%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : AGT036^1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 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 : n006.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 10:07:12 AM UTC 2026
% Result : Theorem 0.12s 0.24s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 50
% Syntax : Number of formulae : 185 ( 132 unt; 0 typ; 33 def)
% Number of atoms : 828 ( 226 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 1181 ( 152 ~; 156 |; 19 &; 835 @)
% ( 0 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 65 ( 65 >; 0 *; 0 +; 0 <<)
% Number of symbols : 52 ( 49 usr; 8 con; 0-3 aty)
% Number of variables : 384 ( 53 ^; 323 !; 8 ?; 384 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_mu,type,
mu: $tType ).
thf(tp_a1,type,
a1: $i > $i > $o ).
thf(tp_a2,type,
a2: $i > $i > $o ).
thf(tp_a3,type,
a3: $i > $i > $o ).
thf(tp_beer,type,
beer: mu ).
thf(tp_cola,type,
cola: mu ).
thf(tp_cond4s,type,
cond4s: ( $i > $i > $o ) > ( $i > $i > $o ) > $o ).
thf(tp_jan,type,
jan: mu ).
thf(tp_likes,type,
likes: mu > mu > $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_pepsi,type,
pepsi: mu ).
thf(tp_piotr,type,
piotr: mu ).
thf(tp_possibly_likes,type,
possibly_likes: mu > mu > $i > $o ).
thf(tp_sK1_SY0,type,
sK1_SY0: $i ).
thf(tp_sK2_SY62,type,
sK2_SY62: $i > $i ).
thf(tp_sK3_SY66,type,
sK3_SY66: $i > $i ).
thf(tp_sK4_SY89,type,
sK4_SY89: $i > $i ).
thf(tp_sK5_SY122,type,
sK5_SY122: $i > $i ).
thf(tp_subrel,type,
subrel: ( $i > $i > $o ) > ( $i > $i > $o ) > $o ).
thf(tp_very_much_likes,type,
very_much_likes: mu > mu > $i > $o ).
thf(cond4s,definition,
( cond4s
= ( ^ [R1: $i > $i > $o,R2: $i > $i > $o] :
! [U: $i,V: $i,W: $i] :
( ( ( R1 @ U @ V )
& ( R2 @ V @ W ) )
=> ( R2 @ U @ W ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cond4s_def) ).
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(subrel,definition,
( subrel
= ( ^ [R1: $i > $i > $o,R2: $i > $i > $o] :
! [X: $i,Y: $i] :
( ( R1 @ X @ Y )
=> ( R2 @ X @ Y ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subrel_def) ).
thf(1,axiom,
meuclidean @ a3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axioms_5_a3) ).
thf(3,axiom,
meuclidean @ a1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axioms_5_a1) ).
thf(4,axiom,
cond4s @ a3 @ a3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axioms_Is_a3_a3) ).
thf(6,axiom,
cond4s @ a1 @ a1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axioms_Is_a3_a1) ).
thf(10,axiom,
cond4s @ a1 @ a3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axioms_Is_a1_a3) ).
thf(12,axiom,
cond4s @ a1 @ a1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axioms_Is_a1_a1) ).
thf(14,axiom,
subrel @ a1 @ a3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_I_a1_a3) ).
thf(16,axiom,
mserial @ a3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axioms_D_a3) ).
thf(18,axiom,
mserial @ a1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axioms_D_a1) ).
thf(19,axiom,
msymmetric @ a3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axioms_B_a3) ).
thf(21,axiom,
msymmetric @ a1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axioms_B_a1) ).
thf(28,axiom,
mvalid @ ( mdia @ a1 @ ( likes @ piotr @ beer ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_a3_3) ).
thf(29,axiom,
mvalid @ ( mdia @ a3 @ ( likes @ piotr @ pepsi ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_a3_2) ).
thf(33,axiom,
mvalid @ ( mbox @ a1 @ ( likes @ piotr @ beer ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_a2_3) ).
thf(34,axiom,
mvalid @ ( mbox @ a1 @ ( likes @ piotr @ cola ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_a2_2) ).
thf(38,axiom,
mvalid @ ( mbox @ a1 @ ( likes @ piotr @ pepsi ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_a1_2) ).
thf(40,conjecture,
mvalid @ ( likes @ piotr @ pepsi ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj) ).
thf(41,negated_conjecture,
( ( mvalid @ ( likes @ piotr @ pepsi ) )
= $false ),
inference(negate_conjecture,[status(cth)],[40]) ).
thf(42,plain,
( ( ! [SY0: $i] : ( likes @ piotr @ pepsi @ SY0 ) )
= $false ),
inference(unfold_def,[status(thm)],[41,cond4s,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,subrel]) ).
thf(43,plain,
( ( ! [SY2: $i,SY3: $i,SY4: $i] :
( ( ( a3 @ SY2 @ SY3 )
& ( a3 @ SY2 @ SY4 ) )
=> ( a3 @ SY3 @ SY4 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1,cond4s,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,subrel]) ).
