%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO506^1 : TPTP v9.2.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n023.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 09:54:25 AM UTC 2026
% Result : Theorem 1.46s 1.26s
% Output : Refutation 1.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of formulae : 29 ( 7 unt; 0 typ; 3 def)
% Number of atoms : 135 ( 53 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 150 ( 42 ~; 25 |; 4 &; 75 @)
% ( 3 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 7 con; 0-3 aty)
% Number of variables : 50 ( 0 ^; 46 !; 4 ?; 50 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
c: $o > $i > $i > $i ).
thf(func_def_8,type,
ph3:
!>[X0: $tType] : X0 ).
thf(f42,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f33,f37,f39,f41]) ).
thf(f41,plain,
~ spl2_1,
inference(avatar_contradiction_clause,[status(thm)],[f40]) ).
thf(f40,plain,
( $false
| ~ spl2_1 ),
inference(equality_resolution,[status(thm)],[f21]) ).
thf(f21,plain,
( ! [X1: $i] : ( sK0 != X1 )
| ~ spl2_1 ),
inference(avatar_component_clause,[status(thm)],[f20]) ).
thf(f20,definition,
( spl2_1
<=> ! [X1: $i] : ( sK0 != X1 ) ),
introduced(definition,[new_symbols(naming,[spl2_1])],[avatar_definition]) ).
thf(f39,plain,
~ spl2_4,
inference(avatar_contradiction_clause,[status(thm)],[f38]) ).
thf(f38,plain,
( $false
| ~ spl2_4 ),
inference(equality_resolution,[status(thm)],[f32]) ).
thf(f32,plain,
( ! [X0: $i] : ( sK1 != X0 )
| ~ spl2_4 ),
inference(avatar_component_clause,[status(thm)],[f31]) ).
thf(f31,definition,
( spl2_4
<=> ! [X0: $i] : ( sK1 != X0 ) ),
introduced(definition,[new_symbols(naming,[spl2_4])],[avatar_definition]) ).
thf(f37,plain,
~ spl2_3,
inference(avatar_contradiction_clause,[status(thm)],[f36]) ).
thf(f36,plain,
( $false
| ~ spl2_3 ),
inference(subsumption_resolution,[status(thm)],[f35,f10]) ).
thf(f10,plain,
! [X2: $i,X3: $i] :
( ( c @ $true @ X3 @ X2 )
= X3 ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
( ! [X0: $i,X1: $i] :
( ( c @ $false @ X0 @ X1 )
= X1 )
& ! [X2: $i,X3: $i] :
( ( c @ $true @ X3 @ X2 )
= X3 )
& ( sK0
!= ( c @ ( sK0 = sK1 ) @ sK1 @ sK0 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f6,f7]) ).
thf(f7,plain,
( ? [X4: $i,X5: $i] :
( ( c @ ( X4 = X5 ) @ X5 @ X4 )
!= X4 )
=> ( sK0
!= ( c @ ( sK0 = sK1 ) @ sK1 @ sK0 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f6,plain,
( ! [X0: $i,X1: $i] :
( ( c @ $false @ X0 @ X1 )
= X1 )
& ! [X2: $i,X3: $i] :
( ( c @ $true @ X3 @ X2 )
= X3 )
& ? [X4: $i,X5: $i] :
( ( c @ ( X4 = X5 ) @ X5 @ X4 )
!= X4 ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ~ ! [X2: $i,X3: $i] :
( ( c @ $true @ X3 @ X2 )
= X3 )
| ! [X4: $i,X5: $i] :
( ( c @ ( X4 = X5 ) @ X5 @ X4 )
= X4 )
| ~ ! [X0: $i,X1: $i] :
( ( c @ $false @ X0 @ X1 )
= X1 ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ~ ! [X0: $i,X1: $i] :
( X1
= ( c @ $false @ X0 @ X1 ) )
| ~ ! [X2: $i,X3: $i] :
( X3
= ( c @ $true @ X3 @ X2 ) )
| ! [X4: $i,X5: $i] :
( X4
= ( c @ ( X4 = X5 ) @ X5 @ X4 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ~ ! [X0: $i,X1: $i] :
( X1
= ( c @ $false @ X0 @ X1 ) )
| ~ ! [X1: $i,X0: $i] :
( X0
= ( c @ $true @ X0 @ X1 ) )
| ! [X1: $i,X0: $i] :
( X1
= ( c @ ( X0 = X1 ) @ X0 @ X1 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ~ ! [X0: $i,X1: $i] :
( X1
= ( c @ $false @ X0 @ X1 ) )
| ~ ! [X1: $i,X0: $i] :
( X0
= ( c @ $true @ X0 @ X1 ) )
| ! [X1: $i,X0: $i] :
( X1
= ( c @ ( X0 = X1 ) @ X0 @ X1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.jb79BhwE8k/DTF2THF_30979.p',claim) ).
