%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : LCL710^1 : TPTP v9.3.1. Bugfixed v5.0.0.
% 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 : 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 10:30:03 AM UTC 2026
% Result : Theorem 0.08s 0.14s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 32
% Syntax : Number of formulae : 77 ( 50 unt; 0 typ; 31 def)
% Number of atoms : 373 ( 140 equ; 0 cnn)
% Maximal formula atoms : 6 ( 4 avg)
% Number of connectives : 559 ( 77 ~; 80 |; 8 &; 377 @)
% ( 0 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 87 ( 87 >; 0 *; 0 +; 0 <<)
% Number of symbols : 38 ( 35 usr; 4 con; 0-3 aty)
% Number of variables : 213 ( 66 ^; 141 !; 6 ?; 213 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_mu,type,
mu: $tType ).
thf(tp_mand,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_mbox,type,
mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_mcountersatisfiable,type,
mcountersatisfiable: ( $i > $o ) > $o ).
thf(tp_mdia,type,
mdia: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_meq_ind,type,
meq_ind: mu > mu > $i > $o ).
thf(tp_meq_prop,type,
meq_prop: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_mequiv,type,
mequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_meuclidean,type,
meuclidean: ( $i > $i > $o ) > $o ).
thf(tp_mexists_ind,type,
mexists_ind: ( mu > $i > $o ) > $i > $o ).
thf(tp_mexists_prop,type,
mexists_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(tp_mfalse,type,
mfalse: $i > $o ).
thf(tp_mforall_ind,type,
mforall_ind: ( mu > $i > $o ) > $i > $o ).
thf(tp_mforall_prop,type,
mforall_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(tp_mfunctional,type,
mfunctional: ( $i > $i > $o ) > $o ).
thf(tp_mimplied,type,
mimplied: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_mimplies,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_minvalid,type,
minvalid: ( $i > $o ) > $o ).
thf(tp_mnot,type,
mnot: ( $i > $o ) > $i > $o ).
thf(tp_mor,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_mpartially_functional,type,
mpartially_functional: ( $i > $i > $o ) > $o ).
thf(tp_mreflexive,type,
mreflexive: ( $i > $i > $o ) > $o ).
thf(tp_msatisfiable,type,
msatisfiable: ( $i > $o ) > $o ).
thf(tp_mserial,type,
mserial: ( $i > $i > $o ) > $o ).
thf(tp_msymmetric,type,
msymmetric: ( $i > $i > $o ) > $o ).
thf(tp_mtransitive,type,
mtransitive: ( $i > $i > $o ) > $o ).
thf(tp_mtrue,type,
mtrue: $i > $o ).
thf(tp_mvalid,type,
mvalid: ( $i > $o ) > $o ).
thf(tp_mweakly_connected,type,
mweakly_connected: ( $i > $i > $o ) > $o ).
thf(tp_mweakly_dense,type,
mweakly_dense: ( $i > $i > $o ) > $o ).
thf(tp_mweakly_directed,type,
mweakly_directed: ( $i > $i > $o ) > $o ).
thf(tp_mxor,type,
mxor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_sK1_SY0,type,
sK1_SY0: $i > $i > $o ).
thf(tp_sK2_SX0,type,
sK2_SX0: $i ).
thf(tp_sK3_SY58,type,
sK3_SY58: $i ).
thf(tp_sK4_SY59,type,
sK4_SY59: $i > ( $i > $o ) > $i > $i ).
thf(mand,definition,
( mand
= ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mnot @ ( mor @ ( mnot @ Phi ) @ ( mnot @ Psi ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mand) ).
thf(mbox,definition,
( mbox
= ( ^ [R: $i > $i > $o,Phi: $i > $o,W: $i] :
! [V: $i] :
( ~ ( R @ W @ V )
| ( Phi @ V ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mbox) ).
thf(mcountersatisfiable,definition,
( mcountersatisfiable
= ( ^ [Phi: $i > $o] :
? [W: $i] :
~ ( Phi @ W ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mcountersatisfiable) ).
