%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV017^5 : 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 : n023.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 09:40:04 AM UTC 2026
% Result : Theorem 1.45s 1.29s
% Output : Refutation 1.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 3
% Syntax : Number of formulae : 19 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 205 ( 83 equ; 0 cnn)
% Maximal formula atoms : 18 ( 10 avg)
% Number of connectives : 348 ( 40 ~; 24 |; 46 &; 216 @)
% ( 0 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 7 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 16 ( 16 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 4 usr; 5 con; 0-2 aty)
% Number of variables : 103 ( 0 ^; 81 !; 22 ?; 103 :)
% 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 ).
thf(f34,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f31,f16]) ).
thf(f16,plain,
( ( sK0 @ sK3 @ sK1 )
= $true ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( ( $true
= ( sK0 @ sK1 @ sK2 ) )
& ( ( sK0 @ sK3 @ sK1 )
= $true )
& ( $true
!= ( sK0 @ sK3 @ sK2 ) )
& ! [X4: a,X5: a,X6: a] :
( ( $true
!= ( sK0 @ X6 @ X4 ) )
| ( $true
= ( sK0 @ X5 @ X4 ) )
| ( ( sK0 @ X5 @ X6 )
!= $true ) )
& ! [X7: a,X8: a] :
( ( ( sK0 @ X8 @ X7 )
= $true )
| ( $true
!= ( sK0 @ X7 @ X8 ) ) )
& ! [X9: a] :
( $true
= ( sK0 @ X9 @ X9 ) ) ),
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] :
( ( ( X0 @ X1 @ X2 )
= $true )
& ( $true
= ( X0 @ X3 @ X1 ) )
& ( ( X0 @ X3 @ X2 )
!= $true ) )
& ! [X4: a,X5: a,X6: a] :
( ( $true
!= ( X0 @ X6 @ X4 ) )
| ( $true
= ( X0 @ X5 @ X4 ) )
| ( $true
!= ( X0 @ X5 @ X6 ) ) )
& ! [X7: a,X8: a] :
( ( $true
= ( X0 @ X8 @ X7 ) )
| ( $true
!= ( X0 @ X7 @ X8 ) ) )
& ! [X9: a] :
( $true
= ( X0 @ X9 @ X9 ) ) )
=> ( ? [X3: a,X2: a,X1: a] :
( ( $true
= ( sK0 @ X1 @ X2 ) )
& ( $true
= ( sK0 @ X3 @ X1 ) )
& ( ( sK0 @ X3 @ X2 )
!= $true ) )
& ! [X6: a,X5: a,X4: a] :
( ( $true
!= ( sK0 @ X6 @ X4 ) )
| ( $true
= ( sK0 @ X5 @ X4 ) )
| ( ( sK0 @ X5 @ X6 )
!= $true ) )
& ! [X8: a,X7: a] :
( ( ( sK0 @ X8 @ X7 )
= $true )
| ( $true
!= ( sK0 @ X7 @ X8 ) ) )
& ! [X9: a] :
( $true
= ( sK0 @ X9 @ X9 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f10,plain,
( ? [X3: a,X2: a,X1: a] :
( ( $true
= ( sK0 @ X1 @ X2 ) )
& ( $true
= ( sK0 @ X3 @ X1 ) )
& ( ( sK0 @ X3 @ X2 )
!= $true ) )
=> ( ( $true
= ( sK0 @ sK1 @ sK2 ) )
& ( ( sK0 @ sK3 @ sK1 )
= $true )
& ( $true
!= ( sK0 @ sK3 @ sK2 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f8,plain,
? [X0: a > a > $o] :
( ? [X1: a,X2: a,X3: a] :
( ( ( X0 @ X1 @ X2 )
= $true )
& ( $true
= ( X0 @ X3 @ X1 ) )
& ( ( X0 @ X3 @ X2 )
!= $true ) )
& ! [X4: a,X5: a,X6: a] :
