%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO095^5 : 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 : n008.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 09:53:22 AM UTC 2026
% Result : Theorem 1.46s 1.28s
% Output : Refutation 1.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 3
% Syntax : Number of formulae : 25 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 169 ( 44 equ; 0 cnn)
% Maximal formula atoms : 6 ( 6 avg)
% Number of connectives : 189 ( 11 ~; 6 |; 16 &; 140 @)
% ( 6 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 3 usr; 4 con; 0-2 aty)
% Number of variables : 62 ( 0 ^; 50 !; 12 ?; 62 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
cR: $i > $i > $o ).
thf(f62,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f55]) ).
thf(f55,plain,
$false = $true,
inference(superposition,[status(thm)],[f51,f29]) ).
thf(f29,plain,
( $false
= ( cR @ sK0 @ sK0 ) ),
inference(trivial_inequality_removal,[status(thm)],[f26]) ).
thf(f26,plain,
( ( $false
= ( cR @ sK0 @ sK0 ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f15,f17]) ).
thf(f17,plain,
! [X4: $i,X5: $i] :
( ( $true
= ( cR @ X4 @ X5 ) )
| ( ( cR @ X4 @ X4 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f12]) ).
thf(f12,plain,
! [X4: $i,X5: $i] :
( ( cR @ X4 @ X4 )
= ( cR @ X4 @ X5 ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( ( ( cR @ sK0 @ sK0 )
!= $true )
& ( ( cR @ sK1 @ sK1 )
= $true )
& ! [X2: $i,X3: $i] :
( ( cR @ X2 @ X3 )
= ( cR @ X3 @ X3 ) )
& ! [X4: $i,X5: $i] :
( ( cR @ X4 @ X4 )
= ( cR @ X4 @ X5 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f8,f10,f9]) ).
thf(f9,plain,
( ? [X0: $i] :
( ( cR @ X0 @ X0 )
!= $true )
=> ( ( cR @ sK0 @ sK0 )
!= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f10,plain,
( ? [X1: $i] :
( ( cR @ X1 @ X1 )
= $true )
=> ( ( cR @ sK1 @ sK1 )
= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f8,plain,
( ? [X0: $i] :
( ( cR @ X0 @ X0 )
!= $true )
& ? [X1: $i] :
( ( cR @ X1 @ X1 )
= $true )
& ! [X2: $i,X3: $i] :
( ( cR @ X2 @ X3 )
= ( cR @ X3 @ X3 ) )
& ! [X4: $i,X5: $i] :
( ( cR @ X4 @ X4 )
= ( cR @ X4 @ X5 ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,plain,
( ? [X5: $i] :
( ( cR @ X5 @ X5 )
!= $true )
& ? [X4: $i] :
( ( cR @ X4 @ X4 )
= $true )
& ! [X2: $i,X3: $i] :
( ( cR @ X2 @ X3 )
= ( cR @ X3 @ X3 ) )
& ! [X1: $i,X0: $i] :
( ( cR @ X1 @ X0 )
= ( cR @ X1 @ X1 ) ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
( ? [X5: $i] :
( ( cR @ X5 @ X5 )
!= $true )
& ? [X4: $i] :
( ( cR @ X4 @ X4 )
= $true )
& ! [X2: $i,X3: $i] :
( ( cR @ X2 @ X3 )
= ( cR @ X3 @ X3 ) )
& ! [X1: $i,X0: $i] :
( ( cR @ X1 @ X0 )
= ( cR @ X1 @ X1 ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ( ! [X2: $i,X3: $i] :
( ( cR @ X2 @ X3 )
= ( cR @ X3 @ X3 ) )
& ! [X1: $i,X0: $i] :
( ( cR @ X1 @ X0 )
= ( cR @ X1 @ X1 ) ) )
=> ( ? [X4: $i] :
( ( cR @ X4 @ X4 )
= $true )
=> ! [X5: $i] :
( ( cR @ X5 @ X5 )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ( ! [X0: $i,X1: $i] :
( ( cR @ X1 @ X0 )
<=> ( cR @ X1 @ X1 ) )
& ! [X2: $i,X3: $i] :
( ( cR @ X2 @ X3 )
<=> ( cR @ X3 @ X3 ) ) )
=> ( ? [X4: $i] : ( cR @ X4 @ X4 )
=> ! [X5: $i] : ( cR @ X5 @ X5 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ( ! [X1: $i,X0: $i] :
( ( cR @ X0 @ X1 )
<=> ( cR @ X0 @ X0 ) )
& ! [X3: $i,X2: $i] :
( ( cR @ X3 @ X2 )
<=> ( cR @ X2 @ X2 ) ) )
=> ( ? [X4: $i] : ( cR @ X4 @ X4 )
=> ! [X5: $i] : ( cR @ X5 @ X5 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ( ! [X1: $i,X0: $i] :
( ( cR @ X0 @ X1 )
<=> ( cR @ X0 @ X0 ) )
& ! [X3: $i,X2: $i] :
( ( cR @ X3 @ X2 )
<=> ( cR @ X2 @ X2 ) ) )
=> ( ? [X4: $i] : ( cR @ X4 @ X4 )
=> ! [X5: $i] : ( cR @ X5 @ X5 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JKpKJce31C/DTF2THF_21538.p',cTHM81) ).
