%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV434^1 : TPTP v9.2.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n028.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 09:41:14 AM UTC 2026
% Result : Theorem 0.31s 1.39s
% Output : Refutation 0.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 6
% Syntax : Number of formulae : 51 ( 9 unt; 0 typ; 2 def)
% Number of atoms : 244 ( 122 equ; 0 cnn)
% Maximal formula atoms : 7 ( 4 avg)
% Number of connectives : 198 ( 54 ~; 84 |; 10 &; 46 @)
% ( 2 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 7 con; 0-2 aty)
% Number of variables : 87 ( 0 ^; 76 !; 11 ?; 87 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
f: $o > $i ).
thf(func_def_4,type,
sK0: $i > $o ).
thf(func_def_9,type,
ph5:
!>[X0: $tType] : X0 ).
thf(f337,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f46,f83,f335]) ).
thf(f335,plain,
~ spl4_1,
inference(avatar_contradiction_clause,[status(thm)],[f334]) ).
thf(f334,plain,
( $false
| ~ spl4_1 ),
inference(equality_resolution,[status(thm)],[f318]) ).
thf(f318,plain,
( ! [X0: $i] : ( sK1 != X0 )
| ~ spl4_1 ),
inference(duplicate_literal_removal,[status(thm)],[f309]) ).
thf(f309,plain,
( ! [X0: $i] :
( ( sK1 != X0 )
| ( sK1 != X0 ) )
| ~ spl4_1 ),
inference(superposition,[status(thm)],[f14,f275]) ).
thf(f275,plain,
( ! [X0: $i] :
( ( sK3 = X0 )
| ( sK1 != X0 ) )
| ~ spl4_1 ),
inference(trivial_inequality_removal,[status(thm)],[f262]) ).
thf(f262,plain,
( ! [X0: $i] :
( ( sK3 = X0 )
| ( sK1 != X0 )
| ( sK2 != sK2 ) )
| ~ spl4_1 ),
inference(superposition,[status(thm)],[f15,f232]) ).
thf(f232,plain,
( ! [X0: $i,X1: $i] :
( ( sK2 = X1 )
| ( X0 = X1 )
| ( sK1 != X0 ) )
| ~ spl4_1 ),
inference(superposition,[status(thm)],[f13,f231]) ).
thf(f231,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 ) )
| ~ spl4_1 ),
inference(subsumption_resolution,[status(thm)],[f220,f230]) ).
thf(f230,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( X2 = X3 )
| ( X0 = X1 )
| ( X1 = X3 )
| ( X1 = X2 ) )
| ~ spl4_1 ),
inference(subsumption_resolution,[status(thm)],[f204,f196]) ).
thf(f196,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( X3 = X4 )
| ( X0 = X2 )
| ( X0 = X1 )
| ( X0 = X4 )
| ( X1 = X2 )
| ( ( sK0 @ X3 )
= $false ) ),
inference(trivial_inequality_removal,[status(thm)],[f189]) ).
thf(f189,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( $true != $true )
| ( X0 = X1 )
| ( X3 = X4 )
| ( X1 = X2 )
| ( X0 = X2 )
| ( ( sK0 @ X3 )
= $false )
| ( X0 = X4 ) ),
inference(superposition,[status(thm)],[f174,f26]) ).
thf(f26,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( sK0 @ X1 ) )
| ( ( sK0 @ X2 )
= $false )
| ( X0 = X1 )
| ( X0 = X2 ) ),
inference(trivial_inequality_removal,[status(thm)],[f22]) ).
thf(f22,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( sK0 @ X2 )
= $false )
| ( X0 = X1 )
| ( $true = $false )
| ( $true
= ( sK0 @ X1 ) )
| ( X0 = X2 ) ),
inference(superposition,[status(thm)],[f17,f18]) ).
thf(f18,plain,
! [X0: $i,X1: $i] :
( ( ( sK0 @ X1 )
= $false )
| ( ( sK0 @ X0 )
= $false )
| ( X0 = X1 ) ),
inference(binary_proxy_clausification,[status(thm)],[f16]) ).
thf(f16,plain,
! [X0: $i,X1: $i] :
( ( ( sK0 @ X1 )
!= ( sK0 @ X0 ) )
| ( X0 = X1 ) ),
inference(constrained_superposition,[status(thm)],[f12,f12]) ).
thf(f12,plain,
! [X0: $i] :
( ( f @ ( sK0 @ X0 ) )
= X0 ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
! [X0: $i] :
( ( f @ ( sK0 @ X0 ) )
= X0 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f1,f7]) ).
thf(f7,plain,
! [X0: $i] :
( ? [X1: $o] :
( ( f @ X1 )
= X0 )
=> ( ( f @ ( sK0 @ X0 ) )
= X0 ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1,axiom,
! [X0: $i] :
? [X1: $o] :
( ( f @ X1 )
= X0 ),
file('/export/starexec/sandbox2/tmp/tmp.DoU9jji1Ik/DTF2THF_7414.p',fsurj) ).
thf(f17,plain,
! [X0: $i,X1: $i] :
( ( $true
= ( sK0 @ X1 ) )
| ( $true
= ( sK0 @ X0 ) )
| ( X0 = X1 ) ),
inference(binary_proxy_clausification,[status(thm)],[f16]) ).
thf(f174,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( sK0 @ X0 ) )
| ( X1 = X2 )
| ( X0 = X1 )
| ( X0 = X2 ) ),
inference(constrained_superposition,[status(thm)],[f29,f12]) ).
thf(f29,plain,
! [X0: $i,X1: $i] :
( ( ( f @ $true )
= X1 )
| ( ( f @ $true )
= X0 )
| ( X0 = X1 ) ),
inference(superposition,[status(thm)],[f12,f19]) ).
