%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM906_1 : TPTP v9.3.1. Released v5.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n019.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 12:26:02 PM UTC 2026
% Result : Theorem 0.15s 0.44s
% Output : Refutation 0.15s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM906_1 : TPTP v9.3.1. Released v5.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.13/0.37 % Computer : n019.cluster.edu
% 0.13/0.37 % Model : x86_64 x86_64
% 0.13/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.37 % Memory : 8046.5625MB
% 0.13/0.37 % OS : Linux 6.8.0-71-generic
% 0.13/0.37 % CPULimit : 300
% 0.13/0.37 % WCLimit : 300
% 0.13/0.37 % DateTime : Sun Sep 27 21:39:18 UTC 2026
% 0.13/0.38 % CPUTime :
% 0.13/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.15/0.41 Running first-order model finding
% 0.15/0.41 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
% 0.15/0.44 % (3432444)Will run a generic schedule for satisfiability detection.
% 0.15/0.44 % (3432454)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2323277298:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.15/0.44 % (3432454) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3432444-3432454"...
% 0.15/0.44 % (3432454)...printing done.
% 0.15/0.44 % (3432454)Refutation found. Thanks to Tanya!
% 0.15/0.44 % SZS status Theorem for theBenchmark
% 0.15/0.44 % SZS output start Proof for theBenchmark
% 0.15/0.44 tff(func_def_4, type, sK0: $rat).
% 0.15/0.44 tff(func_def_5, type, sK1: $rat).
% 0.15/0.44 tff(f1,conjecture,(
% 0.15/0.44 ! [X0 : $rat,X1 : $rat] : ($lesseq(X0,X1) <=> ($less(X0,X1) | X0 = X1))),
% 0.15/0.44 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rat_combined_problem_1)).
% 0.15/0.44 tff(f2,negated_conjecture,(
% 0.15/0.44 ~ ! [X0 : $rat,X1 : $rat] : ($lesseq(X0,X1) <=> ($less(X0,X1) | X0 = X1))),
% 0.15/0.44 inference(negated_conjecture,[status(cth)],[f1])).
% 0.15/0.44 tff(f3,plain,(
% 0.15/0.44 ~ ! [X0 : $rat,X1 : $rat] : (~$less(X1,X0) <=> ($less(X0,X1) | X0 = X1))),
% 0.15/0.44 inference(theory_normalization,[],[f2])).
% 0.15/0.44 tff(f9,definition,(
% 0.15/0.44 ( ! [X0 : $rat] : (~$less(X0,X0)) )),
% 0.15/0.44 introduced(theory,[tha_non-reflexivity])).
% 0.15/0.44 tff(f10,definition,(
% 0.15/0.44 ( ! [X2 : $rat,X0 : $rat,X1 : $rat] : (~$less(X0,X1) | ~$less(X1,X2) | $less(X0,X2)) )),
% 0.15/0.44 introduced(theory,[tha_transitivity])).
% 0.15/0.44 tff(f11,definition,(
% 0.15/0.44 ( ! [X0 : $rat,X1 : $rat] : ($less(X0,X1) | $less(X1,X0) | X0 = X1) )),
% 0.15/0.44 introduced(theory,[tha_order_totality])).
% 0.15/0.44 tff(f15,plain,(
% 0.15/0.44 ? [X0 : $rat,X1 : $rat] : (~$less(X1,X0) <~> ($less(X0,X1) | X0 = X1))),
% 0.15/0.44 inference(ennf_transformation,[],[f3])).
% 0.15/0.44 tff(f16,plain,(
% 0.15/0.44 ? [X0 : $rat,X1 : $rat] : (((~$less(X0,X1) & X0 != X1) | $less(X1,X0)) & (($less(X0,X1) | X0 = X1) | ~$less(X1,X0)))),
% 0.15/0.44 inference(nnf_transformation,[],[f15])).
% 0.15/0.44 tff(f17,plain,(
% 0.15/0.44 ? [X0 : $rat,X1 : $rat] : (((~$less(X0,X1) & X0 != X1) | $less(X1,X0)) & ($less(X0,X1) | X0 = X1 | ~$less(X1,X0)))),
% 0.15/0.44 inference(flattening,[],[f16])).
