%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV396^5 : 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 : n011.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 09:41:10 AM UTC 2026
% Result : Theorem 1.79s 1.56s
% Output : Refutation 1.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 6
% Syntax : Number of formulae : 50 ( 1 unt; 0 typ; 4 def)
% Number of atoms : 370 ( 83 equ; 0 cnn)
% Maximal formula atoms : 6 ( 7 avg)
% Number of connectives : 283 ( 49 ~; 69 |; 33 &; 116 @)
% ( 9 <=>; 6 =>; 0 <=; 1 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 9 usr; 8 con; 0-2 aty)
% Number of variables : 39 ( 20 ^; 16 !; 3 ?; 39 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
cR: $i > $o ).
thf(func_def_1,type,
cS: $i > $o ).
thf(func_def_10,type,
ph2:
!>[X0: $tType] : X0 ).
thf(f64,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f22,f27,f32,f47,f63]) ).
thf(f63,plain,
( ~ spl1_1
| ~ spl1_3
| spl1_4 ),
inference(avatar_contradiction_clause,[status(thm)],[f62]) ).
thf(f62,plain,
( $false
| ~ spl1_1
| ~ spl1_3
| spl1_4 ),
inference(trivial_inequality_removal,[status(thm)],[f61]) ).
thf(f61,plain,
( ( $false = $true )
| ~ spl1_1
| ~ spl1_3
| spl1_4 ),
inference(backward_demodulation,[status(thm)],[f26,f60]) ).
thf(f60,plain,
( ( $false
= ( cR @ sK0 ) )
| ~ spl1_1
| spl1_4 ),
inference(trivial_inequality_removal,[status(thm)],[f59]) ).
thf(f59,plain,
( ( $true != $true )
| ( $false
= ( cR @ sK0 ) )
| ~ spl1_1
| spl1_4 ),
inference(superposition,[status(thm)],[f31,f57]) ).
thf(f57,plain,
( ! [X1: $i] :
( ( $true
= ( cS @ X1 ) )
| ( $false
= ( cR @ X1 ) ) )
| ~ spl1_1 ),
inference(binary_proxy_clausification,[status(thm)],[f54]) ).
thf(f54,plain,
( ! [X1: $i] :
( ( $false
= ( cR @ X1 ) )
| ( ( ( cR @ X1 )
& ( cS @ X1 ) )
= $true ) )
| ~ spl1_1 ),
inference(binary_proxy_clausification,[status(thm)],[f53]) ).
thf(f53,plain,
( ! [X1: $i] :
( ( ( cR @ X1 )
& ( cS @ X1 ) )
= ( cR @ X1 ) )
| ~ spl1_1 ),
inference(beta_eta_normalization,[status(thm)],[f52]) ).
thf(f52,plain,
( ! [X1: $i] :
( ( cR @ X1 )
= ( ^ [Y0: $i] :
( ( cR @ Y0 )
& ( cS @ Y0 ) )
@ X1 ) )
| ~ spl1_1 ),
inference(argument_congruence,[status(thm)],[f18]) ).
thf(f18,plain,
( ( cR
= ( ^ [Y0: $i] :
( ( cR @ Y0 )
& ( cS @ Y0 ) ) ) )
| ~ spl1_1 ),
inference(avatar_component_clause,[status(thm)],[f16]) ).
thf(f16,definition,
( spl1_1
<=> ( cR
= ( ^ [Y0: $i] :
( ( cR @ Y0 )
& ( cS @ Y0 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl1_1])],[avatar_definition]) ).
thf(f31,plain,
( ( $true
!= ( cS @ sK0 ) )
| spl1_4 ),
inference(avatar_component_clause,[status(thm)],[f29]) ).
thf(f29,definition,
( spl1_4
<=> ( $true
= ( cS @ sK0 ) ) ),
introduced(definition,[new_symbols(naming,[spl1_4])],[avatar_definition]) ).
thf(f26,plain,
( ( $true
= ( cR @ sK0 ) )
| ~ spl1_3 ),
inference(avatar_component_clause,[status(thm)],[f24]) ).
thf(f24,definition,
( spl1_3
<=> ( $true
= ( cR @ sK0 ) ) ),
introduced(definition,[new_symbols(naming,[spl1_3])],[avatar_definition]) ).
thf(f47,plain,
( spl1_1
| ~ spl1_2 ),
inference(avatar_contradiction_clause,[status(thm)],[f46]) ).
thf(f46,plain,
( $false
| spl1_1
| ~ spl1_2 ),
inference(trivial_inequality_removal,[status(thm)],[f45]) ).
