%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV194^5 : 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 : n021.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 09:40:31 AM UTC 2026
% Result : Theorem 1.48s 1.29s
% Output : Refutation 1.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 2
% Syntax : Number of formulae : 14 ( 3 unt; 0 typ; 0 def)
% Number of atoms : 154 ( 105 equ; 0 cnn)
% Maximal formula atoms : 22 ( 11 avg)
% Number of connectives : 358 ( 58 ~; 48 |; 49 &; 192 @)
% ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 14 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 24 ( 24 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 4 usr; 4 con; 0-3 aty)
% Number of variables : 104 ( 0 ^; 71 !; 33 ?; 104 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_1,type,
x: a ).
thf(func_def_2,type,
c0: a ).
thf(func_def_3,type,
cP: a > a > a ).
thf(func_def_7,type,
sK0: a > a > a > $o ).
thf(f22,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f14,f21]) ).
thf(f21,plain,
! [X2: a] :
( $true
= ( sK0 @ c0 @ X2 @ X2 ) ),
inference(equality_resolution,[status(thm)],[f20]) ).
thf(f20,plain,
! [X2: a,X3: a] :
( ( c0 != X3 )
| ( $true
= ( sK0 @ X3 @ X2 @ X2 ) ) ),
inference(equality_resolution,[status(thm)],[f11]) ).
thf(f11,plain,
! [X2: a,X3: a,X1: a] :
( ( X1 != X2 )
| ( c0 != X3 )
| ( ( sK0 @ X3 @ X1 @ X2 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
( ( $true
!= ( sK0 @ c0 @ x @ x ) )
& ! [X1: a,X2: a,X3: a] :
( ( ! [X4: a,X5: a,X6: a,X7: a,X8: a,X9: a] :
( ( ( cP @ X5 @ X9 )
!= X1 )
| ( ( cP @ X7 @ X6 )
!= X2 )
| ( $true
!= ( sK0 @ X8 @ X9 @ X6 ) )
| ( ( cP @ X4 @ X8 )
!= X3 )
| ( $true
!= ( sK0 @ X4 @ X5 @ X7 ) ) )
& ( ( c0 != X1 )
| ( X2 != X3 ) )
& ( ( X1 != X2 )
| ( c0 != X3 ) ) )
| ( ( sK0 @ X3 @ X1 @ X2 )
= $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f8,f9]) ).
thf(f9,plain,
( ? [X0: a > a > a > $o] :
( ( ( X0 @ c0 @ x @ x )
!= $true )
& ! [X1: a,X2: a,X3: a] :
( ( ! [X4: a,X5: a,X6: a,X7: a,X8: a,X9: a] :
( ( ( cP @ X5 @ X9 )
!= X1 )
| ( ( cP @ X7 @ X6 )
!= X2 )
| ( $true
!= ( X0 @ X8 @ X9 @ X6 ) )
| ( ( cP @ X4 @ X8 )
!= X3 )
| ( $true
!= ( X0 @ X4 @ X5 @ X7 ) ) )
& ( ( c0 != X1 )
| ( X2 != X3 ) )
& ( ( X1 != X2 )
| ( c0 != X3 ) ) )
| ( $true
= ( X0 @ X3 @ X1 @ X2 ) ) ) )
=> ( ( $true
!= ( sK0 @ c0 @ x @ x ) )
& ! [X3: a,X2: a,X1: a] :
( ( ! [X9: a,X8: a,X7: a,X6: a,X5: a,X4: a] :
( ( ( cP @ X5 @ X9 )
!= X1 )
| ( ( cP @ X7 @ X6 )
!= X2 )
| ( $true
!= ( sK0 @ X8 @ X9 @ X6 ) )
| ( ( cP @ X4 @ X8 )
!= X3 )
| ( $true
!= ( sK0 @ X4 @ X5 @ X7 ) ) )
& ( ( c0 != X1 )
| ( X2 != X3 ) )
& ( ( X1 != X2 )
| ( c0 != X3 ) ) )
| ( ( sK0 @ X3 @ X1 @ X2 )
= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f8,plain,
? [X0: a > a > a > $o] :
( ( ( X0 @ c0 @ x @ x )
!= $true )
& ! [X1: a,X2: a,X3: a] :
( ( ! [X4: a,X5: a,X6: a,X7: a,X8: a,X9: a] :
( ( ( cP @ X5 @ X9 )
!= X1 )
| ( ( cP @ X7 @ X6 )
!= X2 )
| ( $true
!= ( X0 @ X8 @ X9 @ X6 ) )
| ( ( cP @ X4 @ X8 )
!= X3 )
| ( $true
!= ( X0 @ X4 @ X5 @ X7 ) ) )
& ( ( c0 != X1 )
| ( X2 != X3 ) )
& ( ( X1 != X2 )
| ( c0 != X3 ) ) )
| ( $true
= ( X0 @ X3 @ X1 @ X2 ) ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,plain,
? [X0: a > a > a > $o] :
( ( ( X0 @ c0 @ x @ x )
!= $true )
& ! [X1: a,X3: a,X2: a] :
( ( ! [X5: a,X4: a,X6: a,X9: a,X7: a,X8: a] :
( ( ( cP @ X4 @ X8 )
!= X1 )
| ( ( cP @ X9 @ X6 )
!= X3 )
| ( $true
!= ( X0 @ X7 @ X8 @ X6 ) )
| ( ( cP @ X5 @ X7 )
!= X2 )
| ( $true
!= ( X0 @ X5 @ X4 @ X9 ) ) )
& ( ( c0 != X1 )
| ( X2 != X3 ) )
& ( ( X1 != X3 )
| ( c0 != X2 ) ) )
| ( $true
= ( X0 @ X2 @ X1 @ X3 ) ) ) ),
inference(ennf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
~ ! [X0: a > a > a > $o] :
( ! [X1: a,X3: a,X2: a] :
( ( ? [X4: a,X9: a,X7: a,X6: a,X5: a,X8: a] :
( ( ( cP @ X9 @ X6 )
= X3 )
& ( ( cP @ X4 @ X8 )
= X1 )
& ( ( cP @ X5 @ X7 )
= X2 )
& ( $true
= ( X0 @ X7 @ X8 @ X6 ) )
& ( $true
= ( X0 @ X5 @ X4 @ X9 ) ) )
| ( ( c0 = X2 )
& ( X1 = X3 ) )
| ( ( c0 = X1 )
& ( X2 = X3 ) ) )
=> ( $true
= ( X0 @ X2 @ X1 @ X3 ) ) )
=> ( ( X0 @ c0 @ x @ x )
= $true ) ),
inference(true_and_false_elimination,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X0: a > a > a > $o] :
( ( ! [X1: a,X3: a,X2: a] :
( ( ? [X4: a,X9: a,X7: a,X6: a,X5: a,X8: a] :
( ( ( cP @ X9 @ X6 )
= X3 )
& ( ( cP @ X4 @ X8 )
= X1 )
& ( ( cP @ X5 @ X7 )
= X2 )
& ( $true
= ( X0 @ X7 @ X8 @ X6 ) )
& ( $true
= ( X0 @ X5 @ X4 @ X9 ) ) )
| ( ( c0 = X2 )
& ( X1 = X3 ) )
| ( ( c0 = X1 )
& ( X2 = X3 ) ) )
=> ( $true
= ( X0 @ X2 @ X1 @ X3 ) ) )
& $true )
=> ( ( X0 @ c0 @ x @ x )
= $true ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: a > a > a > $o] :
( ( ! [X1: a,X2: a,X3: a] :
( ( ( ( c0 = X2 )
& ( X1 = X3 ) )
| ( ( c0 = X1 )
& ( X2 = X3 ) )
| ? [X4: a,X5: a,X6: a,X7: a,X8: a,X9: a] :
( ( X0 @ X7 @ X8 @ X6 )
& ( ( cP @ X4 @ X8 )
= X1 )
& ( X0 @ X5 @ X4 @ X9 )
& ( ( cP @ X5 @ X7 )
= X2 )
& ( ( cP @ X9 @ X6 )
= X3 ) ) )
=> ( X0 @ X2 @ X1 @ X3 ) )
& $true )
=> ( X0 @ c0 @ x @ x ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X0: a > a > a > $o] :
( ( ! [X2: a,X1: a,X3: a] :
( ( ( ( c0 = X1 )
& ( X2 = X3 ) )
| ( ( c0 = X2 )
& ( X1 = X3 ) )
| ? [X6: a,X4: a,X9: a,X5: a,X7: a,X8: a] :
( ( X0 @ X5 @ X7 @ X9 )
& ( ( cP @ X6 @ X7 )
= X2 )
& ( X0 @ X4 @ X6 @ X8 )
& ( ( cP @ X4 @ X5 )
= X1 )
& ( ( cP @ X8 @ X9 )