thf(f19,plain,
! [X0: $i,X1: $i] :
( ( $true
= ( sK0 @ X1 ) )
| ( X0 = X1 )
| ( ( f @ $true )
= X0 ) ),
inference(superposition,[status(thm)],[f12,f17]) ).
thf(f204,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( X0 = X1 )
| ( ( sK0 @ X0 )
!= $false )
| ( X1 = X3 )
| ( X1 = X2 )
| ( X2 = X3 ) )
| ~ spl4_1 ),
inference(constrained_superposition,[status(thm)],[f12,f172]) ).
thf(f172,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( ( f @ $false )
= X0 )
| ( X0 = X1 )
| ( X1 = X2 )
| ( X0 = X2 ) )
| ~ spl4_1 ),
inference(superposition,[status(thm)],[f29,f97]) ).
thf(f97,plain,
( ! [X0: $i] :
( ( ( f @ $true )
= X0 )
| ( ( f @ $false )
= X0 ) )
| ~ spl4_1 ),
inference(trivial_inequality_removal,[status(thm)],[f87]) ).
thf(f87,plain,
( ! [X0: $i] :
( ( ( f @ $false )
= X0 )
| ( $true = $false )
| ( ( f @ $true )
= X0 ) )
| ~ spl4_1 ),
inference(superposition,[status(thm)],[f42,f19]) ).
thf(f42,plain,
( ( ( sK0 @ ( f @ $false ) )
= $false )
| ~ spl4_1 ),
inference(avatar_component_clause,[status(thm)],[f40]) ).
thf(f40,definition,
( spl4_1
<=> ( ( sK0 @ ( f @ $false ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl4_1])],[avatar_definition]) ).
thf(f220,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( ( f @ $false )
!= X1 )
| ( X0 = X2 )
| ( X0 = X1 )
| ( X1 = X2 ) )
| ~ spl4_1 ),
inference(equality_factoring,[status(thm)],[f172]) ).
thf(f13,plain,
sK2 != sK1,
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( ( sK3 != sK2 )
& ( sK3 != sK1 )
& ( sK2 != sK1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3])],[f9,f10]) ).
thf(f10,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( X1 != X2 )
& ( X0 != X2 )
& ( X0 != X1 ) )
=> ( ( sK3 != sK2 )
& ( sK3 != sK1 )
& ( sK2 != sK1 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f9,plain,
? [X0: $i,X1: $i,X2: $i] :
( ( X1 != X2 )
& ( X0 != X2 )
& ( X0 != X1 ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,plain,
? [X1: $i,X2: $i,X0: $i] :
( ( X0 != X2 )
& ( X0 != X1 )
& ( X1 != X2 ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X2: $i,X0: $i,X1: $i] :
( ( X1 = X2 )
| ( X0 = X1 )
| ( X0 = X2 ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,negated_conjecture,
~ ! [X2: $i,X1: $i,X0: $i] :
( ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f2,conjecture,
! [X2: $i,X1: $i,X0: $i] :
( ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 ) ),
file('/export/starexec/sandbox2/tmp/tmp.DoU9jji1Ik/DTF2THF_7414.p',less3) ).
thf(f15,plain,
sK3 != sK2,
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f14,plain,
sK3 != sK1,
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f83,plain,
~ spl4_2,
inference(avatar_contradiction_clause,[status(thm)],[f82]) ).
thf(f82,plain,
( $false
| ~ spl4_2 ),
inference(subsumption_resolution,[status(thm)],[f68,f47]) ).
thf(f47,plain,
( ! [X0: $i,X1: $i] : ( X0 = X1 )
| ~ spl4_2 ),
inference(superposition,[status(thm)],[f45,f45]) ).
thf(f45,plain,
( ! [X0: $i] :
( ( f @ $false )
= X0 )
| ~ spl4_2 ),
inference(avatar_component_clause,[status(thm)],[f44]) ).
thf(f44,definition,
( spl4_2
<=> ! [X0: $i] :
( ( f @ $false )
= X0 ) ),
introduced(definition,[new_symbols(naming,[spl4_2])],[avatar_definition]) ).
thf(f68,plain,
( ! [X0: $i] : ( sK1 != X0 )
| ~ spl4_2 ),
inference(superposition,[status(thm)],[f14,f47]) ).
thf(f46,plain,
( spl4_1
| spl4_2 ),
inference(avatar_split_clause,[status(thm)],[f38,f44,f40]) ).
thf(f38,plain,
! [X0: $i] :
( ( ( f @ $false )
= X0 )
| ( ( sK0 @ ( f @ $false ) )
= $false ) ),
inference(trivial_inequality_removal,[status(thm)],[f36]) ).
thf(f36,plain,
! [X0: $i] :
( ( ( sK0 @ ( f @ $false ) )
= $false )
| ( ( f @ $false )
= X0 )
| ( X0 != X0 ) ),
inference(equality_factoring,[status(thm)],[f23]) ).
thf(f23,plain,
! [X0: $i,X1: $i] :
( ( ( f @ $false )
= X0 )
| ( ( sK0 @ X1 )
= $false )
| ( X0 = X1 ) ),
inference(superposition,[status(thm)],[f12,f18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEV434^1 : TPTP v9.2.1. Released v5.2.0.
% 0.00/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.15/0.34 % Computer : n028.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 12:46:42 EST 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.20/0.46 ---- Original DTF file ---
% 0.20/0.46 thf(spec,logic,$$dhol).
% 0.20/0.46 %------------------------------------------------------------------------------
% 0.20/0.46 % File : SEV434^1 : TPTP v9.2.1. Released v5.2.0.
% 0.20/0.46 % Domain : Set Theory
% 0.20/0.46 % Problem : There are at most 2 individuals if there is a surjection from o
% 0.20/0.46 % Version : Especial.
