%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV413^5 : 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 : n010.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 09:41:12 AM UTC 2026
% Result : Theorem 1.53s 1.31s
% Output : Refutation 1.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of formulae : 36 ( 1 unt; 0 typ; 5 def)
% Number of atoms : 296 ( 69 equ; 0 cnn)
% Maximal formula atoms : 8 ( 8 avg)
% Number of connectives : 237 ( 51 ~; 51 |; 17 &; 91 @)
% ( 5 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 9 usr; 9 con; 0-2 aty)
% Number of variables : 32 ( 0 ^; 26 !; 6 ?; 32 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
cB: $i > $o ).
thf(func_def_1,type,
cA: $i > $o ).
thf(f47,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f24,f29,f34,f35,f39,f44,f46]) ).
thf(f46,plain,
( ~ spl2_2
| spl2_4
| ~ spl2_5 ),
inference(avatar_contradiction_clause,[status(thm)],[f45]) ).
thf(f45,plain,
( $false
| ~ spl2_2
| spl2_4
| ~ spl2_5 ),
inference(subsumption_resolution,[status(thm)],[f42,f23]) ).
thf(f23,plain,
( ( $true
= ( cA @ sK0 ) )
| ~ spl2_2 ),
inference(avatar_component_clause,[status(thm)],[f21]) ).
thf(f21,definition,
( spl2_2
<=> ( $true
= ( cA @ sK0 ) ) ),
introduced(definition,[new_symbols(naming,[spl2_2])],[avatar_definition]) ).
thf(f42,plain,
( ( $true
!= ( cA @ sK0 ) )
| spl2_4
| ~ spl2_5 ),
inference(trivial_inequality_removal,[status(thm)],[f41]) ).
thf(f41,plain,
( ( $true
!= ( cA @ sK0 ) )
| ( $true != $true )
| spl2_4
| ~ spl2_5 ),
inference(superposition,[status(thm)],[f33,f38]) ).
thf(f38,plain,
( ! [X2: $i] :
( ( $true
= ( cB @ X2 ) )
| ( $true
!= ( cA @ X2 ) ) )
| ~ spl2_5 ),
inference(avatar_component_clause,[status(thm)],[f37]) ).
thf(f37,definition,
( spl2_5
<=> ! [X2: $i] :
( ( $true
!= ( cA @ X2 ) )
| ( $true
= ( cB @ X2 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl2_5])],[avatar_definition]) ).
thf(f33,plain,
( ( ( cB @ sK0 )
!= $true )
| spl2_4 ),
inference(avatar_component_clause,[status(thm)],[f31]) ).
thf(f31,definition,
( spl2_4
<=> ( ( cB @ sK0 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl2_4])],[avatar_definition]) ).
thf(f44,plain,
( ~ spl2_3
| spl2_1
| ~ spl2_5 ),
inference(avatar_split_clause,[status(thm)],[f43,f37,f17,f26]) ).
thf(f26,definition,
( spl2_3
<=> ( $true
= ( cA @ sK1 ) ) ),
introduced(definition,[new_symbols(naming,[spl2_3])],[avatar_definition]) ).
thf(f17,definition,
( spl2_1
<=> ( ( cB @ sK1 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl2_1])],[avatar_definition]) ).
thf(f43,plain,
( ( $true
!= ( cA @ sK1 ) )
| spl2_1
| ~ spl2_5 ),
inference(trivial_inequality_removal,[status(thm)],[f40]) ).
thf(f40,plain,
( ( $true != $true )
| ( $true
!= ( cA @ sK1 ) )
| spl2_1
| ~ spl2_5 ),
inference(superposition,[status(thm)],[f19,f38]) ).
thf(f19,plain,
( ( ( cB @ sK1 )
!= $true )
| spl2_1 ),
inference(avatar_component_clause,[status(thm)],[f17]) ).
thf(f39,plain,
( spl2_5
| spl2_5 ),
inference(avatar_split_clause,[status(thm)],[f11,f37,f37]) ).
