TSTP Solution File: LCL957^6 by LEO-II---1.7.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : LCL957^6 : TPTP v8.1.0. Released v8.1.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n018.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 : 600s
% DateTime : Sun Jul 17 12:27:50 EDT 2022
% Result : Theorem 0.18s 0.38s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 32
% Syntax : Number of formulae : 97 ( 49 unt; 20 typ; 10 def)
% Number of atoms : 646 ( 140 equ; 0 cnn)
% Maximal formula atoms : 21 ( 8 avg)
% Number of connectives : 1285 ( 205 ~; 218 |; 2 &; 857 @)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 3 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 66 ( 66 >; 0 *; 0 +; 0 <<)
% Number of symbols : 22 ( 19 usr; 4 con; 0-3 aty)
% Number of variables : 315 ( 39 ^ 274 !; 2 ?; 315 :)
% 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_SX0,type,
sK1_SX0: mworld ).
thf(tp_sK2_SY18,type,
sK2_SY18: $i > mworld ).
thf(tp_sK3_SY23,type,
sK3_SY23: $i > $i ).
thf(tp_sK4_SY27,type,
sK4_SY27: $i > mworld ).
thf(tp_sK5_SY32,type,
sK5_SY32: $i > mworld > mworld ).
thf(tp_sK6_SY31,type,
sK6_SY31: $i > mworld ).
thf(mand,definition,
( mand
= ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
( ( A @ W )
& ( B @ W ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mand) ).
thf(mbox,definition,
( mbox
= ( ^ [Phi: mworld > $o,W: mworld] :
! [V: mworld] :
( ( mrel @ W @ V )
=> ( Phi @ V ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mbox) ).
thf(mdia,definition,
( mdia
= ( ^ [Phi: mworld > $o,W: mworld] :
? [V: mworld] :
( ( mrel @ W @ V )
& ( Phi @ V ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mdia) ).
thf(mequiv,definition,
( mequiv
= ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
( ( A @ W )
<=> ( B @ W ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mequiv) ).
thf(mexists_di,definition,
( mexists_di
= ( ^ [A: $i > mworld > $o,W: mworld] :
? [X: $i] : ( A @ X @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mexists_di) ).
thf(mforall_di,definition,
( mforall_di
= ( ^ [A: $i > mworld > $o,W: mworld] :
! [X: $i] : ( A @ X @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mforall_di) ).
thf(mimplies,definition,
( mimplies
= ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
( ( A @ W )
=> ( B @ W ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mimplies) ).
thf(mlocal,definition,
( mlocal
= ( ^ [Phi: mworld > $o] : ( Phi @ mactual ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mlocal) ).
thf(mnot,definition,
( mnot
= ( ^ [A: mworld > $o,W: mworld] :
~ ( A @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mnot) ).
thf(mor,definition,
( mor
= ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
( ( A @ W )
| ( B @ W ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mor) ).
thf(1,axiom,
! [W: mworld,V: mworld] : ( mrel @ W @ V ),
file('/export/starexec/sandbox/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/sandbox/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,
( ( ~ ( 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 ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [W: mworld,V: mworld] : ( mrel @ W @ V ) )
= $true ),
inference(copy,[status(thm)],[1]) ).
thf(6,plain,
( ( ~ ( 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 ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[4]) ).
thf(7,plain,
( ( ~ ! [SX0: mworld] :
( ~ ( mrel @ mactual @ SX0 )
| ~ ! [SX1: mworld] :
( ~ ( mrel @ SX0 @ SX1 )
| ~ ~ ! [SX2: $i] :
~ ! [SX3: mworld] :
( ~ ( mrel @ SX1 @ SX3 )
| ( big_r @ SX2 @ SX2 @ SX3 ) )
| ! [SX2: mworld] :
( ~ ( mrel @ SX1 @ SX2 )
| ! [SX3: $i,SX4: mworld] :
( ~ ( mrel @ SX2 @ SX4 )
| ( big_r @ SX3 @ SX3 @ SX4 ) ) ) )
| ~ ! [SX1: $i] :
~ ! [SX2: mworld] :
( ~ ( mrel @ SX0 @ SX2 )
| ! [SX3: $i,SX4: mworld] :
( ~ ( mrel @ SX2 @ SX4 )
| ~ ! [SX5: mworld] :
( ~ ( mrel @ SX4 @ SX5 )
| ( big_r @ SX1 @ SX1 @ SX5 ) )
| ! [SX5: mworld] :
( ~ ( mrel @ SX4 @ SX5 )
| ( big_r @ SX3 @ SX3 @ SX5 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(8,plain,
! [SV1: mworld] :
( ( ! [SY0: mworld] : ( mrel @ SV1 @ SY0 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5]) ).
