%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SWV154+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n008.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 01:20:21 PM UTC 2026
% Result : Theorem 0.21s 0.29s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 1
% Syntax : Number of formulae : 12 ( 6 unt; 0 def)
% Number of atoms : 96 ( 35 equ)
% Maximal formula atoms : 15 ( 8 avg)
% Number of connectives : 108 ( 24 ~; 16 |; 58 &)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 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 : 17 ( 14 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
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,pv12) )
=> ( pv12 = X2
=> divide(sqrt(times(minus(a_select3(center,pv12,n0),a_select2(x,pv10)),minus(a_select3(center,pv12,n0),a_select2(x,pv10)))),pv70) = divide(sqrt(times(minus(a_select3(center,X2,n0),a_select2(x,pv10)),minus(a_select3(center,X2,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)))))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cl5_nebula_norm_0004) ).
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,pv12) )
=> ( pv12 = X2
=> divide(sqrt(times(minus(a_select3(center,pv12,n0),a_select2(x,pv10)),minus(a_select3(center,pv12,n0),a_select2(x,pv10)))),pv70) = divide(sqrt(times(minus(a_select3(center,X2,n0),a_select2(x,pv10)),minus(a_select3(center,X2,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)))))) ) ) ),
inference(negated_conjecture,[status(cth)],[f53]) ).
fof(f143,plain,
( ? [X2] :
( divide(sqrt(times(minus(a_select3(center,pv12,n0),a_select2(x,pv10)),minus(a_select3(center,pv12,n0),a_select2(x,pv10)))),pv70) != divide(sqrt(times(minus(a_select3(center,X2,n0),a_select2(x,pv10)),minus(a_select3(center,X2,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))))))
& pv12 = X2
& leq(n0,X2)
& leq(X2,pv12) )
& 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(f144,plain,
( ? [X2] :
( divide(sqrt(times(minus(a_select3(center,pv12,n0),a_select2(x,pv10)),minus(a_select3(center,pv12,n0),a_select2(x,pv10)))),pv70) != divide(sqrt(times(minus(a_select3(center,X2,n0),a_select2(x,pv10)),minus(a_select3(center,X2,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))))))
& pv12 = X2
& leq(n0,X2)
& leq(X2,pv12) )
& 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,[],[f143]) ).
fof(f197,plain,
( ? [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)))))) != divide(sqrt(times(minus(a_select3(center,pv12,n0),a_select2(x,pv10)),minus(a_select3(center,pv12,n0),a_select2(x,pv10)))),pv70)
& pv12 = X0
& leq(n0,X0)
& leq(X0,pv12) )
& 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,[],[f144]) ).
fof(f198,plain,
( divide(sqrt(times(minus(a_select3(center,pv12,n0),a_select2(x,pv10)),minus(a_select3(center,pv12,n0),a_select2(x,pv10)))),pv70) != divide(sqrt(times(minus(a_select3(center,sK31,n0),a_select2(x,pv10)),minus(a_select3(center,sK31,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))))))
& pv12 = sK31
& leq(n0,sK31)
& leq(sK31,pv12)
& 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,[sK31]),skolemize(X0,sK31)],[f197]) ).
fof(f315,plain,
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))))),
inference(cnf_transformation,[],[f198]) ).
fof(f318,plain,
pv12 = sK31,
inference(cnf_transformation,[],[f198]) ).
fof(f319,plain,
divide(sqrt(times(minus(a_select3(center,pv12,n0),a_select2(x,pv10)),minus(a_select3(center,pv12,n0),a_select2(x,pv10)))),pv70) != divide(sqrt(times(minus(a_select3(center,sK31,n0),a_select2(x,pv10)),minus(a_select3(center,sK31,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)))))),
inference(cnf_transformation,[],[f198]) ).
fof(f380,plain,
divide(sqrt(times(minus(a_select3(center,sK31,n0),a_select2(x,pv10)),minus(a_select3(center,sK31,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)))))) != divide(sqrt(times(minus(a_select3(center,sK31,n0),a_select2(x,pv10)),minus(a_select3(center,sK31,n0),a_select2(x,pv10)))),pv70),
inference(definition_unfolding,[],[f319,f318,f318]) ).
fof(f410,plain,
divide(sqrt(times(minus(a_select3(center,sK31,n0),a_select2(x,pv10)),minus(a_select3(center,sK31,n0),a_select2(x,pv10)))),pv70) != divide(sqrt(times(minus(a_select3(center,sK31,n0),a_select2(x,pv10)),minus(a_select3(center,sK31,n0),a_select2(x,pv10)))),pv70),
inference(forward_demodulation,[],[f380,f315]) ).
fof(f411,plain,
$false,
inference(trivial_inequality_removal,[],[f410]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV154+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.20 % Computer : n008.cluster.edu
% 0.10/0.20 % Model : x86_64 x86_64
% 0.10/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.20 % Memory : 8046.5625MB
% 0.10/0.20 % OS : Linux 6.8.0-71-generic
% 0.10/0.20 % CPULimit : 300
% 0.10/0.20 % WCLimit : 300
% 0.10/0.20 % DateTime : Mon Sep 28 10:02:25 UTC 2026
% 0.10/0.21 % CPUTime :
% 0.10/0.21 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.24 Running first-order model finding
% 0.10/0.24 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.29 % (2145551)Will run a generic schedule for satisfiability detection.
% 0.21/0.29 % (2145556)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2585277881_2999 on theBenchmark for (2999ds/0Mi)
% 0.21/0.29 % (2145557)% WARNING: option uhcvi not known.
% 0.21/0.29 % (2145557)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1037756860:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.21/0.29 % (2145560)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=321109896:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.21/0.29 % (2145561)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1688766141:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.21/0.29 % (2145558)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2596713741:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.21/0.29 % (2145559)dis+10_1_sil=32000:sp=arity:random_seed=264842881:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.21/0.29 % (2145562)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3379857127:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.21/0.29 % (2145561) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2145551-2145561"...
% 0.21/0.29 % (2145561)...printing done.
% 0.21/0.29 % (2145559) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2145551-2145559"...
% 0.21/0.29 % (2145558) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2145551-2145558"...
% 0.21/0.29 % (2145561)Refutation found. Thanks to Tanya!
% 0.21/0.29 % SZS status Theorem for theBenchmark
% 0.21/0.29 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.29 % (2145561)------------------------------
% 0.21/0.29 % (2145561)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.29 % (2145561)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.29 % (2145561)CaDiCaL version: 2.1.3
% 0.21/0.29 % (2145561)Termination reason: Refutation
% 0.21/0.29 % (2145561)Time elapsed: 0.006 s
% 0.21/0.29 % (2145561)Peak memory usage: 11 MB
% 0.21/0.29 % (2145561)Instructions burned: 11 (million)
% 0.21/0.29 % (2145551)Success in time 0.041 s
% 0.21/0.29 % Vampire exiting
%------------------------------------------------------------------------------