thf(f45,plain,
( ( $false = $true )
| spl1_1
| ~ spl1_2 ),
inference(backward_demodulation,[status(thm)],[f42,f44]) ).
thf(f44,plain,
( ( $false
= ( cS @ sK3 ) )
| spl1_1 ),
inference(trivial_inequality_removal,[status(thm)],[f43]) ).
thf(f43,plain,
( ( $false
= ( cS @ sK3 ) )
| ( $false = $true )
| spl1_1 ),
inference(forward_demodulation,[status(thm)],[f38,f41]) ).
thf(f41,plain,
( ( ( cR @ sK3 )
= $true )
| spl1_1 ),
inference(duplicate_literal_removal,[status(thm)],[f40]) ).
thf(f40,plain,
( ( ( cR @ sK3 )
= $true )
| ( ( cR @ sK3 )
= $true )
| spl1_1 ),
inference(binary_proxy_clausification,[status(thm)],[f35]) ).
thf(f35,plain,
( ( ( cR @ sK3 )
= $true )
| ( $true
= ( ( cR @ sK3 )
& ( cS @ sK3 ) ) )
| spl1_1 ),
inference(binary_proxy_clausification,[status(thm)],[f34]) ).
thf(f34,plain,
( ( ( cR @ sK3 )
!= ( ( cR @ sK3 )
& ( cS @ sK3 ) ) )
| spl1_1 ),
inference(beta_eta_normalization,[status(thm)],[f33]) ).
thf(f33,plain,
( ( ( ^ [Y0: $i] :
( ( cR @ Y0 )
& ( cS @ Y0 ) )
@ sK3 )
!= ( cR @ sK3 ) )
| spl1_1 ),
inference(negative_extensionality,[status(thm)],[f17]) ).
thf(f17,plain,
( ( cR
!= ( ^ [Y0: $i] :
( ( cR @ Y0 )
& ( cS @ Y0 ) ) ) )
| spl1_1 ),
inference(avatar_component_clause,[status(thm)],[f16]) ).
thf(f38,plain,
( ( $false
= ( cS @ sK3 ) )
| ( $false
= ( cR @ sK3 ) )
| spl1_1 ),
inference(duplicate_literal_removal,[status(thm)],[f37]) ).
thf(f37,plain,
( ( $false
= ( cR @ sK3 ) )
| ( $false
= ( cR @ sK3 ) )
| ( $false
= ( cS @ sK3 ) )
| spl1_1 ),
inference(binary_proxy_clausification,[status(thm)],[f36]) ).
thf(f36,plain,
( ( $false
= ( cR @ sK3 ) )
| ( $false
= ( ( cR @ sK3 )
& ( cS @ sK3 ) ) )
| spl1_1 ),
inference(binary_proxy_clausification,[status(thm)],[f34]) ).
thf(f42,plain,
( ( $true
= ( cS @ sK3 ) )
| spl1_1
| ~ spl1_2 ),
inference(subsumption_resolution,[status(thm)],[f39,f21]) ).
thf(f21,plain,
( ! [X1: $i] :
( ( $true
!= ( cR @ X1 ) )
| ( $true
= ( cS @ X1 ) ) )
| ~ spl1_2 ),
inference(avatar_component_clause,[status(thm)],[f20]) ).
thf(f20,definition,
( spl1_2
<=> ! [X1: $i] :
( ( $true
= ( cS @ X1 ) )
| ( $true
!= ( cR @ X1 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl1_2])],[avatar_definition]) ).
thf(f39,plain,
( ( ( cR @ sK3 )
= $true )
| ( $true
= ( cS @ sK3 ) )
| spl1_1 ),
inference(binary_proxy_clausification,[status(thm)],[f35]) ).
thf(f32,plain,
( ~ spl1_1
| ~ spl1_4 ),
inference(avatar_split_clause,[status(thm)],[f13,f29,f16]) ).
thf(f13,plain,
( ( $true
!= ( cS @ sK0 ) )
| ( cR
!= ( ^ [Y0: $i] :
( ( cR @ Y0 )
& ( cS @ Y0 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( ( ( cR
!= ( ^ [Y0: $i] :
( ( cR @ Y0 )
& ( cS @ Y0 ) ) ) )
| ( ( $true
= ( cR @ sK0 ) )
& ( $true
!= ( cS @ sK0 ) ) ) )
& ( ( cR
= ( ^ [Y0: $i] :
( ( cR @ Y0 )
& ( cS @ Y0 ) ) ) )
| ! [X1: $i] :
( ( $true
!= ( cR @ X1 ) )
| ( $true
= ( cS @ X1 ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f9,f10]) ).
