TSTP Solution File: SEV200^5 by Vampire---4.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.9
% Problem : SEV200^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire %s %d THM
% Computer : n025.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 16:02:14 EDT 2024
% Result : Theorem 0.12s 0.38s
% Output : Refutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 3
% Syntax : Number of formulae : 16 ( 3 unt; 0 typ; 0 def)
% Number of atoms : 277 ( 188 equ; 0 cnn)
% Maximal formula atoms : 22 ( 17 avg)
% Number of connectives : 640 ( 91 ~; 67 |; 105 &; 345 @)
% ( 0 <=>; 32 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 15 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 37 ( 37 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 4 con; 0-3 aty)
% Number of variables : 205 ( 0 ^ 163 !; 42 ?; 205 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_1,type,
x: a ).
thf(func_def_2,type,
cZ: a ).
thf(func_def_3,type,
cP: a > a > a ).
thf(func_def_7,type,
sK0: a > a > a > $o ).
thf(func_def_8,type,
sK1: ( a > $o ) > a ).
thf(func_def_9,type,
sK2: ( a > $o ) > a ).
thf(f30,plain,
$false,
inference(subsumption_resolution,[],[f19,f26]) ).
thf(f26,plain,
! [X2: a] :
( ( sK0 @ cZ @ X2 @ X2 )
= $true ),
inference(equality_resolution,[],[f25]) ).
thf(f25,plain,
! [X2: a,X1: a] :
( ( ( sK0 @ cZ @ X1 @ X2 )
= $true )
| ( X1 != X2 ) ),
inference(equality_resolution,[],[f21]) ).
thf(f21,plain,
! [X2: a,X3: a,X1: a] :
( ( ( sK0 @ X3 @ X1 @ X2 )
= $true )
| ( cZ != X3 )
| ( X1 != X2 ) ),
inference(cnf_transformation,[],[f12]) ).
thf(f12,plain,
( ! [X1: a,X2: a,X3: a] :
( ( ( sK0 @ X3 @ X1 @ X2 )
= $true )
| ( ( ( X2 != X3 )
| ( cZ != X1 ) )
& ( ( cZ != X3 )
| ( X1 != X2 ) )
& ! [X4: a,X5: a,X6: a,X7: a,X8: a,X9: a] :
( ( ( cP @ X5 @ X4 )
!= X1 )
| ( $true
!= ( sK0 @ X6 @ X4 @ X9 ) )
| ( ( cP @ X8 @ X9 )
!= X2 )
| ( ( cP @ X7 @ X6 )
!= X3 )
| ( $true
!= ( sK0 @ X7 @ X5 @ X8 ) ) ) ) )
& ( ( sK0 @ cZ @ x @ x )
!= $true )
& ! [X10: a,X11: a] :
( cZ
!= ( cP @ X10 @ X11 ) )
& ! [X12: a,X13: a,X14: a,X15: a] :
( ( ( X13 = X15 )
& ( X12 = X14 ) )
| ( ( cP @ X14 @ X13 )
!= ( cP @ X12 @ X15 ) ) )
& ! [X16: a > $o] :
( ( $true
!= ( X16 @ cZ ) )
| ! [X17: a] :
( $true
= ( X16 @ X17 ) )
| ( ( ( X16 @ ( sK1 @ X16 ) )
= $true )
& ( ( X16 @ ( sK2 @ X16 ) )
= $true )
& ( ( X16 @ ( cP @ ( sK1 @ X16 ) @ ( sK2 @ X16 ) ) )
!= $true ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f9,f11,f10]) ).
