%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO108^5 : 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 : n010.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 09:53:23 AM UTC 2026
% Result : Theorem 1.55s 1.31s
% Output : Refutation 1.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 8
% Syntax : Number of formulae : 33 ( 5 unt; 0 typ; 4 def)
% Number of atoms : 209 ( 51 equ; 0 cnn)
% Maximal formula atoms : 6 ( 6 avg)
% Number of connectives : 189 ( 60 ~; 45 |; 9 &; 68 @)
% ( 4 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 10 usr; 9 con; 0-2 aty)
% Number of variables : 55 ( 0 ^; 36 !; 19 ?; 55 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
cG: $i > $o ).
thf(func_def_1,type,
cN: $i > $o ).
thf(func_def_2,type,
cM: $i > $o ).
thf(f40,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f24,f32,f34,f37,f39]) ).
thf(f39,plain,
( ~ spl3_2
| ~ spl3_4 ),
inference(avatar_contradiction_clause,[status(thm)],[f38]) ).
thf(f38,plain,
( $false
| ~ spl3_2
| ~ spl3_4 ),
inference(subsumption_resolution,[status(thm)],[f31,f23]) ).
thf(f23,plain,
( ! [X2: $i] :
( $true
!= ( cN @ X2 ) )
| ~ spl3_2 ),
inference(avatar_component_clause,[status(thm)],[f22]) ).
thf(f22,definition,
( spl3_2
<=> ! [X2: $i] :
( $true
!= ( cN @ X2 ) ) ),
introduced(definition,[new_symbols(naming,[spl3_2])],[avatar_definition]) ).
thf(f31,plain,
( ( $true
= ( cN @ sK2 ) )
| ~ spl3_4 ),
inference(avatar_component_clause,[status(thm)],[f29]) ).
thf(f29,definition,
( spl3_4
<=> ( $true
= ( cN @ sK2 ) ) ),
introduced(definition,[new_symbols(naming,[spl3_4])],[avatar_definition]) ).
thf(f37,plain,
~ spl3_3,
inference(avatar_contradiction_clause,[status(thm)],[f36]) ).
thf(f36,plain,
( $false
| ~ spl3_3 ),
inference(trivial_inequality_removal,[status(thm)],[f35]) ).
thf(f35,plain,
( ( $true != $true )
| ~ spl3_3 ),
inference(superposition,[status(thm)],[f15,f27]) ).
thf(f27,plain,
( ! [X4: $i] :
( ( cM @ X4 )
= $true )
| ~ spl3_3 ),
inference(avatar_component_clause,[status(thm)],[f26]) ).
thf(f26,definition,
( spl3_3
<=> ! [X4: $i] :
( ( cM @ X4 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl3_3])],[avatar_definition]) ).
thf(f15,plain,
( ( cM @ sK0 )
!= $true ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
( ! [X0: $i] :
( ( cG @ X0 )
= $true )
& ( ( cM @ sK0 )
!= $true )
& ! [X2: $i] :
( ( ( cG @ sK1 )
!= $true )
| ( $true
!= ( cN @ X2 ) ) )
& ! [X4: $i] :
( ( $true
= ( cN @ sK2 ) )
| ( ( cM @ X4 )
= $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f8,f11,f10,f9]) ).
