TSTP Solution File: ALG279^5 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : ALG279^5 : TPTP v8.1.2. Bugfixed v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% Computer : n002.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 : Sun May 5 04:13:46 EDT 2024
% Result : Theorem 0.16s 0.40s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 13
% Syntax : Number of formulae : 49 ( 32 unt; 8 typ; 0 def)
% Number of atoms : 144 ( 79 equ; 0 cnn)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 318 ( 12 ~; 0 |; 23 &; 263 @)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 41 ( 41 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 6 usr; 6 con; 0-2 aty)
% ( 8 !!; 6 ??; 0 @@+; 0 @@-)
% Number of variables : 110 ( 33 ^ 65 !; 12 ?; 110 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
g: $tType ).
thf(func_def_0,type,
g: $tType ).
thf(func_def_1,type,
cGRP_RIGHT_INVERSE: ( g > g > g ) > g > $o ).
thf(func_def_2,type,
cGRP_RIGHT_UNIT: ( g > g > g ) > g > $o ).
thf(func_def_14,type,
sK0: g ).
thf(func_def_15,type,
sK1: g > g > g ).
thf(func_def_16,type,
sK2: g ).
thf(func_def_18,type,
sK4: g > g ).
thf(f100,plain,
$false,
inference(trivial_inequality_removal,[],[f94]) ).
thf(f94,plain,
sK2 != sK2,
inference(superposition,[],[f15,f87]) ).
thf(f87,plain,
! [X1: g] :
( ( sK1 @ sK0 @ X1 )
= X1 ),
inference(backward_demodulation,[],[f34,f86]) ).
thf(f86,plain,
! [X0: g,X1: g] :
( ( sK1 @ X0 @ ( sK1 @ ( sK4 @ X0 ) @ X1 ) )
= X1 ),
inference(forward_demodulation,[],[f82,f65]) ).
thf(f65,plain,
! [X0: g] :
( ( sK1 @ sK0 @ ( sK4 @ ( sK4 @ X0 ) ) )
= X0 ),
inference(forward_demodulation,[],[f56,f26]) ).
thf(f26,plain,
! [X1: g] :
( ( sK1 @ X1 @ sK0 )
= X1 ),
inference(equality_proxy_clausification,[],[f25]) ).
thf(f25,plain,
! [X1: g] :
( ( ( sK1 @ X1 @ sK0 )
= X1 )
= $true ),
inference(beta_eta_normalization,[],[f24]) ).
thf(f24,plain,
! [X1: g] :
( $true
= ( ^ [Y0: g] :
( ( sK1 @ Y0 @ sK0 )
= Y0 )
@ X1 ) ),
inference(pi_clausification,[],[f23]) ).
thf(f23,plain,
( $true
= ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ Y0 @ sK0 )
= Y0 ) ) ),
inference(beta_eta_normalization,[],[f22]) ).
thf(f22,plain,
( ( ^ [Y0: g > g > g,Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( Y0 @ Y2 @ Y1 )
= Y2 ) )
@ sK1
@ sK0 )
= $true ),
inference(definition_unfolding,[],[f17,f20]) ).
thf(f20,plain,
( cGRP_RIGHT_UNIT
= ( ^ [Y0: g > g > g,Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( Y0 @ Y2 @ Y1 )
= Y2 ) ) ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f9,plain,
( cGRP_RIGHT_UNIT
= ( ^ [Y0: g > g > g,Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( Y0 @ Y2 @ Y1 )
= Y2 ) ) ) ),
inference(fool_elimination,[],[f2]) ).
thf(f2,axiom,
( ( ^ [X0: g > g > g,X1: g] :
! [X2: g] :
( ( X0 @ X2 @ X1 )
= X2 ) )
= cGRP_RIGHT_UNIT ),
file('/export/starexec/sandbox/tmp/tmp.5nAfkS80yg/Vampire---4.8_31257',cGRP_RIGHT_UNIT_def) ).
