%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWV221+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 : n004.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 01:08:25 PM UTC 2026
% Result : Theorem 3.61s 1.20s
% Output : Refutation 3.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 1
% Syntax : Number of formulae : 18 ( 7 unt; 0 def)
% Number of atoms : 308 ( 69 equ)
% Maximal formula atoms : 47 ( 17 avg)
% Number of connectives : 439 ( 149 ~; 126 |; 138 &)
% ( 0 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 9 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 13 con; 0-3 aty)
% Number of variables : 84 ( 78 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f53,conjecture,
( ( leq(n0,pv5)
& leq(n0,pv57)
& leq(pv5,n998)
& leq(pv57,n5)
& leq(pv58,n5)
& gt(pv58,pv57)
& ! [X0,X1] :
( ( leq(n0,X0)
& leq(n0,X1)
& leq(X0,n5)
& leq(X1,n5) )
=> a_select3(q_ds1_filter,X0,X1) = a_select3(q_ds1_filter,X1,X0) )
& ! [X2,X3] :
( ( leq(n0,X2)
& leq(n0,X3)
& leq(X2,n2)
& leq(X3,n2) )
=> a_select3(r_ds1_filter,X2,X3) = a_select3(r_ds1_filter,X3,X2) )
& ! [X4,X5] :
( ( leq(n0,X4)
& leq(n0,X5)
& leq(X4,n5)
& leq(X5,n5) )
=> a_select3(pminus_ds1_filter,X4,X5) = a_select3(pminus_ds1_filter,X5,X4) )
& ! [X6,X7] :
( ( leq(n0,X6)
& leq(n0,X7)
& leq(X6,n5)
& leq(X7,n5) )
=> ( ( X6 = pv57
& gt(pv58,X7) )
=> a_select3(id_ds1_filter,X6,X7) = a_select3(id_ds1_filter,X7,X6) ) )
& ! [X8,X9] :
( ( leq(n0,X8)
& leq(n0,X9)
& leq(X8,n5)
& leq(X9,n5) )
=> ( gt(pv57,X8)
=> a_select3(id_ds1_filter,X8,X9) = a_select3(id_ds1_filter,X9,X8) ) )
& ! [X10] :
( ( leq(n0,X10)
& leq(X10,pred(pv57)) )
=> ! [X11] :
( ( leq(n0,X11)
& leq(X11,n5) )
=> a_select3(id_ds1_filter,X10,X11) = a_select3(id_ds1_filter,X11,X10) ) ) )
=> ! [X12] :
( ( leq(n0,X12)
& leq(X12,pred(pv57)) )
=> ! [X13] :
( ( leq(n0,X13)
& leq(X13,n5) )
=> ( ( ~ ( pv57 = X13
& X13 = X12 )
& pv57 != X12 )
=> a_select3(id_ds1_filter,X12,X13) = a_select3(id_ds1_filter,X13,X12) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quaternion_ds1_symm_0401) ).
