%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO500^1 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n011.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 09:54:23 AM UTC 2026
% Result : Theorem 1.60s 1.30s
% Output : Refutation 1.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 10
% Syntax : Number of formulae : 73 ( 5 unt; 0 typ; 9 def)
% Number of atoms : 397 ( 60 equ; 0 cnn)
% Maximal formula atoms : 5 ( 5 avg)
% Number of connectives : 325 ( 121 ~; 125 |; 0 &; 70 @)
% ( 9 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 4 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 12 usr; 12 con; 0-2 aty)
% Number of variables : 0 ( 0 ^; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
f: $o > $o ).
thf(func_def_6,type,
ph1:
!>[X0: $tType] : X0 ).
thf(f140,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f16,f25,f28,f49,f65,f66,f68,f72,f81,f90,f119,f123,f127,f139]) ).
thf(f139,plain,
( ~ spl0_1
| ~ spl0_8
| ~ spl0_9 ),
inference(avatar_contradiction_clause,[status(thm)],[f138]) ).
thf(f138,plain,
( $false
| ~ spl0_1
| ~ spl0_8
| ~ spl0_9 ),
inference(trivial_inequality_removal,[status(thm)],[f137]) ).
thf(f137,plain,
( ( $true = $false )
| ~ spl0_1
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[status(thm)],[f132,f63]) ).
thf(f63,plain,
( ( $false
= ( f @ $false ) )
| ~ spl0_9 ),
inference(avatar_component_clause,[status(thm)],[f61]) ).
thf(f61,definition,
( spl0_9
<=> ( $false
= ( f @ $false ) ) ),
introduced(definition,[new_symbols(naming,[spl0_9])],[avatar_definition]) ).
thf(f132,plain,
( ( $true
= ( f @ $false ) )
| ~ spl0_1
| ~ spl0_8 ),
inference(backward_demodulation,[status(thm)],[f11,f58]) ).
thf(f58,plain,
( ( x = $false )
| ~ spl0_8 ),
inference(avatar_component_clause,[status(thm)],[f56]) ).
thf(f56,definition,
( spl0_8
<=> ( x = $false ) ),
introduced(definition,[new_symbols(naming,[spl0_8])],[avatar_definition]) ).
thf(f11,plain,
( ( ( f @ x )
= $true )
| ~ spl0_1 ),
inference(avatar_component_clause,[status(thm)],[f9]) ).
thf(f9,definition,
( spl0_1
<=> ( ( f @ x )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition]) ).
thf(f127,plain,
( ~ spl0_1
| spl0_2
| ~ spl0_7 ),
inference(avatar_contradiction_clause,[status(thm)],[f126]) ).
thf(f126,plain,
( $false
| ~ spl0_1
| spl0_2
| ~ spl0_7 ),
inference(subsumption_resolution,[status(thm)],[f125,f53]) ).
thf(f53,plain,
( ( $true
= ( f @ $true ) )
| ~ spl0_7 ),
inference(avatar_component_clause,[status(thm)],[f51]) ).
thf(f51,definition,
( spl0_7
<=> ( $true
= ( f @ $true ) ) ),
introduced(definition,[new_symbols(naming,[spl0_7])],[avatar_definition]) ).
thf(f125,plain,
( ( $true
!= ( f @ $true ) )
| ~ spl0_1
| spl0_2
| ~ spl0_7 ),
inference(forward_demodulation,[status(thm)],[f124,f53]) ).
thf(f124,plain,
( ( ( f @ ( f @ $true ) )
!= $true )
| ~ spl0_1
| spl0_2 ),
inference(forward_demodulation,[status(thm)],[f14,f11]) ).
thf(f14,plain,
( ( ( f @ ( f @ ( f @ x ) ) )
!= $true )
| spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f13]) ).
thf(f13,definition,
( spl0_2
<=> ( ( f @ ( f @ ( f @ x ) ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition]) ).
thf(f123,plain,
( ~ spl0_1
| ~ spl0_4 ),
inference(avatar_contradiction_clause,[status(thm)],[f122]) ).
thf(f122,plain,
( $false
| ~ spl0_1
| ~ spl0_4 ),
inference(trivial_inequality_removal,[status(thm)],[f121]) ).
thf(f121,plain,
( ( $true = $false )
| ~ spl0_1
| ~ spl0_4 ),
inference(forward_demodulation,[status(thm)],[f11,f24]) ).
thf(f24,plain,
( ( ( f @ x )
= $false )
| ~ spl0_4 ),
inference(avatar_component_clause,[status(thm)],[f22]) ).
thf(f22,definition,
( spl0_4
<=> ( ( f @ x )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition]) ).
thf(f119,plain,
( ~ spl0_2
| ~ spl0_4
| spl0_8
| spl0_9 ),
inference(avatar_contradiction_clause,[status(thm)],[f118]) ).
thf(f118,plain,
( $false
| ~ spl0_2
| ~ spl0_4
| spl0_8
| spl0_9 ),
inference(subsumption_resolution,[status(thm)],[f117,f62]) ).
thf(f62,plain,
( ( $false
!= ( f @ $false ) )
| spl0_9 ),
inference(avatar_component_clause,[status(thm)],[f61]) ).
