%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO208^5 : 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 : n026.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 09:53:40 AM UTC 2026
% Result : Theorem 1.60s 1.36s
% Output : Refutation 1.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 1
% Syntax : Number of formulae : 35 ( 23 unt; 0 typ; 0 def)
% Number of atoms : 194 ( 82 equ; 0 cnn)
% Maximal formula atoms : 4 ( 5 avg)
% Number of connectives : 327 ( 55 ~; 20 |; 0 &; 234 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 58 ( 58 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 2 usr; 4 con; 0-2 aty)
% ( 6 !!; 12 ??; 0 @@+; 0 @@-)
% Number of variables : 112 ( 72 ^; 36 !; 4 ?; 112 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_13,type,
sK1: a > a > $o ).
thf(func_def_14,type,
sK2: ( a > $o ) > a ).
thf(f64,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f63]) ).
thf(f63,plain,
$true = $false,
inference(forward_demodulation,[status(thm)],[f62,f58]) ).
thf(f58,plain,
( $false
= ( sK1
@ ( sK2
@ ^ [Y0: a] :
~ ( sK1 @ Y0 @ Y0 ) )
@ ( sK2
@ ^ [Y0: a] :
~ ( sK1 @ Y0 @ Y0 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f55]) ).
thf(f55,plain,
( $false
= ( sK1
@ ( sK2
@ ^ [Y0: a] :
~ ( sK1 @ Y0
@ ( ^ [Y1: a] : Y1
@ Y0 ) ) )
@ ( ^ [Y0: a] : Y0
@ ( sK2
@ ^ [Y0: a] :
~ ( sK1 @ Y0
@ ( ^ [Y1: a] : Y1
@ Y0 ) ) ) ) ) ),
inference(equality_resolution,[status(thm)],[f49]) ).
thf(f49,plain,
! [X0: a > a] :
( ( ( sK2
@ ^ [Y0: a] :
~ ( sK1 @ Y0 @ ( X0 @ Y0 ) ) )
!= ( X0
@ ( sK2
@ ^ [Y0: a] :
~ ( sK1 @ Y0 @ ( X0 @ Y0 ) ) ) ) )
| ( ( sK1
@ ( sK2
@ ^ [Y0: a] :
~ ( sK1 @ Y0 @ ( X0 @ Y0 ) ) )
@ ( X0
@ ( sK2
@ ^ [Y0: a] :
~ ( sK1 @ Y0 @ ( X0 @ Y0 ) ) ) ) )
= $false ) ),
inference(equality_resolution,[status(thm)],[f41]) ).
thf(f41,plain,
! [X0: a > a,X1: a] :
( ( ( sK2
@ ^ [Y0: a] :
~ ( sK1 @ Y0 @ ( X0 @ Y0 ) ) )
!= X1 )
| ( $false
= ( sK1 @ X1 @ ( X0 @ X1 ) ) )
| ( ( X0 @ X1 )
!= X1 ) ),
inference(beta_eta_normalization,[status(thm)],[f40]) ).
thf(f40,plain,
! [X0: a > a,X1: a] :
( ( ( ^ [Y0: a] :
( sK1
@ ( ^ [Y1: a] : Y1
@ Y0 )
@ ( X0 @ Y0 ) )
@ X1 )
= $false )
| ( ( sK2
@ ^ [Y0: a] :
~ ( ^ [Y1: a] :
( sK1
@ ( ^ [Y2: a] : Y2
@ Y1 )
@ ( X0 @ Y1 ) )
@ Y0 ) )
!= X1 )
| ( ( X0 @ X1 )
!= X1 ) ),
inference(trivial_inequality_removal,[status(thm)],[f36]) ).
thf(f36,plain,
! [X0: a > a,X1: a] :
( ( ( sK2
@ ^ [Y0: a] :
~ ( ^ [Y1: a] :
( sK1
@ ( ^ [Y2: a] : Y2
@ Y1 )
@ ( X0 @ Y1 ) )
@ Y0 ) )
!= X1 )
| ( $false != $false )
| ( ( ^ [Y0: a] :
( sK1
@ ( ^ [Y1: a] : Y1
@ Y0 )
@ ( X0 @ Y0 ) )
@ X1 )
= $false )
| ( ( X0 @ X1 )
!= X1 ) ),
inference(equality_factoring,[status(thm)],[f35]) ).
thf(f35,plain,
! [X2: a,X5: a > $o] :
( ( $false
= ( sK1
@ ( sK2
@ ^ [Y0: a] :
~ ( X5 @ Y0 ) )
@ X2 ) )
| ( $false
= ( X5 @ X2 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f33]) ).
thf(f33,plain,
! [X2: a,X5: a > $o] :
( ( $false
= ( sK1
@ ( sK2
@ ^ [Y0: a] :
~ ( X5 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ~ ( X5 @ X2 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f24]) ).
thf(f24,plain,
! [X2: a,X5: a > $o] :
( ( ~ ( X5 @ X2 ) )
= ( sK1
@ ( sK2
@ ^ [Y0: a] :
~ ( X5 @ Y0 ) )
@ X2 ) ),
inference(beta_eta_normalization,[status(thm)],[f21]) ).
thf(f21,plain,
! [X2: a,X5: a > $o] :
( ( ^ [Y0: a] :
~ ( X5 @ Y0 )
@ X2 )
= ( sK1
@ ( sK2
@ ^ [Y0: a] :
~ ( X5 @ Y0 ) )
@ X2 ) ),
inference(primitive_instantiation,[status(thm)],[f16]) ).
thf(f16,plain,
! [X2: a,X1: a > $o] :
( ( sK1 @ ( sK2 @ X1 ) @ X2 )
= ( X1 @ X2 ) ),
inference(argument_congruence,[status(thm)],[f15]) ).
thf(f15,plain,
! [X1: a > $o] :
( ( sK1 @ ( sK2 @ X1 ) )
= X1 ),
inference(equality_proxy_clausification,[status(thm)],[f14]) ).
thf(f14,plain,
! [X1: a > $o] :
( ( ( sK1 @ ( sK2 @ X1 ) )
= X1 )
= $true ),
inference(equality_proxy_clausification,[status(thm)],[f13]) ).
thf(f13,plain,
! [X1: a > $o] :
( $true
= ( ( ( sK1 @ ( sK2 @ X1 ) )
= X1 )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f12]) ).
