TSTP Solution File: GEO273+1 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : GEO273+1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n028.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 11:10:20 EDT 2023
% Result : Theorem 73.09s 14.76s
% Output : Refutation 73.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 171
% Syntax : Number of formulae : 309 ( 17 unt; 35 typ; 0 def)
% Number of atoms : 2990 (1352 equ; 0 cnn)
% Maximal formula atoms : 57 ( 10 avg)
% Number of connectives : 7274 ( 392 ~; 24 |;2256 &;4166 @)
% ( 8 <=>; 428 =>; 0 <=; 0 <~>)
% Maximal formula depth : 47 ( 14 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 82 ( 82 >; 0 *; 0 +; 0 <<)
% Number of symbols : 37 ( 35 usr; 9 con; 0-8 aty)
% Number of variables : 1871 ( 0 ^;1246 !; 625 ?;1871 :)
% Comments :
%------------------------------------------------------------------------------
thf(vf_type,type,
vf: $i > $i > $i ).
thf(vd1069_type,type,
vd1069: $i ).
thf(vd1070_type,type,
vd1070: $i ).
thf(vd1074_type,type,
vd1074: $i ).
thf(rpoint_type,type,
rpoint: $i > $o ).
thf(vplus_type,type,
vplus: $i > $i > $i ).
thf(rreal_type,type,
rreal: $i > $o ).
thf(rless_type,type,
rless: $i > $i > $o ).
thf(v0_type,type,
v0: $i ).
thf(rcenter_type,type,
rcenter: $i > $i > $o ).
thf(rcircle_type,type,
rcircle: $i > $o ).
thf(rinside_type,type,
rinside: $i > $i > $o ).
thf(vd684_type,type,
vd684: $i ).
thf(ron_type,type,
ron: $i > $i > $o ).
thf(rline_type,type,
rline: $i > $o ).
thf(rR_type,type,
rR: $i > $i > $i > $o ).
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(rintersect_type,type,
rintersect: $i > $i > $o ).
thf(vskolem1092_type,type,
vskolem1092: $i > $i > $i > $i > $i ).
thf(vskolem1095_type,type,
vskolem1095: $i > $i > $i > $i > $i > $i ).
thf(vskolem1089_type,type,
vskolem1089: $i > $i > $i > $i > $i ).
thf(vskolem1099_type,type,
vskolem1099: $i > $i > $i > $i > $i > $i > $i ).
thf(vg_type,type,
vg: $i > $i > $i > $i ).
thf(vtriangle_type,type,
vtriangle: $i > $i > $i > $i ).
thf(rtriangle_type,type,
rtriangle: $i > $o ).
thf(vskolem1102_type,type,
vskolem1102: $i > $i > $i > $i > $i > $i > $i > $i ).
thf(vskolem1096_type,type,
vskolem1096: $i > $i > $i > $i > $i > $i > $i ).
thf(vskolem1103_type,type,
vskolem1103: $i > $i > $i > $i > $i > $i > $i > $i > $i ).
thf(vd1075_type,type,
vd1075: $i ).
thf(vskolem1052_type,type,
vskolem1052: $i > $i > $i > $i > $i ).
thf(rgeq_type,type,
rgeq: $i > $i > $o ).
thf(vd14_type,type,
vd14: $i ).
thf(rleq_type,type,
rleq: $i > $i > $o ).
thf(114,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 ) )
=> ! [E: $i] :
( ( E
= ( vskolem1092 @ C @ D @ A @ B ) )
=> ! [F: $i] :
( ( F
= ( vskolem1095 @ E @ C @ D @ A @ B ) )
=> ( rpoint @ ( vskolem1096 @ F @ E @ C @ D @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(proof(223), 0), 15)') ).
thf(981,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 ) )
=> ! [E: $i] :
( ( E
= ( vskolem1092 @ C @ D @ A @ B ) )
=> ! [F: $i] :
( ( F
= ( vskolem1095 @ E @ C @ D @ A @ B ) )
=> ( rpoint @ ( vskolem1096 @ F @ E @ C @ D @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(18,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(212,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)],[18]) ).
thf(92,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 ) )
=> ! [E: $i] :
( ( E
= ( vskolem1092 @ C @ D @ A @ B ) )
=> ! [F: $i] :
( ( F
= ( vskolem1095 @ E @ C @ D @ A @ B ) )
=> ( ( ron @ C @ ( vskolem1099 @ F @ E @ C @ D @ A @ B ) )
& ( ron @ ( vskolem1089 @ C @ D @ A @ B ) @ ( vskolem1099 @ F @ E @ C @ D @ A @ B ) )
& ( rline @ ( vskolem1099 @ F @ E @ C @ D @ A @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(proof(223), 0), 11)') ).
thf(809,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 ) )
=> ! [E: $i] :
( ( E
= ( vskolem1092 @ C @ D @ A @ B ) )
=> ! [F: $i] :
( ( F
= ( vskolem1095 @ E @ C @ D @ A @ B ) )
=> ( ( ron @ C @ ( vskolem1099 @ F @ E @ C @ D @ A @ B ) )
& ( ron @ ( vskolem1089 @ C @ D @ A @ B ) @ ( vskolem1099 @ F @ E @ C @ D @ A @ B ) )
& ( rline @ ( vskolem1099 @ F @ E @ C @ D @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(50,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(479,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)],[50]) ).
