TSTP Solution File: GEO284+1 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : GEO284+1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n014.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 11:10:23 EDT 2023
% Result : Theorem 11.52s 3.88s
% Output : Refutation 12.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 171
% Syntax : Number of formulae : 304 ( 9 unt; 40 typ; 0 def)
% Number of atoms : 2568 (1051 equ; 0 cnn)
% Maximal formula atoms : 57 ( 9 avg)
% Number of connectives : 5635 ( 320 ~; 24 |;1998 &;3011 @)
% ( 8 <=>; 274 =>; 0 <=; 0 <~>)
% Maximal formula depth : 47 ( 13 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 46 ( 46 >; 0 *; 0 +; 0 <<)
% Number of symbols : 42 ( 40 usr; 20 con; 0-4 aty)
% Number of variables : 1506 ( 0 ^; 966 !; 540 ?;1506 :)
% Comments :
%------------------------------------------------------------------------------
thf(ron_type,type,
ron: $i > $i > $o ).
thf(vd1127_type,type,
vd1127: $i ).
thf(rcenter_type,type,
rcenter: $i > $i > $o ).
thf(vd1123_type,type,
vd1123: $i ).
thf(rcircle_type,type,
rcircle: $i > $o ).
thf(vd1125_type,type,
vd1125: $i ).
thf(rline_type,type,
rline: $i > $o ).
thf(rreal_type,type,
rreal: $i > $o ).
thf(vd684_type,type,
vd684: $i ).
thf(vplus_type,type,
vplus: $i > $i > $i ).
thf(rless_type,type,
rless: $i > $i > $o ).
thf(vtriangle_type,type,
vtriangle: $i > $i > $i > $i ).
thf(rtriangle_type,type,
rtriangle: $i > $o ).
thf(rpoint_type,type,
rpoint: $i > $o ).
thf(vg_type,type,
vg: $i > $i > $i > $i ).
thf(v0_type,type,
v0: $i ).
thf(vf_type,type,
vf: $i > $i > $i ).
thf(vskolem1078_type,type,
vskolem1078: $i > $i > $i > $i > $i ).
thf(vskolem1052_type,type,
vskolem1052: $i > $i > $i > $i > $i ).
thf(vangle_type,type,
vangle: $i > $i > $i > $i ).
thf(rR_type,type,
rR: $i > $i > $i > $o ).
thf(rleq_type,type,
rleq: $i > $i > $o ).
thf(rgeq_type,type,
rgeq: $i > $i > $o ).
thf(vd14_type,type,
vd14: $i ).
thf(vperp_type,type,
vperp: $i ).
thf(vskolem1147_type,type,
vskolem1147: $i ).
thf(vskolem1145_type,type,
vskolem1145: $i ).
thf(rS_type,type,
rS: $i > $i > $i > $o ).
thf(rintersect_type,type,
rintersect: $i > $i > $o ).
thf(vd1129_type,type,
vd1129: $i ).
thf(vskolem1140_type,type,
vskolem1140: $i ).
thf(vskolem1136_type,type,
vskolem1136: $i ).
thf(vskolem1139_type,type,
vskolem1139: $i ).
thf(vskolem1138_type,type,
vskolem1138: $i ).
thf(vskolem1146_type,type,
vskolem1146: $i ).
thf(rinside_type,type,
rinside: $i > $i > $o ).
thf(vd1130_type,type,
vd1130: $i ).
thf(vd1128_type,type,
vd1128: $i ).
thf(vd1126_type,type,
vd1126: $i ).
thf(vd1124_type,type,
vd1124: $i ).
thf(70,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(629,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)],[70]) ).
thf(39,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(365,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)],[39]) ).
thf(132,axiom,
( ( ( vd1123 != vd1129 )
& ( vd1123 != vd1127 ) )
=> ~ ( rinside @ vd1125 @ vskolem1139 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(conseq(242), 0), 7)') ).
