%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV176^5 : 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 : n007.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 09:40:29 AM UTC 2026
% Result : Theorem 1.48s 1.28s
% Output : Refutation 1.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 3
% Syntax : Number of formulae : 24 ( 3 unt; 0 typ; 0 def)
% Number of atoms : 260 ( 71 equ; 0 cnn)
% Maximal formula atoms : 12 ( 10 avg)
% Number of connectives : 279 ( 45 ~; 32 |; 17 &; 177 @)
% ( 6 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 3 usr; 3 con; 0-2 aty)
% Number of variables : 44 ( 0 ^; 25 !; 19 ?; 44 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
cR: $i > $i > $o ).
thf(func_def_5,type,
sK1: $i > $i ).
thf(f25,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f24,f15]) ).
thf(f15,plain,
! [X2: $i,X1: $i] :
( ( $true
!= ( cR @ X1 @ sK0 ) )
| ( ( cR @ X1 @ X2 )
!= $true )
| ( ( cR @ X2 @ X1 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
! [X1: $i] :
( ( ! [X2: $i] :
( ( ( cR @ X1 @ X2 )
!= $true )
| ( ( cR @ X2 @ X1 )
!= $true ) )
| ( $true
!= ( cR @ X1 @ sK0 ) ) )
& ( ( $true
= ( cR @ X1 @ sK0 ) )
| ( ( $true
= ( cR @ X1 @ ( sK1 @ X1 ) ) )
& ( $true
= ( cR @ ( sK1 @ X1 ) @ X1 ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f9,f11,f10]) ).
thf(f10,plain,
( ? [X0: $i] :
! [X1: $i] :
( ( ! [X2: $i] :
( ( ( cR @ X1 @ X2 )
!= $true )
| ( ( cR @ X2 @ X1 )
!= $true ) )
| ( ( cR @ X1 @ X0 )
!= $true ) )
& ( ( ( cR @ X1 @ X0 )
= $true )
| ? [X3: $i] :
( ( $true
= ( cR @ X1 @ X3 ) )
& ( $true
= ( cR @ X3 @ X1 ) ) ) ) )
=> ! [X1: $i] :
( ( ! [X2: $i] :
( ( ( cR @ X1 @ X2 )
!= $true )
| ( ( cR @ X2 @ X1 )
!= $true ) )
| ( $true
!= ( cR @ X1 @ sK0 ) ) )
& ( ( $true
= ( cR @ X1 @ sK0 ) )
| ? [X3: $i] :
( ( $true
= ( cR @ X1 @ X3 ) )
& ( $true
= ( cR @ X3 @ X1 ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f11,plain,
! [X1: $i] :
( ? [X3: $i] :
( ( $true
= ( cR @ X1 @ X3 ) )
& ( $true
= ( cR @ X3 @ X1 ) ) )
=> ( ( $true
= ( cR @ X1 @ ( sK1 @ X1 ) ) )
& ( $true
= ( cR @ ( sK1 @ X1 ) @ X1 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f9,plain,
? [X0: $i] :
! [X1: $i] :
( ( ! [X2: $i] :
( ( ( cR @ X1 @ X2 )
!= $true )
| ( ( cR @ X2 @ X1 )
!= $true ) )
| ( ( cR @ X1 @ X0 )
!= $true ) )
& ( ( ( cR @ X1 @ X0 )
= $true )
| ? [X3: $i] :
( ( $true
= ( cR @ X1 @ X3 ) )
& ( $true
= ( cR @ X3 @ X1 ) ) ) ) ),
inference(rectify,[status(thm)],[f8]) ).