thf(f10,plain,
( ? [X0: $i] :
( ( ( cR @ X0 )
= $true )
& ( ( cS @ X0 )
!= $true ) )
=> ( ( $true
= ( cR @ sK0 ) )
& ( $true
!= ( cS @ sK0 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f9,plain,
( ( ( cR
!= ( ^ [Y0: $i] :
( ( cR @ Y0 )
& ( cS @ Y0 ) ) ) )
| ? [X0: $i] :
( ( ( cR @ X0 )
= $true )
& ( ( cS @ X0 )
!= $true ) ) )
& ( ( cR
= ( ^ [Y0: $i] :
( ( cR @ Y0 )
& ( cS @ Y0 ) ) ) )
| ! [X1: $i] :
( ( $true
!= ( cR @ X1 ) )
| ( $true
= ( cS @ X1 ) ) ) ) ),
inference(rectify,[status(thm)],[f8]) ).
thf(f8,plain,
( ( ( cR
!= ( ^ [Y0: $i] :
( ( cR @ Y0 )
& ( cS @ Y0 ) ) ) )
| ? [X0: $i] :
( ( ( cR @ X0 )
= $true )
& ( ( cS @ X0 )
!= $true ) ) )
& ( ( cR
= ( ^ [Y0: $i] :
( ( cR @ Y0 )
& ( cS @ Y0 ) ) ) )
| ! [X0: $i] :
( ( ( cR @ X0 )
!= $true )
| ( ( cS @ X0 )
= $true ) ) ) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
( ! [X0: $i] :
( ( ( cR @ X0 )
!= $true )
| ( ( cS @ X0 )
= $true ) )
<~> ( cR
= ( ^ [Y0: $i] :
( ( cR @ Y0 )
& ( cS @ Y0 ) ) ) ) ),
inference(ennf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
~ ( ! [X0: $i] :
( ( ( cR @ X0 )
= $true )
=> ( ( cS @ X0 )
= $true ) )
<=> ( cR
= ( ^ [Y0: $i] :
( ( cR @ Y0 )
& ( cS @ Y0 ) ) ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ( cR
= ( ^ [Y0: $i] :
( ( cR @ Y0 )
& ( cS @ Y0 ) ) ) )
<=> ! [X1: $i] :
( ( $true
= ( cR @ X1 ) )
=> ( $true
= ( cS @ X1 ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ( cR
= ( ^ [X0: $i] :
( ( cS @ X0 )
& ( cR @ X0 ) ) ) )
<=> ! [X1: $i] :
( ( cR @ X1 )
=> ( cS @ X1 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ( cR
= ( ^ [X0: $i] :
( ( cS @ X0 )
& ( cR @ X0 ) ) ) )
<=> ! [X0: $i] :
( ( cR @ X0 )
=> ( cS @ X0 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ( cR
= ( ^ [X0: $i] :
( ( cS @ X0 )
& ( cR @ X0 ) ) ) )
<=> ! [X0: $i] :
( ( cR @ X0 )
=> ( cS @ X0 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.dNtt4mRPlU/DTF2THF_6866.p',cTHM31_pme) ).
thf(f27,plain,
( spl1_3
| ~ spl1_1 ),
inference(avatar_split_clause,[status(thm)],[f14,f16,f24]) ).
thf(f14,plain,
( ( $true
= ( cR @ sK0 ) )
| ( cR
!= ( ^ [Y0: $i] :
( ( cR @ Y0 )
& ( cS @ Y0 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f22,plain,
( spl1_1
| spl1_2 ),
inference(avatar_split_clause,[status(thm)],[f12,f20,f16]) ).
thf(f12,plain,
! [X1: $i] :
( ( cR
= ( ^ [Y0: $i] :
( ( cR @ Y0 )
& ( cS @ Y0 ) ) ) )
| ( $true
= ( cS @ X1 ) )
| ( $true
!= ( cR @ X1 ) ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEV396^5 : TPTP v9.2.1. Released v4.0.0.
% 0.11/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.15/0.32 % Computer : n011.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Tue Feb 24 12:45:47 EST 2026
% 0.15/0.32 % CPUTime :
% 0.15/0.32 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.19/0.47 ---- Original DTF file ---
% 0.19/0.47 thf(spec,logic,$$dhol).
% 0.19/0.47 %------------------------------------------------------------------------------
% 0.19/0.47 % File : SEV396^5 : TPTP v9.2.1. Released v4.0.0.
