%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV230^5 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n001.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 09:40:37 AM UTC 2026
% Result : Theorem 1.53s 1.21s
% Output : Refutation 1.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 23 ( 6 unt; 0 typ; 0 def)
% Number of atoms : 226 ( 89 equ; 0 cnn)
% Maximal formula atoms : 16 ( 9 avg)
% Number of connectives : 247 ( 46 ~; 27 |; 32 &; 110 @)
% ( 0 <=>; 32 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 55 ( 55 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 83 ( 0 ^; 56 !; 27 ?; 83 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_4,type,
sK0: a > $o ).
thf(func_def_5,type,
sK1: a > $o ).
thf(func_def_6,type,
sK2: ( a > $o ) > $o ).
thf(func_def_7,type,
sK3: a > $o ).
thf(func_def_8,type,
sK4: a ).
thf(func_def_11,type,
ph6:
!>[X0: $tType] : X0 ).
thf(f24,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f23,f14]) ).
thf(f14,plain,
( $true
= ( sK3 @ sK4 ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
( ! [X2: a] :
( ( ( sK0 @ X2 )
!= $true )
| ( ( sK1 @ X2 )
= $true ) )
& ! [X4: a > $o] :
( ! [X5: a] :
( ( ( sK0 @ X5 )
= $true )
| ( $true
!= ( X4 @ X5 ) ) )
| ( ( sK2 @ X4 )
!= $true ) )
& ( ( sK1 @ sK4 )
!= $true )
& ( $true
= ( sK3 @ sK4 ) )
& ( ( sK2 @ sK3 )
= $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4])],[f7,f11,f10,f9,f8]) ).
thf(f8,plain,
( ? [X0: a > $o,X1: a > $o] :
( ! [X2: a] :
( ( ( X0 @ X2 )
!= $true )
| ( ( X1 @ X2 )
= $true ) )
& ? [X3: ( a > $o ) > $o] :
( ! [X4: a > $o] :
( ! [X5: a] :
( ( ( X0 @ X5 )
= $true )
| ( $true
!= ( X4 @ X5 ) ) )
| ( $true
!= ( X3 @ X4 ) ) )
& ? [X6: a > $o] :
( ? [X7: a] :
( ( ( X1 @ X7 )
!= $true )
& ( ( X6 @ X7 )
= $true ) )
& ( ( X3 @ X6 )
= $true ) ) ) )
=> ( ! [X2: a] :
( ( ( sK0 @ X2 )
!= $true )
| ( ( sK1 @ X2 )
= $true ) )
& ? [X3: ( a > $o ) > $o] :
( ! [X4: a > $o] :
( ! [X5: a] :
( ( ( sK0 @ X5 )
= $true )
| ( $true
!= ( X4 @ X5 ) ) )
| ( $true
!= ( X3 @ X4 ) ) )
& ? [X6: a > $o] :
( ? [X7: a] :
( ( ( sK1 @ X7 )
!= $true )
& ( ( X6 @ X7 )
= $true ) )
& ( ( X3 @ X6 )
= $true ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f9,plain,
( ? [X3: ( a > $o ) > $o] :
( ! [X4: a > $o] :
( ! [X5: a] :
( ( ( sK0 @ X5 )
= $true )
| ( $true
!= ( X4 @ X5 ) ) )
| ( $true
!= ( X3 @ X4 ) ) )
& ? [X6: a > $o] :
( ? [X7: a] :
( ( ( sK1 @ X7 )
!= $true )
& ( ( X6 @ X7 )
= $true ) )
& ( ( X3 @ X6 )
= $true ) ) )
=> ( ! [X4: a > $o] :
( ! [X5: a] :
( ( ( sK0 @ X5 )
= $true )
| ( $true
!= ( X4 @ X5 ) ) )
| ( ( sK2 @ X4 )
!= $true ) )
& ? [X6: a > $o] :
( ? [X7: a] :
( ( ( sK1 @ X7 )
!= $true )
& ( ( X6 @ X7 )
= $true ) )
& ( $true
= ( sK2 @ X6 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f10,plain,