thf(f117,plain,
( ( $false
= ( f @ $false ) )
| ~ spl0_2
| ~ spl0_4
| spl0_8 ),
inference(subsumption_resolution,[status(thm)],[f107,f57]) ).
thf(f57,plain,
( ( x != $false )
| spl0_8 ),
inference(avatar_component_clause,[status(thm)],[f56]) ).
thf(f107,plain,
( ( x = $false )
| ( $false
= ( f @ $false ) )
| ~ spl0_2
| ~ spl0_4 ),
inference(binary_proxy_clausification,[status(thm)],[f105]) ).
thf(f105,plain,
( ( x
!= ( f @ $false ) )
| ~ spl0_2
| ~ spl0_4 ),
inference(trivial_inequality_removal,[status(thm)],[f101]) ).
thf(f101,plain,
( ( $true = $false )
| ( x
!= ( f @ $false ) )
| ~ spl0_2
| ~ spl0_4 ),
inference(constrained_superposition,[status(thm)],[f77,f24]) ).
thf(f77,plain,
( ( ( f @ ( f @ $false ) )
= $true )
| ~ spl0_2
| ~ spl0_4 ),
inference(forward_demodulation,[status(thm)],[f15,f24]) ).
thf(f15,plain,
( ( ( f @ ( f @ ( f @ x ) ) )
= $true )
| ~ spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f13]) ).
thf(f90,plain,
( ~ spl0_8
| ~ spl0_4
| spl0_9 ),
inference(avatar_split_clause,[status(thm)],[f89,f61,f22,f56]) ).
thf(f89,plain,
( ( x != $false )
| ~ spl0_4
| spl0_9 ),
inference(trivial_inequality_removal,[status(thm)],[f88]) ).
thf(f88,plain,
( ( x != $false )
| ( $false != $false )
| ~ spl0_4
| spl0_9 ),
inference(constrained_superposition,[status(thm)],[f62,f24]) ).
thf(f81,plain,
( ~ spl0_2
| ~ spl0_4
| ~ spl0_9 ),
inference(avatar_contradiction_clause,[status(thm)],[f80]) ).
thf(f80,plain,
( $false
| ~ spl0_2
| ~ spl0_4
| ~ spl0_9 ),
inference(trivial_inequality_removal,[status(thm)],[f79]) ).
thf(f79,plain,
( ( $true = $false )
| ~ spl0_2
| ~ spl0_4
| ~ spl0_9 ),
inference(forward_demodulation,[status(thm)],[f78,f63]) ).
thf(f78,plain,
( ( $true
= ( f @ $false ) )
| ~ spl0_2
| ~ spl0_4
| ~ spl0_9 ),
inference(forward_demodulation,[status(thm)],[f77,f63]) ).
thf(f72,plain,
( ~ spl0_1
| ~ spl0_5
| ~ spl0_6 ),
inference(avatar_contradiction_clause,[status(thm)],[f71]) ).
thf(f71,plain,
( $false
| ~ spl0_1
| ~ spl0_5
| ~ spl0_6 ),
inference(trivial_inequality_removal,[status(thm)],[f70]) ).
thf(f70,plain,
( ( $true = $false )
| ~ spl0_1
| ~ spl0_5
| ~ spl0_6 ),
inference(forward_demodulation,[status(thm)],[f69,f44]) ).
thf(f44,plain,
( ( $false
= ( f @ $true ) )
| ~ spl0_5 ),
inference(avatar_component_clause,[status(thm)],[f42]) ).
thf(f42,definition,
( spl0_5
<=> ( $false
= ( f @ $true ) ) ),
introduced(definition,[new_symbols(naming,[spl0_5])],[avatar_definition]) ).
thf(f69,plain,
( ( $true
= ( f @ $true ) )
| ~ spl0_1
| ~ spl0_6 ),
inference(backward_demodulation,[status(thm)],[f11,f47]) ).
thf(f47,plain,
( ( x = $true )
| ~ spl0_6 ),
inference(avatar_component_clause,[status(thm)],[f46]) ).
thf(f46,definition,
( spl0_6
<=> ( x = $true ) ),
introduced(definition,[new_symbols(naming,[spl0_6])],[avatar_definition]) ).
thf(f68,plain,
( spl0_9
| ~ spl0_1
| ~ spl0_3
| ~ spl0_5 ),
inference(avatar_split_clause,[status(thm)],[f67,f42,f18,f9,f61]) ).
thf(f18,definition,
( spl0_3
<=> ( ( f @ ( f @ ( f @ x ) ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition]) ).
thf(f67,plain,
( ( $false
= ( f @ $false ) )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_5 ),
inference(backward_demodulation,[status(thm)],[f30,f44]) ).
thf(f30,plain,
( ( ( f @ ( f @ $true ) )
= $false )
| ~ spl0_1
| ~ spl0_3 ),
inference(backward_demodulation,[status(thm)],[f20,f11]) ).
thf(f20,plain,
( ( ( f @ ( f @ ( f @ x ) ) )
= $false )
| ~ spl0_3 ),
inference(avatar_component_clause,[status(thm)],[f18]) ).