thf(f35,plain,
( ( sK0
!= ( c @ $true @ sK0 @ sK0 ) )
| ~ spl2_3 ),
inference(boolean_simplification,[status(thm)],[f34]) ).
thf(f34,plain,
( ( sK0
!= ( c @ ( sK0 = sK0 ) @ sK0 @ sK0 ) )
| ~ spl2_3 ),
inference(superposition,[status(thm)],[f9,f27]) ).
thf(f27,plain,
( ( sK0 = sK1 )
| ~ spl2_3 ),
inference(avatar_component_clause,[status(thm)],[f26]) ).
thf(f26,definition,
( spl2_3
<=> ( sK0 = sK1 ) ),
introduced(definition,[new_symbols(naming,[spl2_3])],[avatar_definition]) ).
thf(f9,plain,
( sK0
!= ( c @ ( sK0 = sK1 ) @ sK1 @ sK0 ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f33,plain,
( spl2_3
| spl2_4
| spl2_1 ),
inference(avatar_split_clause,[status(thm)],[f17,f20,f31,f26]) ).
thf(f17,plain,
! [X0: $i,X1: $i] :
( ( sK0 != X1 )
| ( sK1 != X0 )
| ( sK0 = sK1 ) ),
inference(equality_proxy_clausification,[status(thm)],[f16]) ).
thf(f16,plain,
! [X0: $i,X1: $i] :
( ( ( sK0 = sK1 )
!= $false )
| ( sK0 != X1 )
| ( sK1 != X0 ) ),
inference(duplicate_literal_removal,[status(thm)],[f14]) ).
thf(f14,plain,
! [X0: $i,X1: $i] :
( ( sK0 != X1 )
| ( sK0 != X1 )
| ( ( sK0 = sK1 )
!= $false )
| ( sK1 != X0 ) ),
inference(constrained_superposition,[status(thm)],[f9,f11]) ).
thf(f11,plain,
! [X0: $i,X1: $i] :
( ( c @ $false @ X0 @ X1 )
= X1 ),
inference(cnf_transformation,[status(thm)],[f8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SYO506^1 : TPTP v9.2.1. Released v4.1.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n023.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 14:33:34 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.28/0.46 ---- Original DTF file ---
% 0.28/0.46 thf(spec,logic,$$dhol).
% 0.28/0.46 %------------------------------------------------------------------------------
% 0.28/0.46 % File : SYO506^1 : TPTP v9.2.1. Released v4.1.0.
% 0.28/0.46 % Domain : Syntactic
% 0.28/0.46 % Problem : (if (X = Y) then X else Y) = Y
% 0.28/0.46 % Version : Especial.
% 0.28/0.46 % English :
% 0.28/0.46
% 0.28/0.46 % Refs : [Bro09] Brown E. (2009), Email to Geoff Sutcliffe
% 0.28/0.46 % : [BS09] Brown E. & Smolka (2009), Extended First-Order Logic
% 0.28/0.46 % Source : [Bro09]
% 0.28/0.46 % Names : efo1 [Bro09]
% 0.28/0.46
% 0.28/0.46 % Status : Theorem
% 0.28/0.46 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.20 v8.2.0, 0.15 v8.1.0, 0.09 v7.5.0, 0.14 v7.4.0, 0.33 v7.2.0, 0.25 v7.0.0, 0.29 v6.4.0, 0.33 v6.3.0, 0.40 v6.2.0, 0.43 v6.1.0, 0.29 v5.5.0, 0.17 v5.4.0, 0.20 v5.3.0, 0.40 v5.0.0, 0.80 v4.1.0
% 0.28/0.46 % Syntax : Number of formulae : 2 ( 0 unt; 1 typ; 0 def)
% 0.28/0.46 % Number of atoms : 6 ( 4 equ; 0 cnn)
% 0.28/0.46 % Maximal formula atoms : 3 ( 6 avg)
% 0.28/0.46 % Number of connectives : 13 ( 2 ~; 2 |; 0 &; 9 @)
% 0.28/0.46 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.28/0.46 % Maximal formula depth : 6 ( 6 avg)
% 0.28/0.46 % Number of types : 2 ( 0 usr)
% 0.28/0.46 % Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% 0.28/0.46 % Number of symbols : 4 ( 1 usr; 2 con; 0-3 aty)
% 0.28/0.46 % Number of variables : 6 ( 0 ^; 6 !; 0 ?; 6 :)
% 0.28/0.46 % SPC : TH0_THM_EQU_NAR
% 0.28/0.46
% 0.28/0.46 % Comments :
% 0.28/0.46 %------------------------------------------------------------------------------
% 0.28/0.46 thf(c,type,
% 0.28/0.46 c: $o > $i > $i > $i ).
