%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : GEO524+1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 10:19:02 AM UTC 2026
% Result : Theorem 2.34s 0.67s
% Output : CNFRefutation 2.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 6
% Syntax : Number of formulae : 85 ( 59 unt; 0 typ; 0 def)
% Number of atoms : 541 ( 351 equ; 0 cnn)
% Maximal formula atoms : 8 ( 6 avg)
% Number of connectives : 1137 ( 129 ~; 216 |; 6 &; 786 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 59 ( 56 usr; 15 con; 0-8 aty)
% Number of variables : 264 ( 0 ^; 264 !; 0 ?; 264 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_alpha,type,
alpha: $i ).
thf(tp_beta,type,
beta: $i ).
thf(tp_c63,type,
c63: $i > $i > $i > $i ).
thf(tp_crossbar,type,
crossbar: $i > $i > $i > $i > $i > $i > $i ).
thf(tp_erect,type,
erect: $i > $i > $i > $i ).
thf(tp_erect21a,type,
erect21a: $i > $i > $i > $i ).
thf(tp_erectAux,type,
erectAux: $i > $i > $i > $i ).
thf(tp_erectAux21a,type,
erectAux21a: $i > $i > $i > $i ).
thf(tp_ext,type,
ext: $i > $i > $i > $i > $i ).
thf(tp_f811,type,
f811: $i > $i > $i > $i > $i > $i ).
thf(tp_f813,type,
f813: $i > $i > $i > $i > $i > $i ).
thf(tp_foot,type,
foot: $i > $i > $i > $i ).
thf(tp_g811,type,
g811: $i > $i > $i > $i > $i > $i ).
thf(tp_g813,type,
g813: $i > $i > $i > $i > $i > $i ).
thf(tp_gamma,type,
gamma: $i ).
thf(tp_il,type,
il: $i > $i > $i > $i > $i ).
thf(tp_ins,type,
ins: $i > $i > $i > $i > $i ).
thf(tp_insert,type,
insert: $i > $i > $i > $i > $i ).
thf(tp_insert5,type,
insert5: $i > $i > $i > $i > $i > $i ).
thf(tp_ip,type,
ip: $i > $i > $i > $i > $i > $i ).
thf(tp_isomidpoint,type,
isomidpoint: $i > $i > $i > $i ).
thf(tp_le,type,
le: $i > $i > $i > $i > $o ).
thf(tp_midpoint,type,
midpoint: $i > $i > $i ).
thf(tp_midpointAux,type,
midpointAux: $i > $i > $i > $i > $i > $i ).
thf(tp_op,type,
op: $i > $i > $i > $i > $i > $i ).
thf(tp_opposite,type,
opposite: $i > $i > $i > $i > $o ).
thf(tp_perp,type,
perp: $i > $i > $i > $i > $o ).
thf(tp_perpAt,type,
perpAt: $i > $i > $i > $i > $i > $o ).
thf(tp_pointOffLine,type,
pointOffLine: $i > $i > $i ).
thf(tp_reflect,type,
reflect: $i > $i > $i > $i ).
thf(tp_s,type,
s: $i > $i > $i ).
thf(tp_sK1_Xa,type,
sK1_Xa: $i ).
thf(tp_sK2_SY22,type,
sK2_SY22: $i ).
thf(tp_sK3_SY25,type,
sK3_SY25: $i ).
thf(tp_sK4_SY27,type,
sK4_SY27: $i ).
thf(tp_s_afs,type,
s_afs: $i > $i > $i > $i > $i > $i > $i > $i > $o ).
thf(tp_s_col,type,
s_col: $i > $i > $i > $o ).
thf(tp_s_e,type,
s_e: $i > $i > $i > $i > $o ).
thf(tp_s_e3,type,
s_e3: $i > $i > $i > $i > $i > $i > $o ).
thf(tp_s_fs,type,
s_fs: $i > $i > $i > $i > $i > $i > $i > $i > $o ).
thf(tp_s_ifs,type,
s_ifs: $i > $i > $i > $i > $i > $i > $i > $i > $o ).
thf(tp_s_kf,type,
s_kf: $i > $i > $i > $i > $i > $i > $i > $o ).
thf(tp_s_m,type,
s_m: $i > $i > $i > $o ).
thf(tp_s_r,type,
s_r: $i > $i > $i > $o ).
thf(tp_s_t,type,
s_t: $i > $i > $i > $o ).
thf(tp_sameside,type,
sameside: $i > $i > $i > $o ).
thf(tp_samesideline,type,
samesideline: $i > $i > $i > $i > $o ).
thf(tp_ss1,type,
ss1: $i > $i > $i > $i > $i ).
thf(tp_ss2,type,
ss2: $i > $i > $i > $i > $i ).
thf(tp_ss3,type,
ss3: $i > $i > $i > $i > $i ).
thf(tp_xa,type,
xa: $i ).
thf(tp_xb,type,
xb: $i ).
thf(tp_xc,type,
xc: $i ).
thf(tp_xd,type,
xd: $i ).
