%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV135^5 : 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 : n013.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 09:40:22 AM UTC 2026
% Result : Theorem 1.51s 1.36s
% Output : Refutation 1.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 3
% Syntax : Number of formulae : 16 ( 4 unt; 0 typ; 0 def)
% Number of atoms : 162 ( 68 equ; 0 cnn)
% Maximal formula atoms : 14 ( 10 avg)
% Number of connectives : 236 ( 38 ~; 26 |; 30 &; 124 @)
% ( 0 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 8 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 26 ( 26 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 4 usr; 4 con; 0-2 aty)
% Number of variables : 71 ( 0 ^; 53 !; 18 ?; 71 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_4,type,
sK0: a > a > $o ).
thf(func_def_5,type,
sK1: a ).
thf(func_def_6,type,
sK2: a ).
thf(func_def_7,type,
sK3: a > $o ).
thf(f18,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f17,f14]) ).
thf(f14,plain,
( ( sK3 @ sK2 )
!= $true ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( ! [X4: a,X5: a] :
( ( ( sK3 @ X4 )
= $true )
| ( ( sK3 @ X5 )
!= $true )
| ( $true
!= ( sK0 @ X5 @ X4 ) ) )
& ( ( sK3 @ sK2 )
!= $true )
& ! [X6: a] :
( ( ( sK3 @ X6 )
= $true )
| ( ( sK0 @ sK1 @ X6 )
!= $true ) )
& ( $true
= ( sK0 @ sK1 @ sK2 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f8,f10,f9]) ).
thf(f9,plain,
( ? [X0: a > a > $o,X1: a,X2: a] :
( ? [X3: a > $o] :
( ! [X4: a,X5: a] :
( ( ( X3 @ X4 )
= $true )
| ( ( X3 @ X5 )
!= $true )
| ( ( X0 @ X5 @ X4 )
!= $true ) )
& ( ( X3 @ X2 )
!= $true )
& ! [X6: a] :
( ( ( X3 @ X6 )
= $true )
| ( ( X0 @ X1 @ X6 )
!= $true ) ) )
& ( ( X0 @ X1 @ X2 )
= $true ) )
=> ( ? [X3: a > $o] :
( ! [X5: a,X4: a] :
( ( ( X3 @ X4 )
= $true )
| ( ( X3 @ X5 )
!= $true )
| ( $true
!= ( sK0 @ X5 @ X4 ) ) )
& ( ( X3 @ sK2 )
!= $true )
& ! [X6: a] :
( ( ( X3 @ X6 )
= $true )
| ( ( sK0 @ sK1 @ X6 )
!= $true ) ) )
& ( $true
= ( sK0 @ sK1 @ sK2 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f10,plain,
( ? [X3: a > $o] :
( ! [X5: a,X4: a] :
( ( ( X3 @ X4 )
= $true )
| ( ( X3 @ X5 )
!= $true )
| ( $true
!= ( sK0 @ X5 @ X4 ) ) )
& ( ( X3 @ sK2 )
!= $true )
& ! [X6: a] :
( ( ( X3 @ X6 )
= $true )
| ( ( sK0 @ sK1 @ X6 )
!= $true ) ) )
=> ( ! [X5: a,X4: a] :
( ( ( sK3 @ X4 )
= $true )
| ( ( sK3 @ X5 )
!= $true )
| ( $true
!= ( sK0 @ X5 @ X4 ) ) )
& ( ( sK3 @ sK2 )
!= $true )
& ! [X6: a] :
( ( ( sK3 @ X6 )
= $true )
| ( ( sK0 @ sK1 @ X6 )
!= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f8,plain,
? [X0: a > a > $o,X1: a,X2: a] :
( ? [X3: a > $o] :
( ! [X4: a,X5: a] :
( ( ( X3 @ X4 )
= $true )
| ( ( X3 @ X5 )
!= $true )
| ( ( X0 @ X5 @ X4 )
!= $true ) )
& ( ( X3 @ X2 )
!= $true )
& ! [X6: a] :
( ( ( X3 @ X6 )
= $true )
| ( ( X0 @ X1 @ X6 )
!= $true ) ) )
& ( ( X0 @ X1 @ X2 )
= $true ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,plain,