thf(53,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(518,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)],[53]) ).
thf(34,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(365,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)],[34]) ).
thf(1,conjecture,
? [A: $i] :
( ( ( vf @ vd1069 @ vd1070 )
= ( vf @ vd1074 @ A ) )
& ( rpoint @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qe(222)') ).
thf(2,negated_conjecture,
~ ? [A: $i] :
( ( ( vf @ vd1069 @ vd1070 )
= ( vf @ vd1074 @ A ) )
& ( rpoint @ A ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(138,plain,
~ ? [A: $i] :
( ( ( vf @ vd1069 @ vd1070 )
= ( vf @ vd1074 @ A ) )
& ( rpoint @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(113,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(977,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)],[113]) ).
thf(54,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(523,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)],[54]) ).
thf(127,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(1068,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)],[127]) ).
thf(65,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(614,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)],[65]) ).
thf(98,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 ) )
=> ! [E: $i] :
( ( E
= ( vskolem1092 @ C @ D @ A @ B ) )
=> ! [F: $i] :
( ( F
= ( vskolem1095 @ E @ C @ D @ A @ B ) )
=> ! [G: $i] :
( ( G
= ( vskolem1099 @ F @ E @ C @ D @ A @ B ) )
=> ! [H: $i] :
( ( H
= ( vskolem1102 @ G @ F @ E @ C @ D @ A @ B ) )
=> ( ron @ ( vskolem1103 @ H @ G @ F @ E @ C @ D @ A @ B ) @ H ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(proof(223), 0), 6)') ).
thf(861,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 ) )
=> ! [E: $i] :
( ( E
= ( vskolem1092 @ C @ D @ A @ B ) )
=> ! [F: $i] :
( ( F
= ( vskolem1095 @ E @ C @ D @ A @ B ) )
=> ! [G: $i] :
( ( G
= ( vskolem1099 @ F @ E @ C @ D @ A @ B ) )
=> ! [H: $i] :
( ( H
= ( vskolem1102 @ G @ F @ E @ C @ D @ A @ B ) )
=> ( ron @ ( vskolem1103 @ H @ G @ F @ E @ C @ D @ A @ B ) @ H ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(37,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 ) )
=> ( ( ron @ ( vskolem1089 @ C @ D @ A @ B ) @ ( vskolem1092 @ C @ D @ A @ B ) )
& ( ron @ A @ ( vskolem1092 @ C @ D @ A @ B ) )
& ( rline @ ( vskolem1092 @ C @ D @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(proof(223), 0), 19)') ).
thf(384,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 ) )
=> ( ( ron @ ( vskolem1089 @ C @ D @ A @ B ) @ ( vskolem1092 @ C @ D @ A @ B ) )
& ( ron @ A @ ( vskolem1092 @ C @ D @ A @ B ) )
& ( rline @ ( vskolem1092 @ C @ D @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(56,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(533,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)],[56]) ).
thf(57,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(538,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)],[57]) ).
thf(105,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(917,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)],[105]) ).
thf(15,axiom,
v0 = vd684,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pred(axiom(137), 2)') ).
thf(196,plain,
v0 = vd684,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(118,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(1013,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)],[118]) ).
thf(135,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(1115,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)],[135]) ).
thf(21,axiom,
vd1069 != vd1070,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pred(220, 5)') ).
thf(228,plain,
vd1069 != vd1070,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(46,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 ) )
=> ! [E: $i] :
( ( E
= ( vskolem1092 @ C @ D @ A @ B ) )
=> ! [F: $i] :
( ( F
= ( vskolem1095 @ E @ C @ D @ A @ B ) )
=> ! [G: $i] :
( ( G
= ( vskolem1099 @ F @ E @ C @ D @ A @ B ) )
=> ! [H: $i] :
( ( H
= ( vskolem1102 @ G @ F @ E @ C @ D @ A @ B ) )
=> ( rR @ C @ ( vskolem1103 @ H @ G @ F @ E @ C @ D @ A @ B ) @ ( vskolem1089 @ C @ D @ A @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(proof(223), 0), 4)') ).
thf(448,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 ) )
=> ! [E: $i] :
( ( E
= ( vskolem1092 @ C @ D @ A @ B ) )
=> ! [F: $i] :
( ( F
= ( vskolem1095 @ E @ C @ D @ A @ B ) )
=> ! [G: $i] :
( ( G
= ( vskolem1099 @ F @ E @ C @ D @ A @ B ) )
=> ! [H: $i] :
( ( H
= ( vskolem1102 @ G @ F @ E @ C @ D @ A @ B ) )
=> ( rR @ C @ ( vskolem1103 @ H @ G @ F @ E @ C @ D @ A @ B ) @ ( vskolem1089 @ C @ D @ A @ B ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(122,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(1040,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)],[122]) ).
thf(68,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(646,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)],[68]) ).
thf(27,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(292,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)],[27]) ).
thf(47,axiom,
? [A: $i] :
( ( vd1069 = A )
& ( rpoint @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qe(s1(plural(220)))') ).
thf(452,plain,
? [A: $i] :
( ( vd1069 = A )
& ( rpoint @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(107,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(925,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)],[107]) ).