( ? [X6: a > $o] :
( ? [X7: a] :
( ( ( sK1 @ X7 )
!= $true )
& ( ( X6 @ X7 )
= $true ) )
& ( $true
= ( sK2 @ X6 ) ) )
=> ( ? [X7: a] :
( ( ( sK1 @ X7 )
!= $true )
& ( ( sK3 @ X7 )
= $true ) )
& ( ( sK2 @ sK3 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f11,plain,
( ? [X7: a] :
( ( ( sK1 @ X7 )
!= $true )
& ( ( sK3 @ X7 )
= $true ) )
=> ( ( ( sK1 @ sK4 )
!= $true )
& ( $true
= ( sK3 @ sK4 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f7,plain,
? [X0: a > $o,X1: a > $o] :
( ! [X2: a] :
( ( ( X0 @ X2 )
!= $true )
| ( ( X1 @ X2 )
= $true ) )
& ? [X3: ( a > $o ) > $o] :
( ! [X4: a > $o] :
( ! [X5: a] :
( ( ( X0 @ X5 )
= $true )
| ( $true
!= ( X4 @ X5 ) ) )
| ( $true
!= ( X3 @ X4 ) ) )
& ? [X6: a > $o] :
( ? [X7: a] :
( ( ( X1 @ X7 )
!= $true )
& ( ( X6 @ X7 )
= $true ) )
& ( ( X3 @ X6 )
= $true ) ) ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,plain,
? [X1: a > $o,X0: a > $o] :
( ! [X2: a] :
( ( ( X1 @ X2 )
!= $true )
| ( ( X0 @ X2 )
= $true ) )
& ? [X3: ( a > $o ) > $o] :
( ! [X4: a > $o] :
( ! [X5: a] :
( ( ( X1 @ X5 )
= $true )
| ( $true
!= ( X4 @ X5 ) ) )
| ( $true
!= ( X3 @ X4 ) ) )
& ? [X6: a > $o] :
( ? [X7: a] :
( ( $true
!= ( X0 @ X7 ) )
& ( ( X6 @ X7 )
= $true ) )
& ( ( X3 @ X6 )
= $true ) ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X1: a > $o,X0: a > $o] :
( ! [X2: a] :
( ( ( X1 @ X2 )
= $true )
=> ( ( X0 @ X2 )
= $true ) )
=> ! [X3: ( a > $o ) > $o] :
( ! [X4: a > $o] :
( ( $true
= ( X3 @ X4 ) )
=> ! [X5: a] :
( ( $true
= ( X4 @ X5 ) )
=> ( ( X1 @ X5 )
= $true ) ) )
=> ! [X6: a > $o] :
( ( ( X3 @ X6 )
= $true )
=> ! [X7: a] :
( ( ( X6 @ X7 )
= $true )
=> ( $true
= ( X0 @ X7 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: a > $o,X1: a > $o] :
( ! [X2: a] :
( ( X1 @ X2 )
=> ( X0 @ X2 ) )
=> ! [X3: ( a > $o ) > $o] :
( ! [X4: a > $o] :
( ( X3 @ X4 )
=> ! [X5: a] :
( ( X4 @ X5 )
=> ( X1 @ X5 ) ) )
=> ! [X6: a > $o] :
( ( X3 @ X6 )
=> ! [X7: a] :
( ( X6 @ X7 )
=> ( X0 @ X7 ) ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X1: a > $o,X0: a > $o] :
( ! [X2: a] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) )
=> ! [X2: ( a > $o ) > $o] :
( ! [X3: a > $o] :
( ( X2 @ X3 )
=> ! [X4: a] :
( ( X3 @ X4 )
=> ( X0 @ X4 ) ) )
=> ! [X3: a > $o] :
( ( X2 @ X3 )
=> ! [X4: a] :
( ( X3 @ X4 )
=> ( X1 @ X4 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X1: a > $o,X0: a > $o] :
( ! [X2: a] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) )
=> ! [X2: ( a > $o ) > $o] :
( ! [X3: a > $o] :
( ( X2 @ X3 )
=> ! [X4: a] :
( ( X3 @ X4 )
=> ( X0 @ X4 ) ) )
=> ! [X3: a > $o] :
( ( X2 @ X3 )
=> ! [X4: a] :
( ( X3 @ X4 )
=> ( X1 @ X4 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.LbWT5Y56ZO/DTF2THF_11675.p',cTHM88_pme) ).
