%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWV212+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 : n014.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 01:08:24 PM UTC 2026
% Result : Theorem 3.10s 0.99s
% Output : Refutation 3.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 1
% Syntax : Number of formulae : 13 ( 6 unt; 0 def)
% Number of atoms : 400 ( 379 equ)
% Maximal formula atoms : 78 ( 30 avg)
% Number of connectives : 676 ( 289 ~; 107 |; 276 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 47 ( 19 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 10 con; 0-2 aty)
% Number of variables : 8 ( 4 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f53,conjecture,
! [X0,X1] :
( ( leq(n0,X0)
& leq(n0,X1)
& leq(X0,n5)
& leq(X1,n5) )
=> ( ( ~ ( n0 = X0
& n1 = X1 )
& ~ ( n0 = X0
& n2 = X1 )
& ~ ( n0 = X0
& n3 = X1 )
& ~ ( n0 = X0
& n4 = X1 )
& ~ ( n0 = X0
& n5 = X1 )
& ~ ( n0 = X1
& n1 = X0 )
& ~ ( n0 = X1
& n2 = X0 )
& ~ ( n0 = X1
& n3 = X0 )
& ~ ( n0 = X1
& n4 = X0 )
& ~ ( n0 = X1
& n5 = X0 )
& ~ ( n1 = X0
& n1 = X1 )
& ~ ( n1 = X0
& n2 = X1 )
& ~ ( n1 = X0
& n3 = X1 )
& ~ ( n1 = X0
& n4 = X1 )
& ~ ( n1 = X0
& n5 = X1 )
& ~ ( n1 = X1
& n2 = X0 )
& ~ ( n1 = X1
& n3 = X0 )
& ~ ( n1 = X1
& n4 = X0 )
& ~ ( n1 = X1
& n5 = X0 )
& ~ ( n2 = X0
& n2 = X1 )
& ~ ( n2 = X0
& n3 = X1 )
& ~ ( n2 = X0
& n4 = X1 )
& ~ ( n2 = X0
& n5 = X1 )
& ~ ( n2 = X1
& n3 = X0 )
& ~ ( n2 = X1
& n4 = X0 )
& ~ ( n2 = X1
& n5 = X0 )
& ~ ( n3 = X0
& n3 = X1 )
& ~ ( n3 = X0
& n4 = X1 )
& ~ ( n3 = X0
& n5 = X1 )
& ~ ( n3 = X1
& n4 = X0 )
& ~ ( n3 = X1
& n5 = X0 )
& ~ ( n4 = X0
& n4 = X1 )
& ~ ( n4 = X0
& n5 = X1 )
& ~ ( n4 = X1
& n5 = X0 )
& ~ ( n5 = X0
& n5 = X1 )
& n0 = X0
& n0 = X1
& n3 = X0 )
=> n0 = times(divide(n1,n400),a_select2(sigma,n0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quaternion_ds1_symm_0041) ).
fof(f54,negated_conjecture,
~ ! [X0,X1] :
( ( leq(n0,X0)
& leq(n0,X1)
& leq(X0,n5)
& leq(X1,n5) )
=> ( ( ~ ( n0 = X0
& n1 = X1 )
& ~ ( n0 = X0
& n2 = X1 )
& ~ ( n0 = X0
& n3 = X1 )
& ~ ( n0 = X0
& n4 = X1 )
& ~ ( n0 = X0
& n5 = X1 )
& ~ ( n0 = X1
& n1 = X0 )
& ~ ( n0 = X1
& n2 = X0 )
& ~ ( n0 = X1
& n3 = X0 )
& ~ ( n0 = X1
& n4 = X0 )
& ~ ( n0 = X1
& n5 = X0 )
& ~ ( n1 = X0
& n1 = X1 )
& ~ ( n1 = X0
& n2 = X1 )
& ~ ( n1 = X0
& n3 = X1 )
& ~ ( n1 = X0
& n4 = X1 )
& ~ ( n1 = X0
& n5 = X1 )
& ~ ( n1 = X1
& n2 = X0 )
& ~ ( n1 = X1
& n3 = X0 )
& ~ ( n1 = X1
& n4 = X0 )
& ~ ( n1 = X1
& n5 = X0 )
& ~ ( n2 = X0
& n2 = X1 )
& ~ ( n2 = X0
& n3 = X1 )
& ~ ( n2 = X0
& n4 = X1 )
& ~ ( n2 = X0
& n5 = X1 )
& ~ ( n2 = X1
& n3 = X0 )
& ~ ( n2 = X1
& n4 = X0 )
& ~ ( n2 = X1
& n5 = X0 )
& ~ ( n3 = X0
& n3 = X1 )
& ~ ( n3 = X0
& n4 = X1 )
& ~ ( n3 = X0
& n5 = X1 )
& ~ ( n3 = X1
& n4 = X0 )
& ~ ( n3 = X1
& n5 = X0 )
& ~ ( n4 = X0
& n4 = X1 )
& ~ ( n4 = X0
& n5 = X1 )
& ~ ( n4 = X1
& n5 = X0 )
& ~ ( n5 = X0
& n5 = X1 )
& n0 = X0
& n0 = X1
& n3 = X0 )
=> n0 = times(divide(n1,n400),a_select2(sigma,n0)) ) ),
inference(negated_conjecture,[status(cth)],[f53]) ).