thf(19,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 ) )
=> ! [E: $i] :
( ( E
= ( vskolem1092 @ C @ D @ A @ B ) )
=> ! [F: $i] :
( ( F
= ( vskolem1095 @ E @ C @ D @ A @ B ) )
=> ! [G: $i] :
( ( ( ron @ C @ G )
& ( ron @ ( vskolem1089 @ C @ D @ A @ B ) @ G )
& ( rline @ G ) )
=> ( G
= ( vskolem1099 @ F @ E @ C @ D @ A @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(proof(223), 0), 10)') ).
thf(220,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 ) )
=> ! [E: $i] :
( ( E
= ( vskolem1092 @ C @ D @ A @ B ) )
=> ! [F: $i] :
( ( F
= ( vskolem1095 @ E @ C @ D @ A @ B ) )
=> ! [G: $i] :
( ( ( ron @ C @ G )
& ( ron @ ( vskolem1089 @ C @ D @ A @ B ) @ G )
& ( rline @ G ) )
=> ( G
= ( vskolem1099 @ F @ E @ C @ D @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(76,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(714,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)],[76]) ).
thf(23,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(260,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)],[23]) ).
thf(7,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(160,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)],[7]) ).
thf(8,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(165,plain,
! [A: $i,B: $i] :
( ( rcenter @ A @ B )
=> ( rinside @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(97,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(847,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)],[97]) ).
thf(33,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 ) )
=> ! [E: $i] :
( ( ( ron @ ( vskolem1089 @ C @ D @ A @ B ) @ E )
& ( ron @ A @ E )
& ( rline @ E ) )
=> ( E
= ( vskolem1092 @ C @ D @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(proof(223), 0), 18)') ).
thf(361,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 ) )
=> ! [E: $i] :
( ( ( ron @ ( vskolem1089 @ C @ D @ A @ B ) @ E )
& ( ron @ A @ E )
& ( rline @ E ) )
=> ( E
= ( vskolem1092 @ C @ D @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(66,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(625,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)],[66]) ).
thf(48,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(456,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)],[48]) ).
thf(20,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(224,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)],[20]) ).
thf(130,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(1089,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)],[130]) ).
thf(119,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(1017,plain,
! [A: $i,B: $i] :
( ( ( A = B )
& ( rpoint @ B ) )
=> ? [C: $i] :
( ( C != A )
& ( rpoint @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(6,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(156,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)],[6]) ).
thf(41,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(420,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)],[41]) ).
thf(3,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(141,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)],[3]) ).
thf(100,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(869,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)],[100]) ).
thf(115,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(985,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)],[115]) ).
thf(78,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(738,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)],[78]) ).
thf(137,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(1131,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)],[137]) ).
thf(126,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(1060,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)],[126]) ).
thf(88,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 ) )
=> ! [E: $i] :
( ( E
= ( vskolem1092 @ C @ D @ A @ B ) )
=> ! [F: $i] :
( ( F
= ( vskolem1095 @ E @ C @ D @ A @ B ) )
=> ! [G: $i] :
( ( G
= ( vskolem1099 @ F @ E @ C @ D @ A @ B ) )
=> ! [H: $i] :
( ( ( ron @ ( vskolem1096 @ F @ E @ C @ D @ A @ B ) @ H )
& ( rcenter @ ( vskolem1089 @ C @ D @ A @ B ) @ H )
& ( rcircle @ H ) )
=> ( H
= ( vskolem1102 @ G @ F @ E @ C @ D @ A @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(proof(223), 0), 8)') ).
thf(792,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 ) )
=> ! [E: $i] :
( ( E
= ( vskolem1092 @ C @ D @ A @ B ) )
=> ! [F: $i] :
( ( F
= ( vskolem1095 @ E @ C @ D @ A @ B ) )
=> ! [G: $i] :
( ( G
= ( vskolem1099 @ F @ E @ C @ D @ A @ B ) )
=> ! [H: $i] :
( ( ( ron @ ( vskolem1096 @ F @ E @ C @ D @ A @ B ) @ H )
& ( rcenter @ ( vskolem1089 @ C @ D @ A @ B ) @ H )
& ( rcircle @ H ) )
=> ( H
= ( vskolem1102 @ G @ F @ E @ C @ D @ A @ B ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(67,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(633,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)],[67]) ).
thf(106,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 ) )
=> ! [E: $i] :
( ( E
= ( vskolem1092 @ C @ D @ A @ B ) )
=> ! [F: $i] :
( ( F
= ( vskolem1095 @ E @ C @ D @ A @ B ) )
=> ! [G: $i] :
( ( G
= ( vskolem1099 @ F @ E @ C @ D @ A @ B ) )
=> ! [H: $i] :
( ( H
= ( vskolem1102 @ G @ F @ E @ C @ D @ A @ B ) )
=> ( ( vf @ A @ B )
= ( vf @ C @ ( vskolem1103 @ H @ G @ F @ E @ C @ D @ A @ B ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(proof(223), 0), 0)') ).
