%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ARI610_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 : n008.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 09:34:58 AM UTC 2026
% Result : Theorem 0.25s 0.33s
% Output : Refutation 0.25s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ARI610_1 : TPTP v9.3.1. Released v5.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.23 % Computer : n008.cluster.edu
% 0.11/0.23 % Model : x86_64 x86_64
% 0.11/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.23 % Memory : 8046.5625MB
% 0.11/0.23 % OS : Linux 6.8.0-71-generic
% 0.11/0.23 % CPULimit : 300
% 0.11/0.23 % WCLimit : 300
% 0.11/0.23 % DateTime : Mon Sep 28 20:54:24 UTC 2026
% 0.11/0.24 % CPUTime :
% 0.11/0.24 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.25/0.29 Running first-order model finding
% 0.25/0.29 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
% 0.25/0.33 % (2634485)Will run a generic schedule for satisfiability detection.
% 0.25/0.33 % (2634492)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2534093589:i=88024:add=on:rawr=on_3000 on theBenchmark for (3000ds/88024Mi)
% 0.25/0.33 % (2634493)dis+10_1_sil=32000:sp=arity:random_seed=1071098868:i=103:fgj=on_3000 on theBenchmark for (3000ds/103Mi)
% 0.25/0.33 % (2634491)% WARNING: option uhcvi not known.
% 0.25/0.33 % (2634493) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2634485-2634493"...
% 0.25/0.33 % (2634493)...printing done.
% 0.25/0.33 % (2634493)Refutation found. Thanks to Tanya!
% 0.25/0.33 % SZS status Theorem for theBenchmark
% 0.25/0.33 % SZS output start Proof for theBenchmark
% 0.25/0.33 tff(func_def_0, type, f: $int > $int).
% 0.25/0.33 tff(func_def_1, type, a: $int).
% 0.25/0.33 tff(func_def_2, type, b: $int).
% 0.25/0.33 tff(f1,conjecture,(
% 0.25/0.33 (! [X0 : $int,X1 : $int] : ($lesseq(X0,X1) => $lesseq(f(X0),f(X1))) & $less(f(b),f(a))) => $lesseq(f(0),f($sum(a,$uminus(b))))),
% 0.25/0.33 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f_mon_implies_f_a_b_2)).
% 0.25/0.33 tff(f2,negated_conjecture,(
% 0.25/0.33 ~((! [X0 : $int,X1 : $int] : ($lesseq(X0,X1) => $lesseq(f(X0),f(X1))) & $less(f(b),f(a))) => $lesseq(f(0),f($sum(a,$uminus(b)))))),
% 0.25/0.33 inference(negated_conjecture,[status(cth)],[f1])).
% 0.25/0.33 tff(f3,plain,(
% 0.25/0.33 ~((! [X0 : $int,X1 : $int] : (~$less(X1,X0) => ~$less(f(X1),f(X0))) & $less(f(b),f(a))) => ~$less(f($sum(a,$uminus(b))),f(0)))),
% 0.25/0.33 inference(theory_normalization,[],[f2])).
% 0.25/0.33 tff(f8,definition,(
% 0.25/0.33 ( ! [X0 : $int] : (0 = $sum(X0,$uminus(X0))) )),
% 0.25/0.33 introduced(theory,[tha_inverse_op_unit])).
% 0.25/0.33 tff(f10,definition,(
% 0.25/0.33 ( ! [X2 : $int,X0 : $int,X1 : $int] : (~$less(X1,X2) | ~$less(X0,X1) | $less(X0,X2)) )),
% 0.25/0.33 introduced(theory,[tha_transitivity])).
% 0.25/0.33 tff(f12,definition,(
% 0.25/0.33 ( ! [X2 : $int,X0 : $int,X1 : $int] : ($less($sum(X0,X2),$sum(X1,X2)) | ~$less(X0,X1)) )),
% 0.25/0.33 introduced(theory,[tha_order_monotonicity])).
% 0.25/0.33 tff(f16,plain,(
% 0.25/0.33 $less(f($sum(a,$uminus(b))),f(0)) & (! [X0 : $int,X1 : $int] : (~$less(f(X1),f(X0)) | $less(X1,X0)) & $less(f(b),f(a)))),
% 0.25/0.33 inference(ennf_transformation,[],[f3])).
% 0.25/0.33 tff(f17,plain,(
% 0.25/0.33 $less(f($sum(a,$uminus(b))),f(0)) & ! [X0 : $int,X1 : $int] : (~$less(f(X1),f(X0)) | $less(X1,X0)) & $less(f(b),f(a))),
% 0.25/0.33 inference(flattening,[],[f16])).
% 0.25/0.33 tff(f18,plain,(
% 0.25/0.33 $less(f(b),f(a))),
% 0.25/0.33 inference(cnf_transformation,[],[f17])).
% 0.25/0.33 tff(f19,plain,(
% 0.25/0.33 ( ! [X0 : $int,X1 : $int] : (~$less(f(X1),f(X0)) | $less(X1,X0)) )),
% 0.25/0.33 inference(cnf_transformation,[],[f17])).
% 0.25/0.33 tff(f20,plain,(
% 0.25/0.33 $less(f($sum(a,$uminus(b))),f(0))),
% 0.25/0.33 inference(cnf_transformation,[],[f17])).
% 0.25/0.33 tff(f21,plain,(
% 0.25/0.33 $less(b,a)),
% 0.25/0.33 inference(resolution,[],[f19,f18])).
% 0.25/0.33 tff(f22,plain,(
% 0.25/0.33 $less($sum(a,$uminus(b)),0)),
% 0.25/0.33 inference(resolution,[],[f20,f19])).
% 0.25/0.33 tff(f49,plain,(
% 0.25/0.33 ( ! [X0 : $int] : (~$less(X0,$sum(a,$uminus(b))) | $less(X0,0)) )),
% 0.25/0.33 inference(resolution,[],[f10,f22])).
% 0.25/0.33 tff(f76,plain,(
% 0.25/0.33 ( ! [X0 : $int] : ($less($sum(X0,$uminus(b)),0) | ~$less(X0,a)) )),
% 0.25/0.33 inference(resolution,[],[f12,f49])).
% 0.25/0.33 tff(f121,plain,(
% 0.25/0.33 $less(0,0) | ~$less(b,a)),
% 0.25/0.33 inference(superposition,[],[f76,f8])).
% 0.25/0.33 tff(f126,plain,(
% 0.25/0.33 ~$less(b,a)),
% 0.25/0.33 inference(evaluation,[],[f121])).
% 0.25/0.33 tff(f127,plain,(
% 0.25/0.33 $false),
% 0.25/0.33 inference(forward_subsumption_resolution,[],[f126,f21])).
% 0.25/0.33 % SZS output end Proof for theBenchmark
% 0.25/0.33 % (2634493)------------------------------
% 0.25/0.33 % (2634493)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.25/0.33 % (2634493)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.25/0.33 % (2634493)CaDiCaL version: 2.1.3
% 0.25/0.33 % (2634493)Termination reason: Refutation
% 0.25/0.33 % (2634493)Time elapsed: 0.006 s
% 0.25/0.33 % (2634493)Peak memory usage: 12 MB
% 0.25/0.33 % (2634493)Instructions burned: 6 (million)
% 0.25/0.33 % (2634485)Success in time 0.031 s
% 0.25/0.33 % Vampire exiting
%------------------------------------------------------------------------------