%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO042^1 : 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 : n015.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 09:53:13 AM UTC 2026
% Result : Unsatisfiable 1.66s 1.43s
% Output : Refutation 1.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 11
% Syntax : Number of formulae : 83 ( 10 unt; 0 typ; 10 def)
% Number of atoms : 455 ( 91 equ; 7 cnn)
% Maximal formula atoms : 7 ( 5 avg)
% Number of connectives : 296 ( 106 ~; 102 |; 16 &; 62 @)
% ( 10 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 20 ( 16 usr; 16 con; 0-2 aty)
% Number of variables : 0 ( 0 ^; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
g: $o > $o ).
thf(func_def_1,type,
p: ( $o > $o ) > $o ).
thf(func_def_9,type,
ph1:
!>[X0: $tType] : X0 ).
thf(f309,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f25,f34,f39,f44,f50,f68,f77,f104,f203,f216,f223,f297,f305]) ).
thf(f305,plain,
( ~ spl0_2
| spl0_5
| ~ spl0_8
| ~ spl0_9 ),
inference(avatar_contradiction_clause,[status(thm)],[f304]) ).
thf(f304,plain,
( $false
| ~ spl0_2
| spl0_5
| ~ spl0_8
| ~ spl0_9 ),
inference(subsumption_resolution,[status(thm)],[f299,f270]) ).
thf(f270,plain,
( ( $true
= ( g @ $true ) )
| ~ spl0_8
| ~ spl0_9 ),
inference(superposition,[status(thm)],[f67,f72]) ).
thf(f72,plain,
( ( sK2 = $true )
| ~ spl0_9 ),
inference(avatar_component_clause,[status(thm)],[f70]) ).
thf(f70,definition,
( spl0_9
<=> ( sK2 = $true ) ),
introduced(definition,[new_symbols(naming,[spl0_9])],[avatar_definition]) ).
thf(f67,plain,
( ( $true
= ( g @ sK2 ) )
| ~ spl0_8 ),
inference(avatar_component_clause,[status(thm)],[f65]) ).
thf(f65,definition,
( spl0_8
<=> ( $true
= ( g @ sK2 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_8])],[avatar_definition]) ).
thf(f299,plain,
( ( $true
!= ( g @ $true ) )
| ~ spl0_2
| spl0_5 ),
inference(superposition,[status(thm)],[f37,f24]) ).
thf(f24,plain,
( ( y = $true )
| ~ spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f22]) ).
thf(f22,definition,
( spl0_2
<=> ( y = $true ) ),
introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition]) ).
thf(f37,plain,
( ( ( g @ y )
!= $true )
| spl0_5 ),
inference(avatar_component_clause,[status(thm)],[f36]) ).
thf(f36,definition,
( spl0_5
<=> ( ( g @ y )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_5])],[avatar_definition]) ).
thf(f297,plain,
( ~ spl0_1
| spl0_6
| spl0_7
| ~ spl0_8 ),
inference(avatar_contradiction_clause,[status(thm)],[f296]) ).
thf(f296,plain,
( $false
| ~ spl0_1
| spl0_6
| spl0_7
| ~ spl0_8 ),
inference(subsumption_resolution,[status(thm)],[f295,f42]) ).
thf(f42,plain,
( ( ( g @ y )
!= $false )
| spl0_6 ),
inference(avatar_component_clause,[status(thm)],[f41]) ).
thf(f41,definition,
( spl0_6
<=> ( ( g @ y )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_6])],[avatar_definition]) ).
thf(f295,plain,
( ( ( g @ y )
= $false )
| ~ spl0_1
| spl0_7
| ~ spl0_8 ),
inference(subsumption_resolution,[status(thm)],[f288,f62]) ).
thf(f62,plain,
( ( sK2 != $false )
| spl0_7 ),
inference(avatar_component_clause,[status(thm)],[f61]) ).
thf(f61,definition,
( spl0_7
<=> ( sK2 = $false ) ),
introduced(definition,[new_symbols(naming,[spl0_7])],[avatar_definition]) ).
thf(f288,plain,
( ( sK2 = $false )
| ( ( g @ y )
= $false )
| ~ spl0_1
| ~ spl0_8 ),
inference(binary_proxy_clausification,[status(thm)],[f286]) ).
thf(f286,plain,
( ( ( g @ y )
!= sK2 )
| ~ spl0_1
| ~ spl0_8 ),
inference(trivial_inequality_removal,[status(thm)],[f274]) ).
thf(f274,plain,
( ( $true = $false )
| ( ( g @ y )
!= sK2 )
| ~ spl0_1
| ~ spl0_8 ),
inference(constrained_superposition,[status(thm)],[f20,f67]) ).
thf(f20,plain,
( ( ( g @ ( g @ y ) )
= $false )
| ~ spl0_1 ),
inference(avatar_component_clause,[status(thm)],[f18]) ).
thf(f18,definition,
( spl0_1
<=> ( ( g @ ( g @ y ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition]) ).
thf(f223,plain,
( spl0_9
| spl0_2
| ~ spl0_5
| ~ spl0_10 ),
inference(avatar_split_clause,[status(thm)],[f222,f74,f36,f22,f70]) ).
