%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : LCL957^6 : 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 : n012.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 10:31:09 AM UTC 2026
% Result : Theorem 0.09s 0.13s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 12
% Syntax : Number of formulae : 79 ( 51 unt; 0 typ; 10 def)
% Number of atoms : 614 ( 142 equ; 0 cnn)
% Maximal formula atoms : 21 ( 7 avg)
% Number of connectives : 1180 ( 140 ~; 171 |; 2 &; 815 @)
% ( 1 <=>; 51 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 3 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 16 ( 16 >; 0 *; 0 +; 0 <<)
% Number of symbols : 22 ( 19 usr; 4 con; 0-3 aty)
% Number of variables : 314 ( 31 ^; 272 !; 11 ?; 314 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_mworld,type,
mworld: $tType ).
thf(tp_big_r,type,
big_r: $i > $i > mworld > $o ).
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_mexists_di,type,
mexists_di: ( $i > mworld > $o ) > mworld > $o ).
thf(tp_mforall_di,type,
mforall_di: ( $i > 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_sK1_SY116,type,
sK1_SY116: mworld ).
thf(tp_sK2_SY162,type,
sK2_SY162: $i > mworld ).
thf(tp_sK3_SY167,type,
sK3_SY167: $i > $i ).
thf(tp_sK4_SY171,type,
sK4_SY171: $i > mworld ).
thf(tp_sK5_SY174,type,
sK5_SY174: $i > mworld > mworld ).
thf(tp_sK6_SY176,type,
sK6_SY176: $i > 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(mexists_di,definition,
( mexists_di
= ( ^ [A: $i > mworld > $o,W: mworld] :
? [X: $i] : ( A @ X @ W ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mexists_di_def) ).
thf(mforall_di,definition,
( mforall_di
= ( ^ [A: $i > mworld > $o,W: mworld] :
! [X: $i] : ( A @ X @ W ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mforall_di_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] : ( mrel @ W @ V ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mrel_universal) ).
thf(2,conjecture,
( mlocal
@ ( mbox
@ ( mimplies
@ ( mbox
@ ( mimplies
@ ( mexists_di
@ ^ [X: $i] : ( mbox @ ( big_r @ X @ X ) ) )
@ ( mbox
@ ( mforall_di
@ ^ [Y: $i] : ( mbox @ ( big_r @ Y @ Y ) ) ) ) ) )
@ ( mexists_di
@ ^ [U: $i] :
( mbox
@ ( mforall_di
@ ^ [V: $i] : ( mbox @ ( mimplies @ ( mbox @ ( big_r @ U @ U ) ) @ ( mbox @ ( big_r @ V @ V ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x2122) ).
thf(3,negated_conjecture,
( ( mlocal
@ ( mbox
@ ( mimplies
@ ( mbox
@ ( mimplies
@ ( mexists_di
@ ^ [X: $i] : ( mbox @ ( big_r @ X @ X ) ) )
@ ( mbox
@ ( mforall_di
@ ^ [Y: $i] : ( mbox @ ( big_r @ Y @ Y ) ) ) ) ) )
@ ( mexists_di
@ ^ [U: $i] :
( mbox
@ ( mforall_di
@ ^ [V: $i] : ( mbox @ ( mimplies @ ( mbox @ ( big_r @ U @ U ) ) @ ( mbox @ ( big_r @ V @ V ) ) ) ) ) ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[2]) ).
