TSTP Solution File: SWV159+1 by SnakeForV-SAT---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV-SAT---1.0
% Problem : SWV159+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% Computer : n022.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 : Wed Aug 31 18:55:41 EDT 2022
% Result : Theorem 0.18s 0.51s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 23 ( 12 unt; 0 def)
% Number of atoms : 133 ( 50 equ)
% Maximal formula atoms : 15 ( 5 avg)
% Number of connectives : 150 ( 40 ~; 21 |; 73 &)
% ( 0 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 29 ( 29 usr; 20 con; 0-3 aty)
% Number of variables : 23 ( 19 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f471,plain,
$false,
inference(subsumption_resolution,[],[f470,f432]) ).
fof(f432,plain,
n1 != sF34,
inference(definition_folding,[],[f326,f431,f430]) ).
fof(f430,plain,
sF33 = a_select3(q,sK13,tptp_sum_index),
introduced(function_definition,[]) ).
fof(f431,plain,
sF34 = sum(n0,n4,sF33),
introduced(function_definition,[]) ).
fof(f326,plain,
n1 != sum(n0,n4,a_select3(q,sK13,tptp_sum_index)),
inference(cnf_transformation,[],[f213]) ).
fof(f213,plain,
( leq(n0,pv47)
& pv10 != sK13
& leq(sK13,pred(pv10))
& n1 != sum(n0,n4,a_select3(q,sK13,tptp_sum_index))
& leq(n0,sK13)
& leq(pv10,n135299)
& ! [X1] :
( n1 = sum(n0,n4,a_select3(q,X1,tptp_sum_index))
| ~ leq(n0,X1)
| ~ leq(X1,pred(pv10)) )
& leq(pv47,n4)
& pv84 = sum(n0,n4,divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index)),minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index))),tptp_minus_2),times(a_select2(sigma,tptp_sum_index),a_select2(sigma,tptp_sum_index)))),a_select2(rho,tptp_sum_index)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,tptp_sum_index))))
& ! [X2] :
( ~ leq(X2,pred(pv47))
| ~ leq(n0,X2)
| a_select3(q,pv10,X2) = divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,X2)),minus(a_select2(x,pv10),a_select2(mu,X2))),tptp_minus_2),times(a_select2(sigma,X2),a_select2(sigma,X2)))),a_select2(rho,X2)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,X2))),sum(n0,n4,divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index)),minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index))),tptp_minus_2),times(a_select2(sigma,tptp_sum_index),a_select2(sigma,tptp_sum_index)))),a_select2(rho,tptp_sum_index)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,tptp_sum_index))))) )
& leq(n0,pv10) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK13])],[f211,f212]) ).
fof(f212,plain,
( ? [X0] :
( pv10 != X0
& leq(X0,pred(pv10))
& n1 != sum(n0,n4,a_select3(q,X0,tptp_sum_index))
& leq(n0,X0) )
=> ( pv10 != sK13
& leq(sK13,pred(pv10))
& n1 != sum(n0,n4,a_select3(q,sK13,tptp_sum_index))
& leq(n0,sK13) ) ),
introduced(choice_axiom,[]) ).
fof(f211,plain,
( leq(n0,pv47)
& ? [X0] :
( pv10 != X0
& leq(X0,pred(pv10))
& n1 != sum(n0,n4,a_select3(q,X0,tptp_sum_index))
& leq(n0,X0) )
& leq(pv10,n135299)
& ! [X1] :
( n1 = sum(n0,n4,a_select3(q,X1,tptp_sum_index))
| ~ leq(n0,X1)
| ~ leq(X1,pred(pv10)) )
& leq(pv47,n4)
& pv84 = sum(n0,n4,divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index)),minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index))),tptp_minus_2),times(a_select2(sigma,tptp_sum_index),a_select2(sigma,tptp_sum_index)))),a_select2(rho,tptp_sum_index)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,tptp_sum_index))))
& ! [X2] :
( ~ leq(X2,pred(pv47))
| ~ leq(n0,X2)
| a_select3(q,pv10,X2) = divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,X2)),minus(a_select2(x,pv10),a_select2(mu,X2))),tptp_minus_2),times(a_select2(sigma,X2),a_select2(sigma,X2)))),a_select2(rho,X2)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,X2))),sum(n0,n4,divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index)),minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index))),tptp_minus_2),times(a_select2(sigma,tptp_sum_index),a_select2(sigma,tptp_sum_index)))),a_select2(rho,tptp_sum_index)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,tptp_sum_index))))) )
& leq(n0,pv10) ),
inference(rectify,[],[f143]) ).
