%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU889^5 : 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 : n002.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 09:37:40 AM UTC 2026
% Result : Theorem 1.47s 1.25s
% Output : Refutation 1.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 4
% Syntax : Number of formulae : 18 ( 6 unt; 0 typ; 0 def)
% Number of atoms : 105 ( 58 equ; 0 cnn)
% Maximal formula atoms : 10 ( 5 avg)
% Number of connectives : 143 ( 18 ~; 7 |; 33 &; 78 @)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 38 ( 0 ^; 11 !; 27 ?; 38 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
c: $tType ).
thf(type_def_6,type,
b: $tType ).
thf(type_def_8,type,
a: $tType ).
thf(func_def_0,type,
c: $tType ).
thf(func_def_1,type,
b: $tType ).
thf(func_def_2,type,
a: $tType ).
thf(func_def_3,type,
cG: c > b ).
thf(func_def_4,type,
cF: b > a ).
thf(func_def_5,type,
cS: c > $o ).
thf(func_def_9,type,
sK0: a ).
thf(func_def_10,type,
sK1: b ).
thf(func_def_11,type,
sK2: c ).
thf(f19,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f18,f13]) ).
thf(f13,plain,
( $true
= ( cS @ sK2 ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( ! [X1: c] :
( ( ( cF @ ( cG @ X1 ) )
!= sK0 )
| ( ( cS @ X1 )
!= $true ) )
& ( ( cF @ sK1 )
= sK0 )
& ( $true
= ( cS @ sK2 ) )
& ( ( cG @ sK2 )
= sK1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f7,f10,f9,f8]) ).
thf(f8,plain,
( ? [X0: a] :
( ! [X1: c] :
( ( ( cF @ ( cG @ X1 ) )
!= X0 )
| ( ( cS @ X1 )
!= $true ) )
& ? [X2: b] :
( ( ( cF @ X2 )
= X0 )
& ? [X3: c] :
( ( ( cS @ X3 )
= $true )
& ( ( cG @ X3 )
= X2 ) ) ) )
=> ( ! [X1: c] :
( ( ( cF @ ( cG @ X1 ) )
!= sK0 )
| ( ( cS @ X1 )
!= $true ) )
& ? [X2: b] :
( ( sK0
= ( cF @ X2 ) )
& ? [X3: c] :
( ( ( cS @ X3 )
= $true )
& ( ( cG @ X3 )
= X2 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f9,plain,
( ? [X2: b] :
( ( sK0
= ( cF @ X2 ) )
& ? [X3: c] :
( ( ( cS @ X3 )
= $true )
& ( ( cG @ X3 )
= X2 ) ) )
=> ( ( ( cF @ sK1 )
= sK0 )
& ? [X3: c] :
( ( ( cS @ X3 )
= $true )
& ( ( cG @ X3 )
= sK1 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f10,plain,
( ? [X3: c] :
( ( ( cS @ X3 )
= $true )
& ( ( cG @ X3 )
= sK1 ) )
=> ( ( $true
= ( cS @ sK2 ) )
& ( ( cG @ sK2 )
= sK1 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f7,plain,
? [X0: a] :
( ! [X1: c] :
( ( ( cF @ ( cG @ X1 ) )
!= X0 )
| ( ( cS @ X1 )
!= $true ) )
& ? [X2: b] :
( ( ( cF @ X2 )
= X0 )
& ? [X3: c] :
( ( ( cS @ X3 )
= $true )
& ( ( cG @ X3 )
= X2 ) ) ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,plain,
? [X0: a] :
( ! [X3: c] :
( ( ( cF @ ( cG @ X3 ) )
!= X0 )
| ( ( cS @ X3 )
!= $true ) )
& ? [X1: b] :
( ( ( cF @ X1 )
= X0 )
& ? [X2: c] :
( ( ( cS @ X2 )
= $true )
& ( ( cG @ X2 )
= X1 ) ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X0: a] :
( ? [X1: b] :
( ( ( cF @ X1 )
= X0 )
& ? [X2: c] :
( ( ( cS @ X2 )
= $true )
& ( ( cG @ X2 )
= X1 ) ) )
=> ? [X3: c] :
( ( ( cF @ ( cG @ X3 ) )
= X0 )
& ( ( cS @ X3 )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: a] :
( ? [X1: b] :
( ? [X2: c] :
( ( ( cG @ X2 )
= X1 )
& ( cS @ X2 ) )
& ( ( cF @ X1 )
= X0 ) )
=> ? [X3: c] :
( ( ( cF @ ( cG @ X3 ) )
= X0 )
& ( cS @ X3 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X0: a] :
( ? [X1: b] :
( ? [X2: c] :
( ( ( cG @ X2 )
= X1 )
& ( cS @ X2 ) )
& ( ( cF @ X1 )
= X0 ) )
=> ? [X1: c] :
( ( ( cF @ ( cG @ X1 ) )
= X0 )
& ( cS @ X1 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X0: a] :
( ? [X1: b] :
( ? [X2: c] :
( ( ( cG @ X2 )
= X1 )
& ( cS @ X2 ) )
& ( ( cF @ X1 )
= X0 ) )
=> ? [X1: c] :
( ( ( cF @ ( cG @ X1 ) )
= X0 )
& ( cS @ X1 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.XYqADiLPqy/DTF2THF_23677.p',cTHM29A_pme) ).
