%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO364^5 : 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 : n008.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 1.55s 1.26s
% Output : Refutation 1.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 2
% Syntax : Number of formulae : 22 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 98 ( 49 equ; 0 cnn)
% Maximal formula atoms : 6 ( 4 avg)
% Number of connectives : 227 ( 27 ~; 11 |; 18 &; 154 @)
% ( 0 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 44 ( 44 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 56 ( 0 ^; 52 !; 4 ?; 56 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_1,type,
j: a > a ).
thf(func_def_2,type,
g: ( a > a ) > a > a ).
thf(func_def_3,type,
h: a > a ).
thf(func_def_4,type,
f: ( a > a ) > a > a ).
thf(func_def_8,type,
sK0: ( a > a ) > $o ).
thf(func_def_11,type,
ph2:
!>[X0: $tType] : X0 ).
thf(func_def_16,type,
sK3: a ).
thf(func_def_17,type,
sK4: a ).
thf(f126,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f125,f18]) ).
thf(f18,plain,
! [X0: a] :
( ( h @ X0 )
= ( j @ X0 ) ),
inference(leibniz_equality_elimination,[status(thm)],[f14]) ).
thf(f14,plain,
! [X0: a > $o,X1: a] :
( ( $true
!= ( X0 @ ( h @ X1 ) ) )
| ( $true
= ( X0 @ ( j @ X1 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
( ! [X0: a > $o,X1: a] :
( ( $true
!= ( X0 @ ( h @ X1 ) ) )
| ( $true
= ( X0 @ ( j @ X1 ) ) ) )
& ( $true
!= ( sK0 @ ( g @ j ) ) )
& ( $true
= ( sK0 @ ( f @ h ) ) )
& ! [X3: a > a,X4: a > $o,X5: a] :
( ( $true
!= ( X4 @ ( f @ X3 @ X5 ) ) )
| ( $true
= ( X4 @ ( g @ X3 @ X5 ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f8,f9]) ).
thf(f9,plain,
( ? [X2: ( a > a ) > $o] :
( ( ( X2 @ ( g @ j ) )
!= $true )
& ( ( X2 @ ( f @ h ) )
= $true ) )
=> ( ( $true
!= ( sK0 @ ( g @ j ) ) )
& ( $true
= ( sK0 @ ( f @ h ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f8,plain,
( ! [X0: a > $o,X1: a] :
( ( $true
!= ( X0 @ ( h @ X1 ) ) )
| ( $true
= ( X0 @ ( j @ X1 ) ) ) )
& ? [X2: ( a > a ) > $o] :
( ( ( X2 @ ( g @ j ) )
!= $true )
& ( ( X2 @ ( f @ h ) )
= $true ) )
& ! [X3: a > a,X4: a > $o,X5: a] :
( ( $true
!= ( X4 @ ( f @ X3 @ X5 ) ) )
| ( $true
= ( X4 @ ( g @ X3 @ X5 ) ) ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,plain,
( ! [X4: a > $o,X3: a] :
( ( $true
!= ( X4 @ ( h @ X3 ) ) )
| ( ( X4 @ ( j @ X3 ) )
= $true ) )
& ? [X5: ( a > a ) > $o] :
( ( $true
!= ( X5 @ ( g @ j ) ) )
& ( $true
= ( X5 @ ( f @ h ) ) ) )
& ! [X1: a > a,X2: a > $o,X0: a] :
( ( $true
!= ( X2 @ ( f @ X1 @ X0 ) ) )
| ( $true
= ( X2 @ ( g @ X1 @ X0 ) ) ) ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
( ? [X5: ( a > a ) > $o] :
( ( $true
!= ( X5 @ ( g @ j ) ) )
& ( $true
= ( X5 @ ( f @ h ) ) ) )
& ! [X1: a > a,X2: a > $o,X0: a] :
( ( $true
!= ( X2 @ ( f @ X1 @ X0 ) ) )
| ( $true
= ( X2 @ ( g @ X1 @ X0 ) ) ) )
& ! [X4: a > $o,X3: a] :
( ( $true
!= ( X4 @ ( h @ X3 ) ) )
| ( ( X4 @ ( j @ X3 ) )
= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ( ! [X0: a,X2: a > $o,X1: a > a] :
( ( $true
= ( X2 @ ( f @ X1 @ X0 ) ) )
=> ( $true
= ( X2 @ ( g @ X1 @ X0 ) ) ) )
& ! [X4: a > $o,X3: a] :
( ( $true
= ( X4 @ ( h @ X3 ) ) )
=> ( ( X4 @ ( j @ X3 ) )
= $true ) ) )
=> ! [X5: ( a > a ) > $o] :
( ( $true
= ( X5 @ ( f @ h ) ) )
=> ( $true
= ( X5 @ ( g @ j ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ( ! [X0: a,X1: a > a,X2: a > $o] :
( ( X2 @ ( f @ X1 @ X0 ) )
=> ( X2 @ ( g @ X1 @ X0 ) ) )
& ! [X3: a,X4: a > $o] :
( ( X4 @ ( h @ X3 ) )
=> ( X4 @ ( j @ X3 ) ) ) )
=> ! [X5: ( a > a ) > $o] :
( ( X5 @ ( f @ h ) )
=> ( X5 @ ( g @ j ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ( ! [X1: a,X0: a > a,X2: a > $o] :
( ( X2 @ ( f @ X0 @ X1 ) )
=> ( X2 @ ( g @ X0 @ X1 ) ) )
& ! [X3: a,X2: a > $o] :
( ( X2 @ ( h @ X3 ) )
=> ( X2 @ ( j @ X3 ) ) ) )
=> ! [X2: ( a > a ) > $o] :
( ( X2 @ ( f @ h ) )
=> ( X2 @ ( g @ j ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ( ! [X1: a,X0: a > a,X2: a > $o] :
( ( X2 @ ( f @ X0 @ X1 ) )
=> ( X2 @ ( g @ X0 @ X1 ) ) )
& ! [X3: a,X2: a > $o] :
( ( X2 @ ( h @ X3 ) )
=> ( X2 @ ( j @ X3 ) ) ) )
=> ! [X2: ( a > a ) > $o] :
( ( X2 @ ( f @ h ) )
=> ( X2 @ ( g @ j ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JttXFTXNJg/DTF2THF_5385.p',cEDEC_pme) ).
thf(f125,plain,
( ( j @ sK4 )
!= ( h @ sK4 ) ),
inference(negative_extensionality,[status(thm)],[f124]) ).
thf(f124,plain,
h != j,
inference(equality_resolution,[status(thm)],[f123]) ).
thf(f123,plain,
( ( g @ j @ sK3 )
!= ( g @ h @ sK3 ) ),
inference(superposition,[status(thm)],[f50,f52]) ).
thf(f52,plain,
! [X0: a > a,X1: a] :
( ( f @ X0 @ X1 )
= ( g @ X0 @ X1 ) ),
inference(leibniz_equality_elimination,[status(thm)],[f11]) ).
thf(f11,plain,
! [X3: a > a,X4: a > $o,X5: a] :
( ( $true
!= ( X4 @ ( f @ X3 @ X5 ) ) )
| ( $true
= ( X4 @ ( g @ X3 @ X5 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f50,plain,
( ( g @ j @ sK3 )
!= ( f @ h @ sK3 ) ),
inference(negative_extensionality,[status(thm)],[f16]) ).
thf(f16,plain,
( ( f @ h )
!= ( g @ j ) ),
inference(trivial_inequality_removal,[status(thm)],[f15]) ).
thf(f15,plain,
( ( $true != $true )
| ( ( f @ h )
!= ( g @ j ) ) ),
inference(constrained_superposition,[status(thm)],[f13,f12]) ).
thf(f12,plain,
( $true
= ( sK0 @ ( f @ h ) ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f13,plain,
( $true
!= ( sK0 @ ( g @ j ) ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO364^5 : 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
% 0.15/0.34 % Computer : n008.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Tue Feb 24 14:28:54 EST 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.19/0.46 ---- Original DTF file ---
% 0.19/0.46 thf(spec,logic,$$dhol).
% 0.19/0.46 %------------------------------------------------------------------------------
% 0.19/0.46 % File : SYO364^5 : TPTP v9.2.1. Released v4.0.0.