% 0.20/0.46 % English :
% 0.20/0.46
% 0.20/0.46 % Refs : [Bro11] Brown (2011), Email to Geoff Sutcliffe
% 0.20/0.46 % Source : [Bro11]
% 0.20/0.46 % Names : SURJO [Bro11]
% 0.20/0.46
% 0.20/0.46 % Status : Theorem
% 0.20/0.46 % Rating : 0.00 v9.0.0, 0.10 v8.2.0, 0.08 v8.1.0, 0.09 v7.5.0, 0.14 v7.4.0, 0.33 v7.2.0, 0.25 v7.1.0, 0.38 v7.0.0, 0.29 v6.4.0, 0.33 v6.3.0, 0.40 v6.2.0, 0.29 v6.0.0, 0.43 v5.5.0, 0.33 v5.4.0, 0.40 v5.3.0, 0.60 v5.2.0
% 0.20/0.46 % Syntax : Number of formulae : 3 ( 1 unt; 1 typ; 0 def)
% 0.20/0.46 % Number of atoms : 4 ( 4 equ; 0 cnn)
% 0.20/0.46 % Maximal formula atoms : 3 ( 2 avg)
% 0.20/0.46 % Number of connectives : 3 ( 0 ~; 2 |; 0 &; 1 @)
% 0.20/0.46 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.20/0.46 % Maximal formula depth : 6 ( 5 avg)
% 0.20/0.46 % Number of types : 2 ( 0 usr)
% 0.20/0.46 % Number of type conns : 1 ( 1 >; 0 *; 0 +; 0 <<)
% 0.20/0.46 % Number of symbols : 2 ( 1 usr; 0 con; 1-2 aty)
% 0.20/0.46 % Number of variables : 5 ( 0 ^; 4 !; 1 ?; 5 :)
% 0.20/0.46 % SPC : TH0_THM_EQU_NAR
% 0.20/0.46
% 0.20/0.46 % Comments :
% 0.20/0.46 %------------------------------------------------------------------------------
% 0.20/0.46 thf(f,type,
% 0.20/0.46 f: $o > $i ).
% 0.20/0.46
% 0.20/0.46 thf(fsurj,axiom,
% 0.20/0.46 ! [Y: $i] :
% 0.20/0.46 ? [X: $o] :
% 0.20/0.46 ( ( f @ X )
% 0.20/0.46 = Y ) ).
% 0.20/0.46
% 0.20/0.46 thf(less3,conjecture,
% 0.20/0.46 ! [X: $i,Y: $i,Z: $i] :
% 0.20/0.46 ( ( X = Y )
% 0.20/0.46 | ( X = Z )
% 0.20/0.46 | ( Y = Z ) ) ).
% 0.20/0.46
% 0.20/0.46 %------------------------------------------------------------------------------
% 0.20/0.46 ------------------------
% 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 12:46:43 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/sandbox2/tmp/tmp.DoU9jji1Ik/DTF2DTF7414.p
% See solution above
% 0.31/1.30 ------------------------
% 0.31/1.31 ---- Cleaned THF ---
% 0.31/1.32 thf(f,type,
% 0.31/1.32 f: $o > $i ).
% 0.31/1.32
% 0.31/1.32 thf(fsurj,axiom,
% 0.31/1.32 ! [Y: $i] :
% 0.31/1.32 ? [X: $o] :
% 0.31/1.32 ( ( f @ X )
% 0.31/1.32 = Y ) ).
% 0.31/1.32
% 0.31/1.32 thf(less3,conjecture,
% 0.31/1.32 ! [X: $i,Y: $i,Z: $i] :
% 0.31/1.32 ( ( X = Y )
% 0.31/1.32 | ( X = Z )
% 0.31/1.32 | ( Y = Z ) ) ).
% 0.31/1.32 ------------------------
% 0.31/1.33 % (7570)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_7414 for (2999ds/4Mi)
% 0.31/1.33 % (7574)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_7414 for (2999ds/275Mi)
% 0.31/1.33 % (7573)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_7414 for (2999ds/2Mi)
% 0.31/1.33 % (7574)Refutation not found, incomplete strategy
% 0.31/1.33 % (7574)------------------------------
% 0.31/1.33 % (7574)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.33 % (7574)Termination reason: Refutation not found, incomplete strategy
% 0.31/1.33
% 0.31/1.33
% 0.31/1.33 % (7574)Memory used [KB]: 5373
% 0.31/1.33 % (7574)Time elapsed: 0.002 s
% 0.31/1.33 % (7574)Instructions burned: 1 (million)
% 0.31/1.33 % (7574)------------------------------
% 0.31/1.33 % (7574)------------------------------
% 0.31/1.33 % (7573)Instruction limit reached!
% 0.31/1.33 % (7573)------------------------------
% 0.31/1.33 % (7573)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.33 % (7573)Termination reason: Unknown
% 0.31/1.33 % (7573)Termination phase: Saturation
% 0.31/1.33
% 0.31/1.33 % (7573)Memory used [KB]: 5500
% 0.31/1.33 % (7573)Time elapsed: 0.002 s
% 0.31/1.33 % (7573)Instructions burned: 2 (million)
% 0.31/1.33 % (7573)------------------------------
% 0.31/1.33 % (7573)------------------------------
% 0.31/1.33 % (7570)Instruction limit reached!
