircle @ I ) ) )
=> ~ ( rS @ C @ D @ G ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(125), 0), imp(cond(axiom(125), 0)))') ).
thf(280,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( ron @ F @ G )
& ( ron @ E @ G )
& ( G = H )
& ( rline @ H )
& ( rcenter @ F @ B )
& ( rcenter @ E @ A )
& ( C != D )
& ( ron @ D @ B )
& ( ron @ D @ A )
& ( ron @ C @ B )
& ( ron @ C @ A )
& ? [I: $i] :
( ( D = I )
& ( rpoint @ I ) )
& ? [I: $i] :
( ( C = I )
& ( rpoint @ I ) )
& ( rintersect @ A @ B )
& ( A != B )
& ? [I: $i] :
( ( B = I )
& ( rcircle @ I ) )
& ? [I: $i] :
( ( A = I )
& ( rcircle @ I ) ) )
=> ~ ( rS @ C @ D @ G ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(140,axiom,
! [A: $i,B: $i] :
( ( ? [C: $i] :
( ( B = C )
& ( rpoint @ C ) )
& ? [C: $i] :
( ( A = C )
& ( rpoint @ C ) ) )
=> ( rleq @ v0 @ ( vf @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(164), 0), imp(cond(axiom(164), 0)))') ).
thf(1447,plain,
! [A: $i,B: $i] :
( ( ? [C: $i] :
( ( B = C )
& ( rpoint @ C ) )
& ? [C: $i] :
( ( A = C )
& ( rpoint @ C ) ) )
=> ( rleq @ v0 @ ( vf @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(155,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ? [G: $i] :
( ( ron @ F @ G )
& ( ron @ E @ G )
& ( ron @ D @ G )
& ( rline @ G ) )
& ( ( vangle @ B @ A @ C )
= ( vangle @ E @ D @ F ) )
& ( ( vf @ A @ C )
= ( vf @ D @ F ) )
& ( ( vf @ A @ B )
= ( vf @ D @ E ) )
& ? [G: $i] :
( ( F = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( E = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( D = G )
& ( rpoint @ G ) )
& ( B != C )
& ( A != C )
& ( A != B )
& ? [G: $i] :
( ( C = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( B = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( A = G )
& ( rpoint @ G ) ) )
=> ! [G: $i,H: $i,I: $i] :
( ( ( rS @ I @ F @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) )
& ~ ( rR @ E @ G @ D )
& ( ron @ G @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) )
& ( H = E )
& ( ( vf @ A @ C )
= ( vf @ G @ I ) )
& ( ( vf @ B @ C )
= ( vf @ H @ I ) )
& ( ( vf @ A @ B )
= ( vf @ G @ H ) )
& ( ( vangle @ I @ H @ G )
= ( vangle @ C @ B @ A ) )
& ( ( vangle @ G @ I @ H )
= ( vangle @ A @ C @ B ) )
& ( ( vangle @ H @ G @ I )
= ( vangle @ B @ A @ C ) )
& ? [J: $i] :
( ( I = J )
& ( rpoint @ J ) )
& ? [J: $i] :
( ( H = J )
& ( rpoint @ J ) )
& ? [J: $i] :
( ( G = J )
& ( rpoint @ J ) ) )
=> ( ( vangle @ H @ G @ I )
= ( vangle @ E @ D @ F ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(proof(267), 0), 28)') ).
thf(1622,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ? [G: $i] :
( ( ron @ F @ G )
& ( ron @ E @ G )
& ( ron @ D @ G )
& ( rline @ G ) )
& ( ( vangle @ B @ A @ C )
= ( vangle @ E @ D @ F ) )
& ( ( vf @ A @ C )
= ( vf @ D @ F ) )
& ( ( vf @ A @ B )
= ( vf @ D @ E ) )
& ? [G: $i] :
( ( F = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( E = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( D = G )
& ( rpoint @ G ) )
& ( B != C )
& ( A != C )
& ( A != B )
& ? [G: $i] :
( ( C = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( B = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( A = G )
& ( rpoint @ G ) ) )
=> ! [G: $i,H: $i,I: $i] :
( ( ( rS @ I @ F @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) )
& ~ ( rR @ E @ G @ D )
& ( ron @ G @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) )
& ( H = E )
& ( ( vf @ A @ C )
= ( vf @ G @ I ) )
& ( ( vf @ B @ C )
= ( vf @ H @ I ) )
& ( ( vf @ A @ B )
= ( vf @ G @ H ) )
& ( ( vangle @ I @ H @ G )
= ( vangle @ C @ B @ A ) )
& ( ( vangle @ G @ I @ H )
= ( vangle @ A @ C @ B ) )
& ( ( vangle @ H @ G @ I )
= ( vangle @ B @ A @ C ) )
& ? [J: $i] :
( ( I = J )
& ( rpoint @ J ) )
& ? [J: $i] :
( ( H = J )
& ( rpoint @ J ) )
& ? [J: $i] :
( ( G = J )
& ( rpoint @ J ) ) )
=> ( ( vangle @ H @ G @ I )
= ( vangle @ E @ D @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(62,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( ron @ A @ C )
& ( C = D )
& ( rline @ D )
& ( A = B )
& ( rpoint @ B ) )
=> ( rS @ A @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(95), 0), imp(cond(axiom(95), 0)))') ).
thf(660,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( ron @ A @ C )
& ( C = D )
& ( rline @ D )
& ( A = B )
& ( rpoint @ B ) )
=> ( rS @ A @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(139,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ? [G: $i] :
( ( ron @ F @ G )
& ( ron @ E @ G )
& ( ron @ D @ G )
& ( rline @ G ) )
& ( ( vangle @ B @ A @ C )
= ( vangle @ E @ D @ F ) )
& ( ( vf @ A @ C )
= ( vf @ D @ F ) )
& ( ( vf @ A @ B )
= ( vf @ D @ E ) )
& ? [G: $i] :
( ( F = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( E = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( D = G )
& ( rpoint @ G ) )
& ( B != C )
& ( A != C )
& ( A != B )
& ? [G: $i] :
( ( C = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( B = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( A = G )
& ( rpoint @ G ) ) )
=> ! [G: $i,H: $i,I: $i] :
( ( ( rS @ I @ F @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) )
& ~ ( rR @ E @ G @ D )
& ( ron @ G @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) )
& ( H = E )
& ( ( vf @ A @ C )
= ( vf @ G @ I ) )
& ( ( vf @ B @ C )
= ( vf @ H @ I ) )
& ( ( vf @ A @ B )
= ( vf @ G @ H ) )
& ( ( vangle @ I @ H @ G )
= ( vangle @ C @ B @ A ) )
& ( ( vangle @ G @ I @ H )
= ( vangle @ A @ C @ B ) )
& ( ( vangle @ H @ G @ I )
= ( vangle @ B @ A @ C ) )
& ? [J: $i] :
( ( I = J )
& ( rpoint @ J ) )
& ? [J: $i] :
( ( H = J )
& ( rpoint @ J ) )
& ? [J: $i] :
( ( G = J )
& ( rpoint @ J ) ) )
=> ( ( G != D )
=> ~ ( rR @ D @ G @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(proof(267), 0), 31)') ).
thf(1433,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ? [G: $i] :
( ( ron @ F @ G )
& ( ron @ E @ G )
& ( ron @ D @ G )
& ( rline @ G ) )
& ( ( vangle @ B @ A @ C )
= ( vangle @ E @ D @ F ) )
& ( ( vf @ A @ C )
= ( vf @ D @ F ) )
& ( ( vf @ A @ B )
= ( vf @ D @ E ) )
& ? [G: $i] :
( ( F = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( E = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( D = G )
& ( rpoint @ G ) )
& ( B != C )
& ( A != C )
& ( A != B )
& ? [G: $i] :
( ( C = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( B = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( A = G )
& ( rpoint @ G ) ) )
=> ! [G: $i,H: $i,I: $i] :
( ( ( rS @ I @ F @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) )
& ~ ( rR @ E @ G @ D )
& ( ron @ G @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) )
& ( H = E )
& ( ( vf @ A @ C )
= ( vf @ G @ I ) )
& ( ( vf @ B @ C )
= ( vf @ H @ I ) )
& ( ( vf @ A @ B )
= ( vf @ G @ H ) )
& ( ( vangle @ I @ H @ G )
= ( vangle @ C @ B @ A ) )
& ( ( vangle @ G @ I @ H )
= ( vangle @ A @ C @ B ) )
& ( ( vangle @ H @ G @ I )
= ( vangle @ B @ A @ C ) )
& ? [J: $i] :
( ( I = J )
& ( rpoint @ J ) )
& ? [J: $i] :
( ( H = J )
& ( rpoint @ J ) )
& ? [J: $i] :
( ( G = J )
& ( rpoint @ J ) ) )
=> ( ( G != D )
=> ~ ( rR @ D @ G @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(44,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ? [E: $i] :
( ( D = E )
& ( rpoint @ E ) )
& ? [E: $i] :
( ( C = E )
& ( rpoint @ E ) )
& ? [E: $i] :
( ( B = E )
& ( rpoint @ E ) )
& ? [E: $i] :
( ( A = E )
& ( rpoint @ E ) ) )
=> ? [E: $i] :
( ( E != D )
& ( E != C )
& ( E != B )
& ( E != A )
& ( rpoint @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(13), 0), imp(cond(axiom(13), 0)))') ).
thf(527,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ? [E: $i] :
( ( D = E )
& ( rpoint @ E ) )
& ? [E: $i] :
( ( C = E )
& ( rpoint @ E ) )
& ? [E: $i] :
( ( B = E )
& ( rpoint @ E ) )
& ? [E: $i] :
( ( A = E )
& ( rpoint @ E ) ) )
=> ? [E: $i] :
( ( E != D )
& ( E != C )
& ( E != B )
& ( E != A )
& ( rpoint @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(152,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ? [G: $i] :
( ( ron @ F @ G )
& ( ron @ E @ G )
& ( ron @ D @ G )
& ( rline @ G ) )
& ( ( vangle @ B @ A @ C )
= ( vangle @ E @ D @ F ) )
& ( ( vf @ A @ C )
= ( vf @ D @ F ) )
& ( ( vf @ A @ B )
= ( vf @ D @ E ) )
& ? [G: $i] :
( ( F = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( E = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( D = G )
& ( rpoint @ G ) )
& ( B != C )
& ( A != C )
& ( A != B )
& ? [G: $i] :
( ( C = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( B = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( A = G )
& ( rpoint @ G ) ) )
=> ! [G: $i,H: $i,I: $i] :
( ( ( rS @ I @ F @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) )
& ~ ( rR @ E @ G @ D )
& ( ron @ G @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) )
& ( H = E )
& ( ( vf @ A @ C )
= ( vf @ G @ I ) )
& ( ( vf @ B @ C )
= ( vf @ H @ I ) )
& ( ( vf @ A @ B )
= ( vf @ G @ H ) )
& ( ( vangle @ I @ H @ G )
= ( vangle @ C @ B @ A ) )
& ( ( vangle @ G @ I @ H )
= ( vangle @ A @ C @ B ) )
& ( ( vangle @ H @ G @ I )
= ( vangle @ B @ A @ C ) )
& ? [J: $i] :
( ( I = J )
& ( rpoint @ J ) )
& ? [J: $i] :
( ( H = J )
& ( rpoint @ J ) )
& ? [J: $i] :
( ( G = J )
& ( rpoint @ J ) ) )
=> ( rline @ ( vskolem1232 @ G @ H @ I @ A @ B @ C @ D @ E @ F ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(proof(267), 0), 27)') ).
thf(1564,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ? [G: $i] :
( ( ron @ F @ G )
& ( ron @ E @ G )
& ( ron @ D @ G )
& ( rline @ G ) )
& ( ( vangle @ B @ A @ C )
= ( vangle @ E @ D @ F ) )
& ( ( vf @ A @ C )
= ( vf @ D @ F ) )
& ( ( vf @ A @ B )
= ( vf @ D @ E ) )
& ? [G: $i] :
( ( F = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( E = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( D = G )
& ( rpoint @ G ) )
& ( B != C )
& ( A != C )
& ( A != B )
& ? [G: $i] :
( ( C = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( B = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( A = G )
& ( rpoint @ G ) ) )
=> ! [G: $i,H: $i,I: $i] :
( ( ( rS @ I @ F @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) )
& ~ ( rR @ E @ G @ D )
& ( ron @ G @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) )
& ( H = E )
& ( ( vf @ A @ C )
= ( vf @ G @ I ) )
& ( ( vf @ B @ C )
= ( vf @ H @ I ) )
& ( ( vf @ A @ B )
= ( vf @ G @ H ) )
& ( ( vangle @ I @ H @ G )
= ( vangle @ C @ B @ A ) )
& ( ( vangle @ G @ I @ H )
= ( vangle @ A @ C @ B ) )
& ( ( vangle @ H @ G @ I )
= ( vangle @ B @ A @ C ) )
& ? [J: $i] :
( ( I = J )
& ( rpoint @ J ) )
& ? [J: $i] :
( ( H = J )
& ( rpoint @ J ) )
& ? [J: $i] :
( ( G = J )
& ( rpoint @ J ) ) )
=> ( rline @ ( vskolem1232 @ G @ H @ I @ A @ B @ C @ D @ E @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(52,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( E != D )
& ~ ( ron @ G @ B )
& ~ ( rS @ E @ G @ B )
& ( rS @ F @ G @ A )
& ( ron @ G @ C )
& ( ron @ F @ B )
& ( ron @ E @ A )
& ( ron @ D @ C )
& ( ron @ D @ B )
& ( ron @ D @ A )
& ? [H: $i] :
( ( G = H )
& ( rpoint @ H ) )
& ? [H: $i] :
( ( F = H )
& ( rpoint @ H ) )
& ? [H: $i] :
( ( E = H )
& ( rpoint @ H ) )
& ? [H: $i] :
( ( D = H )
& ( rpoint @ H ) )
& ? [H: $i] :
( ( C = H )
& ( rline @ H ) )
& ? [H: $i] :
( ( B = H )
& ( rline @ H ) )
& ? [H: $i] :
( ( A = H )
& ( rline @ H ) ) )
=> ( rS @ E @ F @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(115), 0), imp(cond(axiom(115), 0)))') ).
thf(602,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( E != D )
& ~ ( ron @ G @ B )
& ~ ( rS @ E @ G @ B )
& ( rS @ F @ G @ A )
& ( ron @ G @ C )
& ( ron @ F @ B )
& ( ron @ E @ A )
& ( ron @ D @ C )
& ( ron @ D @ B )
& ( ron @ D @ A )
& ? [H: $i] :
( ( G = H )
& ( rpoint @ H ) )
& ? [H: $i] :
( ( F = H )
& ( rpoint @ H ) )
& ? [H: $i] :
( ( E = H )
& ( rpoint @ H ) )
& ? [H: $i] :
( ( D = H )
& ( rpoint @ H ) )
& ? [H: $i] :
( ( C = H )
& ( rline @ H ) )
& ? [H: $i] :
( ( B = H )
& ( rline @ H ) )
& ? [H: $i] :
( ( A = H )
& ( rline @ H ) ) )
=> ( rS @ E @ F @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(75,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( rinside @ B @ D )
& ~ ( ron @ B @ D )
& ( rinside @ A @ D )
& ( ( ron @ B @ C )
| ( rinside @ B @ C ) )
& ( ron @ A @ C )
& ? [E: $i] :
( ( D = E )
& ( rcircle @ E ) )
& ? [E: $i] :
( ( C = E )
& ( rcircle @ E ) )
& ? [E: $i] :
( ( B = E )
& ( rpoint @ E ) )
& ? [E: $i] :
( ( A = E )
& ( rpoint @ E ) ) )
=> ( rintersect @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(133), 0), imp(cond(axiom(133), 0)))') ).
thf(766,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( rinside @ B @ D )
& ~ ( ron @ B @ D )
& ( rinside @ A @ D )
& ( ( ron @ B @ C )
| ( rinside @ B @ C ) )
& ( ron @ A @ C )
& ? [E: $i] :
( ( D = E )
& ( rcircle @ E ) )
& ? [E: $i] :
( ( C = E )
& ( rcircle @ E ) )
& ? [E: $i] :
( ( B = E )
& ( rpoint @ E ) )
& ? [E: $i] :
( ( A = E )
& ( rpoint @ E ) ) )
=> ( rintersect @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(93,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( rS @ A @ C @ D )
& ( rS @ A @ B @ D )
& ( D = E )
& ( rline @ E )
& ? [F: $i] :
( ( C = F )
& ( rpoint @ F ) )
& ? [F: $i] :
( ( B = F )
& ( rpoint @ F ) )
& ? [F: $i] :
( ( A = F )
& ( rpoint @ F ) ) )
=> ( rS @ B @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(101), 0), imp(cond(axiom(101), 0)))') ).
thf(894,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( rS @ A @ C @ D )
& ( rS @ A @ B @ D )
& ( D = E )
& ( rline @ E )
& ? [F: $i] :
( ( C = F )
& ( rpoint @ F ) )
& ? [F: $i] :
( ( B = F )
& ( rpoint @ F ) )
& ? [F: $i] :
( ( A = F )
& ( rpoint @ F ) ) )
=> ( rS @ B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(113,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ? [G: $i] :
( ( ron @ F @ G )
& ( ron @ E @ G )
& ( ron @ D @ G )
& ( rline @ G ) )
& ( ( vangle @ B @ A @ C )
= ( vangle @ E @ D @ F ) )
& ( ( vf @ A @ C )
= ( vf @ D @ F ) )
& ( ( vf @ A @ B )
= ( vf @ D @ E ) )
& ? [G: $i] :
( ( F = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( E = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( D = G )
& ( rpoint @ G ) )
& ( B != C )
& ( A != C )
& ( A != B )
& ? [G: $i] :
( ( C = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( B = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( A = G )
& ( rpoint @ G ) ) )
=> ! [G: $i,H: $i,I: $i] :
( ( ( rS @ I @ F @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) )
& ~ ( rR @ E @ G @ D )
& ( ron @ G @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) )
& ( H = E )
& ( ( vf @ A @ C )
= ( vf @ G @ I ) )
& ( ( vf @ B @ C )
= ( vf @ H @ I ) )
& ( ( vf @ A @ B )
= ( vf @ G @ H ) )
& ( ( vangle @ I @ H @ G )
= ( vangle @ C @ B @ A ) )
& ( ( vangle @ G @ I @ H )
= ( vangle @ A @ C @ B ) )
& ( ( vangle @ H @ G @ I )
= ( vangle @ B @ A @ C ) )
& ? [J: $i] :
( ( I = J )
& ( rpoint @ J ) )
& ? [J: $i] :
( ( H = J )
& ( rpoint @ J ) )
& ? [J: $i] :
( ( G = J )
& ( rpoint @ J ) ) )
=> ( ron @ D @ ( vskolem1232 @ G @ H @ I @ A @ B @ C @ D @ E @ F ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(proof(267), 0), 15)') ).
thf(1123,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ? [G: $i] :
( ( ron @ F @ G )
& ( ron @ E @ G )
& ( ron @ D @ G )
& ( rline @ G ) )
& ( ( vangle @ B @ A @ C )
= ( vangle @ E @ D @ F ) )
& ( ( vf @ A @ C )
= ( vf @ D @ F ) )
& ( ( vf @ A @ B )
= ( vf @ D @ E ) )
& ? [G: $i] :
( ( F = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( E = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( D = G )
& ( rpoint @ G ) )
& ( B != C )
& ( A != C )
& ( A != B )
& ? [G: $i] :
( ( C = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( B = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( A = G )
& ( rpoint @ G ) ) )
=> ! [G: $i,H: $i,I: $i] :
( ( ( rS @ I @ F @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) )
& ~ ( rR @ E @ G @ D )
& ( ron @ G @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) )
& ( H = E )
& ( ( vf @ A @ C )
= ( vf @ G @ I ) )
& ( ( vf @ B @ C )
= ( vf @ H @ I ) )
& ( ( vf @ A @ B )
= ( vf @ G @ H ) )
& ( ( vangle @ I @ H @ G )
= ( vangle @ C @ B @ A ) )
& ( ( vangle @ G @ I @ H )
= ( vangle @ A @ C @ B ) )
& ( ( vangle @ H @ G @ I )
= ( vangle @ B @ A @ C ) )
& ? [J: $i] :
( ( I = J )
& ( rpoint @ J ) )
& ? [J: $i] :
( ( H = J )
& ( rpoint @ J ) )
& ? [J: $i] :
( ( G = J )
& ( rpoint @ J ) ) )
=> ( ron @ D @ ( vskolem1232 @ G @ H @ I @ A @ B @ C @ D @ E @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(30,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( ron @ B @ D )
& ( ron @ A @ D )
& ( rR @ B @ A @ C )
& ( D = E )
& ( rline @ E )
& ? [F: $i] :
( ( C = F )
& ( rpoint @ F ) )
& ? [F: $i] :
( ( B = F )
& ( rpoint @ F ) )
& ? [F: $i] :
( ( A = F )
& ( rpoint @ F ) ) )
=> ( rS @ B @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(107), 0), imp(cond(axiom(107), 0)))') ).
thf(392,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( ron @ B @ D )
& ( ron @ A @ D )
& ( rR @ B @ A @ C )
& ( D = E )
& ( rline @ E )
& ? [F: $i] :
( ( C = F )
& ( rpoint @ F ) )
& ? [F: $i] :
( ( B = F )
& ( rpoint @ F ) )
& ? [F: $i] :
( ( A = F )
& ( rpoint @ F ) ) )
=> ( rS @ B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(5,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( rless @ ( vplus @ ( vangle @ A @ B @ C ) @ ( vangle @ B @ C @ D ) ) @ ( vplus @ vperp @ vperp ) )
& ( rS @ A @ D @ G )
& ( B != C )
& ( ron @ D @ H )
& ( ron @ C @ H )
& ( ron @ C @ G )
& ( ron @ B @ G )
& ( ron @ B @ F )
& ( ron @ A @ F )
& ? [I: $i] :
( ( H = I )
& ( rline @ I ) )
& ? [I: $i] :
( ( G = I )
& ( rline @ I ) )
& ? [I: $i] :
( ( F = I )
& ( rline @ I ) )
& ? [I: $i] :
( ( E = I )
& ( rpoint @ I ) )
& ? [I: $i] :
( ( D = I )
& ( rpoint @ I ) )
& ? [I: $i] :
( ( C = I )
& ( rpoint @ I ) )
& ? [I: $i] :
( ( B = I )
& ( rpoint @ I ) )
& ? [I: $i] :
( ( A = I )
& ( rpoint @ I ) ) )
=> ( ( ( ( ron @ E @ G )
& ( ron @ E @ F ) )
=> ( rS @ E @ A @ G ) )
& ( rintersect @ F @ G ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(196), 0), imp(cond(axiom(196), 0)))') ).