? [X2: a > a > $o,X1: a,X0: a] :
( ? [X3: a > $o] :
( ! [X5: a,X4: a] :
( ( ( X3 @ X5 )
= $true )
| ( ( X3 @ X4 )
!= $true )
| ( ( X2 @ X4 @ X5 )
!= $true ) )
& ( $true
!= ( X3 @ X0 ) )
& ! [X6: a] :
( ( ( X3 @ X6 )
= $true )
| ( ( X2 @ X1 @ X6 )
!= $true ) ) )
& ( ( X2 @ X1 @ X0 )
= $true ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
? [X0: a,X2: a > a > $o,X1: a] :
( ? [X3: a > $o] :
( ( $true
!= ( X3 @ X0 ) )
& ! [X6: a] :
( ( ( X3 @ X6 )
= $true )
| ( ( X2 @ X1 @ X6 )
!= $true ) )
& ! [X5: a,X4: a] :
( ( ( X3 @ X5 )
= $true )
| ( ( X2 @ X4 @ X5 )
!= $true )
| ( ( X3 @ X4 )
!= $true ) ) )
& ( ( X2 @ X1 @ X0 )
= $true ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X0: a,X2: a > a > $o,X1: a] :
( ( ( X2 @ X1 @ X0 )
= $true )
=> ! [X3: a > $o] :
( ( ! [X6: a] :
( ( ( X2 @ X1 @ X6 )
= $true )
=> ( ( X3 @ X6 )
= $true ) )
& ! [X5: a,X4: a] :
( ( ( ( X2 @ X4 @ X5 )
= $true )
& ( ( X3 @ X4 )
= $true ) )
=> ( ( X3 @ X5 )
= $true ) ) )
=> ( $true
= ( X3 @ X0 ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: a,X1: a,X2: a > a > $o] :
( ( X2 @ X1 @ X0 )
=> ! [X3: a > $o] :
( ( ! [X4: a,X5: a] :
( ( ( X3 @ X4 )
& ( X2 @ X4 @ X5 ) )
=> ( X3 @ X5 ) )
& ! [X6: a] :
( ( X2 @ X1 @ X6 )
=> ( X3 @ X6 ) ) )
=> ( X3 @ X0 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X2: a,X1: a,X0: a > a > $o] :
( ( X0 @ X1 @ X2 )
=> ! [X3: a > $o] :
( ( ! [X5: a,X6: a] :
( ( ( X3 @ X5 )
& ( X0 @ X5 @ X6 ) )
=> ( X3 @ X6 ) )
& ! [X4: a] :
( ( X0 @ X1 @ X4 )
=> ( X3 @ X4 ) ) )
=> ( X3 @ X2 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X2: a,X1: a,X0: a > a > $o] :
( ( X0 @ X1 @ X2 )
=> ! [X3: a > $o] :
( ( ! [X5: a,X6: a] :
( ( ( X3 @ X5 )
& ( X0 @ X5 @ X6 ) )
=> ( X3 @ X6 ) )
& ! [X4: a] :
( ( X0 @ X1 @ X4 )
=> ( X3 @ X4 ) ) )
=> ( X3 @ X2 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.FUPAyY9zSH/DTF2THF_1577.p',cTHM151_pme) ).
thf(f17,plain,
( ( sK3 @ sK2 )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f16]) ).
thf(f16,plain,
( ( ( sK3 @ sK2 )
= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f13,f12]) ).
thf(f12,plain,
( $true
= ( sK0 @ sK1 @ sK2 ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f13,plain,
! [X6: a] :
( ( ( sK0 @ sK1 @ X6 )
!= $true )
| ( ( sK3 @ X6 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SEV135^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.10 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/0.30 % Computer : n013.cluster.edu
% 0.11/0.30 % Model : x86_64 x86_64
% 0.11/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.30 % Memory : 8042.1875MB
% 0.11/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.30 % CPULimit : 300
% 0.11/0.30 % WCLimit : 300
% 0.11/0.30 % DateTime : Tue Feb 24 12:40:23 EST 2026
% 0.11/0.30 % CPUTime :
% 0.11/0.30 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.39 ---- Original DTF file ---
% 0.16/0.39 thf(spec,logic,$$dhol).
