%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU898^5 : 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 09:37:42 AM UTC 2026
% Result : Theorem 1.43s 1.28s
% Output : Refutation 1.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 3
% Syntax : Number of formulae : 23 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 192 ( 97 equ; 0 cnn)
% Maximal formula atoms : 20 ( 8 avg)
% Number of connectives : 416 ( 42 ~; 29 |; 44 &; 275 @)
% ( 0 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 24 ( 24 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 76 ( 0 ^; 58 !; 18 ?; 76 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_2,type,
vEPSILON:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_5,type,
sK0: a > a ).
thf(func_def_6,type,
sK1: a > a ).
thf(func_def_7,type,
sK2: a > $o ).
thf(func_def_8,type,
sK3: a ).
thf(f75,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f74]) ).
thf(f74,plain,
( ( sK1 @ ( sK1 @ ( sK0 @ sK3 ) ) )
!= ( sK1 @ ( sK1 @ ( sK0 @ sK3 ) ) ) ),
inference(superposition,[status(thm)],[f13,f61]) ).
thf(f61,plain,
( ( sK1 @ ( sK1 @ ( sK0 @ sK3 ) ) )
= ( sK0 @ ( sK1 @ ( sK1 @ sK3 ) ) ) ),
inference(forward_demodulation,[status(thm)],[f35,f33]) ).
thf(f33,plain,
( ( sK1 @ ( sK0 @ sK3 ) )
= ( sK0 @ ( sK1 @ sK3 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f30]) ).
thf(f30,plain,
( ( ( sK1 @ ( sK0 @ sK3 ) )
= ( sK0 @ ( sK1 @ sK3 ) ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f12,f14]) ).
thf(f14,plain,
( $true
= ( sK2 @ sK3 ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( ! [X3: a] :
( ( $true
= ( sK2 @ ( sK1 @ X3 ) ) )
| ( ( sK2 @ X3 )
!= $true ) )
& ! [X4: a] :
( ( $true
= ( sK2 @ ( sK0 @ X4 ) ) )
| ( ( sK2 @ X4 )
!= $true ) )
& ! [X5: a] :
( ( $true
!= ( sK2 @ X5 ) )
| ( ( sK2 @ ( sK0 @ X5 ) )
= $true ) )
& ( $true
= ( sK2 @ sK3 ) )
& ( ( sK1 @ ( sK1 @ ( sK0 @ sK3 ) ) )
!= ( sK0 @ ( sK1 @ ( sK1 @ sK3 ) ) ) )
& ! [X7: a] :
( ( ( sK0 @ ( sK1 @ X7 ) )
= ( sK1 @ ( sK0 @ X7 ) ) )
| ( $true
!= ( sK2 @ X7 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f8,f10,f9]) ).
thf(f9,plain,
( ? [X0: a > a,X1: a > a,X2: a > $o] :
( ! [X3: a] :
( ( $true
= ( X2 @ ( X1 @ X3 ) ) )
| ( $true
!= ( X2 @ X3 ) ) )
& ! [X4: a] :
( ( ( X2 @ ( X0 @ X4 ) )
= $true )
| ( $true
!= ( X2 @ X4 ) ) )
& ! [X5: a] :
( ( $true
!= ( X2 @ X5 ) )
| ( $true
= ( X2 @ ( X0 @ X5 ) ) ) )
& ? [X6: a] :
( ( $true
= ( X2 @ X6 ) )
& ( ( X0 @ ( X1 @ ( X1 @ X6 ) ) )
!= ( X1 @ ( X1 @ ( X0 @ X6 ) ) ) ) )
& ! [X7: a] :