fof(f94,plain,
? [X0,X1] :
( n0 != times(divide(n1,n400),a_select2(sigma,n0))
& ( n0 != X0
| n1 != X1 )
& ( n0 != X0
| n2 != X1 )
& ( n0 != X0
| n3 != X1 )
& ( n0 != X0
| n4 != X1 )
& ( n0 != X0
| n5 != X1 )
& ( n0 != X1
| n1 != X0 )
& ( n0 != X1
| n2 != X0 )
& ( n0 != X1
| n3 != X0 )
& ( n0 != X1
| n4 != X0 )
& ( n0 != X1
| n5 != X0 )
& ( n1 != X0
| n1 != X1 )
& ( n1 != X0
| n2 != X1 )
& ( n1 != X0
| n3 != X1 )
& ( n1 != X0
| n4 != X1 )
& ( n1 != X0
| n5 != X1 )
& ( n1 != X1
| n2 != X0 )
& ( n1 != X1
| n3 != X0 )
& ( n1 != X1
| n4 != X0 )
& ( n1 != X1
| n5 != X0 )
& ( n2 != X0
| n2 != X1 )
& ( n2 != X0
| n3 != X1 )
& ( n2 != X0
| n4 != X1 )
& ( n2 != X0
| n5 != X1 )
& ( n2 != X1
| n3 != X0 )
& ( n2 != X1
| n4 != X0 )
& ( n2 != X1
| n5 != X0 )
& ( n3 != X0
| n3 != X1 )
& ( n3 != X0
| n4 != X1 )
& ( n3 != X0
| n5 != X1 )
& ( n3 != X1
| n4 != X0 )
& ( n3 != X1
| n5 != X0 )
& ( n4 != X0
| n4 != X1 )
& ( n4 != X0
| n5 != X1 )
& ( n4 != X1
| n5 != X0 )
& ( n5 != X0
| n5 != X1 )
& n0 = X0
& n0 = X1
& n3 = X0
& leq(n0,X0)
& leq(n0,X1)
& leq(X0,n5)
& leq(X1,n5) ),
inference(ennf_transformation,[],[f54]) ).
fof(f95,plain,
? [X0,X1] :
( n0 != times(divide(n1,n400),a_select2(sigma,n0))
& ( n0 != X0
| n1 != X1 )
& ( n0 != X0
| n2 != X1 )
& ( n0 != X0
| n3 != X1 )
& ( n0 != X0
| n4 != X1 )
& ( n0 != X0
| n5 != X1 )
& ( n0 != X1
| n1 != X0 )
& ( n0 != X1
| n2 != X0 )
& ( n0 != X1
| n3 != X0 )
& ( n0 != X1
| n4 != X0 )
& ( n0 != X1
| n5 != X0 )
& ( n1 != X0
| n1 != X1 )
& ( n1 != X0
| n2 != X1 )
& ( n1 != X0
| n3 != X1 )
& ( n1 != X0
| n4 != X1 )
& ( n1 != X0
| n5 != X1 )
& ( n1 != X1
| n2 != X0 )
& ( n1 != X1
| n3 != X0 )
& ( n1 != X1
| n4 != X0 )
& ( n1 != X1
| n5 != X0 )
& ( n2 != X0
| n2 != X1 )
& ( n2 != X0
| n3 != X1 )
& ( n2 != X0
| n4 != X1 )
& ( n2 != X0
| n5 != X1 )
& ( n2 != X1
| n3 != X0 )
& ( n2 != X1
| n4 != X0 )
& ( n2 != X1
| n5 != X0 )
& ( n3 != X0
| n3 != X1 )
& ( n3 != X0
| n4 != X1 )
& ( n3 != X0
| n5 != X1 )
& ( n3 != X1
| n4 != X0 )
& ( n3 != X1
| n5 != X0 )
& ( n4 != X0
| n4 != X1 )
& ( n4 != X0
| n5 != X1 )
& ( n4 != X1
| n5 != X0 )
& ( n5 != X0
| n5 != X1 )
& n0 = X0
& n0 = X1
& n3 = X0
& leq(n0,X0)
& leq(n0,X1)
& leq(X0,n5)
& leq(X1,n5) ),
inference(flattening,[],[f94]) ).
