TSTP Solution File: NUM902_1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : NUM902_1 : TPTP v8.1.2. Released v5.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n017.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 : Tue Apr 30 14:38:21 EDT 2024
% Result : Theorem 0.10s 0.36s
% Output : Refutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 34
% Syntax : Number of formulae : 79 ( 23 unt; 2 typ; 0 def)
% Number of atoms : 166 ( 45 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 153 ( 64 ~; 62 |; 4 &)
% ( 19 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number arithmetic : 257 ( 39 atm; 105 fun; 29 num; 84 var)
% Number of types : 1 ( 0 usr; 1 ari)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 22 ( 19 usr; 20 prp; 0-2 aty)
% Number of functors : 7 ( 2 usr; 4 con; 0-2 aty)
% Number of variables : 84 ( 80 !; 4 ?; 84 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_5,type,
sK0: $rat ).
tff(func_def_6,type,
sK1: $rat ).
tff(f186,plain,
$false,
inference(avatar_sat_refutation,[],[f24,f29,f33,f37,f41,f45,f49,f53,f60,f64,f74,f78,f104,f108,f131,f146,f166,f174,f178,f185]) ).
tff(f185,plain,
( spl2_1
| ~ spl2_6
| ~ spl2_15 ),
inference(avatar_split_clause,[],[f139,f129,f43,f21]) ).
tff(f21,plain,
( spl2_1
<=> ( sK0 = sK1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1])]) ).
tff(f43,plain,
( spl2_6
<=> ! [X0: $rat] : ( 0/1 = $sum(X0,$uminus(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_6])]) ).
tff(f129,plain,
( spl2_15
<=> ! [X0: $rat] : ( $sum(sK0,$sum($uminus(sK1),X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_15])]) ).
tff(f139,plain,
( ( sK0 = sK1 )
| ~ spl2_6
| ~ spl2_15 ),
inference(evaluation,[],[f135]) ).
tff(f135,plain,
( ( $uminus($uminus(sK1)) = $sum(sK0,0/1) )
| ~ spl2_6
| ~ spl2_15 ),
inference(superposition,[],[f130,f44]) ).
tff(f44,plain,
( ! [X0: $rat] : ( 0/1 = $sum(X0,$uminus(X0)) )
| ~ spl2_6 ),
inference(avatar_component_clause,[],[f43]) ).
tff(f130,plain,
( ! [X0: $rat] : ( $sum(sK0,$sum($uminus(sK1),X0)) = X0 )
| ~ spl2_15 ),
inference(avatar_component_clause,[],[f129]) ).
tff(f178,plain,
( spl2_19
| ~ spl2_6
| ~ spl2_13 ),
inference(avatar_split_clause,[],[f124,f102,f43,f176]) ).
tff(f176,plain,
( spl2_19
<=> ! [X0: $rat,X1: $rat] : ( $sum(X0,$sum($uminus(X0),X1)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_19])]) ).
tff(f102,plain,
( spl2_13
<=> ! [X2: $rat,X0: $rat,X1: $rat] : ( $sum(X0,$sum(X1,X2)) = $sum($sum(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_13])]) ).
tff(f124,plain,
( ! [X0: $rat,X1: $rat] : ( $sum(X0,$sum($uminus(X0),X1)) = X1 )
| ~ spl2_6
| ~ spl2_13 ),
inference(evaluation,[],[f110]) ).
tff(f110,plain,
( ! [X0: $rat,X1: $rat] : ( $sum(X0,$sum($uminus(X0),X1)) = $sum(0/1,X1) )
| ~ spl2_6
| ~ spl2_13 ),
inference(superposition,[],[f103,f44]) ).
tff(f103,plain,
( ! [X2: $rat,X0: $rat,X1: $rat] : ( $sum(X0,$sum(X1,X2)) = $sum($sum(X0,X1),X2) )
| ~ spl2_13 ),
inference(avatar_component_clause,[],[f102]) ).
tff(f174,plain,
( spl2_18
| ~ spl2_7
| ~ spl2_8 ),
inference(avatar_split_clause,[],[f55,f51,f47,f172]) ).
tff(f172,plain,
( spl2_18
<=> ! [X0: $rat,X1: $rat] :
( $less(X1,$sum(1/1,X0))
| $less(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_18])]) ).
tff(f47,plain,
( spl2_7
<=> ! [X0: $rat,X1: $rat] : ( $sum(X0,X1) = $sum(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_7])]) ).