thf(f15,plain,
( ( cR @ sK0 @ sK0 )
!= $true ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f51,plain,
! [X0: $i] :
( ( cR @ X0 @ X0 )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f45]) ).
thf(f45,plain,
! [X0: $i] :
( ( ( cR @ X0 @ X0 )
= $true )
| ( $false = $true ) ),
inference(superposition,[status(thm)],[f44,f16]) ).
thf(f16,plain,
! [X4: $i,X5: $i] :
( ( $false
= ( cR @ X4 @ X5 ) )
| ( ( cR @ X4 @ X4 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f12]) ).
thf(f44,plain,
! [X0: $i] :
( ( cR @ X0 @ sK1 )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f38]) ).
thf(f38,plain,
! [X0: $i] :
( ( ( cR @ X0 @ sK1 )
= $true )
| ( $false = $true ) ),
inference(superposition,[status(thm)],[f14,f18]) ).
thf(f18,plain,
! [X2: $i,X3: $i] :
( ( $false
= ( cR @ X3 @ X3 ) )
| ( ( cR @ X2 @ X3 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f13]) ).
thf(f13,plain,
! [X2: $i,X3: $i] :
( ( cR @ X2 @ X3 )
= ( cR @ X3 @ X3 ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f14,plain,
( ( cR @ sK1 @ sK1 )
= $true ),
inference(cnf_transformation,[status(thm)],[f11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO095^5 : 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
% 0.16/0.33 % Computer : n008.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 14:24:24 EST 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.30/0.46 ---- Original DTF file ---
% 0.30/0.46 thf(spec,logic,$$dhol).
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 % File : SYO095^5 : TPTP v9.2.1. Released v4.0.0.
% 0.30/0.46 % Domain : Syntactic
% 0.30/0.46 % Problem : TPS problem THM81
% 0.30/0.46 % Version : Especial.
% 0.30/0.46 % English :
% 0.30/0.46
% 0.30/0.46 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.30/0.46 % Source : [Bro09]
% 0.30/0.46 % Names : tps_0256 [Bro09]
% 0.30/0.46 % : THM81 [TPS]
% 0.30/0.46
% 0.30/0.46 % Status : Theorem
% 0.30/0.46 % Rating : 0.08 v9.1.0, 0.12 v9.0.0, 0.08 v8.2.0, 0.09 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 v5.1.0, 0.25 v5.0.0, 0.00 v4.0.0
% 0.30/0.46 % Syntax : Number of formulae : 2 ( 0 unt; 1 typ; 0 def)
% 0.30/0.46 % Number of atoms : 6 ( 0 equ; 0 cnn)
% 0.30/0.46 % Maximal formula atoms : 6 ( 6 avg)
% 0.30/0.46 % Number of connectives : 17 ( 0 ~; 0 |; 1 &; 12 @)
% 0.30/0.46 % ( 2 <=>; 2 =>; 0 <=; 0 <~>)
% 0.30/0.46 % Maximal formula depth : 8 ( 8 avg)
% 0.30/0.46 % Number of types : 2 ( 0 usr)
% 0.30/0.46 % Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% 0.30/0.46 % Number of symbols : 1 ( 1 usr; 0 con; 2-2 aty)
% 0.30/0.46 % Number of variables : 6 ( 0 ^; 5 !; 1 ?; 6 :)
% 0.30/0.46 % SPC : TH0_THM_NEQ_NAR
% 0.30/0.46
% 0.30/0.46 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.30/0.46 % project in the Department of Mathematical Sciences at Carnegie
% 0.30/0.46 % Mellon University. Distributed under the Creative Commons copyleft
% 0.30/0.46 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 thf(cR,type,
% 0.30/0.46 cR: $i > $i > $o ).