thf(192,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( rless @ ( vplus @ ( vangle @ A @ B @ C ) @ ( vangle @ B @ C @ D ) ) @ ( vplus @ vperp @ vperp ) )
& ( rS @ A @ D @ G )
& ( B != C )
& ( ron @ D @ H )
& ( ron @ C @ H )
& ( ron @ C @ G )
& ( ron @ B @ G )
& ( ron @ B @ F )
& ( ron @ A @ F )
& ? [I: $i] :
( ( H = I )
& ( rline @ I ) )
& ? [I: $i] :
( ( G = I )
& ( rline @ I ) )
& ? [I: $i] :
( ( F = I )
& ( rline @ I ) )
& ? [I: $i] :
( ( E = I )
& ( rpoint @ I ) )
& ? [I: $i] :
( ( D = I )
& ( rpoint @ I ) )
& ? [I: $i] :
( ( C = I )
& ( rpoint @ I ) )
& ? [I: $i] :
( ( B = I )
& ( rpoint @ I ) )
& ? [I: $i] :
( ( A = I )
& ( rpoint @ I ) ) )
=> ( ( ( ( ron @ E @ G )
& ( ron @ E @ F ) )
=> ( rS @ E @ A @ G ) )
& ( rintersect @ F @ G ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(78,axiom,
! [A: $i,B: $i] :
( ( ( A = B )
& ( rpoint @ B ) )
=> ? [C: $i] :
( ( C != A )
& ( rpoint @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(7), 0), imp(cond(axiom(7), 0)))') ).
thf(788,plain,
! [A: $i,B: $i] :
( ( ( A = B )
& ( rpoint @ B ) )
=> ? [C: $i] :
( ( C != A )
& ( rpoint @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(23,axiom,
! [A: $i,B: $i] :
( ( rcenter @ A @ B )
=> ( rinside @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(77), 0), imp(cond(axiom(77), 0)))') ).
thf(329,plain,
! [A: $i,B: $i] :
( ( rcenter @ A @ B )
=> ( rinside @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(63,axiom,
rreal @ vd684,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pred(axiom(137), 1)') ).
thf(665,plain,
rreal @ vd684,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(127,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( rR @ B @ A @ C )
& ? [D: $i] :
( ( C = D )
& ( rpoint @ D ) )
& ? [D: $i] :
( ( B = D )
& ( rpoint @ D ) )
& ? [D: $i] :
( ( A = D )
& ( rpoint @ D ) ) )
=> ( ( vplus @ ( vf @ A @ B ) @ ( vf @ B @ C ) )
= ( vf @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(180), 0), imp(cond(axiom(180), 0)))') ).
thf(1291,plain,
! [A: $i,B: $i,C: $i] :
( ( ( rR @ B @ A @ C )
& ? [D: $i] :
( ( C = D )
& ( rpoint @ D ) )
& ? [D: $i] :
( ( B = D )
& ( rpoint @ D ) )
& ? [D: $i] :
( ( A = D )
& ( rpoint @ D ) ) )
=> ( ( vplus @ ( vf @ A @ B ) @ ( vf @ B @ C ) )
= ( vf @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(86,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ~ ( ron @ G @ C )
& ( ron @ F @ C )
& ( ron @ E @ C )
& ( rcenter @ F @ B )
& ( rcenter @ E @ A )
& ( rintersect @ A @ B )
& ( C = D )
& ( rline @ D )
& ? [H: $i] :
( ( B = H )
& ( rcircle @ H ) )
& ? [H: $i] :
( ( A = H )
& ( rcircle @ H ) ) )
=> ? [H: $i] :
( ~ ( rS @ H @ G @ C )
& ( ron @ H @ B )
& ( ron @ H @ A )
& ( rpoint @ H ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(71), 0), imp(cond(axiom(71), 0)))') ).
thf(842,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ~ ( ron @ G @ C )
& ( ron @ F @ C )
& ( ron @ E @ C )
& ( rcenter @ F @ B )
& ( rcenter @ E @ A )
& ( rintersect @ A @ B )
& ( C = D )
& ( rline @ D )
& ? [H: $i] :
( ( B = H )
& ( rcircle @ H ) )
& ? [H: $i] :
( ( A = H )
& ( rcircle @ H ) ) )
=> ? [H: $i] :
( ~ ( rS @ H @ G @ C )
& ( ron @ H @ B )
& ( ron @ H @ A )
& ( rpoint @ H ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(16,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( rless @ C @ E )
& ( rless @ A @ C )
& ( E = F )
& ( rreal @ F )
& ( C = D )
& ( rreal @ D )
& ( A = B )
& ( rreal @ B ) )
=> ( rless @ A @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(151), 0), imp(cond(axiom(151), 0)))') ).
thf(285,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( rless @ C @ E )
& ( rless @ A @ C )
& ( E = F )
& ( rreal @ F )
& ( C = D )
& ( rreal @ D )
& ( A = B )
& ( rreal @ B ) )
=> ( rless @ A @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(136,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ? [G: $i] :
( ( ron @ F @ G )
& ( ron @ E @ G )
& ( ron @ D @ G )
& ( rline @ G ) )
& ( ( vangle @ B @ A @ C )
= ( vangle @ E @ D @ F ) )
& ( ( vf @ A @ C )
= ( vf @ D @ F ) )
& ( ( vf @ A @ B )
= ( vf @ D @ E ) )
& ? [G: $i] :
( ( F = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( E = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( D = G )
& ( rpoint @ G ) )
& ( B != C )
& ( A != C )
& ( A != B )
& ? [G: $i] :
( ( C = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( B = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( A = G )
& ( rpoint @ G ) ) )
=> ! [G: $i,H: $i,I: $i] :
( ( ( rS @ I @ F @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) )
& ~ ( rR @ E @ G @ D )
& ( ron @ G @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) )
& ( H = E )
& ( ( vf @ A @ C )
= ( vf @ G @ I ) )
& ( ( vf @ B @ C )
= ( vf @ H @ I ) )
& ( ( vf @ A @ B )
= ( vf @ G @ H ) )
& ( ( vangle @ I @ H @ G )
= ( vangle @ C @ B @ A ) )
& ( ( vangle @ G @ I @ H )
= ( vangle @ A @ C @ B ) )
& ( ( vangle @ H @ G @ I )
= ( vangle @ B @ A @ C ) )
& ? [J: $i] :
( ( I = J )
& ( rpoint @ J ) )
& ? [J: $i] :
( ( H = J )
& ( rpoint @ J ) )
& ? [J: $i] :
( ( G = J )
& ( rpoint @ J ) ) )
=> ( ( G != D )
=> ( ( rR @ D @ G @ E )
| ( rR @ G @ D @ E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(proof(267), 0), 30)') ).
thf(1402,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ? [G: $i] :
( ( ron @ F @ G )
& ( ron @ E @ G )
& ( ron @ D @ G )
& ( rline @ G ) )
& ( ( vangle @ B @ A @ C )
= ( vangle @ E @ D @ F ) )
& ( ( vf @ A @ C )
= ( vf @ D @ F ) )
& ( ( vf @ A @ B )
= ( vf @ D @ E ) )
& ? [G: $i] :
( ( F = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( E = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( D = G )
& ( rpoint @ G ) )
& ( B != C )
& ( A != C )
& ( A != B )
& ? [G: $i] :
( ( C = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( B = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( A = G )
& ( rpoint @ G ) ) )
=> ! [G: $i,H: $i,I: $i] :
( ( ( rS @ I @ F @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) )
& ~ ( rR @ E @ G @ D )
& ( ron @ G @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) )
& ( H = E )
& ( ( vf @ A @ C )
= ( vf @ G @ I ) )
& ( ( vf @ B @ C )
= ( vf @ H @ I ) )
& ( ( vf @ A @ B )
= ( vf @ G @ H ) )
& ( ( vangle @ I @ H @ G )
= ( vangle @ C @ B @ A ) )
& ( ( vangle @ G @ I @ H )
= ( vangle @ A @ C @ B ) )
& ( ( vangle @ H @ G @ I )
= ( vangle @ B @ A @ C ) )
& ? [J: $i] :
( ( I = J )
& ( rpoint @ J ) )
& ? [J: $i] :
( ( H = J )
& ( rpoint @ J ) )
& ? [J: $i] :
( ( G = J )
& ( rpoint @ J ) ) )
=> ( ( G != D )
=> ( ( rR @ D @ G @ E )
| ( rR @ G @ D @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(132,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ? [G: $i] :
( ( ron @ F @ G )
& ( ron @ E @ G )
& ( ron @ D @ G )
& ( rline @ G ) )
& ( ( vangle @ B @ A @ C )
= ( vangle @ E @ D @ F ) )
& ( ( vf @ A @ C )
= ( vf @ D @ F ) )
& ( ( vf @ A @ B )
= ( vf @ D @ E ) )
& ? [G: $i] :
( ( F = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( E = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( D = G )
& ( rpoint @ G ) )
& ( B != C )
& ( A != C )
& ( A != B )
& ? [G: $i] :
( ( C = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( B = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( A = G )
& ( rpoint @ G ) ) )
=> ! [G: $i,H: $i,I: $i] :
( ( ( rS @ I @ F @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) )
& ~ ( rR @ E @ G @ D )
& ( ron @ G @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) )
& ( H = E )
& ( ( vf @ A @ C )
= ( vf @ G @ I ) )
& ( ( vf @ B @ C )
= ( vf @ H @ I ) )
& ( ( vf @ A @ B )
= ( vf @ G @ H ) )
& ( ( vangle @ I @ H @ G )
= ( vangle @ C @ B @ A ) )
& ( ( vangle @ G @ I @ H )
= ( vangle @ A @ C @ B ) )
& ( ( vangle @ H @ G @ I )
= ( vangle @ B @ A @ C ) )
& ? [J: $i] :
( ( I = J )
& ( rpoint @ J ) )
& ? [J: $i] :
( ( H = J )
& ( rpoint @ J ) )
& ? [J: $i] :
( ( G = J )
& ( rpoint @ J ) ) )
=> ( ron @ D @ ( vskolem1232 @ G @ H @ I @ A @ B @ C @ D @ E @ F ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(proof(267), 0), 26)') ).
thf(1350,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ? [G: $i] :
( ( ron @ F @ G )
& ( ron @ E @ G )
& ( ron @ D @ G )
& ( rline @ G ) )
& ( ( vangle @ B @ A @ C )
= ( vangle @ E @ D @ F ) )
& ( ( vf @ A @ C )
= ( vf @ D @ F ) )
& ( ( vf @ A @ B )
= ( vf @ D @ E ) )
& ? [G: $i] :
( ( F = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( E = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( D = G )
& ( rpoint @ G ) )
& ( B != C )
& ( A != C )
& ( A != B )
& ? [G: $i] :
( ( C = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( B = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( A = G )
& ( rpoint @ G ) ) )
=> ! [G: $i,H: $i,I: $i] :
( ( ( rS @ I @ F @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) )
& ~ ( rR @ E @ G @ D )
& ( ron @ G @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) )
& ( H = E )
& ( ( vf @ A @ C )
= ( vf @ G @ I ) )
& ( ( vf @ B @ C )
= ( vf @ H @ I ) )
& ( ( vf @ A @ B )
= ( vf @ G @ H ) )
& ( ( vangle @ I @ H @ G )
= ( vangle @ C @ B @ A ) )
& ( ( vangle @ G @ I @ H )
= ( vangle @ A @ C @ B ) )
& ( ( vangle @ H @ G @ I )
= ( vangle @ B @ A @ C ) )
& ? [J: $i] :
( ( I = J )
& ( rpoint @ J ) )
& ? [J: $i] :
( ( H = J )
& ( rpoint @ J ) )
& ? [J: $i] :
( ( G = J )
& ( rpoint @ J ) ) )
=> ( ron @ D @ ( vskolem1232 @ G @ H @ I @ A @ B @ C @ D @ E @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(110,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ? [G: $i] :
( ( ron @ F @ G )
& ( ron @ E @ G )
& ( ron @ D @ G )
& ( rline @ G ) )
& ( ( vangle @ B @ A @ C )
= ( vangle @ E @ D @ F ) )
& ( ( vf @ A @ C )
= ( vf @ D @ F ) )
& ( ( vf @ A @ B )
= ( vf @ D @ E ) )
& ? [G: $i] :
( ( F = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( E = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( D = G )
& ( rpoint @ G ) )
& ( B != C )
& ( A != C )
& ( A != B )
& ? [G: $i] :
( ( C = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( B = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( A = G )
& ( rpoint @ G ) ) )
=> ! [G: $i,H: $i,I: $i] :
( ( ( rS @ I @ F @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) )
& ~ ( rR @ E @ G @ D )
& ( ron @ G @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) )
& ( H = E )
& ( ( vf @ A @ C )
= ( vf @ G @ I ) )
& ( ( vf @ B @ C )
= ( vf @ H @ I ) )
& ( ( vf @ A @ B )
= ( vf @ G @ H ) )
& ( ( vangle @ I @ H @ G )
= ( vangle @ C @ B @ A ) )
& ( ( vangle @ G @ I @ H )
= ( vangle @ A @ C @ B ) )
& ( ( vangle @ H @ G @ I )
= ( vangle @ B @ A @ C ) )
& ? [J: $i] :
( ( I = J )
& ( rpoint @ J ) )
& ? [J: $i] :
( ( H = J )
& ( rpoint @ J ) )
& ? [J: $i] :
( ( G = J )
& ( rpoint @ J ) ) )
=> ( ron @ I @ ( vskolem1232 @ G @ H @ I @ A @ B @ C @ D @ E @ F ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(proof(267), 0), 14)') ).
thf(1089,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ? [G: $i] :
( ( ron @ F @ G )
& ( ron @ E @ G )
& ( ron @ D @ G )
& ( rline @ G ) )
& ( ( vangle @ B @ A @ C )
= ( vangle @ E @ D @ F ) )
& ( ( vf @ A @ C )
= ( vf @ D @ F ) )
& ( ( vf @ A @ B )
= ( vf @ D @ E ) )
& ? [G: $i] :
( ( F = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( E = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( D = G )
& ( rpoint @ G ) )
& ( B != C )
& ( A != C )
& ( A != B )
& ? [G: $i] :
( ( C = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( B = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( A = G )
& ( rpoint @ G ) ) )
=> ! [G: $i,H: $i,I: $i] :
( ( ( rS @ I @ F @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) )
& ~ ( rR @ E @ G @ D )
& ( ron @ G @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) )
& ( H = E )
& ( ( vf @ A @ C )
= ( vf @ G @ I ) )
& ( ( vf @ B @ C )
= ( vf @ H @ I ) )
& ( ( vf @ A @ B )
= ( vf @ G @ H ) )
& ( ( vangle @ I @ H @ G )
= ( vangle @ C @ B @ A ) )
& ( ( vangle @ G @ I @ H )
= ( vangle @ A @ C @ B ) )
& ( ( vangle @ H @ G @ I )
= ( vangle @ B @ A @ C ) )
& ? [J: $i] :
( ( I = J )
& ( rpoint @ J ) )
& ? [J: $i] :
( ( H = J )
& ( rpoint @ J ) )
& ? [J: $i] :
( ( G = J )
& ( rpoint @ J ) ) )
=> ( ron @ I @ ( vskolem1232 @ G @ H @ I @ A @ B @ C @ D @ E @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(90,axiom,
v0 = vd684,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pred(axiom(137), 2)') ).
thf(874,plain,
v0 = vd684,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(102,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ? [G: $i] :
( ( ron @ F @ G )
& ( ron @ E @ G )
& ( ron @ D @ G )
& ( rline @ G ) )
& ( ( vangle @ B @ A @ C )
= ( vangle @ E @ D @ F ) )
& ( ( vf @ A @ C )
= ( vf @ D @ F ) )
& ( ( vf @ A @ B )
= ( vf @ D @ E ) )
& ? [G: $i] :
( ( F = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( E = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( D = G )
& ( rpoint @ G ) )
& ( B != C )
& ( A != C )
& ( A != B )
& ? [G: $i] :
( ( C = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( B = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( A = G )
& ( rpoint @ G ) ) )
=> ! [G: $i,H: $i,I: $i] :
( ( ( rS @ I @ F @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) )
& ~ ( rR @ E @ G @ D )
& ( ron @ G @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) )
& ( H = E )
& ( ( vf @ A @ C )
= ( vf @ G @ I ) )
& ( ( vf @ B @ C )
= ( vf @ H @ I ) )
& ( ( vf @ A @ B )
= ( vf @ G @ H ) )
& ( ( vangle @ I @ H @ G )
= ( vangle @ C @ B @ A ) )
& ( ( vangle @ G @ I @ H )
= ( vangle @ A @ C @ B ) )
& ( ( vangle @ H @ G @ I )
= ( vangle @ B @ A @ C ) )
& ? [J: $i] :
( ( I = J )
& ( rpoint @ J ) )
& ? [J: $i] :
( ( H = J )
& ( rpoint @ J ) )
& ? [J: $i] :
( ( G = J )
& ( rpoint @ J ) ) )
=> ( ( I != F )
=> ( ( rR @ I @ D @ F )
| ( rR @ F @ D @ I ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(proof(267), 0), 10)') ).
thf(1017,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ? [G: $i] :
( ( ron @ F @ G )
& ( ron @ E @ G )
& ( ron @ D @ G )
& ( rline @ G ) )
& ( ( vangle @ B @ A @ C )
= ( vangle @ E @ D @ F ) )
& ( ( vf @ A @ C )
= ( vf @ D @ F ) )
& ( ( vf @ A @ B )
= ( vf @ D @ E ) )
& ? [G: $i] :
( ( F = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( E = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( D = G )
& ( rpoint @ G ) )
& ( B != C )
& ( A != C )
& ( A != B )
& ? [G: $i] :
( ( C = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( B = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( A = G )
& ( rpoint @ G ) ) )
=> ! [G: $i,H: $i,I: $i] :
( ( ( rS @ I @ F @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) )
& ~ ( rR @ E @ G @ D )
& ( ron @ G @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) )
& ( H = E )
& ( ( vf @ A @ C )
= ( vf @ G @ I ) )
& ( ( vf @ B @ C )
= ( vf @ H @ I ) )
& ( ( vf @ A @ B )
= ( vf @ G @ H ) )
& ( ( vangle @ I @ H @ G )
= ( vangle @ C @ B @ A ) )
& ( ( vangle @ G @ I @ H )
= ( vangle @ A @ C @ B ) )
& ( ( vangle @ H @ G @ I )
= ( vangle @ B @ A @ C ) )
& ? [J: $i] :
( ( I = J )
& ( rpoint @ J ) )
& ? [J: $i] :
( ( H = J )
& ( rpoint @ J ) )
& ? [J: $i] :
( ( G = J )
& ( rpoint @ J ) ) )
=> ( ( I != F )
=> ( ( rR @ I @ D @ F )
| ( rR @ F @ D @ I ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(149,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C = D )
& ( A != C )
& ( rpoint @ D )
& ( A = B )
& ( rpoint @ B ) )
=> ( ( vf @ C @ ( vskolem1052 @ A @ B @ C @ D ) )
= ( vf @ ( vskolem1052 @ A @ B @ C @ D ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(206), 0), 0)') ).
thf(1540,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C = D )
& ( A != C )
& ( rpoint @ D )
& ( A = B )
& ( rpoint @ B ) )
=> ( ( vf @ C @ ( vskolem1052 @ A @ B @ C @ D ) )
= ( vf @ ( vskolem1052 @ A @ B @ C @ D ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(109,axiom,
! [A: $i,B: $i] :
( ( ? [C: $i] :
( ( B = C )
& ( rpoint @ C ) )
& ? [C: $i] :
( ( A = C )
& ( rpoint @ C ) ) )
=> ? [C: $i] :
( ( ( vf @ A @ B )
= C )
& ( rreal @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(160), 0), imp(cond(axiom(160), 0)))') ).
thf(1082,plain,
! [A: $i,B: $i] :
( ( ? [C: $i] :
( ( B = C )
& ( rpoint @ C ) )
& ? [C: $i] :
( ( A = C )
& ( rpoint @ C ) ) )
=> ? [C: $i] :
( ( ( vf @ A @ B )
= C )
& ( rreal @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(40,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ( ron @ D @ E )
& ( rR @ C @ A @ B )
& ( E = F )
& ( rline @ F )
& ? [G: $i] :
( ( D = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( C = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( B = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( A = G )
& ( rpoint @ G ) ) )
=> ( ( ( vangle @ A @ C @ D )
= ( vangle @ D @ C @ B ) )
<=> ( ( vangle @ A @ C @ D )
= vperp ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(192), 0), imp(cond(axiom(192), 0)))') ).
thf(488,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ( ron @ D @ E )
& ( rR @ C @ A @ B )
& ( E = F )
& ( rline @ F )
& ? [G: $i] :
( ( D = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( C = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( B = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( A = G )
& ( rpoint @ G ) ) )
=> ( ( ( ( vangle @ A @ C @ D )
= ( vangle @ D @ C @ B ) )
=> ( ( vangle @ A @ C @ D )
= vperp ) )
& ( ( ( vangle @ A @ C @ D )
= vperp )
=> ( ( vangle @ A @ C @ D )
= ( vangle @ D @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(46,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( ron @ A @ E )
& ( rinside @ A @ C )
& ( E = F )
& ( rline @ F )
& ( C = D )
& ( rcircle @ D )
& ( A = B )
& ( rpoint @ B ) )
=> ( rintersect @ E @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(131), 0), imp(cond(axiom(131), 0)))') ).
thf(554,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( ron @ A @ E )
& ( rinside @ A @ C )
& ( E = F )
& ( rline @ F )
& ( C = D )
& ( rcircle @ D )
& ( A = B )
& ( rpoint @ B ) )
=> ( rintersect @ E @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(38,axiom,
rpoint @ vd14,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pred(axiom(5), 0)') ).
thf(476,plain,
rpoint @ vd14,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(115,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ? [G: $i] :
( ( ron @ F @ G )
& ( ron @ E @ G )
& ( ron @ D @ G )
& ( rline @ G ) )
& ( ( vangle @ B @ A @ C )
= ( vangle @ E @ D @ F ) )
& ( ( vf @ A @ C )
= ( vf @ D @ F ) )
& ( ( vf @ A @ B )
= ( vf @ D @ E ) )
& ? [G: $i] :
( ( F = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( E = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( D = G )
& ( rpoint @ G ) )
& ( B != C )
& ( A != C )
& ( A != B )
& ? [G: $i] :
( ( C = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( B = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( A = G )
& ( rpoint @ G ) ) )
=> ! [G: $i,H: $i,I: $i] :
( ( ( rS @ I @ F @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) )
& ~ ( rR @ E @ G @ D )
& ( ron @ G @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) )
& ( H = E )
& ( ( vf @ A @ C )
= ( vf @ G @ I ) )
& ( ( vf @ B @ C )
= ( vf @ H @ I ) )
& ( ( vf @ A @ B )
= ( vf @ G @ H ) )
& ( ( vangle @ I @ H @ G )
= ( vangle @ C @ B @ A ) )
& ( ( vangle @ G @ I @ H )
= ( vangle @ A @ C @ B ) )
& ( ( vangle @ H @ G @ I )
= ( vangle @ B @ A @ C ) )
& ? [J: $i] :
( ( I = J )
& ( rpoint @ J ) )
& ? [J: $i] :
( ( H = J )
& ( rpoint @ J ) )
& ? [J: $i] :
( ( G = J )
& ( rpoint @ J ) ) )
=> ( ( vangle @ D @ E @ F )
= ( vangle @ A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(proof(267), 0), 4)') ).