thf(f12,plain,
! [X1: a > $o] :
( $true
= ( ^ [Y0: a] :
( ( ( sK1 @ Y0 )
= X1 )
= $true )
@ ( sK2 @ X1 ) ) ),
inference(sigma_clausification,[status(thm)],[f11]) ).
thf(f11,plain,
! [X1: a > $o] :
( ( ?? @ a
@ ^ [Y0: a] :
( ( ( sK1 @ Y0 )
= X1 )
= $true ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f10]) ).
thf(f10,plain,
! [X1: a > $o] :
( $true
= ( ^ [Y0: a > $o] :
( ?? @ a
@ ^ [Y1: a] :
( ( ( sK1 @ Y1 )
= Y0 )
= $true ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f9]) ).
thf(f9,plain,
( $true
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ?? @ a
@ ^ [Y1: a] :
( ( ( sK1 @ Y1 )
= Y0 )
= $true ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f8]) ).
thf(f8,plain,
( ( ^ [Y0: a > a > $o] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ?? @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
= Y1 )
= $true ) ) )
@ sK1 )
= $true ),
inference(sigma_clausification,[status(thm)],[f7]) ).
thf(f7,plain,
( $true
= ( ?? @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ?? @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
= Y1 )
= $true ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f6]) ).
thf(f6,plain,
( $true
= ( ?? @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ?? @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
= Y1 )
= ( Y1 = Y1 ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f5]) ).
thf(f5,plain,
( ( ~ ~ ( ?? @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ?? @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
= Y1 )
= ( Y1 = Y1 ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f4]) ).
thf(f4,plain,
( ( ~ ~ ( ?? @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ?? @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
= Y1 )
= ( Y1 = Y1 ) ) ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ~ ? [X0: a > a > $o] :
! [X1: a > $o] :
? [X2: a] :
( ( ( X0 @ X2 )
= X1 )
= ( X1 = X1 ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
~ ? [X0: a > a > $o] :
! [X1: a > $o] :
? [X2: a] :
( ( ( X0 @ X2 )
= X1 )
= ( X1 = X1 ) ),
file('/export/starexec/sandbox/tmp/tmp.8RDVElAklK/DTF2THF_17671.p',cCT31) ).
thf(f62,plain,
( $true
= ( sK1
@ ( sK2
@ ^ [Y0: a] :
~ ( sK1 @ Y0 @ Y0 ) )
@ ( sK2
@ ^ [Y0: a] :
~ ( sK1 @ Y0 @ Y0 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f59]) ).
thf(f59,plain,
( $true
= ( sK1
@ ( sK2
@ ^ [Y0: a] :
~ ( sK1 @ Y0
@ ( ^ [Y1: a] : Y1
@ Y0 ) ) )
@ ( ^ [Y0: a] : Y0
@ ( sK2
@ ^ [Y0: a] :
~ ( sK1 @ Y0
@ ( ^ [Y1: a] : Y1
@ Y0 ) ) ) ) ) ),
inference(equality_resolution,[status(thm)],[f50]) ).
thf(f50,plain,
! [X0: a > a] :
( ( ( sK2
@ ^ [Y0: a] :
~ ( sK1 @ Y0 @ ( X0 @ Y0 ) ) )
!= ( X0
@ ( sK2
@ ^ [Y0: a] :
~ ( sK1 @ Y0 @ ( X0 @ Y0 ) ) ) ) )
| ( ( sK1
@ ( sK2
@ ^ [Y0: a] :
~ ( sK1 @ Y0 @ ( X0 @ Y0 ) ) )
@ ( X0
@ ( sK2
@ ^ [Y0: a] :
~ ( sK1 @ Y0 @ ( X0 @ Y0 ) ) ) ) )
= $true ) ),
inference(equality_resolution,[status(thm)],[f46]) ).
thf(f46,plain,
! [X0: a > a,X1: a] :
( ( ( sK2
@ ^ [Y0: a] :
~ ( sK1 @ Y0 @ ( X0 @ Y0 ) ) )
!= X1 )
| ( $true
= ( sK1 @ X1 @ ( X0 @ X1 ) ) )
| ( ( X0 @ X1 )
!= X1 ) ),
inference(beta_eta_normalization,[status(thm)],[f45]) ).
thf(f45,plain,
! [X0: a > a,X1: a] :
( ( ( sK2
@ ^ [Y0: a] :
~ ( ^ [Y1: a] :
( sK1
@ ( ^ [Y2: a] : Y2
@ Y1 )
@ ( X0 @ Y1 ) )
@ Y0 ) )
!= X1 )
| ( $true
= ( ^ [Y0: a] :
( sK1
@ ( ^ [Y1: a] : Y1
@ Y0 )
@ ( X0 @ Y0 ) )
@ X1 ) )
| ( ( X0 @ X1 )
!= X1 ) ),
inference(trivial_inequality_removal,[status(thm)],[f43]) ).
thf(f43,plain,
! [X0: a > a,X1: a] :
( ( $true
= ( ^ [Y0: a] :
( sK1
@ ( ^ [Y1: a] : Y1
@ Y0 )
@ ( X0 @ Y0 ) )
@ X1 ) )
| ( ( sK2
@ ^ [Y0: a] :
~ ( ^ [Y1: a] :
( sK1
@ ( ^ [Y2: a] : Y2
@ Y1 )
@ ( X0 @ Y1 ) )
@ Y0 ) )
!= X1 )
| ( ( X0 @ X1 )
!= X1 )
| ( $true != $true ) ),
inference(equality_factoring,[status(thm)],[f42]) ).
thf(f42,plain,
! [X2: a,X5: a > $o] :
( ( $true
= ( sK1
@ ( sK2
@ ^ [Y0: a] :
~ ( X5 @ Y0 ) )
@ X2 ) )
| ( $true
= ( X5 @ X2 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f34]) ).
thf(f34,plain,
! [X2: a,X5: a > $o] :
( ( $true
= ( sK1
@ ( sK2
@ ^ [Y0: a] :
~ ( X5 @ Y0 ) )
@ X2 ) )
| ( $false
= ( ~ ( X5 @ X2 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO208^5 : 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 : n026.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 14:26:10 EST 2026
% 0.16/0.35 % CPUTime :
% 0.16/0.35 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.30/0.47 ---- Original DTF file ---
% 0.30/0.47 thf(spec,logic,$$dhol).
% 0.30/0.47 %------------------------------------------------------------------------------
% 0.30/0.47 % File : SYO208^5 : TPTP v9.2.1. Released v4.0.0.
