%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SET046^5 : 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 : n009.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 09:31:04 AM UTC 2026
% Result : Theorem 1.66s 1.46s
% Output : Refutation 1.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 3
% Syntax : Number of formulae : 19 ( 2 unt; 0 typ; 0 def)
% Number of atoms : 232 ( 62 equ; 0 cnn)
% Maximal formula atoms : 12 ( 12 avg)
% Number of connectives : 274 ( 42 ~; 25 |; 25 &; 170 @)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 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 : 42 ( 0 ^; 21 !; 21 ?; 42 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
cF: $i > $i > $o ).
thf(func_def_5,type,
sK1: $i > $i ).
thf(f23,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f22,f13]) ).
thf(f13,plain,
! [X2: $i,X1: $i] :
( ( $true
!= ( cF @ X1 @ sK0 ) )
| ( ( cF @ X1 @ X2 )
!= $true )
| ( ( cF @ X2 @ X1 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
! [X1: $i] :
( ( ! [X2: $i] :
( ( ( cF @ X2 @ X1 )
!= $true )
| ( ( cF @ X1 @ X2 )
!= $true ) )
| ( $true
!= ( cF @ X1 @ sK0 ) ) )
& ( ( $true
= ( cF @ X1 @ sK0 ) )
| ( ( ( cF @ ( sK1 @ X1 ) @ X1 )
= $true )
& ( $true
= ( cF @ X1 @ ( sK1 @ X1 ) ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f7,f9,f8]) ).
thf(f8,plain,
( ? [X0: $i] :
! [X1: $i] :
( ( ! [X2: $i] :
( ( ( cF @ X2 @ X1 )
!= $true )
| ( ( cF @ X1 @ X2 )
!= $true ) )
| ( ( cF @ X1 @ X0 )
!= $true ) )
& ( ( ( cF @ X1 @ X0 )
= $true )
| ? [X3: $i] :
( ( $true
= ( cF @ X3 @ X1 ) )
& ( $true
= ( cF @ X1 @ X3 ) ) ) ) )
=> ! [X1: $i] :
( ( ! [X2: $i] :
( ( ( cF @ X2 @ X1 )
!= $true )
| ( ( cF @ X1 @ X2 )
!= $true ) )
| ( $true
!= ( cF @ X1 @ sK0 ) ) )
& ( ( $true
= ( cF @ X1 @ sK0 ) )
| ? [X3: $i] :
( ( $true
= ( cF @ X3 @ X1 ) )
& ( $true
= ( cF @ X1 @ X3 ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f9,plain,
! [X1: $i] :
( ? [X3: $i] :
( ( $true
= ( cF @ X3 @ X1 ) )
& ( $true
= ( cF @ X1 @ X3 ) ) )
=> ( ( ( cF @ ( sK1 @ X1 ) @ X1 )
= $true )
& ( $true
= ( cF @ X1 @ ( sK1 @ X1 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f7,plain,
? [X0: $i] :
! [X1: $i] :
( ( ! [X2: $i] :
( ( ( cF @ X2 @ X1 )
!= $true )
| ( ( cF @ X1 @ X2 )
!= $true ) )
| ( ( cF @ X1 @ X0 )
!= $true ) )
& ( ( ( cF @ X1 @ X0 )
= $true )
| ? [X3: $i] :
( ( $true
= ( cF @ X3 @ X1 ) )
& ( $true
= ( cF @ X1 @ X3 ) ) ) ) ),
inference(ennf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
? [X0: $i] :
! [X1: $i] :
( ( ( ( cF @ X1 @ X0 )
= $true )
=> ~ ? [X2: $i] :
( ( ( cF @ X1 @ X2 )
= $true )
& ( ( cF @ X2 @ X1 )
= $true ) ) )
& ( ~ ? [X3: $i] :
( ( $true
= ( cF @ X3 @ X1 ) )
& ( $true
= ( cF @ X1 @ X3 ) ) )
=> ( ( cF @ X1 @ X0 )
= $true ) ) ),
inference(flattening,[status(thm)],[f5]) ).