thf(44,plain,
( ( ! [SY8: $i,SY9: $i,SY10: $i] :
( ( ( a1 @ SY8 @ SY9 )
& ( a1 @ SY8 @ SY10 ) )
=> ( a1 @ SY9 @ SY10 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3,cond4s,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,subrel]) ).
thf(45,plain,
( ( ! [SY18: $i,SY19: $i,SY20: $i] :
( ( ( a3 @ SY18 @ SY19 )
& ( a3 @ SY19 @ SY20 ) )
=> ( a3 @ SY18 @ SY20 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4,cond4s,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,subrel]) ).
thf(46,plain,
( ( ! [SY28: $i,SY29: $i,SY30: $i] :
( ( ( a1 @ SY28 @ SY29 )
& ( a1 @ SY29 @ SY30 ) )
=> ( a1 @ SY28 @ SY30 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6,cond4s,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,subrel]) ).
thf(47,plain,
( ( ! [SY38: $i,SY39: $i,SY40: $i] :
( ( ( a1 @ SY38 @ SY39 )
& ( a3 @ SY39 @ SY40 ) )
=> ( a3 @ SY38 @ SY40 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10,cond4s,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,subrel]) ).
thf(48,plain,
( ( ! [SY48: $i,SY49: $i,SY50: $i] :
( ( ( a1 @ SY48 @ SY49 )
& ( a1 @ SY49 @ SY50 ) )
=> ( a1 @ SY48 @ SY50 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12,cond4s,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,subrel]) ).
thf(49,plain,
( ( ! [SY57: $i,SY58: $i] :
( ( a1 @ SY57 @ SY58 )
=> ( a3 @ SY57 @ SY58 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14,cond4s,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,subrel]) ).
thf(50,plain,
( ( ! [SY61: $i] :
? [SY62: $i] : ( a3 @ SY61 @ SY62 ) )
= $true ),
inference(unfold_def,[status(thm)],[16,cond4s,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,subrel]) ).
thf(51,plain,
( ( ! [SY65: $i] :
? [SY66: $i] : ( a1 @ SY65 @ SY66 ) )
= $true ),
inference(unfold_def,[status(thm)],[18,cond4s,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,subrel]) ).
thf(52,plain,
( ( ! [SY69: $i,SY70: $i] :
( ( a3 @ SY69 @ SY70 )
=> ( a3 @ SY70 @ SY69 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19,cond4s,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,subrel]) ).
thf(53,plain,
( ( ! [SY73: $i,SY74: $i] :
( ( a1 @ SY73 @ SY74 )
=> ( a1 @ SY74 @ SY73 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[21,cond4s,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,subrel]) ).
thf(54,plain,
( ( ! [SY88: $i] :
~ ! [SY89: $i] :
( ~ ( a1 @ SY88 @ SY89 )
| ~ ( likes @ piotr @ beer @ SY89 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[28,cond4s,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,subrel]) ).
thf(55,plain,
( ( ! [SY97: $i,SY98: $i] :
( ~ ( a1 @ SY97 @ SY98 )
| ( likes @ piotr @ beer @ SY98 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[33,cond4s,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,subrel]) ).
thf(56,plain,
( ( ! [SY106: $i,SY107: $i] :
( ~ ( a1 @ SY106 @ SY107 )
| ( likes @ piotr @ cola @ SY107 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[34,cond4s,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,subrel]) ).
thf(57,plain,
( ( ! [SY121: $i] :
~ ! [SY122: $i] :
( ~ ( a3 @ SY121 @ SY122 )
| ~ ( likes @ piotr @ pepsi @ SY122 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[29,cond4s,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,subrel]) ).
thf(58,plain,
( ( ! [SY130: $i,SY131: $i] :
( ~ ( a1 @ SY130 @ SY131 )
| ( likes @ piotr @ pepsi @ SY131 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[38,cond4s,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,subrel]) ).
thf(59,plain,
( ( likes @ piotr @ pepsi @ sK1_SY0 )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[42]) ).
thf(60,plain,
( ( ~ ( likes @ piotr @ pepsi @ sK1_SY0 ) )
= $true ),
inference(polarity_switch,[status(thm)],[59]) ).
thf(61,plain,
( ( ! [SY2: $i,SY3: $i,SY4: $i] :
( ~ ( a3 @ SY2 @ SY3 )
| ~ ( a3 @ SY2 @ SY4 )
| ( a3 @ SY3 @ SY4 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[43]) ).
thf(62,plain,
( ( ! [SY8: $i,SY9: $i,SY10: $i] :
( ~ ( a1 @ SY8 @ SY9 )
| ~ ( a1 @ SY8 @ SY10 )
| ( a1 @ SY9 @ SY10 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[44]) ).
thf(63,plain,
( ( ! [SY18: $i,SY19: $i,SY20: $i] :
( ~ ( a3 @ SY18 @ SY19 )
| ~ ( a3 @ SY19 @ SY20 )
| ( a3 @ SY18 @ SY20 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[45]) ).
