TSTP Solution File: SEV065^5 by Vampire---4.9
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.9
% Problem : SEV065^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire %s %d THM
% Computer : n001.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 : Mon Jun 24 16:01:41 EDT 2024
% Result : Theorem 0.12s 0.38s
% Output : Refutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 6
% Syntax : Number of formulae : 56 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 313 ( 164 equ; 0 cnn)
% Maximal formula atoms : 4 ( 5 avg)
% Number of connectives : 317 ( 60 ~; 70 |; 60 &; 118 @)
% ( 4 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 10 usr; 10 con; 0-2 aty)
% Number of variables : 40 ( 22 ^ 12 !; 6 ?; 40 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
b: $tType ).
thf(type_def_6,type,
a: $tType ).
thf(func_def_0,type,
b: $tType ).
thf(func_def_1,type,
a: $tType ).
thf(func_def_12,type,
sK0: a ).
thf(func_def_13,type,
sK1: b > a > $o ).
thf(func_def_14,type,
sK2: b ).
thf(func_def_16,type,
ph4:
!>[X0: $tType] : X0 ).
thf(func_def_17,type,
sK5: b ).
thf(func_def_18,type,
sK6: a ).
thf(f87,plain,
$false,
inference(avatar_sat_refutation,[],[f57,f62,f67,f68,f69,f79,f86]) ).
thf(f86,plain,
( ~ spl3_1
| ~ spl3_4 ),
inference(avatar_contradiction_clause,[],[f85]) ).
thf(f85,plain,
( $false
| ~ spl3_1
| ~ spl3_4 ),
inference(trivial_inequality_removal,[],[f81]) ).
thf(f81,plain,
( ( $true = $false )
| ~ spl3_1
| ~ spl3_4 ),
inference(superposition,[],[f52,f66]) ).
thf(f66,plain,
( ( $false
= ( sK1 @ sK5 @ sK6 ) )
| ~ spl3_4 ),
inference(avatar_component_clause,[],[f64]) ).
thf(f64,plain,
( spl3_4
<=> ( $false
= ( sK1 @ sK5 @ sK6 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_4])]) ).
thf(f52,plain,
( ( $true
= ( sK1 @ sK5 @ sK6 ) )
| ~ spl3_1 ),
inference(avatar_component_clause,[],[f50]) ).
thf(f50,plain,
( spl3_1
<=> ( $true
= ( sK1 @ sK5 @ sK6 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_1])]) ).
thf(f79,plain,
( ~ spl3_2
| ~ spl3_3
| ~ spl3_4 ),
inference(avatar_contradiction_clause,[],[f78]) ).
thf(f78,plain,
( $false
| ~ spl3_2
| ~ spl3_3
| ~ spl3_4 ),
inference(trivial_inequality_removal,[],[f75]) ).
thf(f75,plain,
( ( $true = $false )
| ~ spl3_2
| ~ spl3_3
| ~ spl3_4 ),
inference(superposition,[],[f10,f72]) ).
thf(f72,plain,
( ( ( sK1 @ sK2 @ sK0 )
= $false )
| ~ spl3_2
| ~ spl3_3
| ~ spl3_4 ),
inference(superposition,[],[f70,f61]) ).
thf(f61,plain,
( ( sK5 = sK2 )
| ~ spl3_3 ),
inference(avatar_component_clause,[],[f59]) ).
thf(f59,plain,
( spl3_3
<=> ( sK5 = sK2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_3])]) ).
thf(f70,plain,
( ( $false
= ( sK1 @ sK5 @ sK0 ) )
| ~ spl3_2
| ~ spl3_4 ),
inference(superposition,[],[f66,f56]) ).
thf(f56,plain,
( ( sK6 = sK0 )
| ~ spl3_2 ),
inference(avatar_component_clause,[],[f54]) ).
thf(f54,plain,
( spl3_2
<=> ( sK6 = sK0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_2])]) ).
thf(f10,plain,
( ( sK1 @ sK2 @ sK0 )
= $true ),
inference(cnf_transformation,[],[f8]) ).