thf(9,plain,
( ( ! [SX0: mworld] :
( ~ ( mrel @ mactual @ SX0 )
| ~ ! [SX1: mworld] :
( ~ ( mrel @ SX0 @ SX1 )
| ~ ~ ! [SX2: $i] :
~ ! [SX3: mworld] :
( ~ ( mrel @ SX1 @ SX3 )
| ( big_r @ SX2 @ SX2 @ SX3 ) )
| ! [SX2: mworld] :
( ~ ( mrel @ SX1 @ SX2 )
| ! [SX3: $i,SX4: mworld] :
( ~ ( mrel @ SX2 @ SX4 )
| ( big_r @ SX3 @ SX3 @ SX4 ) ) ) )
| ~ ! [SX1: $i] :
~ ! [SX2: mworld] :
( ~ ( mrel @ SX0 @ SX2 )
| ! [SX3: $i,SX4: mworld] :
( ~ ( mrel @ SX2 @ SX4 )
| ~ ! [SX5: mworld] :
( ~ ( mrel @ SX4 @ SX5 )
| ( big_r @ SX1 @ SX1 @ SX5 ) )
| ! [SX5: mworld] :
( ~ ( mrel @ SX4 @ SX5 )
| ( big_r @ SX3 @ SX3 @ SX5 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[7]) ).
thf(10,plain,
! [SV2: mworld,SV1: mworld] :
( ( mrel @ SV1 @ SV2 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[8]) ).
thf(11,plain,
( ( ~ ( mrel @ mactual @ sK1_SX0 )
| ~ ! [SY1: mworld] :
( ~ ( mrel @ sK1_SX0 @ SY1 )
| ~ ~ ! [SX2: $i] :
~ ! [SX3: mworld] :
( ~ ( mrel @ SY1 @ SX3 )
| ( big_r @ SX2 @ SX2 @ SX3 ) )
| ! [SX2: mworld] :
( ~ ( mrel @ SY1 @ SX2 )
| ! [SX3: $i,SX4: mworld] :
( ~ ( mrel @ SX2 @ SX4 )
| ( big_r @ SX3 @ SX3 @ SX4 ) ) ) )
| ~ ! [SY7: $i] :
~ ! [SY8: mworld] :
( ~ ( mrel @ sK1_SX0 @ SY8 )
| ! [SX3: $i,SX4: mworld] :
( ~ ( mrel @ SY8 @ SX4 )
| ~ ! [SX5: mworld] :
( ~ ( mrel @ SX4 @ SX5 )
| ( big_r @ SY7 @ SY7 @ SX5 ) )
| ! [SX5: mworld] :
( ~ ( mrel @ SX4 @ SX5 )
| ( big_r @ SX3 @ SX3 @ SX5 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[9]) ).
thf(12,plain,
( ( ~ ( mrel @ mactual @ sK1_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[11]) ).
thf(13,plain,
( ( ~ ! [SY1: mworld] :
( ~ ( mrel @ sK1_SX0 @ SY1 )
| ~ ~ ! [SX2: $i] :
~ ! [SX3: mworld] :
( ~ ( mrel @ SY1 @ SX3 )
| ( big_r @ SX2 @ SX2 @ SX3 ) )
| ! [SX2: mworld] :
( ~ ( mrel @ SY1 @ SX2 )
| ! [SX3: $i,SX4: mworld] :
( ~ ( mrel @ SX2 @ SX4 )
| ( big_r @ SX3 @ SX3 @ SX4 ) ) ) )
| ~ ! [SY7: $i] :
~ ! [SY8: mworld] :
( ~ ( mrel @ sK1_SX0 @ SY8 )
| ! [SX3: $i,SX4: mworld] :
( ~ ( mrel @ SY8 @ SX4 )
| ~ ! [SX5: mworld] :
( ~ ( mrel @ SX4 @ SX5 )
| ( big_r @ SY7 @ SY7 @ SX5 ) )
| ! [SX5: mworld] :
( ~ ( mrel @ SX4 @ SX5 )
| ( big_r @ SX3 @ SX3 @ SX5 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[11]) ).
thf(14,plain,
( ( mrel @ mactual @ sK1_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[12]) ).
