%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SET044^5 : 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 09:31:03 AM UTC 2026
% Result : Theorem 1.48s 1.28s
% Output : Refutation 1.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 3
% Syntax : Number of formulae : 28 ( 6 unt; 0 typ; 0 def)
% Number of atoms : 217 ( 61 equ; 0 cnn)
% Maximal formula atoms : 8 ( 7 avg)
% Number of connectives : 250 ( 30 ~; 23 |; 7 &; 174 @)
% ( 9 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 56 ( 0 ^; 40 !; 16 ?; 56 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
cF: $i > $i > $o ).
thf(func_def_2,type,
vEPSILON:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_6,type,
sK1: $i > $i ).
thf(f50,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f49]) ).
thf(f49,plain,
$true = $false,
inference(forward_demodulation,[status(thm)],[f48,f33]) ).
thf(f33,plain,
( ( cF @ ( sK1 @ sK0 ) @ ( sK1 @ sK0 ) )
= $false ),
inference(trivial_inequality_removal,[status(thm)],[f32]) ).
thf(f32,plain,
( ( $true != $true )
| ( ( cF @ ( sK1 @ sK0 ) @ ( sK1 @ sK0 ) )
= $false ) ),
inference(duplicate_literal_removal,[status(thm)],[f29]) ).
thf(f29,plain,
( ( $true != $true )
| ( ( cF @ ( sK1 @ sK0 ) @ ( sK1 @ sK0 ) )
= $false )
| ( ( cF @ ( sK1 @ sK0 ) @ ( sK1 @ sK0 ) )
= $false ) ),
inference(superposition,[status(thm)],[f28,f16]) ).
thf(f16,plain,
! [X1: $i] :
( ( $true
= ( cF @ X1 @ sK0 ) )
| ( ( cF @ X1 @ X1 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f14]) ).
thf(f14,plain,
! [X1: $i] :
( ( cF @ X1 @ X1 )
= ( cF @ X1 @ sK0 ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( ! [X1: $i] :
( ( cF @ X1 @ X1 )
= ( cF @ X1 @ sK0 ) )
& ! [X2: $i,X4: $i] :
( ( ( $true
= ( cF @ X4 @ ( sK1 @ X2 ) ) )
| ( $true
= ( cF @ X4 @ X2 ) ) )
& ( ( $true
!= ( cF @ X4 @ X2 ) )
| ( $true
!= ( cF @ X4 @ ( sK1 @ X2 ) ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f8,f10,f9]) ).
thf(f9,plain,
( ? [X0: $i] :
! [X1: $i] :
( ( cF @ X1 @ X0 )
= ( cF @ X1 @ X1 ) )
=> ! [X1: $i] :
( ( cF @ X1 @ X1 )
= ( cF @ X1 @ sK0 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f10,plain,
! [X2: $i] :
( ? [X3: $i] :
! [X4: $i] :
( ( ( $true
= ( cF @ X4 @ X3 ) )
| ( $true
= ( cF @ X4 @ X2 ) ) )
& ( ( $true
!= ( cF @ X4 @ X2 ) )
| ( $true
!= ( cF @ X4 @ X3 ) ) ) )
=> ! [X4: $i] :
( ( ( $true
= ( cF @ X4 @ ( sK1 @ X2 ) ) )
| ( $true
= ( cF @ X4 @ X2 ) ) )
& ( ( $true
!= ( cF @ X4 @ X2 ) )
| ( $true
!= ( cF @ X4 @ ( sK1 @ X2 ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f8,plain,
( ? [X0: $i] :
! [X1: $i] :
( ( cF @ X1 @ X0 )
= ( cF @ X1 @ X1 ) )
& ! [X2: $i] :
? [X3: $i] :
! [X4: $i] :
( ( ( $true
= ( cF @ X4 @ X3 ) )
| ( $true
= ( cF @ X4 @ X2 ) ) )
& ( ( $true
!= ( cF @ X4 @ X2 ) )
| ( $true
!= ( cF @ X4 @ X3 ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
( ? [X0: $i] :
! [X1: $i] :
( ( cF @ X1 @ X0 )
= ( cF @ X1 @ X1 ) )
& ! [X2: $i] :
? [X3: $i] :
! [X4: $i] :
( ( $true
= ( cF @ X4 @ X3 ) )
<=> ( $true