thf(1105,plain,
( ( ( vd1123 != vd1129 )
& ( vd1123 != vd1127 ) )
=> ~ ( rinside @ vd1125 @ vskolem1139 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(128,axiom,
( ( ( vd1123 != vd1129 )
& ( vd1123 != vd1127 ) )
=> ( ( vf @ vd1123 @ vskolem1140 )
= ( vf @ vd1123 @ vskolem1136 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(conseq(242), 0), 1)') ).
thf(1083,plain,
( ( ( vd1123 != vd1129 )
& ( vd1123 != vd1127 ) )
=> ( ( vf @ vd1123 @ vskolem1140 )
= ( vf @ vd1123 @ vskolem1136 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(42,axiom,
( ( vd1123 = vd1127 )
=> ( ron @ vskolem1147 @ vskolem1145 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(conseq(242), 1), 3)') ).
thf(379,plain,
( ( vd1123 = vd1127 )
=> ( ron @ vskolem1147 @ vskolem1145 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(100,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(861,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)],[100]) ).
thf(67,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(614,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)],[67]) ).
thf(24,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(269,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)],[24]) ).
thf(61,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(550,plain,
! [A: $i,B: $i] :
( ( rcenter @ A @ B )
=> ( rinside @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(107,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(913,plain,
! [A: $i,B: $i] :
( ( ( A = B )
& ( rline @ B ) )
=> ? [C: $i] :
( ( ron @ C @ A )
& ( rpoint @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(29,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(301,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)],[29]) ).
thf(63,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(565,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)],[63]) ).
thf(50,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(436,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)],[50]) ).
thf(73,axiom,
( ( vd1123 = vd1127 )
=> ( rline @ vskolem1145 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(conseq(242), 1), 8)') ).
thf(651,plain,
( ( vd1123 = vd1127 )
=> ( rline @ vskolem1145 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(41,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(372,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)],[41]) ).
thf(68,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(619,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)],[68]) ).
thf(59,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(542,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)],[59]) ).
thf(88,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(789,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)],[88]) ).
thf(8,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(179,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)],[8]) ).
thf(91,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(806,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)],[91]) ).
thf(86,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(766,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)],[86]) ).
thf(77,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(687,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)],[77]) ).
thf(71,axiom,
( ( vd1123 = vd1127 )
=> ~ ( ron @ vd1125 @ vskolem1146 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(conseq(242), 1), 5)') ).
thf(634,plain,
( ( vd1123 = vd1127 )
=> ~ ( ron @ vd1125 @ vskolem1146 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(103,axiom,
( ( ( vd1123 != vd1129 )
& ( vd1123 != vd1127 ) )
=> ( ron @ vskolem1140 @ vskolem1138 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(conseq(242), 0), 4)') ).
thf(877,plain,
( ( ( vd1123 != vd1129 )
& ( vd1123 != vd1127 ) )
=> ( ron @ vskolem1140 @ vskolem1138 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(14,axiom,
! [A: $i,B: $i] :
( ( ( A != B )
& ? [C: $i] :
( ( B = C )
& ( rpoint @ C ) )
& ? [C: $i] :
( ( A = C )
& ( rpoint @ C ) ) )
=> ! [C: $i,D: $i] :
( ( ( C = D )
& ( C != B )
& ( C != A )
& ( rpoint @ D ) )
=> ( rpoint @ ( vskolem1078 @ C @ D @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(219), 0), 1)') ).
thf(221,plain,
! [A: $i,B: $i] :
( ( ( A != B )
& ? [C: $i] :
( ( B = C )
& ( rpoint @ C ) )
& ? [C: $i] :
( ( A = C )
& ( rpoint @ C ) ) )
=> ! [C: $i,D: $i] :
( ( ( C = D )
& ( C != B )
& ( C != A )
& ( rpoint @ D ) )
=> ( rpoint @ ( vskolem1078 @ C @ D @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(1,conjecture,
? [A: $i,B: $i] :
( ( ron @ vd1127 @ B )
& ( rcenter @ vd1123 @ B )
& ( rcircle @ B )
& ( ron @ vd1125 @ A )
& ( ron @ vd1123 @ A )
& ( rline @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qe(259)') ).