% 0.28/0.46
% 0.28/0.46 thf(claim,conjecture,
% 0.28/0.46 ( ! [X: $i,Y: $i] :
% 0.28/0.46 ( ( c @ ( X = Y ) @ X @ Y )
% 0.28/0.46 = Y )
% 0.28/0.46 | ~ ! [X: $i,Y: $i] :
% 0.28/0.46 ( ( c @ $true @ X @ Y )
% 0.28/0.46 = X )
% 0.28/0.46 | ~ ! [X: $i,Y: $i] :
% 0.28/0.46 ( ( c @ $false @ X @ Y )
% 0.28/0.46 = Y ) ) ).
% 0.28/0.46
% 0.28/0.46 %------------------------------------------------------------------------------
% 0.28/0.46 ------------------------
% 1.46/1.22 ---- Embedded in THF ---
% 1.46/1.22 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.46/1.22 %%% Generated on Tue Feb 24 14:33:35 EST 2026
% 1.46/1.22 %%% using '$$dhol' embedding, version 1.3.0.
% 1.46/1.22 %%% Logic specification used:
% 1.46/1.22 %%% thf(spec, logic, $$dhol).
% 1.46/1.22
% 1.46/1.22 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.jb79BhwE8k/DTF2DTF30979.p
% See solution above
% 1.46/1.22 ------------------------
% 1.46/1.23 ---- Cleaned THF ---
% 1.46/1.23 thf(c,type,
% 1.46/1.23 c: $o > $i > $i > $i ).
% 1.46/1.23
% 1.46/1.23 thf(claim,conjecture,
% 1.46/1.23 ( ! [X: $i,Y: $i] :
% 1.46/1.23 ( ( c @ ( X = Y ) @ X @ Y )
% 1.46/1.23 = Y )
% 1.46/1.23 | ~ ! [X: $i,Y: $i] :
% 1.46/1.23 ( ( c @ $true @ X @ Y )
% 1.46/1.23 = X )
% 1.46/1.23 | ~ ! [X: $i,Y: $i] :
% 1.46/1.23 ( ( c @ $false @ X @ Y )
% 1.46/1.23 = Y ) ) ).
% 1.46/1.23 ------------------------
% 1.46/1.25 % (31286)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_30979 for (2999ds/2Mi)
% 1.46/1.25 % (31286)Instruction limit reached!