fof(f143,plain,
( leq(n0,pv47)
& ? [X2] :
( pv10 != X2
& leq(X2,pred(pv10))
& n1 != sum(n0,n4,a_select3(q,X2,tptp_sum_index))
& leq(n0,X2) )
& leq(pv10,n135299)
& ! [X0] :
( n1 = sum(n0,n4,a_select3(q,X0,tptp_sum_index))
| ~ leq(n0,X0)
| ~ leq(X0,pred(pv10)) )
& leq(pv47,n4)
& pv84 = sum(n0,n4,divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index)),minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index))),tptp_minus_2),times(a_select2(sigma,tptp_sum_index),a_select2(sigma,tptp_sum_index)))),a_select2(rho,tptp_sum_index)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,tptp_sum_index))))
& ! [X1] :
( ~ leq(X1,pred(pv47))
| ~ leq(n0,X1)
| divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,X1)),minus(a_select2(x,pv10),a_select2(mu,X1))),tptp_minus_2),times(a_select2(sigma,X1),a_select2(sigma,X1)))),a_select2(rho,X1)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,X1))),sum(n0,n4,divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index)),minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index))),tptp_minus_2),times(a_select2(sigma,tptp_sum_index),a_select2(sigma,tptp_sum_index)))),a_select2(rho,tptp_sum_index)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,tptp_sum_index))))) = a_select3(q,pv10,X1) )
& leq(n0,pv10) ),
inference(flattening,[],[f142]) ).
fof(f142,plain,
( ? [X2] :
( n1 != sum(n0,n4,a_select3(q,X2,tptp_sum_index))
& pv10 != X2
& leq(X2,pred(pv10))
& leq(n0,X2) )
& ! [X0] :
( n1 = sum(n0,n4,a_select3(q,X0,tptp_sum_index))
| ~ leq(X0,pred(pv10))
| ~ leq(n0,X0) )
& leq(pv10,n135299)
& leq(n0,pv47)
& leq(n0,pv10)
& pv84 = sum(n0,n4,divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index)),minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index))),tptp_minus_2),times(a_select2(sigma,tptp_sum_index),a_select2(sigma,tptp_sum_index)))),a_select2(rho,tptp_sum_index)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,tptp_sum_index))))
& ! [X1] :
( divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,X1)),minus(a_select2(x,pv10),a_select2(mu,X1))),tptp_minus_2),times(a_select2(sigma,X1),a_select2(sigma,X1)))),a_select2(rho,X1)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,X1))),sum(n0,n4,divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index)),minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index))),tptp_minus_2),times(a_select2(sigma,tptp_sum_index),a_select2(sigma,tptp_sum_index)))),a_select2(rho,tptp_sum_index)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,tptp_sum_index))))) = a_select3(q,pv10,X1)
| ~ leq(n0,X1)
| ~ leq(X1,pred(pv47)) )
& leq(pv47,n4) ),
inference(ennf_transformation,[],[f125]) ).