thf(2,negated_conjecture,
~ ? [A: $i,B: $i] :
( ( ron @ vd1127 @ B )
& ( rcenter @ vd1123 @ B )
& ( rcircle @ B )
& ( ron @ vd1125 @ A )
& ( ron @ vd1123 @ A )
& ( rline @ A ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(133,plain,
~ ? [A: $i,B: $i] :
( ( ron @ vd1127 @ B )
& ( rcenter @ vd1123 @ B )
& ( rcircle @ B )
& ( ron @ vd1125 @ A )
& ( ron @ vd1123 @ A )
& ( rline @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(47,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(411,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)],[47]) ).
thf(23,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(265,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)],[23]) ).
thf(98,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(849,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)],[98]) ).
thf(17,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(233,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)],[17]) ).
thf(56,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(512,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)],[56]) ).
thf(111,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(942,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)],[111]) ).
thf(105,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(894,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)],[105]) ).
thf(122,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(1042,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)],[122]) ).
thf(36,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(349,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)],[36]) ).
thf(65,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(598,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)],[65]) ).
thf(16,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(229,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)],[16]) ).
thf(119,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(1027,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)],[119]) ).
thf(33,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(324,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)],[33]) ).
thf(37,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(356,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)],[37]) ).
thf(5,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(141,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)],[5]) ).
thf(15,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(225,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)],[15]) ).
thf(58,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(537,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)],[58]) ).
thf(126,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(1075,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)],[126]) ).
thf(72,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(637,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)],[72]) ).
thf(121,axiom,
( ( vd1123 = vd1127 )
=> ( ron @ vskolem1147 @ vskolem1146 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(conseq(242), 1), 2)') ).
thf(1039,plain,
( ( vd1123 = vd1127 )
=> ( ron @ vskolem1147 @ vskolem1146 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(60,axiom,
( ( vd1123 = vd1127 )
=> ( rR @ vskolem1147 @ vd1123 @ vd1125 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(conseq(242), 1), 1)') ).
thf(547,plain,
( ( vd1123 = vd1127 )
=> ( rR @ vskolem1147 @ vd1123 @ vd1125 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(45,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(393,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)],[45]) ).
thf(117,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(997,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)],[117]) ).
thf(78,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(701,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)],[78]) ).
thf(74,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(654,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)],[74]) ).
thf(123,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(1050,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)],[123]) ).
thf(18,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(237,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)],[18]) ).
thf(129,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(1086,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)],[129]) ).
thf(38,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(360,plain,
! [A: $i,B: $i] :
( ( ( A = B )
& ( rreal @ B ) )
=> ~ ( rless @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(55,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(508,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)],[55]) ).
thf(108,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(921,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)],[108]) ).
thf(125,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(1071,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)],[125]) ).
thf(112,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(953,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)],[112]) ).
thf(99,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(856,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)],[99]) ).
thf(25,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(279,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)],[25]) ).
thf(28,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(296,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)],[28]) ).
thf(81,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(733,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)],[81]) ).
thf(26,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(286,plain,
! [A: $i,B: $i] :
( ( ( A = B )
& ( rreal @ B ) )
=> ( ( vplus @ A @ v0 )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(102,axiom,
vd1123 = vd1129,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(258, 1150, 0)') ).
thf(875,plain,
vd1123 = vd1129,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(27,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(291,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)],[27]) ).
thf(43,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(382,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)],[43]) ).
thf(124,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(1058,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)],[124]) ).
thf(10,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(187,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)],[10]) ).
thf(104,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(880,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)],[104]) ).
thf(92,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(811,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)],[92]) ).
thf(62,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(552,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)],[62]) ).
thf(93,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(816,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)],[93]) ).
thf(66,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(609,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)],[66]) ).
thf(32,axiom,
rpoint @ vd14,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pred(axiom(5), 0)') ).
thf(323,plain,
rpoint @ vd14,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(57,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(520,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)],[57]) ).