fof(f54,negated_conjecture,
~ ( ( leq(n0,pv5)
& leq(n0,pv57)
& leq(pv5,n998)
& leq(pv57,n5)
& leq(pv58,n5)
& gt(pv58,pv57)
& ! [X0,X1] :
( ( leq(n0,X0)
& leq(n0,X1)
& leq(X0,n5)
& leq(X1,n5) )
=> a_select3(q_ds1_filter,X0,X1) = a_select3(q_ds1_filter,X1,X0) )
& ! [X2,X3] :
( ( leq(n0,X2)
& leq(n0,X3)
& leq(X2,n2)
& leq(X3,n2) )
=> a_select3(r_ds1_filter,X2,X3) = a_select3(r_ds1_filter,X3,X2) )
& ! [X4,X5] :
( ( leq(n0,X4)
& leq(n0,X5)
& leq(X4,n5)
& leq(X5,n5) )
=> a_select3(pminus_ds1_filter,X4,X5) = a_select3(pminus_ds1_filter,X5,X4) )
& ! [X6,X7] :
( ( leq(n0,X6)
& leq(n0,X7)
& leq(X6,n5)
& leq(X7,n5) )
=> ( ( X6 = pv57
& gt(pv58,X7) )
=> a_select3(id_ds1_filter,X6,X7) = a_select3(id_ds1_filter,X7,X6) ) )
& ! [X8,X9] :
( ( leq(n0,X8)
& leq(n0,X9)
& leq(X8,n5)
& leq(X9,n5) )
=> ( gt(pv57,X8)
=> a_select3(id_ds1_filter,X8,X9) = a_select3(id_ds1_filter,X9,X8) ) )
& ! [X10] :
( ( leq(n0,X10)
& leq(X10,pred(pv57)) )
=> ! [X11] :
( ( leq(n0,X11)
& leq(X11,n5) )
=> a_select3(id_ds1_filter,X10,X11) = a_select3(id_ds1_filter,X11,X10) ) ) )
=> ! [X12] :
( ( leq(n0,X12)
& leq(X12,pred(pv57)) )
=> ! [X13] :
( ( leq(n0,X13)
& leq(X13,n5) )
=> ( ( ~ ( pv57 = X13
& X13 = X12 )
& pv57 != X12 )
=> a_select3(id_ds1_filter,X12,X13) = a_select3(id_ds1_filter,X13,X12) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f53]) ).
fof(f94,plain,
( ? [X12] :
( ? [X13] :
( a_select3(id_ds1_filter,X12,X13) != a_select3(id_ds1_filter,X13,X12)
& ( pv57 != X13
| X12 != X13 )
& pv57 != X12
& leq(n0,X13)
& leq(X13,n5) )
& leq(n0,X12)
& leq(X12,pred(pv57)) )
& leq(n0,pv5)
& leq(n0,pv57)
& leq(pv5,n998)
& leq(pv57,n5)
& leq(pv58,n5)
& gt(pv58,pv57)
& ! [X0,X1] :
( a_select3(q_ds1_filter,X0,X1) = a_select3(q_ds1_filter,X1,X0)
| ~ leq(n0,X0)
| ~ leq(n0,X1)
| ~ leq(X0,n5)
| ~ leq(X1,n5) )
& ! [X2,X3] :
( a_select3(r_ds1_filter,X2,X3) = a_select3(r_ds1_filter,X3,X2)
| ~ leq(n0,X2)
| ~ leq(n0,X3)
| ~ leq(X2,n2)
| ~ leq(X3,n2) )
& ! [X4,X5] :
( a_select3(pminus_ds1_filter,X4,X5) = a_select3(pminus_ds1_filter,X5,X4)
| ~ leq(n0,X4)
| ~ leq(n0,X5)
| ~ leq(X4,n5)
| ~ leq(X5,n5) )
& ! [X6,X7] :
( a_select3(id_ds1_filter,X6,X7) = a_select3(id_ds1_filter,X7,X6)
| pv57 != X6
| ~ gt(pv58,X7)
| ~ leq(n0,X6)
| ~ leq(n0,X7)
| ~ leq(X6,n5)
| ~ leq(X7,n5) )
& ! [X8,X9] :
( a_select3(id_ds1_filter,X8,X9) = a_select3(id_ds1_filter,X9,X8)
| ~ gt(pv57,X8)
| ~ leq(n0,X8)
| ~ leq(n0,X9)
| ~ leq(X8,n5)
| ~ leq(X9,n5) )
& ! [X10] :
( ! [X11] :
( a_select3(id_ds1_filter,X10,X11) = a_select3(id_ds1_filter,X11,X10)
| ~ leq(n0,X11)
| ~ leq(X11,n5) )
| ~ leq(n0,X10)
| ~ leq(X10,pred(pv57)) ) ),
inference(ennf_transformation,[],[f54]) ).