thf(tp_xp,type,
xp: $i ).
thf(tp_xq,type,
xq: $i ).
thf(16,axiom,
! [Xa: $i,Xb: $i,Xp: $i,Xp1: $i] :
( ( Xa = Xb )
| ( ( reflect @ Xa @ Xb @ Xp )
!= Xp1 )
| ( Xp
= ( reflect @ Xa @ Xb @ Xp1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz10_6) ).
thf(17,axiom,
! [Xa: $i,Xb: $i,Xp: $i] :
( ( Xa = Xb )
| ( ( reflect @ Xa @ Xb @ ( reflect @ Xa @ Xb @ Xp ) )
= Xp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz10_5) ).
thf(18,axiom,
! [Xa: $i,Xb: $i,Xp: $i,Xp1: $i] :
( ( Xa = Xb )
| ( ( reflect @ Xa @ Xb @ Xp )
!= Xp1 )
| ( ( reflect @ Xa @ Xb @ Xp1 )
= Xp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz10_4) ).
thf(19,axiom,
! [Xa: $i,Xb: $i,Xp: $i,Xp1: $i] :
( ( ( Xa = Xb )
| ~ ( s_col @ Xa @ Xb @ ( midpoint @ Xp @ Xp1 ) )
| ~ ( perp @ Xa @ Xb @ Xp @ Xp1 )
| ( Xp1
= ( reflect @ Xa @ Xb @ Xp ) ) )
& ( ( Xa = Xb )
| ~ ( s_col @ Xa @ Xb @ ( midpoint @ Xp @ Xp1 ) )
| ( Xp != Xp1 )
| ( Xp1
= ( reflect @ Xa @ Xb @ Xp ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz10_2b) ).
thf(20,axiom,
! [Xa: $i,Xb: $i,Xp: $i] :
( ( ( Xa = Xb )
| ( s_col @ Xa @ Xb @ ( midpoint @ Xp @ ( reflect @ Xa @ Xb @ Xp ) ) ) )
& ( ( Xa = Xb )
| ( Xp
= ( reflect @ Xa @ Xb @ Xp ) )
| ( perp @ Xa @ Xb @ Xp @ ( reflect @ Xa @ Xb @ Xp ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz10_2a) ).
thf(204,conjecture,
! [Xa: $i,Xb: $i,Xp: $i,Xq: $i] :
( ( Xa = Xb )
| ( ( reflect @ Xa @ Xb @ Xp )
!= ( reflect @ Xa @ Xb @ Xq ) )
| ( Xp = Xq ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz10_7) ).
thf(205,negated_conjecture,
( ( ! [Xa: $i,Xb: $i,Xp: $i,Xq: $i] :
( ( Xa = Xb )
| ( ( reflect @ Xa @ Xb @ Xp )
!= ( reflect @ Xa @ Xb @ Xq ) )
| ( Xp = Xq ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[204]) ).
thf(206,plain,
( ( ! [Xa: $i,Xb: $i,Xp: $i,Xq: $i] :
( ( Xa = Xb )
| ( ( reflect @ Xa @ Xb @ Xp )
!= ( reflect @ Xa @ Xb @ Xq ) )
| ( Xp = Xq ) ) )
= $false ),
inference(unfold_def,[status(thm)],[205]) ).
thf(207,plain,
( ( ! [Xa: $i,Xb: $i,Xp: $i,Xp1: $i] :
( ( Xa = Xb )
| ( ( reflect @ Xa @ Xb @ Xp )
!= Xp1 )
| ( Xp
= ( reflect @ Xa @ Xb @ Xp1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(208,plain,
( ( ! [Xa: $i,Xb: $i,Xp: $i] :
( ( Xa = Xb )
| ( ( reflect @ Xa @ Xb @ ( reflect @ Xa @ Xb @ Xp ) )
= Xp ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(209,plain,
( ( ! [Xa: $i,Xb: $i,Xp: $i,Xp1: $i] :
( ( Xa = Xb )
| ( ( reflect @ Xa @ Xb @ Xp )
!= Xp1 )
| ( ( reflect @ Xa @ Xb @ Xp1 )
= Xp ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(210,plain,
( ( ! [Xa: $i,Xb: $i,Xp: $i,Xp1: $i] :
( ( ( Xa = Xb )
| ~ ( s_col @ Xa @ Xb @ ( midpoint @ Xp @ Xp1 ) )
| ~ ( perp @ Xa @ Xb @ Xp @ Xp1 )
| ( Xp1
= ( reflect @ Xa @ Xb @ Xp ) ) )
& ( ( Xa = Xb )
| ~ ( s_col @ Xa @ Xb @ ( midpoint @ Xp @ Xp1 ) )
| ( Xp != Xp1 )
| ( Xp1
= ( reflect @ Xa @ Xb @ Xp ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(211,plain,
( ( ! [Xa: $i,Xb: $i,Xp: $i] :
( ( ( Xa = Xb )
| ( s_col @ Xa @ Xb @ ( midpoint @ Xp @ ( reflect @ Xa @ Xb @ Xp ) ) ) )
& ( ( Xa = Xb )
| ( Xp
= ( reflect @ Xa @ Xb @ Xp ) )
| ( perp @ Xa @ Xb @ Xp @ ( reflect @ Xa @ Xb @ Xp ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(212,plain,
( ( ! [SY22: $i,SY23: $i,SY24: $i] :
( ( sK1_Xa = SY22 )
| ( ( reflect @ sK1_Xa @ SY22 @ SY23 )
!= ( reflect @ sK1_Xa @ SY22 @ SY24 ) )
| ( SY23 = SY24 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[206]) ).