thf(114,axiom,
( ( rless @ ( vf @ vd1127 @ vd1129 ) @ ( vf @ vd1123 @ vd1125 ) )
& ( vd1127 != vd1129 )
& ( vd1123 != vd1125 )
& ( vd1129 = vd1130 )
& ( rpoint @ vd1130 )
& ( vd1127 = vd1128 )
& ( rpoint @ vd1128 )
& ( vd1125 = vd1126 )
& ( rpoint @ vd1126 )
& ( vd1123 = vd1124 )
& ( rpoint @ vd1124 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','and(and(and(and(holds(conjunct2(conjunct2(conjunct2(conjunct2(conjunct2(conjunct2(242)))))), 1133, 0), and(holds(conjunct1(conjunct2(conjunct2(conjunct2(conjunct2(conjunct2(242)))))), 1132, 0), and(holds(conjunct1(conjunct2(conjunct2(conjunct2(conjunct2(242))))), 1131, 0), and(pred(conjunct1(conjunct2(conjunct2(conjunct2(242)))), 2), pred(conjunct1(conjunct2(conjunct2(conjunct2(242)))), 1))))), and(pred(conjunct1(conjunct2(conjunct2(242))), 2), pred(conjunct1(conjunct2(conjunct2(242))), 1))), and(pred(conjunct1(conjunct2(242)), 2), pred(conjunct1(conjunct2(242)), 1))), and(pred(conjunct1(242), 2), pred(conjunct1(242), 1)))') ).
thf(964,plain,
( ( rless @ ( vf @ vd1127 @ vd1129 ) @ ( vf @ vd1123 @ vd1125 ) )
& ( vd1127 != vd1129 )
& ( vd1123 != vd1125 )
& ( vd1129 = vd1130 )
& ( rpoint @ vd1130 )
& ( vd1127 = vd1128 )
& ( rpoint @ vd1128 )
& ( vd1125 = vd1126 )
& ( rpoint @ vd1126 )
& ( vd1123 = vd1124 )
& ( rpoint @ vd1124 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(12,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(198,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)],[12]) ).
thf(53,axiom,
( ( ( vd1123 != vd1129 )
& ( vd1123 != vd1127 ) )
=> ~ ( ron @ vd1125 @ vskolem1139 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(conseq(242), 0), 6)') ).
thf(494,plain,
( ( ( vd1123 != vd1129 )
& ( vd1123 != vd1127 ) )
=> ~ ( ron @ vd1125 @ vskolem1139 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(127,axiom,
( ( vd1123 = vd1127 )
=> ( ( vf @ vd1123 @ vskolem1147 )
= ( vf @ vd1127 @ vd1129 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(conseq(242), 1), 0)') ).
thf(1080,plain,
( ( vd1123 = vd1127 )
=> ( ( vf @ vd1123 @ vskolem1147 )
= ( vf @ vd1127 @ vd1129 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(3,axiom,
rreal @ vd684,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pred(axiom(137), 1)') ).
thf(135,plain,
rreal @ vd684,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(131,axiom,
( ( ( vd1123 != vd1129 )
& ( vd1123 != vd1127 ) )
=> ( ron @ vskolem1140 @ vskolem1139 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(conseq(242), 0), 3)') ).
thf(1102,plain,
( ( ( vd1123 != vd1129 )
& ( vd1123 != vd1127 ) )
=> ( ron @ vskolem1140 @ vskolem1139 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(120,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(1034,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)],[120]) ).
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 )
& ( rcenter @ A @ C )
& ( rcircle @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(53), 0), imp(cond(axiom(53), 0)))') ).
thf(426,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)],[49]) ).
thf(83,axiom,
( ( ( vd1123 != vd1129 )
& ( vd1123 != vd1127 ) )
=> ( rline @ vskolem1138 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(conseq(242), 0), 9)') ).
thf(749,plain,
( ( ( vd1123 != vd1129 )
& ( vd1123 != vd1127 ) )
=> ( rline @ vskolem1138 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(110,axiom,
( ( vd1123 = vd1127 )
=> ( rpoint @ vskolem1147 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(conseq(242), 1), 4)') ).