% 0.19/0.47 % Domain : Set Theory
% 0.19/0.47 % Problem : TPS problem THM31
% 0.19/0.47 % Version : Especial.
% 0.19/0.47 % English :
% 0.19/0.47
% 0.19/0.47 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.19/0.47 % Source : [Bro09]
% 0.19/0.47 % Names : tps_0377 [Bro09]
% 0.19/0.47 % : THM31 [TPS]
% 0.19/0.47
% 0.19/0.47 % Status : Theorem
% 0.19/0.47 % Rating : 0.00 v8.2.0, 0.08 v8.1.0, 0.00 v7.4.0, 0.11 v7.2.0, 0.00 v7.1.0, 0.12 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v4.1.0, 0.00 v4.0.1, 0.33 v4.0.0
% 0.19/0.47 % Syntax : Number of formulae : 3 ( 0 unt; 2 typ; 0 def)
% 0.19/0.47 % Number of atoms : 6 ( 1 equ; 0 cnn)
% 0.19/0.47 % Maximal formula atoms : 3 ( 6 avg)
% 0.19/0.47 % Number of connectives : 7 ( 0 ~; 0 |; 1 &; 4 @)
% 0.19/0.47 % ( 1 <=>; 1 =>; 0 <=; 0 <~>)
% 0.19/0.47 % Maximal formula depth : 5 ( 5 avg)
% 0.19/0.47 % Number of types : 2 ( 0 usr)
% 0.19/0.47 % Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% 0.19/0.47 % Number of symbols : 3 ( 2 usr; 0 con; 1-2 aty)
% 0.19/0.47 % Number of variables : 2 ( 1 ^; 1 !; 0 ?; 2 :)
% 0.19/0.47 % SPC : TH0_THM_EQU_NAR
% 0.19/0.47
% 0.19/0.47 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.19/0.47 % project in the Department of Mathematical Sciences at Carnegie
% 0.19/0.47 % Mellon University. Distributed under the Creative Commons copyleft
% 0.19/0.47 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.19/0.47 % : Polymorphic definitions expanded.
% 0.19/0.47 %------------------------------------------------------------------------------
% 0.19/0.47 thf(cR,type,
% 0.19/0.47 cR: $i > $o ).
% 0.19/0.47
% 0.19/0.47 thf(cS,type,
% 0.19/0.47 cS: $i > $o ).
% 0.19/0.47
% 0.19/0.47 thf(cTHM31_pme,conjecture,
% 0.19/0.47 ( ! [Xx: $i] :
% 0.19/0.47 ( ( cR @ Xx )
% 0.19/0.47 => ( cS @ Xx ) )
% 0.19/0.47 <=> ( ( ^ [Xx: $i] :
% 0.19/0.47 ( ( cR @ Xx )
% 0.19/0.47 & ( cS @ Xx ) ) )
% 0.19/0.47 = cR ) ) ).
% 0.19/0.47
% 0.19/0.47 %------------------------------------------------------------------------------
% 0.19/0.47 ------------------------
% 1.79/1.52 ---- Embedded in THF ---
% 1.79/1.52 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.79/1.52 %%% Generated on Tue Feb 24 12:45:48 EST 2026
% 1.79/1.52 %%% using '$$dhol' embedding, version 1.3.0.
% 1.79/1.52 %%% Logic specification used:
% 1.79/1.52 %%% thf(spec, logic, $$dhol).
% 1.79/1.52
% 1.79/1.52 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.dNtt4mRPlU/DTF2DTF6866.p
% See solution above
% 1.79/1.53 ------------------------
% 1.79/1.53 ---- Cleaned THF ---
% 1.79/1.54 thf(cR,type,
% 1.79/1.54 cR: $i > $o ).
% 1.79/1.54
% 1.79/1.54 thf(cS,type,
% 1.79/1.54 cS: $i > $o ).
% 1.79/1.54
% 1.79/1.54 thf(cTHM31_pme,conjecture,
% 1.79/1.54 ( ! [Xx: $i] :
% 1.79/1.54 ( ( cR @ Xx )
% 1.79/1.54 => ( cS @ Xx ) )
% 1.79/1.54 <=> ( ( ^ [Xx: $i] :
% 1.79/1.54 ( ( cR @ Xx )
% 1.79/1.54 & ( cS @ Xx ) ) )
% 1.79/1.54 = cR ) ) ).
