%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO235^5 : 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 : n023.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 09:53:44 AM UTC 2026
% Result : Theorem 1.61s 1.38s
% Output : Refutation 1.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 45 ( 1 unt; 0 typ; 5 def)
% Number of atoms : 279 ( 68 equ; 0 cnn)
% Maximal formula atoms : 7 ( 6 avg)
% Number of connectives : 190 ( 62 ~; 75 |; 5 &; 30 @)
% ( 9 <=>; 8 =>; 0 <=; 1 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 14 ( 14 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 9 con; 0-2 aty)
% Number of variables : 16 ( 2 ^; 14 !; 0 ?; 16 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_7,type,
ph1:
!>[X0: $tType] : X0 ).
thf(f120,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f22,f30,f35,f36,f65,f68,f116,f119]) ).
thf(f119,plain,
( ~ spl0_1
| ~ spl0_4 ),
inference(avatar_contradiction_clause,[status(thm)],[f118]) ).
thf(f118,plain,
( $false
| ~ spl0_1
| ~ spl0_4 ),
inference(trivial_inequality_removal,[status(thm)],[f117]) ).
thf(f117,plain,
( ( $false = $true )
| ~ spl0_1
| ~ spl0_4 ),
inference(backward_demodulation,[status(thm)],[f17,f29]) ).
thf(f29,plain,
( ( cB = $false )
| ~ spl0_4 ),
inference(avatar_component_clause,[status(thm)],[f27]) ).
thf(f27,definition,
( spl0_4
<=> ( cB = $false ) ),
introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition]) ).
thf(f17,plain,
( ( cB = $true )
| ~ spl0_1 ),
inference(avatar_component_clause,[status(thm)],[f15]) ).
thf(f15,definition,
( spl0_1
<=> ( cB = $true ) ),
introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition]) ).
thf(f116,plain,
( ~ spl0_1
| spl0_2
| ~ spl0_3 ),
inference(avatar_contradiction_clause,[status(thm)],[f115]) ).
thf(f115,plain,
( $false
| ~ spl0_1
| spl0_2
| ~ spl0_3 ),
inference(subsumption_resolution,[status(thm)],[f96,f20]) ).
thf(f20,plain,
( ( cA != $true )
| spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f19]) ).
thf(f19,definition,
( spl0_2
<=> ( cA = $true ) ),
introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition]) ).
thf(f96,plain,
( ( cA = $true )
| ~ spl0_1
| ~ spl0_3 ),
inference(leibniz_equality_elimination,[status(thm)],[f95]) ).
thf(f95,plain,
( ! [X0: $o > $o] :
( ( ( X0 @ cA )
!= $true )
| ( ( X0 @ $true )
= $true ) )
| ~ spl0_1
| ~ spl0_3 ),
inference(forward_demodulation,[status(thm)],[f25,f17]) ).
thf(f25,plain,
( ! [X0: $o > $o] :
( ( ( X0 @ cA )
!= $true )
| ( ( X0 @ cB )
= $true ) )
| ~ spl0_3 ),
inference(avatar_component_clause,[status(thm)],[f24]) ).
thf(f24,definition,
( spl0_3
<=> ! [X0: $o > $o] :
( ( ( X0 @ cB )
= $true )
| ( ( X0 @ cA )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition]) ).
thf(f68,plain,
( ~ spl0_2
| ~ spl0_5 ),
inference(avatar_contradiction_clause,[status(thm)],[f67]) ).
thf(f67,plain,
( $false
| ~ spl0_2
| ~ spl0_5 ),
inference(trivial_inequality_removal,[status(thm)],[f66]) ).
thf(f66,plain,
( ( $false = $true )
| ~ spl0_2
| ~ spl0_5 ),
inference(backward_demodulation,[status(thm)],[f21,f34]) ).
thf(f34,plain,
( ( cA = $false )
| ~ spl0_5 ),
inference(avatar_component_clause,[status(thm)],[f32]) ).