( ( ( X1 @ ( X0 @ X7 ) )
= ( X0 @ ( X1 @ X7 ) ) )
| ( ( X2 @ X7 )
!= $true ) ) )
=> ( ! [X3: a] :
( ( $true
= ( sK2 @ ( sK1 @ X3 ) ) )
| ( ( sK2 @ X3 )
!= $true ) )
& ! [X4: a] :
( ( $true
= ( sK2 @ ( sK0 @ X4 ) ) )
| ( ( sK2 @ X4 )
!= $true ) )
& ! [X5: a] :
( ( $true
!= ( sK2 @ X5 ) )
| ( ( sK2 @ ( sK0 @ X5 ) )
= $true ) )
& ? [X6: a] :
( ( $true
= ( sK2 @ X6 ) )
& ( ( sK1 @ ( sK1 @ ( sK0 @ X6 ) ) )
!= ( sK0 @ ( sK1 @ ( sK1 @ X6 ) ) ) ) )
& ! [X7: a] :
( ( ( sK0 @ ( sK1 @ X7 ) )
= ( sK1 @ ( sK0 @ X7 ) ) )
| ( $true
!= ( sK2 @ X7 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f10,plain,
( ? [X6: a] :
( ( $true
= ( sK2 @ X6 ) )
& ( ( sK1 @ ( sK1 @ ( sK0 @ X6 ) ) )
!= ( sK0 @ ( sK1 @ ( sK1 @ X6 ) ) ) ) )
=> ( ( $true
= ( sK2 @ sK3 ) )
& ( ( sK1 @ ( sK1 @ ( sK0 @ sK3 ) ) )
!= ( sK0 @ ( sK1 @ ( sK1 @ sK3 ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f8,plain,
? [X0: a > a,X1: a > a,X2: a > $o] :
( ! [X3: a] :
( ( $true
= ( X2 @ ( X1 @ X3 ) ) )
| ( $true
!= ( X2 @ X3 ) ) )
& ! [X4: a] :
( ( ( X2 @ ( X0 @ X4 ) )
= $true )
| ( $true
!= ( X2 @ X4 ) ) )
& ! [X5: a] :
( ( $true
!= ( X2 @ X5 ) )
| ( $true
= ( X2 @ ( X0 @ X5 ) ) ) )
& ? [X6: a] :
( ( $true
= ( X2 @ X6 ) )
& ( ( X0 @ ( X1 @ ( X1 @ X6 ) ) )
!= ( X1 @ ( X1 @ ( X0 @ X6 ) ) ) ) )
& ! [X7: a] :
( ( ( X1 @ ( X0 @ X7 ) )
= ( X0 @ ( X1 @ X7 ) ) )
| ( ( X2 @ X7 )
!= $true ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,plain,
? [X1: a > a,X0: a > a,X2: a > $o] :
( ! [X4: a] :
( ( ( X2 @ ( X0 @ X4 ) )
= $true )
| ( $true
!= ( X2 @ X4 ) ) )
& ! [X3: a] :
( ( $true
= ( X2 @ ( X1 @ X3 ) ) )
| ( $true
!= ( X2 @ X3 ) ) )
& ! [X6: a] :
( ( $true
!= ( X2 @ X6 ) )
| ( $true
= ( X2 @ ( X1 @ X6 ) ) ) )
& ? [X7: a] :
( ( ( X2 @ X7 )
= $true )
& ( ( X0 @ ( X0 @ ( X1 @ X7 ) ) )
!= ( X1 @ ( X0 @ ( X0 @ X7 ) ) ) ) )
& ! [X5: a] :
( ( ( X1 @ ( X0 @ X5 ) )
= ( X0 @ ( X1 @ X5 ) ) )
| ( $true
!= ( X2 @ X5 ) ) ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
? [X2: a > $o,X0: a > a,X1: a > a] :
( ? [X7: a] :
( ( ( X2 @ X7 )
= $true )
& ( ( X0 @ ( X0 @ ( X1 @ X7 ) ) )
!= ( X1 @ ( X0 @ ( X0 @ X7 ) ) ) ) )
& ! [X3: a] :
( ( $true
= ( X2 @ ( X1 @ X3 ) ) )
| ( $true
!= ( X2 @ X3 ) ) )
& ! [X5: a] :
( ( ( X1 @ ( X0 @ X5 ) )
= ( X0 @ ( X1 @ X5 ) ) )
| ( $true
!= ( X2 @ X5 ) ) )
& ! [X6: a] :
( ( $true
!= ( X2 @ X6 ) )
| ( $true
= ( X2 @ ( X1 @ X6 ) ) ) )
& ! [X4: a] :
( ( ( X2 @ ( X0 @ X4 ) )
= $true )
| ( $true
!= ( X2 @ X4 ) ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X2: a > $o,X0: a > a,X1: a > a] :
