%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO043^1 : 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 09:53:14 AM UTC 2026
% Result : Unsatisfiable 0.32s 1.43s
% Output : Refutation 0.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 43 ( 4 unt; 0 typ; 5 def)
% Number of atoms : 245 ( 39 equ; 0 cnn)
% Maximal formula atoms : 7 ( 5 avg)
% Number of connectives : 166 ( 42 ~; 44 |; 6 &; 69 @)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 9 usr; 8 con; 0-2 aty)
% Number of variables : 0 ( 0 ^; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
f: $o > $o ).
thf(func_def_1,type,
q: ( $o > $o ) > $o > $o ).
thf(func_def_7,type,
ph1:
!>[X0: $tType] : X0 ).
thf(f213,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f18,f27,f41,f56,f95,f104,f212]) ).
thf(f212,plain,
( ~ spl0_1
| spl0_6 ),
inference(avatar_contradiction_clause,[status(thm)],[f211]) ).
thf(f211,plain,
( $false
| ~ spl0_1
| spl0_6 ),
inference(subsumption_resolution,[status(thm)],[f175,f37]) ).
thf(f37,plain,
( ( ( f @ $true )
!= $true )
| spl0_6 ),
inference(avatar_component_clause,[status(thm)],[f36]) ).
thf(f36,definition,
( spl0_6
<=> ( ( f @ $true )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_6])],[avatar_definition]) ).
thf(f175,plain,
( ( ( f @ $true )
= $true )
| ~ spl0_1 ),
inference(superposition,[status(thm)],[f13,f5]) ).
thf(f5,plain,
( ( q @ f @ x )
= $true ),
inference(cnf_transformation,[status(thm)],[f4]) ).
thf(f4,plain,
( ( ( f @ ( f @ x ) )
= $true )
& ( ( f @ x )
!= ( f @ ( q @ f @ x ) ) )
& ( ( q @ f @ x )
= $true ) ),
inference(fool_elimination,[status(thm)],[f3]) ).
thf(f3,plain,
( ( f @ ( f @ x ) )
& ( ( f @ x )
!= ( f @ ( q @ f @ x ) ) )
& ( q @ f @ x ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( ( f @ ( f @ x ) )
& ( ( f @ x )
!= ( f @ ( q @ f @ x ) ) )
& ( q @ f @ x ) ),
file('/export/starexec/sandbox/tmp/tmp.RRxX3ziCB9/DTF2THF_4525.p',5) ).
thf(f13,plain,
( ( ( f @ ( q @ f @ x ) )
= $true )
| ~ spl0_1 ),
inference(avatar_component_clause,[status(thm)],[f11]) ).
thf(f11,definition,
( spl0_1
<=> ( ( f @ ( q @ f @ x ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition]) ).
thf(f104,plain,
( spl0_2
| ~ spl0_6 ),
inference(avatar_contradiction_clause,[status(thm)],[f103]) ).
thf(f103,plain,
( $false
| spl0_2
| ~ spl0_6 ),
inference(subsumption_resolution,[status(thm)],[f98,f102]) ).
thf(f102,plain,
( ( x = $true )
| spl0_2 ),
inference(subsumption_resolution,[status(thm)],[f100,f16]) ).
thf(f16,plain,
( ( ( f @ x )
!= $true )
| spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f15]) ).
thf(f15,definition,
( spl0_2
<=> ( ( f @ x )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition]) ).
thf(f100,plain,
( ( ( f @ x )
= $true )
| ( x = $true )
| spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f99]) ).
thf(f99,plain,
( ( x
!= ( f @ x ) )
| spl0_2 ),
inference(trivial_inequality_removal,[status(thm)],[f97]) ).
thf(f97,plain,
( ( x
!= ( f @ x ) )
| ( $true != $true )
| spl0_2 ),
inference(constrained_superposition,[status(thm)],[f16,f7]) ).
