%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO308^5 : 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 : n019.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 09:53:54 AM UTC 2026
% Result : Theorem 1.65s 1.47s
% Output : Refutation 1.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 28 ( 6 unt; 0 typ; 2 def)
% Number of atoms : 255 ( 76 equ; 0 cnn)
% Maximal formula atoms : 14 ( 9 avg)
% Number of connectives : 236 ( 55 ~; 44 |; 22 &; 95 @)
% ( 2 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 44 ( 0 ^; 34 !; 10 ?; 44 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
cB: $i > $o ).
thf(func_def_1,type,
cA: $i > $o ).
thf(func_def_5,type,
sK0: $i > $o ).
thf(f31,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f22,f26,f30]) ).
thf(f30,plain,
~ spl2_1,
inference(avatar_contradiction_clause,[status(thm)],[f29]) ).
thf(f29,plain,
( $false
| ~ spl2_1 ),
inference(subsumption_resolution,[status(thm)],[f28,f12]) ).
thf(f12,plain,
( $true
= ( sK0 @ sK1 ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( ( ! [X1: $i] :
( ( ( cB @ X1 )
= $true )
| ( $true
!= ( sK0 @ X1 ) ) )
| ! [X2: $i] :
( ( $true
= ( cA @ X2 ) )
| ( ( sK0 @ X2 )
!= $true ) ) )
& ( ( cB @ sK1 )
!= $true )
& ( $true
!= ( cA @ sK1 ) )
& ( $true
= ( sK0 @ sK1 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f8,f10,f9]) ).
thf(f9,plain,
( ? [X0: $i > $o] :
( ( ! [X1: $i] :
( ( ( cB @ X1 )
= $true )
| ( ( X0 @ X1 )
!= $true ) )
| ! [X2: $i] :
( ( $true
= ( cA @ X2 ) )
| ( ( X0 @ X2 )
!= $true ) ) )
& ? [X3: $i] :
( ( ( cB @ X3 )
!= $true )
& ( ( cA @ X3 )
!= $true )
& ( ( X0 @ X3 )
= $true ) ) )
=> ( ( ! [X1: $i] :
( ( ( cB @ X1 )
= $true )
| ( $true
!= ( sK0 @ X1 ) ) )
| ! [X2: $i] :
( ( $true
= ( cA @ X2 ) )
| ( ( sK0 @ X2 )
!= $true ) ) )
& ? [X3: $i] :
( ( ( cB @ X3 )
!= $true )
& ( ( cA @ X3 )
!= $true )
& ( $true
= ( sK0 @ X3 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f10,plain,
( ? [X3: $i] :
( ( ( cB @ X3 )
!= $true )
& ( ( cA @ X3 )
!= $true )
& ( $true
= ( sK0 @ X3 ) ) )
=> ( ( ( cB @ sK1 )
!= $true )
& ( $true
!= ( cA @ sK1 ) )
& ( $true
= ( sK0 @ sK1 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f8,plain,
? [X0: $i > $o] :
( ( ! [X1: $i] :
( ( ( cB @ X1 )
= $true )
| ( ( X0 @ X1 )
!= $true ) )
| ! [X2: $i] :
( ( $true
= ( cA @ X2 ) )
| ( ( X0 @ X2 )
!= $true ) ) )
& ? [X3: $i] :
( ( ( cB @ X3 )
!= $true )
& ( ( cA @ X3 )
!= $true )
& ( ( X0 @ X3 )
= $true ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,plain,
? [X0: $i > $o] :
( ( ! [X2: $i] :
( ( ( cB @ X2 )
= $true )
| ( ( X0 @ X2 )
!= $true ) )
| ! [X1: $i] :
( ( ( cA @ X1 )
= $true )
| ( ( X0 @ X1 )
!= $true ) ) )
& ? [X3: $i] :
( ( ( cB @ X3 )
!= $true )
& ( ( cA @ X3 )
!= $true )
& ( ( X0 @ X3 )
= $true ) ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
? [X0: $i > $o] :
( ? [X3: $i] :
( ( ( cA @ X3 )
!= $true )
& ( ( cB @ X3 )
!= $true )
& ( ( X0 @ X3 )
= $true ) )
& ( ! [X2: $i] :
( ( ( cB @ X2 )
= $true )
| ( ( X0 @ X2 )
!= $true ) )
| ! [X1: $i] :
( ( ( cA @ X1 )
= $true )
| ( ( X0 @ X1 )
!= $true ) ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X0: $i > $o] :