thf(213,plain,
( ( ! [SY25: $i,SY26: $i] :
( ( sK1_Xa = sK2_SY22 )
| ( ( reflect @ sK1_Xa @ sK2_SY22 @ SY25 )
!= ( reflect @ sK1_Xa @ sK2_SY22 @ SY26 ) )
| ( SY25 = SY26 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[212]) ).
thf(214,plain,
( ( ! [SY27: $i] :
( ( sK1_Xa = sK2_SY22 )
| ( ( reflect @ sK1_Xa @ sK2_SY22 @ sK3_SY25 )
!= ( reflect @ sK1_Xa @ sK2_SY22 @ SY27 ) )
| ( sK3_SY25 = SY27 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[213]) ).
thf(215,plain,
( ( ( sK1_Xa = sK2_SY22 )
| ( ( reflect @ sK1_Xa @ sK2_SY22 @ sK3_SY25 )
!= ( reflect @ sK1_Xa @ sK2_SY22 @ sK4_SY27 ) )
| ( sK3_SY25 = sK4_SY27 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[214]) ).
thf(216,plain,
( ( ~ ( ( sK1_Xa = sK2_SY22 )
| ( ( reflect @ sK1_Xa @ sK2_SY22 @ sK3_SY25 )
!= ( reflect @ sK1_Xa @ sK2_SY22 @ sK4_SY27 ) )
| ( sK3_SY25 = sK4_SY27 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[215]) ).
thf(217,plain,
( ( ! [Xa: $i,Xb: $i,Xp: $i] :
( ( ( Xa = Xb )
| ( s_col @ Xa @ Xb @ ( midpoint @ Xp @ ( reflect @ Xa @ Xb @ Xp ) ) ) )
& ( ( Xa = Xb )
| ( Xp
= ( reflect @ Xa @ Xb @ Xp ) )
| ( perp @ Xa @ Xb @ Xp @ ( reflect @ Xa @ Xb @ Xp ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[211]) ).
thf(218,plain,
( ( ! [Xa: $i,Xb: $i,Xp: $i,Xp1: $i] :
( ( ( Xa = Xb )
| ~ ( s_col @ Xa @ Xb @ ( midpoint @ Xp @ Xp1 ) )
| ~ ( perp @ Xa @ Xb @ Xp @ Xp1 )
| ( Xp1
= ( reflect @ Xa @ Xb @ Xp ) ) )
& ( ( Xa = Xb )
| ~ ( s_col @ Xa @ Xb @ ( midpoint @ Xp @ Xp1 ) )
| ( Xp != Xp1 )
| ( Xp1
= ( reflect @ Xa @ Xb @ Xp ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[210]) ).
thf(219,plain,
( ( ! [Xa: $i,Xb: $i,Xp: $i,Xp1: $i] :
( ( Xa = Xb )
| ( ( reflect @ Xa @ Xb @ Xp )
!= Xp1 )
| ( ( reflect @ Xa @ Xb @ Xp1 )
= Xp ) ) )
= $true ),
inference(copy,[status(thm)],[209]) ).
thf(220,plain,
( ( ! [Xa: $i,Xb: $i,Xp: $i] :
( ( Xa = Xb )
| ( ( reflect @ Xa @ Xb @ ( reflect @ Xa @ Xb @ Xp ) )
= Xp ) ) )
= $true ),
inference(copy,[status(thm)],[208]) ).
thf(221,plain,
( ( ! [Xa: $i,Xb: $i,Xp: $i,Xp1: $i] :
( ( Xa = Xb )
| ( ( reflect @ Xa @ Xb @ Xp )
!= Xp1 )
| ( Xp
= ( reflect @ Xa @ Xb @ Xp1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[207]) ).
thf(222,plain,
( ( ~ ( ( sK1_Xa = sK2_SY22 )
| ( ( reflect @ sK1_Xa @ sK2_SY22 @ sK3_SY25 )
!= ( reflect @ sK1_Xa @ sK2_SY22 @ sK4_SY27 ) )
| ( sK3_SY25 = sK4_SY27 ) ) )
= $true ),
inference(copy,[status(thm)],[216]) ).