thf(f74,definition,
( spl0_10
<=> ( $false
= ( g @ sK2 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_10])],[avatar_definition]) ).
thf(f222,plain,
( ( sK2 = $true )
| spl0_2
| ~ spl0_5
| ~ spl0_10 ),
inference(subsumption_resolution,[status(thm)],[f213,f23]) ).
thf(f23,plain,
( ( y != $true )
| spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f22]) ).
thf(f213,plain,
( ( y = $true )
| ( sK2 = $true )
| ~ spl0_5
| ~ spl0_10 ),
inference(binary_proxy_clausification,[status(thm)],[f212]) ).
thf(f212,plain,
( ( y != sK2 )
| ~ spl0_5
| ~ spl0_10 ),
inference(trivial_inequality_removal,[status(thm)],[f209]) ).
thf(f209,plain,
( ( $true = $false )
| ( y != sK2 )
| ~ spl0_5
| ~ spl0_10 ),
inference(constrained_superposition,[status(thm)],[f76,f38]) ).
thf(f38,plain,
( ( ( g @ y )
= $true )
| ~ spl0_5 ),
inference(avatar_component_clause,[status(thm)],[f36]) ).
thf(f76,plain,
( ( $false
= ( g @ sK2 ) )
| ~ spl0_10 ),
inference(avatar_component_clause,[status(thm)],[f74]) ).
thf(f216,plain,
( ~ spl0_5
| ~ spl0_6 ),
inference(avatar_contradiction_clause,[status(thm)],[f215]) ).
thf(f215,plain,
( $false
| ~ spl0_5
| ~ spl0_6 ),
inference(trivial_inequality_removal,[status(thm)],[f208]) ).
thf(f208,plain,
( ( $true = $false )
| ~ spl0_5
| ~ spl0_6 ),
inference(superposition,[status(thm)],[f43,f38]) ).
thf(f43,plain,
( ( ( g @ y )
= $false )
| ~ spl0_6 ),
inference(avatar_component_clause,[status(thm)],[f41]) ).
thf(f203,plain,
( spl0_5
| ~ spl0_4
| spl0_9
| ~ spl0_10 ),
inference(avatar_split_clause,[status(thm)],[f202,f74,f70,f31,f36]) ).
thf(f31,definition,
( spl0_4
<=> ( ( g @ ( g @ y ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition]) ).
thf(f202,plain,
( ( ( g @ y )
= $true )
| ~ spl0_4
| spl0_9
| ~ spl0_10 ),
inference(subsumption_resolution,[status(thm)],[f177,f71]) ).
thf(f71,plain,
( ( sK2 != $true )
| spl0_9 ),
inference(avatar_component_clause,[status(thm)],[f70]) ).
thf(f177,plain,
( ( sK2 = $true )
| ( ( g @ y )
= $true )
| ~ spl0_4
| ~ spl0_10 ),
inference(binary_proxy_clausification,[status(thm)],[f176]) ).
thf(f176,plain,
( ( ( g @ y )
!= sK2 )
| ~ spl0_4
| ~ spl0_10 ),
inference(trivial_inequality_removal,[status(thm)],[f175]) ).
thf(f175,plain,
( ( ( g @ y )
!= sK2 )
| ( $true = $false )
| ~ spl0_4
| ~ spl0_10 ),
inference(constrained_superposition,[status(thm)],[f76,f33]) ).
thf(f33,plain,
( ( ( g @ ( g @ y ) )
= $true )
| ~ spl0_4 ),
inference(avatar_component_clause,[status(thm)],[f31]) ).
thf(f104,plain,
( ~ spl0_7
| ~ spl0_9 ),
inference(avatar_contradiction_clause,[status(thm)],[f103]) ).
thf(f103,plain,
( $false
| ~ spl0_7
| ~ spl0_9 ),
inference(trivial_inequality_removal,[status(thm)],[f99]) ).
thf(f99,plain,
( ( $true = $false )
| ~ spl0_7
| ~ spl0_9 ),
inference(superposition,[status(thm)],[f72,f63]) ).
thf(f63,plain,
( ( sK2 = $false )
| ~ spl0_7 ),
inference(avatar_component_clause,[status(thm)],[f61]) ).
thf(f77,plain,
( spl0_9
| spl0_10 ),
inference(avatar_split_clause,[status(thm)],[f58,f74,f70]) ).
thf(f58,plain,
( ( sK2 = $true )
| ( $false
= ( g @ sK2 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f57]) ).
thf(f57,plain,
( ( $false
= ( g @ sK2 ) )
| ( $false = ( ~ sK2 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f55]) ).
thf(f55,plain,
( ( ~ sK2 )
!= ( g @ sK2 ) ),
inference(negative_extensionality,[status(thm)],[f54]) ).
thf(f54,plain,
g != (~),
inference(trivial_inequality_removal,[status(thm)],[f53]) ).
thf(f53,plain,
( ( g != (~) )
| ( $true != $true ) ),
inference(constrained_superposition,[status(thm)],[f7,f8]) ).
thf(f8,plain,
( ( p @ g )
= $true ),
inference(cnf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
( ( x != y )
& ( x
= ( g @ y ) )
& ( ( p @ g )
= $true )
& ( ( p @ (~) )
!= $true )
& ( y
= ( g @ x ) ) ),
inference(flattening,[status(thm)],[f4]) ).
