%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO374^5 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n024.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 09:54:04 AM UTC 2026
% Result : Theorem 0.83s 0.88s
% Output : Refutation 0.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 6
% Syntax : Number of formulae : 39 ( 4 unt; 0 typ; 4 def)
% Number of atoms : 127 ( 36 equ; 0 cnn)
% Maximal formula atoms : 4 ( 3 avg)
% Number of connectives : 169 ( 44 ~; 37 |; 2 &; 71 @)
% ( 10 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 20 ( 20 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 23 ( 0 ^; 21 !; 2 ?; 23 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
cN: $i > $i ).
thf(func_def_1,type,
cM: $i > $i ).
thf(func_def_5,type,
sK0: ( $i > $i ) > $o ).
thf(func_def_8,type,
ph2:
!>[X0: $tType] : X0 ).
thf(f91,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f23,f32,f73,f76,f90]) ).
thf(f90,plain,
( spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[status(thm)],[f89]) ).
thf(f89,plain,
( $false
| spl1_3
| ~ spl1_4 ),
inference(subsumption_resolution,[status(thm)],[f88,f38]) ).
thf(f38,plain,
! [X0: $i] :
( ( cM @ X0 )
= ( cN @ X0 ) ),
inference(leibniz_equality_elimination,[status(thm)],[f11]) ).
thf(f11,plain,
! [X0: $i,X1: $i > $o] :
( ( ( X1 @ ( cM @ X0 ) )
= $true )
| ( ( X1 @ ( cN @ X0 ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f10]) ).
thf(f10,plain,
! [X0: $i,X1: $i > $o] :
( ( X1 @ ( cM @ X0 ) )
= ( X1 @ ( cN @ X0 ) ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
( ! [X0: $i,X1: $i > $o] :
( ( X1 @ ( cM @ X0 ) )
= ( X1 @ ( cN @ X0 ) ) )
& ( ( sK0 @ cN )
!= ( sK0 @ cM ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f6,f7]) ).
thf(f7,plain,
( ? [X2: ( $i > $i ) > $o] :
( ( X2 @ cM )
!= ( X2 @ cN ) )
=> ( ( sK0 @ cN )
!= ( sK0 @ cM ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f6,plain,
( ! [X0: $i,X1: $i > $o] :
( ( X1 @ ( cM @ X0 ) )
= ( X1 @ ( cN @ X0 ) ) )
& ? [X2: ( $i > $i ) > $o] :
( ( X2 @ cM )
!= ( X2 @ cN ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ! [X0: $i,X1: $i > $o] :
( ( X1 @ ( cM @ X0 ) )
= ( X1 @ ( cN @ X0 ) ) )
=> ! [X2: ( $i > $i ) > $o] :
( ( X2 @ cM )
= ( X2 @ cN ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ! [X0: $i,X1: $i > $o] :
( ( X1 @ ( cN @ X0 ) )
<=> ( X1 @ ( cM @ X0 ) ) )
=> ! [X2: ( $i > $i ) > $o] :
( ( X2 @ cM )
<=> ( X2 @ cN ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ! [X0: $i,X1: $i > $o] :
( ( X1 @ ( cN @ X0 ) )
<=> ( X1 @ ( cM @ X0 ) ) )
=> ! [X2: ( $i > $i ) > $o] :
( ( X2 @ cM )
<=> ( X2 @ cN ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ! [X0: $i,X1: $i > $o] :
( ( X1 @ ( cN @ X0 ) )
<=> ( X1 @ ( cM @ X0 ) ) )
=> ! [X2: ( $i > $i ) > $o] :
( ( X2 @ cM )
<=> ( X2 @ cN ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.VR7BTtFTDX/DTF2THF_15722.p',cEXT_A_LEIB2) ).
thf(f88,plain,
( ( ( cN @ sK4 )
!= ( cM @ sK4 ) )
| spl1_3
| ~ spl1_4 ),
inference(negative_extensionality,[status(thm)],[f87]) ).
thf(f87,plain,
( ( cM != cN )
| spl1_3
| ~ spl1_4 ),
inference(trivial_inequality_removal,[status(thm)],[f83]) ).