thf(f10,plain,
( ? [X0: a > a > a > $o] :
( ! [X1: a,X2: a,X3: a] :
( ( $true
= ( X0 @ X3 @ X1 @ X2 ) )
| ( ( ( X2 != X3 )
| ( cZ != X1 ) )
& ( ( cZ != X3 )
| ( X1 != X2 ) )
& ! [X4: a,X5: a,X6: a,X7: a,X8: a,X9: a] :
( ( ( cP @ X5 @ X4 )
!= X1 )
| ( $true
!= ( X0 @ X6 @ X4 @ X9 ) )
| ( ( cP @ X8 @ X9 )
!= X2 )
| ( ( cP @ X7 @ X6 )
!= X3 )
| ( $true
!= ( X0 @ X7 @ X5 @ X8 ) ) ) ) )
& ( $true
!= ( X0 @ cZ @ x @ x ) ) )
=> ( ! [X3: a,X2: a,X1: a] :
( ( ( sK0 @ X3 @ X1 @ X2 )
= $true )
| ( ( ( X2 != X3 )
| ( cZ != X1 ) )
& ( ( cZ != X3 )
| ( X1 != X2 ) )
& ! [X9: a,X8: a,X7: a,X6: a,X5: a,X4: a] :
( ( ( cP @ X5 @ X4 )
!= X1 )
| ( $true
!= ( sK0 @ X6 @ X4 @ X9 ) )
| ( ( cP @ X8 @ X9 )
!= X2 )
| ( ( cP @ X7 @ X6 )
!= X3 )
| ( $true
!= ( sK0 @ X7 @ X5 @ X8 ) ) ) ) )
& ( ( sK0 @ cZ @ x @ x )
!= $true ) ) ),
introduced(choice_axiom,[]) ).
thf(f11,plain,
! [X16: a > $o] :
( ? [X18: a,X19: a] :
( ( ( X16 @ X18 )
= $true )
& ( ( X16 @ X19 )
= $true )
& ( $true
!= ( X16 @ ( cP @ X18 @ X19 ) ) ) )
=> ( ( ( X16 @ ( sK1 @ X16 ) )
= $true )
& ( ( X16 @ ( sK2 @ X16 ) )
= $true )
& ( ( X16 @ ( cP @ ( sK1 @ X16 ) @ ( sK2 @ X16 ) ) )
!= $true ) ) ),
introduced(choice_axiom,[]) ).
thf(f9,plain,
( ? [X0: a > a > a > $o] :
( ! [X1: a,X2: a,X3: a] :
( ( $true
= ( X0 @ X3 @ X1 @ X2 ) )
| ( ( ( X2 != X3 )
| ( cZ != X1 ) )
& ( ( cZ != X3 )
| ( X1 != X2 ) )
& ! [X4: a,X5: a,X6: a,X7: a,X8: a,X9: a] :
( ( ( cP @ X5 @ X4 )
!= X1 )
| ( $true
!= ( X0 @ X6 @ X4 @ X9 ) )
| ( ( cP @ X8 @ X9 )
!= X2 )
| ( ( cP @ X7 @ X6 )
!= X3 )
| ( $true
!= ( X0 @ X7 @ X5 @ X8 ) ) ) ) )
& ( $true
!= ( X0 @ cZ @ x @ x ) ) )
& ! [X10: a,X11: a] :
( cZ
!= ( cP @ X10 @ X11 ) )
& ! [X12: a,X13: a,X14: a,X15: a] :
( ( ( X13 = X15 )
& ( X12 = X14 ) )
| ( ( cP @ X14 @ X13 )
!= ( cP @ X12 @ X15 ) ) )
& ! [X16: a > $o] :
( ( $true
!= ( X16 @ cZ ) )
| ! [X17: a] :
( $true
= ( X16 @ X17 ) )
| ? [X18: a,X19: a] :
( ( ( X16 @ X18 )
= $true )
& ( ( X16 @ X19 )
= $true )
& ( $true
!= ( X16 @ ( cP @ X18 @ X19 ) ) ) ) ) ),
inference(rectify,[],[f8]) ).