= X3 ) ) )
=> ( X0 @ X1 @ X2 @ X3 ) )
& $true )
=> ( X0 @ c0 @ x @ x ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X0: a > a > a > $o] :
( ( ! [X2: a,X1: a,X3: a] :
( ( ( ( c0 = X1 )
& ( X2 = X3 ) )
| ( ( c0 = X2 )
& ( X1 = X3 ) )
| ? [X6: a,X4: a,X9: a,X5: a,X7: a,X8: a] :
( ( X0 @ X5 @ X7 @ X9 )
& ( ( cP @ X6 @ X7 )
= X2 )
& ( X0 @ X4 @ X6 @ X8 )
& ( ( cP @ X4 @ X5 )
= X1 )
& ( ( cP @ X8 @ X9 )
= X3 ) ) )
=> ( X0 @ X1 @ X2 @ X3 ) )
& $true )
=> ( X0 @ c0 @ x @ x ) ),
file('/export/starexec/sandbox2/tmp/tmp.ygolOv5gjs/DTF2THF_28560.p',cS_INCL_LEM2_pme) ).
thf(f14,plain,
( $true
!= ( sK0 @ c0 @ x @ x ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEV194^5 : TPTP v9.2.1. Released v4.0.0.
% 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.15/0.34 % Computer : n021.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Tue Feb 24 12:41:39 EST 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.19/0.45 ---- Original DTF file ---
% 0.19/0.45 thf(spec,logic,$$dhol).
% 0.19/0.45 %------------------------------------------------------------------------------
% 0.19/0.45 % File : SEV194^5 : TPTP v9.2.1. Released v4.0.0.
% 0.19/0.45 % Domain : Set Theory (Sets of sets)
% 0.19/0.45 % Problem : TPS problem from S-THMS
% 0.19/0.45 % Version : Especial.
% 0.19/0.45 % English :
% 0.19/0.45
% 0.19/0.45 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.19/0.45 % Source : [Bro09]
% 0.19/0.45 % Names : tps_1033 [Bro09]
% 0.19/0.45
% 0.19/0.45 % Status : Theorem
% 0.19/0.45 % Rating : 0.00 v6.2.0, 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
% 0.19/0.45 % Syntax : Number of formulae : 5 ( 0 unt; 4 typ; 0 def)
% 0.19/0.45 % Number of atoms : 8 ( 7 equ; 0 cnn)
% 0.19/0.45 % Maximal formula atoms : 8 ( 8 avg)
% 0.19/0.45 % Number of connectives : 29 ( 0 ~; 2 |; 7 &; 18 @)
% 0.19/0.45 % ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% 0.19/0.45 % Maximal formula depth : 23 ( 23 avg)
% 0.19/0.45 % Number of types : 2 ( 1 usr)
% 0.19/0.45 % Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% 0.19/0.45 % Number of symbols : 5 ( 3 usr; 3 con; 0-2 aty)
% 0.19/0.45 % Number of variables : 10 ( 0 ^; 4 !; 6 ?; 10 :)
% 0.19/0.45 % SPC : TH0_THM_EQU_NAR
% 0.19/0.45
% 0.19/0.45 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.19/0.45 % project in the Department of Mathematical Sciences at Carnegie
% 0.19/0.45 % Mellon University. Distributed under the Creative Commons copyleft
% 0.19/0.45 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.19/0.45 %------------------------------------------------------------------------------
% 0.19/0.45 thf(a_type,type,
% 0.19/0.45 a: $tType ).
