%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV122^5 : 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 : n009.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 09:40:20 AM UTC 2026
% Result : Theorem 0.32s 1.23s
% Output : Refutation 0.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 2
% Syntax : Number of formulae : 10 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 73 ( 10 equ; 0 cnn)
% Maximal formula atoms : 2 ( 7 avg)
% Number of connectives : 378 ( 9 ~; 0 |; 20 &; 252 @)
% ( 0 <=>; 41 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 163 ( 163 >; 0 *; 0 +; 0 <<)
% Number of symbols : 5 ( 1 usr; 3 con; 0-2 aty)
% ( 42 !!; 14 ??; 0 @@+; 0 @@-)
% Number of variables : 129 ( 96 ^; 25 !; 8 ?; 129 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_12,type,
sK0: ( a > a > $o ) > $o ).
thf(f11,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f10]) ).
thf(f10,plain,
( ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK0 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y5: a > a > $o] : ( Y5 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
!= ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK0 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y5: a > a > $o] : ( Y5 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK0 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y5: a > a > $o] : ( Y5 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
!= ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK0 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y5: a > a > $o] : ( Y5 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f7,f8]) ).
thf(f8,plain,
( ? [X0: ( a > a > $o ) > $o] :
( ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( X0 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y5: a > a > $o] : ( Y5 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
!= ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( X0 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y5: a > a > $o] : ( Y5 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) )
=> ( ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK0 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y5: a > a > $o] : ( Y5 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
!= ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK0 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y5: a > a > $o] : ( Y5 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f7,plain,
? [X0: ( a > a > $o ) > $o] :
( ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( X0 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y5: a > a > $o] : ( Y5 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
!= ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( X0 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y5: a > a > $o] : ( Y5 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ),
inference(ennf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
~ ! [X0: ( a > a > $o ) > $o] :
( ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( X0 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y5: a > a > $o] : ( Y5 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
= ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( X0 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y5: a > a > $o] : ( Y5 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X1: ( a > a > $o ) > $o] :
( ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( X1 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y5: a > a > $o] : ( Y5 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
= ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( X1 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y5: a > a > $o] : ( Y5 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X1: ( a > a > $o ) > $o] :
( ( ^ [X2: a,X3: a] :
! [X4: a > a > $o] :
( ( ! [X5: a,X6: a] :
( ? [X7: a > a > $o] : ( X7 @ X6 @ X5 )
=> ( X4 @ X6 @ X5 ) )
& ( X1 @ X4 ) )
=> ( X4 @ X2 @ X3 ) ) )
= ( ^ [X8: a,X9: a] :
! [X10: a > a > $o] :
( ( ! [X11: a,X12: a] :
( ? [X13: a > a > $o] : ( X13 @ X12 @ X11 )
=> ( X10 @ X12 @ X11 ) )
& ( X1 @ X10 ) )
=> ( X10 @ X8 @ X9 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X1: ( a > a > $o ) > $o,X0: ( a > a > $o ) > $o] :
( ( ^ [X2: a,X3: a] :
! [X4: a > a > $o] :
( ( ! [X6: a,X5: a] :
( ? [X7: a > a > $o] : ( X7 @ X5 @ X6 )
=> ( X4 @ X5 @ X6 ) )
& ( X0 @ X4 ) )
=> ( X4 @ X2 @ X3 ) ) )
= ( ^ [X2: a,X3: a] :
! [X4: a > a > $o] :
( ( ! [X6: a,X5: a] :
( ? [X7: a > a > $o] : ( X7 @ X5 @ X6 )
=> ( X4 @ X5 @ X6 ) )
& ( X0 @ X4 ) )
=> ( X4 @ X2 @ X3 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X1: ( a > a > $o ) > $o,X0: ( a > a > $o ) > $o] :
( ( ^ [X2: a,X3: a] :
! [X4: a > a > $o] :
( ( ! [X6: a,X5: a] :
( ? [X7: a > a > $o] : ( X7 @ X5 @ X6 )
=> ( X4 @ X5 @ X6 ) )
& ( X0 @ X4 ) )
=> ( X4 @ X2 @ X3 ) ) )
= ( ^ [X2: a,X3: a] :
! [X4: a > a > $o] :
( ( ! [X6: a,X5: a] :
( ? [X7: a > a > $o] : ( X7 @ X5 @ X6 )
=> ( X4 @ X5 @ X6 ) )
& ( X0 @ X4 ) )
=> ( X4 @ X2 @ X3 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.fHgkMx0ESH/DTF2THF_23379.p',cTHM530_pme) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEV122^5 : TPTP v9.2.1. Released v4.0.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n009.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 12:40:40 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.26/0.48 ---- Original DTF file ---
% 0.26/0.48 thf(spec,logic,$$dhol).