!= ( cF @ X4 @ X2 ) ) ) ),
inference(ennf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
~ ( ? [X0: $i] :
! [X1: $i] :
( ( cF @ X1 @ X0 )
= ( cF @ X1 @ X1 ) )
=> ~ ! [X2: $i] :
? [X3: $i] :
! [X4: $i] :
( ( $true
= ( cF @ X4 @ X3 ) )
<=> ( $true
!= ( cF @ X4 @ X2 ) ) ) ),
inference(flattening,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ? [X0: $i] :
! [X1: $i] :
( ( cF @ X1 @ X0 )
= ( cF @ X1 @ X1 ) )
=> ~ ! [X2: $i] :
? [X3: $i] :
! [X4: $i] :
( ( $true
!= ( cF @ X4 @ X2 ) )
<=> ( $true
= ( cF @ X4 @ X3 ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ? [X0: $i] :
! [X1: $i] :
( ( cF @ X1 @ X1 )
<=> ( cF @ X1 @ X0 ) )
=> ~ ! [X2: $i] :
? [X3: $i] :
! [X4: $i] :
( ~ ( cF @ X4 @ X2 )
<=> ( cF @ X4 @ X3 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ? [X0: $i] :
! [X1: $i] :
( ( cF @ X1 @ X1 )
<=> ( cF @ X1 @ X0 ) )
=> ~ ! [X1: $i] :
? [X0: $i] :
! [X2: $i] :
( ~ ( cF @ X2 @ X1 )
<=> ( cF @ X2 @ X0 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ? [X0: $i] :
! [X1: $i] :
( ( cF @ X1 @ X1 )
<=> ( cF @ X1 @ X0 ) )
=> ~ ! [X1: $i] :
? [X0: $i] :
! [X2: $i] :
( ~ ( cF @ X2 @ X1 )
<=> ( cF @ X2 @ X0 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.Qq9LbLOPMQ/DTF2THF_24613.p',cPELL40) ).
thf(f28,plain,
! [X0: $i] :
( ( $true
!= ( cF @ ( sK1 @ X0 ) @ X0 ) )
| ( ( cF @ ( sK1 @ X0 ) @ ( sK1 @ X0 ) )
= $false ) ),
inference(trivial_inequality_removal,[status(thm)],[f26]) ).
thf(f26,plain,
! [X0: $i] :
( ( ( cF @ ( sK1 @ X0 ) @ ( sK1 @ X0 ) )
= $false )
| ( $true != $true )
| ( $true
!= ( cF @ ( sK1 @ X0 ) @ X0 ) ) ),
inference(superposition,[status(thm)],[f12,f21]) ).
thf(f21,plain,
! [X0: $i] :
( ( $true
= ( cF @ X0 @ X0 ) )
| ( ( cF @ X0 @ X0 )
= $false ) ),
inference(trivial_inequality_removal,[status(thm)],[f18]) ).
thf(f18,plain,
! [X0: $i] :
( ( $true = $false )
| ( $true
= ( cF @ X0 @ X0 ) )
| ( ( cF @ X0 @ X0 )
= $false ) ),
inference(superposition,[status(thm)],[f16,f15]) ).
thf(f15,plain,
! [X1: $i] :
( ( $false
= ( cF @ X1 @ sK0 ) )
| ( ( cF @ X1 @ X1 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f14]) ).
thf(f12,plain,
! [X2: $i,X4: $i] :
( ( $true
!= ( cF @ X4 @ ( sK1 @ X2 ) ) )
| ( $true
!= ( cF @ X4 @ X2 ) ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f48,plain,
( $true
= ( cF @ ( sK1 @ sK0 ) @ ( sK1 @ sK0 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f43]) ).
thf(f43,plain,
( ( $true = $false )
| ( $true
= ( cF @ ( sK1 @ sK0 ) @ ( sK1 @ sK0 ) ) ) ),
inference(superposition,[status(thm)],[f41,f15]) ).
thf(f41,plain,
( $true
= ( cF @ ( sK1 @ sK0 ) @ sK0 ) ),
inference(trivial_inequality_removal,[status(thm)],[f37]) ).
thf(f37,plain,
( ( $true = $false )
| ( $true
= ( cF @ ( sK1 @ sK0 ) @ sK0 ) ) ),
inference(superposition,[status(thm)],[f13,f33]) ).
thf(f13,plain,
! [X2: $i,X4: $i] :
( ( $true
= ( cF @ X4 @ ( sK1 @ X2 ) ) )
| ( $true
= ( cF @ X4 @ X2 ) ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET044^5 : TPTP v9.2.1. Released v4.0.0.