% 0.30/0.46
% 0.30/0.46 thf(cTHM81,conjecture,
% 0.30/0.46 ( ( ! [S: $i,T: $i] :
% 0.30/0.46 ( ( cR @ S @ S )
% 0.30/0.46 <=> ( cR @ S @ T ) )
% 0.30/0.46 & ! [W: $i,Z: $i] :
% 0.30/0.46 ( ( cR @ W @ W )
% 0.30/0.46 <=> ( cR @ Z @ W ) ) )
% 0.30/0.46 => ( ? [X: $i] : ( cR @ X @ X )
% 0.30/0.46 => ! [Y: $i] : ( cR @ Y @ Y ) ) ) ).
% 0.30/0.46
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 ------------------------
% 1.46/1.25 ---- Embedded in THF ---
% 1.46/1.25 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.46/1.25 %%% Generated on Tue Feb 24 14:24:25 EST 2026
% 1.46/1.25 %%% using '$$dhol' embedding, version 1.3.0.
% 1.46/1.25 %%% Logic specification used:
% 1.46/1.25 %%% thf(spec, logic, $$dhol).
% 1.46/1.25
% 1.46/1.25 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.JKpKJce31C/DTF2DTF21538.p
% See solution above
% 1.46/1.25 ------------------------
% 1.46/1.26 ---- Cleaned THF ---
% 1.46/1.26 thf(cR,type,
% 1.46/1.26 cR: $i > $i > $o ).
% 1.46/1.26
% 1.46/1.26 thf(cTHM81,conjecture,
% 1.46/1.26 ( ( ! [S: $i,T: $i] :
% 1.46/1.26 ( ( cR @ S @ S )
% 1.46/1.26 <=> ( cR @ S @ T ) )
% 1.46/1.26 & ! [W: $i,Z: $i] :
% 1.46/1.26 ( ( cR @ W @ W )
% 1.46/1.26 <=> ( cR @ Z @ W ) ) )
% 1.46/1.26 => ( ? [X: $i] : ( cR @ X @ X )
% 1.46/1.26 => ! [Y: $i] : ( cR @ Y @ Y ) ) ) ).
% 1.46/1.26 ------------------------
% 1.46/1.28 % (21817)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_21538 for (2999ds/183Mi)
% 1.46/1.28 % (21818)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_21538 for (2999ds/4Mi)
% 1.46/1.28 % (21817)First to succeed.
% 1.46/1.28 % (21818)Instruction limit reached!
% 1.46/1.28 % (21818)------------------------------
% 1.46/1.28 % (21818)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.46/1.28 % (21818)Termination reason: Unknown
% 1.46/1.28 % (21818)Termination phase: Saturation
% 1.46/1.28
% 1.46/1.28 % (21818)Memory used [KB]: 5500
% 1.46/1.28 % (21818)Time elapsed: 0.003 s
% 1.46/1.28 % (21818)Instructions burned: 5 (million)
% 1.46/1.28 % (21818)------------------------------
% 1.46/1.28 % (21818)------------------------------
% 1.46/1.28 % (21817)Refutation found. Thanks to Tanya!
% 1.46/1.28 % SZS status Theorem for DTF2THF_21538
% 1.46/1.28 % SZS output start Proof for DTF2THF_21538
% 1.46/1.28 thf(func_def_0, type, cR: $i > $i > $o).
% 1.46/1.28 thf(f62,plain,(
% 1.46/1.28 $false),
% 1.46/1.28 inference(trivial_inequality_removal,[status(thm)],[f55])).
% 1.46/1.28 thf(f55,plain,(
% 1.46/1.28 ($false = $true)),
% 1.46/1.28 inference(superposition,[status(thm)],[f51,f29])).
% 1.46/1.28 thf(f29,plain,(
% 1.46/1.28 ($false = (cR @ sK0 @ sK0))),
% 1.46/1.28 inference(trivial_inequality_removal,[status(thm)],[f26])).
% 1.46/1.28 thf(f26,plain,(
% 1.46/1.28 ($false = (cR @ sK0 @ sK0)) | ($true != $true)),
% 1.46/1.28 inference(superposition,[status(thm)],[f15,f17])).