thf(f18,plain,
( $true
!= ( cS @ sK2 ) ),
inference(equality_resolution,[status(thm)],[f17]) ).
thf(f17,plain,
! [X1: c] :
( ( ( cF @ ( cG @ X1 ) )
!= ( cF @ ( cG @ sK2 ) ) )
| ( ( cS @ X1 )
!= $true ) ),
inference(definition_unfolding,[status(thm)],[f15,f16]) ).
thf(f16,plain,
( sK0
= ( cF @ ( cG @ sK2 ) ) ),
inference(definition_unfolding,[status(thm)],[f14,f12]) ).
thf(f12,plain,
( ( cG @ sK2 )
= sK1 ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f14,plain,
( ( cF @ sK1 )
= sK0 ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f15,plain,
! [X1: c] :
( ( ( cF @ ( cG @ X1 ) )
!= sK0 )
| ( ( cS @ X1 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU889^5 : TPTP v9.2.1. Released v4.0.0.
% 0.13/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.33 % Computer : n002.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 12:36:18 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.19/0.46 ---- Original DTF file ---
% 0.19/0.46 thf(spec,logic,$$dhol).
% 0.19/0.46 %------------------------------------------------------------------------------
% 0.19/0.46 % File : SEU889^5 : TPTP v9.2.1. Released v4.0.0.
% 0.19/0.46 % Domain : Set Theory
% 0.19/0.46 % Problem : TPS problem THM29A
% 0.19/0.46 % Version : Especial.
% 0.19/0.46 % English :
% 0.19/0.46
% 0.19/0.46 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.19/0.46 % Source : [Bro09]
% 0.19/0.46 % Names : tps_0298 [Bro09]
% 0.19/0.46 % : THM29A [TPS]
% 0.19/0.46
% 0.19/0.46 % Status : Theorem
% 0.19/0.46 % Rating : 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
% 0.19/0.46 % Syntax : Number of formulae : 7 ( 0 unt; 6 typ; 0 def)
% 0.19/0.46 % Number of atoms : 5 ( 3 equ; 0 cnn)
% 0.19/0.46 % Maximal formula atoms : 5 ( 5 avg)
% 0.19/0.46 % Number of connectives : 10 ( 0 ~; 0 |; 3 &; 6 @)
% 0.19/0.46 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.19/0.46 % Maximal formula depth : 8 ( 8 avg)
% 0.19/0.46 % Number of types : 4 ( 3 usr)
% 0.19/0.46 % Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% 0.19/0.46 % Number of symbols : 4 ( 3 usr; 0 con; 1-2 aty)
% 0.19/0.46 % Number of variables : 4 ( 0 ^; 1 !; 3 ?; 4 :)
% 0.19/0.46 % SPC : TH0_THM_EQU_NAR
% 0.19/0.46
% 0.19/0.46 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.19/0.46 % project in the Department of Mathematical Sciences at Carnegie
% 0.19/0.46 % Mellon University. Distributed under the Creative Commons copyleft
% 0.19/0.46 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.19/0.46 % : Polymorphic definitions expanded.
% 0.19/0.46 %------------------------------------------------------------------------------
% 0.19/0.46 thf(c_type,type,
% 0.19/0.46 c: $tType ).
% 0.19/0.46
% 0.19/0.46 thf(b_type,type,
% 0.19/0.46 b: $tType ).
% 0.19/0.46
% 0.19/0.46 thf(a_type,type,
% 0.19/0.46 a: $tType ).