fof(f95,plain,
( ? [X12] :
( ? [X13] :
( a_select3(id_ds1_filter,X12,X13) != a_select3(id_ds1_filter,X13,X12)
& ( pv57 != X13
| X12 != X13 )
& pv57 != X12
& leq(n0,X13)
& leq(X13,n5) )
& leq(n0,X12)
& leq(X12,pred(pv57)) )
& leq(n0,pv5)
& leq(n0,pv57)
& leq(pv5,n998)
& leq(pv57,n5)
& leq(pv58,n5)
& gt(pv58,pv57)
& ! [X0,X1] :
( a_select3(q_ds1_filter,X0,X1) = a_select3(q_ds1_filter,X1,X0)
| ~ leq(n0,X0)
| ~ leq(n0,X1)
| ~ leq(X0,n5)
| ~ leq(X1,n5) )
& ! [X2,X3] :
( a_select3(r_ds1_filter,X2,X3) = a_select3(r_ds1_filter,X3,X2)
| ~ leq(n0,X2)
| ~ leq(n0,X3)
| ~ leq(X2,n2)
| ~ leq(X3,n2) )
& ! [X4,X5] :
( a_select3(pminus_ds1_filter,X4,X5) = a_select3(pminus_ds1_filter,X5,X4)
| ~ leq(n0,X4)
| ~ leq(n0,X5)
| ~ leq(X4,n5)
| ~ leq(X5,n5) )
& ! [X6,X7] :
( a_select3(id_ds1_filter,X6,X7) = a_select3(id_ds1_filter,X7,X6)
| pv57 != X6
| ~ gt(pv58,X7)
| ~ leq(n0,X6)
| ~ leq(n0,X7)
| ~ leq(X6,n5)
| ~ leq(X7,n5) )
& ! [X8,X9] :
( a_select3(id_ds1_filter,X8,X9) = a_select3(id_ds1_filter,X9,X8)
| ~ gt(pv57,X8)
| ~ leq(n0,X8)
| ~ leq(n0,X9)
| ~ leq(X8,n5)
| ~ leq(X9,n5) )
& ! [X10] :
( ! [X11] :
( a_select3(id_ds1_filter,X10,X11) = a_select3(id_ds1_filter,X11,X10)
| ~ leq(n0,X11)
| ~ leq(X11,n5) )
| ~ leq(n0,X10)
| ~ leq(X10,pred(pv57)) ) ),
inference(flattening,[],[f94]) ).
fof(f117,plain,
( ? [X0] :
( ? [X1] :
( a_select3(id_ds1_filter,X0,X1) != a_select3(id_ds1_filter,X1,X0)
& ( pv57 != X1
| X0 != X1 )
& pv57 != X0
& leq(n0,X1)
& leq(X1,n5) )
& leq(n0,X0)
& leq(X0,pred(pv57)) )
& leq(n0,pv5)
& leq(n0,pv57)
& leq(pv5,n998)
& leq(pv57,n5)
& leq(pv58,n5)
& gt(pv58,pv57)
& ! [X2,X3] :
( a_select3(q_ds1_filter,X2,X3) = a_select3(q_ds1_filter,X3,X2)
| ~ leq(n0,X2)
| ~ leq(n0,X3)
| ~ leq(X2,n5)
| ~ leq(X3,n5) )
& ! [X4,X5] :
( a_select3(r_ds1_filter,X4,X5) = a_select3(r_ds1_filter,X5,X4)
| ~ leq(n0,X4)
| ~ leq(n0,X5)
| ~ leq(X4,n2)
| ~ leq(X5,n2) )
& ! [X6,X7] :
( a_select3(pminus_ds1_filter,X6,X7) = a_select3(pminus_ds1_filter,X7,X6)
| ~ leq(n0,X6)
| ~ leq(n0,X7)
| ~ leq(X6,n5)
| ~ leq(X7,n5) )
& ! [X8,X9] :
( a_select3(id_ds1_filter,X8,X9) = a_select3(id_ds1_filter,X9,X8)
| pv57 != X8
| ~ gt(pv58,X9)
| ~ leq(n0,X8)
| ~ leq(n0,X9)
| ~ leq(X8,n5)
| ~ leq(X9,n5) )
& ! [X10,X11] :
( a_select3(id_ds1_filter,X10,X11) = a_select3(id_ds1_filter,X11,X10)
| ~ gt(pv57,X10)
| ~ leq(n0,X10)
| ~ leq(n0,X11)
| ~ leq(X10,n5)
| ~ leq(X11,n5) )
& ! [X12] :
( ! [X13] :
( a_select3(id_ds1_filter,X12,X13) = a_select3(id_ds1_filter,X13,X12)
| ~ leq(n0,X13)
| ~ leq(X13,n5) )
| ~ leq(n0,X12)
| ~ leq(X12,pred(pv57)) ) ),
inference(rectify,[],[f95]) ).