thf(4,plain,
( ( ! [SY116: mworld] :
( ( mrel @ mactual @ SY116 )
=> ( ! [SY104: mworld] :
( ( mrel @ SY116 @ SY104 )
=> ( ? [SY32: $i] :
! [SY33: mworld] :
( ( mrel @ SY104 @ SY33 )
=> ( big_r @ SY32 @ SY32 @ SY33 ) )
=> ! [SY34: mworld] :
( ( mrel @ SY104 @ SY34 )
=> ! [SY22: $i,SY23: mworld] :
( ( mrel @ SY34 @ SY23 )
=> ( big_r @ SY22 @ SY22 @ SY23 ) ) ) ) )
=> ? [SY110: $i] :
! [SY111: mworld] :
( ( mrel @ SY116 @ SY111 )
=> ! [SY80: $i,SY81: mworld] :
( ( mrel @ SY111 @ SY81 )
=> ( ! [SY82: mworld] :
( ( mrel @ SY81 @ SY82 )
=> ( big_r @ SY110 @ SY110 @ SY82 ) )
=> ! [SY66: mworld] :
( ( mrel @ SY81 @ SY66 )
=> ( big_r @ SY80 @ SY80 @ SY66 ) ) ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[3,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(5,plain,
( ( ! [W: mworld,V: mworld] : ( mrel @ W @ V ) )
= $true ),
inference(unfold_def,[status(thm)],[1,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(6,plain,
( ( ( mrel @ mactual @ sK1_SY116 )
=> ( ! [SY144: mworld] :
( ( mrel @ sK1_SY116 @ SY144 )
=> ( ? [SY32: $i] :
! [SY33: mworld] :
( ( mrel @ SY144 @ SY33 )
=> ( big_r @ SY32 @ SY32 @ SY33 ) )
=> ! [SY34: mworld] :
( ( mrel @ SY144 @ SY34 )
=> ! [SY22: $i,SY23: mworld] :
( ( mrel @ SY34 @ SY23 )
=> ( big_r @ SY22 @ SY22 @ SY23 ) ) ) ) )
=> ? [SY150: $i] :
! [SY151: mworld] :
( ( mrel @ sK1_SY116 @ SY151 )
=> ! [SY80: $i,SY81: mworld] :
( ( mrel @ SY151 @ SY81 )
=> ( ! [SY82: mworld] :
( ( mrel @ SY81 @ SY82 )
=> ( big_r @ SY150 @ SY150 @ SY82 ) )
=> ! [SY66: mworld] :
( ( mrel @ SY81 @ SY66 )
=> ( big_r @ SY80 @ SY80 @ SY66 ) ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[4]) ).
thf(7,plain,
( ( mrel @ mactual @ sK1_SY116 )
= $true ),
inference(standard_cnf,[status(thm)],[6]) ).
thf(8,plain,
( ( ! [SY144: mworld] :
( ( mrel @ sK1_SY116 @ SY144 )
=> ( ? [SY32: $i] :
! [SY33: mworld] :
( ( mrel @ SY144 @ SY33 )
=> ( big_r @ SY32 @ SY32 @ SY33 ) )
=> ! [SY34: mworld] :
( ( mrel @ SY144 @ SY34 )
=> ! [SY22: $i,SY23: mworld] :
( ( mrel @ SY34 @ SY23 )
=> ( big_r @ SY22 @ SY22 @ SY23 ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[6]) ).
thf(9,plain,
( ( ? [SY150: $i] :
! [SY151: mworld] :
( ( mrel @ sK1_SY116 @ SY151 )
=> ! [SY80: $i,SY81: mworld] :
( ( mrel @ SY151 @ SY81 )
=> ( ! [SY82: mworld] :
( ( mrel @ SY81 @ SY82 )
=> ( big_r @ SY150 @ SY150 @ SY82 ) )
=> ! [SY66: mworld] :
( ( mrel @ SY81 @ SY66 )
=> ( big_r @ SY80 @ SY80 @ SY66 ) ) ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[6]) ).
thf(10,plain,
( ( ~ ? [SY150: $i] :
! [SY151: mworld] :
( ( mrel @ sK1_SY116 @ SY151 )
=> ! [SY80: $i,SY81: mworld] :
( ( mrel @ SY151 @ SY81 )
=> ( ! [SY82: mworld] :
( ( mrel @ SY81 @ SY82 )
=> ( big_r @ SY150 @ SY150 @ SY82 ) )
=> ! [SY66: mworld] :
( ( mrel @ SY81 @ SY66 )
=> ( big_r @ SY80 @ SY80 @ SY66 ) ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[9]) ).
