%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : PHI008^4 : TPTP v9.2.1. Released v6.4.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 09:27:41 AM UTC 2026
% Result : Theorem 0.15s 0.97s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 8
% Syntax : Number of formulae : 52 ( 22 unt; 0 typ; 0 def)
% Number of atoms : 210 ( 69 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 286 ( 38 ~; 20 |; 4 &; 202 @)
% ( 0 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 69 ( 69 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 14 usr; 5 con; 0-4 aty)
% ( 4 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 135 ( 42 ^; 80 !; 13 ?; 135 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
qML_mu: $tType ).
thf(type_def_6,type,
qML_i: $tType ).
thf(func_def_0,type,
qML_mu: $tType ).
thf(func_def_1,type,
qML_i: $tType ).
thf(func_def_2,type,
scott_G: qML_mu > qML_i > $o ).
thf(func_def_3,type,
scott_NE_QML_mu: qML_mu > qML_i > $o ).
thf(func_def_4,type,
scott_P: ( qML_mu > qML_i > $o ) > qML_i > $o ).
thf(func_def_5,type,
scott_ess_QML_mu: ( qML_mu > qML_i > $o ) > qML_mu > qML_i > $o ).
thf(func_def_19,type,
sK0: qML_i ).
thf(func_def_20,type,
sK1: qML_i > $o ).
thf(func_def_21,type,
sK2: qML_i ).
thf(func_def_22,type,
sK3: ( qML_mu > qML_i > $o ) > ( qML_mu > qML_i > $o ) > qML_mu ).
thf(func_def_23,type,
sK4: ( qML_mu > qML_i > $o ) > ( qML_mu > qML_i > $o ) > qML_i ).
thf(func_def_24,type,
sK5: qML_i > qML_mu ).
thf(func_def_27,type,
sK7: qML_i > qML_mu > qML_mu > qML_i > $o ).
thf(func_def_28,type,
sK8: qML_mu > qML_i > qML_mu > qML_i > $o ).
thf(func_def_29,type,
sK9: qML_mu > qML_i > qML_mu > qML_i > $o ).
thf(func_def_62,type,
ph10:
!>[X0: $tType] : X0 ).
thf(f229,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f222]) ).
thf(f222,plain,
$false = $true,
inference(superposition,[status(thm)],[f219,f57]) ).
thf(f57,plain,
( ( sK1 @ sK0 )
= $true ),
inference(cnf_transformation,[status(thm)],[f52]) ).
thf(f52,plain,
( ( ( sK1 @ sK2 )
!= $true )
& ( ( sK1 @ sK0 )
= $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f49,f51,f50]) ).
thf(f50,plain,
( ? [X0: qML_i,X1: qML_i > $o] :
( ? [X2: qML_i] :
( ( X1 @ X2 )
!= $true )
& ( ( X1 @ X0 )
= $true ) )
=> ( ? [X2: qML_i] :
( ( sK1 @ X2 )
!= $true )
& ( ( sK1 @ sK0 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f51,plain,
( ? [X2: qML_i] :
( ( sK1 @ X2 )
!= $true )
=> ( ( sK1 @ sK2 )
!= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f49,plain,
? [X0: qML_i,X1: qML_i > $o] :
( ? [X2: qML_i] :
( ( X1 @ X2 )
!= $true )
& ( ( X1 @ X0 )
= $true ) ),
inference(ennf_transformation,[status(thm)],[f39]) ).
thf(f39,plain,
~ ! [X0: qML_i,X1: qML_i > $o] :
( ! [X2: qML_i] :
( ( X1 @ X2 )
= $true )
| ( ( X1 @ X0 )
!= $true ) ),
inference(flattening,[status(thm)],[f16]) ).
thf(f16,plain,
~ ! [X0: qML_i,X1: qML_i > $o] :
( ( ( X1 @ X0 )
!= $true )
| ! [X2: qML_i] :
( ( X1 @ X2 )
= $true ) ),
inference(fool_elimination,[status(thm)],[f15]) ).
thf(f15,plain,
~ ! [X0: qML_i,X1: qML_i > $o] :
( ~ ( X1 @ X0 )
| ! [X2: qML_i] : ( X1 @ X2 ) ),
inference(rectify,[status(thm)],[f13]) ).
thf(f13,negated_conjecture,
~ ! [X14: qML_i,X7: qML_i > $o] :
( ~ ( X7 @ X14 )
| ! [X12: qML_i] : ( X7 @ X12 ) ),
inference(negated_conjecture,[status(cth)],[f12]) ).
thf(f12,conjecture,
! [X14: qML_i,X7: qML_i > $o] :
( ~ ( X7 @ X14 )
| ! [X12: qML_i] : ( X7 @ X12 ) ),
file('/export/starexec/sandbox2/tmp/tmp.YSDwy2w41Y/DTF2THF_30192.p',conj_0) ).
thf(f219,plain,
! [X0: qML_i] :
( ( sK1 @ X0 )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f218]) ).
thf(f218,plain,
! [X0: qML_i] :
( ( ^ [Y0: qML_mu] : sK1
@ ( sK5 @ X0 )
@ X0 )
= $false ),
inference(trivial_inequality_removal,[status(thm)],[f208]) ).
thf(f208,plain,
! [X0: qML_i] :
( ( ( ^ [Y0: qML_mu] : sK1
@ ( sK5 @ X0 )
@ X0 )
= $false )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f124,f165]) ).
thf(f165,plain,
! [X0: qML_mu > qML_i > $o,X1: qML_i] :
( ( ( scott_P @ X0 @ X1 )
= $true )
| ( ( X0 @ ( sK5 @ X1 ) @ X1 )
= $false ) ),
inference(not_proxy_clausification,[status(thm)],[f164]) ).
thf(f164,plain,
! [X0: qML_mu > qML_i > $o,X1: qML_i] :
( ( ( scott_P @ X0 @ X1 )
= $true )
| ( ( ~ ( X0 @ ( sK5 @ X1 ) @ X1 ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f163]) ).
thf(f163,plain,
! [X0: qML_mu > qML_i > $o,X1: qML_i] :
( ( ( ^ [Y0: qML_mu,Y1: qML_i] :
~ ( X0 @ Y0 @ Y1 )
@ ( sK5 @ X1 )
@ X1 )
= $true )
| ( ( scott_P @ X0 @ X1 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f153]) ).
thf(f153,plain,
! [X0: qML_mu > qML_i > $o,X1: qML_i] :
( ( ( ^ [Y0: qML_mu,Y1: qML_i] :
~ ( X0 @ Y0 @ Y1 )
@ ( sK5 @ X1 )
@ X1 )
= $true )
| ( ( scott_P @ X0 @ X1 )
= $true )
| ( $false = $true ) ),
inference(superposition,[status(thm)],[f108,f61]) ).
thf(f61,plain,
! [X0: qML_mu > qML_i > $o,X1: qML_i] :
( ( ( scott_P
@ ^ [Y0: qML_mu,Y1: qML_i] :
~ ( X0 @ Y0 @ Y1 )
@ X1 )
= $true )
| ( ( scott_P @ X0 @ X1 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f47]) ).
thf(f47,plain,
! [X0: qML_mu > qML_i > $o,X1: qML_i] :
( ( ( scott_P @ X0 @ X1 )
= $true )
| ( ( scott_P
@ ^ [Y0: qML_mu,Y1: qML_i] :
~ ( X0 @ Y0 @ Y1 )
@ X1 )
= $true ) ),
inference(ennf_transformation,[status(thm)],[f41]) ).
thf(f41,plain,
! [X0: qML_mu > qML_i > $o,X1: qML_i] :
( ( ( scott_P @ X0 @ X1 )
!= $true )
=> ( ( scott_P
@ ^ [Y0: qML_mu,Y1: qML_i] :
~ ( X0 @ Y0 @ Y1 )
@ X1 )
= $true ) ),
inference(flattening,[status(thm)],[f26]) ).
thf(f26,plain,
! [X0: qML_mu > qML_i > $o,X1: qML_i] :
( ( ( scott_P @ X0 @ X1 )
!= $true )
=> ( ( scott_P
@ ^ [Y0: qML_mu,Y1: qML_i] :
~ ( X0 @ Y0 @ Y1 )
@ X1 )
= $true ) ),
inference(fool_elimination,[status(thm)],[f25]) ).
thf(f25,plain,
! [X0: qML_mu > qML_i > $o,X1: qML_i] :
( ~ ( scott_P @ X0 @ X1 )
=> ( scott_P
@ ^ [X2: qML_mu,X3: qML_i] :
~ ( X0 @ X2 @ X3 )
@ X1 ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,axiom,
! [X4: qML_mu > qML_i > $o,X3: qML_i] :
( ~ ( scott_P @ X4 @ X3 )
=> ( scott_P
@ ^ [X2: qML_mu,X10: qML_i] :
~ ( X4 @ X2 @ X10 )
@ X3 ) ),
file('/export/starexec/sandbox2/tmp/tmp.YSDwy2w41Y/DTF2THF_30192.p',fact_6_A1b) ).