% 1.46/1.25 % (31286)------------------------------
% 1.46/1.25 % (31286)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.46/1.25 % (31286)Termination reason: Unknown
% 1.46/1.25 % (31286)Termination phase: Saturation
% 1.46/1.25
% 1.46/1.25 % (31286)Memory used [KB]: 5500
% 1.46/1.25 % (31286)Time elapsed: 0.002 s
% 1.46/1.25 % (31286)Instructions burned: 2 (million)
% 1.46/1.25 % (31286)------------------------------
% 1.46/1.25 % (31286)------------------------------
% 1.46/1.25 % (31282)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_30979 for (2999ds/183Mi)
% 1.46/1.25 % (31283)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_30979 for (2999ds/4Mi)
% 1.46/1.25 % (31284)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_30979 for (2999ds/27Mi)
% 1.46/1.25 % (31285)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_30979 for (2999ds/2Mi)
% 1.46/1.25 % (31287)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_30979 for (2999ds/275Mi)
% 1.46/1.25 % (31288)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_30979 for (2999ds/18Mi)
% 1.46/1.26 % (31284)Refutation not found, incomplete strategy
% 1.46/1.26 % (31284)------------------------------
% 1.46/1.26 % (31284)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.46/1.26 % (31284)Termination reason: Refutation not found, incomplete strategy
% 1.46/1.26
% 1.46/1.26
% 1.46/1.26 % (31284)Memory used [KB]: 5500
% 1.46/1.26 % (31284)Time elapsed: 0.004 s
% 1.46/1.26 % (31284)Instructions burned: 1 (million)
% 1.46/1.26 % (31284)------------------------------
% 1.46/1.26 % (31284)------------------------------
% 1.46/1.26 % (31285)Refutation not found, incomplete strategy
% 1.46/1.26 % (31285)------------------------------
% 1.46/1.26 % (31285)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.46/1.26 % (31285)Termination reason: Refutation not found, incomplete strategy
% 1.46/1.26
% 1.46/1.26
% 1.46/1.26 % (31285)Memory used [KB]: 5500
% 1.46/1.26 % (31285)Time elapsed: 0.004 s
% 1.46/1.26 % (31285)Instructions burned: 1 (million)
% 1.46/1.26 % (31285)------------------------------
% 1.46/1.26 % (31285)------------------------------
% 1.46/1.26 % (31287)Refutation not found, incomplete strategy
% 1.46/1.26 % (31287)------------------------------
% 1.46/1.26 % (31287)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.46/1.26 % (31287)Termination reason: Refutation not found, incomplete strategy
% 1.46/1.26
% 1.46/1.26
% 1.46/1.26 % (31287)Memory used [KB]: 5500
% 1.46/1.26 % (31287)Time elapsed: 0.003 s
% 1.46/1.26 % (31287)Instructions burned: 1 (million)
% 1.46/1.26 % (31287)------------------------------
% 1.46/1.26 % (31287)------------------------------
% 1.46/1.26 % (31283)Refutation not found, incomplete strategy
% 1.46/1.26 % (31283)------------------------------
% 1.46/1.26 % (31283)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.46/1.26 % (31283)Termination reason: Refutation not found, incomplete strategy
% 1.46/1.26
% 1.46/1.26
% 1.46/1.26 % (31283)Memory used [KB]: 5500
% 1.46/1.26 % (31283)Time elapsed: 0.004 s
% 1.46/1.26 % (31283)Instructions burned: 2 (million)
% 1.46/1.26 % (31283)------------------------------
% 1.46/1.26 % (31283)------------------------------
% 1.46/1.26 % (31282)First to succeed.
% 1.46/1.26 % (31289)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_30979 for (2999ds/3Mi)
% 1.46/1.26 % (31288)Also succeeded, but the first one will report.
% 1.46/1.26 % (31289)Refutation not found, incomplete strategy
% 1.46/1.26 % (31289)------------------------------
% 1.46/1.26 % (31289)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.46/1.26 % (31289)Termination reason: Refutation not found, incomplete strategy
% 1.46/1.26
% 1.46/1.26
% 1.46/1.26 % (31289)Memory used [KB]: 5500
% 1.46/1.26 % (31289)Time elapsed: 0.002 s
% 1.46/1.26 % (31289)Instructions burned: 2 (million)
% 1.46/1.26 % (31289)------------------------------
% 1.46/1.26 % (31289)------------------------------
% 1.46/1.26 % (31282)Refutation found. Thanks to Tanya!
% 1.46/1.26 % SZS status Theorem for DTF2THF_30979
% 1.46/1.26 % SZS output start Proof for DTF2THF_30979
% 1.46/1.26 thf(func_def_0, type, c: $o > $i > $i > $i).
% 1.46/1.26 thf(func_def_8, type, ph3: !>[X0: $tType]:(X0)).
% 1.46/1.26 thf(f42,plain,(
% 1.46/1.26 $false),
% 1.46/1.26 inference(avatar_sat_refutation,[status(thm)],[f33,f37,f39,f41])).
% 1.46/1.26 thf(f41,plain,(
% 1.46/1.26 ~spl2_1),
% 1.46/1.26 inference(avatar_contradiction_clause,[status(thm)],[f40])).
% 1.46/1.26 thf(f40,plain,(
% 1.46/1.26 $false | ~spl2_1),
% 1.46/1.26 inference(equality_resolution,[status(thm)],[f21])).