thf(f32,definition,
( spl0_5
<=> ( cA = $false ) ),
introduced(definition,[new_symbols(naming,[spl0_5])],[avatar_definition]) ).
thf(f21,plain,
( ( cA = $true )
| ~ spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f19]) ).
thf(f65,plain,
( spl0_1
| ~ spl0_2
| ~ spl0_3 ),
inference(avatar_contradiction_clause,[status(thm)],[f64]) ).
thf(f64,plain,
( $false
| spl0_1
| ~ spl0_2
| ~ spl0_3 ),
inference(subsumption_resolution,[status(thm)],[f50,f16]) ).
thf(f16,plain,
( ( cB != $true )
| spl0_1 ),
inference(avatar_component_clause,[status(thm)],[f15]) ).
thf(f50,plain,
( ( cB = $true )
| ~ spl0_2
| ~ spl0_3 ),
inference(trivial_inequality_removal,[status(thm)],[f49]) ).
thf(f49,plain,
( ( $true != $true )
| ( cB = $true )
| ~ spl0_2
| ~ spl0_3 ),
inference(beta_eta_normalization,[status(thm)],[f40]) ).
thf(f40,plain,
( ( ( ^ [Y0: $o] : Y0
@ $true )
!= $true )
| ( ( ^ [Y0: $o] : Y0
@ cB )
= $true )
| ~ spl0_2
| ~ spl0_3 ),
inference(primitive_instantiation,[status(thm)],[f37]) ).
thf(f37,plain,
( ! [X0: $o > $o] :
( ( ( X0 @ $true )
!= $true )
| ( ( X0 @ cB )
= $true ) )
| ~ spl0_2
| ~ spl0_3 ),
inference(forward_demodulation,[status(thm)],[f25,f21]) ).
thf(f36,plain,
( ~ spl0_2
| ~ spl0_1 ),
inference(avatar_split_clause,[status(thm)],[f11,f15,f19]) ).
thf(f11,plain,
( ( cA != $true )
| ( cB != $true ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
( ( ( cA != $true )
| ( cB != $true ) )
& ( ( cA = $true )
| ( cB = $true ) )
& ( ( cA = cB )
| ! [X0: $o > $o] :
( ( ( X0 @ cA )
!= $true )
| ( ( X0 @ cB )
= $true ) ) ) ),
inference(flattening,[status(thm)],[f7]) ).
thf(f7,plain,
( ( ( cA != $true )
| ( cB != $true ) )
& ( ( cA = $true )
| ( cB = $true ) )
& ( ( cA = cB )
| ! [X0: $o > $o] :
( ( ( X0 @ cA )
!= $true )
| ( ( X0 @ cB )
= $true ) ) ) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
( ( ( cB = $true )
<~> ( cA = $true ) )
& ( ( cA = cB )
| ! [X0: $o > $o] :
( ( ( X0 @ cA )
!= $true )
| ( ( X0 @ cB )
= $true ) ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ( ( cA = cB )
| ! [X0: $o > $o] :
( ( ( X0 @ cA )
= $true )
=> ( ( X0 @ cB )
= $true ) ) )
=> ( ( cA = $true )
<=> ( cB = $true ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ( ( cB
<=> cA )
| ! [X0: $o > $o] :
( ( X0 @ cA )
=> ( X0 @ cB ) ) )
=> ( cA = cB ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ( ( cB
<=> cA )
| ! [X0: $o > $o] :
( ( X0 @ cA )
=> ( X0 @ cB ) ) )
=> ( cA = cB ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ( ( cB
<=> cA )
| ! [X0: $o > $o] :
( ( X0 @ cA )
=> ( X0 @ cB ) ) )
=> ( cA = cB ) ),
file('/export/starexec/sandbox/tmp/tmp.0C6SggKD6u/DTF2THF_7604.p',cTHM505) ).
thf(f35,plain,
( spl0_3
| spl0_1
| spl0_5 ),
inference(avatar_split_clause,[status(thm)],[f13,f32,f15,f24]) ).
