%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV406^5 : 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 : n031.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 09:41:11 AM UTC 2026
% Result : Theorem 1.45s 1.18s
% Output : Refutation 1.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 5
% Syntax : Number of formulae : 40 ( 10 unt; 0 typ; 4 def)
% Number of atoms : 248 ( 44 equ; 0 cnn)
% Maximal formula atoms : 6 ( 6 avg)
% Number of connectives : 182 ( 26 ~; 55 |; 1 &; 92 @)
% ( 4 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 18 ( 18 ^; 0 !; 0 ?; 18 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
cA: $i > $o ).
thf(func_def_1,type,
cB: $i > $o ).
thf(func_def_2,type,
cP: ( $i > $o ) > $o ).
thf(func_def_10,type,
ph1:
!>[X0: $tType] : X0 ).
thf(f54,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f34,f44,f45,f49,f52]) ).
thf(f52,plain,
( ~ spl0_1
| ~ spl0_4 ),
inference(avatar_contradiction_clause,[status(thm)],[f51]) ).
thf(f51,plain,
( $false
| ~ spl0_1
| ~ spl0_4 ),
inference(trivial_inequality_removal,[status(thm)],[f50]) ).
thf(f50,plain,
( ( $true = $false )
| ~ spl0_1
| ~ spl0_4 ),
inference(forward_demodulation,[status(thm)],[f29,f42]) ).
thf(f42,plain,
( ( $false
= ( cB @ sK2 ) )
| ~ spl0_4 ),
inference(avatar_component_clause,[status(thm)],[f40]) ).
thf(f40,definition,
( spl0_4
<=> ( $false
= ( cB @ sK2 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition]) ).
thf(f29,plain,
( ( $true
= ( cB @ sK2 ) )
| ~ spl0_1 ),
inference(avatar_component_clause,[status(thm)],[f27]) ).
thf(f27,definition,
( spl0_1
<=> ( $true
= ( cB @ sK2 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition]) ).
thf(f49,plain,
( ~ spl0_2
| ~ spl0_3 ),
inference(avatar_contradiction_clause,[status(thm)],[f48]) ).
thf(f48,plain,
( $false
| ~ spl0_2
| ~ spl0_3 ),
inference(trivial_inequality_removal,[status(thm)],[f47]) ).
thf(f47,plain,
( ( $true = $false )
| ~ spl0_2
| ~ spl0_3 ),
inference(backward_demodulation,[status(thm)],[f33,f38]) ).
thf(f38,plain,
( ( $false
= ( cA @ sK2 ) )
| ~ spl0_3 ),
inference(avatar_component_clause,[status(thm)],[f36]) ).
thf(f36,definition,
( spl0_3
<=> ( $false
= ( cA @ sK2 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition]) ).
thf(f33,plain,
( ( $true
= ( cA @ sK2 ) )
| ~ spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f31]) ).
thf(f31,definition,
( spl0_2
<=> ( $true
= ( cA @ sK2 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition]) ).
thf(f45,plain,
spl0_3,
inference(avatar_split_clause,[status(thm)],[f19,f36]) ).
thf(f19,plain,
( $false
= ( cA @ sK2 ) ),
inference(duplicate_literal_removal,[status(thm)],[f17]) ).
thf(f17,plain,
( ( $false
= ( cA @ sK2 ) )
| ( $false
= ( cA @ sK2 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f16]) ).
thf(f16,plain,
( ( $false
= ( cA @ sK2 ) )
| ( $false
= ( ( cB @ sK2 )
| ( cA @ sK2 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f14]) ).
thf(f14,plain,
( ( $false
= ( ( cA @ sK2 )
| ( cB @ sK2 ) ) )
| ( $false
= ( ( cB @ sK2 )
| ( cA @ sK2 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f12]) ).
thf(f12,plain,
( ( ( cB @ sK2 )
| ( cA @ sK2 ) )
!= ( ( cA @ sK2 )
| ( cB @ sK2 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f11]) ).
thf(f11,plain,
( ( ^ [Y0: $i] :
( ( cA @ Y0 )
| ( cB @ Y0 ) )
@ sK2 )
!= ( ^ [Y0: $i] :
( ( cB @ Y0 )
| ( cA @ Y0 ) )
@ sK2 ) ),
inference(negative_extensionality,[status(thm)],[f10]) ).
