%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SYO893^11 : TPTP v9.3.1. Released v8.1.0.
% 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 : n003.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 11:09:17 AM UTC 2026
% Result : Theorem 0.07s 0.25s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 11
% Syntax : Number of formulae : 130 ( 70 unt; 0 typ; 8 def)
% Number of atoms : 823 ( 196 equ; 0 cnn)
% Maximal formula atoms : 12 ( 6 avg)
% Number of connectives : 1608 ( 519 ~; 229 |; 27 &; 798 @)
% ( 2 <=>; 33 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% Number of symbols : 20 ( 17 usr; 5 con; 0-3 aty)
% Number of variables : 313 ( 19 ^; 272 !; 22 ?; 313 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_mworld,type,
mworld: $tType ).
thf(tp_mactual,type,
mactual: mworld ).
thf(tp_mand,type,
mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(tp_mbox,type,
mbox: ( mworld > $o ) > mworld > $o ).
thf(tp_mdia,type,
mdia: ( mworld > $o ) > mworld > $o ).
thf(tp_mequiv,type,
mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(tp_mimplies,type,
mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(tp_mlocal,type,
mlocal: ( mworld > $o ) > $o ).
thf(tp_mnot,type,
mnot: ( mworld > $o ) > mworld > $o ).
thf(tp_mor,type,
mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(tp_mrel,type,
mrel: mworld > mworld > $o ).
thf(tp_p,type,
p: mworld > $o ).
thf(tp_sK1_SX0,type,
sK1_SX0: mworld ).
thf(tp_sK2_SY54,type,
sK2_SY54: mworld > mworld ).
thf(tp_sK3_SY58,type,
sK3_SY58: mworld > mworld ).
thf(tp_sK4_SX0,type,
sK4_SX0: mworld ).
thf(tp_sK5_SY63,type,
sK5_SY63: mworld > mworld ).
thf(tp_sK6_SY68,type,
sK6_SY68: mworld > mworld ).
thf(mand,definition,
( mand
= ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
( ( A @ W )
& ( B @ W ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mand_def) ).
thf(mbox,definition,
( mbox
= ( ^ [Phi: mworld > $o,W: mworld] :
! [V: mworld] :
( ( mrel @ W @ V )
=> ( Phi @ V ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mbox_def) ).
thf(mdia,definition,
( mdia
= ( ^ [Phi: mworld > $o,W: mworld] :
? [V: mworld] :
( ( mrel @ W @ V )
& ( Phi @ V ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mdia_def) ).
thf(mequiv,definition,
( mequiv
= ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
( ( A @ W )
<=> ( B @ W ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mequiv_def) ).
thf(mimplies,definition,
( mimplies
= ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
( ( A @ W )
=> ( B @ W ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mimplies_def) ).
thf(mlocal,definition,
( mlocal
= ( ^ [Phi: mworld > $o] : ( Phi @ mactual ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mlocal_def) ).
thf(mnot,definition,
( mnot
= ( ^ [A: mworld > $o,W: mworld] :
~ ( A @ W ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mnot_def) ).
thf(mor,definition,
( mor
= ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
( ( A @ W )
| ( B @ W ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mor_def) ).
thf(1,axiom,
! [W: mworld,V: mworld,U: mworld] :
( ( ( mrel @ W @ U )
& ( mrel @ W @ V ) )
=> ( mrel @ U @ V ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mrel_euclidean) ).
thf(2,axiom,
! [W: mworld] : ( mrel @ W @ W ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mrel_reflexive) ).
thf(3,conjecture,
mlocal @ ( mequiv @ ( mnot @ ( mbox @ ( mdia @ ( mbox @ p ) ) ) ) @ ( mdia @ ( mbox @ ( mdia @ ( mnot @ p ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
thf(4,negated_conjecture,
( ( mlocal @ ( mequiv @ ( mnot @ ( mbox @ ( mdia @ ( mbox @ p ) ) ) ) @ ( mdia @ ( mbox @ ( mdia @ ( mnot @ p ) ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[3]) ).
thf(5,plain,
( ( ~ ! [SY35: mworld] :
( ( mrel @ mactual @ SY35 )
=> ? [SY7: mworld] :
( ( mrel @ SY35 @ SY7 )
& ! [SY4: mworld] :
( ( mrel @ SY7 @ SY4 )
=> ( p @ SY4 ) ) ) )
<=> ? [SY38: mworld] :
( ( mrel @ mactual @ SY38 )
& ! [SY26: mworld] :
( ( mrel @ SY38 @ SY26 )
=> ? [SY23: mworld] :
( ( mrel @ SY26 @ SY23 )
& ~ ( p @ SY23 ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[4,mand,mbox,mdia,mequiv,mimplies,mlocal,mnot,mor]) ).
thf(6,plain,
( ( ! [W: mworld,V: mworld,U: mworld] :
( ( ( mrel @ W @ U )
& ( mrel @ W @ V ) )
=> ( mrel @ U @ V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1,mand,mbox,mdia,mequiv,mimplies,mlocal,mnot,mor]) ).
thf(7,plain,
( ( ! [W: mworld] : ( mrel @ W @ W ) )
= $true ),
inference(unfold_def,[status(thm)],[2,mand,mbox,mdia,mequiv,mimplies,mlocal,mnot,mor]) ).
thf(8,plain,
( ( ~ ! [SY35: mworld] :
( ( mrel @ mactual @ SY35 )
=> ? [SY7: mworld] :
( ( mrel @ SY35 @ SY7 )
& ! [SY4: mworld] :
( ( mrel @ SY7 @ SY4 )
=> ( p @ SY4 ) ) ) )
=> ? [SY38: mworld] :
( ( mrel @ mactual @ SY38 )
& ! [SY26: mworld] :
( ( mrel @ SY38 @ SY26 )
=> ? [SY23: mworld] :
( ( mrel @ SY26 @ SY23 )
& ~ ( p @ SY23 ) ) ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[5]) ).