% 0.30/0.47 % Domain : Syntactic
% 0.30/0.47 % Problem : TPS problem CT31
% 0.30/0.47 % Version : Especial.
% 0.30/0.47 % English :
% 0.30/0.47
% 0.30/0.47 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.30/0.47 % Source : [Bro09]
% 0.30/0.47 % Names : tps_0179 [Bro09]
% 0.30/0.47 % : CT31 [TPS]
% 0.30/0.47
% 0.30/0.47 % Status : Theorem
% 0.30/0.47 % Rating : 0.44 v9.1.0, 0.38 v9.0.0, 0.50 v8.2.0, 0.69 v8.1.0, 0.45 v7.5.0, 0.29 v7.4.0, 0.44 v7.2.0, 0.38 v7.0.0, 0.57 v6.4.0, 0.50 v6.3.0, 0.60 v6.2.0, 0.71 v6.1.0, 0.57 v6.0.0, 0.71 v5.5.0, 0.67 v5.4.0, 0.40 v4.1.0, 0.33 v4.0.1, 0.67 v4.0.0
% 0.30/0.47 % Syntax : Number of formulae : 2 ( 1 unt; 1 typ; 0 def)
% 0.30/0.47 % Number of atoms : 3 ( 3 equ; 0 cnn)
% 0.30/0.47 % Maximal formula atoms : 1 ( 3 avg)
% 0.30/0.47 % Number of connectives : 2 ( 1 ~; 0 |; 0 &; 1 @)
% 0.30/0.47 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.30/0.47 % Maximal formula depth : 5 ( 5 avg)
% 0.30/0.47 % Number of types : 2 ( 1 usr)
% 0.30/0.47 % Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% 0.30/0.47 % Number of symbols : 1 ( 0 usr; 0 con; 2-2 aty)
% 0.30/0.47 % Number of variables : 3 ( 0 ^; 1 !; 2 ?; 3 :)
% 0.30/0.47 % SPC : TH0_THM_EQU_NAR
% 0.30/0.47
% 0.30/0.47 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.30/0.47 % project in the Department of Mathematical Sciences at Carnegie
% 0.30/0.47 % Mellon University. Distributed under the Creative Commons copyleft
% 0.30/0.47 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.30/0.47 %------------------------------------------------------------------------------
% 0.30/0.47 thf(a_type,type,
% 0.30/0.47 a: $tType ).
% 0.30/0.47
% 0.30/0.47 thf(cCT31,conjecture,
% 0.30/0.47 ~ ? [Xg: a > a > $o] :
% 0.30/0.47 ! [Xf: a > $o] :
% 0.30/0.47 ? [Xj: a] :
% 0.30/0.47 ( ( ( Xg @ Xj )
% 0.30/0.47 = Xf )
% 0.30/0.47 = ( Xf = Xf ) ) ).
% 0.30/0.47
% 0.30/0.47 %------------------------------------------------------------------------------
% 0.30/0.47 ------------------------
% 1.46/1.25 ---- Embedded in THF ---
% 1.46/1.25 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.46/1.25 %%% Generated on Tue Feb 24 14:26:11 EST 2026
% 1.46/1.25 %%% using '$$dhol' embedding, version 1.3.0.
% 1.46/1.25 %%% Logic specification used:
% 1.46/1.25 %%% thf(spec, logic, $$dhol).
% 1.46/1.25
% 1.46/1.25 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.8RDVElAklK/DTF2DTF17671.p
% See solution above
% 1.46/1.26 ------------------------
% 1.46/1.26 ---- Cleaned THF ---
% 1.46/1.26 thf(a_type,type,
% 1.46/1.26 a: $tType ).
% 1.46/1.26
% 1.46/1.26 thf(cCT31,conjecture,
% 1.46/1.26 ~ ? [Xg: a > a > $o] :
% 1.46/1.26 ! [Xf: a > $o] :
% 1.46/1.26 ? [Xj: a] :
% 1.46/1.26 ( ( ( Xg @ Xj )
% 1.46/1.26 = Xf )
% 1.46/1.26 = ( Xf = Xf ) ) ).
% 1.46/1.27 ------------------------
% 1.46/1.28 % (18001)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_17671 for (2999ds/27Mi)
% 1.46/1.28 % (18000)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_17671 for (2999ds/4Mi)
% 1.46/1.28 % (18001)Refutation not found, incomplete strategy
% 1.46/1.28 % (18001)------------------------------
% 1.46/1.28 % (18001)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.46/1.28 % (18001)Termination reason: Refutation not found, incomplete strategy
% 1.46/1.28
% 1.46/1.28
% 1.46/1.28 % (18001)Memory used [KB]: 5500
% 1.46/1.28 % (18001)Time elapsed: 0.003 s
% 1.46/1.28 % (18001)Instructions burned: 2 (million)
% 1.46/1.28 % (18001)------------------------------
% 1.46/1.28 % (18001)------------------------------
% 1.46/1.28 % (18000)Instruction limit reached!
% 1.46/1.28 % (18000)------------------------------
% 1.46/1.28 % (18000)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.46/1.28 % (18000)Termination reason: Unknown
% 1.46/1.28 % (18000)Termination phase: Saturation
% 1.46/1.28
% 1.46/1.28 % (18000)Memory used [KB]: 5500
% 1.46/1.28 % (18000)Time elapsed: 0.003 s
% 1.46/1.28 % (18000)Instructions burned: 4 (million)
% 1.46/1.28 % (18000)------------------------------
% 1.46/1.28 % (18000)------------------------------
% 1.46/1.29 % (17999)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_17671 for (2999ds/183Mi)
% 1.46/1.29 % (18002)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_17671 for (2999ds/2Mi)
% 1.46/1.29 % (18003)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_17671 for (2999ds/2Mi)
% 1.46/1.29 % (18004)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_17671 for (2999ds/275Mi)
% 1.46/1.29 % (18005)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_17671 for (2999ds/18Mi)
% 1.46/1.29 % (18002)Instruction limit reached!
% 1.46/1.29 % (18002)------------------------------
% 1.46/1.29 % (18002)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.46/1.29 % (18002)Termination reason: Unknown
% 1.46/1.29 % (18002)Termination phase: Saturation
% 1.46/1.29
% 1.46/1.29 % (18002)Memory used [KB]: 5500
% 1.46/1.29 % (18002)Time elapsed: 0.004 s
% 1.46/1.29 % (18002)Instructions burned: 2 (million)
% 1.46/1.29 % (18002)------------------------------
% 1.46/1.29 % (18002)------------------------------
% 1.46/1.29 % (18003)Instruction limit reached!
