%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : PUZ149^13 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n026.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 Sep 30 08:21:17 AM UTC 2026
% Result : Theorem 0.11s 0.28s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 16
% Syntax : Number of formulae : 131 ( 55 unt; 0 typ; 6 def)
% Number of atoms : 748 ( 159 equ; 0 cnn)
% Maximal formula atoms : 9 ( 5 avg)
% Number of connectives : 1033 ( 102 ~; 115 |; 39 &; 695 @)
% ( 6 <=>; 40 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 51 ( 51 >; 0 *; 0 +; 0 <<)
% Number of symbols : 47 ( 42 usr; 23 con; 0-4 aty)
% ( 18 !!; 18 ??; 0 @@+; 0 @@-)
% Number of variables : 202 ( 0 sgn 49 !; 2 ?; 202 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
mworld: $tType ).
thf(type_def_6,type,
mindex: $tType ).
thf(type_def_7,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
mrel: mindex > mworld > mworld > $o ).
thf(func_def_1,type,
'#pour_b': mindex ).
thf(func_def_2,type,
'#make_c': mindex ).
thf(func_def_3,type,
'#pour_a': mindex ).
thf(func_def_4,type,
mactual: mworld ).
thf(func_def_5,type,
mlocal: ( mworld > $o ) > $o ).
thf(func_def_7,type,
mnot: ( mworld > $o ) > mworld > $o ).
thf(func_def_8,type,
mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(func_def_9,type,
mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(func_def_10,type,
mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(func_def_11,type,
mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(func_def_12,type,
mbox: mindex > ( mworld > $o ) > mworld > $o ).
thf(func_def_13,type,
mdia: mindex > ( mworld > $o ) > mworld > $o ).
thf(func_def_14,type,
acid: mworld > $o ).
thf(func_def_15,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_16,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_17,type,
vNOT: $o > $o ).
thf(func_def_18,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_19,type,
vAND: $o > $o > $o ).
thf(func_def_20,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_21,type,
vOR: $o > $o > $o ).
thf(func_def_22,type,
vIMP: $o > $o > $o ).
thf(func_def_23,type,
vIFF: $o > $o > $o ).
thf(func_def_24,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_25,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_26,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_29,type,
sK0: mworld ).
thf(func_def_30,type,
sK1: mworld ).
thf(func_def_31,type,
sK2: mworld ).
thf(func_def_32,type,
sK3: mworld ).
thf(func_def_33,type,
sK4: mworld ).
thf(func_def_34,type,
sK5: mworld ).
thf(func_def_35,type,
sK6: mworld ).
thf(func_def_36,type,
sK7: mworld ).
thf(func_def_37,type,
sK8: mworld ).
thf(f1,axiom,
( mlocal
= ( ^ [X0: mworld > $o] : ( X0 @ mactual ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mlocal_def) ).
thf(f2,axiom,
( mnot
= ( ^ [X0: mworld > $o,X1: mworld] :
~ ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mnot_def) ).
thf(f3,axiom,
( mand
= ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X1 @ X2 )
& ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mand_def) ).
thf(f5,axiom,
( mimplies
= ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mimplies_def) ).
thf(f7,axiom,
( mbox
= ( ^ [X0: mindex,X1: mworld > $o,X2: mworld] :
! [X3: mworld] :
( ( mrel @ X0 @ X2 @ X3 )
=> ( X1 @ X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mbox_def) ).
thf(f8,axiom,
( mdia
= ( ^ [X0: mindex,X1: mworld > $o,X2: mworld] :
? [X3: mworld] :
( ( X1 @ X3 )
& ( mrel @ X0 @ X2 @ X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mdia_def) ).
thf(f10,axiom,
mlocal @ ( mimplies @ ( mbox @ '#pour_a' @ ( mbox @ '#pour_b' @ ( mnot @ acid ) ) ) @ ( mbox @ '#make_c' @ ( mnot @ acid ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pour_ab_make_axiom_2) ).
thf(f13,axiom,
mlocal @ ( mbox @ '#pour_a' @ ( mnot @ acid ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pour_a_acid) ).
thf(f14,axiom,
mlocal @ ( mdia @ '#make_c' @ acid ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',make_c_acid) ).
