%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO362^5 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n018.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 09:54:02 AM UTC 2026
% Result : Theorem 1.65s 1.41s
% Output : Refutation 1.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 3
% Syntax : Number of formulae : 35 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 260 ( 77 equ; 0 cnn)
% Maximal formula atoms : 8 ( 7 avg)
% Number of connectives : 344 ( 24 ~; 51 |; 15 &; 232 @)
% ( 0 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 53 ( 53 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 114 ( 36 ^; 67 !; 11 ?; 114 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
cK: ( $i > $o ) > $i > $o ).
thf(func_def_7,type,
sK0: $i > $o ).
thf(func_def_8,type,
sK1: $i > $o ).
thf(func_def_12,type,
ph4:
!>[X0: $tType] : X0 ).
thf(func_def_14,type,
sK6: ( $i > $o ) > $i ).
thf(f89,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f88]) ).
thf(f88,plain,
$false = $true,
inference(duplicate_literal_removal,[status(thm)],[f82]) ).
thf(f82,plain,
( ( $false = $true )
| ( $false = $true ) ),
inference(superposition,[status(thm)],[f63,f69]) ).
thf(f69,plain,
( $true
= ( sK1 @ ( sK6 @ sK1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f68]) ).
thf(f68,plain,
( ( ^ [Y0: $i] :
( sK1
@ ( ^ [Y1: $i] : Y1
@ Y0 ) )
@ ( sK6
@ ^ [Y0: $i] :
( sK1
@ ( ^ [Y1: $i] : Y1
@ Y0 ) ) ) )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f66]) ).
thf(f66,plain,
( ( ( ^ [Y0: $i] :
( sK1
@ ( ^ [Y1: $i] : Y1
@ Y0 ) )
@ ( sK6
@ ^ [Y0: $i] :
( sK1
@ ( ^ [Y1: $i] : Y1
@ Y0 ) ) ) )
= $true )
| ( $true != $true ) ),
inference(equality_factoring,[status(thm)],[f65]) ).
thf(f65,plain,
! [X0: $i > $o] :
( ( $true
= ( sK1 @ ( sK6 @ X0 ) ) )
| ( ( X0 @ ( sK6 @ X0 ) )
= $true ) ),
inference(subsumption_resolution,[status(thm)],[f64,f15]) ).
thf(f15,plain,
! [X2: $i] :
( ( ( sK0 @ X2 )
!= $true )
| ( ( sK1 @ X2 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( ! [X2: $i] :
( ( ( sK1 @ X2 )
= $true )
| ( ( sK0 @ X2 )
!= $true ) )
& ( $true
!= ( cK @ sK1 @ sK2 ) )
& ( $true
= ( cK @ sK0 @ sK2 ) )
& ! [X4: $i > $o,X5: $i > $o] :
( ( cK
@ ^ [Y0: $i] :
( ( X5 @ Y0 )
| ( X4 @ Y0 ) ) )
= ( ^ [Y0: $i] :
( ( cK @ X5 @ Y0 )
| ( cK @ X4 @ Y0 ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f8,f10,f9]) ).
thf(f9,plain,
( ? [X0: $i > $o,X1: $i > $o] :
( ! [X2: $i] :
( ( ( X1 @ X2 )
= $true )
| ( ( X0 @ X2 )
!= $true ) )
& ? [X3: $i] :
( ( ( cK @ X1 @ X3 )
!= $true )
& ( ( cK @ X0 @ X3 )
= $true ) ) )
=> ( ! [X2: $i] :
( ( ( sK1 @ X2 )
= $true )
| ( ( sK0 @ X2 )
!= $true ) )
& ? [X3: $i] :
( ( ( cK @ sK1 @ X3 )
!= $true )
& ( $true
= ( cK @ sK0 @ X3 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f10,plain,
( ? [X3: $i] :
( ( ( cK @ sK1 @ X3 )
!= $true )
& ( $true
= ( cK @ sK0 @ X3 ) ) )
=> ( ( $true
!= ( cK @ sK1 @ sK2 ) )
& ( $true
= ( cK @ sK0 @ sK2 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f8,plain,
( ? [X0: $i > $o,X1: $i > $o] :
( ! [X2: $i] :
( ( ( X1 @ X2 )
= $true )
| ( ( X0 @ X2 )
!= $true ) )
& ? [X3: $i] :
( ( ( cK @ X1 @ X3 )
!= $true )
& ( ( cK @ X0 @ X3 )
= $true ) ) )
& ! [X4: $i > $o,X5: $i > $o] :