% 0.26/0.48 %------------------------------------------------------------------------------
% 0.26/0.48 % File : SEV122^5 : TPTP v9.2.1. Released v4.0.0.
% 0.26/0.48 % Domain : Set Theory (Relations)
% 0.26/0.48 % Problem : TPS problem THM530
% 0.26/0.48 % Version : Especial.
% 0.26/0.48 % English :
% 0.26/0.48
% 0.26/0.48 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.26/0.48 % Source : [Bro09]
% 0.26/0.48 % Names : tps_0494 [Bro09]
% 0.26/0.48 % : THM530 [TPS]
% 0.26/0.48
% 0.26/0.48 % Status : Theorem
% 0.26/0.48 % Rating : 0.00 v8.2.0, 0.08 v8.1.0, 0.09 v7.5.0, 0.00 v6.2.0, 0.14 v6.1.0, 0.00 v6.0.0, 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
% 0.26/0.48 % Syntax : Number of formulae : 2 ( 1 unt; 1 typ; 0 def)
% 0.26/0.48 % Number of atoms : 1 ( 1 equ; 0 cnn)
% 0.26/0.48 % Maximal formula atoms : 1 ( 1 avg)
% 0.26/0.48 % Number of connectives : 20 ( 0 ~; 0 |; 2 &; 14 @)
% 0.26/0.48 % ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% 0.26/0.48 % Maximal formula depth : 3 ( 3 avg)
% 0.26/0.48 % Number of types : 2 ( 1 usr)
% 0.26/0.48 % Number of type conns : 14 ( 14 >; 0 *; 0 +; 0 <<)
% 0.26/0.48 % Number of symbols : 1 ( 0 usr; 0 con; 2-2 aty)
% 0.26/0.48 % Number of variables : 14 ( 4 ^; 8 !; 2 ?; 14 :)
% 0.26/0.48 % SPC : TH0_THM_EQU_NAR
% 0.26/0.48
% 0.26/0.48 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.26/0.48 % project in the Department of Mathematical Sciences at Carnegie
% 0.26/0.48 % Mellon University. Distributed under the Creative Commons copyleft
% 0.26/0.48 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.26/0.48 % : Polymorphic definitions expanded.
% 0.26/0.48 %------------------------------------------------------------------------------
% 0.26/0.48 thf(a_type,type,
% 0.26/0.48 a: $tType ).
% 0.26/0.48
% 0.26/0.48 thf(cTHM530_pme,conjecture,
% 0.26/0.48 ! [PROP: ( a > a > $o ) > $o,F: ( a > a > $o ) > $o] :
% 0.26/0.48 ( ( ^ [Xx: a,Xy: a] :
% 0.26/0.48 ! [Xp: a > a > $o] :
% 0.26/0.48 ( ( ! [Xx0: a,Xy0: a] :
% 0.26/0.48 ( ? [R: a > a > $o] : ( R @ Xx0 @ Xy0 )
% 0.26/0.48 => ( Xp @ Xx0 @ Xy0 ) )
% 0.26/0.48 & ( PROP @ Xp ) )
% 0.26/0.48 => ( Xp @ Xx @ Xy ) ) )
% 0.26/0.48 = ( ^ [Xx: a,Xy: a] :
% 0.26/0.48 ! [Xp: a > a > $o] :
% 0.26/0.48 ( ( ! [Xx0: a,Xy0: a] :
% 0.26/0.48 ( ? [R: a > a > $o] : ( R @ Xx0 @ Xy0 )
% 0.26/0.48 => ( Xp @ Xx0 @ Xy0 ) )
% 0.26/0.48 & ( PROP @ Xp ) )
% 0.26/0.48 => ( Xp @ Xx @ Xy ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 %------------------------------------------------------------------------------
% 0.26/0.48 ------------------------
% 0.32/1.20 ---- Embedded in THF ---
% 0.32/1.20 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 0.32/1.20 %%% Generated on Tue Feb 24 12:40:41 EST 2026
% 0.32/1.20 %%% using '$$dhol' embedding, version 1.3.0.
