%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWV155+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n012.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 01:08:16 PM UTC 2026
% Result : Theorem 2.09s 0.68s
% Output : Refutation 2.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 2
% Syntax : Number of formulae : 18 ( 8 unt; 0 def)
% Number of atoms : 109 ( 36 equ)
% Maximal formula atoms : 15 ( 6 avg)
% Number of connectives : 129 ( 38 ~; 23 |; 58 &)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 20 ( 20 usr; 12 con; 0-3 aty)
% Number of variables : 21 ( 18 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f39,axiom,
! [X0] : minus(X0,n1) = pred(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pred_minus_1) ).
fof(f53,conjecture,
( ( pv70 = sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)))))
& leq(n0,pv10)
& leq(n0,pv12)
& leq(pv10,n135299)
& leq(pv12,n4)
& ! [X0] :
( ( leq(n0,X0)
& leq(X0,pred(pv12)) )
=> a_select3(q,pv10,X0) = divide(sqrt(times(minus(a_select3(center,X0,n0),a_select2(x,pv10)),minus(a_select3(center,X0,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)))))) )
& ! [X1] :
( ( leq(n0,X1)
& leq(X1,pred(pv10)) )
=> sum(n0,n4,a_select3(q,X1,tptp_sum_index)) = n1 ) )
=> ! [X2] :
( ( leq(n0,X2)
& leq(X2,pred(pv10)) )
=> ( pv10 != X2
=> sum(n0,n4,a_select3(q,X2,tptp_sum_index)) = n1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cl5_nebula_norm_0005) ).
fof(f54,negated_conjecture,
~ ( ( pv70 = sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)))))
& leq(n0,pv10)
& leq(n0,pv12)
& leq(pv10,n135299)
& leq(pv12,n4)
& ! [X0] :
( ( leq(n0,X0)
& leq(X0,pred(pv12)) )
=> a_select3(q,pv10,X0) = divide(sqrt(times(minus(a_select3(center,X0,n0),a_select2(x,pv10)),minus(a_select3(center,X0,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)))))) )
& ! [X1] :
( ( leq(n0,X1)
& leq(X1,pred(pv10)) )
=> sum(n0,n4,a_select3(q,X1,tptp_sum_index)) = n1 ) )
=> ! [X2] :
( ( leq(n0,X2)
& leq(X2,pred(pv10)) )
=> ( pv10 != X2
=> sum(n0,n4,a_select3(q,X2,tptp_sum_index)) = n1 ) ) ),
inference(negated_conjecture,[status(cth)],[f53]) ).
fof(f94,plain,
( ? [X2] :
( n1 != sum(n0,n4,a_select3(q,X2,tptp_sum_index))
& pv10 != X2
& leq(n0,X2)
& leq(X2,pred(pv10)) )
& pv70 = sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)))))
& leq(n0,pv10)
& leq(n0,pv12)
& leq(pv10,n135299)
& leq(pv12,n4)
& ! [X0] :
( a_select3(q,pv10,X0) = divide(sqrt(times(minus(a_select3(center,X0,n0),a_select2(x,pv10)),minus(a_select3(center,X0,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10))))))
| ~ leq(n0,X0)
| ~ leq(X0,pred(pv12)) )
& ! [X1] :
( sum(n0,n4,a_select3(q,X1,tptp_sum_index)) = n1
| ~ leq(n0,X1)
| ~ leq(X1,pred(pv10)) ) ),
inference(ennf_transformation,[],[f54]) ).
fof(f95,plain,
( ? [X2] :
( n1 != sum(n0,n4,a_select3(q,X2,tptp_sum_index))
& pv10 != X2
& leq(n0,X2)
& leq(X2,pred(pv10)) )
& pv70 = sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)))))
& leq(n0,pv10)
& leq(n0,pv12)
& leq(pv10,n135299)
& leq(pv12,n4)
& ! [X0] :
( a_select3(q,pv10,X0) = divide(sqrt(times(minus(a_select3(center,X0,n0),a_select2(x,pv10)),minus(a_select3(center,X0,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10))))))
| ~ leq(n0,X0)
| ~ leq(X0,pred(pv12)) )
& ! [X1] :
( sum(n0,n4,a_select3(q,X1,tptp_sum_index)) = n1
| ~ leq(n0,X1)
| ~ leq(X1,pred(pv10)) ) ),
inference(flattening,[],[f94]) ).
fof(f118,plain,
( ? [X0] :
( n1 != sum(n0,n4,a_select3(q,X0,tptp_sum_index))
& pv10 != X0
& leq(n0,X0)
& leq(X0,pred(pv10)) )
& pv70 = sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)))))
& leq(n0,pv10)
& leq(n0,pv12)
& leq(pv10,n135299)
& leq(pv12,n4)
& ! [X1] :
( a_select3(q,pv10,X1) = divide(sqrt(times(minus(a_select3(center,X1,n0),a_select2(x,pv10)),minus(a_select3(center,X1,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10))))))
| ~ leq(n0,X1)
| ~ leq(X1,pred(pv12)) )
& ! [X2] :
( n1 = sum(n0,n4,a_select3(q,X2,tptp_sum_index))
| ~ leq(n0,X2)
| ~ leq(X2,pred(pv10)) ) ),
inference(rectify,[],[f95]) ).