thf(9,plain,
( ( ? [SY38: mworld] :
( ( mrel @ mactual @ SY38 )
& ! [SY26: mworld] :
( ( mrel @ SY38 @ SY26 )
=> ? [SY23: mworld] :
( ( mrel @ SY26 @ SY23 )
& ~ ( p @ SY23 ) ) ) )
=> ~ ! [SY35: mworld] :
( ( mrel @ mactual @ SY35 )
=> ? [SY7: mworld] :
( ( mrel @ SY35 @ SY7 )
& ! [SY4: mworld] :
( ( mrel @ SY7 @ SY4 )
=> ( p @ SY4 ) ) ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[5]) ).
thf(10,plain,
( ( ~ ( ~ ! [SY35: mworld] :
( ( mrel @ mactual @ SY35 )
=> ? [SY7: mworld] :
( ( mrel @ SY35 @ SY7 )
& ! [SY4: mworld] :
( ( mrel @ SY7 @ SY4 )
=> ( p @ SY4 ) ) ) )
=> ? [SY38: mworld] :
( ( mrel @ mactual @ SY38 )
& ! [SY26: mworld] :
( ( mrel @ SY38 @ SY26 )
=> ? [SY23: mworld] :
( ( mrel @ SY26 @ SY23 )
& ~ ( p @ SY23 ) ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[8]) ).
thf(11,plain,
( ( ~ ( ? [SY38: mworld] :
( ( mrel @ mactual @ SY38 )
& ! [SY26: mworld] :
( ( mrel @ SY38 @ SY26 )
=> ? [SY23: mworld] :
( ( mrel @ SY26 @ SY23 )
& ~ ( p @ SY23 ) ) ) )
=> ~ ! [SY35: mworld] :
( ( mrel @ mactual @ SY35 )
=> ? [SY7: mworld] :
( ( mrel @ SY35 @ SY7 )
& ! [SY4: mworld] :
( ( mrel @ SY7 @ SY4 )
=> ( p @ SY4 ) ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[9]) ).
thf(12,plain,
( ( ! [W: mworld] : ( mrel @ W @ W ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(13,plain,
( ( ! [W: mworld,V: mworld,U: mworld] :
( ( ( mrel @ W @ U )
& ( mrel @ W @ V ) )
=> ( mrel @ U @ V ) ) )
= $true ),
inference(copy,[status(thm)],[6]) ).
thf(14,plain,
( ( ~ ( ~ ! [SY35: mworld] :
( ( mrel @ mactual @ SY35 )
=> ? [SY7: mworld] :
( ( mrel @ SY35 @ SY7 )
& ! [SY4: mworld] :
( ( mrel @ SY7 @ SY4 )
=> ( p @ SY4 ) ) ) )
=> ? [SY38: mworld] :
( ( mrel @ mactual @ SY38 )
& ! [SY26: mworld] :
( ( mrel @ SY38 @ SY26 )
=> ? [SY23: mworld] :
( ( mrel @ SY26 @ SY23 )
& ~ ( p @ SY23 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(15,plain,
( ( ~ ( ~ ~ ! [SX0: mworld] :
( ~ ( mrel @ mactual @ SX0 )
| ~ ! [SX1: mworld] :
~ ~ ( ~ ( mrel @ SX0 @ SX1 )
| ~ ! [SX2: mworld] :
( ~ ( mrel @ SX1 @ SX2 )
| ( p @ SX2 ) ) ) )
| ~ ! [SX0: mworld] :
~ ~ ( ~ ( mrel @ mactual @ SX0 )
| ~ ! [SX1: mworld] :
( ~ ( mrel @ SX0 @ SX1 )
| ~ ! [SX2: mworld] :
~ ~ ( ~ ( mrel @ SX1 @ SX2 )
| ~ ~ ( p @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14,mand,mbox,mdia,mequiv,mimplies,mlocal,mnot,mor]) ).
thf(16,plain,
( ( ! [SX0: mworld,SX1: mworld,SX2: mworld] :
( ~ ~ ( ~ ( mrel @ SX0 @ SX2 )
| ~ ( mrel @ SX0 @ SX1 ) )
| ( mrel @ SX2 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13,mand,mbox,mdia,mequiv,mimplies,mlocal,mnot,mor]) ).
thf(17,plain,
! [SV1: mworld] :
( ( mrel @ SV1 @ SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[12]) ).
thf(18,plain,
( ( ~ ~ ! [SX0: mworld] :
( ~ ( mrel @ mactual @ SX0 )
| ~ ! [SX1: mworld] :
~ ~ ( ~ ( mrel @ SX0 @ SX1 )
| ~ ! [SX2: mworld] :
( ~ ( mrel @ SX1 @ SX2 )
| ( p @ SX2 ) ) ) )
| ~ ! [SX0: mworld] :
~ ~ ( ~ ( mrel @ mactual @ SX0 )
| ~ ! [SX1: mworld] :
( ~ ( mrel @ SX0 @ SX1 )
| ~ ! [SX2: mworld] :
~ ~ ( ~ ( mrel @ SX1 @ SX2 )
| ~ ~ ( p @ SX2 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[15]) ).
thf(19,plain,
! [SV2: mworld] :
( ( ! [SY51: mworld,SY52: mworld] :
( ~ ~ ( ~ ( mrel @ SV2 @ SY52 )
| ~ ( mrel @ SV2 @ SY51 ) )
| ( mrel @ SY52 @ SY51 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[16]) ).