thf(921,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 ) )
=> ! [E: $i] :
( ( E
= ( vskolem1092 @ C @ D @ A @ B ) )
=> ! [F: $i] :
( ( F
= ( vskolem1095 @ E @ C @ D @ A @ B ) )
=> ! [G: $i] :
( ( G
= ( vskolem1099 @ F @ E @ C @ D @ A @ B ) )
=> ! [H: $i] :
( ( H
= ( vskolem1102 @ G @ F @ E @ C @ D @ A @ B ) )
=> ( ( vf @ A @ B )
= ( vf @ C @ ( vskolem1103 @ H @ G @ F @ E @ C @ D @ A @ B ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(69,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(657,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)],[69]) ).
thf(39,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(398,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)],[39]) ).
thf(60,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(558,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)],[60]) ).
thf(102,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(888,plain,
! [A: $i,B: $i] :
( ( ( A = B )
& ( rline @ B ) )
=> ? [C: $i] :
( ( ron @ C @ A )
& ( rpoint @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(91,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 ) )
=> ! [E: $i] :
( ( E
= ( vskolem1092 @ C @ D @ A @ B ) )
=> ! [F: $i] :
( ( F
= ( vskolem1095 @ E @ C @ D @ A @ B ) )
=> ( ron @ ( vskolem1096 @ F @ E @ C @ D @ A @ B ) @ E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(proof(223), 0), 13)') ).
thf(805,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 ) )
=> ! [E: $i] :
( ( E
= ( vskolem1092 @ C @ D @ A @ B ) )
=> ! [F: $i] :
( ( F
= ( vskolem1095 @ E @ C @ D @ A @ B ) )
=> ( ron @ ( vskolem1096 @ F @ E @ C @ D @ A @ B ) @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(17,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(205,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)],[17]) ).
thf(42,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(425,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)],[42]) ).
thf(45,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(444,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)],[45]) ).
thf(52,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(513,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)],[52]) ).
thf(43,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 @ ( vskolem1089 @ C @ D @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(proof(223), 0), 22)') ).
thf(430,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 @ ( vskolem1089 @ C @ D @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(93,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(819,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)],[93]) ).
thf(14,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(191,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)],[14]) ).
thf(84,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(772,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)],[84]) ).
thf(79,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(743,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)],[79]) ).
thf(94,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(826,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)],[94]) ).
thf(108,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(936,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)],[108]) ).
thf(75,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(704,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)],[75]) ).
thf(83,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(764,plain,
! [A: $i,B: $i] :
( ( ( A = B )
& ( rcircle @ B ) )
=> ? [C: $i] :
( ( ron @ C @ A )
& ( rpoint @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(87,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(784,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)],[87]) ).
thf(124,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 ) )
=> ! [E: $i] :
( ( E
= ( vskolem1092 @ C @ D @ A @ B ) )
=> ! [F: $i] :
( ( F
= ( vskolem1095 @ E @ C @ D @ A @ B ) )
=> ! [G: $i] :
( ( G
= ( vskolem1099 @ F @ E @ C @ D @ A @ B ) )
=> ! [H: $i] :
( ( H
= ( vskolem1102 @ G @ F @ E @ C @ D @ A @ B ) )
=> ( ron @ ( vskolem1103 @ H @ G @ F @ E @ C @ D @ A @ B ) @ G ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(proof(223), 0), 5)') ).
thf(1048,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 ) )
=> ! [E: $i] :
( ( E
= ( vskolem1092 @ C @ D @ A @ B ) )
=> ! [F: $i] :
( ( F
= ( vskolem1095 @ E @ C @ D @ A @ B ) )
=> ! [G: $i] :
( ( G
= ( vskolem1099 @ F @ E @ C @ D @ A @ B ) )
=> ! [H: $i] :
( ( H
= ( vskolem1102 @ G @ F @ E @ C @ D @ A @ B ) )
=> ( ron @ ( vskolem1103 @ H @ G @ F @ E @ C @ D @ A @ B ) @ G ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(36,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(377,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)],[36]) ).
thf(44,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 ) )
=> ! [E: $i] :
( ( E
= ( vskolem1092 @ C @ D @ A @ B ) )
=> ( ( ron @ B @ ( vskolem1095 @ E @ C @ D @ A @ B ) )
& ( rcenter @ A @ ( vskolem1095 @ E @ C @ D @ A @ B ) )
& ( rcircle @ ( vskolem1095 @ E @ C @ D @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(proof(223), 0), 17)') ).
thf(434,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 ) )
=> ! [E: $i] :
( ( E
= ( vskolem1092 @ C @ D @ A @ B ) )
=> ( ( ron @ B @ ( vskolem1095 @ E @ C @ D @ A @ B ) )
& ( rcenter @ A @ ( vskolem1095 @ E @ C @ D @ A @ B ) )
& ( rcircle @ ( vskolem1095 @ E @ C @ D @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(63,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(599,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)],[63]) ).
thf(10,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(172,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)],[10]) ).
thf(95,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 ) )
=> ! [E: $i] :
( ( E
= ( vskolem1092 @ C @ D @ A @ B ) )
=> ! [F: $i] :
( ( F
= ( vskolem1095 @ E @ C @ D @ A @ B ) )
=> ! [G: $i] :
( ( G
= ( vskolem1099 @ F @ E @ C @ D @ A @ B ) )
=> ! [H: $i] :
( ( H
= ( vskolem1102 @ G @ F @ E @ C @ D @ A @ B ) )
=> ( ( vf @ A @ B )
= ( vf @ A @ ( vskolem1096 @ F @ E @ C @ D @ A @ B ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(proof(223), 0), 3)') ).