thf(f83,plain,
( ( $false != $false )
| ( cM != cN )
| spl1_3
| ~ spl1_4 ),
inference(constrained_superposition,[status(thm)],[f26,f31]) ).
thf(f31,plain,
( ( ( sK0 @ cN )
= $false )
| ~ spl1_4 ),
inference(avatar_component_clause,[status(thm)],[f29]) ).
thf(f29,definition,
( spl1_4
<=> ( ( sK0 @ cN )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl1_4])],[avatar_definition]) ).
thf(f26,plain,
( ( ( sK0 @ cM )
!= $false )
| spl1_3 ),
inference(avatar_component_clause,[status(thm)],[f25]) ).
thf(f25,definition,
( spl1_3
<=> ( ( sK0 @ cM )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl1_3])],[avatar_definition]) ).
thf(f76,plain,
( ~ spl1_1
| ~ spl1_3 ),
inference(avatar_contradiction_clause,[status(thm)],[f75]) ).
thf(f75,plain,
( $false
| ~ spl1_1
| ~ spl1_3 ),
inference(trivial_inequality_removal,[status(thm)],[f74]) ).
thf(f74,plain,
( ( $true = $false )
| ~ spl1_1
| ~ spl1_3 ),
inference(forward_demodulation,[status(thm)],[f18,f27]) ).
thf(f27,plain,
( ( ( sK0 @ cM )
= $false )
| ~ spl1_3 ),
inference(avatar_component_clause,[status(thm)],[f25]) ).
thf(f18,plain,
( ( ( sK0 @ cM )
= $true )
| ~ spl1_1 ),
inference(avatar_component_clause,[status(thm)],[f16]) ).
thf(f16,definition,
( spl1_1
<=> ( ( sK0 @ cM )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl1_1])],[avatar_definition]) ).
thf(f73,plain,
( ~ spl1_2
| ~ spl1_3 ),
inference(avatar_contradiction_clause,[status(thm)],[f72]) ).
thf(f72,plain,
( $false
| ~ spl1_2
| ~ spl1_3 ),
inference(trivial_inequality_removal,[status(thm)],[f71]) ).
thf(f71,plain,
( ( ( cN @ sK3 )
!= ( cN @ sK3 ) )
| ~ spl1_2
| ~ spl1_3 ),
inference(superposition,[status(thm)],[f37,f38]) ).
thf(f37,plain,
( ( ( cN @ sK3 )
!= ( cM @ sK3 ) )
| ~ spl1_2
| ~ spl1_3 ),
inference(negative_extensionality,[status(thm)],[f36]) ).
thf(f36,plain,
( ( cM != cN )
| ~ spl1_2
| ~ spl1_3 ),
inference(trivial_inequality_removal,[status(thm)],[f34]) ).
thf(f34,plain,
( ( cM != cN )
| ( $true = $false )
| ~ spl1_2
| ~ spl1_3 ),
inference(constrained_superposition,[status(thm)],[f22,f27]) ).
thf(f22,plain,
( ( ( sK0 @ cN )
= $true )
| ~ spl1_2 ),
inference(avatar_component_clause,[status(thm)],[f20]) ).
thf(f20,definition,
( spl1_2
<=> ( ( sK0 @ cN )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl1_2])],[avatar_definition]) ).
thf(f32,plain,
( spl1_3
| spl1_4 ),
inference(avatar_split_clause,[status(thm)],[f14,f29,f25]) ).
thf(f14,plain,
( ( ( sK0 @ cM )
= $false )
| ( ( sK0 @ cN )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f9]) ).
thf(f9,plain,
( ( sK0 @ cN )
!= ( sK0 @ cM ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f23,plain,
( spl1_1
| spl1_2 ),
inference(avatar_split_clause,[status(thm)],[f13,f20,f16]) ).
thf(f13,plain,
( ( ( sK0 @ cM )
= $true )
| ( ( sK0 @ cN )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : SYO374^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.06 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.07/0.24 % Computer : n024.cluster.edu
% 0.07/0.24 % Model : x86_64 x86_64
% 0.07/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.24 % Memory : 8042.1875MB
% 0.07/0.24 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.24 % CPULimit : 300
% 0.07/0.24 % WCLimit : 300
% 0.07/0.24 % DateTime : Tue Feb 24 09:28:55 EST 2026
% 0.07/0.25 % CPUTime :
% 0.07/0.25 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.07/0.31 ---- Original DTF file ---
% 0.07/0.31 thf(spec,logic,$$dhol).