thf(f4,plain,
( ( y
= ( g @ x ) )
& ( ( p @ g )
= $true )
& ( x != y )
& ( x
= ( g @ y ) )
& ( ( p @ (~) )
!= $true ) ),
inference(fool_elimination,[status(thm)],[f3]) ).
thf(f3,plain,
( ( y
= ( g @ x ) )
& ( p @ g )
& ( x != y )
& ( x
= ( g @ y ) )
& ~ ( p @ (~) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( ( y
= ( g @ x ) )
& ( p @ g )
& ( x != y )
& ( x
= ( g @ y ) )
& ~ ( p @ (~) ) ),
file('/export/starexec/sandbox/tmp/tmp.4ffxeAIhVl/DTF2THF_9877.p',4) ).
thf(f7,plain,
( ( p @ (~) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f5]) ).
thf(f68,plain,
( spl0_7
| spl0_8 ),
inference(avatar_split_clause,[status(thm)],[f59,f65,f61]) ).
thf(f59,plain,
( ( $true
= ( g @ sK2 ) )
| ( sK2 = $false ) ),
inference(not_proxy_clausification,[status(thm)],[f56]) ).
thf(f56,plain,
( ( $true = ( ~ sK2 ) )
| ( $true
= ( g @ sK2 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f55]) ).
thf(f50,plain,
( ~ spl0_2
| ~ spl0_3 ),
inference(avatar_contradiction_clause,[status(thm)],[f49]) ).
thf(f49,plain,
( $false
| ~ spl0_2
| ~ spl0_3 ),
inference(trivial_inequality_removal,[status(thm)],[f45]) ).
thf(f45,plain,
( ( $true = $false )
| ~ spl0_2
| ~ spl0_3 ),
inference(superposition,[status(thm)],[f29,f24]) ).
thf(f29,plain,
( ( y = $false )
| ~ spl0_3 ),
inference(avatar_component_clause,[status(thm)],[f27]) ).
thf(f27,definition,
( spl0_3
<=> ( y = $false ) ),
introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition]) ).
thf(f44,plain,
( spl0_6
| spl0_3 ),
inference(avatar_split_clause,[status(thm)],[f14,f27,f41]) ).
thf(f14,plain,
( ( ( g @ y )
= $false )
| ( y = $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f12]) ).
thf(f12,plain,
( y
!= ( g @ y ) ),
inference(definition_unfolding,[status(thm)],[f10,f9]) ).
thf(f9,plain,
( x
= ( g @ y ) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
thf(f10,plain,
x != y,
inference(cnf_transformation,[status(thm)],[f5]) ).
thf(f39,plain,
( spl0_2
| spl0_5 ),
inference(avatar_split_clause,[status(thm)],[f13,f36,f22]) ).
thf(f13,plain,
( ( ( g @ y )
= $true )
| ( y = $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f12]) ).
thf(f34,plain,
( spl0_3
| spl0_4 ),
inference(avatar_split_clause,[status(thm)],[f16,f31,f27]) ).
thf(f16,plain,
( ( ( g @ ( g @ y ) )
= $true )
| ( y = $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f11]) ).
thf(f11,plain,
( y
= ( g @ ( g @ y ) ) ),
inference(definition_unfolding,[status(thm)],[f6,f9]) ).
thf(f6,plain,
( y
= ( g @ x ) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
thf(f25,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f15,f22,f18]) ).
thf(f15,plain,
( ( ( g @ ( g @ y ) )
= $false )
| ( y = $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO042^1 : 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 : n015.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 14:22:46 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 : SYO042^1 : TPTP v9.2.1. Released v4.0.0.
% 0.20/0.46 % Domain : Syntactic
% 0.20/0.46 % Problem : Unsatisfiable basic formula 4
% 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 v5.4.0, 0.33 v5.3.0, 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 : 5 ( 0 unt; 4 typ; 0 def)
% 0.20/0.46 % Number of atoms : 15 ( 3 equ; 1 cnn)
% 0.20/0.46 % Maximal formula atoms : 7 ( 15 avg)
% 0.20/0.46 % Number of connectives : 11 ( 3 ~; 0 |; 4 &; 4 @)
% 0.20/0.46 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.20/0.46 % Maximal formula depth : 7 ( 7 avg)
% 0.20/0.46 % Number of types : 1 ( 0 usr)
% 0.20/0.46 % Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% 0.20/0.46 % Number of symbols : 6 ( 4 usr; 3 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(g,type,
% 0.20/0.46 g: $o > $o ).
% 0.20/0.46
% 0.20/0.46 thf(p,type,
% 0.20/0.46 p: ( $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(y,type,
% 0.20/0.46 y: $o ).
% 0.20/0.46
% 0.20/0.46 thf(4,axiom,
% 0.20/0.46 ( ( x != y )
% 0.20/0.46 & ( ( g @ x )
% 0.20/0.46 = y )
% 0.20/0.46 & ( ( g @ y )
% 0.20/0.46 = x )
% 0.20/0.46 & ( p @ g )
% 0.20/0.46 & ~ ( p @ (~) ) ) ).
