%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWW220+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n006.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 01:29:52 PM UTC 2026
% Result : Theorem 2.59s 1.29s
% Output : Refutation 3.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of formulae : 37 ( 11 unt; 2 def)
% Number of atoms : 86 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 89 ( 40 ~; 32 |; 9 &)
% ( 2 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 7 ( 6 usr; 4 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 5 con; 0-3 aty)
% Number of variables : 52 ( 0 sgn 40 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
? [X0] :
( c_SEQ_Osubseq(X0)
& ? [X1] :
! [X2] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2)
=> ? [X3] :
! [X4] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3),X4))
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_g____(hAPP(X0,X4)),X1)),X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096EX_Af_Az_O_Asubseq_Af_A_G_A_IALL_Ae_0620_O_AEX_AN_O_AALL_An_062_061N_O_Acmod_A_Ig_A_If_An_J_A_N_Az_J_A_060_Ae_J_096) ).
fof(f1269,axiom,
! [X0] :
( c_SEQ_Osubseq(X0)
=> ( ? [X1] :
! [X2] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2)
=> ? [X3] :
! [X4] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3),X4))
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_g____(hAPP(X0,X4)),X1)),X2) ) )
=> v_thesis____ ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
fof(f1270,conjecture,
v_thesis____,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).
fof(f1271,negated_conjecture,
~ v_thesis____,
inference(negated_conjecture,[status(cth)],[f1270]) ).
fof(f1272,plain,
~ v_thesis____,
inference(flattening,[],[f1271]) ).
fof(f1274,plain,
! [X0] :
( v_thesis____
| ! [X1] :
? [X2] :
( ! [X3] :
? [X4] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_g____(hAPP(X0,X4)),X1)),X2)
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3),X4)) )
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2) )
| ~ c_SEQ_Osubseq(X0) ),
inference(ennf_transformation,[],[f1269]) ).
fof(f1275,plain,
! [X0] :
( v_thesis____
| ! [X1] :
? [X2] :
( ! [X3] :
? [X4] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_g____(hAPP(X0,X4)),X1)),X2)
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3),X4)) )
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2) )
| ~ c_SEQ_Osubseq(X0) ),
inference(flattening,[],[f1274]) ).
fof(f1314,plain,
? [X0] :
( c_SEQ_Osubseq(X0)
& ? [X1] :
! [X2] :
( ? [X3] :
! [X4] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_g____(hAPP(X0,X4)),X1)),X2)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3),X4)) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2) ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f1359,plain,
! [X0] :
( v_thesis____
| ! [X1] :
( ! [X3] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_g____(hAPP(X0,sK1(X0,X1,X3))),X1)),sK0(X0,X1))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3),sK1(X0,X1,X3))) )
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK0(X0,X1)) )
| ~ c_SEQ_Osubseq(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X2,sK0(X0,X1)),skolemize(X4,sK1(X0,X1,X3))],[f1275]) ).
fof(f1388,plain,
( c_SEQ_Osubseq(sK7)
& ! [X2] :
( ! [X4] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_g____(hAPP(sK7,X4)),sK8)),X2)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK9(X2)),X4)) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8,sK9]),skolemize(X0,sK7),skolemize(X1,sK8),skolemize(X3,sK9(X2))],[f1314]) ).
fof(f1416,plain,
! [X0,X1] :
( v_thesis____
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK0(X0,X1))
| ~ c_SEQ_Osubseq(X0) ),
inference(cnf_transformation,[],[f1359]) ).
fof(f1417,plain,
! [X3,X0,X1] :
( v_thesis____
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3),sK1(X0,X1,X3)))
| ~ c_SEQ_Osubseq(X0) ),
inference(cnf_transformation,[],[f1359]) ).
fof(f1418,plain,
! [X3,X0,X1] :
( v_thesis____
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_g____(hAPP(X0,sK1(X0,X1,X3))),X1)),sK0(X0,X1))
| ~ c_SEQ_Osubseq(X0) ),
inference(cnf_transformation,[],[f1359]) ).