% 1.46/1.29 % (18003)------------------------------
% 1.46/1.29 % (18003)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.46/1.29 % (18003)Termination reason: Unknown
% 1.46/1.29 % (18003)Termination phase: Saturation
% 1.46/1.29
% 1.46/1.29 % (18003)Memory used [KB]: 5500
% 1.46/1.29 % (18003)Time elapsed: 0.004 s
% 1.46/1.29 % (18003)Instructions burned: 2 (million)
% 1.46/1.29 % (18003)------------------------------
% 1.46/1.29 % (18003)------------------------------
% 1.46/1.29 % (18004)Refutation not found, incomplete strategy
% 1.46/1.29 % (18004)------------------------------
% 1.46/1.29 % (18004)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.46/1.29 % (18004)Termination reason: Refutation not found, incomplete strategy
% 1.46/1.29
% 1.46/1.29
% 1.46/1.29 % (18004)Memory used [KB]: 5500
% 1.46/1.29 % (18004)Time elapsed: 0.004 s
% 1.46/1.29 % (18004)Instructions burned: 2 (million)
% 1.46/1.29 % (18004)------------------------------
% 1.46/1.29 % (18004)------------------------------
% 1.46/1.29 % (18006)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_17671 for (2999ds/3Mi)
% 1.46/1.29 % (18006)Refutation not found, incomplete strategy
% 1.46/1.29 % (18006)------------------------------
% 1.46/1.29 % (18006)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.46/1.29 % (18006)Termination reason: Refutation not found, incomplete strategy
% 1.46/1.29
% 1.46/1.29
% 1.46/1.29 % (18006)Memory used [KB]: 5500
% 1.46/1.29 % (18006)Time elapsed: 0.001 s
% 1.46/1.29 % (18006)------------------------------
% 1.46/1.29 % (18006)------------------------------
% 1.46/1.29 % (18007)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_17671 for (2999ds/37Mi)
% 1.60/1.30 % (18005)Instruction limit reached!
% 1.60/1.30 % (18005)------------------------------
% 1.60/1.30 % (18005)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.60/1.30 % (18005)Termination reason: Unknown
% 1.60/1.30 % (18005)Termination phase: Saturation
% 1.60/1.30
% 1.60/1.30 % (18005)Memory used [KB]: 5628
% 1.60/1.30 % (18005)Time elapsed: 0.014 s
% 1.60/1.30 % (18005)Instructions burned: 18 (million)
% 1.60/1.30 % (18005)------------------------------
% 1.60/1.30 % (18005)------------------------------
% 1.60/1.30 % (18011)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_17671 for (2999ds/7Mi)
% 1.60/1.30 % (18011)Instruction limit reached!
% 1.60/1.30 % (18011)------------------------------
% 1.60/1.30 % (18011)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.60/1.30 % (18011)Termination reason: Unknown
% 1.60/1.30 % (18011)Termination phase: Saturation
% 1.60/1.30
% 1.60/1.30 % (18011)Memory used [KB]: 1023
% 1.60/1.30 % (18011)Time elapsed: 0.004 s
% 1.60/1.30 % (18011)Instructions burned: 8 (million)
% 1.60/1.30 % (18011)------------------------------
% 1.60/1.30 % (18011)------------------------------
% 1.60/1.30 % (18007)Instruction limit reached!
% 1.60/1.30 % (18007)------------------------------
% 1.60/1.30 % (18007)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.60/1.30 % (18007)Termination reason: Unknown
% 1.60/1.30 % (18007)Termination phase: Saturation
% 1.60/1.30
% 1.60/1.30 % (18007)Memory used [KB]: 5756
% 1.60/1.30 % (18007)Time elapsed: 0.015 s
% 1.60/1.30 % (18007)Instructions burned: 37 (million)
% 1.60/1.30 % (18007)------------------------------
% 1.60/1.30 % (18007)------------------------------
% 1.60/1.31 % (18008)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_17671 for (2999ds/15Mi)
% 1.60/1.31 % (18009)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_17671 for (2999ds/3Mi)
% 1.60/1.31 % (18010)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_17671 for (2999ds/1041Mi)
% 1.60/1.31 % (18009)Refutation not found, incomplete strategy
% 1.60/1.31 % (18009)------------------------------
% 1.60/1.31 % (18009)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.60/1.31 % (18009)Termination reason: Refutation not found, incomplete strategy
% 1.60/1.31
% 1.60/1.31
% 1.60/1.31 % (18009)Memory used [KB]: 5500
% 1.60/1.31 % (18009)Time elapsed: 0.003 s
% 1.60/1.31 % (18009)Instructions burned: 1 (million)
% 1.60/1.31 % (18009)------------------------------
% 1.60/1.31 % (18009)------------------------------
% 1.60/1.31 % (18008)Refutation not found, incomplete strategy
% 1.60/1.31 % (18008)------------------------------
% 1.60/1.31 % (18008)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.60/1.31 % (18008)Termination reason: Refutation not found, incomplete strategy
% 1.60/1.31
% 1.60/1.31
% 1.60/1.31 % (18008)Memory used [KB]: 5500
% 1.60/1.31 % (18008)Time elapsed: 0.004 s
% 1.60/1.31 % (18008)Instructions burned: 2 (million)
% 1.60/1.31 % (18008)------------------------------
% 1.60/1.31 % (18008)------------------------------
% 1.60/1.31 % (18013)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_17671 for (2999ds/3Mi)
% 1.60/1.31 % (18013)Instruction limit reached!
% 1.60/1.31 % (18013)------------------------------
% 1.60/1.31 % (18013)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.60/1.31 % (18013)Termination reason: Unknown
% 1.60/1.31 % (18013)Termination phase: Saturation
% 1.60/1.31
% 1.60/1.31 % (18013)Memory used [KB]: 5500
% 1.60/1.31 % (18013)Time elapsed: 0.002 s
% 1.60/1.31 % (18013)Instructions burned: 3 (million)
% 1.60/1.31 % (18013)------------------------------
% 1.60/1.31 % (18013)------------------------------
% 1.60/1.32 % (18014)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_17671 for (2999ds/3Mi)
% 1.60/1.32 % (18014)Instruction limit reached!