thf(939,plain,
( ( vd1123 = vd1127 )
=> ( rpoint @ vskolem1147 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(94,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(823,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)],[94]) ).
thf(96,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(836,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)],[96]) ).
thf(11,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(194,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)],[11]) ).
thf(87,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(776,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)],[87]) ).
thf(79,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(712,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)],[79]) ).
thf(101,axiom,
( ( ( vd1123 != vd1129 )
& ( vd1123 != vd1127 ) )
=> ( rpoint @ vskolem1140 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(conseq(242), 0), 5)') ).
thf(872,plain,
( ( ( vd1123 != vd1129 )
& ( vd1123 != vd1127 ) )
=> ( rpoint @ vskolem1140 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(31,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(310,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)],[31]) ).
thf(116,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(993,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)],[116]) ).
thf(76,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(673,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)],[76]) ).
thf(40,axiom,
v0 = vd684,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pred(axiom(137), 2)') ).
thf(370,plain,
v0 = vd684,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(82,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(744,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)],[82]) ).
thf(7,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(175,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)],[7]) ).
thf(54,axiom,
( ( vd1123 = vd1127 )
=> ( ( ron @ vd1129 @ vskolem1146 )
& ( rcenter @ vd1123 @ vskolem1146 )
& ( rcircle @ vskolem1146 )
& ( ron @ vd1125 @ vskolem1145 )
& ( ron @ vd1123 @ vskolem1145 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(conseq(242), 1), 7)') ).
thf(497,plain,
( ( vd1123 = vd1127 )
=> ( ( ron @ vd1129 @ vskolem1146 )
& ( rcenter @ vd1123 @ vskolem1146 )
& ( rcircle @ vskolem1146 )
& ( ron @ vd1125 @ vskolem1145 )
& ( ron @ vd1123 @ vskolem1145 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(21,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(250,plain,
! [A: $i,B: $i] :
( ( ( A = B )
& ( rpoint @ B ) )
=> ? [C: $i] :
( ( C != A )
& ( rpoint @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(97,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(844,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)],[97]) ).
thf(22,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(258,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)],[22]) ).
thf(44,axiom,
( ( ( vd1123 != vd1129 )
& ( vd1123 != vd1127 ) )
=> ( ( vf @ vd1123 @ vskolem1140 )
= ( vf @ vd1127 @ vd1129 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(conseq(242), 0), 0)') ).
thf(390,plain,
( ( ( vd1123 != vd1129 )
& ( vd1123 != vd1127 ) )
=> ( ( vf @ vd1123 @ vskolem1140 )
= ( vf @ vd1127 @ vd1129 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(46,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(401,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)],[46]) ).
thf(20,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(246,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)],[20]) ).
thf(85,axiom,
( ( ( vd1123 != vd1129 )
& ( vd1123 != vd1127 ) )
=> ( rR @ vskolem1140 @ vd1123 @ vd1125 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(conseq(242), 0), 2)') ).
thf(763,plain,
( ( ( vd1123 != vd1129 )
& ( vd1123 != vd1127 ) )
=> ( rR @ vskolem1140 @ vd1123 @ vd1125 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(13,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(214,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)],[13]) ).
thf(89,axiom,
( ( ( vd1123 != vd1129 )
& ( vd1123 != vd1127 ) )
=> ( rpoint @ vskolem1136 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(conseq(242), 0), 11)') ).
thf(800,plain,
( ( ( vd1123 != vd1129 )
& ( vd1123 != vd1127 ) )
=> ( rpoint @ vskolem1136 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(84,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(752,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)],[84]) ).
thf(130,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(1097,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)],[130]) ).
thf(6,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(146,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)],[6]) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( ( A != B )
& ? [C: $i] :
( ( B = C )
& ( rpoint @ C ) )
& ? [C: $i] :
( ( A = C )
& ( rpoint @ C ) ) )
=> ! [C: $i,D: $i] :
( ( ( C = D )
& ( C != B )
& ( C != A )
& ( rpoint @ D ) )
=> ( ( vf @ A @ B )
= ( vf @ C @ ( vskolem1078 @ C @ D @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(219), 0), 0)') ).