% 0.19/0.46
% 0.19/0.46 thf(cG,type,
% 0.19/0.46 cG: c > b ).
% 0.19/0.46
% 0.19/0.46 thf(cF,type,
% 0.19/0.46 cF: b > a ).
% 0.19/0.46
% 0.19/0.46 thf(cS,type,
% 0.19/0.46 cS: c > $o ).
% 0.19/0.46
% 0.19/0.46 thf(cTHM29A_pme,conjecture,
% 0.19/0.46 ! [Xx: a] :
% 0.19/0.46 ( ? [Xt: b] :
% 0.19/0.46 ( ? [Xt0: c] :
% 0.19/0.46 ( ( cS @ Xt0 )
% 0.19/0.46 & ( Xt
% 0.19/0.46 = ( cG @ Xt0 ) ) )
% 0.19/0.46 & ( Xx
% 0.19/0.46 = ( cF @ Xt ) ) )
% 0.19/0.46 => ? [Xt: c] :
% 0.19/0.46 ( ( cS @ Xt )
% 0.19/0.46 & ( Xx
% 0.19/0.46 = ( cF @ ( cG @ Xt ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 %------------------------------------------------------------------------------
% 0.19/0.46 ------------------------
% 1.47/1.23 ---- Embedded in THF ---
% 1.47/1.23 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.47/1.23 %%% Generated on Tue Feb 24 12:36:19 EST 2026
% 1.47/1.23 %%% using '$$dhol' embedding, version 1.3.0.
% 1.47/1.23 %%% Logic specification used:
% 1.47/1.23 %%% thf(spec, logic, $$dhol).
% 1.47/1.23
% 1.47/1.23 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.XYqADiLPqy/DTF2DTF23677.p
% See solution above
% 1.47/1.23 ------------------------
% 1.47/1.23 ---- Cleaned THF ---
% 1.47/1.23 thf(c_type,type,
% 1.47/1.23 c: $tType ).
% 1.47/1.23
% 1.47/1.23 thf(b_type,type,
% 1.47/1.23 b: $tType ).
% 1.47/1.23
% 1.47/1.23 thf(a_type,type,
% 1.47/1.23 a: $tType ).
% 1.47/1.23
% 1.47/1.23 thf(cG,type,
% 1.47/1.23 cG: c > b ).
% 1.47/1.23
% 1.47/1.23 thf(cF,type,
% 1.47/1.23 cF: b > a ).
% 1.47/1.23
% 1.47/1.23 thf(cS,type,
% 1.47/1.23 cS: c > $o ).
% 1.47/1.23
% 1.47/1.23 thf(cTHM29A_pme,conjecture,
% 1.47/1.23 ! [Xx: a] :
% 1.47/1.23 ( ? [Xt: b] :
% 1.47/1.23 ( ? [Xt0: c] :
% 1.47/1.23 ( ( cS @ Xt0 )
% 1.47/1.23 & ( Xt
% 1.47/1.23 = ( cG @ Xt0 ) ) )
% 1.47/1.23 & ( Xx
% 1.47/1.23 = ( cF @ Xt ) ) )
% 1.47/1.23 => ? [Xt: c] :
% 1.47/1.23 ( ( cS @ Xt )
% 1.47/1.23 & ( Xx
% 1.47/1.23 = ( cF @ ( cG @ Xt ) ) ) ) ) ).
% 1.47/1.23 ------------------------
% 1.47/1.25 % (23820)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_23677 for (2999ds/2Mi)
% 1.47/1.25 % (23820)Instruction limit reached!
% 1.47/1.25 % (23820)------------------------------
% 1.47/1.25 % (23820)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.47/1.25 % (23820)Termination reason: Unknown
% 1.47/1.25 % (23820)Termination phase: Saturation
% 1.47/1.25
% 1.47/1.25 % (23820)Memory used [KB]: 5500
% 1.47/1.25 % (23820)Time elapsed: 0.002 s
% 1.47/1.25 % (23820)Instructions burned: 2 (million)
% 1.47/1.25 % (23820)------------------------------
% 1.47/1.25 % (23820)------------------------------
% 1.47/1.25 % (23821)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_23677 for (2999ds/2Mi)
% 1.47/1.25 % (23817)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_23677 for (2999ds/183Mi)
% 1.47/1.25 % (23821)Instruction limit reached!