thf(f11,plain,
! [X2: $i,X3: $i] :
( ( $true
!= ( cA @ X2 ) )
| ( $true
= ( cB @ X2 ) )
| ( ( cB @ X3 )
= $true )
| ( ( cA @ X3 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
( ( ( ( $true
= ( cA @ sK0 ) )
& ( ( cB @ sK0 )
!= $true ) )
| ( ( ( cB @ sK1 )
!= $true )
& ( $true
= ( cA @ sK1 ) ) ) )
& ( ! [X2: $i] :
( ( $true
= ( cB @ X2 ) )
| ( $true
!= ( cA @ X2 ) ) )
| ! [X3: $i] :
( ( ( cA @ X3 )
!= $true )
| ( ( cB @ X3 )
= $true ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f7,f9,f8]) ).
thf(f8,plain,
( ? [X0: $i] :
( ( ( cA @ X0 )
= $true )
& ( ( cB @ X0 )
!= $true ) )
=> ( ( $true
= ( cA @ sK0 ) )
& ( ( cB @ sK0 )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f9,plain,
( ? [X1: $i] :
( ( $true
!= ( cB @ X1 ) )
& ( $true
= ( cA @ X1 ) ) )
=> ( ( ( cB @ sK1 )
!= $true )
& ( $true
= ( cA @ sK1 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f7,plain,
( ( ? [X0: $i] :
( ( ( cA @ X0 )
= $true )
& ( ( cB @ X0 )
!= $true ) )
| ? [X1: $i] :
( ( $true
!= ( cB @ X1 ) )
& ( $true
= ( cA @ X1 ) ) ) )
& ( ! [X2: $i] :
( ( $true
= ( cB @ X2 ) )
| ( $true
!= ( cA @ X2 ) ) )
| ! [X3: $i] :
( ( ( cA @ X3 )
!= $true )
| ( ( cB @ X3 )
= $true ) ) ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,plain,
( ( ? [X3: $i] :
( ( ( cA @ X3 )
= $true )
& ( ( cB @ X3 )
!= $true ) )
| ? [X2: $i] :
( ( $true
!= ( cB @ X2 ) )
& ( $true
= ( cA @ X2 ) ) ) )
& ( ! [X1: $i] :
( ( $true
= ( cB @ X1 ) )
| ( $true
!= ( cA @ X1 ) ) )
| ! [X0: $i] :
( ( ( cA @ X0 )
!= $true )
| ( ( cB @ X0 )
= $true ) ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ( ! [X1: $i] :
( ( $true
= ( cA @ X1 ) )
=> ( $true
= ( cB @ X1 ) ) )
| ! [X0: $i] :
( ( ( cA @ X0 )
= $true )
=> ( ( cB @ X0 )
= $true ) ) )
=> ( ! [X3: $i] :
( ( ( cA @ X3 )
= $true )
=> ( ( cB @ X3 )
= $true ) )
& ! [X2: $i] :
( ( $true
= ( cA @ X2 ) )
=> ( $true
= ( cB @ X2 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ( ! [X0: $i] :
( ( cA @ X0 )
=> ( cB @ X0 ) )
| ! [X1: $i] :
( ( cA @ X1 )
=> ( cB @ X1 ) ) )
=> ( ! [X2: $i] :
( ( cA @ X2 )
=> ( cB @ X2 ) )
& ! [X3: $i] :
( ( cA @ X3 )
=> ( cB @ X3 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ( ! [X0: $i] :
( ( cA @ X0 )
=> ( cB @ X0 ) )
| ! [X0: $i] :
( ( cA @ X0 )
=> ( cB @ X0 ) ) )
=> ( ! [X0: $i] :
( ( cA @ X0 )
=> ( cB @ X0 ) )
& ! [X0: $i] :
( ( cA @ X0 )
=> ( cB @ X0 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ( ! [X0: $i] :
( ( cA @ X0 )
=> ( cB @ X0 ) )
| ! [X0: $i] :
( ( cA @ X0 )
=> ( cB @ X0 ) ) )
=> ( ! [X0: $i] :
( ( cA @ X0 )
=> ( cB @ X0 ) )
& ! [X0: $i] :
( ( cA @ X0 )
=> ( cB @ X0 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.hia5ng53e2/DTF2THF_29646.p',cDUAL_EG5_pme) ).