thf(f66,plain,
( spl0_5
| spl0_8
| ~ spl0_1
| ~ spl0_3 ),
inference(avatar_split_clause,[status(thm)],[f37,f18,f9,f56,f42]) ).
thf(f37,plain,
( ( $false
= ( f @ $true ) )
| ( x = $false )
| ~ spl0_1
| ~ spl0_3 ),
inference(binary_proxy_clausification,[status(thm)],[f35]) ).
thf(f35,plain,
( ( x
!= ( f @ $true ) )
| ~ spl0_1
| ~ spl0_3 ),
inference(trivial_inequality_removal,[status(thm)],[f34]) ).
thf(f34,plain,
( ( $true = $false )
| ( x
!= ( f @ $true ) )
| ~ spl0_1
| ~ spl0_3 ),
inference(constrained_superposition,[status(thm)],[f11,f30]) ).
thf(f65,plain,
( spl0_6
| spl0_7
| ~ spl0_1
| ~ spl0_3 ),
inference(avatar_split_clause,[status(thm)],[f36,f18,f9,f51,f46]) ).
thf(f36,plain,
( ( x = $true )
| ( $true
= ( f @ $true ) )
| ~ spl0_1
| ~ spl0_3 ),
inference(binary_proxy_clausification,[status(thm)],[f35]) ).
thf(f49,plain,
( spl0_5
| ~ spl0_6
| ~ spl0_1
| ~ spl0_3 ),
inference(avatar_split_clause,[status(thm)],[f32,f18,f9,f46,f42]) ).
thf(f32,plain,
( ( $false
= ( f @ $true ) )
| ( x != $true )
| ~ spl0_1
| ~ spl0_3 ),
inference(constrained_superposition,[status(thm)],[f30,f11]) ).
thf(f28,plain,
( ~ spl0_2
| ~ spl0_3 ),
inference(avatar_contradiction_clause,[status(thm)],[f27]) ).
thf(f27,plain,
( $false
| ~ spl0_2
| ~ spl0_3 ),
inference(trivial_inequality_removal,[status(thm)],[f26]) ).
thf(f26,plain,
( ( $true = $false )
| ~ spl0_2
| ~ spl0_3 ),
inference(backward_demodulation,[status(thm)],[f15,f20]) ).
thf(f25,plain,
( spl0_3
| spl0_4 ),
inference(avatar_split_clause,[status(thm)],[f7,f22,f18]) ).
thf(f7,plain,
( ( ( f @ ( f @ ( f @ x ) ) )
= $false )
| ( ( f @ x )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f5]) ).
thf(f5,plain,
( ( f @ x )
!= ( f @ ( f @ ( f @ x ) ) ) ),
inference(cnf_transformation,[status(thm)],[f4]) ).
thf(f4,plain,
( ( f @ x )
!= ( f @ ( f @ ( f @ x ) ) ) ),
inference(flattening,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
( ( f @ x )
!= ( f @ ( f @ ( f @ x ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ( f @ x )
= ( f @ ( f @ ( f @ x ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.UZcIHmZ2ap/DTF2THF_30495.p',con) ).
thf(f16,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f6,f13,f9]) ).
thf(f6,plain,
( ( ( f @ ( f @ ( f @ x ) ) )
= $true )
| ( ( f @ x )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO500^1 : TPTP v9.2.1. Released v4.0.0.
% 0.13/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.17/0.34 % Computer : n011.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 14:32:32 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.30/0.46 ---- Original DTF file ---
% 0.30/0.46 thf(spec,logic,$$dhol).
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 % File : SYO500^1 : TPTP v9.2.1. Released v4.0.0.
% 0.30/0.46 % Domain : Syntactic
% 0.30/0.46 % Problem : The Kaminski equation
% 0.30/0.46 % Version : Especial.
% 0.30/0.46 % English :
% 0.30/0.46
% 0.30/0.46 % Refs : [Kam09] Kaminski (2009), Email to Chris Benzmueller
% 0.30/0.46 % Source : [Kam09]
% 0.30/0.46 % Names :
% 0.30/0.46
% 0.30/0.46 % Status : Theorem
% 0.30/0.46 % Rating : 0.00 v9.0.0, 0.10 v8.2.0, 0.08 v8.1.0, 0.09 v7.5.0, 0.14 v7.4.0, 0.22 v7.2.0, 0.12 v7.1.0, 0.25 v7.0.0, 0.29 v6.4.0, 0.33 v6.3.0, 0.40 v6.2.0, 0.29 v5.5.0, 0.17 v5.4.0, 0.40 v5.3.0, 0.60 v4.1.0, 0.67 v4.0.1, 1.00 v4.0.0
% 0.30/0.46 % Syntax : Number of formulae : 3 ( 1 unt; 2 typ; 0 def)
% 0.30/0.46 % Number of atoms : 7 ( 1 equ; 0 cnn)
% 0.30/0.46 % Maximal formula atoms : 1 ( 7 avg)
% 0.30/0.46 % Number of connectives : 4 ( 0 ~; 0 |; 0 &; 4 @)
% 0.30/0.46 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.30/0.46 % Maximal formula depth : 1 ( 1 avg)
% 0.30/0.46 % Number of types : 1 ( 0 usr)
% 0.30/0.46 % Number of type conns : 1 ( 1 >; 0 *; 0 +; 0 <<)
% 0.30/0.46 % Number of symbols : 3 ( 2 usr; 1 con; 0-2 aty)
% 0.30/0.46 % Number of variables : 0 ( 0 ^; 0 !; 0 ?; 0 :)
% 0.30/0.46 % SPC : TH0_THM_EQU_NAR
% 0.30/0.46
% 0.30/0.46 % Comments : The fragment of simple type theory that restricts equations to
% 0.30/0.46 % base types and disallows lambda abstraction and quantification is
% 0.30/0.46 % decidable. This is an example.