thf(f15,conjecture,
mlocal @ ( mand @ ( mdia @ '#pour_a' @ ( mnot @ acid ) ) @ ( mdia @ '#pour_a' @ ( mdia @ '#pour_b' @ acid ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj) ).
thf(f16,negated_conjecture,
~ ( mlocal @ ( mand @ ( mdia @ '#pour_a' @ ( mnot @ acid ) ) @ ( mdia @ '#pour_a' @ ( mdia @ '#pour_b' @ acid ) ) ) ),
inference(negated_conjecture,[status(cth)],[f15]) ).
thf(f17,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(fool_elimination,[],[f1]) ).
thf(f18,plain,
( mnot
= ( ^ [X0: mworld > $o,X1: mworld] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f2]) ).
thf(f19,plain,
( mnot
= ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f18]) ).
thf(f20,plain,
( mand
= ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X1 @ X2 )
& ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f21,plain,
( mand
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f20]) ).
thf(f24,plain,
( mimplies
= ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f25,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f24]) ).
thf(f28,plain,
( mbox
= ( ^ [X0: mindex,X1: mworld > $o,X2: mworld] :
! [X3: mworld] :
( ( mrel @ X0 @ X2 @ X3 )
=> ( X1 @ X3 ) ) ) ),
inference(rectify,[],[f7]) ).
thf(f29,plain,
( mbox
= ( ^ [Y0: mindex,Y1: mworld > $o,Y2: mworld] :
( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) ) ) ),
inference(fool_elimination,[],[f28]) ).
thf(f30,plain,
( mdia
= ( ^ [X0: mindex,X1: mworld > $o,X2: mworld] :
? [X3: mworld] :
( ( X1 @ X3 )
& ( mrel @ X0 @ X2 @ X3 ) ) ) ),
inference(rectify,[],[f8]) ).
thf(f31,plain,
( mdia
= ( ^ [Y0: mindex,Y1: mworld > $o,Y2: mworld] :
( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y0 @ Y2 @ Y3 )
& ( Y1 @ Y3 ) ) ) ) ),
inference(fool_elimination,[],[f30]) ).
thf(f34,plain,
mlocal @ ( mimplies @ ( mbox @ '#pour_a' @ ( mbox @ '#pour_b' @ ( mnot @ acid ) ) ) @ ( mbox @ '#make_c' @ ( mnot @ acid ) ) ),
inference(rectify,[],[f10]) ).
thf(f35,plain,
( ( mlocal @ ( mimplies @ ( mbox @ '#pour_a' @ ( mbox @ '#pour_b' @ ( mnot @ acid ) ) ) @ ( mbox @ '#make_c' @ ( mnot @ acid ) ) ) )
= $true ),
inference(fool_elimination,[],[f34]) ).
thf(f40,plain,
mlocal @ ( mbox @ '#pour_a' @ ( mnot @ acid ) ),
inference(rectify,[],[f13]) ).
thf(f41,plain,
( ( mlocal @ ( mbox @ '#pour_a' @ ( mnot @ acid ) ) )
= $true ),
inference(fool_elimination,[],[f40]) ).
thf(f42,plain,
mlocal @ ( mdia @ '#make_c' @ acid ),
inference(rectify,[],[f14]) ).
thf(f43,plain,
( ( mlocal @ ( mdia @ '#make_c' @ acid ) )
= $true ),
inference(fool_elimination,[],[f42]) ).
thf(f44,plain,
~ ( mlocal @ ( mand @ ( mdia @ '#pour_a' @ ( mnot @ acid ) ) @ ( mdia @ '#pour_a' @ ( mdia @ '#pour_b' @ acid ) ) ) ),
inference(rectify,[],[f16]) ).
thf(f45,plain,
( ( mlocal @ ( mand @ ( mdia @ '#pour_a' @ ( mnot @ acid ) ) @ ( mdia @ '#pour_a' @ ( mdia @ '#pour_b' @ acid ) ) ) )
!= $true ),
inference(fool_elimination,[],[f44]) ).
thf(f46,plain,
( ( mlocal @ ( mand @ ( mdia @ '#pour_a' @ ( mnot @ acid ) ) @ ( mdia @ '#pour_a' @ ( mdia @ '#pour_b' @ acid ) ) ) )
!= $true ),
inference(flattening,[],[f45]) ).
thf(f47,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(cnf_transformation,[],[f17]) ).