thf(f13,plain,
! [X0: $o > $o] :
( ( ( X0 @ cB )
= $true )
| ( cB = $true )
| ( ( X0 @ cA )
!= $true )
| ( cA = $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f9]) ).
thf(f9,plain,
! [X0: $o > $o] :
( ( ( X0 @ cB )
= $true )
| ( ( X0 @ cA )
!= $true )
| ( cA = cB ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f30,plain,
( spl0_2
| spl0_3
| spl0_4 ),
inference(avatar_split_clause,[status(thm)],[f12,f27,f24,f19]) ).
thf(f12,plain,
! [X0: $o > $o] :
( ( ( X0 @ cB )
= $true )
| ( cA = $true )
| ( cB = $false )
| ( ( X0 @ cA )
!= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f9]) ).
thf(f22,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f10,f19,f15]) ).
thf(f10,plain,
( ( cA = $true )
| ( cB = $true ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SYO235^5 : 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 : n023.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 14:27:19 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
% 0.18/0.45 ---- Original DTF file ---
% 0.18/0.45 thf(spec,logic,$$dhol).
% 0.18/0.45 %------------------------------------------------------------------------------
% 0.18/0.45 % File : SYO235^5 : TPTP v9.2.1. Released v4.0.0.
% 0.18/0.45 % Domain : Syntactic
% 0.18/0.45 % Problem : TPS problem from BASIC-HO-EQ-THMS
% 0.18/0.45 % Version : Especial.
% 0.18/0.45 % English :
% 0.18/0.45
% 0.18/0.45 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.18/0.45 % Source : [Bro09]
% 0.18/0.45 % Names : tps_0713 [Bro09]
% 0.18/0.45
% 0.18/0.45 % Status : Theorem
% 0.18/0.45 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.10 v8.2.0, 0.31 v8.1.0, 0.36 v7.5.0, 0.14 v7.4.0, 0.11 v7.2.0, 0.00 v7.1.0, 0.12 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.29 v6.1.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.40 v4.1.0, 0.33 v4.0.0
% 0.18/0.45 % Syntax : Number of formulae : 3 ( 0 unt; 2 typ; 0 def)
% 0.18/0.45 % Number of atoms : 7 ( 1 equ; 0 cnn)
% 0.18/0.45 % Maximal formula atoms : 5 ( 7 avg)
% 0.18/0.45 % Number of connectives : 6 ( 0 ~; 1 |; 0 &; 2 @)
% 0.18/0.45 % ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% 0.18/0.45 % Maximal formula depth : 6 ( 6 avg)
% 0.18/0.45 % Number of types : 1 ( 0 usr)
% 0.18/0.45 % Number of type conns : 1 ( 1 >; 0 *; 0 +; 0 <<)
% 0.18/0.45 % Number of symbols : 3 ( 2 usr; 2 con; 0-2 aty)
% 0.18/0.45 % Number of variables : 1 ( 0 ^; 1 !; 0 ?; 1 :)
% 0.18/0.45 % SPC : TH0_THM_EQU_NAR
% 0.18/0.45
% 0.18/0.45 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.18/0.45 % project in the Department of Mathematical Sciences at Carnegie
% 0.18/0.45 % Mellon University. Distributed under the Creative Commons copyleft
% 0.18/0.45 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.18/0.45 %------------------------------------------------------------------------------
% 0.18/0.45 thf(cB,type,
% 0.18/0.45 cB: $o ).
% 0.18/0.45
% 0.18/0.45 thf(cA,type,
% 0.18/0.45 cA: $o ).
% 0.18/0.45
% 0.18/0.45 thf(cTHM505,conjecture,
% 0.18/0.45 ( ( ! [Q: $o > $o] :
% 0.18/0.45 ( ( Q @ cA )
% 0.18/0.45 => ( Q @ cB ) )
% 0.18/0.45 | ( cA
% 0.18/0.45 <=> cB ) )
% 0.18/0.45 => ( cA = cB ) ) ).