thf(223,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
~ ( ~ ( ( SX0 = SX1 )
| ~ ( s_col @ SX0 @ SX1 @ ( midpoint @ SX2 @ SX3 ) )
| ~ ( perp @ SX0 @ SX1 @ SX2 @ SX3 )
| ( SX3
= ( reflect @ SX0 @ SX1 @ SX2 ) ) )
| ~ ( ( SX0 = SX1 )
| ~ ( s_col @ SX0 @ SX1 @ ( midpoint @ SX2 @ SX3 ) )
| ( SX2 != SX3 )
| ( SX3
= ( reflect @ SX0 @ SX1 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[218]) ).
thf(224,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ( SX0 = SX1 )
| ( s_col @ SX0 @ SX1 @ ( midpoint @ SX2 @ ( reflect @ SX0 @ SX1 @ SX2 ) ) ) )
| ~ ( ( SX0 = SX1 )
| ( SX2
= ( reflect @ SX0 @ SX1 @ SX2 ) )
| ( perp @ SX0 @ SX1 @ SX2 @ ( reflect @ SX0 @ SX1 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[217]) ).
thf(225,plain,
( ( ~ ( ( sK1_Xa = sK2_SY22 )
| ( ( reflect @ sK1_Xa @ sK2_SY22 @ sK3_SY25 )
!= ( reflect @ sK1_Xa @ sK2_SY22 @ sK4_SY27 ) )
| ( sK3_SY25 = sK4_SY27 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[222]) ).
thf(226,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( SX0 = SX1 )
| ( ( reflect @ SX0 @ SX1 @ SX2 )
!= SX3 )
| ( SX2
= ( reflect @ SX0 @ SX1 @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[221]) ).
thf(227,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( SX0 = SX1 )
| ( ( reflect @ SX0 @ SX1 @ SX2 )
!= SX3 )
| ( ( reflect @ SX0 @ SX1 @ SX3 )
= SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[219]) ).
thf(228,plain,
! [SV1: $i] :
( ( ! [SY28: $i,SY29: $i] :
( ( SV1 = SY28 )
| ( ( reflect @ SV1 @ SY28 @ ( reflect @ SV1 @ SY28 @ SY29 ) )
= SY29 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[220]) ).
thf(229,plain,
! [SV2: $i] :
( ( ! [SY30: $i,SY31: $i,SY32: $i] :
~ ( ~ ( ( SV2 = SY30 )
| ~ ( s_col @ SV2 @ SY30 @ ( midpoint @ SY31 @ SY32 ) )
| ~ ( perp @ SV2 @ SY30 @ SY31 @ SY32 )
| ( SY32
= ( reflect @ SV2 @ SY30 @ SY31 ) ) )
| ~ ( ( SV2 = SY30 )
| ~ ( s_col @ SV2 @ SY30 @ ( midpoint @ SY31 @ SY32 ) )
| ( SY31 != SY32 )
| ( SY32
= ( reflect @ SV2 @ SY30 @ SY31 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[223]) ).
thf(230,plain,
! [SV3: $i] :
( ( ! [SY33: $i,SY34: $i] :
~ ( ~ ( ( SV3 = SY33 )
| ( s_col @ SV3 @ SY33 @ ( midpoint @ SY34 @ ( reflect @ SV3 @ SY33 @ SY34 ) ) ) )
| ~ ( ( SV3 = SY33 )
| ( SY34
= ( reflect @ SV3 @ SY33 @ SY34 ) )
| ( perp @ SV3 @ SY33 @ SY34 @ ( reflect @ SV3 @ SY33 @ SY34 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[224]) ).
thf(231,plain,
( ( ( sK1_Xa = sK2_SY22 )
| ( ( reflect @ sK1_Xa @ sK2_SY22 @ sK3_SY25 )
!= ( reflect @ sK1_Xa @ sK2_SY22 @ sK4_SY27 ) )
| ( sK3_SY25 = sK4_SY27 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[225]) ).
thf(232,plain,
! [SV4: $i] :
( ( ! [SY35: $i,SY36: $i,SY37: $i] :
( ( SV4 = SY35 )
| ( ( reflect @ SV4 @ SY35 @ SY36 )
!= SY37 )
| ( SY36
= ( reflect @ SV4 @ SY35 @ SY37 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[226]) ).
thf(233,plain,
! [SV5: $i] :
( ( ! [SY38: $i,SY39: $i,SY40: $i] :
( ( SV5 = SY38 )
| ( ( reflect @ SV5 @ SY38 @ SY39 )
!= SY40 )
| ( ( reflect @ SV5 @ SY38 @ SY40 )
= SY39 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[227]) ).
thf(234,plain,
! [SV6: $i,SV1: $i] :
( ( ! [SY41: $i] :
( ( SV1 = SV6 )
| ( ( reflect @ SV1 @ SV6 @ ( reflect @ SV1 @ SV6 @ SY41 ) )
= SY41 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[228]) ).