fof(f1419,plain,
~ v_thesis____,
inference(cnf_transformation,[],[f1272]) ).
fof(f1507,plain,
! [X2,X4] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_g____(hAPP(sK7,X4)),sK8)),X2)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK9(X2)),X4))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2) ),
inference(cnf_transformation,[],[f1388]) ).
fof(f1508,plain,
c_SEQ_Osubseq(sK7),
inference(cnf_transformation,[],[f1388]) ).
fof(f1634,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK0(X0,X1))
| ~ c_SEQ_Osubseq(X0) ),
inference(forward_subsumption_resolution,[],[f1416,f1419]) ).
fof(f1635,plain,
! [X3,X0,X1] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3),sK1(X0,X1,X3)))
| ~ c_SEQ_Osubseq(X0) ),
inference(forward_subsumption_resolution,[],[f1417,f1419]) ).
fof(f1636,plain,
! [X3,X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_g____(hAPP(X0,sK1(X0,X1,X3))),X1)),sK0(X0,X1))
| ~ c_SEQ_Osubseq(X0) ),
inference(forward_subsumption_resolution,[],[f1418,f1419]) ).
fof(f1645,plain,
! [X0] :
( ~ c_SEQ_Osubseq(sK7)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK9(sK0(sK7,sK8))),sK1(sK7,sK8,X0)))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK0(sK7,sK8)) ),
inference(resolution,[],[f1636,f1507]) ).
fof(f1647,plain,
! [X0] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK9(sK0(sK7,sK8))),sK1(sK7,sK8,X0)))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK0(sK7,sK8)) ),
inference(forward_subsumption_resolution,[],[f1645,f1508]) ).
fof(f1649,definition,
( spl24_1
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK0(sK7,sK8)) ),
introduced(definition,[new_symbols(definition,[spl24_1])],[avatar_definition]) ).
fof(f1651,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK0(sK7,sK8))
| spl24_1 ),
inference(avatar_component_clause,[],[f1649]) ).
fof(f1653,definition,
( spl24_2
<=> ! [X0] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK9(sK0(sK7,sK8))),sK1(sK7,sK8,X0))) ),
introduced(definition,[new_symbols(definition,[spl24_2])],[avatar_definition]) ).
fof(f1654,plain,
( ! [X0] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK9(sK0(sK7,sK8))),sK1(sK7,sK8,X0)))
| ~ spl24_2 ),
inference(avatar_component_clause,[],[f1653]) ).
fof(f1655,plain,
( ~ spl24_1
| spl24_2 ),
inference(avatar_split_clause,[],[f1647,f1653,f1649]) ).
fof(f1656,plain,
( ~ c_SEQ_Osubseq(sK7)
| spl24_1 ),
inference(resolution,[],[f1651,f1634]) ).
fof(f1658,plain,
( $false
| spl24_1 ),
inference(forward_subsumption_resolution,[],[f1656,f1508]) ).
fof(f1659,plain,
spl24_1,
inference(avatar_contradiction_clause,[],[f1658]) ).
fof(f1661,plain,
( ~ c_SEQ_Osubseq(sK7)
| ~ spl24_2 ),
inference(resolution,[],[f1654,f1635]) ).
fof(f1669,plain,
( $false
| ~ spl24_2 ),
inference(forward_subsumption_resolution,[],[f1661,f1508]) ).
fof(f1670,plain,
~ spl24_2,
inference(avatar_contradiction_clause,[],[f1669]) ).
cnf(s1,plain,
( ~ spl24_1
| spl24_2 ),
inference(sat_conversion,[],[f1655]) ).
cnf(s2,plain,
spl24_1,
inference(sat_conversion,[],[f1659]) ).
cnf(s3,plain,
~ spl24_2,
inference(sat_conversion,[],[f1670]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s1,s3,s2]) ).
fof(f1671,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW220+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.21 % Computer : n006.cluster.edu
% 0.11/0.21 % Model : x86_64 x86_64
% 0.11/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.21 % Memory : 8046.5625MB
% 0.11/0.21 % OS : Linux 6.8.0-71-generic
% 0.11/0.21 % CPULimit : 300
% 0.11/0.21 % WCLimit : 300
% 0.11/0.21 % DateTime : Mon Sep 28 13:18:10 UTC 2026
% 0.11/0.22 % CPUTime :
% 0.11/0.22 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.28 Running first-order theorem proving
% 0.11/0.28 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
% 2.59/1.29 % (3959359)Detected formulas, will run a generic FOF schedule.