thf(f35,plain,
( ~ spl2_4
| spl2_3 ),
inference(avatar_split_clause,[status(thm)],[f12,f26,f31]) ).
thf(f12,plain,
( ( $true
= ( cA @ sK1 ) )
| ( ( cB @ sK0 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f34,plain,
( ~ spl2_1
| ~ spl2_4 ),
inference(avatar_split_clause,[status(thm)],[f13,f31,f17]) ).
thf(f13,plain,
( ( ( cB @ sK0 )
!= $true )
| ( ( cB @ sK1 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f29,plain,
( spl2_2
| spl2_3 ),
inference(avatar_split_clause,[status(thm)],[f14,f26,f21]) ).
thf(f14,plain,
( ( $true
= ( cA @ sK0 ) )
| ( $true
= ( cA @ sK1 ) ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f24,plain,
( ~ spl2_1
| spl2_2 ),
inference(avatar_split_clause,[status(thm)],[f15,f21,f17]) ).
thf(f15,plain,
( ( $true
= ( cA @ sK0 ) )
| ( ( cB @ sK1 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SEV413^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.09 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.12/0.29 % Computer : n010.cluster.edu
% 0.12/0.29 % Model : x86_64 x86_64
% 0.12/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.29 % Memory : 8042.1875MB
% 0.12/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.29 % CPULimit : 300
% 0.12/0.29 % WCLimit : 300
% 0.12/0.29 % DateTime : Tue Feb 24 12:46:03 EST 2026
% 0.12/0.29 % CPUTime :
% 0.12/0.29 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.20/0.38 ---- Original DTF file ---
% 0.20/0.39 thf(spec,logic,$$dhol).
% 0.20/0.39 %------------------------------------------------------------------------------
% 0.20/0.39 % File : SEV413^5 : TPTP v9.2.1. Released v4.0.0.
% 0.20/0.39 % Domain : Set Theory
% 0.20/0.39 % Problem : TPS problem from SETS-THMS
% 0.20/0.39 % Version : Especial.
% 0.20/0.39 % English :
% 0.20/0.39
% 0.20/0.39 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.20/0.39 % Source : [Bro09]
% 0.20/0.39 % Names : tps_0852 [Bro09]
% 0.20/0.39
% 0.20/0.39 % Status : Theorem
% 0.20/0.39 % Rating : 0.00 v6.2.0, 0.17 v6.1.0, 0.00 v4.0.0
% 0.20/0.39 % Syntax : Number of formulae : 3 ( 0 unt; 2 typ; 0 def)
% 0.20/0.39 % Number of atoms : 8 ( 0 equ; 0 cnn)
% 0.20/0.39 % Maximal formula atoms : 8 ( 8 avg)
% 0.20/0.39 % Number of connectives : 15 ( 0 ~; 1 |; 1 &; 8 @)
% 0.20/0.39 % ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% 0.20/0.39 % Maximal formula depth : 6 ( 6 avg)
% 0.20/0.39 % Number of types : 2 ( 0 usr)
% 0.20/0.39 % Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% 0.20/0.39 % Number of symbols : 2 ( 2 usr; 0 con; 1-1 aty)
% 0.20/0.39 % Number of variables : 4 ( 0 ^; 4 !; 0 ?; 4 :)
% 0.20/0.39 % SPC : TH0_THM_NEQ_NAR
% 0.20/0.39
% 0.20/0.39 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.20/0.39 % project in the Department of Mathematical Sciences at Carnegie
% 0.20/0.39 % Mellon University. Distributed under the Creative Commons copyleft
% 0.20/0.39 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.20/0.39 %------------------------------------------------------------------------------
% 0.20/0.39 thf(cB,type,
% 0.20/0.39 cB: $i > $o ).
% 0.20/0.39
% 0.20/0.39 thf(cA,type,
% 0.20/0.39 cA: $i > $o ).