thf(f7,plain,
( ( f @ ( f @ x ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f4]) ).
thf(f98,plain,
( ( x != $true )
| spl0_2
| ~ spl0_6 ),
inference(trivial_inequality_removal,[status(thm)],[f96]) ).
thf(f96,plain,
( ( $true != $true )
| ( x != $true )
| spl0_2
| ~ spl0_6 ),
inference(constrained_superposition,[status(thm)],[f16,f38]) ).
thf(f38,plain,
( ( ( f @ $true )
= $true )
| ~ spl0_6 ),
inference(avatar_component_clause,[status(thm)],[f36]) ).
thf(f95,plain,
( ~ spl0_3
| ~ spl0_6 ),
inference(avatar_contradiction_clause,[status(thm)],[f94]) ).
thf(f94,plain,
( $false
| ~ spl0_3
| ~ spl0_6 ),
inference(subsumption_resolution,[status(thm)],[f75,f5]) ).
thf(f75,plain,
( ( ( q @ f @ x )
!= $true )
| ~ spl0_3
| ~ spl0_6 ),
inference(trivial_inequality_removal,[status(thm)],[f67]) ).
thf(f67,plain,
( ( ( q @ f @ x )
!= $true )
| ( $false = $true )
| ~ spl0_3
| ~ spl0_6 ),
inference(constrained_superposition,[status(thm)],[f38,f22]) ).
thf(f22,plain,
( ( ( f @ ( q @ f @ x ) )
= $false )
| ~ spl0_3 ),
inference(avatar_component_clause,[status(thm)],[f20]) ).
thf(f20,definition,
( spl0_3
<=> ( ( f @ ( q @ f @ x ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition]) ).
thf(f56,plain,
( ~ spl0_2
| ~ spl0_4 ),
inference(avatar_contradiction_clause,[status(thm)],[f55]) ).
thf(f55,plain,
( $false
| ~ spl0_2
| ~ spl0_4 ),
inference(trivial_inequality_removal,[status(thm)],[f44]) ).
thf(f44,plain,
( ( $false = $true )
| ~ spl0_2
| ~ spl0_4 ),
inference(superposition,[status(thm)],[f17,f26]) ).
thf(f26,plain,
( ( ( f @ x )
= $false )
| ~ spl0_4 ),
inference(avatar_component_clause,[status(thm)],[f24]) ).
thf(f24,definition,
( spl0_4
<=> ( ( f @ x )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition]) ).
thf(f17,plain,
( ( ( f @ x )
= $true )
| ~ spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f15]) ).
thf(f41,plain,
( spl0_6
| ~ spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f40,f15,f36]) ).
thf(f40,plain,
( ( ( f @ $true )
= $true )
| ~ spl0_2 ),
inference(superposition,[status(thm)],[f7,f17]) ).
thf(f27,plain,
( spl0_3
| spl0_4 ),
inference(avatar_split_clause,[status(thm)],[f9,f24,f20]) ).
thf(f9,plain,
( ( ( f @ ( q @ f @ x ) )
= $false )
| ( ( f @ x )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f6]) ).
thf(f6,plain,
( ( f @ x )
!= ( f @ ( q @ f @ x ) ) ),
inference(cnf_transformation,[status(thm)],[f4]) ).
thf(f18,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f8,f15,f11]) ).
thf(f8,plain,
( ( ( f @ x )
= $true )
| ( ( f @ ( q @ f @ x ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO043^1 : 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 : n031.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 14:23:33 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
% 0.20/0.46 ---- Original DTF file ---
% 0.20/0.46 thf(spec,logic,$$dhol).
% 0.20/0.46 %------------------------------------------------------------------------------
% 0.20/0.46 % File : SYO043^1 : TPTP v9.2.1. Released v4.0.0.
% 0.20/0.46 % Domain : Syntactic
% 0.20/0.46 % Problem : Unsatisfiable basic formula 5
% 0.20/0.46 % Version : Especial.