thf(f5,plain,
~ ~ ? [X0: $i] :
! [X1: $i] :
( ( ( ( cF @ X1 @ X0 )
= $true )
=> ~ ? [X2: $i] :
( ( ( cF @ X1 @ X2 )
= $true )
& ( ( cF @ X2 @ X1 )
= $true ) ) )
& ( ~ ? [X3: $i] :
( ( $true
= ( cF @ X3 @ X1 ) )
& ( $true
= ( cF @ X1 @ X3 ) ) )
=> ( ( cF @ X1 @ X0 )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ~ ? [X0: $i] :
! [X1: $i] :
( ( ( cF @ X1 @ X0 )
=> ~ ? [X2: $i] :
( ( cF @ X1 @ X2 )
& ( cF @ X2 @ X1 ) ) )
& ( ~ ? [X3: $i] :
( ( cF @ X3 @ X1 )
& ( cF @ X1 @ X3 ) )
=> ( cF @ X1 @ X0 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ~ ? [X0: $i] :
! [X1: $i] :
( ( ( cF @ X1 @ X0 )
=> ~ ? [X2: $i] :
( ( cF @ X1 @ X2 )
& ( cF @ X2 @ X1 ) ) )
& ( ~ ? [X2: $i] :
( ( cF @ X2 @ X1 )
& ( cF @ X1 @ X2 ) )
=> ( cF @ X1 @ X0 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
~ ? [X0: $i] :
! [X1: $i] :
( ( ( cF @ X1 @ X0 )
=> ~ ? [X2: $i] :
( ( cF @ X1 @ X2 )
& ( cF @ X2 @ X1 ) ) )
& ( ~ ? [X2: $i] :
( ( cF @ X2 @ X1 )
& ( cF @ X1 @ X2 ) )
=> ( cF @ X1 @ X0 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.67W7WZ6ymG/DTF2THF_11304.p',cPELL42) ).
thf(f22,plain,
( ( cF @ sK0 @ sK0 )
= $true ),
inference(subsumption_resolution,[status(thm)],[f19,f11]) ).
thf(f11,plain,
! [X1: $i] :
( ( $true
= ( cF @ X1 @ ( sK1 @ X1 ) ) )
| ( $true
= ( cF @ X1 @ sK0 ) ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f19,plain,
( ( $true
!= ( cF @ sK0 @ ( sK1 @ sK0 ) ) )
| ( ( cF @ sK0 @ sK0 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f17]) ).
thf(f17,plain,
( ( $true
!= ( cF @ sK0 @ ( sK1 @ sK0 ) ) )
| ( $true != $true )
| ( ( cF @ sK0 @ sK0 )
= $true ) ),
inference(superposition,[status(thm)],[f16,f12]) ).
thf(f12,plain,
! [X1: $i] :
( ( ( cF @ ( sK1 @ X1 ) @ X1 )
= $true )
| ( $true
= ( cF @ X1 @ sK0 ) ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f16,plain,
! [X0: $i] :
( ( $true
!= ( cF @ ( sK1 @ sK0 ) @ X0 ) )
| ( $true
!= ( cF @ X0 @ ( sK1 @ sK0 ) ) ) ),
inference(subsumption_resolution,[status(thm)],[f15,f13]) ).
thf(f15,plain,
! [X0: $i] :
( ( $true
!= ( cF @ X0 @ ( sK1 @ sK0 ) ) )
| ( $true
!= ( cF @ ( sK1 @ sK0 ) @ X0 ) )
| ( ( cF @ sK0 @ sK0 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f14]) ).
thf(f14,plain,
! [X0: $i] :
( ( ( cF @ sK0 @ sK0 )
= $true )
| ( $true
!= ( cF @ X0 @ ( sK1 @ sK0 ) ) )
| ( $true
!= ( cF @ ( sK1 @ sK0 ) @ X0 ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f13,f12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET046^5 : TPTP v9.2.1. Released v4.0.0.
% 0.11/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.18/0.34 % Computer : n009.cluster.edu
% 0.18/0.34 % Model : x86_64 x86_64
% 0.18/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.34 % Memory : 8042.1875MB
% 0.18/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.34 % CPULimit : 300
% 0.18/0.34 % WCLimit : 300
% 0.18/0.34 % DateTime : Tue Feb 24 11:50:25 EST 2026
% 0.18/0.35 % CPUTime :
% 0.18/0.35 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.30/0.49 ---- Original DTF file ---
% 0.30/0.50 thf(spec,logic,$$dhol).