thf(mdia,definition,
( mdia
= ( ^ [R: $i > $i > $o,Phi: $i > $o] : ( mnot @ ( mbox @ R @ ( mnot @ Phi ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mdia) ).
thf(meq_ind,definition,
( meq_ind
= ( ^ [X: mu,Y: mu,W: $i] : ( X = Y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',meq_ind) ).
thf(meq_prop,definition,
( meq_prop
= ( ^ [X: $i > $o,Y: $i > $o,W: $i] :
( ( X @ W )
= ( Y @ W ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',meq_prop) ).
thf(mequiv,definition,
( mequiv
= ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mand @ ( mimplies @ Phi @ Psi ) @ ( mimplies @ Psi @ Phi ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mequiv) ).
thf(meuclidean,definition,
( meuclidean
= ( ^ [R: $i > $i > $o] :
! [S: $i,T: $i,U: $i] :
( ( ( R @ S @ T )
& ( R @ S @ U ) )
=> ( R @ T @ U ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',meuclidean) ).
thf(mexists_ind,definition,
( mexists_ind
= ( ^ [Phi: mu > $i > $o] :
( mnot
@ ( mforall_ind
@ ^ [X: mu] : ( mnot @ ( Phi @ X ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mexists_ind) ).
thf(mexists_prop,definition,
( mexists_prop
= ( ^ [Phi: ( $i > $o ) > $i > $o] :
( mnot
@ ( mforall_prop
@ ^ [P: $i > $o] : ( mnot @ ( Phi @ P ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mexists_prop) ).
thf(mfalse,definition,
( mfalse
= ( mnot @ mtrue ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mfalse) ).
thf(mforall_ind,definition,
( mforall_ind
= ( ^ [Phi: mu > $i > $o,W: $i] :
! [X: mu] : ( Phi @ X @ W ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mforall_ind) ).
thf(mforall_prop,definition,
( mforall_prop
= ( ^ [Phi: ( $i > $o ) > $i > $o,W: $i] :
! [P: $i > $o] : ( Phi @ P @ W ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mforall_prop) ).
thf(mfunctional,definition,
( mfunctional
= ( ^ [R: $i > $i > $o] :
! [S: $i] :
? [T: $i] :
( ( R @ S @ T )
& ! [U: $i] :
( ( R @ S @ U )
=> ( T = U ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mfunctional) ).
thf(mimplied,definition,
( mimplied
= ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mor @ ( mnot @ Psi ) @ Phi ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mimplied) ).
thf(mimplies,definition,
( mimplies
= ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mor @ ( mnot @ Phi ) @ Psi ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mimplies) ).
thf(minvalid,definition,
( minvalid
= ( ^ [Phi: $i > $o] :
! [W: $i] :
~ ( Phi @ W ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',minvalid) ).
thf(mnot,definition,
( mnot
= ( ^ [Phi: $i > $o,W: $i] :
~ ( Phi @ W ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mnot) ).
thf(mor,definition,
( mor
= ( ^ [Phi: $i > $o,Psi: $i > $o,W: $i] :
( ( Phi @ W )
| ( Psi @ W ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mor) ).
thf(mpartially_functional,definition,
( mpartially_functional
= ( ^ [R: $i > $i > $o] :
! [S: $i,T: $i,U: $i] :
( ( ( R @ S @ T )
& ( R @ S @ U ) )
=> ( T = U ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mpartially_functional) ).
thf(mreflexive,definition,
( mreflexive
= ( ^ [R: $i > $i > $o] :
! [S: $i] : ( R @ S @ S ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mreflexive) ).
thf(msatisfiable,definition,
( msatisfiable
= ( ^ [Phi: $i > $o] :
? [W: $i] : ( Phi @ W ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',msatisfiable) ).
thf(mserial,definition,
( mserial
= ( ^ [R: $i > $i > $o] :
! [S: $i] :
? [T: $i] : ( R @ S @ T ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mserial) ).
thf(msymmetric,definition,
( msymmetric
= ( ^ [R: $i > $i > $o] :
! [S: $i,T: $i] :
( ( R @ S @ T )
=> ( R @ T @ S ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',msymmetric) ).