thf(1150,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ? [G: $i] :
( ( ron @ F @ G )
& ( ron @ E @ G )
& ( ron @ D @ G )
& ( rline @ G ) )
& ( ( vangle @ B @ A @ C )
= ( vangle @ E @ D @ F ) )
& ( ( vf @ A @ C )
= ( vf @ D @ F ) )
& ( ( vf @ A @ B )
= ( vf @ D @ E ) )
& ? [G: $i] :
( ( F = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( E = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( D = G )
& ( rpoint @ G ) )
& ( B != C )
& ( A != C )
& ( A != B )
& ? [G: $i] :
( ( C = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( B = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( A = G )
& ( rpoint @ G ) ) )
=> ! [G: $i,H: $i,I: $i] :
( ( ( rS @ I @ F @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) )
& ~ ( rR @ E @ G @ D )
& ( ron @ G @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) )
& ( H = E )
& ( ( vf @ A @ C )
= ( vf @ G @ I ) )
& ( ( vf @ B @ C )
= ( vf @ H @ I ) )
& ( ( vf @ A @ B )
= ( vf @ G @ H ) )
& ( ( vangle @ I @ H @ G )
= ( vangle @ C @ B @ A ) )
& ( ( vangle @ G @ I @ H )
= ( vangle @ A @ C @ B ) )
& ( ( vangle @ H @ G @ I )
= ( vangle @ B @ A @ C ) )
& ? [J: $i] :
( ( I = J )
& ( rpoint @ J ) )
& ? [J: $i] :
( ( H = J )
& ( rpoint @ J ) )
& ? [J: $i] :
( ( G = J )
& ( rpoint @ J ) ) )
=> ( ( vangle @ D @ E @ F )
= ( vangle @ A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(141,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ? [G: $i] :
( ( ron @ F @ G )
& ( ron @ E @ G )
& ( ron @ D @ G )
& ( rline @ G ) )
& ( ( vangle @ B @ A @ C )
= ( vangle @ E @ D @ F ) )
& ( ( vf @ A @ C )
= ( vf @ D @ F ) )
& ( ( vf @ A @ B )
= ( vf @ D @ E ) )
& ? [G: $i] :
( ( F = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( E = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( D = G )
& ( rpoint @ G ) )
& ( B != C )
& ( A != C )
& ( A != B )
& ? [G: $i] :
( ( C = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( B = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( A = G )
& ( rpoint @ G ) ) )
=> ! [G: $i,H: $i,I: $i] :
( ( ( rS @ I @ F @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) )
& ~ ( rR @ E @ G @ D )
& ( ron @ G @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) )
& ( H = E )
& ( ( vf @ A @ C )
= ( vf @ G @ I ) )
& ( ( vf @ B @ C )
= ( vf @ H @ I ) )
& ( ( vf @ A @ B )
= ( vf @ G @ H ) )
& ( ( vangle @ I @ H @ G )
= ( vangle @ C @ B @ A ) )
& ( ( vangle @ G @ I @ H )
= ( vangle @ A @ C @ B ) )
& ( ( vangle @ H @ G @ I )
= ( vangle @ B @ A @ C ) )
& ? [J: $i] :
( ( I = J )
& ( rpoint @ J ) )
& ? [J: $i] :
( ( H = J )
& ( rpoint @ J ) )
& ? [J: $i] :
( ( G = J )
& ( rpoint @ J ) ) )
=> ( ron @ F @ ( vskolem1232 @ G @ H @ I @ A @ B @ C @ D @ E @ F ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(proof(267), 0), 25)') ).
thf(1451,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ? [G: $i] :
( ( ron @ F @ G )
& ( ron @ E @ G )
& ( ron @ D @ G )
& ( rline @ G ) )
& ( ( vangle @ B @ A @ C )
= ( vangle @ E @ D @ F ) )
& ( ( vf @ A @ C )
= ( vf @ D @ F ) )
& ( ( vf @ A @ B )
= ( vf @ D @ E ) )
& ? [G: $i] :
( ( F = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( E = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( D = G )
& ( rpoint @ G ) )
& ( B != C )
& ( A != C )
& ( A != B )
& ? [G: $i] :
( ( C = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( B = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( A = G )
& ( rpoint @ G ) ) )
=> ! [G: $i,H: $i,I: $i] :
( ( ( rS @ I @ F @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) )
& ~ ( rR @ E @ G @ D )
& ( ron @ G @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) )
& ( H = E )
& ( ( vf @ A @ C )
= ( vf @ G @ I ) )
& ( ( vf @ B @ C )
= ( vf @ H @ I ) )
& ( ( vf @ A @ B )
= ( vf @ G @ H ) )
& ( ( vangle @ I @ H @ G )
= ( vangle @ C @ B @ A ) )
& ( ( vangle @ G @ I @ H )
= ( vangle @ A @ C @ B ) )
& ( ( vangle @ H @ G @ I )
= ( vangle @ B @ A @ C ) )
& ? [J: $i] :
( ( I = J )
& ( rpoint @ J ) )
& ? [J: $i] :
( ( H = J )
& ( rpoint @ J ) )
& ? [J: $i] :
( ( G = J )
& ( rpoint @ J ) ) )
=> ( ron @ F @ ( vskolem1232 @ G @ H @ I @ A @ B @ C @ D @ E @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(123,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ? [G: $i] :
( ( ron @ F @ G )
& ( ron @ E @ G )
& ( ron @ D @ G )
& ( rline @ G ) )
& ( ( vangle @ B @ A @ C )
= ( vangle @ E @ D @ F ) )
& ( ( vf @ A @ C )
= ( vf @ D @ F ) )
& ( ( vf @ A @ B )
= ( vf @ D @ E ) )
& ? [G: $i] :
( ( F = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( E = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( D = G )
& ( rpoint @ G ) )
& ( B != C )
& ( A != C )
& ( A != B )
& ? [G: $i] :
( ( C = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( B = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( A = G )
& ( rpoint @ G ) ) )
=> ! [G: $i,H: $i,I: $i] :
( ( ( rS @ I @ F @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) )
& ~ ( rR @ E @ G @ D )
& ( ron @ G @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) )
& ( H = E )
& ( ( vf @ A @ C )
= ( vf @ G @ I ) )
& ( ( vf @ B @ C )
= ( vf @ H @ I ) )
& ( ( vf @ A @ B )
= ( vf @ G @ H ) )
& ( ( vangle @ I @ H @ G )
= ( vangle @ C @ B @ A ) )
& ( ( vangle @ G @ I @ H )
= ( vangle @ A @ C @ B ) )
& ( ( vangle @ H @ G @ I )
= ( vangle @ B @ A @ C ) )
& ? [J: $i] :
( ( I = J )
& ( rpoint @ J ) )
& ? [J: $i] :
( ( H = J )
& ( rpoint @ J ) )
& ? [J: $i] :
( ( G = J )
& ( rpoint @ J ) ) )
=> ( ron @ H @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(proof(267), 0), 35)') ).
thf(1246,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ? [G: $i] :
( ( ron @ F @ G )
& ( ron @ E @ G )
& ( ron @ D @ G )
& ( rline @ G ) )
& ( ( vangle @ B @ A @ C )
= ( vangle @ E @ D @ F ) )
& ( ( vf @ A @ C )
= ( vf @ D @ F ) )
& ( ( vf @ A @ B )
= ( vf @ D @ E ) )
& ? [G: $i] :
( ( F = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( E = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( D = G )
& ( rpoint @ G ) )
& ( B != C )
& ( A != C )
& ( A != B )
& ? [G: $i] :
( ( C = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( B = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( A = G )
& ( rpoint @ G ) ) )
=> ! [G: $i,H: $i,I: $i] :
( ( ( rS @ I @ F @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) )
& ~ ( rR @ E @ G @ D )
& ( ron @ G @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) )
& ( H = E )
& ( ( vf @ A @ C )
= ( vf @ G @ I ) )
& ( ( vf @ B @ C )
= ( vf @ H @ I ) )
& ( ( vf @ A @ B )
= ( vf @ G @ H ) )
& ( ( vangle @ I @ H @ G )
= ( vangle @ C @ B @ A ) )
& ( ( vangle @ G @ I @ H )
= ( vangle @ A @ C @ B ) )
& ( ( vangle @ H @ G @ I )
= ( vangle @ B @ A @ C ) )
& ? [J: $i] :
( ( I = J )
& ( rpoint @ J ) )
& ? [J: $i] :
( ( H = J )
& ( rpoint @ J ) )
& ? [J: $i] :
( ( G = J )
& ( rpoint @ J ) ) )
=> ( ron @ H @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(13,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( rcenter @ D @ A )
& ( rcenter @ C @ A )
& ( A = B )
& ( rcircle @ B ) )
=> ( C = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(75), 0), imp(cond(axiom(75), 0)))') ).
thf(266,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( rcenter @ D @ A )
& ( rcenter @ C @ A )
& ( A = B )
& ( rcircle @ B ) )
=> ( C = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(7,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( rless @ A @ C )
& ( E = F )
& ( rreal @ F )
& ( C = D )
& ( rreal @ D )
& ( A = B )
& ( rreal @ B ) )
=> ( rless @ ( vplus @ A @ E ) @ ( vplus @ C @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(153), 0), imp(cond(axiom(153), 0)))') ).
thf(205,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( rless @ A @ C )
& ( E = F )
& ( rreal @ F )
& ( C = D )
& ( rreal @ D )
& ( A = B )
& ( rreal @ B ) )
=> ( rless @ ( vplus @ A @ E ) @ ( vplus @ C @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(100,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ? [G: $i] :
( ( ron @ F @ G )
& ( ron @ E @ G )
& ( ron @ D @ G )
& ( rline @ G ) )
& ( ( vangle @ B @ A @ C )
= ( vangle @ E @ D @ F ) )
& ( ( vf @ A @ C )
= ( vf @ D @ F ) )
& ( ( vf @ A @ B )
= ( vf @ D @ E ) )
& ? [G: $i] :
( ( F = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( E = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( D = G )
& ( rpoint @ G ) )
& ( B != C )
& ( A != C )
& ( A != B )
& ? [G: $i] :
( ( C = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( B = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( A = G )
& ( rpoint @ G ) ) )
=> ! [G: $i,H: $i,I: $i] :
( ( ( rS @ I @ F @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) )
& ~ ( rR @ E @ G @ D )
& ( ron @ G @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) )
& ( H = E )
& ( ( vf @ A @ C )
= ( vf @ G @ I ) )
& ( ( vf @ B @ C )
= ( vf @ H @ I ) )
& ( ( vf @ A @ B )
= ( vf @ G @ H ) )
& ( ( vangle @ I @ H @ G )
= ( vangle @ C @ B @ A ) )
& ( ( vangle @ G @ I @ H )
= ( vangle @ A @ C @ B ) )
& ( ( vangle @ H @ G @ I )
= ( vangle @ B @ A @ C ) )
& ? [J: $i] :
( ( I = J )
& ( rpoint @ J ) )
& ? [J: $i] :
( ( H = J )
& ( rpoint @ J ) )
& ? [J: $i] :
( ( G = J )
& ( rpoint @ J ) ) )
=> ( ( G != D )
=> ( ( rR @ G @ D @ E )
| ( rR @ D @ G @ E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(proof(267), 0), 33)') ).
thf(953,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ? [G: $i] :
( ( ron @ F @ G )
& ( ron @ E @ G )
& ( ron @ D @ G )
& ( rline @ G ) )
& ( ( vangle @ B @ A @ C )
= ( vangle @ E @ D @ F ) )
& ( ( vf @ A @ C )
= ( vf @ D @ F ) )
& ( ( vf @ A @ B )
= ( vf @ D @ E ) )
& ? [G: $i] :
( ( F = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( E = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( D = G )
& ( rpoint @ G ) )
& ( B != C )
& ( A != C )
& ( A != B )
& ? [G: $i] :
( ( C = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( B = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( A = G )
& ( rpoint @ G ) ) )
=> ! [G: $i,H: $i,I: $i] :
( ( ( rS @ I @ F @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) )
& ~ ( rR @ E @ G @ D )
& ( ron @ G @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) )
& ( H = E )
& ( ( vf @ A @ C )
= ( vf @ G @ I ) )
& ( ( vf @ B @ C )
= ( vf @ H @ I ) )
& ( ( vf @ A @ B )
= ( vf @ G @ H ) )
& ( ( vangle @ I @ H @ G )
= ( vangle @ C @ B @ A ) )
& ( ( vangle @ G @ I @ H )
= ( vangle @ A @ C @ B ) )
& ( ( vangle @ H @ G @ I )
= ( vangle @ B @ A @ C ) )
& ? [J: $i] :
( ( I = J )
& ( rpoint @ J ) )
& ? [J: $i] :
( ( H = J )
& ( rpoint @ J ) )
& ? [J: $i] :
( ( G = J )
& ( rpoint @ J ) ) )
=> ( ( G != D )
=> ( ( rR @ G @ D @ E )
| ( rR @ D @ G @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(69,axiom,
! [A: $i,B: $i] :
( ( ( A = B )
& ( rline @ B ) )
=> ? [C: $i] :
( ( ron @ C @ A )
& ( rpoint @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(15), 0), imp(cond(axiom(15), 0)))') ).
thf(718,plain,
! [A: $i,B: $i] :
( ( ( A = B )
& ( rline @ B ) )
=> ? [C: $i] :
( ( ron @ C @ A )
& ( rpoint @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(76,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ron @ B @ D )
& ( ron @ B @ C )
& ( ron @ A @ D )
& ( ron @ A @ C )
& ? [E: $i] :
( ( D = E )
& ( rline @ E ) )
& ? [E: $i] :
( ( C = E )
& ( rline @ E ) )
& ( A != B )
& ? [E: $i] :
( ( B = E )
& ( rpoint @ E ) )
& ? [E: $i] :
( ( A = E )
& ( rpoint @ E ) ) )
=> ( C = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(73), 0), imp(cond(axiom(73), 0)))') ).
thf(773,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ron @ B @ D )
& ( ron @ B @ C )
& ( ron @ A @ D )
& ( ron @ A @ C )
& ? [E: $i] :
( ( D = E )
& ( rline @ E ) )
& ? [E: $i] :
( ( C = E )
& ( rline @ E ) )
& ( A != B )
& ? [E: $i] :
( ( B = E )
& ( rpoint @ E ) )
& ? [E: $i] :
( ( A = E )
& ( rpoint @ E ) ) )
=> ( C = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(50,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( rintersect @ C @ A )
& ( C = D )
& ( rline @ D )
& ( A = B )
& ( rcircle @ B ) )
=> ? [E: $i] :
( ( ron @ E @ A )
& ( ron @ E @ C )
& ( rpoint @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(57), 0), imp(cond(axiom(57), 0)))') ).
thf(586,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( rintersect @ C @ A )
& ( C = D )
& ( rline @ D )
& ( A = B )
& ( rcircle @ B ) )
=> ? [E: $i] :
( ( ron @ E @ A )
& ( ron @ E @ C )
& ( rpoint @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(49,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( rR @ F @ C @ D )
& ( rR @ E @ C @ D )
& ( ron @ E @ A )
& ( ron @ D @ A )
& ( ron @ C @ A )
& ? [G: $i] :
( ( F = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( E = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( D = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( C = G )
& ( rpoint @ G ) )
& ( A = B )
& ( rline @ B ) )
=> ? [G: $i] :
( ( G != F )
& ( G != E )
& ( rR @ G @ C @ D )
& ( rpoint @ G ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(27), 0), imp(cond(axiom(27), 0)))') ).
thf(573,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( rR @ F @ C @ D )
& ( rR @ E @ C @ D )
& ( ron @ E @ A )
& ( ron @ D @ A )
& ( ron @ C @ A )
& ? [G: $i] :
( ( F = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( E = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( D = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( C = G )
& ( rpoint @ G ) )
& ( A = B )
& ( rline @ B ) )
=> ? [G: $i] :
( ( G != F )
& ( G != E )
& ( rR @ G @ C @ D )
& ( rpoint @ G ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(71,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( C = D )
& ( E = F )
& ( rS @ E @ C @ A )
& ( rpoint @ F )
& ~ ( ron @ C @ A )
& ( rpoint @ D )
& ( A = B )
& ( rline @ B ) )
=> ? [G: $i] :
( ( G != E )
& ( G != C )
& ( rS @ G @ C @ A )
& ( rpoint @ G ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(35), 0), imp(cond(axiom(35), 0)))') ).
thf(733,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( C = D )
& ( E = F )
& ( rS @ E @ C @ A )
& ( rpoint @ F )
& ~ ( ron @ C @ A )
& ( rpoint @ D )
& ( A = B )
& ( rline @ B ) )
=> ? [G: $i] :
( ( G != E )
& ( G != C )
& ( rS @ G @ C @ A )
& ( rpoint @ G ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(126,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ? [G: $i] :
( ( ron @ F @ G )
& ( ron @ E @ G )
& ( ron @ D @ G )
& ( rline @ G ) )
& ( ( vangle @ B @ A @ C )
= ( vangle @ E @ D @ F ) )
& ( ( vf @ A @ C )
= ( vf @ D @ F ) )
& ( ( vf @ A @ B )
= ( vf @ D @ E ) )
& ? [G: $i] :
( ( F = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( E = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( D = G )
& ( rpoint @ G ) )
& ( B != C )
& ( A != C )
& ( A != B )
& ? [G: $i] :
( ( C = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( B = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( A = G )
& ( rpoint @ G ) ) )
=> ! [G: $i,H: $i,I: $i] :
( ( ( rS @ I @ F @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) )
& ~ ( rR @ E @ G @ D )
& ( ron @ G @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) )
& ( H = E )
& ( ( vf @ A @ C )
= ( vf @ G @ I ) )
& ( ( vf @ B @ C )
= ( vf @ H @ I ) )
& ( ( vf @ A @ B )
= ( vf @ G @ H ) )
& ( ( vangle @ I @ H @ G )
= ( vangle @ C @ B @ A ) )
& ( ( vangle @ G @ I @ H )
= ( vangle @ A @ C @ B ) )
& ( ( vangle @ H @ G @ I )
= ( vangle @ B @ A @ C ) )
& ? [J: $i] :
( ( I = J )
& ( rpoint @ J ) )
& ? [J: $i] :
( ( H = J )
& ( rpoint @ J ) )
& ? [J: $i] :
( ( G = J )
& ( rpoint @ J ) ) )
=> ( ~ ( ron @ I @ ( vskolem1232 @ G @ H @ I @ A @ B @ C @ D @ E @ F ) )
=> ~ ( rS @ H @ F @ ( vskolem1234 @ G @ H @ I @ A @ B @ C @ D @ E @ F ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(proof(267), 0), 19)') ).
thf(1278,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ? [G: $i] :
( ( ron @ F @ G )
& ( ron @ E @ G )
& ( ron @ D @ G )
& ( rline @ G ) )
& ( ( vangle @ B @ A @ C )
= ( vangle @ E @ D @ F ) )
& ( ( vf @ A @ C )
= ( vf @ D @ F ) )
& ( ( vf @ A @ B )
= ( vf @ D @ E ) )
& ? [G: $i] :
( ( F = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( E = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( D = G )
& ( rpoint @ G ) )
& ( B != C )
& ( A != C )
& ( A != B )
& ? [G: $i] :
( ( C = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( B = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( A = G )
& ( rpoint @ G ) ) )
=> ! [G: $i,H: $i,I: $i] :
( ( ( rS @ I @ F @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) )
& ~ ( rR @ E @ G @ D )
& ( ron @ G @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) )
& ( H = E )
& ( ( vf @ A @ C )
= ( vf @ G @ I ) )
& ( ( vf @ B @ C )
= ( vf @ H @ I ) )
& ( ( vf @ A @ B )
= ( vf @ G @ H ) )
& ( ( vangle @ I @ H @ G )
= ( vangle @ C @ B @ A ) )
& ( ( vangle @ G @ I @ H )
= ( vangle @ A @ C @ B ) )
& ( ( vangle @ H @ G @ I )
= ( vangle @ B @ A @ C ) )
& ? [J: $i] :
( ( I = J )
& ( rpoint @ J ) )
& ? [J: $i] :
( ( H = J )
& ( rpoint @ J ) )
& ? [J: $i] :
( ( G = J )
& ( rpoint @ J ) ) )
=> ( ~ ( ron @ I @ ( vskolem1232 @ G @ H @ I @ A @ B @ C @ D @ E @ F ) )
=> ~ ( rS @ H @ F @ ( vskolem1234 @ G @ H @ I @ A @ B @ C @ D @ E @ F ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(19,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( C = D )
& ( E = F )
& ( G = H )
& ( rS @ G @ C @ A )
& ( rpoint @ H )
& ( rS @ E @ C @ A )
& ( rpoint @ F )
& ~ ( ron @ C @ A )
& ( rpoint @ D )
& ( A = B )
& ( rline @ B ) )
=> ? [I: $i] :
( ( I != G )
& ( I != E )
& ( I != C )
& ( rS @ I @ C @ A )
& ( rpoint @ I ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(37), 0), imp(cond(axiom(37), 0)))') ).
thf(298,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( C = D )
& ( E = F )
& ( G = H )
& ( rS @ G @ C @ A )
& ( rpoint @ H )
& ( rS @ E @ C @ A )
& ( rpoint @ F )
& ~ ( ron @ C @ A )
& ( rpoint @ D )
& ( A = B )
& ( rline @ B ) )
=> ? [I: $i] :
( ( I != G )
& ( I != E )
& ( I != C )
& ( rS @ I @ C @ A )
& ( rpoint @ I ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(95,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C = D )
& ( rreal @ D )
& ( A = B )
& ( rreal @ B ) )
=> ( ( vplus @ A @ C )
= ( vplus @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(143), 0), imp(cond(axiom(143), 0)))') ).
thf(904,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C = D )
& ( rreal @ D )
& ( A = B )
& ( rreal @ B ) )
=> ( ( vplus @ A @ C )
= ( vplus @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(32,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ? [E: $i] : ( rS @ A @ B @ E )
& ( ( ron @ B @ C )
| ( rinside @ B @ C ) )
& ( ( ron @ A @ C )
| ( rinside @ A @ C ) )
& ? [E: $i] :
( ( D = E )
& ( rcircle @ E ) )
& ? [E: $i] :
( ( C = E )
& ( rcircle @ E ) )
& ? [E: $i] :
( ( B = E )
& ( rpoint @ E ) )
& ? [E: $i] :
( ( A = E )
& ( rpoint @ E ) ) )
=> ? [E: $i] : ( rintersect @ E @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(129), 0), imp(cond(axiom(129), 0)))') ).