( ( $true
!= ( X0 @ X6 @ X4 ) )
| ( $true
= ( X0 @ X5 @ X4 ) )
| ( $true
!= ( X0 @ X5 @ X6 ) ) )
& ! [X7: a,X8: a] :
( ( $true
= ( X0 @ X8 @ X7 ) )
| ( $true
!= ( X0 @ X7 @ X8 ) ) )
& ! [X9: a] :
( $true
= ( X0 @ X9 @ X9 ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,plain,
? [X0: a > a > $o] :
( ? [X9: a,X7: a,X8: a] :
( ( $true
= ( X0 @ X9 @ X7 ) )
& ( $true
= ( X0 @ X8 @ X9 ) )
& ( $true
!= ( X0 @ X8 @ X7 ) ) )
& ! [X4: a,X5: a,X6: a] :
( ( $true
!= ( X0 @ X6 @ X4 ) )
| ( $true
= ( X0 @ X5 @ X4 ) )
| ( $true
!= ( X0 @ X5 @ X6 ) ) )
& ! [X3: a,X2: a] :
( ( ( X0 @ X2 @ X3 )
= $true )
| ( ( X0 @ X3 @ X2 )
!= $true ) )
& ! [X1: a] :
( ( X0 @ X1 @ X1 )
= $true ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
? [X0: a > a > $o] :
( ? [X8: a,X7: a,X9: a] :
( ( $true
!= ( X0 @ X8 @ X7 ) )
& ( $true
= ( X0 @ X9 @ X7 ) )
& ( $true
= ( X0 @ X8 @ X9 ) ) )
& ! [X1: a] :
( ( X0 @ X1 @ X1 )
= $true )
& ! [X6: a,X4: a,X5: a] :
( ( $true
= ( X0 @ X5 @ X4 ) )
| ( $true
!= ( X0 @ X6 @ X4 ) )
| ( $true
!= ( X0 @ X5 @ X6 ) ) )
& ! [X3: a,X2: a] :
( ( ( X0 @ X2 @ X3 )
= $true )
| ( ( X0 @ X3 @ X2 )
!= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X0: a > a > $o] :
( ( ! [X1: a] :
( ( X0 @ X1 @ X1 )
= $true )
& ! [X6: a,X4: a,X5: a] :
( ( ( $true
= ( X0 @ X6 @ X4 ) )
& ( $true
= ( X0 @ X5 @ X6 ) ) )
=> ( $true
= ( X0 @ X5 @ X4 ) ) )
& ! [X2: a,X3: a] :
( ( ( X0 @ X3 @ X2 )
= $true )
=> ( ( X0 @ X2 @ X3 )
= $true ) ) )
=> ! [X8: a,X7: a,X9: a] :
( ( $true
= ( X0 @ X8 @ X9 ) )
=> ( ( $true
= ( X0 @ X9 @ X7 ) )
=> ( $true
= ( X0 @ X8 @ X7 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: a > a > $o] :
( ( ! [X1: a] : ( X0 @ X1 @ X1 )
& ! [X2: a,X3: a] :
( ( X0 @ X3 @ X2 )
=> ( X0 @ X2 @ X3 ) )
& ! [X4: a,X5: a,X6: a] :
( ( ( X0 @ X5 @ X6 )
& ( X0 @ X6 @ X4 ) )
=> ( X0 @ X5 @ X4 ) ) )
=> ! [X7: a,X8: a,X9: a] :
( ( X0 @ X8 @ X9 )
=> ( ( X0 @ X9 @ X7 )
=> ( X0 @ X8 @ X7 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X0: a > a > $o] :
( ( ! [X1: a] : ( X0 @ X1 @ X1 )
& ! [X2: a,X1: a] :
( ( X0 @ X1 @ X2 )
=> ( X0 @ X2 @ X1 ) )
& ! [X3: a,X1: a,X2: a] :
( ( ( X0 @ X1 @ X2 )
& ( X0 @ X2 @ X3 ) )
=> ( X0 @ X1 @ X3 ) ) )
=> ! [X3: a,X1: a,X2: a] :
( ( X0 @ X1 @ X2 )
=> ( ( X0 @ X2 @ X3 )
=> ( X0 @ X1 @ X3 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X0: a > a > $o] :
( ( ! [X1: a] : ( X0 @ X1 @ X1 )
& ! [X2: a,X1: a] :
( ( X0 @ X1 @ X2 )
=> ( X0 @ X2 @ X1 ) )
& ! [X3: a,X1: a,X2: a] :
( ( ( X0 @ X1 @ X2 )
& ( X0 @ X2 @ X3 ) )
=> ( X0 @ X1 @ X3 ) ) )
=> ! [X3: a,X1: a,X2: a] :
( ( X0 @ X1 @ X2 )
=> ( ( X0 @ X2 @ X3 )
=> ( X0 @ X1 @ X3 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.o6uQ0qr2Xl/DTF2THF_29221.p',cTHM514_pme) ).