% 1.60/1.32 % (18014)------------------------------
% 1.60/1.32 % (18014)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.60/1.32 % (18014)Termination reason: Unknown
% 1.60/1.32 % (18014)Termination phase: Saturation
% 1.60/1.32
% 1.60/1.32 % (18014)Memory used [KB]: 5500
% 1.60/1.32 % (18014)Time elapsed: 0.003 s
% 1.60/1.32 % (18014)Instructions burned: 3 (million)
% 1.60/1.32 % (18014)------------------------------
% 1.60/1.32 % (18014)------------------------------
% 1.60/1.32 % (18012)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_17671 for (2999ds/16Mi)
% 1.60/1.32 % (18010)Refutation not found, incomplete strategy
% 1.60/1.32 % (18010)------------------------------
% 1.60/1.32 % (18010)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.60/1.32 % (18010)Termination reason: Refutation not found, incomplete strategy
% 1.60/1.32
% 1.60/1.32
% 1.60/1.32 % (18010)Memory used [KB]: 5500
% 1.60/1.32 % (18010)Time elapsed: 0.018 s
% 1.60/1.32 % (18010)Instructions burned: 26 (million)
% 1.60/1.32 % (18010)------------------------------
% 1.60/1.32 % (18010)------------------------------
% 1.60/1.32 % (18017)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_17671 for (2999ds/4Mi)
% 1.60/1.33 % (18015)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_17671 for (2999ds/7Mi)
% 1.60/1.33 % (18017)Instruction limit reached!
% 1.60/1.33 % (18017)------------------------------
% 1.60/1.33 % (18017)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.60/1.33 % (18017)Termination reason: Unknown
% 1.60/1.33 % (18017)Termination phase: Saturation
% 1.60/1.33
% 1.60/1.33 % (18017)Memory used [KB]: 5500
% 1.60/1.33 % (18017)Time elapsed: 0.003 s
% 1.60/1.33 % (18017)Instructions burned: 5 (million)
% 1.60/1.33 % (18017)------------------------------
% 1.60/1.33 % (18017)------------------------------
% 1.60/1.33 % (18018)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_17671 for (2999ds/18Mi)
% 1.60/1.33 % (18016)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_17671 for (2999ds/3Mi)
% 1.60/1.33 % (18015)Refutation not found, incomplete strategy
% 1.60/1.33 % (18015)------------------------------
% 1.60/1.33 % (18015)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.60/1.33 % (18015)Termination reason: Refutation not found, incomplete strategy
% 1.60/1.33
% 1.60/1.33
% 1.60/1.33 % (18015)Memory used [KB]: 5373
% 1.60/1.33 % (18015)Time elapsed: 0.003 s
% 1.60/1.33 % (18015)Instructions burned: 1 (million)
% 1.60/1.33 % (18015)------------------------------
% 1.60/1.33 % (18015)------------------------------
% 1.60/1.33 % (18018)Refutation not found, incomplete strategy
% 1.60/1.33 % (18018)------------------------------
% 1.60/1.33 % (18018)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.60/1.33 % (18018)Termination reason: Refutation not found, incomplete strategy
% 1.60/1.33
% 1.60/1.33
% 1.60/1.33 % (18018)Memory used [KB]: 5500
% 1.60/1.33 % (18018)Time elapsed: 0.002 s
% 1.60/1.33 % (18018)Instructions burned: 1 (million)
% 1.60/1.33 % (18018)------------------------------
% 1.60/1.33 % (18018)------------------------------
% 1.60/1.33 % (18012)Instruction limit reached!
% 1.60/1.33 % (18012)------------------------------
% 1.60/1.33 % (18012)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.60/1.33 % (18012)Termination reason: Unknown
% 1.60/1.33 % (18012)Termination phase: Saturation
% 1.60/1.33
% 1.60/1.33 % (18012)Memory used [KB]: 5628
% 1.60/1.33 % (18012)Time elapsed: 0.013 s
% 1.60/1.33 % (18012)Instructions burned: 17 (million)
% 1.60/1.33 % (18012)------------------------------
% 1.60/1.33 % (18012)------------------------------
% 1.60/1.33 % (18016)Instruction limit reached!
% 1.60/1.33 % (18016)------------------------------
% 1.60/1.33 % (18016)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.60/1.33 % (18016)Termination reason: Unknown
% 1.60/1.33 % (18016)Termination phase: Saturation
% 1.60/1.33
% 1.60/1.33 % (18016)Memory used [KB]: 5500
% 1.60/1.33 % (18016)Time elapsed: 0.004 s
% 1.60/1.33 % (18016)Instructions burned: 3 (million)
% 1.60/1.33 % (18016)------------------------------
% 1.60/1.33 % (18016)------------------------------
% 1.60/1.34 % (18020)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_17671 for (2999ds/6Mi)
% 1.60/1.34 % (18023)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_17671 for (2999ds/5Mi)
% 1.60/1.34 % (18020)Instruction limit reached!
% 1.60/1.34 % (18020)------------------------------
% 1.60/1.34 % (18020)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.60/1.34 % (18020)Termination reason: Unknown
% 1.60/1.34 % (18020)Termination phase: Saturation
% 1.60/1.34
% 1.60/1.34 % (18020)Memory used [KB]: 5500
% 1.60/1.34 % (18020)Time elapsed: 0.004 s
% 1.60/1.34 % (18020)Instructions burned: 8 (million)
% 1.60/1.34 % (18020)------------------------------
% 1.60/1.34 % (18020)------------------------------
% 1.60/1.34 % (18023)Instruction limit reached!
% 1.60/1.34 % (18023)------------------------------
% 1.60/1.34 % (18023)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.60/1.34 % (18023)Termination reason: Unknown
% 1.60/1.34 % (18023)Termination phase: Saturation
% 1.60/1.34
% 1.60/1.34 % (18023)Memory used [KB]: 5500
% 1.60/1.34 % (18023)Time elapsed: 0.004 s
% 1.60/1.34 % (18023)Instructions burned: 6 (million)
% 1.60/1.34 % (18023)------------------------------
% 1.60/1.34 % (18023)------------------------------
% 1.60/1.34 % (18019)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_17671 for (2999ds/710Mi)
% 1.60/1.34 % (18021)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_17671 for (2999ds/902Mi)
% 1.60/1.34 % (18022)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_17671 for (2999ds/21Mi)
% 1.60/1.35 % (18024)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_17671 for (2999ds/6Mi)
% 1.60/1.35 % (18025)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_17671 for (2999ds/377Mi)
% 1.60/1.35 % (18025)Refutation not found, incomplete strategy
% 1.60/1.35 % (18025)------------------------------
% 1.60/1.35 % (18025)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.60/1.35 % (18025)Termination reason: Refutation not found, incomplete strategy
% 1.60/1.35
% 1.60/1.35
% 1.60/1.35 % (18025)Memory used [KB]: 5500
% 1.60/1.35 % (18025)Time elapsed: 0.002 s
% 1.60/1.35 % (18025)Instructions burned: 3 (million)
% 1.60/1.35 % (18025)------------------------------
% 1.60/1.35 % (18025)------------------------------
% 1.60/1.35 % (18024)Instruction limit reached!