% 0.07/0.31 %------------------------------------------------------------------------------
% 0.07/0.31 % File : SYO374^5 : TPTP v9.2.1. Released v4.0.0.
% 0.07/0.31 % Domain : Syntactic
% 0.07/0.31 % Problem : TPS problem from EXTENSIONALITY
% 0.07/0.31 % Version : Especial.
% 0.07/0.31 % English :
% 0.07/0.31
% 0.07/0.31 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.07/0.31 % Source : [Bro09]
% 0.07/0.31 % Names : tps_0758 [Bro09]
% 0.07/0.31
% 0.07/0.31 % Status : Theorem
% 0.07/0.31 % Rating : 0.25 v9.1.0, 0.38 v9.0.0, 0.25 v8.2.0, 0.27 v8.1.0, 0.25 v7.4.0, 0.22 v7.3.0, 0.20 v7.2.0, 0.25 v7.1.0, 0.29 v7.0.0, 0.25 v6.4.0, 0.29 v6.3.0, 0.33 v6.2.0, 0.50 v6.1.0, 0.33 v5.5.0, 0.40 v5.4.0, 0.75 v4.1.0, 0.67 v4.0.1, 1.00 v4.0.0
% 0.07/0.31 % Syntax : Number of formulae : 3 ( 0 unt; 2 typ; 0 def)
% 0.07/0.31 % Number of atoms : 0 ( 0 equ; 0 cnn)
% 0.07/0.31 % Maximal formula atoms : 0 ( 0 avg)
% 0.07/0.31 % Number of connectives : 9 ( 0 ~; 0 |; 0 &; 6 @)
% 0.07/0.31 % ( 2 <=>; 1 =>; 0 <=; 0 <~>)
% 0.07/0.31 % Maximal formula depth : 7 ( 7 avg)
% 0.07/0.31 % Number of types : 2 ( 0 usr)
% 0.07/0.31 % Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% 0.07/0.31 % Number of symbols : 2 ( 2 usr; 0 con; 1-1 aty)
% 0.07/0.31 % Number of variables : 3 ( 0 ^; 3 !; 0 ?; 3 :)
% 0.07/0.31 % SPC : TH0_THM_NEQ_NAR
% 0.07/0.31
% 0.07/0.31 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.07/0.31 % project in the Department of Mathematical Sciences at Carnegie
% 0.07/0.31 % Mellon University. Distributed under the Creative Commons copyleft
% 0.07/0.31 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.07/0.31 %------------------------------------------------------------------------------
% 0.07/0.31 thf(cN,type,
% 0.07/0.31 cN: $i > $i ).
% 0.07/0.31
% 0.07/0.31 thf(cM,type,
% 0.07/0.31 cM: $i > $i ).
% 0.07/0.31
% 0.07/0.31 thf(cEXT_A_LEIB2,conjecture,
% 0.07/0.31 ( ! [Xx: $i,Xp: $i > $o] :
% 0.07/0.31 ( ( Xp @ ( cM @ Xx ) )
% 0.07/0.31 <=> ( Xp @ ( cN @ Xx ) ) )
% 0.07/0.31 => ! [Xq: ( $i > $i ) > $o] :
% 0.07/0.31 ( ( Xq @ cM )
% 0.07/0.31 <=> ( Xq @ cN ) ) ) ).
% 0.07/0.31
% 0.07/0.31 %------------------------------------------------------------------------------
% 0.07/0.31 ------------------------
% 0.83/0.86 ---- Embedded in THF ---
% 0.83/0.86 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 0.83/0.86 %%% Generated on Tue Feb 24 09:28:56 EST 2026
% 0.83/0.86 %%% using '$$dhol' embedding, version 1.3.0.
% 0.83/0.86 %%% Logic specification used:
% 0.83/0.86 %%% thf(spec, logic, $$dhol).