thf(402,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ? [E: $i] : ( rS @ A @ B @ E )
& ( ( ron @ B @ C )
| ( rinside @ B @ C ) )
& ( ( ron @ A @ C )
| ( rinside @ A @ C ) )
& ? [E: $i] :
( ( D = E )
& ( rcircle @ E ) )
& ? [E: $i] :
( ( C = E )
& ( rcircle @ E ) )
& ? [E: $i] :
( ( B = E )
& ( rpoint @ E ) )
& ? [E: $i] :
( ( A = E )
& ( rpoint @ E ) ) )
=> ? [E: $i] : ( rintersect @ E @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(135,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ? [G: $i] :
( ( ron @ F @ G )
& ( ron @ E @ G )
& ( ron @ D @ G )
& ( rline @ G ) )
& ( ( vangle @ B @ A @ C )
= ( vangle @ E @ D @ F ) )
& ( ( vf @ A @ C )
= ( vf @ D @ F ) )
& ( ( vf @ A @ B )
= ( vf @ D @ E ) )
& ? [G: $i] :
( ( F = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( E = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( D = G )
& ( rpoint @ G ) )
& ( B != C )
& ( A != C )
& ( A != B )
& ? [G: $i] :
( ( C = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( B = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( A = G )
& ( rpoint @ G ) ) )
=> ! [G: $i,H: $i,I: $i] :
( ( ( rS @ I @ F @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) )
& ~ ( rR @ E @ G @ D )
& ( ron @ G @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) )
& ( H = E )
& ( ( vf @ A @ C )
= ( vf @ G @ I ) )
& ( ( vf @ B @ C )
= ( vf @ H @ I ) )
& ( ( vf @ A @ B )
= ( vf @ G @ H ) )
& ( ( vangle @ I @ H @ G )
= ( vangle @ C @ B @ A ) )
& ( ( vangle @ G @ I @ H )
= ( vangle @ A @ C @ B ) )
& ( ( vangle @ H @ G @ I )
= ( vangle @ B @ A @ C ) )
& ? [J: $i] :
( ( I = J )
& ( rpoint @ J ) )
& ? [J: $i] :
( ( H = J )
& ( rpoint @ J ) )
& ? [J: $i] :
( ( G = J )
& ( rpoint @ J ) ) )
=> ( ~ ( ron @ I @ ( vskolem1232 @ G @ H @ I @ A @ B @ C @ D @ E @ F ) )
=> ( ( rS @ H @ F @ ( vskolem1234 @ G @ H @ I @ A @ B @ C @ D @ E @ F ) )
| ( rS @ E @ I @ ( vskolem1232 @ G @ H @ I @ A @ B @ C @ D @ E @ F ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(proof(267), 0), 18)') ).
thf(1389,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ? [G: $i] :
( ( ron @ F @ G )
& ( ron @ E @ G )
& ( ron @ D @ G )
& ( rline @ G ) )
& ( ( vangle @ B @ A @ C )
= ( vangle @ E @ D @ F ) )
& ( ( vf @ A @ C )
= ( vf @ D @ F ) )
& ( ( vf @ A @ B )
= ( vf @ D @ E ) )
& ? [G: $i] :
( ( F = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( E = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( D = G )
& ( rpoint @ G ) )
& ( B != C )
& ( A != C )
& ( A != B )
& ? [G: $i] :
( ( C = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( B = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( A = G )
& ( rpoint @ G ) ) )
=> ! [G: $i,H: $i,I: $i] :
( ( ( rS @ I @ F @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) )
& ~ ( rR @ E @ G @ D )
& ( ron @ G @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) )
& ( H = E )
& ( ( vf @ A @ C )
= ( vf @ G @ I ) )
& ( ( vf @ B @ C )
= ( vf @ H @ I ) )
& ( ( vf @ A @ B )
= ( vf @ G @ H ) )
& ( ( vangle @ I @ H @ G )
= ( vangle @ C @ B @ A ) )
& ( ( vangle @ G @ I @ H )
= ( vangle @ A @ C @ B ) )
& ( ( vangle @ H @ G @ I )
= ( vangle @ B @ A @ C ) )
& ? [J: $i] :
( ( I = J )
& ( rpoint @ J ) )
& ? [J: $i] :
( ( H = J )
& ( rpoint @ J ) )
& ? [J: $i] :
( ( G = J )
& ( rpoint @ J ) ) )
=> ( ~ ( ron @ I @ ( vskolem1232 @ G @ H @ I @ A @ B @ C @ D @ E @ F ) )
=> ( ( rS @ H @ F @ ( vskolem1234 @ G @ H @ I @ A @ B @ C @ D @ E @ F ) )
| ( rS @ E @ I @ ( vskolem1232 @ G @ H @ I @ A @ B @ C @ D @ E @ F ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(84,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C = D )
& ~ ( ron @ C @ A )
& ( rpoint @ D )
& ( A = B )
& ( rline @ B ) )
=> ? [E: $i] :
( ~ ( rS @ E @ C @ A )
& ( rpoint @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(39), 0), imp(cond(axiom(39), 0)))') ).
thf(826,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C = D )
& ~ ( ron @ C @ A )
& ( rpoint @ D )
& ( A = B )
& ( rline @ B ) )
=> ? [E: $i] :
( ~ ( rS @ E @ C @ A )
& ( rpoint @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(145,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ? [G: $i] :
( ( ron @ F @ G )
& ( ron @ E @ G )
& ( ron @ D @ G )
& ( rline @ G ) )
& ( ( vangle @ B @ A @ C )
= ( vangle @ E @ D @ F ) )
& ( ( vf @ A @ C )
= ( vf @ D @ F ) )
& ( ( vf @ A @ B )
= ( vf @ D @ E ) )
& ? [G: $i] :
( ( F = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( E = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( D = G )
& ( rpoint @ G ) )
& ( B != C )
& ( A != C )
& ( A != B )
& ? [G: $i] :
( ( C = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( B = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( A = G )
& ( rpoint @ G ) ) )
=> ( ( vangle @ D @ F @ E )
= ( vangle @ A @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(proof(267), 0), 0)') ).
thf(1488,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ? [G: $i] :
( ( ron @ F @ G )
& ( ron @ E @ G )
& ( ron @ D @ G )
& ( rline @ G ) )
& ( ( vangle @ B @ A @ C )
= ( vangle @ E @ D @ F ) )
& ( ( vf @ A @ C )
= ( vf @ D @ F ) )
& ( ( vf @ A @ B )
= ( vf @ D @ E ) )
& ? [G: $i] :
( ( F = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( E = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( D = G )
& ( rpoint @ G ) )
& ( B != C )
& ( A != C )
& ( A != B )
& ? [G: $i] :
( ( C = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( B = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( A = G )
& ( rpoint @ G ) ) )
=> ( ( vangle @ D @ F @ E )
= ( vangle @ A @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(28,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( rS @ A @ B @ C )
& ( C = D )
& ( rline @ D )
& ? [E: $i] :
( ( B = E )
& ( rpoint @ E ) )
& ? [E: $i] :
( ( A = E )
& ( rpoint @ E ) ) )
=> ( rS @ B @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(97), 0), imp(cond(axiom(97), 0)))') ).
thf(382,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( rS @ A @ B @ C )
& ( C = D )
& ( rline @ D )
& ? [E: $i] :
( ( B = E )
& ( rpoint @ E ) )
& ? [E: $i] :
( ( A = E )
& ( rpoint @ E ) ) )
=> ( rS @ B @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(68,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( rS @ A @ B @ D )
& ~ ( ron @ C @ D )
& ~ ( ron @ B @ D )
& ~ ( ron @ A @ D )
& ( D = E )
& ( rline @ E )
& ? [F: $i] :
( ( C = F )
& ( rpoint @ F ) )
& ? [F: $i] :
( ( B = F )
& ( rpoint @ F ) )
& ? [F: $i] :
( ( A = F )
& ( rpoint @ F ) ) )
=> ( ( rS @ A @ C @ D )
| ( rS @ B @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(103), 0), imp(cond(axiom(103), 0)))') ).
thf(713,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( rS @ A @ B @ D )
& ~ ( ron @ C @ D )
& ~ ( ron @ B @ D )
& ~ ( ron @ A @ D )
& ( D = E )
& ( rline @ E )
& ? [F: $i] :
( ( C = F )
& ( rpoint @ F ) )
& ? [F: $i] :
( ( B = F )
& ( rpoint @ F ) )
& ? [F: $i] :
( ( A = F )
& ( rpoint @ F ) ) )
=> ( ( rS @ A @ C @ D )
| ( rS @ B @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(156,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ? [G: $i] :
( ( ron @ F @ G )
& ( ron @ E @ G )
& ( ron @ D @ G )
& ( rline @ G ) )
& ( ( vangle @ B @ A @ C )
= ( vangle @ E @ D @ F ) )
& ( ( vf @ A @ C )
= ( vf @ D @ F ) )
& ( ( vf @ A @ B )
= ( vf @ D @ E ) )
& ? [G: $i] :
( ( F = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( E = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( D = G )
& ( rpoint @ G ) )
& ( B != C )
& ( A != C )
& ( A != B )
& ? [G: $i] :
( ( C = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( B = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( A = G )
& ( rpoint @ G ) ) )
=> ! [G: $i,H: $i,I: $i] :
( ( ( rS @ I @ F @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) )
& ~ ( rR @ E @ G @ D )
& ( ron @ G @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) )
& ( H = E )
& ( ( vf @ A @ C )
= ( vf @ G @ I ) )
& ( ( vf @ B @ C )
= ( vf @ H @ I ) )
& ( ( vf @ A @ B )
= ( vf @ G @ H ) )
& ( ( vangle @ I @ H @ G )
= ( vangle @ C @ B @ A ) )
& ( ( vangle @ G @ I @ H )
= ( vangle @ A @ C @ B ) )
& ( ( vangle @ H @ G @ I )
= ( vangle @ B @ A @ C ) )
& ? [J: $i] :
( ( I = J )
& ( rpoint @ J ) )
& ? [J: $i] :
( ( H = J )
& ( rpoint @ J ) )
& ? [J: $i] :
( ( G = J )
& ( rpoint @ J ) ) )
=> ( ( G != D )
=> ~ ( rR @ G @ D @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(proof(267), 0), 32)') ).
thf(1635,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ? [G: $i] :
( ( ron @ F @ G )
& ( ron @ E @ G )
& ( ron @ D @ G )
& ( rline @ G ) )
& ( ( vangle @ B @ A @ C )
= ( vangle @ E @ D @ F ) )
& ( ( vf @ A @ C )
= ( vf @ D @ F ) )
& ( ( vf @ A @ B )
= ( vf @ D @ E ) )
& ? [G: $i] :
( ( F = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( E = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( D = G )
& ( rpoint @ G ) )
& ( B != C )
& ( A != C )
& ( A != B )
& ? [G: $i] :
( ( C = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( B = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( A = G )
& ( rpoint @ G ) ) )
=> ! [G: $i,H: $i,I: $i] :
( ( ( rS @ I @ F @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) )
& ~ ( rR @ E @ G @ D )
& ( ron @ G @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) )
& ( H = E )
& ( ( vf @ A @ C )
= ( vf @ G @ I ) )
& ( ( vf @ B @ C )
= ( vf @ H @ I ) )
& ( ( vf @ A @ B )
= ( vf @ G @ H ) )
& ( ( vangle @ I @ H @ G )
= ( vangle @ C @ B @ A ) )
& ( ( vangle @ G @ I @ H )
= ( vangle @ A @ C @ B ) )
& ( ( vangle @ H @ G @ I )
= ( vangle @ B @ A @ C ) )
& ? [J: $i] :
( ( I = J )
& ( rpoint @ J ) )
& ? [J: $i] :
( ( H = J )
& ( rpoint @ J ) )
& ? [J: $i] :
( ( G = J )
& ( rpoint @ J ) ) )
=> ( ( G != D )
=> ~ ( rR @ G @ D @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(80,axiom,
! [A: $i,B: $i,C: $i] :
( ( ? [D: $i] :
( ( C = D )
& ( rpoint @ D ) )
& ? [D: $i] :
( ( B = D )
& ( rpoint @ D ) )
& ? [D: $i] :
( ( A = D )
& ( rpoint @ D ) ) )
=> ( ( ( vg @ A @ B @ C )
= ( vg @ A @ C @ B ) )
& ( ( vg @ A @ B @ C )
= ( vg @ C @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(176), 0), imp(cond(axiom(176), 0)))') ).
thf(804,plain,
! [A: $i,B: $i,C: $i] :
( ( ? [D: $i] :
( ( C = D )
& ( rpoint @ D ) )
& ? [D: $i] :
( ( B = D )
& ( rpoint @ D ) )
& ? [D: $i] :
( ( A = D )
& ( rpoint @ D ) ) )
=> ( ( ( vg @ A @ B @ C )
= ( vg @ A @ C @ B ) )
& ( ( vg @ A @ B @ C )
= ( vg @ C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(142,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( ( vf @ C @ A )
= ( vf @ C @ B ) )
& ( ron @ B @ E )
& ( ron @ A @ D )
& ( rcenter @ C @ E )
& ( rcenter @ C @ D )
& ? [F: $i] :
( ( B = F )
& ( rpoint @ F ) )
& ? [F: $i] :
( ( A = F )
& ( rpoint @ F ) ) )
=> ( D = E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(182), 0), imp(cond(axiom(182), 0)))') ).
thf(1464,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( ( vf @ C @ A )
= ( vf @ C @ B ) )
& ( ron @ B @ E )
& ( ron @ A @ D )
& ( rcenter @ C @ E )
& ( rcenter @ C @ D )
& ? [F: $i] :
( ( B = F )
& ( rpoint @ F ) )
& ? [F: $i] :
( ( A = F )
& ( rpoint @ F ) ) )
=> ( D = E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(3,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( rintersect @ A @ C )
& ( C = D )
& ( rcircle @ D )
& ( A = B )
& ( rcircle @ B ) )
=> ? [E: $i] :
( ( ron @ E @ C )
& ( ron @ E @ A )
& ( rpoint @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(65), 0), imp(cond(axiom(65), 0)))') ).
thf(159,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( rintersect @ A @ C )
& ( C = D )
& ( rcircle @ D )
& ( A = B )
& ( rcircle @ B ) )
=> ? [E: $i] :
( ( ron @ E @ C )
& ( ron @ E @ A )
& ( rpoint @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(105,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( rless @ ( vf @ E @ G ) @ ( vf @ A @ C ) )
& ( E != G )
& ( A != C )
& ( G = H )
& ( rpoint @ H )
& ( E = F )
& ( rpoint @ F )
& ( C = D )
& ( rpoint @ D )
& ( A = B )
& ( rpoint @ B ) )
=> ( rR @ ( vskolem1120 @ A @ B @ C @ D @ E @ F @ G @ H ) @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(238), 0), 1)') ).
thf(1048,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( rless @ ( vf @ E @ G ) @ ( vf @ A @ C ) )
& ( E != G )
& ( A != C )
& ( G = H )
& ( rpoint @ H )
& ( E = F )
& ( rpoint @ F )
& ( C = D )
& ( rpoint @ D )
& ( A = B )
& ( rpoint @ B ) )
=> ( rR @ ( vskolem1120 @ A @ B @ C @ D @ E @ F @ G @ H ) @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(27,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( rinside @ A @ C )
& ( C = D )
& ( rcircle @ D )
& ( A = B )
& ( rpoint @ B ) )
=> ~ ( ron @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(79), 0), imp(cond(axiom(79), 0)))') ).
thf(377,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( rinside @ A @ C )
& ( C = D )
& ( rcircle @ D )
& ( A = B )
& ( rpoint @ B ) )
=> ~ ( ron @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(134,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ? [G: $i] :
( ( ron @ F @ G )
& ( ron @ E @ G )
& ( ron @ D @ G )
& ( rline @ G ) )
& ( ( vangle @ B @ A @ C )
= ( vangle @ E @ D @ F ) )
& ( ( vf @ A @ C )
= ( vf @ D @ F ) )
& ( ( vf @ A @ B )
= ( vf @ D @ E ) )
& ? [G: $i] :
( ( F = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( E = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( D = G )
& ( rpoint @ G ) )
& ( B != C )
& ( A != C )
& ( A != B )
& ? [G: $i] :
( ( C = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( B = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( A = G )
& ( rpoint @ G ) ) )
=> ! [G: $i,H: $i,I: $i] :
( ( ( rS @ I @ F @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) )
& ~ ( rR @ E @ G @ D )
& ( ron @ G @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) )
& ( H = E )
& ( ( vf @ A @ C )
= ( vf @ G @ I ) )
& ( ( vf @ B @ C )
= ( vf @ H @ I ) )
& ( ( vf @ A @ B )
= ( vf @ G @ H ) )
& ( ( vangle @ I @ H @ G )
= ( vangle @ C @ B @ A ) )
& ( ( vangle @ G @ I @ H )
= ( vangle @ A @ C @ B ) )
& ( ( vangle @ H @ G @ I )
= ( vangle @ B @ A @ C ) )
& ? [J: $i] :
( ( I = J )
& ( rpoint @ J ) )
& ? [J: $i] :
( ( H = J )
& ( rpoint @ J ) )
& ? [J: $i] :
( ( G = J )
& ( rpoint @ J ) ) )
=> ( ron @ D @ ( vskolem1234 @ G @ H @ I @ A @ B @ C @ D @ E @ F ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(proof(267), 0), 23)') ).
thf(1376,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ? [G: $i] :
( ( ron @ F @ G )
& ( ron @ E @ G )
& ( ron @ D @ G )
& ( rline @ G ) )
& ( ( vangle @ B @ A @ C )
= ( vangle @ E @ D @ F ) )
& ( ( vf @ A @ C )
= ( vf @ D @ F ) )
& ( ( vf @ A @ B )
= ( vf @ D @ E ) )
& ? [G: $i] :
( ( F = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( E = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( D = G )
& ( rpoint @ G ) )
& ( B != C )
& ( A != C )
& ( A != B )
& ? [G: $i] :
( ( C = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( B = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( A = G )
& ( rpoint @ G ) ) )
=> ! [G: $i,H: $i,I: $i] :
( ( ( rS @ I @ F @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) )
& ~ ( rR @ E @ G @ D )
& ( ron @ G @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) )
& ( H = E )
& ( ( vf @ A @ C )
= ( vf @ G @ I ) )
& ( ( vf @ B @ C )
= ( vf @ H @ I ) )
& ( ( vf @ A @ B )
= ( vf @ G @ H ) )
& ( ( vangle @ I @ H @ G )
= ( vangle @ C @ B @ A ) )
& ( ( vangle @ G @ I @ H )
= ( vangle @ A @ C @ B ) )
& ( ( vangle @ H @ G @ I )
= ( vangle @ B @ A @ C ) )
& ? [J: $i] :
( ( I = J )
& ( rpoint @ J ) )
& ? [J: $i] :
( ( H = J )
& ( rpoint @ J ) )
& ? [J: $i] :
( ( G = J )
& ( rpoint @ J ) ) )
=> ( ron @ D @ ( vskolem1234 @ G @ H @ I @ A @ B @ C @ D @ E @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(42,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ron @ C @ A )
& ( C = D )
& ( rpoint @ D )
& ( A = B )
& ( rline @ B ) )
=> ? [E: $i] :
( ( E != C )
& ( ron @ E @ A )
& ( rpoint @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(17), 0), imp(cond(axiom(17), 0)))') ).
thf(509,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ron @ C @ A )
& ( C = D )
& ( rpoint @ D )
& ( A = B )
& ( rline @ B ) )
=> ? [E: $i] :
( ( E != C )
& ( ron @ E @ A )
& ( rpoint @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(35,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( rR @ C @ A @ B )
& ( ( ron @ B @ F )
| ( rinside @ B @ F ) )
& ( ( ron @ A @ F )
| ( rinside @ A @ F ) )
& ( F = G )
& ( rcircle @ G )
& ( D = E )
& ( rline @ E )
& ? [H: $i] :
( ( C = H )
& ( rpoint @ H ) )
& ? [H: $i] :
( ( B = H )
& ( rpoint @ H ) )
& ? [H: $i] :
( ( A = H )
& ( rpoint @ H ) ) )
=> ( rinside @ C @ F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(121), 0), imp(cond(axiom(121), 0)))') ).
thf(434,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( rR @ C @ A @ B )
& ( ( ron @ B @ F )
| ( rinside @ B @ F ) )
& ( ( ron @ A @ F )
| ( rinside @ A @ F ) )
& ( F = G )
& ( rcircle @ G )
& ( D = E )
& ( rline @ E )
& ? [H: $i] :
( ( C = H )
& ( rpoint @ H ) )
& ? [H: $i] :
( ( B = H )
& ( rpoint @ H ) )
& ? [H: $i] :
( ( A = H )
& ( rpoint @ H ) ) )
=> ( rinside @ C @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(39,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( E = F )
& ( rR @ D @ C @ E )
& ( rpoint @ F )
& ( ron @ D @ A )
& ( ron @ C @ A )
& ? [G: $i] :
( ( D = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( C = G )
& ( rpoint @ G ) )
& ( A = B )
& ( rline @ B ) )
=> ? [G: $i] :
( ( G != E )
& ( rR @ D @ C @ G )
& ( rpoint @ G ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(31), 0), imp(cond(axiom(31), 0)))') ).
thf(477,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( E = F )
& ( rR @ D @ C @ E )
& ( rpoint @ F )
& ( ron @ D @ A )
& ( ron @ C @ A )
& ? [G: $i] :
( ( D = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( C = G )
& ( rpoint @ G ) )
& ( A = B )
& ( rline @ B ) )
=> ? [G: $i] :
( ( G != E )
& ( rR @ D @ C @ G )
& ( rpoint @ G ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(57,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( rR @ C @ B @ D )
& ( rR @ B @ A @ C )
& ? [E: $i] :
( ( D = E )
& ( rpoint @ E ) )
& ? [E: $i] :
( ( C = E )
& ( rpoint @ E ) )
& ? [E: $i] :
( ( B = E )
& ( rpoint @ E ) )
& ? [E: $i] :
( ( A = E )
& ( rpoint @ E ) ) )
=> ( rR @ B @ A @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(89), 0), imp(cond(axiom(89), 0)))') ).
thf(631,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( rR @ C @ B @ D )
& ( rR @ B @ A @ C )
& ? [E: $i] :
( ( D = E )
& ( rpoint @ E ) )
& ? [E: $i] :
( ( C = E )
& ( rpoint @ E ) )
& ? [E: $i] :
( ( B = E )
& ( rpoint @ E ) )
& ? [E: $i] :
( ( A = E )
& ( rpoint @ E ) ) )
=> ( rR @ B @ A @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(82,axiom,
! [A: $i,B: $i] :
( ( ( A = B )
& ( rreal @ B ) )
=> ~ ( rless @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(149), 0), imp(cond(axiom(149), 0)))') ).
thf(816,plain,
! [A: $i,B: $i] :
( ( ( A = B )
& ( rreal @ B ) )
=> ~ ( rless @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(70,axiom,
! [A: $i,B: $i,C: $i] :
( ( ? [D: $i] :
( ( C = D )
& ( rpoint @ D ) )
& ? [D: $i] :
( ( B = D )
& ( rpoint @ D ) )
& ? [D: $i] :
( ( A = D )
& ( rpoint @ D ) ) )
=> ( ( rleq @ ( vangle @ A @ B @ C ) @ ( vplus @ vperp @ vperp ) )
& ( rleq @ v0 @ ( vangle @ A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(170), 0), imp(cond(axiom(170), 0)))') ).
thf(726,plain,
! [A: $i,B: $i,C: $i] :
( ( ? [D: $i] :
( ( C = D )
& ( rpoint @ D ) )
& ? [D: $i] :
( ( B = D )
& ( rpoint @ D ) )
& ? [D: $i] :
( ( A = D )
& ( rpoint @ D ) ) )
=> ( ( rleq @ ( vangle @ A @ B @ C ) @ ( vplus @ vperp @ vperp ) )
& ( rleq @ v0 @ ( vangle @ A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(43,axiom,
! [A: $i,B: $i,C: $i] :
( ( ? [D: $i] :
( ( C = D )
& ( rpoint @ D ) )
& ? [D: $i] :
( ( B = D )
& ( rpoint @ D ) )
& ? [D: $i] :
( ( A = D )
& ( rpoint @ D ) ) )
=> ? [D: $i] :
( ( ( vg @ A @ B @ C )
= D )
& ( rreal @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(198), 0), imp(cond(axiom(198), 0)))') ).