% 1.60/1.35 % (18024)------------------------------
% 1.60/1.35 % (18024)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.60/1.35 % (18024)Termination reason: Unknown
% 1.60/1.35 % (18024)Termination phase: Saturation
% 1.60/1.35
% 1.60/1.35 % (18024)Memory used [KB]: 5500
% 1.60/1.35 % (18024)Time elapsed: 0.006 s
% 1.60/1.35 % (18024)Instructions burned: 6 (million)
% 1.60/1.35 % (18024)------------------------------
% 1.60/1.35 % (18024)------------------------------
% 1.60/1.35 % (18026)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on DTF2THF_17671 for (2999ds/779Mi)
% 1.60/1.35 % (18026)Refutation not found, incomplete strategy
% 1.60/1.35 % (18026)------------------------------
% 1.60/1.35 % (18026)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.60/1.35 % (18026)Termination reason: Refutation not found, incomplete strategy
% 1.60/1.35
% 1.60/1.35
% 1.60/1.35 % (18026)Memory used [KB]: 5500
% 1.60/1.35 % (18026)Time elapsed: 0.003 s
% 1.60/1.35 % (18026)Instructions burned: 3 (million)
% 1.60/1.35 % (18026)------------------------------
% 1.60/1.35 % (18026)------------------------------
% 1.60/1.36 % (18027)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on DTF2THF_17671 for (2999ds/19Mi)
% 1.60/1.36 % (18022)Instruction limit reached!
% 1.60/1.36 % (18022)------------------------------
% 1.60/1.36 % (18022)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.60/1.36 % (18022)Termination reason: Unknown
% 1.60/1.36 % (18022)Termination phase: Saturation
% 1.60/1.36
% 1.60/1.36 % (18022)Memory used [KB]: 5628
% 1.60/1.36 % (18022)Time elapsed: 0.016 s
% 1.60/1.36 % (18022)Instructions burned: 21 (million)
% 1.60/1.36 % (18022)------------------------------
% 1.60/1.36 % (18022)------------------------------
% 1.60/1.36 % (17999)Instruction limit reached!
% 1.60/1.36 % (17999)------------------------------
% 1.60/1.36 % (17999)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.60/1.36 % (17999)Termination reason: Unknown
% 1.60/1.36 % (17999)Termination phase: Saturation
% 1.60/1.36
% 1.60/1.36 % (17999)Memory used [KB]: 6268
% 1.60/1.36 % (17999)Time elapsed: 0.077 s
% 1.60/1.36 % (17999)Instructions burned: 183 (million)
% 1.60/1.36 % (17999)------------------------------
% 1.60/1.36 % (17999)------------------------------
% 1.60/1.36 % (18029)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_17671 for (2999ds/17Mi)
% 1.60/1.36 % (18027)First to succeed.
% 1.60/1.36 % (18027)Refutation found. Thanks to Tanya!
% 1.60/1.36 % SZS status Theorem for DTF2THF_17671
% 1.60/1.36 % SZS output start Proof for DTF2THF_17671
% 1.60/1.36 thf(type_def_5, type, a: $tType).
% 1.60/1.36 thf(func_def_0, type, a: $tType).
% 1.60/1.36 thf(func_def_13, type, sK1: a > a > $o).
% 1.60/1.36 thf(func_def_14, type, sK2: (a > $o) > a).
% 1.60/1.36 thf(f64,plain,(
% 1.60/1.36 $false),
% 1.60/1.36 inference(trivial_inequality_removal,[status(thm)],[f63])).
% 1.60/1.36 thf(f63,plain,(
% 1.60/1.36 ($true = $false)),
% 1.60/1.36 inference(forward_demodulation,[status(thm)],[f62,f58])).
% 1.60/1.36 thf(f58,plain,(
% 1.60/1.36 ($false = (sK1 @ (sK2 @ (^[Y0 : a]: (~ (sK1 @ Y0 @ Y0)))) @ (sK2 @ (^[Y0 : a]: (~ (sK1 @ Y0 @ Y0))))))),
% 1.60/1.36 inference(beta_eta_normalization,[status(thm)],[f55])).
% 1.60/1.36 thf(f55,plain,(
% 1.60/1.36 ($false = (sK1 @ (sK2 @ (^[Y0 : a]: (~ (sK1 @ Y0 @ ((^[Y1 : a]: (Y1)) @ Y0))))) @ ((^[Y0 : a]: (Y0)) @ (sK2 @ (^[Y0 : a]: (~ (sK1 @ Y0 @ ((^[Y1 : a]: (Y1)) @ Y0))))))))),
% 1.60/1.36 inference(equality_resolution,[status(thm)],[f49])).
% 1.60/1.36 thf(f49,plain,(
% 1.60/1.36 ( ! [X0 : a > a] : (((sK2 @ (^[Y0 : a]: (~ (sK1 @ Y0 @ (X0 @ Y0))))) != (X0 @ (sK2 @ (^[Y0 : a]: (~ (sK1 @ Y0 @ (X0 @ Y0))))))) | ((sK1 @ (sK2 @ (^[Y0 : a]: (~ (sK1 @ Y0 @ (X0 @ Y0))))) @ (X0 @ (sK2 @ (^[Y0 : a]: (~ (sK1 @ Y0 @ (X0 @ Y0))))))) = $false)) )),
% 1.60/1.36 inference(equality_resolution,[status(thm)],[f41])).
% 1.60/1.36 thf(f41,plain,(
% 1.60/1.36 ( ! [X0 : a > a,X1 : a] : (((sK2 @ (^[Y0 : a]: (~ (sK1 @ Y0 @ (X0 @ Y0))))) != X1) | ($false = (sK1 @ X1 @ (X0 @ X1))) | ((X0 @ X1) != X1)) )),
% 1.60/1.36 inference(beta_eta_normalization,[status(thm)],[f40])).