thf(f9,plain,
( ? [X1: $i] :
( ( cM @ X1 )
!= $true )
=> ( ( cM @ sK0 )
!= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f10,plain,
( ? [X3: $i] :
( ( cG @ X3 )
!= $true )
=> ( ( cG @ sK1 )
!= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f11,plain,
( ? [X5: $i] :
( ( cN @ X5 )
= $true )
=> ( $true
= ( cN @ sK2 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f8,plain,
( ! [X0: $i] :
( ( cG @ X0 )
= $true )
& ? [X1: $i] :
( ( cM @ X1 )
!= $true )
& ! [X2: $i] :
( ? [X3: $i] :
( ( cG @ X3 )
!= $true )
| ( $true
!= ( cN @ X2 ) ) )
& ! [X4: $i] :
( ? [X5: $i] :
( ( cN @ X5 )
= $true )
| ( ( cM @ X4 )
= $true ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,plain,
( ! [X2: $i] :
( $true
= ( cG @ X2 ) )
& ? [X3: $i] :
( ( cM @ X3 )
!= $true )
& ! [X0: $i] :
( ? [X1: $i] :
( ( cG @ X1 )
!= $true )
| ( ( cN @ X0 )
!= $true ) )
& ! [X4: $i] :
( ? [X5: $i] :
( ( cN @ X5 )
= $true )
| ( ( cM @ X4 )
= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
~ ( ? [X2: $i] :
( $true
!= ( cG @ X2 ) )
| ~ ! [X0: $i] :
( ~ ! [X1: $i] :
( ( cG @ X1 )
= $true )
| ( ( cN @ X0 )
!= $true ) )
| ~ ! [X4: $i] :
( ? [X5: $i] :
( ( cN @ X5 )
= $true )
| ( ( cM @ X4 )
= $true ) )
| ! [X3: $i] :
( ( cM @ X3 )
= $true ) ),
inference(flattening,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ~ ! [X0: $i] :
( ( ( cN @ X0 )
!= $true )
| ~ ! [X1: $i] :
( ( cG @ X1 )
= $true ) )
| ? [X2: $i] :
( $true
!= ( cG @ X2 ) )
| ! [X3: $i] :
( ( cM @ X3 )
= $true )
| ~ ! [X4: $i] :
( ? [X5: $i] :
( ( cN @ X5 )
= $true )
| ( ( cM @ X4 )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ~ ! [X0: $i] :
( ~ ( cN @ X0 )
| ~ ! [X1: $i] : ( cG @ X1 ) )
| ? [X2: $i] :
~ ( cG @ X2 )
| ! [X3: $i] : ( cM @ X3 )
| ~ ! [X4: $i] :
( ? [X5: $i] : ( cN @ X5 )
| ( cM @ X4 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ~ ! [X4: $i] :
( ~ ( cN @ X4 )
| ~ ! [X5: $i] : ( cG @ X5 ) )
| ? [X1: $i] :
~ ( cG @ X1 )
| ! [X0: $i] : ( cM @ X0 )
| ~ ! [X2: $i] :
( ? [X3: $i] : ( cN @ X3 )
| ( cM @ X2 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ~ ! [X4: $i] :
( ~ ( cN @ X4 )
| ~ ! [X5: $i] : ( cG @ X5 ) )
| ? [X1: $i] :
~ ( cG @ X1 )
| ! [X0: $i] : ( cM @ X0 )
| ~ ! [X2: $i] :
( ? [X3: $i] : ( cN @ X3 )
| ( cM @ X2 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.eVYjGbSBa5/DTF2THF_15482.p',cTHM79) ).
thf(f34,plain,
spl3_1,
inference(avatar_contradiction_clause,[status(thm)],[f33]) ).
thf(f33,plain,
( $false
| spl3_1 ),
inference(subsumption_resolution,[status(thm)],[f20,f16]) ).
thf(f16,plain,
! [X0: $i] :
( ( cG @ X0 )
= $true ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f20,plain,
( ( ( cG @ sK1 )
!= $true )
| spl3_1 ),
inference(avatar_component_clause,[status(thm)],[f18]) ).
thf(f18,definition,
( spl3_1
<=> ( ( cG @ sK1 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl3_1])],[avatar_definition]) ).
thf(f32,plain,
( spl3_3
| spl3_4 ),
inference(avatar_split_clause,[status(thm)],[f13,f29,f26]) ).
thf(f13,plain,
! [X4: $i] :
( ( $true
= ( cN @ sK2 ) )
| ( ( cM @ X4 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f24,plain,
( ~ spl3_1
| spl3_2 ),
inference(avatar_split_clause,[status(thm)],[f14,f22,f18]) ).
thf(f14,plain,
! [X2: $i] :
( ( $true
!= ( cN @ X2 ) )
| ( ( cG @ sK1 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SYO108^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.10 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/0.29 % Computer : n010.cluster.edu
% 0.11/0.29 % Model : x86_64 x86_64
% 0.11/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.29 % Memory : 8042.1875MB
% 0.11/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.29 % CPULimit : 300
% 0.11/0.29 % WCLimit : 300
% 0.11/0.29 % DateTime : Tue Feb 24 14:24:03 EST 2026
% 0.11/0.29 % CPUTime :
% 0.11/0.29 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.39 ---- Original DTF file ---
% 0.16/0.39 thf(spec,logic,$$dhol).
% 0.16/0.39 %------------------------------------------------------------------------------
% 0.16/0.39 % File : SYO108^5 : TPTP v9.2.1. Released v4.0.0.