% 0.16/0.39 %------------------------------------------------------------------------------
% 0.16/0.39 % File : SEV135^5 : TPTP v9.2.1. Released v4.0.0.
% 0.16/0.39 % Domain : Set Theory (Relations)
% 0.16/0.39 % Problem : TPS problem THM151
% 0.16/0.39 % Version : Especial.
% 0.16/0.39 % English :
% 0.16/0.39
% 0.16/0.39 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.16/0.39 % Source : [Bro09]
% 0.16/0.39 % Names : tps_0156 [Bro09]
% 0.16/0.39 % : THM151 [TPS]
% 0.16/0.39
% 0.16/0.39 % Status : Theorem
% 0.16/0.39 % Rating : 0.00 v6.2.0, 0.17 v6.1.0, 0.00 v4.0.0
% 0.16/0.39 % Syntax : Number of formulae : 2 ( 0 unt; 1 typ; 0 def)
% 0.16/0.39 % Number of atoms : 0 ( 0 equ; 0 cnn)
% 0.16/0.39 % Maximal formula atoms : 0 ( 0 avg)
% 0.16/0.39 % Number of connectives : 16 ( 0 ~; 0 |; 2 &; 10 @)
% 0.16/0.39 % ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% 0.16/0.39 % Maximal formula depth : 14 ( 14 avg)
% 0.16/0.39 % Number of types : 2 ( 1 usr)
% 0.16/0.39 % Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% 0.16/0.39 % Number of symbols : 0 ( 0 usr; 0 con; --- aty)
% 0.16/0.39 % Number of variables : 7 ( 0 ^; 7 !; 0 ?; 7 :)
% 0.16/0.39 % SPC : TH0_THM_NEQ_NAR
% 0.16/0.39
% 0.16/0.39 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.16/0.39 % project in the Department of Mathematical Sciences at Carnegie
% 0.16/0.39 % Mellon University. Distributed under the Creative Commons copyleft
% 0.16/0.39 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.16/0.39 % : Polymorphic definitions expanded.
% 0.16/0.39 %------------------------------------------------------------------------------
% 0.16/0.39 thf(a_type,type,
% 0.16/0.39 a: $tType ).
% 0.16/0.39
% 0.16/0.39 thf(cTHM151_pme,conjecture,
% 0.16/0.39 ! [Xr: a > a > $o,Xx: a,Xy: a] :
% 0.16/0.39 ( ( Xr @ Xx @ Xy )
% 0.16/0.39 => ! [Xq: a > $o] :
% 0.16/0.39 ( ( ! [Xw: a] :
% 0.16/0.39 ( ( Xr @ Xx @ Xw )
% 0.16/0.39 => ( Xq @ Xw ) )
% 0.16/0.39 & ! [Xu: a,Xv: a] :
% 0.16/0.39 ( ( ( Xq @ Xu )
% 0.16/0.39 & ( Xr @ Xu @ Xv ) )
% 0.16/0.39 => ( Xq @ Xv ) ) )
% 0.16/0.39 => ( Xq @ Xy ) ) ) ).
% 0.16/0.39
% 0.16/0.39 %------------------------------------------------------------------------------
% 0.16/0.39 ------------------------
% 1.51/1.33 ---- Embedded in THF ---
% 1.51/1.33 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.51/1.33 %%% Generated on Tue Feb 24 12:40:24 EST 2026
% 1.51/1.33 %%% using '$$dhol' embedding, version 1.3.0.
% 1.51/1.33 %%% Logic specification used:
% 1.51/1.33 %%% thf(spec, logic, $$dhol).
% 1.51/1.33
% 1.51/1.33 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.FUPAyY9zSH/DTF2DTF1577.p
% See solution above
% 1.51/1.33 ------------------------
% 1.51/1.34 ---- Cleaned THF ---
% 1.51/1.34 thf(a_type,type,
% 1.51/1.34 a: $tType ).