thf(f8,plain,
( ? [X10: a > a > a > $o] :
( ! [X12: a,X13: a,X11: a] :
( ( $true
= ( X10 @ X11 @ X12 @ X13 ) )
| ( ( ( X11 != X13 )
| ( cZ != X12 ) )
& ( ( cZ != X11 )
| ( X12 != X13 ) )
& ! [X15: a,X18: a,X17: a,X14: a,X19: a,X16: a] :
( ( ( cP @ X18 @ X15 )
!= X12 )
| ( ( X10 @ X17 @ X15 @ X16 )
!= $true )
| ( ( cP @ X19 @ X16 )
!= X13 )
| ( ( cP @ X14 @ X17 )
!= X11 )
| ( ( X10 @ X14 @ X18 @ X19 )
!= $true ) ) ) )
& ( ( X10 @ cZ @ x @ x )
!= $true ) )
& ! [X4: a,X5: a] :
( cZ
!= ( cP @ X4 @ X5 ) )
& ! [X9: a,X8: a,X7: a,X6: a] :
( ( ( X6 = X8 )
& ( X7 = X9 ) )
| ( ( cP @ X9 @ X6 )
!= ( cP @ X7 @ X8 ) ) )
& ! [X0: a > $o] :
( ( ( X0 @ cZ )
!= $true )
| ! [X3: a] :
( $true
= ( X0 @ X3 ) )
| ? [X2: a,X1: a] :
( ( $true
= ( X0 @ X2 ) )
& ( $true
= ( X0 @ X1 ) )
& ( $true
!= ( X0 @ ( cP @ X2 @ X1 ) ) ) ) ) ),
inference(flattening,[],[f7]) ).
thf(f7,plain,
( ? [X10: a > a > a > $o] :
( ! [X12: a,X13: a,X11: a] :
( ( $true
= ( X10 @ X11 @ X12 @ X13 ) )
| ( ( ( X11 != X13 )
| ( cZ != X12 ) )
& ( ( cZ != X11 )
| ( X12 != X13 ) )
& ! [X15: a,X18: a,X17: a,X14: a,X19: a,X16: a] :
( ( ( cP @ X18 @ X15 )
!= X12 )
| ( ( X10 @ X17 @ X15 @ X16 )
!= $true )
| ( ( cP @ X19 @ X16 )
!= X13 )
| ( ( cP @ X14 @ X17 )
!= X11 )
| ( ( X10 @ X14 @ X18 @ X19 )
!= $true ) ) ) )
& ( ( X10 @ cZ @ x @ x )
!= $true ) )
& ! [X0: a > $o] :
( ! [X3: a] :
( $true
= ( X0 @ X3 ) )
| ? [X2: a,X1: a] :
( ( $true
!= ( X0 @ ( cP @ X2 @ X1 ) ) )
& ( $true
= ( X0 @ X1 ) )
& ( $true
= ( X0 @ X2 ) ) )
| ( ( X0 @ cZ )
!= $true ) )
& ! [X9: a,X8: a,X7: a,X6: a] :
( ( ( X6 = X8 )
& ( X7 = X9 ) )
| ( ( cP @ X9 @ X6 )
!= ( cP @ X7 @ X8 ) ) )
& ! [X4: a,X5: a] :
( cZ
!= ( cP @ X4 @ X5 ) ) ),
inference(ennf_transformation,[],[f6]) ).
thf(f6,plain,
~ ( ( ! [X0: a > $o] :
( ( ! [X2: a,X1: a] :
( ( ( $true
= ( X0 @ X1 ) )
& ( $true
= ( X0 @ X2 ) ) )
=> ( $true
= ( X0 @ ( cP @ X2 @ X1 ) ) ) )
& ( ( X0 @ cZ )
= $true ) )
=> ! [X3: a] :
( $true
= ( X0 @ X3 ) ) )
& ! [X7: a,X9: a,X8: a,X6: a] :
( ( ( cP @ X9 @ X6 )
= ( cP @ X7 @ X8 ) )
=> ( ( X6 = X8 )
& ( X7 = X9 ) ) )
& ! [X4: a,X5: a] :
( cZ
!= ( cP @ X4 @ X5 ) ) )
=> ! [X10: a > a > a > $o] :
( ! [X12: a,X13: a,X11: a] :
( ( ( ( cZ = X12 )
& ( X11 = X13 ) )
| ( ( cZ = X11 )
& ( X12 = X13 ) )
| ? [X15: a,X14: a,X19: a,X17: a,X16: a,X18: a] :
( ( ( cP @ X19 @ X16 )
= X13 )
& ( ( cP @ X14 @ X17 )
= X11 )
& ( ( X10 @ X14 @ X18 @ X19 )
= $true )
& ( ( X10 @ X17 @ X15 @ X16 )
= $true )
& ( ( cP @ X18 @ X15 )
= X12 ) ) )
=> ( $true
= ( X10 @ X11 @ X12 @ X13 ) ) )
=> ( ( X10 @ cZ @ x @ x )
= $true ) ) ),
inference(true_and_false_elimination,[],[f5]) ).