% 0.20/0.46
% 0.20/0.46 %------------------------------------------------------------------------------
% 0.20/0.46 ------------------------
% 1.47/1.40 ---- Embedded in THF ---
% 1.66/1.40 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.66/1.40 %%% Generated on Tue Feb 24 14:22:47 EST 2026
% 1.66/1.40 %%% using '$$dhol' embedding, version 1.3.0.
% 1.66/1.40 %%% Logic specification used:
% 1.66/1.40 %%% thf(spec, logic, $$dhol).
% 1.66/1.40
% 1.66/1.40 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.4ffxeAIhVl/DTF2DTF9877.p
% See solution above
% 1.66/1.40 ------------------------
% 1.66/1.41 ---- Cleaned THF ---
% 1.66/1.41 thf(g,type,
% 1.66/1.41 g: $o > $o ).
% 1.66/1.41
% 1.66/1.41 thf(p,type,
% 1.66/1.41 p: ( $o > $o ) > $o ).
% 1.66/1.41
% 1.66/1.41 thf(x,type,
% 1.66/1.41 x: $o ).
% 1.66/1.41
% 1.66/1.41 thf(y,type,
% 1.66/1.41 y: $o ).
% 1.66/1.41
% 1.66/1.41 thf(4,axiom,
% 1.66/1.41 ( ( x != y )
% 1.66/1.41 & ( ( g @ x )
% 1.66/1.41 = y )
% 1.66/1.41 & ( ( g @ y )
% 1.66/1.41 = x )
% 1.66/1.41 & ( p @ g )
% 1.66/1.41 & ~ ( p @ (~) ) ) ).
% 1.66/1.41 ------------------------
% 1.66/1.43 % (9976)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_9877 for (3000ds/27Mi)
% 1.66/1.43 % (9975)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_9877 for (3000ds/4Mi)
% 1.66/1.43 % (9974)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_9877 for (3000ds/183Mi)
% 1.66/1.43 % (9977)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_9877 for (3000ds/2Mi)
% 1.66/1.43 % (9978)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_9877 for (3000ds/2Mi)
% 1.66/1.43 % (9980)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_9877 for (3000ds/18Mi)
% 1.66/1.43 % (9979)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_9877 for (3000ds/275Mi)
% 1.66/1.43 % (9979)Refutation not found, incomplete strategy
% 1.66/1.43 % (9979)------------------------------
% 1.66/1.43 % (9979)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.43 % (9979)Termination reason: Refutation not found, incomplete strategy
% 1.66/1.43
% 1.66/1.43
% 1.66/1.43 % (9979)Memory used [KB]: 5373
% 1.66/1.43 % (9979)Time elapsed: 0.002 s
% 1.66/1.43 % (9979)Instructions burned: 1 (million)
% 1.66/1.43 % (9979)------------------------------
% 1.66/1.43 % (9979)------------------------------
% 1.66/1.43 % (9978)Refutation not found, incomplete strategy
% 1.66/1.43 % (9978)------------------------------
% 1.66/1.43 % (9978)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.43 % (9978)Termination reason: Refutation not found, incomplete strategy
% 1.66/1.43
% 1.66/1.43
% 1.66/1.43 % (9978)Memory used [KB]: 5500
% 1.66/1.43 % (9978)Time elapsed: 0.002 s
% 1.66/1.43 % (9978)Instructions burned: 1 (million)
% 1.66/1.43 % (9978)------------------------------
% 1.66/1.43 % (9978)------------------------------
% 1.66/1.43 % (9976)Refutation not found, incomplete strategy
% 1.66/1.43 % (9976)------------------------------
% 1.66/1.43 % (9976)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.43 % (9976)Termination reason: Refutation not found, incomplete strategy
% 1.66/1.43
% 1.66/1.43
% 1.66/1.43 % (9976)Memory used [KB]: 5500
% 1.66/1.43 % (9976)Time elapsed: 0.004 s
% 1.66/1.43 % (9976)Instructions burned: 1 (million)
% 1.66/1.43 % (9977)Instruction limit reached!
% 1.66/1.43 % (9977)------------------------------
% 1.66/1.43 % (9977)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.43 % (9976)------------------------------
% 1.66/1.43 % (9976)------------------------------
% 1.66/1.43 % (9977)Termination reason: Unknown
% 1.66/1.43 % (9977)Termination phase: Saturation
% 1.66/1.43
% 1.66/1.43 % (9977)Memory used [KB]: 5500
% 1.66/1.43 % (9977)Time elapsed: 0.003 s
% 1.66/1.43 % (9977)Instructions burned: 2 (million)
% 1.66/1.43 % (9977)------------------------------
% 1.66/1.43 % (9977)------------------------------
% 1.66/1.43 % (9975)Refutation not found, incomplete strategy
% 1.66/1.43 % (9975)------------------------------
% 1.66/1.43 % (9975)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.43 % (9975)Termination reason: Refutation not found, incomplete strategy
% 1.66/1.43
% 1.66/1.43
% 1.66/1.43 % (9975)Memory used [KB]: 5500
% 1.66/1.43 % (9975)Time elapsed: 0.004 s
% 1.66/1.43 % (9975)Instructions burned: 2 (million)
% 1.66/1.43 % (9975)------------------------------
% 1.66/1.43 % (9975)------------------------------
% 1.66/1.43 % (9980)Refutation not found, incomplete strategy
% 1.66/1.43 % (9980)------------------------------
% 1.66/1.43 % (9980)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.43 % (9980)Termination reason: Refutation not found, incomplete strategy
% 1.66/1.43
% 1.66/1.43
% 1.66/1.43 % (9980)Memory used [KB]: 5500
% 1.66/1.43 % (9980)Time elapsed: 0.004 s
% 1.66/1.43 % (9980)Instructions burned: 4 (million)
% 1.66/1.43 % (9980)------------------------------
% 1.66/1.43 % (9980)------------------------------
% 1.66/1.43 % (9974)First to succeed.