% 1.79/1.54 ------------------------
% 1.79/1.56 % (6977)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_6866 for (3000ds/18Mi)
% 1.79/1.56 % (6974)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_6866 for (3000ds/2Mi)
% 1.79/1.56 % (6975)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_6866 for (3000ds/2Mi)
% 1.79/1.56 % (6973)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_6866 for (3000ds/27Mi)
% 1.79/1.56 % (6971)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_6866 for (3000ds/183Mi)
% 1.79/1.56 % (6976)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_6866 for (3000ds/275Mi)
% 1.79/1.56 % (6974)Instruction limit reached!
% 1.79/1.56 % (6974)------------------------------
% 1.79/1.56 % (6974)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.79/1.56 % (6974)Termination reason: Unknown
% 1.79/1.56 % (6974)Termination phase: Saturation
% 1.79/1.56
% 1.79/1.56 % (6975)Instruction limit reached!
% 1.79/1.56 % (6975)------------------------------
% 1.79/1.56 % (6975)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.79/1.56 % (6975)Termination reason: Unknown
% 1.79/1.56 % (6975)Termination phase: Saturation
% 1.79/1.56
% 1.79/1.56 % (6975)Memory used [KB]: 5500
% 1.79/1.56 % (6975)Time elapsed: 0.003 s
% 1.79/1.56 % (6975)Instructions burned: 2 (million)
% 1.79/1.56 % (6975)------------------------------
% 1.79/1.56 % (6975)------------------------------
% 1.79/1.56 % (6974)Memory used [KB]: 5500
% 1.79/1.56 % (6974)Time elapsed: 0.003 s
% 1.79/1.56 % (6974)Instructions burned: 2 (million)
% 1.79/1.56 % (6974)------------------------------
% 1.79/1.56 % (6974)------------------------------
% 1.79/1.56 % (6972)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_6866 for (3000ds/4Mi)
% 1.79/1.56 % (6977)First to succeed.
% 1.79/1.56 % (6971)Also succeeded, but the first one will report.
% 1.79/1.56 % (6973)Also succeeded, but the first one will report.
% 1.79/1.56 % (6977)Refutation found. Thanks to Tanya!
% 1.79/1.56 % SZS status Theorem for DTF2THF_6866
% 1.79/1.56 % SZS output start Proof for DTF2THF_6866
% 1.79/1.56 thf(func_def_0, type, cR: $i > $o).
% 1.79/1.56 thf(func_def_1, type, cS: $i > $o).
% 1.79/1.56 thf(func_def_10, type, ph2: !>[X0: $tType]:(X0)).
% 1.79/1.56 thf(f64,plain,(
% 1.79/1.56 $false),
% 1.79/1.56 inference(avatar_sat_refutation,[status(thm)],[f22,f27,f32,f47,f63])).
% 1.79/1.56 thf(f63,plain,(
% 1.79/1.56 ~spl1_1 | ~spl1_3 | spl1_4),
% 1.79/1.56 inference(avatar_contradiction_clause,[status(thm)],[f62])).
% 1.79/1.56 thf(f62,plain,(
% 1.79/1.56 $false | (~spl1_1 | ~spl1_3 | spl1_4)),
% 1.79/1.56 inference(trivial_inequality_removal,[status(thm)],[f61])).
% 1.79/1.56 thf(f61,plain,(
% 1.79/1.56 ($false = $true) | (~spl1_1 | ~spl1_3 | spl1_4)),
% 1.79/1.56 inference(backward_demodulation,[status(thm)],[f26,f60])).
% 1.79/1.56 thf(f60,plain,(
% 1.79/1.56 ($false = (cR @ sK0)) | (~spl1_1 | spl1_4)),
% 1.79/1.56 inference(trivial_inequality_removal,[status(thm)],[f59])).
% 1.79/1.56 thf(f59,plain,(
% 1.79/1.56 ($true != $true) | ($false = (cR @ sK0)) | (~spl1_1 | spl1_4)),
% 1.79/1.56 inference(superposition,[status(thm)],[f31,f57])).
% 1.79/1.56 thf(f57,plain,(
% 1.79/1.56 ( ! [X1 : $i] : (($true = (cS @ X1)) | ($false = (cR @ X1))) ) | ~spl1_1),
% 1.79/1.56 inference(binary_proxy_clausification,[status(thm)],[f54])).
% 1.79/1.56 thf(f54,plain,(
% 1.79/1.56 ( ! [X1 : $i] : (($false = (cR @ X1)) | (((cR @ X1) & (cS @ X1)) = $true)) ) | ~spl1_1),
% 1.79/1.56 inference(binary_proxy_clausification,[status(thm)],[f53])).
