%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWV156+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 2.05s 0.67s
% Output : Refutation 2.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 19 ( 9 unt; 0 def)
% Number of atoms : 109 ( 33 equ)
% Maximal formula atoms : 15 ( 5 avg)
% Number of connectives : 117 ( 27 ~; 20 |; 59 &)
% ( 1 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 22 ( 22 usr; 12 con; 0-3 aty)
% Number of variables : 29 ( 26 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] : ~ gt(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',irreflexivity_gt) ).
fof(f10,axiom,
! [X0,X1] :
( leq(X0,pred(X1))
<=> gt(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',leq_gt_pred) ).
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,cond(tptp_term_equals(pv12,tptp_sum_index),divide(sqrt(times(minus(a_select3(center,pv12,n0),a_select2(x,pv10)),minus(a_select3(center,pv12,n0),a_select2(x,pv10)))),pv70),a_select3(q,X2,tptp_sum_index))) = n1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cl5_nebula_norm_0006) ).
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,cond(tptp_term_equals(pv12,tptp_sum_index),divide(sqrt(times(minus(a_select3(center,pv12,n0),a_select2(x,pv10)),minus(a_select3(center,pv12,n0),a_select2(x,pv10)))),pv70),a_select3(q,X2,tptp_sum_index))) = n1 ) ) ),
inference(negated_conjecture,[status(cth)],[f53]) ).
fof(f94,plain,
( ? [X2] :
( n1 != sum(n0,n4,cond(tptp_term_equals(pv12,tptp_sum_index),divide(sqrt(times(minus(a_select3(center,pv12,n0),a_select2(x,pv10)),minus(a_select3(center,pv12,n0),a_select2(x,pv10)))),pv70),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,cond(tptp_term_equals(pv12,tptp_sum_index),divide(sqrt(times(minus(a_select3(center,pv12,n0),a_select2(x,pv10)),minus(a_select3(center,pv12,n0),a_select2(x,pv10)))),pv70),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,cond(tptp_term_equals(pv12,tptp_sum_index),divide(sqrt(times(minus(a_select3(center,pv12,n0),a_select2(x,pv10)),minus(a_select3(center,pv12,n0),a_select2(x,pv10)))),pv70),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,cond(tptp_term_equals(pv12,tptp_sum_index),divide(sqrt(times(minus(a_select3(center,pv12,n0),a_select2(x,pv10)),minus(a_select3(center,pv12,n0),a_select2(x,pv10)))),pv70),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(f120,plain,
! [X0,X1] :
( ( leq(X0,pred(X1))
| ~ gt(X1,X0) )
& ( gt(X1,X0)
| ~ leq(X0,pred(X1)) ) ),
inference(nnf_transformation,[],[f10]) ).
fof(f130,plain,
leq(sK0,pred(pv10)),
inference(cnf_transformation,[],[f119]) ).
fof(f132,plain,
pv10 = sK0,
inference(cnf_transformation,[],[f119]) ).
fof(f136,plain,
! [X0,X1] :
( gt(X1,X0)
| ~ leq(X0,pred(X1)) ),
inference(cnf_transformation,[],[f120]) ).
fof(f154,plain,
! [X0] : minus(X0,n1) = pred(X0),
inference(cnf_transformation,[],[f39]) ).
fof(f169,plain,
! [X0] : ~ gt(X0,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f196,plain,
leq(sK0,minus(sK0,n1)),
inference(definition_unfolding,[],[f130,f154,f132]) ).
fof(f205,plain,
! [X0,X1] :
( ~ leq(X0,minus(X1,n1))
| gt(X1,X0) ),
inference(definition_unfolding,[],[f136,f154]) ).
fof(f345,plain,
gt(sK0,sK0),
inference(resolution,[],[f205,f196]) ).
fof(f351,plain,
$false,
inference(forward_subsumption_resolution,[],[f345,f169]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SWV156+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 10:00:49 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
% 2.05/0.67 % (3277973)Detected formulas, will run a generic FOF schedule.
