TSTP Solution File: SEV179^5 by Vampire---4.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.9
% Problem : SEV179^5 : TPTP v8.2.0. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire %s %d THM
% Computer : n029.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 16:02:08 EDT 2024
% Result : Theorem 0.21s 0.38s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 3
% Syntax : Number of formulae : 31 ( 23 unt; 0 typ; 0 def)
% Number of atoms : 141 ( 60 equ; 0 cnn)
% Maximal formula atoms : 2 ( 4 avg)
% Number of connectives : 277 ( 39 ~; 4 |; 25 &; 189 @)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 72 ( 72 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 7 usr; 3 con; 0-2 aty)
% ( 0 !!; 19 ??; 0 @@+; 0 @@-)
% Number of variables : 60 ( 46 ^ 10 !; 4 ?; 60 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
cD_FOR_X5309: ( ( $i > $o ) > $i ) > $i > $o ).
thf(func_def_2,type,
vEPSILON:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_13,type,
sK0: ( $i > $o ) > $i ).
thf(func_def_15,type,
ph2:
!>[X0: $tType] : X0 ).
thf(func_def_16,type,
sK3: $i > $o ).
thf(func_def_17,type,
sK4: $i > $o ).
thf(func_def_18,type,
sK5: $i > $o ).
thf(f53,plain,
$false,
inference(trivial_inequality_removal,[],[f52]) ).
thf(f52,plain,
$false = $true,
inference(forward_demodulation,[],[f42,f27]) ).
thf(f27,plain,
( ( sK3 @ ( sK0 @ sK3 ) )
= $false ),
inference(not_proxy_clausification,[],[f26]) ).
thf(f26,plain,
( ( ~ ( sK3 @ ( sK0 @ sK3 ) ) )
= $true ),
inference(binary_proxy_clausification,[],[f24]) ).
thf(f24,plain,
( ( ~ ( sK3 @ ( sK0 @ sK3 ) )
& ( ( sK0 @ sK3 )
= ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK0 @ Y1 ) )
& ( ( sK0 @ Y1 )
= Y0 ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[],[f23]) ).
thf(f23,plain,
( ( ^ [Y0: $i > $o] :
( ~ ( Y0 @ ( sK0 @ Y0 ) )
& ( ( sK0 @ Y0 )
= ( sK0
@ ^ [Y1: $i] :
( ?? @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( Y2 @ ( sK0 @ Y2 ) )
& ( ( sK0 @ Y2 )
= Y1 ) ) ) ) ) )
@ sK3 )
= $true ),
inference(sigma_clausification,[],[f22]) ).
thf(f22,plain,
( ( ?? @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ~ ( Y0 @ ( sK0 @ Y0 ) )
& ( ( sK0 @ Y0 )
= ( sK0
@ ^ [Y1: $i] :
( ?? @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( Y2 @ ( sK0 @ Y2 ) )
& ( ( sK0 @ Y2 )
= Y1 ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[],[f21]) ).
thf(f21,plain,
( ( ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK0 @ Y1 ) )
& ( ( sK0 @ Y1 )
= Y0 ) ) )
@ ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK0 @ Y1 ) )
& ( ( sK0 @ Y1 )
= Y0 ) ) ) ) )
= $true ),
inference(equality_resolution,[],[f20]) ).
thf(f20,plain,
! [X1: $i > $o] :
( ( ( sK0 @ X1 )
!= ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK0 @ Y1 ) )
& ( ( sK0 @ Y1 )
= Y0 ) ) ) ) )
| ( ( X1 @ ( sK0 @ X1 ) )
= $true ) ),
inference(equality_proxy_clausification,[],[f19]) ).
thf(f19,plain,
! [X1: $i > $o] :
( ( ( X1 @ ( sK0 @ X1 ) )
= $true )
| ( $false
= ( ( sK0 @ X1 )
= ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK0 @ Y1 ) )
& ( ( sK0 @ Y1 )
= Y0 ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f18]) ).
thf(f18,plain,
! [X1: $i > $o] :
( ( $false
= ( ~ ( X1 @ ( sK0 @ X1 ) ) ) )
| ( $false
= ( ( sK0 @ X1 )
= ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK0 @ Y1 ) )
& ( ( sK0 @ Y1 )
= Y0 ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f17]) ).
thf(f17,plain,
! [X1: $i > $o] :
( ( ~ ( X1 @ ( sK0 @ X1 ) )
& ( ( sK0 @ X1 )
= ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK0 @ Y1 ) )
& ( ( sK0 @ Y1 )
= Y0 ) ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[],[f16]) ).
thf(f16,plain,
! [X1: $i > $o] :
( ( ^ [Y0: $i > $o] :
( ~ ( Y0 @ ( sK0 @ Y0 ) )
& ( ( sK0 @ Y0 )
= ( sK0
@ ^ [Y1: $i] :
( ?? @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( Y2 @ ( sK0 @ Y2 ) )
& ( ( sK0 @ Y2 )
= Y1 ) ) ) ) ) )
@ X1 )
= $false ),
inference(pi_clausification,[],[f15]) ).