thf(f23,plain,
( $true
!= ( sK3 @ sK4 ) ),
inference(trivial_inequality_removal,[status(thm)],[f22]) ).
thf(f22,plain,
( ( $true != $true )
| ( $true
!= ( sK3 @ sK4 ) ) ),
inference(superposition,[status(thm)],[f19,f21]) ).
thf(f21,plain,
! [X0: a] :
( ( $true
= ( sK0 @ X0 ) )
| ( $true
!= ( sK3 @ X0 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f20]) ).
thf(f20,plain,
! [X0: a] :
( ( $true
!= ( sK3 @ X0 ) )
| ( $true != $true )
| ( $true
= ( sK0 @ X0 ) ) ),
inference(superposition,[status(thm)],[f16,f13]) ).
thf(f13,plain,
( ( sK2 @ sK3 )
= $true ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f16,plain,
! [X4: a > $o,X5: a] :
( ( ( sK2 @ X4 )
!= $true )
| ( ( sK0 @ X5 )
= $true )
| ( $true
!= ( X4 @ X5 ) ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f19,plain,
( ( sK0 @ sK4 )
!= $true ),
inference(trivial_inequality_removal,[status(thm)],[f18]) ).
thf(f18,plain,
( ( $true != $true )
| ( ( sK0 @ sK4 )
!= $true ) ),
inference(superposition,[status(thm)],[f15,f17]) ).
thf(f17,plain,
! [X2: a] :
( ( ( sK1 @ X2 )
= $true )
| ( ( sK0 @ X2 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f15,plain,
( ( sK1 @ sK4 )
!= $true ),
inference(cnf_transformation,[status(thm)],[f12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SEV230^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.11 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.14/0.31 % Computer : n001.cluster.edu
% 0.14/0.31 % Model : x86_64 x86_64
% 0.14/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.31 % Memory : 8042.1875MB
% 0.14/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.31 % CPULimit : 300
% 0.14/0.31 % WCLimit : 300
% 0.14/0.31 % DateTime : Tue Feb 24 12:43:05 EST 2026
% 0.14/0.31 % CPUTime :
% 0.14/0.31 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.20/0.42 ---- Original DTF file ---
% 0.20/0.42 thf(spec,logic,$$dhol).
% 0.20/0.42 %------------------------------------------------------------------------------
% 0.20/0.42 % File : SEV230^5 : TPTP v9.2.1. Released v4.0.0.
% 0.20/0.42 % Domain : Set Theory (Sets of sets)
% 0.20/0.42 % Problem : TPS problem THM88
% 0.20/0.42 % Version : Especial.
% 0.20/0.42 % English :
% 0.20/0.42
% 0.20/0.42 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.20/0.42 % Source : [Bro09]
% 0.20/0.42 % Names : tps_0320 [Bro09]
% 0.20/0.42 % : THM88 [TPS]
% 0.20/0.42
% 0.20/0.42 % Status : Theorem
% 0.20/0.42 % Rating : 0.00 v8.1.0, 0.08 v7.4.0, 0.00 v6.2.0, 0.17 v6.1.0, 0.00 v5.1.0, 0.25 v5.0.0, 0.00 v4.0.0
% 0.20/0.42 % Syntax : Number of formulae : 2 ( 0 unt; 1 typ; 0 def)
% 0.20/0.42 % Number of atoms : 0 ( 0 equ; 0 cnn)
% 0.20/0.42 % Maximal formula atoms : 0 ( 0 avg)
% 0.20/0.42 % Number of connectives : 15 ( 0 ~; 0 |; 0 &; 8 @)
% 0.20/0.42 % ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% 0.20/0.42 % Maximal formula depth : 11 ( 11 avg)
% 0.20/0.42 % Number of types : 2 ( 1 usr)
% 0.20/0.42 % Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% 0.20/0.42 % Number of symbols : 0 ( 0 usr; 0 con; --- aty)
% 0.20/0.42 % Number of variables : 8 ( 0 ^; 8 !; 0 ?; 8 :)
% 0.20/0.42 % SPC : TH0_THM_NEQ_NAR
% 0.20/0.42
% 0.20/0.42 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.20/0.42 % project in the Department of Mathematical Sciences at Carnegie
% 0.20/0.42 % Mellon University. Distributed under the Creative Commons copyleft
% 0.20/0.42 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.20/0.42 % : Polymorphic definitions expanded.