thf(15,plain,
( ( ~ ! [SY1: mworld] :
( ~ ( mrel @ sK1_SX0 @ SY1 )
| ~ ~ ! [SX2: $i] :
~ ! [SX3: mworld] :
( ~ ( mrel @ SY1 @ SX3 )
| ( big_r @ SX2 @ SX2 @ SX3 ) )
| ! [SX2: mworld] :
( ~ ( mrel @ SY1 @ SX2 )
| ! [SX3: $i,SX4: mworld] :
( ~ ( mrel @ SX2 @ SX4 )
| ( big_r @ SX3 @ SX3 @ SX4 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[13]) ).
thf(16,plain,
( ( ~ ! [SY7: $i] :
~ ! [SY8: mworld] :
( ~ ( mrel @ sK1_SX0 @ SY8 )
| ! [SX3: $i,SX4: mworld] :
( ~ ( mrel @ SY8 @ SX4 )
| ~ ! [SX5: mworld] :
( ~ ( mrel @ SX4 @ SX5 )
| ( big_r @ SY7 @ SY7 @ SX5 ) )
| ! [SX5: mworld] :
( ~ ( mrel @ SX4 @ SX5 )
| ( big_r @ SX3 @ SX3 @ SX5 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[13]) ).
thf(17,plain,
( ( ! [SY1: mworld] :
( ~ ( mrel @ sK1_SX0 @ SY1 )
| ~ ~ ! [SX2: $i] :
~ ! [SX3: mworld] :
( ~ ( mrel @ SY1 @ SX3 )
| ( big_r @ SX2 @ SX2 @ SX3 ) )
| ! [SX2: mworld] :
( ~ ( mrel @ SY1 @ SX2 )
| ! [SX3: $i,SX4: mworld] :
( ~ ( mrel @ SX2 @ SX4 )
| ( big_r @ SX3 @ SX3 @ SX4 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[15]) ).
thf(18,plain,
( ( ! [SY7: $i] :
~ ! [SY8: mworld] :
( ~ ( mrel @ sK1_SX0 @ SY8 )
| ! [SX3: $i,SX4: mworld] :
( ~ ( mrel @ SY8 @ SX4 )
| ~ ! [SX5: mworld] :
( ~ ( mrel @ SX4 @ SX5 )
| ( big_r @ SY7 @ SY7 @ SX5 ) )
| ! [SX5: mworld] :
( ~ ( mrel @ SX4 @ SX5 )
| ( big_r @ SX3 @ SX3 @ SX5 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[16]) ).
thf(19,plain,
! [SV3: mworld] :
( ( ~ ( mrel @ sK1_SX0 @ SV3 )
| ~ ~ ! [SY13: $i] :
~ ! [SY14: mworld] :
( ~ ( mrel @ SV3 @ SY14 )
| ( big_r @ SY13 @ SY13 @ SY14 ) )
| ! [SY15: mworld] :
( ~ ( mrel @ SV3 @ SY15 )
| ! [SX3: $i,SX4: mworld] :
( ~ ( mrel @ SY15 @ SX4 )
| ( big_r @ SX3 @ SX3 @ SX4 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[17]) ).
thf(20,plain,
! [SV4: $i] :
( ( ~ ! [SY18: mworld] :
( ~ ( mrel @ sK1_SX0 @ SY18 )
| ! [SY19: $i,SY20: mworld] :
( ~ ( mrel @ SY18 @ SY20 )
| ~ ! [SY21: mworld] :
( ~ ( mrel @ SY20 @ SY21 )
| ( big_r @ SV4 @ SV4 @ SY21 ) )
| ! [SX5: mworld] :
( ~ ( mrel @ SY20 @ SX5 )
| ( big_r @ SY19 @ SY19 @ SX5 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[18]) ).
thf(21,plain,
! [SV3: mworld] :
( ( ( ~ ( mrel @ sK1_SX0 @ SV3 ) )
= $true )
| ( ( ~ ~ ! [SY13: $i] :
~ ! [SY14: mworld] :
( ~ ( mrel @ SV3 @ SY14 )
| ( big_r @ SY13 @ SY13 @ SY14 ) )
| ! [SY15: mworld] :
( ~ ( mrel @ SV3 @ SY15 )
| ! [SX3: $i,SX4: mworld] :
( ~ ( mrel @ SY15 @ SX4 )
| ( big_r @ SX3 @ SX3 @ SX4 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[19]) ).