% 0.32/1.20 %%% Logic specification used:
% 0.32/1.20 %%% thf(spec, logic, $$dhol).
% 0.32/1.20
% 0.32/1.20 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.fHgkMx0ESH/DTF2DTF23379.p
% See solution above
% 0.32/1.20 ------------------------
% 0.32/1.21 ---- Cleaned THF ---
% 0.32/1.21 thf(a_type,type,
% 0.32/1.21 a: $tType ).
% 0.32/1.21
% 0.32/1.21 thf(cTHM530_pme,conjecture,
% 0.32/1.21 ! [PROP: ( a > a > $o ) > $o,F: ( a > a > $o ) > $o] :
% 0.32/1.21 ( ( ^ [Xx: a,Xy: a] :
% 0.32/1.21 ! [Xp: a > a > $o] :
% 0.32/1.21 ( ( ! [Xx0: a,Xy0: a] :
% 0.32/1.21 ( ? [R: a > a > $o] : ( R @ Xx0 @ Xy0 )
% 0.32/1.21 => ( Xp @ Xx0 @ Xy0 ) )
% 0.32/1.21 & ( PROP @ Xp ) )
% 0.32/1.21 => ( Xp @ Xx @ Xy ) ) )
% 0.32/1.21 = ( ^ [Xx: a,Xy: a] :
% 0.32/1.21 ! [Xp: a > a > $o] :
% 0.32/1.21 ( ( ! [Xx0: a,Xy0: a] :
% 0.32/1.21 ( ? [R: a > a > $o] : ( R @ Xx0 @ Xy0 )
% 0.32/1.21 => ( Xp @ Xx0 @ Xy0 ) )
% 0.32/1.21 & ( PROP @ Xp ) )
% 0.32/1.21 => ( Xp @ Xx @ Xy ) ) ) ) ).
% 0.32/1.21 ------------------------
% 0.32/1.23 % (23568)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_23379 for (2999ds/183Mi)
% 0.32/1.23 % (23572)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_23379 for (2999ds/2Mi)
% 0.32/1.23 % (23568)First to succeed.
% 0.32/1.23 % (23570)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_23379 for (2999ds/27Mi)
% 0.32/1.23 % (23572)Also succeeded, but the first one will report.
% 0.32/1.23 % (23568)Refutation found. Thanks to Tanya!
% 0.32/1.23 % SZS status Theorem for DTF2THF_23379
% 0.32/1.23 % SZS output start Proof for DTF2THF_23379
% 0.32/1.23 thf(type_def_5, type, a: $tType).
% 0.32/1.23 thf(func_def_0, type, a: $tType).
% 0.32/1.23 thf(func_def_12, type, sK0: (a > a > $o) > $o).
% 0.32/1.23 thf(f11,plain,(
% 0.32/1.23 $false),
% 0.32/1.23 inference(trivial_inequality_removal,[status(thm)],[f10])).
% 0.32/1.23 thf(f10,plain,(
% 0.32/1.23 ((^[Y0 : a]: ((^[Y1 : a]: (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((sK0 @ Y2) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((?? @ (a > a > $o) @ (^[Y5 : a > a > $o]: (Y5 @ Y3 @ Y4))) => (Y2 @ Y3 @ Y4))))))) => (Y2 @ Y0 @ Y1))))))) != (^[Y0 : a]: ((^[Y1 : a]: (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((sK0 @ Y2) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((?? @ (a > a > $o) @ (^[Y5 : a > a > $o]: (Y5 @ Y3 @ Y4))) => (Y2 @ Y3 @ Y4))))))) => (Y2 @ Y0 @ Y1))))))))),
% 0.32/1.23 inference(cnf_transformation,[status(thm)],[f9])).