% 0.83/0.86
% 0.83/0.86 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.VR7BTtFTDX/DTF2DTF15722.p
% See solution above
% 0.83/0.86 ------------------------
% 0.83/0.87 ---- Cleaned THF ---
% 0.83/0.87 thf(cN,type,
% 0.83/0.87 cN: $i > $i ).
% 0.83/0.87
% 0.83/0.87 thf(cM,type,
% 0.83/0.87 cM: $i > $i ).
% 0.83/0.87
% 0.83/0.87 thf(cEXT_A_LEIB2,conjecture,
% 0.83/0.87 ( ! [Xx: $i,Xp: $i > $o] :
% 0.83/0.87 ( ( Xp @ ( cM @ Xx ) )
% 0.83/0.87 <=> ( Xp @ ( cN @ Xx ) ) )
% 0.83/0.87 => ! [Xq: ( $i > $i ) > $o] :
% 0.83/0.87 ( ( Xq @ cM )
% 0.83/0.87 <=> ( Xq @ cN ) ) ) ).
% 0.83/0.87 ------------------------
% 0.83/0.88 % (15926)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_15722 for (3000ds/4Mi)
% 0.83/0.88 % (15925)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_15722 for (3000ds/183Mi)
% 0.83/0.88 % (15927)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_15722 for (3000ds/27Mi)
% 0.83/0.88 % (15928)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_15722 for (3000ds/2Mi)
% 0.83/0.88 % (15929)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_15722 for (3000ds/2Mi)
% 0.83/0.88 % (15930)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_15722 for (3000ds/275Mi)
% 0.83/0.88 % (15931)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_15722 for (3000ds/18Mi)
% 0.83/0.88 % (15928)Instruction limit reached!
% 0.83/0.88 % (15928)------------------------------
% 0.83/0.88 % (15928)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.83/0.88 % (15928)Termination reason: Unknown
% 0.83/0.88 % (15928)Termination phase: Saturation
% 0.83/0.88
% 0.83/0.88 % (15928)Memory used [KB]: 5500
% 0.83/0.88 % (15928)Time elapsed: 0.002 s
% 0.83/0.88 % (15928)Instructions burned: 2 (million)
% 0.83/0.88 % (15928)------------------------------
% 0.83/0.88 % (15928)------------------------------
% 0.83/0.88 % (15929)Instruction limit reached!
% 0.83/0.88 % (15929)------------------------------
% 0.83/0.88 % (15929)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.83/0.88 % (15929)Termination reason: Unknown
% 0.83/0.88 % (15929)Termination phase: Saturation
% 0.83/0.88
% 0.83/0.88 % (15929)Memory used [KB]: 5500
% 0.83/0.88 % (15929)Time elapsed: 0.002 s
% 0.83/0.88 % (15929)Instructions burned: 3 (million)
% 0.83/0.88 % (15929)------------------------------
% 0.83/0.88 % (15929)------------------------------
% 0.83/0.88 % (15927)Refutation not found, incomplete strategy
% 0.83/0.88 % (15927)------------------------------
% 0.83/0.88 % (15927)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.83/0.88 % (15927)Termination reason: Refutation not found, incomplete strategy
% 0.83/0.88
% 0.83/0.88
% 0.83/0.88 % (15927)Memory used [KB]: 5500
% 0.83/0.88 % (15927)Time elapsed: 0.002 s
% 0.83/0.88 % (15927)Instructions burned: 2 (million)
% 0.83/0.88 % (15927)------------------------------
% 0.83/0.88 % (15927)------------------------------
% 0.83/0.88 % (15930)Refutation not found, incomplete strategy
% 0.83/0.88 % (15930)------------------------------
% 0.83/0.88 % (15930)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.83/0.88 % (15930)Termination reason: Refutation not found, incomplete strategy
% 0.83/0.88
% 0.83/0.88
% 0.83/0.88 % (15930)Memory used [KB]: 5500
% 0.83/0.88 % (15930)Time elapsed: 0.002 s
% 0.83/0.88 % (15930)Instructions burned: 2 (million)
% 0.83/0.88 % (15930)------------------------------
% 0.83/0.88 % (15930)------------------------------
% 0.83/0.88 % (15926)Instruction limit reached!