% 0.31/1.33 % (7570)------------------------------
% 0.31/1.33 % (7570)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.33 % (7570)Termination reason: Unknown
% 0.31/1.33 % (7570)Termination phase: Saturation
% 0.31/1.33
% 0.31/1.33 % (7570)Memory used [KB]: 5500
% 0.31/1.33 % (7570)Time elapsed: 0.004 s
% 0.31/1.33 % (7570)Instructions burned: 5 (million)
% 0.31/1.33 % (7570)------------------------------
% 0.31/1.33 % (7570)------------------------------
% 0.31/1.34 % (7571)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_7414 for (2999ds/27Mi)
% 0.31/1.34 % (7572)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_7414 for (2999ds/2Mi)
% 0.31/1.34 % (7575)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_7414 for (2999ds/18Mi)
% 0.31/1.34 % (7572)Refutation not found, incomplete strategy
% 0.31/1.34 % (7572)------------------------------
% 0.31/1.34 % (7572)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.34 % (7572)Termination reason: Refutation not found, incomplete strategy
% 0.31/1.34
% 0.31/1.34
% 0.31/1.34 % (7572)Memory used [KB]: 5500
% 0.31/1.34 % (7572)Time elapsed: 0.003 s
% 0.31/1.34 % (7572)Instructions burned: 1 (million)
% 0.31/1.34 % (7571)Refutation not found, incomplete strategy
% 0.31/1.34 % (7571)------------------------------
% 0.31/1.34 % (7571)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.34 % (7572)------------------------------
% 0.31/1.34 % (7572)------------------------------
% 0.31/1.34 % (7571)Termination reason: Refutation not found, incomplete strategy
% 0.31/1.34
% 0.31/1.34
% 0.31/1.34 % (7571)Memory used [KB]: 5500
% 0.31/1.34 % (7571)Time elapsed: 0.003 s
% 0.31/1.34 % (7571)Instructions burned: 1 (million)
% 0.31/1.34 % (7571)------------------------------
% 0.31/1.34 % (7571)------------------------------
% 0.31/1.34 % (7576)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_7414 for (2999ds/3Mi)
% 0.31/1.34 % (7576)Refutation not found, incomplete strategy
% 0.31/1.34 % (7576)------------------------------
% 0.31/1.34 % (7576)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.34 % (7576)Termination reason: Refutation not found, incomplete strategy
% 0.31/1.34
% 0.31/1.34
% 0.31/1.34 % (7576)Memory used [KB]: 5500
% 0.31/1.34 % (7576)Time elapsed: 0.002 s
% 0.31/1.34 % (7576)Instructions burned: 2 (million)
% 0.31/1.34 % (7576)------------------------------
% 0.31/1.34 % (7576)------------------------------
% 0.31/1.34 % (7577)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_7414 for (2999ds/37Mi)
% 0.31/1.34 % (7578)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_7414 for (2999ds/15Mi)
% 0.31/1.34 % (7578)Refutation not found, incomplete strategy
% 0.31/1.34 % (7578)------------------------------
% 0.31/1.34 % (7578)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.34 % (7578)Termination reason: Refutation not found, incomplete strategy
% 0.31/1.34
% 0.31/1.34
% 0.31/1.34 % (7578)Memory used [KB]: 5500
% 0.31/1.34 % (7578)Time elapsed: 0.001 s
% 0.31/1.34 % (7578)------------------------------
% 0.31/1.34 % (7578)------------------------------
% 0.31/1.34 % (7569)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_7414 for (2999ds/183Mi)
% 0.31/1.35 % (7575)Instruction limit reached!
% 0.31/1.35 % (7575)------------------------------
% 0.31/1.35 % (7575)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.35 % (7575)Termination reason: Unknown
% 0.31/1.35 % (7575)Termination phase: Saturation
% 0.31/1.35
% 0.31/1.35 % (7575)Memory used [KB]: 5500
% 0.31/1.35 % (7575)Time elapsed: 0.014 s
% 0.31/1.35 % (7575)Instructions burned: 18 (million)
% 0.31/1.35 % (7575)------------------------------
% 0.31/1.35 % (7575)------------------------------
% 0.31/1.35 % (7581)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_7414 for (2999ds/7Mi)
% 0.31/1.35 % (7582)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_7414 for (2999ds/16Mi)
% 0.31/1.35 % (7581)Instruction limit reached!
% 0.31/1.35 % (7581)------------------------------
% 0.31/1.35 % (7581)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.35 % (7581)Termination reason: Unknown
% 0.31/1.35 % (7581)Termination phase: Saturation
% 0.31/1.35
% 0.31/1.35 % (7581)Memory used [KB]: 1023
% 0.31/1.35 % (7581)Time elapsed: 0.004 s
% 0.31/1.35 % (7581)Instructions burned: 9 (million)
% 0.31/1.35 % (7581)------------------------------
% 0.31/1.35 % (7581)------------------------------
% 0.31/1.36 % (7577)Instruction limit reached!
% 0.31/1.36 % (7577)------------------------------
% 0.31/1.36 % (7577)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.36 % (7577)Termination reason: Unknown
% 0.31/1.36 % (7577)Termination phase: Saturation
% 0.31/1.36
% 0.31/1.36 % (7577)Memory used [KB]: 5628
% 0.31/1.36 % (7577)Time elapsed: 0.016 s
% 0.31/1.36 % (7577)Instructions burned: 37 (million)
% 0.31/1.36 % (7577)------------------------------
% 0.31/1.36 % (7577)------------------------------
% 0.31/1.36 % (7579)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_7414 for (2999ds/3Mi)
% 0.31/1.36 % (7580)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_7414 for (2999ds/1041Mi)
% 0.31/1.36 % (7582)Instruction limit reached!
% 0.31/1.36 % (7582)------------------------------
% 0.31/1.36 % (7582)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.36 % (7582)Termination reason: Unknown
% 0.31/1.36 % (7582)Termination phase: Saturation
% 0.31/1.36
% 0.31/1.36 % (7582)Memory used [KB]: 5500
% 0.31/1.36 % (7582)Time elapsed: 0.007 s
% 0.31/1.36 % (7582)Instructions burned: 17 (million)
% 0.31/1.36 % (7582)------------------------------
% 0.31/1.36 % (7582)------------------------------
% 0.31/1.36 % (7579)Instruction limit reached!