% 0.19/0.46 % Domain : Syntactic
% 0.19/0.46 % Problem : TPS problem EDEC
% 0.19/0.46 % Version : Especial.
% 0.19/0.46 % English : Example from [Ben99] about decomposition (using Leibniz equality).
% 0.19/0.46
% 0.19/0.46 % Refs : [Ben99] Benzmueller (1999), Equality and Extensionality in Hig
% 0.19/0.46 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.19/0.46 % Source : [Bro09]
% 0.19/0.46 % Names : tps_0575 [Bro09]
% 0.19/0.46 % : EDEC [TPS]
% 0.19/0.46
% 0.19/0.46 % Status : Theorem
% 0.19/0.46 % Rating : 0.25 v9.0.0, 0.17 v8.2.0, 0.18 v8.1.0, 0.25 v7.4.0, 0.22 v7.3.0, 0.30 v7.2.0, 0.38 v7.1.0, 0.29 v7.0.0, 0.38 v6.4.0, 0.43 v6.3.0, 0.50 v5.5.0, 0.80 v5.4.0, 0.75 v5.0.0, 0.50 v4.1.0, 0.67 v4.0.1, 1.00 v4.0.0
% 0.19/0.46 % Syntax : Number of formulae : 6 ( 0 unt; 5 typ; 0 def)
% 0.19/0.46 % Number of atoms : 0 ( 0 equ; 0 cnn)
% 0.19/0.46 % Maximal formula atoms : 0 ( 0 avg)
% 0.19/0.46 % Number of connectives : 19 ( 0 ~; 0 |; 1 &; 14 @)
% 0.19/0.46 % ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% 0.19/0.46 % Maximal formula depth : 10 ( 10 avg)
% 0.19/0.46 % Number of types : 2 ( 1 usr)
% 0.19/0.46 % Number of type conns : 13 ( 13 >; 0 *; 0 +; 0 <<)
% 0.19/0.46 % Number of symbols : 4 ( 4 usr; 0 con; 1-2 aty)
% 0.19/0.46 % Number of variables : 6 ( 0 ^; 6 !; 0 ?; 6 :)
% 0.19/0.46 % SPC : TH0_THM_NEQ_NAR
% 0.19/0.46
% 0.19/0.46 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.19/0.46 % project in the Department of Mathematical Sciences at Carnegie
% 0.19/0.46 % Mellon University. Distributed under the Creative Commons copyleft
% 0.19/0.46 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.19/0.46 % : Polymorphic definitions expanded.
% 0.19/0.46 %------------------------------------------------------------------------------
% 0.19/0.46 thf(a_type,type,
% 0.19/0.46 a: $tType ).
% 0.19/0.46
% 0.19/0.46 thf(j,type,
% 0.19/0.46 j: a > a ).
% 0.19/0.46
% 0.19/0.46 thf(g,type,
% 0.19/0.46 g: ( a > a ) > a > a ).
% 0.19/0.46
% 0.19/0.46 thf(h,type,
% 0.19/0.46 h: a > a ).
% 0.19/0.46
% 0.19/0.46 thf(f,type,
% 0.19/0.46 f: ( a > a ) > a > a ).
% 0.19/0.46
% 0.19/0.46 thf(cEDEC_pme,conjecture,
% 0.19/0.46 ( ( ! [X: a > a,Y: a,Xq: a > $o] :
% 0.19/0.46 ( ( Xq @ ( f @ X @ Y ) )
% 0.19/0.46 => ( Xq @ ( g @ X @ Y ) ) )
% 0.19/0.46 & ! [Z: a,Xq: a > $o] :
% 0.19/0.46 ( ( Xq @ ( h @ Z ) )
% 0.19/0.46 => ( Xq @ ( j @ Z ) ) ) )
% 0.19/0.46 => ! [Xq: ( a > a ) > $o] :
% 0.19/0.46 ( ( Xq @ ( f @ h ) )
% 0.19/0.46 => ( Xq @ ( g @ j ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 %------------------------------------------------------------------------------
% 0.19/0.46 ------------------------
% 1.55/1.22 ---- Embedded in THF ---
% 1.55/1.22 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.55/1.22 %%% Generated on Tue Feb 24 14:28:55 EST 2026
% 1.55/1.22 %%% using '$$dhol' embedding, version 1.3.0.