( ( ! [X1: $i] :
( ( ( X0 @ X1 )
= $true )
=> ( ( cA @ X1 )
= $true ) )
| ! [X2: $i] :
( ( ( X0 @ X2 )
= $true )
=> ( ( cB @ X2 )
= $true ) ) )
=> ! [X3: $i] :
( ( ( X0 @ X3 )
= $true )
=> ( ( ( cA @ X3 )
= $true )
| ( ( cB @ X3 )
= $true ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: $i > $o] :
( ( ! [X1: $i] :
( ( X0 @ X1 )
=> ( cA @ X1 ) )
| ! [X2: $i] :
( ( X0 @ X2 )
=> ( cB @ X2 ) ) )
=> ! [X3: $i] :
( ( X0 @ X3 )
=> ( ( cA @ X3 )
| ( cB @ X3 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X0: $i > $o] :
( ( ! [X1: $i] :
( ( X0 @ X1 )
=> ( cA @ X1 ) )
| ! [X2: $i] :
( ( X0 @ X2 )
=> ( cB @ X2 ) ) )
=> ! [X3: $i] :
( ( X0 @ X3 )
=> ( ( cA @ X3 )
| ( cB @ X3 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X0: $i > $o] :
( ( ! [X1: $i] :
( ( X0 @ X1 )
=> ( cA @ X1 ) )
| ! [X2: $i] :
( ( X0 @ X2 )
=> ( cB @ X2 ) ) )
=> ! [X3: $i] :
( ( X0 @ X3 )
=> ( ( cA @ X3 )
| ( cB @ X3 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.VgJvwDf4pQ/DTF2THF_27098.p',cSET81_pme) ).
thf(f28,plain,
( ( $true
!= ( sK0 @ sK1 ) )
| ~ spl2_1 ),
inference(trivial_inequality_removal,[status(thm)],[f27]) ).
thf(f27,plain,
( ( $true != $true )
| ( $true
!= ( sK0 @ sK1 ) )
| ~ spl2_1 ),
inference(superposition,[status(thm)],[f14,f18]) ).
thf(f18,plain,
( ! [X1: $i] :
( ( ( cB @ X1 )
= $true )
| ( $true
!= ( sK0 @ X1 ) ) )
| ~ spl2_1 ),
inference(avatar_component_clause,[status(thm)],[f17]) ).
thf(f17,definition,
( spl2_1
<=> ! [X1: $i] :
( ( ( cB @ X1 )
= $true )
| ( $true
!= ( sK0 @ X1 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl2_1])],[avatar_definition]) ).
thf(f14,plain,
( ( cB @ sK1 )
!= $true ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f26,plain,
~ spl2_2,
inference(avatar_contradiction_clause,[status(thm)],[f25]) ).
thf(f25,plain,
( $false
| ~ spl2_2 ),
inference(subsumption_resolution,[status(thm)],[f24,f12]) ).
thf(f24,plain,
( ( $true
!= ( sK0 @ sK1 ) )
| ~ spl2_2 ),
inference(trivial_inequality_removal,[status(thm)],[f23]) ).
thf(f23,plain,
( ( $true
!= ( sK0 @ sK1 ) )
| ( $true != $true )
| ~ spl2_2 ),
inference(superposition,[status(thm)],[f13,f21]) ).
thf(f21,plain,
( ! [X2: $i] :
( ( $true
= ( cA @ X2 ) )
| ( ( sK0 @ X2 )
!= $true ) )
| ~ spl2_2 ),
inference(avatar_component_clause,[status(thm)],[f20]) ).
thf(f20,definition,
( spl2_2
<=> ! [X2: $i] :
( ( ( sK0 @ X2 )
!= $true )
| ( $true
= ( cA @ X2 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl2_2])],[avatar_definition]) ).
thf(f13,plain,
( $true
!= ( cA @ sK1 ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f22,plain,
( spl2_1
| spl2_2 ),
inference(avatar_split_clause,[status(thm)],[f15,f20,f17]) ).
thf(f15,plain,
! [X2: $i,X1: $i] :
( ( ( sK0 @ X2 )
!= $true )
| ( ( cB @ X1 )
= $true )
| ( $true
!= ( sK0 @ X1 ) )
| ( $true
= ( cA @ X2 ) ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO308^5 : 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
% 0.17/0.34 % Computer : n019.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue Feb 24 14:27:54 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.31/0.49 ---- Original DTF file ---
% 0.31/0.49 thf(spec,logic,$$dhol).