thf(64,plain,
( ( ! [SY28: $i,SY29: $i,SY30: $i] :
( ~ ( a1 @ SY28 @ SY29 )
| ~ ( a1 @ SY29 @ SY30 )
| ( a1 @ SY28 @ SY30 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[46]) ).
thf(65,plain,
( ( ! [SY38: $i,SY39: $i,SY40: $i] :
( ~ ( a1 @ SY38 @ SY39 )
| ~ ( a3 @ SY39 @ SY40 )
| ( a3 @ SY38 @ SY40 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[47]) ).
thf(66,plain,
( ( ! [SY48: $i,SY49: $i,SY50: $i] :
( ~ ( a1 @ SY48 @ SY49 )
| ~ ( a1 @ SY49 @ SY50 )
| ( a1 @ SY48 @ SY50 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[48]) ).
thf(67,plain,
( ( ! [SY57: $i,SY58: $i] :
( ~ ( a1 @ SY57 @ SY58 )
| ( a3 @ SY57 @ SY58 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[49]) ).
thf(68,plain,
( ( ! [SY61: $i] : ( a3 @ SY61 @ ( sK2_SY62 @ SY61 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[50]) ).
thf(69,plain,
( ( ! [SY65: $i] : ( a1 @ SY65 @ ( sK3_SY66 @ SY65 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[51]) ).
thf(70,plain,
( ( ! [SY69: $i,SY70: $i] :
( ~ ( a3 @ SY69 @ SY70 )
| ( a3 @ SY70 @ SY69 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[52]) ).
thf(71,plain,
( ( ! [SY73: $i,SY74: $i] :
( ~ ( a1 @ SY73 @ SY74 )
| ( a1 @ SY74 @ SY73 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[53]) ).
thf(72,plain,
( ( ! [SY88: $i] :
( ( a1 @ SY88 @ ( sK4_SY89 @ SY88 ) )
& ( likes @ piotr @ beer @ ( sK4_SY89 @ SY88 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[54]) ).
thf(73,plain,
( ( ! [SY121: $i] :
( ( a3 @ SY121 @ ( sK5_SY122 @ SY121 ) )
& ( likes @ piotr @ pepsi @ ( sK5_SY122 @ SY121 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[57]) ).
thf(74,plain,
( ( ! [SY130: $i,SY131: $i] :
( ~ ( a1 @ SY130 @ SY131 )
| ( likes @ piotr @ pepsi @ SY131 ) ) )
= $true ),
inference(copy,[status(thm)],[58]) ).
thf(75,plain,
( ( ! [SY121: $i] :
( ( a3 @ SY121 @ ( sK5_SY122 @ SY121 ) )
& ( likes @ piotr @ pepsi @ ( sK5_SY122 @ SY121 ) ) ) )
= $true ),
inference(copy,[status(thm)],[73]) ).
thf(76,plain,
( ( ! [SY106: $i,SY107: $i] :
( ~ ( a1 @ SY106 @ SY107 )
| ( likes @ piotr @ cola @ SY107 ) ) )
= $true ),
inference(copy,[status(thm)],[56]) ).
thf(77,plain,
( ( ! [SY97: $i,SY98: $i] :
( ~ ( a1 @ SY97 @ SY98 )
| ( likes @ piotr @ beer @ SY98 ) ) )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(78,plain,
( ( ! [SY88: $i] :
( ( a1 @ SY88 @ ( sK4_SY89 @ SY88 ) )
& ( likes @ piotr @ beer @ ( sK4_SY89 @ SY88 ) ) ) )
= $true ),
inference(copy,[status(thm)],[72]) ).
thf(79,plain,
( ( ! [SY73: $i,SY74: $i] :
( ~ ( a1 @ SY73 @ SY74 )
| ( a1 @ SY74 @ SY73 ) ) )
= $true ),
inference(copy,[status(thm)],[71]) ).
thf(80,plain,
( ( ! [SY69: $i,SY70: $i] :
( ~ ( a3 @ SY69 @ SY70 )
| ( a3 @ SY70 @ SY69 ) ) )
= $true ),
inference(copy,[status(thm)],[70]) ).
thf(81,plain,
( ( ! [SY65: $i] : ( a1 @ SY65 @ ( sK3_SY66 @ SY65 ) ) )
= $true ),
inference(copy,[status(thm)],[69]) ).
thf(82,plain,
( ( ! [SY61: $i] : ( a3 @ SY61 @ ( sK2_SY62 @ SY61 ) ) )
= $true ),
inference(copy,[status(thm)],[68]) ).
thf(83,plain,
( ( ! [SY57: $i,SY58: $i] :
( ~ ( a1 @ SY57 @ SY58 )
| ( a3 @ SY57 @ SY58 ) ) )
= $true ),
inference(copy,[status(thm)],[67]) ).