thf(235,plain,
! [SV7: $i,SV2: $i] :
( ( ! [SY42: $i,SY43: $i] :
~ ( ~ ( ( SV2 = SV7 )
| ~ ( s_col @ SV2 @ SV7 @ ( midpoint @ SY42 @ SY43 ) )
| ~ ( perp @ SV2 @ SV7 @ SY42 @ SY43 )
| ( SY43
= ( reflect @ SV2 @ SV7 @ SY42 ) ) )
| ~ ( ( SV2 = SV7 )
| ~ ( s_col @ SV2 @ SV7 @ ( midpoint @ SY42 @ SY43 ) )
| ( SY42 != SY43 )
| ( SY43
= ( reflect @ SV2 @ SV7 @ SY42 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[229]) ).
thf(236,plain,
! [SV8: $i,SV3: $i] :
( ( ! [SY44: $i] :
~ ( ~ ( ( SV3 = SV8 )
| ( s_col @ SV3 @ SV8 @ ( midpoint @ SY44 @ ( reflect @ SV3 @ SV8 @ SY44 ) ) ) )
| ~ ( ( SV3 = SV8 )
| ( SY44
= ( reflect @ SV3 @ SV8 @ SY44 ) )
| ( perp @ SV3 @ SV8 @ SY44 @ ( reflect @ SV3 @ SV8 @ SY44 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[230]) ).
thf(237,plain,
( ( ( sK1_Xa = sK2_SY22 )
| ( ( reflect @ sK1_Xa @ sK2_SY22 @ sK3_SY25 )
!= ( reflect @ sK1_Xa @ sK2_SY22 @ sK4_SY27 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[231]) ).
thf(238,plain,
( ( sK3_SY25 = sK4_SY27 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[231]) ).
thf(239,plain,
! [SV9: $i,SV4: $i] :
( ( ! [SY45: $i,SY46: $i] :
( ( SV4 = SV9 )
| ( ( reflect @ SV4 @ SV9 @ SY45 )
!= SY46 )
| ( SY45
= ( reflect @ SV4 @ SV9 @ SY46 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[232]) ).
thf(240,plain,
! [SV10: $i,SV5: $i] :
( ( ! [SY47: $i,SY48: $i] :
( ( SV5 = SV10 )
| ( ( reflect @ SV5 @ SV10 @ SY47 )
!= SY48 )
| ( ( reflect @ SV5 @ SV10 @ SY48 )
= SY47 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[233]) ).
thf(241,plain,
! [SV11: $i,SV6: $i,SV1: $i] :
( ( ( SV1 = SV6 )
| ( ( reflect @ SV1 @ SV6 @ ( reflect @ SV1 @ SV6 @ SV11 ) )
= SV11 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[234]) ).
thf(242,plain,
! [SV12: $i,SV7: $i,SV2: $i] :
( ( ! [SY49: $i] :
~ ( ~ ( ( SV2 = SV7 )
| ~ ( s_col @ SV2 @ SV7 @ ( midpoint @ SV12 @ SY49 ) )
| ~ ( perp @ SV2 @ SV7 @ SV12 @ SY49 )
| ( SY49
= ( reflect @ SV2 @ SV7 @ SV12 ) ) )
| ~ ( ( SV2 = SV7 )
| ~ ( s_col @ SV2 @ SV7 @ ( midpoint @ SV12 @ SY49 ) )
| ( SV12 != SY49 )
| ( SY49
= ( reflect @ SV2 @ SV7 @ SV12 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[235]) ).
thf(243,plain,
! [SV13: $i,SV8: $i,SV3: $i] :
( ( ~ ( ~ ( ( SV3 = SV8 )
| ( s_col @ SV3 @ SV8 @ ( midpoint @ SV13 @ ( reflect @ SV3 @ SV8 @ SV13 ) ) ) )
| ~ ( ( SV3 = SV8 )
| ( SV13
= ( reflect @ SV3 @ SV8 @ SV13 ) )
| ( perp @ SV3 @ SV8 @ SV13 @ ( reflect @ SV3 @ SV8 @ SV13 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[236]) ).
thf(244,plain,
( ( sK1_Xa = sK2_SY22 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[237]) ).
thf(245,plain,
( ( ( reflect @ sK1_Xa @ sK2_SY22 @ sK3_SY25 )
!= ( reflect @ sK1_Xa @ sK2_SY22 @ sK4_SY27 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[237]) ).
thf(246,plain,
! [SV14: $i,SV9: $i,SV4: $i] :
( ( ! [SY50: $i] :
( ( SV4 = SV9 )
| ( ( reflect @ SV4 @ SV9 @ SV14 )
!= SY50 )
| ( SV14
= ( reflect @ SV4 @ SV9 @ SY50 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[239]) ).
thf(247,plain,
! [SV15: $i,SV10: $i,SV5: $i] :
( ( ! [SY51: $i] :
( ( SV5 = SV10 )
| ( ( reflect @ SV5 @ SV10 @ SV15 )
!= SY51 )
| ( ( reflect @ SV5 @ SV10 @ SY51 )
= SV15 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[240]) ).
thf(248,plain,
! [SV11: $i,SV6: $i,SV1: $i] :
( ( ( SV1 = SV6 )
= $true )
| ( ( ( reflect @ SV1 @ SV6 @ ( reflect @ SV1 @ SV6 @ SV11 ) )
= SV11 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[241]) ).
