%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWV164+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 01:08:17 PM UTC 2026
% Result : Theorem 3.68s 1.29s
% Output : Refutation 3.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 8
% Syntax : Number of formulae : 37 ( 13 unt; 0 def)
% Number of atoms : 108 ( 23 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 111 ( 40 ~; 30 |; 31 &)
% ( 1 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 26 ( 26 usr; 16 con; 0-3 aty)
% Number of variables : 43 ( 40 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] : ~ gt(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',irreflexivity_gt) ).
fof(f5,axiom,
! [X0,X1,X2] :
( ( leq(X0,X1)
& leq(X1,X2) )
=> leq(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity_leq) ).
fof(f8,axiom,
! [X0,X1] :
( gt(X1,X0)
=> leq(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',leq_gt1) ).
fof(f13,axiom,
! [X0,X1] :
( leq(X0,X1)
<=> gt(succ(X1),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',leq_succ_gt_equiv) ).
fof(f28,axiom,
succ(tptp_minus_1) = n0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',succ_tptp_minus_1) ).
fof(f53,conjecture,
( ( leq(n0,pv10)
& leq(pv10,n135299)
& ! [X0] :
( ( leq(n0,X0)
& leq(X0,pred(pv10)) )
=> sum(n0,n4,a_select3(q,X0,tptp_sum_index)) = n1 ) )
=> ! [X1] :
( ( leq(n0,X1)
& leq(X1,tptp_minus_1) )
=> a_select3(q,pv10,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))))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cl5_nebula_norm_0014) ).
fof(f54,negated_conjecture,
~ ( ( leq(n0,pv10)
& leq(pv10,n135299)
& ! [X0] :
( ( leq(n0,X0)
& leq(X0,pred(pv10)) )
=> sum(n0,n4,a_select3(q,X0,tptp_sum_index)) = n1 ) )
=> ! [X1] :
( ( leq(n0,X1)
& leq(X1,tptp_minus_1) )
=> a_select3(q,pv10,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))))) ) ),
inference(negated_conjecture,[status(cth)],[f53]) ).
fof(f61,axiom,
gt(n0,tptp_minus_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_0_tptp_minus_1) ).
fof(f93,axiom,
! [X0] :
( ( leq(n0,X0)
& leq(X0,n0) )
=> X0 = n0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',finite_domain_0) ).
fof(f102,plain,
( ? [X1] :
( a_select3(q,pv10,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)))))
& leq(n0,X1)
& leq(X1,tptp_minus_1) )
& leq(n0,pv10)
& leq(pv10,n135299)
& ! [X0] :
( sum(n0,n4,a_select3(q,X0,tptp_sum_index)) = n1
| ~ leq(n0,X0)
| ~ leq(X0,pred(pv10)) ) ),
inference(ennf_transformation,[],[f54]) ).
fof(f103,plain,
( ? [X1] :
( a_select3(q,pv10,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)))))
& leq(n0,X1)
& leq(X1,tptp_minus_1) )
& leq(n0,pv10)
& leq(pv10,n135299)
& ! [X0] :
( sum(n0,n4,a_select3(q,X0,tptp_sum_index)) = n1
| ~ leq(n0,X0)
| ~ leq(X0,pred(pv10)) ) ),
inference(flattening,[],[f102]) ).
fof(f104,plain,
! [X0] :
( X0 = n0
| ~ leq(n0,X0)
| ~ leq(X0,n0) ),
inference(ennf_transformation,[],[f93]) ).
fof(f105,plain,
! [X0] :
( X0 = n0
| ~ leq(n0,X0)
| ~ leq(X0,n0) ),
inference(flattening,[],[f104]) ).
fof(f108,plain,
! [X0,X1] :
( leq(X0,X1)
| ~ gt(X1,X0) ),
inference(ennf_transformation,[],[f8]) ).
fof(f109,plain,
! [X0,X1,X2] :
( leq(X0,X2)
| ~ leq(X0,X1)
| ~ leq(X1,X2) ),
inference(ennf_transformation,[],[f5]) ).
