%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ANA139_1 : TPTP v9.3.1. Released v8.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n017.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 09:31:34 AM UTC 2026
% Result : Theorem 0.23s 0.35s
% Output : Refutation 0.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : ANA139_1 : TPTP v9.3.1. Released v8.2.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.23/0.27 % Computer : n017.cluster.edu
% 0.23/0.27 % Model : x86_64 x86_64
% 0.23/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.23/0.27 % Memory : 8046.5625MB
% 0.23/0.27 % OS : Linux 6.8.0-71-generic
% 0.23/0.28 % CPULimit : 300
% 0.23/0.28 % WCLimit : 300
% 0.23/0.28 % DateTime : Mon Sep 28 20:34:21 UTC 2026
% 0.23/0.28 % CPUTime :
% 0.23/0.28 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.23/0.31 Running first-order model finding
% 0.23/0.31 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
% 0.23/0.35 % (3980727)Will run a generic schedule for satisfiability detection.
% 0.23/0.35 % (3980737)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3939449299:i=131_3000 on theBenchmark for (3000ds/131Mi)
% 0.23/0.35 % (3980737) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3980727-3980737"...
% 0.23/0.35 % (3980737)...printing done.
% 0.23/0.35 % (3980737)Refutation found. Thanks to Tanya!
% 0.23/0.35 % SZS status Theorem for theBenchmark
% 0.23/0.35 % SZS output start Proof for theBenchmark
% 0.23/0.35 tff(func_def_0, type, a: $real).
% 0.23/0.35 tff(func_def_1, type, c: $real).
% 0.23/0.35 tff(func_def_7, type, sK0: $real).
% 0.23/0.35 tff(func_def_8, type, sK1: $real > $real).
% 0.23/0.35 tff(f1,conjecture,(
% 0.23/0.35 ! [X0 : $real] : ($less(0/1,X0) => ? [X1 : $real] : ($less(0/1,X1) & ! [X2 : $real] : ((X2 != a & ($greatereq($difference(X2,a),0/1) => $less($difference(X2,a),X1)) & (~$greatereq($difference(X2,a),0/1) => $less($uminus($difference(X2,a)),X1))) => (($greatereq($difference(c,c),0/1) => $less($difference(c,c),X0)) & (~$greatereq($difference(c,c),0/1) => $less($uminus($difference(c,c)),X0))))))),
% 0.23/0.35 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',formula_1)).
% 0.23/0.35 tff(f2,negated_conjecture,(
% 0.23/0.35 ~ ! [X0 : $real] : ($less(0/1,X0) => ? [X1 : $real] : ($less(0/1,X1) & ! [X2 : $real] : ((X2 != a & ($greatereq($difference(X2,a),0/1) => $less($difference(X2,a),X1)) & (~$greatereq($difference(X2,a),0/1) => $less($uminus($difference(X2,a)),X1))) => (($greatereq($difference(c,c),0/1) => $less($difference(c,c),X0)) & (~$greatereq($difference(c,c),0/1) => $less($uminus($difference(c,c)),X0))))))),
% 0.23/0.35 inference(negated_conjecture,[status(cth)],[f1])).
% 0.23/0.35 tff(f3,plain,(
% 0.23/0.35 ~ ! [X0 : $real] : ($less(0/1,X0) => ? [X1 : $real] : ($less(0/1,X1) & ! [X2 : $real] : ((X2 != a & (~$less($sum(X2,$uminus(a)),0/1) => $less($sum(X2,$uminus(a)),X1)) & ($less($sum(X2,$uminus(a)),0/1) => $less($uminus($sum(X2,$uminus(a))),X1))) => ((~$less($sum(c,$uminus(c)),0/1) => $less($sum(c,$uminus(c)),X0)) & ($less($sum(c,$uminus(c)),0/1) => $less($uminus($sum(c,$uminus(c))),X0))))))),
% 0.23/0.35 inference(theory_normalization,[],[f2])).
% 0.23/0.35 tff(f7,definition,(
% 0.23/0.35 ( ! [X0 : $real,X1 : $real] : ($uminus($sum(X0,X1)) = $sum($uminus(X1),$uminus(X0))) )),
% 0.23/0.35 introduced(theory,[tha_inverse_op_op_inverses])).
