%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO079^5 : 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 : n012.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 09:53:20 AM UTC 2026
% Result : Theorem 1.42s 1.21s
% Output : Refutation 1.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 52 ( 1 unt; 0 typ; 4 def)
% Number of atoms : 294 ( 64 equ)
% Maximal formula atoms : 8 ( 5 avg)
% Number of connectives : 180 ( 64 ~; 85 |; 7 &)
% ( 19 <=>; 4 =>; 0 <=; 1 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 128 ( 126 fml; 2 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 10 ( 7 usr; 9 prp; 0-2 aty)
% Number of functors : 0 ( 0 usr; 0 con; --- aty)
% Number of variables : 1 ( 1 !; 0 ?; 1 :)
% Comments :
%------------------------------------------------------------------------------
tff(f65,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f22,f23,f32,f33,f46,f54,f60,f64]) ).
tff(f64,plain,
( spl0_1
| ~ spl0_2
| ~ spl0_3
| ~ spl0_4 ),
inference(avatar_contradiction_clause,[status(thm)],[f63]) ).
tff(f63,plain,
( $false
| spl0_1
| ~ spl0_2
| ~ spl0_3
| ~ spl0_4 ),
inference(subsumption_resolution,[status(thm)],[f62,f61]) ).
tff(f61,plain,
( ( cQ != $true )
| spl0_1
| ~ spl0_4 ),
inference(forward_demodulation,[status(thm)],[f17,f31]) ).
tff(f31,plain,
( ( cR = $true )
| ~ spl0_4 ),
inference(avatar_component_clause,[status(thm)],[f29]) ).
tff(f29,definition,
( spl0_4
<=> ( cR = $true ) ),
introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition]) ).
tff(f17,plain,
( ( cQ != cR )
| spl0_1 ),
inference(avatar_component_clause,[status(thm)],[f15]) ).
tff(f15,definition,
( spl0_1
<=> ( cQ = cR ) ),
introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition]) ).
tff(f62,plain,
( ( cQ = $true )
| ~ spl0_2
| ~ spl0_3 ),
inference(forward_demodulation,[status(thm)],[f26,f20]) ).
tff(f20,plain,
( ( cP = $true )
| ~ spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f19]) ).
tff(f19,definition,
( spl0_2
<=> ( cP = $true ) ),
introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition]) ).
tff(f26,plain,
( ( cP = cQ )
| ~ spl0_3 ),
inference(avatar_component_clause,[status(thm)],[f25]) ).
tff(f25,definition,
( spl0_3
<=> ( cP = cQ ) ),
introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition]) ).
tff(f60,plain,
( ~ spl0_1
| spl0_2
| ~ spl0_3
| ~ spl0_4 ),
inference(avatar_contradiction_clause,[status(thm)],[f59]) ).
tff(f59,plain,
( $false
| ~ spl0_1
| spl0_2
| ~ spl0_3
| ~ spl0_4 ),
inference(trivial_inequality_removal,[status(thm)],[f58]) ).
tff(f58,plain,
( ( $true = $false )
| ~ spl0_1
| spl0_2
| ~ spl0_3
| ~ spl0_4 ),
inference(forward_demodulation,[status(thm)],[f57,f55]) ).
tff(f55,plain,
( ( cQ = $false )
| spl0_2
| ~ spl0_3 ),
inference(backward_demodulation,[status(thm)],[f26,f52]) ).
tff(f52,plain,
( ( cP = $false )
| spl0_2 ),
inference(trivial_inequality_removal,[status(thm)],[f51]) ).
tff(f51,plain,
( ( cP = $false )
| ( $true != $true )
| spl0_2 ),
inference(superposition,[status(thm)],[f21,f4]) ).
tff(f4,plain,
! [X0: $o] :
( ( $true = (X0) )
| ( $false = (X0) ) ),
introduced(definition,[],[fool_axiom]) ).
tff(f21,plain,
( ( cP != $true )
| spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f19]) ).
tff(f57,plain,
( ( cQ = $true )
| ~ spl0_1
| ~ spl0_4 ),
inference(forward_demodulation,[status(thm)],[f16,f31]) ).