thf(f15,plain,
( ( ?? @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ~ ( Y0 @ ( sK0 @ Y0 ) )
& ( ( sK0 @ Y0 )
= ( sK0
@ ^ [Y1: $i] :
( ?? @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( Y2 @ ( sK0 @ Y2 ) )
& ( ( sK0 @ Y2 )
= Y1 ) ) ) ) ) ) )
!= $true ),
inference(beta_eta_normalization,[],[f14]) ).
thf(f14,plain,
( ( ^ [Y0: ( $i > $o ) > $i,Y1: $i] :
( ?? @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( Y2 @ ( Y0 @ Y2 ) )
& ( ( Y0 @ Y2 )
= Y1 ) ) )
@ sK0
@ ( sK0
@ ( ^ [Y0: ( $i > $o ) > $i,Y1: $i] :
( ?? @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( Y2 @ ( Y0 @ Y2 ) )
& ( ( Y0 @ Y2 )
= Y1 ) ) )
@ sK0 ) ) )
!= $true ),
inference(definition_unfolding,[],[f12,f13,f13]) ).
thf(f13,plain,
( cD_FOR_X5309
= ( ^ [Y0: ( $i > $o ) > $i,Y1: $i] :
( ?? @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( Y2 @ ( Y0 @ Y2 ) )
& ( ( Y0 @ Y2 )
= Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f8,plain,
( cD_FOR_X5309
= ( ^ [Y0: ( $i > $o ) > $i,Y1: $i] :
( ?? @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( Y2 @ ( Y0 @ Y2 ) )
& ( ( Y0 @ Y2 )
= Y1 ) ) ) ) ),
inference(fool_elimination,[],[f7]) ).
thf(f7,plain,
( cD_FOR_X5309
= ( ^ [X0: ( $i > $o ) > $i,X1: $i] :
? [X2: $i > $o] :
( ( ( X0 @ X2 )
= X1 )
& ~ ( X2 @ ( X0 @ X2 ) ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f1,axiom,
( cD_FOR_X5309
= ( ^ [X0: ( $i > $o ) > $i,X1: $i] :
? [X2: $i > $o] :
( ( ( X0 @ X2 )
= X1 )
& ~ ( X2 @ ( X0 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cD_FOR_X5309_def) ).
thf(f12,plain,
( ( cD_FOR_X5309 @ sK0 @ ( sK0 @ ( cD_FOR_X5309 @ sK0 ) ) )
!= $true ),
inference(cnf_transformation,[],[f11]) ).
thf(f11,plain,
( ( cD_FOR_X5309 @ sK0 @ ( sK0 @ ( cD_FOR_X5309 @ sK0 ) ) )
!= $true ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f9,f10]) ).
thf(f10,plain,
( ? [X0: ( $i > $o ) > $i] :
( ( cD_FOR_X5309 @ X0 @ ( X0 @ ( cD_FOR_X5309 @ X0 ) ) )
!= $true )
=> ( ( cD_FOR_X5309 @ sK0 @ ( sK0 @ ( cD_FOR_X5309 @ sK0 ) ) )
!= $true ) ),
introduced(choice_axiom,[]) ).
thf(f9,plain,
? [X0: ( $i > $o ) > $i] :
( ( cD_FOR_X5309 @ X0 @ ( X0 @ ( cD_FOR_X5309 @ X0 ) ) )
!= $true ),
inference(ennf_transformation,[],[f6]) ).
thf(f6,plain,
~ ! [X0: ( $i > $o ) > $i] :
( ( cD_FOR_X5309 @ X0 @ ( X0 @ ( cD_FOR_X5309 @ X0 ) ) )
= $true ),
inference(fool_elimination,[],[f5]) ).
thf(f5,plain,
~ ! [X0: ( $i > $o ) > $i] : ( cD_FOR_X5309 @ X0 @ ( X0 @ ( cD_FOR_X5309 @ X0 ) ) ),
inference(rectify,[],[f3]) ).
thf(f3,negated_conjecture,
~ ! [X0: ( $i > $o ) > $i] : ( cD_FOR_X5309 @ X0 @ ( X0 @ ( cD_FOR_X5309 @ X0 ) ) ),
inference(negated_conjecture,[],[f2]) ).
thf(f2,conjecture,
! [X0: ( $i > $o ) > $i] : ( cD_FOR_X5309 @ X0 @ ( X0 @ ( cD_FOR_X5309 @ X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM144C_pme) ).
thf(f42,plain,
( ( sK3 @ ( sK0 @ sK3 ) )
= $true ),
inference(equality_resolution,[],[f30]) ).