% 0.13/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n008.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 11:50:24 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
% 0.31/0.46 ---- Original DTF file ---
% 0.31/0.46 thf(spec,logic,$$dhol).
% 0.31/0.46 %------------------------------------------------------------------------------
% 0.31/0.46 % File : SET044^5 : TPTP v9.2.1. Released v4.0.0.
% 0.31/0.46 % Domain : Set Theory
% 0.31/0.46 % Problem : TPS problem PELL40
% 0.31/0.46 % Version : Especial.
% 0.31/0.46 % English : If there were an anti-Russell set (a set that contains exactly
% 0.31/0.46 % those sets that are members of themselves), then not every set
% 0.31/0.46 % has a complement.
% 0.31/0.46
% 0.31/0.46 % Refs : [Pel86] Pelletier (1986), Seventy-five Problems for Testing Au
% 0.31/0.46 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.31/0.46 % Source : [Bro09]
% 0.31/0.46 % Names : tps_0236 [Bro09]
% 0.31/0.46 % : PELL40 [TPS]
% 0.31/0.46 % : Pelletier 40 [Pel86]
% 0.31/0.46
% 0.31/0.46 % Status : Theorem
% 0.31/0.46 % 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 v6.2.0, 0.00 v6.1.0, 0.17 v6.0.0, 0.00 v5.3.0, 0.25 v5.2.0, 0.00 v4.0.0
% 0.31/0.46 % Syntax : Number of formulae : 2 ( 0 unt; 1 typ; 0 def)
% 0.31/0.46 % Number of atoms : 4 ( 0 equ; 0 cnn)
% 0.31/0.46 % Maximal formula atoms : 4 ( 4 avg)
% 0.31/0.46 % Number of connectives : 13 ( 2 ~; 0 |; 0 &; 8 @)
% 0.31/0.46 % ( 2 <=>; 1 =>; 0 <=; 0 <~>)
% 0.31/0.46 % Maximal formula depth : 10 ( 10 avg)
% 0.31/0.46 % Number of types : 2 ( 0 usr)
% 0.31/0.46 % Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% 0.31/0.46 % Number of symbols : 1 ( 1 usr; 0 con; 2-2 aty)
% 0.31/0.46 % Number of variables : 5 ( 0 ^; 3 !; 2 ?; 5 :)
% 0.31/0.46 % SPC : TH0_THM_NEQ_NAR
% 0.31/0.46
% 0.31/0.46 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.31/0.46 % project in the Department of Mathematical Sciences at Carnegie
% 0.31/0.46 % Mellon University. Distributed under the Creative Commons copyleft
% 0.31/0.46 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.31/0.46 %------------------------------------------------------------------------------
% 0.31/0.46 thf(cF,type,
% 0.31/0.46 cF: $i > $i > $o ).
% 0.31/0.46
% 0.31/0.46 thf(cPELL40,conjecture,
% 0.31/0.46 ( ? [Xy: $i] :
% 0.31/0.46 ! [Xx: $i] :
% 0.31/0.46 ( ( cF @ Xx @ Xy )
% 0.31/0.46 <=> ( cF @ Xx @ Xx ) )
% 0.31/0.46 => ~ ! [Xx: $i] :
% 0.31/0.46 ? [Xy: $i] :
% 0.31/0.46 ! [Xz: $i] :
% 0.31/0.46 ( ( cF @ Xz @ Xy )
% 0.31/0.46 <=> ~ ( cF @ Xz @ Xx ) ) ) ).