% 0.18/0.45
% 0.18/0.45 %------------------------------------------------------------------------------
% 0.18/0.45 ------------------------
% 1.61/1.35 ---- Embedded in THF ---
% 1.61/1.35 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.61/1.35 %%% Generated on Tue Feb 24 14:27:20 EST 2026
% 1.61/1.35 %%% using '$$dhol' embedding, version 1.3.0.
% 1.61/1.35 %%% Logic specification used:
% 1.61/1.35 %%% thf(spec, logic, $$dhol).
% 1.61/1.35
% 1.61/1.35 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.0C6SggKD6u/DTF2DTF7604.p
% See solution above
% 1.61/1.35 ------------------------
% 1.61/1.36 ---- Cleaned THF ---
% 1.61/1.36 thf(cB,type,
% 1.61/1.36 cB: $o ).
% 1.61/1.36
% 1.61/1.36 thf(cA,type,
% 1.61/1.36 cA: $o ).
% 1.61/1.36
% 1.61/1.36 thf(cTHM505,conjecture,
% 1.61/1.36 ( ( ! [Q: $o > $o] :
% 1.61/1.36 ( ( Q @ cA )
% 1.61/1.36 => ( Q @ cB ) )
% 1.61/1.36 | ( cA
% 1.61/1.36 <=> cB ) )
% 1.61/1.36 => ( cA = cB ) ) ).
% 1.61/1.36 ------------------------
% 1.61/1.38 % (7813)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_7604 for (3000ds/18Mi)
% 1.61/1.38 % (7808)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_7604 for (3000ds/4Mi)
% 1.61/1.38 % (7809)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_7604 for (3000ds/27Mi)
% 1.61/1.38 % (7808)Instruction limit reached!
% 1.61/1.38 % (7808)------------------------------
% 1.61/1.38 % (7808)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.38 % (7808)Termination reason: Unknown
% 1.61/1.38 % (7808)Termination phase: Saturation
% 1.61/1.38
% 1.61/1.38 % (7808)Memory used [KB]: 5500
% 1.61/1.38 % (7808)Time elapsed: 0.003 s
% 1.61/1.38 % (7808)Instructions burned: 4 (million)
% 1.61/1.38 % (7808)------------------------------
% 1.61/1.38 % (7808)------------------------------
% 1.61/1.38 % (7813)First to succeed.
% 1.61/1.38 % (7809)Refutation not found, incomplete strategy
% 1.61/1.38 % (7809)------------------------------
% 1.61/1.38 % (7809)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.38 % (7809)Termination reason: Refutation not found, incomplete strategy
% 1.61/1.38
% 1.61/1.38
% 1.61/1.38 % (7809)Memory used [KB]: 5500
% 1.61/1.38 % (7809)Time elapsed: 0.002 s
% 1.61/1.38 % (7809)Instructions burned: 1 (million)
% 1.61/1.38 % (7809)------------------------------
% 1.61/1.38 % (7809)------------------------------
% 1.61/1.38 % (7813)Refutation found. Thanks to Tanya!
% 1.61/1.38 % SZS status Theorem for DTF2THF_7604
% 1.61/1.38 % SZS output start Proof for DTF2THF_7604
% 1.61/1.38 thf(func_def_7, type, ph1: !>[X0: $tType]:(X0)).
% 1.61/1.38 thf(f120,plain,(
% 1.61/1.38 $false),
% 1.61/1.38 inference(avatar_sat_refutation,[status(thm)],[f22,f30,f35,f36,f65,f68,f116,f119])).
% 1.61/1.38 thf(f119,plain,(
% 1.61/1.38 ~spl0_1 | ~spl0_4),
% 1.61/1.38 inference(avatar_contradiction_clause,[status(thm)],[f118])).
