%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU850^5 : 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 09:37:35 AM UTC 2026
% Result : Theorem 0.31s 1.34s
% Output : Refutation 0.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 8
% Syntax : Number of formulae : 43 ( 4 unt; 0 typ; 3 def)
% Number of atoms : 350 ( 128 equ; 0 cnn)
% Maximal formula atoms : 16 ( 8 avg)
% Number of connectives : 317 ( 63 ~; 60 |; 48 &; 123 @)
% ( 3 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 24 ( 24 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 9 usr; 8 con; 0-2 aty)
% Number of variables : 54 ( 0 ^; 24 !; 30 ?; 54 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_4,type,
sK0: a > $o ).
thf(func_def_5,type,
sK1: a > $o ).
thf(func_def_6,type,
sK2: a > $o ).
thf(func_def_7,type,
sK3: a ).
thf(func_def_8,type,
sK4: a ).
thf(func_def_9,type,
sK5: a ).
thf(f53,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f45,f46,f47,f48,f49,f50,f51,f52]) ).
thf(f52,plain,
( spl6_3
| ~ spl6_1
| ~ spl6_2 ),
inference(avatar_split_clause,[status(thm)],[f27,f38,f34,f42]) ).
thf(f42,definition,
( spl6_3
<=> ( $true
= ( sK1 @ sK5 ) ) ),
introduced(definition,[new_symbols(naming,[spl6_3])],[avatar_definition]) ).
thf(f34,definition,
( spl6_1
<=> ( $true
= ( sK1 @ sK3 ) ) ),
introduced(definition,[new_symbols(naming,[spl6_1])],[avatar_definition]) ).
thf(f38,definition,
( spl6_2
<=> ( $true
= ( sK1 @ sK4 ) ) ),
introduced(definition,[new_symbols(naming,[spl6_2])],[avatar_definition]) ).
thf(f27,plain,
( ( $true
!= ( sK1 @ sK4 ) )
| ( $true
= ( sK1 @ sK5 ) )
| ( $true
!= ( sK1 @ sK3 ) ) ),
inference(definition_unfolding,[status(thm)],[f21,f15,f15]) ).
thf(f15,plain,
sK0 = sK1,
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
( ( ( ( $true
!= ( sK0 @ sK3 ) )
& ( $true
= ( sK1 @ sK3 ) ) )
| ( ( $true
= ( sK2 @ sK4 ) )
& ( $true
!= ( sK1 @ sK4 ) ) )
| ( ( $true
= ( sK0 @ sK5 ) )
& ( $true
!= ( sK2 @ sK5 ) ) ) )
& ( sK0 = sK1 )
& ( sK2 = sK0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5])],[f8,f12,f11,f10,f9]) ).
thf(f9,plain,
( ? [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ? [X3: a] :
( ( ( X0 @ X3 )
!= $true )
& ( ( X1 @ X3 )
= $true ) )
| ? [X4: a] :
( ( $true
= ( X2 @ X4 ) )
& ( ( X1 @ X4 )
!= $true ) )
| ? [X5: a] :
( ( $true
= ( X0 @ X5 ) )
& ( $true
!= ( X2 @ X5 ) ) ) )
& ( X0 = X1 )
& ( X0 = X2 ) )
=> ( ( ? [X3: a] :
( ( $true
!= ( sK0 @ X3 ) )
& ( $true
= ( sK1 @ X3 ) ) )
| ? [X4: a] :
( ( $true
= ( sK2 @ X4 ) )
& ( $true
!= ( sK1 @ X4 ) ) )
| ? [X5: a] :
( ( $true
= ( sK0 @ X5 ) )
& ( $true
!= ( sK2 @ X5 ) ) ) )
& ( sK0 = sK1 )
& ( sK2 = sK0 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f10,plain,
( ? [X3: a] :
( ( $true
!= ( sK0 @ X3 ) )
& ( $true
= ( sK1 @ X3 ) ) )
=> ( ( $true
!= ( sK0 @ sK3 ) )
& ( $true
= ( sK1 @ sK3 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f11,plain,
( ? [X4: a] :
( ( $true
= ( sK2 @ X4 ) )
& ( $true
!= ( sK1 @ X4 ) ) )
=> ( ( $true
= ( sK2 @ sK4 ) )
& ( $true
!= ( sK1 @ sK4 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f12,plain,
( ? [X5: a] :
( ( $true
= ( sK0 @ X5 ) )
& ( $true