thf(84,plain,
( ( ! [SY48: $i,SY49: $i,SY50: $i] :
( ~ ( a1 @ SY48 @ SY49 )
| ~ ( a1 @ SY49 @ SY50 )
| ( a1 @ SY48 @ SY50 ) ) )
= $true ),
inference(copy,[status(thm)],[66]) ).
thf(85,plain,
( ( ! [SY38: $i,SY39: $i,SY40: $i] :
( ~ ( a1 @ SY38 @ SY39 )
| ~ ( a3 @ SY39 @ SY40 )
| ( a3 @ SY38 @ SY40 ) ) )
= $true ),
inference(copy,[status(thm)],[65]) ).
thf(86,plain,
( ( ! [SY28: $i,SY29: $i,SY30: $i] :
( ~ ( a1 @ SY28 @ SY29 )
| ~ ( a1 @ SY29 @ SY30 )
| ( a1 @ SY28 @ SY30 ) ) )
= $true ),
inference(copy,[status(thm)],[64]) ).
thf(87,plain,
( ( ! [SY18: $i,SY19: $i,SY20: $i] :
( ~ ( a3 @ SY18 @ SY19 )
| ~ ( a3 @ SY19 @ SY20 )
| ( a3 @ SY18 @ SY20 ) ) )
= $true ),
inference(copy,[status(thm)],[63]) ).
thf(88,plain,
( ( ! [SY8: $i,SY9: $i,SY10: $i] :
( ~ ( a1 @ SY8 @ SY9 )
| ~ ( a1 @ SY8 @ SY10 )
| ( a1 @ SY9 @ SY10 ) ) )
= $true ),
inference(copy,[status(thm)],[62]) ).
thf(89,plain,
( ( ! [SY2: $i,SY3: $i,SY4: $i] :
( ~ ( a3 @ SY2 @ SY3 )
| ~ ( a3 @ SY2 @ SY4 )
| ( a3 @ SY3 @ SY4 ) ) )
= $true ),
inference(copy,[status(thm)],[61]) ).
thf(90,plain,
( ( ~ ( likes @ piotr @ pepsi @ sK1_SY0 ) )
= $true ),
inference(copy,[status(thm)],[60]) ).
thf(91,plain,
( ( ! [SX0: $i] :
~ ( ~ ( a3 @ SX0 @ ( sK5_SY122 @ SX0 ) )
| ~ ( likes @ piotr @ pepsi @ ( sK5_SY122 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[75,cond4s,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,subrel]) ).
thf(92,plain,
( ( ! [SX0: $i] :
~ ( ~ ( a1 @ SX0 @ ( sK4_SY89 @ SX0 ) )
| ~ ( likes @ piotr @ beer @ ( sK4_SY89 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[78,cond4s,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,subrel]) ).
thf(93,plain,
! [SV1: $i] :
( ( ! [SY134: $i] :
( ~ ( a1 @ SV1 @ SY134 )
| ( likes @ piotr @ pepsi @ SY134 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[74]) ).
thf(94,plain,
! [SV2: $i] :
( ( ! [SY135: $i] :
( ~ ( a1 @ SV2 @ SY135 )
| ( likes @ piotr @ cola @ SY135 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[76]) ).
thf(95,plain,
! [SV3: $i] :
( ( ! [SY136: $i] :
( ~ ( a1 @ SV3 @ SY136 )
| ( likes @ piotr @ beer @ SY136 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[77]) ).
thf(96,plain,
! [SV4: $i] :
( ( ! [SY137: $i] :
( ~ ( a1 @ SV4 @ SY137 )
| ( a1 @ SY137 @ SV4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[79]) ).
thf(97,plain,
! [SV5: $i] :
( ( ! [SY138: $i] :
( ~ ( a3 @ SV5 @ SY138 )
| ( a3 @ SY138 @ SV5 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[80]) ).
thf(98,plain,
! [SV6: $i] :
( ( a1 @ SV6 @ ( sK3_SY66 @ SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[81]) ).
thf(99,plain,
! [SV7: $i] :
( ( a3 @ SV7 @ ( sK2_SY62 @ SV7 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[82]) ).
thf(100,plain,
! [SV8: $i] :
( ( ! [SY139: $i] :
( ~ ( a1 @ SV8 @ SY139 )
| ( a3 @ SV8 @ SY139 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[83]) ).
thf(101,plain,
! [SV9: $i] :
( ( ! [SY140: $i,SY141: $i] :
( ~ ( a1 @ SV9 @ SY140 )
| ~ ( a1 @ SY140 @ SY141 )
| ( a1 @ SV9 @ SY141 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).
thf(102,plain,
! [SV10: $i] :
( ( ! [SY142: $i,SY143: $i] :
( ~ ( a1 @ SV10 @ SY142 )
| ~ ( a3 @ SY142 @ SY143 )
| ( a3 @ SV10 @ SY143 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(103,plain,
! [SV11: $i] :
( ( ! [SY144: $i,SY145: $i] :
( ~ ( a1 @ SV11 @ SY144 )
| ~ ( a1 @ SY144 @ SY145 )
| ( a1 @ SV11 @ SY145 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[86]) ).