thf(f108,plain,
! [X0: qML_i,X1: qML_mu > qML_i > $o] :
( ( ( scott_P @ X1 @ X0 )
= $false )
| ( ( X1 @ ( sK5 @ X0 ) @ X0 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f107]) ).
thf(f107,plain,
! [X0: qML_i,X1: qML_mu > qML_i > $o] :
( ( ( scott_P @ X1 @ X0 )
=> ( X1 @ ( sK5 @ X0 ) @ X0 ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f106]) ).
thf(f106,plain,
! [X0: qML_i,X1: qML_mu > qML_i > $o] :
( ( ^ [Y0: qML_mu > qML_i > $o] :
( ( scott_P @ Y0 @ X0 )
=> ( Y0 @ ( sK5 @ X0 ) @ X0 ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f105]) ).
thf(f105,plain,
! [X0: qML_i] :
( ( !! @ ( qML_mu > qML_i > $o )
@ ^ [Y0: qML_mu > qML_i > $o] :
( ( scott_P @ Y0 @ X0 )
=> ( Y0 @ ( sK5 @ X0 ) @ X0 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f75]) ).
thf(f75,plain,
! [X0: qML_i] :
( ( ^ [Y0: qML_mu,Y1: qML_i] :
( !! @ ( qML_mu > qML_i > $o )
@ ^ [Y2: qML_mu > qML_i > $o] :
( ( scott_P @ Y2 @ Y1 )
=> ( Y2 @ Y0 @ Y1 ) ) )
@ ( sK5 @ X0 )
@ X0 )
= $true ),
inference(definition_unfolding,[status(thm)],[f70,f67]) ).
thf(f67,plain,
( scott_G
= ( ^ [Y0: qML_mu,Y1: qML_i] :
( !! @ ( qML_mu > qML_i > $o )
@ ^ [Y2: qML_mu > qML_i > $o] :
( ( scott_P @ Y2 @ Y1 )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
thf(f24,plain,
( scott_G
= ( ^ [Y0: qML_mu,Y1: qML_i] :
( !! @ ( qML_mu > qML_i > $o )
@ ^ [Y2: qML_mu > qML_i > $o] :
( ( scott_P @ Y2 @ Y1 )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f23]) ).
thf(f23,plain,
( scott_G
= ( ^ [X0: qML_mu,X1: qML_i] :
! [X2: qML_mu > qML_i > $o] :
( ( scott_P @ X2 @ X1 )
=> ( X2 @ X0 @ X1 ) ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( scott_G
= ( ^ [X0: qML_mu,X1: qML_i] :
! [X2: qML_mu > qML_i > $o] :
( ( scott_P @ X2 @ X1 )
=> ( X2 @ X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.YSDwy2w41Y/DTF2THF_30192.p',fact_0_G__def) ).
thf(f70,plain,
! [X0: qML_i] :
( ( scott_G @ ( sK5 @ X0 ) @ X0 )
= $true ),
inference(cnf_transformation,[status(thm)],[f56]) ).
thf(f56,plain,
! [X0: qML_i] :
( ( scott_G @ ( sK5 @ X0 ) @ X0 )
= $true ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f42,f55]) ).
thf(f55,plain,
! [X0: qML_i] :
( ? [X1: qML_mu] :
( ( scott_G @ X1 @ X0 )
= $true )
=> ( ( scott_G @ ( sK5 @ X0 ) @ X0 )
= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f42,plain,
! [X0: qML_i] :
? [X1: qML_mu] :
( ( scott_G @ X1 @ X0 )
= $true ),
inference(rectify,[status(thm)],[f34]) ).
thf(f34,plain,
! [X1: qML_i] :
? [X2: qML_mu] :
( ( scott_G @ X2 @ X1 )
= $true ),
inference(fool_elimination,[status(thm)],[f33]) ).
thf(f33,plain,
! [X1: qML_i] :
? [X2: qML_mu] : ( scott_G @ X2 @ X1 ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
! [X3: qML_i,X6: qML_i] :
? [X7: qML_mu] : ( scott_G @ X7 @ X6 ),
file('/export/starexec/sandbox2/tmp/tmp.YSDwy2w41Y/DTF2THF_30192.p',fact_2_T3) ).
thf(f124,plain,
! [X0: qML_i] :
( ( scott_P
@ ^ [Y0: qML_mu] : sK1
@ X0 )
!= $true ),
inference(beta_eta_normalization,[status(thm)],[f123]) ).
thf(f123,plain,
! [X0: qML_i] :
( ( scott_P
@ ^ [Y0: qML_mu,Y1: qML_i] :
( sK1
@ ( ^ [Y2: qML_mu,Y3: qML_i] : Y3
@ Y0
@ Y1 ) )
@ X0 )
!= $true ),
inference(trivial_inequality_removal,[status(thm)],[f119]) ).
thf(f119,plain,
! [X0: qML_i] :
( ( ( scott_P
@ ^ [Y0: qML_mu,Y1: qML_i] :
( sK1
@ ( ^ [Y2: qML_mu,Y3: qML_i] : Y3
@ Y0
@ Y1 ) )
@ X0 )
!= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f58,f114]) ).
thf(f114,plain,
! [X2: qML_i,X0: qML_mu > qML_i > $o,X1: qML_i] :
( ( ( X0 @ ( sK5 @ X1 ) @ X1 )
= $true )
| ( ( scott_P @ X0 @ X2 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f110]) ).
thf(f110,plain,
! [X2: qML_i,X0: qML_mu > qML_i > $o,X1: qML_i] :
( ( $false = $true )
| ( ( X0 @ ( sK5 @ X1 ) @ X1 )
= $true )
| ( ( scott_P @ X0 @ X2 )
!= $true ) ),
inference(superposition,[status(thm)],[f66,f108]) ).
thf(f66,plain,
! [X2: qML_i,X0: qML_mu > qML_i > $o,X1: qML_i] :
( ( ( scott_P @ X0 @ X2 )
= $true )
| ( ( scott_P @ X0 @ X1 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f46]) ).
thf(f46,plain,
! [X0: qML_mu > qML_i > $o,X1: qML_i] :
( ! [X2: qML_i] :
( ( scott_P @ X0 @ X2 )
= $true )
| ( ( scott_P @ X0 @ X1 )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f22]) ).
thf(f22,plain,
! [X0: qML_mu > qML_i > $o,X1: qML_i] :
( ( ( scott_P @ X0 @ X1 )
= $true )
=> ! [X2: qML_i] :
( ( scott_P @ X0 @ X2 )
= $true ) ),
inference(fool_elimination,[status(thm)],[f21]) ).
thf(f21,plain,
! [X0: qML_mu > qML_i > $o,X1: qML_i] :
( ( scott_P @ X0 @ X1 )
=> ! [X2: qML_i] : ( scott_P @ X0 @ X2 ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X4: qML_mu > qML_i > $o,X3: qML_i] :
( ( scott_P @ X4 @ X3 )
=> ! [X5: qML_i] : ( scott_P @ X4 @ X5 ) ),
file('/export/starexec/sandbox2/tmp/tmp.YSDwy2w41Y/DTF2THF_30192.p',fact_1_A4) ).
thf(f58,plain,
( ( sK1 @ sK2 )
!= $true ),
inference(cnf_transformation,[status(thm)],[f52]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : PHI008^4 : TPTP v9.2.1. Released v6.4.0.
% 0.00/0.06 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.07/0.25 % Computer : n012.cluster.edu
% 0.07/0.25 % Model : x86_64 x86_64
% 0.07/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.25 % Memory : 8042.1875MB
% 0.07/0.25 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.25 % CPULimit : 300
% 0.07/0.25 % WCLimit : 300
% 0.07/0.25 % DateTime : Tue Feb 24 11:25:00 EST 2026
% 0.07/0.25 % CPUTime :
% 0.07/0.25 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.07/0.31 ---- Original DTF file ---
% 0.07/0.31 thf(spec,logic,$$dhol).
% 0.07/0.31 %------------------------------------------------------------------------------
% 0.07/0.31 % File : PHI008^4 : TPTP v9.2.1. Released v6.4.0.
% 0.07/0.31 % Domain : Philosophy
% 0.07/0.31 % Problem : Modal Collapse of Goedel's ontological argument in Scott's variant
% 0.07/0.31 % Version : [Ben16] axioms : Biased.