thf(20,plain,
( ( ~ ~ ! [SX0: mworld] :
( ~ ( mrel @ mactual @ SX0 )
| ~ ! [SX1: mworld] :
~ ~ ( ~ ( mrel @ SX0 @ SX1 )
| ~ ! [SX2: mworld] :
( ~ ( mrel @ SX1 @ SX2 )
| ( p @ SX2 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[18]) ).
thf(21,plain,
( ( ~ ! [SX0: mworld] :
~ ~ ( ~ ( mrel @ mactual @ SX0 )
| ~ ! [SX1: mworld] :
( ~ ( mrel @ SX0 @ SX1 )
| ~ ! [SX2: mworld] :
~ ~ ( ~ ( mrel @ SX1 @ SX2 )
| ~ ~ ( p @ SX2 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[18]) ).
thf(22,plain,
! [SV3: mworld,SV2: mworld] :
( ( ! [SY53: mworld] :
( ~ ~ ( ~ ( mrel @ SV2 @ SY53 )
| ~ ( mrel @ SV2 @ SV3 ) )
| ( mrel @ SY53 @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[19]) ).
thf(23,plain,
( ( ~ ! [SX0: mworld] :
( ~ ( mrel @ mactual @ SX0 )
| ~ ! [SX1: mworld] :
~ ~ ( ~ ( mrel @ SX0 @ SX1 )
| ~ ! [SX2: mworld] :
( ~ ( mrel @ SX1 @ SX2 )
| ( p @ SX2 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[20]) ).
thf(24,plain,
( ( ! [SX0: mworld] :
~ ~ ( ~ ( mrel @ mactual @ SX0 )
| ~ ! [SX1: mworld] :
( ~ ( mrel @ SX0 @ SX1 )
| ~ ! [SX2: mworld] :
~ ~ ( ~ ( mrel @ SX1 @ SX2 )
| ~ ~ ( p @ SX2 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[21]) ).
thf(25,plain,
! [SV3: mworld,SV4: mworld,SV2: mworld] :
( ( ~ ~ ( ~ ( mrel @ SV2 @ SV4 )
| ~ ( mrel @ SV2 @ SV3 ) )
| ( mrel @ SV4 @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[22]) ).
thf(26,plain,
( ( ! [SX0: mworld] :
( ~ ( mrel @ mactual @ SX0 )
| ~ ! [SX1: mworld] :
~ ~ ( ~ ( mrel @ SX0 @ SX1 )
| ~ ! [SX2: mworld] :
( ~ ( mrel @ SX1 @ SX2 )
| ( p @ SX2 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[23]) ).
thf(27,plain,
! [SV5: mworld] :
( ( ~ ~ ( ~ ( mrel @ mactual @ SV5 )
| ~ ! [SY54: mworld] :
( ~ ( mrel @ SV5 @ SY54 )
| ~ ! [SX2: mworld] :
~ ~ ( ~ ( mrel @ SY54 @ SX2 )
| ~ ~ ( p @ SX2 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[24]) ).
thf(28,plain,
! [SV3: mworld,SV4: mworld,SV2: mworld] :
( ( ( ~ ~ ( ~ ( mrel @ SV2 @ SV4 )
| ~ ( mrel @ SV2 @ SV3 ) ) )
= $true )
| ( ( mrel @ SV4 @ SV3 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[25]) ).
thf(29,plain,
( ( ~ ( mrel @ mactual @ sK1_SX0 )
| ~ ! [SY56: mworld] :
~ ~ ( ~ ( mrel @ sK1_SX0 @ SY56 )
| ~ ! [SX2: mworld] :
( ~ ( mrel @ SY56 @ SX2 )
| ( p @ SX2 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[26]) ).
thf(30,plain,
! [SV5: mworld] :
( ( ~ ( ~ ( mrel @ mactual @ SV5 )
| ~ ! [SY54: mworld] :
( ~ ( mrel @ SV5 @ SY54 )
| ~ ! [SX2: mworld] :
~ ~ ( ~ ( mrel @ SY54 @ SX2 )
| ~ ~ ( p @ SX2 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[27]) ).
thf(31,plain,
! [SV3: mworld,SV4: mworld,SV2: mworld] :
( ( ( ~ ( ~ ( mrel @ SV2 @ SV4 )
| ~ ( mrel @ SV2 @ SV3 ) ) )
= $false )
| ( ( mrel @ SV4 @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[28]) ).
thf(32,plain,
( ( ~ ( mrel @ mactual @ sK1_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[29]) ).
thf(33,plain,
( ( ~ ! [SY56: mworld] :
~ ~ ( ~ ( mrel @ sK1_SX0 @ SY56 )
| ~ ! [SX2: mworld] :
( ~ ( mrel @ SY56 @ SX2 )
| ( p @ SX2 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[29]) ).
thf(34,plain,
! [SV5: mworld] :
( ( ~ ( mrel @ mactual @ SV5 )
| ~ ! [SY54: mworld] :
( ~ ( mrel @ SV5 @ SY54 )
| ~ ! [SX2: mworld] :
~ ~ ( ~ ( mrel @ SY54 @ SX2 )
| ~ ~ ( p @ SX2 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[30]) ).
thf(35,plain,
! [SV3: mworld,SV4: mworld,SV2: mworld] :
( ( ( ~ ( mrel @ SV2 @ SV4 )
| ~ ( mrel @ SV2 @ SV3 ) )
= $true )
| ( ( mrel @ SV4 @ SV3 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[31]) ).
thf(36,plain,
( ( mrel @ mactual @ sK1_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[32]) ).