thf(f48,plain,
( mnot
= ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f19]) ).
thf(f49,plain,
( mand
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f21]) ).
thf(f51,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f25]) ).
thf(f53,plain,
( mbox
= ( ^ [Y0: mindex,Y1: mworld > $o,Y2: mworld] :
( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) ) ) ),
inference(cnf_transformation,[],[f29]) ).
thf(f54,plain,
( mdia
= ( ^ [Y0: mindex,Y1: mworld > $o,Y2: mworld] :
( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y0 @ Y2 @ Y3 )
& ( Y1 @ Y3 ) ) ) ) ),
inference(cnf_transformation,[],[f31]) ).
thf(f56,plain,
( ( mlocal @ ( mimplies @ ( mbox @ '#pour_a' @ ( mbox @ '#pour_b' @ ( mnot @ acid ) ) ) @ ( mbox @ '#make_c' @ ( mnot @ acid ) ) ) )
= $true ),
inference(cnf_transformation,[],[f35]) ).
thf(f59,plain,
( ( mlocal @ ( mbox @ '#pour_a' @ ( mnot @ acid ) ) )
= $true ),
inference(cnf_transformation,[],[f41]) ).
thf(f60,plain,
( ( mlocal @ ( mdia @ '#make_c' @ acid ) )
= $true ),
inference(cnf_transformation,[],[f43]) ).
thf(f61,plain,
( ( mlocal @ ( mand @ ( mdia @ '#pour_a' @ ( mnot @ acid ) ) @ ( mdia @ '#pour_a' @ ( mdia @ '#pour_b' @ acid ) ) ) )
!= $true ),
inference(cnf_transformation,[],[f46]) ).
thf(f65,plain,
( $true
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) )
@ ( ^ [Y0: mindex,Y1: mworld > $o,Y2: mworld] :
( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ '#pour_a'
@ ( ^ [Y0: mindex,Y1: mworld > $o,Y2: mworld] :
( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ '#pour_b'
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ acid ) ) )
@ ( ^ [Y0: mindex,Y1: mworld > $o,Y2: mworld] :
( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ '#make_c'
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ acid ) ) ) ) ),
inference(definition_unfolding,[],[f56,f47,f51,f53,f53,f48,f53,f48]) ).
thf(f68,plain,
( $true
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: mindex,Y1: mworld > $o,Y2: mworld] :
( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ '#pour_a'
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ acid ) ) ) ),
inference(definition_unfolding,[],[f59,f47,f53,f48]) ).
thf(f69,plain,
( $true
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: mindex,Y1: mworld > $o,Y2: mworld] :
( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y0 @ Y2 @ Y3 )
& ( Y1 @ Y3 ) ) )
@ '#make_c'
@ acid ) ) ),
inference(definition_unfolding,[],[f60,f47,f54]) ).
thf(f70,plain,
( $true
!= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) )
@ ( ^ [Y0: mindex,Y1: mworld > $o,Y2: mworld] :
( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y0 @ Y2 @ Y3 )
& ( Y1 @ Y3 ) ) )
@ '#pour_a'
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ acid ) )
@ ( ^ [Y0: mindex,Y1: mworld > $o,Y2: mworld] :
( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y0 @ Y2 @ Y3 )
& ( Y1 @ Y3 ) ) )
@ '#pour_a'
@ ( ^ [Y0: mindex,Y1: mworld > $o,Y2: mworld] :
( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y0 @ Y2 @ Y3 )
& ( Y1 @ Y3 ) ) )
@ '#pour_b'
@ acid ) ) ) ) ),
inference(definition_unfolding,[],[f61,f47,f49,f54,f48,f54,f54]) ).
thf(f71,plain,
( $true
!= ( ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#pour_a' @ mactual @ Y0 )
& ~ ( acid @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#pour_a' @ mactual @ Y0 )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ '#pour_b' @ Y0 @ Y1 )
& ( acid @ Y1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f70]) ).
thf(f72,plain,
( ( $false
= ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#pour_a' @ mactual @ Y0 )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ '#pour_b' @ Y0 @ Y1 )
& ( acid @ Y1 ) ) ) ) ) )
| ( $false
= ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#pour_a' @ mactual @ Y0 )
& ~ ( acid @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f71]) ).