thf(22,plain,
! [SV4: $i] :
( ( ! [SY18: mworld] :
( ~ ( mrel @ sK1_SX0 @ SY18 )
| ! [SY19: $i,SY20: mworld] :
( ~ ( mrel @ SY18 @ SY20 )
| ~ ! [SY21: mworld] :
( ~ ( mrel @ SY20 @ SY21 )
| ( big_r @ SV4 @ SV4 @ SY21 ) )
| ! [SX5: mworld] :
( ~ ( mrel @ SY20 @ SX5 )
| ( big_r @ SY19 @ SY19 @ SX5 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[20]) ).
thf(23,plain,
! [SV3: mworld] :
( ( ( mrel @ sK1_SX0 @ SV3 )
= $false )
| ( ( ~ ~ ! [SY13: $i] :
~ ! [SY14: mworld] :
( ~ ( mrel @ SV3 @ SY14 )
| ( big_r @ SY13 @ SY13 @ SY14 ) )
| ! [SY15: mworld] :
( ~ ( mrel @ SV3 @ SY15 )
| ! [SX3: $i,SX4: mworld] :
( ~ ( mrel @ SY15 @ SX4 )
| ( big_r @ SX3 @ SX3 @ SX4 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[21]) ).
thf(24,plain,
! [SV4: $i] :
( ( ~ ( mrel @ sK1_SX0 @ ( sK2_SY18 @ SV4 ) )
| ! [SY23: $i,SY24: mworld] :
( ~ ( mrel @ ( sK2_SY18 @ SV4 ) @ SY24 )
| ~ ! [SY21: mworld] :
( ~ ( mrel @ SY24 @ SY21 )
| ( big_r @ SV4 @ SV4 @ SY21 ) )
| ! [SX5: mworld] :
( ~ ( mrel @ SY24 @ SX5 )
| ( big_r @ SY23 @ SY23 @ SX5 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[22]) ).
thf(25,plain,
! [SV3: mworld] :
( ( ( ~ ~ ! [SY13: $i] :
~ ! [SY14: mworld] :
( ~ ( mrel @ SV3 @ SY14 )
| ( big_r @ SY13 @ SY13 @ SY14 ) ) )
= $true )
| ( ( ! [SY15: mworld] :
( ~ ( mrel @ SV3 @ SY15 )
| ! [SX3: $i,SX4: mworld] :
( ~ ( mrel @ SY15 @ SX4 )
| ( big_r @ SX3 @ SX3 @ SX4 ) ) ) )
= $true )
| ( ( mrel @ sK1_SX0 @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[23]) ).
thf(26,plain,
! [SV4: $i] :
( ( ~ ( mrel @ sK1_SX0 @ ( sK2_SY18 @ SV4 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[24]) ).
thf(27,plain,
! [SV4: $i] :
( ( ! [SY23: $i,SY24: mworld] :
( ~ ( mrel @ ( sK2_SY18 @ SV4 ) @ SY24 )
| ~ ! [SY21: mworld] :
( ~ ( mrel @ SY24 @ SY21 )
| ( big_r @ SV4 @ SV4 @ SY21 ) )
| ! [SX5: mworld] :
( ~ ( mrel @ SY24 @ SX5 )
| ( big_r @ SY23 @ SY23 @ SX5 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[24]) ).
thf(28,plain,
! [SV3: mworld] :
( ( ( ~ ! [SY13: $i] :
~ ! [SY14: mworld] :
( ~ ( mrel @ SV3 @ SY14 )
| ( big_r @ SY13 @ SY13 @ SY14 ) ) )
= $false )
| ( ( ! [SY15: mworld] :
( ~ ( mrel @ SV3 @ SY15 )
| ! [SX3: $i,SX4: mworld] :
( ~ ( mrel @ SY15 @ SX4 )
| ( big_r @ SX3 @ SX3 @ SX4 ) ) ) )
= $true )
| ( ( mrel @ sK1_SX0 @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[25]) ).
thf(29,plain,
! [SV4: $i] :
( ( mrel @ sK1_SX0 @ ( sK2_SY18 @ SV4 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[26]) ).
thf(30,plain,
! [SV4: $i] :
( ( ! [SY27: mworld] :
( ~ ( mrel @ ( sK2_SY18 @ SV4 ) @ SY27 )
| ~ ! [SY21: mworld] :
( ~ ( mrel @ SY27 @ SY21 )
| ( big_r @ SV4 @ SV4 @ SY21 ) )
| ! [SY29: mworld] :
( ~ ( mrel @ SY27 @ SY29 )
| ( big_r @ ( sK3_SY23 @ SV4 ) @ ( sK3_SY23 @ SV4 ) @ SY29 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[27]) ).