thf(249,plain,
! [SV16: $i,SV12: $i,SV7: $i,SV2: $i] :
( ( ~ ( ~ ( ( SV2 = SV7 )
| ~ ( s_col @ SV2 @ SV7 @ ( midpoint @ SV12 @ SV16 ) )
| ~ ( perp @ SV2 @ SV7 @ SV12 @ SV16 )
| ( SV16
= ( reflect @ SV2 @ SV7 @ SV12 ) ) )
| ~ ( ( SV2 = SV7 )
| ~ ( s_col @ SV2 @ SV7 @ ( midpoint @ SV12 @ SV16 ) )
| ( SV12 != SV16 )
| ( SV16
= ( reflect @ SV2 @ SV7 @ SV12 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[242]) ).
thf(250,plain,
! [SV13: $i,SV8: $i,SV3: $i] :
( ( ~ ( ( SV3 = SV8 )
| ( s_col @ SV3 @ SV8 @ ( midpoint @ SV13 @ ( reflect @ SV3 @ SV8 @ SV13 ) ) ) )
| ~ ( ( SV3 = SV8 )
| ( SV13
= ( reflect @ SV3 @ SV8 @ SV13 ) )
| ( perp @ SV3 @ SV8 @ SV13 @ ( reflect @ SV3 @ SV8 @ SV13 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[243]) ).
thf(251,plain,
( ( ( reflect @ sK1_Xa @ sK2_SY22 @ sK3_SY25 )
= ( reflect @ sK1_Xa @ sK2_SY22 @ sK4_SY27 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[245]) ).
thf(252,plain,
! [SV17: $i,SV14: $i,SV9: $i,SV4: $i] :
( ( ( SV4 = SV9 )
| ( ( reflect @ SV4 @ SV9 @ SV14 )
!= SV17 )
| ( SV14
= ( reflect @ SV4 @ SV9 @ SV17 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[246]) ).
thf(253,plain,
! [SV18: $i,SV15: $i,SV10: $i,SV5: $i] :
( ( ( SV5 = SV10 )
| ( ( reflect @ SV5 @ SV10 @ SV15 )
!= SV18 )
| ( ( reflect @ SV5 @ SV10 @ SV18 )
= SV15 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[247]) ).
thf(254,plain,
! [SV16: $i,SV12: $i,SV7: $i,SV2: $i] :
( ( ~ ( ( SV2 = SV7 )
| ~ ( s_col @ SV2 @ SV7 @ ( midpoint @ SV12 @ SV16 ) )
| ~ ( perp @ SV2 @ SV7 @ SV12 @ SV16 )
| ( SV16
= ( reflect @ SV2 @ SV7 @ SV12 ) ) )
| ~ ( ( SV2 = SV7 )
| ~ ( s_col @ SV2 @ SV7 @ ( midpoint @ SV12 @ SV16 ) )
| ( SV12 != SV16 )
| ( SV16
= ( reflect @ SV2 @ SV7 @ SV12 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[249]) ).
thf(255,plain,
! [SV13: $i,SV8: $i,SV3: $i] :
( ( ~ ( ( SV3 = SV8 )
| ( s_col @ SV3 @ SV8 @ ( midpoint @ SV13 @ ( reflect @ SV3 @ SV8 @ SV13 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[250]) ).
thf(256,plain,
! [SV13: $i,SV8: $i,SV3: $i] :
( ( ~ ( ( SV3 = SV8 )
| ( SV13
= ( reflect @ SV3 @ SV8 @ SV13 ) )
| ( perp @ SV3 @ SV8 @ SV13 @ ( reflect @ SV3 @ SV8 @ SV13 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[250]) ).
thf(257,plain,
! [SV17: $i,SV14: $i,SV9: $i,SV4: $i] :
( ( ( ( SV4 = SV9 )
| ( ( reflect @ SV4 @ SV9 @ SV14 )
!= SV17 ) )
= $true )
| ( ( SV14
= ( reflect @ SV4 @ SV9 @ SV17 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[252]) ).
thf(258,plain,
! [SV18: $i,SV15: $i,SV10: $i,SV5: $i] :
( ( ( ( SV5 = SV10 )
| ( ( reflect @ SV5 @ SV10 @ SV15 )
!= SV18 ) )
= $true )
| ( ( ( reflect @ SV5 @ SV10 @ SV18 )
= SV15 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[253]) ).
thf(259,plain,
! [SV16: $i,SV12: $i,SV7: $i,SV2: $i] :
( ( ~ ( ( SV2 = SV7 )
| ~ ( s_col @ SV2 @ SV7 @ ( midpoint @ SV12 @ SV16 ) )
| ~ ( perp @ SV2 @ SV7 @ SV12 @ SV16 )
| ( SV16
= ( reflect @ SV2 @ SV7 @ SV12 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[254]) ).
thf(260,plain,
! [SV16: $i,SV12: $i,SV7: $i,SV2: $i] :
( ( ~ ( ( SV2 = SV7 )
| ~ ( s_col @ SV2 @ SV7 @ ( midpoint @ SV12 @ SV16 ) )
| ( SV12 != SV16 )
| ( SV16
= ( reflect @ SV2 @ SV7 @ SV12 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[254]) ).