% 0.16/0.39 % Domain : Syntactic
% 0.16/0.39 % Problem : TPS problem THM79
% 0.16/0.39 % Version : Especial.
% 0.16/0.39 % English :
% 0.16/0.39
% 0.16/0.39 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.16/0.39 % Source : [Bro09]
% 0.16/0.39 % Names : tps_0415 [Bro09]
% 0.16/0.39 % : THM79 [TPS]
% 0.16/0.39
% 0.16/0.39 % Status : Theorem
% 0.16/0.39 % Rating : 0.17 v9.1.0, 0.12 v9.0.0, 0.17 v8.2.0, 0.18 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 v6.0.0, 0.00 v4.0.0
% 0.16/0.39 % Syntax : Number of formulae : 4 ( 0 unt; 3 typ; 0 def)
% 0.16/0.39 % Number of atoms : 6 ( 0 equ; 0 cnn)
% 0.16/0.39 % Maximal formula atoms : 6 ( 6 avg)
% 0.16/0.39 % Number of connectives : 16 ( 5 ~; 5 |; 0 &; 6 @)
% 0.16/0.39 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.16/0.39 % Maximal formula depth : 10 ( 10 avg)
% 0.16/0.39 % Number of types : 2 ( 0 usr)
% 0.16/0.39 % Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% 0.16/0.39 % Number of symbols : 3 ( 3 usr; 0 con; 1-1 aty)
% 0.16/0.39 % Number of variables : 6 ( 0 ^; 4 !; 2 ?; 6 :)
% 0.16/0.39 % SPC : TH0_THM_NEQ_NAR
% 0.16/0.39
% 0.16/0.39 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.16/0.39 % project in the Department of Mathematical Sciences at Carnegie
% 0.16/0.39 % Mellon University. Distributed under the Creative Commons copyleft
% 0.16/0.39 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.16/0.39 %------------------------------------------------------------------------------
% 0.16/0.39 thf(cG,type,
% 0.16/0.39 cG: $i > $o ).
% 0.16/0.39
% 0.16/0.39 thf(cN,type,
% 0.16/0.39 cN: $i > $o ).
% 0.16/0.39
% 0.16/0.39 thf(cM,type,
% 0.16/0.39 cM: $i > $o ).
% 0.16/0.39
% 0.16/0.39 thf(cTHM79,conjecture,
% 0.16/0.39 ( ! [R: $i] : ( cM @ R )
% 0.16/0.39 | ? [X: $i] :
% 0.16/0.39 ~ ( cG @ X )
% 0.16/0.39 | ~ ! [Y: $i] :
% 0.16/0.39 ( ( cM @ Y )
% 0.16/0.39 | ? [S: $i] : ( cN @ S ) )
% 0.16/0.39 | ~ ! [Z: $i] :
% 0.16/0.39 ( ~ ( cN @ Z )
% 0.16/0.39 | ~ ! [T: $i] : ( cG @ T ) ) ) ).
% 0.16/0.39
% 0.16/0.39 %------------------------------------------------------------------------------
% 0.16/0.39 ------------------------
% 1.37/1.28 ---- Embedded in THF ---
% 1.37/1.28 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.37/1.28 %%% Generated on Tue Feb 24 14:24:04 EST 2026
% 1.37/1.28 %%% using '$$dhol' embedding, version 1.3.0.
% 1.37/1.28 %%% Logic specification used:
% 1.37/1.28 %%% thf(spec, logic, $$dhol).
% 1.37/1.28
% 1.37/1.28 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.eVYjGbSBa5/DTF2DTF15482.p
% See solution above
% 1.37/1.28 ------------------------
% 1.37/1.29 ---- Cleaned THF ---
% 1.37/1.29 thf(cG,type,
% 1.37/1.29 cG: $i > $o ).
% 1.37/1.29
% 1.37/1.29 thf(cN,type,
% 1.37/1.29 cN: $i > $o ).
% 1.37/1.29
% 1.37/1.29 thf(cM,type,
% 1.37/1.29 cM: $i > $o ).