thf(f73,plain,
! [X1: mworld] :
( ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ '#pour_a' @ mactual @ Y0 )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ '#pour_b' @ Y0 @ Y1 )
& ( acid @ Y1 ) ) ) )
@ X1 ) )
| ( $false
= ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#pour_a' @ mactual @ Y0 )
& ~ ( acid @ Y0 ) ) ) ) ),
inference(pi_proxy_clausification,[],[f72]) ).
thf(f74,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ '#pour_a' @ mactual @ Y0 )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ '#pour_b' @ Y0 @ Y1 )
& ( acid @ Y1 ) ) ) )
@ X1 ) )
| ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ '#pour_a' @ mactual @ Y0 )
& ~ ( acid @ Y0 ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f73]) ).
thf(f75,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( ( mrel @ '#pour_a' @ mactual @ X1 )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#pour_b' @ X1 @ Y0 )
& ( acid @ Y0 ) ) ) ) )
| ( $false
= ( ( mrel @ '#pour_a' @ mactual @ X2 )
& ~ ( acid @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f74]) ).
thf(f76,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#pour_b' @ X1 @ Y0 )
& ( acid @ Y0 ) ) ) )
| ( $false
= ( ( mrel @ '#pour_a' @ mactual @ X2 )
& ~ ( acid @ X2 ) ) )
| ( $false
= ( mrel @ '#pour_a' @ mactual @ X1 ) ) ),
inference(and_proxy_clausification,[],[f75]) ).
thf(f77,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ '#pour_b' @ X1 @ Y0 )
& ( acid @ Y0 ) )
@ X3 ) )
| ( $false
= ( ( mrel @ '#pour_a' @ mactual @ X2 )
& ~ ( acid @ X2 ) ) )
| ( $false
= ( mrel @ '#pour_a' @ mactual @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f76]) ).
thf(f78,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ '#pour_b' @ X1 @ Y0 )
& ( acid @ Y0 ) )
@ X3 ) )
| ( $false
= ( ~ ( acid @ X2 ) ) )
| ( $false
= ( mrel @ '#pour_a' @ mactual @ X1 ) )
| ( $false
= ( mrel @ '#pour_a' @ mactual @ X2 ) ) ),
inference(and_proxy_clausification,[],[f77]) ).
thf(f79,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ '#pour_b' @ X1 @ Y0 )
& ( acid @ Y0 ) )
@ X3 ) )
| ( $true
= ( acid @ X2 ) )
| ( $false
= ( mrel @ '#pour_a' @ mactual @ X1 ) )
| ( $false
= ( mrel @ '#pour_a' @ mactual @ X2 ) ) ),
inference(not_proxy_clausification,[],[f78]) ).
thf(f80,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( ( mrel @ '#pour_b' @ X1 @ X3 )
& ( acid @ X3 ) ) )
| ( $true
= ( acid @ X2 ) )
| ( $false
= ( mrel @ '#pour_a' @ mactual @ X1 ) )
| ( $false
= ( mrel @ '#pour_a' @ mactual @ X2 ) ) ),
inference(beta-eta_normalization,[],[f79]) ).
thf(f81,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( acid @ X3 ) )
| ( $true
= ( acid @ X2 ) )
| ( $false
= ( mrel @ '#pour_a' @ mactual @ X1 ) )
| ( $false
= ( mrel @ '#pour_a' @ mactual @ X2 ) )
| ( $false
= ( mrel @ '#pour_b' @ X1 @ X3 ) ) ),
inference(and_proxy_clausification,[],[f80]) ).
thf(f82,plain,
( $true
= ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#make_c' @ mactual @ Y0 )
& ( acid @ Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f69]) ).
thf(f83,plain,
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ '#make_c' @ mactual @ Y0 )
& ( acid @ Y0 ) )
@ sK0 ) ),
inference(sigma_proxy_clausification,[],[f82]) ).
thf(f84,plain,
( $true
= ( ( mrel @ '#make_c' @ mactual @ sK0 )
& ( acid @ sK0 ) ) ),
inference(beta-eta_normalization,[],[f83]) ).
thf(f85,plain,
( $true
= ( acid @ sK0 ) ),
inference(and_proxy_clausification,[],[f84]) ).
thf(f86,plain,
( $true
= ( mrel @ '#make_c' @ mactual @ sK0 ) ),
inference(and_proxy_clausification,[],[f84]) ).