!= ( sK2 @ X5 ) ) )
=> ( ( $true
= ( sK0 @ sK5 ) )
& ( $true
!= ( sK2 @ sK5 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f8,plain,
? [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ? [X3: a] :
( ( ( X0 @ X3 )
!= $true )
& ( ( X1 @ X3 )
= $true ) )
| ? [X4: a] :
( ( $true
= ( X2 @ X4 ) )
& ( ( X1 @ X4 )
!= $true ) )
| ? [X5: a] :
( ( $true
= ( X0 @ X5 ) )
& ( $true
!= ( X2 @ X5 ) ) ) )
& ( X0 = X1 )
& ( X0 = X2 ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,plain,
? [X2: a > $o,X1: a > $o,X0: a > $o] :
( ( ? [X5: a] :
( ( $true
!= ( X2 @ X5 ) )
& ( $true
= ( X1 @ X5 ) ) )
| ? [X3: a] :
( ( ( X0 @ X3 )
= $true )
& ( ( X1 @ X3 )
!= $true ) )
| ? [X4: a] :
( ( $true
= ( X2 @ X4 ) )
& ( $true
!= ( X0 @ X4 ) ) ) )
& ( X1 = X2 )
& ( X0 = X2 ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
? [X1: a > $o,X2: a > $o,X0: a > $o] :
( ( ? [X5: a] :
( ( $true
!= ( X2 @ X5 ) )
& ( $true
= ( X1 @ X5 ) ) )
| ? [X3: a] :
( ( ( X0 @ X3 )
= $true )
& ( ( X1 @ X3 )
!= $true ) )
| ? [X4: a] :
( ( $true
= ( X2 @ X4 ) )
& ( $true
!= ( X0 @ X4 ) ) ) )
& ( X0 = X2 )
& ( X1 = X2 ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X1: a > $o,X2: a > $o,X0: a > $o] :
( ( ( X0 = X2 )
& ( X1 = X2 ) )
=> ( ! [X3: a] :
( ( ( X0 @ X3 )
= $true )
=> ( ( X1 @ X3 )
= $true ) )
& ! [X5: a] :
( ( $true
= ( X1 @ X5 ) )
=> ( $true
= ( X2 @ X5 ) ) )
& ! [X4: a] :
( ( $true
= ( X2 @ X4 ) )
=> ( $true
= ( X0 @ X4 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ( X1 = X2 )
& ( X0 = X2 ) )
=> ( ! [X3: a] :
( ( X0 @ X3 )
=> ( X1 @ X3 ) )
& ! [X4: a] :
( ( X2 @ X4 )
=> ( X0 @ X4 ) )
& ! [X5: a] :
( ( X1 @ X5 )
=> ( X2 @ X5 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X2: a > $o,X0: a > $o,X1: a > $o] :
( ( ( X0 = X1 )
& ( X1 = X2 ) )
=> ( ! [X3: a] :
( ( X2 @ X3 )
=> ( X0 @ X3 ) )
& ! [X3: a] :
( ( X1 @ X3 )
=> ( X2 @ X3 ) )
& ! [X3: a] :
( ( X0 @ X3 )
=> ( X1 @ X3 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X2: a > $o,X0: a > $o,X1: a > $o] :
( ( ( X0 = X1 )
& ( X1 = X2 ) )
=> ( ! [X3: a] :
( ( X2 @ X3 )
=> ( X0 @ X3 ) )
& ! [X3: a] :
( ( X1 @ X3 )
=> ( X2 @ X3 ) )
& ! [X3: a] :
( ( X0 @ X3 )
=> ( X1 @ X3 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.cmezRSdI3t/DTF2THF_16900.p',cGAZING_THM9_pme) ).
thf(f21,plain,
( ( $true
!= ( sK0 @ sK3 ) )
| ( $true
!= ( sK1 @ sK4 ) )
| ( $true
= ( sK0 @ sK5 ) ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f51,plain,
( spl6_1
| spl6_2
| ~ spl6_3 ),
inference(avatar_split_clause,[status(thm)],[f30,f42,f38,f34]) ).
thf(f30,plain,
( ( $true
!= ( sK1 @ sK5 ) )
| ( $true
= ( sK1 @ sK3 ) )
| ( $true
= ( sK1 @ sK4 ) ) ),
inference(definition_unfolding,[status(thm)],[f18,f24,f24]) ).
thf(f24,plain,
sK2 = sK1,
inference(definition_unfolding,[status(thm)],[f14,f15]) ).
thf(f14,plain,
sK2 = sK0,
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f18,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ( $true
= ( sK2 @ sK4 ) )
| ( $true
!= ( sK2 @ sK5 ) ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f50,plain,
( spl6_3
| ~ spl6_1
| spl6_2 ),
inference(avatar_split_clause,[status(thm)],[f25,f38,f34,f42]) ).