tff(f16,plain,
( ( cQ = cR )
| ~ spl0_1 ),
inference(avatar_component_clause,[status(thm)],[f15]) ).
tff(f54,plain,
( ~ spl0_1
| spl0_2
| spl0_3
| spl0_4 ),
inference(avatar_contradiction_clause,[status(thm)],[f53]) ).
tff(f53,plain,
( $false
| ~ spl0_1
| spl0_2
| spl0_3
| spl0_4 ),
inference(subsumption_resolution,[status(thm)],[f52,f50]) ).
tff(f50,plain,
( ( cP != $false )
| ~ spl0_1
| spl0_3
| spl0_4 ),
inference(forward_demodulation,[status(thm)],[f27,f49]) ).
tff(f49,plain,
( ( cQ = $false )
| ~ spl0_1
| spl0_4 ),
inference(forward_demodulation,[status(thm)],[f16,f42]) ).
tff(f42,plain,
( ( cR = $false )
| spl0_4 ),
inference(trivial_inequality_removal,[status(thm)],[f37]) ).
tff(f37,plain,
( ( $true != $true )
| ( cR = $false )
| spl0_4 ),
inference(superposition,[status(thm)],[f30,f4]) ).
tff(f30,plain,
( ( cR != $true )
| spl0_4 ),
inference(avatar_component_clause,[status(thm)],[f29]) ).
tff(f27,plain,
( ( cP != cQ )
| spl0_3 ),
inference(avatar_component_clause,[status(thm)],[f25]) ).
tff(f46,plain,
( spl0_1
| ~ spl0_2
| spl0_3
| spl0_4 ),
inference(avatar_contradiction_clause,[status(thm)],[f45]) ).
tff(f45,plain,
( $false
| spl0_1
| ~ spl0_2
| spl0_3
| spl0_4 ),
inference(subsumption_resolution,[status(thm)],[f41,f44]) ).
tff(f44,plain,
( ( cQ != $false )
| spl0_1
| spl0_4 ),
inference(backward_demodulation,[status(thm)],[f17,f42]) ).
tff(f41,plain,
( ( cQ = $false )
| ~ spl0_2
| spl0_3 ),
inference(trivial_inequality_removal,[status(thm)],[f38]) ).
tff(f38,plain,
( ( cQ = $false )
| ( $true != $true )
| ~ spl0_2
| spl0_3 ),
inference(superposition,[status(thm)],[f34,f4]) ).
tff(f34,plain,
( ( cQ != $true )
| ~ spl0_2
| spl0_3 ),
inference(backward_demodulation,[status(thm)],[f27,f20]) ).
tff(f33,plain,
( ~ spl0_4
| spl0_3 ),
inference(avatar_split_clause,[status(thm)],[f13,f25,f29]) ).
tff(f13,plain,
( ( cR != $true )
| ( cP = cQ ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
tff(f9,plain,
( ( ( cP = cQ )
| ( cR != $true ) )
& ( ( cR = $true )
| ( cP != cQ ) )
& ( ( cQ != cR )
| ( cP != $true ) )
& ( ( cQ = cR )
| ( cP = $true ) ) ),
inference(flattening,[status(thm)],[f8]) ).
tff(f8,plain,
( ( ( cP = cQ )
| ( cR != $true ) )
& ( ( cR = $true )
| ( cP != cQ ) )
& ( ( cQ != cR )
| ( cP != $true ) )
& ( ( cQ = cR )
| ( cP = $true ) ) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
tff(f7,plain,
( ( ( cP = cQ )
<=> ( cR = $true ) )
& ( ( cP = $true )
<~> ( cQ = cR ) ) ),
inference(ennf_transformation,[status(thm)],[f6]) ).
tff(f6,plain,
~ ( ( ( cP = cQ )
<=> ( cR = $true ) )
=> ( ( cP = $true )
<=> ( cQ = cR ) ) ),
inference(fool_elimination,[status(thm)],[f5]) ).
tff(f5,plain,
~ ( ( ( cP
<=> cQ )
<=> cR )
=> ( ( cQ
<=> cR )
<=> cP ) ),
inference(rectify,[status(thm)],[f2]) ).