% 1.37/1.29
% 1.37/1.29 thf(cTHM79,conjecture,
% 1.37/1.29 ( ! [R: $i] : ( cM @ R )
% 1.37/1.29 | ? [X: $i] :
% 1.37/1.29 ~ ( cG @ X )
% 1.37/1.29 | ~ ! [Y: $i] :
% 1.37/1.29 ( ( cM @ Y )
% 1.37/1.29 | ? [S: $i] : ( cN @ S ) )
% 1.37/1.29 | ~ ! [Z: $i] :
% 1.37/1.29 ( ~ ( cN @ Z )
% 1.37/1.29 | ~ ! [T: $i] : ( cG @ T ) ) ) ).
% 1.37/1.29 ------------------------
% 1.55/1.31 % (15584)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_15482 for (3000ds/2Mi)
% 1.55/1.31 % (15581)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_15482 for (3000ds/4Mi)
% 1.55/1.31 % (15580)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_15482 for (3000ds/183Mi)
% 1.55/1.31 % (15583)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_15482 for (3000ds/2Mi)
% 1.55/1.31 % (15582)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_15482 for (3000ds/27Mi)
% 1.55/1.31 % (15585)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_15482 for (3000ds/275Mi)
% 1.55/1.31 % (15586)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_15482 for (3000ds/18Mi)
% 1.55/1.31 % (15584)Instruction limit reached!
% 1.55/1.31 % (15584)------------------------------
% 1.55/1.31 % (15584)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.31 % (15584)Termination reason: Unknown
% 1.55/1.31 % (15584)Termination phase: Saturation
% 1.55/1.31
% 1.55/1.31 % (15584)Memory used [KB]: 5500
% 1.55/1.31 % (15584)Time elapsed: 0.003 s
% 1.55/1.31 % (15584)Instructions burned: 2 (million)
% 1.55/1.31 % (15584)------------------------------
% 1.55/1.31 % (15584)------------------------------
% 1.55/1.31 % (15580)First to succeed.
% 1.55/1.31 % (15582)Also succeeded, but the first one will report.
% 1.55/1.31 % (15586)Also succeeded, but the first one will report.
% 1.55/1.31 % (15580)Refutation found. Thanks to Tanya!
% 1.55/1.31 % SZS status Theorem for DTF2THF_15482
% 1.55/1.31 % SZS output start Proof for DTF2THF_15482
% 1.55/1.31 thf(func_def_0, type, cG: $i > $o).
% 1.55/1.31 thf(func_def_1, type, cN: $i > $o).
% 1.55/1.31 thf(func_def_2, type, cM: $i > $o).
% 1.55/1.31 thf(f40,plain,(
% 1.55/1.31 $false),
% 1.55/1.31 inference(avatar_sat_refutation,[status(thm)],[f24,f32,f34,f37,f39])).
% 1.55/1.31 thf(f39,plain,(
% 1.55/1.31 ~spl3_2 | ~spl3_4),
% 1.55/1.31 inference(avatar_contradiction_clause,[status(thm)],[f38])).
% 1.55/1.31 thf(f38,plain,(
% 1.55/1.31 $false | (~spl3_2 | ~spl3_4)),
% 1.55/1.31 inference(subsumption_resolution,[status(thm)],[f31,f23])).
% 1.55/1.31 thf(f23,plain,(
% 1.55/1.31 ( ! [X2 : $i] : (($true != (cN @ X2))) ) | ~spl3_2),
% 1.55/1.31 inference(avatar_component_clause,[status(thm)],[f22])).
% 1.55/1.31 thf(f22,definition,(
% 1.55/1.31 spl3_2 <=> ! [X2 : $i] : ($true != (cN @ X2))),
% 1.55/1.31 introduced(definition,[new_symbols(naming,[spl3_2])],[avatar_definition])).
% 1.55/1.31 thf(f31,plain,(
% 1.55/1.31 ($true = (cN @ sK2)) | ~spl3_4),
% 1.55/1.31 inference(avatar_component_clause,[status(thm)],[f29])).
% 1.55/1.31 thf(f29,definition,(
% 1.55/1.31 spl3_4 <=> ($true = (cN @ sK2))),
% 1.55/1.31 introduced(definition,[new_symbols(naming,[spl3_4])],[avatar_definition])).
% 1.55/1.31 thf(f37,plain,(
% 1.55/1.31 ~spl3_3),
% 1.55/1.31 inference(avatar_contradiction_clause,[status(thm)],[f36])).
% 1.55/1.31 thf(f36,plain,(
% 1.55/1.31 $false | ~spl3_3),
% 1.55/1.31 inference(trivial_inequality_removal,[status(thm)],[f35])).