% 1.61/1.38 thf(f118,plain,(
% 1.61/1.38 $false | (~spl0_1 | ~spl0_4)),
% 1.61/1.38 inference(trivial_inequality_removal,[status(thm)],[f117])).
% 1.61/1.38 thf(f117,plain,(
% 1.61/1.38 ($false = $true) | (~spl0_1 | ~spl0_4)),
% 1.61/1.38 inference(backward_demodulation,[status(thm)],[f17,f29])).
% 1.61/1.38 thf(f29,plain,(
% 1.61/1.38 (cB = $false) | ~spl0_4),
% 1.61/1.38 inference(avatar_component_clause,[status(thm)],[f27])).
% 1.61/1.38 thf(f27,definition,(
% 1.61/1.38 spl0_4 <=> (cB = $false)),
% 1.61/1.38 introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition])).
% 1.61/1.38 thf(f17,plain,(
% 1.61/1.38 (cB = $true) | ~spl0_1),
% 1.61/1.38 inference(avatar_component_clause,[status(thm)],[f15])).
% 1.61/1.38 thf(f15,definition,(
% 1.61/1.38 spl0_1 <=> (cB = $true)),
% 1.61/1.38 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 1.61/1.38 thf(f116,plain,(
% 1.61/1.38 ~spl0_1 | spl0_2 | ~spl0_3),
% 1.61/1.38 inference(avatar_contradiction_clause,[status(thm)],[f115])).
% 1.61/1.38 thf(f115,plain,(
% 1.61/1.38 $false | (~spl0_1 | spl0_2 | ~spl0_3)),
% 1.61/1.38 inference(subsumption_resolution,[status(thm)],[f96,f20])).
% 1.61/1.38 thf(f20,plain,(
% 1.61/1.38 (cA != $true) | spl0_2),
% 1.61/1.38 inference(avatar_component_clause,[status(thm)],[f19])).
% 1.61/1.38 thf(f19,definition,(
% 1.61/1.38 spl0_2 <=> (cA = $true)),
% 1.61/1.38 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])).
% 1.61/1.38 thf(f96,plain,(
% 1.61/1.38 (cA = $true) | (~spl0_1 | ~spl0_3)),
% 1.61/1.38 inference(leibniz_equality_elimination,[status(thm)],[f95])).
% 1.61/1.38 thf(f95,plain,(
% 1.61/1.38 ( ! [X0 : $o > $o] : (((X0 @ cA) != $true) | ((X0 @ $true) = $true)) ) | (~spl0_1 | ~spl0_3)),
% 1.61/1.38 inference(forward_demodulation,[status(thm)],[f25,f17])).
% 1.61/1.38 thf(f25,plain,(
% 1.61/1.38 ( ! [X0 : $o > $o] : (((X0 @ cA) != $true) | ((X0 @ cB) = $true)) ) | ~spl0_3),
% 1.61/1.38 inference(avatar_component_clause,[status(thm)],[f24])).
% 1.61/1.38 thf(f24,definition,(
% 1.61/1.38 spl0_3 <=> ! [X0 : $o > $o] : (((X0 @ cB) = $true) | ((X0 @ cA) != $true))),
% 1.61/1.38 introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition])).
% 1.61/1.38 thf(f68,plain,(
% 1.61/1.38 ~spl0_2 | ~spl0_5),
% 1.61/1.38 inference(avatar_contradiction_clause,[status(thm)],[f67])).
% 1.61/1.38 thf(f67,plain,(
% 1.61/1.38 $false | (~spl0_2 | ~spl0_5)),
% 1.61/1.38 inference(trivial_inequality_removal,[status(thm)],[f66])).
% 1.61/1.38 thf(f66,plain,(
% 1.61/1.38 ($false = $true) | (~spl0_2 | ~spl0_5)),
% 1.61/1.38 inference(backward_demodulation,[status(thm)],[f21,f34])).
% 1.61/1.38 thf(f34,plain,(
% 1.61/1.38 (cA = $false) | ~spl0_5),
% 1.61/1.38 inference(avatar_component_clause,[status(thm)],[f32])).