% 0.31/1.36 % (7579)------------------------------
% 0.31/1.36 % (7579)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.36 % (7579)Termination reason: Unknown
% 0.31/1.36 % (7579)Termination phase: Saturation
% 0.31/1.36
% 0.31/1.36 % (7579)Memory used [KB]: 5500
% 0.31/1.36 % (7579)Time elapsed: 0.004 s
% 0.31/1.36 % (7579)Instructions burned: 3 (million)
% 0.31/1.36 % (7579)------------------------------
% 0.31/1.36 % (7579)------------------------------
% 0.31/1.36 % (7580)Refutation not found, incomplete strategy
% 0.31/1.36 % (7580)------------------------------
% 0.31/1.36 % (7580)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.36 % (7580)Termination reason: Refutation not found, incomplete strategy
% 0.31/1.36
% 0.31/1.36
% 0.31/1.36 % (7580)Memory used [KB]: 5500
% 0.31/1.36 % (7580)Time elapsed: 0.006 s
% 0.31/1.36 % (7580)Instructions burned: 6 (million)
% 0.31/1.36 % (7580)------------------------------
% 0.31/1.36 % (7580)------------------------------
% 0.31/1.36 % (7584)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_7414 for (2999ds/3Mi)
% 0.31/1.36 % (7584)Instruction limit reached!
% 0.31/1.36 % (7584)------------------------------
% 0.31/1.36 % (7584)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.36 % (7584)Termination reason: Unknown
% 0.31/1.36 % (7584)Termination phase: Saturation
% 0.31/1.36
% 0.31/1.36 % (7584)Memory used [KB]: 5500
% 0.31/1.36 % (7584)Time elapsed: 0.002 s
% 0.31/1.36 % (7584)Instructions burned: 3 (million)
% 0.31/1.36 % (7584)------------------------------
% 0.31/1.36 % (7584)------------------------------
% 0.31/1.37 % (7585)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_7414 for (2999ds/7Mi)
% 0.31/1.37 % (7585)Refutation not found, incomplete strategy
% 0.31/1.37 % (7585)------------------------------
% 0.31/1.37 % (7585)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.37 % (7585)Termination reason: Refutation not found, incomplete strategy
% 0.31/1.37
% 0.31/1.37
% 0.31/1.37 % (7585)Memory used [KB]: 5500
% 0.31/1.37 % (7585)Time elapsed: 0.002 s
% 0.31/1.37 % (7585)Instructions burned: 1 (million)
% 0.31/1.37 % (7585)------------------------------
% 0.31/1.37 % (7585)------------------------------
% 0.31/1.37 % (7583)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_7414 for (2999ds/3Mi)
% 0.31/1.37 % (7586)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_7414 for (2999ds/3Mi)
% 0.31/1.37 % (7583)Refutation not found, incomplete strategy
% 0.31/1.37 % (7583)------------------------------
% 0.31/1.37 % (7583)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.37 % (7583)Termination reason: Refutation not found, incomplete strategy
% 0.31/1.37
% 0.31/1.37
% 0.31/1.37 % (7583)Memory used [KB]: 5500
% 0.31/1.37 % (7583)Time elapsed: 0.003 s
% 0.31/1.37 % (7583)Instructions burned: 1 (million)
% 0.31/1.37 % (7583)------------------------------
% 0.31/1.37 % (7583)------------------------------
% 0.31/1.37 % (7586)Refutation not found, incomplete strategy
% 0.31/1.37 % (7586)------------------------------
% 0.31/1.37 % (7586)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.37 % (7586)Termination reason: Refutation not found, incomplete strategy
% 0.31/1.37
% 0.31/1.37
% 0.31/1.37 % (7586)Memory used [KB]: 5500
% 0.31/1.37 % (7586)Time elapsed: 0.003 s
% 0.31/1.37 % (7586)Instructions burned: 2 (million)
% 0.31/1.37 % (7586)------------------------------
% 0.31/1.37 % (7586)------------------------------
% 0.31/1.37 % (7587)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_7414 for (2999ds/4Mi)
% 0.31/1.37 % (7589)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_7414 for (2999ds/710Mi)
% 0.31/1.38 % (7587)Instruction limit reached!
% 0.31/1.38 % (7587)------------------------------
% 0.31/1.38 % (7587)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.38 % (7587)Termination reason: Unknown
% 0.31/1.38 % (7587)Termination phase: Saturation
% 0.31/1.38
% 0.31/1.38 % (7587)Memory used [KB]: 5500
% 0.31/1.38 % (7587)Time elapsed: 0.004 s
% 0.31/1.38 % (7587)Instructions burned: 5 (million)
% 0.31/1.38 % (7587)------------------------------
% 0.31/1.38 % (7587)------------------------------
% 0.31/1.38 % (7590)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_7414 for (2999ds/6Mi)
% 0.31/1.38 % (7592)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_7414 for (2999ds/21Mi)
% 0.31/1.38 % (7590)Instruction limit reached!