% 0.20/0.39
% 0.20/0.39 thf(cDUAL_EG5_pme,conjecture,
% 0.20/0.39 ( ( ! [Xx: $i] :
% 0.20/0.39 ( ( cA @ Xx )
% 0.20/0.39 => ( cB @ Xx ) )
% 0.20/0.39 | ! [Xx: $i] :
% 0.20/0.39 ( ( cA @ Xx )
% 0.20/0.39 => ( cB @ Xx ) ) )
% 0.20/0.39 => ( ! [Xx: $i] :
% 0.20/0.39 ( ( cA @ Xx )
% 0.20/0.39 => ( cB @ Xx ) )
% 0.20/0.39 & ! [Xx: $i] :
% 0.20/0.39 ( ( cA @ Xx )
% 0.20/0.39 => ( cB @ Xx ) ) ) ) ).
% 0.20/0.39
% 0.20/0.39 %------------------------------------------------------------------------------
% 0.20/0.39 ------------------------
% 1.36/1.28 ---- Embedded in THF ---
% 1.36/1.28 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.36/1.28 %%% Generated on Tue Feb 24 12:46:04 EST 2026
% 1.36/1.28 %%% using '$$dhol' embedding, version 1.3.0.
% 1.36/1.28 %%% Logic specification used:
% 1.36/1.28 %%% thf(spec, logic, $$dhol).
% 1.36/1.28
% 1.36/1.28 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.hia5ng53e2/DTF2DTF29646.p
% See solution above
% 1.36/1.28 ------------------------
% 1.36/1.29 ---- Cleaned THF ---
% 1.36/1.29 thf(cB,type,
% 1.36/1.29 cB: $i > $o ).
% 1.36/1.29
% 1.36/1.29 thf(cA,type,
% 1.36/1.29 cA: $i > $o ).
% 1.36/1.29
% 1.36/1.29 thf(cDUAL_EG5_pme,conjecture,
% 1.36/1.29 ( ( ! [Xx: $i] :
% 1.36/1.29 ( ( cA @ Xx )
% 1.36/1.29 => ( cB @ Xx ) )
% 1.36/1.29 | ! [Xx: $i] :
% 1.36/1.29 ( ( cA @ Xx )
% 1.36/1.29 => ( cB @ Xx ) ) )
% 1.36/1.29 => ( ! [Xx: $i] :
% 1.36/1.29 ( ( cA @ Xx )
% 1.36/1.29 => ( cB @ Xx ) )
% 1.36/1.29 & ! [Xx: $i] :
% 1.36/1.29 ( ( cA @ Xx )
% 1.36/1.29 => ( cB @ Xx ) ) ) ) ).
% 1.36/1.29 ------------------------
% 1.53/1.31 % (29746)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_29646 for (3000ds/2Mi)
% 1.53/1.31 % (29748)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_29646 for (3000ds/275Mi)
% 1.53/1.31 % (29743)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_29646 for (3000ds/183Mi)
% 1.53/1.31 % (29744)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_29646 for (3000ds/4Mi)
% 1.53/1.31 % (29747)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_29646 for (3000ds/2Mi)
% 1.53/1.31 % (29745)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_29646 for (3000ds/27Mi)
% 1.53/1.31 % (29749)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_29646 for (3000ds/18Mi)
% 1.53/1.31 % (29747)Instruction limit reached!
% 1.53/1.31 % (29747)------------------------------
% 1.53/1.31 % (29747)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.31 % (29747)Termination reason: Unknown
% 1.53/1.31 % (29747)Termination phase: Saturation
% 1.53/1.31
% 1.53/1.31 % (29747)Memory used [KB]: 5373
% 1.53/1.31 % (29747)Time elapsed: 0.003 s
% 1.53/1.31 % (29747)Instructions burned: 2 (million)
% 1.53/1.31 % (29747)------------------------------
% 1.53/1.31 % (29747)------------------------------
% 1.53/1.31 % (29748)First to succeed.
% 1.53/1.31 % (29746)Instruction limit reached!
% 1.53/1.31 % (29746)------------------------------
% 1.53/1.31 % (29746)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.31 % (29746)Termination reason: Unknown
% 1.53/1.31 % (29746)Termination phase: Saturation
% 1.53/1.31
% 1.53/1.31 % (29746)Memory used [KB]: 5500
% 1.53/1.31 % (29746)Time elapsed: 0.004 s
% 1.53/1.31 % (29746)Instructions burned: 3 (million)
% 1.53/1.31 % (29746)------------------------------
% 1.53/1.31 % (29746)------------------------------
% 1.53/1.31 % (29743)Also succeeded, but the first one will report.