% 1.55/1.22 %%% Logic specification used:
% 1.55/1.22 %%% thf(spec, logic, $$dhol).
% 1.55/1.22
% 1.55/1.22 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.JttXFTXNJg/DTF2DTF5385.p
% See solution above
% 1.55/1.22 ------------------------
% 1.55/1.23 ---- Cleaned THF ---
% 1.55/1.23 thf(a_type,type,
% 1.55/1.23 a: $tType ).
% 1.55/1.23
% 1.55/1.23 thf(j,type,
% 1.55/1.23 j: a > a ).
% 1.55/1.23
% 1.55/1.23 thf(g,type,
% 1.55/1.23 g: ( a > a ) > a > a ).
% 1.55/1.23
% 1.55/1.23 thf(h,type,
% 1.55/1.23 h: a > a ).
% 1.55/1.23
% 1.55/1.23 thf(f,type,
% 1.55/1.23 f: ( a > a ) > a > a ).
% 1.55/1.23
% 1.55/1.23 thf(cEDEC_pme,conjecture,
% 1.55/1.23 ( ( ! [X: a > a,Y: a,Xq: a > $o] :
% 1.55/1.23 ( ( Xq @ ( f @ X @ Y ) )
% 1.55/1.23 => ( Xq @ ( g @ X @ Y ) ) )
% 1.55/1.23 & ! [Z: a,Xq: a > $o] :
% 1.55/1.23 ( ( Xq @ ( h @ Z ) )
% 1.55/1.23 => ( Xq @ ( j @ Z ) ) ) )
% 1.55/1.23 => ! [Xq: ( a > a ) > $o] :
% 1.55/1.23 ( ( Xq @ ( f @ h ) )
% 1.55/1.23 => ( Xq @ ( g @ j ) ) ) ) ).
% 1.55/1.23 ------------------------
% 1.55/1.24 % (5574)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_5385 for (2999ds/4Mi)
% 1.55/1.24 % (5575)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_5385 for (2999ds/27Mi)
% 1.55/1.24 % (5574)Instruction limit reached!
% 1.55/1.24 % (5574)------------------------------
% 1.55/1.24 % (5574)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.24 % (5574)Termination reason: Unknown
% 1.55/1.24 % (5574)Termination phase: Saturation
% 1.55/1.24
% 1.55/1.24 % (5574)Memory used [KB]: 5500
% 1.55/1.24 % (5574)Time elapsed: 0.003 s
% 1.55/1.24 % (5574)Instructions burned: 4 (million)
% 1.55/1.24 % (5574)------------------------------
% 1.55/1.24 % (5574)------------------------------
% 1.55/1.24 % (5575)Refutation not found, incomplete strategy
% 1.55/1.24 % (5575)------------------------------
% 1.55/1.24 % (5575)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.24 % (5575)Termination reason: Refutation not found, incomplete strategy
% 1.55/1.24
% 1.55/1.24
% 1.55/1.24 % (5575)Memory used [KB]: 5500
% 1.55/1.24 % (5575)Time elapsed: 0.002 s
% 1.55/1.24 % (5575)Instructions burned: 2 (million)
% 1.55/1.24 % (5575)------------------------------
% 1.55/1.24 % (5575)------------------------------
% 1.55/1.25 % (5573)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_5385 for (2999ds/183Mi)
% 1.55/1.25 % (5576)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_5385 for (2999ds/2Mi)
% 1.55/1.25 % (5577)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_5385 for (2999ds/2Mi)
% 1.55/1.25 % (5579)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_5385 for (2999ds/18Mi)
% 1.55/1.25 % (5576)Instruction limit reached!
% 1.55/1.25 % (5576)------------------------------
% 1.55/1.25 % (5576)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.25 % (5576)Termination reason: Unknown
% 1.55/1.25 % (5576)Termination phase: Saturation
% 1.55/1.25
% 1.55/1.25 % (5577)Instruction limit reached!