% 1.51/1.34
% 1.51/1.34 thf(cTHM151_pme,conjecture,
% 1.51/1.34 ! [Xr: a > a > $o,Xx: a,Xy: a] :
% 1.51/1.34 ( ( Xr @ Xx @ Xy )
% 1.51/1.34 => ! [Xq: a > $o] :
% 1.51/1.34 ( ( ! [Xw: a] :
% 1.51/1.34 ( ( Xr @ Xx @ Xw )
% 1.51/1.34 => ( Xq @ Xw ) )
% 1.51/1.34 & ! [Xu: a,Xv: a] :
% 1.51/1.34 ( ( ( Xq @ Xu )
% 1.51/1.34 & ( Xr @ Xu @ Xv ) )
% 1.51/1.34 => ( Xq @ Xv ) ) )
% 1.51/1.34 => ( Xq @ Xy ) ) ) ).
% 1.51/1.34 ------------------------
% 1.51/1.36 % (1681)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_1577 for (3000ds/275Mi)
% 1.51/1.36 % (1677)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_1577 for (3000ds/4Mi)
% 1.51/1.36 % (1679)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_1577 for (3000ds/2Mi)
% 1.51/1.36 % (1682)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_1577 for (3000ds/18Mi)
% 1.51/1.36 % (1680)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_1577 for (3000ds/2Mi)
% 1.51/1.36 % (1678)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_1577 for (3000ds/27Mi)
% 1.51/1.36 % (1676)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_1577 for (3000ds/183Mi)
% 1.51/1.36 % (1679)Instruction limit reached!
% 1.51/1.36 % (1679)------------------------------
% 1.51/1.36 % (1679)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.51/1.36 % (1679)Termination reason: Unknown
% 1.51/1.36 % (1679)Termination phase: Saturation
% 1.51/1.36 % (1680)Instruction limit reached!
% 1.51/1.36 % (1680)------------------------------
% 1.51/1.36 % (1680)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.51/1.36
% 1.51/1.36 % (1679)Memory used [KB]: 5373
% 1.51/1.36 % (1679)Time elapsed: 0.003 s
% 1.51/1.36 % (1679)Instructions burned: 2 (million)
% 1.51/1.36 % (1679)------------------------------
% 1.51/1.36 % (1679)------------------------------
% 1.51/1.36 % (1680)Termination reason: Unknown
% 1.51/1.36 % (1680)Termination phase: Saturation
% 1.51/1.36
% 1.51/1.36 % (1680)Memory used [KB]: 5373
% 1.51/1.36 % (1680)Time elapsed: 0.003 s
% 1.51/1.36 % (1680)Instructions burned: 2 (million)
% 1.51/1.36 % (1680)------------------------------
% 1.51/1.36 % (1680)------------------------------
% 1.51/1.36 % (1676)First to succeed.
% 1.51/1.36 % (1678)Also succeeded, but the first one will report.
% 1.51/1.36 % (1677)Also succeeded, but the first one will report.
% 1.51/1.36 % (1676)Refutation found. Thanks to Tanya!
% 1.51/1.36 % SZS status Theorem for DTF2THF_1577
% 1.51/1.36 % SZS output start Proof for DTF2THF_1577
% 1.51/1.36 thf(type_def_5, type, a: $tType).
% 1.51/1.36 thf(func_def_0, type, a: $tType).
% 1.51/1.36 thf(func_def_4, type, sK0: a > a > $o).
% 1.51/1.36 thf(func_def_5, type, sK1: a).
% 1.51/1.36 thf(func_def_6, type, sK2: a).
% 1.51/1.36 thf(func_def_7, type, sK3: a > $o).
% 1.51/1.36 thf(f18,plain,(
% 1.51/1.36 $false),
% 1.51/1.36 inference(subsumption_resolution,[status(thm)],[f17,f14])).
% 1.51/1.36 thf(f14,plain,(
% 1.51/1.36 ((sK3 @ sK2) != $true)),
% 1.51/1.36 inference(cnf_transformation,[status(thm)],[f11])).