% 1.53/1.31 % (29744)Also succeeded, but the first one will report.
% 1.53/1.31 % (29748)Refutation found. Thanks to Tanya!
% 1.53/1.31 % SZS status Theorem for DTF2THF_29646
% 1.53/1.31 % SZS output start Proof for DTF2THF_29646
% 1.53/1.31 thf(func_def_0, type, cB: $i > $o).
% 1.53/1.31 thf(func_def_1, type, cA: $i > $o).
% 1.53/1.31 thf(f47,plain,(
% 1.53/1.31 $false),
% 1.53/1.31 inference(avatar_sat_refutation,[status(thm)],[f24,f29,f34,f35,f39,f44,f46])).
% 1.53/1.31 thf(f46,plain,(
% 1.53/1.31 ~spl2_2 | spl2_4 | ~spl2_5),
% 1.53/1.31 inference(avatar_contradiction_clause,[status(thm)],[f45])).
% 1.53/1.31 thf(f45,plain,(
% 1.53/1.31 $false | (~spl2_2 | spl2_4 | ~spl2_5)),
% 1.53/1.31 inference(subsumption_resolution,[status(thm)],[f42,f23])).
% 1.53/1.31 thf(f23,plain,(
% 1.53/1.31 ($true = (cA @ sK0)) | ~spl2_2),
% 1.53/1.31 inference(avatar_component_clause,[status(thm)],[f21])).
% 1.53/1.31 thf(f21,definition,(
% 1.53/1.31 spl2_2 <=> ($true = (cA @ sK0))),
% 1.53/1.31 introduced(definition,[new_symbols(naming,[spl2_2])],[avatar_definition])).
% 1.53/1.31 thf(f42,plain,(
% 1.53/1.31 ($true != (cA @ sK0)) | (spl2_4 | ~spl2_5)),
% 1.53/1.31 inference(trivial_inequality_removal,[status(thm)],[f41])).
% 1.53/1.31 thf(f41,plain,(
% 1.53/1.31 ($true != (cA @ sK0)) | ($true != $true) | (spl2_4 | ~spl2_5)),
% 1.53/1.31 inference(superposition,[status(thm)],[f33,f38])).
% 1.53/1.31 thf(f38,plain,(
% 1.53/1.31 ( ! [X2 : $i] : (($true = (cB @ X2)) | ($true != (cA @ X2))) ) | ~spl2_5),
% 1.53/1.31 inference(avatar_component_clause,[status(thm)],[f37])).
% 1.53/1.31 thf(f37,definition,(
% 1.53/1.31 spl2_5 <=> ! [X2 : $i] : (($true != (cA @ X2)) | ($true = (cB @ X2)))),
% 1.53/1.31 introduced(definition,[new_symbols(naming,[spl2_5])],[avatar_definition])).
% 1.53/1.31 thf(f33,plain,(
% 1.53/1.31 ((cB @ sK0) != $true) | spl2_4),
% 1.53/1.31 inference(avatar_component_clause,[status(thm)],[f31])).
% 1.53/1.31 thf(f31,definition,(
% 1.53/1.31 spl2_4 <=> ((cB @ sK0) = $true)),
% 1.53/1.31 introduced(definition,[new_symbols(naming,[spl2_4])],[avatar_definition])).
% 1.53/1.31 thf(f44,plain,(
% 1.53/1.31 ~spl2_3 | spl2_1 | ~spl2_5),
% 1.53/1.31 inference(avatar_split_clause,[status(thm)],[f43,f37,f17,f26])).
% 1.53/1.31 thf(f26,definition,(
% 1.53/1.31 spl2_3 <=> ($true = (cA @ sK1))),
% 1.53/1.31 introduced(definition,[new_symbols(naming,[spl2_3])],[avatar_definition])).
% 1.53/1.31 thf(f17,definition,(
% 1.53/1.31 spl2_1 <=> ((cB @ sK1) = $true)),
% 1.53/1.31 introduced(definition,[new_symbols(naming,[spl2_1])],[avatar_definition])).