thf(31,plain,
! [SV3: mworld] :
( ( ( ! [SY13: $i] :
~ ! [SY14: mworld] :
( ~ ( mrel @ SV3 @ SY14 )
| ( big_r @ SY13 @ SY13 @ SY14 ) ) )
= $true )
| ( ( ! [SY15: mworld] :
( ~ ( mrel @ SV3 @ SY15 )
| ! [SX3: $i,SX4: mworld] :
( ~ ( mrel @ SY15 @ SX4 )
| ( big_r @ SX3 @ SX3 @ SX4 ) ) ) )
= $true )
| ( ( mrel @ sK1_SX0 @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[28]) ).
thf(32,plain,
! [SV4: $i] :
( ( ~ ( mrel @ ( sK2_SY18 @ SV4 ) @ ( sK4_SY27 @ SV4 ) )
| ~ ! [SY30: mworld] :
( ~ ( mrel @ ( sK4_SY27 @ SV4 ) @ SY30 )
| ( big_r @ SV4 @ SV4 @ SY30 ) )
| ! [SY31: mworld] :
( ~ ( mrel @ ( sK4_SY27 @ SV4 ) @ SY31 )
| ( big_r @ ( sK3_SY23 @ SV4 ) @ ( sK3_SY23 @ SV4 ) @ SY31 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[30]) ).
thf(33,plain,
! [SV5: $i,SV3: mworld] :
( ( ( ~ ! [SY32: mworld] :
( ~ ( mrel @ SV3 @ SY32 )
| ( big_r @ SV5 @ SV5 @ SY32 ) ) )
= $true )
| ( ( ! [SY15: mworld] :
( ~ ( mrel @ SV3 @ SY15 )
| ! [SX3: $i,SX4: mworld] :
( ~ ( mrel @ SY15 @ SX4 )
| ( big_r @ SX3 @ SX3 @ SX4 ) ) ) )
= $true )
| ( ( mrel @ sK1_SX0 @ SV3 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[31]) ).
thf(34,plain,
! [SV4: $i] :
( ( ~ ( mrel @ ( sK2_SY18 @ SV4 ) @ ( sK4_SY27 @ SV4 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[32]) ).
thf(35,plain,
! [SV4: $i] :
( ( ~ ! [SY30: mworld] :
( ~ ( mrel @ ( sK4_SY27 @ SV4 ) @ SY30 )
| ( big_r @ SV4 @ SV4 @ SY30 ) )
| ! [SY31: mworld] :
( ~ ( mrel @ ( sK4_SY27 @ SV4 ) @ SY31 )
| ( big_r @ ( sK3_SY23 @ SV4 ) @ ( sK3_SY23 @ SV4 ) @ SY31 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[32]) ).
thf(36,plain,
! [SV5: $i,SV3: mworld] :
( ( ( ! [SY32: mworld] :
( ~ ( mrel @ SV3 @ SY32 )
| ( big_r @ SV5 @ SV5 @ SY32 ) ) )
= $false )
| ( ( ! [SY15: mworld] :
( ~ ( mrel @ SV3 @ SY15 )
| ! [SX3: $i,SX4: mworld] :
( ~ ( mrel @ SY15 @ SX4 )
| ( big_r @ SX3 @ SX3 @ SX4 ) ) ) )
= $true )
| ( ( mrel @ sK1_SX0 @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[33]) ).
thf(37,plain,
! [SV4: $i] :
( ( mrel @ ( sK2_SY18 @ SV4 ) @ ( sK4_SY27 @ SV4 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[34]) ).
thf(38,plain,
! [SV4: $i] :
( ( ~ ! [SY30: mworld] :
( ~ ( mrel @ ( sK4_SY27 @ SV4 ) @ SY30 )
| ( big_r @ SV4 @ SV4 @ SY30 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[35]) ).
thf(39,plain,
! [SV4: $i] :
( ( ! [SY31: mworld] :
( ~ ( mrel @ ( sK4_SY27 @ SV4 ) @ SY31 )
| ( big_r @ ( sK3_SY23 @ SV4 ) @ ( sK3_SY23 @ SV4 ) @ SY31 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[35]) ).