tff(f51,plain,
( spl2_8
<=> ! [X0: $rat,X1: $rat] :
( $less(X0,X1)
| $less(X1,$sum(X0,1/1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_8])]) ).
tff(f55,plain,
( ! [X0: $rat,X1: $rat] :
( $less(X1,$sum(1/1,X0))
| $less(X0,X1) )
| ~ spl2_7
| ~ spl2_8 ),
inference(superposition,[],[f52,f48]) ).
tff(f48,plain,
( ! [X0: $rat,X1: $rat] : ( $sum(X0,X1) = $sum(X1,X0) )
| ~ spl2_7 ),
inference(avatar_component_clause,[],[f47]) ).
tff(f52,plain,
( ! [X0: $rat,X1: $rat] :
( $less(X1,$sum(X0,1/1))
| $less(X0,X1) )
| ~ spl2_8 ),
inference(avatar_component_clause,[],[f51]) ).
tff(f166,plain,
( spl2_17
| ~ spl2_3
| ~ spl2_8 ),
inference(avatar_split_clause,[],[f54,f51,f31,f164]) ).
tff(f164,plain,
( spl2_17
<=> ! [X0: $rat] : $less(X0,$sum(X0,1/1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_17])]) ).
tff(f31,plain,
( spl2_3
<=> ! [X0: $rat] : ~ $less(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_3])]) ).
tff(f54,plain,
( ! [X0: $rat] : $less(X0,$sum(X0,1/1))
| ~ spl2_3
| ~ spl2_8 ),
inference(resolution,[],[f52,f32]) ).
tff(f32,plain,
( ! [X0: $rat] : ~ $less(X0,X0)
| ~ spl2_3 ),
inference(avatar_component_clause,[],[f31]) ).
tff(f146,plain,
( spl2_16
| ~ spl2_2
| ~ spl2_12 ),
inference(avatar_split_clause,[],[f96,f76,f26,f144]) ).
tff(f144,plain,
( spl2_16
<=> ! [X0: $rat] :
( $less($sum(X0,$uminus(sK1)),0/1)
| ~ $less(X0,sK0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_16])]) ).
tff(f26,plain,
( spl2_2
<=> ( 0/1 = $sum(sK0,$uminus(sK1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_2])]) ).
tff(f76,plain,
( spl2_12
<=> ! [X2: $rat,X0: $rat,X1: $rat] :
( ~ $less(X0,X1)
| $less($sum(X0,X2),$sum(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_12])]) ).
tff(f96,plain,
( ! [X0: $rat] :
( $less($sum(X0,$uminus(sK1)),0/1)
| ~ $less(X0,sK0) )
| ~ spl2_2
| ~ spl2_12 ),
inference(superposition,[],[f77,f28]) ).
tff(f28,plain,
( ( 0/1 = $sum(sK0,$uminus(sK1)) )
| ~ spl2_2 ),
inference(avatar_component_clause,[],[f26]) ).
tff(f77,plain,
( ! [X2: $rat,X0: $rat,X1: $rat] :
( $less($sum(X0,X2),$sum(X1,X2))
| ~ $less(X0,X1) )
| ~ spl2_12 ),
inference(avatar_component_clause,[],[f76]) ).
tff(f131,plain,
( spl2_15
| ~ spl2_2
| ~ spl2_13 ),
inference(avatar_split_clause,[],[f125,f102,f26,f129]) ).
tff(f125,plain,
( ! [X0: $rat] : ( $sum(sK0,$sum($uminus(sK1),X0)) = X0 )
| ~ spl2_2
| ~ spl2_13 ),
inference(evaluation,[],[f109]) ).
tff(f109,plain,
( ! [X0: $rat] : ( $sum(sK0,$sum($uminus(sK1),X0)) = $sum(0/1,X0) )
| ~ spl2_2
| ~ spl2_13 ),
inference(superposition,[],[f103,f28]) ).
tff(f108,plain,
( spl2_14
| ~ spl2_2
| ~ spl2_12 ),
inference(avatar_split_clause,[],[f91,f76,f26,f106]) ).
tff(f106,plain,
( spl2_14
<=> ! [X0: $rat] :
( $less(0/1,$sum(X0,$uminus(sK1)))
| ~ $less(sK0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_14])]) ).