% 0.31/0.46
% 0.31/0.46 %------------------------------------------------------------------------------
% 0.31/0.46 ------------------------
% 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 11:50:25 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/sandbox/tmp/tmp.Qq9LbLOPMQ/DTF2DTF24613.p
% See solution above
% 1.48/1.25 ------------------------
% 1.48/1.26 ---- Cleaned THF ---
% 1.48/1.26 thf(cF,type,
% 1.48/1.26 cF: $i > $i > $o ).
% 1.48/1.26
% 1.48/1.26 thf(cPELL40,conjecture,
% 1.48/1.26 ( ? [Xy: $i] :
% 1.48/1.26 ! [Xx: $i] :
% 1.48/1.26 ( ( cF @ Xx @ Xy )
% 1.48/1.26 <=> ( cF @ Xx @ Xx ) )
% 1.48/1.26 => ~ ! [Xx: $i] :
% 1.48/1.26 ? [Xy: $i] :
% 1.48/1.26 ! [Xz: $i] :
% 1.48/1.26 ( ( cF @ Xz @ Xy )
% 1.48/1.26 <=> ~ ( cF @ Xz @ Xx ) ) ) ).
% 1.48/1.26 ------------------------
% 1.48/1.28 % (24721)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_24613 for (2999ds/27Mi)
% 1.48/1.28 % (24724)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_24613 for (2999ds/275Mi)
% 1.48/1.28 % (24724)Refutation not found, incomplete strategy
% 1.48/1.28 % (24724)------------------------------
% 1.48/1.28 % (24724)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.28 % (24724)Termination reason: Refutation not found, incomplete strategy
% 1.48/1.28
% 1.48/1.28
% 1.48/1.28 % (24724)Memory used [KB]: 5500
% 1.48/1.28 % (24724)Time elapsed: 0.003 s
% 1.48/1.28 % (24724)Instructions burned: 3 (million)
% 1.48/1.28 % (24724)------------------------------
% 1.48/1.28 % (24724)------------------------------
% 1.48/1.28 % (24721)First to succeed.
% 1.48/1.28 % (24722)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_24613 for (2999ds/2Mi)
% 1.48/1.28 % (24721)Refutation found. Thanks to Tanya!
% 1.48/1.28 % SZS status Theorem for DTF2THF_24613
% 1.48/1.28 % SZS output start Proof for DTF2THF_24613
% 1.48/1.28 thf(func_def_0, type, cF: $i > $i > $o).
% 1.48/1.28 thf(func_def_2, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.48/1.28 thf(func_def_6, type, sK1: $i > $i).
% 1.48/1.28 thf(f50,plain,(
% 1.48/1.28 $false),
% 1.48/1.28 inference(trivial_inequality_removal,[status(thm)],[f49])).
% 1.48/1.28 thf(f49,plain,(
% 1.48/1.28 ($true = $false)),
% 1.48/1.28 inference(forward_demodulation,[status(thm)],[f48,f33])).
% 1.48/1.28 thf(f33,plain,(
% 1.48/1.28 ((cF @ (sK1 @ sK0) @ (sK1 @ sK0)) = $false)),
% 1.48/1.28 inference(trivial_inequality_removal,[status(thm)],[f32])).
% 1.48/1.28 thf(f32,plain,(
% 1.48/1.28 ($true != $true) | ((cF @ (sK1 @ sK0) @ (sK1 @ sK0)) = $false)),
% 1.48/1.28 inference(duplicate_literal_removal,[status(thm)],[f29])).
% 1.48/1.28 thf(f29,plain,(
% 1.48/1.28 ($true != $true) | ((cF @ (sK1 @ sK0) @ (sK1 @ sK0)) = $false) | ((cF @ (sK1 @ sK0) @ (sK1 @ sK0)) = $false)),
% 1.48/1.28 inference(superposition,[status(thm)],[f28,f16])).
% 1.48/1.28 thf(f16,plain,(
% 1.48/1.28 ( ! [X1 : $i] : (($true = (cF @ X1 @ sK0)) | ((cF @ X1 @ X1) = $false)) )),
% 1.48/1.28 inference(binary_proxy_clausification,[status(thm)],[f14])).