% 0.20/0.46 % English :
% 0.20/0.46
% 0.20/0.46 % Refs : [BS09a] Brown E. & Smolka (2009), Terminating Tableaux for the
% 0.20/0.46 % : [BS09b] Brown E. & Smolka (2009), Extended First-Order Logic
% 0.20/0.46 % Source : [BS09a]
% 0.20/0.46 % Names :
% 0.20/0.46
% 0.20/0.46 % Status : Unsatisfiable
% 0.20/0.46 % Rating : 0.00 v5.3.0, 0.33 v5.2.0, 0.67 v5.0.0, 0.33 v4.1.0, 0.67 v4.0.1, 1.00 v4.0.0
% 0.20/0.46 % Syntax : Number of formulae : 4 ( 0 unt; 3 typ; 0 def)
% 0.20/0.46 % Number of atoms : 13 ( 1 equ; 0 cnn)
% 0.20/0.46 % Maximal formula atoms : 7 ( 13 avg)
% 0.20/0.46 % Number of connectives : 11 ( 1 ~; 0 |; 2 &; 8 @)
% 0.20/0.46 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.20/0.46 % Maximal formula depth : 5 ( 5 avg)
% 0.20/0.46 % Number of types : 1 ( 0 usr)
% 0.20/0.46 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.20/0.46 % Number of symbols : 4 ( 3 usr; 1 con; 0-2 aty)
% 0.20/0.46 % Number of variables : 0 ( 0 ^; 0 !; 0 ?; 0 :)
% 0.20/0.46 % SPC : TH0_UNS_EQU_NAR
% 0.20/0.46
% 0.20/0.46 % Comments : The fragment of simple type theory that restricts equations to
% 0.20/0.46 % base types and disallows lambda abstraction and quantification is
% 0.20/0.46 % decidable. This is an example.
% 0.20/0.46 %------------------------------------------------------------------------------
% 0.20/0.46 thf(f,type,
% 0.20/0.46 f: $o > $o ).
% 0.20/0.46
% 0.20/0.46 thf(q,type,
% 0.20/0.46 q: ( $o > $o ) > $o > $o ).
% 0.20/0.46
% 0.20/0.46 thf(x,type,
% 0.20/0.46 x: $o ).
% 0.20/0.46
% 0.20/0.46 thf(5,axiom,
% 0.20/0.46 ( ( q @ f @ x )
% 0.20/0.46 & ( f @ ( f @ x ) )
% 0.20/0.46 & ( ( f @ ( q @ f @ x ) )
% 0.20/0.46 != ( f @ x ) ) ) ).
% 0.20/0.46
% 0.20/0.46 %------------------------------------------------------------------------------
% 0.20/0.46 ------------------------
% 0.32/1.40 ---- Embedded in THF ---
% 0.32/1.40 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 0.32/1.40 %%% Generated on Tue Feb 24 14:23:34 EST 2026
% 0.32/1.40 %%% using '$$dhol' embedding, version 1.3.0.
% 0.32/1.40 %%% Logic specification used:
% 0.32/1.40 %%% thf(spec, logic, $$dhol).
% 0.32/1.40
% 0.32/1.40 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.RRxX3ziCB9/DTF2DTF4525.p
% See solution above
% 0.32/1.40 ------------------------
% 0.32/1.41 ---- Cleaned THF ---
% 0.32/1.41 thf(f,type,
% 0.32/1.41 f: $o > $o ).
% 0.32/1.41
% 0.32/1.41 thf(q,type,
% 0.32/1.41 q: ( $o > $o ) > $o > $o ).
% 0.32/1.41
% 0.32/1.41 thf(x,type,
% 0.32/1.41 x: $o ).
% 0.32/1.41
% 0.32/1.41 thf(5,axiom,
% 0.32/1.41 ( ( q @ f @ x )
% 0.32/1.41 & ( f @ ( f @ x ) )
% 0.32/1.41 & ( ( f @ ( q @ f @ x ) )
% 0.32/1.41 != ( f @ x ) ) ) ).