thf(mtransitive,definition,
( mtransitive
= ( ^ [R: $i > $i > $o] :
! [S: $i,T: $i,U: $i] :
( ( ( R @ S @ T )
& ( R @ T @ U ) )
=> ( R @ S @ U ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mtransitive) ).
thf(mtrue,definition,
( mtrue
= ( ^ [W: $i] : $true ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mtrue) ).
thf(mvalid,definition,
( mvalid
= ( ^ [Phi: $i > $o] :
! [W: $i] : ( Phi @ W ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mvalid) ).
thf(mweakly_connected,definition,
( mweakly_connected
= ( ^ [R: $i > $i > $o] :
! [S: $i,T: $i,U: $i] :
( ( ( R @ S @ T )
& ( R @ S @ U ) )
=> ( ( R @ T @ U )
| ( T = U )
| ( R @ U @ T ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mweakly_connected) ).
thf(mweakly_dense,definition,
( mweakly_dense
= ( ^ [R: $i > $i > $o] :
! [S: $i,T: $i,U: $i] :
( ( R @ S @ T )
=> ? [U: $i] :
( ( R @ S @ U )
& ( R @ U @ T ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mweakly_dense) ).
thf(mweakly_directed,definition,
( mweakly_directed
= ( ^ [R: $i > $i > $o] :
! [S: $i,T: $i,U: $i] :
( ( ( R @ S @ T )
& ( R @ S @ U ) )
=> ? [V: $i] :
( ( R @ T @ V )
& ( R @ U @ V ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mweakly_directed) ).
thf(mxor,definition,
( mxor
= ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mnot @ ( mequiv @ Phi @ Psi ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mxor) ).
thf(1,conjecture,
! [R: $i > $i > $o] :
( ( mvalid
@ ( mforall_prop
@ ^ [A: $i > $o] : ( mimplies @ A @ ( mbox @ R @ ( mdia @ R @ A ) ) ) ) )
=> ( msymmetric @ R ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj) ).
thf(2,negated_conjecture,
( ( ! [R: $i > $i > $o] :
( ( mvalid
@ ( mforall_prop
@ ^ [A: $i > $o] : ( mimplies @ A @ ( mbox @ R @ ( mdia @ R @ A ) ) ) ) )
=> ( msymmetric @ R ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [SY0: $i > $i > $o] :
( ! [SY34: $i,SY35: $i > $o] :
( ~ ( SY35 @ SY34 )
| ! [SY36: $i] :
( ~ ( SY0 @ SY34 @ SY36 )
| ~ ! [SY31: $i] :
( ~ ( SY0 @ SY36 @ SY31 )
| ~ ( SY35 @ SY31 ) ) ) )
=> ! [SY38: $i,SY39: $i] :
( ( SY0 @ SY38 @ SY39 )
=> ( SY0 @ SY39 @ SY38 ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2,mand,mbox,mcountersatisfiable,mdia,meq_ind,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(4,plain,
( ( ! [SY47: $i,SY48: $i > $o] :
( ~ ( SY48 @ SY47 )
| ! [SY49: $i] :
( ~ ( sK1_SY0 @ SY47 @ SY49 )
| ~ ! [SY50: $i] :
( ~ ( sK1_SY0 @ SY49 @ SY50 )
| ~ ( SY48 @ SY50 ) ) ) )
=> ! [SY51: $i,SY52: $i] :
( ( sK1_SY0 @ SY51 @ SY52 )
=> ( sK1_SY0 @ SY52 @ SY51 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[3]) ).
thf(5,plain,
( ( ! [SY47: $i,SY48: $i > $o] :
( ~ ( SY48 @ SY47 )
| ! [SY49: $i] :
( ~ ( sK1_SY0 @ SY47 @ SY49 )
| ~ ! [SY50: $i] :
( ~ ( sK1_SY0 @ SY49 @ SY50 )
| ~ ( SY48 @ SY50 ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[4]) ).
thf(6,plain,
( ( ! [SY51: $i,SY52: $i] :
( ( sK1_SY0 @ SY51 @ SY52 )
=> ( sK1_SY0 @ SY52 @ SY51 ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[4]) ).