thf(f87,plain,
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#pour_a' @ mactual @ Y0 )
=> ~ ( acid @ Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f68]) ).
thf(f88,plain,
! [X1: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ '#pour_a' @ mactual @ Y0 )
=> ~ ( acid @ Y0 ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f87]) ).
thf(f89,plain,
! [X1: mworld] :
( $true
= ( ( mrel @ '#pour_a' @ mactual @ X1 )
=> ~ ( acid @ X1 ) ) ),
inference(beta-eta_normalization,[],[f88]) ).
thf(f90,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ '#pour_a' @ mactual @ X1 ) )
| ( $true
= ( ~ ( acid @ X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f89]) ).
thf(f91,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ '#pour_a' @ mactual @ X1 ) )
| ( $false
= ( acid @ X1 ) ) ),
inference(not_proxy_clausification,[],[f90]) ).
thf(f121,plain,
( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#pour_a' @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ '#pour_b' @ Y0 @ Y1 )
=> ~ ( acid @ Y1 ) ) ) ) )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#make_c' @ mactual @ Y0 )
=> ~ ( acid @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f65]) ).
thf(f122,plain,
( ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#pour_a' @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ '#pour_b' @ Y0 @ Y1 )
=> ~ ( acid @ Y1 ) ) ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#make_c' @ mactual @ Y0 )
=> ~ ( acid @ Y0 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f121]) ).
thf(f123,plain,
( ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ '#pour_a' @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ '#pour_b' @ Y0 @ Y1 )
=> ~ ( acid @ Y1 ) ) ) )
@ sK5 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#make_c' @ mactual @ Y0 )
=> ~ ( acid @ Y0 ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f122]) ).
thf(f124,plain,
! [X1: mworld] :
( ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ '#pour_a' @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ '#pour_b' @ Y0 @ Y1 )
=> ~ ( acid @ Y1 ) ) ) )
@ sK5 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ '#make_c' @ mactual @ Y0 )
=> ~ ( acid @ Y0 ) )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f123]) ).
thf(f125,plain,
! [X1: mworld] :
( ( $false
= ( ( mrel @ '#pour_a' @ mactual @ sK5 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#pour_b' @ sK5 @ Y0 )
=> ~ ( acid @ Y0 ) ) ) ) )
| ( $true
= ( ( mrel @ '#make_c' @ mactual @ X1 )
=> ~ ( acid @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f124]) ).
thf(f126,plain,
! [X1: mworld] :
( ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#pour_b' @ sK5 @ Y0 )
=> ~ ( acid @ Y0 ) ) ) )
| ( $true
= ( ( mrel @ '#make_c' @ mactual @ X1 )
=> ~ ( acid @ X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f125]) ).
thf(f127,plain,
! [X1: mworld] :
( ( $true
= ( mrel @ '#pour_a' @ mactual @ sK5 ) )
| ( $true
= ( ( mrel @ '#make_c' @ mactual @ X1 )
=> ~ ( acid @ X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f125]) ).
thf(f128,plain,
! [X1: mworld] :
( ( $true
= ( mrel @ '#pour_a' @ mactual @ sK5 ) )
| ( $false
= ( mrel @ '#make_c' @ mactual @ X1 ) )
| ( $true
= ( ~ ( acid @ X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f127]) ).
thf(f129,plain,
! [X1: mworld] :
( ( $true
= ( mrel @ '#pour_a' @ mactual @ sK5 ) )
| ( $false
= ( mrel @ '#make_c' @ mactual @ X1 ) )
| ( $false
= ( acid @ X1 ) ) ),
inference(not_proxy_clausification,[],[f128]) ).
thf(f130,plain,
! [X1: mworld] :
( ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ '#pour_b' @ sK5 @ Y0 )
=> ~ ( acid @ Y0 ) )
@ sK6 ) )
| ( $true
= ( ( mrel @ '#make_c' @ mactual @ X1 )
=> ~ ( acid @ X1 ) ) ) ),
inference(sigma_proxy_clausification,[],[f126]) ).
thf(f131,plain,
! [X1: mworld] :
( ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ '#pour_b' @ sK5 @ Y0 )
=> ~ ( acid @ Y0 ) )
@ sK6 ) )
| ( $false
= ( mrel @ '#make_c' @ mactual @ X1 ) )
| ( $true
= ( ~ ( acid @ X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f130]) ).