% 0.31/1.38 % (7590)------------------------------
% 0.31/1.38 % (7590)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.38 % (7590)Termination reason: Unknown
% 0.31/1.38 % (7590)Termination phase: Saturation
% 0.31/1.38
% 0.31/1.38 % (7590)Memory used [KB]: 5500
% 0.31/1.38 % (7590)Time elapsed: 0.004 s
% 0.31/1.38 % (7590)Instructions burned: 6 (million)
% 0.31/1.38 % (7590)------------------------------
% 0.31/1.38 % (7590)------------------------------
% 0.31/1.38 % (7588)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_7414 for (2999ds/18Mi)
% 0.31/1.38 % (7588)Refutation not found, incomplete strategy
% 0.31/1.38 % (7588)------------------------------
% 0.31/1.38 % (7588)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.38 % (7588)Termination reason: Refutation not found, incomplete strategy
% 0.31/1.38
% 0.31/1.38
% 0.31/1.38 % (7588)Memory used [KB]: 5500
% 0.31/1.38 % (7588)Time elapsed: 0.003 s
% 0.31/1.38 % (7588)Instructions burned: 1 (million)
% 0.31/1.38 % (7588)------------------------------
% 0.31/1.38 % (7588)------------------------------
% 0.31/1.39 % (7591)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_7414 for (2999ds/902Mi)
% 0.31/1.39 % (7593)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_7414 for (2999ds/5Mi)
% 0.31/1.39 % (7592)Instruction limit reached!
% 0.31/1.39 % (7592)------------------------------
% 0.31/1.39 % (7592)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.39 % (7592)Termination reason: Unknown
% 0.31/1.39 % (7592)Termination phase: Saturation
% 0.31/1.39 % (7569)First to succeed.
% 0.31/1.39
% 0.31/1.39 % (7592)Memory used [KB]: 5628
% 0.31/1.39 % (7592)Time elapsed: 0.009 s
% 0.31/1.39 % (7592)Instructions burned: 23 (million)
% 0.31/1.39 % (7592)------------------------------
% 0.31/1.39 % (7592)------------------------------
% 0.31/1.39 % (7591)Refutation not found, incomplete strategy
% 0.31/1.39 % (7591)------------------------------
% 0.31/1.39 % (7591)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.39 % (7591)Termination reason: Refutation not found, incomplete strategy
% 0.31/1.39
% 0.31/1.39
% 0.31/1.39 % (7591)Memory used [KB]: 5373
% 0.31/1.39 % (7591)Time elapsed: 0.003 s
% 0.31/1.39 % (7591)Instructions burned: 1 (million)
% 0.31/1.39 % (7591)------------------------------
% 0.31/1.39 % (7591)------------------------------
% 0.31/1.39 % (7569)Refutation found. Thanks to Tanya!
% 0.31/1.39 % SZS status Theorem for DTF2THF_7414
% 0.31/1.39 % SZS output start Proof for DTF2THF_7414
% 0.31/1.39 thf(func_def_0, type, f: $o > $i).
% 0.31/1.39 thf(func_def_4, type, sK0: $i > $o).
% 0.31/1.39 thf(func_def_9, type, ph5: !>[X0: $tType]:(X0)).
% 0.31/1.39 thf(f337,plain,(
% 0.31/1.39 $false),
% 0.31/1.39 inference(avatar_sat_refutation,[status(thm)],[f46,f83,f335])).
% 0.31/1.39 thf(f335,plain,(
% 0.31/1.39 ~spl4_1),
% 0.31/1.39 inference(avatar_contradiction_clause,[status(thm)],[f334])).
% 0.31/1.39 thf(f334,plain,(
% 0.31/1.39 $false | ~spl4_1),
% 0.31/1.39 inference(equality_resolution,[status(thm)],[f318])).
% 0.31/1.39 thf(f318,plain,(
% 0.31/1.39 ( ! [X0 : $i] : ((sK1 != X0)) ) | ~spl4_1),
% 0.31/1.39 inference(duplicate_literal_removal,[status(thm)],[f309])).
% 0.31/1.39 thf(f309,plain,(
% 0.31/1.39 ( ! [X0 : $i] : ((sK1 != X0) | (sK1 != X0)) ) | ~spl4_1),
% 0.31/1.39 inference(superposition,[status(thm)],[f14,f275])).
% 0.31/1.39 thf(f275,plain,(
% 0.31/1.39 ( ! [X0 : $i] : ((sK3 = X0) | (sK1 != X0)) ) | ~spl4_1),
% 0.31/1.39 inference(trivial_inequality_removal,[status(thm)],[f262])).
% 0.31/1.39 thf(f262,plain,(
% 0.31/1.39 ( ! [X0 : $i] : ((sK3 = X0) | (sK1 != X0) | (sK2 != sK2)) ) | ~spl4_1),
% 0.31/1.39 inference(superposition,[status(thm)],[f15,f232])).
% 0.31/1.39 thf(f232,plain,(
% 0.31/1.39 ( ! [X0 : $i,X1 : $i] : ((sK2 = X1) | (X0 = X1) | (sK1 != X0)) ) | ~spl4_1),
% 0.31/1.39 inference(superposition,[status(thm)],[f13,f231])).
% 0.31/1.39 thf(f231,plain,(
% 0.31/1.39 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((X1 = X2) | (X0 = X2) | (X0 = X1)) ) | ~spl4_1),
% 0.31/1.39 inference(subsumption_resolution,[status(thm)],[f220,f230])).
% 0.31/1.39 thf(f230,plain,(
% 0.31/1.39 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : ((X2 = X3) | (X0 = X1) | (X1 = X3) | (X1 = X2)) ) | ~spl4_1),
% 0.31/1.39 inference(subsumption_resolution,[status(thm)],[f204,f196])).
% 0.31/1.39 thf(f196,plain,(
% 0.31/1.39 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i] : ((X3 = X4) | (X0 = X2) | (X0 = X1) | (X0 = X4) | (X1 = X2) | ((sK0 @ X3) = $false)) )),
% 0.31/1.39 inference(trivial_inequality_removal,[status(thm)],[f189])).
% 0.31/1.39 thf(f189,plain,(
% 0.31/1.39 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i] : (($true != $true) | (X0 = X1) | (X3 = X4) | (X1 = X2) | (X0 = X2) | ((sK0 @ X3) = $false) | (X0 = X4)) )),
% 0.31/1.39 inference(superposition,[status(thm)],[f174,f26])).