thf(7,plain,
( ( ~ ! [SY51: $i,SY52: $i] :
( ( sK1_SY0 @ SY51 @ SY52 )
=> ( sK1_SY0 @ SY52 @ SY51 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[6]) ).
thf(8,plain,
( ( ! [SY47: $i,SY48: $i > $o] :
( ~ ( SY48 @ SY47 )
| ! [SY49: $i] :
( ~ ( sK1_SY0 @ SY47 @ SY49 )
| ~ ! [SY50: $i] :
( ~ ( sK1_SY0 @ SY49 @ SY50 )
| ~ ( SY48 @ SY50 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(9,plain,
( ( ~ ! [SY51: $i,SY52: $i] :
( ( sK1_SY0 @ SY51 @ SY52 )
=> ( sK1_SY0 @ SY52 @ SY51 ) ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(10,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( sK1_SY0 @ SX0 @ SX1 )
| ( sK1_SY0 @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9,mand,mbox,mcountersatisfiable,mdia,meq_ind,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(11,plain,
! [SV1: $i] :
( ( ! [SY53: $i > $o] :
( ~ ( SY53 @ SV1 )
| ! [SY54: $i] :
( ~ ( sK1_SY0 @ SV1 @ SY54 )
| ~ ! [SY50: $i] :
( ~ ( sK1_SY0 @ SY54 @ SY50 )
| ~ ( SY53 @ SY50 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[8]) ).
thf(12,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( sK1_SY0 @ SX0 @ SX1 )
| ( sK1_SY0 @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[10]) ).
thf(13,plain,
! [SV1: $i,SV2: $i > $o] :
( ( ~ ( SV2 @ SV1 )
| ! [SY56: $i] :
( ~ ( sK1_SY0 @ SV1 @ SY56 )
| ~ ! [SY57: $i] :
( ~ ( sK1_SY0 @ SY56 @ SY57 )
| ~ ( SV2 @ SY57 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[11]) ).
thf(14,plain,
( ( ! [SY58: $i] :
( ~ ( sK1_SY0 @ sK2_SX0 @ SY58 )
| ( sK1_SY0 @ SY58 @ sK2_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[12]) ).
thf(15,plain,
! [SV1: $i,SV2: $i > $o] :
( ( ( ~ ( SV2 @ SV1 ) )
= $true )
| ( ( ! [SY56: $i] :
( ~ ( sK1_SY0 @ SV1 @ SY56 )
| ~ ! [SY57: $i] :
( ~ ( sK1_SY0 @ SY56 @ SY57 )
| ~ ( SV2 @ SY57 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[13]) ).
thf(16,plain,
( ( ~ ( sK1_SY0 @ sK2_SX0 @ sK3_SY58 )
| ( sK1_SY0 @ sK3_SY58 @ sK2_SX0 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[14]) ).
thf(17,plain,
! [SV1: $i,SV2: $i > $o] :
( ( ( SV2 @ SV1 )
= $false )
| ( ( ! [SY56: $i] :
( ~ ( sK1_SY0 @ SV1 @ SY56 )
| ~ ! [SY57: $i] :
( ~ ( sK1_SY0 @ SY56 @ SY57 )
| ~ ( SV2 @ SY57 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[15]) ).
thf(18,plain,
( ( ~ ( sK1_SY0 @ sK2_SX0 @ sK3_SY58 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[16]) ).
thf(19,plain,
( ( sK1_SY0 @ sK3_SY58 @ sK2_SX0 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[16]) ).
thf(20,plain,
! [SV2: $i > $o,SV3: $i,SV1: $i] :
( ( ( ~ ( sK1_SY0 @ SV1 @ SV3 )
| ~ ! [SY59: $i] :
( ~ ( sK1_SY0 @ SV3 @ SY59 )
| ~ ( SV2 @ SY59 ) ) )
= $true )
| ( ( SV2 @ SV1 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[17]) ).
thf(21,plain,
( ( sK1_SY0 @ sK2_SX0 @ sK3_SY58 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[18]) ).