% 0.32/1.41 ------------------------
% 0.32/1.43 % (4623)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_4525 for (3000ds/4Mi)
% 0.32/1.43 % (4624)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_4525 for (3000ds/27Mi)
% 0.32/1.43 % (4622)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_4525 for (3000ds/183Mi)
% 0.32/1.43 % (4625)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_4525 for (3000ds/2Mi)
% 0.32/1.43 % (4626)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_4525 for (3000ds/2Mi)
% 0.32/1.43 % (4627)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_4525 for (3000ds/275Mi)
% 0.32/1.43 % (4628)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_4525 for (3000ds/18Mi)
% 0.32/1.43 % (4627)Refutation not found, incomplete strategy
% 0.32/1.43 % (4627)------------------------------
% 0.32/1.43 % (4627)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.43 % (4627)Termination reason: Refutation not found, incomplete strategy
% 0.32/1.43
% 0.32/1.43
% 0.32/1.43 % (4627)Memory used [KB]: 5373
% 0.32/1.43 % (4627)Time elapsed: 0.002 s
% 0.32/1.43 % (4627)Instructions burned: 1 (million)
% 0.32/1.43 % (4627)------------------------------
% 0.32/1.43 % (4627)------------------------------
% 0.32/1.43 % (4626)Refutation not found, incomplete strategy
% 0.32/1.43 % (4626)------------------------------
% 0.32/1.43 % (4626)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.43 % (4626)Termination reason: Refutation not found, incomplete strategy
% 0.32/1.43
% 0.32/1.43
% 0.32/1.43 % (4626)Memory used [KB]: 5373
% 0.32/1.43 % (4626)Time elapsed: 0.002 s
% 0.32/1.43 % (4626)Instructions burned: 1 (million)
% 0.32/1.43 % (4626)------------------------------
% 0.32/1.43 % (4626)------------------------------
% 0.32/1.43 % (4625)Instruction limit reached!
% 0.32/1.43 % (4625)------------------------------
% 0.32/1.43 % (4625)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.43 % (4625)Termination reason: Unknown
% 0.32/1.43 % (4625)Termination phase: Saturation
% 0.32/1.43
% 0.32/1.43 % (4625)Memory used [KB]: 5500
% 0.32/1.43 % (4625)Time elapsed: 0.003 s
% 0.32/1.43 % (4625)Instructions burned: 2 (million)
% 0.32/1.43 % (4625)------------------------------
% 0.32/1.43 % (4625)------------------------------
% 0.32/1.43 % (4624)Refutation not found, incomplete strategy
% 0.32/1.43 % (4624)------------------------------
% 0.32/1.43 % (4624)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.43 % (4624)Termination reason: Refutation not found, incomplete strategy
% 0.32/1.43
% 0.32/1.43
% 0.32/1.43 % (4624)Memory used [KB]: 5500
% 0.32/1.43 % (4624)Time elapsed: 0.003 s
% 0.32/1.43 % (4624)Instructions burned: 2 (million)
% 0.32/1.43 % (4624)------------------------------
% 0.32/1.43 % (4624)------------------------------
% 0.32/1.43 % (4628)Refutation not found, incomplete strategy
% 0.32/1.43 % (4628)------------------------------
% 0.32/1.43 % (4628)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.43 % (4628)Termination reason: Refutation not found, incomplete strategy
% 0.32/1.43
% 0.32/1.43
% 0.32/1.43 % (4628)Memory used [KB]: 5500
% 0.32/1.43 % (4628)Time elapsed: 0.004 s
% 0.32/1.43 % (4628)Instructions burned: 2 (million)
% 0.32/1.43 % (4628)------------------------------
% 0.32/1.43 % (4628)------------------------------
% 0.32/1.43 % (4623)Instruction limit reached!