% 1.53/1.31 thf(f43,plain,(
% 1.53/1.31 ($true != (cA @ sK1)) | (spl2_1 | ~spl2_5)),
% 1.53/1.31 inference(trivial_inequality_removal,[status(thm)],[f40])).
% 1.53/1.31 thf(f40,plain,(
% 1.53/1.31 ($true != $true) | ($true != (cA @ sK1)) | (spl2_1 | ~spl2_5)),
% 1.53/1.31 inference(superposition,[status(thm)],[f19,f38])).
% 1.53/1.31 thf(f19,plain,(
% 1.53/1.31 ((cB @ sK1) != $true) | spl2_1),
% 1.53/1.31 inference(avatar_component_clause,[status(thm)],[f17])).
% 1.53/1.31 thf(f39,plain,(
% 1.53/1.31 spl2_5 | spl2_5),
% 1.53/1.31 inference(avatar_split_clause,[status(thm)],[f11,f37,f37])).
% 1.53/1.31 thf(f11,plain,(
% 1.53/1.31 ( ! [X2 : $i,X3 : $i] : (($true != (cA @ X2)) | ($true = (cB @ X2)) | ((cB @ X3) = $true) | ((cA @ X3) != $true)) )),
% 1.53/1.31 inference(cnf_transformation,[status(thm)],[f10])).
% 1.53/1.31 thf(f10,plain,(
% 1.53/1.31 ((($true = (cA @ sK0)) & ((cB @ sK0) != $true)) | (((cB @ sK1) != $true) & ($true = (cA @ sK1)))) & (! [X2 : $i] : (($true = (cB @ X2)) | ($true != (cA @ X2))) | ! [X3 : $i] : (((cA @ X3) != $true) | ((cB @ X3) = $true)))),
% 1.53/1.31 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f7,f9,f8])).
% 1.53/1.31 thf(f8,plain,(
% 1.53/1.31 ? [X0 : $i] : (((cA @ X0) = $true) & ((cB @ X0) != $true)) => (($true = (cA @ sK0)) & ((cB @ sK0) != $true))),
% 1.53/1.31 introduced(definition,[],[choice_axiom])).
% 1.53/1.31 thf(f9,plain,(
% 1.53/1.31 ? [X1 : $i] : (($true != (cB @ X1)) & ($true = (cA @ X1))) => (((cB @ sK1) != $true) & ($true = (cA @ sK1)))),
% 1.53/1.31 introduced(definition,[],[choice_axiom])).
% 1.53/1.31 thf(f7,plain,(
% 1.53/1.31 (? [X0 : $i] : (((cA @ X0) = $true) & ((cB @ X0) != $true)) | ? [X1 : $i] : (($true != (cB @ X1)) & ($true = (cA @ X1)))) & (! [X2 : $i] : (($true = (cB @ X2)) | ($true != (cA @ X2))) | ! [X3 : $i] : (((cA @ X3) != $true) | ((cB @ X3) = $true)))),
% 1.53/1.31 inference(rectify,[status(thm)],[f6])).
% 1.53/1.31 thf(f6,plain,(
% 1.53/1.31 (? [X3 : $i] : (((cA @ X3) = $true) & ((cB @ X3) != $true)) | ? [X2 : $i] : (($true != (cB @ X2)) & ($true = (cA @ X2)))) & (! [X1 : $i] : (($true = (cB @ X1)) | ($true != (cA @ X1))) | ! [X0 : $i] : (((cA @ X0) != $true) | ((cB @ X0) = $true)))),
% 1.53/1.31 inference(ennf_transformation,[status(thm)],[f5])).
% 1.53/1.31 thf(f5,plain,(
% 1.53/1.31 ~((! [X1 : $i] : (($true = (cA @ X1)) => ($true = (cB @ X1))) | ! [X0 : $i] : (((cA @ X0) = $true) => ((cB @ X0) = $true))) => (! [X3 : $i] : (((cA @ X3) = $true) => ((cB @ X3) = $true)) & ! [X2 : $i] : (($true = (cA @ X2)) => ($true = (cB @ X2)))))),
% 1.53/1.31 inference(fool_elimination,[status(thm)],[f4])).