thf(f31,plain,
( ( sK0 @ sK3 @ sK1 )
!= $true ),
inference(trivial_inequality_removal,[status(thm)],[f29]) ).
thf(f29,plain,
( ( ( sK0 @ sK3 @ sK1 )
!= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f24,f17]) ).
thf(f17,plain,
( $true
= ( sK0 @ sK1 @ sK2 ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f24,plain,
! [X0: a] :
( ( $true
!= ( sK0 @ X0 @ sK2 ) )
| ( ( sK0 @ sK3 @ X0 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f23]) ).
thf(f23,plain,
! [X0: a] :
( ( $true
!= ( sK0 @ X0 @ sK2 ) )
| ( ( sK0 @ sK3 @ X0 )
!= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f15,f14]) ).
thf(f14,plain,
! [X6: a,X4: a,X5: a] :
( ( $true
= ( sK0 @ X5 @ X4 ) )
| ( ( sK0 @ X5 @ X6 )
!= $true )
| ( $true
!= ( sK0 @ X6 @ X4 ) ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f15,plain,
( $true
!= ( sK0 @ sK3 @ sK2 ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEV017^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.33 % Computer : n023.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue Feb 24 12:39:19 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
% 0.31/0.47 ---- Original DTF file ---
% 0.31/0.47 thf(spec,logic,$$dhol).
% 0.31/0.47 %------------------------------------------------------------------------------
% 0.31/0.47 % File : SEV017^5 : TPTP v9.2.1. Released v4.0.0.
% 0.31/0.47 % Domain : Set Theory (Relations)
% 0.31/0.47 % Problem : TPS problem from EQUIVALENCE-RELATIONS-THMS
% 0.31/0.47 % Version : Especial.
% 0.31/0.47 % English :
% 0.31/0.47
% 0.31/0.47 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.31/0.47 % Source : [Bro09]
% 0.31/0.47 % Names : tps_0968 [Bro09]
% 0.31/0.47
% 0.31/0.47 % Status : Theorem
% 0.31/0.47 % Rating : 0.00 v6.2.0, 0.17 v6.1.0, 0.00 v5.1.0, 0.25 v5.0.0, 0.00 v4.0.1, 0.33 v4.0.0
% 0.31/0.47 % Syntax : Number of formulae : 2 ( 0 unt; 1 typ; 0 def)
% 0.31/0.47 % Number of atoms : 0 ( 0 equ; 0 cnn)
% 0.31/0.47 % Maximal formula atoms : 0 ( 0 avg)
% 0.31/0.47 % Number of connectives : 26 ( 0 ~; 0 |; 3 &; 18 @)
% 0.31/0.47 % ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% 0.31/0.47 % Maximal formula depth : 12 ( 12 avg)
% 0.31/0.47 % Number of types : 2 ( 1 usr)
% 0.31/0.47 % Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% 0.31/0.47 % Number of symbols : 0 ( 0 usr; 0 con; --- aty)
% 0.31/0.47 % Number of variables : 10 ( 0 ^; 10 !; 0 ?; 10 :)
% 0.31/0.47 % SPC : TH0_THM_NEQ_NAR
% 0.31/0.47
% 0.31/0.47 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.31/0.47 % project in the Department of Mathematical Sciences at Carnegie
% 0.31/0.47 % Mellon University. Distributed under the Creative Commons copyleft
% 0.31/0.47 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.31/0.47 %------------------------------------------------------------------------------
% 0.31/0.47 thf(a_type,type,
% 0.31/0.47 a: $tType ).