% 0.32/1.43 % (4623)------------------------------
% 0.32/1.43 % (4623)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.43 % (4623)Termination reason: Unknown
% 0.32/1.43 % (4623)Termination phase: Saturation
% 0.32/1.43
% 0.32/1.43 % (4623)Memory used [KB]: 5500
% 0.32/1.43 % (4623)Time elapsed: 0.005 s
% 0.32/1.43 % (4623)Instructions burned: 5 (million)
% 0.32/1.43 % (4623)------------------------------
% 0.32/1.43 % (4623)------------------------------
% 0.32/1.43 % (4622)First to succeed.
% 0.32/1.43 % (4622)Refutation found. Thanks to Tanya!
% 0.32/1.43 % SZS status Unsatisfiable for DTF2THF_4525
% 0.32/1.43 % SZS output start Proof for DTF2THF_4525
% 0.32/1.43 thf(func_def_0, type, f: $o > $o).
% 0.32/1.43 thf(func_def_1, type, q: ($o > $o) > $o > $o).
% 0.32/1.43 thf(func_def_7, type, ph1: !>[X0: $tType]:(X0)).
% 0.32/1.43 thf(f213,plain,(
% 0.32/1.43 $false),
% 0.32/1.43 inference(avatar_sat_refutation,[status(thm)],[f18,f27,f41,f56,f95,f104,f212])).
% 0.32/1.43 thf(f212,plain,(
% 0.32/1.43 ~spl0_1 | spl0_6),
% 0.32/1.43 inference(avatar_contradiction_clause,[status(thm)],[f211])).
% 0.32/1.43 thf(f211,plain,(
% 0.32/1.43 $false | (~spl0_1 | spl0_6)),
% 0.32/1.43 inference(subsumption_resolution,[status(thm)],[f175,f37])).
% 0.32/1.43 thf(f37,plain,(
% 0.32/1.43 ((f @ $true) != $true) | spl0_6),
% 0.32/1.43 inference(avatar_component_clause,[status(thm)],[f36])).
% 0.32/1.43 thf(f36,definition,(
% 0.32/1.43 spl0_6 <=> ((f @ $true) = $true)),
% 0.32/1.43 introduced(definition,[new_symbols(naming,[spl0_6])],[avatar_definition])).
% 0.32/1.43 thf(f175,plain,(
% 0.32/1.43 ((f @ $true) = $true) | ~spl0_1),
% 0.32/1.43 inference(superposition,[status(thm)],[f13,f5])).
% 0.32/1.43 thf(f5,plain,(
% 0.32/1.43 ((q @ f @ x) = $true)),
% 0.32/1.43 inference(cnf_transformation,[status(thm)],[f4])).
% 0.32/1.43 thf(f4,plain,(
% 0.32/1.43 ((f @ (f @ x)) = $true) & ((f @ x) != (f @ (q @ f @ x))) & ((q @ f @ x) = $true)),
% 0.32/1.43 inference(fool_elimination,[status(thm)],[f3])).
% 0.32/1.43 thf(f3,plain,(
% 0.32/1.43 (f @ (f @ x)) & ((f @ x) != (f @ (q @ f @ x))) & (q @ f @ x)),
% 0.32/1.43 inference(rectify,[status(thm)],[f1])).
% 0.32/1.43 thf(f1,axiom,(
% 0.32/1.43 (f @ (f @ x)) & ((f @ x) != (f @ (q @ f @ x))) & (q @ f @ x)),
% 0.32/1.43 file('/export/starexec/sandbox/tmp/tmp.RRxX3ziCB9/DTF2THF_4525.p',5)).
% 0.32/1.43 thf(f13,plain,(
% 0.32/1.43 ((f @ (q @ f @ x)) = $true) | ~spl0_1),
% 0.32/1.43 inference(avatar_component_clause,[status(thm)],[f11])).