thf(f30,plain,
! [X0: $i > $o] :
( ( ( sK0 @ sK3 )
!= ( sK0 @ X0 ) )
| ( ( X0 @ ( sK0 @ X0 ) )
= $true ) ),
inference(superposition,[],[f20,f28]) ).
thf(f28,plain,
( ( sK0 @ sK3 )
= ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK0 @ Y1 ) )
& ( ( sK0 @ Y1 )
= Y0 ) ) ) ) ),
inference(equality_proxy_clausification,[],[f25]) ).
thf(f25,plain,
( ( ( sK0 @ sK3 )
= ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK0 @ Y1 ) )
& ( ( sK0 @ Y1 )
= Y0 ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[],[f24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEV179^5 : TPTP v8.2.0. Bugfixed v5.2.0.
% 0.03/0.12 % Command : run_vampire %s %d THM
% 0.12/0.34 % Computer : n029.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 21 18:54:09 EDT 2024
% 0.12/0.34 % CPUTime :
% 0.12/0.36 This is a TH0_THM_EQU_NAR problem
% 0.12/0.36 Running higher-order theorem proving
% 0.12/0.36 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
% 0.21/0.38 % (4880)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.21/0.38 % (4881)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)
% 0.21/0.38 % (4883)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.21/0.38 % (4884)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)
% 0.21/0.38 % (4882)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)
% 0.21/0.38 % (4885)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)
% 0.21/0.38 % (4886)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.21/0.38 % (4885)Refutation not found, incomplete strategy
% 0.21/0.38 % (4885)------------------------------
% 0.21/0.38 % (4885)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.21/0.38 % (4885)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.38
% 0.21/0.38
% 0.21/0.38 % (4885)Memory used [KB]: 5373
% 0.21/0.38 % (4885)Time elapsed: 0.003 s
% 0.21/0.38 % (4885)Instructions burned: 1 (million)
% 0.21/0.38 % (4885)------------------------------
% 0.21/0.38 % (4885)------------------------------
% 0.21/0.38 % (4883)Instruction limit reached!
% 0.21/0.38 % (4883)------------------------------
% 0.21/0.38 % (4883)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.21/0.38 % (4883)Termination reason: Unknown
% 0.21/0.38 % (4884)Instruction limit reached!
% 0.21/0.38 % (4884)------------------------------
% 0.21/0.38 % (4884)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.21/0.38 % (4884)Termination reason: Unknown
% 0.21/0.38 % (4884)Termination phase: Saturation
% 0.21/0.38
% 0.21/0.38 % (4884)Memory used [KB]: 5500
% 0.21/0.38 % (4884)Time elapsed: 0.004 s
% 0.21/0.38 % (4884)Instructions burned: 2 (million)
% 0.21/0.38 % (4884)------------------------------
% 0.21/0.38 % (4884)------------------------------
% 0.21/0.38 % (4883)Termination phase: Saturation
% 0.21/0.38
% 0.21/0.38 % (4883)Memory used [KB]: 5500
% 0.21/0.38 % (4883)Time elapsed: 0.004 s
% 0.21/0.38 % (4883)Instructions burned: 2 (million)
% 0.21/0.38 % (4883)------------------------------
% 0.21/0.38 % (4883)------------------------------
% 0.21/0.38 % (4881)Instruction limit reached!
% 0.21/0.38 % (4881)------------------------------
% 0.21/0.38 % (4881)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.21/0.38 % (4881)Termination reason: Unknown
% 0.21/0.38 % (4881)Termination phase: Saturation
% 0.21/0.38
% 0.21/0.38 % (4881)Memory used [KB]: 5500
% 0.21/0.38 % (4881)Time elapsed: 0.006 s
% 0.21/0.38 % (4881)Instructions burned: 4 (million)
% 0.21/0.38 % (4881)------------------------------
% 0.21/0.38 % (4881)------------------------------
% 0.21/0.38 % (4882)First to succeed.
% 0.21/0.38 % (4886)Also succeeded, but the first one will report.
% 0.21/0.38 % (4880)Also succeeded, but the first one will report.
% 0.21/0.38 % (4882)Refutation found. Thanks to Tanya!
% 0.21/0.38 % SZS status Theorem for theBenchmark
% 0.21/0.38 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.39 % (4882)------------------------------
% 0.21/0.39 % (4882)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.21/0.39 % (4882)Termination reason: Refutation
% 0.21/0.39
% 0.21/0.39 % (4882)Memory used [KB]: 5500
% 0.21/0.39 % (4882)Time elapsed: 0.007 s
% 0.21/0.39 % (4882)Instructions burned: 4 (million)
% 0.21/0.39 % (4882)------------------------------
% 0.21/0.39 % (4882)------------------------------
% 0.21/0.39 % (4879)Success in time 0.011 s
%------------------------------------------------------------------------------