fof(f119,plain,
( n1 != sum(n0,n4,a_select3(q,sK0,tptp_sum_index))
& pv10 != sK0
& leq(n0,sK0)
& leq(sK0,pred(pv10))
& pv70 = sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)))))
& leq(n0,pv10)
& leq(n0,pv12)
& leq(pv10,n135299)
& leq(pv12,n4)
& ! [X1] :
( a_select3(q,pv10,X1) = divide(sqrt(times(minus(a_select3(center,X1,n0),a_select2(x,pv10)),minus(a_select3(center,X1,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10))))))
| ~ leq(n0,X1)
| ~ leq(X1,pred(pv12)) )
& ! [X2] :
( n1 = sum(n0,n4,a_select3(q,X2,tptp_sum_index))
| ~ leq(n0,X2)
| ~ leq(X2,pred(pv10)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f118]) ).
fof(f123,plain,
! [X2] :
( n1 = sum(n0,n4,a_select3(q,X2,tptp_sum_index))
| ~ leq(n0,X2)
| ~ leq(X2,pred(pv10)) ),
inference(cnf_transformation,[],[f119]) ).
fof(f130,plain,
leq(sK0,pred(pv10)),
inference(cnf_transformation,[],[f119]) ).
fof(f131,plain,
leq(n0,sK0),
inference(cnf_transformation,[],[f119]) ).
fof(f133,plain,
n1 != sum(n0,n4,a_select3(q,sK0,tptp_sum_index)),
inference(cnf_transformation,[],[f119]) ).
fof(f154,plain,
! [X0] : minus(X0,n1) = pred(X0),
inference(cnf_transformation,[],[f39]) ).
fof(f195,plain,
leq(sK0,minus(pv10,n1)),
inference(definition_unfolding,[],[f130,f154]) ).
fof(f197,plain,
! [X2] :
( n1 = sum(n0,n4,a_select3(q,X2,tptp_sum_index))
| ~ leq(n0,X2)
| ~ leq(X2,minus(pv10,n1)) ),
inference(definition_unfolding,[],[f123,f154]) ).
fof(f202,plain,
( n1 != n1
| ~ leq(n0,sK0)
| ~ leq(sK0,minus(pv10,n1)) ),
inference(superposition,[],[f133,f197]) ).
fof(f203,plain,
( ~ leq(n0,sK0)
| ~ leq(sK0,minus(pv10,n1)) ),
inference(trivial_inequality_removal,[],[f202]) ).
fof(f204,plain,
~ leq(sK0,minus(pv10,n1)),
inference(forward_subsumption_resolution,[],[f203,f131]) ).
fof(f205,plain,
$false,
inference(forward_subsumption_resolution,[],[f204,f195]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SWV155+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.00/0.10 % Computer : n012.cluster.edu
% 0.00/0.10 % Model : x86_64 x86_64
% 0.00/0.10 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.10 % Memory : 8046.5625MB
% 0.00/0.10 % OS : Linux 6.8.0-71-generic
% 0.00/0.10 % CPULimit : 300
% 0.00/0.10 % WCLimit : 300
% 0.00/0.10 % DateTime : Mon Sep 28 10:01:04 UTC 2026
% 0.00/0.10 % CPUTime :
% 0.00/0.10 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.12 Running first-order theorem proving
% 0.08/0.12 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.09/0.68 % (3278399)Detected formulas, will run a generic FOF schedule.
% 2.09/0.68 % (3278404)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=3467365314:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.09/0.68 % (3278406)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=3331444704:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.09/0.68 % (3278410)dis-21_1_sil=8000:lcm=predicate:random_seed=2748406750: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)
% 2.09/0.68 % (3278408)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2805048481:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.09/0.68 % (3278405)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=4008436177:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.09/0.68 % (3278407)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3698449640:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.09/0.68 % (3278409)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2578199019:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.09/0.68 % (3278408)First to succeed.
% 2.09/0.68 % (3278408)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3278399"
% 2.09/0.68 % (3278407)Also succeeded, but the first one will report.
% 2.09/0.68 % (3278409)Also succeeded, but the first one will report.
% 2.09/0.68 % (3278410)Also succeeded, but the first one will report.
% 2.09/0.68 % (3278408)Refutation found. Thanks to Tanya!
% 2.09/0.68 % SZS status Theorem for theBenchmark
% 2.09/0.68 % SZS output start Proof for theBenchmark
% See solution above
% 2.09/0.68 % (3278408)------------------------------
% 2.09/0.68 % (3278408)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.09/0.68 % (3278408)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.09/0.68 % (3278408)CaDiCaL version: 2.1.3
% 2.09/0.68 % (3278408)Termination reason: Refutation
% 2.09/0.68 % (3278408)Time elapsed: 0.002 s
% 2.09/0.68 % (3278408)Peak memory usage: 88 MB
% 2.09/0.68 % (3278408)Instructions burned: 4 (million)
% 2.09/0.68 % (3278408)------------------------------
% 2.09/0.68 % (3278408)------------------------------
% 2.09/0.68 % (3278399)Success in time 0.274 s
% 2.09/0.68 % Vampire exiting
%------------------------------------------------------------------------------