% 0.07/0.31 % English :
% 0.07/0.31
% 0.07/0.31 % Refs : [Ben16] Benzmueller (2016), Email to Geoff Sutcliffe
% 0.07/0.31 % Source : [Ben16]
% 0.07/0.31 % Names : Sledgehammer_MC_S5U_direct_satallax.p [Ben16]
% 0.07/0.31
% 0.07/0.31 % Status : Theorem
% 0.07/0.31 % Rating : 0.44 v9.1.0, 0.38 v9.0.0, 0.40 v8.2.0, 0.62 v8.1.0, 0.55 v7.5.0, 0.29 v7.4.0, 0.67 v7.2.0, 0.62 v7.0.0, 0.57 v6.4.0
% 0.07/0.31 % Syntax : Number of formulae : 18 ( 4 unt; 6 typ; 0 def)
% 0.07/0.31 % Number of atoms : 24 ( 3 equ; 0 cnn)
% 0.07/0.31 % Maximal formula atoms : 3 ( 2 avg)
% 0.07/0.31 % Number of connectives : 72 ( 5 ~; 1 |; 2 &; 54 @)
% 0.07/0.31 % ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% 0.07/0.31 % Maximal formula depth : 11 ( 6 avg)
% 0.07/0.31 % Number of types : 3 ( 2 usr)
% 0.07/0.31 % Number of type conns : 32 ( 32 >; 0 *; 0 +; 0 <<)
% 0.07/0.31 % Number of symbols : 5 ( 4 usr; 0 con; 2-3 aty)
% 0.07/0.31 % Number of variables : 40 ( 11 ^; 27 !; 2 ?; 40 :)
% 0.07/0.31 % SPC : TH0_THM_EQU_NAR
% 0.07/0.31
% 0.07/0.31 % Comments : This problem file has been generated by Sledgehammer (satallax
% 0.07/0.31 % translation) in default setting.
% 0.07/0.31 %------------------------------------------------------------------------------
% 0.07/0.31 %----Could-be-implicit typings (2)
% 0.07/0.31 thf(ty_n_t__QML____S5U__O__092__060mu__062,type,
% 0.07/0.31 qML_mu: $tType ).
% 0.07/0.31
% 0.07/0.31 thf(ty_n_t__QML____S5U__Oi,type,
% 0.07/0.31 qML_i: $tType ).
% 0.07/0.31
% 0.07/0.31 %----Explicit typings (4)
% 0.07/0.31 thf(sy_c_Scott__S5U_OG,type,
% 0.07/0.31 scott_G: qML_mu > qML_i > $o ).
% 0.07/0.31
% 0.07/0.31 thf(sy_c_Scott__S5U_ONE_001t__QML____S5U__O__092__060mu__062,type,
% 0.07/0.31 scott_NE_QML_mu: qML_mu > qML_i > $o ).
% 0.07/0.31
% 0.07/0.31 thf(sy_c_Scott__S5U_OP,type,
% 0.07/0.31 scott_P: ( qML_mu > qML_i > $o ) > qML_i > $o ).
% 0.07/0.31
% 0.07/0.31 thf(sy_c_Scott__S5U_Oess_001t__QML____S5U__O__092__060mu__062,type,
% 0.07/0.31 scott_ess_QML_mu: ( qML_mu > qML_i > $o ) > qML_mu > qML_i > $o ).
% 0.07/0.31
% 0.07/0.31 %----Relevant facts (11)
% 0.07/0.31 thf(fact_0_G__def,axiom,
% 0.07/0.31 ( scott_G
% 0.07/0.31 = ( ^ [X: qML_mu,W: qML_i] :
% 0.07/0.31 ! [Y: qML_mu > qML_i > $o] :
% 0.07/0.31 ( ( scott_P @ Y @ W )
% 0.07/0.31 => ( Y @ X @ W ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % G_def
% 0.07/0.31 thf(fact_1_A4,axiom,
% 0.07/0.31 ! [W2: qML_i,X2: qML_mu > qML_i > $o] :
% 0.07/0.31 ( ( scott_P @ X2 @ W2 )
% 0.07/0.31 => ! [X_1: qML_i] : ( scott_P @ X2 @ X_1 ) ) ).
% 0.07/0.31
% 0.07/0.31 % A4
% 0.07/0.31 thf(fact_2_T3,axiom,
% 0.07/0.31 ! [W2: qML_i,V: qML_i] :
% 0.07/0.31 ? [X3: qML_mu] : ( scott_G @ X3 @ V ) ).
% 0.07/0.31
% 0.07/0.31 % T3
% 0.07/0.31 thf(fact_3_A3,axiom,
% 0.07/0.31 ! [X_1: qML_i] : ( scott_P @ scott_G @ X_1 ) ).
% 0.07/0.31
% 0.07/0.31 % A3
% 0.07/0.31 thf(fact_4_ess__def,axiom,
% 0.07/0.31 ( scott_ess_QML_mu
% 0.07/0.31 = ( ^ [Phi: qML_mu > qML_i > $o,X: qML_mu,W: qML_i] :
% 0.07/0.31 ( ( Phi @ X @ W )
% 0.07/0.31 & ! [Y: qML_mu > qML_i > $o] :
% 0.07/0.31 ( ( Y @ X @ W )
% 0.07/0.31 => ! [V2: qML_i,Z: qML_mu] :
% 0.07/0.31 ( ( Phi @ Z @ V2 )
% 0.07/0.31 => ( Y @ Z @ V2 ) ) ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % ess_def
% 0.07/0.31 thf(fact_5_A2,axiom,
% 0.07/0.31 ! [W2: qML_i,X2: qML_mu > qML_i > $o,Xa: qML_mu > qML_i > $o] :
% 0.07/0.31 ( ( ( scott_P @ X2 @ W2 )
% 0.07/0.31 & ! [V3: qML_i,Xb: qML_mu] :
% 0.07/0.31 ( ( X2 @ Xb @ V3 )
% 0.07/0.31 => ( Xa @ Xb @ V3 ) ) )
% 0.07/0.31 => ( scott_P @ Xa @ W2 ) ) ).
% 0.07/0.31
% 0.07/0.31 % A2
% 0.07/0.31 thf(fact_6_A1b,axiom,
% 0.07/0.31 ! [W2: qML_i,X2: qML_mu > qML_i > $o] :
% 0.07/0.31 ( ~ ( scott_P @ X2 @ W2 )
% 0.07/0.31 => ( scott_P
% 0.07/0.31 @ ^ [Y: qML_mu,Z: qML_i] :
% 0.07/0.31 ~ ( X2 @ Y @ Z )
% 0.07/0.31 @ W2 ) ) ).
% 0.07/0.31
% 0.07/0.31 % A1b
% 0.07/0.31 thf(fact_7_A5,axiom,
% 0.07/0.31 ! [X_1: qML_i] : ( scott_P @ scott_NE_QML_mu @ X_1 ) ).
% 0.07/0.31
% 0.07/0.31 % A5
% 0.07/0.31 thf(fact_8_A1a,axiom,
% 0.07/0.31 ! [W2: qML_i,X2: qML_mu > qML_i > $o] :
% 0.07/0.31 ( ( scott_P
% 0.07/0.31 @ ^ [Y: qML_mu,Z: qML_i] :
% 0.07/0.31 ~ ( X2 @ Y @ Z )
% 0.07/0.31 @ W2 )
% 0.07/0.31 => ~ ( scott_P @ X2 @ W2 ) ) ).
% 0.07/0.31
% 0.07/0.31 % A1a
% 0.07/0.31 thf(fact_9_T2,axiom,
% 0.07/0.31 ! [W2: qML_i,X2: qML_mu] :
% 0.07/0.31 ( ( scott_G @ X2 @ W2 )
% 0.07/0.31 => ( scott_ess_QML_mu @ scott_G @ X2 @ W2 ) ) ).
% 0.07/0.31
% 0.07/0.31 % T2
% 0.07/0.31 thf(fact_10_NE__def,axiom,
% 0.07/0.31 ( scott_NE_QML_mu
% 0.07/0.31 = ( ^ [X: qML_mu,W: qML_i] :
% 0.07/0.31 ! [Y: qML_mu > qML_i > $o] :
% 0.07/0.31 ( ( scott_ess_QML_mu @ Y @ X @ W )
% 0.07/0.31 => ! [V2: qML_i] :
% 0.07/0.31 ? [Z: qML_mu] : ( Y @ Z @ V2 ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % NE_def
% 0.07/0.31
% 0.07/0.31 %----Conjectures (1)
% 0.07/0.31 thf(conj_0,conjecture,
% 0.07/0.31 ! [W3: qML_i,X3: qML_i > $o] :
% 0.07/0.31 ( ~ ( X3 @ W3 )
% 0.07/0.31 | ! [V3: qML_i] : ( X3 @ V3 ) ) ).
% 0.07/0.31
% 0.07/0.31 %------------------------------------------------------------------------------
% 0.07/0.31 ------------------------
% 0.15/0.90 ---- Embedded in THF ---
% 0.15/0.90 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 0.15/0.90 %%% Generated on Tue Feb 24 11:25:01 EST 2026
% 0.15/0.90 %%% using '$$dhol' embedding, version 1.3.0.