thf(f8,plain,
? [X0: $i] :
! [X1: $i] :
( ( ! [X2: $i] :
( ( ( cR @ X1 @ X2 )
!= $true )
| ( ( cR @ X2 @ X1 )
!= $true ) )
| ( ( cR @ X1 @ X0 )
!= $true ) )
& ( ( ( cR @ X1 @ X0 )
= $true )
| ? [X2: $i] :
( ( ( cR @ X1 @ X2 )
= $true )
& ( ( cR @ X2 @ X1 )
= $true ) ) ) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
? [X0: $i] :
! [X1: $i] :
( ! [X2: $i] :
( ( ( cR @ X1 @ X2 )
!= $true )
| ( ( cR @ X2 @ X1 )
!= $true ) )
<=> ( ( cR @ X1 @ X0 )
= $true ) ),
inference(ennf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
? [X0: $i] :
! [X1: $i] :
( ~ ? [X2: $i] :
( ( ( cR @ X1 @ X2 )
= $true )
& ( ( cR @ X2 @ X1 )
= $true ) )
<=> ( ( cR @ X1 @ X0 )
= $true ) ),
inference(flattening,[status(thm)],[f5]) ).
thf(f5,plain,
~ ~ ? [X0: $i] :
! [X1: $i] :
( ~ ? [X2: $i] :
( ( ( cR @ X1 @ X2 )
= $true )
& ( ( cR @ X2 @ X1 )
= $true ) )
<=> ( ( cR @ X1 @ X0 )
= $true ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ~ ? [X0: $i] :
! [X1: $i] :
( ( cR @ X1 @ X0 )
<=> ~ ? [X2: $i] :
( ( cR @ X1 @ X2 )
& ( cR @ X2 @ X1 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ~ ? [X0: $i] :
! [X1: $i] :
( ( cR @ X1 @ X0 )
<=> ~ ? [X2: $i] :
( ( cR @ X1 @ X2 )
& ( cR @ X2 @ X1 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
~ ? [X0: $i] :
! [X1: $i] :
( ( cR @ X1 @ X0 )
<=> ~ ? [X2: $i] :
( ( cR @ X1 @ X2 )
& ( cR @ X2 @ X1 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.vWs2C2ViRo/DTF2THF_6833.p',cTHM25) ).
thf(f24,plain,
( ( cR @ sK0 @ sK0 )
= $true ),
inference(subsumption_resolution,[status(thm)],[f21,f23]) ).
thf(f23,plain,
( $true
= ( cR @ ( sK1 @ sK0 ) @ sK0 ) ),
inference(subsumption_resolution,[status(thm)],[f22,f14]) ).
thf(f14,plain,
! [X1: $i] :
( ( $true
= ( cR @ X1 @ ( sK1 @ X1 ) ) )
| ( $true
= ( cR @ X1 @ sK0 ) ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f22,plain,
( ( $true
!= ( cR @ ( sK1 @ sK0 ) @ ( sK1 @ ( sK1 @ sK0 ) ) ) )
| ( $true
= ( cR @ ( sK1 @ sK0 ) @ sK0 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f19]) ).
thf(f19,plain,
( ( $true
= ( cR @ ( sK1 @ sK0 ) @ sK0 ) )
| ( $true
!= ( cR @ ( sK1 @ sK0 ) @ ( sK1 @ ( sK1 @ sK0 ) ) ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f18,f13]) ).
thf(f13,plain,
! [X1: $i] :
( ( $true
= ( cR @ ( sK1 @ X1 ) @ X1 ) )
| ( $true
= ( cR @ X1 @ sK0 ) ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f18,plain,
! [X0: $i] :
( ( $true
!= ( cR @ X0 @ ( sK1 @ sK0 ) ) )
| ( ( cR @ ( sK1 @ sK0 ) @ X0 )
!= $true ) ),
inference(subsumption_resolution,[status(thm)],[f17,f15]) ).
thf(f17,plain,
! [X0: $i] :
( ( ( cR @ ( sK1 @ sK0 ) @ X0 )
!= $true )
| ( ( cR @ sK0 @ sK0 )
= $true )
| ( $true
!= ( cR @ X0 @ ( sK1 @ sK0 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f16]) ).