% 0.20/0.42 %------------------------------------------------------------------------------
% 0.20/0.42 thf(a_type,type,
% 0.20/0.42 a: $tType ).
% 0.20/0.42
% 0.20/0.42 thf(cTHM88_pme,conjecture,
% 0.20/0.42 ! [U: a > $o,V: a > $o] :
% 0.20/0.42 ( ! [Xx: a] :
% 0.20/0.42 ( ( U @ Xx )
% 0.20/0.42 => ( V @ Xx ) )
% 0.20/0.42 => ! [Xx: ( a > $o ) > $o] :
% 0.20/0.42 ( ! [Xx0: a > $o] :
% 0.20/0.42 ( ( Xx @ Xx0 )
% 0.20/0.42 => ! [Xx1: a] :
% 0.20/0.42 ( ( Xx0 @ Xx1 )
% 0.20/0.42 => ( U @ Xx1 ) ) )
% 0.20/0.42 => ! [Xx0: a > $o] :
% 0.20/0.42 ( ( Xx @ Xx0 )
% 0.20/0.42 => ! [Xx1: a] :
% 0.20/0.42 ( ( Xx0 @ Xx1 )
% 0.20/0.42 => ( V @ Xx1 ) ) ) ) ) ).
% 0.20/0.42
% 0.20/0.42 %------------------------------------------------------------------------------
% 0.20/0.42 ------------------------
% 1.37/1.18 ---- Embedded in THF ---
% 1.37/1.18 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.37/1.18 %%% Generated on Tue Feb 24 12:43:06 EST 2026
% 1.37/1.18 %%% using '$$dhol' embedding, version 1.3.0.
% 1.37/1.18 %%% Logic specification used:
% 1.37/1.18 %%% thf(spec, logic, $$dhol).
% 1.37/1.18
% 1.37/1.18 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.LbWT5Y56ZO/DTF2DTF11675.p
% See solution above
% 1.37/1.18 ------------------------
% 1.37/1.19 ---- Cleaned THF ---
% 1.37/1.19 thf(a_type,type,
% 1.37/1.19 a: $tType ).
% 1.37/1.19
% 1.37/1.19 thf(cTHM88_pme,conjecture,
% 1.37/1.19 ! [U: a > $o,V: a > $o] :
% 1.37/1.19 ( ! [Xx: a] :
% 1.37/1.19 ( ( U @ Xx )
% 1.37/1.19 => ( V @ Xx ) )
% 1.37/1.19 => ! [Xx: ( a > $o ) > $o] :
% 1.37/1.19 ( ! [Xx0: a > $o] :
% 1.37/1.19 ( ( Xx @ Xx0 )
% 1.37/1.19 => ! [Xx1: a] :
% 1.37/1.19 ( ( Xx0 @ Xx1 )
% 1.37/1.19 => ( U @ Xx1 ) ) )
% 1.37/1.19 => ! [Xx0: a > $o] :
% 1.37/1.19 ( ( Xx @ Xx0 )
% 1.37/1.19 => ! [Xx1: a] :
% 1.37/1.19 ( ( Xx0 @ Xx1 )
% 1.37/1.19 => ( V @ Xx1 ) ) ) ) ) ).
% 1.37/1.19 ------------------------
% 1.53/1.21 % (11843)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_11675 for (2999ds/183Mi)
% 1.53/1.21 % (11848)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_11675 for (2999ds/275Mi)
% 1.53/1.21 % (11843)First to succeed.