% 0.30/0.50 %------------------------------------------------------------------------------
% 0.30/0.50 % File : SET046^5 : TPTP v9.2.1. Released v4.0.0.
% 0.30/0.50 % Domain : Set Theory
% 0.30/0.50 % Problem : TPS problem PELL42
% 0.30/0.50 % Version : Especial.
% 0.30/0.50 % English : There is no set of non-circular sets (where a circular set is a
% 0.30/0.50 % set x s.t. there is a set y, s.t. x belongs to y and reversely).
% 0.30/0.50
% 0.30/0.50 % Refs : [Pel86] Pelletier (1986), Seventy-five Problems for Testing Au
% 0.30/0.50 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.30/0.50 % Source : [Bro09]
% 0.30/0.50 % Names : tps_0525 [Bro09]
% 0.30/0.50 % : PELL42 [TPS]
% 0.30/0.50 % : Pelletier 42 [Pel86]
% 0.30/0.50
% 0.30/0.50 % Status : Theorem
% 0.30/0.50 % 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
% 0.30/0.50 % Syntax : Number of formulae : 2 ( 0 unt; 1 typ; 0 def)
% 0.30/0.50 % Number of atoms : 6 ( 0 equ; 0 cnn)
% 0.30/0.50 % Maximal formula atoms : 6 ( 6 avg)
% 0.30/0.50 % Number of connectives : 20 ( 3 ~; 0 |; 3 &; 12 @)
% 0.30/0.50 % ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% 0.30/0.50 % Maximal formula depth : 11 ( 11 avg)
% 0.30/0.50 % Number of types : 2 ( 0 usr)
% 0.30/0.50 % Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% 0.30/0.50 % Number of symbols : 1 ( 1 usr; 0 con; 2-2 aty)
% 0.30/0.50 % Number of variables : 4 ( 0 ^; 1 !; 3 ?; 4 :)
% 0.30/0.50 % SPC : TH0_THM_NEQ_NAR
% 0.30/0.50
% 0.30/0.50 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.30/0.50 % project in the Department of Mathematical Sciences at Carnegie
% 0.30/0.50 % Mellon University. Distributed under the Creative Commons copyleft
% 0.30/0.50 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.30/0.50 %------------------------------------------------------------------------------
% 0.30/0.50 thf(cF,type,
% 0.30/0.50 cF: $i > $i > $o ).
% 0.30/0.50
% 0.30/0.50 thf(cPELL42,conjecture,
% 0.30/0.50 ~ ? [Xy: $i] :
% 0.30/0.50 ! [Xx: $i] :
% 0.30/0.50 ( ( ( cF @ Xx @ Xy )
% 0.30/0.50 => ~ ? [Xz: $i] :
% 0.30/0.50 ( ( cF @ Xx @ Xz )
% 0.30/0.50 & ( cF @ Xz @ Xx ) ) )
% 0.30/0.50 & ( ~ ? [Xz: $i] :
% 0.30/0.50 ( ( cF @ Xx @ Xz )
% 0.30/0.50 & ( cF @ Xz @ Xx ) )
% 0.30/0.50 => ( cF @ Xx @ Xy ) ) ) ).
% 0.30/0.50
% 0.30/0.50 %------------------------------------------------------------------------------
% 0.30/0.50 ------------------------
% 1.66/1.43 ---- Embedded in THF ---
% 1.66/1.43 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.66/1.43 %%% Generated on Tue Feb 24 11:50:26 EST 2026
% 1.66/1.43 %%% using '$$dhol' embedding, version 1.3.0.
% 1.66/1.43 %%% Logic specification used:
% 1.66/1.43 %%% thf(spec, logic, $$dhol).
% 1.66/1.43
% 1.66/1.43 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.67W7WZ6ymG/DTF2DTF11304.p
% See solution above
% 1.66/1.43 ------------------------
% 1.66/1.43 ---- Cleaned THF ---
% 1.66/1.44 thf(cF,type,
% 1.66/1.44 cF: $i > $i > $o ).