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 thf(f,type,
% 0.30/0.46 f: $o > $o ).
% 0.30/0.46
% 0.30/0.46 thf(x,type,
% 0.30/0.46 x: $o ).
% 0.30/0.46
% 0.30/0.46 thf(con,conjecture,
% 0.30/0.46 ( ( f @ ( f @ ( f @ x ) ) )
% 0.30/0.46 = ( f @ x ) ) ).
% 0.30/0.46
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 ------------------------
% 1.47/1.26 ---- Embedded in THF ---
% 1.47/1.26 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.47/1.26 %%% Generated on Tue Feb 24 14:32:33 EST 2026
% 1.47/1.26 %%% using '$$dhol' embedding, version 1.3.0.
% 1.47/1.26 %%% Logic specification used:
% 1.47/1.26 %%% thf(spec, logic, $$dhol).
% 1.47/1.26
% 1.47/1.26 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.UZcIHmZ2ap/DTF2DTF30495.p
% See solution above
% 1.47/1.26 ------------------------
% 1.47/1.27 ---- Cleaned THF ---
% 1.47/1.27 thf(f,type,
% 1.47/1.27 f: $o > $o ).
% 1.47/1.27
% 1.47/1.27 thf(x,type,
% 1.47/1.27 x: $o ).
% 1.47/1.27
% 1.47/1.27 thf(con,conjecture,
% 1.47/1.27 ( ( f @ ( f @ ( f @ x ) ) )
% 1.47/1.27 = ( f @ x ) ) ).
% 1.47/1.27 ------------------------
% 1.47/1.29 % (30707)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_30495 for (2999ds/275Mi)
% 1.47/1.29 % (30705)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_30495 for (2999ds/2Mi)
% 1.47/1.29 % (30707)Refutation not found, incomplete strategy
% 1.47/1.29 % (30707)------------------------------
% 1.47/1.29 % (30707)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.47/1.29 % (30707)Termination reason: Refutation not found, incomplete strategy
% 1.47/1.29
% 1.47/1.29
% 1.47/1.29 % (30707)Memory used [KB]: 5500
% 1.47/1.29 % (30707)Time elapsed: 0.002 s
% 1.47/1.29 % (30707)Instructions burned: 1 (million)
% 1.47/1.29 % (30707)------------------------------
% 1.47/1.29 % (30707)------------------------------
% 1.47/1.29 % (30705)Refutation not found, incomplete strategy
% 1.47/1.29 % (30705)------------------------------
% 1.47/1.29 % (30705)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.47/1.29 % (30705)Termination reason: Refutation not found, incomplete strategy
% 1.47/1.29
% 1.47/1.29
% 1.47/1.29 % (30705)Memory used [KB]: 5500
% 1.47/1.29 % (30705)Time elapsed: 0.002 s
% 1.47/1.29 % (30705)Instructions burned: 1 (million)
% 1.47/1.29 % (30705)------------------------------
% 1.47/1.29 % (30705)------------------------------
% 1.47/1.29 % (30702)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_30495 for (2999ds/183Mi)
% 1.47/1.29 % (30703)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_30495 for (2999ds/4Mi)
% 1.47/1.29 % (30704)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_30495 for (2999ds/27Mi)
% 1.47/1.29 % (30706)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_30495 for (2999ds/2Mi)
% 1.47/1.29 % (30708)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_30495 for (2999ds/18Mi)
% 1.47/1.30 % (30706)Refutation not found, incomplete strategy
% 1.47/1.30 % (30706)------------------------------
% 1.47/1.30 % (30706)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.47/1.30 % (30706)Termination reason: Refutation not found, incomplete strategy
% 1.47/1.30
% 1.47/1.30
% 1.47/1.30 % (30706)Memory used [KB]: 5500
% 1.47/1.30 % (30706)Time elapsed: 0.003 s
% 1.47/1.30 % (30706)Instructions burned: 1 (million)
% 1.47/1.30 % (30706)------------------------------
% 1.47/1.30 % (30706)------------------------------
% 1.47/1.30 % (30704)Refutation not found, incomplete strategy
% 1.47/1.30 % (30704)------------------------------
% 1.47/1.30 % (30704)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.47/1.30 % (30704)Termination reason: Refutation not found, incomplete strategy
% 1.47/1.30
% 1.47/1.30
% 1.47/1.30 % (30704)Memory used [KB]: 5500
% 1.47/1.30 % (30704)Time elapsed: 0.004 s
% 1.47/1.30 % (30704)Instructions burned: 1 (million)
% 1.47/1.30 % (30704)------------------------------
% 1.47/1.30 % (30704)------------------------------
% 1.60/1.30 % (30703)Instruction limit reached!