thf(37,plain,
( ( ! [SY56: mworld] :
~ ~ ( ~ ( mrel @ sK1_SX0 @ SY56 )
| ~ ! [SX2: mworld] :
( ~ ( mrel @ SY56 @ SX2 )
| ( p @ SX2 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[33]) ).
thf(38,plain,
! [SV5: mworld] :
( ( ( ~ ( mrel @ mactual @ SV5 ) )
= $true )
| ( ( ~ ! [SY54: mworld] :
( ~ ( mrel @ SV5 @ SY54 )
| ~ ! [SX2: mworld] :
~ ~ ( ~ ( mrel @ SY54 @ SX2 )
| ~ ~ ( p @ SX2 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[34]) ).
thf(39,plain,
! [SV3: mworld,SV4: mworld,SV2: mworld] :
( ( ( ~ ( mrel @ SV2 @ SV4 ) )
= $true )
| ( ( ~ ( mrel @ SV2 @ SV3 ) )
= $true )
| ( ( mrel @ SV4 @ SV3 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[35]) ).
thf(40,plain,
! [SV6: mworld] :
( ( ~ ~ ( ~ ( mrel @ sK1_SX0 @ SV6 )
| ~ ! [SY58: mworld] :
( ~ ( mrel @ SV6 @ SY58 )
| ( p @ SY58 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[37]) ).
thf(41,plain,
! [SV5: mworld] :
( ( ( mrel @ mactual @ SV5 )
= $false )
| ( ( ~ ! [SY54: mworld] :
( ~ ( mrel @ SV5 @ SY54 )
| ~ ! [SX2: mworld] :
~ ~ ( ~ ( mrel @ SY54 @ SX2 )
| ~ ~ ( p @ SX2 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[38]) ).
thf(42,plain,
! [SV3: mworld,SV4: mworld,SV2: mworld] :
( ( ( mrel @ SV2 @ SV4 )
= $false )
| ( ( ~ ( mrel @ SV2 @ SV3 ) )
= $true )
| ( ( mrel @ SV4 @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[39]) ).
thf(43,plain,
! [SV6: mworld] :
( ( ~ ( ~ ( mrel @ sK1_SX0 @ SV6 )
| ~ ! [SY58: mworld] :
( ~ ( mrel @ SV6 @ SY58 )
| ( p @ SY58 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[40]) ).
thf(44,plain,
! [SV5: mworld] :
( ( ( ! [SY54: mworld] :
( ~ ( mrel @ SV5 @ SY54 )
| ~ ! [SX2: mworld] :
~ ~ ( ~ ( mrel @ SY54 @ SX2 )
| ~ ~ ( p @ SX2 ) ) ) )
= $false )
| ( ( mrel @ mactual @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[41]) ).
thf(45,plain,
! [SV4: mworld,SV3: mworld,SV2: mworld] :
( ( ( mrel @ SV2 @ SV3 )
= $false )
| ( ( mrel @ SV2 @ SV4 )
= $false )
| ( ( mrel @ SV4 @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[42]) ).
thf(46,plain,
! [SV6: mworld] :
( ( ~ ( mrel @ sK1_SX0 @ SV6 )
| ~ ! [SY58: mworld] :
( ~ ( mrel @ SV6 @ SY58 )
| ( p @ SY58 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[43]) ).
thf(47,plain,
! [SV5: mworld] :
( ( ( ~ ( mrel @ SV5 @ ( sK2_SY54 @ SV5 ) )
| ~ ! [SY59: mworld] :
~ ~ ( ~ ( mrel @ ( sK2_SY54 @ SV5 ) @ SY59 )
| ~ ~ ( p @ SY59 ) ) )
= $false )
| ( ( mrel @ mactual @ SV5 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[44]) ).
thf(48,plain,
! [SV6: mworld] :
( ( ( ~ ( mrel @ sK1_SX0 @ SV6 ) )
= $true )
| ( ( ~ ! [SY58: mworld] :
( ~ ( mrel @ SV6 @ SY58 )
| ( p @ SY58 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[46]) ).
thf(49,plain,
! [SV5: mworld] :
( ( ( ~ ( mrel @ SV5 @ ( sK2_SY54 @ SV5 ) ) )
= $false )
| ( ( mrel @ mactual @ SV5 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[47]) ).
thf(50,plain,
! [SV5: mworld] :
( ( ( ~ ! [SY59: mworld] :
~ ~ ( ~ ( mrel @ ( sK2_SY54 @ SV5 ) @ SY59 )
| ~ ~ ( p @ SY59 ) ) )
= $false )
| ( ( mrel @ mactual @ SV5 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[47]) ).
thf(51,plain,
! [SV6: mworld] :
( ( ( mrel @ sK1_SX0 @ SV6 )
= $false )
| ( ( ~ ! [SY58: mworld] :
( ~ ( mrel @ SV6 @ SY58 )
| ( p @ SY58 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[48]) ).
thf(52,plain,
! [SV5: mworld] :
( ( ( mrel @ SV5 @ ( sK2_SY54 @ SV5 ) )
= $true )
| ( ( mrel @ mactual @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[49]) ).
thf(53,plain,
! [SV5: mworld] :
( ( ( ! [SY59: mworld] :
~ ~ ( ~ ( mrel @ ( sK2_SY54 @ SV5 ) @ SY59 )
| ~ ~ ( p @ SY59 ) ) )
= $true )
| ( ( mrel @ mactual @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[50]) ).
thf(54,plain,
! [SV6: mworld] :
( ( ( ! [SY58: mworld] :
( ~ ( mrel @ SV6 @ SY58 )
| ( p @ SY58 ) ) )
= $false )
| ( ( mrel @ sK1_SX0 @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[51]) ).