% 1.66/1.44
% 1.66/1.44 thf(cPELL42,conjecture,
% 1.66/1.44 ~ ? [Xy: $i] :
% 1.66/1.44 ! [Xx: $i] :
% 1.66/1.44 ( ( ( cF @ Xx @ Xy )
% 1.66/1.44 => ~ ? [Xz: $i] :
% 1.66/1.44 ( ( cF @ Xx @ Xz )
% 1.66/1.44 & ( cF @ Xz @ Xx ) ) )
% 1.66/1.44 & ( ~ ? [Xz: $i] :
% 1.66/1.44 ( ( cF @ Xx @ Xz )
% 1.66/1.44 & ( cF @ Xz @ Xx ) )
% 1.66/1.44 => ( cF @ Xx @ Xy ) ) ) ).
% 1.66/1.44 ------------------------
% 1.66/1.46 % (11402)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_11304 for (3000ds/4Mi)
% 1.66/1.46 % (11404)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_11304 for (3000ds/2Mi)
% 1.66/1.46 % (11403)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_11304 for (3000ds/27Mi)
% 1.66/1.46 % (11401)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_11304 for (3000ds/183Mi)
% 1.66/1.46 % (11407)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_11304 for (3000ds/18Mi)
% 1.66/1.46 % (11406)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_11304 for (3000ds/275Mi)
% 1.66/1.46 % (11405)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_11304 for (3000ds/2Mi)
% 1.66/1.46 % (11404)Instruction limit reached!
% 1.66/1.46 % (11404)------------------------------
% 1.66/1.46 % (11404)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.46 % (11404)Termination reason: Unknown
% 1.66/1.46 % (11404)Termination phase: Saturation
% 1.66/1.46 % (11405)Instruction limit reached!
% 1.66/1.46 % (11405)------------------------------
% 1.66/1.46 % (11405)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.46 % (11405)Termination reason: Unknown
% 1.66/1.46 % (11405)Termination phase: Saturation
% 1.66/1.46
% 1.66/1.46 % (11405)Memory used [KB]: 5500
% 1.66/1.46 % (11405)Time elapsed: 0.003 s
% 1.66/1.46 % (11405)Instructions burned: 2 (million)
% 1.66/1.46 % (11405)------------------------------
% 1.66/1.46 % (11405)------------------------------
% 1.66/1.46
% 1.66/1.46 % (11404)Memory used [KB]: 5500
% 1.66/1.46 % (11404)Time elapsed: 0.003 s
% 1.66/1.46 % (11404)Instructions burned: 2 (million)
% 1.66/1.46 % (11404)------------------------------
% 1.66/1.46 % (11404)------------------------------
% 1.66/1.46 % (11406)First to succeed.
% 1.66/1.46 % (11403)Also succeeded, but the first one will report.
% 1.66/1.46 % (11401)Also succeeded, but the first one will report.
% 1.66/1.46 % (11406)Refutation found. Thanks to Tanya!
% 1.66/1.46 % SZS status Theorem for DTF2THF_11304
% 1.66/1.46 % SZS output start Proof for DTF2THF_11304
% 1.66/1.46 thf(func_def_0, type, cF: $i > $i > $o).
% 1.66/1.46 thf(func_def_5, type, sK1: $i > $i).
% 1.66/1.46 thf(f23,plain,(
% 1.66/1.46 $false),
% 1.66/1.46 inference(subsumption_resolution,[status(thm)],[f22,f13])).
% 1.66/1.46 thf(f13,plain,(
% 1.66/1.46 ( ! [X2 : $i,X1 : $i] : (($true != (cF @ X1 @ sK0)) | ((cF @ X1 @ X2) != $true) | ((cF @ X2 @ X1) != $true)) )),
% 1.66/1.46 inference(cnf_transformation,[status(thm)],[f10])).