tff(f91,plain,
( ! [X0: $rat] :
( $less(0/1,$sum(X0,$uminus(sK1)))
| ~ $less(sK0,X0) )
| ~ spl2_2
| ~ spl2_12 ),
inference(superposition,[],[f77,f28]) ).
tff(f104,plain,
spl2_13,
inference(avatar_split_clause,[],[f5,f102]) ).
tff(f5,plain,
! [X2: $rat,X0: $rat,X1: $rat] : ( $sum(X0,$sum(X1,X2)) = $sum($sum(X0,X1),X2) ),
introduced(theory_axiom_136,[]) ).
tff(f78,plain,
spl2_12,
inference(avatar_split_clause,[],[f12,f76]) ).
tff(f12,plain,
! [X2: $rat,X0: $rat,X1: $rat] :
( ~ $less(X0,X1)
| $less($sum(X0,X2),$sum(X1,X2)) ),
introduced(theory_axiom_145,[]) ).
tff(f74,plain,
spl2_11,
inference(avatar_split_clause,[],[f7,f72]) ).
tff(f72,plain,
( spl2_11
<=> ! [X0: $rat,X1: $rat] : ( $uminus($sum(X0,X1)) = $sum($uminus(X1),$uminus(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_11])]) ).
tff(f7,plain,
! [X0: $rat,X1: $rat] : ( $uminus($sum(X0,X1)) = $sum($uminus(X1),$uminus(X0)) ),
introduced(theory_axiom_139,[]) ).
tff(f64,plain,
spl2_10,
inference(avatar_split_clause,[],[f11,f62]) ).
tff(f62,plain,
( spl2_10
<=> ! [X0: $rat,X1: $rat] :
( $less(X0,X1)
| $less(X1,X0)
| ( X0 = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_10])]) ).
tff(f11,plain,
! [X0: $rat,X1: $rat] :
( $less(X0,X1)
| $less(X1,X0)
| ( X0 = X1 ) ),
introduced(theory_axiom_144,[]) ).
tff(f60,plain,
spl2_9,
inference(avatar_split_clause,[],[f10,f58]) ).
tff(f58,plain,
( spl2_9
<=> ! [X2: $rat,X0: $rat,X1: $rat] :
( ~ $less(X0,X1)
| ~ $less(X1,X2)
| $less(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_9])]) ).
tff(f10,plain,
! [X2: $rat,X0: $rat,X1: $rat] :
( ~ $less(X0,X1)
| ~ $less(X1,X2)
| $less(X0,X2) ),
introduced(theory_axiom_143,[]) ).
tff(f53,plain,
spl2_8,
inference(avatar_split_clause,[],[f13,f51]) ).
tff(f13,plain,
! [X0: $rat,X1: $rat] :
( $less(X0,X1)
| $less(X1,$sum(X0,1/1)) ),
introduced(theory_axiom_147,[]) ).
tff(f49,plain,
spl2_7,
inference(avatar_split_clause,[],[f4,f47]) ).
tff(f4,plain,
! [X0: $rat,X1: $rat] : ( $sum(X0,X1) = $sum(X1,X0) ),
introduced(theory_axiom_135,[]) ).
tff(f45,plain,
spl2_6,
inference(avatar_split_clause,[],[f8,f43]) ).
tff(f8,plain,
! [X0: $rat] : ( 0/1 = $sum(X0,$uminus(X0)) ),
introduced(theory_axiom_140,[]) ).
tff(f41,plain,
spl2_5,
inference(avatar_split_clause,[],[f14,f39]) ).
tff(f39,plain,
( spl2_5
<=> ! [X0: $rat] : ( $uminus($uminus(X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_5])]) ).
tff(f14,plain,
! [X0: $rat] : ( $uminus($uminus(X0)) = X0 ),
introduced(theory_axiom_148,[]) ).
tff(f37,plain,
spl2_4,
inference(avatar_split_clause,[],[f6,f35]) ).
tff(f35,plain,
( spl2_4
<=> ! [X0: $rat] : ( $sum(X0,0/1) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_4])]) ).
tff(f6,plain,
! [X0: $rat] : ( $sum(X0,0/1) = X0 ),
introduced(theory_axiom_137,[]) ).
tff(f33,plain,
spl2_3,
inference(avatar_split_clause,[],[f9,f31]) ).
tff(f9,plain,
! [X0: $rat] : ~ $less(X0,X0),
introduced(theory_axiom_142,[]) ).