thf(40,plain,
! [SV5: $i,SV3: mworld] :
( ( ( ~ ( mrel @ SV3 @ ( sK5_SY32 @ SV5 @ SV3 ) )
| ( big_r @ SV5 @ SV5 @ ( sK5_SY32 @ SV5 @ SV3 ) ) )
= $false )
| ( ( ! [SY15: mworld] :
( ~ ( mrel @ SV3 @ SY15 )
| ! [SX3: $i,SX4: mworld] :
( ~ ( mrel @ SY15 @ SX4 )
| ( big_r @ SX3 @ SX3 @ SX4 ) ) ) )
= $true )
| ( ( mrel @ sK1_SX0 @ SV3 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[36]) ).
thf(41,plain,
! [SV4: $i] :
( ( ! [SY30: mworld] :
( ~ ( mrel @ ( sK4_SY27 @ SV4 ) @ SY30 )
| ( big_r @ SV4 @ SV4 @ SY30 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[38]) ).
thf(42,plain,
! [SV4: $i] :
( ( ~ ( mrel @ ( sK4_SY27 @ SV4 ) @ ( sK6_SY31 @ SV4 ) )
| ( big_r @ ( sK3_SY23 @ SV4 ) @ ( sK3_SY23 @ SV4 ) @ ( sK6_SY31 @ SV4 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[39]) ).
thf(43,plain,
! [SV5: $i,SV3: mworld] :
( ( ( ~ ( mrel @ SV3 @ ( sK5_SY32 @ SV5 @ SV3 ) ) )
= $false )
| ( ( ! [SY15: mworld] :
( ~ ( mrel @ SV3 @ SY15 )
| ! [SX3: $i,SX4: mworld] :
( ~ ( mrel @ SY15 @ SX4 )
| ( big_r @ SX3 @ SX3 @ SX4 ) ) ) )
= $true )
| ( ( mrel @ sK1_SX0 @ SV3 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[40]) ).
thf(44,plain,
! [SV3: mworld,SV5: $i] :
( ( ( big_r @ SV5 @ SV5 @ ( sK5_SY32 @ SV5 @ SV3 ) )
= $false )
| ( ( ! [SY15: mworld] :
( ~ ( mrel @ SV3 @ SY15 )
| ! [SX3: $i,SX4: mworld] :
( ~ ( mrel @ SY15 @ SX4 )
| ( big_r @ SX3 @ SX3 @ SX4 ) ) ) )
= $true )
| ( ( mrel @ sK1_SX0 @ SV3 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[40]) ).
thf(45,plain,
! [SV6: mworld,SV4: $i] :
( ( ~ ( mrel @ ( sK4_SY27 @ SV4 ) @ SV6 )
| ( big_r @ SV4 @ SV4 @ SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[41]) ).
thf(46,plain,
! [SV4: $i] :
( ( ~ ( mrel @ ( sK4_SY27 @ SV4 ) @ ( sK6_SY31 @ SV4 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[42]) ).
thf(47,plain,
! [SV4: $i] :
( ( big_r @ ( sK3_SY23 @ SV4 ) @ ( sK3_SY23 @ SV4 ) @ ( sK6_SY31 @ SV4 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[42]) ).
thf(48,plain,
! [SV5: $i,SV3: mworld] :
( ( ( mrel @ SV3 @ ( sK5_SY32 @ SV5 @ SV3 ) )
= $true )
| ( ( ! [SY15: mworld] :
( ~ ( mrel @ SV3 @ SY15 )
| ! [SX3: $i,SX4: mworld] :
( ~ ( mrel @ SY15 @ SX4 )
| ( big_r @ SX3 @ SX3 @ SX4 ) ) ) )
= $true )
| ( ( mrel @ sK1_SX0 @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[43]) ).
thf(49,plain,
! [SV5: $i,SV7: mworld,SV3: mworld] :
( ( ( ~ ( mrel @ SV3 @ SV7 )
| ! [SY33: $i,SY34: mworld] :
( ~ ( mrel @ SV7 @ SY34 )
| ( big_r @ SY33 @ SY33 @ SY34 ) ) )
= $true )
| ( ( big_r @ SV5 @ SV5 @ ( sK5_SY32 @ SV5 @ SV3 ) )
= $false )
| ( ( mrel @ sK1_SX0 @ SV3 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[44]) ).
thf(50,plain,
! [SV6: mworld,SV4: $i] :
( ( ( ~ ( mrel @ ( sK4_SY27 @ SV4 ) @ SV6 ) )
= $true )
| ( ( big_r @ SV4 @ SV4 @ SV6 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[45]) ).
thf(51,plain,
! [SV4: $i] :
( ( mrel @ ( sK4_SY27 @ SV4 ) @ ( sK6_SY31 @ SV4 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[46]) ).