thf(f10,plain,
( ( ^ [Y0: $i] :
( ( cB @ Y0 )
| ( cA @ Y0 ) ) )
!= ( ^ [Y0: $i] :
( ( cA @ Y0 )
| ( cB @ Y0 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f9]) ).
thf(f9,plain,
( ( $true != $true )
| ( ( ^ [Y0: $i] :
( ( cB @ Y0 )
| ( cA @ Y0 ) ) )
!= ( ^ [Y0: $i] :
( ( cA @ Y0 )
| ( cB @ Y0 ) ) ) ) ),
inference(constrained_superposition,[status(thm)],[f7,f8]) ).
thf(f8,plain,
( $true
= ( cP
@ ^ [Y0: $i] :
( ( cB @ Y0 )
| ( cA @ Y0 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
( ( $true
= ( cP
@ ^ [Y0: $i] :
( ( cB @ Y0 )
| ( cA @ Y0 ) ) ) )
& ( $true
!= ( cP
@ ^ [Y0: $i] :
( ( cA @ Y0 )
| ( cB @ Y0 ) ) ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ( $true
= ( cP
@ ^ [Y0: $i] :
( ( cB @ Y0 )
| ( cA @ Y0 ) ) ) )
=> ( $true
= ( cP
@ ^ [Y0: $i] :
( ( cA @ Y0 )
| ( cB @ Y0 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ( cP
@ ^ [X0: $i] :
( ( cA @ X0 )
| ( cB @ X0 ) ) )
=> ( cP
@ ^ [X1: $i] :
( ( cB @ X1 )
| ( cA @ X1 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ( cP
@ ^ [X0: $i] :
( ( cA @ X0 )
| ( cB @ X0 ) ) )
=> ( cP
@ ^ [X0: $i] :
( ( cB @ X0 )
| ( cA @ X0 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ( cP
@ ^ [X0: $i] :
( ( cA @ X0 )
| ( cB @ X0 ) ) )
=> ( cP
@ ^ [X0: $i] :
( ( cB @ X0 )
| ( cA @ X0 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.RgHhpkbIRf/DTF2THF_12270.p',cTRIVEXT2_pme) ).
thf(f7,plain,
( $true
!= ( cP
@ ^ [Y0: $i] :
( ( cA @ Y0 )
| ( cB @ Y0 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
thf(f44,plain,
spl0_4,
inference(avatar_split_clause,[status(thm)],[f22,f40]) ).
thf(f22,plain,
( $false
= ( cB @ sK2 ) ),
inference(duplicate_literal_removal,[status(thm)],[f21]) ).
thf(f21,plain,
( ( $false
= ( cB @ sK2 ) )
| ( $false
= ( cB @ sK2 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f15]) ).
thf(f15,plain,
( ( $false
= ( ( cB @ sK2 )
| ( cA @ sK2 ) ) )
| ( $false
= ( cB @ sK2 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f14]) ).
thf(f34,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f25,f31,f27]) ).
thf(f25,plain,
( ( $true
= ( cB @ sK2 ) )
| ( $true
= ( cA @ sK2 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f24]) ).
thf(f24,plain,
( ( $true
= ( cA @ sK2 ) )
| ( $true
= ( cB @ sK2 ) )
| ( $true
= ( cB @ sK2 ) )
| ( $true
= ( cA @ sK2 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f23]) ).
thf(f23,plain,
( ( $true
= ( ( cA @ sK2 )
| ( cB @ sK2 ) ) )
| ( $true
= ( cB @ sK2 ) )
| ( $true
= ( cA @ sK2 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f13]) ).
thf(f13,plain,
( ( $true
= ( ( cB @ sK2 )
| ( cA @ sK2 ) ) )
| ( $true
= ( ( cA @ sK2 )
| ( cB @ sK2 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEV406^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.15/0.33 % Computer : n031.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue Feb 24 12:47:03 EST 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.33 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.19/0.45 ---- Original DTF file ---
% 0.19/0.45 thf(spec,logic,$$dhol).
