%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : PUZ085^1 : TPTP v9.3.1. Released v4.0.0.
% 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 : n020.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 10:36:54 AM UTC 2026
% Result : Theorem 0.10s 0.22s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 38
% Syntax : Number of formulae : 106 ( 79 unt; 0 typ; 31 def)
% Number of atoms : 564 ( 132 equ; 0 cnn)
% Maximal formula atoms : 12 ( 5 avg)
% Number of connectives : 781 ( 127 ~; 99 |; 14 &; 527 @)
% ( 0 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 61 ( 61 >; 0 *; 0 +; 0 <<)
% Number of symbols : 41 ( 38 usr; 5 con; 0-3 aty)
% Number of variables : 233 ( 51 ^; 176 !; 6 ?; 233 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_mu,type,
mu: $tType ).
thf(tp_john,type,
john: $i > $i > $o ).
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_peter,type,
peter: $i > $i > $o ).
thf(tp_sK1_SY38,type,
sK1_SY38: $i ).
thf(tp_sK2_SY72,type,
sK2_SY72: $i > $o ).
thf(tp_sK3_SY77,type,
sK3_SY77: $i ).
thf(tp_sK4_SY88,type,
sK4_SY88: $i ).
thf(tp_wife,type,
wife: ( $i > $i > $o ) > $i > $i > $o ).
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,axiom,
mtransitive @ ( wife @ peter ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',trans_wife_peter) ).
thf(2,axiom,
mtransitive @ john,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',trans_john) ).
thf(3,axiom,
mtransitive @ peter,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',trans_peter) ).
thf(4,axiom,
mreflexive @ ( wife @ peter ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',refl_wife_peter) ).
thf(5,axiom,
mreflexive @ john,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',refl_john) ).
thf(6,axiom,
mreflexive @ peter,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',refl_peter) ).
thf(7,conjecture,
( mvalid
@ ( mforall_prop
@ ^ [A: $i > $o] : ( mimplies @ ( mbox @ ( wife @ peter ) @ A ) @ ( mbox @ ( wife @ peter ) @ ( mbox @ ( wife @ peter ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj) ).
thf(8,negated_conjecture,
( ( mvalid
@ ( mforall_prop
@ ^ [A: $i > $o] : ( mimplies @ ( mbox @ ( wife @ peter ) @ A ) @ ( mbox @ ( wife @ peter ) @ ( mbox @ ( wife @ peter ) @ A ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[7]) ).
thf(9,plain,
( ( ! [SY38: $i,SY39: $i > $o] :
( ~ ! [SY40: $i] :
( ~ ( wife @ peter @ SY38 @ SY40 )
| ( SY39 @ SY40 ) )
| ! [SY41: $i] :
( ~ ( wife @ peter @ SY38 @ SY41 )
| ! [SY34: $i] :
( ~ ( wife @ peter @ SY41 @ SY34 )
| ( SY39 @ SY34 ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[8,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(10,plain,
( ( ! [SY48: $i,SY49: $i,SY50: $i] :
( ( ( wife @ peter @ SY48 @ SY49 )
& ( wife @ peter @ SY49 @ SY50 ) )
=> ( wife @ peter @ SY48 @ SY50 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1,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,
( ( ! [SY54: $i,SY55: $i,SY56: $i] :
( ( ( john @ SY54 @ SY55 )
& ( john @ SY55 @ SY56 ) )
=> ( john @ SY54 @ SY56 ) ) )
= $true ),
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(12,plain,
( ( ! [SY60: $i,SY61: $i,SY62: $i] :
( ( ( peter @ SY60 @ SY61 )
& ( peter @ SY61 @ SY62 ) )
=> ( peter @ SY60 @ SY62 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3,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(13,plain,
( ( ! [SY66: $i] : ( wife @ peter @ SY66 @ SY66 ) )
= $true ),
inference(unfold_def,[status(thm)],[4,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(14,plain,
( ( ! [SY68: $i] : ( john @ SY68 @ SY68 ) )
= $true ),
inference(unfold_def,[status(thm)],[5,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(15,plain,
( ( ! [SY70: $i] : ( peter @ SY70 @ SY70 ) )
= $true ),
inference(unfold_def,[status(thm)],[6,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(16,plain,
( ( ! [SY72: $i > $o] :
( ~ ! [SY73: $i] :
( ~ ( wife @ peter @ sK1_SY38 @ SY73 )
| ( SY72 @ SY73 ) )
| ! [SY74: $i] :
( ~ ( wife @ peter @ sK1_SY38 @ SY74 )
| ! [SY34: $i] :
( ~ ( wife @ peter @ SY74 @ SY34 )
| ( SY72 @ SY34 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[9]) ).