tff(f2,negated_conjecture,
~ ( ( ( cP
<=> cQ )
<=> cR )
=> ( ( cQ
<=> cR )
<=> cP ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
tff(f1,conjecture,
( ( ( cP
<=> cQ )
<=> cR )
=> ( ( cQ
<=> cR )
<=> cP ) ),
file('/export/starexec/sandbox/tmp/tmp.8COsbiWISf/DTF2THF_9895.p',cTHM50_A) ).
tff(f32,plain,
( ~ spl0_3
| spl0_4 ),
inference(avatar_split_clause,[status(thm)],[f12,f29,f25]) ).
tff(f12,plain,
( ( cR = $true )
| ( cP != cQ ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
tff(f23,plain,
( spl0_2
| spl0_1 ),
inference(avatar_split_clause,[status(thm)],[f10,f15,f19]) ).
tff(f10,plain,
( ( cP = $true )
| ( cQ = cR ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
tff(f22,plain,
( ~ spl0_1
| ~ spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f11,f19,f15]) ).
tff(f11,plain,
( ( cP != $true )
| ( cQ != cR ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : SYO079^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.07 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.07/0.25 % Computer : n012.cluster.edu
% 0.07/0.25 % Model : x86_64 x86_64
% 0.07/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.25 % Memory : 8042.1875MB
% 0.07/0.25 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.25 % CPULimit : 300
% 0.07/0.25 % WCLimit : 300
% 0.07/0.25 % DateTime : Tue Feb 24 14:23:45 EST 2026
% 0.07/0.25 % CPUTime :
% 0.07/0.25 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.07/0.32 ---- Original DTF file ---
% 0.07/0.32 thf(spec,logic,$$dhol).
% 0.07/0.32 %------------------------------------------------------------------------------
% 0.07/0.32 % File : SYO079^5 : TPTP v9.2.1. Released v4.0.0.
% 0.07/0.32 % Domain : Syntactic
% 0.07/0.32 % Problem : TPS problem THM50-A
% 0.07/0.32 % Version : Especial.
% 0.07/0.32 % English : Associativity of equivalence.
% 0.07/0.32
% 0.07/0.32 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.07/0.32 % Source : [Bro09]
% 0.07/0.32 % Names : tps_0044 [Bro09]
% 0.07/0.32 % : THM50-A [TPS]
% 0.07/0.32 % : THM52 [TPS]
% 0.07/0.32
% 0.07/0.32 % Status : Theorem
% 0.07/0.32 % 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, 0.10 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, 0.33 v6.1.0, 0.17 v6.0.0, 0.00 v4.0.0
% 0.07/0.32 % Syntax : Number of formulae : 4 ( 0 unt; 3 typ; 0 def)
% 0.07/0.32 % Number of atoms : 6 ( 0 equ; 0 cnn)
% 0.07/0.32 % Maximal formula atoms : 6 ( 6 avg)
% 0.07/0.32 % Number of connectives : 5 ( 0 ~; 0 |; 0 &; 0 @)
% 0.07/0.32 % ( 4 <=>; 1 =>; 0 <=; 0 <~>)
% 0.07/0.32 % Maximal formula depth : 4 ( 4 avg)
% 0.07/0.32 % Number of types : 1 ( 0 usr)
% 0.07/0.32 % Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% 0.07/0.32 % Number of symbols : 3 ( 3 usr; 3 con; 0-0 aty)
% 0.07/0.32 % Number of variables : 0 ( 0 ^; 0 !; 0 ?; 0 :)
% 0.07/0.32 % SPC : TH0_THM_NEQ_NAR
% 0.07/0.32
% 0.07/0.32 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.07/0.32 % project in the Department of Mathematical Sciences at Carnegie
% 0.07/0.32 % Mellon University. Distributed under the Creative Commons copyleft
% 0.07/0.32 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.07/0.32 %------------------------------------------------------------------------------
% 0.07/0.32 thf(cR,type,
% 0.07/0.32 cR: $o ).
% 0.07/0.32
% 0.07/0.32 thf(cQ,type,
% 0.07/0.32 cQ: $o ).
% 0.07/0.32
% 0.07/0.32 thf(cP,type,
% 0.07/0.32 cP: $o ).