thf(520,plain,
! [A: $i,B: $i,C: $i] :
( ( ? [D: $i] :
( ( C = D )
& ( rpoint @ D ) )
& ? [D: $i] :
( ( B = D )
& ( rpoint @ D ) )
& ? [D: $i] :
( ( A = D )
& ( rpoint @ D ) ) )
=> ? [D: $i] :
( ( ( vg @ A @ B @ C )
= D )
& ( rreal @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(11,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( E != F )
& ~ ( ron @ D @ F )
& ~ ( ron @ D @ E )
& ( A != C )
& ( A != B )
& ( ron @ C @ F )
& ( ron @ B @ E )
& ( ron @ A @ F )
& ( ron @ A @ E )
& ? [G: $i] :
( ( F = G )
& ( rline @ G ) )
& ? [G: $i] :
( ( E = G )
& ( rline @ G ) )
& ? [G: $i] :
( ( D = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( C = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( B = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( A = G )
& ( rpoint @ G ) ) )
=> ( ( ( vangle @ B @ A @ C )
= ( vplus @ ( vangle @ B @ A @ D ) @ ( vangle @ D @ A @ C ) ) )
<=> ( ( rS @ C @ D @ E )
& ( rS @ B @ D @ F ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(190), 0), imp(cond(axiom(190), 0)))') ).
thf(251,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( E != F )
& ~ ( ron @ D @ F )
& ~ ( ron @ D @ E )
& ( A != C )
& ( A != B )
& ( ron @ C @ F )
& ( ron @ B @ E )
& ( ron @ A @ F )
& ( ron @ A @ E )
& ? [G: $i] :
( ( F = G )
& ( rline @ G ) )
& ? [G: $i] :
( ( E = G )
& ( rline @ G ) )
& ? [G: $i] :
( ( D = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( C = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( B = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( A = G )
& ( rpoint @ G ) ) )
=> ( ( ( ( vangle @ B @ A @ C )
= ( vplus @ ( vangle @ B @ A @ D ) @ ( vangle @ D @ A @ C ) ) )
=> ( ( rS @ C @ D @ E )
& ( rS @ B @ D @ F ) ) )
& ( ( ( rS @ C @ D @ E )
& ( rS @ B @ D @ F ) )
=> ( ( vangle @ B @ A @ C )
= ( vplus @ ( vangle @ B @ A @ D ) @ ( vangle @ D @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(117,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ? [G: $i] :
( ( ron @ F @ G )
& ( ron @ E @ G )
& ( ron @ D @ G )
& ( rline @ G ) )
& ( ( vangle @ B @ A @ C )
= ( vangle @ E @ D @ F ) )
& ( ( vf @ A @ C )
= ( vf @ D @ F ) )
& ( ( vf @ A @ B )
= ( vf @ D @ E ) )
& ? [G: $i] :
( ( F = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( E = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( D = G )
& ( rpoint @ G ) )
& ( B != C )
& ( A != C )
& ( A != B )
& ? [G: $i] :
( ( C = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( B = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( A = G )
& ( rpoint @ G ) ) )
=> ( ( vf @ E @ F )
= ( vf @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(proof(267), 0), 2)') ).
thf(1177,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ? [G: $i] :
( ( ron @ F @ G )
& ( ron @ E @ G )
& ( ron @ D @ G )
& ( rline @ G ) )
& ( ( vangle @ B @ A @ C )
= ( vangle @ E @ D @ F ) )
& ( ( vf @ A @ C )
= ( vf @ D @ F ) )
& ( ( vf @ A @ B )
= ( vf @ D @ E ) )
& ? [G: $i] :
( ( F = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( E = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( D = G )
& ( rpoint @ G ) )
& ( B != C )
& ( A != C )
& ( A != B )
& ? [G: $i] :
( ( C = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( B = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( A = G )
& ( rpoint @ G ) ) )
=> ( ( vf @ E @ F )
= ( vf @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(37,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( ron @ E @ A )
& ( ron @ C @ A )
& ( E = F )
& ( rpoint @ F )
& ( C = D )
& ( rpoint @ D )
& ( A = B )
& ( rline @ B ) )
=> ? [G: $i] :
( ( G != E )
& ( G != C )
& ( ron @ G @ A )
& ( rpoint @ G ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(19), 0), imp(cond(axiom(19), 0)))') ).
thf(462,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( ron @ E @ A )
& ( ron @ C @ A )
& ( E = F )
& ( rpoint @ F )
& ( C = D )
& ( rpoint @ D )
& ( A = B )
& ( rline @ B ) )
=> ? [G: $i] :
( ( G != E )
& ( G != C )
& ( ron @ G @ A )
& ( rpoint @ G ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(81,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( rS @ A @ B @ C )
& ( C = D )
& ( rline @ D )
& ? [E: $i] :
( ( B = E )
& ( rpoint @ E ) )
& ? [E: $i] :
( ( A = E )
& ( rpoint @ E ) ) )
=> ~ ( ron @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(99), 0), imp(cond(axiom(99), 0)))') ).
thf(811,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( rS @ A @ B @ C )
& ( C = D )
& ( rline @ D )
& ? [E: $i] :
( ( B = E )
& ( rpoint @ E ) )
& ? [E: $i] :
( ( A = E )
& ( rpoint @ E ) ) )
=> ~ ( ron @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(29,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( D = E )
& ( ron @ C @ D )
& ( ron @ B @ D )
& ( ron @ A @ D )
& ( rline @ E )
& ( B != C )
& ( A != C )
& ( A != B )
& ? [F: $i] :
( ( C = F )
& ( rpoint @ F ) )
& ? [F: $i] :
( ( B = F )
& ( rpoint @ F ) )
& ? [F: $i] :
( ( A = F )
& ( rpoint @ F ) ) )
=> ( ( rR @ B @ A @ C )
| ( rR @ A @ B @ C )
| ( rR @ C @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(91), 0), imp(cond(axiom(91), 0)))') ).
thf(387,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( D = E )
& ( ron @ C @ D )
& ( ron @ B @ D )
& ( ron @ A @ D )
& ( rline @ E )
& ( B != C )
& ( A != C )
& ( A != B )
& ? [F: $i] :
( ( C = F )
& ( rpoint @ F ) )
& ? [F: $i] :
( ( B = F )
& ( rpoint @ F ) )
& ? [F: $i] :
( ( A = F )
& ( rpoint @ F ) ) )
=> ( ( rR @ B @ A @ C )
| ( rR @ A @ B @ C )
| ( rR @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(66,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( ron @ G @ C )
& ~ ( ron @ G @ A )
& ~ ( rinside @ G @ A )
& ( G = H )
& ( rpoint @ H )
& ( ron @ E @ C )
& ( rinside @ E @ A )
& ( E = F )
& ( rpoint @ F )
& ( C = D )
& ( rline @ D )
& ( A = B )
& ( rcircle @ B ) )
=> ? [I: $i] :
( ( rR @ I @ E @ G )
& ( ron @ I @ A )
& ( ron @ I @ C )
& ( rpoint @ I ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(61), 0), imp(cond(axiom(61), 0)))') ).
thf(685,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( ron @ G @ C )
& ~ ( ron @ G @ A )
& ~ ( rinside @ G @ A )
& ( G = H )
& ( rpoint @ H )
& ( ron @ E @ C )
& ( rinside @ E @ A )
& ( E = F )
& ( rpoint @ F )
& ( C = D )
& ( rline @ D )
& ( A = B )
& ( rcircle @ B ) )
=> ? [I: $i] :
( ( rR @ I @ E @ G )
& ( ron @ I @ A )
& ( ron @ I @ C )
& ( rpoint @ I ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(104,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( rless @ ( vf @ E @ G ) @ ( vf @ A @ C ) )
& ( E != G )
& ( A != C )
& ( G = H )
& ( rpoint @ H )
& ( E = F )
& ( rpoint @ F )
& ( C = D )
& ( rpoint @ D )
& ( A = B )
& ( rpoint @ B ) )
=> ( rpoint @ ( vskolem1120 @ A @ B @ C @ D @ E @ F @ G @ H ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(238), 0), 2)') ).
thf(1044,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( rless @ ( vf @ E @ G ) @ ( vf @ A @ C ) )
& ( E != G )
& ( A != C )
& ( G = H )
& ( rpoint @ H )
& ( E = F )
& ( rpoint @ F )
& ( C = D )
& ( rpoint @ D )
& ( A = B )
& ( rpoint @ B ) )
=> ( rpoint @ ( vskolem1120 @ A @ B @ C @ D @ E @ F @ G @ H ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(48,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( rR @ E @ C @ D )
& ( ron @ D @ A )
& ( ron @ C @ A )
& ? [F: $i] :
( ( E = F )
& ( rpoint @ F ) )
& ? [F: $i] :
( ( D = F )
& ( rpoint @ F ) )
& ? [F: $i] :
( ( C = F )
& ( rpoint @ F ) )
& ( A = B )
& ( rline @ B ) )
=> ? [F: $i] :
( ( F != E )
& ( rR @ F @ C @ D )
& ( rpoint @ F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(25), 0), imp(cond(axiom(25), 0)))') ).
thf(563,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( rR @ E @ C @ D )
& ( ron @ D @ A )
& ( ron @ C @ A )
& ? [F: $i] :
( ( E = F )
& ( rpoint @ F ) )
& ? [F: $i] :
( ( D = F )
& ( rpoint @ F ) )
& ? [F: $i] :
( ( C = F )
& ( rpoint @ F ) )
& ( A = B )
& ( rline @ B ) )
=> ? [F: $i] :
( ( F != E )
& ( rR @ F @ C @ D )
& ( rpoint @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(111,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( ron @ E @ D )
& ( E = F )
& ( rpoint @ F )
& ( rcenter @ C @ D )
& ( A = B )
& ( rpoint @ B ) )
=> ( ( ( vf @ C @ A )
= ( vf @ C @ E ) )
<=> ( ron @ A @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(184), 0), imp(cond(axiom(184), 0)))') ).
thf(1102,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( ron @ E @ D )
& ( E = F )
& ( rpoint @ F )
& ( rcenter @ C @ D )
& ( A = B )
& ( rpoint @ B ) )
=> ( ( ( ( vf @ C @ A )
= ( vf @ C @ E ) )
=> ( ron @ A @ D ) )
& ( ( ron @ A @ D )
=> ( ( vf @ C @ A )
= ( vf @ C @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(61,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C != D )
& ( ron @ D @ A )
& ( ron @ C @ A )
& ? [E: $i] :
( ( D = E )
& ( rpoint @ E ) )
& ? [E: $i] :
( ( C = E )
& ( rpoint @ E ) )
& ( A = B )
& ( rline @ B ) )
=> ? [E: $i] :
( ( rR @ D @ C @ E )
& ( rpoint @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(29), 0), imp(cond(axiom(29), 0)))') ).
thf(653,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C != D )
& ( ron @ D @ A )
& ( ron @ C @ A )
& ? [E: $i] :
( ( D = E )
& ( rpoint @ E ) )
& ? [E: $i] :
( ( C = E )
& ( rpoint @ E ) )
& ( A = B )
& ( rline @ B ) )
=> ? [E: $i] :
( ( rR @ D @ C @ E )
& ( rpoint @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(97,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ? [G: $i] :
( ( ron @ F @ G )
& ( ron @ E @ G )
& ( ron @ D @ G )
& ( rline @ G ) )
& ( ( vangle @ B @ A @ C )
= ( vangle @ E @ D @ F ) )
& ( ( vf @ A @ C )
= ( vf @ D @ F ) )
& ( ( vf @ A @ B )
= ( vf @ D @ E ) )
& ? [G: $i] :
( ( F = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( E = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( D = G )
& ( rpoint @ G ) )
& ( B != C )
& ( A != C )
& ( A != B )
& ? [G: $i] :
( ( C = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( B = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( A = G )
& ( rpoint @ G ) ) )
=> ( ( vangle @ D @ E @ F )
= ( vangle @ A @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(proof(267), 0), 1)') ).
thf(922,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ? [G: $i] :
( ( ron @ F @ G )
& ( ron @ E @ G )
& ( ron @ D @ G )
& ( rline @ G ) )
& ( ( vangle @ B @ A @ C )
= ( vangle @ E @ D @ F ) )
& ( ( vf @ A @ C )
= ( vf @ D @ F ) )
& ( ( vf @ A @ B )
= ( vf @ D @ E ) )
& ? [G: $i] :
( ( F = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( E = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( D = G )
& ( rpoint @ G ) )
& ( B != C )
& ( A != C )
& ( A != B )
& ? [G: $i] :
( ( C = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( B = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( A = G )
& ( rpoint @ G ) ) )
=> ( ( vangle @ D @ E @ F )
= ( vangle @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(119,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ? [G: $i] :
( ( ron @ F @ G )
& ( ron @ E @ G )
& ( ron @ D @ G )
& ( rline @ G ) )
& ( ( vangle @ B @ A @ C )
= ( vangle @ E @ D @ F ) )
& ( ( vf @ A @ C )
= ( vf @ D @ F ) )
& ( ( vf @ A @ B )
= ( vf @ D @ E ) )
& ? [G: $i] :
( ( F = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( E = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( D = G )
& ( rpoint @ G ) )
& ( B != C )
& ( A != C )
& ( A != B )
& ? [G: $i] :
( ( C = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( B = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( A = G )
& ( rpoint @ G ) ) )
=> ! [G: $i,H: $i,I: $i] :
( ( ( rS @ I @ F @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) )
& ~ ( rR @ E @ G @ D )
& ( ron @ G @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) )
& ( H = E )
& ( ( vf @ A @ C )
= ( vf @ G @ I ) )
& ( ( vf @ B @ C )
= ( vf @ H @ I ) )
& ( ( vf @ A @ B )
= ( vf @ G @ H ) )
& ( ( vangle @ I @ H @ G )
= ( vangle @ C @ B @ A ) )
& ( ( vangle @ G @ I @ H )
= ( vangle @ A @ C @ B ) )
& ( ( vangle @ H @ G @ I )
= ( vangle @ B @ A @ C ) )
& ? [J: $i] :
( ( I = J )
& ( rpoint @ J ) )
& ? [J: $i] :
( ( H = J )
& ( rpoint @ J ) )
& ? [J: $i] :
( ( G = J )
& ( rpoint @ J ) ) )
=> ( ( I != F )
=> ~ ( rR @ I @ D @ F ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(proof(267), 0), 9)') ).
thf(1203,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ? [G: $i] :
( ( ron @ F @ G )
& ( ron @ E @ G )
& ( ron @ D @ G )
& ( rline @ G ) )
& ( ( vangle @ B @ A @ C )
= ( vangle @ E @ D @ F ) )
& ( ( vf @ A @ C )
= ( vf @ D @ F ) )
& ( ( vf @ A @ B )
= ( vf @ D @ E ) )
& ? [G: $i] :
( ( F = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( E = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( D = G )
& ( rpoint @ G ) )
& ( B != C )
& ( A != C )
& ( A != B )
& ? [G: $i] :
( ( C = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( B = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( A = G )
& ( rpoint @ G ) ) )
=> ! [G: $i,H: $i,I: $i] :
( ( ( rS @ I @ F @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) )
& ~ ( rR @ E @ G @ D )
& ( ron @ G @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) )
& ( H = E )
& ( ( vf @ A @ C )
= ( vf @ G @ I ) )
& ( ( vf @ B @ C )
= ( vf @ H @ I ) )
& ( ( vf @ A @ B )
= ( vf @ G @ H ) )
& ( ( vangle @ I @ H @ G )
= ( vangle @ C @ B @ A ) )
& ( ( vangle @ G @ I @ H )
= ( vangle @ A @ C @ B ) )
& ( ( vangle @ H @ G @ I )
= ( vangle @ B @ A @ C ) )
& ? [J: $i] :
( ( I = J )
& ( rpoint @ J ) )
& ? [J: $i] :
( ( H = J )
& ( rpoint @ J ) )
& ? [J: $i] :
( ( G = J )
& ( rpoint @ J ) ) )
=> ( ( I != F )
=> ~ ( rR @ I @ D @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(138,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ? [G: $i] :
( ( ron @ F @ G )
& ( ron @ E @ G )
& ( ron @ D @ G )
& ( rline @ G ) )
& ( ( vangle @ B @ A @ C )
= ( vangle @ E @ D @ F ) )
& ( ( vf @ A @ C )
= ( vf @ D @ F ) )
& ( ( vf @ A @ B )
= ( vf @ D @ E ) )
& ? [G: $i] :
( ( F = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( E = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( D = G )
& ( rpoint @ G ) )
& ( B != C )
& ( A != C )
& ( A != B )
& ? [G: $i] :
( ( C = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( B = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( A = G )
& ( rpoint @ G ) ) )
=> ! [G: $i,H: $i,I: $i] :
( ( ( rS @ I @ F @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) )
& ~ ( rR @ E @ G @ D )
& ( ron @ G @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) )
& ( H = E )
& ( ( vf @ A @ C )
= ( vf @ G @ I ) )
& ( ( vf @ B @ C )
= ( vf @ H @ I ) )
& ( ( vf @ A @ B )
= ( vf @ G @ H ) )
& ( ( vangle @ I @ H @ G )
= ( vangle @ C @ B @ A ) )
& ( ( vangle @ G @ I @ H )
= ( vangle @ A @ C @ B ) )
& ( ( vangle @ H @ G @ I )
= ( vangle @ B @ A @ C ) )
& ? [J: $i] :
( ( I = J )
& ( rpoint @ J ) )
& ? [J: $i] :
( ( H = J )
& ( rpoint @ J ) )
& ? [J: $i] :
( ( G = J )
& ( rpoint @ J ) ) )
=> ~ ( rR @ D @ I @ F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(proof(267), 0), 11)') ).
thf(1420,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ? [G: $i] :
( ( ron @ F @ G )
& ( ron @ E @ G )
& ( ron @ D @ G )
& ( rline @ G ) )
& ( ( vangle @ B @ A @ C )
= ( vangle @ E @ D @ F ) )
& ( ( vf @ A @ C )
= ( vf @ D @ F ) )
& ( ( vf @ A @ B )
= ( vf @ D @ E ) )
& ? [G: $i] :
( ( F = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( E = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( D = G )
& ( rpoint @ G ) )
& ( B != C )
& ( A != C )
& ( A != B )
& ? [G: $i] :
( ( C = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( B = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( A = G )
& ( rpoint @ G ) ) )
=> ! [G: $i,H: $i,I: $i] :
( ( ( rS @ I @ F @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) )
& ~ ( rR @ E @ G @ D )
& ( ron @ G @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) )
& ( H = E )
& ( ( vf @ A @ C )
= ( vf @ G @ I ) )
& ( ( vf @ B @ C )
= ( vf @ H @ I ) )
& ( ( vf @ A @ B )
= ( vf @ G @ H ) )
& ( ( vangle @ I @ H @ G )
= ( vangle @ C @ B @ A ) )
& ( ( vangle @ G @ I @ H )
= ( vangle @ A @ C @ B ) )
& ( ( vangle @ H @ G @ I )
= ( vangle @ B @ A @ C ) )
& ? [J: $i] :
( ( I = J )
& ( rpoint @ J ) )
& ? [J: $i] :
( ( H = J )
& ( rpoint @ J ) )
& ? [J: $i] :
( ( G = J )
& ( rpoint @ J ) ) )
=> ~ ( rR @ D @ I @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(60,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ~ ( rR @ A @ C @ E )
& ~ ( rR @ A @ B @ D )
& ( E != A )
& ( D != A )
& ( C != A )
& ( B != A )
& ( ron @ E @ G )
& ( ron @ C @ G )
& ( ron @ D @ F )
& ( ron @ B @ F )
& ( ron @ A @ F )
& ? [H: $i] :
( ( G = H )
& ( rline @ H ) )
& ? [H: $i] :
( ( F = H )
& ( rline @ H ) )
& ? [H: $i] :
( ( E = H )
& ( rpoint @ H ) )
& ? [H: $i] :
( ( D = H )
& ( rpoint @ H ) )
& ? [H: $i] :
( ( C = H )
& ( rpoint @ H ) )
& ? [H: $i] :
( ( B = H )
& ( rpoint @ H ) )
& ? [H: $i] :
( ( A = H )
& ( rpoint @ H ) ) )
=> ( ( vangle @ B @ A @ C )
= ( vangle @ D @ A @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(194), 0), imp(cond(axiom(194), 0)))') ).
thf(648,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ~ ( rR @ A @ C @ E )
& ~ ( rR @ A @ B @ D )
& ( E != A )
& ( D != A )
& ( C != A )
& ( B != A )
& ( ron @ E @ G )
& ( ron @ C @ G )
& ( ron @ D @ F )
& ( ron @ B @ F )
& ( ron @ A @ F )
& ? [H: $i] :
( ( G = H )
& ( rline @ H ) )
& ? [H: $i] :
( ( F = H )
& ( rline @ H ) )
& ? [H: $i] :
( ( E = H )
& ( rpoint @ H ) )
& ? [H: $i] :
( ( D = H )
& ( rpoint @ H ) )
& ? [H: $i] :
( ( C = H )
& ( rpoint @ H ) )
& ? [H: $i] :
( ( B = H )
& ( rpoint @ H ) )
& ? [H: $i] :
( ( A = H )
& ( rpoint @ H ) ) )
=> ( ( vangle @ B @ A @ C )
= ( vangle @ D @ A @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(99,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ? [G: $i] :
( ( ron @ F @ G )
& ( ron @ E @ G )
& ( ron @ D @ G )
& ( rline @ G ) )
& ( ( vangle @ B @ A @ C )
= ( vangle @ E @ D @ F ) )
& ( ( vf @ A @ C )
= ( vf @ D @ F ) )
& ( ( vf @ A @ B )
= ( vf @ D @ E ) )
& ? [G: $i] :
( ( F = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( E = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( D = G )
& ( rpoint @ G ) )
& ( B != C )
& ( A != C )
& ( A != B )
& ? [G: $i] :
( ( C = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( B = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( A = G )
& ( rpoint @ G ) ) )
=> ! [G: $i,H: $i,I: $i] :
( ( ( rS @ I @ F @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) )
& ~ ( rR @ E @ G @ D )
& ( ron @ G @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) )
& ( H = E )
& ( ( vf @ A @ C )
= ( vf @ G @ I ) )
& ( ( vf @ B @ C )
= ( vf @ H @ I ) )
& ( ( vf @ A @ B )
= ( vf @ G @ H ) )
& ( ( vangle @ I @ H @ G )
= ( vangle @ C @ B @ A ) )
& ( ( vangle @ G @ I @ H )
= ( vangle @ A @ C @ B ) )
& ( ( vangle @ H @ G @ I )
= ( vangle @ B @ A @ C ) )
& ? [J: $i] :
( ( I = J )
& ( rpoint @ J ) )
& ? [J: $i] :
( ( H = J )
& ( rpoint @ J ) )
& ? [J: $i] :
( ( G = J )
& ( rpoint @ J ) ) )
=> ( ( vf @ G @ H )
= ( vf @ D @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(proof(267), 0), 37)') ).