thf(f25,plain,
( ( $true
= ( sK1 @ sK5 ) )
| ( $true
= ( sK1 @ sK4 ) )
| ( $true
!= ( sK1 @ sK3 ) ) ),
inference(definition_unfolding,[status(thm)],[f23,f15,f24,f15]) ).
thf(f23,plain,
( ( $true
!= ( sK0 @ sK3 ) )
| ( $true
= ( sK2 @ sK4 ) )
| ( $true
= ( sK0 @ sK5 ) ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f49,plain,
( spl6_1
| spl6_2
| spl6_3 ),
inference(avatar_split_clause,[status(thm)],[f29,f42,f38,f34]) ).
thf(f29,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ( $true
= ( sK1 @ sK5 ) )
| ( $true
= ( sK1 @ sK4 ) ) ),
inference(definition_unfolding,[status(thm)],[f19,f24,f15]) ).
thf(f19,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ( $true
= ( sK2 @ sK4 ) )
| ( $true
= ( sK0 @ sK5 ) ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f48,plain,
( ~ spl6_1
| spl6_2
| ~ spl6_3 ),
inference(avatar_split_clause,[status(thm)],[f26,f42,f38,f34]) ).
thf(f26,plain,
( ( $true
= ( sK1 @ sK4 ) )
| ( $true
!= ( sK1 @ sK3 ) )
| ( $true
!= ( sK1 @ sK5 ) ) ),
inference(definition_unfolding,[status(thm)],[f22,f15,f24,f24]) ).
thf(f22,plain,
( ( $true
!= ( sK0 @ sK3 ) )
| ( $true
= ( sK2 @ sK4 ) )
| ( $true
!= ( sK2 @ sK5 ) ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f47,plain,
( spl6_3
| ~ spl6_2
| spl6_1 ),
inference(avatar_split_clause,[status(thm)],[f31,f34,f38,f42]) ).
thf(f31,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ( $true
!= ( sK1 @ sK4 ) )
| ( $true
= ( sK1 @ sK5 ) ) ),
inference(definition_unfolding,[status(thm)],[f17,f15]) ).
thf(f17,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ( $true
!= ( sK1 @ sK4 ) )
| ( $true
= ( sK0 @ sK5 ) ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f46,plain,
( ~ spl6_3
| ~ spl6_2
| spl6_1 ),
inference(avatar_split_clause,[status(thm)],[f32,f34,f38,f42]) ).
thf(f32,plain,
( ( $true
!= ( sK1 @ sK5 ) )
| ( $true
= ( sK1 @ sK3 ) )
| ( $true
!= ( sK1 @ sK4 ) ) ),
inference(definition_unfolding,[status(thm)],[f16,f24]) ).
thf(f16,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ( $true
!= ( sK1 @ sK4 ) )
| ( $true
!= ( sK2 @ sK5 ) ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f45,plain,
( ~ spl6_1
| ~ spl6_2
| ~ spl6_3 ),
inference(avatar_split_clause,[status(thm)],[f28,f42,f38,f34]) ).
thf(f28,plain,
( ( $true
!= ( sK1 @ sK4 ) )
| ( $true
!= ( sK1 @ sK5 ) )
| ( $true
!= ( sK1 @ sK3 ) ) ),
inference(definition_unfolding,[status(thm)],[f20,f15,f24]) ).
thf(f20,plain,
( ( $true
!= ( sK0 @ sK3 ) )
| ( $true
!= ( sK1 @ sK4 ) )
| ( $true
!= ( sK2 @ sK5 ) ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU850^5 : 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
% 0.17/0.34 % Computer : n018.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue Feb 24 12:35:31 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.31/0.46 ---- Original DTF file ---
% 0.31/0.46 thf(spec,logic,$$dhol).
% 0.31/0.46 %------------------------------------------------------------------------------
% 0.31/0.46 % File : SEU850^5 : TPTP v9.2.1. Released v4.0.0.
% 0.31/0.46 % Domain : Set Theory
% 0.31/0.46 % Problem : TPS problem GAZING-THM9
% 0.31/0.46 % Version : Especial.