% 1.48/1.28 thf(f14,plain,(
% 1.48/1.28 ( ! [X1 : $i] : (((cF @ X1 @ X1) = (cF @ X1 @ sK0))) )),
% 1.48/1.28 inference(cnf_transformation,[status(thm)],[f11])).
% 1.48/1.28 thf(f11,plain,(
% 1.48/1.28 ! [X1 : $i] : ((cF @ X1 @ X1) = (cF @ X1 @ sK0)) & ! [X2 : $i] : ! [X4 : $i] : ((($true = (cF @ X4 @ (sK1 @ X2))) | ($true = (cF @ X4 @ X2))) & (($true != (cF @ X4 @ X2)) | ($true != (cF @ X4 @ (sK1 @ X2)))))),
% 1.48/1.28 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f8,f10,f9])).
% 1.48/1.28 thf(f9,plain,(
% 1.48/1.28 ? [X0 : $i] : ! [X1 : $i] : ((cF @ X1 @ X0) = (cF @ X1 @ X1)) => ! [X1 : $i] : ((cF @ X1 @ X1) = (cF @ X1 @ sK0))),
% 1.48/1.28 introduced(definition,[],[choice_axiom])).
% 1.48/1.28 thf(f10,plain,(
% 1.48/1.28 ! [X2 : $i] : (? [X3 : $i] : ! [X4 : $i] : ((($true = (cF @ X4 @ X3)) | ($true = (cF @ X4 @ X2))) & (($true != (cF @ X4 @ X2)) | ($true != (cF @ X4 @ X3)))) => ! [X4 : $i] : ((($true = (cF @ X4 @ (sK1 @ X2))) | ($true = (cF @ X4 @ X2))) & (($true != (cF @ X4 @ X2)) | ($true != (cF @ X4 @ (sK1 @ X2))))))),
% 1.48/1.28 introduced(definition,[],[choice_axiom])).
% 1.48/1.28 thf(f8,plain,(
% 1.48/1.28 ? [X0 : $i] : ! [X1 : $i] : ((cF @ X1 @ X0) = (cF @ X1 @ X1)) & ! [X2 : $i] : ? [X3 : $i] : ! [X4 : $i] : ((($true = (cF @ X4 @ X3)) | ($true = (cF @ X4 @ X2))) & (($true != (cF @ X4 @ X2)) | ($true != (cF @ X4 @ X3))))),
% 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] : ((cF @ X1 @ X0) = (cF @ X1 @ X1)) & ! [X2 : $i] : ? [X3 : $i] : ! [X4 : $i] : (($true = (cF @ X4 @ X3)) <=> ($true != (cF @ X4 @ X2)))),
% 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] : ((cF @ X1 @ X0) = (cF @ X1 @ X1)) => ~! [X2 : $i] : ? [X3 : $i] : ! [X4 : $i] : (($true = (cF @ X4 @ X3)) <=> ($true != (cF @ X4 @ X2))))),
% 1.48/1.28 inference(flattening,[status(thm)],[f5])).
% 1.48/1.28 thf(f5,plain,(
% 1.48/1.28 ~(? [X0 : $i] : ! [X1 : $i] : ((cF @ X1 @ X0) = (cF @ X1 @ X1)) => ~! [X2 : $i] : ? [X3 : $i] : ! [X4 : $i] : (~($true = (cF @ X4 @ X2)) <=> ($true = (cF @ X4 @ X3))))),
% 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] : ((cF @ X1 @ X1) <=> (cF @ X1 @ X0)) => ~! [X2 : $i] : ? [X3 : $i] : ! [X4 : $i] : (~(cF @ X4 @ X2) <=> (cF @ X4 @ X3)))),
% 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] : ((cF @ X1 @ X1) <=> (cF @ X1 @ X0)) => ~! [X1 : $i] : ? [X0 : $i] : ! [X2 : $i] : (~(cF @ X2 @ X1) <=> (cF @ X2 @ X0)))),
% 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] : ((cF @ X1 @ X1) <=> (cF @ X1 @ X0)) => ~! [X1 : $i] : ? [X0 : $i] : ! [X2 : $i] : (~(cF @ X2 @ X1) <=> (cF @ X2 @ X0))),
% 1.48/1.28 file('/export/starexec/sandbox/tmp/tmp.Qq9LbLOPMQ/DTF2THF_24613.p',cPELL40)).