thf(f17,plain,
( ( cGRP_RIGHT_UNIT @ sK1 @ sK0 )
= $true ),
inference(cnf_transformation,[],[f14]) ).
thf(f14,plain,
( ( ( cGRP_RIGHT_INVERSE @ sK1 @ sK0 )
= $true )
& ( ( cGRP_RIGHT_UNIT @ sK1 @ sK0 )
= $true )
& ! [X2: g,X3: g,X4: g] :
( ( sK1 @ ( sK1 @ X4 @ X2 ) @ X3 )
= ( sK1 @ X4 @ ( sK1 @ X2 @ X3 ) ) )
& ( sK2
!= ( sK1 @ sK0 @ sK2 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f11,f13,f12]) ).
thf(f12,plain,
( ? [X0: g,X1: g > g > g] :
( ( $true
= ( cGRP_RIGHT_INVERSE @ X1 @ X0 ) )
& ( $true
= ( cGRP_RIGHT_UNIT @ X1 @ X0 ) )
& ! [X2: g,X3: g,X4: g] :
( ( X1 @ X4 @ ( X1 @ X2 @ X3 ) )
= ( X1 @ ( X1 @ X4 @ X2 ) @ X3 ) )
& ? [X5: g] :
( ( X1 @ X0 @ X5 )
!= X5 ) )
=> ( ( ( cGRP_RIGHT_INVERSE @ sK1 @ sK0 )
= $true )
& ( ( cGRP_RIGHT_UNIT @ sK1 @ sK0 )
= $true )
& ! [X4: g,X3: g,X2: g] :
( ( sK1 @ ( sK1 @ X4 @ X2 ) @ X3 )
= ( sK1 @ X4 @ ( sK1 @ X2 @ X3 ) ) )
& ? [X5: g] :
( ( sK1 @ sK0 @ X5 )
!= X5 ) ) ),
introduced(choice_axiom,[]) ).
thf(f13,plain,
( ? [X5: g] :
( ( sK1 @ sK0 @ X5 )
!= X5 )
=> ( sK2
!= ( sK1 @ sK0 @ sK2 ) ) ),
introduced(choice_axiom,[]) ).
thf(f11,plain,
? [X0: g,X1: g > g > g] :
( ( $true
= ( cGRP_RIGHT_INVERSE @ X1 @ X0 ) )
& ( $true
= ( cGRP_RIGHT_UNIT @ X1 @ X0 ) )
& ! [X2: g,X3: g,X4: g] :
( ( X1 @ X4 @ ( X1 @ X2 @ X3 ) )
= ( X1 @ ( X1 @ X4 @ X2 ) @ X3 ) )
& ? [X5: g] :
( ( X1 @ X0 @ X5 )
!= X5 ) ),
inference(flattening,[],[f10]) ).
thf(f10,plain,
? [X0: g,X1: g > g > g] :
( ? [X5: g] :
( ( X1 @ X0 @ X5 )
!= X5 )
& ( $true
= ( cGRP_RIGHT_INVERSE @ X1 @ X0 ) )
& ( $true
= ( cGRP_RIGHT_UNIT @ X1 @ X0 ) )
& ! [X2: g,X3: g,X4: g] :
( ( X1 @ X4 @ ( X1 @ X2 @ X3 ) )
= ( X1 @ ( X1 @ X4 @ X2 ) @ X3 ) ) ),
inference(ennf_transformation,[],[f7]) ).
thf(f7,plain,
~ ! [X0: g,X1: g > g > g] :
( ( ( $true
= ( cGRP_RIGHT_INVERSE @ X1 @ X0 ) )
& ( $true
= ( cGRP_RIGHT_UNIT @ X1 @ X0 ) )
& ! [X2: g,X3: g,X4: g] :
( ( X1 @ X4 @ ( X1 @ X2 @ X3 ) )
= ( X1 @ ( X1 @ X4 @ X2 ) @ X3 ) ) )
=> ! [X5: g] :
( ( X1 @ X0 @ X5 )
= X5 ) ),
inference(fool_elimination,[],[f6]) ).