% 1.60/1.36 thf(f40,plain,(
% 1.60/1.36 ( ! [X0 : a > a,X1 : a] : ((((^[Y0 : a]: (sK1 @ ((^[Y1 : a]: (Y1)) @ Y0) @ (X0 @ Y0))) @ X1) = $false) | ((sK2 @ (^[Y0 : a]: (~ ((^[Y1 : a]: (sK1 @ ((^[Y2 : a]: (Y2)) @ Y1) @ (X0 @ Y1))) @ Y0)))) != X1) | ((X0 @ X1) != X1)) )),
% 1.60/1.36 inference(trivial_inequality_removal,[status(thm)],[f36])).
% 1.60/1.36 thf(f36,plain,(
% 1.60/1.36 ( ! [X0 : a > a,X1 : a] : (((sK2 @ (^[Y0 : a]: (~ ((^[Y1 : a]: (sK1 @ ((^[Y2 : a]: (Y2)) @ Y1) @ (X0 @ Y1))) @ Y0)))) != X1) | ($false != $false) | (((^[Y0 : a]: (sK1 @ ((^[Y1 : a]: (Y1)) @ Y0) @ (X0 @ Y0))) @ X1) = $false) | ((X0 @ X1) != X1)) )),
% 1.60/1.36 inference(equality_factoring,[status(thm)],[f35])).
% 1.60/1.36 thf(f35,plain,(
% 1.60/1.36 ( ! [X2 : a,X5 : a > $o] : (($false = (sK1 @ (sK2 @ (^[Y0 : a]: (~ (X5 @ Y0)))) @ X2)) | ($false = (X5 @ X2))) )),
% 1.60/1.36 inference(not_proxy_clausification,[status(thm)],[f33])).
% 1.60/1.36 thf(f33,plain,(
% 1.60/1.36 ( ! [X2 : a,X5 : a > $o] : (($false = (sK1 @ (sK2 @ (^[Y0 : a]: (~ (X5 @ Y0)))) @ X2)) | ($true = (~ (X5 @ X2)))) )),
% 1.60/1.36 inference(binary_proxy_clausification,[status(thm)],[f24])).
% 1.60/1.36 thf(f24,plain,(
% 1.60/1.36 ( ! [X2 : a,X5 : a > $o] : (((~ (X5 @ X2)) = (sK1 @ (sK2 @ (^[Y0 : a]: (~ (X5 @ Y0)))) @ X2))) )),
% 1.60/1.36 inference(beta_eta_normalization,[status(thm)],[f21])).
% 1.60/1.36 thf(f21,plain,(
% 1.60/1.36 ( ! [X2 : a,X5 : a > $o] : ((((^[Y0 : a]: (~ (X5 @ Y0))) @ X2) = (sK1 @ (sK2 @ (^[Y0 : a]: (~ (X5 @ Y0)))) @ X2))) )),
% 1.60/1.36 inference(primitive_instantiation,[status(thm)],[f16])).
% 1.60/1.36 thf(f16,plain,(
% 1.60/1.36 ( ! [X2 : a,X1 : a > $o] : (((sK1 @ (sK2 @ X1) @ X2) = (X1 @ X2))) )),
% 1.60/1.36 inference(argument_congruence,[status(thm)],[f15])).
% 1.60/1.36 thf(f15,plain,(
% 1.60/1.36 ( ! [X1 : a > $o] : (((sK1 @ (sK2 @ X1)) = X1)) )),
% 1.60/1.36 inference(equality_proxy_clausification,[status(thm)],[f14])).
% 1.60/1.36 thf(f14,plain,(
% 1.60/1.36 ( ! [X1 : a > $o] : ((((sK1 @ (sK2 @ X1)) = X1) = $true)) )),
% 1.60/1.36 inference(equality_proxy_clausification,[status(thm)],[f13])).
% 1.60/1.36 thf(f13,plain,(
% 1.60/1.36 ( ! [X1 : a > $o] : (($true = (((sK1 @ (sK2 @ X1)) = X1) = $true))) )),
% 1.60/1.36 inference(beta_eta_normalization,[status(thm)],[f12])).
% 1.60/1.36 thf(f12,plain,(
% 1.60/1.36 ( ! [X1 : a > $o] : (($true = ((^[Y0 : a]: (((sK1 @ Y0) = X1) = $true)) @ (sK2 @ X1)))) )),
% 1.60/1.36 inference(sigma_clausification,[status(thm)],[f11])).
% 1.60/1.36 thf(f11,plain,(
% 1.60/1.36 ( ! [X1 : a > $o] : (((?? @ a @ (^[Y0 : a]: (((sK1 @ Y0) = X1) = $true))) = $true)) )),
% 1.60/1.36 inference(beta_eta_normalization,[status(thm)],[f10])).
% 1.60/1.36 thf(f10,plain,(
% 1.60/1.36 ( ! [X1 : a > $o] : (($true = ((^[Y0 : a > $o]: (?? @ a @ (^[Y1 : a]: (((sK1 @ Y1) = Y0) = $true)))) @ X1))) )),
% 1.60/1.36 inference(pi_clausification,[status(thm)],[f9])).
% 1.60/1.36 thf(f9,plain,(
% 1.60/1.36 ($true = (!! @ (a > $o) @ (^[Y0 : a > $o]: (?? @ a @ (^[Y1 : a]: (((sK1 @ Y1) = Y0) = $true))))))),
% 1.60/1.36 inference(beta_eta_normalization,[status(thm)],[f8])).
% 1.60/1.36 thf(f8,plain,(
% 1.60/1.36 (((^[Y0 : a > a > $o]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (?? @ a @ (^[Y2 : a]: (((Y0 @ Y2) = Y1) = $true)))))) @ sK1) = $true)),
% 1.60/1.36 inference(sigma_clausification,[status(thm)],[f7])).
% 1.60/1.36 thf(f7,plain,(
% 1.60/1.36 ($true = (?? @ (a > a > $o) @ (^[Y0 : a > a > $o]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (?? @ a @ (^[Y2 : a]: (((Y0 @ Y2) = Y1) = $true))))))))),
% 1.60/1.36 inference(boolean_simplification,[status(thm)],[f6])).
% 1.60/1.36 thf(f6,plain,(
% 1.60/1.36 ($true = (?? @ (a > a > $o) @ (^[Y0 : a > a > $o]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (?? @ a @ (^[Y2 : a]: (((Y0 @ Y2) = Y1) = (Y1 = Y1)))))))))),
% 1.60/1.36 inference(boolean_simplification,[status(thm)],[f5])).