thf(22,plain,
! [SV2: $i > $o,SV3: $i,SV1: $i] :
( ( ( ~ ( sK1_SY0 @ SV1 @ SV3 ) )
= $true )
| ( ( ~ ! [SY59: $i] :
( ~ ( sK1_SY0 @ SV3 @ SY59 )
| ~ ( SV2 @ SY59 ) ) )
= $true )
| ( ( SV2 @ SV1 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[20]) ).
thf(23,plain,
! [SV2: $i > $o,SV3: $i,SV1: $i] :
( ( ( sK1_SY0 @ SV1 @ SV3 )
= $false )
| ( ( ~ ! [SY59: $i] :
( ~ ( sK1_SY0 @ SV3 @ SY59 )
| ~ ( SV2 @ SY59 ) ) )
= $true )
| ( ( SV2 @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[22]) ).
thf(24,plain,
! [SV1: $i,SV2: $i > $o,SV3: $i] :
( ( ( ! [SY59: $i] :
( ~ ( sK1_SY0 @ SV3 @ SY59 )
| ~ ( SV2 @ SY59 ) ) )
= $false )
| ( ( sK1_SY0 @ SV1 @ SV3 )
= $false )
| ( ( SV2 @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[23]) ).
thf(25,plain,
! [SV2: $i > $o,SV1: $i,SV3: $i] :
( ( ( ~ ( sK1_SY0 @ SV3 @ ( sK4_SY59 @ SV1 @ SV2 @ SV3 ) )
| ~ ( SV2 @ ( sK4_SY59 @ SV1 @ SV2 @ SV3 ) ) )
= $false )
| ( ( sK1_SY0 @ SV1 @ SV3 )
= $false )
| ( ( SV2 @ SV1 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[24]) ).
thf(26,plain,
! [SV2: $i > $o,SV1: $i,SV3: $i] :
( ( ( ~ ( sK1_SY0 @ SV3 @ ( sK4_SY59 @ SV1 @ SV2 @ SV3 ) ) )
= $false )
| ( ( sK1_SY0 @ SV1 @ SV3 )
= $false )
| ( ( SV2 @ SV1 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[25]) ).
thf(27,plain,
! [SV3: $i,SV1: $i,SV2: $i > $o] :
( ( ( ~ ( SV2 @ ( sK4_SY59 @ SV1 @ SV2 @ SV3 ) ) )
= $false )
| ( ( sK1_SY0 @ SV1 @ SV3 )
= $false )
| ( ( SV2 @ SV1 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[25]) ).
thf(28,plain,
! [SV2: $i > $o,SV1: $i,SV3: $i] :
( ( ( sK1_SY0 @ SV3 @ ( sK4_SY59 @ SV1 @ SV2 @ SV3 ) )
= $true )
| ( ( sK1_SY0 @ SV1 @ SV3 )
= $false )
| ( ( SV2 @ SV1 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[26]) ).
thf(29,plain,
! [SV3: $i,SV1: $i,SV2: $i > $o] :
( ( ( SV2 @ ( sK4_SY59 @ SV1 @ SV2 @ SV3 ) )
= $true )
| ( ( sK1_SY0 @ SV1 @ SV3 )
= $false )
| ( ( SV2 @ SV1 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[27]) ).
thf(30,plain,
! [SV1: $i,SV3: $i] :
( ( ( sK1_SY0 @ SV3
@ ( sK4_SY59 @ SV1
@ ^ [SX0: $i] : $true
@ SV3 ) )
= $true )
| ( ( sK1_SY0 @ SV1 @ SV3 )
= $false )
| ( $true = $false ) ),
inference(prim_subst,[status(thm)],[28:[bind(SV2,$thf( ^ [SV9: $i] : $true ))]]) ).
thf(32,plain,
! [SV7: $i > $o,SV1: $i,SV3: $i] :
( ( ( sK1_SY0 @ SV3
@ ( sK4_SY59 @ SV1
@ ^ [SX0: $i] :
~ ( SV7 @ SX0 )
@ SV3 ) )
= $true )
| ( ( sK1_SY0 @ SV1 @ SV3 )
= $false )
| ( ( ~ ( SV7 @ SV1 ) )
= $false ) ),
inference(prim_subst,[status(thm)],[28:[bind(SV2,$thf( ^ [SV6: $i] : ~ ( SV7 @ SV6 ) ))]]) ).