% 1.66/1.43 % (9974)Refutation found. Thanks to Tanya!
% 1.66/1.43 % SZS status Unsatisfiable for DTF2THF_9877
% 1.66/1.43 % SZS output start Proof for DTF2THF_9877
% 1.66/1.43 thf(func_def_0, type, g: $o > $o).
% 1.66/1.43 thf(func_def_1, type, p: ($o > $o) > $o).
% 1.66/1.43 thf(func_def_9, type, ph1: !>[X0: $tType]:(X0)).
% 1.66/1.43 thf(f309,plain,(
% 1.66/1.43 $false),
% 1.66/1.43 inference(avatar_sat_refutation,[status(thm)],[f25,f34,f39,f44,f50,f68,f77,f104,f203,f216,f223,f297,f305])).
% 1.66/1.43 thf(f305,plain,(
% 1.66/1.43 ~spl0_2 | spl0_5 | ~spl0_8 | ~spl0_9),
% 1.66/1.43 inference(avatar_contradiction_clause,[status(thm)],[f304])).
% 1.66/1.43 thf(f304,plain,(
% 1.66/1.43 $false | (~spl0_2 | spl0_5 | ~spl0_8 | ~spl0_9)),
% 1.66/1.43 inference(subsumption_resolution,[status(thm)],[f299,f270])).
% 1.66/1.43 thf(f270,plain,(
% 1.66/1.43 ($true = (g @ $true)) | (~spl0_8 | ~spl0_9)),
% 1.66/1.43 inference(superposition,[status(thm)],[f67,f72])).
% 1.66/1.43 thf(f72,plain,(
% 1.66/1.43 (sK2 = $true) | ~spl0_9),
% 1.66/1.43 inference(avatar_component_clause,[status(thm)],[f70])).
% 1.66/1.43 thf(f70,definition,(
% 1.66/1.43 spl0_9 <=> (sK2 = $true)),
% 1.66/1.43 introduced(definition,[new_symbols(naming,[spl0_9])],[avatar_definition])).
% 1.66/1.43 thf(f67,plain,(
% 1.66/1.43 ($true = (g @ sK2)) | ~spl0_8),
% 1.66/1.44 inference(avatar_component_clause,[status(thm)],[f65])).
% 1.66/1.44 thf(f65,definition,(
% 1.66/1.44 spl0_8 <=> ($true = (g @ sK2))),
% 1.66/1.44 introduced(definition,[new_symbols(naming,[spl0_8])],[avatar_definition])).
% 1.66/1.44 thf(f299,plain,(
% 1.66/1.44 ($true != (g @ $true)) | (~spl0_2 | spl0_5)),
% 1.66/1.44 inference(superposition,[status(thm)],[f37,f24])).
% 1.66/1.44 thf(f24,plain,(
% 1.66/1.44 (y = $true) | ~spl0_2),
% 1.66/1.44 inference(avatar_component_clause,[status(thm)],[f22])).
% 1.66/1.44 thf(f22,definition,(
% 1.66/1.44 spl0_2 <=> (y = $true)),
% 1.66/1.44 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])).
% 1.66/1.44 thf(f37,plain,(
% 1.66/1.44 ((g @ y) != $true) | spl0_5),
% 1.66/1.44 inference(avatar_component_clause,[status(thm)],[f36])).
% 1.66/1.44 thf(f36,definition,(
% 1.66/1.44 spl0_5 <=> ((g @ y) = $true)),
% 1.66/1.44 introduced(definition,[new_symbols(naming,[spl0_5])],[avatar_definition])).
% 1.66/1.44 thf(f297,plain,(
% 1.66/1.44 ~spl0_1 | spl0_6 | spl0_7 | ~spl0_8),
% 1.66/1.44 inference(avatar_contradiction_clause,[status(thm)],[f296])).
% 1.66/1.44 thf(f296,plain,(
% 1.66/1.44 $false | (~spl0_1 | spl0_6 | spl0_7 | ~spl0_8)),
% 1.66/1.44 inference(subsumption_resolution,[status(thm)],[f295,f42])).
% 1.66/1.44 thf(f42,plain,(
% 1.66/1.44 ((g @ y) != $false) | spl0_6),
% 1.66/1.44 inference(avatar_component_clause,[status(thm)],[f41])).
% 1.66/1.44 thf(f41,definition,(
% 1.66/1.44 spl0_6 <=> ((g @ y) = $false)),
% 1.66/1.44 introduced(definition,[new_symbols(naming,[spl0_6])],[avatar_definition])).
% 1.66/1.44 thf(f295,plain,(
% 1.66/1.44 ((g @ y) = $false) | (~spl0_1 | spl0_7 | ~spl0_8)),
% 1.66/1.44 inference(subsumption_resolution,[status(thm)],[f288,f62])).