( ( cK
@ ^ [Y0: $i] :
( ( X5 @ Y0 )
| ( X4 @ Y0 ) ) )
= ( ^ [Y0: $i] :
( ( cK @ X5 @ Y0 )
| ( cK @ X4 @ Y0 ) ) ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,plain,
( ? [X2: $i > $o,X3: $i > $o] :
( ! [X4: $i] :
( ( $true
= ( X3 @ X4 ) )
| ( ( X2 @ X4 )
!= $true ) )
& ? [X5: $i] :
( ( $true
!= ( cK @ X3 @ X5 ) )
& ( ( cK @ X2 @ X5 )
= $true ) ) )
& ! [X0: $i > $o,X1: $i > $o] :
( ( ^ [Y0: $i] :
( ( cK @ X1 @ Y0 )
| ( cK @ X0 @ Y0 ) ) )
= ( cK
@ ^ [Y0: $i] :
( ( X1 @ Y0 )
| ( X0 @ Y0 ) ) ) ) ),
inference(ennf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
~ ( ! [X0: $i > $o,X1: $i > $o] :
( ( ^ [Y0: $i] :
( ( cK @ X1 @ Y0 )
| ( cK @ X0 @ Y0 ) ) )
= ( cK
@ ^ [Y0: $i] :
( ( X1 @ Y0 )
| ( X0 @ Y0 ) ) ) )
=> ! [X2: $i > $o,X3: $i > $o] :
( ! [X4: $i] :
( ( ( X2 @ X4 )
= $true )
=> ( $true
= ( X3 @ X4 ) ) )
=> ! [X5: $i] :
( ( ( cK @ X2 @ X5 )
= $true )
=> ( $true
= ( cK @ X3 @ X5 ) ) ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ! [X0: $i > $o,X1: $i > $o] :
( ( ^ [Y0: $i] :
( ( cK @ X1 @ Y0 )
| ( cK @ X0 @ Y0 ) ) )
= ( cK
@ ^ [Y0: $i] :
( ( X1 @ Y0 )
| ( X0 @ Y0 ) ) ) )
=> ! [X4: $i > $o,X5: $i > $o] :
( ! [X6: $i] :
( ( $true
= ( X4 @ X6 ) )
=> ( ( X5 @ X6 )
= $true ) )
=> ! [X7: $i] :
( ( ( cK @ X4 @ X7 )
= $true )
=> ( ( cK @ X5 @ X7 )
= $true ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ! [X0: $i > $o,X1: $i > $o] :
( ( cK
@ ^ [X2: $i] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) )
= ( ^ [X3: $i] :
( ( cK @ X0 @ X3 )
| ( cK @ X1 @ X3 ) ) ) )
=> ! [X4: $i > $o,X5: $i > $o] :
( ! [X6: $i] :
( ( X4 @ X6 )
=> ( X5 @ X6 ) )
=> ! [X7: $i] :
( ( cK @ X4 @ X7 )
=> ( cK @ X5 @ X7 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ! [X1: $i > $o,X0: $i > $o] :
( ( cK
@ ^ [X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) )
= ( ^ [X3: $i] :
( ( cK @ X1 @ X3 )
| ( cK @ X0 @ X3 ) ) ) )
=> ! [X0: $i > $o,X1: $i > $o] :
( ! [X4: $i] :
( ( X0 @ X4 )
=> ( X1 @ X4 ) )
=> ! [X4: $i] :
( ( cK @ X0 @ X4 )
=> ( cK @ X1 @ X4 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ! [X1: $i > $o,X0: $i > $o] :
( ( cK
@ ^ [X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) )
= ( ^ [X3: $i] :
( ( cK @ X1 @ X3 )
| ( cK @ X0 @ X3 ) ) ) )
=> ! [X0: $i > $o,X1: $i > $o] :
( ! [X4: $i] :
( ( X0 @ X4 )
=> ( X1 @ X4 ) )
=> ! [X4: $i] :
( ( cK @ X0 @ X4 )
=> ( cK @ X1 @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JLlLF4KaAw/DTF2THF_11649.p',cTHM631A_pme) ).
thf(f64,plain,
! [X0: $i > $o] :
( ( $true
= ( sK1 @ ( sK6 @ X0 ) ) )
| ( ( sK0 @ ( sK6 @ X0 ) )
= $true )
| ( ( X0 @ ( sK6 @ X0 ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f60]) ).
thf(f60,plain,
! [X0: $i > $o] :
( ( $true
= ( sK1 @ ( sK6 @ X0 ) ) )
| ( $true
= ( ( X0 @ ( sK6 @ X0 ) )
| ( sK0 @ ( sK6 @ X0 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f59]) ).
thf(f59,plain,
! [X0: $i > $o] :
( ( sK1 @ ( sK6 @ X0 ) )
!= ( ( X0 @ ( sK6 @ X0 ) )
| ( sK0 @ ( sK6 @ X0 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f57]) ).
thf(f57,plain,
! [X0: $i > $o] :
( ( sK1 @ ( sK6 @ X0 ) )
!= ( ^ [Y0: $i] :
( ( X0 @ Y0 )
| ( sK0 @ Y0 ) )
@ ( sK6 @ X0 ) ) ),
inference(negative_extensionality,[status(thm)],[f55]) ).
