%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SWW209+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n005.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 01:39:37 PM UTC 2026
% Result : Theorem 0.57s 0.46s
% Output : Refutation 0.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 18 ( 9 unt; 0 def)
% Number of atoms : 27 ( 2 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 20 ( 11 ~; 4 |; 1 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 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 : 30 ( 28 !; 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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',fact__096ALL_Am_An_O_Am_A_060_An_A_N_N_062_Ag_Am_A_060_Ag_An_096) ).
fof(f7,axiom,
! [X0,X1,X2,X3,X4,X5] : hAPP(hAPP(c_Fun_Ocomp(X5,X4,X3,X2),X1),X0) = hAPP(X2,hAPP(X1,X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_o__apply) ).
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/sandbox2/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(f1174,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(f1175,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(f2156,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(f2158,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,[],[f1174]) ).
fof(f2159,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,[],[f1175]) ).
fof(f2163,plain,
! [X2,X3,X0,X1,X4,X5] : hAPP(hAPP(c_Fun_Ocomp(X5,X4,X3,X2),X1),X0) = hAPP(X2,hAPP(X1,X0)),
inference(cnf_transformation,[],[f7]) ).
fof(f3774,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK53,sK54),
inference(cnf_transformation,[],[f2156]) ).
fof(f3775,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____),sK53),hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____),v_ga____),sK54)),
inference(cnf_transformation,[],[f2156]) ).
fof(f4204,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____),sK53),hAPP(v_f____,hAPP(v_ga____,sK54))),
inference(superposition,[],[f3775,f2163]) ).
fof(f4205,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(v_f____,hAPP(v_ga____,sK53)),hAPP(v_f____,hAPP(v_ga____,sK54))),
inference(forward_demodulation,[],[f4204,f2163]) ).
fof(f4209,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(v_ga____,sK53),hAPP(v_ga____,sK54)),
inference(resolution,[],[f4205,f2158]) ).
fof(f4222,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK53,sK54),
inference(resolution,[],[f4209,f2159]) ).
fof(f4235,plain,
$false,
inference(forward_subsumption_resolution,[],[f4222,f3774]) ).
%------------------------------------------------------------------------------
%----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/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.20 % Computer : n005.cluster.edu
% 0.08/0.20 % Model : x86_64 x86_64
% 0.08/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.20 % Memory : 8046.5625MB
% 0.08/0.20 % OS : Linux 6.8.0-71-generic
% 0.08/0.20 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.20 % DateTime : Mon Sep 28 13:17:17 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.23 Running first-order model finding
% 0.08/0.23 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.57/0.46 % (777452)Will run a generic schedule for satisfiability detection.
% 0.57/0.46 % (777461)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1217751211:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.57/0.46 % (777458)% WARNING: option uhcvi not known.
% 0.57/0.46 % (777457)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1251805617_2999 on theBenchmark for (2999ds/0Mi)
% 0.57/0.46 % (777458)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2528700334:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.57/0.46 % (777459)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1648461902:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.57/0.46 % (777460)dis+10_1_sil=32000:sp=arity:random_seed=3895819612:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.57/0.46 % (777462)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2664826568:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.57/0.46 % (777463)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2524537560:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.57/0.46 % (777461)Instruction limit reached!
% 0.57/0.46 % (777461)------------------------------
% 0.57/0.46 % (777461)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.57/0.46 % (777461)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.57/0.46 % (777461)CaDiCaL version: 2.1.3
% 0.57/0.46 % (777461)Termination reason: Instruction limit
% 0.57/0.46 % (777461)Termination phase: Property scanning
% 0.57/0.46 % (777461)Time elapsed: 0.030 s
% 0.57/0.46 % (777461)Peak memory usage: 13 MB
% 0.57/0.46 % (777461)Instructions burned: 118 (million)
% 0.57/0.46 % (777471)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=3735463503:i=714:nm=2_2998 on theBenchmark for (2998ds/714Mi)
% 0.57/0.46 % (777460)Instruction limit reached!
% 0.57/0.46 % (777460)------------------------------
% 0.57/0.46 % (777460)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.57/0.46 % (777460)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.57/0.46 % (777460)CaDiCaL version: 2.1.3
% 0.57/0.46 % (777460)Termination reason: Instruction limit
% 0.57/0.46 % (777460)Termination phase: Saturation
% 0.57/0.46 % (777460)Time elapsed: 0.055 s
% 0.57/0.46 % (777460)Peak memory usage: 14 MB
% 0.57/0.46 % (777460)Instructions burned: 103 (million)
% 0.57/0.46 % (777462)Instruction limit reached!
% 0.57/0.46 % (777462)------------------------------
% 0.57/0.46 % (777462)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.57/0.46 % (777462)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.57/0.46 % (777462)CaDiCaL version: 2.1.3
% 0.57/0.46 % (777462)Termination reason: Instruction limit
% 0.57/0.46 % (777462)Termination phase: Saturation
% 0.57/0.46 % (777462)Time elapsed: 0.066 s
% 0.57/0.46 % (777462)Peak memory usage: 14 MB
% 0.57/0.46 % (777462)Instructions burned: 132 (million)
% 0.57/0.46 % (777473)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=1227376749:i=131:bd=preordered:fsd=on_2998 on theBenchmark for (2998ds/131Mi)
% 0.57/0.46 % (777474)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=2062429551:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 0.57/0.46 % (777463)Instruction limit reached!
% 0.57/0.46 % (777463)------------------------------
% 0.57/0.46 % (777463)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.57/0.46 % (777463)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.57/0.46 % (777463)CaDiCaL version: 2.1.3
% 0.57/0.46 % (777463)Termination reason: Instruction limit
% 0.57/0.46 % (777463)Termination phase: Saturation
% 0.57/0.46 % (777463)Time elapsed: 0.091 s
% 0.57/0.46 % (777463)Peak memory usage: 15 MB
% 0.57/0.46 % (777463)Instructions burned: 160 (million)
% 0.57/0.46 % (777477)ott-21_1_sil=16000:fs=off:random_seed=3666475664:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 0.57/0.46 % (777474) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-777452-777474"...
% 0.57/0.46 % (777473)Instruction limit reached!
% 0.57/0.46 % (777473)------------------------------
% 0.57/0.46 % (777473)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.57/0.46 % (777473)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.57/0.46 % (777473)CaDiCaL version: 2.1.3
% 0.57/0.46 % (777473)Termination reason: Instruction limit
% 0.57/0.46 % (777473)Termination phase: Saturation
% 0.57/0.46 % (777473)Time elapsed: 0.060 s
% 0.57/0.46 % (777473)Peak memory usage: 14 MB
% 0.57/0.46 % (777473)Instructions burned: 132 (million)
% 0.57/0.46 % (777474)...printing done.
% 0.57/0.46 % (777474)Refutation found. Thanks to Tanya!
% 0.57/0.46 % SZS status Theorem for theBenchmark
% 0.57/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.57/0.46 % (777474)------------------------------
% 0.57/0.46 % (777474)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.57/0.46 % (777474)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.57/0.46 % (777474)CaDiCaL version: 2.1.3
% 0.57/0.46 % (777474)Termination reason: Refutation
% 0.57/0.46 % (777474)Time elapsed: 0.047 s
% 0.57/0.46 % (777474)Peak memory usage: 15 MB
% 0.57/0.46 % (777474)Instructions burned: 95 (million)
% 0.57/0.46 % (777452)Success in time 0.223 s
% 0.57/0.46 % Vampire exiting
%------------------------------------------------------------------------------