% 1.55/1.25 % (5577)------------------------------
% 1.55/1.25 % (5577)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.25 % (5577)Termination reason: Unknown
% 1.55/1.25 % (5577)Termination phase: Saturation
% 1.55/1.25
% 1.55/1.25 % (5577)Memory used [KB]: 895
% 1.55/1.25 % (5577)Time elapsed: 0.003 s
% 1.55/1.25 % (5577)Instructions burned: 2 (million)
% 1.55/1.25 % (5577)------------------------------
% 1.55/1.25 % (5577)------------------------------
% 1.55/1.25 % (5576)Memory used [KB]: 5373
% 1.55/1.25 % (5576)Time elapsed: 0.003 s
% 1.55/1.25 % (5576)Instructions burned: 2 (million)
% 1.55/1.25 % (5576)------------------------------
% 1.55/1.25 % (5576)------------------------------
% 1.55/1.25 % (5580)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_5385 for (2999ds/3Mi)
% 1.55/1.25 % (5580)Instruction limit reached!
% 1.55/1.25 % (5580)------------------------------
% 1.55/1.25 % (5580)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.25 % (5580)Termination reason: Unknown
% 1.55/1.25 % (5580)Termination phase: Saturation
% 1.55/1.25
% 1.55/1.25 % (5580)Memory used [KB]: 5500
% 1.55/1.25 % (5580)Time elapsed: 0.002 s
% 1.55/1.25 % (5580)Instructions burned: 3 (million)
% 1.55/1.25 % (5580)------------------------------
% 1.55/1.25 % (5580)------------------------------
% 1.55/1.25 % (5581)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_5385 for (2999ds/37Mi)
% 1.55/1.25 % (5578)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_5385 for (2999ds/275Mi)
% 1.55/1.26 % (5578)Refutation not found, incomplete strategy
% 1.55/1.26 % (5578)------------------------------
% 1.55/1.26 % (5578)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.26 % (5578)Termination reason: Refutation not found, incomplete strategy
% 1.55/1.26
% 1.55/1.26
% 1.55/1.26 % (5578)Memory used [KB]: 5500
% 1.55/1.26 % (5578)Time elapsed: 0.006 s
% 1.55/1.26 % (5578)Instructions burned: 7 (million)
% 1.55/1.26 % (5578)------------------------------
% 1.55/1.26 % (5578)------------------------------
% 1.55/1.26 % (5579)First to succeed.
% 1.55/1.26 % (5579)Refutation found. Thanks to Tanya!
% 1.55/1.26 % SZS status Theorem for DTF2THF_5385
% 1.55/1.26 % SZS output start Proof for DTF2THF_5385
% 1.55/1.26 thf(type_def_5, type, a: $tType).
% 1.55/1.26 thf(func_def_0, type, a: $tType).
% 1.55/1.26 thf(func_def_1, type, j: a > a).
% 1.55/1.26 thf(func_def_2, type, g: (a > a) > a > a).
% 1.55/1.26 thf(func_def_3, type, h: a > a).
% 1.55/1.26 thf(func_def_4, type, f: (a > a) > a > a).
% 1.55/1.26 thf(func_def_8, type, sK0: (a > a) > $o).
% 1.55/1.26 thf(func_def_11, type, ph2: !>[X0: $tType]:(X0)).
% 1.55/1.26 thf(func_def_16, type, sK3: a).
% 1.55/1.26 thf(func_def_17, type, sK4: a).
% 1.55/1.26 thf(f126,plain,(
% 1.55/1.26 $false),
% 1.55/1.26 inference(subsumption_resolution,[status(thm)],[f125,f18])).
% 1.55/1.26 thf(f18,plain,(
% 1.55/1.26 ( ! [X0 : a] : (((h @ X0) = (j @ X0))) )),
% 1.55/1.26 inference(leibniz_equality_elimination,[status(thm)],[f14])).
% 1.55/1.26 thf(f14,plain,(
% 1.55/1.26 ( ! [X0 : a > $o,X1 : a] : (($true != (X0 @ (h @ X1))) | ($true = (X0 @ (j @ X1)))) )),
% 1.55/1.26 inference(cnf_transformation,[status(thm)],[f10])).