% 0.15/0.90 %%% Logic specification used:
% 0.15/0.90 %%% thf(spec, logic, $$dhol).
% 0.15/0.90
% 0.15/0.90 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.YSDwy2w41Y/DTF2DTF30192.p
% See solution above
% 0.15/0.90 ------------------------
% 0.15/0.91 ---- Cleaned THF ---
% 0.15/0.91 thf(ty_n_t__QML____S5U__O__092__060mu__062,type,
% 0.15/0.91 qML_mu: $tType ).
% 0.15/0.91
% 0.15/0.91 thf(ty_n_t__QML____S5U__Oi,type,
% 0.15/0.91 qML_i: $tType ).
% 0.15/0.91
% 0.15/0.91 thf(sy_c_Scott__S5U_OG,type,
% 0.15/0.91 scott_G: qML_mu > qML_i > $o ).
% 0.15/0.91
% 0.15/0.91 thf(sy_c_Scott__S5U_ONE_001t__QML____S5U__O__092__060mu__062,type,
% 0.15/0.91 scott_NE_QML_mu: qML_mu > qML_i > $o ).
% 0.15/0.91
% 0.15/0.91 thf(sy_c_Scott__S5U_OP,type,
% 0.15/0.91 scott_P: ( qML_mu > qML_i > $o ) > qML_i > $o ).
% 0.15/0.91
% 0.15/0.91 thf(sy_c_Scott__S5U_Oess_001t__QML____S5U__O__092__060mu__062,type,
% 0.15/0.91 scott_ess_QML_mu: ( qML_mu > qML_i > $o ) > qML_mu > qML_i > $o ).
% 0.15/0.91
% 0.15/0.91 thf(fact_0_G__def,axiom,
% 0.15/0.91 ( scott_G
% 0.15/0.91 = ( ^ [X: qML_mu,W: qML_i] :
% 0.15/0.91 ! [Y: qML_mu > qML_i > $o] :
% 0.15/0.91 ( ( scott_P @ Y @ W )
% 0.15/0.91 => ( Y @ X @ W ) ) ) ) ).
% 0.15/0.91
% 0.15/0.91 thf(fact_1_A4,axiom,
% 0.15/0.91 ! [W2: qML_i,X2: qML_mu > qML_i > $o] :
% 0.15/0.91 ( ( scott_P @ X2 @ W2 )
% 0.15/0.91 => ! [X_1: qML_i] : ( scott_P @ X2 @ X_1 ) ) ).
% 0.15/0.91
% 0.15/0.91 thf(fact_2_T3,axiom,
% 0.15/0.91 ! [W2: qML_i,V: qML_i] :
% 0.15/0.91 ? [X3: qML_mu] : ( scott_G @ X3 @ V ) ).
% 0.15/0.91
% 0.15/0.91 thf(fact_3_A3,axiom,
% 0.15/0.91 ! [X_1: qML_i] : ( scott_P @ scott_G @ X_1 ) ).
% 0.15/0.91
% 0.15/0.91 thf(fact_4_ess__def,axiom,
% 0.15/0.91 ( scott_ess_QML_mu
% 0.15/0.91 = ( ^ [Phi: qML_mu > qML_i > $o,X: qML_mu,W: qML_i] :
% 0.15/0.91 ( ( Phi @ X @ W )
% 0.15/0.91 & ! [Y: qML_mu > qML_i > $o] :
% 0.15/0.91 ( ( Y @ X @ W )
% 0.15/0.91 => ! [V2: qML_i,Z: qML_mu] :
% 0.15/0.91 ( ( Phi @ Z @ V2 )
% 0.15/0.91 => ( Y @ Z @ V2 ) ) ) ) ) ) ).
% 0.15/0.91
% 0.15/0.91 thf(fact_5_A2,axiom,
% 0.15/0.91 ! [W2: qML_i,X2: qML_mu > qML_i > $o,Xa: qML_mu > qML_i > $o] :
% 0.15/0.91 ( ( ( scott_P @ X2 @ W2 )
% 0.15/0.91 & ! [V3: qML_i,Xb: qML_mu] :
% 0.15/0.91 ( ( X2 @ Xb @ V3 )
% 0.15/0.91 => ( Xa @ Xb @ V3 ) ) )
% 0.15/0.91 => ( scott_P @ Xa @ W2 ) ) ).
% 0.15/0.91
% 0.15/0.91 thf(fact_6_A1b,axiom,
% 0.15/0.91 ! [W2: qML_i,X2: qML_mu > qML_i > $o] :
% 0.15/0.91 ( ~ ( scott_P @ X2 @ W2 )
% 0.15/0.91 => ( scott_P
% 0.15/0.91 @ ^ [Y: qML_mu,Z: qML_i] :
% 0.15/0.91 ~ ( X2 @ Y @ Z )
% 0.15/0.91 @ W2 ) ) ).
% 0.15/0.91
% 0.15/0.91 thf(fact_7_A5,axiom,
% 0.15/0.91 ! [X_1: qML_i] : ( scott_P @ scott_NE_QML_mu @ X_1 ) ).
% 0.15/0.91
% 0.15/0.91 thf(fact_8_A1a,axiom,
% 0.15/0.91 ! [W2: qML_i,X2: qML_mu > qML_i > $o] :
% 0.15/0.91 ( ( scott_P
% 0.15/0.91 @ ^ [Y: qML_mu,Z: qML_i] :
% 0.15/0.91 ~ ( X2 @ Y @ Z )
% 0.15/0.91 @ W2 )
% 0.15/0.91 => ~ ( scott_P @ X2 @ W2 ) ) ).
% 0.15/0.91
% 0.15/0.91 thf(fact_9_T2,axiom,
% 0.15/0.91 ! [W2: qML_i,X2: qML_mu] :
% 0.15/0.91 ( ( scott_G @ X2 @ W2 )
% 0.15/0.91 => ( scott_ess_QML_mu @ scott_G @ X2 @ W2 ) ) ).
% 0.15/0.91
% 0.15/0.91 thf(fact_10_NE__def,axiom,
% 0.15/0.91 ( scott_NE_QML_mu
% 0.15/0.91 = ( ^ [X: qML_mu,W: qML_i] :
% 0.15/0.91 ! [Y: qML_mu > qML_i > $o] :
% 0.15/0.91 ( ( scott_ess_QML_mu @ Y @ X @ W )
% 0.15/0.91 => ! [V2: qML_i] :
% 0.15/0.91 ? [Z: qML_mu] : ( Y @ Z @ V2 ) ) ) ) ).
% 0.15/0.91
% 0.15/0.91 thf(conj_0,conjecture,
% 0.15/0.91 ! [W3: qML_i,X3: qML_i > $o] :
% 0.15/0.91 ( ~ ( X3 @ W3 )
% 0.15/0.91 | ! [V3: qML_i] : ( X3 @ V3 ) ) ).
% 0.15/0.91 ------------------------
% 0.15/0.92 % (30308)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on DTF2THF_30192 for (2999ds/27Mi)
% 0.15/0.92 % (30311)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on DTF2THF_30192 for (2999ds/275Mi)
% 0.15/0.92 % (30307)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on DTF2THF_30192 for (2999ds/4Mi)
% 0.15/0.92 % (30306)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_30192 for (2999ds/183Mi)
% 0.15/0.92 % (30309)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_30192 for (2999ds/2Mi)
% 0.15/0.92 % (30310)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on DTF2THF_30192 for (2999ds/2Mi)
% 0.15/0.92 % (30312)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_30192 for (2999ds/18Mi)
% 0.15/0.92 % (30309)Instruction limit reached!
% 0.15/0.92 % (30309)------------------------------
% 0.15/0.92 % (30309)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.15/0.92 % (30310)Instruction limit reached!
% 0.15/0.92 % (30310)------------------------------
% 0.15/0.92 % (30310)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.15/0.92 % (30309)Termination reason: Unknown
% 0.15/0.92 % (30309)Termination phase: Preprocessing 1
% 0.15/0.92
% 0.15/0.92 % (30309)Memory used [KB]: 1023
% 0.15/0.92 % (30309)Time elapsed: 0.002 s
% 0.15/0.92 % (30309)Instructions burned: 3 (million)
% 0.15/0.92 % (30309)------------------------------
% 0.15/0.92 % (30309)------------------------------
% 0.15/0.92 % (30310)Termination reason: Unknown
% 0.15/0.92 % (30310)Termination phase: Property scanning
% 0.15/0.92
% 0.15/0.92 % (30310)Memory used [KB]: 1023
% 0.15/0.92 % (30310)Time elapsed: 0.002 s
% 0.15/0.92 % (30310)Instructions burned: 3 (million)
% 0.15/0.92 % (30310)------------------------------
% 0.15/0.92 % (30310)------------------------------
% 0.15/0.92 % (30311)Refutation not found, incomplete strategy
% 0.15/0.92 % (30311)------------------------------
% 0.15/0.92 % (30311)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.15/0.92 % (30311)Termination reason: Refutation not found, incomplete strategy
% 0.15/0.92
% 0.15/0.92
% 0.15/0.92 % (30311)Memory used [KB]: 5500
% 0.15/0.92 % (30311)Time elapsed: 0.002 s
% 0.15/0.92 % (30311)Instructions burned: 3 (million)
% 0.15/0.92 % (30311)------------------------------
% 0.15/0.92 % (30311)------------------------------
% 0.15/0.92 % (30307)Instruction limit reached!