% 0.31/0.49 %------------------------------------------------------------------------------
% 0.31/0.49 % File : SYO308^5 : TPTP v9.2.1. Released v4.0.0.
% 0.31/0.49 % Domain : Syntactic
% 0.31/0.49 % Problem : TPS problem from BASIC-HO-THMS
% 0.31/0.49 % Version : Especial.
% 0.31/0.49 % English :
% 0.31/0.49
% 0.31/0.49 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.31/0.49 % Source : [Bro09]
% 0.31/0.49 % Names : tps_0830 [Bro09]
% 0.31/0.49
% 0.31/0.49 % Status : Theorem
% 0.31/0.49 % Rating : 0.00 v6.2.0, 0.17 v6.1.0, 0.00 v4.0.0
% 0.31/0.49 % Syntax : Number of formulae : 3 ( 0 unt; 2 typ; 0 def)
% 0.31/0.49 % Number of atoms : 4 ( 0 equ; 0 cnn)
% 0.31/0.49 % Maximal formula atoms : 4 ( 4 avg)
% 0.31/0.49 % Number of connectives : 13 ( 0 ~; 2 |; 0 &; 7 @)
% 0.31/0.49 % ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% 0.31/0.49 % Maximal formula depth : 7 ( 7 avg)
% 0.31/0.49 % Number of types : 2 ( 0 usr)
% 0.31/0.49 % Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% 0.31/0.49 % Number of symbols : 2 ( 2 usr; 0 con; 1-1 aty)
% 0.31/0.49 % Number of variables : 4 ( 0 ^; 4 !; 0 ?; 4 :)
% 0.31/0.49 % SPC : TH0_THM_NEQ_NAR
% 0.31/0.49
% 0.31/0.49 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.31/0.49 % project in the Department of Mathematical Sciences at Carnegie
% 0.31/0.49 % Mellon University. Distributed under the Creative Commons copyleft
% 0.31/0.49 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.31/0.49 %------------------------------------------------------------------------------
% 0.31/0.49 thf(cB,type,
% 0.31/0.49 cB: $i > $o ).
% 0.31/0.49
% 0.31/0.49 thf(cA,type,
% 0.31/0.49 cA: $i > $o ).
% 0.31/0.49
% 0.31/0.49 thf(cSET81_pme,conjecture,
% 0.31/0.49 ! [Z1: $i > $o] :
% 0.31/0.49 ( ( ! [Z3: $i] :
% 0.31/0.49 ( ( Z1 @ Z3 )
% 0.31/0.49 => ( cA @ Z3 ) )
% 0.31/0.49 | ! [Z4: $i] :
% 0.31/0.49 ( ( Z1 @ Z4 )
% 0.31/0.49 => ( cB @ Z4 ) ) )
% 0.31/0.49 => ! [Z5: $i] :
% 0.31/0.49 ( ( Z1 @ Z5 )
% 0.31/0.49 => ( ( cA @ Z5 )
% 0.31/0.49 | ( cB @ Z5 ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 %------------------------------------------------------------------------------
% 0.31/0.49 ------------------------
% 1.65/1.44 ---- Embedded in THF ---
% 1.65/1.44 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.65/1.44 %%% Generated on Tue Feb 24 14:27:55 EST 2026
% 1.65/1.44 %%% using '$$dhol' embedding, version 1.3.0.
% 1.65/1.44 %%% Logic specification used:
% 1.65/1.44 %%% thf(spec, logic, $$dhol).
% 1.65/1.44
% 1.65/1.44 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.VgJvwDf4pQ/DTF2DTF27098.p
% See solution above
% 1.65/1.44 ------------------------
% 1.65/1.45 ---- Cleaned THF ---
% 1.65/1.45 thf(cB,type,
% 1.65/1.45 cB: $i > $o ).
% 1.65/1.45
% 1.65/1.45 thf(cA,type,
% 1.65/1.45 cA: $i > $o ).
% 1.65/1.45
% 1.65/1.45 thf(cSET81_pme,conjecture,
% 1.65/1.45 ! [Z1: $i > $o] :
% 1.65/1.45 ( ( ! [Z3: $i] :
% 1.65/1.45 ( ( Z1 @ Z3 )
% 1.65/1.45 => ( cA @ Z3 ) )
% 1.65/1.45 | ! [Z4: $i] :
% 1.65/1.45 ( ( Z1 @ Z4 )
% 1.65/1.45 => ( cB @ Z4 ) ) )
% 1.65/1.45 => ! [Z5: $i] :
% 1.65/1.45 ( ( Z1 @ Z5 )
% 1.65/1.45 => ( ( cA @ Z5 )
% 1.65/1.45 | ( cB @ Z5 ) ) ) ) ).