fof(f125,plain,
~ ( ( ! [X0] :
( ( leq(X0,pred(pv10))
& leq(n0,X0) )
=> n1 = sum(n0,n4,a_select3(q,X0,tptp_sum_index)) )
& leq(pv10,n135299)
& leq(n0,pv47)
& leq(n0,pv10)
& pv84 = sum(n0,n4,divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index)),minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index))),tptp_minus_2),times(a_select2(sigma,tptp_sum_index),a_select2(sigma,tptp_sum_index)))),a_select2(rho,tptp_sum_index)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,tptp_sum_index))))
& ! [X1] :
( ( leq(n0,X1)
& leq(X1,pred(pv47)) )
=> divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,X1)),minus(a_select2(x,pv10),a_select2(mu,X1))),tptp_minus_2),times(a_select2(sigma,X1),a_select2(sigma,X1)))),a_select2(rho,X1)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,X1))),sum(n0,n4,divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index)),minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index))),tptp_minus_2),times(a_select2(sigma,tptp_sum_index),a_select2(sigma,tptp_sum_index)))),a_select2(rho,tptp_sum_index)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,tptp_sum_index))))) = a_select3(q,pv10,X1) )
& leq(pv47,n4) )
=> ! [X2] :
( ( leq(X2,pred(pv10))
& leq(n0,X2) )
=> ( pv10 != X2
=> n1 = sum(n0,n4,a_select3(q,X2,tptp_sum_index)) ) ) ),
inference(rectify,[],[f54]) ).
fof(f54,negated_conjecture,
~ ( ( leq(n0,pv10)
& ! [X17] :
( ( leq(n0,X17)
& leq(X17,pred(pv10)) )
=> n1 = sum(n0,n4,a_select3(q,X17,tptp_sum_index)) )
& pv84 = sum(n0,n4,divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index)),minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index))),tptp_minus_2),times(a_select2(sigma,tptp_sum_index),a_select2(sigma,tptp_sum_index)))),a_select2(rho,tptp_sum_index)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,tptp_sum_index))))
& leq(n0,pv47)
& ! [X13] :
( ( leq(X13,pred(pv47))
& leq(n0,X13) )
=> a_select3(q,pv10,X13) = divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,X13)),minus(a_select2(x,pv10),a_select2(mu,X13))),tptp_minus_2),times(a_select2(sigma,X13),a_select2(sigma,X13)))),a_select2(rho,X13)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,X13))),sum(n0,n4,divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index)),minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index))),tptp_minus_2),times(a_select2(sigma,tptp_sum_index),a_select2(sigma,tptp_sum_index)))),a_select2(rho,tptp_sum_index)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,tptp_sum_index))))) )
& leq(pv10,n135299)
& leq(pv47,n4) )
=> ! [X3] :
( ( leq(n0,X3)
& leq(X3,pred(pv10)) )
=> ( pv10 != X3
=> n1 = sum(n0,n4,a_select3(q,X3,tptp_sum_index)) ) ) ),
inference(negated_conjecture,[],[f53]) ).
fof(f53,conjecture,
( ( leq(n0,pv10)
& ! [X17] :
( ( leq(n0,X17)
& leq(X17,pred(pv10)) )
=> n1 = sum(n0,n4,a_select3(q,X17,tptp_sum_index)) )
& pv84 = sum(n0,n4,divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index)),minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index))),tptp_minus_2),times(a_select2(sigma,tptp_sum_index),a_select2(sigma,tptp_sum_index)))),a_select2(rho,tptp_sum_index)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,tptp_sum_index))))
& leq(n0,pv47)
& ! [X13] :
( ( leq(X13,pred(pv47))
& leq(n0,X13) )
=> a_select3(q,pv10,X13) = divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,X13)),minus(a_select2(x,pv10),a_select2(mu,X13))),tptp_minus_2),times(a_select2(sigma,X13),a_select2(sigma,X13)))),a_select2(rho,X13)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,X13))),sum(n0,n4,divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index)),minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index))),tptp_minus_2),times(a_select2(sigma,tptp_sum_index),a_select2(sigma,tptp_sum_index)))),a_select2(rho,tptp_sum_index)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,tptp_sum_index))))) )
& leq(pv10,n135299)
& leq(pv47,n4) )
=> ! [X3] :
( ( leq(n0,X3)
& leq(X3,pred(pv10)) )
=> ( pv10 != X3
=> n1 = sum(n0,n4,a_select3(q,X3,tptp_sum_index)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cl5_nebula_norm_0009) ).
