%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ARI609_1 : TPTP v9.3.1. Released v5.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 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 09:34:57 AM UTC 2026
% Result : Theorem 0.09s 0.25s
% Output : Refutation 0.09s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ARI609_1 : TPTP v9.3.1. Released v5.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.16 % Computer : n014.cluster.edu
% 0.09/0.16 % Model : x86_64 x86_64
% 0.09/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.16 % Memory : 8046.5625MB
% 0.09/0.16 % OS : Linux 6.8.0-71-generic
% 0.09/0.16 % CPULimit : 300
% 0.09/0.16 % WCLimit : 300
% 0.09/0.16 % DateTime : Mon Sep 28 20:53:30 UTC 2026
% 0.09/0.16 % CPUTime :
% 0.09/0.17 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.20 Running first-order model finding
% 0.09/0.20 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
% 0.09/0.25 % (2175422)Will run a generic schedule for satisfiability detection.
% 0.09/0.25 % (2175437)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1050352691:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.09/0.25 % (2175432)% WARNING: option uhcvi not known.
% 0.09/0.25 % (2175431)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=75210902_2999 on theBenchmark for (2999ds/0Mi)
% 0.09/0.25 % (2175433)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1463645583:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.09/0.25 % (2175434)dis+10_1_sil=32000:sp=arity:random_seed=4007187529:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.09/0.25 % (2175435)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=318177043:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.09/0.25 % (2175438)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3219357503:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.09/0.25 % (2175431)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.09/0.25 % (2175431)Terminated due to inappropriate strategy.
% 0.09/0.25 % (2175431)------------------------------
% 0.09/0.25 % (2175431)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.25 % (2175431)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.25 % (2175431)CaDiCaL version: 2.1.3
% 0.09/0.25 % (2175431)Termination reason: Inappropriate
% 0.09/0.25 % (2175431)Time elapsed: 0.0000 s
% 0.09/0.25 % (2175431)Peak memory usage: 10 MB
% 0.09/0.25 % (2175431)------------------------------
% 0.09/0.25 % (2175431)------------------------------
% 0.09/0.25 % (2175432)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3447528099:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.09/0.25 % (2175434) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2175422-2175434"...
% 0.09/0.25 % (2175437) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2175422-2175437"...
% 0.09/0.25 % (2175434)...printing done.
% 0.09/0.25 % (2175437)...printing done.
% 0.09/0.25 % (2175432) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2175422-2175432"...
% 0.09/0.25 % (2175434)Refutation found. Thanks to Tanya!
% 0.09/0.25 % SZS status Theorem for theBenchmark
% 0.09/0.25 % SZS output start Proof for theBenchmark
% 0.09/0.25 tff(func_def_0, type, f: $int > $int).
% 0.09/0.25 tff(func_def_1, type, a: $int).
% 0.09/0.25 tff(func_def_2, type, b: $int).
% 0.09/0.25 tff(f1,conjecture,(
% 0.09/0.25 (! [X0 : $int,X1 : $int] : ($lesseq(X0,X1) => $lesseq(f(X0),f(X1))) & $lesseq(0,$sum(a,$uminus(b)))) => $lesseq(0,$sum(f(a),$uminus(f(b))))),
% 0.09/0.25 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f_mon_implies_f_a_b_1)).
% 0.09/0.25 tff(f2,negated_conjecture,(
% 0.09/0.25 ~((! [X0 : $int,X1 : $int] : ($lesseq(X0,X1) => $lesseq(f(X0),f(X1))) & $lesseq(0,$sum(a,$uminus(b)))) => $lesseq(0,$sum(f(a),$uminus(f(b)))))),
% 0.09/0.25 inference(negated_conjecture,[status(cth)],[f1])).
% 0.09/0.25 tff(f3,plain,(
% 0.09/0.25 ~((! [X0 : $int,X1 : $int] : (~$less(X1,X0) => ~$less(f(X1),f(X0))) & ~$less($sum(a,$uminus(b)),0)) => ~$less($sum(f(a),$uminus(f(b))),0))),
% 0.09/0.25 inference(theory_normalization,[],[f2])).