% 1.55/1.31 thf(f35,plain,(
% 1.55/1.31 ($true != $true) | ~spl3_3),
% 1.55/1.31 inference(superposition,[status(thm)],[f15,f27])).
% 1.55/1.31 thf(f27,plain,(
% 1.55/1.31 ( ! [X4 : $i] : (((cM @ X4) = $true)) ) | ~spl3_3),
% 1.55/1.31 inference(avatar_component_clause,[status(thm)],[f26])).
% 1.55/1.31 thf(f26,definition,(
% 1.55/1.31 spl3_3 <=> ! [X4 : $i] : ((cM @ X4) = $true)),
% 1.55/1.31 introduced(definition,[new_symbols(naming,[spl3_3])],[avatar_definition])).
% 1.55/1.31 thf(f15,plain,(
% 1.55/1.31 ((cM @ sK0) != $true)),
% 1.55/1.31 inference(cnf_transformation,[status(thm)],[f12])).
% 1.55/1.31 thf(f12,plain,(
% 1.55/1.31 ! [X0 : $i] : ((cG @ X0) = $true) & ((cM @ sK0) != $true) & ! [X2 : $i] : (((cG @ sK1) != $true) | ($true != (cN @ X2))) & ! [X4 : $i] : (($true = (cN @ sK2)) | ((cM @ X4) = $true))),
% 1.55/1.31 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f8,f11,f10,f9])).
% 1.55/1.31 thf(f9,plain,(
% 1.55/1.31 ? [X1 : $i] : ((cM @ X1) != $true) => ((cM @ sK0) != $true)),
% 1.55/1.31 introduced(definition,[],[choice_axiom])).
% 1.55/1.31 thf(f10,plain,(
% 1.55/1.31 ? [X3 : $i] : ((cG @ X3) != $true) => ((cG @ sK1) != $true)),
% 1.55/1.31 introduced(definition,[],[choice_axiom])).
% 1.55/1.31 thf(f11,plain,(
% 1.55/1.31 ? [X5 : $i] : ((cN @ X5) = $true) => ($true = (cN @ sK2))),
% 1.55/1.31 introduced(definition,[],[choice_axiom])).
% 1.55/1.31 thf(f8,plain,(
% 1.55/1.31 ! [X0 : $i] : ((cG @ X0) = $true) & ? [X1 : $i] : ((cM @ X1) != $true) & ! [X2 : $i] : (? [X3 : $i] : ((cG @ X3) != $true) | ($true != (cN @ X2))) & ! [X4 : $i] : (? [X5 : $i] : ((cN @ X5) = $true) | ((cM @ X4) = $true))),
% 1.55/1.31 inference(rectify,[status(thm)],[f7])).
% 1.55/1.31 thf(f7,plain,(
% 1.55/1.31 ! [X2 : $i] : ($true = (cG @ X2)) & ? [X3 : $i] : ((cM @ X3) != $true) & ! [X0 : $i] : (? [X1 : $i] : ((cG @ X1) != $true) | ((cN @ X0) != $true)) & ! [X4 : $i] : (? [X5 : $i] : ((cN @ X5) = $true) | ((cM @ X4) = $true))),
% 1.55/1.31 inference(ennf_transformation,[status(thm)],[f6])).
% 1.55/1.31 thf(f6,plain,(
% 1.55/1.31 ~(? [X2 : $i] : ($true != (cG @ X2)) | ~! [X0 : $i] : (~! [X1 : $i] : ((cG @ X1) = $true) | ((cN @ X0) != $true)) | ~! [X4 : $i] : (? [X5 : $i] : ((cN @ X5) = $true) | ((cM @ X4) = $true)) | ! [X3 : $i] : ((cM @ X3) = $true))),
% 1.55/1.31 inference(flattening,[status(thm)],[f5])).
% 1.55/1.31 thf(f5,plain,(
% 1.55/1.31 ~(~! [X0 : $i] : (~((cN @ X0) = $true) | ~! [X1 : $i] : ((cG @ X1) = $true)) | ? [X2 : $i] : ~($true = (cG @ X2)) | ! [X3 : $i] : ((cM @ X3) = $true) | ~! [X4 : $i] : (? [X5 : $i] : ((cN @ X5) = $true) | ((cM @ X4) = $true)))),
% 1.55/1.31 inference(fool_elimination,[status(thm)],[f4])).