% 0.31/0.46 % English :
% 0.31/0.46
% 0.31/0.46 % Refs : [Bar92] Barker-Plummer D (1992), Gazing: An Approach to the Pr
% 0.31/0.46 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.31/0.46 % Source : [Bro09]
% 0.31/0.46 % Names : tps_0358 [Bro09]
% 0.31/0.46 % : 9 [Bar92]
% 0.31/0.46 % : GAZING-THM9 [TPS]
% 0.31/0.46
% 0.31/0.46 % Status : Theorem
% 0.31/0.46 % Rating : 0.00 v7.4.0, 0.11 v7.2.0, 0.00 v7.1.0, 0.12 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.00 v6.1.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v5.3.0, 0.40 v5.2.0, 0.20 v4.1.0, 0.00 v4.0.0
% 0.31/0.46 % Syntax : Number of formulae : 2 ( 0 unt; 1 typ; 0 def)
% 0.31/0.46 % Number of atoms : 2 ( 2 equ; 0 cnn)
% 0.31/0.46 % Maximal formula atoms : 2 ( 2 avg)
% 0.31/0.46 % Number of connectives : 13 ( 0 ~; 0 |; 3 &; 6 @)
% 0.31/0.46 % ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% 0.31/0.46 % Maximal formula depth : 10 ( 10 avg)
% 0.31/0.46 % Number of types : 2 ( 1 usr)
% 0.31/0.46 % Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% 0.31/0.46 % Number of symbols : 1 ( 0 usr; 0 con; 2-2 aty)
% 0.31/0.46 % Number of variables : 6 ( 0 ^; 6 !; 0 ?; 6 :)
% 0.31/0.46 % SPC : TH0_THM_EQU_NAR
% 0.31/0.46
% 0.31/0.46 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.31/0.46 % project in the Department of Mathematical Sciences at Carnegie
% 0.31/0.46 % Mellon University. Distributed under the Creative Commons copyleft
% 0.31/0.46 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.31/0.46 % : Polymorphic definitions expanded.
% 0.31/0.46 %------------------------------------------------------------------------------
% 0.31/0.46 thf(a_type,type,
% 0.31/0.46 a: $tType ).
% 0.31/0.46
% 0.31/0.46 thf(cGAZING_THM9_pme,conjecture,
% 0.31/0.46 ! [S: a > $o,T: a > $o,U: a > $o] :
% 0.31/0.46 ( ( ( S = T )
% 0.31/0.46 & ( T = U ) )
% 0.31/0.46 => ( ! [Xx: a] :
% 0.31/0.46 ( ( S @ Xx )
% 0.31/0.46 => ( T @ Xx ) )
% 0.31/0.46 & ! [Xx: a] :
% 0.31/0.46 ( ( T @ Xx )
% 0.31/0.46 => ( U @ Xx ) )
% 0.31/0.46 & ! [Xx: a] :
% 0.31/0.46 ( ( U @ Xx )
% 0.31/0.46 => ( S @ Xx ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 %------------------------------------------------------------------------------
% 0.31/0.46 ------------------------
% 0.31/1.30 ---- Embedded in THF ---
% 0.31/1.30 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 0.31/1.30 %%% Generated on Tue Feb 24 12:35:32 EST 2026
% 0.31/1.30 %%% using '$$dhol' embedding, version 1.3.0.
% 0.31/1.30 %%% Logic specification used:
% 0.31/1.30 %%% thf(spec, logic, $$dhol).
% 0.31/1.30
% 0.31/1.30 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.cmezRSdI3t/DTF2DTF16900.p
% See solution above
% 0.31/1.30 ------------------------
% 0.31/1.31 ---- Cleaned THF ---
% 0.31/1.31 thf(a_type,type,
% 0.31/1.31 a: $tType ).
% 0.31/1.31
% 0.31/1.31 thf(cGAZING_THM9_pme,conjecture,
% 0.31/1.31 ! [S: a > $o,T: a > $o,U: a > $o] :
% 0.31/1.31 ( ( ( S = T )
% 0.31/1.31 & ( T = U ) )
% 0.31/1.31 => ( ! [Xx: a] :
% 0.31/1.31 ( ( S @ Xx )
% 0.31/1.31 => ( T @ Xx ) )
% 0.31/1.31 & ! [Xx: a] :
% 0.31/1.31 ( ( T @ Xx )
% 0.31/1.31 => ( U @ Xx ) )
% 0.31/1.31 & ! [Xx: a] :
% 0.31/1.31 ( ( U @ Xx )
% 0.31/1.31 => ( S @ Xx ) ) ) ) ).