% 1.55/1.26 thf(f10,plain,(
% 1.55/1.26 ! [X0 : a > $o,X1 : a] : (($true != (X0 @ (h @ X1))) | ($true = (X0 @ (j @ X1)))) & (($true != (sK0 @ (g @ j))) & ($true = (sK0 @ (f @ h)))) & ! [X3 : a > a,X4 : a > $o,X5 : a] : (($true != (X4 @ (f @ X3 @ X5))) | ($true = (X4 @ (g @ X3 @ X5))))),
% 1.55/1.26 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f8,f9])).
% 1.55/1.26 thf(f9,plain,(
% 1.55/1.26 ? [X2 : (a > a) > $o] : (((X2 @ (g @ j)) != $true) & ((X2 @ (f @ h)) = $true)) => (($true != (sK0 @ (g @ j))) & ($true = (sK0 @ (f @ h))))),
% 1.55/1.26 introduced(definition,[],[choice_axiom])).
% 1.55/1.26 thf(f8,plain,(
% 1.55/1.26 ! [X0 : a > $o,X1 : a] : (($true != (X0 @ (h @ X1))) | ($true = (X0 @ (j @ X1)))) & ? [X2 : (a > a) > $o] : (((X2 @ (g @ j)) != $true) & ((X2 @ (f @ h)) = $true)) & ! [X3 : a > a,X4 : a > $o,X5 : a] : (($true != (X4 @ (f @ X3 @ X5))) | ($true = (X4 @ (g @ X3 @ X5))))),
% 1.55/1.26 inference(rectify,[status(thm)],[f7])).
% 1.55/1.26 thf(f7,plain,(
% 1.55/1.26 ! [X4 : a > $o,X3 : a] : (($true != (X4 @ (h @ X3))) | ((X4 @ (j @ X3)) = $true)) & ? [X5 : (a > a) > $o] : (($true != (X5 @ (g @ j))) & ($true = (X5 @ (f @ h)))) & ! [X1 : a > a,X2 : a > $o,X0 : a] : (($true != (X2 @ (f @ X1 @ X0))) | ($true = (X2 @ (g @ X1 @ X0))))),
% 1.55/1.26 inference(flattening,[status(thm)],[f6])).
% 1.55/1.26 thf(f6,plain,(
% 1.55/1.26 ? [X5 : (a > a) > $o] : (($true != (X5 @ (g @ j))) & ($true = (X5 @ (f @ h)))) & (! [X1 : a > a,X2 : a > $o,X0 : a] : (($true != (X2 @ (f @ X1 @ X0))) | ($true = (X2 @ (g @ X1 @ X0)))) & ! [X4 : a > $o,X3 : a] : (($true != (X4 @ (h @ X3))) | ((X4 @ (j @ X3)) = $true)))),
% 1.55/1.26 inference(ennf_transformation,[status(thm)],[f5])).
% 1.55/1.26 thf(f5,plain,(
% 1.55/1.26 ~((! [X0 : a,X2 : a > $o,X1 : a > a] : (($true = (X2 @ (f @ X1 @ X0))) => ($true = (X2 @ (g @ X1 @ X0)))) & ! [X4 : a > $o,X3 : a] : (($true = (X4 @ (h @ X3))) => ((X4 @ (j @ X3)) = $true))) => ! [X5 : (a > a) > $o] : (($true = (X5 @ (f @ h))) => ($true = (X5 @ (g @ j)))))),
% 1.55/1.26 inference(fool_elimination,[status(thm)],[f4])).
% 1.55/1.26 thf(f4,plain,(
% 1.55/1.26 ~((! [X0 : a,X1 : a > a,X2 : a > $o] : ((X2 @ (f @ X1 @ X0)) => (X2 @ (g @ X1 @ X0))) & ! [X3 : a,X4 : a > $o] : ((X4 @ (h @ X3)) => (X4 @ (j @ X3)))) => ! [X5 : (a > a) > $o] : ((X5 @ (f @ h)) => (X5 @ (g @ j))))),
% 1.55/1.26 inference(rectify,[status(thm)],[f2])).