% 0.09/0.25 tff(f8,definition,(
% 0.09/0.25 ( ! [X0 : $int] : (0 = $sum(X0,$uminus(X0))) )),
% 0.09/0.25 introduced(theory,[tha_inverse_op_unit])).
% 0.09/0.25 tff(f10,definition,(
% 0.09/0.25 ( ! [X2 : $int,X0 : $int,X1 : $int] : (~$less(X1,X2) | ~$less(X0,X1) | $less(X0,X2)) )),
% 0.09/0.25 introduced(theory,[tha_transitivity])).
% 0.09/0.25 tff(f11,definition,(
% 0.09/0.25 ( ! [X0 : $int,X1 : $int] : ($less(X1,X0) | $less(X0,X1) | X0 = X1) )),
% 0.09/0.25 introduced(theory,[tha_order_totality])).
% 0.09/0.25 tff(f12,definition,(
% 0.09/0.25 ( ! [X2 : $int,X0 : $int,X1 : $int] : ($less($sum(X0,X2),$sum(X1,X2)) | ~$less(X0,X1)) )),
% 0.09/0.25 introduced(theory,[tha_order_monotonicity])).
% 0.09/0.25 tff(f16,plain,(
% 0.09/0.25 $less($sum(f(a),$uminus(f(b))),0) & (! [X0 : $int,X1 : $int] : (~$less(f(X1),f(X0)) | $less(X1,X0)) & ~$less($sum(a,$uminus(b)),0))),
% 0.09/0.25 inference(ennf_transformation,[],[f3])).
% 0.09/0.25 tff(f17,plain,(
% 0.09/0.25 $less($sum(f(a),$uminus(f(b))),0) & ! [X0 : $int,X1 : $int] : (~$less(f(X1),f(X0)) | $less(X1,X0)) & ~$less($sum(a,$uminus(b)),0)),
% 0.09/0.25 inference(flattening,[],[f16])).
% 0.09/0.25 tff(f18,plain,(
% 0.09/0.25 ~$less($sum(a,$uminus(b)),0)),
% 0.09/0.25 inference(cnf_transformation,[],[f17])).
% 0.09/0.25 tff(f19,plain,(
% 0.09/0.25 ( ! [X0 : $int,X1 : $int] : (~$less(f(X1),f(X0)) | $less(X1,X0)) )),
% 0.09/0.25 inference(cnf_transformation,[],[f17])).
% 0.09/0.25 tff(f20,plain,(
% 0.09/0.25 $less($sum(f(a),$uminus(f(b))),0)),
% 0.09/0.25 inference(cnf_transformation,[],[f17])).
% 0.09/0.25 tff(f41,plain,(
% 0.09/0.25 ( ! [X0 : $int] : (~$less(X0,$sum(f(a),$uminus(f(b)))) | $less(X0,0)) )),
% 0.09/0.25 inference(resolution,[],[f10,f20])).
% 0.09/0.25 tff(f46,plain,(
% 0.09/0.25 ( ! [X0 : $int,X1 : $int] : ($less(f(X1),f(X0)) | f(X0) = f(X1) | $less(X0,X1)) )),
% 0.09/0.25 inference(resolution,[],[f11,f19])).
% 0.09/0.25 tff(f82,plain,(
% 0.09/0.25 ( ! [X0 : $int] : ($less($sum(X0,$uminus(f(b))),0) | ~$less(X0,f(a))) )),
% 0.09/0.25 inference(resolution,[],[f12,f41])).
% 0.09/0.25 tff(f91,plain,(
% 0.09/0.25 ( ! [X0 : $int,X1 : $int] : ($less($sum(X0,$uminus(X1)),0) | ~$less(X0,X1)) )),
% 0.09/0.25 inference(superposition,[],[f12,f8])).
% 0.09/0.25 tff(f98,plain,(
% 0.09/0.25 $less(0,0) | ~$less(f(b),f(a))),
% 0.09/0.25 inference(superposition,[],[f82,f8])).