% 1.46/1.28 thf(f17,plain,(
% 1.46/1.28 ( ! [X4 : $i,X5 : $i] : (($true = (cR @ X4 @ X5)) | ((cR @ X4 @ X4) = $false)) )),
% 1.46/1.28 inference(binary_proxy_clausification,[status(thm)],[f12])).
% 1.46/1.28 thf(f12,plain,(
% 1.46/1.28 ( ! [X4 : $i,X5 : $i] : (((cR @ X4 @ X4) = (cR @ X4 @ X5))) )),
% 1.46/1.28 inference(cnf_transformation,[status(thm)],[f11])).
% 1.46/1.28 thf(f11,plain,(
% 1.46/1.28 ((cR @ sK0 @ sK0) != $true) & ((cR @ sK1 @ sK1) = $true) & ! [X2 : $i,X3 : $i] : ((cR @ X2 @ X3) = (cR @ X3 @ X3)) & ! [X4 : $i,X5 : $i] : ((cR @ X4 @ X4) = (cR @ X4 @ X5))),
% 1.46/1.28 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f8,f10,f9])).
% 1.46/1.28 thf(f9,plain,(
% 1.46/1.28 ? [X0 : $i] : ((cR @ X0 @ X0) != $true) => ((cR @ sK0 @ sK0) != $true)),
% 1.46/1.28 introduced(definition,[],[choice_axiom])).
% 1.46/1.28 thf(f10,plain,(
% 1.46/1.28 ? [X1 : $i] : ((cR @ X1 @ X1) = $true) => ((cR @ sK1 @ sK1) = $true)),
% 1.46/1.28 introduced(definition,[],[choice_axiom])).
% 1.46/1.28 thf(f8,plain,(
% 1.46/1.28 ? [X0 : $i] : ((cR @ X0 @ X0) != $true) & ? [X1 : $i] : ((cR @ X1 @ X1) = $true) & ! [X2 : $i,X3 : $i] : ((cR @ X2 @ X3) = (cR @ X3 @ X3)) & ! [X4 : $i,X5 : $i] : ((cR @ X4 @ X4) = (cR @ X4 @ X5))),
% 1.46/1.28 inference(rectify,[status(thm)],[f7])).
% 1.46/1.28 thf(f7,plain,(
% 1.46/1.28 ? [X5 : $i] : ((cR @ X5 @ X5) != $true) & ? [X4 : $i] : ((cR @ X4 @ X4) = $true) & ! [X2 : $i,X3 : $i] : ((cR @ X2 @ X3) = (cR @ X3 @ X3)) & ! [X1 : $i,X0 : $i] : ((cR @ X1 @ X0) = (cR @ X1 @ X1))),
% 1.46/1.28 inference(flattening,[status(thm)],[f6])).
% 1.46/1.28 thf(f6,plain,(
% 1.46/1.28 (? [X5 : $i] : ((cR @ X5 @ X5) != $true) & ? [X4 : $i] : ((cR @ X4 @ X4) = $true)) & (! [X2 : $i,X3 : $i] : ((cR @ X2 @ X3) = (cR @ X3 @ X3)) & ! [X1 : $i,X0 : $i] : ((cR @ X1 @ X0) = (cR @ X1 @ X1)))),
% 1.46/1.28 inference(ennf_transformation,[status(thm)],[f5])).
% 1.46/1.28 thf(f5,plain,(
% 1.46/1.28 ~((! [X2 : $i,X3 : $i] : ((cR @ X2 @ X3) = (cR @ X3 @ X3)) & ! [X1 : $i,X0 : $i] : ((cR @ X1 @ X0) = (cR @ X1 @ X1))) => (? [X4 : $i] : ((cR @ X4 @ X4) = $true) => ! [X5 : $i] : ((cR @ X5 @ X5) = $true)))),
% 1.46/1.28 inference(fool_elimination,[status(thm)],[f4])).
% 1.46/1.28 thf(f4,plain,(
% 1.46/1.28 ~((! [X0 : $i,X1 : $i] : ((cR @ X1 @ X0) <=> (cR @ X1 @ X1)) & ! [X2 : $i,X3 : $i] : ((cR @ X2 @ X3) <=> (cR @ X3 @ X3))) => (? [X4 : $i] : (cR @ X4 @ X4) => ! [X5 : $i] : (cR @ X5 @ X5)))),
% 1.46/1.28 inference(rectify,[status(thm)],[f2])).