% 1.61/1.38 thf(f32,definition,(
% 1.61/1.38 spl0_5 <=> (cA = $false)),
% 1.61/1.38 introduced(definition,[new_symbols(naming,[spl0_5])],[avatar_definition])).
% 1.61/1.38 thf(f21,plain,(
% 1.61/1.38 (cA = $true) | ~spl0_2),
% 1.61/1.38 inference(avatar_component_clause,[status(thm)],[f19])).
% 1.61/1.38 thf(f65,plain,(
% 1.61/1.38 spl0_1 | ~spl0_2 | ~spl0_3),
% 1.61/1.38 inference(avatar_contradiction_clause,[status(thm)],[f64])).
% 1.61/1.38 thf(f64,plain,(
% 1.61/1.38 $false | (spl0_1 | ~spl0_2 | ~spl0_3)),
% 1.61/1.38 inference(subsumption_resolution,[status(thm)],[f50,f16])).
% 1.61/1.38 thf(f16,plain,(
% 1.61/1.38 (cB != $true) | spl0_1),
% 1.61/1.38 inference(avatar_component_clause,[status(thm)],[f15])).
% 1.61/1.38 thf(f50,plain,(
% 1.61/1.38 (cB = $true) | (~spl0_2 | ~spl0_3)),
% 1.61/1.38 inference(trivial_inequality_removal,[status(thm)],[f49])).
% 1.61/1.38 thf(f49,plain,(
% 1.61/1.38 ($true != $true) | (cB = $true) | (~spl0_2 | ~spl0_3)),
% 1.61/1.38 inference(beta_eta_normalization,[status(thm)],[f40])).
% 1.61/1.38 thf(f40,plain,(
% 1.61/1.38 (((^[Y0 : $o]: (Y0)) @ $true) != $true) | (((^[Y0 : $o]: (Y0)) @ cB) = $true) | (~spl0_2 | ~spl0_3)),
% 1.61/1.38 inference(primitive_instantiation,[status(thm)],[f37])).
% 1.61/1.38 thf(f37,plain,(
% 1.61/1.38 ( ! [X0 : $o > $o] : (((X0 @ $true) != $true) | ((X0 @ cB) = $true)) ) | (~spl0_2 | ~spl0_3)),
% 1.61/1.38 inference(forward_demodulation,[status(thm)],[f25,f21])).
% 1.61/1.38 thf(f36,plain,(
% 1.61/1.38 ~spl0_2 | ~spl0_1),
% 1.61/1.38 inference(avatar_split_clause,[status(thm)],[f11,f15,f19])).
% 1.61/1.38 thf(f11,plain,(
% 1.61/1.38 (cA != $true) | (cB != $true)),
% 1.61/1.38 inference(cnf_transformation,[status(thm)],[f8])).
% 1.61/1.38 thf(f8,plain,(
% 1.61/1.38 ((cA != $true) | (cB != $true)) & ((cA = $true) | (cB = $true)) & ((cA = cB) | ! [X0 : $o > $o] : (((X0 @ cA) != $true) | ((X0 @ cB) = $true)))),
% 1.61/1.38 inference(flattening,[status(thm)],[f7])).
% 1.61/1.38 thf(f7,plain,(
% 1.61/1.38 (((cA != $true) | (cB != $true)) & ((cA = $true) | (cB = $true))) & ((cA = cB) | ! [X0 : $o > $o] : (((X0 @ cA) != $true) | ((X0 @ cB) = $true)))),
% 1.61/1.38 inference(nnf_transformation,[status(thm)],[f6])).
% 1.61/1.38 thf(f6,plain,(
% 1.61/1.38 ((cB = $true) <~> (cA = $true)) & ((cA = cB) | ! [X0 : $o > $o] : (((X0 @ cA) != $true) | ((X0 @ cB) = $true)))),
% 1.61/1.38 inference(ennf_transformation,[status(thm)],[f5])).