thf(f55,plain,
! [X0: $i > $o] :
( ( ^ [Y0: $i] :
( ( X0 @ Y0 )
| ( sK0 @ Y0 ) ) )
!= sK1 ),
inference(trivial_inequality_removal,[status(thm)],[f49]) ).
thf(f49,plain,
! [X0: $i > $o] :
( ( ( ^ [Y0: $i] :
( ( X0 @ Y0 )
| ( sK0 @ Y0 ) ) )
!= sK1 )
| ( $true != $true ) ),
inference(constrained_superposition,[status(thm)],[f14,f46]) ).
thf(f46,plain,
! [X0: $i > $o] :
( ( cK
@ ^ [Y0: $i] :
( ( X0 @ Y0 )
| ( sK0 @ Y0 ) )
@ sK2 )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f40]) ).
thf(f40,plain,
! [X0: $i > $o] :
( ( ( cK
@ ^ [Y0: $i] :
( ( X0 @ Y0 )
| ( sK0 @ Y0 ) )
@ sK2 )
= $true )
| ( $false = $true ) ),
inference(superposition,[status(thm)],[f37,f13]) ).
thf(f13,plain,
( $true
= ( cK @ sK0 @ sK2 ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f37,plain,
! [X6: $i,X4: $i > $o,X5: $i > $o] :
( ( ( cK @ X4 @ X6 )
= $false )
| ( $true
= ( cK
@ ^ [Y0: $i] :
( ( X5 @ Y0 )
| ( X4 @ Y0 ) )
@ X6 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f36]) ).
thf(f36,plain,
! [X6: $i,X4: $i > $o,X5: $i > $o] :
( ( ( ( cK @ X5 @ X6 )
| ( cK @ X4 @ X6 ) )
= $false )
| ( $true
= ( cK
@ ^ [Y0: $i] :
( ( X5 @ Y0 )
| ( X4 @ Y0 ) )
@ X6 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f34]) ).
thf(f34,plain,
! [X6: $i,X4: $i > $o,X5: $i > $o] :
( ( ( cK @ X5 @ X6 )
| ( cK @ X4 @ X6 ) )
= ( cK
@ ^ [Y0: $i] :
( ( X5 @ Y0 )
| ( X4 @ Y0 ) )
@ X6 ) ),
inference(beta_eta_normalization,[status(thm)],[f32]) ).
thf(f32,plain,
! [X6: $i,X4: $i > $o,X5: $i > $o] :
( ( ^ [Y0: $i] :
( ( cK @ X5 @ Y0 )
| ( cK @ X4 @ Y0 ) )
@ X6 )
= ( cK
@ ^ [Y0: $i] :
( ( X5 @ Y0 )
| ( X4 @ Y0 ) )
@ X6 ) ),
inference(argument_congruence,[status(thm)],[f12]) ).
thf(f12,plain,
! [X4: $i > $o,X5: $i > $o] :
( ( cK
@ ^ [Y0: $i] :
( ( X5 @ Y0 )
| ( X4 @ Y0 ) ) )
= ( ^ [Y0: $i] :
( ( cK @ X5 @ Y0 )
| ( cK @ X4 @ Y0 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f14,plain,
( $true
!= ( cK @ sK1 @ sK2 ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f63,plain,
! [X0: $i > $o] :
( ( $false
= ( sK1 @ ( sK6 @ X0 ) ) )
| ( ( X0 @ ( sK6 @ X0 ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f61]) ).
thf(f61,plain,
! [X0: $i > $o] :
( ( $false
= ( ( X0 @ ( sK6 @ X0 ) )
| ( sK0 @ ( sK6 @ X0 ) ) ) )
| ( $false
= ( sK1 @ ( sK6 @ X0 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f59]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO362^5 : TPTP v9.2.1. Released v4.0.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n018.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 14:28:31 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.21/0.45 ---- Original DTF file ---
% 0.21/0.45 thf(spec,logic,$$dhol).
% 0.21/0.45 %------------------------------------------------------------------------------
% 0.21/0.45 % File : SYO362^5 : TPTP v9.2.1. Released v4.0.0.
% 0.21/0.45 % Domain : Syntactic
% 0.21/0.45 % Problem : TPS problem THM631A
% 0.21/0.45 % Version : Especial.
% 0.21/0.45 % English : If a set function preserves unions, then it is monotone.