thf(f5,plain,
~ ( ( ! [X0: a > $o] :
( ( ! [X2: a,X1: a] :
( ( ( $true
= ( X0 @ X1 ) )
& ( $true
= ( X0 @ X2 ) ) )
=> ( $true
= ( X0 @ ( cP @ X2 @ X1 ) ) ) )
& ( ( X0 @ cZ )
= $true ) )
=> ! [X3: a] :
( $true
= ( X0 @ X3 ) ) )
& ! [X7: a,X9: a,X8: a,X6: a] :
( ( ( cP @ X9 @ X6 )
= ( cP @ X7 @ X8 ) )
=> ( ( X6 = X8 )
& ( X7 = X9 ) ) )
& ! [X4: a,X5: a] :
( cZ
!= ( cP @ X4 @ X5 ) ) )
=> ! [X10: a > a > a > $o] :
( ( ! [X12: a,X13: a,X11: a] :
( ( ( ( cZ = X12 )
& ( X11 = X13 ) )
| ( ( cZ = X11 )
& ( X12 = X13 ) )
| ? [X15: a,X14: a,X19: a,X17: a,X16: a,X18: a] :
( ( ( cP @ X19 @ X16 )
= X13 )
& ( ( cP @ X14 @ X17 )
= X11 )
& ( ( X10 @ X14 @ X18 @ X19 )
= $true )
& ( ( X10 @ X17 @ X15 @ X16 )
= $true )
& ( ( cP @ X18 @ X15 )
= X12 ) ) )
=> ( $true
= ( X10 @ X11 @ X12 @ X13 ) ) )
& $true )
=> ( ( X10 @ cZ @ x @ x )
= $true ) ) ),
inference(fool_elimination,[],[f4]) ).
thf(f4,plain,
~ ( ( ! [X0: a > $o] :
( ( ! [X1: a,X2: a] :
( ( ( X0 @ X2 )
& ( X0 @ X1 ) )
=> ( X0 @ ( cP @ X2 @ X1 ) ) )
& ( X0 @ cZ ) )
=> ! [X3: a] : ( X0 @ X3 ) )
& ! [X4: a,X5: a] :
( cZ
!= ( cP @ X4 @ X5 ) )
& ! [X6: a,X7: a,X8: a,X9: a] :
( ( ( cP @ X9 @ X6 )
= ( cP @ X7 @ X8 ) )
=> ( ( X6 = X8 )
& ( X7 = X9 ) ) ) )
=> ! [X10: a > a > a > $o] :
( ( ! [X11: a,X12: a,X13: a] :
( ( ( ( X11 = X13 )
& ( cZ = X12 ) )
| ? [X14: a,X15: a,X16: a,X17: a,X18: a,X19: a] :
( ( ( cP @ X14 @ X17 )
= X11 )
& ( X10 @ X17 @ X15 @ X16 )
& ( ( cP @ X19 @ X16 )
= X13 )
& ( ( cP @ X18 @ X15 )
= X12 )
& ( X10 @ X14 @ X18 @ X19 ) )
| ( ( X12 = X13 )
& ( cZ = X11 ) ) )
=> ( X10 @ X11 @ X12 @ X13 ) )
& $true )
=> ( X10 @ cZ @ x @ x ) ) ),
inference(rectify,[],[f2]) ).