thf(831,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 ) )
=> ! [E: $i] :
( ( E
= ( vskolem1092 @ C @ D @ A @ B ) )
=> ! [F: $i] :
( ( F
= ( vskolem1095 @ E @ C @ D @ A @ B ) )
=> ! [G: $i] :
( ( G
= ( vskolem1099 @ F @ E @ C @ D @ A @ B ) )
=> ! [H: $i] :
( ( H
= ( vskolem1102 @ G @ F @ E @ C @ D @ A @ B ) )
=> ( ( vf @ A @ B )
= ( vf @ A @ ( vskolem1096 @ F @ E @ C @ D @ A @ B ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(58,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(552,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)],[58]) ).
thf(74,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 ) )
=> ! [E: $i] :
( ( E
= ( vskolem1092 @ C @ D @ A @ B ) )
=> ! [F: $i] :
( ( F
= ( vskolem1095 @ E @ C @ D @ A @ B ) )
=> ( ron @ ( vskolem1096 @ F @ E @ C @ D @ A @ B ) @ F ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(proof(223), 0), 14)') ).
thf(700,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 ) )
=> ! [E: $i] :
( ( E
= ( vskolem1092 @ C @ D @ A @ B ) )
=> ! [F: $i] :
( ( F
= ( vskolem1095 @ E @ C @ D @ A @ B ) )
=> ( ron @ ( vskolem1096 @ F @ E @ C @ D @ A @ B ) @ F ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(16,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(198,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)],[16]) ).
thf(134,axiom,
vd1074 != vd1070,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(conjunct2(221), 1077, 0)') ).
thf(1112,plain,
vd1074 != vd1070,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(25,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(278,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)],[25]) ).
thf(86,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(780,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)],[86]) ).
thf(101,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(883,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)],[101]) ).
thf(38,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(394,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)],[38]) ).
thf(133,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(1102,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)],[133]) ).
thf(9,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(167,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)],[9]) ).
thf(110,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(944,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)],[110]) ).
thf(71,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(680,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)],[71]) ).
thf(128,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 ) )
=> ! [E: $i] :
( ( E
= ( vskolem1092 @ C @ D @ A @ B ) )
=> ! [F: $i] :
( ( F
= ( vskolem1095 @ E @ C @ D @ A @ B ) )
=> ! [G: $i] :
( ( G
= ( vskolem1099 @ F @ E @ C @ D @ A @ B ) )
=> ! [H: $i] :
( ( H
= ( vskolem1102 @ G @ F @ E @ C @ D @ A @ B ) )
=> ( ( vf @ ( vskolem1089 @ C @ D @ A @ B ) @ ( vskolem1096 @ F @ E @ C @ D @ A @ B ) )
= ( vf @ ( vskolem1089 @ C @ D @ A @ B ) @ ( vskolem1103 @ H @ G @ F @ E @ C @ D @ A @ B ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(proof(223), 0), 2)') ).
thf(1081,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 ) )
=> ! [E: $i] :
( ( E
= ( vskolem1092 @ C @ D @ A @ B ) )
=> ! [F: $i] :
( ( F
= ( vskolem1095 @ E @ C @ D @ A @ B ) )
=> ! [G: $i] :
( ( G
= ( vskolem1099 @ F @ E @ C @ D @ A @ B ) )
=> ! [H: $i] :
( ( H
= ( vskolem1102 @ G @ F @ E @ C @ D @ A @ B ) )
=> ( ( vf @ ( vskolem1089 @ C @ D @ A @ B ) @ ( vskolem1096 @ F @ E @ C @ D @ A @ B ) )
= ( vf @ ( vskolem1089 @ C @ D @ A @ B ) @ ( vskolem1103 @ H @ G @ F @ E @ C @ D @ A @ B ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(28,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 ) )
=> ! [E: $i] :
( ( E
= ( vskolem1092 @ C @ D @ A @ B ) )
=> ! [F: $i] :
( ( F
= ( vskolem1095 @ E @ C @ D @ A @ B ) )
=> ! [G: $i] :
( ( G
= ( vskolem1099 @ F @ E @ C @ D @ A @ B ) )
=> ! [H: $i] :
( ( H
= ( vskolem1102 @ G @ F @ E @ C @ D @ A @ B ) )
=> ( ( vf @ A @ ( vskolem1096 @ F @ E @ C @ D @ A @ B ) )
= ( vf @ C @ ( vskolem1103 @ H @ G @ F @ E @ C @ D @ A @ B ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(proof(223), 0), 1)') ).
thf(342,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 ) )
=> ! [E: $i] :
( ( E
= ( vskolem1092 @ C @ D @ A @ B ) )
=> ! [F: $i] :
( ( F
= ( vskolem1095 @ E @ C @ D @ A @ B ) )
=> ! [G: $i] :
( ( G
= ( vskolem1099 @ F @ E @ C @ D @ A @ B ) )
=> ! [H: $i] :
( ( H
= ( vskolem1102 @ G @ F @ E @ C @ D @ A @ B ) )
=> ( ( vf @ A @ ( vskolem1096 @ F @ E @ C @ D @ A @ B ) )
= ( vf @ C @ ( vskolem1103 @ H @ G @ F @ E @ C @ D @ A @ B ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(31,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 ) )
=> ! [E: $i] :
( ( E
= ( vskolem1092 @ C @ D @ A @ B ) )
=> ! [F: $i] :
( ( F
= ( vskolem1095 @ E @ C @ D @ A @ B ) )
=> ( rR @ A @ ( vskolem1089 @ C @ D @ A @ B ) @ ( vskolem1096 @ F @ E @ C @ D @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(proof(223), 0), 12)') ).