% 0.31/0.47
% 0.31/0.47 thf(cTHM514_pme,conjecture,
% 0.31/0.47 ! [Xr: a > a > $o] :
% 0.31/0.47 ( ( ! [Xx: a] : ( Xr @ Xx @ Xx )
% 0.31/0.47 & ! [Xx: a,Xy: a] :
% 0.31/0.47 ( ( Xr @ Xx @ Xy )
% 0.31/0.47 => ( Xr @ Xy @ Xx ) )
% 0.31/0.47 & ! [Xx: a,Xy: a,Xz: a] :
% 0.31/0.47 ( ( ( Xr @ Xx @ Xy )
% 0.31/0.47 & ( Xr @ Xy @ Xz ) )
% 0.31/0.47 => ( Xr @ Xx @ Xz ) ) )
% 0.31/0.47 => ! [Xx: a,Xy: a,Xz: a] :
% 0.31/0.47 ( ( Xr @ Xx @ Xy )
% 0.31/0.47 => ( ( Xr @ Xy @ Xz )
% 0.31/0.47 => ( Xr @ Xx @ Xz ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 %------------------------------------------------------------------------------
% 0.31/0.47 ------------------------
% 1.45/1.26 ---- Embedded in THF ---
% 1.45/1.26 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.45/1.26 %%% Generated on Tue Feb 24 12:39:20 EST 2026
% 1.45/1.26 %%% using '$$dhol' embedding, version 1.3.0.
% 1.45/1.26 %%% Logic specification used:
% 1.45/1.26 %%% thf(spec, logic, $$dhol).
% 1.45/1.26
% 1.45/1.26 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.o6uQ0qr2Xl/DTF2DTF29221.p
% See solution above
% 1.45/1.26 ------------------------
% 1.45/1.27 ---- Cleaned THF ---
% 1.45/1.27 thf(a_type,type,
% 1.45/1.27 a: $tType ).
% 1.45/1.27
% 1.45/1.27 thf(cTHM514_pme,conjecture,
% 1.45/1.27 ! [Xr: a > a > $o] :
% 1.45/1.27 ( ( ! [Xx: a] : ( Xr @ Xx @ Xx )
% 1.45/1.27 & ! [Xx: a,Xy: a] :
% 1.45/1.27 ( ( Xr @ Xx @ Xy )
% 1.45/1.27 => ( Xr @ Xy @ Xx ) )
% 1.45/1.27 & ! [Xx: a,Xy: a,Xz: a] :
% 1.45/1.27 ( ( ( Xr @ Xx @ Xy )
% 1.45/1.27 & ( Xr @ Xy @ Xz ) )
% 1.45/1.27 => ( Xr @ Xx @ Xz ) ) )
% 1.45/1.27 => ! [Xx: a,Xy: a,Xz: a] :
% 1.45/1.27 ( ( Xr @ Xx @ Xy )
% 1.45/1.27 => ( ( Xr @ Xy @ Xz )
% 1.45/1.27 => ( Xr @ Xx @ Xz ) ) ) ) ).
% 1.45/1.27 ------------------------
% 1.45/1.28 % (29500)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_29221 for (2999ds/4Mi)
% 1.45/1.29 % (29499)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_29221 for (2999ds/183Mi)
% 1.45/1.29 % (29500)Instruction limit reached!
% 1.45/1.29 % (29500)------------------------------
% 1.45/1.29 % (29500)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.45/1.29 % (29500)Termination reason: Unknown
% 1.45/1.29 % (29500)Termination phase: Saturation
% 1.45/1.29
% 1.45/1.29 % (29500)Memory used [KB]: 5500
% 1.45/1.29 % (29500)Time elapsed: 0.004 s
% 1.45/1.29 % (29500)Instructions burned: 6 (million)
% 1.45/1.29 % (29500)------------------------------
% 1.45/1.29 % (29500)------------------------------
% 1.45/1.29 % (29499)First to succeed.