( ( ! [X3: a] :
( ( $true
= ( X2 @ X3 ) )
=> ( $true
= ( X2 @ ( X1 @ X3 ) ) ) )
& ! [X5: a] :
( ( $true
= ( X2 @ X5 ) )
=> ( ( X1 @ ( X0 @ X5 ) )
= ( X0 @ ( X1 @ X5 ) ) ) )
& ! [X6: a] :
( ( $true
= ( X2 @ X6 ) )
=> ( $true
= ( X2 @ ( X1 @ X6 ) ) ) )
& ! [X4: a] :
( ( $true
= ( X2 @ X4 ) )
=> ( ( X2 @ ( X0 @ X4 ) )
= $true ) ) )
=> ! [X7: a] :
( ( ( X2 @ X7 )
= $true )
=> ( ( X0 @ ( X0 @ ( X1 @ X7 ) ) )
= ( X1 @ ( X0 @ ( X0 @ X7 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: a > a,X1: a > a,X2: a > $o] :
( ( ! [X3: a] :
( ( X2 @ X3 )
=> ( X2 @ ( X1 @ X3 ) ) )
& ! [X4: a] :
( ( X2 @ X4 )
=> ( X2 @ ( X0 @ X4 ) ) )
& ! [X5: a] :
( ( X2 @ X5 )
=> ( ( X1 @ ( X0 @ X5 ) )
= ( X0 @ ( X1 @ X5 ) ) ) )
& ! [X6: a] :
( ( X2 @ X6 )
=> ( X2 @ ( X1 @ X6 ) ) ) )
=> ! [X7: a] :
( ( X2 @ X7 )
=> ( ( X0 @ ( X0 @ ( X1 @ X7 ) ) )
= ( X1 @ ( X0 @ ( X0 @ X7 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X0: a > a,X2: a > a,X1: a > $o] :
( ( ! [X3: a] :
( ( X1 @ X3 )
=> ( X1 @ ( X2 @ X3 ) ) )
& ! [X3: a] :
( ( X1 @ X3 )
=> ( X1 @ ( X0 @ X3 ) ) )
& ! [X3: a] :
( ( X1 @ X3 )
=> ( ( X0 @ ( X2 @ X3 ) )
= ( X2 @ ( X0 @ X3 ) ) ) )
& ! [X3: a] :
( ( X1 @ X3 )
=> ( X1 @ ( X2 @ X3 ) ) ) )
=> ! [X3: a] :
( ( X1 @ X3 )
=> ( ( X0 @ ( X0 @ ( X2 @ X3 ) ) )
= ( X2 @ ( X0 @ ( X0 @ X3 ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X0: a > a,X2: a > a,X1: a > $o] :
( ( ! [X3: a] :
( ( X1 @ X3 )
=> ( X1 @ ( X2 @ X3 ) ) )
& ! [X3: a] :
( ( X1 @ X3 )
=> ( X1 @ ( X0 @ X3 ) ) )
& ! [X3: a] :
( ( X1 @ X3 )
=> ( ( X0 @ ( X2 @ X3 ) )
= ( X2 @ ( X0 @ X3 ) ) ) )
& ! [X3: a] :
( ( X1 @ X3 )
=> ( X1 @ ( X2 @ X3 ) ) ) )
=> ! [X3: a] :
( ( X1 @ X3 )
=> ( ( X0 @ ( X0 @ ( X2 @ X3 ) ) )
= ( X2 @ ( X0 @ ( X0 @ X3 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.dGrsKvLo7w/DTF2THF_9732.p',cTHM132_pme) ).
thf(f12,plain,
! [X7: a] :
( ( $true
!= ( sK2 @ X7 ) )
| ( ( sK0 @ ( sK1 @ X7 ) )
= ( sK1 @ ( sK0 @ X7 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f35,plain,
( ( sK1 @ ( sK0 @ ( sK1 @ sK3 ) ) )
= ( sK0 @ ( sK1 @ ( sK1 @ sK3 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f32]) ).
thf(f32,plain,
( ( ( sK1 @ ( sK0 @ ( sK1 @ sK3 ) ) )
= ( sK0 @ ( sK1 @ ( sK1 @ sK3 ) ) ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f12,f21]) ).
thf(f21,plain,
( ( sK2 @ ( sK1 @ sK3 ) )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f20]) ).
thf(f20,plain,
( ( $true != $true )
| ( ( sK2 @ ( sK1 @ sK3 ) )
= $true ) ),
inference(superposition,[status(thm)],[f17,f14]) ).