% 0.21/0.45
% 0.21/0.45 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.21/0.45 % Source : [Bro09]
% 0.21/0.45 % Names : tps_0419 [Bro09]
% 0.21/0.45 % : THM631 [TPS]
% 0.21/0.45 % : THM631A [TPS]
% 0.21/0.45
% 0.21/0.45 % Status : Theorem
% 0.21/0.45 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.10 v8.2.0, 0.23 v8.1.0, 0.27 v7.5.0, 0.14 v7.4.0, 0.22 v7.2.0, 0.12 v7.1.0, 0.25 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.29 v6.1.0, 0.14 v6.0.0, 0.29 v5.5.0, 0.50 v5.4.0, 0.60 v5.3.0, 0.80 v4.1.0, 1.00 v4.0.0
% 0.21/0.45 % Syntax : Number of formulae : 2 ( 0 unt; 1 typ; 0 def)
% 0.21/0.45 % Number of atoms : 6 ( 1 equ; 0 cnn)
% 0.21/0.45 % Maximal formula atoms : 3 ( 6 avg)
% 0.21/0.45 % Number of connectives : 19 ( 0 ~; 2 |; 0 &; 13 @)
% 0.21/0.45 % ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% 0.21/0.45 % Maximal formula depth : 9 ( 9 avg)
% 0.21/0.45 % Number of types : 2 ( 0 usr)
% 0.21/0.45 % Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% 0.21/0.45 % Number of symbols : 2 ( 1 usr; 0 con; 2-2 aty)
% 0.21/0.45 % Number of variables : 8 ( 2 ^; 6 !; 0 ?; 8 :)
% 0.21/0.45 % SPC : TH0_THM_EQU_NAR
% 0.21/0.45
% 0.21/0.45 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.21/0.45 % project in the Department of Mathematical Sciences at Carnegie
% 0.21/0.45 % Mellon University. Distributed under the Creative Commons copyleft
% 0.21/0.45 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.21/0.45 % : Polymorphic definitions expanded.
% 0.21/0.45 %------------------------------------------------------------------------------
% 0.21/0.45 thf(cK,type,
% 0.21/0.45 cK: ( $i > $o ) > $i > $o ).
% 0.21/0.45
% 0.21/0.45 thf(cTHM631A_pme,conjecture,
% 0.21/0.45 ( ! [X: $i > $o,Y: $i > $o] :
% 0.21/0.45 ( ( cK
% 0.21/0.45 @ ^ [Xz: $i] :
% 0.21/0.45 ( ( X @ Xz )
% 0.21/0.45 | ( Y @ Xz ) ) )
% 0.21/0.45 = ( ^ [Xw: $i] :
% 0.21/0.45 ( ( cK @ X @ Xw )
% 0.21/0.45 | ( cK @ Y @ Xw ) ) ) )
% 0.21/0.45 => ! [X: $i > $o,Y: $i > $o] :
% 0.21/0.45 ( ! [Xx: $i] :
% 0.21/0.45 ( ( X @ Xx )
% 0.21/0.45 => ( Y @ Xx ) )
% 0.21/0.45 => ! [Xx: $i] :
% 0.21/0.45 ( ( cK @ X @ Xx )
% 0.21/0.45 => ( cK @ Y @ Xx ) ) ) ) ).
% 0.21/0.45
% 0.21/0.45 %------------------------------------------------------------------------------
% 0.21/0.45 ------------------------
% 1.49/1.37 ---- Embedded in THF ---
% 1.49/1.37 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.49/1.37 %%% Generated on Tue Feb 24 14:28:32 EST 2026
% 1.49/1.37 %%% using '$$dhol' embedding, version 1.3.0.
% 1.49/1.37 %%% Logic specification used:
% 1.49/1.37 %%% thf(spec, logic, $$dhol).
% 1.49/1.37
% 1.49/1.37 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.JLlLF4KaAw/DTF2DTF11649.p
% See solution above
% 1.49/1.37 ------------------------
% 1.49/1.38 ---- Cleaned THF ---
% 1.49/1.38 thf(cK,type,
% 1.49/1.38 cK: ( $i > $o ) > $i > $o ).
% 1.49/1.38
% 1.49/1.38 thf(cTHM631A_pme,conjecture,
% 1.49/1.38 ( ! [X: $i > $o,Y: $i > $o] :
% 1.49/1.38 ( ( cK
% 1.49/1.38 @ ^ [Xz: $i] :
% 1.49/1.38 ( ( X @ Xz )
% 1.49/1.38 | ( Y @ Xz ) ) )
% 1.49/1.38 = ( ^ [Xw: $i] :
% 1.49/1.38 ( ( cK @ X @ Xw )
% 1.49/1.38 | ( cK @ Y @ Xw ) ) ) )
% 1.49/1.38 => ! [X: $i > $o,Y: $i > $o] :
% 1.49/1.38 ( ! [Xx: $i] :
% 1.49/1.38 ( ( X @ Xx )
% 1.49/1.38 => ( Y @ Xx ) )
% 1.49/1.38 => ! [Xx: $i] :
% 1.49/1.38 ( ( cK @ X @ Xx )
% 1.49/1.38 => ( cK @ Y @ Xx ) ) ) ) ).