% 1.45/1.29 % (29499)Refutation found. Thanks to Tanya!
% 1.45/1.29 % SZS status Theorem for DTF2THF_29221
% 1.45/1.29 % SZS output start Proof for DTF2THF_29221
% 1.45/1.29 thf(type_def_5, type, a: $tType).
% 1.45/1.29 thf(func_def_0, type, a: $tType).
% 1.45/1.29 thf(func_def_4, type, sK0: a > a > $o).
% 1.45/1.29 thf(func_def_5, type, sK1: a).
% 1.45/1.29 thf(func_def_6, type, sK2: a).
% 1.45/1.29 thf(func_def_7, type, sK3: a).
% 1.45/1.29 thf(f34,plain,(
% 1.45/1.29 $false),
% 1.45/1.29 inference(subsumption_resolution,[status(thm)],[f31,f16])).
% 1.45/1.29 thf(f16,plain,(
% 1.45/1.29 ((sK0 @ sK3 @ sK1) = $true)),
% 1.45/1.29 inference(cnf_transformation,[status(thm)],[f11])).
% 1.45/1.29 thf(f11,plain,(
% 1.45/1.29 (($true = (sK0 @ sK1 @ sK2)) & ((sK0 @ sK3 @ sK1) = $true) & ($true != (sK0 @ sK3 @ sK2))) & ! [X4 : a,X5 : a,X6 : a] : (($true != (sK0 @ X6 @ X4)) | ($true = (sK0 @ X5 @ X4)) | ((sK0 @ X5 @ X6) != $true)) & ! [X7 : a,X8 : a] : (((sK0 @ X8 @ X7) = $true) | ($true != (sK0 @ X7 @ X8))) & ! [X9 : a] : ($true = (sK0 @ X9 @ X9))),
% 1.45/1.29 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f8,f10,f9])).
% 1.45/1.29 thf(f9,plain,(
% 1.45/1.29 ? [X0 : a > a > $o] : (? [X1 : a,X2 : a,X3 : a] : (((X0 @ X1 @ X2) = $true) & ($true = (X0 @ X3 @ X1)) & ((X0 @ X3 @ X2) != $true)) & ! [X4 : a,X5 : a,X6 : a] : (($true != (X0 @ X6 @ X4)) | ($true = (X0 @ X5 @ X4)) | ($true != (X0 @ X5 @ X6))) & ! [X7 : a,X8 : a] : (($true = (X0 @ X8 @ X7)) | ($true != (X0 @ X7 @ X8))) & ! [X9 : a] : ($true = (X0 @ X9 @ X9))) => (? [X3 : a,X2 : a,X1 : a] : (($true = (sK0 @ X1 @ X2)) & ($true = (sK0 @ X3 @ X1)) & ((sK0 @ X3 @ X2) != $true)) & ! [X6 : a,X5 : a,X4 : a] : (($true != (sK0 @ X6 @ X4)) | ($true = (sK0 @ X5 @ X4)) | ((sK0 @ X5 @ X6) != $true)) & ! [X8 : a,X7 : a] : (((sK0 @ X8 @ X7) = $true) | ($true != (sK0 @ X7 @ X8))) & ! [X9 : a] : ($true = (sK0 @ X9 @ X9)))),
% 1.45/1.29 introduced(definition,[],[choice_axiom])).
% 1.45/1.29 thf(f10,plain,(
% 1.45/1.29 ? [X3 : a,X2 : a,X1 : a] : (($true = (sK0 @ X1 @ X2)) & ($true = (sK0 @ X3 @ X1)) & ((sK0 @ X3 @ X2) != $true)) => (($true = (sK0 @ sK1 @ sK2)) & ((sK0 @ sK3 @ sK1) = $true) & ($true != (sK0 @ sK3 @ sK2)))),
% 1.45/1.29 introduced(definition,[],[choice_axiom])).