thf(f16,plain,
! [X0: $i] :
( ( $true != $true )
| ( ( cR @ ( sK1 @ sK0 ) @ X0 )
!= $true )
| ( $true
!= ( cR @ X0 @ ( sK1 @ sK0 ) ) )
| ( ( cR @ sK0 @ sK0 )
= $true ) ),
inference(superposition,[status(thm)],[f15,f13]) ).
thf(f21,plain,
( ( ( cR @ sK0 @ sK0 )
= $true )
| ( $true
!= ( cR @ ( sK1 @ sK0 ) @ sK0 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f20]) ).
thf(f20,plain,
( ( $true
!= ( cR @ ( sK1 @ sK0 ) @ sK0 ) )
| ( ( cR @ sK0 @ sK0 )
= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f18,f14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEV176^5 : 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
% 0.16/0.34 % Computer : n007.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 12:40:38 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
% 0.29/0.46 ---- Original DTF file ---
% 0.29/0.46 thf(spec,logic,$$dhol).
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 % File : SEV176^5 : TPTP v9.2.1. Released v4.0.0.
% 0.29/0.46 % Domain : Set Theory
% 0.29/0.46 % Problem : TPS problem THM25
% 0.29/0.46 % Version : Especial.
% 0.29/0.46 % English : Quine's modification of Russell's paradox.
% 0.29/0.46
% 0.29/0.46 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.29/0.46 % Source : [Bro09]
% 0.29/0.46 % Names : tps_0281 [Bro09]
% 0.29/0.46 % : THM25 [TPS]
% 0.29/0.46
% 0.29/0.46 % Status : Theorem
% 0.29/0.46 % Rating : 0.17 v9.1.0, 0.12 v9.0.0, 0.17 v8.2.0, 0.18 v8.1.0, 0.08 v7.4.0, 0.11 v7.3.0, 0.10 v7.2.0, 0.12 v7.1.0, 0.14 v7.0.0, 0.12 v6.4.0, 0.14 v6.3.0, 0.17 v6.0.0, 0.00 v4.0.0
% 0.29/0.46 % Syntax : Number of formulae : 2 ( 0 unt; 1 typ; 0 def)
% 0.29/0.46 % Number of atoms : 3 ( 0 equ; 0 cnn)
% 0.29/0.46 % Maximal formula atoms : 3 ( 3 avg)
% 0.29/0.46 % Number of connectives : 10 ( 2 ~; 0 |; 1 &; 6 @)
% 0.29/0.46 % ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% 0.29/0.46 % Maximal formula depth : 10 ( 10 avg)
% 0.29/0.46 % Number of types : 2 ( 0 usr)
% 0.29/0.46 % Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% 0.29/0.46 % Number of symbols : 1 ( 1 usr; 0 con; 2-2 aty)
% 0.29/0.46 % Number of variables : 3 ( 0 ^; 1 !; 2 ?; 3 :)
% 0.29/0.46 % SPC : TH0_THM_NEQ_NAR
% 0.29/0.46
% 0.29/0.46 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.29/0.46 % project in the Department of Mathematical Sciences at Carnegie
% 0.29/0.46 % Mellon University. Distributed under the Creative Commons copyleft
% 0.29/0.46 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 thf(cR,type,
% 0.29/0.46 cR: $i > $i > $o ).
% 0.29/0.46
% 0.29/0.46 thf(cTHM25,conjecture,
% 0.29/0.46 ~ ? [Y: $i] :
% 0.29/0.46 ! [X: $i] :
% 0.29/0.46 ( ( cR @ X @ Y )
% 0.29/0.46 <=> ~ ? [Z: $i] :
% 0.29/0.46 ( ( cR @ X @ Z )
% 0.29/0.46 & ( cR @ Z @ X ) ) ) ).
% 0.29/0.46
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 ------------------------
% 1.48/1.25 ---- Embedded in THF ---
% 1.48/1.25 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.48/1.25 %%% Generated on Tue Feb 24 12:40:39 EST 2026
% 1.48/1.25 %%% using '$$dhol' embedding, version 1.3.0.