% 1.46/1.26 thf(f21,plain,(
% 1.46/1.26 ( ! [X1 : $i] : ((sK0 != X1)) ) | ~spl2_1),
% 1.46/1.26 inference(avatar_component_clause,[status(thm)],[f20])).
% 1.46/1.26 thf(f20,definition,(
% 1.46/1.26 spl2_1 <=> ! [X1 : $i] : (sK0 != X1)),
% 1.46/1.26 introduced(definition,[new_symbols(naming,[spl2_1])],[avatar_definition])).
% 1.46/1.26 thf(f39,plain,(
% 1.46/1.26 ~spl2_4),
% 1.46/1.26 inference(avatar_contradiction_clause,[status(thm)],[f38])).
% 1.46/1.26 thf(f38,plain,(
% 1.46/1.26 $false | ~spl2_4),
% 1.46/1.26 inference(equality_resolution,[status(thm)],[f32])).
% 1.46/1.26 thf(f32,plain,(
% 1.46/1.26 ( ! [X0 : $i] : ((sK1 != X0)) ) | ~spl2_4),
% 1.46/1.26 inference(avatar_component_clause,[status(thm)],[f31])).
% 1.46/1.26 thf(f31,definition,(
% 1.46/1.26 spl2_4 <=> ! [X0 : $i] : (sK1 != X0)),
% 1.46/1.26 introduced(definition,[new_symbols(naming,[spl2_4])],[avatar_definition])).
% 1.46/1.26 thf(f37,plain,(
% 1.46/1.26 ~spl2_3),
% 1.46/1.26 inference(avatar_contradiction_clause,[status(thm)],[f36])).
% 1.46/1.26 thf(f36,plain,(
% 1.46/1.26 $false | ~spl2_3),
% 1.46/1.26 inference(subsumption_resolution,[status(thm)],[f35,f10])).
% 1.46/1.26 thf(f10,plain,(
% 1.46/1.26 ( ! [X2 : $i,X3 : $i] : (((c @ $true @ X3 @ X2) = X3)) )),
% 1.46/1.26 inference(cnf_transformation,[status(thm)],[f8])).
% 1.46/1.26 thf(f8,plain,(
% 1.46/1.26 ! [X0 : $i,X1 : $i] : ((c @ $false @ X0 @ X1) = X1) & ! [X2 : $i,X3 : $i] : ((c @ $true @ X3 @ X2) = X3) & (sK0 != (c @ (sK0 = sK1) @ sK1 @ sK0))),
% 1.46/1.26 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f6,f7])).
% 1.46/1.26 thf(f7,plain,(
% 1.46/1.26 ? [X4 : $i,X5 : $i] : ((c @ (X4 = X5) @ X5 @ X4) != X4) => (sK0 != (c @ (sK0 = sK1) @ sK1 @ sK0))),
% 1.46/1.26 introduced(definition,[],[choice_axiom])).
% 1.46/1.26 thf(f6,plain,(
% 1.46/1.26 ! [X0 : $i,X1 : $i] : ((c @ $false @ X0 @ X1) = X1) & ! [X2 : $i,X3 : $i] : ((c @ $true @ X3 @ X2) = X3) & ? [X4 : $i,X5 : $i] : ((c @ (X4 = X5) @ X5 @ X4) != X4)),
% 1.46/1.26 inference(ennf_transformation,[status(thm)],[f5])).
% 1.46/1.26 thf(f5,plain,(
% 1.46/1.26 ~(~! [X2 : $i,X3 : $i] : ((c @ $true @ X3 @ X2) = X3) | ! [X4 : $i,X5 : $i] : ((c @ (X4 = X5) @ X5 @ X4) = X4) | ~! [X0 : $i,X1 : $i] : ((c @ $false @ X0 @ X1) = X1))),
% 1.46/1.26 inference(fool_elimination,[status(thm)],[f4])).
% 1.46/1.26 thf(f4,plain,(
% 1.46/1.26 ~(~! [X0 : $i,X1 : $i] : (X1 = (c @ $false @ X0 @ X1)) | ~! [X2 : $i,X3 : $i] : (X3 = (c @ $true @ X3 @ X2)) | ! [X4 : $i,X5 : $i] : (X4 = (c @ (X4 = X5) @ X5 @ X4)))),
% 1.46/1.26 inference(rectify,[status(thm)],[f2])).