thf(261,plain,
! [SV13: $i,SV8: $i,SV3: $i] :
( ( ( SV3 = SV8 )
| ( s_col @ SV3 @ SV8 @ ( midpoint @ SV13 @ ( reflect @ SV3 @ SV8 @ SV13 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[255]) ).
thf(262,plain,
! [SV13: $i,SV8: $i,SV3: $i] :
( ( ( SV3 = SV8 )
| ( SV13
= ( reflect @ SV3 @ SV8 @ SV13 ) )
| ( perp @ SV3 @ SV8 @ SV13 @ ( reflect @ SV3 @ SV8 @ SV13 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[256]) ).
thf(263,plain,
! [SV17: $i,SV14: $i,SV9: $i,SV4: $i] :
( ( ( SV4 = SV9 )
= $true )
| ( ( ( reflect @ SV4 @ SV9 @ SV14 )
!= SV17 )
= $true )
| ( ( SV14
= ( reflect @ SV4 @ SV9 @ SV17 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[257]) ).
thf(264,plain,
! [SV18: $i,SV15: $i,SV10: $i,SV5: $i] :
( ( ( SV5 = SV10 )
= $true )
| ( ( ( reflect @ SV5 @ SV10 @ SV15 )
!= SV18 )
= $true )
| ( ( ( reflect @ SV5 @ SV10 @ SV18 )
= SV15 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[258]) ).
thf(265,plain,
! [SV16: $i,SV12: $i,SV7: $i,SV2: $i] :
( ( ( SV2 = SV7 )
| ~ ( s_col @ SV2 @ SV7 @ ( midpoint @ SV12 @ SV16 ) )
| ~ ( perp @ SV2 @ SV7 @ SV12 @ SV16 )
| ( SV16
= ( reflect @ SV2 @ SV7 @ SV12 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[259]) ).
thf(266,plain,
! [SV16: $i,SV12: $i,SV7: $i,SV2: $i] :
( ( ( SV2 = SV7 )
| ~ ( s_col @ SV2 @ SV7 @ ( midpoint @ SV12 @ SV16 ) )
| ( SV12 != SV16 )
| ( SV16
= ( reflect @ SV2 @ SV7 @ SV12 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[260]) ).
thf(267,plain,
! [SV13: $i,SV8: $i,SV3: $i] :
( ( ( SV3 = SV8 )
= $true )
| ( ( s_col @ SV3 @ SV8 @ ( midpoint @ SV13 @ ( reflect @ SV3 @ SV8 @ SV13 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[261]) ).
thf(268,plain,
! [SV13: $i,SV8: $i,SV3: $i] :
( ( ( ( SV3 = SV8 )
| ( SV13
= ( reflect @ SV3 @ SV8 @ SV13 ) ) )
= $true )
| ( ( perp @ SV3 @ SV8 @ SV13 @ ( reflect @ SV3 @ SV8 @ SV13 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[262]) ).
thf(269,plain,
! [SV17: $i,SV14: $i,SV9: $i,SV4: $i] :
( ( ( ( reflect @ SV4 @ SV9 @ SV14 )
= SV17 )
= $false )
| ( ( SV4 = SV9 )
= $true )
| ( ( SV14
= ( reflect @ SV4 @ SV9 @ SV17 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[263]) ).
thf(270,plain,
! [SV18: $i,SV15: $i,SV10: $i,SV5: $i] :
( ( ( ( reflect @ SV5 @ SV10 @ SV15 )
= SV18 )
= $false )
| ( ( SV5 = SV10 )
= $true )
| ( ( ( reflect @ SV5 @ SV10 @ SV18 )
= SV15 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[264]) ).
thf(271,plain,
! [SV16: $i,SV12: $i,SV7: $i,SV2: $i] :
( ( ( ( SV2 = SV7 )
| ~ ( s_col @ SV2 @ SV7 @ ( midpoint @ SV12 @ SV16 ) )
| ~ ( perp @ SV2 @ SV7 @ SV12 @ SV16 ) )
= $true )
| ( ( SV16
= ( reflect @ SV2 @ SV7 @ SV12 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[265]) ).
thf(272,plain,
! [SV16: $i,SV12: $i,SV7: $i,SV2: $i] :
( ( ( ( SV2 = SV7 )
| ~ ( s_col @ SV2 @ SV7 @ ( midpoint @ SV12 @ SV16 ) )
| ( SV12 != SV16 ) )
= $true )
| ( ( SV16
= ( reflect @ SV2 @ SV7 @ SV12 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[266]) ).
thf(273,plain,
! [SV13: $i,SV8: $i,SV3: $i] :
( ( ( SV3 = SV8 )
= $true )
| ( ( SV13
= ( reflect @ SV3 @ SV8 @ SV13 ) )
= $true )
| ( ( perp @ SV3 @ SV8 @ SV13 @ ( reflect @ SV3 @ SV8 @ SV13 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[268]) ).