% 1.66/1.46 thf(f10,plain,(
% 1.66/1.46 ! [X1 : $i] : ((! [X2 : $i] : (((cF @ X2 @ X1) != $true) | ((cF @ X1 @ X2) != $true)) | ($true != (cF @ X1 @ sK0))) & (($true = (cF @ X1 @ sK0)) | (((cF @ (sK1 @ X1) @ X1) = $true) & ($true = (cF @ X1 @ (sK1 @ X1))))))),
% 1.66/1.46 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f7,f9,f8])).
% 1.66/1.46 thf(f8,plain,(
% 1.66/1.46 ? [X0 : $i] : ! [X1 : $i] : ((! [X2 : $i] : (((cF @ X2 @ X1) != $true) | ((cF @ X1 @ X2) != $true)) | ((cF @ X1 @ X0) != $true)) & (((cF @ X1 @ X0) = $true) | ? [X3 : $i] : (($true = (cF @ X3 @ X1)) & ($true = (cF @ X1 @ X3))))) => ! [X1 : $i] : ((! [X2 : $i] : (((cF @ X2 @ X1) != $true) | ((cF @ X1 @ X2) != $true)) | ($true != (cF @ X1 @ sK0))) & (($true = (cF @ X1 @ sK0)) | ? [X3 : $i] : (($true = (cF @ X3 @ X1)) & ($true = (cF @ X1 @ X3)))))),
% 1.66/1.46 introduced(definition,[],[choice_axiom])).
% 1.66/1.46 thf(f9,plain,(
% 1.66/1.46 ! [X1 : $i] : (? [X3 : $i] : (($true = (cF @ X3 @ X1)) & ($true = (cF @ X1 @ X3))) => (((cF @ (sK1 @ X1) @ X1) = $true) & ($true = (cF @ X1 @ (sK1 @ X1)))))),
% 1.66/1.46 introduced(definition,[],[choice_axiom])).
% 1.66/1.46 thf(f7,plain,(
% 1.66/1.46 ? [X0 : $i] : ! [X1 : $i] : ((! [X2 : $i] : (((cF @ X2 @ X1) != $true) | ((cF @ X1 @ X2) != $true)) | ((cF @ X1 @ X0) != $true)) & (((cF @ X1 @ X0) = $true) | ? [X3 : $i] : (($true = (cF @ X3 @ X1)) & ($true = (cF @ X1 @ X3)))))),
% 1.66/1.46 inference(ennf_transformation,[status(thm)],[f6])).
% 1.66/1.46 thf(f6,plain,(
% 1.66/1.46 ? [X0 : $i] : ! [X1 : $i] : ((((cF @ X1 @ X0) = $true) => ~? [X2 : $i] : (((cF @ X1 @ X2) = $true) & ((cF @ X2 @ X1) = $true))) & (~? [X3 : $i] : (($true = (cF @ X3 @ X1)) & ($true = (cF @ X1 @ X3))) => ((cF @ X1 @ X0) = $true)))),
% 1.66/1.46 inference(flattening,[status(thm)],[f5])).
% 1.66/1.46 thf(f5,plain,(
% 1.66/1.46 ~~? [X0 : $i] : ! [X1 : $i] : ((((cF @ X1 @ X0) = $true) => ~? [X2 : $i] : (((cF @ X1 @ X2) = $true) & ((cF @ X2 @ X1) = $true))) & (~? [X3 : $i] : (($true = (cF @ X3 @ X1)) & ($true = (cF @ X1 @ X3))) => ((cF @ X1 @ X0) = $true)))),
% 1.66/1.46 inference(fool_elimination,[status(thm)],[f4])).
% 1.66/1.46 thf(f4,plain,(
% 1.66/1.46 ~~? [X0 : $i] : ! [X1 : $i] : (((cF @ X1 @ X0) => ~? [X2 : $i] : ((cF @ X1 @ X2) & (cF @ X2 @ X1))) & (~? [X3 : $i] : ((cF @ X3 @ X1) & (cF @ X1 @ X3)) => (cF @ X1 @ X0)))),
% 1.66/1.46 inference(rectify,[status(thm)],[f2])).