thf(f17,plain,
! [X3: a] :
( ( ( sK2 @ X3 )
!= $true )
| ( $true
= ( sK2 @ ( sK1 @ X3 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f13,plain,
( ( sK1 @ ( sK1 @ ( sK0 @ sK3 ) ) )
!= ( sK0 @ ( sK1 @ ( sK1 @ sK3 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU898^5 : 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
% 0.18/0.34 % Computer : n011.cluster.edu
% 0.18/0.34 % Model : x86_64 x86_64
% 0.18/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.34 % Memory : 8042.1875MB
% 0.18/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.34 % CPULimit : 300
% 0.18/0.34 % WCLimit : 300
% 0.18/0.34 % DateTime : Tue Feb 24 12:36:02 EST 2026
% 0.18/0.34 % CPUTime :
% 0.18/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.20/0.48 ---- Original DTF file ---
% 0.20/0.48 thf(spec,logic,$$dhol).
% 0.20/0.48 %------------------------------------------------------------------------------
% 0.20/0.48 % File : SEU898^5 : TPTP v9.2.1. Released v4.0.0.
% 0.20/0.48 % Domain : Set Theory
% 0.20/0.48 % Problem : TPS problem THM132
% 0.20/0.48 % Version : Especial.
% 0.20/0.48 % English :
% 0.20/0.48
% 0.20/0.48 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.20/0.48 % Source : [Bro09]
% 0.20/0.48 % Names : tps_0424 [Bro09]
% 0.20/0.48 % : THM132 [TPS]
% 0.20/0.48
% 0.20/0.48 % Status : Theorem
% 0.20/0.48 % Rating : 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, 0.00 v6.1.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v5.3.0, 0.40 v5.2.0, 0.20 v4.1.0, 0.00 v4.0.0
% 0.20/0.48 % Syntax : Number of formulae : 2 ( 0 unt; 1 typ; 0 def)
% 0.20/0.48 % Number of atoms : 2 ( 2 equ; 0 cnn)
% 0.20/0.48 % Maximal formula atoms : 2 ( 2 avg)
% 0.20/0.48 % Number of connectives : 30 ( 0 ~; 0 |; 3 &; 21 @)
% 0.20/0.48 % ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% 0.20/0.48 % Maximal formula depth : 12 ( 12 avg)
% 0.20/0.48 % Number of types : 2 ( 1 usr)
% 0.20/0.48 % Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% 0.20/0.48 % Number of symbols : 1 ( 0 usr; 0 con; 2-2 aty)
% 0.20/0.48 % Number of variables : 8 ( 0 ^; 8 !; 0 ?; 8 :)
% 0.20/0.48 % SPC : TH0_THM_EQU_NAR
% 0.20/0.48
% 0.20/0.48 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.20/0.48 % project in the Department of Mathematical Sciences at Carnegie
% 0.20/0.48 % Mellon University. Distributed under the Creative Commons copyleft
% 0.20/0.48 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.20/0.48 % : Polymorphic definitions expanded.
% 0.20/0.48 %------------------------------------------------------------------------------
% 0.20/0.48 thf(a_type,type,
% 0.20/0.48 a: $tType ).
% 0.20/0.48
% 0.20/0.48 thf(cTHM132_pme,conjecture,
% 0.20/0.48 ! [Xh: a > a,Xs: a > $o,Xf: a > a] :
% 0.20/0.48 ( ( ! [Xx: a] :
% 0.20/0.48 ( ( Xs @ Xx )
% 0.20/0.48 => ( Xs @ ( Xf @ Xx ) ) )
% 0.20/0.48 & ! [Xx: a] :
% 0.20/0.48 ( ( Xs @ Xx )
% 0.20/0.48 => ( Xs @ ( Xf @ Xx ) ) )
% 0.20/0.48 & ! [Xx: a] :
% 0.20/0.48 ( ( Xs @ Xx )
% 0.20/0.48 => ( Xs @ ( Xh @ Xx ) ) )
% 0.20/0.48 & ! [Xx: a] :
% 0.20/0.48 ( ( Xs @ Xx )
% 0.20/0.48 => ( ( Xh @ ( Xf @ Xx ) )
% 0.20/0.48 = ( Xf @ ( Xh @ Xx ) ) ) ) )
% 0.20/0.48 => ! [Xx: a] :
% 0.20/0.48 ( ( Xs @ Xx )
% 0.20/0.48 => ( ( Xh @ ( Xh @ ( Xf @ Xx ) ) )
% 0.20/0.48 = ( Xf @ ( Xh @ ( Xh @ Xx ) ) ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 %------------------------------------------------------------------------------
% 0.20/0.48 ------------------------
% 1.43/1.26 ---- Embedded in THF ---
% 1.43/1.26 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.43/1.26 %%% Generated on Tue Feb 24 12:36:03 EST 2026
% 1.43/1.26 %%% using '$$dhol' embedding, version 1.3.0.