% 1.45/1.29 thf(f8,plain,(
% 1.45/1.29 ? [X0 : a > a > $o] : (? [X1 : a,X2 : a,X3 : a] : (((X0 @ X1 @ X2) = $true) & ($true = (X0 @ X3 @ X1)) & ((X0 @ X3 @ X2) != $true)) & ! [X4 : a,X5 : a,X6 : a] : (($true != (X0 @ X6 @ X4)) | ($true = (X0 @ X5 @ X4)) | ($true != (X0 @ X5 @ X6))) & ! [X7 : a,X8 : a] : (($true = (X0 @ X8 @ X7)) | ($true != (X0 @ X7 @ X8))) & ! [X9 : a] : ($true = (X0 @ X9 @ X9)))),
% 1.45/1.29 inference(rectify,[status(thm)],[f7])).
% 1.45/1.29 thf(f7,plain,(
% 1.45/1.29 ? [X0 : a > a > $o] : (? [X9 : a,X7 : a,X8 : a] : (($true = (X0 @ X9 @ X7)) & ($true = (X0 @ X8 @ X9)) & ($true != (X0 @ X8 @ X7))) & ! [X4 : a,X5 : a,X6 : a] : (($true != (X0 @ X6 @ X4)) | ($true = (X0 @ X5 @ X4)) | ($true != (X0 @ X5 @ X6))) & ! [X3 : a,X2 : a] : (((X0 @ X2 @ X3) = $true) | ((X0 @ X3 @ X2) != $true)) & ! [X1 : a] : ((X0 @ X1 @ X1) = $true))),
% 1.45/1.29 inference(flattening,[status(thm)],[f6])).
% 1.45/1.29 thf(f6,plain,(
% 1.45/1.29 ? [X0 : a > a > $o] : (? [X8 : a,X7 : a,X9 : a] : ((($true != (X0 @ X8 @ X7)) & ($true = (X0 @ X9 @ X7))) & ($true = (X0 @ X8 @ X9))) & (! [X1 : a] : ((X0 @ X1 @ X1) = $true) & ! [X6 : a,X4 : a,X5 : a] : (($true = (X0 @ X5 @ X4)) | (($true != (X0 @ X6 @ X4)) | ($true != (X0 @ X5 @ X6)))) & ! [X3 : a,X2 : a] : (((X0 @ X2 @ X3) = $true) | ((X0 @ X3 @ X2) != $true))))),
% 1.45/1.29 inference(ennf_transformation,[status(thm)],[f5])).
% 1.45/1.29 thf(f5,plain,(
% 1.45/1.29 ~! [X0 : a > a > $o] : ((! [X1 : a] : ((X0 @ X1 @ X1) = $true) & ! [X6 : a,X4 : a,X5 : a] : ((($true = (X0 @ X6 @ X4)) & ($true = (X0 @ X5 @ X6))) => ($true = (X0 @ X5 @ X4))) & ! [X2 : a,X3 : a] : (((X0 @ X3 @ X2) = $true) => ((X0 @ X2 @ X3) = $true))) => ! [X8 : a,X7 : a,X9 : a] : (($true = (X0 @ X8 @ X9)) => (($true = (X0 @ X9 @ X7)) => ($true = (X0 @ X8 @ X7)))))),
% 1.45/1.29 inference(fool_elimination,[status(thm)],[f4])).
% 1.45/1.29 thf(f4,plain,(
% 1.45/1.29 ~! [X0 : a > a > $o] : ((! [X1 : a] : (X0 @ X1 @ X1) & ! [X2 : a,X3 : a] : ((X0 @ X3 @ X2) => (X0 @ X2 @ X3)) & ! [X4 : a,X5 : a,X6 : a] : (((X0 @ X5 @ X6) & (X0 @ X6 @ X4)) => (X0 @ X5 @ X4))) => ! [X7 : a,X8 : a,X9 : a] : ((X0 @ X8 @ X9) => ((X0 @ X9 @ X7) => (X0 @ X8 @ X7))))),
% 1.45/1.29 inference(rectify,[status(thm)],[f2])).