thf(11,plain,
( ( ! [W: mworld,V: mworld] : ( mrel @ W @ V ) )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(12,plain,
( ( ! [SY144: mworld] :
( ( mrel @ sK1_SY116 @ SY144 )
=> ( ? [SY32: $i] :
! [SY33: mworld] :
( ( mrel @ SY144 @ SY33 )
=> ( big_r @ SY32 @ SY32 @ SY33 ) )
=> ! [SY34: mworld] :
( ( mrel @ SY144 @ SY34 )
=> ! [SY22: $i,SY23: mworld] :
( ( mrel @ SY34 @ SY23 )
=> ( big_r @ SY22 @ SY22 @ SY23 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(13,plain,
( ( mrel @ mactual @ sK1_SY116 )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(14,plain,
( ( ~ ? [SY150: $i] :
! [SY151: mworld] :
( ( mrel @ sK1_SY116 @ SY151 )
=> ! [SY80: $i,SY81: mworld] :
( ( mrel @ SY151 @ SY81 )
=> ( ! [SY82: mworld] :
( ( mrel @ SY81 @ SY82 )
=> ( big_r @ SY150 @ SY150 @ SY82 ) )
=> ! [SY66: mworld] :
( ( mrel @ SY81 @ SY66 )
=> ( big_r @ SY80 @ SY80 @ SY66 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(15,plain,
( ( ~ ~ ! [SX0: $i] :
~ ! [SX1: mworld] :
( ~ ( mrel @ sK1_SY116 @ SX1 )
| ! [SX2: $i,SX3: mworld] :
( ~ ( mrel @ SX1 @ SX3 )
| ~ ! [SX4: mworld] :
( ~ ( mrel @ SX3 @ SX4 )
| ( big_r @ SX0 @ SX0 @ SX4 ) )
| ! [SX4: mworld] :
( ~ ( mrel @ SX3 @ SX4 )
| ( big_r @ SX2 @ SX2 @ SX4 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(16,plain,
( ( ! [SX0: mworld] :
( ~ ( mrel @ sK1_SY116 @ SX0 )
| ~ ~ ! [SX1: $i] :
~ ! [SX2: mworld] :
( ~ ( mrel @ SX0 @ SX2 )
| ( big_r @ SX1 @ SX1 @ SX2 ) )
| ! [SX1: mworld] :
( ~ ( mrel @ SX0 @ SX1 )
| ! [SX2: $i,SX3: mworld] :
( ~ ( mrel @ SX1 @ SX3 )
| ( big_r @ SX2 @ SX2 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(17,plain,
! [SV1: mworld] :
( ( ! [SY156: mworld] : ( mrel @ SV1 @ SY156 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[11]) ).
thf(18,plain,
( ( ~ ! [SX0: $i] :
~ ! [SX1: mworld] :
( ~ ( mrel @ sK1_SY116 @ SX1 )
| ! [SX2: $i,SX3: mworld] :
( ~ ( mrel @ SX1 @ SX3 )
| ~ ! [SX4: mworld] :
( ~ ( mrel @ SX3 @ SX4 )
| ( big_r @ SX0 @ SX0 @ SX4 ) )
| ! [SX4: mworld] :
( ~ ( mrel @ SX3 @ SX4 )
| ( big_r @ SX2 @ SX2 @ SX4 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[15]) ).
thf(19,plain,
! [SV2: mworld] :
( ( ~ ( mrel @ sK1_SY116 @ SV2 )
| ~ ~ ! [SY157: $i] :
~ ! [SY158: mworld] :
( ~ ( mrel @ SV2 @ SY158 )
| ( big_r @ SY157 @ SY157 @ SY158 ) )
| ! [SY159: mworld] :
( ~ ( mrel @ SV2 @ SY159 )
| ! [SX2: $i,SX3: mworld] :
( ~ ( mrel @ SY159 @ SX3 )
| ( big_r @ SX2 @ SX2 @ SX3 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[16]) ).
thf(20,plain,
! [SV3: mworld,SV1: mworld] :
( ( mrel @ SV1 @ SV3 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[17]) ).
thf(21,plain,
( ( ! [SX0: $i] :
~ ! [SX1: mworld] :
( ~ ( mrel @ sK1_SY116 @ SX1 )
| ! [SX2: $i,SX3: mworld] :
( ~ ( mrel @ SX1 @ SX3 )
| ~ ! [SX4: mworld] :
( ~ ( mrel @ SX3 @ SX4 )
| ( big_r @ SX0 @ SX0 @ SX4 ) )
| ! [SX4: mworld] :
( ~ ( mrel @ SX3 @ SX4 )
| ( big_r @ SX2 @ SX2 @ SX4 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[18]) ).
thf(22,plain,
! [SV2: mworld] :
( ( ( ~ ( mrel @ sK1_SY116 @ SV2 ) )
= $true )
| ( ( ~ ~ ! [SY157: $i] :
~ ! [SY158: mworld] :
( ~ ( mrel @ SV2 @ SY158 )
| ( big_r @ SY157 @ SY157 @ SY158 ) )
| ! [SY159: mworld] :
( ~ ( mrel @ SV2 @ SY159 )
| ! [SX2: $i,SX3: mworld] :
( ~ ( mrel @ SY159 @ SX3 )
| ( big_r @ SX2 @ SX2 @ SX3 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[19]) ).
thf(23,plain,
! [SV4: $i] :
( ( ~ ! [SY162: mworld] :
( ~ ( mrel @ sK1_SY116 @ SY162 )
| ! [SY163: $i,SY164: mworld] :
( ~ ( mrel @ SY162 @ SY164 )
| ~ ! [SY165: mworld] :
( ~ ( mrel @ SY164 @ SY165 )
| ( big_r @ SV4 @ SV4 @ SY165 ) )
| ! [SX4: mworld] :
( ~ ( mrel @ SY164 @ SX4 )
| ( big_r @ SY163 @ SY163 @ SX4 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[21]) ).