fof(f110,plain,
! [X0,X1,X2] :
( leq(X0,X2)
| ~ leq(X0,X1)
| ~ leq(X1,X2) ),
inference(flattening,[],[f109]) ).
fof(f126,plain,
( ? [X0] :
( a_select3(q,pv10,X0) != divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,X0)),minus(a_select2(x,pv10),a_select2(mu,X0))),tptp_minus_2),times(a_select2(sigma,X0),a_select2(sigma,X0)))),a_select2(rho,X0)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,X0))),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,X0)
& leq(X0,tptp_minus_1) )
& leq(n0,pv10)
& leq(pv10,n135299)
& ! [X1] :
( n1 = sum(n0,n4,a_select3(q,X1,tptp_sum_index))
| ~ leq(n0,X1)
| ~ leq(X1,pred(pv10)) ) ),
inference(rectify,[],[f103]) ).
fof(f127,plain,
( a_select3(q,pv10,sK0) != divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,sK0)),minus(a_select2(x,pv10),a_select2(mu,sK0))),tptp_minus_2),times(a_select2(sigma,sK0),a_select2(sigma,sK0)))),a_select2(rho,sK0)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,sK0))),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,sK0)
& leq(sK0,tptp_minus_1)
& leq(n0,pv10)
& leq(pv10,n135299)
& ! [X1] :
( n1 = sum(n0,n4,a_select3(q,X1,tptp_sum_index))
| ~ leq(n0,X1)
| ~ leq(X1,pred(pv10)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f126]) ).
fof(f130,plain,
! [X0,X1] :
( ( leq(X0,X1)
| ~ gt(succ(X1),X0) )
& ( gt(succ(X1),X0)
| ~ leq(X0,X1) ) ),
inference(nnf_transformation,[],[f13]) ).
fof(f134,plain,
leq(sK0,tptp_minus_1),
inference(cnf_transformation,[],[f127]) ).
fof(f135,plain,
leq(n0,sK0),
inference(cnf_transformation,[],[f127]) ).
fof(f141,plain,
! [X0] :
( ~ leq(n0,X0)
| n0 = X0
| ~ leq(X0,n0) ),
inference(cnf_transformation,[],[f105]) ).
fof(f143,plain,
! [X0,X1] :
( leq(X0,X1)
| ~ gt(X1,X0) ),
inference(cnf_transformation,[],[f108]) ).
fof(f144,plain,
! [X2,X0,X1] :
( leq(X0,X2)
| ~ leq(X0,X1)
| ~ leq(X1,X2) ),
inference(cnf_transformation,[],[f110]) ).
fof(f149,plain,
gt(n0,tptp_minus_1),
inference(cnf_transformation,[],[f61]) ).
fof(f152,plain,
n0 = succ(tptp_minus_1),
inference(cnf_transformation,[],[f28]) ).
fof(f187,plain,
! [X0,X1] :
( gt(succ(X1),X0)
| ~ leq(X0,X1) ),
inference(cnf_transformation,[],[f130]) ).
fof(f191,plain,
! [X0] : ~ gt(X0,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f243,plain,
! [X0] : ~ leq(succ(X0),X0),
inference(resolution,[],[f187,f191]) ).
fof(f252,plain,
~ leq(n0,tptp_minus_1),
inference(superposition,[],[f243,f152]) ).
fof(f366,plain,
( ~ leq(sK0,n0)
| n0 = sK0 ),
inference(resolution,[],[f141,f135]) ).
fof(f398,plain,
! [X0] :
( ~ leq(sK0,X0)
| ~ leq(X0,n0)
| n0 = sK0 ),
inference(resolution,[],[f144,f366]) ).
fof(f461,plain,
( ~ leq(tptp_minus_1,n0)
| n0 = sK0 ),
inference(resolution,[],[f398,f134]) ).
fof(f475,plain,
( n0 = sK0
| ~ gt(n0,tptp_minus_1) ),
inference(resolution,[],[f461,f143]) ).
fof(f476,plain,
n0 = sK0,
inference(forward_subsumption_resolution,[],[f475,f149]) ).