% 0.83/0.88 % (15926)------------------------------
% 0.83/0.88 % (15926)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.83/0.88 % (15926)Termination reason: Unknown
% 0.83/0.88 % (15926)Termination phase: Saturation
% 0.83/0.88
% 0.83/0.88 % (15926)Memory used [KB]: 5500
% 0.83/0.88 % (15926)Time elapsed: 0.003 s
% 0.83/0.88 % (15926)Instructions burned: 5 (million)
% 0.83/0.88 % (15926)------------------------------
% 0.83/0.88 % (15926)------------------------------
% 0.83/0.88 % (15931)First to succeed.
% 0.83/0.88 % (15925)Also succeeded, but the first one will report.
% 0.83/0.88 % (15931)Refutation found. Thanks to Tanya!
% 0.83/0.88 % SZS status Theorem for DTF2THF_15722
% 0.83/0.88 % SZS output start Proof for DTF2THF_15722
% 0.83/0.88 thf(func_def_0, type, cN: $i > $i).
% 0.83/0.88 thf(func_def_1, type, cM: $i > $i).
% 0.83/0.88 thf(func_def_5, type, sK0: ($i > $i) > $o).
% 0.83/0.88 thf(func_def_8, type, ph2: !>[X0: $tType]:(X0)).
% 0.83/0.88 thf(f91,plain,(
% 0.83/0.88 $false),
% 0.83/0.88 inference(avatar_sat_refutation,[status(thm)],[f23,f32,f73,f76,f90])).
% 0.83/0.88 thf(f90,plain,(
% 0.83/0.88 spl1_3 | ~spl1_4),
% 0.83/0.88 inference(avatar_contradiction_clause,[status(thm)],[f89])).
% 0.83/0.88 thf(f89,plain,(
% 0.83/0.88 $false | (spl1_3 | ~spl1_4)),
% 0.83/0.88 inference(subsumption_resolution,[status(thm)],[f88,f38])).
% 0.83/0.88 thf(f38,plain,(
% 0.83/0.88 ( ! [X0 : $i] : (((cM @ X0) = (cN @ X0))) )),
% 0.83/0.88 inference(leibniz_equality_elimination,[status(thm)],[f11])).
% 0.83/0.88 thf(f11,plain,(
% 0.83/0.88 ( ! [X0 : $i,X1 : $i > $o] : (((X1 @ (cM @ X0)) = $true) | ((X1 @ (cN @ X0)) = $false)) )),
% 0.83/0.88 inference(binary_proxy_clausification,[status(thm)],[f10])).
% 0.83/0.88 thf(f10,plain,(
% 0.83/0.88 ( ! [X0 : $i,X1 : $i > $o] : (((X1 @ (cM @ X0)) = (X1 @ (cN @ X0)))) )),
% 0.83/0.88 inference(cnf_transformation,[status(thm)],[f8])).
% 0.83/0.88 thf(f8,plain,(
% 0.83/0.88 ! [X0 : $i,X1 : $i > $o] : ((X1 @ (cM @ X0)) = (X1 @ (cN @ X0))) & ((sK0 @ cN) != (sK0 @ cM))),
% 0.83/0.88 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f6,f7])).
% 0.83/0.88 thf(f7,plain,(
% 0.83/0.88 ? [X2 : ($i > $i) > $o] : ((X2 @ cM) != (X2 @ cN)) => ((sK0 @ cN) != (sK0 @ cM))),
% 0.83/0.88 introduced(definition,[],[choice_axiom])).
% 0.83/0.88 thf(f6,plain,(
% 0.83/0.88 ! [X0 : $i,X1 : $i > $o] : ((X1 @ (cM @ X0)) = (X1 @ (cN @ X0))) & ? [X2 : ($i > $i) > $o] : ((X2 @ cM) != (X2 @ cN))),
% 0.83/0.88 inference(ennf_transformation,[status(thm)],[f5])).
% 0.83/0.88 thf(f5,plain,(
% 0.83/0.88 ~(! [X0 : $i,X1 : $i > $o] : ((X1 @ (cM @ X0)) = (X1 @ (cN @ X0))) => ! [X2 : ($i > $i) > $o] : ((X2 @ cM) = (X2 @ cN)))),
% 0.83/0.88 inference(fool_elimination,[status(thm)],[f4])).