thf(104,plain,
! [SV12: $i] :
( ( ! [SY146: $i,SY147: $i] :
( ~ ( a3 @ SV12 @ SY146 )
| ~ ( a3 @ SY146 @ SY147 )
| ( a3 @ SV12 @ SY147 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).
thf(105,plain,
! [SV13: $i] :
( ( ! [SY148: $i,SY149: $i] :
( ~ ( a1 @ SV13 @ SY148 )
| ~ ( a1 @ SV13 @ SY149 )
| ( a1 @ SY148 @ SY149 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(106,plain,
! [SV14: $i] :
( ( ! [SY150: $i,SY151: $i] :
( ~ ( a3 @ SV14 @ SY150 )
| ~ ( a3 @ SV14 @ SY151 )
| ( a3 @ SY150 @ SY151 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[89]) ).
thf(107,plain,
( ( likes @ piotr @ pepsi @ sK1_SY0 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[90]) ).
thf(108,plain,
! [SV15: $i] :
( ( ~ ( ~ ( a3 @ SV15 @ ( sK5_SY122 @ SV15 ) )
| ~ ( likes @ piotr @ pepsi @ ( sK5_SY122 @ SV15 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[91]) ).
thf(109,plain,
! [SV16: $i] :
( ( ~ ( ~ ( a1 @ SV16 @ ( sK4_SY89 @ SV16 ) )
| ~ ( likes @ piotr @ beer @ ( sK4_SY89 @ SV16 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[92]) ).
thf(110,plain,
! [SV17: $i,SV1: $i] :
( ( ~ ( a1 @ SV1 @ SV17 )
| ( likes @ piotr @ pepsi @ SV17 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[93]) ).
thf(111,plain,
! [SV18: $i,SV2: $i] :
( ( ~ ( a1 @ SV2 @ SV18 )
| ( likes @ piotr @ cola @ SV18 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[94]) ).
thf(112,plain,
! [SV19: $i,SV3: $i] :
( ( ~ ( a1 @ SV3 @ SV19 )
| ( likes @ piotr @ beer @ SV19 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[95]) ).
thf(113,plain,
! [SV20: $i,SV4: $i] :
( ( ~ ( a1 @ SV4 @ SV20 )
| ( a1 @ SV20 @ SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[96]) ).
thf(114,plain,
! [SV21: $i,SV5: $i] :
( ( ~ ( a3 @ SV5 @ SV21 )
| ( a3 @ SV21 @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[97]) ).
thf(115,plain,
! [SV22: $i,SV8: $i] :
( ( ~ ( a1 @ SV8 @ SV22 )
| ( a3 @ SV8 @ SV22 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[100]) ).
thf(116,plain,
! [SV23: $i,SV9: $i] :
( ( ! [SY152: $i] :
( ~ ( a1 @ SV9 @ SV23 )
| ~ ( a1 @ SV23 @ SY152 )
| ( a1 @ SV9 @ SY152 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[101]) ).
thf(117,plain,
! [SV24: $i,SV10: $i] :
( ( ! [SY153: $i] :
( ~ ( a1 @ SV10 @ SV24 )
| ~ ( a3 @ SV24 @ SY153 )
| ( a3 @ SV10 @ SY153 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[102]) ).
thf(118,plain,
! [SV25: $i,SV11: $i] :
( ( ! [SY154: $i] :
( ~ ( a1 @ SV11 @ SV25 )
| ~ ( a1 @ SV25 @ SY154 )
| ( a1 @ SV11 @ SY154 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[103]) ).
thf(119,plain,
! [SV26: $i,SV12: $i] :
( ( ! [SY155: $i] :
( ~ ( a3 @ SV12 @ SV26 )
| ~ ( a3 @ SV26 @ SY155 )
| ( a3 @ SV12 @ SY155 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[104]) ).
thf(120,plain,
! [SV27: $i,SV13: $i] :
( ( ! [SY156: $i] :
( ~ ( a1 @ SV13 @ SV27 )
| ~ ( a1 @ SV13 @ SY156 )
| ( a1 @ SV27 @ SY156 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[105]) ).
thf(121,plain,
! [SV28: $i,SV14: $i] :
( ( ! [SY157: $i] :
( ~ ( a3 @ SV14 @ SV28 )
| ~ ( a3 @ SV14 @ SY157 )
| ( a3 @ SV28 @ SY157 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[106]) ).
thf(122,plain,
! [SV15: $i] :
( ( ~ ( a3 @ SV15 @ ( sK5_SY122 @ SV15 ) )
| ~ ( likes @ piotr @ pepsi @ ( sK5_SY122 @ SV15 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[108]) ).