% 0.19/0.45 %------------------------------------------------------------------------------
% 0.19/0.45 % File : SEV406^5 : TPTP v9.2.1. Released v4.0.0.
% 0.19/0.45 % Domain : Set Theory
% 0.19/0.45 % Problem : TPS problem from SETS-THMS
% 0.19/0.45 % Version : Especial.
% 0.19/0.45 % English :
% 0.19/0.45
% 0.19/0.45 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.19/0.45 % Source : [Bro09]
% 0.19/0.45 % Names : tps_0743 [Bro09]
% 0.19/0.45
% 0.19/0.45 % Status : Theorem
% 0.19/0.45 % 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, 0.20 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, 0.33 v6.1.0, 0.17 v5.5.0, 0.20 v5.4.0, 0.25 v5.3.0, 0.50 v4.1.0, 0.67 v4.0.0
% 0.19/0.45 % Syntax : Number of formulae : 4 ( 0 unt; 3 typ; 0 def)
% 0.19/0.45 % Number of atoms : 6 ( 0 equ; 0 cnn)
% 0.19/0.45 % Maximal formula atoms : 6 ( 6 avg)
% 0.19/0.45 % Number of connectives : 9 ( 0 ~; 2 |; 0 &; 6 @)
% 0.19/0.45 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.19/0.45 % Maximal formula depth : 6 ( 6 avg)
% 0.19/0.45 % Number of types : 2 ( 0 usr)
% 0.19/0.45 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.19/0.45 % Number of symbols : 3 ( 3 usr; 0 con; 1-1 aty)
% 0.19/0.45 % Number of variables : 2 ( 2 ^; 0 !; 0 ?; 2 :)
% 0.19/0.45 % SPC : TH0_THM_NEQ_NAR
% 0.19/0.45
% 0.19/0.45 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.19/0.45 % project in the Department of Mathematical Sciences at Carnegie
% 0.19/0.45 % Mellon University. Distributed under the Creative Commons copyleft
% 0.19/0.45 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.19/0.45 %------------------------------------------------------------------------------
% 0.19/0.45 thf(cA,type,
% 0.19/0.45 cA: $i > $o ).
% 0.19/0.45
% 0.19/0.45 thf(cB,type,
% 0.19/0.45 cB: $i > $o ).
% 0.19/0.45
% 0.19/0.45 thf(cP,type,
% 0.19/0.45 cP: ( $i > $o ) > $o ).
% 0.19/0.45
% 0.19/0.45 thf(cTRIVEXT2_pme,conjecture,
% 0.19/0.45 ( ( cP
% 0.19/0.45 @ ^ [Xz: $i] :
% 0.19/0.45 ( ( cA @ Xz )
% 0.19/0.45 | ( cB @ Xz ) ) )
% 0.19/0.45 => ( cP
% 0.19/0.45 @ ^ [Xz: $i] :
% 0.19/0.45 ( ( cB @ Xz )
% 0.19/0.45 | ( cA @ Xz ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 %------------------------------------------------------------------------------
% 0.19/0.45 ------------------------
% 1.45/1.15 ---- Embedded in THF ---
% 1.45/1.15 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.45/1.15 %%% Generated on Tue Feb 24 12:47:04 EST 2026
% 1.45/1.15 %%% using '$$dhol' embedding, version 1.3.0.
% 1.45/1.15 %%% Logic specification used:
% 1.45/1.15 %%% thf(spec, logic, $$dhol).
% 1.45/1.15
% 1.45/1.15 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.RgHhpkbIRf/DTF2DTF12270.p
% See solution above
% 1.45/1.15 ------------------------
% 1.45/1.16 ---- Cleaned THF ---
% 1.45/1.16 thf(cA,type,
% 1.45/1.16 cA: $i > $o ).
% 1.45/1.16
% 1.45/1.16 thf(cB,type,
% 1.45/1.16 cB: $i > $o ).
% 1.45/1.16
% 1.45/1.16 thf(cP,type,
% 1.45/1.16 cP: ( $i > $o ) > $o ).