% 1.55/1.26 thf(f2,negated_conjecture,(
% 1.55/1.26 ~((! [X1 : a,X0 : a > a,X2 : a > $o] : ((X2 @ (f @ X0 @ X1)) => (X2 @ (g @ X0 @ X1))) & ! [X3 : a,X2 : a > $o] : ((X2 @ (h @ X3)) => (X2 @ (j @ X3)))) => ! [X2 : (a > a) > $o] : ((X2 @ (f @ h)) => (X2 @ (g @ j))))),
% 1.55/1.26 inference(negated_conjecture,[status(cth)],[f1])).
% 1.55/1.26 thf(f1,conjecture,(
% 1.55/1.26 (! [X1 : a,X0 : a > a,X2 : a > $o] : ((X2 @ (f @ X0 @ X1)) => (X2 @ (g @ X0 @ X1))) & ! [X3 : a,X2 : a > $o] : ((X2 @ (h @ X3)) => (X2 @ (j @ X3)))) => ! [X2 : (a > a) > $o] : ((X2 @ (f @ h)) => (X2 @ (g @ j)))),
% 1.55/1.26 file('/export/starexec/sandbox/tmp/tmp.JttXFTXNJg/DTF2THF_5385.p',cEDEC_pme)).
% 1.55/1.26 thf(f125,plain,(
% 1.55/1.26 ((j @ sK4) != (h @ sK4))),
% 1.55/1.26 inference(negative_extensionality,[status(thm)],[f124])).
% 1.55/1.26 thf(f124,plain,(
% 1.55/1.26 (h != j)),
% 1.55/1.26 inference(equality_resolution,[status(thm)],[f123])).
% 1.55/1.26 thf(f123,plain,(
% 1.55/1.26 ((g @ j @ sK3) != (g @ h @ sK3))),
% 1.55/1.26 inference(superposition,[status(thm)],[f50,f52])).
% 1.55/1.26 thf(f52,plain,(
% 1.55/1.26 ( ! [X0 : a > a,X1 : a] : (((f @ X0 @ X1) = (g @ X0 @ X1))) )),
% 1.55/1.26 inference(leibniz_equality_elimination,[status(thm)],[f11])).
% 1.55/1.26 thf(f11,plain,(
% 1.55/1.26 ( ! [X3 : a > a,X4 : a > $o,X5 : a] : (($true != (X4 @ (f @ X3 @ X5))) | ($true = (X4 @ (g @ X3 @ X5)))) )),
% 1.55/1.26 inference(cnf_transformation,[status(thm)],[f10])).
% 1.55/1.26 thf(f50,plain,(
% 1.55/1.26 ((g @ j @ sK3) != (f @ h @ sK3))),
% 1.55/1.26 inference(negative_extensionality,[status(thm)],[f16])).
% 1.55/1.26 thf(f16,plain,(
% 1.55/1.26 ((f @ h) != (g @ j))),
% 1.55/1.26 inference(trivial_inequality_removal,[status(thm)],[f15])).
% 1.55/1.26 thf(f15,plain,(
% 1.55/1.26 ($true != $true) | ((f @ h) != (g @ j))),
% 1.55/1.26 inference(constrained_superposition,[status(thm)],[f13,f12])).
% 1.55/1.26 thf(f12,plain,(
% 1.55/1.26 ($true = (sK0 @ (f @ h)))),
% 1.55/1.26 inference(cnf_transformation,[status(thm)],[f10])).
% 1.55/1.26 thf(f13,plain,(
% 1.55/1.26 ($true != (sK0 @ (g @ j)))),
% 1.55/1.26 inference(cnf_transformation,[status(thm)],[f10])).
% 1.55/1.26 % SZS output end Proof for DTF2THF_5385
% 1.55/1.26 % (5579)------------------------------
% 1.55/1.26 % (5579)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.26 % (5579)Termination reason: Refutation
% 1.55/1.26
% 1.55/1.26 % (5579)Memory used [KB]: 5628
% 1.55/1.26 % (5579)Time elapsed: 0.015 s
% 1.55/1.26 % (5579)Instructions burned: 15 (million)
% 1.55/1.26 % (5579)------------------------------
% 1.55/1.26 % (5579)------------------------------
% 1.55/1.26 % (5572)Success in time 0.029 s
%------------------------------------------------------------------------------