% 0.07/0.32
% 0.07/0.32 thf(cTHM50_A,conjecture,
% 0.07/0.32 ( ( ( cP
% 0.07/0.32 <=> cQ )
% 0.07/0.32 <=> cR )
% 0.07/0.32 => ( cP
% 0.07/0.32 <=> ( cQ
% 0.07/0.32 <=> cR ) ) ) ).
% 0.07/0.32
% 0.07/0.32 %------------------------------------------------------------------------------
% 0.07/0.32 ------------------------
% 1.34/1.17 ---- Embedded in THF ---
% 1.34/1.17 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.34/1.17 %%% Generated on Tue Feb 24 14:23:46 EST 2026
% 1.34/1.17 %%% using '$$dhol' embedding, version 1.3.0.
% 1.34/1.17 %%% Logic specification used:
% 1.34/1.17 %%% thf(spec, logic, $$dhol).
% 1.34/1.17
% 1.34/1.17 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.8COsbiWISf/DTF2DTF9895.p
% See solution above
% 1.34/1.17 ------------------------
% 1.34/1.18 ---- Cleaned THF ---
% 1.34/1.18 thf(cR,type,
% 1.34/1.18 cR: $o ).
% 1.34/1.18
% 1.34/1.18 thf(cQ,type,
% 1.34/1.18 cQ: $o ).
% 1.34/1.18
% 1.34/1.18 thf(cP,type,
% 1.34/1.18 cP: $o ).
% 1.34/1.18
% 1.34/1.18 thf(cTHM50_A,conjecture,
% 1.34/1.18 ( ( ( cP
% 1.34/1.18 <=> cQ )
% 1.34/1.18 <=> cR )
% 1.34/1.18 => ( cP
% 1.34/1.18 <=> ( cQ
% 1.34/1.18 <=> cR ) ) ) ).
% 1.34/1.18 ------------------------
% 1.42/1.20 % (10010)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_9895 for (3000ds/27Mi)
% 1.42/1.20 % (10011)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_9895 for (3000ds/2Mi)
% 1.42/1.20 % (10012)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_9895 for (3000ds/2Mi)
% 1.42/1.20 % (10013)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_9895 for (3000ds/275Mi)
% 1.42/1.20 % (10009)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_9895 for (3000ds/4Mi)
% 1.42/1.20 % (10008)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_9895 for (3000ds/183Mi)
% 1.42/1.20 % (10014)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_9895 for (3000ds/18Mi)
% 1.42/1.20 % (10013)Refutation not found, incomplete strategy
% 1.42/1.20 % (10013)------------------------------
% 1.42/1.20 % (10013)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.42/1.20 % (10013)Termination reason: Refutation not found, incomplete strategy
% 1.42/1.20
% 1.42/1.20
% 1.42/1.20 % (10013)Memory used [KB]: 5500
% 1.42/1.20 % (10013)Time elapsed: 0.002 s
% 1.42/1.20 % (10013)Instructions burned: 1 (million)
% 1.42/1.20 % (10013)------------------------------
% 1.42/1.20 % (10013)------------------------------
% 1.42/1.20 % (10012)Instruction limit reached!
% 1.42/1.20 % (10012)------------------------------
% 1.42/1.20 % (10012)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.42/1.20 % (10012)Termination reason: Unknown
% 1.42/1.20 % (10012)Termination phase: Saturation
% 1.42/1.20
% 1.42/1.20 % (10012)Memory used [KB]: 5500
% 1.42/1.20 % (10012)Time elapsed: 0.003 s
% 1.42/1.20 % (10012)Instructions burned: 2 (million)
% 1.42/1.20 % (10012)------------------------------
% 1.42/1.20 % (10012)------------------------------
% 1.42/1.20 % (10011)First to succeed.
% 1.42/1.21 % (10009)Also succeeded, but the first one will report.
% 1.42/1.21 % (10011)Refutation found. Thanks to Tanya!
% 1.42/1.21 % SZS status Theorem for DTF2THF_9895
% 1.42/1.21 % SZS output start Proof for DTF2THF_9895
% 1.42/1.21 tff(f65,plain,(
% 1.42/1.21 $false),
% 1.42/1.21 inference(avatar_sat_refutation,[status(thm)],[f22,f23,f32,f33,f46,f54,f60,f64])).