thf(f8,plain,
( ( ( sK1 @ sK2 @ sK0 )
= $true )
& ( sK1
!= ( ^ [Y0: b,Y1: a] :
( ( ( sK2 = Y0 )
& ( sK0 = Y1 ) )
| ( ~ ( ( sK0 = Y1 )
& ( sK2 = Y0 ) )
& ( sK1 @ Y0 @ Y1 ) ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f6,f7]) ).
thf(f7,plain,
( ? [X0: a,X1: b > a > $o,X2: b] :
( ( ( X1 @ X2 @ X0 )
= $true )
& ( ( ^ [Y0: b,Y1: a] :
( ( ( X2 = Y0 )
& ( X0 = Y1 ) )
| ( ~ ( ( X0 = Y1 )
& ( X2 = Y0 ) )
& ( X1 @ Y0 @ Y1 ) ) ) )
!= X1 ) )
=> ( ( ( sK1 @ sK2 @ sK0 )
= $true )
& ( sK1
!= ( ^ [Y0: b,Y1: a] :
( ( ( sK2 = Y0 )
& ( sK0 = Y1 ) )
| ( ~ ( ( sK0 = Y1 )
& ( sK2 = Y0 ) )
& ( sK1 @ Y0 @ Y1 ) ) ) ) ) ) ),
introduced(choice_axiom,[]) ).
thf(f6,plain,
? [X0: a,X1: b > a > $o,X2: b] :
( ( ( X1 @ X2 @ X0 )
= $true )
& ( ( ^ [Y0: b,Y1: a] :
( ( ( X2 = Y0 )
& ( X0 = Y1 ) )
| ( ~ ( ( X0 = Y1 )
& ( X2 = Y0 ) )
& ( X1 @ Y0 @ Y1 ) ) ) )
!= X1 ) ),
inference(ennf_transformation,[],[f5]) ).
thf(f5,plain,
~ ! [X0: a,X1: b > a > $o,X2: b] :
( ( ( X1 @ X2 @ X0 )
= $true )
=> ( ( ^ [Y0: b,Y1: a] :
( ( ( X2 = Y0 )
& ( X0 = Y1 ) )
| ( ~ ( ( X0 = Y1 )
& ( X2 = Y0 ) )
& ( X1 @ Y0 @ Y1 ) ) ) )
= X1 ) ),
inference(fool_elimination,[],[f4]) ).
thf(f4,plain,
~ ! [X0: a,X1: b > a > $o,X2: b] :
( ( X1 @ X2 @ X0 )
=> ( X1
= ( ^ [X3: b,X4: a] :
( ( ( X1 @ X3 @ X4 )
& ~ ( ( X2 = X3 )
& ( X0 = X4 ) ) )
| ( ( X0 = X4 )
& ( X2 = X3 ) ) ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X1: a,X2: b > a > $o,X0: b] :
( ( X2 @ X0 @ X1 )
=> ( X2
= ( ^ [X3: b,X4: a] :
( ( ( X2 @ X3 @ X4 )
& ~ ( ( X0 = X3 )
& ( X1 = X4 ) ) )
| ( ( X1 = X4 )
& ( X0 = X3 ) ) ) ) ) ),
inference(negated_conjecture,[],[f1]) ).
thf(f1,conjecture,
! [X1: a,X2: b > a > $o,X0: b] :
( ( X2 @ X0 @ X1 )
=> ( X2
= ( ^ [X3: b,X4: a] :
( ( ( X2 @ X3 @ X4 )
& ~ ( ( X0 = X3 )
& ( X1 = X4 ) ) )
| ( ( X1 = X4 )
& ( X0 = X3 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM177_pme) ).
thf(f69,plain,
( ~ spl3_2
| ~ spl3_3
| spl3_4 ),
inference(avatar_split_clause,[],[f21,f64,f59,f54]) ).
thf(f21,plain,
( ( $false
= ( sK1 @ sK5 @ sK6 ) )
| ( sK5 != sK2 )
| ( sK6 != sK0 ) ),
inference(equality_proxy_clausification,[],[f20]) ).