% 0.15/0.92 % (30307)------------------------------
% 0.15/0.92 % (30307)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.15/0.92 % (30307)Termination reason: Unknown
% 0.15/0.92 % (30307)Termination phase: Saturation
% 0.15/0.92
% 0.15/0.92 % (30307)Memory used [KB]: 5500
% 0.15/0.92 % (30307)Time elapsed: 0.003 s
% 0.15/0.92 % (30307)Instructions burned: 6 (million)
% 0.15/0.92 % (30307)------------------------------
% 0.15/0.92 % (30307)------------------------------
% 0.15/0.92 % (30312)Instruction limit reached!
% 0.15/0.92 % (30312)------------------------------
% 0.15/0.92 % (30312)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.15/0.92 % (30312)Termination reason: Unknown
% 0.15/0.92 % (30312)Termination phase: Saturation
% 0.15/0.92
% 0.15/0.92 % (30312)Memory used [KB]: 5628
% 0.15/0.92 % (30312)Time elapsed: 0.007 s
% 0.15/0.92 % (30312)Instructions burned: 18 (million)
% 0.15/0.92 % (30312)------------------------------
% 0.15/0.92 % (30312)------------------------------
% 0.15/0.93 % (30308)Instruction limit reached!
% 0.15/0.93 % (30308)------------------------------
% 0.15/0.93 % (30308)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.15/0.93 % (30308)Termination reason: Unknown
% 0.15/0.93 % (30308)Termination phase: Saturation
% 0.15/0.93
% 0.15/0.93 % (30308)Memory used [KB]: 5628
% 0.15/0.93 % (30308)Time elapsed: 0.010 s
% 0.15/0.93 % (30308)Instructions burned: 29 (million)
% 0.15/0.93 % (30308)------------------------------
% 0.15/0.93 % (30308)------------------------------
% 0.15/0.93 % (30313)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_30192 for (2999ds/3Mi)
% 0.15/0.93 % (30314)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_30192 for (2999ds/37Mi)
% 0.15/0.93 % (30315)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on DTF2THF_30192 for (2999ds/15Mi)
% 0.15/0.93 % (30316)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_30192 for (2999ds/3Mi)
% 0.15/0.93 % (30313)Instruction limit reached!
% 0.15/0.93 % (30313)------------------------------
% 0.15/0.93 % (30313)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.15/0.93 % (30313)Termination reason: Unknown
% 0.15/0.93 % (30313)Termination phase: Property scanning
% 0.15/0.93
% 0.15/0.93 % (30313)Memory used [KB]: 1023
% 0.15/0.93 % (30313)Time elapsed: 0.002 s
% 0.15/0.93 % (30313)Instructions burned: 4 (million)
% 0.15/0.93 % (30313)------------------------------
% 0.15/0.93 % (30313)------------------------------
% 0.15/0.93 % (30316)Instruction limit reached!
% 0.15/0.93 % (30316)------------------------------
% 0.15/0.93 % (30316)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.15/0.93 % (30316)Termination reason: Unknown
% 0.15/0.93 % (30316)Termination phase: Property scanning
% 0.15/0.93
% 0.15/0.93 % (30316)Memory used [KB]: 1023
% 0.15/0.93 % (30316)Time elapsed: 0.002 s
% 0.15/0.93 % (30316)Instructions burned: 4 (million)
% 0.15/0.93 % (30316)------------------------------
% 0.15/0.93 % (30316)------------------------------
% 0.15/0.93 % (30315)Refutation not found, incomplete strategy
% 0.15/0.93 % (30315)------------------------------
% 0.15/0.93 % (30315)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.15/0.93 % (30315)Termination reason: Refutation not found, incomplete strategy
% 0.15/0.93
% 0.15/0.93
% 0.15/0.93 % (30315)Memory used [KB]: 5500
% 0.15/0.93 % (30315)Time elapsed: 0.003 s
% 0.15/0.93 % (30315)Instructions burned: 7 (million)
% 0.15/0.93 % (30315)------------------------------
% 0.15/0.93 % (30315)------------------------------
% 0.15/0.93 % (30317)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on DTF2THF_30192 for (2999ds/1041Mi)
% 0.15/0.94 % (30318)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_30192 for (2999ds/7Mi)
% 0.15/0.94 % (30318)Instruction limit reached!
% 0.15/0.94 % (30318)------------------------------
% 0.15/0.94 % (30318)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.15/0.94 % (30318)Termination reason: Unknown
% 0.15/0.94 % (30318)Termination phase: Saturation
% 0.15/0.94
% 0.15/0.94 % (30318)Memory used [KB]: 1023
% 0.15/0.94 % (30318)Time elapsed: 0.003 s
% 0.15/0.94 % (30318)Instructions burned: 7 (million)
% 0.15/0.94 % (30318)------------------------------
% 0.15/0.94 % (30318)------------------------------
% 0.15/0.94 % (30319)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_30192 for (2999ds/16Mi)
% 0.15/0.94 % (30314)Instruction limit reached!
% 0.15/0.94 % (30314)------------------------------
% 0.15/0.94 % (30314)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.15/0.94 % (30314)Termination reason: Unknown
% 0.15/0.94 % (30320)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on DTF2THF_30192 for (2999ds/3Mi)
% 0.15/0.94 % (30314)Termination phase: Saturation
% 0.15/0.94
% 0.15/0.94 % (30314)Memory used [KB]: 6140
% 0.15/0.94 % (30314)Time elapsed: 0.012 s
% 0.15/0.94 % (30314)Instructions burned: 40 (million)
% 0.15/0.94 % (30314)------------------------------
% 0.15/0.94 % (30314)------------------------------
% 0.15/0.94 % (30320)Instruction limit reached!
% 0.15/0.94 % (30320)------------------------------
% 0.15/0.94 % (30320)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.15/0.94 % (30320)Termination reason: Unknown
% 0.15/0.94 % (30320)Termination phase: Twee Goal Transformation
% 0.15/0.94
% 0.15/0.94 % (30320)Memory used [KB]: 1023
% 0.15/0.94 % (30320)Time elapsed: 0.002 s
% 0.15/0.94 % (30320)Instructions burned: 4 (million)
% 0.15/0.94 % (30320)------------------------------
% 0.15/0.94 % (30320)------------------------------
% 0.15/0.94 % (30321)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_30192 for (2999ds/3Mi)
% 0.15/0.94 % (30321)Instruction limit reached!
% 0.15/0.94 % (30321)------------------------------
% 0.15/0.94 % (30321)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.15/0.94 % (30321)Termination reason: Unknown
% 0.15/0.94 % (30321)Termination phase: Function definition elimination
% 0.15/0.94
% 0.15/0.94 % (30321)Memory used [KB]: 1023
% 0.15/0.94 % (30321)Time elapsed: 0.002 s
% 0.15/0.94 % (30321)Instructions burned: 4 (million)
% 0.15/0.94 % (30321)------------------------------
% 0.15/0.94 % (30321)------------------------------
% 0.15/0.94 % (30319)Instruction limit reached!
% 0.15/0.94 % (30319)------------------------------
% 0.15/0.94 % (30319)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.15/0.94 % (30319)Termination reason: Unknown
% 0.15/0.94 % (30319)Termination phase: Saturation
% 0.15/0.94
% 0.15/0.94 % (30319)Memory used [KB]: 5628
% 0.15/0.94 % (30319)Time elapsed: 0.006 s
% 0.15/0.94 % (30319)Instructions burned: 18 (million)
% 0.15/0.94 % (30319)------------------------------
% 0.15/0.94 % (30319)------------------------------
% 0.15/0.95 % (30322)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_30192 for (2999ds/7Mi)
% 0.15/0.95 % (30323)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_30192 for (2999ds/3Mi)
% 0.15/0.95 % (30322)Instruction limit reached!
% 0.15/0.95 % (30322)------------------------------
% 0.15/0.95 % (30322)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.15/0.95 % (30322)Termination reason: Unknown
% 0.15/0.95 % (30322)Termination phase: Saturation
% 0.15/0.95
% 0.15/0.95 % (30322)Memory used [KB]: 5500
% 0.15/0.95 % (30322)Time elapsed: 0.003 s
% 0.15/0.95 % (30322)Instructions burned: 7 (million)
% 0.15/0.95 % (30322)------------------------------
% 0.15/0.95 % (30322)------------------------------
% 0.15/0.95 % (30324)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_30192 for (2999ds/4Mi)
% 0.15/0.95 % (30323)Instruction limit reached!
