TSTP Solution File: SEV239^5 by Vampire---4.9
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.9
% Problem : SEV239^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire %s %d THM
% Computer : n028.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 16:02:25 EDT 2024
% Result : Theorem 0.14s 0.31s
% Output : Refutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 7
% Syntax : Number of formulae : 61 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 365 ( 140 equ; 23 cnn)
% Maximal formula atoms : 5 ( 5 avg)
% Number of connectives : 351 ( 50 ~; 75 |; 36 &; 162 @)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 30 ( 30 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 12 usr; 13 con; 0-2 aty)
% ( 0 !!; 22 ??; 0 @@+; 0 @@-)
% Number of variables : 72 ( 46 ^ 20 !; 6 ?; 72 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_1,type,
y: a > $o ).
thf(func_def_13,type,
ph1:
!>[X0: $tType] : X0 ).
thf(func_def_14,type,
sK2: a ).
thf(func_def_15,type,
sK3: a > $o ).
thf(func_def_16,type,
sK4: a ).
thf(func_def_17,type,
sK5: a ).
thf(f123,plain,
$false,
inference(avatar_sat_refutation,[],[f37,f42,f47,f55,f63,f69,f122]) ).
thf(f122,plain,
( ~ spl0_1
| spl0_2
| ~ spl0_3
| ~ spl0_4 ),
inference(avatar_contradiction_clause,[],[f121]) ).
thf(f121,plain,
( $false
| ~ spl0_1
| spl0_2
| ~ spl0_3
| ~ spl0_4 ),
inference(subsumption_resolution,[],[f120,f35]) ).
thf(f35,plain,
( ( ( y @ sK2 )
!= $true )
| spl0_2 ),
inference(avatar_component_clause,[],[f34]) ).
thf(f34,plain,
( spl0_2
<=> ( ( y @ sK2 )
= $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
thf(f120,plain,
( ( ( y @ sK2 )
= $true )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_4 ),
inference(superposition,[],[f41,f118]) ).
thf(f118,plain,
( ( sK2 = sK4 )
| ~ spl0_1
| ~ spl0_4 ),
inference(trivial_inequality_removal,[],[f113]) ).
thf(f113,plain,
( ( sK2 = sK4 )
| ( $true = $false )
| ~ spl0_1
| ~ spl0_4 ),
inference(superposition,[],[f76,f32]) ).
thf(f32,plain,
( ( $true
= ( sK3 @ sK2 ) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f30]) ).
thf(f30,plain,
( spl0_1
<=> ( $true
= ( sK3 @ sK2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
thf(f76,plain,
( ! [X1: a] :
( ( $false
= ( sK3 @ X1 ) )
| ( sK4 = X1 ) )
| ~ spl0_4 ),
inference(equality_proxy_clausification,[],[f73]) ).
thf(f73,plain,
( ! [X1: a] :
( ( $true
= ( sK4 = X1 ) )
| ( $false
= ( sK3 @ X1 ) ) )
| ~ spl0_4 ),
inference(binary_proxy_clausification,[],[f71]) ).
thf(f71,plain,
( ! [X1: a] :
( ( sK4 = X1 )
= ( sK3 @ X1 ) )
| ~ spl0_4 ),
inference(argument_congruence,[],[f46]) ).
thf(f46,plain,
( ( sK3
= ( (=) @ sK4 ) )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f44]) ).
thf(f44,plain,
( spl0_4
<=> ( sK3
= ( (=) @ sK4 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
thf(f41,plain,
( ( $true
= ( y @ sK4 ) )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f39]) ).
thf(f39,plain,
( spl0_3
<=> ( $true
= ( y @ sK4 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
thf(f69,plain,
( ~ spl0_2
| ~ spl0_6 ),
inference(avatar_contradiction_clause,[],[f68]) ).
thf(f68,plain,
( $false
| ~ spl0_2
| ~ spl0_6 ),
inference(trivial_inequality_removal,[],[f64]) ).
thf(f64,plain,
( ( $true = $false )
| ~ spl0_2
| ~ spl0_6 ),
inference(superposition,[],[f54,f36]) ).
thf(f36,plain,
( ( ( y @ sK2 )
= $true )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f34]) ).
thf(f54,plain,
( ( ( y @ sK2 )
= $false )
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f52]) ).
thf(f52,plain,
( spl0_6
<=> ( ( y @ sK2 )
= $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
thf(f63,plain,
( ~ spl0_2
| ~ spl0_5 ),
inference(avatar_contradiction_clause,[],[f62]) ).