thf(f132,plain,
! [X1: mworld] :
( ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ '#pour_b' @ sK5 @ Y0 )
=> ~ ( acid @ Y0 ) )
@ sK6 ) )
| ( $false
= ( mrel @ '#make_c' @ mactual @ X1 ) )
| ( $false
= ( acid @ X1 ) ) ),
inference(not_proxy_clausification,[],[f131]) ).
thf(f133,plain,
! [X1: mworld] :
( ( $false
= ( ( mrel @ '#pour_b' @ sK5 @ sK6 )
=> ~ ( acid @ sK6 ) ) )
| ( $false
= ( mrel @ '#make_c' @ mactual @ X1 ) )
| ( $false
= ( acid @ X1 ) ) ),
inference(beta-eta_normalization,[],[f132]) ).
thf(f134,plain,
! [X1: mworld] :
( ( $false
= ( ~ ( acid @ sK6 ) ) )
| ( $false
= ( mrel @ '#make_c' @ mactual @ X1 ) )
| ( $false
= ( acid @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f133]) ).
thf(f135,plain,
! [X1: mworld] :
( ( $true
= ( mrel @ '#pour_b' @ sK5 @ sK6 ) )
| ( $false
= ( mrel @ '#make_c' @ mactual @ X1 ) )
| ( $false
= ( acid @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f133]) ).
thf(f136,plain,
! [X1: mworld] :
( ( $true
= ( acid @ sK6 ) )
| ( $false
= ( mrel @ '#make_c' @ mactual @ X1 ) )
| ( $false
= ( acid @ X1 ) ) ),
inference(not_proxy_clausification,[],[f134]) ).
thf(f157,definition,
( spl9_3
<=> ! [X2: mworld] :
( ( $true
= ( acid @ X2 ) )
| ( $false
= ( mrel @ '#pour_a' @ mactual @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl9_3])],[avatar_definition]) ).
thf(f158,plain,
( ! [X2: mworld] :
( ( $false
= ( mrel @ '#pour_a' @ mactual @ X2 ) )
| ( $true
= ( acid @ X2 ) ) )
| ~ spl9_3 ),
inference(avatar_component_clause,[],[f157]) ).
thf(f166,definition,
( spl9_6
<=> ! [X1: mworld,X3: mworld] :
( ( $false
= ( acid @ X3 ) )
| ( $false
= ( mrel @ '#pour_a' @ mactual @ X1 ) )
| ( $false
= ( mrel @ '#pour_b' @ X1 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl9_6])],[avatar_definition]) ).
thf(f167,plain,
( ! [X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ '#pour_b' @ X1 @ X3 ) )
| ( $false
= ( mrel @ '#pour_a' @ mactual @ X1 ) )
| ( $false
= ( acid @ X3 ) ) )
| ~ spl9_6 ),
inference(avatar_component_clause,[],[f166]) ).
thf(f168,plain,
( spl9_3
| spl9_6 ),
inference(avatar_split_clause,[],[f81,f166,f157]) ).
thf(f266,definition,
( spl9_11
<=> ! [X1: mworld] :
( ( $false
= ( mrel @ '#make_c' @ mactual @ X1 ) )
| ( $false
= ( acid @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl9_11])],[avatar_definition]) ).
thf(f267,plain,
( ! [X1: mworld] :
( ( $false
= ( mrel @ '#make_c' @ mactual @ X1 ) )
| ( $false
= ( acid @ X1 ) ) )
| ~ spl9_11 ),
inference(avatar_component_clause,[],[f266]) ).
thf(f285,plain,
( ( $true = $false )
| ( $false
= ( acid @ sK0 ) )
| ~ spl9_11 ),
inference(constrained_superposition,[],[f86,f267]) ).
thf(f286,plain,
( ( $false
= ( acid @ sK0 ) )
| ~ spl9_11 ),
inference(trivial_inequality_removal,[],[f285]) ).
thf(f290,plain,
( ( $true = $false )
| ~ spl9_11 ),
inference(constrained_superposition,[],[f286,f85]) ).
thf(f294,plain,
( $false
| ~ spl9_11 ),
inference(trivial_inequality_removal,[],[f290]) ).