% 0.15/0.95 % (30323)------------------------------
% 0.15/0.95 % (30323)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.15/0.95 % (30323)Termination reason: Unknown
% 0.15/0.95 % (30323)Termination phase: Function definition elimination
% 0.15/0.95
% 0.15/0.95 % (30323)Memory used [KB]: 1023
% 0.15/0.95 % (30323)Time elapsed: 0.002 s
% 0.15/0.95 % (30323)Instructions burned: 5 (million)
% 0.15/0.95 % (30323)------------------------------
% 0.15/0.95 % (30323)------------------------------
% 0.15/0.95 % (30324)Instruction limit reached!
% 0.15/0.95 % (30324)------------------------------
% 0.15/0.95 % (30324)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.15/0.95 % (30324)Termination reason: Unknown
% 0.15/0.95 % (30324)Termination phase: Property scanning
% 0.15/0.95
% 0.15/0.95 % (30324)Memory used [KB]: 1023
% 0.15/0.95 % (30324)Time elapsed: 0.002 s
% 0.15/0.95 % (30324)Instructions burned: 4 (million)
% 0.15/0.95 % (30324)------------------------------
% 0.15/0.95 % (30324)------------------------------
% 0.15/0.95 % (30325)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_30192 for (2999ds/18Mi)
% 0.15/0.95 % (30326)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_30192 for (2999ds/710Mi)
% 0.15/0.95 % (30326)Refutation not found, incomplete strategy
% 0.15/0.95 % (30326)------------------------------
% 0.15/0.95 % (30326)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.15/0.95 % (30326)Termination reason: Refutation not found, incomplete strategy
% 0.15/0.95
% 0.15/0.95
% 0.15/0.95 % (30326)Memory used [KB]: 5500
% 0.15/0.95 % (30326)Time elapsed: 0.002 s
% 0.15/0.95 % (30326)Instructions burned: 3 (million)
% 0.15/0.95 % (30326)------------------------------
% 0.15/0.95 % (30326)------------------------------
% 0.15/0.96 % (30325)Instruction limit reached!
% 0.15/0.96 % (30325)------------------------------
% 0.15/0.96 % (30325)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.15/0.96 % (30325)Termination reason: Unknown
% 0.15/0.96 % (30325)Termination phase: Saturation
% 0.15/0.96
% 0.15/0.96 % (30325)Memory used [KB]: 5628
% 0.15/0.96 % (30325)Time elapsed: 0.007 s
% 0.15/0.96 % (30325)Instructions burned: 19 (million)
% 0.15/0.96 % (30325)------------------------------
% 0.15/0.96 % (30325)------------------------------
% 0.15/0.96 % (30327)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_30192 for (2999ds/6Mi)
% 0.15/0.96 % (30328)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on DTF2THF_30192 for (2999ds/902Mi)
% 0.15/0.96 % (30329)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on DTF2THF_30192 for (2999ds/21Mi)
% 0.15/0.96 % (30328)Refutation not found, incomplete strategy
% 0.15/0.96 % (30328)------------------------------
% 0.15/0.96 % (30328)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.15/0.96 % (30328)Termination reason: Refutation not found, incomplete strategy
% 0.15/0.96
% 0.15/0.96
% 0.15/0.96 % (30328)Memory used [KB]: 5500
% 0.15/0.96 % (30328)Time elapsed: 0.002 s
% 0.15/0.96 % (30328)Instructions burned: 4 (million)
% 0.15/0.96 % (30328)------------------------------
% 0.15/0.96 % (30328)------------------------------
% 0.15/0.96 % (30327)Instruction limit reached!
% 0.15/0.96 % (30327)------------------------------
% 0.15/0.96 % (30327)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.15/0.96 % (30327)Termination reason: Unknown
% 0.15/0.96 % (30327)Termination phase: Saturation
% 0.15/0.96
% 0.15/0.96 % (30327)Memory used [KB]: 5500
% 0.15/0.96 % (30327)Time elapsed: 0.003 s
% 0.15/0.96 % (30327)Instructions burned: 7 (million)
% 0.15/0.96 % (30327)------------------------------
% 0.15/0.96 % (30327)------------------------------
% 0.15/0.96 % (30306)First to succeed.
% 0.15/0.96 % (30330)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_30192 for (2999ds/5Mi)
% 0.15/0.97 % (30306)Refutation found. Thanks to Tanya!
% 0.15/0.97 % SZS status Theorem for DTF2THF_30192
% 0.15/0.97 % SZS output start Proof for DTF2THF_30192
% 0.15/0.97 thf(type_def_5, type, qML_mu: $tType).
% 0.15/0.97 thf(type_def_6, type, qML_i: $tType).
% 0.15/0.97 thf(func_def_0, type, qML_mu: $tType).
% 0.15/0.97 thf(func_def_1, type, qML_i: $tType).
% 0.15/0.97 thf(func_def_2, type, scott_G: qML_mu > qML_i > $o).
% 0.15/0.97 thf(func_def_3, type, scott_NE_QML_mu: qML_mu > qML_i > $o).
% 0.15/0.97 thf(func_def_4, type, scott_P: (qML_mu > qML_i > $o) > qML_i > $o).
% 0.15/0.97 thf(func_def_5, type, scott_ess_QML_mu: (qML_mu > qML_i > $o) > qML_mu > qML_i > $o).
% 0.15/0.97 thf(func_def_19, type, sK0: qML_i).
% 0.15/0.97 thf(func_def_20, type, sK1: qML_i > $o).
% 0.15/0.97 thf(func_def_21, type, sK2: qML_i).
% 0.15/0.97 thf(func_def_22, type, sK3: (qML_mu > qML_i > $o) > (qML_mu > qML_i > $o) > qML_mu).
% 0.15/0.97 thf(func_def_23, type, sK4: (qML_mu > qML_i > $o) > (qML_mu > qML_i > $o) > qML_i).
% 0.15/0.97 thf(func_def_24, type, sK5: qML_i > qML_mu).
% 0.15/0.97 thf(func_def_27, type, sK7: qML_i > qML_mu > qML_mu > qML_i > $o).
% 0.15/0.97 thf(func_def_28, type, sK8: qML_mu > qML_i > qML_mu > qML_i > $o).
% 0.15/0.97 thf(func_def_29, type, sK9: qML_mu > qML_i > qML_mu > qML_i > $o).
% 0.15/0.97 thf(func_def_62, type, ph10: !>[X0: $tType]:(X0)).
% 0.15/0.97 thf(f229,plain,(
% 0.15/0.97 $false),
% 0.15/0.97 inference(trivial_inequality_removal,[status(thm)],[f222])).
% 0.15/0.97 thf(f222,plain,(
% 0.15/0.97 ($false = $true)),
% 0.15/0.97 inference(superposition,[status(thm)],[f219,f57])).
% 0.15/0.97 thf(f57,plain,(
% 0.15/0.97 ((sK1 @ sK0) = $true)),
% 0.15/0.97 inference(cnf_transformation,[status(thm)],[f52])).
% 0.15/0.97 thf(f52,plain,(
% 0.15/0.97 ((sK1 @ sK2) != $true) & ((sK1 @ sK0) = $true)),
% 0.15/0.97 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f49,f51,f50])).
% 0.15/0.97 thf(f50,plain,(
% 0.15/0.97 ? [X0 : qML_i,X1 : qML_i > $o] : (? [X2 : qML_i] : ((X1 @ X2) != $true) & ((X1 @ X0) = $true)) => (? [X2 : qML_i] : ((sK1 @ X2) != $true) & ((sK1 @ sK0) = $true))),
% 0.15/0.97 introduced(definition,[],[choice_axiom])).
% 0.15/0.97 thf(f51,plain,(
% 0.15/0.97 ? [X2 : qML_i] : ((sK1 @ X2) != $true) => ((sK1 @ sK2) != $true)),
% 0.15/0.97 introduced(definition,[],[choice_axiom])).
% 0.15/0.97 thf(f49,plain,(
% 0.15/0.97 ? [X0 : qML_i,X1 : qML_i > $o] : (? [X2 : qML_i] : ((X1 @ X2) != $true) & ((X1 @ X0) = $true))),
% 0.15/0.97 inference(ennf_transformation,[status(thm)],[f39])).
% 0.15/0.97 thf(f39,plain,(
% 0.15/0.97 ~! [X0 : qML_i,X1 : qML_i > $o] : (! [X2 : qML_i] : ((X1 @ X2) = $true) | ((X1 @ X0) != $true))),
% 0.15/0.97 inference(flattening,[status(thm)],[f16])).