% 1.45/1.16
% 1.45/1.16 thf(cTRIVEXT2_pme,conjecture,
% 1.45/1.16 ( ( cP
% 1.45/1.16 @ ^ [Xz: $i] :
% 1.45/1.16 ( ( cA @ Xz )
% 1.45/1.16 | ( cB @ Xz ) ) )
% 1.45/1.16 => ( cP
% 1.45/1.16 @ ^ [Xz: $i] :
% 1.45/1.16 ( ( cB @ Xz )
% 1.45/1.16 | ( cA @ Xz ) ) ) ) ).
% 1.45/1.16 ------------------------
% 1.45/1.17 % (12374)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_12270 for (3000ds/18Mi)
% 1.45/1.17 % (12368)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_12270 for (3000ds/183Mi)
% 1.45/1.18 % (12374)First to succeed.
% 1.45/1.18 % (12368)Also succeeded, but the first one will report.
% 1.45/1.18 % (12374)Refutation found. Thanks to Tanya!
% 1.45/1.18 % SZS status Theorem for DTF2THF_12270
% 1.45/1.18 % SZS output start Proof for DTF2THF_12270
% 1.45/1.18 thf(func_def_0, type, cA: $i > $o).
% 1.45/1.18 thf(func_def_1, type, cB: $i > $o).
% 1.45/1.18 thf(func_def_2, type, cP: ($i > $o) > $o).
% 1.45/1.18 thf(func_def_10, type, ph1: !>[X0: $tType]:(X0)).
% 1.45/1.18 thf(f54,plain,(
% 1.45/1.18 $false),
% 1.45/1.18 inference(avatar_sat_refutation,[status(thm)],[f34,f44,f45,f49,f52])).
% 1.45/1.18 thf(f52,plain,(
% 1.45/1.18 ~spl0_1 | ~spl0_4),
% 1.45/1.18 inference(avatar_contradiction_clause,[status(thm)],[f51])).
% 1.45/1.18 thf(f51,plain,(
% 1.45/1.18 $false | (~spl0_1 | ~spl0_4)),
% 1.45/1.18 inference(trivial_inequality_removal,[status(thm)],[f50])).
% 1.45/1.18 thf(f50,plain,(
% 1.45/1.18 ($true = $false) | (~spl0_1 | ~spl0_4)),
% 1.45/1.18 inference(forward_demodulation,[status(thm)],[f29,f42])).
% 1.45/1.18 thf(f42,plain,(
% 1.45/1.18 ($false = (cB @ sK2)) | ~spl0_4),
% 1.45/1.18 inference(avatar_component_clause,[status(thm)],[f40])).
% 1.45/1.18 thf(f40,definition,(
% 1.45/1.18 spl0_4 <=> ($false = (cB @ sK2))),
% 1.45/1.18 introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition])).
% 1.45/1.18 thf(f29,plain,(
% 1.45/1.18 ($true = (cB @ sK2)) | ~spl0_1),
% 1.45/1.18 inference(avatar_component_clause,[status(thm)],[f27])).
% 1.45/1.18 thf(f27,definition,(
% 1.45/1.18 spl0_1 <=> ($true = (cB @ sK2))),
% 1.45/1.18 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 1.45/1.18 thf(f49,plain,(
% 1.45/1.18 ~spl0_2 | ~spl0_3),
% 1.45/1.18 inference(avatar_contradiction_clause,[status(thm)],[f48])).
% 1.45/1.18 thf(f48,plain,(
% 1.45/1.18 $false | (~spl0_2 | ~spl0_3)),
% 1.45/1.18 inference(trivial_inequality_removal,[status(thm)],[f47])).
% 1.45/1.18 thf(f47,plain,(
% 1.45/1.18 ($true = $false) | (~spl0_2 | ~spl0_3)),
% 1.45/1.18 inference(backward_demodulation,[status(thm)],[f33,f38])).
% 1.45/1.18 thf(f38,plain,(
% 1.45/1.18 ($false = (cA @ sK2)) | ~spl0_3),
% 1.45/1.18 inference(avatar_component_clause,[status(thm)],[f36])).
% 1.45/1.18 thf(f36,definition,(
% 1.45/1.18 spl0_3 <=> ($false = (cA @ sK2))),
% 1.45/1.18 introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition])).
% 1.45/1.18 thf(f33,plain,(
% 1.45/1.18 ($true = (cA @ sK2)) | ~spl0_2),
% 1.45/1.18 inference(avatar_component_clause,[status(thm)],[f31])).