% 1.55/1.31 thf(f4,plain,(
% 1.55/1.31 ~(~! [X0 : $i] : (~(cN @ X0) | ~! [X1 : $i] : (cG @ X1)) | ? [X2 : $i] : ~(cG @ X2) | ! [X3 : $i] : (cM @ X3) | ~! [X4 : $i] : (? [X5 : $i] : (cN @ X5) | (cM @ X4)))),
% 1.55/1.31 inference(rectify,[status(thm)],[f2])).
% 1.55/1.31 thf(f2,negated_conjecture,(
% 1.55/1.31 ~(~! [X4 : $i] : (~(cN @ X4) | ~! [X5 : $i] : (cG @ X5)) | ? [X1 : $i] : ~(cG @ X1) | ! [X0 : $i] : (cM @ X0) | ~! [X2 : $i] : (? [X3 : $i] : (cN @ X3) | (cM @ X2)))),
% 1.55/1.31 inference(negated_conjecture,[status(cth)],[f1])).
% 1.55/1.31 thf(f1,conjecture,(
% 1.55/1.31 ~! [X4 : $i] : (~(cN @ X4) | ~! [X5 : $i] : (cG @ X5)) | ? [X1 : $i] : ~(cG @ X1) | ! [X0 : $i] : (cM @ X0) | ~! [X2 : $i] : (? [X3 : $i] : (cN @ X3) | (cM @ X2))),
% 1.55/1.31 file('/export/starexec/sandbox/tmp/tmp.eVYjGbSBa5/DTF2THF_15482.p',cTHM79)).
% 1.55/1.31 thf(f34,plain,(
% 1.55/1.31 spl3_1),
% 1.55/1.31 inference(avatar_contradiction_clause,[status(thm)],[f33])).
% 1.55/1.31 thf(f33,plain,(
% 1.55/1.31 $false | spl3_1),
% 1.55/1.31 inference(subsumption_resolution,[status(thm)],[f20,f16])).
% 1.55/1.31 thf(f16,plain,(
% 1.55/1.31 ( ! [X0 : $i] : (((cG @ X0) = $true)) )),
% 1.55/1.31 inference(cnf_transformation,[status(thm)],[f12])).
% 1.55/1.31 thf(f20,plain,(
% 1.55/1.31 ((cG @ sK1) != $true) | spl3_1),
% 1.55/1.31 inference(avatar_component_clause,[status(thm)],[f18])).
% 1.55/1.31 thf(f18,definition,(
% 1.55/1.31 spl3_1 <=> ((cG @ sK1) = $true)),
% 1.55/1.31 introduced(definition,[new_symbols(naming,[spl3_1])],[avatar_definition])).
% 1.55/1.31 thf(f32,plain,(
% 1.55/1.31 spl3_3 | spl3_4),
% 1.55/1.31 inference(avatar_split_clause,[status(thm)],[f13,f29,f26])).
% 1.55/1.31 thf(f13,plain,(
% 1.55/1.31 ( ! [X4 : $i] : (($true = (cN @ sK2)) | ((cM @ X4) = $true)) )),
% 1.55/1.31 inference(cnf_transformation,[status(thm)],[f12])).
% 1.55/1.31 thf(f24,plain,(
% 1.55/1.31 ~spl3_1 | spl3_2),
% 1.55/1.31 inference(avatar_split_clause,[status(thm)],[f14,f22,f18])).
% 1.55/1.31 thf(f14,plain,(
% 1.55/1.31 ( ! [X2 : $i] : (($true != (cN @ X2)) | ((cG @ sK1) != $true)) )),
% 1.55/1.31 inference(cnf_transformation,[status(thm)],[f12])).
% 1.55/1.31 % SZS output end Proof for DTF2THF_15482
% 1.55/1.31 % (15580)------------------------------
% 1.55/1.31 % (15580)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.31 % (15580)Termination reason: Refutation
% 1.55/1.31
% 1.55/1.31 % (15580)Memory used [KB]: 5500
% 1.55/1.31 % (15580)Time elapsed: 0.004 s
% 1.55/1.31 % (15580)Instructions burned: 1 (million)
% 1.55/1.31 % (15580)------------------------------
% 1.55/1.31 % (15580)------------------------------
% 1.55/1.31 % (15579)Success in time 0.016 s
%------------------------------------------------------------------------------