thf(939,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ? [G: $i] :
( ( ron @ F @ G )
& ( ron @ E @ G )
& ( ron @ D @ G )
& ( rline @ G ) )
& ( ( vangle @ B @ A @ C )
= ( vangle @ E @ D @ F ) )
& ( ( vf @ A @ C )
= ( vf @ D @ F ) )
& ( ( vf @ A @ B )
= ( vf @ D @ E ) )
& ? [G: $i] :
( ( F = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( E = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( D = G )
& ( rpoint @ G ) )
& ( B != C )
& ( A != C )
& ( A != B )
& ? [G: $i] :
( ( C = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( B = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( A = G )
& ( rpoint @ G ) ) )
=> ! [G: $i,H: $i,I: $i] :
( ( ( rS @ I @ F @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) )
& ~ ( rR @ E @ G @ D )
& ( ron @ G @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) )
& ( H = E )
& ( ( vf @ A @ C )
= ( vf @ G @ I ) )
& ( ( vf @ B @ C )
= ( vf @ H @ I ) )
& ( ( vf @ A @ B )
= ( vf @ G @ H ) )
& ( ( vangle @ I @ H @ G )
= ( vangle @ C @ B @ A ) )
& ( ( vangle @ G @ I @ H )
= ( vangle @ A @ C @ B ) )
& ( ( vangle @ H @ G @ I )
= ( vangle @ B @ A @ C ) )
& ? [J: $i] :
( ( I = J )
& ( rpoint @ J ) )
& ? [J: $i] :
( ( H = J )
& ( rpoint @ J ) )
& ? [J: $i] :
( ( G = J )
& ( rpoint @ J ) ) )
=> ( ( vf @ G @ H )
= ( vf @ D @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(151,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ? [G: $i] :
( ( ron @ F @ G )
& ( ron @ E @ G )
& ( ron @ D @ G )
& ( rline @ G ) )
& ( ( vangle @ B @ A @ C )
= ( vangle @ E @ D @ F ) )
& ( ( vf @ A @ C )
= ( vf @ D @ F ) )
& ( ( vf @ A @ B )
= ( vf @ D @ E ) )
& ? [G: $i] :
( ( F = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( E = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( D = G )
& ( rpoint @ G ) )
& ( B != C )
& ( A != C )
& ( A != B )
& ? [G: $i] :
( ( C = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( B = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( A = G )
& ( rpoint @ G ) ) )
=> ! [G: $i,H: $i,I: $i] :
( ( ( rS @ I @ F @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) )
& ~ ( rR @ E @ G @ D )
& ( ron @ G @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) )
& ( H = E )
& ( ( vf @ A @ C )
= ( vf @ G @ I ) )
& ( ( vf @ B @ C )
= ( vf @ H @ I ) )
& ( ( vf @ A @ B )
= ( vf @ G @ H ) )
& ( ( vangle @ I @ H @ G )
= ( vangle @ C @ B @ A ) )
& ( ( vangle @ G @ I @ H )
= ( vangle @ A @ C @ B ) )
& ( ( vangle @ H @ G @ I )
= ( vangle @ B @ A @ C ) )
& ? [J: $i] :
( ( I = J )
& ( rpoint @ J ) )
& ? [J: $i] :
( ( H = J )
& ( rpoint @ J ) )
& ? [J: $i] :
( ( G = J )
& ( rpoint @ J ) ) )
=> ( ron @ I @ ( vskolem1232 @ G @ H @ I @ A @ B @ C @ D @ E @ F ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(proof(267), 0), 17)') ).
thf(1551,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ? [G: $i] :
( ( ron @ F @ G )
& ( ron @ E @ G )
& ( ron @ D @ G )
& ( rline @ G ) )
& ( ( vangle @ B @ A @ C )
= ( vangle @ E @ D @ F ) )
& ( ( vf @ A @ C )
= ( vf @ D @ F ) )
& ( ( vf @ A @ B )
= ( vf @ D @ E ) )
& ? [G: $i] :
( ( F = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( E = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( D = G )
& ( rpoint @ G ) )
& ( B != C )
& ( A != C )
& ( A != B )
& ? [G: $i] :
( ( C = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( B = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( A = G )
& ( rpoint @ G ) ) )
=> ! [G: $i,H: $i,I: $i] :
( ( ( rS @ I @ F @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) )
& ~ ( rR @ E @ G @ D )
& ( ron @ G @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) )
& ( H = E )
& ( ( vf @ A @ C )
= ( vf @ G @ I ) )
& ( ( vf @ B @ C )
= ( vf @ H @ I ) )
& ( ( vf @ A @ B )
= ( vf @ G @ H ) )
& ( ( vangle @ I @ H @ G )
= ( vangle @ C @ B @ A ) )
& ( ( vangle @ G @ I @ H )
= ( vangle @ A @ C @ B ) )
& ( ( vangle @ H @ G @ I )
= ( vangle @ B @ A @ C ) )
& ? [J: $i] :
( ( I = J )
& ( rpoint @ J ) )
& ? [J: $i] :
( ( H = J )
& ( rpoint @ J ) )
& ? [J: $i] :
( ( G = J )
& ( rpoint @ J ) ) )
=> ( ron @ I @ ( vskolem1232 @ G @ H @ I @ A @ B @ C @ D @ E @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(87,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( rS @ F @ H @ C )
& ( rS @ G @ H @ B )
& ( rS @ E @ F @ C )
& ( rS @ F @ G @ A )
& ( ron @ G @ C )
& ( ron @ F @ B )
& ( ron @ E @ A )
& ( ron @ D @ C )
& ( ron @ D @ B )
& ( ron @ D @ A )
& ? [I: $i] :
( ( G = I )
& ( rpoint @ I ) )
& ? [I: $i] :
( ( F = I )
& ( rpoint @ I ) )
& ? [I: $i] :
( ( E = I )
& ( rpoint @ I ) )
& ? [I: $i] :
( ( D = I )
& ( rpoint @ I ) )
& ? [I: $i] :
( ( C = I )
& ( rline @ I ) )
& ? [I: $i] :
( ( B = I )
& ( rline @ I ) )
& ? [I: $i] :
( ( A = I )
& ( rline @ I ) ) )
=> ( rS @ F @ H @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(117), 0), imp(cond(axiom(117), 0)))') ).
thf(855,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( rS @ F @ H @ C )
& ( rS @ G @ H @ B )
& ( rS @ E @ F @ C )
& ( rS @ F @ G @ A )
& ( ron @ G @ C )
& ( ron @ F @ B )
& ( ron @ E @ A )
& ( ron @ D @ C )
& ( ron @ D @ B )
& ( ron @ D @ A )
& ? [I: $i] :
( ( G = I )
& ( rpoint @ I ) )
& ? [I: $i] :
( ( F = I )
& ( rpoint @ I ) )
& ? [I: $i] :
( ( E = I )
& ( rpoint @ I ) )
& ? [I: $i] :
( ( D = I )
& ( rpoint @ I ) )
& ? [I: $i] :
( ( C = I )
& ( rline @ I ) )
& ? [I: $i] :
( ( B = I )
& ( rline @ I ) )
& ? [I: $i] :
( ( A = I )
& ( rline @ I ) ) )
=> ( rS @ F @ H @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(92,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C != D )
& ( ron @ D @ A )
& ( ron @ C @ A )
& ? [E: $i] :
( ( D = E )
& ( rpoint @ E ) )
& ? [E: $i] :
( ( C = E )
& ( rpoint @ E ) )
& ( A = B )
& ( rline @ B ) )
=> ? [E: $i] :
( ( rR @ E @ C @ D )
& ( rpoint @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(23), 0), imp(cond(axiom(23), 0)))') ).
thf(887,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C != D )
& ( ron @ D @ A )
& ( ron @ C @ A )
& ? [E: $i] :
( ( D = E )
& ( rpoint @ E ) )
& ? [E: $i] :
( ( C = E )
& ( rpoint @ E ) )
& ( A = B )
& ( rline @ B ) )
=> ? [E: $i] :
( ( rR @ E @ C @ D )
& ( rpoint @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(24,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ~ ( ron @ G @ C )
& ( ron @ F @ C )
& ( ron @ E @ C )
& ( rcenter @ F @ B )
& ( rcenter @ E @ A )
& ( rintersect @ A @ B )
& ( C = D )
& ( rline @ D )
& ? [H: $i] :
( ( B = H )
& ( rcircle @ H ) )
& ? [H: $i] :
( ( A = H )
& ( rcircle @ H ) ) )
=> ? [H: $i] :
( ( rS @ H @ G @ C )
& ( ron @ H @ B )
& ( ron @ H @ A )
& ( rpoint @ H ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(69), 0), imp(cond(axiom(69), 0)))') ).
thf(331,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ~ ( ron @ G @ C )
& ( ron @ F @ C )
& ( ron @ E @ C )
& ( rcenter @ F @ B )
& ( rcenter @ E @ A )
& ( rintersect @ A @ B )
& ( C = D )
& ( rline @ D )
& ? [H: $i] :
( ( B = H )
& ( rcircle @ H ) )
& ? [H: $i] :
( ( A = H )
& ( rcircle @ H ) ) )
=> ? [H: $i] :
( ( rS @ H @ G @ C )
& ( ron @ H @ B )
& ( ron @ H @ A )
& ( rpoint @ H ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(121,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ? [G: $i] :
( ( ron @ F @ G )
& ( ron @ E @ G )
& ( ron @ D @ G )
& ( rline @ G ) )
& ( ( vangle @ B @ A @ C )
= ( vangle @ E @ D @ F ) )
& ( ( vf @ A @ C )
= ( vf @ D @ F ) )
& ( ( vf @ A @ B )
= ( vf @ D @ E ) )
& ? [G: $i] :
( ( F = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( E = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( D = G )
& ( rpoint @ G ) )
& ( B != C )
& ( A != C )
& ( A != B )
& ? [G: $i] :
( ( C = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( B = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( A = G )
& ( rpoint @ G ) ) )
=> ! [G: $i,H: $i,I: $i] :
( ( ( rS @ I @ F @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) )
& ~ ( rR @ E @ G @ D )
& ( ron @ G @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) )
& ( H = E )
& ( ( vf @ A @ C )
= ( vf @ G @ I ) )
& ( ( vf @ B @ C )
= ( vf @ H @ I ) )
& ( ( vf @ A @ B )
= ( vf @ G @ H ) )
& ( ( vangle @ I @ H @ G )
= ( vangle @ C @ B @ A ) )
& ( ( vangle @ G @ I @ H )
= ( vangle @ A @ C @ B ) )
& ( ( vangle @ H @ G @ I )
= ( vangle @ B @ A @ C ) )
& ? [J: $i] :
( ( I = J )
& ( rpoint @ J ) )
& ? [J: $i] :
( ( H = J )
& ( rpoint @ J ) )
& ? [J: $i] :
( ( G = J )
& ( rpoint @ J ) ) )
=> ( ( I != F )
=> ~ ( rR @ F @ D @ I ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(proof(267), 0), 8)') ).
thf(1220,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ? [G: $i] :
( ( ron @ F @ G )
& ( ron @ E @ G )
& ( ron @ D @ G )
& ( rline @ G ) )
& ( ( vangle @ B @ A @ C )
= ( vangle @ E @ D @ F ) )
& ( ( vf @ A @ C )
= ( vf @ D @ F ) )
& ( ( vf @ A @ B )
= ( vf @ D @ E ) )
& ? [G: $i] :
( ( F = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( E = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( D = G )
& ( rpoint @ G ) )
& ( B != C )
& ( A != C )
& ( A != B )
& ? [G: $i] :
( ( C = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( B = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( A = G )
& ( rpoint @ G ) ) )
=> ! [G: $i,H: $i,I: $i] :
( ( ( rS @ I @ F @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) )
& ~ ( rR @ E @ G @ D )
& ( ron @ G @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) )
& ( H = E )
& ( ( vf @ A @ C )
= ( vf @ G @ I ) )
& ( ( vf @ B @ C )
= ( vf @ H @ I ) )
& ( ( vf @ A @ B )
= ( vf @ G @ H ) )
& ( ( vangle @ I @ H @ G )
= ( vangle @ C @ B @ A ) )
& ( ( vangle @ G @ I @ H )
= ( vangle @ A @ C @ B ) )
& ( ( vangle @ H @ G @ I )
= ( vangle @ B @ A @ C ) )
& ? [J: $i] :
( ( I = J )
& ( rpoint @ J ) )
& ? [J: $i] :
( ( H = J )
& ( rpoint @ J ) )
& ? [J: $i] :
( ( G = J )
& ( rpoint @ J ) ) )
=> ( ( I != F )
=> ~ ( rR @ F @ D @ I ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(131,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ? [G: $i] :
( ( ron @ F @ G )
& ( ron @ E @ G )
& ( ron @ D @ G )
& ( rline @ G ) )
& ( ( vangle @ B @ A @ C )
= ( vangle @ E @ D @ F ) )
& ( ( vf @ A @ C )
= ( vf @ D @ F ) )
& ( ( vf @ A @ B )
= ( vf @ D @ E ) )
& ? [G: $i] :
( ( F = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( E = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( D = G )
& ( rpoint @ G ) )
& ( B != C )
& ( A != C )
& ( A != B )
& ? [G: $i] :
( ( C = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( B = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( A = G )
& ( rpoint @ G ) ) )
=> ! [G: $i,H: $i,I: $i] :
( ( ( rS @ I @ F @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) )
& ~ ( rR @ E @ G @ D )
& ( ron @ G @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) )
& ( H = E )
& ( ( vf @ A @ C )
= ( vf @ G @ I ) )
& ( ( vf @ B @ C )
= ( vf @ H @ I ) )
& ( ( vf @ A @ B )
= ( vf @ G @ H ) )
& ( ( vangle @ I @ H @ G )
= ( vangle @ C @ B @ A ) )
& ( ( vangle @ G @ I @ H )
= ( vangle @ A @ C @ B ) )
& ( ( vangle @ H @ G @ I )
= ( vangle @ B @ A @ C ) )
& ? [J: $i] :
( ( I = J )
& ( rpoint @ J ) )
& ? [J: $i] :
( ( H = J )
& ( rpoint @ J ) )
& ? [J: $i] :
( ( G = J )
& ( rpoint @ J ) ) )
=> ( ( vf @ E @ F )
= ( vf @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(proof(267), 0), 5)') ).
thf(1336,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ? [G: $i] :
( ( ron @ F @ G )
& ( ron @ E @ G )
& ( ron @ D @ G )
& ( rline @ G ) )
& ( ( vangle @ B @ A @ C )
= ( vangle @ E @ D @ F ) )
& ( ( vf @ A @ C )
= ( vf @ D @ F ) )
& ( ( vf @ A @ B )
= ( vf @ D @ E ) )
& ? [G: $i] :
( ( F = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( E = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( D = G )
& ( rpoint @ G ) )
& ( B != C )
& ( A != C )
& ( A != B )
& ? [G: $i] :
( ( C = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( B = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( A = G )
& ( rpoint @ G ) ) )
=> ! [G: $i,H: $i,I: $i] :
( ( ( rS @ I @ F @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) )
& ~ ( rR @ E @ G @ D )
& ( ron @ G @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) )
& ( H = E )
& ( ( vf @ A @ C )
= ( vf @ G @ I ) )
& ( ( vf @ B @ C )
= ( vf @ H @ I ) )
& ( ( vf @ A @ B )
= ( vf @ G @ H ) )
& ( ( vangle @ I @ H @ G )
= ( vangle @ C @ B @ A ) )
& ( ( vangle @ G @ I @ H )
= ( vangle @ A @ C @ B ) )
& ( ( vangle @ H @ G @ I )
= ( vangle @ B @ A @ C ) )
& ? [J: $i] :
( ( I = J )
& ( rpoint @ J ) )
& ? [J: $i] :
( ( H = J )
& ( rpoint @ J ) )
& ? [J: $i] :
( ( G = J )
& ( rpoint @ J ) ) )
=> ( ( vf @ E @ F )
= ( vf @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(59,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( rless @ A @ C )
& ( C = D )
& ( rreal @ D )
& ( A = B )
& ( rreal @ B ) )
=> ( ~ ( rless @ C @ A )
| ( A = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(147), 0), imp(cond(axiom(147), 0)))') ).
thf(643,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( rless @ A @ C )
& ( C = D )
& ( rreal @ D )
& ( A = B )
& ( rreal @ B ) )
=> ( ~ ( rless @ C @ A )
| ( A = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(106,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ? [G: $i] :
( ( ron @ F @ G )
& ( ron @ E @ G )
& ( ron @ D @ G )
& ( rline @ G ) )
& ( ( vangle @ B @ A @ C )
= ( vangle @ E @ D @ F ) )
& ( ( vf @ A @ C )
= ( vf @ D @ F ) )
& ( ( vf @ A @ B )
= ( vf @ D @ E ) )
& ? [G: $i] :
( ( F = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( E = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( D = G )
& ( rpoint @ G ) )
& ( B != C )
& ( A != C )
& ( A != B )
& ? [G: $i] :
( ( C = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( B = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( A = G )
& ( rpoint @ G ) ) )
=> ~ ( ron @ F @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(proof(267), 0), 39)') ).
thf(1052,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ? [G: $i] :
( ( ron @ F @ G )
& ( ron @ E @ G )
& ( ron @ D @ G )
& ( rline @ G ) )
& ( ( vangle @ B @ A @ C )
= ( vangle @ E @ D @ F ) )
& ( ( vf @ A @ C )
= ( vf @ D @ F ) )
& ( ( vf @ A @ B )
= ( vf @ D @ E ) )
& ? [G: $i] :
( ( F = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( E = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( D = G )
& ( rpoint @ G ) )
& ( B != C )
& ( A != C )
& ( A != B )
& ? [G: $i] :
( ( C = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( B = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( A = G )
& ( rpoint @ G ) ) )
=> ~ ( ron @ F @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(89,axiom,
! [A: $i,B: $i] :
( ( ? [C: $i] :
( ( B = C )
& ( rpoint @ C ) )
& ? [C: $i] :
( ( A = C )
& ( rpoint @ C ) ) )
=> ? [C: $i] :
( ( C != B )
& ( C != A )
& ( rpoint @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(9), 0), imp(cond(axiom(9), 0)))') ).
thf(864,plain,
! [A: $i,B: $i] :
( ( ? [C: $i] :
( ( B = C )
& ( rpoint @ C ) )
& ? [C: $i] :
( ( A = C )
& ( rpoint @ C ) ) )
=> ? [C: $i] :
( ( C != B )
& ( C != A )
& ( rpoint @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(91,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C = D )
& ~ ( ron @ C @ A )
& ( rpoint @ D )
& ( A = B )
& ( rline @ B ) )
=> ? [E: $i] :
( ( E != C )
& ( rS @ E @ C @ A )
& ( rpoint @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(33), 0), imp(cond(axiom(33), 0)))') ).
thf(876,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C = D )
& ~ ( ron @ C @ A )
& ( rpoint @ D )
& ( A = B )
& ( rline @ B ) )
=> ? [E: $i] :
( ( E != C )
& ( rS @ E @ C @ A )
& ( rpoint @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(88,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( D = E )
& ( ron @ C @ D )
& ( ron @ A @ D )
& ( rR @ B @ A @ C )
& ( rline @ E )
& ? [F: $i] :
( ( C = F )
& ( rpoint @ F ) )
& ? [F: $i] :
( ( B = F )
& ( rpoint @ F ) )
& ? [F: $i] :
( ( A = F )
& ( rpoint @ F ) ) )
=> ( ron @ B @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(85), 0), imp(cond(axiom(85), 0)))') ).
thf(859,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( D = E )
& ( ron @ C @ D )
& ( ron @ A @ D )
& ( rR @ B @ A @ C )
& ( rline @ E )
& ? [F: $i] :
( ( C = F )
& ( rpoint @ F ) )
& ? [F: $i] :
( ( B = F )
& ( rpoint @ F ) )
& ? [F: $i] :
( ( A = F )
& ( rpoint @ F ) ) )
=> ( ron @ B @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(56,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A != C )
& ( A != B )
& ? [D: $i] :
( ( C = D )
& ( rpoint @ D ) )
& ? [D: $i] :
( ( B = D )
& ( rpoint @ D ) )
& ? [D: $i] :
( ( A = D )
& ( rpoint @ D ) ) )
=> ( ( vangle @ A @ B @ C )
= ( vangle @ C @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(168), 0), imp(cond(axiom(168), 0)))') ).
thf(627,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A != C )
& ( A != B )
& ? [D: $i] :
( ( C = D )
& ( rpoint @ D ) )
& ? [D: $i] :
( ( B = D )
& ( rpoint @ D ) )
& ? [D: $i] :
( ( A = D )
& ( rpoint @ D ) ) )
=> ( ( vangle @ A @ B @ C )
= ( vangle @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(120,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C = D )
& ( A != C )
& ( rpoint @ D )
& ( A = B )
& ( rpoint @ B ) )
=> ( ( vf @ A @ C )
= ( vf @ C @ ( vskolem1052 @ A @ B @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(206), 0), 1)') ).
thf(1216,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C = D )
& ( A != C )
& ( rpoint @ D )
& ( A = B )
& ( rpoint @ B ) )
=> ( ( vf @ A @ C )
= ( vf @ C @ ( vskolem1052 @ A @ B @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(67,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( G != E )
& ( ron @ G @ C )
& ( G = H )
& ( rpoint @ H )
& ( ron @ E @ C )
& ( rinside @ E @ A )
& ( E = F )
& ( rpoint @ F )
& ( C = D )
& ( rline @ D )
& ( A = B )
& ( rcircle @ B ) )
=> ? [I: $i] :
( ( rR @ E @ I @ G )
& ( ron @ I @ C )
& ( ron @ I @ A )
& ( rpoint @ I ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(63), 0), imp(cond(axiom(63), 0)))') ).
thf(699,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( G != E )
& ( ron @ G @ C )
& ( G = H )
& ( rpoint @ H )
& ( ron @ E @ C )
& ( rinside @ E @ A )
& ( E = F )
& ( rpoint @ F )
& ( C = D )
& ( rline @ D )
& ( A = B )
& ( rcircle @ B ) )
=> ? [I: $i] :
( ( rR @ E @ I @ G )
& ( ron @ I @ C )
& ( ron @ I @ A )
& ( rpoint @ I ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(144,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ron @ B @ D )
& ( rcenter @ C @ D )
& ? [E: $i] :
( ( B = E )
& ( rpoint @ E ) )
& ? [E: $i] :
( ( A = E )
& ( rpoint @ E ) ) )
=> ( ( rless @ ( vf @ C @ A ) @ ( vf @ C @ B ) )
<=> ( rinside @ A @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(186), 0), imp(cond(axiom(186), 0)))') ).