thf(183,plain,
! [A: $i,B: $i] :
( ( ( A != B )
& ? [C: $i] :
( ( B = C )
& ( rpoint @ C ) )
& ? [C: $i] :
( ( A = C )
& ( rpoint @ C ) ) )
=> ! [C: $i,D: $i] :
( ( ( C = D )
& ( C != B )
& ( C != A )
& ( rpoint @ D ) )
=> ( ( vf @ A @ B )
= ( vf @ C @ ( vskolem1078 @ C @ D @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(30,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(305,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)],[30]) ).
thf(19,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(242,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)],[19]) ).
thf(4,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(136,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)],[4]) ).
thf(35,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(341,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)],[35]) ).
thf(95,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(828,plain,
! [A: $i,B: $i] :
( ( ( A = B )
& ( rcircle @ B ) )
=> ? [C: $i] :
( ( ron @ C @ A )
& ( rpoint @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(113,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(960,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)],[113]) ).
thf(80,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(720,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)],[80]) ).
thf(48,axiom,
( ( ( vd1123 != vd1129 )
& ( vd1123 != vd1127 ) )
=> ( ( ron @ vskolem1136 @ vskolem1139 )
& ( rcenter @ vd1123 @ vskolem1139 )
& ( rcircle @ vskolem1139 )
& ( ron @ vd1125 @ vskolem1138 )
& ( ron @ vd1123 @ vskolem1138 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(conseq(242), 0), 8)') ).
thf(415,plain,
( ( ( vd1123 != vd1129 )
& ( vd1123 != vd1127 ) )
=> ( ( ron @ vskolem1136 @ vskolem1139 )
& ( rcenter @ vd1123 @ vskolem1139 )
& ( rcircle @ vskolem1139 )
& ( ron @ vd1125 @ vskolem1138 )
& ( ron @ vd1123 @ vskolem1138 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(69,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(624,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)],[69]) ).
thf(64,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(575,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)],[64]) ).
thf(118,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(1019,plain,
! [A: $i,B: $i] :
( ( ( A = B )
& ( rcircle @ B ) )
=> ? [C: $i] :
( ( rinside @ C @ A )
& ( rpoint @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(106,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(908,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)],[106]) ).
thf(115,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(982,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)],[115]) ).
thf(51,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(486,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)],[51]) ).
thf(90,axiom,
( ( vd1123 = vd1127 )
=> ~ ( rinside @ vd1125 @ vskolem1146 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(conseq(242), 1), 6)') ).
thf(803,plain,
( ( vd1123 = vd1127 )
=> ~ ( rinside @ vd1125 @ vskolem1146 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(34,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(337,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)],[34]) ).
thf(109,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(935,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)],[109]) ).
thf(75,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(659,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)],[75]) ).
thf(52,axiom,
( ( ( vd1123 != vd1129 )
& ( vd1123 != vd1127 ) )
=> ( ( vf @ vd1127 @ vd1129 )
= ( vf @ vd1123 @ vskolem1136 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(conseq(242), 0), 10)') ).
thf(491,plain,
( ( ( vd1123 != vd1129 )
& ( vd1123 != vd1127 ) )
=> ( ( vf @ vd1127 @ vd1129 )
= ( vf @ vd1123 @ vskolem1136 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(1127,plain,
$false,
inference(e,[status(thm)],[629,365,1105,1083,379,861,614,269,550,913,301,565,436,651,372,619,542,789,179,806,766,687,634,877,221,133,411,265,849,233,512,942,894,1042,349,598,229,1027,324,356,141,225,537,1075,637,1039,547,393,997,701,654,1050,237,1086,360,508,921,1071,953,856,279,296,733,286,875,291,382,1058,187,880,811,552,816,609,323,520,964,198,494,1080,135,1102,1034,426,749,939,823,836,194,776,712,872,310,993,673,370,744,175,497,250,844,258,390,401,246,763,214,800,752,1097,146,183,305,242,136,341,828,960,720,415,624,575,1019,908,982,486,803,337,935,659,491]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GEO284+1 : TPTP v8.1.2. Released v4.1.0.