% 0.31/1.39 thf(f26,plain,(
% 0.31/1.39 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = (sK0 @ X1)) | ((sK0 @ X2) = $false) | (X0 = X1) | (X0 = X2)) )),
% 0.31/1.39 inference(trivial_inequality_removal,[status(thm)],[f22])).
% 0.31/1.39 thf(f22,plain,(
% 0.31/1.39 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((sK0 @ X2) = $false) | (X0 = X1) | ($true = $false) | ($true = (sK0 @ X1)) | (X0 = X2)) )),
% 0.31/1.39 inference(superposition,[status(thm)],[f17,f18])).
% 0.31/1.39 thf(f18,plain,(
% 0.31/1.39 ( ! [X0 : $i,X1 : $i] : (((sK0 @ X1) = $false) | ((sK0 @ X0) = $false) | (X0 = X1)) )),
% 0.31/1.39 inference(binary_proxy_clausification,[status(thm)],[f16])).
% 0.31/1.39 thf(f16,plain,(
% 0.31/1.39 ( ! [X0 : $i,X1 : $i] : (((sK0 @ X1) != (sK0 @ X0)) | (X0 = X1)) )),
% 0.31/1.39 inference(constrained_superposition,[status(thm)],[f12,f12])).
% 0.31/1.39 thf(f12,plain,(
% 0.31/1.39 ( ! [X0 : $i] : (((f @ (sK0 @ X0)) = X0)) )),
% 0.31/1.39 inference(cnf_transformation,[status(thm)],[f8])).
% 0.31/1.39 thf(f8,plain,(
% 0.31/1.39 ! [X0 : $i] : ((f @ (sK0 @ X0)) = X0)),
% 0.31/1.39 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f1,f7])).
% 0.31/1.39 thf(f7,plain,(
% 0.31/1.39 ! [X0 : $i] : (? [X1 : $o] : ((f @ X1) = X0) => ((f @ (sK0 @ X0)) = X0))),
% 0.31/1.39 introduced(definition,[],[choice_axiom])).
% 0.31/1.39 thf(f1,axiom,(
% 0.31/1.39 ! [X0 : $i] : ? [X1 : $o] : ((f @ X1) = X0)),
% 0.31/1.39 file('/export/starexec/sandbox2/tmp/tmp.DoU9jji1Ik/DTF2THF_7414.p',fsurj)).
% 0.31/1.39 thf(f17,plain,(
% 0.31/1.39 ( ! [X0 : $i,X1 : $i] : (($true = (sK0 @ X1)) | ($true = (sK0 @ X0)) | (X0 = X1)) )),
% 0.31/1.39 inference(binary_proxy_clausification,[status(thm)],[f16])).
% 0.31/1.39 thf(f174,plain,(
% 0.31/1.39 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != (sK0 @ X0)) | (X1 = X2) | (X0 = X1) | (X0 = X2)) )),
% 0.31/1.39 inference(constrained_superposition,[status(thm)],[f29,f12])).
% 0.31/1.39 thf(f29,plain,(
% 0.31/1.39 ( ! [X0 : $i,X1 : $i] : (((f @ $true) = X1) | ((f @ $true) = X0) | (X0 = X1)) )),
% 0.31/1.39 inference(superposition,[status(thm)],[f12,f19])).
% 0.31/1.39 thf(f19,plain,(
% 0.31/1.39 ( ! [X0 : $i,X1 : $i] : (($true = (sK0 @ X1)) | (X0 = X1) | ((f @ $true) = X0)) )),
% 0.31/1.39 inference(superposition,[status(thm)],[f12,f17])).
% 0.31/1.39 thf(f204,plain,(
% 0.31/1.39 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : ((X0 = X1) | ((sK0 @ X0) != $false) | (X1 = X3) | (X1 = X2) | (X2 = X3)) ) | ~spl4_1),
% 0.31/1.39 inference(constrained_superposition,[status(thm)],[f12,f172])).
% 0.31/1.39 thf(f172,plain,(
% 0.31/1.39 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((f @ $false) = X0) | (X0 = X1) | (X1 = X2) | (X0 = X2)) ) | ~spl4_1),
% 0.31/1.39 inference(superposition,[status(thm)],[f29,f97])).
% 0.31/1.39 thf(f97,plain,(
% 0.31/1.39 ( ! [X0 : $i] : (((f @ $true) = X0) | ((f @ $false) = X0)) ) | ~spl4_1),
% 0.31/1.39 inference(trivial_inequality_removal,[status(thm)],[f87])).
% 0.31/1.39 thf(f87,plain,(
% 0.31/1.39 ( ! [X0 : $i] : (((f @ $false) = X0) | ($true = $false) | ((f @ $true) = X0)) ) | ~spl4_1),
% 0.31/1.39 inference(superposition,[status(thm)],[f42,f19])).
% 0.31/1.39 thf(f42,plain,(
% 0.31/1.39 ((sK0 @ (f @ $false)) = $false) | ~spl4_1),
% 0.31/1.39 inference(avatar_component_clause,[status(thm)],[f40])).
% 0.31/1.39 thf(f40,definition,(
% 0.31/1.39 spl4_1 <=> ((sK0 @ (f @ $false)) = $false)),
% 0.31/1.39 introduced(definition,[new_symbols(naming,[spl4_1])],[avatar_definition])).
% 0.31/1.39 thf(f220,plain,(
% 0.31/1.39 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((f @ $false) != X1) | (X0 = X2) | (X0 = X1) | (X1 = X2)) ) | ~spl4_1),
% 0.31/1.39 inference(equality_factoring,[status(thm)],[f172])).
% 0.31/1.39 thf(f13,plain,(
% 0.31/1.39 (sK2 != sK1)),
% 0.31/1.39 inference(cnf_transformation,[status(thm)],[f11])).