% 1.79/1.56 thf(f53,plain,(
% 1.79/1.56 ( ! [X1 : $i] : ((((cR @ X1) & (cS @ X1)) = (cR @ X1))) ) | ~spl1_1),
% 1.79/1.56 inference(beta_eta_normalization,[status(thm)],[f52])).
% 1.79/1.56 thf(f52,plain,(
% 1.79/1.56 ( ! [X1 : $i] : (((cR @ X1) = ((^[Y0 : $i]: ((cR @ Y0) & (cS @ Y0))) @ X1))) ) | ~spl1_1),
% 1.79/1.56 inference(argument_congruence,[status(thm)],[f18])).
% 1.79/1.56 thf(f18,plain,(
% 1.79/1.56 (cR = (^[Y0 : $i]: ((cR @ Y0) & (cS @ Y0)))) | ~spl1_1),
% 1.79/1.56 inference(avatar_component_clause,[status(thm)],[f16])).
% 1.79/1.56 thf(f16,definition,(
% 1.79/1.56 spl1_1 <=> (cR = (^[Y0 : $i]: ((cR @ Y0) & (cS @ Y0))))),
% 1.79/1.56 introduced(definition,[new_symbols(naming,[spl1_1])],[avatar_definition])).
% 1.79/1.56 thf(f31,plain,(
% 1.79/1.56 ($true != (cS @ sK0)) | spl1_4),
% 1.79/1.56 inference(avatar_component_clause,[status(thm)],[f29])).
% 1.79/1.56 thf(f29,definition,(
% 1.79/1.56 spl1_4 <=> ($true = (cS @ sK0))),
% 1.79/1.56 introduced(definition,[new_symbols(naming,[spl1_4])],[avatar_definition])).
% 1.79/1.56 thf(f26,plain,(
% 1.79/1.56 ($true = (cR @ sK0)) | ~spl1_3),
% 1.79/1.56 inference(avatar_component_clause,[status(thm)],[f24])).
% 1.79/1.56 thf(f24,definition,(
% 1.79/1.56 spl1_3 <=> ($true = (cR @ sK0))),
% 1.79/1.56 introduced(definition,[new_symbols(naming,[spl1_3])],[avatar_definition])).
% 1.79/1.56 thf(f47,plain,(
% 1.79/1.56 spl1_1 | ~spl1_2),
% 1.79/1.56 inference(avatar_contradiction_clause,[status(thm)],[f46])).
% 1.79/1.56 thf(f46,plain,(
% 1.79/1.56 $false | (spl1_1 | ~spl1_2)),
% 1.79/1.56 inference(trivial_inequality_removal,[status(thm)],[f45])).
% 1.79/1.56 thf(f45,plain,(
% 1.79/1.56 ($false = $true) | (spl1_1 | ~spl1_2)),
% 1.79/1.56 inference(backward_demodulation,[status(thm)],[f42,f44])).
% 1.79/1.56 thf(f44,plain,(
% 1.79/1.56 ($false = (cS @ sK3)) | spl1_1),
% 1.79/1.56 inference(trivial_inequality_removal,[status(thm)],[f43])).
% 1.79/1.56 thf(f43,plain,(
% 1.79/1.56 ($false = (cS @ sK3)) | ($false = $true) | spl1_1),
% 1.79/1.56 inference(forward_demodulation,[status(thm)],[f38,f41])).
% 1.79/1.56 thf(f41,plain,(
% 1.79/1.56 ((cR @ sK3) = $true) | spl1_1),
% 1.79/1.56 inference(duplicate_literal_removal,[status(thm)],[f40])).
% 1.79/1.56 thf(f40,plain,(
% 1.79/1.56 ((cR @ sK3) = $true) | ((cR @ sK3) = $true) | spl1_1),
% 1.79/1.56 inference(binary_proxy_clausification,[status(thm)],[f35])).
% 1.79/1.56 thf(f35,plain,(
% 1.79/1.56 ((cR @ sK3) = $true) | ($true = ((cR @ sK3) & (cS @ sK3))) | spl1_1),
% 1.79/1.56 inference(binary_proxy_clausification,[status(thm)],[f34])).
% 1.79/1.56 thf(f34,plain,(
% 1.79/1.56 ((cR @ sK3) != ((cR @ sK3) & (cS @ sK3))) | spl1_1),
% 1.79/1.56 inference(beta_eta_normalization,[status(thm)],[f33])).