thf(123,plain,
! [SV16: $i] :
( ( ~ ( a1 @ SV16 @ ( sK4_SY89 @ SV16 ) )
| ~ ( likes @ piotr @ beer @ ( sK4_SY89 @ SV16 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[109]) ).
thf(124,plain,
! [SV17: $i,SV1: $i] :
( ( ( ~ ( a1 @ SV1 @ SV17 ) )
= $true )
| ( ( likes @ piotr @ pepsi @ SV17 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[110]) ).
thf(125,plain,
! [SV18: $i,SV2: $i] :
( ( ( ~ ( a1 @ SV2 @ SV18 ) )
= $true )
| ( ( likes @ piotr @ cola @ SV18 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[111]) ).
thf(126,plain,
! [SV19: $i,SV3: $i] :
( ( ( ~ ( a1 @ SV3 @ SV19 ) )
= $true )
| ( ( likes @ piotr @ beer @ SV19 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[112]) ).
thf(127,plain,
! [SV20: $i,SV4: $i] :
( ( ( ~ ( a1 @ SV4 @ SV20 ) )
= $true )
| ( ( a1 @ SV20 @ SV4 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[113]) ).
thf(128,plain,
! [SV21: $i,SV5: $i] :
( ( ( ~ ( a3 @ SV5 @ SV21 ) )
= $true )
| ( ( a3 @ SV21 @ SV5 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[114]) ).
thf(129,plain,
! [SV22: $i,SV8: $i] :
( ( ( ~ ( a1 @ SV8 @ SV22 ) )
= $true )
| ( ( a3 @ SV8 @ SV22 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[115]) ).
thf(130,plain,
! [SV29: $i,SV23: $i,SV9: $i] :
( ( ~ ( a1 @ SV9 @ SV23 )
| ~ ( a1 @ SV23 @ SV29 )
| ( a1 @ SV9 @ SV29 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[116]) ).
thf(131,plain,
! [SV30: $i,SV24: $i,SV10: $i] :
( ( ~ ( a1 @ SV10 @ SV24 )
| ~ ( a3 @ SV24 @ SV30 )
| ( a3 @ SV10 @ SV30 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[117]) ).
thf(132,plain,
! [SV31: $i,SV25: $i,SV11: $i] :
( ( ~ ( a1 @ SV11 @ SV25 )
| ~ ( a1 @ SV25 @ SV31 )
| ( a1 @ SV11 @ SV31 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[118]) ).
thf(133,plain,
! [SV32: $i,SV26: $i,SV12: $i] :
( ( ~ ( a3 @ SV12 @ SV26 )
| ~ ( a3 @ SV26 @ SV32 )
| ( a3 @ SV12 @ SV32 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[119]) ).
thf(134,plain,
! [SV33: $i,SV27: $i,SV13: $i] :
( ( ~ ( a1 @ SV13 @ SV27 )
| ~ ( a1 @ SV13 @ SV33 )
| ( a1 @ SV27 @ SV33 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[120]) ).
thf(135,plain,
! [SV34: $i,SV28: $i,SV14: $i] :
( ( ~ ( a3 @ SV14 @ SV28 )
| ~ ( a3 @ SV14 @ SV34 )
| ( a3 @ SV28 @ SV34 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[121]) ).
thf(136,plain,
! [SV15: $i] :
( ( ~ ( a3 @ SV15 @ ( sK5_SY122 @ SV15 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[122]) ).
thf(137,plain,
! [SV15: $i] :
( ( ~ ( likes @ piotr @ pepsi @ ( sK5_SY122 @ SV15 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[122]) ).
thf(138,plain,
! [SV16: $i] :
( ( ~ ( a1 @ SV16 @ ( sK4_SY89 @ SV16 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[123]) ).
thf(139,plain,
! [SV16: $i] :
( ( ~ ( likes @ piotr @ beer @ ( sK4_SY89 @ SV16 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[123]) ).
thf(140,plain,
! [SV17: $i,SV1: $i] :
( ( ( a1 @ SV1 @ SV17 )
= $false )
| ( ( likes @ piotr @ pepsi @ SV17 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[124]) ).
thf(141,plain,
! [SV18: $i,SV2: $i] :
( ( ( a1 @ SV2 @ SV18 )
= $false )
| ( ( likes @ piotr @ cola @ SV18 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[125]) ).
thf(142,plain,
! [SV19: $i,SV3: $i] :
( ( ( a1 @ SV3 @ SV19 )
= $false )
| ( ( likes @ piotr @ beer @ SV19 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[126]) ).
thf(143,plain,
! [SV20: $i,SV4: $i] :
( ( ( a1 @ SV4 @ SV20 )
= $false )
| ( ( a1 @ SV20 @ SV4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[127]) ).
thf(144,plain,
! [SV21: $i,SV5: $i] :
( ( ( a3 @ SV5 @ SV21 )
= $false )
| ( ( a3 @ SV21 @ SV5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[128]) ).