% 1.48/1.25 %%% Logic specification used:
% 1.48/1.25 %%% thf(spec, logic, $$dhol).
% 1.48/1.25
% 1.48/1.25 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.vWs2C2ViRo/DTF2DTF6833.p
% See solution above
% 1.48/1.25 ------------------------
% 1.48/1.26 ---- Cleaned THF ---
% 1.48/1.26 thf(cR,type,
% 1.48/1.26 cR: $i > $i > $o ).
% 1.48/1.26
% 1.48/1.26 thf(cTHM25,conjecture,
% 1.48/1.26 ~ ? [Y: $i] :
% 1.48/1.26 ! [X: $i] :
% 1.48/1.26 ( ( cR @ X @ Y )
% 1.48/1.26 <=> ~ ? [Z: $i] :
% 1.48/1.26 ( ( cR @ X @ Z )
% 1.48/1.26 & ( cR @ Z @ X ) ) ) ).
% 1.48/1.26 ------------------------
% 1.48/1.27 % (7051)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_6833 for (2999ds/275Mi)
% 1.48/1.27 % (7048)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_6833 for (2999ds/27Mi)
% 1.48/1.27 % (7051)First to succeed.
% 1.48/1.28 % (7051)Refutation found. Thanks to Tanya!
% 1.48/1.28 % SZS status Theorem for DTF2THF_6833
% 1.48/1.28 % SZS output start Proof for DTF2THF_6833
% 1.48/1.28 thf(func_def_0, type, cR: $i > $i > $o).
% 1.48/1.28 thf(func_def_5, type, sK1: $i > $i).
% 1.48/1.28 thf(f25,plain,(
% 1.48/1.28 $false),
% 1.48/1.28 inference(subsumption_resolution,[status(thm)],[f24,f15])).
% 1.48/1.28 thf(f15,plain,(
% 1.48/1.28 ( ! [X2 : $i,X1 : $i] : (($true != (cR @ X1 @ sK0)) | ((cR @ X1 @ X2) != $true) | ((cR @ X2 @ X1) != $true)) )),
% 1.48/1.28 inference(cnf_transformation,[status(thm)],[f12])).
% 1.48/1.28 thf(f12,plain,(
% 1.48/1.28 ! [X1 : $i] : ((! [X2 : $i] : (((cR @ X1 @ X2) != $true) | ((cR @ X2 @ X1) != $true)) | ($true != (cR @ X1 @ sK0))) & (($true = (cR @ X1 @ sK0)) | (($true = (cR @ X1 @ (sK1 @ X1))) & ($true = (cR @ (sK1 @ X1) @ X1)))))),
% 1.48/1.28 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f9,f11,f10])).
% 1.48/1.28 thf(f10,plain,(
% 1.48/1.28 ? [X0 : $i] : ! [X1 : $i] : ((! [X2 : $i] : (((cR @ X1 @ X2) != $true) | ((cR @ X2 @ X1) != $true)) | ((cR @ X1 @ X0) != $true)) & (((cR @ X1 @ X0) = $true) | ? [X3 : $i] : (($true = (cR @ X1 @ X3)) & ($true = (cR @ X3 @ X1))))) => ! [X1 : $i] : ((! [X2 : $i] : (((cR @ X1 @ X2) != $true) | ((cR @ X2 @ X1) != $true)) | ($true != (cR @ X1 @ sK0))) & (($true = (cR @ X1 @ sK0)) | ? [X3 : $i] : (($true = (cR @ X1 @ X3)) & ($true = (cR @ X3 @ X1)))))),
% 1.48/1.28 introduced(definition,[],[choice_axiom])).
% 1.48/1.28 thf(f11,plain,(
% 1.48/1.28 ! [X1 : $i] : (? [X3 : $i] : (($true = (cR @ X1 @ X3)) & ($true = (cR @ X3 @ X1))) => (($true = (cR @ X1 @ (sK1 @ X1))) & ($true = (cR @ (sK1 @ X1) @ X1))))),
% 1.48/1.28 introduced(definition,[],[choice_axiom])).