% 0.15/0.97 thf(f16,plain,(
% 0.15/0.97 ~! [X0 : qML_i,X1 : qML_i > $o] : (~((X1 @ X0) = $true) | ! [X2 : qML_i] : ((X1 @ X2) = $true))),
% 0.15/0.97 inference(fool_elimination,[status(thm)],[f15])).
% 0.15/0.97 thf(f15,plain,(
% 0.15/0.97 ~! [X0 : qML_i,X1 : qML_i > $o] : (~(X1 @ X0) | ! [X2 : qML_i] : (X1 @ X2))),
% 0.15/0.97 inference(rectify,[status(thm)],[f13])).
% 0.15/0.97 thf(f13,negated_conjecture,(
% 0.15/0.97 ~! [X14 : qML_i,X7 : qML_i > $o] : (~(X7 @ X14) | ! [X12 : qML_i] : (X7 @ X12))),
% 0.15/0.97 inference(negated_conjecture,[status(cth)],[f12])).
% 0.15/0.97 thf(f12,conjecture,(
% 0.15/0.97 ! [X14 : qML_i,X7 : qML_i > $o] : (~(X7 @ X14) | ! [X12 : qML_i] : (X7 @ X12))),
% 0.15/0.97 file('/export/starexec/sandbox2/tmp/tmp.YSDwy2w41Y/DTF2THF_30192.p',conj_0)).
% 0.15/0.97 thf(f219,plain,(
% 0.15/0.97 ( ! [X0 : qML_i] : (((sK1 @ X0) = $false)) )),
% 0.15/0.97 inference(beta_eta_normalization,[status(thm)],[f218])).
% 0.15/0.97 thf(f218,plain,(
% 0.15/0.97 ( ! [X0 : qML_i] : ((((^[Y0 : qML_mu]: (sK1)) @ (sK5 @ X0) @ X0) = $false)) )),
% 0.15/0.97 inference(trivial_inequality_removal,[status(thm)],[f208])).
% 0.15/0.97 thf(f208,plain,(
% 0.15/0.97 ( ! [X0 : qML_i] : ((((^[Y0 : qML_mu]: (sK1)) @ (sK5 @ X0) @ X0) = $false) | ($true != $true)) )),
% 0.15/0.97 inference(superposition,[status(thm)],[f124,f165])).
% 0.15/0.97 thf(f165,plain,(
% 0.15/0.97 ( ! [X0 : qML_mu > qML_i > $o,X1 : qML_i] : (((scott_P @ X0 @ X1) = $true) | ((X0 @ (sK5 @ X1) @ X1) = $false)) )),
% 0.15/0.97 inference(not_proxy_clausification,[status(thm)],[f164])).
% 0.15/0.97 thf(f164,plain,(
% 0.15/0.97 ( ! [X0 : qML_mu > qML_i > $o,X1 : qML_i] : (((scott_P @ X0 @ X1) = $true) | ((~ (X0 @ (sK5 @ X1) @ X1)) = $true)) )),
% 0.15/0.97 inference(beta_eta_normalization,[status(thm)],[f163])).
% 0.15/0.97 thf(f163,plain,(
% 0.15/0.97 ( ! [X0 : qML_mu > qML_i > $o,X1 : qML_i] : ((((^[Y0 : qML_mu]: ((^[Y1 : qML_i]: (~ (X0 @ Y0 @ Y1))))) @ (sK5 @ X1) @ X1) = $true) | ((scott_P @ X0 @ X1) = $true)) )),
% 0.15/0.97 inference(trivial_inequality_removal,[status(thm)],[f153])).
% 0.15/0.97 thf(f153,plain,(
% 0.15/0.97 ( ! [X0 : qML_mu > qML_i > $o,X1 : qML_i] : ((((^[Y0 : qML_mu]: ((^[Y1 : qML_i]: (~ (X0 @ Y0 @ Y1))))) @ (sK5 @ X1) @ X1) = $true) | ((scott_P @ X0 @ X1) = $true) | ($false = $true)) )),
% 0.15/0.97 inference(superposition,[status(thm)],[f108,f61])).
% 0.15/0.97 thf(f61,plain,(
% 0.15/0.97 ( ! [X0 : qML_mu > qML_i > $o,X1 : qML_i] : (((scott_P @ (^[Y0 : qML_mu]: ((^[Y1 : qML_i]: (~ (X0 @ Y0 @ Y1))))) @ X1) = $true) | ((scott_P @ X0 @ X1) = $true)) )),
% 0.15/0.97 inference(cnf_transformation,[status(thm)],[f47])).
% 0.15/0.97 thf(f47,plain,(
% 0.15/0.97 ! [X0 : qML_mu > qML_i > $o,X1 : qML_i] : (((scott_P @ X0 @ X1) = $true) | ((scott_P @ (^[Y0 : qML_mu]: ((^[Y1 : qML_i]: (~ (X0 @ Y0 @ Y1))))) @ X1) = $true))),
% 0.15/0.97 inference(ennf_transformation,[status(thm)],[f41])).
% 0.15/0.97 thf(f41,plain,(
% 0.15/0.97 ! [X0 : qML_mu > qML_i > $o,X1 : qML_i] : (((scott_P @ X0 @ X1) != $true) => ((scott_P @ (^[Y0 : qML_mu]: ((^[Y1 : qML_i]: (~ (X0 @ Y0 @ Y1))))) @ X1) = $true))),
% 0.15/0.97 inference(flattening,[status(thm)],[f26])).
% 0.15/0.97 thf(f26,plain,(
% 0.15/0.97 ! [X0 : qML_mu > qML_i > $o,X1 : qML_i] : (~((scott_P @ X0 @ X1) = $true) => ((scott_P @ (^[Y0 : qML_mu]: ((^[Y1 : qML_i]: (~ (X0 @ Y0 @ Y1))))) @ X1) = $true))),
% 0.15/0.97 inference(fool_elimination,[status(thm)],[f25])).
% 0.15/0.97 thf(f25,plain,(
% 0.15/0.97 ! [X0 : qML_mu > qML_i > $o,X1 : qML_i] : (~(scott_P @ X0 @ X1) => (scott_P @ (^[X2 : qML_mu, X3 : qML_i] : (~(X0 @ X2 @ X3))) @ X1))),
% 0.15/0.97 inference(rectify,[status(thm)],[f7])).
% 0.15/0.97 thf(f7,axiom,(
% 0.15/0.97 ! [X4 : qML_mu > qML_i > $o,X3 : qML_i] : (~(scott_P @ X4 @ X3) => (scott_P @ (^[X2 : qML_mu, X10 : qML_i] : (~(X4 @ X2 @ X10))) @ X3))),
% 0.15/0.97 file('/export/starexec/sandbox2/tmp/tmp.YSDwy2w41Y/DTF2THF_30192.p',fact_6_A1b)).
% 0.15/0.97 thf(f108,plain,(
% 0.15/0.97 ( ! [X0 : qML_i,X1 : qML_mu > qML_i > $o] : (((scott_P @ X1 @ X0) = $false) | ((X1 @ (sK5 @ X0) @ X0) = $true)) )),
% 0.15/0.97 inference(binary_proxy_clausification,[status(thm)],[f107])).
% 0.15/0.97 thf(f107,plain,(
% 0.15/0.97 ( ! [X0 : qML_i,X1 : qML_mu > qML_i > $o] : ((((scott_P @ X1 @ X0) => (X1 @ (sK5 @ X0) @ X0)) = $true)) )),
% 0.15/0.97 inference(beta_eta_normalization,[status(thm)],[f106])).
% 0.15/0.97 thf(f106,plain,(
% 0.15/0.97 ( ! [X0 : qML_i,X1 : qML_mu > qML_i > $o] : ((((^[Y0 : qML_mu > qML_i > $o]: ((scott_P @ Y0 @ X0) => (Y0 @ (sK5 @ X0) @ X0))) @ X1) = $true)) )),
% 0.15/0.97 inference(pi_clausification,[status(thm)],[f105])).
% 0.15/0.97 thf(f105,plain,(
% 0.15/0.97 ( ! [X0 : qML_i] : (((!! @ (qML_mu > qML_i > $o) @ (^[Y0 : qML_mu > qML_i > $o]: ((scott_P @ Y0 @ X0) => (Y0 @ (sK5 @ X0) @ X0)))) = $true)) )),
% 0.15/0.97 inference(beta_eta_normalization,[status(thm)],[f75])).
% 0.15/0.97 thf(f75,plain,(
% 0.15/0.97 ( ! [X0 : qML_i] : ((((^[Y0 : qML_mu]: ((^[Y1 : qML_i]: (!! @ (qML_mu > qML_i > $o) @ (^[Y2 : qML_mu > qML_i > $o]: ((scott_P @ Y2 @ Y1) => (Y2 @ Y0 @ Y1))))))) @ (sK5 @ X0) @ X0) = $true)) )),
% 0.15/0.97 inference(definition_unfolding,[status(thm)],[f70,f67])).