% 1.43/1.26 %%% Logic specification used:
% 1.43/1.26 %%% thf(spec, logic, $$dhol).
% 1.43/1.26
% 1.43/1.26 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.dGrsKvLo7w/DTF2DTF9732.p
% See solution above
% 1.43/1.26 ------------------------
% 1.43/1.26 ---- Cleaned THF ---
% 1.43/1.27 thf(a_type,type,
% 1.43/1.27 a: $tType ).
% 1.43/1.27
% 1.43/1.27 thf(cTHM132_pme,conjecture,
% 1.43/1.27 ! [Xh: a > a,Xs: a > $o,Xf: a > a] :
% 1.43/1.27 ( ( ! [Xx: a] :
% 1.43/1.27 ( ( Xs @ Xx )
% 1.43/1.27 => ( Xs @ ( Xf @ Xx ) ) )
% 1.43/1.27 & ! [Xx: a] :
% 1.43/1.27 ( ( Xs @ Xx )
% 1.43/1.27 => ( Xs @ ( Xf @ Xx ) ) )
% 1.43/1.27 & ! [Xx: a] :
% 1.43/1.27 ( ( Xs @ Xx )
% 1.43/1.27 => ( Xs @ ( Xh @ Xx ) ) )
% 1.43/1.27 & ! [Xx: a] :
% 1.43/1.27 ( ( Xs @ Xx )
% 1.43/1.27 => ( ( Xh @ ( Xf @ Xx ) )
% 1.43/1.27 = ( Xf @ ( Xh @ Xx ) ) ) ) )
% 1.43/1.27 => ! [Xx: a] :
% 1.43/1.27 ( ( Xs @ Xx )
% 1.43/1.27 => ( ( Xh @ ( Xh @ ( Xf @ Xx ) ) )
% 1.43/1.27 = ( Xf @ ( Xh @ ( Xh @ Xx ) ) ) ) ) ) ).
% 1.43/1.27 ------------------------
% 1.43/1.28 % (9832)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_9732 for (3000ds/27Mi)
% 1.43/1.28 % (9830)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_9732 for (3000ds/183Mi)
% 1.43/1.28 % (9832)First to succeed.
% 1.43/1.28 % (9832)Refutation found. Thanks to Tanya!
% 1.43/1.28 % SZS status Theorem for DTF2THF_9732
% 1.43/1.28 % SZS output start Proof for DTF2THF_9732
% 1.43/1.28 thf(type_def_5, type, a: $tType).
% 1.43/1.28 thf(func_def_0, type, a: $tType).
% 1.43/1.28 thf(func_def_2, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.43/1.28 thf(func_def_5, type, sK0: a > a).
% 1.43/1.28 thf(func_def_6, type, sK1: a > a).
% 1.43/1.28 thf(func_def_7, type, sK2: a > $o).
% 1.43/1.28 thf(func_def_8, type, sK3: a).
% 1.43/1.28 thf(f75,plain,(
% 1.43/1.28 $false),
% 1.43/1.28 inference(trivial_inequality_removal,[status(thm)],[f74])).
% 1.43/1.28 thf(f74,plain,(
% 1.43/1.28 ((sK1 @ (sK1 @ (sK0 @ sK3))) != (sK1 @ (sK1 @ (sK0 @ sK3))))),
% 1.43/1.28 inference(superposition,[status(thm)],[f13,f61])).
% 1.43/1.28 thf(f61,plain,(
% 1.43/1.28 ((sK1 @ (sK1 @ (sK0 @ sK3))) = (sK0 @ (sK1 @ (sK1 @ sK3))))),
% 1.43/1.28 inference(forward_demodulation,[status(thm)],[f35,f33])).