% 0.23/0.35 tff(f8,definition,(
% 0.23/0.35 ( ! [X0 : $real] : (0/1 = $sum(X0,$uminus(X0))) )),
% 0.23/0.35 introduced(theory,[tha_inverse_op_unit])).
% 0.23/0.35 tff(f15,plain,(
% 0.23/0.35 ? [X0 : $real] : (! [X1 : $real] : (~$less(0/1,X1) | ? [X2 : $real] : (((~$less($sum(c,$uminus(c)),X0) & ~$less($sum(c,$uminus(c)),0/1)) | (~$less($uminus($sum(c,$uminus(c))),X0) & $less($sum(c,$uminus(c)),0/1))) & (X2 != a & ($less($sum(X2,$uminus(a)),X1) | $less($sum(X2,$uminus(a)),0/1)) & ($less($uminus($sum(X2,$uminus(a))),X1) | ~$less($sum(X2,$uminus(a)),0/1))))) & $less(0/1,X0))),
% 0.23/0.35 inference(ennf_transformation,[],[f3])).
% 0.23/0.35 tff(f16,plain,(
% 0.23/0.35 ? [X0 : $real] : (! [X1 : $real] : (~$less(0/1,X1) | ? [X2 : $real] : (((~$less($sum(c,$uminus(c)),X0) & ~$less($sum(c,$uminus(c)),0/1)) | (~$less($uminus($sum(c,$uminus(c))),X0) & $less($sum(c,$uminus(c)),0/1))) & X2 != a & ($less($sum(X2,$uminus(a)),X1) | $less($sum(X2,$uminus(a)),0/1)) & ($less($uminus($sum(X2,$uminus(a))),X1) | ~$less($sum(X2,$uminus(a)),0/1)))) & $less(0/1,X0))),
% 0.23/0.35 inference(flattening,[],[f15])).
% 0.23/0.35 tff(f17,plain,(
% 0.23/0.35 ! [X1 : $real] : (~$less(0/1,X1) | (((~$less($sum(c,$uminus(c)),sK0) & ~$less($sum(c,$uminus(c)),0/1)) | (~$less($uminus($sum(c,$uminus(c))),sK0) & $less($sum(c,$uminus(c)),0/1))) & a != sK1(X1) & ($less($sum(sK1(X1),$uminus(a)),X1) | $less($sum(sK1(X1),$uminus(a)),0/1)) & ($less($uminus($sum(sK1(X1),$uminus(a))),X1) | ~$less($sum(sK1(X1),$uminus(a)),0/1)))) & $less(0/1,sK0)),
% 0.23/0.35 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X2,sK1(X1))],[f16])).
% 0.23/0.35 tff(f18,plain,(
% 0.23/0.35 $less(0/1,sK0)),
% 0.23/0.35 inference(cnf_transformation,[],[f17])).
% 0.23/0.35 tff(f25,plain,(
% 0.23/0.35 ( ! [X1 : $real] : (~$less(0/1,X1) | ~$less($sum(c,$uminus(c)),sK0) | ~$less($uminus($sum(c,$uminus(c))),sK0)) )),
% 0.23/0.35 inference(cnf_transformation,[],[f17])).
% 0.23/0.35 tff(f27,definition,(
% 0.23/0.35 spl2_1 <=> $less($uminus($sum(c,$uminus(c))),sK0)),
% 0.23/0.35 introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition])).
% 0.23/0.35 tff(f29,plain,(
% 0.23/0.35 ~$less($uminus($sum(c,$uminus(c))),sK0) | spl2_1),
% 0.23/0.35 inference(avatar_component_clause,[],[f27])).
% 0.23/0.35 tff(f35,definition,(
% 0.23/0.35 spl2_3 <=> ! [X1 : $real] : ~$less(0/1,X1)),
% 0.23/0.35 introduced(definition,[new_symbols(definition,[spl2_3])],[avatar_definition])).
% 0.23/0.35 tff(f36,plain,(
% 0.23/0.35 ( ! [X1 : $real] : (~$less(0/1,X1)) ) | ~spl2_3),
% 0.23/0.35 inference(avatar_component_clause,[],[f35])).