thf(24,plain,
! [SV2: mworld] :
( ( ( mrel @ sK1_SY116 @ SV2 )
= $false )
| ( ( ~ ~ ! [SY157: $i] :
~ ! [SY158: mworld] :
( ~ ( mrel @ SV2 @ SY158 )
| ( big_r @ SY157 @ SY157 @ SY158 ) )
| ! [SY159: mworld] :
( ~ ( mrel @ SV2 @ SY159 )
| ! [SX2: $i,SX3: mworld] :
( ~ ( mrel @ SY159 @ SX3 )
| ( big_r @ SX2 @ SX2 @ SX3 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[22]) ).
thf(25,plain,
! [SV4: $i] :
( ( ! [SY162: mworld] :
( ~ ( mrel @ sK1_SY116 @ SY162 )
| ! [SY163: $i,SY164: mworld] :
( ~ ( mrel @ SY162 @ SY164 )
| ~ ! [SY165: mworld] :
( ~ ( mrel @ SY164 @ SY165 )
| ( big_r @ SV4 @ SV4 @ SY165 ) )
| ! [SX4: mworld] :
( ~ ( mrel @ SY164 @ SX4 )
| ( big_r @ SY163 @ SY163 @ SX4 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[23]) ).
thf(26,plain,
! [SV2: mworld] :
( ( ( ~ ~ ! [SY157: $i] :
~ ! [SY158: mworld] :
( ~ ( mrel @ SV2 @ SY158 )
| ( big_r @ SY157 @ SY157 @ SY158 ) ) )
= $true )
| ( ( ! [SY159: mworld] :
( ~ ( mrel @ SV2 @ SY159 )
| ! [SX2: $i,SX3: mworld] :
( ~ ( mrel @ SY159 @ SX3 )
| ( big_r @ SX2 @ SX2 @ SX3 ) ) ) )
= $true )
| ( ( mrel @ sK1_SY116 @ SV2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[24]) ).
thf(27,plain,
! [SV4: $i] :
( ( ~ ( mrel @ sK1_SY116 @ ( sK2_SY162 @ SV4 ) )
| ! [SY167: $i,SY168: mworld] :
( ~ ( mrel @ ( sK2_SY162 @ SV4 ) @ SY168 )
| ~ ! [SY165: mworld] :
( ~ ( mrel @ SY168 @ SY165 )
| ( big_r @ SV4 @ SV4 @ SY165 ) )
| ! [SX4: mworld] :
( ~ ( mrel @ SY168 @ SX4 )
| ( big_r @ SY167 @ SY167 @ SX4 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[25]) ).
thf(28,plain,
! [SV2: mworld] :
( ( ( ~ ! [SY157: $i] :
~ ! [SY158: mworld] :
( ~ ( mrel @ SV2 @ SY158 )
| ( big_r @ SY157 @ SY157 @ SY158 ) ) )
= $false )
| ( ( ! [SY159: mworld] :
( ~ ( mrel @ SV2 @ SY159 )
| ! [SX2: $i,SX3: mworld] :
( ~ ( mrel @ SY159 @ SX3 )
| ( big_r @ SX2 @ SX2 @ SX3 ) ) ) )
= $true )
| ( ( mrel @ sK1_SY116 @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[26]) ).
thf(29,plain,
! [SV4: $i] :
( ( ~ ( mrel @ sK1_SY116 @ ( sK2_SY162 @ SV4 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[27]) ).
thf(30,plain,
! [SV4: $i] :
( ( ! [SY167: $i,SY168: mworld] :
( ~ ( mrel @ ( sK2_SY162 @ SV4 ) @ SY168 )
| ~ ! [SY165: mworld] :
( ~ ( mrel @ SY168 @ SY165 )
| ( big_r @ SV4 @ SV4 @ SY165 ) )
| ! [SX4: mworld] :
( ~ ( mrel @ SY168 @ SX4 )
| ( big_r @ SY167 @ SY167 @ SX4 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[27]) ).
thf(31,plain,
! [SV2: mworld] :
( ( ( ! [SY157: $i] :
~ ! [SY158: mworld] :
( ~ ( mrel @ SV2 @ SY158 )
| ( big_r @ SY157 @ SY157 @ SY158 ) ) )
= $true )
| ( ( ! [SY159: mworld] :
( ~ ( mrel @ SV2 @ SY159 )
| ! [SX2: $i,SX3: mworld] :
( ~ ( mrel @ SY159 @ SX3 )
| ( big_r @ SX2 @ SX2 @ SX3 ) ) ) )
= $true )
| ( ( mrel @ sK1_SY116 @ SV2 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[28]) ).