% 1.65/1.45 ------------------------
% 1.65/1.47 % (27215)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_27098 for (2999ds/2Mi)
% 1.65/1.47 % (27211)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_27098 for (2999ds/183Mi)
% 1.65/1.47 % (27212)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_27098 for (2999ds/4Mi)
% 1.65/1.47 % (27213)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_27098 for (2999ds/27Mi)
% 1.65/1.47 % (27217)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_27098 for (2999ds/18Mi)
% 1.65/1.47 % (27216)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_27098 for (2999ds/275Mi)
% 1.65/1.47 % (27214)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_27098 for (2999ds/2Mi)
% 1.65/1.47 % (27215)Instruction limit reached!
% 1.65/1.47 % (27215)------------------------------
% 1.65/1.47 % (27215)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.47 % (27215)Termination reason: Unknown
% 1.65/1.47 % (27215)Termination phase: Saturation
% 1.65/1.47
% 1.65/1.47 % (27215)Memory used [KB]: 895
% 1.65/1.47 % (27215)Time elapsed: 0.003 s
% 1.65/1.47 % (27215)Instructions burned: 2 (million)
% 1.65/1.47 % (27215)------------------------------
% 1.65/1.47 % (27215)------------------------------
% 1.65/1.47 % (27214)Instruction limit reached!
% 1.65/1.47 % (27214)------------------------------
% 1.65/1.47 % (27214)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.47 % (27214)Termination reason: Unknown
% 1.65/1.47 % (27214)Termination phase: Saturation
% 1.65/1.47
% 1.65/1.47 % (27214)Memory used [KB]: 5500
% 1.65/1.47 % (27214)Time elapsed: 0.003 s
% 1.65/1.47 % (27214)Instructions burned: 2 (million)
% 1.65/1.47 % (27214)------------------------------
% 1.65/1.47 % (27214)------------------------------
% 1.65/1.47 % (27216)First to succeed.
% 1.65/1.47 % (27217)Also succeeded, but the first one will report.
% 1.65/1.47 % (27211)Also succeeded, but the first one will report.
% 1.65/1.47 % (27216)Refutation found. Thanks to Tanya!
% 1.65/1.47 % SZS status Theorem for DTF2THF_27098
% 1.65/1.47 % SZS output start Proof for DTF2THF_27098
% 1.65/1.47 thf(func_def_0, type, cB: $i > $o).
% 1.65/1.47 thf(func_def_1, type, cA: $i > $o).
% 1.65/1.47 thf(func_def_5, type, sK0: $i > $o).
% 1.65/1.47 thf(f31,plain,(
% 1.65/1.47 $false),
% 1.65/1.47 inference(avatar_sat_refutation,[status(thm)],[f22,f26,f30])).
% 1.65/1.47 thf(f30,plain,(
% 1.65/1.47 ~spl2_1),
% 1.65/1.47 inference(avatar_contradiction_clause,[status(thm)],[f29])).
% 1.65/1.47 thf(f29,plain,(
% 1.65/1.47 $false | ~spl2_1),
% 1.65/1.47 inference(subsumption_resolution,[status(thm)],[f28,f12])).
% 1.65/1.47 thf(f12,plain,(
% 1.65/1.47 ($true = (sK0 @ sK1))),
% 1.65/1.47 inference(cnf_transformation,[status(thm)],[f11])).
% 1.65/1.47 thf(f11,plain,(
% 1.65/1.47 (! [X1 : $i] : (((cB @ X1) = $true) | ($true != (sK0 @ X1))) | ! [X2 : $i] : (($true = (cA @ X2)) | ((sK0 @ X2) != $true))) & (((cB @ sK1) != $true) & ($true != (cA @ sK1)) & ($true = (sK0 @ sK1)))),
% 1.65/1.47 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f8,f10,f9])).