% 1.49/1.38 ------------------------
% 1.65/1.40 % (11750)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_11649 for (3000ds/27Mi)
% 1.65/1.40 % (11748)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_11649 for (3000ds/183Mi)
% 1.65/1.40 % (11751)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_11649 for (3000ds/2Mi)
% 1.65/1.40 % (11749)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_11649 for (3000ds/4Mi)
% 1.65/1.40 % (11753)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_11649 for (3000ds/275Mi)
% 1.65/1.40 % (11752)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_11649 for (3000ds/2Mi)
% 1.65/1.40 % (11754)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_11649 for (3000ds/18Mi)
% 1.65/1.40 % (11751)Instruction limit reached!
% 1.65/1.40 % (11751)------------------------------
% 1.65/1.40 % (11751)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.40 % (11751)Termination reason: Unknown
% 1.65/1.40 % (11751)Termination phase: Saturation
% 1.65/1.40
% 1.65/1.40 % (11751)Memory used [KB]: 5500
% 1.65/1.40 % (11751)Time elapsed: 0.003 s
% 1.65/1.40 % (11751)Instructions burned: 2 (million)
% 1.65/1.40 % (11751)------------------------------
% 1.65/1.40 % (11751)------------------------------
% 1.65/1.40 % (11752)Instruction limit reached!
% 1.65/1.40 % (11752)------------------------------
% 1.65/1.40 % (11752)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.40 % (11752)Termination reason: Unknown
% 1.65/1.40 % (11752)Termination phase: Saturation
% 1.65/1.40
% 1.65/1.40 % (11752)Memory used [KB]: 895
% 1.65/1.40 % (11752)Time elapsed: 0.003 s
% 1.65/1.40 % (11752)Instructions burned: 2 (million)
% 1.65/1.40 % (11752)------------------------------
% 1.65/1.40 % (11752)------------------------------
% 1.65/1.40 % (11749)Instruction limit reached!
% 1.65/1.40 % (11749)------------------------------
% 1.65/1.40 % (11749)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.40 % (11749)Termination reason: Unknown
% 1.65/1.40 % (11749)Termination phase: Saturation
% 1.65/1.40
% 1.65/1.40 % (11749)Memory used [KB]: 5500
% 1.65/1.40 % (11749)Time elapsed: 0.005 s
% 1.65/1.40 % (11749)Instructions burned: 5 (million)
% 1.65/1.40 % (11749)------------------------------
% 1.65/1.40 % (11749)------------------------------
% 1.65/1.41 % (11754)First to succeed.
% 1.65/1.41 % (11754)Refutation found. Thanks to Tanya!
% 1.65/1.41 % SZS status Theorem for DTF2THF_11649
% 1.65/1.41 % SZS output start Proof for DTF2THF_11649
% 1.65/1.41 thf(func_def_0, type, cK: ($i > $o) > $i > $o).
% 1.65/1.41 thf(func_def_7, type, sK0: $i > $o).
% 1.65/1.41 thf(func_def_8, type, sK1: $i > $o).
% 1.65/1.41 thf(func_def_12, type, ph4: !>[X0: $tType]:(X0)).
% 1.65/1.41 thf(func_def_14, type, sK6: ($i > $o) > $i).
% 1.65/1.41 thf(f89,plain,(
% 1.65/1.41 $false),
% 1.65/1.41 inference(trivial_inequality_removal,[status(thm)],[f88])).
% 1.65/1.41 thf(f88,plain,(
% 1.65/1.41 ($false = $true)),
% 1.65/1.41 inference(duplicate_literal_removal,[status(thm)],[f82])).
% 1.65/1.41 thf(f82,plain,(
% 1.65/1.41 ($false = $true) | ($false = $true)),
% 1.65/1.41 inference(superposition,[status(thm)],[f63,f69])).
% 1.65/1.41 thf(f69,plain,(
% 1.65/1.41 ($true = (sK1 @ (sK6 @ sK1)))),
% 1.65/1.41 inference(beta_eta_normalization,[status(thm)],[f68])).
% 1.65/1.41 thf(f68,plain,(
% 1.65/1.41 (((^[Y0 : $i]: (sK1 @ ((^[Y1 : $i]: (Y1)) @ Y0))) @ (sK6 @ (^[Y0 : $i]: (sK1 @ ((^[Y1 : $i]: (Y1)) @ Y0))))) = $true)),
% 1.65/1.41 inference(trivial_inequality_removal,[status(thm)],[f66])).
% 1.65/1.41 thf(f66,plain,(
% 1.65/1.41 (((^[Y0 : $i]: (sK1 @ ((^[Y1 : $i]: (Y1)) @ Y0))) @ (sK6 @ (^[Y0 : $i]: (sK1 @ ((^[Y1 : $i]: (Y1)) @ Y0))))) = $true) | ($true != $true)),
% 1.65/1.41 inference(equality_factoring,[status(thm)],[f65])).