thf(f6,plain,
~ ! [X0: g,X1: g > g > g] :
( ( ( cGRP_RIGHT_UNIT @ X1 @ X0 )
& ( cGRP_RIGHT_INVERSE @ X1 @ X0 )
& ! [X2: g,X3: g,X4: g] :
( ( X1 @ X4 @ ( X1 @ X2 @ X3 ) )
= ( X1 @ ( X1 @ X4 @ X2 ) @ X3 ) ) )
=> ! [X5: g] :
( ( X1 @ X0 @ X5 )
= X5 ) ),
inference(rectify,[],[f4]) ).
thf(f4,negated_conjecture,
~ ! [X1: g,X0: g > g > g] :
( ( ( cGRP_RIGHT_UNIT @ X0 @ X1 )
& ( cGRP_RIGHT_INVERSE @ X0 @ X1 )
& ! [X3: g,X4: g,X2: g] :
( ( X0 @ ( X0 @ X2 @ X3 ) @ X4 )
= ( X0 @ X2 @ ( X0 @ X3 @ X4 ) ) ) )
=> ! [X2: g] :
( ( X0 @ X1 @ X2 )
= X2 ) ),
inference(negated_conjecture,[],[f3]) ).
thf(f3,conjecture,
! [X1: g,X0: g > g > g] :
( ( ( cGRP_RIGHT_UNIT @ X0 @ X1 )
& ( cGRP_RIGHT_INVERSE @ X0 @ X1 )
& ! [X3: g,X4: g,X2: g] :
( ( X0 @ ( X0 @ X2 @ X3 ) @ X4 )
= ( X0 @ X2 @ ( X0 @ X3 @ X4 ) ) ) )
=> ! [X2: g] :
( ( X0 @ X1 @ X2 )
= X2 ) ),
file('/export/starexec/sandbox/tmp/tmp.5nAfkS80yg/Vampire---4.8_31257',cE13A2A) ).
thf(f56,plain,
! [X0: g] :
( ( sK1 @ X0 @ sK0 )
= ( sK1 @ sK0 @ ( sK4 @ ( sK4 @ X0 ) ) ) ),
inference(superposition,[],[f34,f32]) ).
thf(f32,plain,
! [X1: g] :
( sK0
= ( sK1 @ X1 @ ( sK4 @ X1 ) ) ),
inference(equality_proxy_clausification,[],[f31]) ).
thf(f31,plain,
! [X1: g] :
( ( ( sK1 @ X1 @ ( sK4 @ X1 ) )
= sK0 )
= $true ),
inference(beta_eta_normalization,[],[f30]) ).
thf(f30,plain,
! [X1: g] :
( ( ^ [Y0: g] :
( ( sK1 @ X1 @ Y0 )
= sK0 )
@ ( sK4 @ X1 ) )
= $true ),
inference(sigma_clausification,[],[f29]) ).
thf(f29,plain,
! [X1: g] :
( $true
= ( ?? @ g
@ ^ [Y0: g] :
( ( sK1 @ X1 @ Y0 )
= sK0 ) ) ),
inference(beta_eta_normalization,[],[f28]) ).
thf(f28,plain,
! [X1: g] :
( ( ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y0 @ Y1 )
= sK0 ) )
@ X1 )
= $true ),
inference(pi_clausification,[],[f27]) ).
thf(f27,plain,
( $true
= ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y0 @ Y1 )
= sK0 ) ) ) ),
inference(beta_eta_normalization,[],[f21]) ).
thf(f21,plain,
( $true
= ( ^ [Y0: g > g > g,Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ?? @ g
@ ^ [Y3: g] :
( ( Y0 @ Y2 @ Y3 )
= Y1 ) ) )
@ sK1
@ sK0 ) ),
inference(definition_unfolding,[],[f18,f19]) ).