thf(33,plain,
! [SV1: $i,SV3: $i] :
( ( ( sK1_SY0 @ SV3
@ ( sK4_SY59 @ SV1
@ ^ [SX0: $i] : ( SX0 = sK3_SY58 )
@ SV3 ) )
= $true )
| ( ( sK1_SY0 @ SV1 @ SV3 )
= $false )
| ( ( SV1 = sK3_SY58 )
= $false ) ),
inference(prim_subst,[status(thm)],[28:[bind(SV2,$thf( ^ [SV4: $i] : ( SV4 = sK3_SY58 ) ))]]) ).
thf(34,plain,
! [SV1: $i,SV3: $i] :
( ( ( sK1_SY0 @ SV3
@ ( sK4_SY59 @ SV1
@ ^ [SX0: $i] : ( SX0 = sK2_SX0 )
@ SV3 ) )
= $true )
| ( ( sK1_SY0 @ SV1 @ SV3 )
= $false )
| ( ( SV1 = sK2_SX0 )
= $false ) ),
inference(prim_subst,[status(thm)],[28:[bind(SV2,$thf( ^ [SV5: $i] : ( SV5 = sK2_SX0 ) ))]]) ).
thf(37,plain,
! [SV3: $i,SV1: $i,SV7: $i > $o] :
( ( ( ~ ( SV7
@ ( sK4_SY59 @ SV1
@ ^ [SX0: $i] :
~ ( SV7 @ SX0 )
@ SV3 ) ) )
= $true )
| ( ( sK1_SY0 @ SV1 @ SV3 )
= $false )
| ( ( ~ ( SV7 @ SV1 ) )
= $false ) ),
inference(prim_subst,[status(thm)],[29:[bind(SV2,$thf( ^ [SV6: $i] : ~ ( SV7 @ SV6 ) ))]]) ).
thf(38,plain,
! [SV3: $i,SV1: $i] :
( ( ( ( sK4_SY59 @ SV1
@ ^ [SX0: $i] : ( SX0 = sK3_SY58 )
@ SV3 )
= sK3_SY58 )
= $true )
| ( ( sK1_SY0 @ SV1 @ SV3 )
= $false )
| ( ( SV1 = sK3_SY58 )
= $false ) ),
inference(prim_subst,[status(thm)],[29:[bind(SV2,$thf( ^ [SV4: $i] : ( SV4 = sK3_SY58 ) ))]]) ).
thf(39,plain,
! [SV3: $i,SV1: $i] :
( ( ( ( sK4_SY59 @ SV1
@ ^ [SX0: $i] : ( SX0 = sK2_SX0 )
@ SV3 )
= sK2_SX0 )
= $true )
| ( ( sK1_SY0 @ SV1 @ SV3 )
= $false )
| ( ( SV1 = sK2_SX0 )
= $false ) ),
inference(prim_subst,[status(thm)],[29:[bind(SV2,$thf( ^ [SV5: $i] : ( SV5 = sK2_SX0 ) ))]]) ).
thf(40,plain,
! [SV3: $i,SV1: $i,SV7: $i > $o] :
( ( ( SV7 @ SV1 )
= $true )
| ( ( sK1_SY0 @ SV1 @ SV3 )
= $false )
| ( ( sK1_SY0 @ SV3
@ ( sK4_SY59 @ SV1
@ ^ [SX0: $i] :
~ ( SV7 @ SX0 )
@ SV3 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[32]) ).
thf(41,plain,
! [SV3: $i,SV1: $i,SV7: $i > $o] :
( ( ( SV7
@ ( sK4_SY59 @ SV1
@ ^ [SX0: $i] :
~ ( SV7 @ SX0 )
@ SV3 ) )
= $false )
| ( ( sK1_SY0 @ SV1 @ SV3 )
= $false )
| ( ( ~ ( SV7 @ SV1 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[37]) ).