% 0.19/0.45
% 0.19/0.45 thf(x,type,
% 0.19/0.45 x: a ).
% 0.19/0.45
% 0.19/0.45 thf(c0,type,
% 0.19/0.45 c0: a ).
% 0.19/0.45
% 0.19/0.45 thf(cP,type,
% 0.19/0.45 cP: a > a > a ).
% 0.19/0.45
% 0.19/0.45 thf(cS_INCL_LEM2_pme,conjecture,
% 0.19/0.45 ! [R: a > a > a > $o] :
% 0.19/0.45 ( ( $true
% 0.19/0.45 & ! [Xa: a,Xb: a,Xc: a] :
% 0.19/0.45 ( ( ( ( Xa = c0 )
% 0.19/0.45 & ( Xb = Xc ) )
% 0.19/0.45 | ( ( Xb = c0 )
% 0.19/0.45 & ( Xa = Xc ) )
% 0.19/0.45 | ? [Xx1: a,Xx2: a,Xy1: a,Xy2: a,Xz1: a,Xz2: a] :
% 0.19/0.45 ( ( Xa
% 0.19/0.45 = ( cP @ Xx1 @ Xx2 ) )
% 0.19/0.45 & ( Xb
% 0.19/0.45 = ( cP @ Xy1 @ Xy2 ) )
% 0.19/0.45 & ( Xc
% 0.19/0.45 = ( cP @ Xz1 @ Xz2 ) )
% 0.19/0.45 & ( R @ Xx1 @ Xy1 @ Xz1 )
% 0.19/0.45 & ( R @ Xx2 @ Xy2 @ Xz2 ) ) )
% 0.19/0.45 => ( R @ Xa @ Xb @ Xc ) ) )
% 0.19/0.45 => ( R @ c0 @ x @ x ) ) ).
% 0.19/0.45
% 0.19/0.45 %------------------------------------------------------------------------------
% 0.19/0.45 ------------------------
% 1.48/1.26 ---- Embedded in THF ---
% 1.48/1.26 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.48/1.26 %%% Generated on Tue Feb 24 12:41:39 EST 2026
% 1.48/1.26 %%% using '$$dhol' embedding, version 1.3.0.
% 1.48/1.26 %%% Logic specification used:
% 1.48/1.26 %%% thf(spec, logic, $$dhol).
% 1.48/1.26
% 1.48/1.26 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.ygolOv5gjs/DTF2DTF28560.p
% See solution above
% 1.48/1.26 ------------------------
% 1.48/1.28 ---- Cleaned THF ---
% 1.48/1.28 thf(a_type,type,
% 1.48/1.28 a: $tType ).
% 1.48/1.28
% 1.48/1.28 thf(x,type,
% 1.48/1.28 x: a ).
% 1.48/1.28
% 1.48/1.28 thf(c0,type,
% 1.48/1.28 c0: a ).
% 1.48/1.28
% 1.48/1.28 thf(cP,type,
% 1.48/1.28 cP: a > a > a ).