% 0.07/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n014.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Fri May 19 04:24:43 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.86/0.85 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.53/1.06 % [INFO] Parsing done (204ms).
% 1.53/1.06 % [INFO] Running in sequential loop mode.
% 2.18/1.26 % [INFO] eprover registered as external prover.
% 2.18/1.26 % [INFO] cvc4 registered as external prover.
% 2.18/1.27 % [INFO] Scanning for conjecture ...
% 2.41/1.35 % [INFO] Found a conjecture and 130 axioms. Running axiom selection ...
% 2.58/1.43 % [INFO] Axiom selection finished. Selected 130 axioms (removed 0 axioms).
% 3.35/1.63 % [INFO] Problem is first-order (TPTP FOF).
% 3.35/1.65 % [INFO] Type checking passed.
% 3.35/1.66 % [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 ...
% 11.52/3.87 % External prover 'e' found a proof!
% 11.52/3.87 % [INFO] Killing All external provers ...
% 11.52/3.88 % Time passed: 3347ms (effective reasoning time: 2808ms)
% 11.52/3.88 % 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)>
% 11.52/3.88 % Axioms used in derivation (130): qu(cond(axiom(41), 0), imp(cond(axiom(41), 0))), qu(cond(axiom(103), 0), imp(cond(axiom(103), 0))), qu(cond(axiom(73), 0), imp(cond(axiom(73), 0))), qu(cond(axiom(119), 0), imp(cond(axiom(119), 0))), qu(cond(axiom(3), 0), imp(cond(axiom(3), 0))), ass(cond(conseq(242), 0), 8), ass(cond(conseq(242), 0), 4), qu(cond(axiom(164), 0), imp(cond(axiom(164), 0))), ass(cond(conseq(242), 0), 0), qu(cond(axiom(145), 0), imp(cond(axiom(145), 0))), ass(cond(goal(206), 0), 1), holds(258, 1150, 0), qu(cond(axiom(202), 0), imp(cond(axiom(202), 0))), qu(cond(axiom(19), 0), imp(cond(axiom(19), 0))), qu(cond(axiom(95), 0), imp(cond(axiom(95), 0))), qu(cond(axiom(43), 0), imp(cond(axiom(43), 0))), qu(cond(axiom(133), 0), imp(cond(axiom(133), 0))), qu(cond(axiom(21), 0), imp(cond(axiom(21), 0))), qu(cond(axiom(151), 0), imp(cond(axiom(151), 0))), pred(axiom(5), 0), qu(cond(axiom(75), 0), imp(cond(axiom(75), 0))), qu(cond(axiom(194), 0), imp(cond(axiom(194), 0))), ass(cond(conseq(242), 1), 3), qu(cond(axiom(190), 0), imp(cond(axiom(190), 0))), ass(cond(conseq(242), 0), 1), ass(cond(conseq(242), 0), 9), qu(cond(axiom(53), 0), imp(cond(axiom(53), 0))), ass(cond(conseq(242), 0), 5), 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(77), 0), imp(cond(axiom(77), 0))), qu(cond(axiom(113), 0), imp(cond(axiom(113), 0))), qu(cond(axiom(45), 0), imp(cond(axiom(45), 0))), qu(cond(axiom(11), 0), imp(cond(axiom(11), 0))), qu(cond(axiom(176), 0), imp(cond(axiom(176), 0))), qu(cond(axiom(33), 0), imp(cond(axiom(33), 0))), qu(cond(axiom(139), 0), imp(cond(axiom(139), 0))), qu(cond(axiom(59), 0), imp(cond(axiom(59), 0))), qu(cond(axiom(35), 0), imp(cond(axiom(35), 0))), qu(cond(axiom(23), 0), imp(cond(axiom(23), 0))), qu(cond(axiom(87), 0), imp(cond(axiom(87), 0))), 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(conseq(242), 1), 0), ass(cond(conseq(242), 1), 4), qu(cond(axiom(109), 0), imp(cond(axiom(109), 0))), qu(cond(axiom(79), 0), imp(cond(axiom(79), 