% 1.60/1.30 % (30703)------------------------------
% 1.60/1.30 % (30703)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.60/1.30 % (30703)Termination reason: Unknown
% 1.60/1.30 % (30703)Termination phase: Saturation
% 1.60/1.30
% 1.60/1.30 % (30703)Memory used [KB]: 5500
% 1.60/1.30 % (30703)Time elapsed: 0.006 s
% 1.60/1.30 % (30703)Instructions burned: 5 (million)
% 1.60/1.30 % (30703)------------------------------
% 1.60/1.30 % (30703)------------------------------
% 1.60/1.30 % (30709)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_30495 for (2999ds/3Mi)
% 1.60/1.30 % (30709)Refutation not found, incomplete strategy
% 1.60/1.30 % (30709)------------------------------
% 1.60/1.30 % (30709)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.60/1.30 % (30709)Termination reason: Refutation not found, incomplete strategy
% 1.60/1.30
% 1.60/1.30
% 1.60/1.30 % (30709)Memory used [KB]: 5373
% 1.60/1.30 % (30709)Time elapsed: 0.001 s
% 1.60/1.30 % (30709)------------------------------
% 1.60/1.30 % (30709)------------------------------
% 1.60/1.30 % (30710)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_30495 for (2999ds/37Mi)
% 1.60/1.30 % (30708)First to succeed.
% 1.60/1.30 % (30708)Refutation found. Thanks to Tanya!
% 1.60/1.30 % SZS status Theorem for DTF2THF_30495
% 1.60/1.30 % SZS output start Proof for DTF2THF_30495
% 1.60/1.30 thf(func_def_0, type, f: $o > $o).
% 1.60/1.30 thf(func_def_6, type, ph1: !>[X0: $tType]:(X0)).
% 1.60/1.30 thf(f140,plain,(
% 1.60/1.30 $false),
% 1.60/1.30 inference(avatar_sat_refutation,[status(thm)],[f16,f25,f28,f49,f65,f66,f68,f72,f81,f90,f119,f123,f127,f139])).
% 1.60/1.30 thf(f139,plain,(
% 1.60/1.30 ~spl0_1 | ~spl0_8 | ~spl0_9),
% 1.60/1.30 inference(avatar_contradiction_clause,[status(thm)],[f138])).
% 1.60/1.30 thf(f138,plain,(
% 1.60/1.30 $false | (~spl0_1 | ~spl0_8 | ~spl0_9)),
% 1.60/1.30 inference(trivial_inequality_removal,[status(thm)],[f137])).
% 1.60/1.30 thf(f137,plain,(
% 1.60/1.30 ($true = $false) | (~spl0_1 | ~spl0_8 | ~spl0_9)),
% 1.60/1.30 inference(forward_demodulation,[status(thm)],[f132,f63])).
% 1.60/1.30 thf(f63,plain,(
% 1.60/1.30 ($false = (f @ $false)) | ~spl0_9),
% 1.60/1.30 inference(avatar_component_clause,[status(thm)],[f61])).
% 1.60/1.30 thf(f61,definition,(
% 1.60/1.30 spl0_9 <=> ($false = (f @ $false))),
% 1.60/1.30 introduced(definition,[new_symbols(naming,[spl0_9])],[avatar_definition])).
% 1.60/1.30 thf(f132,plain,(
% 1.60/1.30 ($true = (f @ $false)) | (~spl0_1 | ~spl0_8)),
% 1.60/1.30 inference(backward_demodulation,[status(thm)],[f11,f58])).
% 1.60/1.30 thf(f58,plain,(
% 1.60/1.30 (x = $false) | ~spl0_8),
% 1.60/1.30 inference(avatar_component_clause,[status(thm)],[f56])).
% 1.60/1.30 thf(f56,definition,(
% 1.60/1.30 spl0_8 <=> (x = $false)),
% 1.60/1.30 introduced(definition,[new_symbols(naming,[spl0_8])],[avatar_definition])).
% 1.60/1.30 thf(f11,plain,(
% 1.60/1.30 ((f @ x) = $true) | ~spl0_1),
% 1.60/1.30 inference(avatar_component_clause,[status(thm)],[f9])).
% 1.60/1.30 thf(f9,definition,(
% 1.60/1.30 spl0_1 <=> ((f @ x) = $true)),
% 1.60/1.30 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 1.60/1.30 thf(f127,plain,(
% 1.60/1.30 ~spl0_1 | spl0_2 | ~spl0_7),
% 1.60/1.30 inference(avatar_contradiction_clause,[status(thm)],[f126])).
% 1.60/1.30 thf(f126,plain,(
% 1.60/1.30 $false | (~spl0_1 | spl0_2 | ~spl0_7)),
% 1.60/1.30 inference(subsumption_resolution,[status(thm)],[f125,f53])).