% 0.31/1.31 ------------------------
% 0.31/1.34 % (17231)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_16900 for (2999ds/2Mi)
% 0.31/1.34 % (17227)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_16900 for (2999ds/183Mi)
% 0.31/1.34 % (17228)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_16900 for (2999ds/4Mi)
% 0.31/1.34 % (17230)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_16900 for (2999ds/27Mi)
% 0.31/1.34 % (17232)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_16900 for (2999ds/2Mi)
% 0.31/1.34 % (17233)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_16900 for (2999ds/275Mi)
% 0.31/1.34 % (17231)Instruction limit reached!
% 0.31/1.34 % (17231)------------------------------
% 0.31/1.34 % (17231)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.34 % (17231)Termination reason: Unknown
% 0.31/1.34 % (17231)Termination phase: Saturation
% 0.31/1.34
% 0.31/1.34 % (17231)Memory used [KB]: 5500
% 0.31/1.34 % (17231)Time elapsed: 0.004 s
% 0.31/1.34 % (17231)Instructions burned: 2 (million)
% 0.31/1.34 % (17231)------------------------------
% 0.31/1.34 % (17231)------------------------------
% 0.31/1.34 % (17232)Instruction limit reached!
% 0.31/1.34 % (17232)------------------------------
% 0.31/1.34 % (17232)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.34 % (17232)Termination reason: Unknown
% 0.31/1.34 % (17232)Termination phase: Property scanning
% 0.31/1.34
% 0.31/1.34 % (17232)Memory used [KB]: 895
% 0.31/1.34 % (17232)Time elapsed: 0.003 s
% 0.31/1.34 % (17232)Instructions burned: 2 (million)
% 0.31/1.34 % (17232)------------------------------
% 0.31/1.34 % (17232)------------------------------
% 0.31/1.34 % (17234)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_16900 for (2999ds/18Mi)
% 0.31/1.34 % (17227)First to succeed.
% 0.31/1.34 % (17233)Also succeeded, but the first one will report.
% 0.31/1.34 % (17227)Refutation found. Thanks to Tanya!
% 0.31/1.34 % SZS status Theorem for DTF2THF_16900
% 0.31/1.34 % SZS output start Proof for DTF2THF_16900
% 0.31/1.34 thf(type_def_5, type, a: $tType).
% 0.31/1.34 thf(func_def_0, type, a: $tType).
% 0.31/1.34 thf(func_def_4, type, sK0: a > $o).
% 0.31/1.34 thf(func_def_5, type, sK1: a > $o).
% 0.31/1.34 thf(func_def_6, type, sK2: a > $o).
% 0.31/1.34 thf(func_def_7, type, sK3: a).
% 0.31/1.34 thf(func_def_8, type, sK4: a).
% 0.31/1.34 thf(func_def_9, type, sK5: a).
% 0.31/1.34 thf(f53,plain,(
% 0.31/1.34 $false),
% 0.31/1.34 inference(avatar_sat_refutation,[status(thm)],[f45,f46,f47,f48,f49,f50,f51,f52])).
% 0.31/1.34 thf(f52,plain,(
% 0.31/1.34 spl6_3 | ~spl6_1 | ~spl6_2),
% 0.31/1.34 inference(avatar_split_clause,[status(thm)],[f27,f38,f34,f42])).
% 0.31/1.34 thf(f42,definition,(
% 0.31/1.34 spl6_3 <=> ($true = (sK1 @ sK5))),
% 0.31/1.34 introduced(definition,[new_symbols(naming,[spl6_3])],[avatar_definition])).
% 0.31/1.34 thf(f34,definition,(
% 0.31/1.34 spl6_1 <=> ($true = (sK1 @ sK3))),
% 0.31/1.34 introduced(definition,[new_symbols(naming,[spl6_1])],[avatar_definition])).
% 0.31/1.34 thf(f38,definition,(
% 0.31/1.34 spl6_2 <=> ($true = (sK1 @ sK4))),
% 0.31/1.34 introduced(definition,[new_symbols(naming,[spl6_2])],[avatar_definition])).
% 0.31/1.34 thf(f27,plain,(
% 0.31/1.34 ($true != (sK1 @ sK4)) | ($true = (sK1 @ sK5)) | ($true != (sK1 @ sK3))),
% 0.31/1.34 inference(definition_unfolding,[status(thm)],[f21,f15,f15])).
% 0.31/1.34 thf(f15,plain,(
% 0.31/1.34 (sK0 = sK1)),
% 0.31/1.34 inference(cnf_transformation,[status(thm)],[f13])).