thf(55,plain,
! [SV7: mworld,SV5: mworld] :
( ( ( ~ ~ ( ~ ( mrel @ ( sK2_SY54 @ SV5 ) @ SV7 )
| ~ ~ ( p @ SV7 ) ) )
= $true )
| ( ( mrel @ mactual @ SV5 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[53]) ).
thf(56,plain,
! [SV6: mworld] :
( ( ( ~ ( mrel @ SV6 @ ( sK3_SY58 @ SV6 ) )
| ( p @ ( sK3_SY58 @ SV6 ) ) )
= $false )
| ( ( mrel @ sK1_SX0 @ SV6 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[54]) ).
thf(57,plain,
! [SV7: mworld,SV5: mworld] :
( ( ( ~ ( ~ ( mrel @ ( sK2_SY54 @ SV5 ) @ SV7 )
| ~ ~ ( p @ SV7 ) ) )
= $false )
| ( ( mrel @ mactual @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[55]) ).
thf(58,plain,
! [SV6: mworld] :
( ( ( ~ ( mrel @ SV6 @ ( sK3_SY58 @ SV6 ) ) )
= $false )
| ( ( mrel @ sK1_SX0 @ SV6 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[56]) ).
thf(59,plain,
! [SV6: mworld] :
( ( ( p @ ( sK3_SY58 @ SV6 ) )
= $false )
| ( ( mrel @ sK1_SX0 @ SV6 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[56]) ).
thf(60,plain,
! [SV7: mworld,SV5: mworld] :
( ( ( ~ ( mrel @ ( sK2_SY54 @ SV5 ) @ SV7 )
| ~ ~ ( p @ SV7 ) )
= $true )
| ( ( mrel @ mactual @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[57]) ).
thf(61,plain,
! [SV6: mworld] :
( ( ( mrel @ SV6 @ ( sK3_SY58 @ SV6 ) )
= $true )
| ( ( mrel @ sK1_SX0 @ SV6 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[58]) ).
thf(62,plain,
! [SV7: mworld,SV5: mworld] :
( ( ( ~ ( mrel @ ( sK2_SY54 @ SV5 ) @ SV7 ) )
= $true )
| ( ( ~ ~ ( p @ SV7 ) )
= $true )
| ( ( mrel @ mactual @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[60]) ).
thf(63,plain,
! [SV7: mworld,SV5: mworld] :
( ( ( mrel @ ( sK2_SY54 @ SV5 ) @ SV7 )
= $false )
| ( ( ~ ~ ( p @ SV7 ) )
= $true )
| ( ( mrel @ mactual @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[62]) ).
thf(64,plain,
! [SV5: mworld,SV7: mworld] :
( ( ( ~ ( p @ SV7 ) )
= $false )
| ( ( mrel @ ( sK2_SY54 @ SV5 ) @ SV7 )
= $false )
| ( ( mrel @ mactual @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[63]) ).
thf(65,plain,
! [SV5: mworld,SV7: mworld] :
( ( ( p @ SV7 )
= $true )
| ( ( mrel @ ( sK2_SY54 @ SV5 ) @ SV7 )
= $false )
| ( ( mrel @ mactual @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[64]) ).
thf(66,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[17,65,61,59,52,45,36]) ).
thf(67,plain,
( ( ! [W: mworld] : ( mrel @ W @ W ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(68,plain,
( ( ! [W: mworld,V: mworld,U: mworld] :
( ( ( mrel @ W @ U )
& ( mrel @ W @ V ) )
=> ( mrel @ U @ V ) ) )
= $true ),
inference(copy,[status(thm)],[6]) ).
thf(69,plain,
( ( ~ ( ? [SY38: mworld] :
( ( mrel @ mactual @ SY38 )
& ! [SY26: mworld] :
( ( mrel @ SY38 @ SY26 )
=> ? [SY23: mworld] :
( ( mrel @ SY26 @ SY23 )
& ~ ( p @ SY23 ) ) ) )
=> ~ ! [SY35: mworld] :
( ( mrel @ mactual @ SY35 )
=> ? [SY7: mworld] :
( ( mrel @ SY35 @ SY7 )
& ! [SY4: mworld] :
( ( mrel @ SY7 @ SY4 )
=> ( p @ SY4 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(70,plain,
( ( ! [SX0: mworld,SX1: mworld,SX2: mworld] :
( ~ ~ ( ~ ( mrel @ SX0 @ SX2 )
| ~ ( mrel @ SX0 @ SX1 ) )
| ( mrel @ SX2 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[68,mand,mbox,mdia,mequiv,mimplies,mlocal,mnot,mor]) ).
thf(71,plain,
( ( ~ ( ~ ~ ! [SX0: mworld] :
~ ~ ( ~ ( mrel @ mactual @ SX0 )
| ~ ! [SX1: mworld] :
( ~ ( mrel @ SX0 @ SX1 )
| ~ ! [SX2: mworld] :
~ ~ ( ~ ( mrel @ SX1 @ SX2 )
| ~ ~ ( p @ SX2 ) ) ) )
| ~ ! [SX0: mworld] :
( ~ ( mrel @ mactual @ SX0 )
| ~ ! [SX1: mworld] :
~ ~ ( ~ ( mrel @ SX0 @ SX1 )
| ~ ! [SX2: mworld] :
( ~ ( mrel @ SX1 @ SX2 )
| ( p @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[69,mand,mbox,mdia,mequiv,mimplies,mlocal,mnot,mor]) ).
thf(72,plain,
! [SV8: mworld] :
( ( mrel @ SV8 @ SV8 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[67]) ).