% 1.43/1.28 thf(f33,plain,(
% 1.43/1.28 ((sK1 @ (sK0 @ sK3)) = (sK0 @ (sK1 @ sK3)))),
% 1.43/1.28 inference(trivial_inequality_removal,[status(thm)],[f30])).
% 1.43/1.28 thf(f30,plain,(
% 1.43/1.28 ((sK1 @ (sK0 @ sK3)) = (sK0 @ (sK1 @ sK3))) | ($true != $true)),
% 1.43/1.28 inference(superposition,[status(thm)],[f12,f14])).
% 1.43/1.28 thf(f14,plain,(
% 1.43/1.28 ($true = (sK2 @ sK3))),
% 1.43/1.28 inference(cnf_transformation,[status(thm)],[f11])).
% 1.43/1.28 thf(f11,plain,(
% 1.43/1.28 ! [X3 : a] : (($true = (sK2 @ (sK1 @ X3))) | ((sK2 @ X3) != $true)) & ! [X4 : a] : (($true = (sK2 @ (sK0 @ X4))) | ((sK2 @ X4) != $true)) & ! [X5 : a] : (($true != (sK2 @ X5)) | ((sK2 @ (sK0 @ X5)) = $true)) & (($true = (sK2 @ sK3)) & ((sK1 @ (sK1 @ (sK0 @ sK3))) != (sK0 @ (sK1 @ (sK1 @ sK3))))) & ! [X7 : a] : (((sK0 @ (sK1 @ X7)) = (sK1 @ (sK0 @ X7))) | ($true != (sK2 @ X7)))),
% 1.43/1.28 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f8,f10,f9])).
% 1.43/1.28 thf(f9,plain,(
% 1.43/1.28 ? [X0 : a > a,X1 : a > a,X2 : a > $o] : (! [X3 : a] : (($true = (X2 @ (X1 @ X3))) | ($true != (X2 @ X3))) & ! [X4 : a] : (((X2 @ (X0 @ X4)) = $true) | ($true != (X2 @ X4))) & ! [X5 : a] : (($true != (X2 @ X5)) | ($true = (X2 @ (X0 @ X5)))) & ? [X6 : a] : (($true = (X2 @ X6)) & ((X0 @ (X1 @ (X1 @ X6))) != (X1 @ (X1 @ (X0 @ X6))))) & ! [X7 : a] : (((X1 @ (X0 @ X7)) = (X0 @ (X1 @ X7))) | ((X2 @ X7) != $true))) => (! [X3 : a] : (($true = (sK2 @ (sK1 @ X3))) | ((sK2 @ X3) != $true)) & ! [X4 : a] : (($true = (sK2 @ (sK0 @ X4))) | ((sK2 @ X4) != $true)) & ! [X5 : a] : (($true != (sK2 @ X5)) | ((sK2 @ (sK0 @ X5)) = $true)) & ? [X6 : a] : (($true = (sK2 @ X6)) & ((sK1 @ (sK1 @ (sK0 @ X6))) != (sK0 @ (sK1 @ (sK1 @ X6))))) & ! [X7 : a] : (((sK0 @ (sK1 @ X7)) = (sK1 @ (sK0 @ X7))) | ($true != (sK2 @ X7))))),
% 1.43/1.28 introduced(definition,[],[choice_axiom])).
% 1.43/1.28 thf(f10,plain,(
% 1.43/1.28 ? [X6 : a] : (($true = (sK2 @ X6)) & ((sK1 @ (sK1 @ (sK0 @ X6))) != (sK0 @ (sK1 @ (sK1 @ X6))))) => (($true = (sK2 @ sK3)) & ((sK1 @ (sK1 @ (sK0 @ sK3))) != (sK0 @ (sK1 @ (sK1 @ sK3)))))),
% 1.43/1.28 introduced(definition,[],[choice_axiom])).
% 1.43/1.28 thf(f8,plain,(
% 1.43/1.28 ? [X0 : a > a,X1 : a > a,X2 : a > $o] : (! [X3 : a] : (($true = (X2 @ (X1 @ X3))) | ($true != (X2 @ X3))) & ! [X4 : a] : (((X2 @ (X0 @ X4)) = $true) | ($true != (X2 @ X4))) & ! [X5 : a] : (($true != (X2 @ X5)) | ($true = (X2 @ (X0 @ X5)))) & ? [X6 : a] : (($true = (X2 @ X6)) & ((X0 @ (X1 @ (X1 @ X6))) != (X1 @ (X1 @ (X0 @ X6))))) & ! [X7 : a] : (((X1 @ (X0 @ X7)) = (X0 @ (X1 @ X7))) | ((X2 @ X7) != $true)))),
% 1.43/1.28 inference(rectify,[status(thm)],[f7])).