% 1.42/1.21 tff(f64,plain,(
% 1.42/1.21 spl0_1 | ~spl0_2 | ~spl0_3 | ~spl0_4),
% 1.42/1.21 inference(avatar_contradiction_clause,[status(thm)],[f63])).
% 1.42/1.21 tff(f63,plain,(
% 1.42/1.21 $false | (spl0_1 | ~spl0_2 | ~spl0_3 | ~spl0_4)),
% 1.42/1.21 inference(subsumption_resolution,[status(thm)],[f62,f61])).
% 1.42/1.21 tff(f61,plain,(
% 1.42/1.21 (cQ != $true) | (spl0_1 | ~spl0_4)),
% 1.42/1.21 inference(forward_demodulation,[status(thm)],[f17,f31])).
% 1.42/1.21 tff(f31,plain,(
% 1.42/1.21 (cR = $true) | ~spl0_4),
% 1.42/1.21 inference(avatar_component_clause,[status(thm)],[f29])).
% 1.42/1.21 tff(f29,definition,(
% 1.42/1.21 spl0_4 <=> (cR = $true)),
% 1.42/1.21 introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition])).
% 1.42/1.21 tff(f17,plain,(
% 1.42/1.21 (cQ != cR) | spl0_1),
% 1.42/1.21 inference(avatar_component_clause,[status(thm)],[f15])).
% 1.42/1.21 tff(f15,definition,(
% 1.42/1.21 spl0_1 <=> (cQ = cR)),
% 1.42/1.21 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 1.42/1.21 tff(f62,plain,(
% 1.42/1.21 (cQ = $true) | (~spl0_2 | ~spl0_3)),
% 1.42/1.21 inference(forward_demodulation,[status(thm)],[f26,f20])).
% 1.42/1.21 tff(f20,plain,(
% 1.42/1.21 (cP = $true) | ~spl0_2),
% 1.42/1.21 inference(avatar_component_clause,[status(thm)],[f19])).
% 1.42/1.21 tff(f19,definition,(
% 1.42/1.21 spl0_2 <=> (cP = $true)),
% 1.42/1.21 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])).
% 1.42/1.21 tff(f26,plain,(
% 1.42/1.21 (cP = cQ) | ~spl0_3),
% 1.42/1.21 inference(avatar_component_clause,[status(thm)],[f25])).
% 1.42/1.21 tff(f25,definition,(
% 1.42/1.21 spl0_3 <=> (cP = cQ)),
% 1.42/1.21 introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition])).
% 1.42/1.21 tff(f60,plain,(
% 1.42/1.21 ~spl0_1 | spl0_2 | ~spl0_3 | ~spl0_4),
% 1.42/1.21 inference(avatar_contradiction_clause,[status(thm)],[f59])).
% 1.42/1.21 tff(f59,plain,(
% 1.42/1.21 $false | (~spl0_1 | spl0_2 | ~spl0_3 | ~spl0_4)),
% 1.42/1.21 inference(trivial_inequality_removal,[status(thm)],[f58])).
% 1.42/1.21 tff(f58,plain,(
% 1.42/1.21 ($true = $false) | (~spl0_1 | spl0_2 | ~spl0_3 | ~spl0_4)),
% 1.42/1.21 inference(forward_demodulation,[status(thm)],[f57,f55])).
% 1.42/1.21 tff(f55,plain,(
% 1.42/1.21 (cQ = $false) | (spl0_2 | ~spl0_3)),
% 1.42/1.21 inference(backward_demodulation,[status(thm)],[f26,f52])).
% 1.42/1.21 tff(f52,plain,(
% 1.42/1.21 (cP = $false) | spl0_2),
% 1.42/1.21 inference(trivial_inequality_removal,[status(thm)],[f51])).
% 1.42/1.21 tff(f51,plain,(
% 1.42/1.21 (cP = $false) | ($true != $true) | spl0_2),
% 1.42/1.21 inference(superposition,[status(thm)],[f21,f4])).
% 1.42/1.21 tff(f4,plain,(
% 1.42/1.21 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 1.42/1.21 introduced(definition,[],[fool_axiom])).