thf(f2,negated_conjecture,
~ ( ( ! [X4: a > $o] :
( ( ! [X1: a,X0: a] :
( ( ( X4 @ X0 )
& ( X4 @ X1 ) )
=> ( X4 @ ( cP @ X0 @ X1 ) ) )
& ( X4 @ cZ ) )
=> ! [X0: a] : ( X4 @ X0 ) )
& ! [X0: a,X1: a] :
( ( cP @ X0 @ X1 )
!= cZ )
& ! [X3: a,X0: a,X2: a,X1: a] :
( ( ( cP @ X0 @ X2 )
= ( cP @ X1 @ X3 ) )
=> ( ( X2 = X3 )
& ( X0 = X1 ) ) ) )
=> ! [X5: a > a > a > $o] :
( ( ! [X6: a,X7: a,X8: a] :
( ( ( ( X6 = X8 )
& ( cZ = X7 ) )
| ? [X9: a,X12: a,X14: a,X10: a,X11: a,X13: a] :
( ( ( cP @ X9 @ X10 )
= X6 )
& ( X5 @ X10 @ X12 @ X14 )
& ( ( cP @ X13 @ X14 )
= X8 )
& ( ( cP @ X11 @ X12 )
= X7 )
& ( X5 @ X9 @ X11 @ X13 ) )
| ( ( X7 = X8 )
& ( cZ = X6 ) ) )
=> ( X5 @ X6 @ X7 @ X8 ) )
& $true )
=> ( X5 @ cZ @ x @ x ) ) ),
inference(negated_conjecture,[],[f1]) ).
thf(f1,conjecture,
( ( ! [X4: a > $o] :
( ( ! [X1: a,X0: a] :
( ( ( X4 @ X0 )
& ( X4 @ X1 ) )
=> ( X4 @ ( cP @ X0 @ X1 ) ) )
& ( X4 @ cZ ) )
=> ! [X0: a] : ( X4 @ X0 ) )
& ! [X0: a,X1: a] :
( ( cP @ X0 @ X1 )
!= cZ )
& ! [X3: a,X0: a,X2: a,X1: a] :
( ( ( cP @ X0 @ X2 )
= ( cP @ X1 @ X3 ) )
=> ( ( X2 = X3 )
& ( X0 = X1 ) ) ) )
=> ! [X5: a > a > a > $o] :
( ( ! [X6: a,X7: a,X8: a] :
( ( ( ( X6 = X8 )
& ( cZ = X7 ) )
| ? [X9: a,X12: a,X14: a,X10: a,X11: a,X13: a] :
( ( ( cP @ X9 @ X10 )
= X6 )
& ( X5 @ X10 @ X12 @ X14 )
& ( ( cP @ X13 @ X14 )
= X8 )
& ( ( cP @ X11 @ X12 )
= X7 )
& ( X5 @ X9 @ X11 @ X13 ) )
| ( ( X7 = X8 )
& ( cZ = X6 ) ) )
=> ( X5 @ X6 @ X7 @ X8 ) )
& $true )
=> ( X5 @ cZ @ x @ x ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cS_LEM1C_pme) ).
thf(f19,plain,
( ( sK0 @ cZ @ x @ x )
!= $true ),
inference(cnf_transformation,[],[f12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SEV200^5 : TPTP v8.2.0. Released v4.0.0.
% 0.08/0.13 % Command : run_vampire %s %d THM
% 0.12/0.34 % Computer : n025.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 18:39:24 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
% 0.12/0.38 % (2386)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.12/0.38 % (2386)First to succeed.
% 0.12/0.38 % (2386)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 % (2386)------------------------------
% 0.12/0.38 % (2386)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.12/0.38 % (2386)Termination reason: Refutation
% 0.12/0.38
% 0.12/0.38 % (2386)Memory used [KB]: 5500
% 0.12/0.38 % (2386)Time elapsed: 0.004 s
% 0.12/0.38 % (2386)Instructions burned: 3 (million)
% 0.12/0.38 % (2386)------------------------------
% 0.12/0.38 % (2386)------------------------------
% 0.12/0.38 % (2383)Success in time 0.014 s
%------------------------------------------------------------------------------