thf(17,plain,
( ( ~ ! [SY76: $i] :
( ~ ( wife @ peter @ sK1_SY38 @ SY76 )
| ( sK2_SY72 @ SY76 ) )
| ! [SY77: $i] :
( ~ ( wife @ peter @ sK1_SY38 @ SY77 )
| ! [SY78: $i] :
( ~ ( wife @ peter @ SY77 @ SY78 )
| ( sK2_SY72 @ SY78 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[16]) ).
thf(18,plain,
( ( ~ ( ~ ! [SY76: $i] :
( ~ ( wife @ peter @ sK1_SY38 @ SY76 )
| ( sK2_SY72 @ SY76 ) )
| ! [SY77: $i] :
( ~ ( wife @ peter @ sK1_SY38 @ SY77 )
| ! [SY78: $i] :
( ~ ( wife @ peter @ SY77 @ SY78 )
| ( sK2_SY72 @ SY78 ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[17]) ).
thf(19,plain,
( ( ! [SY70: $i] : ( peter @ SY70 @ SY70 ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(20,plain,
( ( ! [SY68: $i] : ( john @ SY68 @ SY68 ) )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(21,plain,
( ( ! [SY66: $i] : ( wife @ peter @ SY66 @ SY66 ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(22,plain,
( ( ! [SY60: $i,SY61: $i,SY62: $i] :
( ( ( peter @ SY60 @ SY61 )
& ( peter @ SY61 @ SY62 ) )
=> ( peter @ SY60 @ SY62 ) ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(23,plain,
( ( ! [SY54: $i,SY55: $i,SY56: $i] :
( ( ( john @ SY54 @ SY55 )
& ( john @ SY55 @ SY56 ) )
=> ( john @ SY54 @ SY56 ) ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(24,plain,
( ( ! [SY48: $i,SY49: $i,SY50: $i] :
( ( ( wife @ peter @ SY48 @ SY49 )
& ( wife @ peter @ SY49 @ SY50 ) )
=> ( wife @ peter @ SY48 @ SY50 ) ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(25,plain,
( ( ~ ( ~ ! [SY76: $i] :
( ~ ( wife @ peter @ sK1_SY38 @ SY76 )
| ( sK2_SY72 @ SY76 ) )
| ! [SY77: $i] :
( ~ ( wife @ peter @ sK1_SY38 @ SY77 )
| ! [SY78: $i] :
( ~ ( wife @ peter @ SY77 @ SY78 )
| ( sK2_SY72 @ SY78 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(26,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( wife @ peter @ SX0 @ SX1 )
| ~ ( wife @ peter @ SX1 @ SX2 ) )
| ( wife @ peter @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[24,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(27,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( john @ SX0 @ SX1 )
| ~ ( john @ SX1 @ SX2 ) )
| ( john @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[23,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(28,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( peter @ SX0 @ SX1 )
| ~ ( peter @ SX1 @ SX2 ) )
| ( peter @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[22,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(29,plain,
! [SV1: $i] :
( ( peter @ SV1 @ SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[19]) ).
thf(30,plain,
! [SV2: $i] :
( ( john @ SV2 @ SV2 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[20]) ).
thf(31,plain,
! [SV3: $i] :
( ( wife @ peter @ SV3 @ SV3 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[21]) ).
thf(32,plain,
( ( ~ ! [SY76: $i] :
( ~ ( wife @ peter @ sK1_SY38 @ SY76 )
| ( sK2_SY72 @ SY76 ) )
| ! [SY77: $i] :
( ~ ( wife @ peter @ sK1_SY38 @ SY77 )
| ! [SY78: $i] :
( ~ ( wife @ peter @ SY77 @ SY78 )
| ( sK2_SY72 @ SY78 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[25]) ).