% 1.51/1.36 thf(f11,plain,(
% 1.51/1.36 (! [X4 : a,X5 : a] : (((sK3 @ X4) = $true) | ((sK3 @ X5) != $true) | ($true != (sK0 @ X5 @ X4))) & ((sK3 @ sK2) != $true) & ! [X6 : a] : (((sK3 @ X6) = $true) | ((sK0 @ sK1 @ X6) != $true))) & ($true = (sK0 @ sK1 @ sK2))),
% 1.51/1.36 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f8,f10,f9])).
% 1.51/1.36 thf(f9,plain,(
% 1.51/1.36 ? [X0 : a > a > $o,X1 : a,X2 : a] : (? [X3 : a > $o] : (! [X4 : a,X5 : a] : (((X3 @ X4) = $true) | ((X3 @ X5) != $true) | ((X0 @ X5 @ X4) != $true)) & ((X3 @ X2) != $true) & ! [X6 : a] : (((X3 @ X6) = $true) | ((X0 @ X1 @ X6) != $true))) & ((X0 @ X1 @ X2) = $true)) => (? [X3 : a > $o] : (! [X5 : a,X4 : a] : (((X3 @ X4) = $true) | ((X3 @ X5) != $true) | ($true != (sK0 @ X5 @ X4))) & ((X3 @ sK2) != $true) & ! [X6 : a] : (((X3 @ X6) = $true) | ((sK0 @ sK1 @ X6) != $true))) & ($true = (sK0 @ sK1 @ sK2)))),
% 1.51/1.36 introduced(definition,[],[choice_axiom])).
% 1.51/1.36 thf(f10,plain,(
% 1.51/1.36 ? [X3 : a > $o] : (! [X5 : a,X4 : a] : (((X3 @ X4) = $true) | ((X3 @ X5) != $true) | ($true != (sK0 @ X5 @ X4))) & ((X3 @ sK2) != $true) & ! [X6 : a] : (((X3 @ X6) = $true) | ((sK0 @ sK1 @ X6) != $true))) => (! [X5 : a,X4 : a] : (((sK3 @ X4) = $true) | ((sK3 @ X5) != $true) | ($true != (sK0 @ X5 @ X4))) & ((sK3 @ sK2) != $true) & ! [X6 : a] : (((sK3 @ X6) = $true) | ((sK0 @ sK1 @ X6) != $true)))),
% 1.51/1.36 introduced(definition,[],[choice_axiom])).
% 1.51/1.36 thf(f8,plain,(
% 1.51/1.36 ? [X0 : a > a > $o,X1 : a,X2 : a] : (? [X3 : a > $o] : (! [X4 : a,X5 : a] : (((X3 @ X4) = $true) | ((X3 @ X5) != $true) | ((X0 @ X5 @ X4) != $true)) & ((X3 @ X2) != $true) & ! [X6 : a] : (((X3 @ X6) = $true) | ((X0 @ X1 @ X6) != $true))) & ((X0 @ X1 @ X2) = $true))),
% 1.51/1.36 inference(rectify,[status(thm)],[f7])).
% 1.51/1.36 thf(f7,plain,(
% 1.51/1.36 ? [X2 : a > a > $o,X1 : a,X0 : a] : (? [X3 : a > $o] : (! [X5 : a,X4 : a] : (((X3 @ X5) = $true) | ((X3 @ X4) != $true) | ((X2 @ X4 @ X5) != $true)) & ($true != (X3 @ X0)) & ! [X6 : a] : (((X3 @ X6) = $true) | ((X2 @ X1 @ X6) != $true))) & ((X2 @ X1 @ X0) = $true))),
% 1.51/1.36 inference(flattening,[status(thm)],[f6])).
% 1.51/1.36 thf(f6,plain,(
% 1.51/1.36 ? [X0 : a,X2 : a > a > $o,X1 : a] : (? [X3 : a > $o] : (($true != (X3 @ X0)) & (! [X6 : a] : (((X3 @ X6) = $true) | ((X2 @ X1 @ X6) != $true)) & ! [X5 : a,X4 : a] : (((X3 @ X5) = $true) | (((X2 @ X4 @ X5) != $true) | ((X3 @ X4) != $true))))) & ((X2 @ X1 @ X0) = $true))),
% 1.51/1.36 inference(ennf_transformation,[status(thm)],[f5])).