thf(274,plain,
! [SV16: $i,SV12: $i,SV7: $i,SV2: $i] :
( ( ( ( SV2 = SV7 )
| ~ ( s_col @ SV2 @ SV7 @ ( midpoint @ SV12 @ SV16 ) ) )
= $true )
| ( ( ~ ( perp @ SV2 @ SV7 @ SV12 @ SV16 ) )
= $true )
| ( ( SV16
= ( reflect @ SV2 @ SV7 @ SV12 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[271]) ).
thf(275,plain,
! [SV16: $i,SV12: $i,SV7: $i,SV2: $i] :
( ( ( ( SV2 = SV7 )
| ~ ( s_col @ SV2 @ SV7 @ ( midpoint @ SV12 @ SV16 ) ) )
= $true )
| ( ( SV12 != SV16 )
= $true )
| ( ( SV16
= ( reflect @ SV2 @ SV7 @ SV12 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[272]) ).
thf(276,plain,
! [SV16: $i,SV12: $i,SV7: $i,SV2: $i] :
( ( ( SV2 = SV7 )
= $true )
| ( ( ~ ( s_col @ SV2 @ SV7 @ ( midpoint @ SV12 @ SV16 ) ) )
= $true )
| ( ( ~ ( perp @ SV2 @ SV7 @ SV12 @ SV16 ) )
= $true )
| ( ( SV16
= ( reflect @ SV2 @ SV7 @ SV12 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[274]) ).
thf(277,plain,
! [SV16: $i,SV12: $i,SV7: $i,SV2: $i] :
( ( ( SV2 = SV7 )
= $true )
| ( ( ~ ( s_col @ SV2 @ SV7 @ ( midpoint @ SV12 @ SV16 ) ) )
= $true )
| ( ( SV12 != SV16 )
= $true )
| ( ( SV16
= ( reflect @ SV2 @ SV7 @ SV12 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[275]) ).
thf(278,plain,
! [SV16: $i,SV12: $i,SV7: $i,SV2: $i] :
( ( ( s_col @ SV2 @ SV7 @ ( midpoint @ SV12 @ SV16 ) )
= $false )
| ( ( SV2 = SV7 )
= $true )
| ( ( ~ ( perp @ SV2 @ SV7 @ SV12 @ SV16 ) )
= $true )
| ( ( SV16
= ( reflect @ SV2 @ SV7 @ SV12 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[276]) ).
thf(279,plain,
! [SV16: $i,SV12: $i,SV7: $i,SV2: $i] :
( ( ( s_col @ SV2 @ SV7 @ ( midpoint @ SV12 @ SV16 ) )
= $false )
| ( ( SV2 = SV7 )
= $true )
| ( ( SV12 != SV16 )
= $true )
| ( ( SV16
= ( reflect @ SV2 @ SV7 @ SV12 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[277]) ).
thf(280,plain,
! [SV16: $i,SV12: $i,SV7: $i,SV2: $i] :
( ( ( perp @ SV2 @ SV7 @ SV12 @ SV16 )
= $false )
| ( ( SV2 = SV7 )
= $true )
| ( ( s_col @ SV2 @ SV7 @ ( midpoint @ SV12 @ SV16 ) )
= $false )
| ( ( SV16
= ( reflect @ SV2 @ SV7 @ SV12 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[278]) ).
thf(281,plain,
! [SV7: $i,SV2: $i,SV16: $i,SV12: $i] :
( ( ( SV12 = SV16 )
= $false )
| ( ( SV2 = SV7 )
= $true )
| ( ( s_col @ SV2 @ SV7 @ ( midpoint @ SV12 @ SV16 ) )
= $false )
| ( ( SV16
= ( reflect @ SV2 @ SV7 @ SV12 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[279]) ).
thf(282,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[238,281,280,273,270,269,267,251,248,244]) ).
thf(283,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[282]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO524+1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.18 % Computer : n019.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Oct 6 10:17:01 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.34/0.67 .
% 2.34/0.67
% 2.34/0.67 No.of.Axioms: 5
% 2.34/0.67
% 2.34/0.67 Length.of.Defs: 0
% 2.34/0.67
% 2.34/0.67 Contains.Choice.Funs: false
% 2.34/0.67 .....
% 2.34/0.67
% 2.34/0.67 ********************************
% 2.34/0.67 * All subproblems solved! *
% 2.34/0.67 ********************************
% 2.34/0.67 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:5,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:282,loop_count:0,foatp_calls:1,translation:fof_full)
% 2.34/0.67
% 2.34/0.67 %**** Beginning of derivation protocol ****
% 2.34/0.67 % SZS output start CNFRefutation
% See solution above
% 2.34/0.67
% 2.34/0.67 %**** End of derivation protocol ****
% 2.34/0.67 %**** no. of clauses in derivation: 85 ****
% 2.34/0.67 %**** clause counter: 282 ****
% 2.34/0.67
% 2.34/0.67 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:5,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:282,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------