thf(f62,plain,
( $false
| ~ spl0_2
| ~ spl0_5 ),
inference(trivial_inequality_removal,[],[f58]) ).
thf(f58,plain,
( ( $true = $false )
| ( sK2 != sK2 )
| ~ spl0_2
| ~ spl0_5 ),
inference(superposition,[],[f57,f36]) ).
thf(f57,plain,
( ! [X0: a] :
( ( $false
= ( y @ X0 ) )
| ( sK2 != X0 ) )
| ~ spl0_5 ),
inference(equality_proxy_clausification,[],[f56]) ).
thf(f56,plain,
( ! [X0: a] :
( ( $false
= ( X0 = sK2 ) )
| ( $false
= ( y @ X0 ) ) )
| ~ spl0_5 ),
inference(equality_resolution,[],[f50]) ).
thf(f50,plain,
( ! [X2: a,X1: a > $o] :
( ( ( (=) @ X2 )
!= X1 )
| ( $false
= ( X1 @ sK2 ) )
| ( ( y @ X2 )
= $false ) )
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f49]) ).
thf(f49,plain,
( spl0_5
<=> ! [X2: a,X1: a > $o] :
( ( ( y @ X2 )
= $false )
| ( $false
= ( X1 @ sK2 ) )
| ( ( (=) @ X2 )
!= X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
thf(f55,plain,
( spl0_5
| spl0_6 ),
inference(avatar_split_clause,[],[f19,f52,f49]) ).
thf(f19,plain,
! [X2: a,X1: a > $o] :
( ( ( y @ X2 )
= $false )
| ( ( y @ sK2 )
= $false )
| ( ( (=) @ X2 )
!= X1 )
| ( $false
= ( X1 @ sK2 ) ) ),
inference(equality_proxy_clausification,[],[f18]) ).
thf(f18,plain,
! [X2: a,X1: a > $o] :
( ( $false
= ( X1 @ sK2 ) )
| ( ( y @ X2 )
= $false )
| ( ( y @ sK2 )
= $false )
| ( $false
= ( X1
= ( (=) @ X2 ) ) ) ),
inference(binary_proxy_clausification,[],[f17]) ).
thf(f17,plain,
! [X2: a,X1: a > $o] :
( ( ( y @ sK2 )
= $false )
| ( $false
= ( ( X1
= ( (=) @ X2 ) )
& ( y @ X2 ) ) )
| ( $false
= ( X1 @ sK2 ) ) ),
inference(beta_eta_normalization,[],[f16]) ).
thf(f16,plain,
! [X2: a,X1: a > $o] :
( ( ( y @ sK2 )
= $false )
| ( $false
= ( X1 @ sK2 ) )
| ( $false
= ( ^ [Y0: a] :
( ( X1
= ( (=) @ Y0 ) )
& ( y @ Y0 ) )
@ X2 ) ) ),
inference(pi_clausification,[],[f15]) ).
thf(f15,plain,
! [X1: a > $o] :
( ( ( y @ sK2 )
= $false )
| ( $false
= ( X1 @ sK2 ) )
| ( $false
= ( ?? @ a
@ ^ [Y0: a] :
( ( X1
= ( (=) @ Y0 ) )
& ( y @ Y0 ) ) ) ) ),
inference(binary_proxy_clausification,[],[f14]) ).
thf(f14,plain,
! [X1: a > $o] :
( ( ( y @ sK2 )
= $false )
| ( $false
= ( ( ?? @ a
@ ^ [Y0: a] :
( ( X1
= ( (=) @ Y0 ) )
& ( y @ Y0 ) ) )
& ( X1 @ sK2 ) ) ) ),
inference(beta_eta_normalization,[],[f13]) ).
thf(f13,plain,
! [X1: a > $o] :
( ( $false
= ( ^ [Y0: a > $o] :
( ( ?? @ a
@ ^ [Y1: a] :
( ( Y0
= ( (=) @ Y1 ) )
& ( y @ Y1 ) ) )
& ( Y0 @ sK2 ) )
@ X1 ) )
| ( ( y @ sK2 )
= $false ) ),
inference(pi_clausification,[],[f12]) ).