% 1.45/1.18 thf(f31,definition,(
% 1.45/1.18 spl0_2 <=> ($true = (cA @ sK2))),
% 1.45/1.18 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])).
% 1.45/1.18 thf(f45,plain,(
% 1.45/1.18 spl0_3),
% 1.45/1.18 inference(avatar_split_clause,[status(thm)],[f19,f36])).
% 1.45/1.18 thf(f19,plain,(
% 1.45/1.18 ($false = (cA @ sK2))),
% 1.45/1.18 inference(duplicate_literal_removal,[status(thm)],[f17])).
% 1.45/1.18 thf(f17,plain,(
% 1.45/1.18 ($false = (cA @ sK2)) | ($false = (cA @ sK2))),
% 1.45/1.18 inference(binary_proxy_clausification,[status(thm)],[f16])).
% 1.45/1.18 thf(f16,plain,(
% 1.45/1.18 ($false = (cA @ sK2)) | ($false = ((cB @ sK2) | (cA @ sK2)))),
% 1.45/1.18 inference(binary_proxy_clausification,[status(thm)],[f14])).
% 1.45/1.18 thf(f14,plain,(
% 1.45/1.18 ($false = ((cA @ sK2) | (cB @ sK2))) | ($false = ((cB @ sK2) | (cA @ sK2)))),
% 1.45/1.18 inference(binary_proxy_clausification,[status(thm)],[f12])).
% 1.45/1.18 thf(f12,plain,(
% 1.45/1.18 (((cB @ sK2) | (cA @ sK2)) != ((cA @ sK2) | (cB @ sK2)))),
% 1.45/1.18 inference(beta_eta_normalization,[status(thm)],[f11])).
% 1.45/1.18 thf(f11,plain,(
% 1.45/1.18 (((^[Y0 : $i]: ((cA @ Y0) | (cB @ Y0))) @ sK2) != ((^[Y0 : $i]: ((cB @ Y0) | (cA @ Y0))) @ sK2))),
% 1.45/1.18 inference(negative_extensionality,[status(thm)],[f10])).
% 1.45/1.18 thf(f10,plain,(
% 1.45/1.18 ((^[Y0 : $i]: ((cB @ Y0) | (cA @ Y0))) != (^[Y0 : $i]: ((cA @ Y0) | (cB @ Y0))))),
% 1.45/1.18 inference(trivial_inequality_removal,[status(thm)],[f9])).
% 1.45/1.18 thf(f9,plain,(
% 1.45/1.18 ($true != $true) | ((^[Y0 : $i]: ((cB @ Y0) | (cA @ Y0))) != (^[Y0 : $i]: ((cA @ Y0) | (cB @ Y0))))),
% 1.45/1.18 inference(constrained_superposition,[status(thm)],[f7,f8])).
% 1.45/1.18 thf(f8,plain,(
% 1.45/1.18 ($true = (cP @ (^[Y0 : $i]: ((cB @ Y0) | (cA @ Y0)))))),
% 1.45/1.18 inference(cnf_transformation,[status(thm)],[f6])).
% 1.45/1.18 thf(f6,plain,(
% 1.45/1.18 ($true = (cP @ (^[Y0 : $i]: ((cB @ Y0) | (cA @ Y0))))) & ($true != (cP @ (^[Y0 : $i]: ((cA @ Y0) | (cB @ Y0)))))),
% 1.45/1.18 inference(ennf_transformation,[status(thm)],[f5])).
% 1.45/1.18 thf(f5,plain,(
% 1.45/1.18 ~(($true = (cP @ (^[Y0 : $i]: ((cB @ Y0) | (cA @ Y0))))) => ($true = (cP @ (^[Y0 : $i]: ((cA @ Y0) | (cB @ Y0))))))),
% 1.45/1.18 inference(fool_elimination,[status(thm)],[f4])).
% 1.45/1.18 thf(f4,plain,(
% 1.45/1.18 ~((cP @ (^[X0 : $i] : ((cA @ X0) | (cB @ X0)))) => (cP @ (^[X1 : $i] : ((cB @ X1) | (cA @ X1)))))),
% 1.45/1.18 inference(rectify,[status(thm)],[f2])).