% 1.79/1.56 thf(f33,plain,(
% 1.79/1.56 (((^[Y0 : $i]: ((cR @ Y0) & (cS @ Y0))) @ sK3) != (cR @ sK3)) | spl1_1),
% 1.79/1.56 inference(negative_extensionality,[status(thm)],[f17])).
% 1.79/1.56 thf(f17,plain,(
% 1.79/1.56 (cR != (^[Y0 : $i]: ((cR @ Y0) & (cS @ Y0)))) | spl1_1),
% 1.79/1.56 inference(avatar_component_clause,[status(thm)],[f16])).
% 1.79/1.56 thf(f38,plain,(
% 1.79/1.56 ($false = (cS @ sK3)) | ($false = (cR @ sK3)) | spl1_1),
% 1.79/1.56 inference(duplicate_literal_removal,[status(thm)],[f37])).
% 1.79/1.56 thf(f37,plain,(
% 1.79/1.56 ($false = (cR @ sK3)) | ($false = (cR @ sK3)) | ($false = (cS @ sK3)) | spl1_1),
% 1.79/1.56 inference(binary_proxy_clausification,[status(thm)],[f36])).
% 1.79/1.56 thf(f36,plain,(
% 1.79/1.56 ($false = (cR @ sK3)) | ($false = ((cR @ sK3) & (cS @ sK3))) | spl1_1),
% 1.79/1.56 inference(binary_proxy_clausification,[status(thm)],[f34])).
% 1.79/1.56 thf(f42,plain,(
% 1.79/1.56 ($true = (cS @ sK3)) | (spl1_1 | ~spl1_2)),
% 1.79/1.56 inference(subsumption_resolution,[status(thm)],[f39,f21])).
% 1.79/1.56 thf(f21,plain,(
% 1.79/1.56 ( ! [X1 : $i] : (($true != (cR @ X1)) | ($true = (cS @ X1))) ) | ~spl1_2),
% 1.79/1.56 inference(avatar_component_clause,[status(thm)],[f20])).
% 1.79/1.56 thf(f20,definition,(
% 1.79/1.56 spl1_2 <=> ! [X1 : $i] : (($true = (cS @ X1)) | ($true != (cR @ X1)))),
% 1.79/1.56 introduced(definition,[new_symbols(naming,[spl1_2])],[avatar_definition])).
% 1.79/1.56 thf(f39,plain,(
% 1.79/1.56 ((cR @ sK3) = $true) | ($true = (cS @ sK3)) | spl1_1),
% 1.79/1.56 inference(binary_proxy_clausification,[status(thm)],[f35])).
% 1.79/1.56 thf(f32,plain,(
% 1.79/1.56 ~spl1_1 | ~spl1_4),
% 1.79/1.56 inference(avatar_split_clause,[status(thm)],[f13,f29,f16])).
% 1.79/1.56 thf(f13,plain,(
% 1.79/1.56 ($true != (cS @ sK0)) | (cR != (^[Y0 : $i]: ((cR @ Y0) & (cS @ Y0))))),
% 1.79/1.56 inference(cnf_transformation,[status(thm)],[f11])).
% 1.79/1.56 thf(f11,plain,(
% 1.79/1.56 ((cR != (^[Y0 : $i]: ((cR @ Y0) & (cS @ Y0)))) | (($true = (cR @ sK0)) & ($true != (cS @ sK0)))) & ((cR = (^[Y0 : $i]: ((cR @ Y0) & (cS @ Y0)))) | ! [X1 : $i] : (($true != (cR @ X1)) | ($true = (cS @ X1))))),
% 1.79/1.56 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f9,f10])).
% 1.79/1.56 thf(f10,plain,(
% 1.79/1.56 ? [X0 : $i] : (((cR @ X0) = $true) & ((cS @ X0) != $true)) => (($true = (cR @ sK0)) & ($true != (cS @ sK0)))),
% 1.79/1.56 introduced(definition,[],[choice_axiom])).
% 1.79/1.56 thf(f9,plain,(
% 1.79/1.56 ((cR != (^[Y0 : $i]: ((cR @ Y0) & (cS @ Y0)))) | ? [X0 : $i] : (((cR @ X0) = $true) & ((cS @ X0) != $true))) & ((cR = (^[Y0 : $i]: ((cR @ Y0) & (cS @ Y0)))) | ! [X1 : $i] : (($true != (cR @ X1)) | ($true = (cS @ X1))))),
% 1.79/1.56 inference(rectify,[status(thm)],[f8])).