% 1.43/1.28 thf(f7,plain,(
% 1.43/1.28 ? [X1 : a > a,X0 : a > a,X2 : a > $o] : (! [X4 : a] : (((X2 @ (X0 @ X4)) = $true) | ($true != (X2 @ X4))) & ! [X3 : a] : (($true = (X2 @ (X1 @ X3))) | ($true != (X2 @ X3))) & ! [X6 : a] : (($true != (X2 @ X6)) | ($true = (X2 @ (X1 @ X6)))) & ? [X7 : a] : (((X2 @ X7) = $true) & ((X0 @ (X0 @ (X1 @ X7))) != (X1 @ (X0 @ (X0 @ X7))))) & ! [X5 : a] : (((X1 @ (X0 @ X5)) = (X0 @ (X1 @ X5))) | ($true != (X2 @ X5))))),
% 1.43/1.28 inference(flattening,[status(thm)],[f6])).
% 1.43/1.28 thf(f6,plain,(
% 1.43/1.28 ? [X2 : a > $o,X0 : a > a,X1 : a > a] : (? [X7 : a] : (((X2 @ X7) = $true) & ((X0 @ (X0 @ (X1 @ X7))) != (X1 @ (X0 @ (X0 @ X7))))) & (! [X3 : a] : (($true = (X2 @ (X1 @ X3))) | ($true != (X2 @ X3))) & ! [X5 : a] : (((X1 @ (X0 @ X5)) = (X0 @ (X1 @ X5))) | ($true != (X2 @ X5))) & ! [X6 : a] : (($true != (X2 @ X6)) | ($true = (X2 @ (X1 @ X6)))) & ! [X4 : a] : (((X2 @ (X0 @ X4)) = $true) | ($true != (X2 @ X4)))))),
% 1.43/1.28 inference(ennf_transformation,[status(thm)],[f5])).
% 1.43/1.28 thf(f5,plain,(
% 1.43/1.28 ~! [X2 : a > $o,X0 : a > a,X1 : a > a] : ((! [X3 : a] : (($true = (X2 @ X3)) => ($true = (X2 @ (X1 @ X3)))) & ! [X5 : a] : (($true = (X2 @ X5)) => ((X1 @ (X0 @ X5)) = (X0 @ (X1 @ X5)))) & ! [X6 : a] : (($true = (X2 @ X6)) => ($true = (X2 @ (X1 @ X6)))) & ! [X4 : a] : (($true = (X2 @ X4)) => ((X2 @ (X0 @ X4)) = $true))) => ! [X7 : a] : (((X2 @ X7) = $true) => ((X0 @ (X0 @ (X1 @ X7))) = (X1 @ (X0 @ (X0 @ X7))))))),
% 1.43/1.28 inference(fool_elimination,[status(thm)],[f4])).
% 1.43/1.28 thf(f4,plain,(
% 1.43/1.28 ~! [X0 : a > a,X1 : a > a,X2 : a > $o] : ((! [X3 : a] : ((X2 @ X3) => (X2 @ (X1 @ X3))) & ! [X4 : a] : ((X2 @ X4) => (X2 @ (X0 @ X4))) & ! [X5 : a] : ((X2 @ X5) => ((X1 @ (X0 @ X5)) = (X0 @ (X1 @ X5)))) & ! [X6 : a] : ((X2 @ X6) => (X2 @ (X1 @ X6)))) => ! [X7 : a] : ((X2 @ X7) => ((X0 @ (X0 @ (X1 @ X7))) = (X1 @ (X0 @ (X0 @ X7))))))),
% 1.43/1.28 inference(rectify,[status(thm)],[f2])).