% 1.66/1.44 thf(f62,plain,(
% 1.66/1.44 (sK2 != $false) | spl0_7),
% 1.66/1.44 inference(avatar_component_clause,[status(thm)],[f61])).
% 1.66/1.44 thf(f61,definition,(
% 1.66/1.44 spl0_7 <=> (sK2 = $false)),
% 1.66/1.44 introduced(definition,[new_symbols(naming,[spl0_7])],[avatar_definition])).
% 1.66/1.44 thf(f288,plain,(
% 1.66/1.44 (sK2 = $false) | ((g @ y) = $false) | (~spl0_1 | ~spl0_8)),
% 1.66/1.44 inference(binary_proxy_clausification,[status(thm)],[f286])).
% 1.66/1.44 thf(f286,plain,(
% 1.66/1.44 ((g @ y) != sK2) | (~spl0_1 | ~spl0_8)),
% 1.66/1.44 inference(trivial_inequality_removal,[status(thm)],[f274])).
% 1.66/1.44 thf(f274,plain,(
% 1.66/1.44 ($true = $false) | ((g @ y) != sK2) | (~spl0_1 | ~spl0_8)),
% 1.66/1.44 inference(constrained_superposition,[status(thm)],[f20,f67])).
% 1.66/1.44 thf(f20,plain,(
% 1.66/1.44 ((g @ (g @ y)) = $false) | ~spl0_1),
% 1.66/1.44 inference(avatar_component_clause,[status(thm)],[f18])).
% 1.66/1.44 thf(f18,definition,(
% 1.66/1.44 spl0_1 <=> ((g @ (g @ y)) = $false)),
% 1.66/1.44 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 1.66/1.44 thf(f223,plain,(
% 1.66/1.44 spl0_9 | spl0_2 | ~spl0_5 | ~spl0_10),
% 1.66/1.44 inference(avatar_split_clause,[status(thm)],[f222,f74,f36,f22,f70])).
% 1.66/1.44 thf(f74,definition,(
% 1.66/1.44 spl0_10 <=> ($false = (g @ sK2))),
% 1.66/1.44 introduced(definition,[new_symbols(naming,[spl0_10])],[avatar_definition])).
% 1.66/1.44 thf(f222,plain,(
% 1.66/1.44 (sK2 = $true) | (spl0_2 | ~spl0_5 | ~spl0_10)),
% 1.66/1.44 inference(subsumption_resolution,[status(thm)],[f213,f23])).
% 1.66/1.44 thf(f23,plain,(
% 1.66/1.44 (y != $true) | spl0_2),
% 1.66/1.44 inference(avatar_component_clause,[status(thm)],[f22])).
% 1.66/1.44 thf(f213,plain,(
% 1.66/1.44 (y = $true) | (sK2 = $true) | (~spl0_5 | ~spl0_10)),
% 1.66/1.44 inference(binary_proxy_clausification,[status(thm)],[f212])).
% 1.66/1.44 thf(f212,plain,(
% 1.66/1.44 (y != sK2) | (~spl0_5 | ~spl0_10)),
% 1.66/1.44 inference(trivial_inequality_removal,[status(thm)],[f209])).
% 1.66/1.44 thf(f209,plain,(
% 1.66/1.44 ($true = $false) | (y != sK2) | (~spl0_5 | ~spl0_10)),
% 1.66/1.44 inference(constrained_superposition,[status(thm)],[f76,f38])).
% 1.66/1.44 thf(f38,plain,(
% 1.66/1.44 ((g @ y) = $true) | ~spl0_5),
% 1.66/1.44 inference(avatar_component_clause,[status(thm)],[f36])).
% 1.66/1.44 thf(f76,plain,(
% 1.66/1.44 ($false = (g @ sK2)) | ~spl0_10),
% 1.66/1.44 inference(avatar_component_clause,[status(thm)],[f74])).
% 1.66/1.44 thf(f216,plain,(
% 1.66/1.44 ~spl0_5 | ~spl0_6),
% 1.66/1.44 inference(avatar_contradiction_clause,[status(thm)],[f215])).
% 1.66/1.44 thf(f215,plain,(
% 1.66/1.44 $false | (~spl0_5 | ~spl0_6)),
% 1.66/1.44 inference(trivial_inequality_removal,[status(thm)],[f208])).
% 1.66/1.44 thf(f208,plain,(
% 1.66/1.44 ($true = $false) | (~spl0_5 | ~spl0_6)),
% 1.66/1.44 inference(superposition,[status(thm)],[f43,f38])).
% 1.66/1.44 thf(f43,plain,(
% 1.66/1.44 ((g @ y) = $false) | ~spl0_6),
% 1.66/1.44 inference(avatar_component_clause,[status(thm)],[f41])).
% 1.66/1.44 thf(f203,plain,(
% 1.66/1.44 spl0_5 | ~spl0_4 | spl0_9 | ~spl0_10),
% 1.66/1.44 inference(avatar_split_clause,[status(thm)],[f202,f74,f70,f31,f36])).
% 1.66/1.44 thf(f31,definition,(
% 1.66/1.44 spl0_4 <=> ((g @ (g @ y)) = $true)),
% 1.66/1.44 introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition])).