% 1.65/1.41 thf(f65,plain,(
% 1.65/1.41 ( ! [X0 : $i > $o] : (($true = (sK1 @ (sK6 @ X0))) | ((X0 @ (sK6 @ X0)) = $true)) )),
% 1.65/1.41 inference(subsumption_resolution,[status(thm)],[f64,f15])).
% 1.65/1.41 thf(f15,plain,(
% 1.65/1.41 ( ! [X2 : $i] : (((sK0 @ X2) != $true) | ((sK1 @ X2) = $true)) )),
% 1.65/1.41 inference(cnf_transformation,[status(thm)],[f11])).
% 1.65/1.41 thf(f11,plain,(
% 1.65/1.41 (! [X2 : $i] : (((sK1 @ X2) = $true) | ((sK0 @ X2) != $true)) & (($true != (cK @ sK1 @ sK2)) & ($true = (cK @ sK0 @ sK2)))) & ! [X4 : $i > $o,X5 : $i > $o] : ((cK @ (^[Y0 : $i]: ((X5 @ Y0) | (X4 @ Y0)))) = (^[Y0 : $i]: ((cK @ X5 @ Y0) | (cK @ X4 @ Y0))))),
% 1.65/1.41 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f8,f10,f9])).
% 1.65/1.41 thf(f9,plain,(
% 1.65/1.41 ? [X0 : $i > $o,X1 : $i > $o] : (! [X2 : $i] : (((X1 @ X2) = $true) | ((X0 @ X2) != $true)) & ? [X3 : $i] : (((cK @ X1 @ X3) != $true) & ((cK @ X0 @ X3) = $true))) => (! [X2 : $i] : (((sK1 @ X2) = $true) | ((sK0 @ X2) != $true)) & ? [X3 : $i] : (((cK @ sK1 @ X3) != $true) & ($true = (cK @ sK0 @ X3))))),
% 1.65/1.41 introduced(definition,[],[choice_axiom])).
% 1.65/1.41 thf(f10,plain,(
% 1.65/1.41 ? [X3 : $i] : (((cK @ sK1 @ X3) != $true) & ($true = (cK @ sK0 @ X3))) => (($true != (cK @ sK1 @ sK2)) & ($true = (cK @ sK0 @ sK2)))),
% 1.65/1.41 introduced(definition,[],[choice_axiom])).
% 1.65/1.41 thf(f8,plain,(
% 1.65/1.41 ? [X0 : $i > $o,X1 : $i > $o] : (! [X2 : $i] : (((X1 @ X2) = $true) | ((X0 @ X2) != $true)) & ? [X3 : $i] : (((cK @ X1 @ X3) != $true) & ((cK @ X0 @ X3) = $true))) & ! [X4 : $i > $o,X5 : $i > $o] : ((cK @ (^[Y0 : $i]: ((X5 @ Y0) | (X4 @ Y0)))) = (^[Y0 : $i]: ((cK @ X5 @ Y0) | (cK @ X4 @ Y0))))),
% 1.65/1.41 inference(rectify,[status(thm)],[f7])).
% 1.65/1.41 thf(f7,plain,(
% 1.65/1.41 ? [X2 : $i > $o,X3 : $i > $o] : (! [X4 : $i] : (($true = (X3 @ X4)) | ((X2 @ X4) != $true)) & ? [X5 : $i] : (($true != (cK @ X3 @ X5)) & ((cK @ X2 @ X5) = $true))) & ! [X0 : $i > $o,X1 : $i > $o] : ((^[Y0 : $i]: ((cK @ X1 @ Y0) | (cK @ X0 @ Y0))) = (cK @ (^[Y0 : $i]: ((X1 @ Y0) | (X0 @ Y0)))))),
% 1.65/1.41 inference(ennf_transformation,[status(thm)],[f6])).
% 1.65/1.41 thf(f6,plain,(
% 1.65/1.41 ~(! [X0 : $i > $o,X1 : $i > $o] : ((^[Y0 : $i]: ((cK @ X1 @ Y0) | (cK @ X0 @ Y0))) = (cK @ (^[Y0 : $i]: ((X1 @ Y0) | (X0 @ Y0))))) => ! [X2 : $i > $o,X3 : $i > $o] : (! [X4 : $i] : (((X2 @ X4) = $true) => ($true = (X3 @ X4))) => ! [X5 : $i] : (((cK @ X2 @ X5) = $true) => ($true = (cK @ X3 @ X5)))))),
% 1.65/1.41 inference(rectify,[status(thm)],[f5])).