thf(32,plain,
! [SV4: $i] :
( ( mrel @ sK1_SY116 @ ( sK2_SY162 @ SV4 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[29]) ).
thf(33,plain,
! [SV4: $i] :
( ( ! [SY171: mworld] :
( ~ ( mrel @ ( sK2_SY162 @ SV4 ) @ SY171 )
| ~ ! [SY165: mworld] :
( ~ ( mrel @ SY171 @ SY165 )
| ( big_r @ SV4 @ SV4 @ SY165 ) )
| ! [SY173: mworld] :
( ~ ( mrel @ SY171 @ SY173 )
| ( big_r @ ( sK3_SY167 @ SV4 ) @ ( sK3_SY167 @ SV4 ) @ SY173 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[30]) ).
thf(34,plain,
! [SV5: $i,SV2: mworld] :
( ( ( ~ ! [SY174: mworld] :
( ~ ( mrel @ SV2 @ SY174 )
| ( big_r @ SV5 @ SV5 @ SY174 ) ) )
= $true )
| ( ( ! [SY159: mworld] :
( ~ ( mrel @ SV2 @ SY159 )
| ! [SX2: $i,SX3: mworld] :
( ~ ( mrel @ SY159 @ SX3 )
| ( big_r @ SX2 @ SX2 @ SX3 ) ) ) )
= $true )
| ( ( mrel @ sK1_SY116 @ SV2 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[31]) ).
thf(35,plain,
! [SV4: $i] :
( ( ~ ( mrel @ ( sK2_SY162 @ SV4 ) @ ( sK4_SY171 @ SV4 ) )
| ~ ! [SY175: mworld] :
( ~ ( mrel @ ( sK4_SY171 @ SV4 ) @ SY175 )
| ( big_r @ SV4 @ SV4 @ SY175 ) )
| ! [SY176: mworld] :
( ~ ( mrel @ ( sK4_SY171 @ SV4 ) @ SY176 )
| ( big_r @ ( sK3_SY167 @ SV4 ) @ ( sK3_SY167 @ SV4 ) @ SY176 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[33]) ).
thf(36,plain,
! [SV5: $i,SV2: mworld] :
( ( ( ! [SY174: mworld] :
( ~ ( mrel @ SV2 @ SY174 )
| ( big_r @ SV5 @ SV5 @ SY174 ) ) )
= $false )
| ( ( ! [SY159: mworld] :
( ~ ( mrel @ SV2 @ SY159 )
| ! [SX2: $i,SX3: mworld] :
( ~ ( mrel @ SY159 @ SX3 )
| ( big_r @ SX2 @ SX2 @ SX3 ) ) ) )
= $true )
| ( ( mrel @ sK1_SY116 @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[34]) ).
thf(37,plain,
! [SV4: $i] :
( ( ~ ( mrel @ ( sK2_SY162 @ SV4 ) @ ( sK4_SY171 @ SV4 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[35]) ).
thf(38,plain,
! [SV4: $i] :
( ( ~ ! [SY175: mworld] :
( ~ ( mrel @ ( sK4_SY171 @ SV4 ) @ SY175 )
| ( big_r @ SV4 @ SV4 @ SY175 ) )
| ! [SY176: mworld] :
( ~ ( mrel @ ( sK4_SY171 @ SV4 ) @ SY176 )
| ( big_r @ ( sK3_SY167 @ SV4 ) @ ( sK3_SY167 @ SV4 ) @ SY176 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[35]) ).
thf(39,plain,
! [SV5: $i,SV2: mworld] :
( ( ( ~ ( mrel @ SV2 @ ( sK5_SY174 @ SV5 @ SV2 ) )
| ( big_r @ SV5 @ SV5 @ ( sK5_SY174 @ SV5 @ SV2 ) ) )
= $false )
| ( ( ! [SY159: mworld] :
( ~ ( mrel @ SV2 @ SY159 )
| ! [SX2: $i,SX3: mworld] :
( ~ ( mrel @ SY159 @ SX3 )
| ( big_r @ SX2 @ SX2 @ SX3 ) ) ) )
= $true )
| ( ( mrel @ sK1_SY116 @ SV2 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[36]) ).
thf(40,plain,
! [SV4: $i] :
( ( mrel @ ( sK2_SY162 @ SV4 ) @ ( sK4_SY171 @ SV4 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[37]) ).