% 0.83/0.88 thf(f4,plain,(
% 0.83/0.88 ~(! [X0 : $i,X1 : $i > $o] : ((X1 @ (cN @ X0)) <=> (X1 @ (cM @ X0))) => ! [X2 : ($i > $i) > $o] : ((X2 @ cM) <=> (X2 @ cN)))),
% 0.83/0.88 inference(rectify,[status(thm)],[f2])).
% 0.83/0.88 thf(f2,negated_conjecture,(
% 0.83/0.88 ~(! [X0 : $i,X1 : $i > $o] : ((X1 @ (cN @ X0)) <=> (X1 @ (cM @ X0))) => ! [X2 : ($i > $i) > $o] : ((X2 @ cM) <=> (X2 @ cN)))),
% 0.83/0.88 inference(negated_conjecture,[status(cth)],[f1])).
% 0.83/0.88 thf(f1,conjecture,(
% 0.83/0.88 ! [X0 : $i,X1 : $i > $o] : ((X1 @ (cN @ X0)) <=> (X1 @ (cM @ X0))) => ! [X2 : ($i > $i) > $o] : ((X2 @ cM) <=> (X2 @ cN))),
% 0.83/0.88 file('/export/starexec/sandbox2/tmp/tmp.VR7BTtFTDX/DTF2THF_15722.p',cEXT_A_LEIB2)).
% 0.83/0.88 thf(f88,plain,(
% 0.83/0.88 ((cN @ sK4) != (cM @ sK4)) | (spl1_3 | ~spl1_4)),
% 0.83/0.88 inference(negative_extensionality,[status(thm)],[f87])).
% 0.83/0.88 thf(f87,plain,(
% 0.83/0.88 (cM != cN) | (spl1_3 | ~spl1_4)),
% 0.83/0.88 inference(trivial_inequality_removal,[status(thm)],[f83])).
% 0.83/0.88 thf(f83,plain,(
% 0.83/0.88 ($false != $false) | (cM != cN) | (spl1_3 | ~spl1_4)),
% 0.83/0.88 inference(constrained_superposition,[status(thm)],[f26,f31])).
% 0.83/0.88 thf(f31,plain,(
% 0.83/0.88 ((sK0 @ cN) = $false) | ~spl1_4),
% 0.83/0.88 inference(avatar_component_clause,[status(thm)],[f29])).
% 0.83/0.88 thf(f29,definition,(
% 0.83/0.88 spl1_4 <=> ((sK0 @ cN) = $false)),
% 0.83/0.88 introduced(definition,[new_symbols(naming,[spl1_4])],[avatar_definition])).
% 0.83/0.88 thf(f26,plain,(
% 0.83/0.88 ((sK0 @ cM) != $false) | spl1_3),
% 0.83/0.88 inference(avatar_component_clause,[status(thm)],[f25])).
% 0.83/0.88 thf(f25,definition,(
% 0.83/0.88 spl1_3 <=> ((sK0 @ cM) = $false)),
% 0.83/0.88 introduced(definition,[new_symbols(naming,[spl1_3])],[avatar_definition])).
% 0.83/0.88 thf(f76,plain,(
% 0.83/0.88 ~spl1_1 | ~spl1_3),
% 0.83/0.88 inference(avatar_contradiction_clause,[status(thm)],[f75])).
% 0.83/0.88 thf(f75,plain,(
% 0.83/0.88 $false | (~spl1_1 | ~spl1_3)),
% 0.83/0.88 inference(trivial_inequality_removal,[status(thm)],[f74])).
% 0.83/0.88 thf(f74,plain,(
% 0.83/0.88 ($true = $false) | (~spl1_1 | ~spl1_3)),
% 0.83/0.88 inference(forward_demodulation,[status(thm)],[f18,f27])).
% 0.83/0.88 thf(f27,plain,(
% 0.83/0.88 ((sK0 @ cM) = $false) | ~spl1_3),
% 0.83/0.88 inference(avatar_component_clause,[status(thm)],[f25])).