% 1.43/1.28 thf(f2,negated_conjecture,(
% 1.43/1.28 ~! [X0 : a > a,X2 : a > a,X1 : a > $o] : ((! [X3 : a] : ((X1 @ X3) => (X1 @ (X2 @ X3))) & ! [X3 : a] : ((X1 @ X3) => (X1 @ (X0 @ X3))) & ! [X3 : a] : ((X1 @ X3) => ((X0 @ (X2 @ X3)) = (X2 @ (X0 @ X3)))) & ! [X3 : a] : ((X1 @ X3) => (X1 @ (X2 @ X3)))) => ! [X3 : a] : ((X1 @ X3) => ((X0 @ (X0 @ (X2 @ X3))) = (X2 @ (X0 @ (X0 @ X3))))))),
% 1.43/1.28 inference(negated_conjecture,[status(cth)],[f1])).
% 1.43/1.28 thf(f1,conjecture,(
% 1.43/1.28 ! [X0 : a > a,X2 : a > a,X1 : a > $o] : ((! [X3 : a] : ((X1 @ X3) => (X1 @ (X2 @ X3))) & ! [X3 : a] : ((X1 @ X3) => (X1 @ (X0 @ X3))) & ! [X3 : a] : ((X1 @ X3) => ((X0 @ (X2 @ X3)) = (X2 @ (X0 @ X3)))) & ! [X3 : a] : ((X1 @ X3) => (X1 @ (X2 @ X3)))) => ! [X3 : a] : ((X1 @ X3) => ((X0 @ (X0 @ (X2 @ X3))) = (X2 @ (X0 @ (X0 @ X3))))))),
% 1.43/1.28 file('/export/starexec/sandbox/tmp/tmp.dGrsKvLo7w/DTF2THF_9732.p',cTHM132_pme)).
% 1.43/1.28 thf(f12,plain,(
% 1.43/1.28 ( ! [X7 : a] : (($true != (sK2 @ X7)) | ((sK0 @ (sK1 @ X7)) = (sK1 @ (sK0 @ X7)))) )),
% 1.43/1.28 inference(cnf_transformation,[status(thm)],[f11])).
% 1.43/1.28 thf(f35,plain,(
% 1.43/1.28 ((sK1 @ (sK0 @ (sK1 @ sK3))) = (sK0 @ (sK1 @ (sK1 @ sK3))))),
% 1.43/1.28 inference(trivial_inequality_removal,[status(thm)],[f32])).
% 1.43/1.28 thf(f32,plain,(
% 1.43/1.28 ((sK1 @ (sK0 @ (sK1 @ sK3))) = (sK0 @ (sK1 @ (sK1 @ sK3)))) | ($true != $true)),
% 1.43/1.28 inference(superposition,[status(thm)],[f12,f21])).
% 1.43/1.28 thf(f21,plain,(
% 1.43/1.28 ((sK2 @ (sK1 @ sK3)) = $true)),
% 1.43/1.28 inference(trivial_inequality_removal,[status(thm)],[f20])).
% 1.43/1.28 thf(f20,plain,(
% 1.43/1.28 ($true != $true) | ((sK2 @ (sK1 @ sK3)) = $true)),
% 1.43/1.28 inference(superposition,[status(thm)],[f17,f14])).
% 1.43/1.28 thf(f17,plain,(
% 1.43/1.28 ( ! [X3 : a] : (((sK2 @ X3) != $true) | ($true = (sK2 @ (sK1 @ X3)))) )),
% 1.43/1.28 inference(cnf_transformation,[status(thm)],[f11])).
% 1.43/1.28 thf(f13,plain,(
% 1.43/1.28 ((sK1 @ (sK1 @ (sK0 @ sK3))) != (sK0 @ (sK1 @ (sK1 @ sK3))))),
% 1.43/1.28 inference(cnf_transformation,[status(thm)],[f11])).
% 1.43/1.28 % SZS output end Proof for DTF2THF_9732
% 1.43/1.28 % (9832)------------------------------
% 1.43/1.28 % (9832)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.43/1.28 % (9832)Termination reason: Refutation
% 1.43/1.28
% 1.43/1.28 % (9832)Memory used [KB]: 5500
% 1.43/1.28 % (9832)Time elapsed: 0.006 s
% 1.43/1.28 % (9832)Instructions burned: 9 (million)
% 1.43/1.28 % (9832)------------------------------
% 1.43/1.28 % (9832)------------------------------
% 1.43/1.28 % (9829)Success in time 0.015 s
%------------------------------------------------------------------------------