thf(145,plain,
! [SV22: $i,SV8: $i] :
( ( ( a1 @ SV8 @ SV22 )
= $false )
| ( ( a3 @ SV8 @ SV22 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[129]) ).
thf(146,plain,
! [SV29: $i,SV23: $i,SV9: $i] :
( ( ( ~ ( a1 @ SV9 @ SV23 )
| ~ ( a1 @ SV23 @ SV29 ) )
= $true )
| ( ( a1 @ SV9 @ SV29 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[130]) ).
thf(147,plain,
! [SV30: $i,SV24: $i,SV10: $i] :
( ( ( ~ ( a1 @ SV10 @ SV24 )
| ~ ( a3 @ SV24 @ SV30 ) )
= $true )
| ( ( a3 @ SV10 @ SV30 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[131]) ).
thf(148,plain,
! [SV31: $i,SV25: $i,SV11: $i] :
( ( ( ~ ( a1 @ SV11 @ SV25 )
| ~ ( a1 @ SV25 @ SV31 ) )
= $true )
| ( ( a1 @ SV11 @ SV31 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[132]) ).
thf(149,plain,
! [SV32: $i,SV26: $i,SV12: $i] :
( ( ( ~ ( a3 @ SV12 @ SV26 )
| ~ ( a3 @ SV26 @ SV32 ) )
= $true )
| ( ( a3 @ SV12 @ SV32 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[133]) ).
thf(150,plain,
! [SV33: $i,SV27: $i,SV13: $i] :
( ( ( ~ ( a1 @ SV13 @ SV27 )
| ~ ( a1 @ SV13 @ SV33 ) )
= $true )
| ( ( a1 @ SV27 @ SV33 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[134]) ).
thf(151,plain,
! [SV34: $i,SV28: $i,SV14: $i] :
( ( ( ~ ( a3 @ SV14 @ SV28 )
| ~ ( a3 @ SV14 @ SV34 ) )
= $true )
| ( ( a3 @ SV28 @ SV34 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[135]) ).
thf(152,plain,
! [SV15: $i] :
( ( a3 @ SV15 @ ( sK5_SY122 @ SV15 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[136]) ).
thf(153,plain,
! [SV15: $i] :
( ( likes @ piotr @ pepsi @ ( sK5_SY122 @ SV15 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[137]) ).
thf(154,plain,
! [SV16: $i] :
( ( a1 @ SV16 @ ( sK4_SY89 @ SV16 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[138]) ).
thf(155,plain,
! [SV16: $i] :
( ( likes @ piotr @ beer @ ( sK4_SY89 @ SV16 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[139]) ).
thf(156,plain,
! [SV29: $i,SV23: $i,SV9: $i] :
( ( ( ~ ( a1 @ SV9 @ SV23 ) )
= $true )
| ( ( ~ ( a1 @ SV23 @ SV29 ) )
= $true )
| ( ( a1 @ SV9 @ SV29 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[146]) ).
thf(157,plain,
! [SV30: $i,SV24: $i,SV10: $i] :
( ( ( ~ ( a1 @ SV10 @ SV24 ) )
= $true )
| ( ( ~ ( a3 @ SV24 @ SV30 ) )
= $true )
| ( ( a3 @ SV10 @ SV30 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[147]) ).
thf(158,plain,
! [SV31: $i,SV25: $i,SV11: $i] :
( ( ( ~ ( a1 @ SV11 @ SV25 ) )
= $true )
| ( ( ~ ( a1 @ SV25 @ SV31 ) )
= $true )
| ( ( a1 @ SV11 @ SV31 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[148]) ).
thf(159,plain,
! [SV32: $i,SV26: $i,SV12: $i] :
( ( ( ~ ( a3 @ SV12 @ SV26 ) )
= $true )
| ( ( ~ ( a3 @ SV26 @ SV32 ) )
= $true )
| ( ( a3 @ SV12 @ SV32 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[149]) ).
thf(160,plain,
! [SV33: $i,SV27: $i,SV13: $i] :
( ( ( ~ ( a1 @ SV13 @ SV27 ) )
= $true )
| ( ( ~ ( a1 @ SV13 @ SV33 ) )
= $true )
| ( ( a1 @ SV27 @ SV33 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[150]) ).
thf(161,plain,
! [SV34: $i,SV28: $i,SV14: $i] :
( ( ( ~ ( a3 @ SV14 @ SV28 ) )
= $true )
| ( ( ~ ( a3 @ SV14 @ SV34 ) )
= $true )
| ( ( a3 @ SV28 @ SV34 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[151]) ).
thf(162,plain,
! [SV29: $i,SV23: $i,SV9: $i] :
( ( ( a1 @ SV9 @ SV23 )
= $false )
| ( ( ~ ( a1 @ SV23 @ SV29 ) )
= $true )
| ( ( a1 @ SV9 @ SV29 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[156]) ).
thf(163,plain,
! [SV30: $i,SV24: $i,SV10: $i] :
( ( ( a1 @ SV10 @ SV24 )
= $false )
| ( ( ~ ( a3 @ SV24 @ SV30 ) )
= $true )
| ( ( a3 @ SV10 @ SV30 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[157]) ).