% 1.53/1.21 % (11848)Also succeeded, but the first one will report.
% 1.53/1.21 % (11843)Refutation found. Thanks to Tanya!
% 1.53/1.21 % SZS status Theorem for DTF2THF_11675
% 1.53/1.21 % SZS output start Proof for DTF2THF_11675
% 1.53/1.21 thf(type_def_5, type, a: $tType).
% 1.53/1.21 thf(func_def_0, type, a: $tType).
% 1.53/1.21 thf(func_def_4, type, sK0: a > $o).
% 1.53/1.21 thf(func_def_5, type, sK1: a > $o).
% 1.53/1.21 thf(func_def_6, type, sK2: (a > $o) > $o).
% 1.53/1.21 thf(func_def_7, type, sK3: a > $o).
% 1.53/1.21 thf(func_def_8, type, sK4: a).
% 1.53/1.21 thf(func_def_11, type, ph6: !>[X0: $tType]:(X0)).
% 1.53/1.21 thf(f24,plain,(
% 1.53/1.21 $false),
% 1.53/1.21 inference(subsumption_resolution,[status(thm)],[f23,f14])).
% 1.53/1.21 thf(f14,plain,(
% 1.53/1.21 ($true = (sK3 @ sK4))),
% 1.53/1.21 inference(cnf_transformation,[status(thm)],[f12])).
% 1.53/1.21 thf(f12,plain,(
% 1.53/1.21 ! [X2 : a] : (((sK0 @ X2) != $true) | ((sK1 @ X2) = $true)) & (! [X4 : a > $o] : (! [X5 : a] : (((sK0 @ X5) = $true) | ($true != (X4 @ X5))) | ((sK2 @ X4) != $true)) & ((((sK1 @ sK4) != $true) & ($true = (sK3 @ sK4))) & ((sK2 @ sK3) = $true)))),
% 1.53/1.21 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4])],[f7,f11,f10,f9,f8])).
% 1.53/1.21 thf(f8,plain,(
% 1.53/1.21 ? [X0 : a > $o,X1 : a > $o] : (! [X2 : a] : (((X0 @ X2) != $true) | ((X1 @ X2) = $true)) & ? [X3 : (a > $o) > $o] : (! [X4 : a > $o] : (! [X5 : a] : (((X0 @ X5) = $true) | ($true != (X4 @ X5))) | ($true != (X3 @ X4))) & ? [X6 : a > $o] : (? [X7 : a] : (((X1 @ X7) != $true) & ((X6 @ X7) = $true)) & ((X3 @ X6) = $true)))) => (! [X2 : a] : (((sK0 @ X2) != $true) | ((sK1 @ X2) = $true)) & ? [X3 : (a > $o) > $o] : (! [X4 : a > $o] : (! [X5 : a] : (((sK0 @ X5) = $true) | ($true != (X4 @ X5))) | ($true != (X3 @ X4))) & ? [X6 : a > $o] : (? [X7 : a] : (((sK1 @ X7) != $true) & ((X6 @ X7) = $true)) & ((X3 @ X6) = $true))))),
% 1.53/1.21 introduced(definition,[],[choice_axiom])).
% 1.53/1.21 thf(f9,plain,(
% 1.53/1.21 ? [X3 : (a > $o) > $o] : (! [X4 : a > $o] : (! [X5 : a] : (((sK0 @ X5) = $true) | ($true != (X4 @ X5))) | ($true != (X3 @ X4))) & ? [X6 : a > $o] : (? [X7 : a] : (((sK1 @ X7) != $true) & ((X6 @ X7) = $true)) & ((X3 @ X6) = $true))) => (! [X4 : a > $o] : (! [X5 : a] : (((sK0 @ X5) = $true) | ($true != (X4 @ X5))) | ((sK2 @ X4) != $true)) & ? [X6 : a > $o] : (? [X7 : a] : (((sK1 @ X7) != $true) & ((X6 @ X7) = $true)) & ($true = (sK2 @ X6))))),
% 1.53/1.21 introduced(definition,[],[choice_axiom])).