% 1.42/1.21 tff(f21,plain,(
% 1.42/1.21 (cP != $true) | spl0_2),
% 1.42/1.21 inference(avatar_component_clause,[status(thm)],[f19])).
% 1.42/1.21 tff(f57,plain,(
% 1.42/1.21 (cQ = $true) | (~spl0_1 | ~spl0_4)),
% 1.42/1.21 inference(forward_demodulation,[status(thm)],[f16,f31])).
% 1.42/1.21 tff(f16,plain,(
% 1.42/1.21 (cQ = cR) | ~spl0_1),
% 1.42/1.21 inference(avatar_component_clause,[status(thm)],[f15])).
% 1.42/1.21 tff(f54,plain,(
% 1.42/1.21 ~spl0_1 | spl0_2 | spl0_3 | spl0_4),
% 1.42/1.21 inference(avatar_contradiction_clause,[status(thm)],[f53])).
% 1.42/1.21 tff(f53,plain,(
% 1.42/1.21 $false | (~spl0_1 | spl0_2 | spl0_3 | spl0_4)),
% 1.42/1.21 inference(subsumption_resolution,[status(thm)],[f52,f50])).
% 1.42/1.21 tff(f50,plain,(
% 1.42/1.21 (cP != $false) | (~spl0_1 | spl0_3 | spl0_4)),
% 1.42/1.21 inference(forward_demodulation,[status(thm)],[f27,f49])).
% 1.42/1.21 tff(f49,plain,(
% 1.42/1.21 (cQ = $false) | (~spl0_1 | spl0_4)),
% 1.42/1.21 inference(forward_demodulation,[status(thm)],[f16,f42])).
% 1.42/1.21 tff(f42,plain,(
% 1.42/1.21 (cR = $false) | spl0_4),
% 1.42/1.21 inference(trivial_inequality_removal,[status(thm)],[f37])).
% 1.42/1.21 tff(f37,plain,(
% 1.42/1.21 ($true != $true) | (cR = $false) | spl0_4),
% 1.42/1.21 inference(superposition,[status(thm)],[f30,f4])).
% 1.42/1.21 tff(f30,plain,(
% 1.42/1.21 (cR != $true) | spl0_4),
% 1.42/1.21 inference(avatar_component_clause,[status(thm)],[f29])).
% 1.42/1.21 tff(f27,plain,(
% 1.42/1.21 (cP != cQ) | spl0_3),
% 1.42/1.21 inference(avatar_component_clause,[status(thm)],[f25])).
% 1.42/1.21 tff(f46,plain,(
% 1.42/1.21 spl0_1 | ~spl0_2 | spl0_3 | spl0_4),
% 1.42/1.21 inference(avatar_contradiction_clause,[status(thm)],[f45])).
% 1.42/1.21 tff(f45,plain,(
% 1.42/1.21 $false | (spl0_1 | ~spl0_2 | spl0_3 | spl0_4)),
% 1.42/1.21 inference(subsumption_resolution,[status(thm)],[f41,f44])).
% 1.42/1.21 tff(f44,plain,(
% 1.42/1.21 (cQ != $false) | (spl0_1 | spl0_4)),
% 1.42/1.21 inference(backward_demodulation,[status(thm)],[f17,f42])).
% 1.42/1.21 tff(f41,plain,(
% 1.42/1.21 (cQ = $false) | (~spl0_2 | spl0_3)),
% 1.42/1.21 inference(trivial_inequality_removal,[status(thm)],[f38])).
% 1.42/1.21 tff(f38,plain,(
% 1.42/1.21 (cQ = $false) | ($true != $true) | (~spl0_2 | spl0_3)),
% 1.42/1.21 inference(superposition,[status(thm)],[f34,f4])).
% 1.42/1.21 tff(f34,plain,(
% 1.42/1.21 (cQ != $true) | (~spl0_2 | spl0_3)),
% 1.42/1.21 inference(backward_demodulation,[status(thm)],[f27,f20])).
% 1.42/1.21 tff(f33,plain,(
% 1.42/1.21 ~spl0_4 | spl0_3),
% 1.42/1.21 inference(avatar_split_clause,[status(thm)],[f13,f25,f29])).