thf(73,plain,
! [SV9: mworld] :
( ( ! [SY60: mworld,SY61: mworld] :
( ~ ~ ( ~ ( mrel @ SV9 @ SY61 )
| ~ ( mrel @ SV9 @ SY60 ) )
| ( mrel @ SY61 @ SY60 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[70]) ).
thf(74,plain,
( ( ~ ~ ! [SX0: mworld] :
~ ~ ( ~ ( mrel @ mactual @ SX0 )
| ~ ! [SX1: mworld] :
( ~ ( mrel @ SX0 @ SX1 )
| ~ ! [SX2: mworld] :
~ ~ ( ~ ( mrel @ SX1 @ SX2 )
| ~ ~ ( p @ SX2 ) ) ) )
| ~ ! [SX0: mworld] :
( ~ ( mrel @ mactual @ SX0 )
| ~ ! [SX1: mworld] :
~ ~ ( ~ ( mrel @ SX0 @ SX1 )
| ~ ! [SX2: mworld] :
( ~ ( mrel @ SX1 @ SX2 )
| ( p @ SX2 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[71]) ).
thf(75,plain,
! [SV10: mworld,SV9: mworld] :
( ( ! [SY62: mworld] :
( ~ ~ ( ~ ( mrel @ SV9 @ SY62 )
| ~ ( mrel @ SV9 @ SV10 ) )
| ( mrel @ SY62 @ SV10 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[73]) ).
thf(76,plain,
( ( ~ ~ ! [SX0: mworld] :
~ ~ ( ~ ( mrel @ mactual @ SX0 )
| ~ ! [SX1: mworld] :
( ~ ( mrel @ SX0 @ SX1 )
| ~ ! [SX2: mworld] :
~ ~ ( ~ ( mrel @ SX1 @ SX2 )
| ~ ~ ( p @ SX2 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[74]) ).
thf(77,plain,
( ( ~ ! [SX0: mworld] :
( ~ ( mrel @ mactual @ SX0 )
| ~ ! [SX1: mworld] :
~ ~ ( ~ ( mrel @ SX0 @ SX1 )
| ~ ! [SX2: mworld] :
( ~ ( mrel @ SX1 @ SX2 )
| ( p @ SX2 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[74]) ).
thf(78,plain,
! [SV10: mworld,SV11: mworld,SV9: mworld] :
( ( ~ ~ ( ~ ( mrel @ SV9 @ SV11 )
| ~ ( mrel @ SV9 @ SV10 ) )
| ( mrel @ SV11 @ SV10 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[75]) ).
thf(79,plain,
( ( ~ ! [SX0: mworld] :
~ ~ ( ~ ( mrel @ mactual @ SX0 )
| ~ ! [SX1: mworld] :
( ~ ( mrel @ SX0 @ SX1 )
| ~ ! [SX2: mworld] :
~ ~ ( ~ ( mrel @ SX1 @ SX2 )
| ~ ~ ( p @ SX2 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[76]) ).
thf(80,plain,
( ( ! [SX0: mworld] :
( ~ ( mrel @ mactual @ SX0 )
| ~ ! [SX1: mworld] :
~ ~ ( ~ ( mrel @ SX0 @ SX1 )
| ~ ! [SX2: mworld] :
( ~ ( mrel @ SX1 @ SX2 )
| ( p @ SX2 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[77]) ).
thf(81,plain,
! [SV10: mworld,SV11: mworld,SV9: mworld] :
( ( ( ~ ~ ( ~ ( mrel @ SV9 @ SV11 )
| ~ ( mrel @ SV9 @ SV10 ) ) )
= $true )
| ( ( mrel @ SV11 @ SV10 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[78]) ).
thf(82,plain,
( ( ! [SX0: mworld] :
~ ~ ( ~ ( mrel @ mactual @ SX0 )
| ~ ! [SX1: mworld] :
( ~ ( mrel @ SX0 @ SX1 )
| ~ ! [SX2: mworld] :
~ ~ ( ~ ( mrel @ SX1 @ SX2 )
| ~ ~ ( p @ SX2 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[79]) ).
thf(83,plain,
! [SV12: mworld] :
( ( ~ ( mrel @ mactual @ SV12 )
| ~ ! [SY63: mworld] :
~ ~ ( ~ ( mrel @ SV12 @ SY63 )
| ~ ! [SX2: mworld] :
( ~ ( mrel @ SY63 @ SX2 )
| ( p @ SX2 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[80]) ).
thf(84,plain,
! [SV10: mworld,SV11: mworld,SV9: mworld] :
( ( ( ~ ( ~ ( mrel @ SV9 @ SV11 )
| ~ ( mrel @ SV9 @ SV10 ) ) )
= $false )
| ( ( mrel @ SV11 @ SV10 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[81]) ).
thf(85,plain,
( ( ~ ~ ( ~ ( mrel @ mactual @ sK4_SX0 )
| ~ ! [SY65: mworld] :
( ~ ( mrel @ sK4_SX0 @ SY65 )
| ~ ! [SX2: mworld] :
~ ~ ( ~ ( mrel @ SY65 @ SX2 )
| ~ ~ ( p @ SX2 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[82]) ).
thf(86,plain,
! [SV12: mworld] :
( ( ( ~ ( mrel @ mactual @ SV12 ) )
= $true )
| ( ( ~ ! [SY63: mworld] :
~ ~ ( ~ ( mrel @ SV12 @ SY63 )
| ~ ! [SX2: mworld] :
( ~ ( mrel @ SY63 @ SX2 )
| ( p @ SX2 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[83]) ).