% 1.48/1.28
% 1.48/1.28 thf(cS_INCL_LEM2_pme,conjecture,
% 1.48/1.28 ! [R: a > a > a > $o] :
% 1.48/1.28 ( ( $true
% 1.48/1.28 & ! [Xa: a,Xb: a,Xc: a] :
% 1.48/1.28 ( ( ( ( Xa = c0 )
% 1.48/1.28 & ( Xb = Xc ) )
% 1.48/1.28 | ( ( Xb = c0 )
% 1.48/1.28 & ( Xa = Xc ) )
% 1.48/1.28 | ? [Xx1: a,Xx2: a,Xy1: a,Xy2: a,Xz1: a,Xz2: a] :
% 1.48/1.28 ( ( Xa
% 1.48/1.28 = ( cP @ Xx1 @ Xx2 ) )
% 1.48/1.28 & ( Xb
% 1.48/1.28 = ( cP @ Xy1 @ Xy2 ) )
% 1.48/1.28 & ( Xc
% 1.48/1.28 = ( cP @ Xz1 @ Xz2 ) )
% 1.48/1.28 & ( R @ Xx1 @ Xy1 @ Xz1 )
% 1.48/1.28 & ( R @ Xx2 @ Xy2 @ Xz2 ) ) )
% 1.48/1.28 => ( R @ Xa @ Xb @ Xc ) ) )
% 1.48/1.28 => ( R @ c0 @ x @ x ) ) ).
% 1.48/1.28 ------------------------
% 1.48/1.29 % (28770)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_28560 for (2999ds/4Mi)
% 1.48/1.29 % (28770)First to succeed.
% 1.48/1.29 % (28775)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_28560 for (2999ds/18Mi)
% 1.48/1.29 % (28770)Refutation found. Thanks to Tanya!
% 1.48/1.29 % SZS status Theorem for DTF2THF_28560
% 1.48/1.29 % SZS output start Proof for DTF2THF_28560
% 1.48/1.29 thf(type_def_5, type, a: $tType).
% 1.48/1.29 thf(func_def_0, type, a: $tType).
% 1.48/1.29 thf(func_def_1, type, x: a).
% 1.48/1.29 thf(func_def_2, type, c0: a).
% 1.48/1.29 thf(func_def_3, type, cP: a > a > a).
% 1.48/1.29 thf(func_def_7, type, sK0: a > a > a > $o).
% 1.48/1.29 thf(f22,plain,(
% 1.48/1.29 $false),
% 1.48/1.29 inference(subsumption_resolution,[status(thm)],[f14,f21])).
% 1.48/1.29 thf(f21,plain,(
% 1.48/1.29 ( ! [X2 : a] : (($true = (sK0 @ c0 @ X2 @ X2))) )),
% 1.48/1.29 inference(equality_resolution,[status(thm)],[f20])).
% 1.48/1.29 thf(f20,plain,(
% 1.48/1.29 ( ! [X2 : a,X3 : a] : ((c0 != X3) | ($true = (sK0 @ X3 @ X2 @ X2))) )),
% 1.48/1.29 inference(equality_resolution,[status(thm)],[f11])).
% 1.48/1.29 thf(f11,plain,(
% 1.48/1.29 ( ! [X2 : a,X3 : a,X1 : a] : ((X1 != X2) | (c0 != X3) | ((sK0 @ X3 @ X1 @ X2) = $true)) )),
% 1.48/1.29 inference(cnf_transformation,[status(thm)],[f10])).
% 1.48/1.29 thf(f10,plain,(
% 1.48/1.29 ($true != (sK0 @ c0 @ x @ x)) & ! [X1 : a,X2 : a,X3 : a] : ((! [X4 : a,X5 : a,X6 : a,X7 : a,X8 : a,X9 : a] : (((cP @ X5 @ X9) != X1) | ((cP @ X7 @ X6) != X2) | ($true != (sK0 @ X8 @ X9 @ X6)) | ((cP @ X4 @ X8) != X3) | ($true != (sK0 @ X4 @ X5 @ X7))) & ((c0 != X1) | (X2 != X3)) & ((X1 != X2) | (c0 != X3))) | ((sK0 @ X3 @ X1 @ X2) = $true))),
% 1.48/1.29 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f8,f9])).