% 1.65/1.47 thf(f9,plain,(
% 1.65/1.47 ? [X0 : $i > $o] : ((! [X1 : $i] : (((cB @ X1) = $true) | ((X0 @ X1) != $true)) | ! [X2 : $i] : (($true = (cA @ X2)) | ((X0 @ X2) != $true))) & ? [X3 : $i] : (((cB @ X3) != $true) & ((cA @ X3) != $true) & ((X0 @ X3) = $true))) => ((! [X1 : $i] : (((cB @ X1) = $true) | ($true != (sK0 @ X1))) | ! [X2 : $i] : (($true = (cA @ X2)) | ((sK0 @ X2) != $true))) & ? [X3 : $i] : (((cB @ X3) != $true) & ((cA @ X3) != $true) & ($true = (sK0 @ X3))))),
% 1.65/1.47 introduced(definition,[],[choice_axiom])).
% 1.65/1.47 thf(f10,plain,(
% 1.65/1.47 ? [X3 : $i] : (((cB @ X3) != $true) & ((cA @ X3) != $true) & ($true = (sK0 @ X3))) => (((cB @ sK1) != $true) & ($true != (cA @ sK1)) & ($true = (sK0 @ sK1)))),
% 1.65/1.47 introduced(definition,[],[choice_axiom])).
% 1.65/1.47 thf(f8,plain,(
% 1.65/1.47 ? [X0 : $i > $o] : ((! [X1 : $i] : (((cB @ X1) = $true) | ((X0 @ X1) != $true)) | ! [X2 : $i] : (($true = (cA @ X2)) | ((X0 @ X2) != $true))) & ? [X3 : $i] : (((cB @ X3) != $true) & ((cA @ X3) != $true) & ((X0 @ X3) = $true)))),
% 1.65/1.47 inference(rectify,[status(thm)],[f7])).
% 1.65/1.47 thf(f7,plain,(
% 1.65/1.47 ? [X0 : $i > $o] : ((! [X2 : $i] : (((cB @ X2) = $true) | ((X0 @ X2) != $true)) | ! [X1 : $i] : (((cA @ X1) = $true) | ((X0 @ X1) != $true))) & ? [X3 : $i] : (((cB @ X3) != $true) & ((cA @ X3) != $true) & ((X0 @ X3) = $true)))),
% 1.65/1.47 inference(flattening,[status(thm)],[f6])).
% 1.65/1.47 thf(f6,plain,(
% 1.65/1.47 ? [X0 : $i > $o] : (? [X3 : $i] : ((((cA @ X3) != $true) & ((cB @ X3) != $true)) & ((X0 @ X3) = $true)) & (! [X2 : $i] : (((cB @ X2) = $true) | ((X0 @ X2) != $true)) | ! [X1 : $i] : (((cA @ X1) = $true) | ((X0 @ X1) != $true))))),
% 1.65/1.47 inference(ennf_transformation,[status(thm)],[f5])).
% 1.65/1.47 thf(f5,plain,(
% 1.65/1.47 ~! [X0 : $i > $o] : ((! [X1 : $i] : (((X0 @ X1) = $true) => ((cA @ X1) = $true)) | ! [X2 : $i] : (((X0 @ X2) = $true) => ((cB @ X2) = $true))) => ! [X3 : $i] : (((X0 @ X3) = $true) => (((cA @ X3) = $true) | ((cB @ X3) = $true))))),
% 1.65/1.47 inference(fool_elimination,[status(thm)],[f4])).
% 1.65/1.47 thf(f4,plain,(
% 1.65/1.47 ~! [X0 : $i > $o] : ((! [X1 : $i] : ((X0 @ X1) => (cA @ X1)) | ! [X2 : $i] : ((X0 @ X2) => (cB @ X2))) => ! [X3 : $i] : ((X0 @ X3) => ((cA @ X3) | (cB @ X3))))),
% 1.65/1.47 inference(rectify,[status(thm)],[f2])).
% 1.65/1.47 thf(f2,negated_conjecture,(
% 1.65/1.47 ~! [X0 : $i > $o] : ((! [X1 : $i] : ((X0 @ X1) => (cA @ X1)) | ! [X2 : $i] : ((X0 @ X2) => (cB @ X2))) => ! [X3 : $i] : ((X0 @ X3) => ((cA @ X3) | (cB @ X3))))),
% 1.65/1.47 inference(negated_conjecture,[status(cth)],[f1])).
% 1.65/1.47 thf(f1,conjecture,(
% 1.65/1.47 ! [X0 : $i > $o] : ((! [X1 : $i] : ((X0 @ X1) => (cA @ X1)) | ! [X2 : $i] : ((X0 @ X2) => (cB @ X2))) => ! [X3 : $i] : ((X0 @ X3) => ((cA @ X3) | (cB @ X3))))),
% 1.65/1.47 file('/export/starexec/sandbox/tmp/tmp.VgJvwDf4pQ/DTF2THF_27098.p',cSET81_pme)).