% 1.46/1.26 thf(f2,negated_conjecture,(
% 1.46/1.26 ~(~! [X0 : $i,X1 : $i] : (X1 = (c @ $false @ X0 @ X1)) | ~! [X1 : $i,X0 : $i] : (X0 = (c @ $true @ X0 @ X1)) | ! [X1 : $i,X0 : $i] : (X1 = (c @ (X0 = X1) @ X0 @ X1)))),
% 1.46/1.26 inference(negated_conjecture,[status(cth)],[f1])).
% 1.46/1.26 thf(f1,conjecture,(
% 1.46/1.26 ~! [X0 : $i,X1 : $i] : (X1 = (c @ $false @ X0 @ X1)) | ~! [X1 : $i,X0 : $i] : (X0 = (c @ $true @ X0 @ X1)) | ! [X1 : $i,X0 : $i] : (X1 = (c @ (X0 = X1) @ X0 @ X1))),
% 1.46/1.26 file('/export/starexec/sandbox/tmp/tmp.jb79BhwE8k/DTF2THF_30979.p',claim)).
% 1.46/1.26 thf(f35,plain,(
% 1.46/1.26 (sK0 != (c @ $true @ sK0 @ sK0)) | ~spl2_3),
% 1.46/1.26 inference(boolean_simplification,[status(thm)],[f34])).
% 1.46/1.26 thf(f34,plain,(
% 1.46/1.26 (sK0 != (c @ (sK0 = sK0) @ sK0 @ sK0)) | ~spl2_3),
% 1.46/1.26 inference(superposition,[status(thm)],[f9,f27])).
% 1.46/1.26 thf(f27,plain,(
% 1.46/1.26 (sK0 = sK1) | ~spl2_3),
% 1.46/1.26 inference(avatar_component_clause,[status(thm)],[f26])).
% 1.46/1.26 thf(f26,definition,(
% 1.46/1.26 spl2_3 <=> (sK0 = sK1)),
% 1.46/1.26 introduced(definition,[new_symbols(naming,[spl2_3])],[avatar_definition])).
% 1.46/1.26 thf(f9,plain,(
% 1.46/1.26 (sK0 != (c @ (sK0 = sK1) @ sK1 @ sK0))),
% 1.46/1.26 inference(cnf_transformation,[status(thm)],[f8])).
% 1.46/1.26 thf(f33,plain,(
% 1.46/1.26 spl2_3 | spl2_4 | spl2_1),
% 1.46/1.26 inference(avatar_split_clause,[status(thm)],[f17,f20,f31,f26])).
% 1.46/1.26 thf(f17,plain,(
% 1.46/1.26 ( ! [X0 : $i,X1 : $i] : ((sK0 != X1) | (sK1 != X0) | (sK0 = sK1)) )),
% 1.46/1.26 inference(equality_proxy_clausification,[status(thm)],[f16])).
% 1.46/1.26 thf(f16,plain,(
% 1.46/1.26 ( ! [X0 : $i,X1 : $i] : (((sK0 = sK1) != $false) | (sK0 != X1) | (sK1 != X0)) )),
% 1.46/1.26 inference(duplicate_literal_removal,[status(thm)],[f14])).
% 1.46/1.26 thf(f14,plain,(
% 1.46/1.26 ( ! [X0 : $i,X1 : $i] : ((sK0 != X1) | (sK0 != X1) | ((sK0 = sK1) != $false) | (sK1 != X0)) )),
% 1.46/1.26 inference(constrained_superposition,[status(thm)],[f9,f11])).
% 1.46/1.26 thf(f11,plain,(
% 1.46/1.26 ( ! [X0 : $i,X1 : $i] : (((c @ $false @ X0 @ X1) = X1)) )),
% 1.46/1.26 inference(cnf_transformation,[status(thm)],[f8])).
% 1.46/1.26 % SZS output end Proof for DTF2THF_30979
% 1.46/1.26 % (31282)------------------------------
% 1.46/1.26 % (31282)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.46/1.26 % (31282)Termination reason: Refutation
% 1.46/1.26
% 1.46/1.26 % (31282)Memory used [KB]: 5500
% 1.46/1.26 % (31282)Time elapsed: 0.005 s
% 1.46/1.26 % (31282)Instructions burned: 2 (million)
% 1.46/1.26 % (31282)------------------------------
% 1.46/1.26 % (31282)------------------------------
% 1.46/1.26 % (31281)Success in time 0.021 s
%------------------------------------------------------------------------------