% 1.60/1.30 thf(f53,plain,(
% 1.60/1.30 ($true = (f @ $true)) | ~spl0_7),
% 1.60/1.30 inference(avatar_component_clause,[status(thm)],[f51])).
% 1.60/1.30 thf(f51,definition,(
% 1.60/1.30 spl0_7 <=> ($true = (f @ $true))),
% 1.60/1.30 introduced(definition,[new_symbols(naming,[spl0_7])],[avatar_definition])).
% 1.60/1.30 thf(f125,plain,(
% 1.60/1.30 ($true != (f @ $true)) | (~spl0_1 | spl0_2 | ~spl0_7)),
% 1.60/1.30 inference(forward_demodulation,[status(thm)],[f124,f53])).
% 1.60/1.30 thf(f124,plain,(
% 1.60/1.30 ((f @ (f @ $true)) != $true) | (~spl0_1 | spl0_2)),
% 1.60/1.30 inference(forward_demodulation,[status(thm)],[f14,f11])).
% 1.60/1.30 thf(f14,plain,(
% 1.60/1.30 ((f @ (f @ (f @ x))) != $true) | spl0_2),
% 1.60/1.30 inference(avatar_component_clause,[status(thm)],[f13])).
% 1.60/1.30 thf(f13,definition,(
% 1.60/1.30 spl0_2 <=> ((f @ (f @ (f @ x))) = $true)),
% 1.60/1.30 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])).
% 1.60/1.30 thf(f123,plain,(
% 1.60/1.30 ~spl0_1 | ~spl0_4),
% 1.60/1.30 inference(avatar_contradiction_clause,[status(thm)],[f122])).
% 1.60/1.30 thf(f122,plain,(
% 1.60/1.30 $false | (~spl0_1 | ~spl0_4)),
% 1.60/1.30 inference(trivial_inequality_removal,[status(thm)],[f121])).
% 1.60/1.30 thf(f121,plain,(
% 1.60/1.30 ($true = $false) | (~spl0_1 | ~spl0_4)),
% 1.60/1.30 inference(forward_demodulation,[status(thm)],[f11,f24])).
% 1.60/1.30 thf(f24,plain,(
% 1.60/1.30 ((f @ x) = $false) | ~spl0_4),
% 1.60/1.30 inference(avatar_component_clause,[status(thm)],[f22])).
% 1.60/1.30 thf(f22,definition,(
% 1.60/1.30 spl0_4 <=> ((f @ x) = $false)),
% 1.60/1.30 introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition])).
% 1.60/1.30 thf(f119,plain,(
% 1.60/1.30 ~spl0_2 | ~spl0_4 | spl0_8 | spl0_9),
% 1.60/1.30 inference(avatar_contradiction_clause,[status(thm)],[f118])).
% 1.60/1.30 thf(f118,plain,(
% 1.60/1.30 $false | (~spl0_2 | ~spl0_4 | spl0_8 | spl0_9)),
% 1.60/1.30 inference(subsumption_resolution,[status(thm)],[f117,f62])).
% 1.60/1.30 thf(f62,plain,(
% 1.60/1.30 ($false != (f @ $false)) | spl0_9),
% 1.60/1.30 inference(avatar_component_clause,[status(thm)],[f61])).
% 1.60/1.30 thf(f117,plain,(
% 1.60/1.30 ($false = (f @ $false)) | (~spl0_2 | ~spl0_4 | spl0_8)),
% 1.60/1.30 inference(subsumption_resolution,[status(thm)],[f107,f57])).
% 1.60/1.30 thf(f57,plain,(
% 1.60/1.30 (x != $false) | spl0_8),
% 1.60/1.30 inference(avatar_component_clause,[status(thm)],[f56])).
% 1.60/1.30 thf(f107,plain,(
% 1.60/1.30 (x = $false) | ($false = (f @ $false)) | (~spl0_2 | ~spl0_4)),
% 1.60/1.30 inference(binary_proxy_clausification,[status(thm)],[f105])).
% 1.60/1.30 thf(f105,plain,(
% 1.60/1.30 (x != (f @ $false)) | (~spl0_2 | ~spl0_4)),
% 1.60/1.30 inference(trivial_inequality_removal,[status(thm)],[f101])).
% 1.60/1.30 thf(f101,plain,(
% 1.60/1.30 ($true = $false) | (x != (f @ $false)) | (~spl0_2 | ~spl0_4)),
% 1.60/1.30 inference(constrained_superposition,[status(thm)],[f77,f24])).
% 1.60/1.30 thf(f77,plain,(
% 1.60/1.30 ((f @ (f @ $false)) = $true) | (~spl0_2 | ~spl0_4)),
% 1.60/1.30 inference(forward_demodulation,[status(thm)],[f15,f24])).
% 1.60/1.30 thf(f15,plain,(
% 1.60/1.30 ((f @ (f @ (f @ x))) = $true) | ~spl0_2),
% 1.60/1.30 inference(avatar_component_clause,[status(thm)],[f13])).