% 0.32/1.23 thf(f9,plain,(
% 0.32/1.23 ((^[Y0 : a]: ((^[Y1 : a]: (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((sK0 @ Y2) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((?? @ (a > a > $o) @ (^[Y5 : a > a > $o]: (Y5 @ Y3 @ Y4))) => (Y2 @ Y3 @ Y4))))))) => (Y2 @ Y0 @ Y1))))))) != (^[Y0 : a]: ((^[Y1 : a]: (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((sK0 @ Y2) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((?? @ (a > a > $o) @ (^[Y5 : a > a > $o]: (Y5 @ Y3 @ Y4))) => (Y2 @ Y3 @ Y4))))))) => (Y2 @ Y0 @ Y1))))))))),
% 0.32/1.23 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f7,f8])).
% 0.32/1.23 thf(f8,plain,(
% 0.32/1.23 ? [X0 : (a > a > $o) > $o] : ((^[Y0 : a]: ((^[Y1 : a]: (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((X0 @ Y2) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((?? @ (a > a > $o) @ (^[Y5 : a > a > $o]: (Y5 @ Y3 @ Y4))) => (Y2 @ Y3 @ Y4))))))) => (Y2 @ Y0 @ Y1))))))) != (^[Y0 : a]: ((^[Y1 : a]: (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((X0 @ Y2) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((?? @ (a > a > $o) @ (^[Y5 : a > a > $o]: (Y5 @ Y3 @ Y4))) => (Y2 @ Y3 @ Y4))))))) => (Y2 @ Y0 @ Y1)))))))) => ((^[Y0 : a]: ((^[Y1 : a]: (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((sK0 @ Y2) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((?? @ (a > a > $o) @ (^[Y5 : a > a > $o]: (Y5 @ Y3 @ Y4))) => (Y2 @ Y3 @ Y4))))))) => (Y2 @ Y0 @ Y1))))))) != (^[Y0 : a]: ((^[Y1 : a]: (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((sK0 @ Y2) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((?? @ (a > a > $o) @ (^[Y5 : a > a > $o]: (Y5 @ Y3 @ Y4))) => (Y2 @ Y3 @ Y4))))))) => (Y2 @ Y0 @ Y1))))))))),
% 0.32/1.23 introduced(definition,[],[choice_axiom])).
% 0.32/1.23 thf(f7,plain,(
% 0.32/1.23 ? [X0 : (a > a > $o) > $o] : ((^[Y0 : a]: ((^[Y1 : a]: (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((X0 @ Y2) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((?? @ (a > a > $o) @ (^[Y5 : a > a > $o]: (Y5 @ Y3 @ Y4))) => (Y2 @ Y3 @ Y4))))))) => (Y2 @ Y0 @ Y1))))))) != (^[Y0 : a]: ((^[Y1 : a]: (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((X0 @ Y2) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((?? @ (a > a > $o) @ (^[Y5 : a > a > $o]: (Y5 @ Y3 @ Y4))) => (Y2 @ Y3 @ Y4))))))) => (Y2 @ Y0 @ Y1))))))))),
% 0.32/1.23 inference(ennf_transformation,[status(thm)],[f6])).
% 0.32/1.23 thf(f6,plain,(
% 0.32/1.23 ~! [X0 : (a > a > $o) > $o] : ((^[Y0 : a]: ((^[Y1 : a]: (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((X0 @ Y2) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((?? @ (a > a > $o) @ (^[Y5 : a > a > $o]: (Y5 @ Y3 @ Y4))) => (Y2 @ Y3 @ Y4))))))) => (Y2 @ Y0 @ Y1))))))) = (^[Y0 : a]: ((^[Y1 : a]: (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((X0 @ Y2) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((?? @ (a > a > $o) @ (^[Y5 : a > a > $o]: (Y5 @ Y3 @ Y4))) => (Y2 @ Y3 @ Y4))))))) => (Y2 @ Y0 @ Y1))))))))),
% 0.32/1.23 inference(rectify,[status(thm)],[f5])).