% 1.53/1.21 thf(f10,plain,(
% 1.53/1.21 ? [X6 : a > $o] : (? [X7 : a] : (((sK1 @ X7) != $true) & ((X6 @ X7) = $true)) & ($true = (sK2 @ X6))) => (? [X7 : a] : (((sK1 @ X7) != $true) & ((sK3 @ X7) = $true)) & ((sK2 @ sK3) = $true))),
% 1.53/1.21 introduced(definition,[],[choice_axiom])).
% 1.53/1.21 thf(f11,plain,(
% 1.53/1.21 ? [X7 : a] : (((sK1 @ X7) != $true) & ((sK3 @ X7) = $true)) => (((sK1 @ sK4) != $true) & ($true = (sK3 @ sK4)))),
% 1.53/1.21 introduced(definition,[],[choice_axiom])).
% 1.53/1.21 thf(f7,plain,(
% 1.53/1.21 ? [X0 : a > $o,X1 : a > $o] : (! [X2 : a] : (((X0 @ X2) != $true) | ((X1 @ X2) = $true)) & ? [X3 : (a > $o) > $o] : (! [X4 : a > $o] : (! [X5 : a] : (((X0 @ X5) = $true) | ($true != (X4 @ X5))) | ($true != (X3 @ X4))) & ? [X6 : a > $o] : (? [X7 : a] : (((X1 @ X7) != $true) & ((X6 @ X7) = $true)) & ((X3 @ X6) = $true))))),
% 1.53/1.21 inference(rectify,[status(thm)],[f6])).
% 1.53/1.21 thf(f6,plain,(
% 1.53/1.21 ? [X1 : a > $o,X0 : a > $o] : (! [X2 : a] : (((X1 @ X2) != $true) | ((X0 @ X2) = $true)) & ? [X3 : (a > $o) > $o] : (! [X4 : a > $o] : (! [X5 : a] : (((X1 @ X5) = $true) | ($true != (X4 @ X5))) | ($true != (X3 @ X4))) & ? [X6 : a > $o] : (? [X7 : a] : (($true != (X0 @ X7)) & ((X6 @ X7) = $true)) & ((X3 @ X6) = $true))))),
% 1.53/1.21 inference(ennf_transformation,[status(thm)],[f5])).
% 1.53/1.21 thf(f5,plain,(
% 1.53/1.21 ~! [X1 : a > $o,X0 : a > $o] : (! [X2 : a] : (((X1 @ X2) = $true) => ((X0 @ X2) = $true)) => ! [X3 : (a > $o) > $o] : (! [X4 : a > $o] : (($true = (X3 @ X4)) => ! [X5 : a] : (($true = (X4 @ X5)) => ((X1 @ X5) = $true))) => ! [X6 : a > $o] : (((X3 @ X6) = $true) => ! [X7 : a] : (((X6 @ X7) = $true) => ($true = (X0 @ X7))))))),
% 1.53/1.21 inference(fool_elimination,[status(thm)],[f4])).
% 1.53/1.21 thf(f4,plain,(
% 1.53/1.21 ~! [X0 : a > $o,X1 : a > $o] : (! [X2 : a] : ((X1 @ X2) => (X0 @ X2)) => ! [X3 : (a > $o) > $o] : (! [X4 : a > $o] : ((X3 @ X4) => ! [X5 : a] : ((X4 @ X5) => (X1 @ X5))) => ! [X6 : a > $o] : ((X3 @ X6) => ! [X7 : a] : ((X6 @ X7) => (X0 @ X7)))))),
% 1.53/1.21 inference(rectify,[status(thm)],[f2])).
% 1.53/1.21 thf(f2,negated_conjecture,(
% 1.53/1.21 ~! [X1 : a > $o,X0 : a > $o] : (! [X2 : a] : ((X0 @ X2) => (X1 @ X2)) => ! [X2 : (a > $o) > $o] : (! [X3 : a > $o] : ((X2 @ X3) => ! [X4 : a] : ((X3 @ X4) => (X0 @ X4))) => ! [X3 : a > $o] : ((X2 @ X3) => ! [X4 : a] : ((X3 @ X4) => (X1 @ X4)))))),
% 1.53/1.21 inference(negated_conjecture,[status(cth)],[f1])).