fof(f118,plain,
( a_select3(id_ds1_filter,sK0,sK1) != a_select3(id_ds1_filter,sK1,sK0)
& ( pv57 != sK1
| sK0 != sK1 )
& pv57 != sK0
& leq(n0,sK1)
& leq(sK1,n5)
& leq(n0,sK0)
& leq(sK0,pred(pv57))
& leq(n0,pv5)
& leq(n0,pv57)
& leq(pv5,n998)
& leq(pv57,n5)
& leq(pv58,n5)
& gt(pv58,pv57)
& ! [X2,X3] :
( a_select3(q_ds1_filter,X2,X3) = a_select3(q_ds1_filter,X3,X2)
| ~ leq(n0,X2)
| ~ leq(n0,X3)
| ~ leq(X2,n5)
| ~ leq(X3,n5) )
& ! [X4,X5] :
( a_select3(r_ds1_filter,X4,X5) = a_select3(r_ds1_filter,X5,X4)
| ~ leq(n0,X4)
| ~ leq(n0,X5)
| ~ leq(X4,n2)
| ~ leq(X5,n2) )
& ! [X6,X7] :
( a_select3(pminus_ds1_filter,X6,X7) = a_select3(pminus_ds1_filter,X7,X6)
| ~ leq(n0,X6)
| ~ leq(n0,X7)
| ~ leq(X6,n5)
| ~ leq(X7,n5) )
& ! [X8,X9] :
( a_select3(id_ds1_filter,X8,X9) = a_select3(id_ds1_filter,X9,X8)
| pv57 != X8
| ~ gt(pv58,X9)
| ~ leq(n0,X8)
| ~ leq(n0,X9)
| ~ leq(X8,n5)
| ~ leq(X9,n5) )
& ! [X10,X11] :
( a_select3(id_ds1_filter,X10,X11) = a_select3(id_ds1_filter,X11,X10)
| ~ gt(pv57,X10)
| ~ leq(n0,X10)
| ~ leq(n0,X11)
| ~ leq(X10,n5)
| ~ leq(X11,n5) )
& ! [X12] :
( ! [X13] :
( a_select3(id_ds1_filter,X12,X13) = a_select3(id_ds1_filter,X13,X12)
| ~ leq(n0,X13)
| ~ leq(X13,n5) )
| ~ leq(n0,X12)
| ~ leq(X12,pred(pv57)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f117]) ).
fof(f122,plain,
! [X12,X13] :
( a_select3(id_ds1_filter,X12,X13) = a_select3(id_ds1_filter,X13,X12)
| ~ leq(n0,X13)
| ~ leq(X13,n5)
| ~ leq(n0,X12)
| ~ leq(X12,pred(pv57)) ),
inference(cnf_transformation,[],[f118]) ).
fof(f134,plain,
leq(sK0,pred(pv57)),
inference(cnf_transformation,[],[f118]) ).
fof(f135,plain,
leq(n0,sK0),
inference(cnf_transformation,[],[f118]) ).
fof(f136,plain,
leq(sK1,n5),
inference(cnf_transformation,[],[f118]) ).