thf(f20,plain,
( ( ( sK2 = sK5 )
= $false )
| ( sK6 != sK0 )
| ( $false
= ( sK1 @ sK5 @ sK6 ) ) ),
inference(equality_proxy_clausification,[],[f19]) ).
thf(f19,plain,
( ( $false
= ( sK0 = sK6 ) )
| ( $false
= ( sK1 @ sK5 @ sK6 ) )
| ( ( sK2 = sK5 )
= $false ) ),
inference(binary_proxy_clausification,[],[f18]) ).
thf(f18,plain,
( ( $false
= ( ( sK2 = sK5 )
& ( sK0 = sK6 ) ) )
| ( $false
= ( sK1 @ sK5 @ sK6 ) ) ),
inference(binary_proxy_clausification,[],[f16]) ).
thf(f16,plain,
( ( $false
= ( sK1 @ sK5 @ sK6 ) )
| ( $false
= ( ( ( sK2 = sK5 )
& ( sK0 = sK6 ) )
| ( ~ ( ( sK0 = sK6 )
& ( sK2 = sK5 ) )
& ( sK1 @ sK5 @ sK6 ) ) ) ) ),
inference(binary_proxy_clausification,[],[f14]) ).
thf(f14,plain,
( ( ( ( sK2 = sK5 )
& ( sK0 = sK6 ) )
| ( ~ ( ( sK0 = sK6 )
& ( sK2 = sK5 ) )
& ( sK1 @ sK5 @ sK6 ) ) )
!= ( sK1 @ sK5 @ sK6 ) ),
inference(beta_eta_normalization,[],[f13]) ).
thf(f13,plain,
( ( ^ [Y0: a] :
( ( ( sK2 = sK5 )
& ( sK0 = Y0 ) )
| ( ~ ( ( sK0 = Y0 )
& ( sK2 = sK5 ) )
& ( sK1 @ sK5 @ Y0 ) ) )
@ sK6 )
!= ( sK1 @ sK5 @ sK6 ) ),
inference(negative_extensionality,[],[f12]) ).
thf(f12,plain,
( ( sK1 @ sK5 )
!= ( ^ [Y0: a] :
( ( ( sK2 = sK5 )
& ( sK0 = Y0 ) )
| ( ~ ( ( sK0 = Y0 )
& ( sK2 = sK5 ) )
& ( sK1 @ sK5 @ Y0 ) ) ) ) ),
inference(beta_eta_normalization,[],[f11]) ).
thf(f11,plain,
( ( ^ [Y0: b,Y1: a] :
( ( ( sK2 = Y0 )
& ( sK0 = Y1 ) )
| ( ~ ( ( sK0 = Y1 )
& ( sK2 = Y0 ) )
& ( sK1 @ Y0 @ Y1 ) ) )
@ sK5 )
!= ( sK1 @ sK5 ) ),
inference(negative_extensionality,[],[f9]) ).
thf(f9,plain,
( sK1
!= ( ^ [Y0: b,Y1: a] :
( ( ( sK2 = Y0 )
& ( sK0 = Y1 ) )
| ( ~ ( ( sK0 = Y1 )
& ( sK2 = Y0 ) )
& ( sK1 @ Y0 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f68,plain,
( spl3_2
| spl3_4 ),
inference(avatar_split_clause,[],[f27,f64,f54]) ).
thf(f27,plain,
( ( sK6 = sK0 )
| ( $false
= ( sK1 @ sK5 @ sK6 ) ) ),
inference(equality_proxy_clausification,[],[f26]) ).
thf(f26,plain,
( ( $true
= ( sK0 = sK6 ) )
| ( $false
= ( sK1 @ sK5 @ sK6 ) ) ),
inference(binary_proxy_clausification,[],[f24]) ).
thf(f24,plain,
( ( $true
= ( ( sK0 = sK6 )
& ( sK2 = sK5 ) ) )
| ( $false
= ( sK1 @ sK5 @ sK6 ) ) ),
inference(not_proxy_clausification,[],[f23]) ).