thf(52,plain,
! [SV5: $i,SV8: mworld,SV3: mworld] :
( ( ( ~ ( mrel @ SV3 @ SV8 )
| ! [SY35: $i,SY36: mworld] :
( ~ ( mrel @ SV8 @ SY36 )
| ( big_r @ SY35 @ SY35 @ SY36 ) ) )
= $true )
| ( ( mrel @ SV3 @ ( sK5_SY32 @ SV5 @ SV3 ) )
= $true )
| ( ( mrel @ sK1_SX0 @ SV3 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[48]) ).
thf(53,plain,
! [SV5: $i,SV7: mworld,SV3: mworld] :
( ( ( ~ ( mrel @ SV3 @ SV7 ) )
= $true )
| ( ( ! [SY33: $i,SY34: mworld] :
( ~ ( mrel @ SV7 @ SY34 )
| ( big_r @ SY33 @ SY33 @ SY34 ) ) )
= $true )
| ( ( big_r @ SV5 @ SV5 @ ( sK5_SY32 @ SV5 @ SV3 ) )
= $false )
| ( ( mrel @ sK1_SX0 @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[49]) ).
thf(54,plain,
! [SV6: mworld,SV4: $i] :
( ( ( mrel @ ( sK4_SY27 @ SV4 ) @ SV6 )
= $false )
| ( ( big_r @ SV4 @ SV4 @ SV6 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[50]) ).
thf(55,plain,
! [SV5: $i,SV8: mworld,SV3: mworld] :
( ( ( ~ ( mrel @ SV3 @ SV8 ) )
= $true )
| ( ( ! [SY35: $i,SY36: mworld] :
( ~ ( mrel @ SV8 @ SY36 )
| ( big_r @ SY35 @ SY35 @ SY36 ) ) )
= $true )
| ( ( mrel @ SV3 @ ( sK5_SY32 @ SV5 @ SV3 ) )
= $true )
| ( ( mrel @ sK1_SX0 @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[52]) ).
thf(56,plain,
! [SV5: $i,SV7: mworld,SV3: mworld] :
( ( ( mrel @ SV3 @ SV7 )
= $false )
| ( ( ! [SY33: $i,SY34: mworld] :
( ~ ( mrel @ SV7 @ SY34 )
| ( big_r @ SY33 @ SY33 @ SY34 ) ) )
= $true )
| ( ( big_r @ SV5 @ SV5 @ ( sK5_SY32 @ SV5 @ SV3 ) )
= $false )
| ( ( mrel @ sK1_SX0 @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[53]) ).
thf(57,plain,
! [SV5: $i,SV8: mworld,SV3: mworld] :
( ( ( mrel @ SV3 @ SV8 )
= $false )
| ( ( ! [SY35: $i,SY36: mworld] :
( ~ ( mrel @ SV8 @ SY36 )
| ( big_r @ SY35 @ SY35 @ SY36 ) ) )
= $true )
| ( ( mrel @ SV3 @ ( sK5_SY32 @ SV5 @ SV3 ) )
= $true )
| ( ( mrel @ sK1_SX0 @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[55]) ).
thf(58,plain,
! [SV5: $i,SV3: mworld,SV9: $i,SV7: mworld] :
( ( ( ! [SY37: mworld] :
( ~ ( mrel @ SV7 @ SY37 )
| ( big_r @ SV9 @ SV9 @ SY37 ) ) )
= $true )
| ( ( mrel @ SV3 @ SV7 )
= $false )
| ( ( big_r @ SV5 @ SV5 @ ( sK5_SY32 @ SV5 @ SV3 ) )
= $false )
| ( ( mrel @ sK1_SX0 @ SV3 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[56]) ).
thf(59,plain,
! [SV5: $i,SV3: mworld,SV10: $i,SV8: mworld] :
( ( ( ! [SY38: mworld] :
( ~ ( mrel @ SV8 @ SY38 )
| ( big_r @ SV10 @ SV10 @ SY38 ) ) )
= $true )
| ( ( mrel @ SV3 @ SV8 )
= $false )
| ( ( mrel @ SV3 @ ( sK5_SY32 @ SV5 @ SV3 ) )
= $true )
| ( ( mrel @ sK1_SX0 @ SV3 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[57]) ).