fof(f470,plain,
n1 = sF34,
inference(backward_demodulation,[],[f431,f469]) ).
fof(f469,plain,
n1 = sum(n0,n4,sF33),
inference(forward_demodulation,[],[f468,f430]) ).
fof(f468,plain,
n1 = sum(n0,n4,a_select3(q,sK13,tptp_sum_index)),
inference(subsumption_resolution,[],[f467,f325]) ).
fof(f325,plain,
leq(n0,sK13),
inference(cnf_transformation,[],[f213]) ).
fof(f467,plain,
( ~ leq(n0,sK13)
| n1 = sum(n0,n4,a_select3(q,sK13,tptp_sum_index)) ),
inference(resolution,[],[f433,f429]) ).
fof(f429,plain,
leq(sK13,sF32),
inference(definition_folding,[],[f327,f428]) ).
fof(f428,plain,
pred(pv10) = sF32,
introduced(function_definition,[]) ).
fof(f327,plain,
leq(sK13,pred(pv10)),
inference(cnf_transformation,[],[f213]) ).
fof(f433,plain,
! [X1] :
( ~ leq(X1,sF32)
| ~ leq(n0,X1)
| n1 = sum(n0,n4,a_select3(q,X1,tptp_sum_index)) ),
inference(definition_folding,[],[f323,f428]) ).
fof(f323,plain,
! [X1] :
( n1 = sum(n0,n4,a_select3(q,X1,tptp_sum_index))
| ~ leq(n0,X1)
| ~ leq(X1,pred(pv10)) ),
inference(cnf_transformation,[],[f213]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SWV159+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% 0.11/0.12 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.18/0.32 % Computer : n022.cluster.edu
% 0.18/0.32 % Model : x86_64 x86_64
% 0.18/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.32 % Memory : 8042.1875MB
% 0.18/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.32 % CPULimit : 300
% 0.18/0.32 % WCLimit : 300
% 0.18/0.32 % DateTime : Tue Aug 30 19:05:55 EDT 2022
% 0.18/0.32 % CPUTime :
% 0.18/0.47 % (24590)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=177:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/177Mi)
% 0.18/0.47 % (24576)ott+10_1:5_bd=off:tgt=full:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.18/0.49 % (24573)ott+2_1:1_fsr=off:gsp=on:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.18/0.49 % (24590)First to succeed.
% 0.18/0.50 % (24582)ott+4_1:1_av=off:bd=off:nwc=5.0:rp=on:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.18/0.50 % (24563)fmb+10_1:1_bce=on:fmbsr=1.5:nm=4:skr=on:i=191324:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/191324Mi)
% 0.18/0.51 % (24585)dis+21_1:1_av=off:er=filter:slsq=on:slsqc=0:slsqr=1,1:sp=frequency:to=lpo:i=498:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/498Mi)
% 0.18/0.51 % (24564)ott+10_1:32_abs=on:br=off:urr=ec_only:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.18/0.51 % (24590)Refutation found. Thanks to Tanya!
% 0.18/0.51 % SZS status Theorem for theBenchmark
% 0.18/0.51 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.51 % (24590)------------------------------
% 0.18/0.51 % (24590)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.18/0.51 % (24590)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.18/0.51 % (24590)Termination reason: Refutation
% 0.18/0.51
% 0.18/0.51 % (24590)Memory used [KB]: 1407
% 0.18/0.51 % (24590)Time elapsed: 0.113 s
% 0.18/0.51 % (24590)Instructions burned: 20 (million)
% 0.18/0.51 % (24590)------------------------------
% 0.18/0.51 % (24590)------------------------------
% 0.18/0.51 % (24562)Success in time 0.178 s
%------------------------------------------------------------------------------