% 1.46/1.28 thf(f2,negated_conjecture,(
% 1.46/1.28 ~((! [X1 : $i,X0 : $i] : ((cR @ X0 @ X1) <=> (cR @ X0 @ X0)) & ! [X3 : $i,X2 : $i] : ((cR @ X3 @ X2) <=> (cR @ X2 @ X2))) => (? [X4 : $i] : (cR @ X4 @ X4) => ! [X5 : $i] : (cR @ X5 @ X5)))),
% 1.46/1.28 inference(negated_conjecture,[status(cth)],[f1])).
% 1.46/1.28 thf(f1,conjecture,(
% 1.46/1.28 (! [X1 : $i,X0 : $i] : ((cR @ X0 @ X1) <=> (cR @ X0 @ X0)) & ! [X3 : $i,X2 : $i] : ((cR @ X3 @ X2) <=> (cR @ X2 @ X2))) => (? [X4 : $i] : (cR @ X4 @ X4) => ! [X5 : $i] : (cR @ X5 @ X5))),
% 1.46/1.28 file('/export/starexec/sandbox/tmp/tmp.JKpKJce31C/DTF2THF_21538.p',cTHM81)).
% 1.46/1.28 thf(f15,plain,(
% 1.46/1.28 ((cR @ sK0 @ sK0) != $true)),
% 1.46/1.28 inference(cnf_transformation,[status(thm)],[f11])).
% 1.46/1.28 thf(f51,plain,(
% 1.46/1.28 ( ! [X0 : $i] : (((cR @ X0 @ X0) = $true)) )),
% 1.46/1.28 inference(trivial_inequality_removal,[status(thm)],[f45])).
% 1.46/1.28 thf(f45,plain,(
% 1.46/1.28 ( ! [X0 : $i] : (((cR @ X0 @ X0) = $true) | ($false = $true)) )),
% 1.46/1.28 inference(superposition,[status(thm)],[f44,f16])).
% 1.46/1.28 thf(f16,plain,(
% 1.46/1.28 ( ! [X4 : $i,X5 : $i] : (($false = (cR @ X4 @ X5)) | ((cR @ X4 @ X4) = $true)) )),
% 1.46/1.28 inference(binary_proxy_clausification,[status(thm)],[f12])).
% 1.46/1.28 thf(f44,plain,(
% 1.46/1.28 ( ! [X0 : $i] : (((cR @ X0 @ sK1) = $true)) )),
% 1.46/1.28 inference(trivial_inequality_removal,[status(thm)],[f38])).
% 1.46/1.28 thf(f38,plain,(
% 1.46/1.28 ( ! [X0 : $i] : (((cR @ X0 @ sK1) = $true) | ($false = $true)) )),
% 1.46/1.28 inference(superposition,[status(thm)],[f14,f18])).
% 1.46/1.28 thf(f18,plain,(
% 1.46/1.28 ( ! [X2 : $i,X3 : $i] : (($false = (cR @ X3 @ X3)) | ((cR @ X2 @ X3) = $true)) )),
% 1.46/1.28 inference(binary_proxy_clausification,[status(thm)],[f13])).
% 1.46/1.28 thf(f13,plain,(
% 1.46/1.28 ( ! [X2 : $i,X3 : $i] : (((cR @ X2 @ X3) = (cR @ X3 @ X3))) )),
% 1.46/1.28 inference(cnf_transformation,[status(thm)],[f11])).
% 1.46/1.28 thf(f14,plain,(
% 1.46/1.28 ((cR @ sK1 @ sK1) = $true)),
% 1.46/1.28 inference(cnf_transformation,[status(thm)],[f11])).
% 1.46/1.28 % SZS output end Proof for DTF2THF_21538
% 1.46/1.28 % (21817)------------------------------
% 1.46/1.28 % (21817)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.46/1.28 % (21817)Termination reason: Refutation
% 1.46/1.28
% 1.46/1.28 % (21817)Memory used [KB]: 5500
% 1.46/1.28 % (21817)Time elapsed: 0.003 s
% 1.46/1.28 % (21817)Instructions burned: 4 (million)
% 1.46/1.28 % (21817)------------------------------
% 1.46/1.28 % (21817)------------------------------
% 1.46/1.28 % (21816)Success in time 0.013 s
%------------------------------------------------------------------------------