% 1.53/1.21 thf(f1,conjecture,(
% 1.53/1.21 ! [X1 : a > $o,X0 : a > $o] : (! [X2 : a] : ((X0 @ X2) => (X1 @ X2)) => ! [X2 : (a > $o) > $o] : (! [X3 : a > $o] : ((X2 @ X3) => ! [X4 : a] : ((X3 @ X4) => (X0 @ X4))) => ! [X3 : a > $o] : ((X2 @ X3) => ! [X4 : a] : ((X3 @ X4) => (X1 @ X4)))))),
% 1.53/1.21 file('/export/starexec/sandbox2/tmp/tmp.LbWT5Y56ZO/DTF2THF_11675.p',cTHM88_pme)).
% 1.53/1.21 thf(f23,plain,(
% 1.53/1.21 ($true != (sK3 @ sK4))),
% 1.53/1.21 inference(trivial_inequality_removal,[status(thm)],[f22])).
% 1.53/1.21 thf(f22,plain,(
% 1.53/1.21 ($true != $true) | ($true != (sK3 @ sK4))),
% 1.53/1.21 inference(superposition,[status(thm)],[f19,f21])).
% 1.53/1.21 thf(f21,plain,(
% 1.53/1.21 ( ! [X0 : a] : (($true = (sK0 @ X0)) | ($true != (sK3 @ X0))) )),
% 1.53/1.21 inference(trivial_inequality_removal,[status(thm)],[f20])).
% 1.53/1.21 thf(f20,plain,(
% 1.53/1.21 ( ! [X0 : a] : (($true != (sK3 @ X0)) | ($true != $true) | ($true = (sK0 @ X0))) )),
% 1.53/1.21 inference(superposition,[status(thm)],[f16,f13])).
% 1.53/1.21 thf(f13,plain,(
% 1.53/1.21 ((sK2 @ sK3) = $true)),
% 1.53/1.21 inference(cnf_transformation,[status(thm)],[f12])).
% 1.53/1.21 thf(f16,plain,(
% 1.53/1.21 ( ! [X4 : a > $o,X5 : a] : (((sK2 @ X4) != $true) | ((sK0 @ X5) = $true) | ($true != (X4 @ X5))) )),
% 1.53/1.21 inference(cnf_transformation,[status(thm)],[f12])).
% 1.53/1.21 thf(f19,plain,(
% 1.53/1.21 ((sK0 @ sK4) != $true)),
% 1.53/1.21 inference(trivial_inequality_removal,[status(thm)],[f18])).
% 1.53/1.21 thf(f18,plain,(
% 1.53/1.21 ($true != $true) | ((sK0 @ sK4) != $true)),
% 1.53/1.21 inference(superposition,[status(thm)],[f15,f17])).
% 1.53/1.21 thf(f17,plain,(
% 1.53/1.21 ( ! [X2 : a] : (((sK1 @ X2) = $true) | ((sK0 @ X2) != $true)) )),
% 1.53/1.21 inference(cnf_transformation,[status(thm)],[f12])).
% 1.53/1.21 thf(f15,plain,(
% 1.53/1.21 ((sK1 @ sK4) != $true)),
% 1.53/1.21 inference(cnf_transformation,[status(thm)],[f12])).
% 1.53/1.21 % SZS output end Proof for DTF2THF_11675
% 1.53/1.21 % (11843)------------------------------
% 1.53/1.21 % (11843)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.21 % (11843)Termination reason: Refutation
% 1.53/1.21
% 1.53/1.21 % (11843)Memory used [KB]: 5500
% 1.53/1.21 % (11843)Time elapsed: 0.003 s
% 1.53/1.21 % (11843)Instructions burned: 2 (million)
% 1.53/1.21 % (11843)------------------------------
% 1.53/1.21 % (11843)------------------------------
% 1.53/1.21 % (11842)Success in time 0.014 s
%------------------------------------------------------------------------------