0))), qu(cond(axiom(55), 0), imp(cond(axiom(55), 0))), qu(cond(axiom(81), 0), imp(cond(axiom(81), 0))), ass(cond(conseq(242), 1), 6), 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))), qu(cond(axiom(188), 0), imp(cond(axiom(188), 0))), qu(cond(axiom(99), 0), imp(cond(axiom(99), 0))), and(and(and(and(holds(conjunct2(conjunct2(conjunct2(conjunct2(conjunct2(conjunct2(242)))))), 1133, 0), and(holds(conjunct1(conjunct2(conjunct2(conjunct2(conjunct2(conjunct2(242)))))), 1132, 0), and(holds(conjunct1(conjunct2(conjunct2(conjunct2(conjunct2(242))))), 1131, 0), and(pred(conjunct1(conjunct2(conjunct2(conjunct2(242)))), 2), pred(conjunct1(conjunct2(conjunct2(conjunct2(242)))), 1))))), and(pred(conjunct1(conjunct2(conjunct2(242))), 2), pred(conjunct1(conjunct2(conjunct2(242))), 1))), and(pred(conjunct1(conjunct2(242)), 2), pred(conjunct1(conjunct2(242)), 1))), and(pred(conjunct1(242), 2), pred(conjunct1(242), 1))), qu(cond(axiom(71), 0), imp(cond(axiom(71), 0))), ass(cond(conseq(242), 0), 6), ass(cond(conseq(242), 0), 2), 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))), 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))), ass(cond(conseq(242), 1), 1), ass(cond(conseq(242), 1), 5), qu(cond(axiom(115), 0), imp(cond(axiom(115), 0))), qu(cond(axiom(131), 0), imp(cond(axiom(131), 0))), qu(cond(axiom(196), 0), imp(cond(axiom(196), 0))), qu(cond(axiom(186), 0), imp(cond(axiom(186), 0))), qu(cond(axiom(127), 0), imp(cond(axiom(127), 0))), ass(cond(conseq(242), 1), 7), 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))), qu(cond(axiom(166), 0), imp(cond(axiom(166), 0))), qu(cond(axiom(105), 0), imp(cond(axiom(105), 0))), qu(cond(axiom(37), 0), imp(cond(axiom(37), 0))), qu(cond(axiom(63), 0), imp(cond(axiom(63), 0))), qu(cond(axiom(192), 0), imp(cond(axiom(192), 0))), ass(cond(goal(219), 0), 0), pred(axiom(137), 1), ass(cond(conseq(242), 0), 7), ass(cond(goal(206), 0), 2), qu(cond(axiom(29), 0), imp(cond(axiom(29), 0))), qu(cond(axiom(39), 0), imp(cond(axiom(39), 0))), qu(cond(axiom(129), 0), imp(cond(axiom(129), 0))), qu(cond(axiom(15), 0), imp(cond(axiom(15), 0))), qu(cond(axiom(85), 0), imp(cond(axiom(85), 0))), ass(cond(conseq(242), 0), 10), qu(cond(axiom(200), 0), imp(cond(axiom(200), 0))), qu(cond(axiom(27), 0), imp(cond(axiom(27), 0))), qu(cond(axiom(91), 0), imp(cond(axiom(91), 0))), ass(cond(conseq(242), 1), 8), ass(cond(goal(219), 0), 1), qu(cond(axiom(49), 0), imp(cond(axiom(49), 0))), qu(cond(axiom(149), 0), imp(cond(axiom(149), 0))), 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))), ass(cond(conseq(242), 1), 2), 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))), 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))), ass(cond(conseq(242), 0), 11), 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))), ass(cond(conseq(242), 0), 3)
% 11.52/3.88 % No. of inferences in proof: 264
% 11.52/3.88 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3347 ms resp. 2808 ms w/o parsing
% 12.48/4.01 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 12.48/4.01 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------