thf(1481,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ron @ B @ D )
& ( rcenter @ C @ D )
& ? [E: $i] :
( ( B = E )
& ( rpoint @ E ) )
& ? [E: $i] :
( ( A = E )
& ( rpoint @ E ) ) )
=> ( ( ( rless @ ( vf @ C @ A ) @ ( vf @ C @ B ) )
=> ( rinside @ A @ D ) )
& ( ( rinside @ A @ D )
=> ( rless @ ( vf @ C @ A ) @ ( vf @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(103,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ? [G: $i] :
( ( ron @ F @ G )
& ( ron @ E @ G )
& ( ron @ D @ G )
& ( rline @ G ) )
& ( ( vangle @ B @ A @ C )
= ( vangle @ E @ D @ F ) )
& ( ( vf @ A @ C )
= ( vf @ D @ F ) )
& ( ( vf @ A @ B )
= ( vf @ D @ E ) )
& ? [G: $i] :
( ( F = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( E = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( D = G )
& ( rpoint @ G ) )
& ( B != C )
& ( A != C )
& ( A != B )
& ? [G: $i] :
( ( C = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( B = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( A = G )
& ( rpoint @ G ) ) )
=> ! [G: $i,H: $i,I: $i] :
( ( ( rS @ I @ F @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) )
& ~ ( rR @ E @ G @ D )
& ( ron @ G @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) )
& ( H = E )
& ( ( vf @ A @ C )
= ( vf @ G @ I ) )
& ( ( vf @ B @ C )
= ( vf @ H @ I ) )
& ( ( vf @ A @ B )
= ( vf @ G @ H ) )
& ( ( vangle @ I @ H @ G )
= ( vangle @ C @ B @ A ) )
& ( ( vangle @ G @ I @ H )
= ( vangle @ A @ C @ B ) )
& ( ( vangle @ H @ G @ I )
= ( vangle @ B @ A @ C ) )
& ? [J: $i] :
( ( I = J )
& ( rpoint @ J ) )
& ? [J: $i] :
( ( H = J )
& ( rpoint @ J ) )
& ? [J: $i] :
( ( G = J )
& ( rpoint @ J ) ) )
=> ( ron @ G @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(proof(267), 0), 36)') ).
thf(1030,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ? [G: $i] :
( ( ron @ F @ G )
& ( ron @ E @ G )
& ( ron @ D @ G )
& ( rline @ G ) )
& ( ( vangle @ B @ A @ C )
= ( vangle @ E @ D @ F ) )
& ( ( vf @ A @ C )
= ( vf @ D @ F ) )
& ( ( vf @ A @ B )
= ( vf @ D @ E ) )
& ? [G: $i] :
( ( F = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( E = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( D = G )
& ( rpoint @ G ) )
& ( B != C )
& ( A != C )
& ( A != B )
& ? [G: $i] :
( ( C = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( B = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( A = G )
& ( rpoint @ G ) ) )
=> ! [G: $i,H: $i,I: $i] :
( ( ( rS @ I @ F @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) )
& ~ ( rR @ E @ G @ D )
& ( ron @ G @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) )
& ( H = E )
& ( ( vf @ A @ C )
= ( vf @ G @ I ) )
& ( ( vf @ B @ C )
= ( vf @ H @ I ) )
& ( ( vf @ A @ B )
= ( vf @ G @ H ) )
& ( ( vangle @ I @ H @ G )
= ( vangle @ C @ B @ A ) )
& ( ( vangle @ G @ I @ H )
= ( vangle @ A @ C @ B ) )
& ( ( vangle @ H @ G @ I )
= ( vangle @ B @ A @ C ) )
& ? [J: $i] :
( ( I = J )
& ( rpoint @ J ) )
& ? [J: $i] :
( ( H = J )
& ( rpoint @ J ) )
& ? [J: $i] :
( ( G = J )
& ( rpoint @ J ) ) )
=> ( ron @ G @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(17,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( rS @ E @ F @ C )
& ( rS @ F @ G @ A )
& ( ron @ G @ C )
& ( ron @ F @ C )
& ( ron @ E @ A )
& ( ron @ D @ C )
& ( ron @ D @ B )
& ( ron @ D @ A )
& ? [H: $i] :
( ( G = H )
& ( rpoint @ H ) )
& ? [H: $i] :
( ( F = H )
& ( rpoint @ H ) )
& ? [H: $i] :
( ( E = H )
& ( rpoint @ H ) )
& ? [H: $i] :
( ( D = H )
& ( rpoint @ H ) )
& ? [H: $i] :
( ( C = H )
& ( rline @ H ) )
& ? [H: $i] :
( ( B = H )
& ( rline @ H ) )
& ? [H: $i] :
( ( A = H )
& ( rline @ H ) ) )
=> ~ ( rS @ E @ G @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(113), 0), imp(cond(axiom(113), 0)))') ).
thf(290,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( rS @ E @ F @ C )
& ( rS @ F @ G @ A )
& ( ron @ G @ C )
& ( ron @ F @ C )
& ( ron @ E @ A )
& ( ron @ D @ C )
& ( ron @ D @ B )
& ( ron @ D @ A )
& ? [H: $i] :
( ( G = H )
& ( rpoint @ H ) )
& ? [H: $i] :
( ( F = H )
& ( rpoint @ H ) )
& ? [H: $i] :
( ( E = H )
& ( rpoint @ H ) )
& ? [H: $i] :
( ( D = H )
& ( rpoint @ H ) )
& ? [H: $i] :
( ( C = H )
& ( rline @ H ) )
& ? [H: $i] :
( ( B = H )
& ( rline @ H ) )
& ? [H: $i] :
( ( A = H )
& ( rline @ H ) ) )
=> ~ ( rS @ E @ G @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(94,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( D = E )
& ( ron @ B @ D )
& ( ron @ A @ D )
& ( rR @ B @ A @ C )
& ( rline @ E )
& ? [F: $i] :
( ( C = F )
& ( rpoint @ F ) )
& ? [F: $i] :
( ( B = F )
& ( rpoint @ F ) )
& ? [F: $i] :
( ( A = F )
& ( rpoint @ F ) ) )
=> ( ron @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(83), 0), imp(cond(axiom(83), 0)))') ).
thf(899,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( D = E )
& ( ron @ B @ D )
& ( ron @ A @ D )
& ( rR @ B @ A @ C )
& ( rline @ E )
& ? [F: $i] :
( ( C = F )
& ( rpoint @ F ) )
& ? [F: $i] :
( ( B = F )
& ( rpoint @ F ) )
& ? [F: $i] :
( ( A = F )
& ( rpoint @ F ) ) )
=> ( ron @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(129,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ? [G: $i] :
( ( ron @ F @ G )
& ( ron @ E @ G )
& ( ron @ D @ G )
& ( rline @ G ) )
& ( ( vangle @ B @ A @ C )
= ( vangle @ E @ D @ F ) )
& ( ( vf @ A @ C )
= ( vf @ D @ F ) )
& ( ( vf @ A @ B )
= ( vf @ D @ E ) )
& ? [G: $i] :
( ( F = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( E = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( D = G )
& ( rpoint @ G ) )
& ( B != C )
& ( A != C )
& ( A != B )
& ? [G: $i] :
( ( C = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( B = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( A = G )
& ( rpoint @ G ) ) )
=> ! [G: $i,H: $i,I: $i] :
( ( ( rS @ I @ F @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) )
& ~ ( rR @ E @ G @ D )
& ( ron @ G @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) )
& ( H = E )
& ( ( vf @ A @ C )
= ( vf @ G @ I ) )
& ( ( vf @ B @ C )
= ( vf @ H @ I ) )
& ( ( vf @ A @ B )
= ( vf @ G @ H ) )
& ( ( vangle @ I @ H @ G )
= ( vangle @ C @ B @ A ) )
& ( ( vangle @ G @ I @ H )
= ( vangle @ A @ C @ B ) )
& ( ( vangle @ H @ G @ I )
= ( vangle @ B @ A @ C ) )
& ? [J: $i] :
( ( I = J )
& ( rpoint @ J ) )
& ? [J: $i] :
( ( H = J )
& ( rpoint @ J ) )
& ? [J: $i] :
( ( G = J )
& ( rpoint @ J ) ) )
=> ~ ( rR @ D @ I @ F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(proof(267), 0), 12)') ).
thf(1309,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ? [G: $i] :
( ( ron @ F @ G )
& ( ron @ E @ G )
& ( ron @ D @ G )
& ( rline @ G ) )
& ( ( vangle @ B @ A @ C )
= ( vangle @ E @ D @ F ) )
& ( ( vf @ A @ C )
= ( vf @ D @ F ) )
& ( ( vf @ A @ B )
= ( vf @ D @ E ) )
& ? [G: $i] :
( ( F = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( E = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( D = G )
& ( rpoint @ G ) )
& ( B != C )
& ( A != C )
& ( A != B )
& ? [G: $i] :
( ( C = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( B = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( A = G )
& ( rpoint @ G ) ) )
=> ! [G: $i,H: $i,I: $i] :
( ( ( rS @ I @ F @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) )
& ~ ( rR @ E @ G @ D )
& ( ron @ G @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) )
& ( H = E )
& ( ( vf @ A @ C )
= ( vf @ G @ I ) )
& ( ( vf @ B @ C )
= ( vf @ H @ I ) )
& ( ( vf @ A @ B )
= ( vf @ G @ H ) )
& ( ( vangle @ I @ H @ G )
= ( vangle @ C @ B @ A ) )
& ( ( vangle @ G @ I @ H )
= ( vangle @ A @ C @ B ) )
& ( ( vangle @ H @ G @ I )
= ( vangle @ B @ A @ C ) )
& ? [J: $i] :
( ( I = J )
& ( rpoint @ J ) )
& ? [J: $i] :
( ( H = J )
& ( rpoint @ J ) )
& ? [J: $i] :
( ( G = J )
& ( rpoint @ J ) ) )
=> ~ ( rR @ D @ I @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(20,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( E = F )
& ( rpoint @ F )
& ( C = D )
& ( rpoint @ D )
& ( A = B )
& ( rpoint @ B ) )
=> ( rgeq @ ( vg @ A @ C @ E ) @ v0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(174), 0), imp(cond(axiom(174), 0)))') ).
thf(315,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( E = F )
& ( rpoint @ F )
& ( C = D )
& ( rpoint @ D )
& ( A = B )
& ( rpoint @ B ) )
=> ( rgeq @ ( vg @ A @ C @ E ) @ v0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(101,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,M: $i,N: $i,O: $i,P: $i,Q: $i,R: $i] :
( ( ( Q = R )
& ! [S: $i,T: $i,U: $i] :
( ( ( rS @ U @ F @ Q )
& ~ ( rR @ D @ T @ E )
& ( ron @ T @ Q )
& ( ( vf @ A @ C )
= ( vf @ S @ U ) )
& ( ( vf @ B @ C )
= ( vf @ T @ U ) )
& ( ( vf @ A @ B )
= ( vf @ S @ T ) )
& ( ( vangle @ S @ U @ T )
= ( vangle @ A @ C @ B ) )
& ( ( vangle @ T @ S @ U )
= ( vangle @ B @ A @ C ) )
& ( ( vangle @ U @ T @ S )
= ( vangle @ C @ B @ A ) )
& ( S = D )
& ( rpoint @ U )
& ( rpoint @ T )
& ( rpoint @ S ) )
=> ( ( ( vangle @ K @ L @ M )
= ( vangle @ N @ O @ P ) )
& ( ( vf @ G @ H )
= ( vf @ I @ J ) ) ) )
& ~ ( ron @ F @ Q )
& ( ron @ E @ Q )
& ( ron @ D @ Q )
& ( rline @ R )
& ? [S: $i] :
( ( P = S )
& ( rpoint @ S ) )
& ? [S: $i] :
( ( O = S )
& ( rpoint @ S ) )
& ? [S: $i] :
( ( N = S )
& ( rpoint @ S ) )
& ? [S: $i] :
( ( M = S )
& ( rpoint @ S ) )
& ? [S: $i] :
( ( L = S )
& ( rpoint @ S ) )
& ? [S: $i] :
( ( K = S )
& ( rpoint @ S ) )
& ? [S: $i] :
( ( J = S )
& ( rpoint @ S ) )
& ? [S: $i] :
( ( I = S )
& ( rpoint @ S ) )
& ? [S: $i] :
( ( H = S )
& ( rpoint @ S ) )
& ? [S: $i] :
( ( G = S )
& ( rpoint @ S ) )
& ? [S: $i] :
( ( F = S )
& ( rpoint @ S ) )
& ? [S: $i] :
( ( E = S )
& ( rpoint @ S ) )
& ? [S: $i] :
( ( D = S )
& ( rpoint @ S ) )
& ( B != C )
& ( A != C )
& ( A != B )
& ? [S: $i] :
( ( C = S )
& ( rpoint @ S ) )
& ? [S: $i] :
( ( B = S )
& ( rpoint @ S ) )
& ? [S: $i] :
( ( A = S )
& ( rpoint @ S ) ) )
=> ( ( ( vangle @ K @ L @ M )
= ( vangle @ N @ O @ P ) )
& ( ( vf @ G @ H )
= ( vf @ I @ J ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(204), 0), imp(cond(axiom(204), 0)))') ).
thf(967,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] :
( ( ( Q = R )
& ! [S: $i,T: $i,U: $i] :
( ( ( rS @ U @ F @ Q )
& ~ ( rR @ D @ T @ E )
& ( ron @ T @ Q )
& ( ( vf @ A @ C )
= ( vf @ S @ U ) )
& ( ( vf @ B @ C )
= ( vf @ T @ U ) )
& ( ( vf @ A @ B )
= ( vf @ S @ T ) )
& ( ( vangle @ S @ U @ T )
= ( vangle @ A @ C @ B ) )
& ( ( vangle @ T @ S @ U )
= ( vangle @ B @ A @ C ) )
& ( ( vangle @ U @ T @ S )
= ( vangle @ C @ B @ A ) )
& ( S = D )
& ( rpoint @ U )
& ( rpoint @ T )
& ( rpoint @ S ) )
=> ( ( ( vangle @ K @ L @ M )
= ( vangle @ N @ O @ P ) )
& ( ( vf @ G @ H )
= ( vf @ I @ J ) ) ) )
& ~ ( ron @ F @ Q )
& ( ron @ E @ Q )
& ( ron @ D @ Q )
& ( rline @ R )
& ? [S: $i] :
( ( P = S )
& ( rpoint @ S ) )
& ? [S: $i] :
( ( O = S )
& ( rpoint @ S ) )
& ? [S: $i] :
( ( N = S )
& ( rpoint @ S ) )
& ? [S: $i] :
( ( M = S )
& ( rpoint @ S ) )
& ? [S: $i] :
( ( L = S )
& ( rpoint @ S ) )
& ? [S: $i] :
( ( K = S )
& ( rpoint @ S ) )
& ? [S: $i] :
( ( J = S )
& ( rpoint @ S ) )
& ? [S: $i] :
( ( I = S )
& ( rpoint @ S ) )
& ? [S: $i] :
( ( H = S )
& ( rpoint @ S ) )
& ? [S: $i] :
( ( G = S )
& ( rpoint @ S ) )
& ? [S: $i] :
( ( F = S )
& ( rpoint @ S ) )
& ? [S: $i] :
( ( E = S )
& ( rpoint @ S ) )
& ? [S: $i] :
( ( D = S )
& ( rpoint @ S ) )
& ( B != C )
& ( A != C )
& ( A != B )
& ? [S: $i] :
( ( C = S )
& ( rpoint @ S ) )
& ? [S: $i] :
( ( B = S )
& ( rpoint @ S ) )
& ? [S: $i] :
( ( A = S )
& ( rpoint @ S ) ) )
=> ( ( ( vangle @ K @ L @ M )
= ( vangle @ N @ O @ P ) )
& ( ( vf @ G @ H )
= ( vf @ I @ J ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(148,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ? [G: $i] :
( ( ron @ F @ G )
& ( ron @ E @ G )
& ( ron @ D @ G )
& ( rline @ G ) )
& ( ( vangle @ B @ A @ C )
= ( vangle @ E @ D @ F ) )
& ( ( vf @ A @ C )
= ( vf @ D @ F ) )
& ( ( vf @ A @ B )
= ( vf @ D @ E ) )
& ? [G: $i] :
( ( F = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( E = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( D = G )
& ( rpoint @ G ) )
& ( B != C )
& ( A != C )
& ( A != B )
& ? [G: $i] :
( ( C = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( B = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( A = G )
& ( rpoint @ G ) ) )
=> ! [G: $i,H: $i,I: $i] :
( ( ( rS @ I @ F @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) )
& ~ ( rR @ E @ G @ D )
& ( ron @ G @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) )
& ( H = E )
& ( ( vf @ A @ C )
= ( vf @ G @ I ) )
& ( ( vf @ B @ C )
= ( vf @ H @ I ) )
& ( ( vf @ A @ B )
= ( vf @ G @ H ) )
& ( ( vangle @ I @ H @ G )
= ( vangle @ C @ B @ A ) )
& ( ( vangle @ G @ I @ H )
= ( vangle @ A @ C @ B ) )
& ( ( vangle @ H @ G @ I )
= ( vangle @ B @ A @ C ) )
& ? [J: $i] :
( ( I = J )
& ( rpoint @ J ) )
& ? [J: $i] :
( ( H = J )
& ( rpoint @ J ) )
& ? [J: $i] :
( ( G = J )
& ( rpoint @ J ) ) )
=> ( ( I != F )
=> ( ( rR @ F @ D @ I )
| ( rR @ I @ D @ F ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(proof(267), 0), 7)') ).
thf(1527,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ? [G: $i] :
( ( ron @ F @ G )
& ( ron @ E @ G )
& ( ron @ D @ G )
& ( rline @ G ) )
& ( ( vangle @ B @ A @ C )
= ( vangle @ E @ D @ F ) )
& ( ( vf @ A @ C )
= ( vf @ D @ F ) )
& ( ( vf @ A @ B )
= ( vf @ D @ E ) )
& ? [G: $i] :
( ( F = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( E = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( D = G )
& ( rpoint @ G ) )
& ( B != C )
& ( A != C )
& ( A != B )
& ? [G: $i] :
( ( C = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( B = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( A = G )
& ( rpoint @ G ) ) )
=> ! [G: $i,H: $i,I: $i] :
( ( ( rS @ I @ F @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) )
& ~ ( rR @ E @ G @ D )
& ( ron @ G @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) )
& ( H = E )
& ( ( vf @ A @ C )
= ( vf @ G @ I ) )
& ( ( vf @ B @ C )
= ( vf @ H @ I ) )
& ( ( vf @ A @ B )
= ( vf @ G @ H ) )
& ( ( vangle @ I @ H @ G )
= ( vangle @ C @ B @ A ) )
& ( ( vangle @ G @ I @ H )
= ( vangle @ A @ C @ B ) )
& ( ( vangle @ H @ G @ I )
= ( vangle @ B @ A @ C ) )
& ? [J: $i] :
( ( I = J )
& ( rpoint @ J ) )
& ? [J: $i] :
( ( H = J )
& ( rpoint @ J ) )
& ? [J: $i] :
( ( G = J )
& ( rpoint @ J ) ) )
=> ( ( I != F )
=> ( ( rR @ F @ D @ I )
| ( rR @ I @ D @ F ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(8,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( vtriangle @ A @ B @ C )
= D )
& ( rtriangle @ D ) )
=> ( ( B != C )
& ( A != C )
& ( A != B )
& ? [E: $i] :
( ( C = E )
& ( rpoint @ E ) )
& ? [E: $i] :
( ( B = E )
& ( rpoint @ E ) )
& ? [E: $i] :
( ( A = E )
& ( rpoint @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(3), 0), imp(cond(axiom(3), 0)))') ).
thf(210,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( vtriangle @ A @ B @ C )
= D )
& ( rtriangle @ D ) )
=> ( ( B != C )
& ( A != C )
& ( A != B )
& ? [E: $i] :
( ( C = E )
& ( rpoint @ E ) )
& ? [E: $i] :
( ( B = E )
& ( rpoint @ E ) )
& ? [E: $i] :
( ( A = E )
& ( rpoint @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(9,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ( ron @ D @ E )
& ( E = F )
& ( rline @ F )
& ( C != D )
& ( B != D )
& ( B != C )
& ( A != D )
& ( A != C )
& ( A != B )
& ? [G: $i] :
( ( D = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( C = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( B = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( A = G )
& ( rpoint @ G ) ) )
=> ( ( rR @ C @ A @ B )
<=> ( ( vplus @ ( vg @ A @ C @ D ) @ ( vg @ D @ C @ B ) )
= ( vg @ A @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(202), 0), imp(cond(axiom(202), 0)))') ).
thf(239,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ( ron @ D @ E )
& ( E = F )
& ( rline @ F )
& ( C != D )
& ( B != D )
& ( B != C )
& ( A != D )
& ( A != C )
& ( A != B )
& ? [G: $i] :
( ( D = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( C = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( B = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( A = G )
& ( rpoint @ G ) ) )
=> ( ( ( rR @ C @ A @ B )
=> ( ( vplus @ ( vg @ A @ C @ D ) @ ( vg @ D @ C @ B ) )
= ( vg @ A @ D @ B ) ) )
& ( ( ( vplus @ ( vg @ A @ C @ D ) @ ( vg @ D @ C @ B ) )
= ( vg @ A @ D @ B ) )
=> ( rR @ C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(18,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C = D )
& ( A != C )
& ( rpoint @ D )
& ( A = B )
& ( rpoint @ B ) )
=> ( rpoint @ ( vskolem1052 @ A @ B @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(206), 0), 2)') ).
thf(294,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C = D )
& ( A != C )
& ( rpoint @ D )
& ( A = B )
& ( rpoint @ B ) )
=> ( rpoint @ ( vskolem1052 @ A @ B @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(133,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ? [G: $i] :
( ( ron @ F @ G )
& ( ron @ E @ G )
& ( ron @ D @ G )
& ( rline @ G ) )
& ( ( vangle @ B @ A @ C )
= ( vangle @ E @ D @ F ) )
& ( ( vf @ A @ C )
= ( vf @ D @ F ) )
& ( ( vf @ A @ B )
= ( vf @ D @ E ) )
& ? [G: $i] :
( ( F = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( E = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( D = G )
& ( rpoint @ G ) )
& ( B != C )
& ( A != C )
& ( A != B )
& ? [G: $i] :
( ( C = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( B = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( A = G )
& ( rpoint @ G ) ) )
=> ! [G: $i,H: $i,I: $i] :
( ( ( rS @ I @ F @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) )
& ~ ( rR @ E @ G @ D )
& ( ron @ G @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) )
& ( H = E )
& ( ( vf @ A @ C )
= ( vf @ G @ I ) )
& ( ( vf @ B @ C )
= ( vf @ H @ I ) )
& ( ( vf @ A @ B )
= ( vf @ G @ H ) )
& ( ( vangle @ I @ H @ G )
= ( vangle @ C @ B @ A ) )
& ( ( vangle @ G @ I @ H )
= ( vangle @ A @ C @ B ) )
& ( ( vangle @ H @ G @ I )
= ( vangle @ B @ A @ C ) )
& ? [J: $i] :
( ( I = J )
& ( rpoint @ J ) )
& ? [J: $i] :
( ( H = J )
& ( rpoint @ J ) )
& ? [J: $i] :
( ( G = J )
& ( rpoint @ J ) ) )
=> ( I = F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(proof(267), 0), 6)') ).