% 1.61/1.38 thf(f5,plain,(
% 1.61/1.38 ~(((cA = cB) | ! [X0 : $o > $o] : (((X0 @ cA) = $true) => ((X0 @ cB) = $true))) => ((cA = $true) <=> (cB = $true)))),
% 1.61/1.38 inference(fool_elimination,[status(thm)],[f4])).
% 1.61/1.38 thf(f4,plain,(
% 1.61/1.38 ~(((cB <=> cA) | ! [X0 : $o > $o] : ((X0 @ cA) => (X0 @ cB))) => (cA = cB))),
% 1.61/1.38 inference(rectify,[status(thm)],[f2])).
% 1.61/1.38 thf(f2,negated_conjecture,(
% 1.61/1.38 ~(((cB <=> cA) | ! [X0 : $o > $o] : ((X0 @ cA) => (X0 @ cB))) => (cA = cB))),
% 1.61/1.38 inference(negated_conjecture,[status(cth)],[f1])).
% 1.61/1.38 thf(f1,conjecture,(
% 1.61/1.38 ((cB <=> cA) | ! [X0 : $o > $o] : ((X0 @ cA) => (X0 @ cB))) => (cA = cB)),
% 1.61/1.38 file('/export/starexec/sandbox/tmp/tmp.0C6SggKD6u/DTF2THF_7604.p',cTHM505)).
% 1.61/1.38 thf(f35,plain,(
% 1.61/1.38 spl0_3 | spl0_1 | spl0_5),
% 1.61/1.38 inference(avatar_split_clause,[status(thm)],[f13,f32,f15,f24])).
% 1.61/1.38 thf(f13,plain,(
% 1.61/1.38 ( ! [X0 : $o > $o] : (((X0 @ cB) = $true) | (cB = $true) | ((X0 @ cA) != $true) | (cA = $false)) )),
% 1.61/1.38 inference(binary_proxy_clausification,[status(thm)],[f9])).
% 1.61/1.38 thf(f9,plain,(
% 1.61/1.38 ( ! [X0 : $o > $o] : (((X0 @ cB) = $true) | ((X0 @ cA) != $true) | (cA = cB)) )),
% 1.61/1.38 inference(cnf_transformation,[status(thm)],[f8])).
% 1.61/1.38 thf(f30,plain,(
% 1.61/1.38 spl0_2 | spl0_3 | spl0_4),
% 1.61/1.38 inference(avatar_split_clause,[status(thm)],[f12,f27,f24,f19])).
% 1.61/1.38 thf(f12,plain,(
% 1.61/1.38 ( ! [X0 : $o > $o] : (((X0 @ cB) = $true) | (cA = $true) | (cB = $false) | ((X0 @ cA) != $true)) )),
% 1.61/1.38 inference(binary_proxy_clausification,[status(thm)],[f9])).
% 1.61/1.38 thf(f22,plain,(
% 1.61/1.38 spl0_1 | spl0_2),
% 1.61/1.38 inference(avatar_split_clause,[status(thm)],[f10,f19,f15])).
% 1.61/1.38 thf(f10,plain,(
% 1.61/1.38 (cA = $true) | (cB = $true)),
% 1.61/1.38 inference(cnf_transformation,[status(thm)],[f8])).
% 1.61/1.38 % SZS output end Proof for DTF2THF_7604
% 1.61/1.38 % (7813)------------------------------
% 1.61/1.38 % (7813)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.38 % (7813)Termination reason: Refutation
% 1.61/1.38
% 1.61/1.38 % (7813)Memory used [KB]: 5500
% 1.61/1.38 % (7813)Time elapsed: 0.005 s
% 1.61/1.38 % (7813)Instructions burned: 3 (million)
% 1.61/1.38 % (7813)------------------------------
% 1.61/1.38 % (7813)------------------------------
% 1.61/1.38 % (7806)Success in time 0.014 s
%------------------------------------------------------------------------------