% 1.48/1.29 thf(f9,plain,(
% 1.48/1.29 ? [X0 : a > a > a > $o] : (((X0 @ c0 @ x @ x) != $true) & ! [X1 : a,X2 : a,X3 : a] : ((! [X4 : a,X5 : a,X6 : a,X7 : a,X8 : a,X9 : a] : (((cP @ X5 @ X9) != X1) | ((cP @ X7 @ X6) != X2) | ($true != (X0 @ X8 @ X9 @ X6)) | ((cP @ X4 @ X8) != X3) | ($true != (X0 @ X4 @ X5 @ X7))) & ((c0 != X1) | (X2 != X3)) & ((X1 != X2) | (c0 != X3))) | ($true = (X0 @ X3 @ X1 @ X2)))) => (($true != (sK0 @ c0 @ x @ x)) & ! [X3 : a,X2 : a,X1 : a] : ((! [X9 : a,X8 : a,X7 : a,X6 : a,X5 : a,X4 : a] : (((cP @ X5 @ X9) != X1) | ((cP @ X7 @ X6) != X2) | ($true != (sK0 @ X8 @ X9 @ X6)) | ((cP @ X4 @ X8) != X3) | ($true != (sK0 @ X4 @ X5 @ X7))) & ((c0 != X1) | (X2 != X3)) & ((X1 != X2) | (c0 != X3))) | ((sK0 @ X3 @ X1 @ X2) = $true)))),
% 1.48/1.29 introduced(definition,[],[choice_axiom])).
% 1.48/1.29 thf(f8,plain,(
% 1.48/1.29 ? [X0 : a > a > a > $o] : (((X0 @ c0 @ x @ x) != $true) & ! [X1 : a,X2 : a,X3 : a] : ((! [X4 : a,X5 : a,X6 : a,X7 : a,X8 : a,X9 : a] : (((cP @ X5 @ X9) != X1) | ((cP @ X7 @ X6) != X2) | ($true != (X0 @ X8 @ X9 @ X6)) | ((cP @ X4 @ X8) != X3) | ($true != (X0 @ X4 @ X5 @ X7))) & ((c0 != X1) | (X2 != X3)) & ((X1 != X2) | (c0 != X3))) | ($true = (X0 @ X3 @ X1 @ X2))))),
% 1.48/1.29 inference(rectify,[status(thm)],[f7])).
% 1.48/1.29 thf(f7,plain,(
% 1.48/1.29 ? [X0 : a > a > a > $o] : (((X0 @ c0 @ x @ x) != $true) & ! [X1 : a,X3 : a,X2 : a] : ((! [X5 : a,X4 : a,X6 : a,X9 : a,X7 : a,X8 : a] : (((cP @ X4 @ X8) != X1) | ((cP @ X9 @ X6) != X3) | ($true != (X0 @ X7 @ X8 @ X6)) | ((cP @ X5 @ X7) != X2) | ($true != (X0 @ X5 @ X4 @ X9))) & ((c0 != X1) | (X2 != X3)) & ((X1 != X3) | (c0 != X2))) | ($true = (X0 @ X2 @ X1 @ X3))))),
% 1.48/1.29 inference(ennf_transformation,[status(thm)],[f6])).
% 1.48/1.29 thf(f6,plain,(
% 1.48/1.29 ~! [X0 : a > a > a > $o] : (! [X1 : a,X3 : a,X2 : a] : ((? [X4 : a,X9 : a,X7 : a,X6 : a,X5 : a,X8 : a] : (((cP @ X9 @ X6) = X3) & ((cP @ X4 @ X8) = X1) & ((cP @ X5 @ X7) = X2) & ($true = (X0 @ X7 @ X8 @ X6)) & ($true = (X0 @ X5 @ X4 @ X9))) | ((c0 = X2) & (X1 = X3)) | ((c0 = X1) & (X2 = X3))) => ($true = (X0 @ X2 @ X1 @ X3))) => ((X0 @ c0 @ x @ x) = $true))),
% 1.48/1.29 inference(true_and_false_elimination,[status(thm)],[f5])).