thf(1363,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ? [G: $i] :
( ( ron @ F @ G )
& ( ron @ E @ G )
& ( ron @ D @ G )
& ( rline @ G ) )
& ( ( vangle @ B @ A @ C )
= ( vangle @ E @ D @ F ) )
& ( ( vf @ A @ C )
= ( vf @ D @ F ) )
& ( ( vf @ A @ B )
= ( vf @ D @ E ) )
& ? [G: $i] :
( ( F = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( E = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( D = G )
& ( rpoint @ G ) )
& ( B != C )
& ( A != C )
& ( A != B )
& ? [G: $i] :
( ( C = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( B = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( A = G )
& ( rpoint @ G ) ) )
=> ! [G: $i,H: $i,I: $i] :
( ( ( rS @ I @ F @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) )
& ~ ( rR @ E @ G @ D )
& ( ron @ G @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) )
& ( H = E )
& ( ( vf @ A @ C )
= ( vf @ G @ I ) )
& ( ( vf @ B @ C )
= ( vf @ H @ I ) )
& ( ( vf @ A @ B )
= ( vf @ G @ H ) )
& ( ( vangle @ I @ H @ G )
= ( vangle @ C @ B @ A ) )
& ( ( vangle @ G @ I @ H )
= ( vangle @ A @ C @ B ) )
& ( ( vangle @ H @ G @ I )
= ( vangle @ B @ A @ C ) )
& ? [J: $i] :
( ( I = J )
& ( rpoint @ J ) )
& ? [J: $i] :
( ( H = J )
& ( rpoint @ J ) )
& ? [J: $i] :
( ( G = J )
& ( rpoint @ J ) ) )
=> ( I = F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(58,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( ron @ B @ D )
& ( ron @ A @ D )
& ( A != B )
& ( D = E )
& ( rline @ E )
& ? [F: $i] :
( ( C = F )
& ( rpoint @ F ) )
& ? [F: $i] :
( ( B = F )
& ( rpoint @ F ) )
& ? [F: $i] :
( ( A = F )
& ( rpoint @ F ) ) )
=> ( ( ( vg @ A @ B @ C )
= v0 )
<=> ( ron @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(200), 0), imp(cond(axiom(200), 0)))') ).
thf(635,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( ron @ B @ D )
& ( ron @ A @ D )
& ( A != B )
& ( D = E )
& ( rline @ E )
& ? [F: $i] :
( ( C = F )
& ( rpoint @ F ) )
& ? [F: $i] :
( ( B = F )
& ( rpoint @ F ) )
& ? [F: $i] :
( ( A = F )
& ( rpoint @ F ) ) )
=> ( ( ( ( vg @ A @ B @ C )
= v0 )
=> ( ron @ C @ D ) )
& ( ( ron @ C @ D )
=> ( ( vg @ A @ B @ C )
= v0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(107,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ? [G: $i] :
( ( ron @ F @ G )
& ( ron @ E @ G )
& ( ron @ D @ G )
& ( rline @ G ) )
& ( ( vangle @ B @ A @ C )
= ( vangle @ E @ D @ F ) )
& ( ( vf @ A @ C )
= ( vf @ D @ F ) )
& ( ( vf @ A @ B )
= ( vf @ D @ E ) )
& ? [G: $i] :
( ( F = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( E = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( D = G )
& ( rpoint @ G ) )
& ( B != C )
& ( A != C )
& ( A != B )
& ? [G: $i] :
( ( C = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( B = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( A = G )
& ( rpoint @ G ) ) )
=> ( rline @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(proof(267), 0), 42)') ).
thf(1065,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ? [G: $i] :
( ( ron @ F @ G )
& ( ron @ E @ G )
& ( ron @ D @ G )
& ( rline @ G ) )
& ( ( vangle @ B @ A @ C )
= ( vangle @ E @ D @ F ) )
& ( ( vf @ A @ C )
= ( vf @ D @ F ) )
& ( ( vf @ A @ B )
= ( vf @ D @ E ) )
& ? [G: $i] :
( ( F = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( E = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( D = G )
& ( rpoint @ G ) )
& ( B != C )
& ( A != C )
& ( A != B )
& ? [G: $i] :
( ( C = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( B = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( A = G )
& ( rpoint @ G ) ) )
=> ( rline @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(79,axiom,
! [A: $i,B: $i] :
( ( ( A = B )
& ( rcircle @ B ) )
=> ? [C: $i] :
( ( rinside @ C @ A )
& ( rpoint @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(47), 0), imp(cond(axiom(47), 0)))') ).
thf(796,plain,
! [A: $i,B: $i] :
( ( ( A = B )
& ( rcircle @ B ) )
=> ? [C: $i] :
( ( rinside @ C @ A )
& ( rpoint @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(6,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( ( vplus @ A @ E )
= ( vplus @ C @ E ) )
& ( E = F )
& ( rreal @ F )
& ( C = D )
& ( rreal @ D )
& ( A = B )
& ( rreal @ B ) )
=> ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(156, 0), 0)') ).
thf(200,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( ( vplus @ A @ E )
= ( vplus @ C @ E ) )
& ( E = F )
& ( rreal @ F )
& ( C = D )
& ( rreal @ D )
& ( A = B )
& ( rreal @ B ) )
=> ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(53,axiom,
! [A: $i,B: $i] :
( ( rcenter @ A @ B )
=> ? [C: $i,D: $i] :
( ( B = D )
& ( rcircle @ D )
& ( A = C )
& ( rpoint @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(1), 0), imp(cond(axiom(1), 0)))') ).
thf(607,plain,
! [A: $i,B: $i] :
( ( rcenter @ A @ B )
=> ? [C: $i,D: $i] :
( ( B = D )
& ( rcircle @ D )
& ( A = C )
& ( rpoint @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(26,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( rintersect @ C @ A )
& ( C = D )
& ( rline @ D )
& ( A = B )
& ( rcircle @ B ) )
=> ? [E: $i,F: $i] :
( ( E != F )
& ( ron @ F @ A )
& ( ron @ F @ C )
& ( rpoint @ F )
& ( ron @ E @ A )
& ( ron @ E @ C )
& ( rpoint @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(59), 0), imp(cond(axiom(59), 0)))') ).
thf(354,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( rintersect @ C @ A )
& ( C = D )
& ( rline @ D )
& ( A = B )
& ( rcircle @ B ) )
=> ? [E: $i,F: $i] :
( ( E != F )
& ( ron @ F @ A )
& ( ron @ F @ C )
& ( rpoint @ F )
& ( ron @ E @ A )
& ( ron @ E @ C )
& ( rpoint @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(98,axiom,
! [A: $i,B: $i] :
( ( ? [C: $i] :
( ( B = C )
& ( rpoint @ C ) )
& ? [C: $i] :
( ( A = C )
& ( rpoint @ C ) ) )
=> ( ( vf @ A @ B )
= ( vf @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(166), 0), imp(cond(axiom(166), 0)))') ).
thf(935,plain,
! [A: $i,B: $i] :
( ( ? [C: $i] :
( ( B = C )
& ( rpoint @ C ) )
& ? [C: $i] :
( ( A = C )
& ( rpoint @ C ) ) )
=> ( ( vf @ A @ B )
= ( vf @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(45,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( rintersect @ A @ C )
& ( C = D )
& ( rline @ D )
& ( A = B )
& ( rline @ B ) )
=> ? [E: $i] :
( ( ron @ E @ C )
& ( ron @ E @ A )
& ( rpoint @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(55), 0), imp(cond(axiom(55), 0)))') ).
thf(543,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( rintersect @ A @ C )
& ( C = D )
& ( rline @ D )
& ( A = B )
& ( rline @ B ) )
=> ? [E: $i] :
( ( ron @ E @ C )
& ( ron @ E @ A )
& ( rpoint @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(137,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( rless @ ( vf @ E @ G ) @ ( vf @ A @ C ) )
& ( E != G )
& ( A != C )
& ( G = H )
& ( rpoint @ H )
& ( E = F )
& ( rpoint @ F )
& ( C = D )
& ( rpoint @ D )
& ( A = B )
& ( rpoint @ B ) )
=> ( ( vf @ A @ ( vskolem1120 @ A @ B @ C @ D @ E @ F @ G @ H ) )
= ( vf @ E @ G ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(238), 0), 0)') ).
thf(1416,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( rless @ ( vf @ E @ G ) @ ( vf @ A @ C ) )
& ( E != G )
& ( A != C )
& ( G = H )
& ( rpoint @ H )
& ( E = F )
& ( rpoint @ F )
& ( C = D )
& ( rpoint @ D )
& ( A = B )
& ( rpoint @ B ) )
=> ( ( vf @ A @ ( vskolem1120 @ A @ B @ C @ D @ E @ F @ G @ H ) )
= ( vf @ E @ G ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(143,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ? [G: $i] :
( ( ron @ F @ G )
& ( ron @ E @ G )
& ( ron @ D @ G )
& ( rline @ G ) )
& ( ( vangle @ B @ A @ C )
= ( vangle @ E @ D @ F ) )
& ( ( vf @ A @ C )
= ( vf @ D @ F ) )
& ( ( vf @ A @ B )
= ( vf @ D @ E ) )
& ? [G: $i] :
( ( F = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( E = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( D = G )
& ( rpoint @ G ) )
& ( B != C )
& ( A != C )
& ( A != B )
& ? [G: $i] :
( ( C = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( B = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( A = G )
& ( rpoint @ G ) ) )
=> ( ron @ D @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(proof(267), 0), 41)') ).
thf(1468,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ? [G: $i] :
( ( ron @ F @ G )
& ( ron @ E @ G )
& ( ron @ D @ G )
& ( rline @ G ) )
& ( ( vangle @ B @ A @ C )
= ( vangle @ E @ D @ F ) )
& ( ( vf @ A @ C )
= ( vf @ D @ F ) )
& ( ( vf @ A @ B )
= ( vf @ D @ E ) )
& ? [G: $i] :
( ( F = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( E = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( D = G )
& ( rpoint @ G ) )
& ( B != C )
& ( A != C )
& ( A != B )
& ? [G: $i] :
( ( C = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( B = G )
& ( rpoint @ G ) )
& ? [G: $i] :
( ( A = G )
& ( rpoint @ G ) ) )
=> ( ron @ D @ ( vskolem1197 @ A @ B @ C @ D @ E @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(41,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ron @ D @ A )
& ( ron @ C @ A )
& ? [E: $i] :
( ( D = E )
& ( rpoint @ E ) )
& ? [E: $i] :
( ( C = E )
& ( rpoint @ E ) )
& ( A = B )
& ( rcircle @ B ) )
=> ? [E: $i] :
( ( E != D )
& ( E != C )
& ( ron @ E @ A )
& ( rpoint @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(45), 0), imp(cond(axiom(45), 0)))') ).
thf(496,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ron @ D @ A )
& ( ron @ C @ A )
& ? [E: $i] :
( ( D = E )
& ( rpoint @ E ) )
& ? [E: $i] :
( ( C = E )
& ( rpoint @ E ) )
& ( A = B )
& ( rcircle @ B ) )
=> ? [E: $i] :
( ( E != D )
& ( E != C )
& ( ron @ E @ A )
& ( rpoint @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(2303,plain,
$false,
inference(cvc4,[status(thm)],[320,270,1322,1501,1190,909,777,1110,666,1295,170,762,1544,247,597,614,677,1078,1164,1233,1260,747,1264,619,751,344,1577,157,559,1514,421,1609,416,325,448,261,821,1136,834,397,280,1447,1622,660,1433,527,1564,602,766,894,1123,392,192,788,329,665,1291,842,285,1402,1350,1089,874,1017,1540,1082,488,554,476,1150,1451,1246,266,205,953,718,773,586,573,733,1278,298,904,402,1389,826,1488,382,713,1635,804,1464,159,1048,377,1376,509,434,477,631,816,726,520,251,1177,462,811,387,685,1044,563,1102,653,922,1203,1420,648,939,1551,855,887,331,1220,1336,643,1052,864,876,859,627,1216,699,1481,1030,290,899,1309,315,967,1527,210,239,294,1363,635,1065,796,200,607,354,935,543,1416,1468,496]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : GEO287+1 : TPTP v8.1.2. Released v4.1.0.
% 0.10/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n031.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 04:36:41 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.91/0.83 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.64/1.07 % [INFO] Parsing done (233ms).
% 1.64/1.07 % [INFO] Running in sequential loop mode.
% 2.34/1.28 % [INFO] eprover registered as external prover.
% 2.34/1.28 % [INFO] cvc4 registered as external prover.
% 2.34/1.29 % [INFO] Scanning for conjecture ...
% 2.78/1.38 % [INFO] Found a conjecture and 154 axioms. Running axiom selection ...
% 2.78/1.47 % [INFO] Axiom selection finished. Selected 154 axioms (removed 0 axioms).
% 4.09/1.85 % [INFO] Problem is first-order (TPTP FOF).
% 4.09/1.89 % [INFO] Type checking passed.
% 4.09/1.90 % [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 ...
% 25.50/7.44 % External prover 'cvc4' found a proof!
% 25.50/7.44 % [INFO] Killing All external provers ...
% 25.50/7.44 % Time passed: 6924ms (effective reasoning time: 6362ms)
% 25.50/7.44 % 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)>
% 25.50/7.44 % Axioms used in derivation (154): qu(cond(axiom(41), 0), imp(cond(axiom(41), 0))), ass(cond(proof(267), 0), 26), qu(cond(axiom(119), 0), imp(cond(axiom(119), 0))), qu(cond(axiom(3), 0), imp(cond(axiom(3), 0))), qu(cond(axiom(164), 0), imp(cond(axiom(164), 0))), qu(cond(axiom(145), 0), imp(cond(axiom(145), 0))), ass(cond(goal(206), 0), 1), qu(cond(axiom(202), 0), imp(cond(axiom(202), 0))), qu(cond(axiom(19), 0), imp(cond(axiom(19), 0))), qu(cond(axiom(95), 0), imp(cond(axiom(95), 0))), qu(cond(axiom(43), 0), imp(cond(axiom(43), 0))), qu(cond(axiom(133), 0), imp(cond(axiom(133), 0))), qu(cond(axiom(21), 0), imp(cond(axiom(21), 0))), qu(cond(axiom(151), 0), imp(cond(axiom(151), 0))), pred(axiom(5), 0), qu(cond(axiom(75), 0), imp(cond(axiom(75), 0))), qu(cond(axiom(194), 0), imp(cond(axiom(194), 0))), qu(cond(axiom(190), 0), imp(cond(axiom(190), 0))), qu(cond(axiom(53), 0), imp(cond(axiom(53), 0))), ass(cond(proof(267), 0), 25), ass(cond(proof(267), 0), 34), qu(cond(axiom(89), 0), imp(cond(axiom(89), 0))), ass(cond(proof(267), 0), 4), pred(axiom(137), 2), qu(cond(axiom(31), 0), imp(cond(axiom(31), 0))), ass(cond(goal(206), 0), 0), ass(cond(proof(267), 0), 29), qu(cond(axiom(107), 0), imp(cond(axiom(107), 0))), qu(cond(axiom(103), 0), imp(cond(axiom(103), 0))), ass(cond(goal(238), 0), 0), ass(cond(proof(267), 0), 16), qu(cond(axiom(77), 0), imp(cond(axiom(77), 0))), qu(cond(axiom(113), 0), imp(cond(axiom(113), 0))), qu(cond(axiom(45), 0), imp(cond(axiom(45), 0))), qu(cond(axiom(11), 0), imp(cond(axiom(11), 0))), qu(cond(axiom(176), 0), imp(cond(axiom(176), 0))), qu(cond(axiom(33), 0), imp(cond(axiom(33), 0))), qu(cond(axiom(139), 0), imp(cond(axiom(139), 0))), qu(cond(axiom(59), 0), imp(cond(axiom(59), 0))), ass(cond(proof(267), 0), 22), qu(cond(axiom(35), 0), imp(cond(axiom(35), 0))), ass(cond(proof(267), 0), 38), qu(cond(axiom(23), 0), imp(cond(axiom(23), 0))), ass(cond(proof(267), 0), 30), qu(cond(axiom(87), 0), imp(cond(axiom(87), 0))), ass(cond(proof(267), 0), 9), ass(cond(proof(267), 0), 18), ass(cond(proof(267), 0), 17), qu(cond(axiom(1), 0), imp(cond(axiom(1), 0))), qu(cond(axiom(121), 0), imp(cond(axiom(121), 0))), qu(cond(axiom(83), 0), imp(cond(axiom(83), 0))), qu(cond(axiom(109), 0), imp(cond(axiom(109), 0))), qu(cond(axiom(79), 0), imp(cond(axiom(79), 0))), qu(cond(axiom(55), 0), imp(cond(axiom(55), 0))), ass(cond(proof(267), 0), 11), qu(cond(axiom(13), 0), imp(cond(axiom(13), 0))), qu(cond(axiom(143), 0), imp(cond(axiom(143), 0))), qu(cond(axiom(81), 0), imp(cond(axiom(81), 0))), ass(cond(proof(267), 0), 31), ass(cond(156, 0), 0), qu(cond(axiom(184), 0), imp(cond(axiom(184), 0))), qu(cond(axiom(188), 0), imp(cond(axiom(188), 0))), qu(cond(axiom(99), 0), imp(cond(axiom(99), 0))), ass(cond(proof(267), 0), 5), ass(cond(proof(267), 0), 21), qu(cond(axiom(71), 0), imp(cond(axiom(71), 0))), ass(cond(proof(267), 0), 13), ass(cond(goal(238), 0), 1), qu(cond(axiom(57), 0), imp(cond(axiom(57), 0))), ass(cond(proof(267), 0), 35), qu(cond(axiom(65), 0), imp(cond(axiom(65), 0))), qu(cond(axiom(174), 0), imp(cond(axiom(174), 0))), qu(cond(axiom(61), 0), imp(cond(axiom(61), 0))), ass(cond(proof(267), 0), 15), ass(cond(proof(267), 0), 0), ass(cond(proof(267), 0), 2), qu(cond(axiom(9), 0), imp(cond(axiom(9), 0))), and(neg(neg(conjunct2(conjunct2(conjunct2(plural(comma_conjunct2(265))))))), and(holds(conjunct1(conjunct2(conjunct2(plural(comma_conjunct2(265))))), 1172, 0), and(holds(conjunct1(conjunct2(plural(comma_conjunct2(265)))), 1171, 0), and(holds(conjunct1(plural(comma_conjunct2(265))), 1170, 0), and(qe(s3(plural(comma_conjunct2(265)))), and(qe(s2(plural(comma_conjunct2(265)))), and(qe(s1(plural(comma_conjunct2(265)))), and(pred(comma_conjunct1(265), 9), and(pred(comma_conjunct1(265), 8), and(pred(comma_conjunct1(265), 7), and(qe(s3(plural(265))), and(qe(s2(plural(265))), qe(s1(plural(265))))))))))))))), ass(cond(proof(267), 0), 8), qu(cond(axiom(182), 0), imp(cond(axiom(182), 0))), qu(cond(axiom(117), 0), imp(cond(axiom(117), 0))), qu(cond(axiom(172), 0), imp(cond(axiom(172), 0))), qu(cond(axiom(115), 0), imp(cond(axiom(115), 0))), qu(cond(axiom(131), 0), imp(cond(axiom(131), 0))), qu(cond(axiom(196), 0), imp(cond(axiom(196), 0))), qu(cond(axiom(186), 0), imp(cond(axiom(186), 0))), qu(cond(axiom(127), 0), imp(cond(axiom(127), 0))), ass(cond(proof(267), 0), 40), ass(cond(proof(267), 0), 19), ass(cond(proof(267), 0), 36), qu(cond(axiom(123), 0), imp(cond(axiom(123), 0))), qu(cond(axiom(25), 0), imp(cond(axiom(25), 0))), qu(cond(axiom(101), 0), imp(cond(axiom(101), 0))), qu(cond(axiom(125), 0), imp(cond(axiom(125), 0))), ass(cond(proof(267), 0), 23), ass(cond(proof(267), 0), 12), qu(cond(axiom(170), 0), imp(cond(axiom(170), 0))), qu(cond(axiom(111), 0), imp(cond(axiom(111), 0))), ass(cond(proof(267), 0), 6), qu(cond(axiom(166), 0), imp(cond(axiom(166), 0))), qu(cond(axiom(105), 0), imp(cond(axiom(105), 0))), qu(cond(axiom(37), 0), imp(cond(axiom(37), 0))), qu(cond(axiom(63), 0), imp(cond(axiom(63), 0))), qu(cond(axiom(192), 0), imp(cond(axiom(192), 0))), ass(cond(proof(267), 0), 7), ass(cond(proof(267), 0), 28), ass(cond(proof(267), 0), 20), ass(cond(goal(219), 0), 0), pred(axiom(137), 1), ass(cond(goal(206), 0), 2), qu(cond(axiom(29), 0), imp(cond(axiom(29), 0))), qu(cond(axiom(39), 0), imp(cond(axiom(39), 0))), qu(cond(axiom(129), 0), imp(cond(axiom(129), 0))), ass(cond(proof(267), 0), 32), qu(cond(axiom(73), 0), imp(cond(axiom(73), 0))), qu(cond(axiom(15), 0), imp(cond(axiom(15), 0))), ass(cond(proof(267), 0), 37), ass(cond(proof(267), 0), 33), qu(cond(axiom(85), 0), imp(cond(axiom(85), 0))), ass(cond(goal(238), 0), 2), qu(cond(axiom(200), 0), imp(cond(axiom(200), 0))), qu(cond(axiom(27), 0), imp(cond(axiom(27), 0))), qu(cond(axiom(91), 0), imp(cond(axiom(91), 0))), ass(cond(goal(219), 0), 1), qu(cond(axiom(49), 0), imp(cond(axiom(49), 0))), qu(cond(axiom(149), 0), imp(cond(axiom(149), 0))), ass(cond(proof(267), 0), 3), qu(cond(axiom(7), 0), imp(cond(axiom(7), 0))), ass(cond(proof(267), 0), 1), ass(cond(proof(267), 0), 41), qu(cond(axiom(17), 0), imp(cond(axiom(17), 0))), ass(cond(proof(267), 0), 10), qu(cond(axiom(51), 0), imp(cond(axiom(51), 0))), ass(cond(proof(267), 0), 27), qu(cond(axiom(141), 0), imp(cond(axiom(141), 0))), qu(cond(axiom(135), 0), imp(cond(axiom(135), 0))), ass(cond(proof(267), 0), 39), qu(cond(axiom(47), 0), imp(cond(axiom(47), 0))), qu(cond(axiom(69), 0), imp(cond(axiom(69), 0))), qu(cond(axiom(147), 0), imp(cond(axiom(147), 0))), qu(cond(axiom(168), 0), imp(cond(axiom(168), 0))), qu(cond(axiom(204), 0), imp(cond(axiom(204), 0))), ass(cond(proof(267), 0), 42), qu(cond(axiom(97), 0), imp(cond(axiom(97), 0))), qu(cond(axiom(162), 0), imp(cond(axiom(162), 0))), qu(cond(axiom(180), 0), imp(cond(axiom(180), 0))), qu(cond(axiom(153), 0), imp(cond(axiom(153), 0))), qu(cond(axiom(178), 0), imp(cond(axiom(178), 0))), ass(cond(proof(267), 0), 14), qu(cond(axiom(160), 0), imp(cond(axiom(160), 0))), ass(cond(proof(267), 0), 24), qu(cond(axiom(67), 0), imp(cond(axiom(67), 0))), qu(cond(axiom(93), 0), imp(cond(axiom(93), 0))), qu(cond(axiom(198), 0), imp(cond(axiom(198), 0)))
% 25.50/7.44 % No. of inferences in proof: 312
% 25.50/7.44 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 6924 ms resp. 6362 ms w/o parsing
% 25.79/7.65 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 25.79/7.65 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------