thf(41,plain,
! [SV4: $i] :
( ( ~ ! [SY175: mworld] :
( ~ ( mrel @ ( sK4_SY171 @ SV4 ) @ SY175 )
| ( big_r @ SV4 @ SV4 @ SY175 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[38]) ).
thf(42,plain,
! [SV4: $i] :
( ( ! [SY176: mworld] :
( ~ ( mrel @ ( sK4_SY171 @ SV4 ) @ SY176 )
| ( big_r @ ( sK3_SY167 @ SV4 ) @ ( sK3_SY167 @ SV4 ) @ SY176 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[38]) ).
thf(43,plain,
! [SV5: $i,SV2: mworld] :
( ( ( ~ ( mrel @ SV2 @ ( sK5_SY174 @ SV5 @ SV2 ) ) )
= $false )
| ( ( ! [SY159: mworld] :
( ~ ( mrel @ SV2 @ SY159 )
| ! [SX2: $i,SX3: mworld] :
( ~ ( mrel @ SY159 @ SX3 )
| ( big_r @ SX2 @ SX2 @ SX3 ) ) ) )
= $true )
| ( ( mrel @ sK1_SY116 @ SV2 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[39]) ).
thf(44,plain,
! [SV2: mworld,SV5: $i] :
( ( ( big_r @ SV5 @ SV5 @ ( sK5_SY174 @ SV5 @ SV2 ) )
= $false )
| ( ( ! [SY159: mworld] :
( ~ ( mrel @ SV2 @ SY159 )
| ! [SX2: $i,SX3: mworld] :
( ~ ( mrel @ SY159 @ SX3 )
| ( big_r @ SX2 @ SX2 @ SX3 ) ) ) )
= $true )
| ( ( mrel @ sK1_SY116 @ SV2 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[39]) ).
thf(45,plain,
! [SV4: $i] :
( ( ! [SY175: mworld] :
( ~ ( mrel @ ( sK4_SY171 @ SV4 ) @ SY175 )
| ( big_r @ SV4 @ SV4 @ SY175 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[41]) ).
thf(46,plain,
! [SV4: $i] :
( ( ~ ( mrel @ ( sK4_SY171 @ SV4 ) @ ( sK6_SY176 @ SV4 ) )
| ( big_r @ ( sK3_SY167 @ SV4 ) @ ( sK3_SY167 @ SV4 ) @ ( sK6_SY176 @ SV4 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[42]) ).
thf(47,plain,
! [SV5: $i,SV2: mworld] :
( ( ( mrel @ SV2 @ ( sK5_SY174 @ SV5 @ SV2 ) )
= $true )
| ( ( ! [SY159: mworld] :
( ~ ( mrel @ SV2 @ SY159 )
| ! [SX2: $i,SX3: mworld] :
( ~ ( mrel @ SY159 @ SX3 )
| ( big_r @ SX2 @ SX2 @ SX3 ) ) ) )
= $true )
| ( ( mrel @ sK1_SY116 @ SV2 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[43]) ).
thf(48,plain,
! [SV5: $i,SV6: mworld,SV2: mworld] :
( ( ( ~ ( mrel @ SV2 @ SV6 )
| ! [SY177: $i,SY178: mworld] :
( ~ ( mrel @ SV6 @ SY178 )
| ( big_r @ SY177 @ SY177 @ SY178 ) ) )
= $true )
| ( ( big_r @ SV5 @ SV5 @ ( sK5_SY174 @ SV5 @ SV2 ) )
= $false )
| ( ( mrel @ sK1_SY116 @ SV2 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[44]) ).
thf(49,plain,
! [SV7: mworld,SV4: $i] :
( ( ~ ( mrel @ ( sK4_SY171 @ SV4 ) @ SV7 )
| ( big_r @ SV4 @ SV4 @ SV7 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[45]) ).
thf(50,plain,
! [SV4: $i] :
( ( ~ ( mrel @ ( sK4_SY171 @ SV4 ) @ ( sK6_SY176 @ SV4 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[46]) ).
thf(51,plain,
! [SV4: $i] :
( ( big_r @ ( sK3_SY167 @ SV4 ) @ ( sK3_SY167 @ SV4 ) @ ( sK6_SY176 @ SV4 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[46]) ).
thf(52,plain,
! [SV5: $i,SV8: mworld,SV2: mworld] :
( ( ( ~ ( mrel @ SV2 @ SV8 )
| ! [SY179: $i,SY180: mworld] :
( ~ ( mrel @ SV8 @ SY180 )
| ( big_r @ SY179 @ SY179 @ SY180 ) ) )
= $true )
| ( ( mrel @ SV2 @ ( sK5_SY174 @ SV5 @ SV2 ) )
= $true )
| ( ( mrel @ sK1_SY116 @ SV2 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[47]) ).