% 1.60/1.30 thf(f90,plain,(
% 1.60/1.30 ~spl0_8 | ~spl0_4 | spl0_9),
% 1.60/1.30 inference(avatar_split_clause,[status(thm)],[f89,f61,f22,f56])).
% 1.60/1.30 thf(f89,plain,(
% 1.60/1.30 (x != $false) | (~spl0_4 | spl0_9)),
% 1.60/1.30 inference(trivial_inequality_removal,[status(thm)],[f88])).
% 1.60/1.30 thf(f88,plain,(
% 1.60/1.30 (x != $false) | ($false != $false) | (~spl0_4 | spl0_9)),
% 1.60/1.30 inference(constrained_superposition,[status(thm)],[f62,f24])).
% 1.60/1.30 thf(f81,plain,(
% 1.60/1.30 ~spl0_2 | ~spl0_4 | ~spl0_9),
% 1.60/1.30 inference(avatar_contradiction_clause,[status(thm)],[f80])).
% 1.60/1.30 thf(f80,plain,(
% 1.60/1.30 $false | (~spl0_2 | ~spl0_4 | ~spl0_9)),
% 1.60/1.30 inference(trivial_inequality_removal,[status(thm)],[f79])).
% 1.60/1.30 thf(f79,plain,(
% 1.60/1.30 ($true = $false) | (~spl0_2 | ~spl0_4 | ~spl0_9)),
% 1.60/1.30 inference(forward_demodulation,[status(thm)],[f78,f63])).
% 1.60/1.30 thf(f78,plain,(
% 1.60/1.30 ($true = (f @ $false)) | (~spl0_2 | ~spl0_4 | ~spl0_9)),
% 1.60/1.30 inference(forward_demodulation,[status(thm)],[f77,f63])).
% 1.60/1.30 thf(f72,plain,(
% 1.60/1.30 ~spl0_1 | ~spl0_5 | ~spl0_6),
% 1.60/1.30 inference(avatar_contradiction_clause,[status(thm)],[f71])).
% 1.60/1.30 thf(f71,plain,(
% 1.60/1.30 $false | (~spl0_1 | ~spl0_5 | ~spl0_6)),
% 1.60/1.30 inference(trivial_inequality_removal,[status(thm)],[f70])).
% 1.60/1.30 thf(f70,plain,(
% 1.60/1.30 ($true = $false) | (~spl0_1 | ~spl0_5 | ~spl0_6)),
% 1.60/1.30 inference(forward_demodulation,[status(thm)],[f69,f44])).
% 1.60/1.30 thf(f44,plain,(
% 1.60/1.30 ($false = (f @ $true)) | ~spl0_5),
% 1.60/1.30 inference(avatar_component_clause,[status(thm)],[f42])).
% 1.60/1.30 thf(f42,definition,(
% 1.60/1.30 spl0_5 <=> ($false = (f @ $true))),
% 1.60/1.30 introduced(definition,[new_symbols(naming,[spl0_5])],[avatar_definition])).
% 1.60/1.30 thf(f69,plain,(
% 1.60/1.30 ($true = (f @ $true)) | (~spl0_1 | ~spl0_6)),
% 1.60/1.30 inference(backward_demodulation,[status(thm)],[f11,f47])).
% 1.60/1.30 thf(f47,plain,(
% 1.60/1.30 (x = $true) | ~spl0_6),
% 1.60/1.30 inference(avatar_component_clause,[status(thm)],[f46])).
% 1.60/1.30 thf(f46,definition,(
% 1.60/1.30 spl0_6 <=> (x = $true)),
% 1.60/1.30 introduced(definition,[new_symbols(naming,[spl0_6])],[avatar_definition])).
% 1.60/1.30 thf(f68,plain,(
% 1.60/1.30 spl0_9 | ~spl0_1 | ~spl0_3 | ~spl0_5),
% 1.60/1.30 inference(avatar_split_clause,[status(thm)],[f67,f42,f18,f9,f61])).
% 1.60/1.30 thf(f18,definition,(
% 1.60/1.30 spl0_3 <=> ((f @ (f @ (f @ x))) = $false)),
% 1.60/1.30 introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition])).
% 1.60/1.30 thf(f67,plain,(
% 1.60/1.30 ($false = (f @ $false)) | (~spl0_1 | ~spl0_3 | ~spl0_5)),
% 1.60/1.30 inference(backward_demodulation,[status(thm)],[f30,f44])).
% 1.60/1.30 thf(f30,plain,(
% 1.60/1.30 ((f @ (f @ $true)) = $false) | (~spl0_1 | ~spl0_3)),
% 1.60/1.30 inference(backward_demodulation,[status(thm)],[f20,f11])).
% 1.60/1.30 thf(f20,plain,(
% 1.60/1.30 ((f @ (f @ (f @ x))) = $false) | ~spl0_3),
% 1.60/1.30 inference(avatar_component_clause,[status(thm)],[f18])).
% 1.60/1.30 thf(f66,plain,(
% 1.60/1.30 spl0_5 | spl0_8 | ~spl0_1 | ~spl0_3),
% 1.60/1.30 inference(avatar_split_clause,[status(thm)],[f37,f18,f9,f56,f42])).