% 2.05/0.67 % (3277984)dis-21_1_sil=8000:lcm=predicate:random_seed=1969105051: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)
% 2.05/0.67 % (3277980)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=2611367313:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.05/0.67 % (3277982)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3485069277:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.05/0.67 % (3277981)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=774691665:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.05/0.67 % (3277979)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=2336336900:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.05/0.67 % (3277983)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3197304199:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.05/0.67 % (3277978)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=1017416582:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.05/0.67 % (3277982)First to succeed.
% 2.05/0.67 % (3277982)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3277973"
% 2.05/0.67 % (3277981)Instruction limit reached!
% 2.05/0.67 % (3277981)------------------------------
% 2.05/0.67 % (3277981)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.05/0.67 % (3277981)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.05/0.67 % (3277981)CaDiCaL version: 2.1.3
% 2.05/0.67 % (3277981)Termination reason: Instruction limit
% 2.05/0.67 % (3277981)Termination phase: Saturation
% 2.05/0.67 % (3277981)Time elapsed: 0.034 s
% 2.05/0.67 % (3277981)Peak memory usage: 89 MB
% 2.05/0.67 % (3277981)Instructions burned: 109 (million)
% 2.05/0.67 % (3277984)Instruction limit reached!
% 2.05/0.67 % (3277984)------------------------------
% 2.05/0.67 % (3277984)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.05/0.67 % (3277984)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.05/0.67 % (3277984)CaDiCaL version: 2.1.3
% 2.05/0.67 % (3277984)Termination reason: Instruction limit
% 2.05/0.67 % (3277984)Termination phase: Saturation
% 2.05/0.67 % (3277984)Time elapsed: 0.034 s
% 2.05/0.67 % (3277984)Peak memory usage: 89 MB
% 2.05/0.67 % (3277984)Instructions burned: 132 (million)
% 2.05/0.67 % (3277983)Instruction limit reached!
% 2.05/0.67 % (3277983)------------------------------
% 2.05/0.67 % (3277983)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.05/0.67 % (3277983)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.05/0.67 % (3277983)CaDiCaL version: 2.1.3
% 2.05/0.67 % (3277983)Termination reason: Instruction limit
% 2.05/0.67 % (3277983)Termination phase: Saturation
% 2.05/0.67 % (3277983)Time elapsed: 0.047 s
% 2.05/0.67 % (3277983)Peak memory usage: 90 MB
% 2.05/0.67 % (3277983)Instructions burned: 140 (million)
% 2.05/0.67 % (3277993)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1156316078:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/157Mi)
% 2.05/0.67 % (3277992)lrs+10_1_sil=8000:sp=occurrence:random_seed=892081760:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 2.05/0.67 % (3277992)Also succeeded, but the first one will report.
% 2.05/0.67 % (3277994)lrs+1011_1_sil=32000:sp=occurrence:random_seed=3991529568:i=325:sd=1:ss=axioms:sgt=32_2998 on theBenchmark for (2998ds/325Mi)
% 2.05/0.67 % (3277982)Refutation found. Thanks to Tanya!
% 2.05/0.67 % SZS status Theorem for theBenchmark
% 2.05/0.67 % SZS output start Proof for theBenchmark
% See solution above
% 2.05/0.67 % (3277982)------------------------------
% 2.05/0.67 % (3277982)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.05/0.67 % (3277982)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.05/0.67 % (3277982)CaDiCaL version: 2.1.3
% 2.05/0.67 % (3277982)Termination reason: Refutation
% 2.05/0.67 % (3277982)Time elapsed: 0.004 s
% 2.05/0.67 % (3277982)Peak memory usage: 88 MB
% 2.05/0.67 % (3277982)Instructions burned: 10 (million)
% 2.05/0.67 % (3277982)------------------------------
% 2.05/0.67 % (3277982)------------------------------
% 2.05/0.67 % (3277973)Success in time 0.261 s
% 2.05/0.67 % Vampire exiting
%------------------------------------------------------------------------------