thf(f295,plain,
~ spl9_11,
inference(avatar_contradiction_clause,[],[f294]) ).
thf(f312,definition,
( spl9_15
<=> ( $true
= ( acid @ sK6 ) ) ),
introduced(definition,[new_symbols(definition,[spl9_15])],[avatar_definition]) ).
thf(f314,plain,
( ( $true
= ( acid @ sK6 ) )
| ~ spl9_15 ),
inference(avatar_component_clause,[],[f312]) ).
thf(f315,plain,
( spl9_11
| spl9_15 ),
inference(avatar_split_clause,[],[f136,f312,f266]) ).
thf(f320,definition,
( spl9_16
<=> ( $true
= ( mrel @ '#pour_a' @ mactual @ sK5 ) ) ),
introduced(definition,[new_symbols(definition,[spl9_16])],[avatar_definition]) ).
thf(f322,plain,
( ( $true
= ( mrel @ '#pour_a' @ mactual @ sK5 ) )
| ~ spl9_16 ),
inference(avatar_component_clause,[],[f320]) ).
thf(f323,plain,
( spl9_11
| spl9_16 ),
inference(avatar_split_clause,[],[f129,f320,f266]) ).
thf(f326,plain,
( ( $true = $false )
| ( $false
= ( acid @ sK5 ) )
| ~ spl9_16 ),
inference(constrained_superposition,[],[f91,f322]) ).
thf(f327,plain,
( ( $true = $false )
| ( $true
= ( acid @ sK5 ) )
| ~ spl9_3
| ~ spl9_16 ),
inference(constrained_superposition,[],[f158,f322]) ).
thf(f328,plain,
( ( $true
= ( acid @ sK5 ) )
| ~ spl9_3
| ~ spl9_16 ),
inference(trivial_inequality_removal,[],[f327]) ).
thf(f329,plain,
( ( $false
= ( acid @ sK5 ) )
| ~ spl9_16 ),
inference(trivial_inequality_removal,[],[f326]) ).
thf(f333,plain,
( ( $true = $false )
| ~ spl9_3
| ~ spl9_16 ),
inference(constrained_superposition,[],[f329,f328]) ).
thf(f337,plain,
( $false
| ~ spl9_3
| ~ spl9_16 ),
inference(trivial_inequality_removal,[],[f333]) ).
thf(f338,plain,
( ~ spl9_3
| ~ spl9_16 ),
inference(avatar_contradiction_clause,[],[f337]) ).
thf(f363,definition,
( spl9_20
<=> ( $true
= ( mrel @ '#pour_b' @ sK5 @ sK6 ) ) ),
introduced(definition,[new_symbols(definition,[spl9_20])],[avatar_definition]) ).
thf(f365,plain,
( ( $true
= ( mrel @ '#pour_b' @ sK5 @ sK6 ) )
| ~ spl9_20 ),
inference(avatar_component_clause,[],[f363]) ).
thf(f366,plain,
( spl9_11
| spl9_20 ),
inference(avatar_split_clause,[],[f135,f363,f266]) ).
thf(f368,plain,
( ( $true = $false )
| ( $false
= ( mrel @ '#pour_a' @ mactual @ sK5 ) )
| ( $false
= ( acid @ sK6 ) )
| ~ spl9_6
| ~ spl9_20 ),
inference(constrained_superposition,[],[f167,f365]) ).
thf(f369,plain,
( ( $false
= ( mrel @ '#pour_a' @ mactual @ sK5 ) )
| ( $false
= ( acid @ sK6 ) )
| ~ spl9_6
| ~ spl9_20 ),
inference(trivial_inequality_removal,[],[f368]) ).
thf(f371,plain,
( ( $true = $false )
| ( $false
= ( acid @ sK6 ) )
| ~ spl9_6
| ~ spl9_16
| ~ spl9_20 ),
inference(forward_demodulation,[],[f369,f322]) ).
thf(f372,plain,
( ( $false
= ( acid @ sK6 ) )
| ~ spl9_6
| ~ spl9_16
| ~ spl9_20 ),
inference(trivial_inequality_removal,[],[f371]) ).
thf(f376,plain,
( ( $true = $false )
| ~ spl9_6
| ~ spl9_15
| ~ spl9_16
| ~ spl9_20 ),
inference(constrained_superposition,[],[f372,f314]) ).