% 0.83/0.88 thf(f18,plain,(
% 0.83/0.88 ((sK0 @ cM) = $true) | ~spl1_1),
% 0.83/0.88 inference(avatar_component_clause,[status(thm)],[f16])).
% 0.83/0.88 thf(f16,definition,(
% 0.83/0.88 spl1_1 <=> ((sK0 @ cM) = $true)),
% 0.83/0.88 introduced(definition,[new_symbols(naming,[spl1_1])],[avatar_definition])).
% 0.83/0.88 thf(f73,plain,(
% 0.83/0.88 ~spl1_2 | ~spl1_3),
% 0.83/0.88 inference(avatar_contradiction_clause,[status(thm)],[f72])).
% 0.83/0.88 thf(f72,plain,(
% 0.83/0.88 $false | (~spl1_2 | ~spl1_3)),
% 0.83/0.88 inference(trivial_inequality_removal,[status(thm)],[f71])).
% 0.83/0.88 thf(f71,plain,(
% 0.83/0.88 ((cN @ sK3) != (cN @ sK3)) | (~spl1_2 | ~spl1_3)),
% 0.83/0.88 inference(superposition,[status(thm)],[f37,f38])).
% 0.83/0.88 thf(f37,plain,(
% 0.83/0.88 ((cN @ sK3) != (cM @ sK3)) | (~spl1_2 | ~spl1_3)),
% 0.83/0.88 inference(negative_extensionality,[status(thm)],[f36])).
% 0.83/0.88 thf(f36,plain,(
% 0.83/0.88 (cM != cN) | (~spl1_2 | ~spl1_3)),
% 0.83/0.88 inference(trivial_inequality_removal,[status(thm)],[f34])).
% 0.83/0.88 thf(f34,plain,(
% 0.83/0.88 (cM != cN) | ($true = $false) | (~spl1_2 | ~spl1_3)),
% 0.83/0.88 inference(constrained_superposition,[status(thm)],[f22,f27])).
% 0.83/0.88 thf(f22,plain,(
% 0.83/0.88 ((sK0 @ cN) = $true) | ~spl1_2),
% 0.83/0.88 inference(avatar_component_clause,[status(thm)],[f20])).
% 0.83/0.88 thf(f20,definition,(
% 0.83/0.88 spl1_2 <=> ((sK0 @ cN) = $true)),
% 0.83/0.88 introduced(definition,[new_symbols(naming,[spl1_2])],[avatar_definition])).
% 0.83/0.88 thf(f32,plain,(
% 0.83/0.88 spl1_3 | spl1_4),
% 0.83/0.88 inference(avatar_split_clause,[status(thm)],[f14,f29,f25])).
% 0.83/0.88 thf(f14,plain,(
% 0.83/0.88 ((sK0 @ cM) = $false) | ((sK0 @ cN) = $false)),
% 0.83/0.88 inference(binary_proxy_clausification,[status(thm)],[f9])).
% 0.83/0.88 thf(f9,plain,(
% 0.83/0.88 ((sK0 @ cN) != (sK0 @ cM))),
% 0.83/0.88 inference(cnf_transformation,[status(thm)],[f8])).
% 0.83/0.88 thf(f23,plain,(
% 0.83/0.88 spl1_1 | spl1_2),
% 0.83/0.88 inference(avatar_split_clause,[status(thm)],[f13,f20,f16])).
% 0.83/0.88 thf(f13,plain,(
% 0.83/0.88 ((sK0 @ cM) = $true) | ((sK0 @ cN) = $true)),
% 0.83/0.88 inference(binary_proxy_clausification,[status(thm)],[f9])).
% 0.83/0.88 % SZS output end Proof for DTF2THF_15722
% 0.83/0.88 % (15931)------------------------------
% 0.83/0.88 % (15931)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.83/0.88 % (15931)Termination reason: Refutation
% 0.83/0.88
% 0.83/0.88 % (15931)Memory used [KB]: 5500
% 0.83/0.88 % (15931)Time elapsed: 0.004 s
% 0.83/0.88 % (15931)Instructions burned: 5 (million)
% 0.83/0.88 % (15931)------------------------------
% 0.83/0.88 % (15931)------------------------------
% 0.83/0.88 % (15924)Success in time 0.011 s
%------------------------------------------------------------------------------