% 2.59/1.29 % (3959367)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3655868736:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.59/1.29 % (3959367)First to succeed.
% 2.59/1.29 % (3959367)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3959359"
% 2.59/1.29 % (3959369)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1398272005:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.59/1.29 % (3959370)dis-21_1_sil=8000:lcm=predicate:random_seed=2994837375: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)
% 2.59/1.29 % (3959368)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1209965322:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.59/1.29 % (3959364)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=4023126774:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.59/1.29 % (3959366)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=1642352961:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.59/1.29 % (3959365)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=2957630732:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.59/1.29 % (3959370)Instruction limit reached!
% 2.59/1.29 % (3959370)------------------------------
% 2.59/1.29 % (3959370)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.59/1.29 % (3959370)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.59/1.29 % (3959370)CaDiCaL version: 2.1.3
% 2.59/1.29 % (3959370)Termination reason: Instruction limit
% 2.59/1.29 % (3959370)Termination phase: Saturation
% 2.59/1.29 % (3959370)Time elapsed: 0.064 s
% 2.59/1.29 % (3959370)Peak memory usage: 90 MB
% 2.59/1.29 % (3959370)Instructions burned: 130 (million)
% 2.59/1.29 % (3959369)Instruction limit reached!
% 2.59/1.29 % (3959369)------------------------------
% 2.59/1.29 % (3959369)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.59/1.29 % (3959369)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.59/1.29 % (3959369)CaDiCaL version: 2.1.3
% 2.59/1.29 % (3959369)Termination reason: Instruction limit
% 2.59/1.29 % (3959369)Termination phase: Saturation
% 2.59/1.29 % (3959369)Time elapsed: 0.072 s
% 2.59/1.29 % (3959369)Peak memory usage: 91 MB
% 2.59/1.29 % (3959369)Instructions burned: 139 (million)
% 2.59/1.29 % (3959368)Instruction limit reached!
% 2.59/1.29 % (3959368)------------------------------
% 2.59/1.29 % (3959368)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.59/1.29 % (3959368)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.59/1.29 % (3959368)CaDiCaL version: 2.1.3
% 2.59/1.29 % (3959368)Termination reason: Instruction limit
% 2.59/1.29 % (3959368)Termination phase: Saturation
% 2.59/1.29 % (3959368)Time elapsed: 0.072 s
% 2.59/1.29 % (3959368)Peak memory usage: 90 MB
% 2.59/1.29 % (3959368)Instructions burned: 120 (million)
% 2.59/1.29 % (3959367)Refutation found. Thanks to Tanya!
% 2.59/1.29 % SZS status Theorem for theBenchmark
% 2.59/1.29 % SZS output start Proof for theBenchmark
% See solution above
% 3.39/1.38 % (3959367)------------------------------
% 3.39/1.38 % (3959367)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.39/1.38 % (3959367)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.39/1.38 % (3959367)CaDiCaL version: 2.1.3
% 3.39/1.38 % (3959367)Termination reason: Refutation
% 3.39/1.38 % (3959367)Time elapsed: 0.010 s
% 3.39/1.38 % (3959367)Peak memory usage: 91 MB
% 3.39/1.38 % (3959367)Instructions burned: 28 (million)
% 3.39/1.38 % (3959367)------------------------------
% 3.39/1.38 % (3959367)------------------------------
% 3.39/1.38 % (3959359)Success in time 0.439 s
% 3.39/1.38 % Vampire exiting
%------------------------------------------------------------------------------