% 1.48/1.28 thf(f9,plain,(
% 1.48/1.28 ? [X0 : $i] : ! [X1 : $i] : ((! [X2 : $i] : (((cR @ X1 @ X2) != $true) | ((cR @ X2 @ X1) != $true)) | ((cR @ X1 @ X0) != $true)) & (((cR @ X1 @ X0) = $true) | ? [X3 : $i] : (($true = (cR @ X1 @ X3)) & ($true = (cR @ X3 @ X1)))))),
% 1.48/1.28 inference(rectify,[status(thm)],[f8])).
% 1.48/1.28 thf(f8,plain,(
% 1.48/1.28 ? [X0 : $i] : ! [X1 : $i] : ((! [X2 : $i] : (((cR @ X1 @ X2) != $true) | ((cR @ X2 @ X1) != $true)) | ((cR @ X1 @ X0) != $true)) & (((cR @ X1 @ X0) = $true) | ? [X2 : $i] : (((cR @ X1 @ X2) = $true) & ((cR @ X2 @ X1) = $true))))),
% 1.48/1.28 inference(nnf_transformation,[status(thm)],[f7])).
% 1.48/1.28 thf(f7,plain,(
% 1.48/1.28 ? [X0 : $i] : ! [X1 : $i] : (! [X2 : $i] : (((cR @ X1 @ X2) != $true) | ((cR @ X2 @ X1) != $true)) <=> ((cR @ X1 @ X0) = $true))),
% 1.48/1.28 inference(ennf_transformation,[status(thm)],[f6])).
% 1.48/1.28 thf(f6,plain,(
% 1.48/1.28 ? [X0 : $i] : ! [X1 : $i] : (~? [X2 : $i] : (((cR @ X1 @ X2) = $true) & ((cR @ X2 @ X1) = $true)) <=> ((cR @ X1 @ X0) = $true))),
% 1.48/1.28 inference(flattening,[status(thm)],[f5])).
% 1.48/1.28 thf(f5,plain,(
% 1.48/1.28 ~~? [X0 : $i] : ! [X1 : $i] : (~? [X2 : $i] : (((cR @ X1 @ X2) = $true) & ((cR @ X2 @ X1) = $true)) <=> ((cR @ X1 @ X0) = $true))),
% 1.48/1.28 inference(fool_elimination,[status(thm)],[f4])).
% 1.48/1.28 thf(f4,plain,(
% 1.48/1.28 ~~? [X0 : $i] : ! [X1 : $i] : ((cR @ X1 @ X0) <=> ~? [X2 : $i] : ((cR @ X1 @ X2) & (cR @ X2 @ X1)))),
% 1.48/1.28 inference(rectify,[status(thm)],[f2])).
% 1.48/1.28 thf(f2,negated_conjecture,(
% 1.48/1.28 ~~? [X0 : $i] : ! [X1 : $i] : ((cR @ X1 @ X0) <=> ~? [X2 : $i] : ((cR @ X1 @ X2) & (cR @ X2 @ X1)))),
% 1.48/1.28 inference(negated_conjecture,[status(cth)],[f1])).
% 1.48/1.28 thf(f1,conjecture,(
% 1.48/1.28 ~? [X0 : $i] : ! [X1 : $i] : ((cR @ X1 @ X0) <=> ~? [X2 : $i] : ((cR @ X1 @ X2) & (cR @ X2 @ X1)))),
% 1.48/1.28 file('/export/starexec/sandbox2/tmp/tmp.vWs2C2ViRo/DTF2THF_6833.p',cTHM25)).
% 1.48/1.28 thf(f24,plain,(
% 1.48/1.28 ((cR @ sK0 @ sK0) = $true)),
% 1.48/1.28 inference(subsumption_resolution,[status(thm)],[f21,f23])).