% 0.09/0.25 tff(f102,plain,(
% 0.09/0.25 ~$less(f(b),f(a))),
% 0.09/0.25 inference(evaluation,[],[f98])).
% 0.09/0.25 tff(f129,definition,(
% 0.09/0.25 spl0_3 <=> f(a) = f(b)),
% 0.09/0.25 introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition])).
% 0.09/0.25 tff(f131,plain,(
% 0.09/0.25 f(a) = f(b) | ~spl0_3),
% 0.09/0.25 inference(avatar_component_clause,[],[f129])).
% 0.09/0.25 tff(f139,plain,(
% 0.09/0.25 f(a) = f(b) | $less(a,b)),
% 0.09/0.25 inference(resolution,[],[f46,f102])).
% 0.09/0.25 tff(f143,definition,(
% 0.09/0.25 spl0_5 <=> $less(a,b)),
% 0.09/0.25 introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition])).
% 0.09/0.25 tff(f145,plain,(
% 0.09/0.25 $less(a,b) | ~spl0_5),
% 0.09/0.25 inference(avatar_component_clause,[],[f143])).
% 0.09/0.25 tff(f146,plain,(
% 0.09/0.25 spl0_5 | spl0_3),
% 0.09/0.25 inference(avatar_split_clause,[],[f139,f129,f143])).
% 0.09/0.25 tff(f150,plain,(
% 0.09/0.25 $less($sum(f(a),$uminus(f(a))),0) | ~spl0_3),
% 0.09/0.25 inference(superposition,[],[f20,f131])).
% 0.09/0.25 tff(f155,plain,(
% 0.09/0.25 $less(0,0) | ~spl0_3),
% 0.09/0.25 inference(forward_demodulation,[],[f150,f8])).
% 0.09/0.25 tff(f156,plain,(
% 0.09/0.25 $false | ~spl0_3),
% 0.09/0.25 inference(evaluation,[],[f155])).
% 0.09/0.25 tff(f157,plain,(
% 0.09/0.25 ~spl0_3),
% 0.09/0.25 inference(avatar_contradiction_clause,[],[f156])).
% 0.09/0.25 tff(f220,plain,(
% 0.09/0.25 ~$less(a,b)),
% 0.09/0.25 inference(resolution,[],[f91,f18])).
% 0.09/0.25 tff(f229,plain,(
% 0.09/0.25 $false | ~spl0_5),
% 0.09/0.25 inference(forward_subsumption_resolution,[],[f220,f145])).
% 0.09/0.25 tff(f230,plain,(
% 0.09/0.25 ~spl0_5),
% 0.09/0.25 inference(avatar_contradiction_clause,[],[f229])).
% 0.09/0.25 cnf(s5, plain, spl0_3 | spl0_5, inference(sat_conversion,[],[f146])).
% 0.09/0.25 cnf(s6, plain, ~spl0_3, inference(sat_conversion,[],[f157])).
% 0.09/0.25 cnf(s7, plain, ~spl0_5, inference(sat_conversion,[],[f230])).
% 0.09/0.25 cnf(s8, plain, $false, inference(rat,[],[s5,s7,s6])).
% 0.09/0.25 tff(f231,plain,(
% 0.09/0.25 $false),
% 0.09/0.25 inference(avatar_sat_refutation,[],[s8])).
% 0.09/0.25 % SZS output end Proof for theBenchmark
% 0.09/0.25 % (2175434)------------------------------
% 0.09/0.25 % (2175434)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.25 % (2175434)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.25 % (2175434)CaDiCaL version: 2.1.3
% 0.09/0.25 % (2175434)Termination reason: Refutation
% 0.09/0.25 % (2175434)Time elapsed: 0.008 s
% 0.09/0.25 % (2175434)Peak memory usage: 12 MB
% 0.09/0.25 % (2175434)Instructions burned: 9 (million)
% 0.09/0.25 % (2175422)Success in time 0.042 s
% 0.09/0.25 % Vampire exiting
%------------------------------------------------------------------------------