thf(164,plain,
! [SV31: $i,SV25: $i,SV11: $i] :
( ( ( a1 @ SV11 @ SV25 )
= $false )
| ( ( ~ ( a1 @ SV25 @ SV31 ) )
= $true )
| ( ( a1 @ SV11 @ SV31 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[158]) ).
thf(165,plain,
! [SV32: $i,SV26: $i,SV12: $i] :
( ( ( a3 @ SV12 @ SV26 )
= $false )
| ( ( ~ ( a3 @ SV26 @ SV32 ) )
= $true )
| ( ( a3 @ SV12 @ SV32 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[159]) ).
thf(166,plain,
! [SV33: $i,SV27: $i,SV13: $i] :
( ( ( a1 @ SV13 @ SV27 )
= $false )
| ( ( ~ ( a1 @ SV13 @ SV33 ) )
= $true )
| ( ( a1 @ SV27 @ SV33 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[160]) ).
thf(167,plain,
! [SV34: $i,SV28: $i,SV14: $i] :
( ( ( a3 @ SV14 @ SV28 )
= $false )
| ( ( ~ ( a3 @ SV14 @ SV34 ) )
= $true )
| ( ( a3 @ SV28 @ SV34 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[161]) ).
thf(168,plain,
! [SV9: $i,SV29: $i,SV23: $i] :
( ( ( a1 @ SV23 @ SV29 )
= $false )
| ( ( a1 @ SV9 @ SV23 )
= $false )
| ( ( a1 @ SV9 @ SV29 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[162]) ).
thf(169,plain,
! [SV10: $i,SV30: $i,SV24: $i] :
( ( ( a3 @ SV24 @ SV30 )
= $false )
| ( ( a1 @ SV10 @ SV24 )
= $false )
| ( ( a3 @ SV10 @ SV30 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[163]) ).
thf(170,plain,
! [SV11: $i,SV31: $i,SV25: $i] :
( ( ( a1 @ SV25 @ SV31 )
= $false )
| ( ( a1 @ SV11 @ SV25 )
= $false )
| ( ( a1 @ SV11 @ SV31 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[164]) ).
thf(171,plain,
! [SV12: $i,SV32: $i,SV26: $i] :
( ( ( a3 @ SV26 @ SV32 )
= $false )
| ( ( a3 @ SV12 @ SV26 )
= $false )
| ( ( a3 @ SV12 @ SV32 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[165]) ).
thf(172,plain,
! [SV27: $i,SV33: $i,SV13: $i] :
( ( ( a1 @ SV13 @ SV33 )
= $false )
| ( ( a1 @ SV13 @ SV27 )
= $false )
| ( ( a1 @ SV27 @ SV33 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[166]) ).
thf(173,plain,
! [SV28: $i,SV34: $i,SV14: $i] :
( ( ( a3 @ SV14 @ SV34 )
= $false )
| ( ( a3 @ SV14 @ SV28 )
= $false )
| ( ( a3 @ SV28 @ SV34 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[167]) ).
thf(174,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[98,173,172,171,170,169,168,155,154,153,152,145,144,143,142,141,140,107,99]) ).
thf(175,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[174]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : AGT036^1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.03 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.15 % Computer : n006.cluster.edu
% 0.12/0.15 % Model : x86_64 x86_64
% 0.12/0.15 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.15 % Memory : 8046.5625MB
% 0.12/0.15 % OS : Linux 6.8.0-71-generic
% 0.12/0.15 % CPULimit : 300
% 0.12/0.15 % WCLimit : 300
% 0.12/0.15 % DateTime : Tue Oct 6 17:59:22 UTC 2026
% 0.12/0.16 % CPUTime :
% 0.12/0.16 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.24
% 0.12/0.24 No.of.Axioms: 39
% 0.12/0.24
% 0.12/0.24 Length.of.Defs: 5718
% 0.12/0.24
% 0.12/0.24 Contains.Choice.Funs: false
% 0.12/0.24 ....
% 0.12/0.24
% 0.12/0.24 ********************************
% 0.12/0.24 * All subproblems solved! *
% 0.12/0.24 ********************************
% 0.12/0.24 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:16,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:15,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:174,loop_count:0,foatp_calls:1,translation:fof_experiment)
% 0.12/0.24
% 0.12/0.24 %**** Beginning of derivation protocol ****
% 0.12/0.24 % SZS output start CNFRefutation
% See solution above
% 0.12/0.24
% 0.12/0.24 %**** End of derivation protocol ****
% 0.12/0.24 %**** no. of clauses in derivation: 152 ****
% 0.12/0.24 %**** clause counter: 174 ****
% 0.12/0.24
% 0.12/0.24 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:16,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:15,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:174,loop_count:0,foatp_calls:1,translation:fof_experiment)
%------------------------------------------------------------------------------