thf(42,plain,
! [SV3: $i,SV1: $i,SV7: $i > $o] :
( ( ( SV7 @ SV1 )
= $true )
| ( ( sK1_SY0 @ SV1 @ SV3 )
= $false )
| ( ( SV7
@ ( sK4_SY59 @ SV1
@ ^ [SX0: $i] :
~ ( SV7 @ SX0 )
@ SV3 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[41]) ).
thf(43,plain,
! [SV3: $i] :
( ( ( sK1_SY0 @ sK3_SY58 @ SV3 )
= $false )
| ( ( sK1_SY0 @ SV3
@ ( sK4_SY59 @ sK3_SY58
@ ^ [SX0: $i] : ( SX0 = sK3_SY58 )
@ SV3 ) )
= $true ) ),
inference(extuni,[status(esa)],[33:[bind(SV1,$thf( sK3_SY58 ))]]) ).
thf(44,plain,
! [SV3: $i] :
( ( ( sK1_SY0 @ sK2_SX0 @ SV3 )
= $false )
| ( ( sK1_SY0 @ SV3
@ ( sK4_SY59 @ sK2_SX0
@ ^ [SX0: $i] : ( SX0 = sK2_SX0 )
@ SV3 ) )
= $true ) ),
inference(extuni,[status(esa)],[34:[bind(SV1,$thf( sK2_SX0 ))]]) ).
thf(45,plain,
! [SV3: $i] :
( ( ( sK1_SY0 @ sK3_SY58 @ SV3 )
= $false )
| ( ( ( sK4_SY59 @ sK3_SY58
@ ^ [SX0: $i] : ( SX0 = sK3_SY58 )
@ SV3 )
= sK3_SY58 )
= $true ) ),
inference(extuni,[status(esa)],[38:[bind(SV1,$thf( sK3_SY58 ))]]) ).
thf(46,plain,
! [SV3: $i] :
( ( ( sK1_SY0 @ sK2_SX0 @ SV3 )
= $false )
| ( ( ( sK4_SY59 @ sK2_SX0
@ ^ [SX0: $i] : ( SX0 = sK2_SX0 )
@ SV3 )
= sK2_SX0 )
= $true ) ),
inference(extuni,[status(esa)],[39:[bind(SV1,$thf( sK2_SX0 ))]]) ).
thf(47,plain,
! [SV1: $i,SV3: $i] :
( ( ( sK1_SY0 @ SV3
@ ( sK4_SY59 @ SV1
@ ^ [SX0: $i] : $true
@ SV3 ) )
= $true )
| ( ( sK1_SY0 @ SV1 @ SV3 )
= $false ) ),
inference(sim,[status(thm)],[30]) ).
thf(48,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[19,47,46,45,44,43,42,40,29,28,21]) ).
thf(49,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[48]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : LCL710^1 : TPTP v9.3.1. Bugfixed v5.0.0.
% 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 12:32:01 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
% 0.08/0.14
% 0.08/0.14 No.of.Axioms: 0
% 0.08/0.14
% 0.08/0.14 Length.of.Defs: 5324
% 0.08/0.14
% 0.08/0.14 Contains.Choice.Funs: false
% 0.08/0.14 .
% 0.08/0.14
% 0.08/0.14 ********************************
% 0.08/0.14 * All subproblems solved! *
% 0.08/0.14 ********************************
% 0.08/0.14 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:1,ps:3,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:48,loop_count:0,foatp_calls:2,translation:fof_full)
% 0.08/0.14
% 0.08/0.14 %**** Beginning of derivation protocol ****
% 0.08/0.14 % SZS output start CNFRefutation
% See solution above
% 0.08/0.14
% 0.08/0.14 %**** End of derivation protocol ****
% 0.08/0.14 %**** no. of clauses in derivation: 46 ****
% 0.08/0.14 %**** clause counter: 48 ****
% 0.08/0.14
% 0.08/0.14 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:1,ps:3,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:48,loop_count:0,foatp_calls:2,translation:fof_full)
%------------------------------------------------------------------------------