fof(f117,plain,
( n0 != times(divide(n1,n400),a_select2(sigma,n0))
& ( n0 != sK0
| n1 != sK1 )
& ( n0 != sK0
| n2 != sK1 )
& ( n0 != sK0
| n3 != sK1 )
& ( n0 != sK0
| n4 != sK1 )
& ( n0 != sK0
| n5 != sK1 )
& ( n0 != sK1
| n1 != sK0 )
& ( n0 != sK1
| n2 != sK0 )
& ( n0 != sK1
| n3 != sK0 )
& ( n0 != sK1
| n4 != sK0 )
& ( n0 != sK1
| n5 != sK0 )
& ( n1 != sK0
| n1 != sK1 )
& ( n1 != sK0
| n2 != sK1 )
& ( n1 != sK0
| n3 != sK1 )
& ( n1 != sK0
| n4 != sK1 )
& ( n1 != sK0
| n5 != sK1 )
& ( n1 != sK1
| n2 != sK0 )
& ( n1 != sK1
| n3 != sK0 )
& ( n1 != sK1
| n4 != sK0 )
& ( n1 != sK1
| n5 != sK0 )
& ( n2 != sK0
| n2 != sK1 )
& ( n2 != sK0
| n3 != sK1 )
& ( n2 != sK0
| n4 != sK1 )
& ( n2 != sK0
| n5 != sK1 )
& ( n2 != sK1
| n3 != sK0 )
& ( n2 != sK1
| n4 != sK0 )
& ( n2 != sK1
| n5 != sK0 )
& ( n3 != sK0
| n3 != sK1 )
& ( n3 != sK0
| n4 != sK1 )
& ( n3 != sK0
| n5 != sK1 )
& ( n3 != sK1
| n4 != sK0 )
& ( n3 != sK1
| n5 != sK0 )
& ( n4 != sK0
| n4 != sK1 )
& ( n4 != sK0
| n5 != sK1 )
& ( n4 != sK1
| n5 != sK0 )
& ( n5 != sK0
| n5 != sK1 )
& n0 = sK0
& n0 = sK1
& n3 = sK0
& leq(n0,sK0)
& leq(n0,sK1)
& leq(sK0,n5)
& leq(sK1,n5) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f95]) ).
fof(f124,plain,
n3 = sK0,
inference(cnf_transformation,[],[f117]) ).
fof(f125,plain,
n0 = sK1,
inference(cnf_transformation,[],[f117]) ).
fof(f126,plain,
n0 = sK0,
inference(cnf_transformation,[],[f117]) ).
fof(f135,plain,
( n3 != sK0
| n3 != sK1 ),
inference(cnf_transformation,[],[f117]) ).
fof(f232,plain,
( sK0 != sK0
| sK0 != sK1 ),
inference(definition_unfolding,[],[f135,f124,f124]) ).
fof(f237,plain,
sK0 = sK1,
inference(definition_unfolding,[],[f125,f126]) ).
fof(f270,plain,
sK0 != sK1,
inference(trivial_inequality_removal,[],[f232]) ).
fof(f295,plain,
$false,
inference(forward_subsumption_resolution,[],[f270,f237]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV212+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.17 % Computer : n014.cluster.edu
% 0.11/0.17 % Model : x86_64 x86_64
% 0.11/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.17 % Memory : 8046.5625MB
% 0.11/0.17 % OS : Linux 6.8.0-71-generic
% 0.11/0.17 % CPULimit : 300
% 0.11/0.17 % WCLimit : 300
% 0.11/0.17 % DateTime : Mon Sep 28 10:10:31 UTC 2026
% 0.11/0.17 % CPUTime :
% 0.11/0.17 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.20 Running first-order theorem proving
% 0.11/0.20 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
% 3.10/0.99 % (1687718)Detected formulas, will run a generic FOF schedule.
% 3.10/0.99 % (1687726)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=4085385778:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.10/0.99 % (1687725)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=4220327593:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.10/0.99 % (1687724)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=881863772:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.10/0.99 % (1687729)dis-21_1_sil=8000:lcm=predicate:random_seed=419643806: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)
% 3.10/0.99 % (1687727)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2927956388:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.10/0.99 % (1687723)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=3510207593:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.10/0.99 % (1687728)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3939929389:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.10/0.99 % (1687727)First to succeed.
% 3.10/0.99 % (1687728)Also succeeded, but the first one will report.
% 3.10/0.99 % (1687727)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1687718"
% 3.10/0.99 % (1687726)Also succeeded, but the first one will report.
% 3.10/0.99 % (1687729)Also succeeded, but the first one will report.
% 3.10/0.99 % (1687737)lrs+10_1_sil=8000:sp=occurrence:random_seed=1029289104:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.10/0.99 % (1687737)Also succeeded, but the first one will report.
% 3.10/0.99 % (1687727)Refutation found. Thanks to Tanya!
% 3.10/0.99 % SZS status Theorem for theBenchmark
% 3.10/0.99 % SZS output start Proof for theBenchmark
% See solution above
% 3.10/0.99 % (1687727)------------------------------
% 3.10/0.99 % (1687727)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.10/0.99 % (1687727)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.10/0.99 % (1687727)CaDiCaL version: 2.1.3
% 3.10/0.99 % (1687727)Termination reason: Refutation
% 3.10/0.99 % (1687727)Time elapsed: 0.004 s
% 3.10/0.99 % (1687727)Peak memory usage: 88 MB
% 3.10/0.99 % (1687727)Instructions burned: 5 (million)
% 3.10/0.99 % (1687727)------------------------------
% 3.10/0.99 % (1687727)------------------------------
% 3.10/0.99 % (1687718)Success in time 0.39 s
% 3.10/0.99 % Vampire exiting
%------------------------------------------------------------------------------