% 0.15/0.44 tff(f18,plain,(
% 0.15/0.44 ((~$less(sK0,sK1) & sK0 != sK1) | $less(sK1,sK0)) & ($less(sK0,sK1) | sK0 = sK1 | ~$less(sK1,sK0))),
% 0.15/0.44 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f17])).
% 0.15/0.44 tff(f19,plain,(
% 0.15/0.44 $less(sK0,sK1) | sK0 = sK1 | ~$less(sK1,sK0)),
% 0.15/0.44 inference(cnf_transformation,[],[f18])).
% 0.15/0.44 tff(f20,plain,(
% 0.15/0.44 sK0 != sK1 | $less(sK1,sK0)),
% 0.15/0.44 inference(cnf_transformation,[],[f18])).
% 0.15/0.44 tff(f21,plain,(
% 0.15/0.44 ~$less(sK0,sK1) | $less(sK1,sK0)),
% 0.15/0.44 inference(cnf_transformation,[],[f18])).
% 0.15/0.44 tff(f23,definition,(
% 0.15/0.44 spl2_1 <=> $less(sK1,sK0)),
% 0.15/0.44 introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition])).
% 0.15/0.44 tff(f24,plain,(
% 0.15/0.44 $less(sK1,sK0) | ~spl2_1),
% 0.15/0.44 inference(avatar_component_clause,[],[f23])).
% 0.15/0.44 tff(f25,plain,(
% 0.15/0.44 ~$less(sK1,sK0) | spl2_1),
% 0.15/0.44 inference(avatar_component_clause,[],[f23])).
% 0.15/0.44 tff(f27,definition,(
% 0.15/0.44 spl2_2 <=> sK0 = sK1),
% 0.15/0.44 introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition])).
% 0.15/0.44 tff(f28,plain,(
% 0.15/0.44 sK0 != sK1 | spl2_2),
% 0.15/0.44 inference(avatar_component_clause,[],[f27])).
% 0.15/0.44 tff(f29,plain,(
% 0.15/0.44 sK0 = sK1 | ~spl2_2),
% 0.15/0.44 inference(avatar_component_clause,[],[f27])).
% 0.15/0.44 tff(f31,definition,(
% 0.15/0.44 spl2_3 <=> $less(sK0,sK1)),
% 0.15/0.44 introduced(definition,[new_symbols(definition,[spl2_3])],[avatar_definition])).
% 0.15/0.44 tff(f32,plain,(
% 0.15/0.44 ~$less(sK0,sK1) | spl2_3),
% 0.15/0.44 inference(avatar_component_clause,[],[f31])).
% 0.15/0.44 tff(f33,plain,(
% 0.15/0.44 $less(sK0,sK1) | ~spl2_3),
% 0.15/0.44 inference(avatar_component_clause,[],[f31])).
% 0.15/0.44 tff(f34,plain,(
% 0.15/0.44 ~spl2_1 | spl2_2 | spl2_3),
% 0.15/0.44 inference(avatar_split_clause,[],[f19,f31,f27,f23])).
% 0.15/0.44 tff(f35,plain,(
% 0.15/0.44 spl2_1 | ~spl2_2),
% 0.15/0.44 inference(avatar_split_clause,[],[f20,f27,f23])).
% 0.15/0.44 tff(f36,plain,(
% 0.15/0.44 spl2_1 | ~spl2_3),
% 0.15/0.44 inference(avatar_split_clause,[],[f21,f31,f23])).
% 0.15/0.44 tff(f51,plain,(
% 0.15/0.44 $less(sK0,sK1) | sK0 = sK1 | spl2_1),
% 0.15/0.44 inference(resolution,[],[f11,f25])).
% 0.15/0.44 tff(f57,plain,(
% 0.15/0.44 sK0 = sK1 | (spl2_1 | spl2_3)),
% 0.15/0.44 inference(forward_subsumption_resolution,[],[f51,f32])).