thf(87,plain,
! [SV10: mworld,SV11: mworld,SV9: mworld] :
( ( ( ~ ( mrel @ SV9 @ SV11 )
| ~ ( mrel @ SV9 @ SV10 ) )
= $true )
| ( ( mrel @ SV11 @ SV10 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[84]) ).
thf(88,plain,
( ( ~ ( ~ ( mrel @ mactual @ sK4_SX0 )
| ~ ! [SY65: mworld] :
( ~ ( mrel @ sK4_SX0 @ SY65 )
| ~ ! [SX2: mworld] :
~ ~ ( ~ ( mrel @ SY65 @ SX2 )
| ~ ~ ( p @ SX2 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[85]) ).
thf(89,plain,
! [SV12: mworld] :
( ( ( mrel @ mactual @ SV12 )
= $false )
| ( ( ~ ! [SY63: mworld] :
~ ~ ( ~ ( mrel @ SV12 @ SY63 )
| ~ ! [SX2: mworld] :
( ~ ( mrel @ SY63 @ SX2 )
| ( p @ SX2 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[86]) ).
thf(90,plain,
! [SV10: mworld,SV11: mworld,SV9: mworld] :
( ( ( ~ ( mrel @ SV9 @ SV11 ) )
= $true )
| ( ( ~ ( mrel @ SV9 @ SV10 ) )
= $true )
| ( ( mrel @ SV11 @ SV10 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[87]) ).
thf(91,plain,
( ( ~ ( mrel @ mactual @ sK4_SX0 )
| ~ ! [SY65: mworld] :
( ~ ( mrel @ sK4_SX0 @ SY65 )
| ~ ! [SX2: mworld] :
~ ~ ( ~ ( mrel @ SY65 @ SX2 )
| ~ ~ ( p @ SX2 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[88]) ).
thf(92,plain,
! [SV12: mworld] :
( ( ( ! [SY63: mworld] :
~ ~ ( ~ ( mrel @ SV12 @ SY63 )
| ~ ! [SX2: mworld] :
( ~ ( mrel @ SY63 @ SX2 )
| ( p @ SX2 ) ) ) )
= $false )
| ( ( mrel @ mactual @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[89]) ).
thf(93,plain,
! [SV10: mworld,SV11: mworld,SV9: mworld] :
( ( ( mrel @ SV9 @ SV11 )
= $false )
| ( ( ~ ( mrel @ SV9 @ SV10 ) )
= $true )
| ( ( mrel @ SV11 @ SV10 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[90]) ).
thf(94,plain,
( ( ~ ( mrel @ mactual @ sK4_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[91]) ).
thf(95,plain,
( ( ~ ! [SY65: mworld] :
( ~ ( mrel @ sK4_SX0 @ SY65 )
| ~ ! [SX2: mworld] :
~ ~ ( ~ ( mrel @ SY65 @ SX2 )
| ~ ~ ( p @ SX2 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[91]) ).
thf(96,plain,
! [SV12: mworld] :
( ( ( ~ ~ ( ~ ( mrel @ SV12 @ ( sK5_SY63 @ SV12 ) )
| ~ ! [SY67: mworld] :
( ~ ( mrel @ ( sK5_SY63 @ SV12 ) @ SY67 )
| ( p @ SY67 ) ) ) )
= $false )
| ( ( mrel @ mactual @ SV12 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[92]) ).
thf(97,plain,
! [SV11: mworld,SV10: mworld,SV9: mworld] :
( ( ( mrel @ SV9 @ SV10 )
= $false )
| ( ( mrel @ SV9 @ SV11 )
= $false )
| ( ( mrel @ SV11 @ SV10 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[93]) ).
thf(98,plain,
( ( mrel @ mactual @ sK4_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[94]) ).
thf(99,plain,
( ( ! [SY65: mworld] :
( ~ ( mrel @ sK4_SX0 @ SY65 )
| ~ ! [SX2: mworld] :
~ ~ ( ~ ( mrel @ SY65 @ SX2 )
| ~ ~ ( p @ SX2 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[95]) ).
thf(100,plain,
! [SV12: mworld] :
( ( ( ~ ( ~ ( mrel @ SV12 @ ( sK5_SY63 @ SV12 ) )
| ~ ! [SY67: mworld] :
( ~ ( mrel @ ( sK5_SY63 @ SV12 ) @ SY67 )
| ( p @ SY67 ) ) ) )
= $true )
| ( ( mrel @ mactual @ SV12 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[96]) ).
thf(101,plain,
! [SV13: mworld] :
( ( ~ ( mrel @ sK4_SX0 @ SV13 )
| ~ ! [SY68: mworld] :
~ ~ ( ~ ( mrel @ SV13 @ SY68 )
| ~ ~ ( p @ SY68 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[99]) ).
thf(102,plain,
! [SV12: mworld] :
( ( ( ~ ( mrel @ SV12 @ ( sK5_SY63 @ SV12 ) )
| ~ ! [SY67: mworld] :
( ~ ( mrel @ ( sK5_SY63 @ SV12 ) @ SY67 )
| ( p @ SY67 ) ) )
= $false )
| ( ( mrel @ mactual @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[100]) ).
thf(103,plain,
! [SV13: mworld] :
( ( ( ~ ( mrel @ sK4_SX0 @ SV13 ) )
= $true )
| ( ( ~ ! [SY68: mworld] :
~ ~ ( ~ ( mrel @ SV13 @ SY68 )
| ~ ~ ( p @ SY68 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[101]) ).
thf(104,plain,
! [SV12: mworld] :
( ( ( ~ ( mrel @ SV12 @ ( sK5_SY63 @ SV12 ) ) )
= $false )
| ( ( mrel @ mactual @ SV12 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[102]) ).