% 1.53/1.31 thf(f4,plain,(
% 1.53/1.31 ~((! [X0 : $i] : ((cA @ X0) => (cB @ X0)) | ! [X1 : $i] : ((cA @ X1) => (cB @ X1))) => (! [X2 : $i] : ((cA @ X2) => (cB @ X2)) & ! [X3 : $i] : ((cA @ X3) => (cB @ X3))))),
% 1.53/1.31 inference(rectify,[status(thm)],[f2])).
% 1.53/1.31 thf(f2,negated_conjecture,(
% 1.53/1.31 ~((! [X0 : $i] : ((cA @ X0) => (cB @ X0)) | ! [X0 : $i] : ((cA @ X0) => (cB @ X0))) => (! [X0 : $i] : ((cA @ X0) => (cB @ X0)) & ! [X0 : $i] : ((cA @ X0) => (cB @ X0))))),
% 1.53/1.31 inference(negated_conjecture,[status(cth)],[f1])).
% 1.53/1.31 thf(f1,conjecture,(
% 1.53/1.31 (! [X0 : $i] : ((cA @ X0) => (cB @ X0)) | ! [X0 : $i] : ((cA @ X0) => (cB @ X0))) => (! [X0 : $i] : ((cA @ X0) => (cB @ X0)) & ! [X0 : $i] : ((cA @ X0) => (cB @ X0)))),
% 1.53/1.31 file('/export/starexec/sandbox/tmp/tmp.hia5ng53e2/DTF2THF_29646.p',cDUAL_EG5_pme)).
% 1.53/1.31 thf(f35,plain,(
% 1.53/1.31 ~spl2_4 | spl2_3),
% 1.53/1.31 inference(avatar_split_clause,[status(thm)],[f12,f26,f31])).
% 1.53/1.31 thf(f12,plain,(
% 1.53/1.31 ($true = (cA @ sK1)) | ((cB @ sK0) != $true)),
% 1.53/1.31 inference(cnf_transformation,[status(thm)],[f10])).
% 1.53/1.31 thf(f34,plain,(
% 1.53/1.31 ~spl2_1 | ~spl2_4),
% 1.53/1.31 inference(avatar_split_clause,[status(thm)],[f13,f31,f17])).
% 1.53/1.31 thf(f13,plain,(
% 1.53/1.31 ((cB @ sK0) != $true) | ((cB @ sK1) != $true)),
% 1.53/1.31 inference(cnf_transformation,[status(thm)],[f10])).
% 1.53/1.31 thf(f29,plain,(
% 1.53/1.31 spl2_2 | spl2_3),
% 1.53/1.31 inference(avatar_split_clause,[status(thm)],[f14,f26,f21])).
% 1.53/1.31 thf(f14,plain,(
% 1.53/1.31 ($true = (cA @ sK0)) | ($true = (cA @ sK1))),
% 1.53/1.31 inference(cnf_transformation,[status(thm)],[f10])).
% 1.53/1.31 thf(f24,plain,(
% 1.53/1.31 ~spl2_1 | spl2_2),
% 1.53/1.31 inference(avatar_split_clause,[status(thm)],[f15,f21,f17])).
% 1.53/1.31 thf(f15,plain,(
% 1.53/1.31 ($true = (cA @ sK0)) | ((cB @ sK1) != $true)),
% 1.53/1.31 inference(cnf_transformation,[status(thm)],[f10])).
% 1.53/1.31 % SZS output end Proof for DTF2THF_29646
% 1.53/1.31 % (29748)------------------------------
% 1.53/1.31 % (29748)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.31 % (29748)Termination reason: Refutation
% 1.53/1.31
% 1.53/1.31 % (29748)Memory used [KB]: 5500
% 1.53/1.31 % (29748)Time elapsed: 0.004 s
% 1.53/1.31 % (29748)Instructions burned: 2 (million)
% 1.53/1.31 % (29748)------------------------------
% 1.53/1.31 % (29748)------------------------------
% 1.53/1.31 % (29742)Success in time 0.018 s
%------------------------------------------------------------------------------