% 1.42/1.21 tff(f13,plain,(
% 1.42/1.21 (cR != $true) | (cP = cQ)),
% 1.42/1.21 inference(cnf_transformation,[status(thm)],[f9])).
% 1.42/1.21 tff(f9,plain,(
% 1.42/1.21 ((cP = cQ) | (cR != $true)) & ((cR = $true) | (cP != cQ)) & ((cQ != cR) | (cP != $true)) & ((cQ = cR) | (cP = $true))),
% 1.42/1.21 inference(flattening,[status(thm)],[f8])).
% 1.42/1.21 tff(f8,plain,(
% 1.42/1.21 (((cP = cQ) | (cR != $true)) & ((cR = $true) | (cP != cQ))) & (((cQ != cR) | (cP != $true)) & ((cQ = cR) | (cP = $true)))),
% 1.42/1.21 inference(nnf_transformation,[status(thm)],[f7])).
% 1.42/1.21 tff(f7,plain,(
% 1.42/1.21 ((cP = cQ) <=> (cR = $true)) & ((cP = $true) <~> (cQ = cR))),
% 1.42/1.21 inference(ennf_transformation,[status(thm)],[f6])).
% 1.42/1.21 tff(f6,plain,(
% 1.42/1.21 ~(((cP = cQ) <=> (cR = $true)) => ((cP = $true) <=> (cQ = cR)))),
% 1.42/1.21 inference(fool_elimination,[status(thm)],[f5])).
% 1.42/1.21 tff(f5,plain,(
% 1.42/1.21 ~(((cP <=> cQ) <=> cR) => ((cQ <=> cR) <=> cP))),
% 1.42/1.21 inference(rectify,[status(thm)],[f2])).
% 1.42/1.21 tff(f2,negated_conjecture,(
% 1.42/1.21 ~(((cP <=> cQ) <=> cR) => ((cQ <=> cR) <=> cP))),
% 1.42/1.21 inference(negated_conjecture,[status(cth)],[f1])).
% 1.42/1.21 tff(f1,conjecture,(
% 1.42/1.21 ((cP <=> cQ) <=> cR) => ((cQ <=> cR) <=> cP)),
% 1.42/1.21 file('/export/starexec/sandbox/tmp/tmp.8COsbiWISf/DTF2THF_9895.p',cTHM50_A)).
% 1.42/1.21 tff(f32,plain,(
% 1.42/1.21 ~spl0_3 | spl0_4),
% 1.42/1.21 inference(avatar_split_clause,[status(thm)],[f12,f29,f25])).
% 1.42/1.21 tff(f12,plain,(
% 1.42/1.21 (cR = $true) | (cP != cQ)),
% 1.42/1.21 inference(cnf_transformation,[status(thm)],[f9])).
% 1.42/1.21 tff(f23,plain,(
% 1.42/1.21 spl0_2 | spl0_1),
% 1.42/1.21 inference(avatar_split_clause,[status(thm)],[f10,f15,f19])).
% 1.42/1.21 tff(f10,plain,(
% 1.42/1.21 (cP = $true) | (cQ = cR)),
% 1.42/1.21 inference(cnf_transformation,[status(thm)],[f9])).
% 1.42/1.21 tff(f22,plain,(
% 1.42/1.21 ~spl0_1 | ~spl0_2),
% 1.42/1.21 inference(avatar_split_clause,[status(thm)],[f11,f19,f15])).
% 1.42/1.21 tff(f11,plain,(
% 1.42/1.21 (cP != $true) | (cQ != cR)),
% 1.42/1.21 inference(cnf_transformation,[status(thm)],[f9])).
% 1.42/1.21 % SZS output end Proof for DTF2THF_9895
% 1.42/1.21 % (10011)------------------------------
% 1.42/1.21 % (10011)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.42/1.21 % (10011)Termination reason: Refutation
% 1.42/1.21
% 1.42/1.21 % (10011)Memory used [KB]: 5500
% 1.42/1.21 % (10011)Time elapsed: 0.004 s
% 1.42/1.21 % (10011)Instructions burned: 1 (million)
% 1.42/1.21 % (10011)------------------------------
% 1.42/1.21 % (10011)------------------------------
% 1.42/1.21 % (10007)Success in time 0.016 s
%------------------------------------------------------------------------------