% 0.31/1.34 thf(f13,plain,(
% 0.31/1.34 ((($true != (sK0 @ sK3)) & ($true = (sK1 @ sK3))) | (($true = (sK2 @ sK4)) & ($true != (sK1 @ sK4))) | (($true = (sK0 @ sK5)) & ($true != (sK2 @ sK5)))) & (sK0 = sK1) & (sK2 = sK0)),
% 0.31/1.34 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5])],[f8,f12,f11,f10,f9])).
% 0.31/1.34 thf(f9,plain,(
% 0.31/1.34 ? [X0 : a > $o,X1 : a > $o,X2 : a > $o] : ((? [X3 : a] : (((X0 @ X3) != $true) & ((X1 @ X3) = $true)) | ? [X4 : a] : (($true = (X2 @ X4)) & ((X1 @ X4) != $true)) | ? [X5 : a] : (($true = (X0 @ X5)) & ($true != (X2 @ X5)))) & (X0 = X1) & (X0 = X2)) => ((? [X3 : a] : (($true != (sK0 @ X3)) & ($true = (sK1 @ X3))) | ? [X4 : a] : (($true = (sK2 @ X4)) & ($true != (sK1 @ X4))) | ? [X5 : a] : (($true = (sK0 @ X5)) & ($true != (sK2 @ X5)))) & (sK0 = sK1) & (sK2 = sK0))),
% 0.31/1.34 introduced(definition,[],[choice_axiom])).
% 0.31/1.34 thf(f10,plain,(
% 0.31/1.34 ? [X3 : a] : (($true != (sK0 @ X3)) & ($true = (sK1 @ X3))) => (($true != (sK0 @ sK3)) & ($true = (sK1 @ sK3)))),
% 0.31/1.34 introduced(definition,[],[choice_axiom])).
% 0.31/1.34 thf(f11,plain,(
% 0.31/1.34 ? [X4 : a] : (($true = (sK2 @ X4)) & ($true != (sK1 @ X4))) => (($true = (sK2 @ sK4)) & ($true != (sK1 @ sK4)))),
% 0.31/1.34 introduced(definition,[],[choice_axiom])).
% 0.31/1.34 thf(f12,plain,(
% 0.31/1.34 ? [X5 : a] : (($true = (sK0 @ X5)) & ($true != (sK2 @ X5))) => (($true = (sK0 @ sK5)) & ($true != (sK2 @ sK5)))),
% 0.31/1.34 introduced(definition,[],[choice_axiom])).
% 0.31/1.34 thf(f8,plain,(
% 0.31/1.34 ? [X0 : a > $o,X1 : a > $o,X2 : a > $o] : ((? [X3 : a] : (((X0 @ X3) != $true) & ((X1 @ X3) = $true)) | ? [X4 : a] : (($true = (X2 @ X4)) & ((X1 @ X4) != $true)) | ? [X5 : a] : (($true = (X0 @ X5)) & ($true != (X2 @ X5)))) & (X0 = X1) & (X0 = X2))),
% 0.31/1.34 inference(rectify,[status(thm)],[f7])).
% 0.31/1.34 thf(f7,plain,(
% 0.31/1.34 ? [X2 : a > $o,X1 : a > $o,X0 : a > $o] : ((? [X5 : a] : (($true != (X2 @ X5)) & ($true = (X1 @ X5))) | ? [X3 : a] : (((X0 @ X3) = $true) & ((X1 @ X3) != $true)) | ? [X4 : a] : (($true = (X2 @ X4)) & ($true != (X0 @ X4)))) & (X1 = X2) & (X0 = X2))),
% 0.31/1.34 inference(flattening,[status(thm)],[f6])).
% 0.31/1.34 thf(f6,plain,(
% 0.31/1.34 ? [X1 : a > $o,X2 : a > $o,X0 : a > $o] : ((? [X5 : a] : (($true != (X2 @ X5)) & ($true = (X1 @ X5))) | ? [X3 : a] : (((X0 @ X3) = $true) & ((X1 @ X3) != $true)) | ? [X4 : a] : (($true = (X2 @ X4)) & ($true != (X0 @ X4)))) & ((X0 = X2) & (X1 = X2)))),
% 0.31/1.34 inference(ennf_transformation,[status(thm)],[f5])).
% 0.31/1.34 thf(f5,plain,(
% 0.31/1.34 ~! [X1 : a > $o,X2 : a > $o,X0 : a > $o] : (((X0 = X2) & (X1 = X2)) => (! [X3 : a] : (((X0 @ X3) = $true) => ((X1 @ X3) = $true)) & ! [X5 : a] : (($true = (X1 @ X5)) => ($true = (X2 @ X5))) & ! [X4 : a] : (($true = (X2 @ X4)) => ($true = (X0 @ X4)))))),
% 0.31/1.34 inference(fool_elimination,[status(thm)],[f4])).