thf(355,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 ) )
=> ! [E: $i] :
( ( E
= ( vskolem1092 @ C @ D @ A @ B ) )
=> ! [F: $i] :
( ( F
= ( vskolem1095 @ E @ C @ D @ A @ B ) )
=> ( rR @ A @ ( vskolem1089 @ C @ D @ A @ B ) @ ( vskolem1096 @ F @ E @ C @ D @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(96,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(836,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)],[96]) ).
thf(85,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(776,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)],[85]) ).
thf(120,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(1025,plain,
! [A: $i,B: $i] :
( ( ( A = B )
& ( rcircle @ B ) )
=> ? [C: $i] :
( ( rinside @ C @ A )
& ( rpoint @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(26,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(282,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)],[26]) ).
thf(132,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 ) )
=> ! [E: $i] :
( ( E
= ( vskolem1092 @ C @ D @ A @ B ) )
=> ! [F: $i] :
( ( F
= ( vskolem1095 @ E @ C @ D @ A @ B ) )
=> ! [G: $i] :
( ( G
= ( vskolem1099 @ F @ E @ C @ D @ A @ B ) )
=> ! [H: $i] :
( ( H
= ( vskolem1102 @ G @ F @ E @ C @ D @ A @ B ) )
=> ( rpoint @ ( vskolem1103 @ H @ G @ F @ E @ C @ D @ A @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(proof(223), 0), 7)') ).
thf(1098,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 ) )
=> ! [E: $i] :
( ( E
= ( vskolem1092 @ C @ D @ A @ B ) )
=> ! [F: $i] :
( ( F
= ( vskolem1095 @ E @ C @ D @ A @ B ) )
=> ! [G: $i] :
( ( G
= ( vskolem1099 @ F @ E @ C @ D @ A @ B ) )
=> ! [H: $i] :
( ( H
= ( vskolem1102 @ G @ F @ E @ C @ D @ A @ B ) )
=> ( rpoint @ ( vskolem1103 @ H @ G @ F @ E @ C @ D @ A @ B ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(59,axiom,
rpoint @ vd1075,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pred(221, 1)') ).
thf(557,plain,
rpoint @ vd1075,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(117,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 ) )
=> ! [E: $i] :
( ( E
= ( vskolem1092 @ C @ D @ A @ B ) )
=> ! [F: $i] :
( ( F
= ( vskolem1095 @ E @ C @ D @ A @ B ) )
=> ! [G: $i] :
( ( G
= ( vskolem1099 @ F @ E @ C @ D @ A @ B ) )
=> ( ( ron @ ( vskolem1096 @ F @ E @ C @ D @ A @ B ) @ ( vskolem1102 @ G @ F @ E @ C @ D @ A @ B ) )
& ( rcenter @ ( vskolem1089 @ C @ D @ A @ B ) @ ( vskolem1102 @ G @ F @ E @ C @ D @ A @ B ) )
& ( rcircle @ ( vskolem1102 @ G @ F @ E @ C @ D @ A @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(proof(223), 0), 9)') ).
thf(1003,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 ) )
=> ! [E: $i] :
( ( E
= ( vskolem1092 @ C @ D @ A @ B ) )
=> ! [F: $i] :
( ( F
= ( vskolem1095 @ E @ C @ D @ A @ B ) )
=> ! [G: $i] :
( ( G
= ( vskolem1099 @ F @ E @ C @ D @ A @ B ) )
=> ( ( ron @ ( vskolem1096 @ F @ E @ C @ D @ A @ B ) @ ( vskolem1102 @ G @ F @ E @ C @ D @ A @ B ) )
& ( rcenter @ ( vskolem1089 @ C @ D @ A @ B ) @ ( vskolem1102 @ G @ F @ E @ C @ D @ A @ B ) )
& ( rcircle @ ( vskolem1102 @ G @ F @ E @ C @ D @ A @ B ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(11,axiom,
rreal @ vd684,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pred(axiom(137), 1)') ).
thf(177,plain,
rreal @ vd684,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(62,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(585,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)],[62]) ).
thf(51,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(502,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)],[51]) ).
thf(129,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(1085,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)],[129]) ).
thf(111,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(951,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)],[111]) ).
thf(32,axiom,
vd1074 = vd1075,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pred(221, 4)') ).
thf(359,plain,
vd1074 = vd1075,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(64,axiom,
rpoint @ vd14,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pred(axiom(5), 0)') ).
thf(613,plain,
rpoint @ vd14,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(125,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(1052,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)],[125]) ).
thf(77,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(727,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)],[77]) ).
thf(131,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(1094,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)],[131]) ).
thf(61,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(571,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)],[61]) ).
thf(22,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(231,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)],[22]) ).