thf(f12,plain,
( ( ( y @ sK2 )
= $false )
| ( ( ?? @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ?? @ a
@ ^ [Y1: a] :
( ( Y0
= ( (=) @ Y1 ) )
& ( y @ Y1 ) ) )
& ( Y0 @ sK2 ) ) )
= $false ) ),
inference(binary_proxy_clausification,[],[f10]) ).
thf(f10,plain,
( ( ?? @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ?? @ a
@ ^ [Y1: a] :
( ( Y0
= ( (=) @ Y1 ) )
& ( y @ Y1 ) ) )
& ( Y0 @ sK2 ) ) )
!= ( y @ sK2 ) ),
inference(beta_eta_normalization,[],[f9]) ).
thf(f9,plain,
( ( ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ?? @ a
@ ^ [Y2: a] :
( ( Y1
= ( (=) @ Y2 ) )
& ( y @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ sK2 )
!= ( y @ sK2 ) ),
inference(negative_extensionality,[],[f8]) ).
thf(f8,plain,
( y
!= ( ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ?? @ a
@ ^ [Y2: a] :
( ( Y1
= ( (=) @ Y2 ) )
& ( y @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) ) ),
inference(beta_eta_normalization,[],[f7]) ).
thf(f7,plain,
( y
!= ( ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ?? @ a
@ ^ [Y2: a] :
( ( Y1
= ( ^ [Y3: a,Y4: a] : ( Y3 = Y4 )
@ Y2 ) )
& ( y @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f6]) ).
thf(f6,plain,
( y
!= ( ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ?? @ a
@ ^ [Y2: a] :
( ( Y1
= ( ^ [Y3: a,Y4: a] : ( Y3 = Y4 )
@ Y2 ) )
& ( y @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) ) ),
inference(flattening,[],[f5]) ).
thf(f5,plain,
( y
!= ( ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ?? @ a
@ ^ [Y2: a] :
( ( Y1
= ( ^ [Y3: a,Y4: a] : ( Y3 = Y4 )
@ Y2 ) )
& ( y @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f4]) ).
thf(f4,plain,
( ( ^ [X0: a] :
? [X1: a > $o] :
( ( X1 @ X0 )
& ? [X2: a] :
( ( y @ X2 )
& ( X1
= ( ^ [X3: a,X4: a] : ( X3 = X4 )
@ X2 ) ) ) ) )
!= y ),
inference(rectify,[],[f2]) ).
thf(f2,negated_conjecture,
( ( ^ [X0: a] :
? [X1: a > $o] :
( ( X1 @ X0 )
& ? [X2: a] :
( ( y @ X2 )
& ( X1
= ( ^ [X0: a,X3: a] : ( X0 = X3 )
@ X2 ) ) ) ) )
!= y ),
inference(negated_conjecture,[],[f1]) ).
thf(f1,conjecture,
( ( ^ [X0: a] :
? [X1: a > $o] :
( ( X1 @ X0 )
& ? [X2: a] :
( ( y @ X2 )
& ( X1
= ( ^ [X0: a,X3: a] : ( X0 = X3 )
@ X2 ) ) ) ) )
= y ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cX5211_pme) ).
thf(f47,plain,
( spl0_2
| spl0_4 ),
inference(avatar_split_clause,[],[f28,f44,f34]) ).
thf(f28,plain,
( ( sK3
= ( (=) @ sK4 ) )
| ( ( y @ sK2 )
= $true ) ),
inference(equality_proxy_clausification,[],[f27]) ).
thf(f27,plain,
( ( ( y @ sK2 )
= $true )
| ( $true
= ( sK3
= ( (=) @ sK4 ) ) ) ),
inference(binary_proxy_clausification,[],[f25]) ).
thf(f25,plain,
( ( ( y @ sK2 )
= $true )
| ( $true
= ( ( sK3
= ( (=) @ sK4 ) )
& ( y @ sK4 ) ) ) ),
inference(beta_eta_normalization,[],[f24]) ).
thf(f24,plain,
( ( ( y @ sK2 )
= $true )
| ( $true
= ( ^ [Y0: a] :
( ( sK3
= ( (=) @ Y0 ) )
& ( y @ Y0 ) )
@ sK4 ) ) ),
inference(sigma_clausification,[],[f23]) ).
thf(f23,plain,
( ( ( y @ sK2 )
= $true )
| ( $true
= ( ?? @ a
@ ^ [Y0: a] :
( ( sK3
= ( (=) @ Y0 ) )
& ( y @ Y0 ) ) ) ) ),
inference(binary_proxy_clausification,[],[f21]) ).