% 1.66/1.44 thf(f202,plain,(
% 1.66/1.44 ((g @ y) = $true) | (~spl0_4 | spl0_9 | ~spl0_10)),
% 1.66/1.44 inference(subsumption_resolution,[status(thm)],[f177,f71])).
% 1.66/1.44 thf(f71,plain,(
% 1.66/1.44 (sK2 != $true) | spl0_9),
% 1.66/1.44 inference(avatar_component_clause,[status(thm)],[f70])).
% 1.66/1.44 thf(f177,plain,(
% 1.66/1.44 (sK2 = $true) | ((g @ y) = $true) | (~spl0_4 | ~spl0_10)),
% 1.66/1.44 inference(binary_proxy_clausification,[status(thm)],[f176])).
% 1.66/1.44 thf(f176,plain,(
% 1.66/1.44 ((g @ y) != sK2) | (~spl0_4 | ~spl0_10)),
% 1.66/1.44 inference(trivial_inequality_removal,[status(thm)],[f175])).
% 1.66/1.44 thf(f175,plain,(
% 1.66/1.44 ((g @ y) != sK2) | ($true = $false) | (~spl0_4 | ~spl0_10)),
% 1.66/1.44 inference(constrained_superposition,[status(thm)],[f76,f33])).
% 1.66/1.44 thf(f33,plain,(
% 1.66/1.44 ((g @ (g @ y)) = $true) | ~spl0_4),
% 1.66/1.44 inference(avatar_component_clause,[status(thm)],[f31])).
% 1.66/1.44 thf(f104,plain,(
% 1.66/1.44 ~spl0_7 | ~spl0_9),
% 1.66/1.44 inference(avatar_contradiction_clause,[status(thm)],[f103])).
% 1.66/1.44 thf(f103,plain,(
% 1.66/1.44 $false | (~spl0_7 | ~spl0_9)),
% 1.66/1.44 inference(trivial_inequality_removal,[status(thm)],[f99])).
% 1.66/1.44 thf(f99,plain,(
% 1.66/1.44 ($true = $false) | (~spl0_7 | ~spl0_9)),
% 1.66/1.44 inference(superposition,[status(thm)],[f72,f63])).
% 1.66/1.44 thf(f63,plain,(
% 1.66/1.44 (sK2 = $false) | ~spl0_7),
% 1.66/1.44 inference(avatar_component_clause,[status(thm)],[f61])).
% 1.66/1.44 thf(f77,plain,(
% 1.66/1.44 spl0_9 | spl0_10),
% 1.66/1.44 inference(avatar_split_clause,[status(thm)],[f58,f74,f70])).
% 1.66/1.44 thf(f58,plain,(
% 1.66/1.44 (sK2 = $true) | ($false = (g @ sK2))),
% 1.66/1.44 inference(not_proxy_clausification,[status(thm)],[f57])).
% 1.66/1.44 thf(f57,plain,(
% 1.66/1.44 ($false = (g @ sK2)) | ($false = (~ sK2))),
% 1.66/1.44 inference(binary_proxy_clausification,[status(thm)],[f55])).
% 1.66/1.44 thf(f55,plain,(
% 1.66/1.44 ((~ sK2) != (g @ sK2))),
% 1.66/1.44 inference(negative_extensionality,[status(thm)],[f54])).
% 1.66/1.44 thf(f54,plain,(
% 1.66/1.44 (g != ~)),
% 1.66/1.44 inference(trivial_inequality_removal,[status(thm)],[f53])).
% 1.66/1.44 thf(f53,plain,(
% 1.66/1.44 (g != ~) | ($true != $true)),
% 1.66/1.44 inference(constrained_superposition,[status(thm)],[f7,f8])).
% 1.66/1.44 thf(f8,plain,(
% 1.66/1.44 ((p @ g) = $true)),
% 1.66/1.44 inference(cnf_transformation,[status(thm)],[f5])).
% 1.66/1.44 thf(f5,plain,(
% 1.66/1.44 (x != y) & (x = (g @ y)) & ((p @ g) = $true) & ((p @ ~) != $true) & (y = (g @ x))),
% 1.66/1.44 inference(flattening,[status(thm)],[f4])).
% 1.66/1.44 thf(f4,plain,(
% 1.66/1.44 (y = (g @ x)) & ((p @ g) = $true) & (x != y) & (x = (g @ y)) & ~((p @ ~) = $true)),
% 1.66/1.44 inference(fool_elimination,[status(thm)],[f3])).
% 1.66/1.44 thf(f3,plain,(
% 1.66/1.44 (y = (g @ x)) & (p @ g) & (x != y) & (x = (g @ y)) & ~(p @ ~)),
% 1.66/1.44 inference(rectify,[status(thm)],[f1])).
% 1.66/1.44 thf(f1,axiom,(
% 1.66/1.44 (y = (g @ x)) & (p @ g) & (x != y) & (x = (g @ y)) & ~(p @ ~)),
% 1.66/1.44 file('/export/starexec/sandbox/tmp/tmp.4ffxeAIhVl/DTF2THF_9877.p',4)).