thf(f380,plain,
( $false
| ~ spl9_6
| ~ spl9_15
| ~ spl9_16
| ~ spl9_20 ),
inference(trivial_inequality_removal,[],[f376]) ).
thf(f381,plain,
( ~ spl9_6
| ~ spl9_15
| ~ spl9_16
| ~ spl9_20 ),
inference(avatar_contradiction_clause,[],[f380]) ).
cnf(s21,plain,
( spl9_3
| spl9_6 ),
inference(sat_conversion,[],[f168]) ).
cnf(s90,plain,
~ spl9_11,
inference(sat_conversion,[],[f295]) ).
cnf(s98,plain,
( spl9_11
| spl9_15 ),
inference(sat_conversion,[],[f315]) ).
cnf(s106,plain,
( spl9_11
| spl9_16 ),
inference(sat_conversion,[],[f323]) ).
cnf(s116,plain,
( ~ spl9_3
| ~ spl9_16 ),
inference(sat_conversion,[],[f338]) ).
cnf(s130,plain,
( spl9_11
| spl9_20 ),
inference(sat_conversion,[],[f366]) ).
cnf(s137,plain,
( ~ spl9_6
| ~ spl9_15
| ~ spl9_16
| ~ spl9_20 ),
inference(sat_conversion,[],[f381]) ).
cnf(s138,plain,
spl9_20,
inference(rat,[],[s130,s90]) ).
cnf(s140,plain,
spl9_16,
inference(rat,[],[s106,s90]) ).
cnf(s142,plain,
spl9_15,
inference(rat,[],[s98,s90]) ).
cnf(s143,plain,
~ spl9_3,
inference(rat,[],[s116,s140]) ).
cnf(s144,plain,
~ spl9_6,
inference(rat,[],[s137,s138,s140,s142]) ).
cnf(s147,plain,
$false,
inference(rat,[],[s21,s144,s143]) ).
thf(f383,plain,
$false,
inference(avatar_sat_refutation,[],[s147]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PUZ149^13 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.19 % Computer : n026.cluster.edu
% 0.11/0.19 % Model : x86_64 x86_64
% 0.11/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.19 % Memory : 8046.5625MB
% 0.11/0.19 % OS : Linux 6.8.0-71-generic
% 0.11/0.19 % CPULimit : 300
% 0.11/0.19 % WCLimit : 300
% 0.11/0.19 % DateTime : Tue Sep 29 13:30:27 UTC 2026
% 0.11/0.19 % CPUTime :
% 0.11/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.22 Running first-order model finding
% 0.11/0.22 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.28 % (583518)Will run a generic schedule for satisfiability detection.
% 0.11/0.28 % (583537)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=905581635:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.11/0.28 % (583536)% WARNING: option uhcvi not known.
% 0.11/0.28 % (583537) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-583518-583537"...
% 0.11/0.28 % (583536)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1423607884:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.11/0.28 % (583535)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3782888114_2999 on theBenchmark for (2999ds/0Mi)
% 0.11/0.28 % (583538)dis+10_1_sil=32000:sp=arity:random_seed=3855219888:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.11/0.28 % (583539)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=4054157644:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.11/0.28 % (583540)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1058450527:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.11/0.28 % (583542)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3235977067:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.11/0.28 % (583536)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.11/0.28 % (583537)...printing done.
% 0.11/0.28 % (583539)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.11/0.28 % (583536)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.11/0.28 % Exception at run slice level
% 0.11/0.28 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.11/0.28 % (583537)Refutation found. Thanks to Tanya!
% 0.11/0.28 % SZS status Theorem for theBenchmark
% 0.11/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.28 % (583537)------------------------------
% 0.20/0.28 % (583537)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.28 % (583537)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.28 % (583537)CaDiCaL version: 2.1.3
% 0.20/0.28 % (583537)Termination reason: Refutation
% 0.20/0.28 % (583537)Time elapsed: 0.009 s
% 0.20/0.28 % (583537)Peak memory usage: 13 MB
% 0.20/0.28 % (583537)Instructions burned: 26 (million)
% 0.20/0.28 % (583518)Success in time 0.049 s
% 0.20/0.28 % Vampire exiting
%------------------------------------------------------------------------------