% 0.15/0.97 thf(f67,plain,(
% 0.15/0.97 (scott_G = (^[Y0 : qML_mu]: ((^[Y1 : qML_i]: (!! @ (qML_mu > qML_i > $o) @ (^[Y2 : qML_mu > qML_i > $o]: ((scott_P @ Y2 @ Y1) => (Y2 @ Y0 @ Y1))))))))),
% 0.15/0.97 inference(cnf_transformation,[status(thm)],[f24])).
% 0.15/0.97 thf(f24,plain,(
% 0.15/0.97 (scott_G = (^[Y0 : qML_mu]: ((^[Y1 : qML_i]: (!! @ (qML_mu > qML_i > $o) @ (^[Y2 : qML_mu > qML_i > $o]: ((scott_P @ Y2 @ Y1) => (Y2 @ Y0 @ Y1))))))))),
% 0.15/0.97 inference(fool_elimination,[status(thm)],[f23])).
% 0.15/0.97 thf(f23,plain,(
% 0.15/0.97 (scott_G = (^[X0 : qML_mu, X1 : qML_i] : (! [X2 : qML_mu > qML_i > $o] : ((scott_P @ X2 @ X1) => (X2 @ X0 @ X1)))))),
% 0.15/0.97 inference(rectify,[status(thm)],[f1])).
% 0.15/0.97 thf(f1,axiom,(
% 0.15/0.97 (scott_G = (^[X0 : qML_mu, X1 : qML_i] : (! [X2 : qML_mu > qML_i > $o] : ((scott_P @ X2 @ X1) => (X2 @ X0 @ X1)))))),
% 0.15/0.97 file('/export/starexec/sandbox2/tmp/tmp.YSDwy2w41Y/DTF2THF_30192.p',fact_0_G__def)).
% 0.15/0.97 thf(f70,plain,(
% 0.15/0.97 ( ! [X0 : qML_i] : (((scott_G @ (sK5 @ X0) @ X0) = $true)) )),
% 0.15/0.97 inference(cnf_transformation,[status(thm)],[f56])).
% 0.15/0.97 thf(f56,plain,(
% 0.15/0.97 ! [X0 : qML_i] : ((scott_G @ (sK5 @ X0) @ X0) = $true)),
% 0.15/0.97 inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f42,f55])).
% 0.15/0.97 thf(f55,plain,(
% 0.15/0.97 ! [X0 : qML_i] : (? [X1 : qML_mu] : ((scott_G @ X1 @ X0) = $true) => ((scott_G @ (sK5 @ X0) @ X0) = $true))),
% 0.15/0.97 introduced(definition,[],[choice_axiom])).
% 0.15/0.97 thf(f42,plain,(
% 0.15/0.97 ! [X0 : qML_i] : ? [X1 : qML_mu] : ((scott_G @ X1 @ X0) = $true)),
% 0.15/0.97 inference(rectify,[status(thm)],[f34])).
% 0.15/0.97 thf(f34,plain,(
% 0.15/0.97 ! [X1 : qML_i] : ? [X2 : qML_mu] : ((scott_G @ X2 @ X1) = $true)),
% 0.15/0.97 inference(fool_elimination,[status(thm)],[f33])).
% 0.15/0.97 thf(f33,plain,(
% 0.15/0.97 ! [X1 : qML_i] : ? [X2 : qML_mu] : (scott_G @ X2 @ X1)),
% 0.15/0.97 inference(rectify,[status(thm)],[f3])).
% 0.15/0.97 thf(f3,axiom,(
% 0.15/0.97 ! [X3 : qML_i,X6 : qML_i] : ? [X7 : qML_mu] : (scott_G @ X7 @ X6)),
% 0.15/0.97 file('/export/starexec/sandbox2/tmp/tmp.YSDwy2w41Y/DTF2THF_30192.p',fact_2_T3)).
% 0.15/0.97 thf(f124,plain,(
% 0.15/0.97 ( ! [X0 : qML_i] : (((scott_P @ (^[Y0 : qML_mu]: (sK1)) @ X0) != $true)) )),
% 0.15/0.97 inference(beta_eta_normalization,[status(thm)],[f123])).
% 0.15/0.97 thf(f123,plain,(
% 0.15/0.97 ( ! [X0 : qML_i] : (((scott_P @ (^[Y0 : qML_mu]: ((^[Y1 : qML_i]: (sK1 @ ((^[Y2 : qML_mu]: ((^[Y3 : qML_i]: (Y3)))) @ Y0 @ Y1))))) @ X0) != $true)) )),
% 0.15/0.97 inference(trivial_inequality_removal,[status(thm)],[f119])).
% 0.15/0.97 thf(f119,plain,(
% 0.15/0.97 ( ! [X0 : qML_i] : (((scott_P @ (^[Y0 : qML_mu]: ((^[Y1 : qML_i]: (sK1 @ ((^[Y2 : qML_mu]: ((^[Y3 : qML_i]: (Y3)))) @ Y0 @ Y1))))) @ X0) != $true) | ($true != $true)) )),
% 0.15/0.97 inference(superposition,[status(thm)],[f58,f114])).
% 0.15/0.97 thf(f114,plain,(
% 0.15/0.97 ( ! [X2 : qML_i,X0 : qML_mu > qML_i > $o,X1 : qML_i] : (((X0 @ (sK5 @ X1) @ X1) = $true) | ((scott_P @ X0 @ X2) != $true)) )),
% 0.15/0.97 inference(trivial_inequality_removal,[status(thm)],[f110])).
% 0.15/0.97 thf(f110,plain,(
% 0.15/0.97 ( ! [X2 : qML_i,X0 : qML_mu > qML_i > $o,X1 : qML_i] : (($false = $true) | ((X0 @ (sK5 @ X1) @ X1) = $true) | ((scott_P @ X0 @ X2) != $true)) )),
% 0.15/0.97 inference(superposition,[status(thm)],[f66,f108])).
% 0.15/0.97 thf(f66,plain,(
% 0.15/0.97 ( ! [X2 : qML_i,X0 : qML_mu > qML_i > $o,X1 : qML_i] : (((scott_P @ X0 @ X2) = $true) | ((scott_P @ X0 @ X1) != $true)) )),
% 0.15/0.97 inference(cnf_transformation,[status(thm)],[f46])).
% 0.15/0.97 thf(f46,plain,(
% 0.15/0.97 ! [X0 : qML_mu > qML_i > $o,X1 : qML_i] : (! [X2 : qML_i] : ((scott_P @ X0 @ X2) = $true) | ((scott_P @ X0 @ X1) != $true))),
% 0.15/0.97 inference(ennf_transformation,[status(thm)],[f22])).
% 0.15/0.97 thf(f22,plain,(
% 0.15/0.97 ! [X0 : qML_mu > qML_i > $o,X1 : qML_i] : (((scott_P @ X0 @ X1) = $true) => ! [X2 : qML_i] : ((scott_P @ X0 @ X2) = $true))),
% 0.15/0.97 inference(fool_elimination,[status(thm)],[f21])).
% 0.15/0.97 thf(f21,plain,(
% 0.15/0.97 ! [X0 : qML_mu > qML_i > $o,X1 : qML_i] : ((scott_P @ X0 @ X1) => ! [X2 : qML_i] : (scott_P @ X0 @ X2))),
% 0.15/0.97 inference(rectify,[status(thm)],[f2])).
% 0.15/0.97 thf(f2,axiom,(
% 0.15/0.97 ! [X4 : qML_mu > qML_i > $o,X3 : qML_i] : ((scott_P @ X4 @ X3) => ! [X5 : qML_i] : (scott_P @ X4 @ X5))),
% 0.15/0.97 file('/export/starexec/sandbox2/tmp/tmp.YSDwy2w41Y/DTF2THF_30192.p',fact_1_A4)).
% 0.15/0.97 thf(f58,plain,(
% 0.15/0.97 ((sK1 @ sK2) != $true)),
% 0.15/0.97 inference(cnf_transformation,[status(thm)],[f52])).
% 0.15/0.97 % SZS output end Proof for DTF2THF_30192
% 0.15/0.97 % (30306)------------------------------
% 0.15/0.97 % (30306)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.15/0.97 % (30306)Termination reason: Refutation
% 0.15/0.97
% 0.15/0.97 % (30306)Memory used [KB]: 7803
% 0.15/0.97 % (30306)Time elapsed: 0.046 s
% 0.15/0.97 % (30306)Instructions burned: 170 (million)
% 0.15/0.97 % (30306)------------------------------
% 0.15/0.97 % (30306)------------------------------
% 0.15/0.97 % (30305)Success in time 0.043 s
%------------------------------------------------------------------------------