% 1.47/1.25 % (23821)------------------------------
% 1.47/1.25 % (23821)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.47/1.25 % (23821)Termination reason: Unknown
% 1.47/1.25 % (23821)Termination phase: Saturation
% 1.47/1.25
% 1.47/1.25 % (23821)Memory used [KB]: 5500
% 1.47/1.25 % (23821)Time elapsed: 0.003 s
% 1.47/1.25 % (23821)Instructions burned: 2 (million)
% 1.47/1.25 % (23821)------------------------------
% 1.47/1.25 % (23821)------------------------------
% 1.47/1.25 % (23817)First to succeed.
% 1.47/1.25 % (23822)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_23677 for (2999ds/275Mi)
% 1.47/1.25 % (23817)Refutation found. Thanks to Tanya!
% 1.47/1.25 % SZS status Theorem for DTF2THF_23677
% 1.47/1.25 % SZS output start Proof for DTF2THF_23677
% 1.47/1.25 thf(type_def_5, type, c: $tType).
% 1.47/1.25 thf(type_def_6, type, b: $tType).
% 1.47/1.25 thf(type_def_8, type, a: $tType).
% 1.47/1.25 thf(func_def_0, type, c: $tType).
% 1.47/1.25 thf(func_def_1, type, b: $tType).
% 1.47/1.25 thf(func_def_2, type, a: $tType).
% 1.47/1.25 thf(func_def_3, type, cG: c > b).
% 1.47/1.25 thf(func_def_4, type, cF: b > a).
% 1.47/1.25 thf(func_def_5, type, cS: c > $o).
% 1.47/1.25 thf(func_def_9, type, sK0: a).
% 1.47/1.25 thf(func_def_10, type, sK1: b).
% 1.47/1.25 thf(func_def_11, type, sK2: c).
% 1.47/1.25 thf(f19,plain,(
% 1.47/1.25 $false),
% 1.47/1.25 inference(subsumption_resolution,[status(thm)],[f18,f13])).
% 1.47/1.25 thf(f13,plain,(
% 1.47/1.25 ($true = (cS @ sK2))),
% 1.47/1.25 inference(cnf_transformation,[status(thm)],[f11])).
% 1.47/1.25 thf(f11,plain,(
% 1.47/1.25 ! [X1 : c] : (((cF @ (cG @ X1)) != sK0) | ((cS @ X1) != $true)) & (((cF @ sK1) = sK0) & (($true = (cS @ sK2)) & ((cG @ sK2) = sK1)))),
% 1.47/1.25 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f7,f10,f9,f8])).
% 1.47/1.25 thf(f8,plain,(
% 1.47/1.25 ? [X0 : a] : (! [X1 : c] : (((cF @ (cG @ X1)) != X0) | ((cS @ X1) != $true)) & ? [X2 : b] : (((cF @ X2) = X0) & ? [X3 : c] : (((cS @ X3) = $true) & ((cG @ X3) = X2)))) => (! [X1 : c] : (((cF @ (cG @ X1)) != sK0) | ((cS @ X1) != $true)) & ? [X2 : b] : ((sK0 = (cF @ X2)) & ? [X3 : c] : (((cS @ X3) = $true) & ((cG @ X3) = X2))))),
% 1.47/1.25 introduced(definition,[],[choice_axiom])).
% 1.47/1.25 thf(f9,plain,(
% 1.47/1.25 ? [X2 : b] : ((sK0 = (cF @ X2)) & ? [X3 : c] : (((cS @ X3) = $true) & ((cG @ X3) = X2))) => (((cF @ sK1) = sK0) & ? [X3 : c] : (((cS @ X3) = $true) & ((cG @ X3) = sK1)))),
% 1.47/1.25 introduced(definition,[],[choice_axiom])).
% 1.47/1.25 thf(f10,plain,(
% 1.47/1.25 ? [X3 : c] : (((cS @ X3) = $true) & ((cG @ X3) = sK1)) => (($true = (cS @ sK2)) & ((cG @ sK2) = sK1))),
% 1.47/1.25 introduced(definition,[],[choice_axiom])).
% 1.47/1.25 thf(f7,plain,(
% 1.47/1.25 ? [X0 : a] : (! [X1 : c] : (((cF @ (cG @ X1)) != X0) | ((cS @ X1) != $true)) & ? [X2 : b] : (((cF @ X2) = X0) & ? [X3 : c] : (((cS @ X3) = $true) & ((cG @ X3) = X2))))),
% 1.47/1.25 inference(rectify,[status(thm)],[f6])).