% 1.45/1.29 thf(f2,negated_conjecture,(
% 1.45/1.29 ~! [X0 : a > a > $o] : ((! [X1 : a] : (X0 @ X1 @ X1) & ! [X2 : a,X1 : a] : ((X0 @ X1 @ X2) => (X0 @ X2 @ X1)) & ! [X3 : a,X1 : a,X2 : a] : (((X0 @ X1 @ X2) & (X0 @ X2 @ X3)) => (X0 @ X1 @ X3))) => ! [X3 : a,X1 : a,X2 : a] : ((X0 @ X1 @ X2) => ((X0 @ X2 @ X3) => (X0 @ X1 @ X3))))),
% 1.45/1.29 inference(negated_conjecture,[status(cth)],[f1])).
% 1.45/1.29 thf(f1,conjecture,(
% 1.45/1.29 ! [X0 : a > a > $o] : ((! [X1 : a] : (X0 @ X1 @ X1) & ! [X2 : a,X1 : a] : ((X0 @ X1 @ X2) => (X0 @ X2 @ X1)) & ! [X3 : a,X1 : a,X2 : a] : (((X0 @ X1 @ X2) & (X0 @ X2 @ X3)) => (X0 @ X1 @ X3))) => ! [X3 : a,X1 : a,X2 : a] : ((X0 @ X1 @ X2) => ((X0 @ X2 @ X3) => (X0 @ X1 @ X3))))),
% 1.45/1.29 file('/export/starexec/sandbox/tmp/tmp.o6uQ0qr2Xl/DTF2THF_29221.p',cTHM514_pme)).
% 1.45/1.29 thf(f31,plain,(
% 1.45/1.29 ((sK0 @ sK3 @ sK1) != $true)),
% 1.45/1.29 inference(trivial_inequality_removal,[status(thm)],[f29])).
% 1.45/1.29 thf(f29,plain,(
% 1.45/1.29 ((sK0 @ sK3 @ sK1) != $true) | ($true != $true)),
% 1.45/1.29 inference(superposition,[status(thm)],[f24,f17])).
% 1.45/1.29 thf(f17,plain,(
% 1.45/1.29 ($true = (sK0 @ sK1 @ sK2))),
% 1.45/1.29 inference(cnf_transformation,[status(thm)],[f11])).
% 1.45/1.29 thf(f24,plain,(
% 1.45/1.29 ( ! [X0 : a] : (($true != (sK0 @ X0 @ sK2)) | ((sK0 @ sK3 @ X0) != $true)) )),
% 1.45/1.29 inference(trivial_inequality_removal,[status(thm)],[f23])).
% 1.45/1.29 thf(f23,plain,(
% 1.45/1.29 ( ! [X0 : a] : (($true != (sK0 @ X0 @ sK2)) | ((sK0 @ sK3 @ X0) != $true) | ($true != $true)) )),
% 1.45/1.29 inference(superposition,[status(thm)],[f15,f14])).
% 1.45/1.29 thf(f14,plain,(
% 1.45/1.29 ( ! [X6 : a,X4 : a,X5 : a] : (($true = (sK0 @ X5 @ X4)) | ((sK0 @ X5 @ X6) != $true) | ($true != (sK0 @ X6 @ X4))) )),
% 1.45/1.29 inference(cnf_transformation,[status(thm)],[f11])).
% 1.45/1.29 thf(f15,plain,(
% 1.45/1.29 ($true != (sK0 @ sK3 @ sK2))),
% 1.45/1.29 inference(cnf_transformation,[status(thm)],[f11])).
% 1.45/1.29 % SZS output end Proof for DTF2THF_29221
% 1.45/1.29 % (29499)------------------------------
% 1.45/1.29 % (29499)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.45/1.29 % (29499)Termination reason: Refutation
% 1.45/1.29
% 1.45/1.29 % (29499)Memory used [KB]: 5500
% 1.45/1.29 % (29499)Time elapsed: 0.003 s
% 1.45/1.29 % (29499)Instructions burned: 4 (million)
% 1.45/1.29 % (29499)------------------------------
% 1.45/1.29 % (29499)------------------------------
% 1.45/1.29 % (29498)Success in time 0.014 s
%------------------------------------------------------------------------------