%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWW209+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 : n010.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 01:29:51 PM UTC 2026
% Result : Theorem 0.20s 1.41s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 21 ( 8 unt; 0 def)
% Number of atoms : 34 ( 7 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 27 ( 14 ~; 6 |; 2 &)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-4 aty)
% Number of variables : 45 ( 43 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(v_f____,X0),hAPP(v_f____,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096ALL_Am_An_O_Am_A_060_An_A_N_N_062_Af_Am_A_060_Af_An_096) ).
fof(f3,axiom,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(v_ga____,X0),hAPP(v_ga____,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096ALL_Am_An_O_Am_A_060_An_A_N_N_062_Ag_Am_A_060_Ag_An_096) ).
fof(f9,axiom,
! [X0,X1,X2,X3,X4,X5,X6] :
( hAPP(c_Fun_Ocomp(X6,X5,X4,X3),X2) = X1
=> hAPP(X3,hAPP(X2,X0)) = hAPP(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_o__eq__dest__lhs) ).
fof(f1161,conjecture,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____),v_ga____),X0),hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____),v_ga____),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
fof(f1162,negated_conjecture,
~ ! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____),v_ga____),X0),hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____),v_ga____),X1)) ),
inference(negated_conjecture,[status(cth)],[f1161]) ).
fof(f1165,plain,
? [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____),v_ga____),X0),hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____),v_ga____),X1))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ),
inference(ennf_transformation,[],[f1162]) ).
fof(f1179,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(v_f____,X0),hAPP(v_f____,X1))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ),
inference(ennf_transformation,[],[f2]) ).
fof(f1180,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(v_ga____,X0),hAPP(v_ga____,X1))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ),
inference(ennf_transformation,[],[f3]) ).
fof(f1183,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( hAPP(X3,hAPP(X2,X0)) = hAPP(X1,X0)
| hAPP(c_Fun_Ocomp(X6,X5,X4,X3),X2) != X1 ),
inference(ennf_transformation,[],[f9]) ).
fof(f1185,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____),v_ga____),sK0),hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____),v_ga____),sK1))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK0,sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f1165]) ).
fof(f1193,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK0,sK1),
inference(cnf_transformation,[],[f1185]) ).
fof(f1194,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____),v_ga____),sK0),hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____),v_ga____),sK1)),
inference(cnf_transformation,[],[f1185]) ).
fof(f1229,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(v_f____,X0),hAPP(v_f____,X1))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ),
inference(cnf_transformation,[],[f1179]) ).
fof(f1230,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(v_ga____,X0),hAPP(v_ga____,X1))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ),
inference(cnf_transformation,[],[f1180]) ).
fof(f1233,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( hAPP(X1,X0) = hAPP(X3,hAPP(X2,X0))
| hAPP(c_Fun_Ocomp(X6,X5,X4,X3),X2) != X1 ),
inference(cnf_transformation,[],[f1183]) ).
fof(f1248,plain,
! [X2,X3,X0,X6,X4,X5] : hAPP(X3,hAPP(X2,X0)) = hAPP(hAPP(c_Fun_Ocomp(X6,X5,X4,X3),X2),X0),
inference(equality_resolution,[],[f1233]) ).
fof(f1255,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____),v_ga____),sK0),hAPP(v_f____,hAPP(v_ga____,sK1))),
inference(forward_demodulation,[],[f1194,f1248]) ).
fof(f1256,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(v_f____,hAPP(v_ga____,sK0)),hAPP(v_f____,hAPP(v_ga____,sK1))),
inference(forward_demodulation,[],[f1255,f1248]) ).
fof(f1258,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(v_ga____,sK0),hAPP(v_ga____,sK1)),
inference(resolution,[],[f1256,f1229]) ).
fof(f1279,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK0,sK1),
inference(resolution,[],[f1258,f1230]) ).
fof(f1292,plain,
$false,
inference(forward_subsumption_resolution,[],[f1279,f1193]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWW209+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.17 % Computer : n010.cluster.edu
% 0.08/0.17 % Model : x86_64 x86_64
% 0.08/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.17 % Memory : 8046.5625MB
% 0.08/0.17 % OS : Linux 6.8.0-71-generic
% 0.08/0.17 % CPULimit : 300
% 0.08/0.17 % WCLimit : 300
% 0.08/0.17 % DateTime : Mon Sep 28 13:17:47 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.24 Running first-order theorem proving
% 0.08/0.24 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
% 0.20/1.41 % (1918781)Detected formulas, will run a generic FOF schedule.
% 0.20/1.41 % (1918792)dis-21_1_sil=8000:lcm=predicate:random_seed=1680577959: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)
% 0.20/1.41 % (1918788)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=3349730568:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.20/1.41 % (1918786)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=163458337:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.20/1.41 % (1918787)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=456587494:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.20/1.41 % (1918789)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1101516974:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.20/1.41 % (1918790)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=667446738:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.20/1.41 % (1918791)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=573660282:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.20/1.41 % (1918792)Instruction limit reached!
% 0.20/1.41 % (1918792)------------------------------
% 0.20/1.41 % (1918792)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.20/1.41 % (1918789)First to succeed.
% 0.20/1.41 % (1918792)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/1.41 % (1918792)CaDiCaL version: 2.1.3
% 0.20/1.41 % (1918792)Termination reason: Instruction limit
% 0.20/1.41 % (1918792)Termination phase: Saturation
% 0.20/1.41 % (1918792)Time elapsed: 0.038 s
% 0.20/1.41 % (1918792)Peak memory usage: 90 MB
% 0.20/1.41 % (1918792)Instructions burned: 131 (million)
% 0.20/1.41 % (1918789)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1918781"
% 0.20/1.41 % (1918790)Also succeeded, but the first one will report.
% 0.20/1.41 % (1918791)Also succeeded, but the first one will report.
% 0.20/1.41 % (1918800)lrs+10_1_sil=8000:sp=occurrence:random_seed=380484799:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 0.20/1.41 % (1918800)Also succeeded, but the first one will report.
% 0.20/1.41 % (1918789)Refutation found. Thanks to Tanya!
% 0.20/1.41 % SZS status Theorem for theBenchmark
% 0.20/1.41 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/1.41 % (1918789)------------------------------
% 0.20/1.41 % (1918789)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.20/1.41 % (1918789)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/1.41 % (1918789)CaDiCaL version: 2.1.3
% 0.20/1.41 % (1918789)Termination reason: Refutation
% 0.20/1.41 % (1918789)Time elapsed: 0.008 s
% 0.20/1.41 % (1918789)Peak memory usage: 89 MB
% 0.20/1.41 % (1918789)Instructions burned: 9 (million)
% 0.20/1.41 % (1918789)------------------------------
% 0.20/1.41 % (1918789)------------------------------
% 0.20/1.41 % (1918781)Success in time 0.449 s
% 0.20/1.41 % Vampire exiting
%------------------------------------------------------------------------------