thf(f23,plain,
( ( $false
= ( ~ ( ( sK0 = sK6 )
& ( sK2 = sK5 ) ) ) )
| ( $false
= ( sK1 @ sK5 @ sK6 ) ) ),
inference(duplicate_literal_removal,[],[f22]) ).
thf(f22,plain,
( ( $false
= ( sK1 @ sK5 @ sK6 ) )
| ( $false
= ( ~ ( ( sK0 = sK6 )
& ( sK2 = sK5 ) ) ) )
| ( $false
= ( sK1 @ sK5 @ sK6 ) ) ),
inference(binary_proxy_clausification,[],[f17]) ).
thf(f17,plain,
( ( ( ~ ( ( sK0 = sK6 )
& ( sK2 = sK5 ) )
& ( sK1 @ sK5 @ sK6 ) )
= $false )
| ( $false
= ( sK1 @ sK5 @ sK6 ) ) ),
inference(binary_proxy_clausification,[],[f16]) ).
thf(f67,plain,
( spl3_4
| spl3_3 ),
inference(avatar_split_clause,[],[f28,f59,f64]) ).
thf(f28,plain,
( ( sK5 = sK2 )
| ( $false
= ( sK1 @ sK5 @ sK6 ) ) ),
inference(equality_proxy_clausification,[],[f25]) ).
thf(f25,plain,
( ( $false
= ( sK1 @ sK5 @ sK6 ) )
| ( ( sK2 = sK5 )
= $true ) ),
inference(binary_proxy_clausification,[],[f24]) ).
thf(f62,plain,
( spl3_3
| spl3_1 ),
inference(avatar_split_clause,[],[f47,f50,f59]) ).
thf(f47,plain,
( ( sK5 = sK2 )
| ( $true
= ( sK1 @ sK5 @ sK6 ) ) ),
inference(equality_proxy_clausification,[],[f46]) ).
thf(f46,plain,
( ( $true
= ( sK1 @ sK5 @ sK6 ) )
| ( ( sK2 = sK5 )
= $true ) ),
inference(binary_proxy_clausification,[],[f44]) ).
thf(f44,plain,
( ( $true
= ( ( sK2 = sK5 )
& ( sK0 = sK6 ) ) )
| ( $true
= ( sK1 @ sK5 @ sK6 ) ) ),
inference(duplicate_literal_removal,[],[f30]) ).
thf(f30,plain,
( ( $true
= ( sK1 @ sK5 @ sK6 ) )
| ( $true
= ( sK1 @ sK5 @ sK6 ) )
| ( $true
= ( ( sK2 = sK5 )
& ( sK0 = sK6 ) ) ) ),
inference(binary_proxy_clausification,[],[f29]) ).
thf(f29,plain,
( ( ( ~ ( ( sK0 = sK6 )
& ( sK2 = sK5 ) )
& ( sK1 @ sK5 @ sK6 ) )
= $true )
| ( $true
= ( ( sK2 = sK5 )
& ( sK0 = sK6 ) ) )
| ( $true
= ( sK1 @ sK5 @ sK6 ) ) ),
inference(binary_proxy_clausification,[],[f15]) ).
thf(f15,plain,
( ( $true
= ( sK1 @ sK5 @ sK6 ) )
| ( $true
= ( ( ( sK2 = sK5 )
& ( sK0 = sK6 ) )
| ( ~ ( ( sK0 = sK6 )
& ( sK2 = sK5 ) )
& ( sK1 @ sK5 @ sK6 ) ) ) ) ),
inference(binary_proxy_clausification,[],[f14]) ).
thf(f57,plain,
( spl3_1
| spl3_2 ),
inference(avatar_split_clause,[],[f48,f54,f50]) ).
thf(f48,plain,
( ( $true
= ( sK1 @ sK5 @ sK6 ) )
| ( sK6 = sK0 ) ),
inference(equality_proxy_clausification,[],[f45]) ).
thf(f45,plain,
( ( $true
= ( sK1 @ sK5 @ sK6 ) )
| ( $true
= ( sK0 = sK6 ) ) ),
inference(binary_proxy_clausification,[],[f44]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SEV065^5 : TPTP v8.2.0. Released v4.0.0.