thf(105,plain,
! [SV12: mworld] :
( ( ( ~ ! [SY67: mworld] :
( ~ ( mrel @ ( sK5_SY63 @ SV12 ) @ SY67 )
| ( p @ SY67 ) ) )
= $false )
| ( ( mrel @ mactual @ SV12 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[102]) ).
thf(106,plain,
! [SV13: mworld] :
( ( ( mrel @ sK4_SX0 @ SV13 )
= $false )
| ( ( ~ ! [SY68: mworld] :
~ ~ ( ~ ( mrel @ SV13 @ SY68 )
| ~ ~ ( p @ SY68 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[103]) ).
thf(107,plain,
! [SV12: mworld] :
( ( ( mrel @ SV12 @ ( sK5_SY63 @ SV12 ) )
= $true )
| ( ( mrel @ mactual @ SV12 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[104]) ).
thf(108,plain,
! [SV12: mworld] :
( ( ( ! [SY67: mworld] :
( ~ ( mrel @ ( sK5_SY63 @ SV12 ) @ SY67 )
| ( p @ SY67 ) ) )
= $true )
| ( ( mrel @ mactual @ SV12 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[105]) ).
thf(109,plain,
! [SV13: mworld] :
( ( ( ! [SY68: mworld] :
~ ~ ( ~ ( mrel @ SV13 @ SY68 )
| ~ ~ ( p @ SY68 ) ) )
= $false )
| ( ( mrel @ sK4_SX0 @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[106]) ).
thf(110,plain,
! [SV14: mworld,SV12: mworld] :
( ( ( ~ ( mrel @ ( sK5_SY63 @ SV12 ) @ SV14 )
| ( p @ SV14 ) )
= $true )
| ( ( mrel @ mactual @ SV12 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[108]) ).
thf(111,plain,
! [SV13: mworld] :
( ( ( ~ ~ ( ~ ( mrel @ SV13 @ ( sK6_SY68 @ SV13 ) )
| ~ ~ ( p @ ( sK6_SY68 @ SV13 ) ) ) )
= $false )
| ( ( mrel @ sK4_SX0 @ SV13 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[109]) ).
thf(112,plain,
! [SV14: mworld,SV12: mworld] :
( ( ( ~ ( mrel @ ( sK5_SY63 @ SV12 ) @ SV14 ) )
= $true )
| ( ( p @ SV14 )
= $true )
| ( ( mrel @ mactual @ SV12 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[110]) ).
thf(113,plain,
! [SV13: mworld] :
( ( ( ~ ( ~ ( mrel @ SV13 @ ( sK6_SY68 @ SV13 ) )
| ~ ~ ( p @ ( sK6_SY68 @ SV13 ) ) ) )
= $true )
| ( ( mrel @ sK4_SX0 @ SV13 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[111]) ).
thf(114,plain,
! [SV14: mworld,SV12: mworld] :
( ( ( mrel @ ( sK5_SY63 @ SV12 ) @ SV14 )
= $false )
| ( ( p @ SV14 )
= $true )
| ( ( mrel @ mactual @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[112]) ).
thf(115,plain,
! [SV13: mworld] :
( ( ( ~ ( mrel @ SV13 @ ( sK6_SY68 @ SV13 ) )
| ~ ~ ( p @ ( sK6_SY68 @ SV13 ) ) )
= $false )
| ( ( mrel @ sK4_SX0 @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[113]) ).
thf(116,plain,
! [SV13: mworld] :
( ( ( ~ ( mrel @ SV13 @ ( sK6_SY68 @ SV13 ) ) )
= $false )
| ( ( mrel @ sK4_SX0 @ SV13 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[115]) ).
thf(117,plain,
! [SV13: mworld] :
( ( ( ~ ~ ( p @ ( sK6_SY68 @ SV13 ) ) )
= $false )
| ( ( mrel @ sK4_SX0 @ SV13 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[115]) ).
thf(118,plain,
! [SV13: mworld] :
( ( ( mrel @ SV13 @ ( sK6_SY68 @ SV13 ) )
= $true )
| ( ( mrel @ sK4_SX0 @ SV13 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[116]) ).
thf(119,plain,
! [SV13: mworld] :
( ( ( ~ ( p @ ( sK6_SY68 @ SV13 ) ) )
= $true )
| ( ( mrel @ sK4_SX0 @ SV13 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[117]) ).
thf(120,plain,
! [SV13: mworld] :
( ( ( p @ ( sK6_SY68 @ SV13 ) )
= $false )
| ( ( mrel @ sK4_SX0 @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[119]) ).
thf(121,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[72,120,118,114,107,98,97]) ).
thf(122,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[121,66]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO893^11 : TPTP v9.3.1. Released v8.1.0.
% 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
% 0.07/0.18 % Computer : n003.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Oct 6 17:55:25 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.25
% 0.07/0.25 No.of.Axioms: 2
% 0.07/0.25
% 0.07/0.25 Length.of.Defs: 1278
% 0.07/0.25
% 0.07/0.25 Contains.Choice.Funs: false
% 0.07/0.25 ...
% 0.07/0.25
% 0.07/0.25 ********************************
% 0.07/0.25 * All subproblems solved! *
% 0.07/0.25 ********************************
% 0.07/0.25 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:2,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:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:121,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.07/0.25
% 0.07/0.25 %**** Beginning of derivation protocol ****
% 0.07/0.25 % SZS output start CNFRefutation
% See solution above
% 0.07/0.25
% 0.07/0.25 %**** End of derivation protocol ****
% 0.07/0.25 %**** no. of clauses in derivation: 122 ****
% 0.07/0.25 %**** clause counter: 121 ****
% 0.07/0.25
% 0.07/0.25 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:2,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:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:121,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------