% 1.45/1.18 thf(f2,negated_conjecture,(
% 1.45/1.18 ~((cP @ (^[X0 : $i] : ((cA @ X0) | (cB @ X0)))) => (cP @ (^[X0 : $i] : ((cB @ X0) | (cA @ X0)))))),
% 1.45/1.18 inference(negated_conjecture,[status(cth)],[f1])).
% 1.45/1.18 thf(f1,conjecture,(
% 1.45/1.18 (cP @ (^[X0 : $i] : ((cA @ X0) | (cB @ X0)))) => (cP @ (^[X0 : $i] : ((cB @ X0) | (cA @ X0))))),
% 1.45/1.18 file('/export/starexec/sandbox/tmp/tmp.RgHhpkbIRf/DTF2THF_12270.p',cTRIVEXT2_pme)).
% 1.45/1.18 thf(f7,plain,(
% 1.45/1.18 ($true != (cP @ (^[Y0 : $i]: ((cA @ Y0) | (cB @ Y0)))))),
% 1.45/1.18 inference(cnf_transformation,[status(thm)],[f6])).
% 1.45/1.18 thf(f44,plain,(
% 1.45/1.18 spl0_4),
% 1.45/1.18 inference(avatar_split_clause,[status(thm)],[f22,f40])).
% 1.45/1.18 thf(f22,plain,(
% 1.45/1.18 ($false = (cB @ sK2))),
% 1.45/1.18 inference(duplicate_literal_removal,[status(thm)],[f21])).
% 1.45/1.18 thf(f21,plain,(
% 1.45/1.18 ($false = (cB @ sK2)) | ($false = (cB @ sK2))),
% 1.45/1.18 inference(binary_proxy_clausification,[status(thm)],[f15])).
% 1.45/1.18 thf(f15,plain,(
% 1.45/1.18 ($false = ((cB @ sK2) | (cA @ sK2))) | ($false = (cB @ sK2))),
% 1.45/1.18 inference(binary_proxy_clausification,[status(thm)],[f14])).
% 1.45/1.18 thf(f34,plain,(
% 1.45/1.18 spl0_1 | spl0_2),
% 1.45/1.18 inference(avatar_split_clause,[status(thm)],[f25,f31,f27])).
% 1.45/1.18 thf(f25,plain,(
% 1.45/1.18 ($true = (cB @ sK2)) | ($true = (cA @ sK2))),
% 1.45/1.18 inference(duplicate_literal_removal,[status(thm)],[f24])).
% 1.45/1.18 thf(f24,plain,(
% 1.45/1.18 ($true = (cA @ sK2)) | ($true = (cB @ sK2)) | ($true = (cB @ sK2)) | ($true = (cA @ sK2))),
% 1.45/1.18 inference(binary_proxy_clausification,[status(thm)],[f23])).
% 1.45/1.18 thf(f23,plain,(
% 1.45/1.18 ($true = ((cA @ sK2) | (cB @ sK2))) | ($true = (cB @ sK2)) | ($true = (cA @ sK2))),
% 1.45/1.18 inference(binary_proxy_clausification,[status(thm)],[f13])).
% 1.45/1.18 thf(f13,plain,(
% 1.45/1.18 ($true = ((cB @ sK2) | (cA @ sK2))) | ($true = ((cA @ sK2) | (cB @ sK2)))),
% 1.45/1.18 inference(binary_proxy_clausification,[status(thm)],[f12])).
% 1.45/1.18 % SZS output end Proof for DTF2THF_12270
% 1.45/1.18 % (12374)------------------------------
% 1.45/1.18 % (12374)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.45/1.18 % (12374)Termination reason: Refutation
% 1.45/1.18
% 1.45/1.18 % (12374)Memory used [KB]: 5500
% 1.45/1.18 % (12374)Time elapsed: 0.002 s
% 1.45/1.18 % (12374)Instructions burned: 2 (million)
% 1.45/1.18 % (12374)------------------------------
% 1.45/1.18 % (12374)------------------------------
% 1.45/1.18 % (12367)Success in time 0.001 s
%------------------------------------------------------------------------------