% 0.06/0.12 % Command : run_vampire %s %d THM
% 0.12/0.33 % Computer : n001.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 21 19:20:24 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.12/0.35 This is a TH0_THM_EQU_NAR problem
% 0.12/0.35 Running higher-order theorem proving
% 0.12/0.35 Running /export/starexec/sandbox2/solver/bin/vampire_ho --cores 7 --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol /export/starexec/sandbox2/benchmark/theBenchmark.p -m 16384 -t 300
% 0.12/0.37 % (16705)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.12/0.37 % (16706)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 theBenchmark for (2999ds/4Mi)
% 0.12/0.37 % (16710)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.12/0.37 % (16707)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 theBenchmark for (2999ds/27Mi)
% 0.12/0.37 % (16711)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on theBenchmark for (2999ds/275Mi)
% 0.12/0.37 % (16708)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.12/0.38 % (16708)Instruction limit reached!
% 0.12/0.38 % (16708)------------------------------
% 0.12/0.38 % (16708)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.12/0.38 % (16708)Termination reason: Unknown
% 0.12/0.38 % (16708)Termination phase: Saturation
% 0.12/0.38
% 0.12/0.38 % (16708)Memory used [KB]: 5500
% 0.12/0.38 % (16710)Instruction limit reached!
% 0.12/0.38 % (16710)------------------------------
% 0.12/0.38 % (16710)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.12/0.38 % (16708)Time elapsed: 0.004 s
% 0.12/0.38 % (16708)Instructions burned: 2 (million)
% 0.12/0.38 % (16708)------------------------------
% 0.12/0.38 % (16708)------------------------------
% 0.12/0.38 % (16710)Termination reason: Unknown
% 0.12/0.38 % (16710)Termination phase: Saturation
% 0.12/0.38
% 0.12/0.38 % (16710)Memory used [KB]: 5500
% 0.12/0.38 % (16710)Time elapsed: 0.004 s
% 0.12/0.38 % (16710)Instructions burned: 2 (million)
% 0.12/0.38 % (16710)------------------------------
% 0.12/0.38 % (16710)------------------------------
% 0.12/0.38 % (16705)First to succeed.
% 0.12/0.38 % (16712)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.12/0.38 % (16706)Instruction limit reached!
% 0.12/0.38 % (16706)------------------------------
% 0.12/0.38 % (16706)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.12/0.38 % (16706)Termination reason: Unknown
% 0.12/0.38 % (16706)Termination phase: Saturation
% 0.12/0.38
% 0.12/0.38 % (16706)Memory used [KB]: 5500
% 0.12/0.38 % (16706)Time elapsed: 0.006 s
% 0.12/0.38 % (16706)Instructions burned: 4 (million)
% 0.12/0.38 % (16706)------------------------------
% 0.12/0.38 % (16706)------------------------------
% 0.12/0.38 % (16711)Also succeeded, but the first one will report.
% 0.12/0.38 % (16705)Refutation found. Thanks to Tanya!
% 0.12/0.38 % SZS status Theorem for theBenchmark
% 0.12/0.38 % SZS output start Proof for theBenchmark
% See solution above
% 0.12/0.38 % (16705)------------------------------
% 0.12/0.38 % (16705)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.12/0.38 % (16705)Termination reason: Refutation
% 0.12/0.38
% 0.12/0.38 % (16705)Memory used [KB]: 5500
% 0.12/0.38 % (16705)Time elapsed: 0.007 s
% 0.12/0.38 % (16705)Instructions burned: 3 (million)
% 0.12/0.38 % (16705)------------------------------
% 0.12/0.38 % (16705)------------------------------
% 0.12/0.38 % (16702)Success in time 0.01 s
%------------------------------------------------------------------------------