tff(f29,plain,
spl2_2,
inference(avatar_split_clause,[],[f18,f26]) ).
tff(f18,plain,
0/1 = $sum(sK0,$uminus(sK1)),
inference(cnf_transformation,[],[f17]) ).
tff(f17,plain,
( ( sK0 != sK1 )
& ( 0/1 = $sum(sK0,$uminus(sK1)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f15,f16]) ).
tff(f16,plain,
( ? [X0: $rat,X1: $rat] :
( ( X0 != X1 )
& ( 0/1 = $sum(X0,$uminus(X1)) ) )
=> ( ( sK0 != sK1 )
& ( 0/1 = $sum(sK0,$uminus(sK1)) ) ) ),
introduced(choice_axiom,[]) ).
tff(f15,plain,
? [X0: $rat,X1: $rat] :
( ( X0 != X1 )
& ( 0/1 = $sum(X0,$uminus(X1)) ) ),
inference(ennf_transformation,[],[f3]) ).
tff(f3,plain,
~ ! [X0: $rat,X1: $rat] :
( ( 0/1 = $sum(X0,$uminus(X1)) )
=> ( X0 = X1 ) ),
inference(theory_normalization,[],[f2]) ).
tff(f2,negated_conjecture,
~ ! [X0: $rat,X1: $rat] :
( ( $difference(X0,X1) = 0/1 )
=> ( X0 = X1 ) ),
inference(negated_conjecture,[],[f1]) ).
tff(f1,conjecture,
! [X0: $rat,X1: $rat] :
( ( $difference(X0,X1) = 0/1 )
=> ( X0 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rat_difference_problem_13) ).
tff(f24,plain,
~ spl2_1,
inference(avatar_split_clause,[],[f19,f21]) ).
tff(f19,plain,
sK0 != sK1,
inference(cnf_transformation,[],[f17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.12 % Problem : NUM902_1 : TPTP v8.1.2. Released v5.0.0.
% 0.02/0.13 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.10/0.33 % Computer : n017.cluster.edu
% 0.10/0.33 % Model : x86_64 x86_64
% 0.10/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.33 % Memory : 8042.1875MB
% 0.10/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.33 % CPULimit : 300
% 0.10/0.33 % WCLimit : 300
% 0.10/0.33 % DateTime : Mon Apr 29 23:17:18 EDT 2024
% 0.10/0.33 % CPUTime :
% 0.10/0.33 % (16494)Running in auto input_syntax mode. Trying TPTP
% 0.10/0.35 % (16497)WARNING: value z3 for option sas not known
% 0.10/0.35 % (16501)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.10/0.35 % (16499)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.10/0.35 % (16500)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.10/0.35 % (16498)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.10/0.35 % (16498)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.10/0.35 % (16498)Terminated due to inappropriate strategy.
% 0.10/0.35 % (16498)------------------------------
% 0.10/0.35 % (16498)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.10/0.35 % (16497)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.10/0.35 % (16498)Termination reason: Inappropriate
% 0.10/0.35
% 0.10/0.35 % (16498)Memory used [KB]: 722
% 0.10/0.35 % (16498)Time elapsed: 0.002 s
% 0.10/0.35 % (16498)Instructions burned: 2 (million)
% 0.10/0.35 % (16498)------------------------------
% 0.10/0.35 % (16498)------------------------------
% 0.10/0.35 % (16499)First to succeed.
% 0.10/0.36 % (16499)Refutation found. Thanks to Tanya!
% 0.10/0.36 % SZS status Theorem for theBenchmark
% 0.10/0.36 % SZS output start Proof for theBenchmark
% See solution above
% 0.10/0.36 % (16499)------------------------------
% 0.10/0.36 % (16499)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.10/0.36 % (16499)Termination reason: Refutation
% 0.10/0.36
% 0.10/0.36 % (16499)Memory used [KB]: 867
% 0.10/0.36 % (16499)Time elapsed: 0.008 s
% 0.10/0.36 % (16499)Instructions burned: 10 (million)
% 0.10/0.36 % (16499)------------------------------
% 0.10/0.36 % (16499)------------------------------
% 0.10/0.36 % (16494)Success in time 0.02 s
% 0.10/0.37 % Exception at proof search level
% 0.10/0.37 System fail: Cannot decrease semaphore. error 22: Invalid argument
%------------------------------------------------------------------------------