% 1.51/1.36 thf(f5,plain,(
% 1.51/1.36 ~! [X0 : a,X2 : a > a > $o,X1 : a] : (((X2 @ X1 @ X0) = $true) => ! [X3 : a > $o] : ((! [X6 : a] : (((X2 @ X1 @ X6) = $true) => ((X3 @ X6) = $true)) & ! [X5 : a,X4 : a] : ((((X2 @ X4 @ X5) = $true) & ((X3 @ X4) = $true)) => ((X3 @ X5) = $true))) => ($true = (X3 @ X0))))),
% 1.51/1.36 inference(fool_elimination,[status(thm)],[f4])).
% 1.51/1.36 thf(f4,plain,(
% 1.51/1.36 ~! [X0 : a,X1 : a,X2 : a > a > $o] : ((X2 @ X1 @ X0) => ! [X3 : a > $o] : ((! [X4 : a,X5 : a] : (((X3 @ X4) & (X2 @ X4 @ X5)) => (X3 @ X5)) & ! [X6 : a] : ((X2 @ X1 @ X6) => (X3 @ X6))) => (X3 @ X0)))),
% 1.51/1.36 inference(rectify,[status(thm)],[f2])).
% 1.51/1.36 thf(f2,negated_conjecture,(
% 1.51/1.36 ~! [X2 : a,X1 : a,X0 : a > a > $o] : ((X0 @ X1 @ X2) => ! [X3 : a > $o] : ((! [X5 : a,X6 : a] : (((X3 @ X5) & (X0 @ X5 @ X6)) => (X3 @ X6)) & ! [X4 : a] : ((X0 @ X1 @ X4) => (X3 @ X4))) => (X3 @ X2)))),
% 1.51/1.36 inference(negated_conjecture,[status(cth)],[f1])).
% 1.51/1.36 thf(f1,conjecture,(
% 1.51/1.36 ! [X2 : a,X1 : a,X0 : a > a > $o] : ((X0 @ X1 @ X2) => ! [X3 : a > $o] : ((! [X5 : a,X6 : a] : (((X3 @ X5) & (X0 @ X5 @ X6)) => (X3 @ X6)) & ! [X4 : a] : ((X0 @ X1 @ X4) => (X3 @ X4))) => (X3 @ X2)))),
% 1.51/1.36 file('/export/starexec/sandbox/tmp/tmp.FUPAyY9zSH/DTF2THF_1577.p',cTHM151_pme)).
% 1.51/1.36 thf(f17,plain,(
% 1.51/1.36 ((sK3 @ sK2) = $true)),
% 1.51/1.36 inference(trivial_inequality_removal,[status(thm)],[f16])).
% 1.51/1.36 thf(f16,plain,(
% 1.51/1.36 ((sK3 @ sK2) = $true) | ($true != $true)),
% 1.51/1.36 inference(superposition,[status(thm)],[f13,f12])).
% 1.51/1.36 thf(f12,plain,(
% 1.51/1.36 ($true = (sK0 @ sK1 @ sK2))),
% 1.51/1.36 inference(cnf_transformation,[status(thm)],[f11])).
% 1.51/1.36 thf(f13,plain,(
% 1.51/1.36 ( ! [X6 : a] : (((sK0 @ sK1 @ X6) != $true) | ((sK3 @ X6) = $true)) )),
% 1.51/1.36 inference(cnf_transformation,[status(thm)],[f11])).
% 1.51/1.36 % SZS output end Proof for DTF2THF_1577
% 1.51/1.36 % (1676)------------------------------
% 1.51/1.36 % (1676)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.51/1.36 % (1676)Termination reason: Refutation
% 1.51/1.36
% 1.51/1.36 % (1676)Memory used [KB]: 5500
% 1.51/1.36 % (1676)Time elapsed: 0.004 s
% 1.51/1.36 % (1676)Instructions burned: 2 (million)
% 1.51/1.36 % (1676)------------------------------
% 1.51/1.36 % (1676)------------------------------
% 1.51/1.36 % (1675)Success in time 0.017 s
%------------------------------------------------------------------------------