thf(33,plain,
! [SV4: $i] :
( ( ! [SY79: $i,SY80: $i] :
( ~ ~ ( ~ ( wife @ peter @ SV4 @ SY79 )
| ~ ( wife @ peter @ SY79 @ SY80 ) )
| ( wife @ peter @ SV4 @ SY80 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[26]) ).
thf(34,plain,
! [SV5: $i] :
( ( ! [SY81: $i,SY82: $i] :
( ~ ~ ( ~ ( john @ SV5 @ SY81 )
| ~ ( john @ SY81 @ SY82 ) )
| ( john @ SV5 @ SY82 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[27]) ).
thf(35,plain,
! [SV6: $i] :
( ( ! [SY83: $i,SY84: $i] :
( ~ ~ ( ~ ( peter @ SV6 @ SY83 )
| ~ ( peter @ SY83 @ SY84 ) )
| ( peter @ SV6 @ SY84 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[28]) ).
thf(36,plain,
( ( ~ ! [SY76: $i] :
( ~ ( wife @ peter @ sK1_SY38 @ SY76 )
| ( sK2_SY72 @ SY76 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[32]) ).
thf(37,plain,
( ( ! [SY77: $i] :
( ~ ( wife @ peter @ sK1_SY38 @ SY77 )
| ! [SY78: $i] :
( ~ ( wife @ peter @ SY77 @ SY78 )
| ( sK2_SY72 @ SY78 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[32]) ).
thf(38,plain,
! [SV7: $i,SV4: $i] :
( ( ! [SY85: $i] :
( ~ ~ ( ~ ( wife @ peter @ SV4 @ SV7 )
| ~ ( wife @ peter @ SV7 @ SY85 ) )
| ( wife @ peter @ SV4 @ SY85 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[33]) ).
thf(39,plain,
! [SV8: $i,SV5: $i] :
( ( ! [SY86: $i] :
( ~ ~ ( ~ ( john @ SV5 @ SV8 )
| ~ ( john @ SV8 @ SY86 ) )
| ( john @ SV5 @ SY86 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[34]) ).
thf(40,plain,
! [SV9: $i,SV6: $i] :
( ( ! [SY87: $i] :
( ~ ~ ( ~ ( peter @ SV6 @ SV9 )
| ~ ( peter @ SV9 @ SY87 ) )
| ( peter @ SV6 @ SY87 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[35]) ).
thf(41,plain,
( ( ! [SY76: $i] :
( ~ ( wife @ peter @ sK1_SY38 @ SY76 )
| ( sK2_SY72 @ SY76 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[36]) ).
thf(42,plain,
( ( ~ ( wife @ peter @ sK1_SY38 @ sK3_SY77 )
| ! [SY88: $i] :
( ~ ( wife @ peter @ sK3_SY77 @ SY88 )
| ( sK2_SY72 @ SY88 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[37]) ).
thf(43,plain,
! [SV10: $i,SV7: $i,SV4: $i] :
( ( ~ ~ ( ~ ( wife @ peter @ SV4 @ SV7 )
| ~ ( wife @ peter @ SV7 @ SV10 ) )
| ( wife @ peter @ SV4 @ SV10 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[38]) ).
thf(44,plain,
! [SV11: $i,SV8: $i,SV5: $i] :
( ( ~ ~ ( ~ ( john @ SV5 @ SV8 )
| ~ ( john @ SV8 @ SV11 ) )
| ( john @ SV5 @ SV11 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[39]) ).
thf(45,plain,
! [SV12: $i,SV9: $i,SV6: $i] :
( ( ~ ~ ( ~ ( peter @ SV6 @ SV9 )
| ~ ( peter @ SV9 @ SV12 ) )
| ( peter @ SV6 @ SV12 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[40]) ).
thf(46,plain,
! [SV13: $i] :
( ( ~ ( wife @ peter @ sK1_SY38 @ SV13 )
| ( sK2_SY72 @ SV13 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[41]) ).
thf(47,plain,
( ( ~ ( wife @ peter @ sK1_SY38 @ sK3_SY77 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[42]) ).