% 0.31/1.34 thf(f4,plain,(
% 0.31/1.34 ~! [X0 : a > $o,X1 : a > $o,X2 : a > $o] : (((X1 = X2) & (X0 = X2)) => (! [X3 : a] : ((X0 @ X3) => (X1 @ X3)) & ! [X4 : a] : ((X2 @ X4) => (X0 @ X4)) & ! [X5 : a] : ((X1 @ X5) => (X2 @ X5))))),
% 0.31/1.34 inference(rectify,[status(thm)],[f2])).
% 0.31/1.34 thf(f2,negated_conjecture,(
% 0.31/1.34 ~! [X2 : a > $o,X0 : a > $o,X1 : a > $o] : (((X0 = X1) & (X1 = X2)) => (! [X3 : a] : ((X2 @ X3) => (X0 @ X3)) & ! [X3 : a] : ((X1 @ X3) => (X2 @ X3)) & ! [X3 : a] : ((X0 @ X3) => (X1 @ X3))))),
% 0.31/1.34 inference(negated_conjecture,[status(cth)],[f1])).
% 0.31/1.34 thf(f1,conjecture,(
% 0.31/1.34 ! [X2 : a > $o,X0 : a > $o,X1 : a > $o] : (((X0 = X1) & (X1 = X2)) => (! [X3 : a] : ((X2 @ X3) => (X0 @ X3)) & ! [X3 : a] : ((X1 @ X3) => (X2 @ X3)) & ! [X3 : a] : ((X0 @ X3) => (X1 @ X3))))),
% 0.31/1.34 file('/export/starexec/sandbox/tmp/tmp.cmezRSdI3t/DTF2THF_16900.p',cGAZING_THM9_pme)).
% 0.31/1.34 thf(f21,plain,(
% 0.31/1.34 ($true != (sK0 @ sK3)) | ($true != (sK1 @ sK4)) | ($true = (sK0 @ sK5))),
% 0.31/1.34 inference(cnf_transformation,[status(thm)],[f13])).
% 0.31/1.34 thf(f51,plain,(
% 0.31/1.34 spl6_1 | spl6_2 | ~spl6_3),
% 0.31/1.34 inference(avatar_split_clause,[status(thm)],[f30,f42,f38,f34])).
% 0.31/1.34 thf(f30,plain,(
% 0.31/1.34 ($true != (sK1 @ sK5)) | ($true = (sK1 @ sK3)) | ($true = (sK1 @ sK4))),
% 0.31/1.34 inference(definition_unfolding,[status(thm)],[f18,f24,f24])).
% 0.31/1.34 thf(f24,plain,(
% 0.31/1.34 (sK2 = sK1)),
% 0.31/1.34 inference(definition_unfolding,[status(thm)],[f14,f15])).
% 0.31/1.34 thf(f14,plain,(
% 0.31/1.34 (sK2 = sK0)),
% 0.31/1.34 inference(cnf_transformation,[status(thm)],[f13])).
% 0.31/1.34 thf(f18,plain,(
% 0.31/1.34 ($true = (sK1 @ sK3)) | ($true = (sK2 @ sK4)) | ($true != (sK2 @ sK5))),
% 0.31/1.34 inference(cnf_transformation,[status(thm)],[f13])).
% 0.31/1.34 thf(f50,plain,(
% 0.31/1.34 spl6_3 | ~spl6_1 | spl6_2),
% 0.31/1.34 inference(avatar_split_clause,[status(thm)],[f25,f38,f34,f42])).
% 0.31/1.34 thf(f25,plain,(
% 0.31/1.34 ($true = (sK1 @ sK5)) | ($true = (sK1 @ sK4)) | ($true != (sK1 @ sK3))),
% 0.31/1.34 inference(definition_unfolding,[status(thm)],[f23,f15,f24,f15])).
% 0.31/1.34 thf(f23,plain,(
% 0.31/1.34 ($true != (sK0 @ sK3)) | ($true = (sK2 @ sK4)) | ($true = (sK0 @ sK5))),
% 0.31/1.34 inference(cnf_transformation,[status(thm)],[f13])).
% 0.31/1.34 thf(f49,plain,(
% 0.31/1.34 spl6_1 | spl6_2 | spl6_3),
% 0.31/1.34 inference(avatar_split_clause,[status(thm)],[f29,f42,f38,f34])).