% 1.66/1.44 thf(f7,plain,(
% 1.66/1.44 ((p @ ~) != $true)),
% 1.66/1.44 inference(cnf_transformation,[status(thm)],[f5])).
% 1.66/1.44 thf(f68,plain,(
% 1.66/1.44 spl0_7 | spl0_8),
% 1.66/1.44 inference(avatar_split_clause,[status(thm)],[f59,f65,f61])).
% 1.66/1.44 thf(f59,plain,(
% 1.66/1.44 ($true = (g @ sK2)) | (sK2 = $false)),
% 1.66/1.44 inference(not_proxy_clausification,[status(thm)],[f56])).
% 1.66/1.44 thf(f56,plain,(
% 1.66/1.44 ($true = (~ sK2)) | ($true = (g @ sK2))),
% 1.66/1.44 inference(binary_proxy_clausification,[status(thm)],[f55])).
% 1.66/1.44 thf(f50,plain,(
% 1.66/1.44 ~spl0_2 | ~spl0_3),
% 1.66/1.44 inference(avatar_contradiction_clause,[status(thm)],[f49])).
% 1.66/1.44 thf(f49,plain,(
% 1.66/1.44 $false | (~spl0_2 | ~spl0_3)),
% 1.66/1.44 inference(trivial_inequality_removal,[status(thm)],[f45])).
% 1.66/1.44 thf(f45,plain,(
% 1.66/1.44 ($true = $false) | (~spl0_2 | ~spl0_3)),
% 1.66/1.44 inference(superposition,[status(thm)],[f29,f24])).
% 1.66/1.44 thf(f29,plain,(
% 1.66/1.44 (y = $false) | ~spl0_3),
% 1.66/1.44 inference(avatar_component_clause,[status(thm)],[f27])).
% 1.66/1.44 thf(f27,definition,(
% 1.66/1.44 spl0_3 <=> (y = $false)),
% 1.66/1.44 introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition])).
% 1.66/1.44 thf(f44,plain,(
% 1.66/1.44 spl0_6 | spl0_3),
% 1.66/1.44 inference(avatar_split_clause,[status(thm)],[f14,f27,f41])).
% 1.66/1.44 thf(f14,plain,(
% 1.66/1.44 ((g @ y) = $false) | (y = $false)),
% 1.66/1.44 inference(binary_proxy_clausification,[status(thm)],[f12])).
% 1.66/1.44 thf(f12,plain,(
% 1.66/1.44 (y != (g @ y))),
% 1.66/1.44 inference(definition_unfolding,[status(thm)],[f10,f9])).
% 1.66/1.44 thf(f9,plain,(
% 1.66/1.44 (x = (g @ y))),
% 1.66/1.44 inference(cnf_transformation,[status(thm)],[f5])).
% 1.66/1.44 thf(f10,plain,(
% 1.66/1.44 (x != y)),
% 1.66/1.44 inference(cnf_transformation,[status(thm)],[f5])).
% 1.66/1.44 thf(f39,plain,(
% 1.66/1.44 spl0_2 | spl0_5),
% 1.66/1.44 inference(avatar_split_clause,[status(thm)],[f13,f36,f22])).
% 1.66/1.44 thf(f13,plain,(
% 1.66/1.44 ((g @ y) = $true) | (y = $true)),
% 1.66/1.44 inference(binary_proxy_clausification,[status(thm)],[f12])).
% 1.66/1.44 thf(f34,plain,(
% 1.66/1.44 spl0_3 | spl0_4),
% 1.66/1.44 inference(avatar_split_clause,[status(thm)],[f16,f31,f27])).
% 1.66/1.44 thf(f16,plain,(
% 1.66/1.44 ((g @ (g @ y)) = $true) | (y = $false)),
% 1.66/1.44 inference(binary_proxy_clausification,[status(thm)],[f11])).
% 1.66/1.44 thf(f11,plain,(
% 1.66/1.44 (y = (g @ (g @ y)))),
% 1.66/1.44 inference(definition_unfolding,[status(thm)],[f6,f9])).
% 1.66/1.44 thf(f6,plain,(
% 1.66/1.44 (y = (g @ x))),
% 1.66/1.44 inference(cnf_transformation,[status(thm)],[f5])).
% 1.66/1.44 thf(f25,plain,(
% 1.66/1.44 spl0_1 | spl0_2),
% 1.66/1.44 inference(avatar_split_clause,[status(thm)],[f15,f22,f18])).
% 1.66/1.44 thf(f15,plain,(
% 1.66/1.44 ((g @ (g @ y)) = $false) | (y = $true)),
% 1.66/1.44 inference(binary_proxy_clausification,[status(thm)],[f11])).
% 1.66/1.44 % SZS output end Proof for DTF2THF_9877
% 1.66/1.44 % (9974)------------------------------
% 1.66/1.44 % (9974)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.44 % (9974)Termination reason: Refutation
% 1.66/1.44
% 1.66/1.44 % (9974)Memory used [KB]: 5628
% 1.66/1.44 % (9974)Time elapsed: 0.009 s
% 1.66/1.44 % (9974)Instructions burned: 11 (million)
% 1.66/1.44 % (9974)------------------------------
% 1.66/1.44 % (9974)------------------------------
% 1.66/1.44 % (9973)Success in time 0.021 s
%------------------------------------------------------------------------------