thf(60,plain,
! [SV5: $i,SV3: mworld,SV9: $i,SV11: mworld,SV7: mworld] :
( ( ( ~ ( mrel @ SV7 @ SV11 )
| ( big_r @ SV9 @ SV9 @ SV11 ) )
= $true )
| ( ( mrel @ SV3 @ SV7 )
= $false )
| ( ( big_r @ SV5 @ SV5 @ ( sK5_SY32 @ SV5 @ SV3 ) )
= $false )
| ( ( mrel @ sK1_SX0 @ SV3 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[58]) ).
thf(61,plain,
! [SV5: $i,SV3: mworld,SV10: $i,SV12: mworld,SV8: mworld] :
( ( ( ~ ( mrel @ SV8 @ SV12 )
| ( big_r @ SV10 @ SV10 @ SV12 ) )
= $true )
| ( ( mrel @ SV3 @ SV8 )
= $false )
| ( ( mrel @ SV3 @ ( sK5_SY32 @ SV5 @ SV3 ) )
= $true )
| ( ( mrel @ sK1_SX0 @ SV3 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[59]) ).
thf(62,plain,
! [SV5: $i,SV3: mworld,SV9: $i,SV11: mworld,SV7: mworld] :
( ( ( ~ ( mrel @ SV7 @ SV11 ) )
= $true )
| ( ( big_r @ SV9 @ SV9 @ SV11 )
= $true )
| ( ( mrel @ SV3 @ SV7 )
= $false )
| ( ( big_r @ SV5 @ SV5 @ ( sK5_SY32 @ SV5 @ SV3 ) )
= $false )
| ( ( mrel @ sK1_SX0 @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[60]) ).
thf(63,plain,
! [SV5: $i,SV3: mworld,SV10: $i,SV12: mworld,SV8: mworld] :
( ( ( ~ ( mrel @ SV8 @ SV12 ) )
= $true )
| ( ( big_r @ SV10 @ SV10 @ SV12 )
= $true )
| ( ( mrel @ SV3 @ SV8 )
= $false )
| ( ( mrel @ SV3 @ ( sK5_SY32 @ SV5 @ SV3 ) )
= $true )
| ( ( mrel @ sK1_SX0 @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[61]) ).
thf(64,plain,
! [SV5: $i,SV3: mworld,SV9: $i,SV11: mworld,SV7: mworld] :
( ( ( mrel @ SV7 @ SV11 )
= $false )
| ( ( big_r @ SV9 @ SV9 @ SV11 )
= $true )
| ( ( mrel @ SV3 @ SV7 )
= $false )
| ( ( big_r @ SV5 @ SV5 @ ( sK5_SY32 @ SV5 @ SV3 ) )
= $false )
| ( ( mrel @ sK1_SX0 @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[62]) ).
thf(65,plain,
! [SV5: $i,SV3: mworld,SV10: $i,SV12: mworld,SV8: mworld] :
( ( ( mrel @ SV8 @ SV12 )
= $false )
| ( ( big_r @ SV10 @ SV10 @ SV12 )
= $true )
| ( ( mrel @ SV3 @ SV8 )
= $false )
| ( ( mrel @ SV3 @ ( sK5_SY32 @ SV5 @ SV3 ) )
= $true )
| ( ( mrel @ sK1_SX0 @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[63]) ).
thf(66,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[10,65,64,54,51,47,37,29,14]) ).
thf(67,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[66]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : LCL957^6 : TPTP v8.1.0. Released v8.1.0.
% 0.00/0.12 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.33 % Computer : n018.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sun Jul 3 14:19:50 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.33
% 0.18/0.33 No.of.Axioms: 1
% 0.18/0.33
% 0.18/0.33 Length.of.Defs: 1574
% 0.18/0.33
% 0.18/0.33 Contains.Choice.Funs: false
% 0.18/0.34 (rf:0,axioms:1,ps:3,u:6,ude:false,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:3,loop_count:0,foatp_calls:0,translation:fof_full)......
% 0.18/0.38
% 0.18/0.38 ********************************
% 0.18/0.38 * All subproblems solved! *
% 0.18/0.38 ********************************
% 0.18/0.38 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:1,ps:3,u:6,ude:false,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:66,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.18/0.39
% 0.18/0.39 %**** Beginning of derivation protocol ****
% 0.18/0.39 % SZS output start CNFRefutation
% See solution above
% 0.18/0.39
% 0.18/0.39 %**** End of derivation protocol ****
% 0.18/0.39 %**** no. of clauses in derivation: 67 ****
% 0.18/0.39 %**** clause counter: 66 ****
% 0.18/0.39
% 0.18/0.39 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:1,ps:3,u:6,ude:false,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:66,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------