thf(48,plain,
( ( ! [SY88: $i] :
( ~ ( wife @ peter @ sK3_SY77 @ SY88 )
| ( sK2_SY72 @ SY88 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[42]) ).
thf(49,plain,
! [SV10: $i,SV7: $i,SV4: $i] :
( ( ( ~ ~ ( ~ ( wife @ peter @ SV4 @ SV7 )
| ~ ( wife @ peter @ SV7 @ SV10 ) ) )
= $true )
| ( ( wife @ peter @ SV4 @ SV10 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[43]) ).
thf(50,plain,
! [SV11: $i,SV8: $i,SV5: $i] :
( ( ( ~ ~ ( ~ ( john @ SV5 @ SV8 )
| ~ ( john @ SV8 @ SV11 ) ) )
= $true )
| ( ( john @ SV5 @ SV11 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[44]) ).
thf(51,plain,
! [SV12: $i,SV9: $i,SV6: $i] :
( ( ( ~ ~ ( ~ ( peter @ SV6 @ SV9 )
| ~ ( peter @ SV9 @ SV12 ) ) )
= $true )
| ( ( peter @ SV6 @ SV12 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[45]) ).
thf(52,plain,
! [SV13: $i] :
( ( ( ~ ( wife @ peter @ sK1_SY38 @ SV13 ) )
= $true )
| ( ( sK2_SY72 @ SV13 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[46]) ).
thf(53,plain,
( ( wife @ peter @ sK1_SY38 @ sK3_SY77 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[47]) ).
thf(54,plain,
( ( ~ ( wife @ peter @ sK3_SY77 @ sK4_SY88 )
| ( sK2_SY72 @ sK4_SY88 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[48]) ).
thf(55,plain,
! [SV10: $i,SV7: $i,SV4: $i] :
( ( ( ~ ( ~ ( wife @ peter @ SV4 @ SV7 )
| ~ ( wife @ peter @ SV7 @ SV10 ) ) )
= $false )
| ( ( wife @ peter @ SV4 @ SV10 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[49]) ).
thf(56,plain,
! [SV11: $i,SV8: $i,SV5: $i] :
( ( ( ~ ( ~ ( john @ SV5 @ SV8 )
| ~ ( john @ SV8 @ SV11 ) ) )
= $false )
| ( ( john @ SV5 @ SV11 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[50]) ).
thf(57,plain,
! [SV12: $i,SV9: $i,SV6: $i] :
( ( ( ~ ( ~ ( peter @ SV6 @ SV9 )
| ~ ( peter @ SV9 @ SV12 ) ) )
= $false )
| ( ( peter @ SV6 @ SV12 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[51]) ).
thf(58,plain,
! [SV13: $i] :
( ( ( wife @ peter @ sK1_SY38 @ SV13 )
= $false )
| ( ( sK2_SY72 @ SV13 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[52]) ).
thf(59,plain,
( ( ~ ( wife @ peter @ sK3_SY77 @ sK4_SY88 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[54]) ).
thf(60,plain,
( ( sK2_SY72 @ sK4_SY88 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[54]) ).
thf(61,plain,
! [SV10: $i,SV7: $i,SV4: $i] :
( ( ( ~ ( wife @ peter @ SV4 @ SV7 )
| ~ ( wife @ peter @ SV7 @ SV10 ) )
= $true )
| ( ( wife @ peter @ SV4 @ SV10 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[55]) ).
thf(62,plain,
! [SV11: $i,SV8: $i,SV5: $i] :
( ( ( ~ ( john @ SV5 @ SV8 )
| ~ ( john @ SV8 @ SV11 ) )
= $true )
| ( ( john @ SV5 @ SV11 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[56]) ).
thf(63,plain,
! [SV12: $i,SV9: $i,SV6: $i] :
( ( ( ~ ( peter @ SV6 @ SV9 )
| ~ ( peter @ SV9 @ SV12 ) )
= $true )
| ( ( peter @ SV6 @ SV12 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[57]) ).
thf(64,plain,
( ( wife @ peter @ sK3_SY77 @ sK4_SY88 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[59]) ).