% 0.31/1.39 thf(f11,plain,(
% 0.31/1.39 (sK3 != sK2) & (sK3 != sK1) & (sK2 != sK1)),
% 0.31/1.39 inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3])],[f9,f10])).
% 0.31/1.39 thf(f10,plain,(
% 0.31/1.39 ? [X0 : $i,X1 : $i,X2 : $i] : ((X1 != X2) & (X0 != X2) & (X0 != X1)) => ((sK3 != sK2) & (sK3 != sK1) & (sK2 != sK1))),
% 0.31/1.39 introduced(definition,[],[choice_axiom])).
% 0.31/1.39 thf(f9,plain,(
% 0.31/1.39 ? [X0 : $i,X1 : $i,X2 : $i] : ((X1 != X2) & (X0 != X2) & (X0 != X1))),
% 0.31/1.39 inference(rectify,[status(thm)],[f6])).
% 0.31/1.39 thf(f6,plain,(
% 0.31/1.39 ? [X1 : $i,X2 : $i,X0 : $i] : ((X0 != X2) & (X0 != X1) & (X1 != X2))),
% 0.31/1.39 inference(ennf_transformation,[status(thm)],[f5])).
% 0.31/1.39 thf(f5,plain,(
% 0.31/1.39 ~! [X2 : $i,X0 : $i,X1 : $i] : ((X1 = X2) | (X0 = X1) | (X0 = X2))),
% 0.31/1.39 inference(rectify,[status(thm)],[f3])).
% 0.31/1.39 thf(f3,negated_conjecture,(
% 0.31/1.39 ~! [X2 : $i,X1 : $i,X0 : $i] : ((X1 = X2) | (X0 = X2) | (X0 = X1))),
% 0.31/1.39 inference(negated_conjecture,[status(cth)],[f2])).
% 0.31/1.39 thf(f2,conjecture,(
% 0.31/1.39 ! [X2 : $i,X1 : $i,X0 : $i] : ((X1 = X2) | (X0 = X2) | (X0 = X1))),
% 0.31/1.39 file('/export/starexec/sandbox2/tmp/tmp.DoU9jji1Ik/DTF2THF_7414.p',less3)).
% 0.31/1.39 thf(f15,plain,(
% 0.31/1.39 (sK3 != sK2)),
% 0.31/1.39 inference(cnf_transformation,[status(thm)],[f11])).
% 0.31/1.39 thf(f14,plain,(
% 0.31/1.39 (sK3 != sK1)),
% 0.31/1.39 inference(cnf_transformation,[status(thm)],[f11])).
% 0.31/1.39 thf(f83,plain,(
% 0.31/1.39 ~spl4_2),
% 0.31/1.39 inference(avatar_contradiction_clause,[status(thm)],[f82])).
% 0.31/1.39 thf(f82,plain,(
% 0.31/1.39 $false | ~spl4_2),
% 0.31/1.39 inference(subsumption_resolution,[status(thm)],[f68,f47])).
% 0.31/1.39 thf(f47,plain,(
% 0.31/1.39 ( ! [X0 : $i,X1 : $i] : ((X0 = X1)) ) | ~spl4_2),
% 0.31/1.39 inference(superposition,[status(thm)],[f45,f45])).
% 0.31/1.39 thf(f45,plain,(
% 0.31/1.39 ( ! [X0 : $i] : (((f @ $false) = X0)) ) | ~spl4_2),
% 0.31/1.39 inference(avatar_component_clause,[status(thm)],[f44])).
% 0.31/1.39 thf(f44,definition,(
% 0.31/1.39 spl4_2 <=> ! [X0 : $i] : ((f @ $false) = X0)),
% 0.31/1.39 introduced(definition,[new_symbols(naming,[spl4_2])],[avatar_definition])).
% 0.31/1.39 thf(f68,plain,(
% 0.31/1.39 ( ! [X0 : $i] : ((sK1 != X0)) ) | ~spl4_2),
% 0.31/1.39 inference(superposition,[status(thm)],[f14,f47])).
% 0.31/1.39 thf(f46,plain,(
% 0.31/1.39 spl4_1 | spl4_2),
% 0.31/1.39 inference(avatar_split_clause,[status(thm)],[f38,f44,f40])).
% 0.31/1.39 thf(f38,plain,(
% 0.31/1.39 ( ! [X0 : $i] : (((f @ $false) = X0) | ((sK0 @ (f @ $false)) = $false)) )),
% 0.31/1.39 inference(trivial_inequality_removal,[status(thm)],[f36])).
% 0.31/1.39 thf(f36,plain,(
% 0.31/1.39 ( ! [X0 : $i] : (((sK0 @ (f @ $false)) = $false) | ((f @ $false) = X0) | (X0 != X0)) )),
% 0.31/1.39 inference(equality_factoring,[status(thm)],[f23])).
% 0.31/1.39 thf(f23,plain,(
% 0.31/1.39 ( ! [X0 : $i,X1 : $i] : (((f @ $false) = X0) | ((sK0 @ X1) = $false) | (X0 = X1)) )),
% 0.31/1.39 inference(superposition,[status(thm)],[f12,f18])).
% 0.31/1.39 % SZS output end Proof for DTF2THF_7414
% 0.31/1.39 % (7569)------------------------------
% 0.31/1.39 % (7569)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.39 % (7569)Termination reason: Refutation
% 0.31/1.39
% 0.31/1.39 % (7569)Memory used [KB]: 5628
% 0.31/1.39 % (7569)Time elapsed: 0.048 s
% 0.31/1.39 % (7569)Instructions burned: 45 (million)
% 0.31/1.39 % (7569)------------------------------
% 0.31/1.39 % (7569)------------------------------
% 0.31/1.39 % (7568)Success in time 0.057 s
%------------------------------------------------------------------------------