% 1.65/1.41 thf(f5,plain,(
% 1.65/1.41 ~(! [X0 : $i > $o,X1 : $i > $o] : ((^[Y0 : $i]: ((cK @ X1 @ Y0) | (cK @ X0 @ Y0))) = (cK @ (^[Y0 : $i]: ((X1 @ Y0) | (X0 @ Y0))))) => ! [X4 : $i > $o,X5 : $i > $o] : (! [X6 : $i] : (($true = (X4 @ X6)) => ((X5 @ X6) = $true)) => ! [X7 : $i] : (((cK @ X4 @ X7) = $true) => ((cK @ X5 @ X7) = $true))))),
% 1.65/1.41 inference(fool_elimination,[status(thm)],[f4])).
% 1.65/1.41 thf(f4,plain,(
% 1.65/1.41 ~(! [X0 : $i > $o,X1 : $i > $o] : ((cK @ (^[X2 : $i] : ((X0 @ X2) | (X1 @ X2)))) = (^[X3 : $i] : ((cK @ X0 @ X3) | (cK @ X1 @ X3)))) => ! [X4 : $i > $o,X5 : $i > $o] : (! [X6 : $i] : ((X4 @ X6) => (X5 @ X6)) => ! [X7 : $i] : ((cK @ X4 @ X7) => (cK @ X5 @ X7))))),
% 1.65/1.41 inference(rectify,[status(thm)],[f2])).
% 1.65/1.41 thf(f2,negated_conjecture,(
% 1.65/1.41 ~(! [X1 : $i > $o,X0 : $i > $o] : ((cK @ (^[X2 : $i] : ((X1 @ X2) | (X0 @ X2)))) = (^[X3 : $i] : ((cK @ X1 @ X3) | (cK @ X0 @ X3)))) => ! [X0 : $i > $o,X1 : $i > $o] : (! [X4 : $i] : ((X0 @ X4) => (X1 @ X4)) => ! [X4 : $i] : ((cK @ X0 @ X4) => (cK @ X1 @ X4))))),
% 1.65/1.41 inference(negated_conjecture,[status(cth)],[f1])).
% 1.65/1.41 thf(f1,conjecture,(
% 1.65/1.41 ! [X1 : $i > $o,X0 : $i > $o] : ((cK @ (^[X2 : $i] : ((X1 @ X2) | (X0 @ X2)))) = (^[X3 : $i] : ((cK @ X1 @ X3) | (cK @ X0 @ X3)))) => ! [X0 : $i > $o,X1 : $i > $o] : (! [X4 : $i] : ((X0 @ X4) => (X1 @ X4)) => ! [X4 : $i] : ((cK @ X0 @ X4) => (cK @ X1 @ X4)))),
% 1.65/1.41 file('/export/starexec/sandbox/tmp/tmp.JLlLF4KaAw/DTF2THF_11649.p',cTHM631A_pme)).
% 1.65/1.41 thf(f64,plain,(
% 1.65/1.41 ( ! [X0 : $i > $o] : (($true = (sK1 @ (sK6 @ X0))) | ((sK0 @ (sK6 @ X0)) = $true) | ((X0 @ (sK6 @ X0)) = $true)) )),
% 1.65/1.41 inference(binary_proxy_clausification,[status(thm)],[f60])).
% 1.65/1.41 thf(f60,plain,(
% 1.65/1.41 ( ! [X0 : $i > $o] : (($true = (sK1 @ (sK6 @ X0))) | ($true = ((X0 @ (sK6 @ X0)) | (sK0 @ (sK6 @ X0))))) )),
% 1.65/1.41 inference(binary_proxy_clausification,[status(thm)],[f59])).
% 1.65/1.41 thf(f59,plain,(
% 1.65/1.41 ( ! [X0 : $i > $o] : (((sK1 @ (sK6 @ X0)) != ((X0 @ (sK6 @ X0)) | (sK0 @ (sK6 @ X0))))) )),
% 1.65/1.41 inference(beta_eta_normalization,[status(thm)],[f57])).
% 1.65/1.41 thf(f57,plain,(
% 1.65/1.41 ( ! [X0 : $i > $o] : (((sK1 @ (sK6 @ X0)) != ((^[Y0 : $i]: ((X0 @ Y0) | (sK0 @ Y0))) @ (sK6 @ X0)))) )),
% 1.65/1.41 inference(negative_extensionality,[status(thm)],[f55])).
% 1.65/1.41 thf(f55,plain,(
% 1.65/1.41 ( ! [X0 : $i > $o] : (((^[Y0 : $i]: ((X0 @ Y0) | (sK0 @ Y0))) != sK1)) )),
% 1.65/1.41 inference(trivial_inequality_removal,[status(thm)],[f49])).
% 1.65/1.41 thf(f49,plain,(
% 1.65/1.41 ( ! [X0 : $i > $o] : (((^[Y0 : $i]: ((X0 @ Y0) | (sK0 @ Y0))) != sK1) | ($true != $true)) )),
% 1.65/1.41 inference(constrained_superposition,[status(thm)],[f14,f46])).