% 1.48/1.29 thf(f5,plain,(
% 1.48/1.29 ~! [X0 : a > a > a > $o] : ((! [X1 : a,X3 : a,X2 : a] : ((? [X4 : a,X9 : a,X7 : a,X6 : a,X5 : a,X8 : a] : (((cP @ X9 @ X6) = X3) & ((cP @ X4 @ X8) = X1) & ((cP @ X5 @ X7) = X2) & ($true = (X0 @ X7 @ X8 @ X6)) & ($true = (X0 @ X5 @ X4 @ X9))) | ((c0 = X2) & (X1 = X3)) | ((c0 = X1) & (X2 = X3))) => ($true = (X0 @ X2 @ X1 @ X3))) & $true) => ((X0 @ c0 @ x @ x) = $true))),
% 1.48/1.29 inference(fool_elimination,[status(thm)],[f4])).
% 1.48/1.29 thf(f4,plain,(
% 1.48/1.29 ~! [X0 : a > a > a > $o] : ((! [X1 : a,X2 : a,X3 : a] : ((((c0 = X2) & (X1 = X3)) | ((c0 = X1) & (X2 = X3)) | ? [X4 : a,X5 : a,X6 : a,X7 : a,X8 : a,X9 : a] : ((X0 @ X7 @ X8 @ X6) & ((cP @ X4 @ X8) = X1) & (X0 @ X5 @ X4 @ X9) & ((cP @ X5 @ X7) = X2) & ((cP @ X9 @ X6) = X3))) => (X0 @ X2 @ X1 @ X3)) & $true) => (X0 @ c0 @ x @ x))),
% 1.48/1.29 inference(rectify,[status(thm)],[f2])).
% 1.48/1.29 thf(f2,negated_conjecture,(
% 1.48/1.29 ~! [X0 : a > a > a > $o] : ((! [X2 : a,X1 : a,X3 : a] : ((((c0 = X1) & (X2 = X3)) | ((c0 = X2) & (X1 = X3)) | ? [X6 : a,X4 : a,X9 : a,X5 : a,X7 : a,X8 : a] : ((X0 @ X5 @ X7 @ X9) & ((cP @ X6 @ X7) = X2) & (X0 @ X4 @ X6 @ X8) & ((cP @ X4 @ X5) = X1) & ((cP @ X8 @ X9) = X3))) => (X0 @ X1 @ X2 @ X3)) & $true) => (X0 @ c0 @ x @ x))),
% 1.48/1.29 inference(negated_conjecture,[status(cth)],[f1])).
% 1.48/1.29 thf(f1,conjecture,(
% 1.48/1.29 ! [X0 : a > a > a > $o] : ((! [X2 : a,X1 : a,X3 : a] : ((((c0 = X1) & (X2 = X3)) | ((c0 = X2) & (X1 = X3)) | ? [X6 : a,X4 : a,X9 : a,X5 : a,X7 : a,X8 : a] : ((X0 @ X5 @ X7 @ X9) & ((cP @ X6 @ X7) = X2) & (X0 @ X4 @ X6 @ X8) & ((cP @ X4 @ X5) = X1) & ((cP @ X8 @ X9) = X3))) => (X0 @ X1 @ X2 @ X3)) & $true) => (X0 @ c0 @ x @ x))),
% 1.48/1.29 file('/export/starexec/sandbox2/tmp/tmp.ygolOv5gjs/DTF2THF_28560.p',cS_INCL_LEM2_pme)).
% 1.48/1.29 thf(f14,plain,(
% 1.48/1.29 ($true != (sK0 @ c0 @ x @ x))),
% 1.48/1.29 inference(cnf_transformation,[status(thm)],[f10])).
% 1.48/1.29 % SZS output end Proof for DTF2THF_28560
% 1.48/1.29 % (28770)------------------------------
% 1.48/1.29 % (28770)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.29 % (28770)Termination reason: Refutation
% 1.48/1.29
% 1.48/1.29 % (28770)Memory used [KB]: 5500
% 1.48/1.29 % (28770)Time elapsed: 0.003 s
% 1.48/1.29 % (28770)Instructions burned: 1 (million)
% 1.48/1.29 % (28770)------------------------------
% 1.48/1.29 % (28770)------------------------------
% 1.48/1.29 % (28768)Success in time 0.013 s
%------------------------------------------------------------------------------