% 0.15/0.44 tff(f60,plain,(
% 0.15/0.44 $false | (spl2_1 | spl2_2 | spl2_3)),
% 0.15/0.44 inference(forward_subsumption_resolution,[],[f57,f28])).
% 0.15/0.44 tff(f61,plain,(
% 0.15/0.44 spl2_1 | spl2_2 | spl2_3),
% 0.15/0.44 inference(avatar_contradiction_clause,[],[f60])).
% 0.15/0.44 tff(f62,plain,(
% 0.15/0.44 ( ! [X0 : $rat] : (~$less(sK0,X0) | $less(sK1,X0)) ) | ~spl2_1),
% 0.15/0.44 inference(resolution,[],[f24,f10])).
% 0.15/0.44 tff(f64,plain,(
% 0.15/0.44 $less(sK0,sK0) | (~spl2_1 | ~spl2_2)),
% 0.15/0.44 inference(superposition,[],[f24,f29])).
% 0.15/0.44 tff(f66,plain,(
% 0.15/0.44 $false | (~spl2_1 | ~spl2_2)),
% 0.15/0.44 inference(forward_subsumption_resolution,[],[f64,f9])).
% 0.15/0.44 tff(f67,plain,(
% 0.15/0.44 ~spl2_1 | ~spl2_2),
% 0.15/0.44 inference(avatar_contradiction_clause,[],[f66])).
% 0.15/0.44 tff(f69,plain,(
% 0.15/0.44 $less(sK1,sK1) | (~spl2_1 | ~spl2_3)),
% 0.15/0.44 inference(resolution,[],[f62,f33])).
% 0.15/0.44 tff(f75,plain,(
% 0.15/0.44 $false | (~spl2_1 | ~spl2_3)),
% 0.15/0.44 inference(forward_subsumption_resolution,[],[f69,f9])).
% 0.15/0.44 tff(f76,plain,(
% 0.15/0.44 ~spl2_1 | ~spl2_3),
% 0.15/0.44 inference(avatar_contradiction_clause,[],[f75])).
% 0.15/0.44 cnf(s1, plain, ~spl2_1 | spl2_2 | spl2_3, inference(sat_conversion,[],[f34])).
% 0.15/0.44 cnf(s2, plain, spl2_1 | ~spl2_2, inference(sat_conversion,[],[f35])).
% 0.15/0.44 cnf(s3, plain, spl2_1 | ~spl2_3, inference(sat_conversion,[],[f36])).
% 0.15/0.44 cnf(s5, plain, spl2_1 | spl2_2 | spl2_3, inference(sat_conversion,[],[f61])).
% 0.15/0.44 cnf(s6, plain, ~spl2_1 | ~spl2_2, inference(sat_conversion,[],[f67])).
% 0.15/0.44 cnf(s7, plain, ~spl2_1 | ~spl2_3, inference(sat_conversion,[],[f76])).
% 0.15/0.44 cnf(s8, plain, spl2_1, inference(rat,[],[s5,s2,s3])).
% 0.15/0.44 cnf(s9, plain, ~spl2_3, inference(rat,[],[s7,s8])).
% 0.15/0.44 cnf(s10, plain, ~spl2_2, inference(rat,[],[s6,s8])).
% 0.15/0.44 cnf(s11, plain, $false, inference(rat,[],[s1,s9,s10,s8])).
% 0.15/0.44 tff(f77,plain,(
% 0.15/0.44 $false),
% 0.15/0.44 inference(avatar_sat_refutation,[],[s11])).
% 0.15/0.44 % SZS output end Proof for theBenchmark
% 0.15/0.44 % (3432454)------------------------------
% 0.15/0.44 % (3432454)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.15/0.44 % (3432454)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/0.44 % (3432454)CaDiCaL version: 2.1.3
% 0.15/0.44 % (3432454)Termination reason: Refutation
% 0.15/0.44 % (3432454)Time elapsed: 0.002 s
% 0.15/0.44 % (3432454)Peak memory usage: 12 MB
% 0.15/0.44 % (3432454)Instructions burned: 3 (million)
% 0.15/0.44 % (3432444)Success in time 0.024 s
% 0.15/0.44 % Vampire exiting
%------------------------------------------------------------------------------