thf(f21,plain,
( ( ( y @ sK2 )
= $true )
| ( $true
= ( ( ?? @ a
@ ^ [Y0: a] :
( ( sK3
= ( (=) @ Y0 ) )
& ( y @ Y0 ) ) )
& ( sK3 @ sK2 ) ) ) ),
inference(beta_eta_normalization,[],[f20]) ).
thf(f20,plain,
( ( $true
= ( ^ [Y0: a > $o] :
( ( ?? @ a
@ ^ [Y1: a] :
( ( Y0
= ( (=) @ Y1 ) )
& ( y @ Y1 ) ) )
& ( Y0 @ sK2 ) )
@ sK3 ) )
| ( ( y @ sK2 )
= $true ) ),
inference(sigma_clausification,[],[f11]) ).
thf(f11,plain,
( ( ( ?? @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ?? @ a
@ ^ [Y1: a] :
( ( Y0
= ( (=) @ Y1 ) )
& ( y @ Y1 ) ) )
& ( Y0 @ sK2 ) ) )
= $true )
| ( ( y @ sK2 )
= $true ) ),
inference(binary_proxy_clausification,[],[f10]) ).
thf(f42,plain,
( spl0_2
| spl0_3 ),
inference(avatar_split_clause,[],[f26,f39,f34]) ).
thf(f26,plain,
( ( $true
= ( y @ sK4 ) )
| ( ( y @ sK2 )
= $true ) ),
inference(binary_proxy_clausification,[],[f25]) ).
thf(f37,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f22,f34,f30]) ).
thf(f22,plain,
( ( $true
= ( sK3 @ sK2 ) )
| ( ( y @ sK2 )
= $true ) ),
inference(binary_proxy_clausification,[],[f21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08 % Problem : SEV239^5 : TPTP v8.2.0. Released v4.0.0.
% 0.00/0.08 % Command : run_vampire %s %d THM
% 0.08/0.28 % Computer : n028.cluster.edu
% 0.08/0.28 % Model : x86_64 x86_64
% 0.08/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.28 % Memory : 8042.1875MB
% 0.08/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.28 % CPULimit : 300
% 0.08/0.28 % WCLimit : 300
% 0.08/0.28 % DateTime : Fri Jun 21 19:12:53 EDT 2024
% 0.08/0.28 % CPUTime :
% 0.13/0.29 This is a TH0_THM_EQU_NAR problem
% 0.13/0.29 Running higher-order theorem proving
% 0.13/0.29 Running /export/starexec/sandbox/solver/bin/vampire_ho --cores 7 --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol /export/starexec/sandbox/benchmark/theBenchmark.p -m 16384 -t 300
% 0.14/0.30 % (15158)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (3000ds/183Mi)
% 0.14/0.30 % (15159)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 (3000ds/4Mi)
% 0.14/0.31 % (15158)First to succeed.
% 0.14/0.31 % (15159)Instruction limit reached!
% 0.14/0.31 % (15159)------------------------------
% 0.14/0.31 % (15159)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.14/0.31 % (15159)Termination reason: Unknown
% 0.14/0.31 % (15159)Termination phase: Saturation
% 0.14/0.31
% 0.14/0.31 % (15159)Memory used [KB]: 5500
% 0.14/0.31 % (15159)Time elapsed: 0.005 s
% 0.14/0.31 % (15159)Instructions burned: 5 (million)
% 0.14/0.31 % (15159)------------------------------
% 0.14/0.31 % (15159)------------------------------
% 0.14/0.31 % (15162)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 (3000ds/2Mi)
% 0.14/0.31 % (15161)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (3000ds/2Mi)
% 0.14/0.31 % (15158)Refutation found. Thanks to Tanya!
% 0.14/0.31 % SZS status Theorem for theBenchmark
% 0.14/0.31 % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.31 % (15158)------------------------------
% 0.14/0.31 % (15158)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.14/0.31 % (15158)Termination reason: Refutation
% 0.14/0.31
% 0.14/0.31 % (15158)Memory used [KB]: 5500
% 0.14/0.31 % (15158)Time elapsed: 0.005 s
% 0.14/0.31 % (15158)Instructions burned: 5 (million)
% 0.14/0.31 % (15158)------------------------------
% 0.14/0.31 % (15158)------------------------------
% 0.14/0.31 % (15157)Success in time 0.004 s
%------------------------------------------------------------------------------