% 1.65/1.41 thf(f46,plain,(
% 1.65/1.41 ( ! [X0 : $i > $o] : (((cK @ (^[Y0 : $i]: ((X0 @ Y0) | (sK0 @ Y0))) @ sK2) = $true)) )),
% 1.65/1.41 inference(trivial_inequality_removal,[status(thm)],[f40])).
% 1.65/1.41 thf(f40,plain,(
% 1.65/1.41 ( ! [X0 : $i > $o] : (((cK @ (^[Y0 : $i]: ((X0 @ Y0) | (sK0 @ Y0))) @ sK2) = $true) | ($false = $true)) )),
% 1.65/1.41 inference(superposition,[status(thm)],[f37,f13])).
% 1.65/1.41 thf(f13,plain,(
% 1.65/1.41 ($true = (cK @ sK0 @ sK2))),
% 1.65/1.41 inference(cnf_transformation,[status(thm)],[f11])).
% 1.65/1.41 thf(f37,plain,(
% 1.65/1.41 ( ! [X6 : $i,X4 : $i > $o,X5 : $i > $o] : (((cK @ X4 @ X6) = $false) | ($true = (cK @ (^[Y0 : $i]: ((X5 @ Y0) | (X4 @ Y0))) @ X6))) )),
% 1.65/1.41 inference(binary_proxy_clausification,[status(thm)],[f36])).
% 1.65/1.41 thf(f36,plain,(
% 1.65/1.41 ( ! [X6 : $i,X4 : $i > $o,X5 : $i > $o] : ((((cK @ X5 @ X6) | (cK @ X4 @ X6)) = $false) | ($true = (cK @ (^[Y0 : $i]: ((X5 @ Y0) | (X4 @ Y0))) @ X6))) )),
% 1.65/1.41 inference(binary_proxy_clausification,[status(thm)],[f34])).
% 1.65/1.41 thf(f34,plain,(
% 1.65/1.41 ( ! [X6 : $i,X4 : $i > $o,X5 : $i > $o] : ((((cK @ X5 @ X6) | (cK @ X4 @ X6)) = (cK @ (^[Y0 : $i]: ((X5 @ Y0) | (X4 @ Y0))) @ X6))) )),
% 1.65/1.41 inference(beta_eta_normalization,[status(thm)],[f32])).
% 1.65/1.41 thf(f32,plain,(
% 1.65/1.41 ( ! [X6 : $i,X4 : $i > $o,X5 : $i > $o] : ((((^[Y0 : $i]: ((cK @ X5 @ Y0) | (cK @ X4 @ Y0))) @ X6) = (cK @ (^[Y0 : $i]: ((X5 @ Y0) | (X4 @ Y0))) @ X6))) )),
% 1.65/1.41 inference(argument_congruence,[status(thm)],[f12])).
% 1.65/1.41 thf(f12,plain,(
% 1.65/1.41 ( ! [X4 : $i > $o,X5 : $i > $o] : (((cK @ (^[Y0 : $i]: ((X5 @ Y0) | (X4 @ Y0)))) = (^[Y0 : $i]: ((cK @ X5 @ Y0) | (cK @ X4 @ Y0))))) )),
% 1.65/1.41 inference(cnf_transformation,[status(thm)],[f11])).
% 1.65/1.41 thf(f14,plain,(
% 1.65/1.41 ($true != (cK @ sK1 @ sK2))),
% 1.65/1.41 inference(cnf_transformation,[status(thm)],[f11])).
% 1.65/1.41 thf(f63,plain,(
% 1.65/1.41 ( ! [X0 : $i > $o] : (($false = (sK1 @ (sK6 @ X0))) | ((X0 @ (sK6 @ X0)) = $false)) )),
% 1.65/1.41 inference(binary_proxy_clausification,[status(thm)],[f61])).
% 1.65/1.41 thf(f61,plain,(
% 1.65/1.41 ( ! [X0 : $i > $o] : (($false = ((X0 @ (sK6 @ X0)) | (sK0 @ (sK6 @ X0)))) | ($false = (sK1 @ (sK6 @ X0)))) )),
% 1.65/1.41 inference(binary_proxy_clausification,[status(thm)],[f59])).
% 1.65/1.41 % SZS output end Proof for DTF2THF_11649
% 1.65/1.41 % (11754)------------------------------
% 1.65/1.41 % (11754)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.41 % (11754)Termination reason: Refutation
% 1.65/1.41
% 1.65/1.41 % (11754)Memory used [KB]: 5500
% 1.65/1.41 % (11754)Time elapsed: 0.010 s
% 1.65/1.41 % (11754)Instructions burned: 14 (million)
% 1.65/1.41 % (11754)------------------------------
% 1.65/1.41 % (11754)------------------------------
% 1.65/1.41 % (11747)Success in time 0.025 s
%------------------------------------------------------------------------------