% 1.47/1.25 thf(f6,plain,(
% 1.47/1.25 ? [X0 : a] : (! [X3 : c] : (((cF @ (cG @ X3)) != X0) | ((cS @ X3) != $true)) & ? [X1 : b] : (((cF @ X1) = X0) & ? [X2 : c] : (((cS @ X2) = $true) & ((cG @ X2) = X1))))),
% 1.47/1.25 inference(ennf_transformation,[status(thm)],[f5])).
% 1.47/1.25 thf(f5,plain,(
% 1.47/1.25 ~! [X0 : a] : (? [X1 : b] : (((cF @ X1) = X0) & ? [X2 : c] : (((cS @ X2) = $true) & ((cG @ X2) = X1))) => ? [X3 : c] : (((cF @ (cG @ X3)) = X0) & ((cS @ X3) = $true)))),
% 1.47/1.25 inference(fool_elimination,[status(thm)],[f4])).
% 1.47/1.25 thf(f4,plain,(
% 1.47/1.25 ~! [X0 : a] : (? [X1 : b] : (? [X2 : c] : (((cG @ X2) = X1) & (cS @ X2)) & ((cF @ X1) = X0)) => ? [X3 : c] : (((cF @ (cG @ X3)) = X0) & (cS @ X3)))),
% 1.47/1.25 inference(rectify,[status(thm)],[f2])).
% 1.47/1.25 thf(f2,negated_conjecture,(
% 1.47/1.25 ~! [X0 : a] : (? [X1 : b] : (? [X2 : c] : (((cG @ X2) = X1) & (cS @ X2)) & ((cF @ X1) = X0)) => ? [X1 : c] : (((cF @ (cG @ X1)) = X0) & (cS @ X1)))),
% 1.47/1.25 inference(negated_conjecture,[status(cth)],[f1])).
% 1.47/1.25 thf(f1,conjecture,(
% 1.47/1.25 ! [X0 : a] : (? [X1 : b] : (? [X2 : c] : (((cG @ X2) = X1) & (cS @ X2)) & ((cF @ X1) = X0)) => ? [X1 : c] : (((cF @ (cG @ X1)) = X0) & (cS @ X1)))),
% 1.47/1.25 file('/export/starexec/sandbox2/tmp/tmp.XYqADiLPqy/DTF2THF_23677.p',cTHM29A_pme)).
% 1.47/1.25 thf(f18,plain,(
% 1.47/1.25 ($true != (cS @ sK2))),
% 1.47/1.25 inference(equality_resolution,[status(thm)],[f17])).
% 1.47/1.25 thf(f17,plain,(
% 1.47/1.25 ( ! [X1 : c] : (((cF @ (cG @ X1)) != (cF @ (cG @ sK2))) | ((cS @ X1) != $true)) )),
% 1.47/1.25 inference(definition_unfolding,[status(thm)],[f15,f16])).
% 1.47/1.25 thf(f16,plain,(
% 1.47/1.25 (sK0 = (cF @ (cG @ sK2)))),
% 1.47/1.25 inference(definition_unfolding,[status(thm)],[f14,f12])).
% 1.47/1.25 thf(f12,plain,(
% 1.47/1.25 ((cG @ sK2) = sK1)),
% 1.47/1.25 inference(cnf_transformation,[status(thm)],[f11])).
% 1.47/1.25 thf(f14,plain,(
% 1.47/1.25 ((cF @ sK1) = sK0)),
% 1.47/1.25 inference(cnf_transformation,[status(thm)],[f11])).
% 1.47/1.25 thf(f15,plain,(
% 1.47/1.25 ( ! [X1 : c] : (((cF @ (cG @ X1)) != sK0) | ((cS @ X1) != $true)) )),
% 1.47/1.25 inference(cnf_transformation,[status(thm)],[f11])).
% 1.47/1.25 % SZS output end Proof for DTF2THF_23677
% 1.47/1.25 % (23817)------------------------------
% 1.47/1.25 % (23817)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.47/1.25 % (23817)Termination reason: Refutation
% 1.47/1.25
% 1.47/1.25 % (23817)Memory used [KB]: 5500
% 1.47/1.25 % (23817)Time elapsed: 0.003 s
% 1.47/1.25 % (23817)Instructions burned: 1 (million)
% 1.47/1.25 % (23817)------------------------------
% 1.47/1.25 % (23817)------------------------------
% 1.47/1.25 % (23816)Success in time 0.013 s
%------------------------------------------------------------------------------