% 1.66/1.46 thf(f2,negated_conjecture,(
% 1.66/1.46 ~~? [X0 : $i] : ! [X1 : $i] : (((cF @ X1 @ X0) => ~? [X2 : $i] : ((cF @ X1 @ X2) & (cF @ X2 @ X1))) & (~? [X2 : $i] : ((cF @ X2 @ X1) & (cF @ X1 @ X2)) => (cF @ X1 @ X0)))),
% 1.66/1.46 inference(negated_conjecture,[status(cth)],[f1])).
% 1.66/1.46 thf(f1,conjecture,(
% 1.66/1.46 ~? [X0 : $i] : ! [X1 : $i] : (((cF @ X1 @ X0) => ~? [X2 : $i] : ((cF @ X1 @ X2) & (cF @ X2 @ X1))) & (~? [X2 : $i] : ((cF @ X2 @ X1) & (cF @ X1 @ X2)) => (cF @ X1 @ X0)))),
% 1.66/1.46 file('/export/starexec/sandbox/tmp/tmp.67W7WZ6ymG/DTF2THF_11304.p',cPELL42)).
% 1.66/1.46 thf(f22,plain,(
% 1.66/1.46 ((cF @ sK0 @ sK0) = $true)),
% 1.66/1.46 inference(subsumption_resolution,[status(thm)],[f19,f11])).
% 1.66/1.46 thf(f11,plain,(
% 1.66/1.46 ( ! [X1 : $i] : (($true = (cF @ X1 @ (sK1 @ X1))) | ($true = (cF @ X1 @ sK0))) )),
% 1.66/1.46 inference(cnf_transformation,[status(thm)],[f10])).
% 1.66/1.46 thf(f19,plain,(
% 1.66/1.46 ($true != (cF @ sK0 @ (sK1 @ sK0))) | ((cF @ sK0 @ sK0) = $true)),
% 1.66/1.46 inference(trivial_inequality_removal,[status(thm)],[f17])).
% 1.66/1.46 thf(f17,plain,(
% 1.66/1.46 ($true != (cF @ sK0 @ (sK1 @ sK0))) | ($true != $true) | ((cF @ sK0 @ sK0) = $true)),
% 1.66/1.46 inference(superposition,[status(thm)],[f16,f12])).
% 1.66/1.46 thf(f12,plain,(
% 1.66/1.46 ( ! [X1 : $i] : (((cF @ (sK1 @ X1) @ X1) = $true) | ($true = (cF @ X1 @ sK0))) )),
% 1.66/1.46 inference(cnf_transformation,[status(thm)],[f10])).
% 1.66/1.46 thf(f16,plain,(
% 1.66/1.46 ( ! [X0 : $i] : (($true != (cF @ (sK1 @ sK0) @ X0)) | ($true != (cF @ X0 @ (sK1 @ sK0)))) )),
% 1.66/1.46 inference(subsumption_resolution,[status(thm)],[f15,f13])).
% 1.66/1.46 thf(f15,plain,(
% 1.66/1.46 ( ! [X0 : $i] : (($true != (cF @ X0 @ (sK1 @ sK0))) | ($true != (cF @ (sK1 @ sK0) @ X0)) | ((cF @ sK0 @ sK0) = $true)) )),
% 1.66/1.46 inference(trivial_inequality_removal,[status(thm)],[f14])).
% 1.66/1.46 thf(f14,plain,(
% 1.66/1.46 ( ! [X0 : $i] : (((cF @ sK0 @ sK0) = $true) | ($true != (cF @ X0 @ (sK1 @ sK0))) | ($true != (cF @ (sK1 @ sK0) @ X0)) | ($true != $true)) )),
% 1.66/1.46 inference(superposition,[status(thm)],[f13,f12])).
% 1.66/1.46 % SZS output end Proof for DTF2THF_11304
% 1.66/1.46 % (11406)------------------------------
% 1.66/1.46 % (11406)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.46 % (11406)Termination reason: Refutation
% 1.66/1.46
% 1.66/1.46 % (11406)Memory used [KB]: 5500
% 1.66/1.46 % (11406)Time elapsed: 0.004 s
% 1.66/1.46 % (11406)Instructions burned: 2 (million)
% 1.66/1.46 % (11406)------------------------------
% 1.66/1.46 % (11406)------------------------------
% 1.66/1.46 % (11400)Success in time 0.019 s
%------------------------------------------------------------------------------