% 1.79/1.56 thf(f8,plain,(
% 1.79/1.56 ((cR != (^[Y0 : $i]: ((cR @ Y0) & (cS @ Y0)))) | ? [X0 : $i] : (((cR @ X0) = $true) & ((cS @ X0) != $true))) & ((cR = (^[Y0 : $i]: ((cR @ Y0) & (cS @ Y0)))) | ! [X0 : $i] : (((cR @ X0) != $true) | ((cS @ X0) = $true)))),
% 1.79/1.56 inference(nnf_transformation,[status(thm)],[f7])).
% 1.79/1.56 thf(f7,plain,(
% 1.79/1.56 ! [X0 : $i] : (((cR @ X0) != $true) | ((cS @ X0) = $true)) <~> (cR = (^[Y0 : $i]: ((cR @ Y0) & (cS @ Y0))))),
% 1.79/1.56 inference(ennf_transformation,[status(thm)],[f6])).
% 1.79/1.56 thf(f6,plain,(
% 1.79/1.56 ~(! [X0 : $i] : (((cR @ X0) = $true) => ((cS @ X0) = $true)) <=> (cR = (^[Y0 : $i]: ((cR @ Y0) & (cS @ Y0)))))),
% 1.79/1.56 inference(rectify,[status(thm)],[f5])).
% 1.79/1.56 thf(f5,plain,(
% 1.79/1.56 ~((cR = (^[Y0 : $i]: ((cR @ Y0) & (cS @ Y0)))) <=> ! [X1 : $i] : (($true = (cR @ X1)) => ($true = (cS @ X1))))),
% 1.79/1.56 inference(fool_elimination,[status(thm)],[f4])).
% 1.79/1.56 thf(f4,plain,(
% 1.79/1.56 ~((cR = (^[X0 : $i] : ((cS @ X0) & (cR @ X0)))) <=> ! [X1 : $i] : ((cR @ X1) => (cS @ X1)))),
% 1.79/1.56 inference(rectify,[status(thm)],[f2])).
% 1.79/1.56 thf(f2,negated_conjecture,(
% 1.79/1.56 ~((cR = (^[X0 : $i] : ((cS @ X0) & (cR @ X0)))) <=> ! [X0 : $i] : ((cR @ X0) => (cS @ X0)))),
% 1.79/1.56 inference(negated_conjecture,[status(cth)],[f1])).
% 1.79/1.56 thf(f1,conjecture,(
% 1.79/1.56 (cR = (^[X0 : $i] : ((cS @ X0) & (cR @ X0)))) <=> ! [X0 : $i] : ((cR @ X0) => (cS @ X0))),
% 1.79/1.56 file('/export/starexec/sandbox/tmp/tmp.dNtt4mRPlU/DTF2THF_6866.p',cTHM31_pme)).
% 1.79/1.56 thf(f27,plain,(
% 1.79/1.56 spl1_3 | ~spl1_1),
% 1.79/1.56 inference(avatar_split_clause,[status(thm)],[f14,f16,f24])).
% 1.79/1.56 thf(f14,plain,(
% 1.79/1.56 ($true = (cR @ sK0)) | (cR != (^[Y0 : $i]: ((cR @ Y0) & (cS @ Y0))))),
% 1.79/1.56 inference(cnf_transformation,[status(thm)],[f11])).
% 1.79/1.56 thf(f22,plain,(
% 1.79/1.56 spl1_1 | spl1_2),
% 1.79/1.56 inference(avatar_split_clause,[status(thm)],[f12,f20,f16])).
% 1.79/1.56 thf(f12,plain,(
% 1.79/1.56 ( ! [X1 : $i] : ((cR = (^[Y0 : $i]: ((cR @ Y0) & (cS @ Y0)))) | ($true = (cS @ X1)) | ($true != (cR @ X1))) )),
% 1.79/1.56 inference(cnf_transformation,[status(thm)],[f11])).
% 1.79/1.56 % SZS output end Proof for DTF2THF_6866
% 1.79/1.56 % (6977)------------------------------
% 1.79/1.56 % (6977)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.79/1.56 % (6977)Termination reason: Refutation
% 1.79/1.56
% 1.79/1.56 % (6977)Memory used [KB]: 5500
% 1.79/1.56 % (6977)Time elapsed: 0.005 s
% 1.79/1.56 % (6977)Instructions burned: 3 (million)
% 1.79/1.56 % (6977)------------------------------
% 1.79/1.56 % (6977)------------------------------
% 1.79/1.56 % (6970)Success in time 0.019 s
%------------------------------------------------------------------------------