% 0.32/1.43 thf(f11,definition,(
% 0.32/1.43 spl0_1 <=> ((f @ (q @ f @ x)) = $true)),
% 0.32/1.43 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 0.32/1.43 thf(f104,plain,(
% 0.32/1.43 spl0_2 | ~spl0_6),
% 0.32/1.43 inference(avatar_contradiction_clause,[status(thm)],[f103])).
% 0.32/1.43 thf(f103,plain,(
% 0.32/1.43 $false | (spl0_2 | ~spl0_6)),
% 0.32/1.43 inference(subsumption_resolution,[status(thm)],[f98,f102])).
% 0.32/1.43 thf(f102,plain,(
% 0.32/1.43 (x = $true) | spl0_2),
% 0.32/1.43 inference(subsumption_resolution,[status(thm)],[f100,f16])).
% 0.32/1.43 thf(f16,plain,(
% 0.32/1.43 ((f @ x) != $true) | spl0_2),
% 0.32/1.43 inference(avatar_component_clause,[status(thm)],[f15])).
% 0.32/1.43 thf(f15,definition,(
% 0.32/1.43 spl0_2 <=> ((f @ x) = $true)),
% 0.32/1.43 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])).
% 0.32/1.43 thf(f100,plain,(
% 0.32/1.43 ((f @ x) = $true) | (x = $true) | spl0_2),
% 0.32/1.43 inference(binary_proxy_clausification,[status(thm)],[f99])).
% 0.32/1.43 thf(f99,plain,(
% 0.32/1.43 (x != (f @ x)) | spl0_2),
% 0.32/1.43 inference(trivial_inequality_removal,[status(thm)],[f97])).
% 0.32/1.43 thf(f97,plain,(
% 0.32/1.43 (x != (f @ x)) | ($true != $true) | spl0_2),
% 0.32/1.43 inference(constrained_superposition,[status(thm)],[f16,f7])).
% 0.32/1.43 thf(f7,plain,(
% 0.32/1.43 ((f @ (f @ x)) = $true)),
% 0.32/1.43 inference(cnf_transformation,[status(thm)],[f4])).
% 0.32/1.43 thf(f98,plain,(
% 0.32/1.43 (x != $true) | (spl0_2 | ~spl0_6)),
% 0.32/1.43 inference(trivial_inequality_removal,[status(thm)],[f96])).
% 0.32/1.43 thf(f96,plain,(
% 0.32/1.43 ($true != $true) | (x != $true) | (spl0_2 | ~spl0_6)),
% 0.32/1.43 inference(constrained_superposition,[status(thm)],[f16,f38])).
% 0.32/1.43 thf(f38,plain,(
% 0.32/1.43 ((f @ $true) = $true) | ~spl0_6),
% 0.32/1.43 inference(avatar_component_clause,[status(thm)],[f36])).
% 0.32/1.43 thf(f95,plain,(
% 0.32/1.43 ~spl0_3 | ~spl0_6),
% 0.32/1.43 inference(avatar_contradiction_clause,[status(thm)],[f94])).
% 0.32/1.43 thf(f94,plain,(
% 0.32/1.43 $false | (~spl0_3 | ~spl0_6)),
% 0.32/1.43 inference(subsumption_resolution,[status(thm)],[f75,f5])).
% 0.32/1.43 thf(f75,plain,(
% 0.32/1.43 ((q @ f @ x) != $true) | (~spl0_3 | ~spl0_6)),
% 0.32/1.43 inference(trivial_inequality_removal,[status(thm)],[f67])).
% 0.32/1.43 thf(f67,plain,(
% 0.32/1.43 ((q @ f @ x) != $true) | ($false = $true) | (~spl0_3 | ~spl0_6)),
% 0.32/1.43 inference(constrained_superposition,[status(thm)],[f38,f22])).