thf(104,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(903,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)],[104]) ).
thf(82,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(759,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)],[82]) ).
thf(136,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(1126,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)],[136]) ).
thf(30,axiom,
? [A: $i] :
( ( vd1070 = A )
& ( rpoint @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qe(s2(plural(220)))') ).
thf(351,plain,
? [A: $i] :
( ( vd1070 = A )
& ( rpoint @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(13,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(186,plain,
! [A: $i,B: $i] :
( ( ( A = B )
& ( rreal @ B ) )
=> ~ ( rless @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(103,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(896,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)],[103]) ).
thf(80,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(748,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)],[80]) ).
thf(29,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(346,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)],[29]) ).
thf(123,axiom,
vd1074 != vd1069,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(conjunct1(221), 1076, 0)') ).
thf(1045,plain,
vd1074 != vd1069,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(90,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(800,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)],[90]) ).
thf(5,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(151,plain,
! [A: $i,B: $i] :
( ( ( A = B )
& ( rreal @ B ) )
=> ( ( vplus @ A @ v0 )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(4,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(146,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)],[4]) ).
thf(99,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 ) )
=> ! [E: $i] :
( ( E
= ( vskolem1092 @ C @ D @ A @ B ) )
=> ! [F: $i] :
( ( ( ron @ B @ F )
& ( rcenter @ A @ F )
& ( rcircle @ F ) )
=> ( F
= ( vskolem1095 @ E @ C @ D @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(proof(223), 0), 16)') ).
thf(865,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 ) )
=> ! [E: $i] :
( ( E
= ( vskolem1092 @ C @ D @ A @ B ) )
=> ! [F: $i] :
( ( ( ron @ B @ F )
& ( rcenter @ A @ F )
& ( rcircle @ F ) )
=> ( F
= ( vskolem1095 @ E @ C @ D @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(24,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(268,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)],[24]) ).
thf(70,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(664,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)],[70]) ).
thf(121,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(1033,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)],[121]) ).
thf(73,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(696,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)],[73]) ).
thf(112,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(955,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)],[112]) ).
thf(89,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(796,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)],[89]) ).
thf(40,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(415,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)],[40]) ).
thf(55,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(528,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)],[55]) ).
thf(116,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(992,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)],[116]) ).
thf(12,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(178,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)],[12]) ).
thf(72,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(691,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)],[72]) ).
thf(35,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(369,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)],[35]) ).
thf(81,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 @ ( vskolem1089 @ C @ D @ A @ B ) @ A )
= ( vf @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(proof(223), 0), 20)') ).
thf(755,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 @ ( vskolem1089 @ C @ D @ A @ B ) @ A )
= ( vf @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(49,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(469,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)],[49]) ).
thf(109,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 @ ( vskolem1089 @ C @ D @ A @ B ) @ C )
= ( vf @ ( vskolem1089 @ C @ D @ A @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(proof(223), 0), 21)') ).
thf(940,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 @ ( vskolem1089 @ C @ D @ A @ B ) @ C )
= ( vf @ ( vskolem1089 @ C @ D @ A @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(17214,plain,
$false,
inference(e,[status(thm)],[981,212,809,479,518,365,138,977,523,1068,614,861,384,533,538,917,196,1013,1115,228,448,1040,646,292,452,925,220,714,260,160,165,847,361,625,456,224,1089,1017,156,420,141,869,985,738,1131,1060,792,633,921,657,398,558,888,805,205,425,444,513,430,819,191,772,743,826,936,704,764,784,1048,377,434,599,172,831,552,700,198,1112,278,780,883,394,1102,167,944,680,1081,342,355,836,776,1025,282,1098,557,1003,177,585,502,1085,951,359,613,1052,727,1094,571,231,903,759,1126,351,186,896,748,346,1045,800,151,146,865,268,664,1033,696,955,796,415,528,992,178,691,369,755,469,940]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GEO273+1 : TPTP v8.1.2. Released v4.1.0.
% 0.14/0.15 % Command : run_Leo-III %s %d
% 0.14/0.35 % Computer : n028.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri May 19 04:12:04 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.96/0.88 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.63/1.12 % [INFO] Parsing done (230ms).
% 1.63/1.12 % [INFO] Running in sequential loop mode.
% 2.36/1.32 % [INFO] eprover registered as external prover.
% 2.36/1.33 % [INFO] cvc4 registered as external prover.
% 2.36/1.33 % [INFO] Scanning for conjecture ...
% 2.53/1.42 % [INFO] Found a conjecture and 135 axioms. Running axiom selection ...
% 2.87/1.49 % [INFO] Axiom selection finished. Selected 135 axioms (removed 0 axioms).
% 3.51/1.72 % [INFO] Problem is first-order (TPTP FOF).
% 3.51/1.74 % [INFO] Type checking passed.
% 3.51/1.75 % [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 ...
% 73.09/14.76 % External prover 'e' found a proof!
% 73.09/14.76 % [INFO] Killing All external provers ...