% 1.48/1.28 thf(f28,plain,(
% 1.48/1.28 ( ! [X0 : $i] : (($true != (cF @ (sK1 @ X0) @ X0)) | ((cF @ (sK1 @ X0) @ (sK1 @ X0)) = $false)) )),
% 1.48/1.28 inference(trivial_inequality_removal,[status(thm)],[f26])).
% 1.48/1.28 thf(f26,plain,(
% 1.48/1.28 ( ! [X0 : $i] : (((cF @ (sK1 @ X0) @ (sK1 @ X0)) = $false) | ($true != $true) | ($true != (cF @ (sK1 @ X0) @ X0))) )),
% 1.48/1.28 inference(superposition,[status(thm)],[f12,f21])).
% 1.48/1.28 thf(f21,plain,(
% 1.48/1.28 ( ! [X0 : $i] : (($true = (cF @ X0 @ X0)) | ((cF @ X0 @ X0) = $false)) )),
% 1.48/1.28 inference(trivial_inequality_removal,[status(thm)],[f18])).
% 1.48/1.28 thf(f18,plain,(
% 1.48/1.28 ( ! [X0 : $i] : (($true = $false) | ($true = (cF @ X0 @ X0)) | ((cF @ X0 @ X0) = $false)) )),
% 1.48/1.28 inference(superposition,[status(thm)],[f16,f15])).
% 1.48/1.28 thf(f15,plain,(
% 1.48/1.28 ( ! [X1 : $i] : (($false = (cF @ X1 @ sK0)) | ((cF @ X1 @ X1) = $true)) )),
% 1.48/1.28 inference(binary_proxy_clausification,[status(thm)],[f14])).
% 1.48/1.28 thf(f12,plain,(
% 1.48/1.28 ( ! [X2 : $i,X4 : $i] : (($true != (cF @ X4 @ (sK1 @ X2))) | ($true != (cF @ X4 @ X2))) )),
% 1.48/1.28 inference(cnf_transformation,[status(thm)],[f11])).
% 1.48/1.28 thf(f48,plain,(
% 1.48/1.28 ($true = (cF @ (sK1 @ sK0) @ (sK1 @ sK0)))),
% 1.48/1.28 inference(trivial_inequality_removal,[status(thm)],[f43])).
% 1.48/1.28 thf(f43,plain,(
% 1.48/1.28 ($true = $false) | ($true = (cF @ (sK1 @ sK0) @ (sK1 @ sK0)))),
% 1.48/1.28 inference(superposition,[status(thm)],[f41,f15])).
% 1.48/1.28 thf(f41,plain,(
% 1.48/1.28 ($true = (cF @ (sK1 @ sK0) @ sK0))),
% 1.48/1.28 inference(trivial_inequality_removal,[status(thm)],[f37])).
% 1.48/1.28 thf(f37,plain,(
% 1.48/1.28 ($true = $false) | ($true = (cF @ (sK1 @ sK0) @ sK0))),
% 1.48/1.28 inference(superposition,[status(thm)],[f13,f33])).
% 1.48/1.28 thf(f13,plain,(
% 1.48/1.28 ( ! [X2 : $i,X4 : $i] : (($true = (cF @ X4 @ (sK1 @ X2))) | ($true = (cF @ X4 @ X2))) )),
% 1.48/1.28 inference(cnf_transformation,[status(thm)],[f11])).
% 1.48/1.28 % SZS output end Proof for DTF2THF_24613
% 1.48/1.28 % (24721)------------------------------
% 1.48/1.28 % (24721)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.28 % (24721)Termination reason: Refutation
% 1.48/1.28
% 1.48/1.28 % (24721)Memory used [KB]: 5500
% 1.48/1.28 % (24721)Time elapsed: 0.004 s
% 1.48/1.28 % (24721)Instructions burned: 5 (million)
% 1.48/1.28 % (24721)------------------------------
% 1.48/1.28 % (24721)------------------------------
% 1.48/1.28 % (24718)Success in time 0.014 s
%------------------------------------------------------------------------------