% 0.32/1.43 thf(f22,plain,(
% 0.32/1.43 ((f @ (q @ f @ x)) = $false) | ~spl0_3),
% 0.32/1.43 inference(avatar_component_clause,[status(thm)],[f20])).
% 0.32/1.43 thf(f20,definition,(
% 0.32/1.43 spl0_3 <=> ((f @ (q @ f @ x)) = $false)),
% 0.32/1.43 introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition])).
% 0.32/1.43 thf(f56,plain,(
% 0.32/1.43 ~spl0_2 | ~spl0_4),
% 0.32/1.43 inference(avatar_contradiction_clause,[status(thm)],[f55])).
% 0.32/1.43 thf(f55,plain,(
% 0.32/1.43 $false | (~spl0_2 | ~spl0_4)),
% 0.32/1.43 inference(trivial_inequality_removal,[status(thm)],[f44])).
% 0.32/1.43 thf(f44,plain,(
% 0.32/1.43 ($false = $true) | (~spl0_2 | ~spl0_4)),
% 0.32/1.43 inference(superposition,[status(thm)],[f17,f26])).
% 0.32/1.43 thf(f26,plain,(
% 0.32/1.43 ((f @ x) = $false) | ~spl0_4),
% 0.32/1.43 inference(avatar_component_clause,[status(thm)],[f24])).
% 0.32/1.43 thf(f24,definition,(
% 0.32/1.43 spl0_4 <=> ((f @ x) = $false)),
% 0.32/1.43 introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition])).
% 0.32/1.43 thf(f17,plain,(
% 0.32/1.43 ((f @ x) = $true) | ~spl0_2),
% 0.32/1.43 inference(avatar_component_clause,[status(thm)],[f15])).
% 0.32/1.43 thf(f41,plain,(
% 0.32/1.43 spl0_6 | ~spl0_2),
% 0.32/1.43 inference(avatar_split_clause,[status(thm)],[f40,f15,f36])).
% 0.32/1.43 thf(f40,plain,(
% 0.32/1.43 ((f @ $true) = $true) | ~spl0_2),
% 0.32/1.43 inference(superposition,[status(thm)],[f7,f17])).
% 0.32/1.43 thf(f27,plain,(
% 0.32/1.43 spl0_3 | spl0_4),
% 0.32/1.43 inference(avatar_split_clause,[status(thm)],[f9,f24,f20])).
% 0.32/1.43 thf(f9,plain,(
% 0.32/1.43 ((f @ (q @ f @ x)) = $false) | ((f @ x) = $false)),
% 0.32/1.43 inference(binary_proxy_clausification,[status(thm)],[f6])).
% 0.32/1.43 thf(f6,plain,(
% 0.32/1.43 ((f @ x) != (f @ (q @ f @ x)))),
% 0.32/1.43 inference(cnf_transformation,[status(thm)],[f4])).
% 0.32/1.43 thf(f18,plain,(
% 0.32/1.43 spl0_1 | spl0_2),
% 0.32/1.43 inference(avatar_split_clause,[status(thm)],[f8,f15,f11])).
% 0.32/1.43 thf(f8,plain,(
% 0.32/1.43 ((f @ x) = $true) | ((f @ (q @ f @ x)) = $true)),
% 0.32/1.43 inference(binary_proxy_clausification,[status(thm)],[f6])).
% 0.32/1.43 % SZS output end Proof for DTF2THF_4525
% 0.32/1.43 % (4622)------------------------------
% 0.32/1.43 % (4622)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.43 % (4622)Termination reason: Refutation
% 0.32/1.43
% 0.32/1.43 % (4622)Memory used [KB]: 5500
% 0.32/1.43 % (4622)Time elapsed: 0.007 s
% 0.32/1.43 % (4622)Instructions burned: 9 (million)
% 0.32/1.43 % (4622)------------------------------
% 0.32/1.43 % (4622)------------------------------
% 0.32/1.43 % (4621)Success in time 0.02 s
%------------------------------------------------------------------------------