% 0.31/1.34 thf(f29,plain,(
% 0.31/1.34 ($true = (sK1 @ sK3)) | ($true = (sK1 @ sK5)) | ($true = (sK1 @ sK4))),
% 0.31/1.34 inference(definition_unfolding,[status(thm)],[f19,f24,f15])).
% 0.31/1.34 thf(f19,plain,(
% 0.31/1.34 ($true = (sK1 @ sK3)) | ($true = (sK2 @ sK4)) | ($true = (sK0 @ sK5))),
% 0.31/1.34 inference(cnf_transformation,[status(thm)],[f13])).
% 0.31/1.34 thf(f48,plain,(
% 0.31/1.34 ~spl6_1 | spl6_2 | ~spl6_3),
% 0.31/1.34 inference(avatar_split_clause,[status(thm)],[f26,f42,f38,f34])).
% 0.31/1.34 thf(f26,plain,(
% 0.31/1.34 ($true = (sK1 @ sK4)) | ($true != (sK1 @ sK3)) | ($true != (sK1 @ sK5))),
% 0.31/1.34 inference(definition_unfolding,[status(thm)],[f22,f15,f24,f24])).
% 0.31/1.34 thf(f22,plain,(
% 0.31/1.34 ($true != (sK0 @ sK3)) | ($true = (sK2 @ sK4)) | ($true != (sK2 @ sK5))),
% 0.31/1.34 inference(cnf_transformation,[status(thm)],[f13])).
% 0.31/1.34 thf(f47,plain,(
% 0.31/1.34 spl6_3 | ~spl6_2 | spl6_1),
% 0.31/1.34 inference(avatar_split_clause,[status(thm)],[f31,f34,f38,f42])).
% 0.31/1.34 thf(f31,plain,(
% 0.31/1.34 ($true = (sK1 @ sK3)) | ($true != (sK1 @ sK4)) | ($true = (sK1 @ sK5))),
% 0.31/1.34 inference(definition_unfolding,[status(thm)],[f17,f15])).
% 0.31/1.34 thf(f17,plain,(
% 0.31/1.34 ($true = (sK1 @ sK3)) | ($true != (sK1 @ sK4)) | ($true = (sK0 @ sK5))),
% 0.31/1.34 inference(cnf_transformation,[status(thm)],[f13])).
% 0.31/1.34 thf(f46,plain,(
% 0.31/1.34 ~spl6_3 | ~spl6_2 | spl6_1),
% 0.31/1.34 inference(avatar_split_clause,[status(thm)],[f32,f34,f38,f42])).
% 0.31/1.34 thf(f32,plain,(
% 0.31/1.34 ($true != (sK1 @ sK5)) | ($true = (sK1 @ sK3)) | ($true != (sK1 @ sK4))),
% 0.31/1.34 inference(definition_unfolding,[status(thm)],[f16,f24])).
% 0.31/1.34 thf(f16,plain,(
% 0.31/1.34 ($true = (sK1 @ sK3)) | ($true != (sK1 @ sK4)) | ($true != (sK2 @ sK5))),
% 0.31/1.34 inference(cnf_transformation,[status(thm)],[f13])).
% 0.31/1.34 thf(f45,plain,(
% 0.31/1.34 ~spl6_1 | ~spl6_2 | ~spl6_3),
% 0.31/1.34 inference(avatar_split_clause,[status(thm)],[f28,f42,f38,f34])).
% 0.31/1.34 thf(f28,plain,(
% 0.31/1.34 ($true != (sK1 @ sK4)) | ($true != (sK1 @ sK5)) | ($true != (sK1 @ sK3))),
% 0.31/1.34 inference(definition_unfolding,[status(thm)],[f20,f15,f24])).
% 0.31/1.34 thf(f20,plain,(
% 0.31/1.34 ($true != (sK0 @ sK3)) | ($true != (sK1 @ sK4)) | ($true != (sK2 @ sK5))),
% 0.31/1.34 inference(cnf_transformation,[status(thm)],[f13])).
% 0.31/1.34 % SZS output end Proof for DTF2THF_16900
% 0.31/1.34 % (17227)------------------------------
% 0.31/1.34 % (17227)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.34 % (17227)Termination reason: Refutation
% 0.31/1.34
% 0.31/1.34 % (17227)Memory used [KB]: 5500
% 0.31/1.34 % (17227)Time elapsed: 0.005 s
% 0.31/1.34 % (17227)Instructions burned: 2 (million)
% 0.31/1.34 % (17227)------------------------------
% 0.31/1.34 % (17227)------------------------------
% 0.31/1.34 % (17226)Success in time 0.021 s
%------------------------------------------------------------------------------