% 73.09/14.76 % Time passed: 14256ms (effective reasoning time: 13633ms)
% 73.09/14.76 % 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)>
% 73.09/14.76 % Axioms used in derivation (135): qu(cond(axiom(71), 0), imp(cond(axiom(71), 0))), qu(cond(axiom(41), 0), imp(cond(axiom(41), 0))), pred(221, 4), ass(cond(proof(223), 0), 8), ass(cond(proof(223), 0), 4), ass(cond(proof(223), 0), 15), 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))), qe(s2(plural(220))), 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))), qe(s1(plural(220))), 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))), qu(cond(axiom(89), 0), imp(cond(axiom(89), 0))), qu(cond(axiom(107), 0), imp(cond(axiom(107), 0))), pred(axiom(137), 2), qu(cond(axiom(31), 0), imp(cond(axiom(31), 0))), ass(cond(goal(206), 0), 0), qu(cond(axiom(103), 0), imp(cond(axiom(103), 0))), ass(cond(proof(223), 0), 21), ass(cond(proof(223), 0), 22), pred(220, 5), qu(cond(axiom(77), 0), imp(cond(axiom(77), 0))), qu(cond(axiom(113), 0), imp(cond(axiom(113), 0))), pred(221, 1), 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))), ass(cond(proof(223), 0), 12), qu(cond(axiom(59), 0), imp(cond(axiom(59), 0))), ass(cond(proof(223), 0), 3), ass(cond(proof(223), 0), 17), qu(cond(axiom(35), 0), imp(cond(axiom(35), 0))), ass(cond(proof(223), 0), 16), qu(cond(axiom(23), 0), imp(cond(axiom(23), 0))), qu(cond(axiom(87), 0), imp(cond(axiom(87), 0))), ass(cond(proof(223), 0), 7), 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))), ass(cond(proof(223), 0), 1), qu(cond(axiom(109), 0), imp(cond(axiom(109), 0))), holds(conjunct2(221), 1077, 0), qu(cond(axiom(79), 0), imp(cond(axiom(79), 0))), qu(cond(axiom(55), 0), imp(cond(axiom(55), 0))), qu(cond(axiom(81), 0), imp(cond(axiom(81), 0))), qu(cond(axiom(13), 0), imp(cond(axiom(13), 0))), qu(cond(axiom(143), 0), imp(cond(axiom(143), 0))), ass(cond(156, 0), 0), qu(cond(axiom(184), 0), imp(cond(axiom(184), 0))), ass(cond(proof(223), 0), 11), ass(cond(proof(223), 0), 2), qu(cond(axiom(188), 0), imp(cond(axiom(188), 0))), qu(cond(axiom(99), 0), imp(cond(axiom(99), 0))), qu(cond(axiom(57), 0), imp(cond(axiom(57), 0))), qu(cond(axiom(65), 0), imp(cond(axiom(65), 0))), qu(cond(axiom(174), 0), imp(cond(axiom(174), 0))), holds(conjunct1(221), 1076, 0), qu(cond(axiom(61), 0), imp(cond(axiom(61), 0))), qu(cond(axiom(9), 0), imp(cond(axiom(9), 0))), 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))), ass(cond(proof(223), 0), 20), 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))), 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))), qu(cond(axiom(170), 0), imp(cond(axiom(170), 0))), qu(cond(axiom(111), 0), imp(cond(axiom(111), 0))), ass(cond(proof(223), 0), 19), 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))), ass(cond(proof(223), 0), 6), qu(cond(axiom(63), 0), imp(cond(axiom(63), 0))), qu(cond(axiom(192), 0), imp(cond(axiom(192), 0))), pred(axiom(137), 1), ass(cond(proof(223), 0), 0), ass(cond(proof(223), 0), 13), qu(cond(axiom(29), 0), imp(cond(axiom(29), 0))), ass(cond(proof(223), 0), 10), ass(cond(goal(206), 0), 2), qu(cond(axiom(39), 0), imp(cond(axiom(39), 0))), qu(cond(axiom(129), 0), imp(cond(axiom(129), 0))), qu(cond(axiom(73), 0), imp(cond(axiom(73), 0))), ass(cond(proof(223), 0), 5), ass(cond(proof(223), 0), 9), qu(cond(axiom(15), 0), imp(cond(axiom(15), 0))), qu(cond(axiom(85), 0), imp(cond(axiom(85), 0))), qu(cond(axiom(200), 0), imp(cond(axiom(200), 0))), qu(cond(axiom(27), 0), imp(cond(axiom(27), 0))), ass(cond(proof(223), 0), 14), qu(cond(axiom(91), 0), imp(cond(axiom(91), 0))), qu(cond(axiom(49), 0), imp(cond(axiom(49), 0))), qu(cond(axiom(149), 0), imp(cond(axiom(149), 0))), qu(cond(axiom(7), 0), imp(cond(axiom(7), 0))), qu(cond(axiom(17), 0), imp(cond(axiom(17), 0))), qu(cond(axiom(51), 0), imp(cond(axiom(51), 0))), qu(cond(axiom(141), 0), imp(cond(axiom(141), 0))), qu(cond(axiom(135), 0), imp(cond(axiom(135), 0))), 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(223), 0), 18), 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))), qu(cond(axiom(160), 0), imp(cond(axiom(160), 0))), 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)))
% 73.09/14.76 % No. of inferences in proof: 274
% 73.09/14.76 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 14256 ms resp. 13633 ms w/o parsing
% 73.48/14.92 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 73.48/14.93 % [INFO] Killing All external provers ...
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