% 1.60/1.30 thf(f37,plain,(
% 1.60/1.30 ($false = (f @ $true)) | (x = $false) | (~spl0_1 | ~spl0_3)),
% 1.60/1.30 inference(binary_proxy_clausification,[status(thm)],[f35])).
% 1.60/1.30 thf(f35,plain,(
% 1.60/1.30 (x != (f @ $true)) | (~spl0_1 | ~spl0_3)),
% 1.60/1.30 inference(trivial_inequality_removal,[status(thm)],[f34])).
% 1.60/1.30 thf(f34,plain,(
% 1.60/1.30 ($true = $false) | (x != (f @ $true)) | (~spl0_1 | ~spl0_3)),
% 1.60/1.30 inference(constrained_superposition,[status(thm)],[f11,f30])).
% 1.60/1.30 thf(f65,plain,(
% 1.60/1.30 spl0_6 | spl0_7 | ~spl0_1 | ~spl0_3),
% 1.60/1.30 inference(avatar_split_clause,[status(thm)],[f36,f18,f9,f51,f46])).
% 1.60/1.30 thf(f36,plain,(
% 1.60/1.30 (x = $true) | ($true = (f @ $true)) | (~spl0_1 | ~spl0_3)),
% 1.60/1.30 inference(binary_proxy_clausification,[status(thm)],[f35])).
% 1.60/1.30 thf(f49,plain,(
% 1.60/1.30 spl0_5 | ~spl0_6 | ~spl0_1 | ~spl0_3),
% 1.60/1.30 inference(avatar_split_clause,[status(thm)],[f32,f18,f9,f46,f42])).
% 1.60/1.30 thf(f32,plain,(
% 1.60/1.30 ($false = (f @ $true)) | (x != $true) | (~spl0_1 | ~spl0_3)),
% 1.60/1.30 inference(constrained_superposition,[status(thm)],[f30,f11])).
% 1.60/1.30 thf(f28,plain,(
% 1.60/1.30 ~spl0_2 | ~spl0_3),
% 1.60/1.30 inference(avatar_contradiction_clause,[status(thm)],[f27])).
% 1.60/1.30 thf(f27,plain,(
% 1.60/1.30 $false | (~spl0_2 | ~spl0_3)),
% 1.60/1.30 inference(trivial_inequality_removal,[status(thm)],[f26])).
% 1.60/1.30 thf(f26,plain,(
% 1.60/1.30 ($true = $false) | (~spl0_2 | ~spl0_3)),
% 1.60/1.30 inference(backward_demodulation,[status(thm)],[f15,f20])).
% 1.60/1.30 thf(f25,plain,(
% 1.60/1.30 spl0_3 | spl0_4),
% 1.60/1.30 inference(avatar_split_clause,[status(thm)],[f7,f22,f18])).
% 1.60/1.30 thf(f7,plain,(
% 1.60/1.30 ((f @ (f @ (f @ x))) = $false) | ((f @ x) = $false)),
% 1.60/1.30 inference(binary_proxy_clausification,[status(thm)],[f5])).
% 1.60/1.30 thf(f5,plain,(
% 1.60/1.30 ((f @ x) != (f @ (f @ (f @ x))))),
% 1.60/1.30 inference(cnf_transformation,[status(thm)],[f4])).
% 1.60/1.30 thf(f4,plain,(
% 1.60/1.30 ((f @ x) != (f @ (f @ (f @ x))))),
% 1.60/1.30 inference(flattening,[status(thm)],[f2])).
% 1.60/1.30 thf(f2,negated_conjecture,(
% 1.60/1.30 ~((f @ x) = (f @ (f @ (f @ x))))),
% 1.60/1.30 inference(negated_conjecture,[status(cth)],[f1])).
% 1.60/1.30 thf(f1,conjecture,(
% 1.60/1.30 ((f @ x) = (f @ (f @ (f @ x))))),
% 1.60/1.30 file('/export/starexec/sandbox2/tmp/tmp.UZcIHmZ2ap/DTF2THF_30495.p',con)).
% 1.60/1.30 thf(f16,plain,(
% 1.60/1.30 spl0_1 | spl0_2),
% 1.60/1.30 inference(avatar_split_clause,[status(thm)],[f6,f13,f9])).
% 1.60/1.30 thf(f6,plain,(
% 1.60/1.30 ((f @ (f @ (f @ x))) = $true) | ((f @ x) = $true)),
% 1.60/1.30 inference(binary_proxy_clausification,[status(thm)],[f5])).
% 1.60/1.30 % SZS output end Proof for DTF2THF_30495
% 1.60/1.30 % (30708)------------------------------
% 1.60/1.30 % (30708)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.60/1.30 % (30708)Termination reason: Refutation
% 1.60/1.30
% 1.60/1.30 % (30708)Memory used [KB]: 5500
% 1.60/1.30 % (30708)Time elapsed: 0.008 s
% 1.60/1.30 % (30708)Instructions burned: 6 (million)
% 1.60/1.30 % (30708)------------------------------
% 1.60/1.30 % (30708)------------------------------
% 1.60/1.30 % (30701)Success in time 0.022 s
%------------------------------------------------------------------------------