thf(53,plain,
! [SV5: $i,SV6: mworld,SV2: mworld] :
( ( ( ~ ( mrel @ SV2 @ SV6 ) )
= $true )
| ( ( ! [SY177: $i,SY178: mworld] :
( ~ ( mrel @ SV6 @ SY178 )
| ( big_r @ SY177 @ SY177 @ SY178 ) ) )
= $true )
| ( ( big_r @ SV5 @ SV5 @ ( sK5_SY174 @ SV5 @ SV2 ) )
= $false )
| ( ( mrel @ sK1_SY116 @ SV2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[48]) ).
thf(54,plain,
! [SV7: mworld,SV4: $i] :
( ( ( ~ ( mrel @ ( sK4_SY171 @ SV4 ) @ SV7 ) )
= $true )
| ( ( big_r @ SV4 @ SV4 @ SV7 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[49]) ).
thf(55,plain,
! [SV4: $i] :
( ( mrel @ ( sK4_SY171 @ SV4 ) @ ( sK6_SY176 @ SV4 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[50]) ).
thf(56,plain,
! [SV5: $i,SV8: mworld,SV2: mworld] :
( ( ( ~ ( mrel @ SV2 @ SV8 ) )
= $true )
| ( ( ! [SY179: $i,SY180: mworld] :
( ~ ( mrel @ SV8 @ SY180 )
| ( big_r @ SY179 @ SY179 @ SY180 ) ) )
= $true )
| ( ( mrel @ SV2 @ ( sK5_SY174 @ SV5 @ SV2 ) )
= $true )
| ( ( mrel @ sK1_SY116 @ SV2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[52]) ).
thf(57,plain,
! [SV5: $i,SV6: mworld,SV2: mworld] :
( ( ( mrel @ SV2 @ SV6 )
= $false )
| ( ( ! [SY177: $i,SY178: mworld] :
( ~ ( mrel @ SV6 @ SY178 )
| ( big_r @ SY177 @ SY177 @ SY178 ) ) )
= $true )
| ( ( big_r @ SV5 @ SV5 @ ( sK5_SY174 @ SV5 @ SV2 ) )
= $false )
| ( ( mrel @ sK1_SY116 @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[53]) ).
thf(58,plain,
! [SV7: mworld,SV4: $i] :
( ( ( mrel @ ( sK4_SY171 @ SV4 ) @ SV7 )
= $false )
| ( ( big_r @ SV4 @ SV4 @ SV7 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[54]) ).
thf(59,plain,
! [SV5: $i,SV8: mworld,SV2: mworld] :
( ( ( mrel @ SV2 @ SV8 )
= $false )
| ( ( ! [SY179: $i,SY180: mworld] :
( ~ ( mrel @ SV8 @ SY180 )
| ( big_r @ SY179 @ SY179 @ SY180 ) ) )
= $true )
| ( ( mrel @ SV2 @ ( sK5_SY174 @ SV5 @ SV2 ) )
= $true )
| ( ( mrel @ sK1_SY116 @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[56]) ).
thf(60,plain,
! [SV5: $i,SV2: mworld,SV9: $i,SV6: mworld] :
( ( ( ! [SY181: mworld] :
( ~ ( mrel @ SV6 @ SY181 )
| ( big_r @ SV9 @ SV9 @ SY181 ) ) )
= $true )
| ( ( mrel @ SV2 @ SV6 )
= $false )
| ( ( big_r @ SV5 @ SV5 @ ( sK5_SY174 @ SV5 @ SV2 ) )
= $false )
| ( ( mrel @ sK1_SY116 @ SV2 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[57]) ).
thf(61,plain,
! [SV5: $i,SV2: mworld,SV10: $i,SV8: mworld] :
( ( ( ! [SY182: mworld] :
( ~ ( mrel @ SV8 @ SY182 )
| ( big_r @ SV10 @ SV10 @ SY182 ) ) )
= $true )
| ( ( mrel @ SV2 @ SV8 )
= $false )
| ( ( mrel @ SV2 @ ( sK5_SY174 @ SV5 @ SV2 ) )
= $true )
| ( ( mrel @ sK1_SY116 @ SV2 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[59]) ).
thf(62,plain,
! [SV5: $i,SV2: mworld,SV9: $i,SV11: mworld,SV6: mworld] :
( ( ( ~ ( mrel @ SV6 @ SV11 )
| ( big_r @ SV9 @ SV9 @ SV11 ) )
= $true )
| ( ( mrel @ SV2 @ SV6 )
= $false )
| ( ( big_r @ SV5 @ SV5 @ ( sK5_SY174 @ SV5 @ SV2 ) )
= $false )
| ( ( mrel @ sK1_SY116 @ SV2 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[60]) ).