fof(f498,plain,
~ leq(sK0,tptp_minus_1),
inference(superposition,[],[f252,f476]) ).
fof(f506,plain,
$false,
inference(forward_subsumption_resolution,[],[f498,f134]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV164+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.18 % Computer : n019.cluster.edu
% 0.10/0.18 % Model : x86_64 x86_64
% 0.10/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.18 % Memory : 8046.5625MB
% 0.10/0.18 % OS : Linux 6.8.0-71-generic
% 0.10/0.18 % CPULimit : 300
% 0.10/0.18 % WCLimit : 300
% 0.10/0.18 % DateTime : Mon Sep 28 10:03:33 UTC 2026
% 0.10/0.18 % CPUTime :
% 0.10/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.21 Running first-order theorem proving
% 0.10/0.21 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.68/1.29 % (3899762)Detected formulas, will run a generic FOF schedule.
% 3.68/1.29 % (3899861)dis-21_1_sil=8000:lcm=predicate:random_seed=2836129633:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 3.68/1.29 % (3899861)Instruction limit reached!
% 3.68/1.29 % (3899861)------------------------------
% 3.68/1.29 % (3899861)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.68/1.29 % (3899861)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.68/1.29 % (3899861)CaDiCaL version: 2.1.3
% 3.68/1.29 % (3899861)Termination reason: Instruction limit
% 3.68/1.29 % (3899861)Termination phase: Saturation
% 3.68/1.29 % (3899861)Time elapsed: 0.037 s
% 3.68/1.29 % (3899861)Peak memory usage: 89 MB
% 3.68/1.29 % (3899861)Instructions burned: 132 (million)
% 3.68/1.29 % (3899859)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3809120977:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.68/1.29 % (3899852)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=2249351782:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.68/1.29 % (3899857)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1275816591:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.68/1.29 % (3899856)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=17199791:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.68/1.29 % (3899854)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=2111792348:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.68/1.29 % (3899860)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=68388500:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.68/1.29 % (3899859)First to succeed.
% 3.68/1.29 % (3899857)Refutation not found, incomplete strategy
% 3.68/1.29 % (3899857)------------------------------
% 3.68/1.29 % (3899857)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.68/1.29 % (3899857)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.68/1.29 % (3899857)CaDiCaL version: 2.1.3
% 3.68/1.29 % (3899857)Termination reason: Refutation not found, incomplete strategy
% 3.68/1.29 % (3899857)Time elapsed: 0.009 s
% 3.68/1.29 % (3899857)Peak memory usage: 88 MB
% 3.68/1.29 % (3899857)Instructions burned: 13 (million)
% 3.68/1.29 % (3899859)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3899762"
% 3.68/1.29 % (3899860)Also succeeded, but the first one will report.
% 3.68/1.29 % (3899904)lrs+10_1_sil=8000:sp=occurrence:random_seed=1651774710:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 3.68/1.29 % (3899904)Also succeeded, but the first one will report.
% 3.68/1.29 % (3899857)------------------------------
% 3.68/1.29 % (3899857)------------------------------
% 3.68/1.29 % (3899859)Refutation found. Thanks to Tanya!
% 3.68/1.29 % SZS status Theorem for theBenchmark
% 3.68/1.29 % SZS output start Proof for theBenchmark
% See solution above
% 3.68/1.29 % (3899859)------------------------------
% 3.68/1.29 % (3899859)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.68/1.29 % (3899859)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.68/1.29 % (3899859)CaDiCaL version: 2.1.3
% 3.68/1.29 % (3899859)Termination reason: Refutation
% 3.68/1.29 % (3899859)Time elapsed: 0.010 s
% 3.68/1.29 % (3899859)Peak memory usage: 88 MB
% 3.68/1.29 % (3899859)Instructions burned: 15 (million)
% 3.68/1.29 % (3899859)------------------------------
% 3.68/1.29 % (3899859)------------------------------
% 3.68/1.29 % (3899762)Success in time 0.436 s
% 3.68/1.29 % Vampire exiting
%------------------------------------------------------------------------------