thf(f19,plain,
( cGRP_RIGHT_INVERSE
= ( ^ [Y0: g > g > g,Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ?? @ g
@ ^ [Y3: g] :
( ( Y0 @ Y2 @ Y3 )
= Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f8,plain,
( cGRP_RIGHT_INVERSE
= ( ^ [Y0: g > g > g,Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ?? @ g
@ ^ [Y3: g] :
( ( Y0 @ Y2 @ Y3 )
= Y1 ) ) ) ) ),
inference(fool_elimination,[],[f1]) ).
thf(f1,axiom,
( cGRP_RIGHT_INVERSE
= ( ^ [X0: g > g > g,X1: g] :
! [X2: g] :
? [X3: g] :
( ( X0 @ X2 @ X3 )
= X1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.5nAfkS80yg/Vampire---4.8_31257',cGRP_RIGHT_INVERSE_def) ).
thf(f18,plain,
( ( cGRP_RIGHT_INVERSE @ sK1 @ sK0 )
= $true ),
inference(cnf_transformation,[],[f14]) ).
thf(f82,plain,
! [X0: g,X1: g] :
( ( sK1 @ X0 @ ( sK1 @ ( sK4 @ X0 ) @ X1 ) )
= ( sK1 @ sK0 @ ( sK4 @ ( sK4 @ X1 ) ) ) ),
inference(superposition,[],[f34,f72]) ).
thf(f72,plain,
! [X0: g,X1: g] :
( ( sK1 @ X1 @ X0 )
= ( sK1 @ X1 @ ( sK4 @ ( sK4 @ X0 ) ) ) ),
inference(superposition,[],[f33,f65]) ).
thf(f33,plain,
! [X0: g,X1: g] :
( ( sK1 @ X0 @ X1 )
= ( sK1 @ X0 @ ( sK1 @ sK0 @ X1 ) ) ),
inference(superposition,[],[f16,f26]) ).
thf(f16,plain,
! [X2: g,X3: g,X4: g] :
( ( sK1 @ ( sK1 @ X4 @ X2 ) @ X3 )
= ( sK1 @ X4 @ ( sK1 @ X2 @ X3 ) ) ),
inference(cnf_transformation,[],[f14]) ).
thf(f34,plain,
! [X0: g,X1: g] :
( ( sK1 @ X0 @ ( sK1 @ ( sK4 @ X0 ) @ X1 ) )
= ( sK1 @ sK0 @ X1 ) ),
inference(superposition,[],[f16,f32]) ).
thf(f15,plain,
( sK2
!= ( sK1 @ sK0 @ sK2 ) ),
inference(cnf_transformation,[],[f14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : ALG279^5 : TPTP v8.1.2. Bugfixed v5.3.0.
% 0.14/0.15 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.16/0.36 % Computer : n002.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Fri May 3 19:59:08 EDT 2024
% 0.16/0.36 % CPUTime :
% 0.16/0.36 This is a TH0_THM_EQU_NAR problem
% 0.16/0.37 Running vampire_ho --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol --cores 8 -m 12000 -t 300 /export/starexec/sandbox/tmp/tmp.5nAfkS80yg/Vampire---4.8_31257
% 0.16/0.38 % (31509)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on Vampire---4 for (2999ds/183Mi)
% 0.16/0.38 % (31510)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 Vampire---4 for (2999ds/4Mi)
% 0.16/0.38 % (31511)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 Vampire---4 for (2999ds/27Mi)
% 0.16/0.38 % (31512)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on Vampire---4 for (2999ds/2Mi)
% 0.16/0.38 % (31514)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on Vampire---4 for (2999ds/275Mi)
% 0.16/0.38 % (31513)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on Vampire---4 for (2999ds/2Mi)
% 0.16/0.38 % (31515)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on Vampire---4 for (2999ds/18Mi)
% 0.16/0.38 % (31516)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on Vampire---4 for (2999ds/3Mi)
% 0.16/0.39 % (31513)Instruction limit reached!