thf(63,plain,
! [SV5: $i,SV2: mworld,SV10: $i,SV12: mworld,SV8: mworld] :
( ( ( ~ ( mrel @ SV8 @ SV12 )
| ( big_r @ SV10 @ SV10 @ SV12 ) )
= $true )
| ( ( mrel @ SV2 @ SV8 )
= $false )
| ( ( mrel @ SV2 @ ( sK5_SY174 @ SV5 @ SV2 ) )
= $true )
| ( ( mrel @ sK1_SY116 @ SV2 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[61]) ).
thf(64,plain,
! [SV5: $i,SV2: mworld,SV9: $i,SV11: mworld,SV6: mworld] :
( ( ( ~ ( mrel @ SV6 @ SV11 ) )
= $true )
| ( ( big_r @ SV9 @ SV9 @ SV11 )
= $true )
| ( ( mrel @ SV2 @ SV6 )
= $false )
| ( ( big_r @ SV5 @ SV5 @ ( sK5_SY174 @ SV5 @ SV2 ) )
= $false )
| ( ( mrel @ sK1_SY116 @ SV2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[62]) ).
thf(65,plain,
! [SV5: $i,SV2: mworld,SV10: $i,SV12: mworld,SV8: mworld] :
( ( ( ~ ( mrel @ SV8 @ SV12 ) )
= $true )
| ( ( big_r @ SV10 @ SV10 @ SV12 )
= $true )
| ( ( mrel @ SV2 @ SV8 )
= $false )
| ( ( mrel @ SV2 @ ( sK5_SY174 @ SV5 @ SV2 ) )
= $true )
| ( ( mrel @ sK1_SY116 @ SV2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[63]) ).
thf(66,plain,
! [SV5: $i,SV2: mworld,SV9: $i,SV11: mworld,SV6: mworld] :
( ( ( mrel @ SV6 @ SV11 )
= $false )
| ( ( big_r @ SV9 @ SV9 @ SV11 )
= $true )
| ( ( mrel @ SV2 @ SV6 )
= $false )
| ( ( big_r @ SV5 @ SV5 @ ( sK5_SY174 @ SV5 @ SV2 ) )
= $false )
| ( ( mrel @ sK1_SY116 @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[64]) ).
thf(67,plain,
! [SV5: $i,SV2: mworld,SV10: $i,SV12: mworld,SV8: mworld] :
( ( ( mrel @ SV8 @ SV12 )
= $false )
| ( ( big_r @ SV10 @ SV10 @ SV12 )
= $true )
| ( ( mrel @ SV2 @ SV8 )
= $false )
| ( ( mrel @ SV2 @ ( sK5_SY174 @ SV5 @ SV2 ) )
= $true )
| ( ( mrel @ sK1_SY116 @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[65]) ).
thf(68,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[13,67,66,58,55,51,40,32,20]) ).
thf(69,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[68]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : LCL957^6 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.02 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.00/0.10 % Computer : n012.cluster.edu
% 0.00/0.10 % Model : x86_64 x86_64
% 0.00/0.10 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.10 % Memory : 8046.5625MB
% 0.00/0.10 % OS : Linux 6.8.0-71-generic
% 0.00/0.10 % CPULimit : 300
% 0.00/0.10 % WCLimit : 300
% 0.00/0.10 % DateTime : Tue Oct 6 12:37:16 UTC 2026
% 0.00/0.10 % CPUTime :
% 0.00/0.10 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.13
% 0.09/0.13 No.of.Axioms: 1
% 0.09/0.13
% 0.09/0.13 Length.of.Defs: 1624
% 0.09/0.13
% 0.09/0.13 Contains.Choice.Funs: false
% 0.09/0.13 ....
% 0.09/0.13
% 0.09/0.13 ********************************
% 0.09/0.13 * All subproblems solved! *
% 0.09/0.13 ********************************
% 0.09/0.13 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:3,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:68,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.09/0.13
% 0.09/0.13 %**** Beginning of derivation protocol ****
% 0.09/0.13 % SZS output start CNFRefutation
% See solution above
% 0.09/0.13
% 0.09/0.13 %**** End of derivation protocol ****
% 0.09/0.13 %**** no. of clauses in derivation: 69 ****
% 0.09/0.13 %**** clause counter: 68 ****
% 0.09/0.13
% 0.09/0.13 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:3,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:68,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------