% 1.65/1.47 thf(f28,plain,(
% 1.65/1.47 ($true != (sK0 @ sK1)) | ~spl2_1),
% 1.65/1.47 inference(trivial_inequality_removal,[status(thm)],[f27])).
% 1.65/1.47 thf(f27,plain,(
% 1.65/1.47 ($true != $true) | ($true != (sK0 @ sK1)) | ~spl2_1),
% 1.65/1.47 inference(superposition,[status(thm)],[f14,f18])).
% 1.65/1.47 thf(f18,plain,(
% 1.65/1.47 ( ! [X1 : $i] : (((cB @ X1) = $true) | ($true != (sK0 @ X1))) ) | ~spl2_1),
% 1.65/1.47 inference(avatar_component_clause,[status(thm)],[f17])).
% 1.65/1.47 thf(f17,definition,(
% 1.65/1.47 spl2_1 <=> ! [X1 : $i] : (((cB @ X1) = $true) | ($true != (sK0 @ X1)))),
% 1.65/1.47 introduced(definition,[new_symbols(naming,[spl2_1])],[avatar_definition])).
% 1.65/1.47 thf(f14,plain,(
% 1.65/1.47 ((cB @ sK1) != $true)),
% 1.65/1.47 inference(cnf_transformation,[status(thm)],[f11])).
% 1.65/1.47 thf(f26,plain,(
% 1.65/1.47 ~spl2_2),
% 1.65/1.47 inference(avatar_contradiction_clause,[status(thm)],[f25])).
% 1.65/1.47 thf(f25,plain,(
% 1.65/1.47 $false | ~spl2_2),
% 1.65/1.47 inference(subsumption_resolution,[status(thm)],[f24,f12])).
% 1.65/1.47 thf(f24,plain,(
% 1.65/1.47 ($true != (sK0 @ sK1)) | ~spl2_2),
% 1.65/1.47 inference(trivial_inequality_removal,[status(thm)],[f23])).
% 1.65/1.47 thf(f23,plain,(
% 1.65/1.47 ($true != (sK0 @ sK1)) | ($true != $true) | ~spl2_2),
% 1.65/1.47 inference(superposition,[status(thm)],[f13,f21])).
% 1.65/1.47 thf(f21,plain,(
% 1.65/1.47 ( ! [X2 : $i] : (($true = (cA @ X2)) | ((sK0 @ X2) != $true)) ) | ~spl2_2),
% 1.65/1.47 inference(avatar_component_clause,[status(thm)],[f20])).
% 1.65/1.47 thf(f20,definition,(
% 1.65/1.47 spl2_2 <=> ! [X2 : $i] : (((sK0 @ X2) != $true) | ($true = (cA @ X2)))),
% 1.65/1.47 introduced(definition,[new_symbols(naming,[spl2_2])],[avatar_definition])).
% 1.65/1.47 thf(f13,plain,(
% 1.65/1.47 ($true != (cA @ sK1))),
% 1.65/1.47 inference(cnf_transformation,[status(thm)],[f11])).
% 1.65/1.47 thf(f22,plain,(
% 1.65/1.47 spl2_1 | spl2_2),
% 1.65/1.47 inference(avatar_split_clause,[status(thm)],[f15,f20,f17])).
% 1.65/1.47 thf(f15,plain,(
% 1.65/1.47 ( ! [X2 : $i,X1 : $i] : (((sK0 @ X2) != $true) | ((cB @ X1) = $true) | ($true != (sK0 @ X1)) | ($true = (cA @ X2))) )),
% 1.65/1.47 inference(cnf_transformation,[status(thm)],[f11])).
% 1.65/1.47 % SZS output end Proof for DTF2THF_27098
% 1.65/1.47 % (27216)------------------------------
% 1.65/1.47 % (27216)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.47 % (27216)Termination reason: Refutation
% 1.65/1.47
% 1.65/1.47 % (27216)Memory used [KB]: 5500
% 1.65/1.47 % (27216)Time elapsed: 0.004 s
% 1.65/1.47 % (27216)Instructions burned: 1 (million)
% 1.65/1.47 % (27216)------------------------------
% 1.65/1.47 % (27216)------------------------------
% 1.65/1.47 % (27210)Success in time 0.019 s
%------------------------------------------------------------------------------