thf(65,plain,
! [SV10: $i,SV7: $i,SV4: $i] :
( ( ( ~ ( wife @ peter @ SV4 @ SV7 ) )
= $true )
| ( ( ~ ( wife @ peter @ SV7 @ SV10 ) )
= $true )
| ( ( wife @ peter @ SV4 @ SV10 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[61]) ).
thf(66,plain,
! [SV11: $i,SV8: $i,SV5: $i] :
( ( ( ~ ( john @ SV5 @ SV8 ) )
= $true )
| ( ( ~ ( john @ SV8 @ SV11 ) )
= $true )
| ( ( john @ SV5 @ SV11 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[62]) ).
thf(67,plain,
! [SV12: $i,SV9: $i,SV6: $i] :
( ( ( ~ ( peter @ SV6 @ SV9 ) )
= $true )
| ( ( ~ ( peter @ SV9 @ SV12 ) )
= $true )
| ( ( peter @ SV6 @ SV12 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[63]) ).
thf(68,plain,
! [SV10: $i,SV7: $i,SV4: $i] :
( ( ( wife @ peter @ SV4 @ SV7 )
= $false )
| ( ( ~ ( wife @ peter @ SV7 @ SV10 ) )
= $true )
| ( ( wife @ peter @ SV4 @ SV10 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[65]) ).
thf(69,plain,
! [SV11: $i,SV8: $i,SV5: $i] :
( ( ( john @ SV5 @ SV8 )
= $false )
| ( ( ~ ( john @ SV8 @ SV11 ) )
= $true )
| ( ( john @ SV5 @ SV11 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[66]) ).
thf(70,plain,
! [SV12: $i,SV9: $i,SV6: $i] :
( ( ( peter @ SV6 @ SV9 )
= $false )
| ( ( ~ ( peter @ SV9 @ SV12 ) )
= $true )
| ( ( peter @ SV6 @ SV12 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[67]) ).
thf(71,plain,
! [SV4: $i,SV10: $i,SV7: $i] :
( ( ( wife @ peter @ SV7 @ SV10 )
= $false )
| ( ( wife @ peter @ SV4 @ SV7 )
= $false )
| ( ( wife @ peter @ SV4 @ SV10 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[68]) ).
thf(72,plain,
! [SV5: $i,SV11: $i,SV8: $i] :
( ( ( john @ SV8 @ SV11 )
= $false )
| ( ( john @ SV5 @ SV8 )
= $false )
| ( ( john @ SV5 @ SV11 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[69]) ).
thf(73,plain,
! [SV6: $i,SV12: $i,SV9: $i] :
( ( ( peter @ SV9 @ SV12 )
= $false )
| ( ( peter @ SV6 @ SV9 )
= $false )
| ( ( peter @ SV6 @ SV12 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[70]) ).
thf(74,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[29,73,72,71,64,60,58,53,31,30]) ).
thf(75,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[74]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PUZ085^1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.17 % Computer : n020.cluster.edu
% 0.10/0.17 % Model : x86_64 x86_64
% 0.10/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.17 % Memory : 8046.5625MB
% 0.10/0.17 % OS : Linux 6.8.0-71-generic
% 0.10/0.17 % CPULimit : 300
% 0.10/0.17 % WCLimit : 300
% 0.10/0.17 % DateTime : Tue Oct 6 14:00:36 UTC 2026
% 0.10/0.17 % CPUTime :
% 0.10/0.17 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.22
% 0.10/0.22 No.of.Axioms: 6
% 0.10/0.22
% 0.10/0.22 Length.of.Defs: 5324
% 0.10/0.22
% 0.10/0.22 Contains.Choice.Funs: false
% 0.10/0.22 ..
% 0.10/0.22
% 0.10/0.22 ********************************
% 0.10/0.22 * All subproblems solved! *
% 0.10/0.22 ********************************
% 0.10/0.22 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:6,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:74,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.10/0.22
% 0.10/0.22 %**** Beginning of derivation protocol ****
% 0.10/0.22 % SZS output start CNFRefutation
% See solution above
% 0.10/0.22
% 0.10/0.22 %**** End of derivation protocol ****
% 0.10/0.22 %**** no. of clauses in derivation: 75 ****
% 0.10/0.22 %**** clause counter: 74 ****
% 0.10/0.22
% 0.10/0.22 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:6,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:74,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------