% 0.23/0.35 tff(f39,definition,(
% 0.23/0.35 spl2_4 <=> $less($sum(c,$uminus(c)),sK0)),
% 0.23/0.35 introduced(definition,[new_symbols(definition,[spl2_4])],[avatar_definition])).
% 0.23/0.35 tff(f41,plain,(
% 0.23/0.35 ~$less($sum(c,$uminus(c)),sK0) | spl2_4),
% 0.23/0.35 inference(avatar_component_clause,[],[f39])).
% 0.23/0.35 tff(f43,plain,(
% 0.23/0.35 ~spl2_1 | ~spl2_4 | spl2_3),
% 0.23/0.35 inference(avatar_split_clause,[],[f25,f35,f39,f27])).
% 0.23/0.35 tff(f44,plain,(
% 0.23/0.35 ~$less($sum($uminus($uminus(c)),$uminus(c)),sK0) | spl2_1),
% 0.23/0.35 inference(forward_demodulation,[],[f29,f7])).
% 0.23/0.35 tff(f45,plain,(
% 0.23/0.35 ~$less($sum(c,$uminus(c)),sK0) | spl2_1),
% 0.23/0.35 inference(evaluation,[],[f44])).
% 0.23/0.35 tff(f46,plain,(
% 0.23/0.35 ~$less(0/1,sK0) | spl2_4),
% 0.23/0.35 inference(forward_demodulation,[],[f41,f8])).
% 0.23/0.35 tff(f47,plain,(
% 0.23/0.35 ~$less(0/1,sK0) | spl2_1),
% 0.23/0.35 inference(forward_demodulation,[],[f45,f8])).
% 0.23/0.35 tff(f48,plain,(
% 0.23/0.35 $false | spl2_4),
% 0.23/0.35 inference(forward_subsumption_resolution,[],[f46,f18])).
% 0.23/0.35 tff(f49,plain,(
% 0.23/0.35 spl2_4),
% 0.23/0.35 inference(avatar_contradiction_clause,[],[f48])).
% 0.23/0.35 tff(f50,plain,(
% 0.23/0.35 $false | spl2_1),
% 0.23/0.35 inference(forward_subsumption_resolution,[],[f47,f18])).
% 0.23/0.35 tff(f51,plain,(
% 0.23/0.35 spl2_1),
% 0.23/0.35 inference(avatar_contradiction_clause,[],[f50])).
% 0.23/0.35 tff(f56,plain,(
% 0.23/0.35 $false | ~spl2_3),
% 0.23/0.35 inference(resolution,[],[f36,f18])).
% 0.23/0.35 tff(f57,plain,(
% 0.23/0.35 ~spl2_3),
% 0.23/0.35 inference(avatar_contradiction_clause,[],[f56])).
% 0.23/0.35 cnf(s3, plain, ~spl2_1 | spl2_3 | ~spl2_4, inference(sat_conversion,[],[f43])).
% 0.23/0.35 cnf(s4, plain, spl2_4, inference(sat_conversion,[],[f49])).
% 0.23/0.35 cnf(s5, plain, spl2_1, inference(sat_conversion,[],[f51])).
% 0.23/0.35 cnf(s6, plain, ~spl2_3, inference(sat_conversion,[],[f57])).
% 0.23/0.35 cnf(s7, plain, $false, inference(rat,[],[s3,s4,s6,s5])).
% 0.23/0.35 tff(f58,plain,(
% 0.23/0.35 $false),
% 0.23/0.35 inference(avatar_sat_refutation,[],[s7])).
% 0.23/0.35 % SZS output end Proof for theBenchmark
% 0.23/0.35 % (3980737)------------------------------
% 0.23/0.35 % (3980737)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.35 % (3980737)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.35 % (3980737)CaDiCaL version: 2.1.3
% 0.23/0.35 % (3980737)Termination reason: Refutation
% 0.23/0.35 % (3980737)Time elapsed: 0.002 s
% 0.23/0.35 % (3980737)Peak memory usage: 12 MB
% 0.23/0.35 % (3980737)Instructions burned: 2 (million)
% 0.23/0.35 % (3980727)Success in time 0.025 s
% 0.23/0.35 % Vampire exiting
%------------------------------------------------------------------------------