% 0.16/0.39 % (31513)------------------------------
% 0.16/0.39 % (31513)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.39 % (31513)Termination reason: Unknown
% 0.16/0.39 % (31513)Termination phase: Property scanning
% 0.16/0.39
% 0.16/0.39 % (31513)Memory used [KB]: 895
% 0.16/0.39 % (31513)Time elapsed: 0.003 s
% 0.16/0.39 % (31513)Instructions burned: 2 (million)
% 0.16/0.39 % (31513)------------------------------
% 0.16/0.39 % (31513)------------------------------
% 0.16/0.39 % (31512)Instruction limit reached!
% 0.16/0.39 % (31512)------------------------------
% 0.16/0.39 % (31512)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.39 % (31512)Termination reason: Unknown
% 0.16/0.39 % (31512)Termination phase: Saturation
% 0.16/0.39
% 0.16/0.39 % (31512)Memory used [KB]: 5500
% 0.16/0.39 % (31512)Time elapsed: 0.004 s
% 0.16/0.39 % (31512)Instructions burned: 3 (million)
% 0.16/0.39 % (31512)------------------------------
% 0.16/0.39 % (31512)------------------------------
% 0.16/0.39 % (31516)Instruction limit reached!
% 0.16/0.39 % (31516)------------------------------
% 0.16/0.39 % (31516)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.39 % (31516)Termination reason: Unknown
% 0.16/0.39 % (31516)Termination phase: Saturation
% 0.16/0.39
% 0.16/0.39 % (31516)Memory used [KB]: 5500
% 0.16/0.39 % (31516)Time elapsed: 0.004 s
% 0.16/0.39 % (31516)Instructions burned: 3 (million)
% 0.16/0.39 % (31516)------------------------------
% 0.16/0.39 % (31516)------------------------------
% 0.16/0.39 % (31510)Instruction limit reached!
% 0.16/0.39 % (31510)------------------------------
% 0.16/0.39 % (31510)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.39 % (31510)Termination reason: Unknown
% 0.16/0.39 % (31510)Termination phase: Saturation
% 0.16/0.39
% 0.16/0.39 % (31510)Memory used [KB]: 5500
% 0.16/0.39 % (31510)Time elapsed: 0.006 s
% 0.16/0.39 % (31510)Instructions burned: 5 (million)
% 0.16/0.39 % (31510)------------------------------
% 0.16/0.39 % (31510)------------------------------
% 0.16/0.39 % (31514)Refutation not found, incomplete strategy
% 0.16/0.39 % (31514)------------------------------
% 0.16/0.39 % (31514)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.39 % (31514)Termination reason: Refutation not found, incomplete strategy
% 0.16/0.39
% 0.16/0.39
% 0.16/0.39 % (31514)Memory used [KB]: 5500
% 0.16/0.39 % (31514)Time elapsed: 0.006 s
% 0.16/0.39 % (31514)Instructions burned: 5 (million)
% 0.16/0.39 % (31514)------------------------------
% 0.16/0.39 % (31514)------------------------------
% 0.16/0.40 % (31515)First to succeed.
% 0.16/0.40 % (31515)Refutation found. Thanks to Tanya!
% 0.16/0.40 % SZS status Theorem for Vampire---4
% 0.16/0.40 % SZS output start Proof for Vampire---4
% See solution above
% 0.16/0.40 % (31515)------------------------------
% 0.16/0.40 % (31515)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.40 % (31515)Termination reason: Refutation
% 0.16/0.40
% 0.16/0.40 % (31515)Memory used [KB]: 5500
% 0.16/0.40 % (31515)Time elapsed: 0.014 s
% 0.16/0.40 % (31515)Instructions burned: 16 (million)
% 0.16/0.40 % (31515)------------------------------
% 0.16/0.40 % (31515)------------------------------
% 0.16/0.40 % (31508)Success in time 0.038 s
% 0.16/0.40 % Vampire---4.8 exiting
%------------------------------------------------------------------------------