% 1.48/1.28 thf(f23,plain,(
% 1.48/1.28 ($true = (cR @ (sK1 @ sK0) @ sK0))),
% 1.48/1.28 inference(subsumption_resolution,[status(thm)],[f22,f14])).
% 1.48/1.28 thf(f14,plain,(
% 1.48/1.28 ( ! [X1 : $i] : (($true = (cR @ X1 @ (sK1 @ X1))) | ($true = (cR @ X1 @ sK0))) )),
% 1.48/1.28 inference(cnf_transformation,[status(thm)],[f12])).
% 1.48/1.28 thf(f22,plain,(
% 1.48/1.28 ($true != (cR @ (sK1 @ sK0) @ (sK1 @ (sK1 @ sK0)))) | ($true = (cR @ (sK1 @ sK0) @ sK0))),
% 1.48/1.28 inference(trivial_inequality_removal,[status(thm)],[f19])).
% 1.48/1.28 thf(f19,plain,(
% 1.48/1.28 ($true = (cR @ (sK1 @ sK0) @ sK0)) | ($true != (cR @ (sK1 @ sK0) @ (sK1 @ (sK1 @ sK0)))) | ($true != $true)),
% 1.48/1.28 inference(superposition,[status(thm)],[f18,f13])).
% 1.48/1.28 thf(f13,plain,(
% 1.48/1.28 ( ! [X1 : $i] : (($true = (cR @ (sK1 @ X1) @ X1)) | ($true = (cR @ X1 @ sK0))) )),
% 1.48/1.28 inference(cnf_transformation,[status(thm)],[f12])).
% 1.48/1.28 thf(f18,plain,(
% 1.48/1.28 ( ! [X0 : $i] : (($true != (cR @ X0 @ (sK1 @ sK0))) | ((cR @ (sK1 @ sK0) @ X0) != $true)) )),
% 1.48/1.28 inference(subsumption_resolution,[status(thm)],[f17,f15])).
% 1.48/1.28 thf(f17,plain,(
% 1.48/1.28 ( ! [X0 : $i] : (((cR @ (sK1 @ sK0) @ X0) != $true) | ((cR @ sK0 @ sK0) = $true) | ($true != (cR @ X0 @ (sK1 @ sK0)))) )),
% 1.48/1.28 inference(trivial_inequality_removal,[status(thm)],[f16])).
% 1.48/1.28 thf(f16,plain,(
% 1.48/1.28 ( ! [X0 : $i] : (($true != $true) | ((cR @ (sK1 @ sK0) @ X0) != $true) | ($true != (cR @ X0 @ (sK1 @ sK0))) | ((cR @ sK0 @ sK0) = $true)) )),
% 1.48/1.28 inference(superposition,[status(thm)],[f15,f13])).
% 1.48/1.28 thf(f21,plain,(
% 1.48/1.28 ((cR @ sK0 @ sK0) = $true) | ($true != (cR @ (sK1 @ sK0) @ sK0))),
% 1.48/1.28 inference(trivial_inequality_removal,[status(thm)],[f20])).
% 1.48/1.28 thf(f20,plain,(
% 1.48/1.28 ($true != (cR @ (sK1 @ sK0) @ sK0)) | ((cR @ sK0 @ sK0) = $true) | ($true != $true)),
% 1.48/1.28 inference(superposition,[status(thm)],[f18,f14])).
% 1.48/1.28 % SZS output end Proof for DTF2THF_6833
% 1.48/1.28 % (7051)------------------------------
% 1.48/1.28 % (7051)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.28 % (7051)Termination reason: Refutation
% 1.48/1.28
% 1.48/1.28 % (7051)Memory used [KB]: 5500
% 1.48/1.28 % (7051)Time elapsed: 0.003 s
% 1.48/1.28 % (7051)Instructions burned: 1 (million)
% 1.48/1.28 % (7051)------------------------------
% 1.48/1.28 % (7051)------------------------------
% 1.48/1.28 % (7045)Success in time 0.013 s
%------------------------------------------------------------------------------