% 0.32/1.23 thf(f5,plain,(
% 0.32/1.23 ~! [X1 : (a > a > $o) > $o] : ((^[Y0 : a]: ((^[Y1 : a]: (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((X1 @ Y2) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((?? @ (a > a > $o) @ (^[Y5 : a > a > $o]: (Y5 @ Y3 @ Y4))) => (Y2 @ Y3 @ Y4))))))) => (Y2 @ Y0 @ Y1))))))) = (^[Y0 : a]: ((^[Y1 : a]: (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((X1 @ Y2) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((?? @ (a > a > $o) @ (^[Y5 : a > a > $o]: (Y5 @ Y3 @ Y4))) => (Y2 @ Y3 @ Y4))))))) => (Y2 @ Y0 @ Y1))))))))),
% 0.32/1.23 inference(fool_elimination,[status(thm)],[f4])).
% 0.32/1.23 thf(f4,plain,(
% 0.32/1.23 ~! [X1 : (a > a > $o) > $o] : ((^[X2 : a, X3 : a] : (! [X4 : a > a > $o] : ((! [X5 : a,X6 : a] : (? [X7 : a > a > $o] : (X7 @ X6 @ X5) => (X4 @ X6 @ X5)) & (X1 @ X4)) => (X4 @ X2 @ X3)))) = (^[X8 : a, X9 : a] : (! [X10 : a > a > $o] : ((! [X11 : a,X12 : a] : (? [X13 : a > a > $o] : (X13 @ X12 @ X11) => (X10 @ X12 @ X11)) & (X1 @ X10)) => (X10 @ X8 @ X9)))))),
% 0.32/1.23 inference(rectify,[status(thm)],[f2])).
% 0.32/1.23 thf(f2,negated_conjecture,(
% 0.32/1.23 ~! [X1 : (a > a > $o) > $o,X0 : (a > a > $o) > $o] : ((^[X2 : a, X3 : a] : (! [X4 : a > a > $o] : ((! [X6 : a,X5 : a] : (? [X7 : a > a > $o] : (X7 @ X5 @ X6) => (X4 @ X5 @ X6)) & (X0 @ X4)) => (X4 @ X2 @ X3)))) = (^[X2 : a, X3 : a] : (! [X4 : a > a > $o] : ((! [X6 : a,X5 : a] : (? [X7 : a > a > $o] : (X7 @ X5 @ X6) => (X4 @ X5 @ X6)) & (X0 @ X4)) => (X4 @ X2 @ X3)))))),
% 0.32/1.23 inference(negated_conjecture,[status(cth)],[f1])).
% 0.32/1.23 thf(f1,conjecture,(
% 0.32/1.23 ! [X1 : (a > a > $o) > $o,X0 : (a > a > $o) > $o] : ((^[X2 : a, X3 : a] : (! [X4 : a > a > $o] : ((! [X6 : a,X5 : a] : (? [X7 : a > a > $o] : (X7 @ X5 @ X6) => (X4 @ X5 @ X6)) & (X0 @ X4)) => (X4 @ X2 @ X3)))) = (^[X2 : a, X3 : a] : (! [X4 : a > a > $o] : ((! [X6 : a,X5 : a] : (? [X7 : a > a > $o] : (X7 @ X5 @ X6) => (X4 @ X5 @ X6)) & (X0 @ X4)) => (X4 @ X2 @ X3)))))),
% 0.32/1.23 file('/export/starexec/sandbox/tmp/tmp.fHgkMx0ESH/DTF2THF_23379.p',cTHM530_pme)).
% 0.32/1.23 % SZS output end Proof for DTF2THF_23379
% 0.32/1.23 % (23568)------------------------------
% 0.32/1.23 % (23568)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.23 % (23568)Termination reason: Refutation
% 0.32/1.23
% 0.32/1.23 % (23568)Memory used [KB]: 5500
% 0.32/1.23 % (23568)Time elapsed: 0.002 s
% 0.32/1.23 % (23568)------------------------------
% 0.32/1.23 % (23568)------------------------------
% 0.32/1.23 % (23567)Success in time 0.004 s
%------------------------------------------------------------------------------