fof(f137,plain,
leq(n0,sK1),
inference(cnf_transformation,[],[f118]) ).
fof(f140,plain,
a_select3(id_ds1_filter,sK0,sK1) != a_select3(id_ds1_filter,sK1,sK0),
inference(cnf_transformation,[],[f118]) ).
fof(f201,plain,
( a_select3(id_ds1_filter,sK0,sK1) != a_select3(id_ds1_filter,sK0,sK1)
| ~ leq(n0,sK1)
| ~ leq(sK1,n5)
| ~ leq(n0,sK0)
| ~ leq(sK0,pred(pv57)) ),
inference(superposition,[],[f140,f122]) ).
fof(f202,plain,
( ~ leq(n0,sK1)
| ~ leq(sK1,n5)
| ~ leq(n0,sK0)
| ~ leq(sK0,pred(pv57)) ),
inference(trivial_inequality_removal,[],[f201]) ).
fof(f204,plain,
( ~ leq(sK1,n5)
| ~ leq(n0,sK0)
| ~ leq(sK0,pred(pv57)) ),
inference(forward_subsumption_resolution,[],[f202,f137]) ).
fof(f206,plain,
( ~ leq(n0,sK0)
| ~ leq(sK0,pred(pv57)) ),
inference(forward_subsumption_resolution,[],[f204,f136]) ).
fof(f208,plain,
~ leq(sK0,pred(pv57)),
inference(forward_subsumption_resolution,[],[f206,f135]) ).
fof(f209,plain,
$false,
inference(forward_subsumption_resolution,[],[f208,f134]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV221+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.17 % Computer : n004.cluster.edu
% 0.09/0.17 % Model : x86_64 x86_64
% 0.09/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.17 % Memory : 8046.5625MB
% 0.09/0.17 % OS : Linux 6.8.0-71-generic
% 0.09/0.17 % CPULimit : 300
% 0.09/0.17 % WCLimit : 300
% 0.09/0.17 % DateTime : Mon Sep 28 10:13:22 UTC 2026
% 0.09/0.17 % CPUTime :
% 0.09/0.17 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.21 Running first-order theorem proving
% 0.09/0.21 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
% 3.61/1.20 % (259503)Detected formulas, will run a generic FOF schedule.
% 3.61/1.20 % (259508)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=1360704228:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.61/1.20 % (259510)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=1356056107:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.61/1.20 % (259513)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1304481285:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.61/1.20 % (259514)dis-21_1_sil=8000:lcm=predicate:random_seed=3006890771: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)
% 3.61/1.20 % (259511)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3583014345:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.61/1.20 % (259512)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3530125565:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.61/1.20 % (259509)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=1443926560:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.61/1.20 % (259512)First to succeed.
% 3.61/1.20 % (259512)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-259503"
% 3.61/1.20 % (259514)Also succeeded, but the first one will report.
% 3.61/1.20 % (259513)Also succeeded, but the first one will report.
% 3.61/1.20 % (259511)Also succeeded, but the first one will report.
% 3.61/1.20 % (259512)Refutation found. Thanks to Tanya!
% 3.61/1.20 % SZS status Theorem for theBenchmark
% 3.61/1.20 % SZS output start Proof for theBenchmark
% See solution above
% 3.61/1.20 % (259512)------------------------------
% 3.61/1.20 % (259512)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.61/1.20 % (259512)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.61/1.20 % (259512)CaDiCaL version: 2.1.3
% 3.61/1.20 % (259512)Termination reason: Refutation
% 3.61/1.20 % (259512)Time elapsed: 0.004 s
% 3.61/1.20 % (259512)Peak memory usage: 88 MB
% 3.61/1.20 % (259512)Instructions burned: 5 (million)
% 3.61/1.20 % (259512)------------------------------
% 3.61/1.20 % (259512)------------------------------
% 3.61/1.20 % (259503)Success in time 0.449 s
% 3.61/1.20 % Vampire exiting
%------------------------------------------------------------------------------