% 1.60/1.36 thf(f5,plain,(
% 1.60/1.36 ((~ (~ (?? @ (a > a > $o) @ (^[Y0 : a > a > $o]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (?? @ a @ (^[Y2 : a]: (((Y0 @ Y2) = Y1) = (Y1 = Y1)))))))))) = $true)),
% 1.60/1.36 inference(cnf_transformation,[status(thm)],[f4])).
% 1.60/1.36 thf(f4,plain,(
% 1.60/1.36 ((~ (~ (?? @ (a > a > $o) @ (^[Y0 : a > a > $o]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (?? @ a @ (^[Y2 : a]: (((Y0 @ Y2) = Y1) = (Y1 = Y1)))))))))) = $true)),
% 1.60/1.36 inference(fool_elimination,[status(thm)],[f2])).
% 1.60/1.36 thf(f2,negated_conjecture,(
% 1.60/1.36 ~~? [X0 : a > a > $o] : ! [X1 : a > $o] : ? [X2 : a] : (((X0 @ X2) = X1) = (X1 = X1))),
% 1.60/1.36 inference(negated_conjecture,[status(cth)],[f1])).
% 1.60/1.36 thf(f1,conjecture,(
% 1.60/1.36 ~? [X0 : a > a > $o] : ! [X1 : a > $o] : ? [X2 : a] : (((X0 @ X2) = X1) = (X1 = X1))),
% 1.60/1.36 file('/export/starexec/sandbox/tmp/tmp.8RDVElAklK/DTF2THF_17671.p',cCT31)).
% 1.60/1.36 thf(f62,plain,(
% 1.60/1.36 ($true = (sK1 @ (sK2 @ (^[Y0 : a]: (~ (sK1 @ Y0 @ Y0)))) @ (sK2 @ (^[Y0 : a]: (~ (sK1 @ Y0 @ Y0))))))),
% 1.60/1.36 inference(beta_eta_normalization,[status(thm)],[f59])).
% 1.60/1.36 thf(f59,plain,(
% 1.60/1.36 ($true = (sK1 @ (sK2 @ (^[Y0 : a]: (~ (sK1 @ Y0 @ ((^[Y1 : a]: (Y1)) @ Y0))))) @ ((^[Y0 : a]: (Y0)) @ (sK2 @ (^[Y0 : a]: (~ (sK1 @ Y0 @ ((^[Y1 : a]: (Y1)) @ Y0))))))))),
% 1.60/1.36 inference(equality_resolution,[status(thm)],[f50])).
% 1.60/1.36 thf(f50,plain,(
% 1.60/1.36 ( ! [X0 : a > a] : (((sK2 @ (^[Y0 : a]: (~ (sK1 @ Y0 @ (X0 @ Y0))))) != (X0 @ (sK2 @ (^[Y0 : a]: (~ (sK1 @ Y0 @ (X0 @ Y0))))))) | ((sK1 @ (sK2 @ (^[Y0 : a]: (~ (sK1 @ Y0 @ (X0 @ Y0))))) @ (X0 @ (sK2 @ (^[Y0 : a]: (~ (sK1 @ Y0 @ (X0 @ Y0))))))) = $true)) )),
% 1.60/1.36 inference(equality_resolution,[status(thm)],[f46])).
% 1.60/1.36 thf(f46,plain,(
% 1.60/1.36 ( ! [X0 : a > a,X1 : a] : (((sK2 @ (^[Y0 : a]: (~ (sK1 @ Y0 @ (X0 @ Y0))))) != X1) | ($true = (sK1 @ X1 @ (X0 @ X1))) | ((X0 @ X1) != X1)) )),
% 1.60/1.36 inference(beta_eta_normalization,[status(thm)],[f45])).
% 1.60/1.36 thf(f45,plain,(
% 1.60/1.36 ( ! [X0 : a > a,X1 : a] : (((sK2 @ (^[Y0 : a]: (~ ((^[Y1 : a]: (sK1 @ ((^[Y2 : a]: (Y2)) @ Y1) @ (X0 @ Y1))) @ Y0)))) != X1) | ($true = ((^[Y0 : a]: (sK1 @ ((^[Y1 : a]: (Y1)) @ Y0) @ (X0 @ Y0))) @ X1)) | ((X0 @ X1) != X1)) )),
% 1.60/1.36 inference(trivial_inequality_removal,[status(thm)],[f43])).
% 1.60/1.36 thf(f43,plain,(
% 1.60/1.36 ( ! [X0 : a > a,X1 : a] : (($true = ((^[Y0 : a]: (sK1 @ ((^[Y1 : a]: (Y1)) @ Y0) @ (X0 @ Y0))) @ X1)) | ((sK2 @ (^[Y0 : a]: (~ ((^[Y1 : a]: (sK1 @ ((^[Y2 : a]: (Y2)) @ Y1) @ (X0 @ Y1))) @ Y0)))) != X1) | ((X0 @ X1) != X1) | ($true != $true)) )),
% 1.60/1.36 inference(equality_factoring,[status(thm)],[f42])).
% 1.60/1.36 thf(f42,plain,(
% 1.60/1.36 ( ! [X2 : a,X5 : a > $o] : (($true = (sK1 @ (sK2 @ (^[Y0 : a]: (~ (X5 @ Y0)))) @ X2)) | ($true = (X5 @ X2))) )),
% 1.60/1.36 inference(not_proxy_clausification,[status(thm)],[f34])).
% 1.60/1.36 thf(f34,plain,(
% 1.60/1.36 ( ! [X2 : a,X5 : a > $o] : (($true = (sK1 @ (sK2 @ (^[Y0 : a]: (~ (X5 @ Y0)))) @ X2)) | ($false = (~ (X5 @ X2)))) )),
% 1.60/1.36 inference(binary_proxy_clausification,[status(thm)],[f24])).
% 1.60/1.36 % SZS output end Proof for DTF2THF_17671
% 1.60/1.36 % (18027)------------------------------
% 1.60/1.36 % (18027)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.60/1.36 % (18027)Termination reason: Refutation
% 1.60/1.36
% 1.60/1.36 % (18027)Memory used [KB]: 5500
% 1.60/1.36 % (18027)Time elapsed: 0.006 s
% 1.60/1.36 % (18027)Instructions burned: 12 (million)
% 1.60/1.36 % (18027)------------------------------
% 1.60/1.36 % (18027)------------------------------
% 1.60/1.36 % (17998)Success in time 0.082 s
%------------------------------------------------------------------------------