%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ARI762_1 : TPTP v9.3.1. Released v9.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 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 09:33:50 AM UTC 2026
% Result : Theorem 2.76s 1.16s
% Output : Refutation 2.76s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ARI762_1 : TPTP v9.3.1. Released v9.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.17 % Computer : n017.cluster.edu
% 0.11/0.17 % Model : x86_64 x86_64
% 0.11/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.17 % Memory : 8046.5625MB
% 0.11/0.17 % OS : Linux 6.8.0-71-generic
% 0.11/0.17 % CPULimit : 300
% 0.11/0.17 % WCLimit : 300
% 0.11/0.17 % DateTime : Mon Sep 28 20:57:37 UTC 2026
% 0.11/0.17 % CPUTime :
% 0.11/0.17 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.20 Running first-order theorem proving
% 0.11/0.20 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.76/1.16 % (4022894)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 2.76/1.16 % (4022930)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=3647965282:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 2.76/1.16 % (4022930)First to succeed.
% 2.76/1.16 % (4022930)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-4022894"
% 2.76/1.16 % (4022929)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=346265231:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 2.76/1.16 % (4022931)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=1393465385:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 2.76/1.16 % (4022935)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=3401428895:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 2.76/1.16 % (4022934)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=3637059481:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 2.76/1.16 % (4022932)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=1037647632:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 2.76/1.16 % (4022936)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=178084355:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 2.76/1.16 % (4022934)Instruction limit reached!
% 2.76/1.16 % (4022934)------------------------------
% 2.76/1.16 % (4022934)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.76/1.16 % (4022934)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.76/1.16 % (4022934)CaDiCaL version: 2.1.3
% 2.76/1.16 % (4022934)Termination reason: Instruction limit
% 2.76/1.16 % (4022934)Termination phase: Saturation
% 2.76/1.16 % (4022934)Time elapsed: 0.004 s
% 2.76/1.16 % (4022934)Peak memory usage: 89 MB
% 2.76/1.16 % (4022934)Instructions burned: 5 (million)
% 2.76/1.16 % (4022932)Instruction limit reached!
% 2.76/1.16 % (4022932)------------------------------
% 2.76/1.16 % (4022932)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.76/1.16 % (4022932)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.76/1.16 % (4022932)CaDiCaL version: 2.1.3
% 2.76/1.16 % (4022932)Termination reason: Instruction limit
% 2.76/1.16 % (4022932)Termination phase: Saturation
% 2.76/1.16 % (4022932)Time elapsed: 0.006 s
% 2.76/1.16 % (4022932)Peak memory usage: 88 MB
% 2.76/1.16 % (4022932)Instructions burned: 8 (million)
% 2.76/1.16 % (4022929)Instruction limit reached!
% 2.76/1.16 % (4022929)------------------------------
% 2.76/1.16 % (4022929)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.76/1.16 % (4022929)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.76/1.16 % (4022929)CaDiCaL version: 2.1.3
% 2.76/1.16 % (4022929)Termination reason: Instruction limit
% 2.76/1.16 % (4022929)Termination phase: Saturation
% 2.76/1.16 % (4022929)Time elapsed: 0.030 s
% 2.76/1.16 % (4022929)Peak memory usage: 115 MB
% 2.76/1.16 % (4022929)Instructions burned: 12 (million)
% 2.76/1.16 % (4022935)Also succeeded, but the first one will report.
% 2.76/1.16 % (4022936)Also succeeded, but the first one will report.
% 2.76/1.16 % (4022931)Also succeeded, but the first one will report.
% 2.76/1.16 % (4022944)dis+11_3_anc=none:drc=ordering:si=on:urr=ec_only:bce=on:tha=off:sac=on:random_seed=3418041666:st=5:i=14:sd=10:rtra=on:ss=axioms:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 2.76/1.16 % (4022930)Refutation found. Thanks to Tanya!
% 2.76/1.16 % SZS status Theorem for theBenchmark
% 2.76/1.16 % SZS output start Proof for theBenchmark
% 2.76/1.16 tff(func_def_0, type, max: ($int * $int) > $int).
% 2.76/1.16 tff(func_def_1, type, iG0: ($int * $int) > $int).
% 2.76/1.16 tff(func_def_2, type, sK2: $int).
% 2.76/1.16 tff(func_def_3, type, sK3: $int).
% 2.76/1.16 tff(pred_def_3, type, iG1: ($int * $int) > $o).
% 2.76/1.16 tff(f1,axiom,(
% 2.76/1.16 ! [X1 : $int,X0 : $int] : max(X0,X1) = $ite($less(X0,X1), (X1,X0)),
% 2.76/1.16 file('/export/starexec/sandbox/benchmark/theBenchmark.p',max_definition)).
% 2.76/1.16 tff(f2,conjecture,(
% 2.76/1.16 ! [X0 : $int,X1 : $int] : $ite(max(X0,X1) = X0, ($greatereq(X0,X1),$greatereq(X1,X0))),
% 2.76/1.16 file('/export/starexec/sandbox/benchmark/theBenchmark.p',max_conjecture)).
% 2.76/1.16 tff(f3,negated_conjecture,(
% 2.76/1.16 ~! [X0 : $int,X1 : $int] : $ite(max(X0,X1) = X0, ($greatereq(X0,X1),$greatereq(X1,X0))),
% 2.76/1.16 inference(negated_conjecture,[status(cth)],[f2])).
% 2.76/1.16 tff(f4,plain,(
% 2.76/1.16 ! [X1 : $int,X0 : $int] : max(X0,X1) = $ite($less(X0,X1), (X1,X0)),
% 2.76/1.16 inference(theory_normalization,[],[f1])).
% 2.76/1.16 tff(f5,plain,(
% 2.76/1.16 ~! [X0 : $int,X1 : $int] : $ite(max(X0,X1) = X0, (~$less(X0,X1),~$less(X1,X0))),
% 2.76/1.16 inference(theory_normalization,[],[f3])).
% 2.76/1.16 tff(f6,plain,(
% 2.76/1.16 ! [X0 : $int,X1 : $int] : max(X1,X0) = $ite($less(X1,X0), (X0,X1)),
% 2.76/1.16 inference(rectify,[],[f4])).
% 2.76/1.16 tff(f7,definition,(
% 2.76/1.16 ! [X0 : $int,X1 : $int] : (~$less(X1,X0) => iG0(X0,X1) = X1) & ! [X0 : $int,X1 : $int] : ($less(X1,X0) => iG0(X0,X1) = X0)),
% 2.76/1.16 introduced(definition,[new_symbols(definition,[iG0])],[fool_ite_definition])).
% 2.76/1.16 tff(f8,plain,(
% 2.76/1.16 ! [X0 : $int,X1 : $int] : iG0(X0,X1) = max(X1,X0)),
% 2.76/1.16 inference(fool_elimination,[],[f6,f7])).
% 2.76/1.16 tff(f9,plain,(
% 2.76/1.16 ~! [X0 : $int,X1 : $int] : $ite(max(X0,X1) = X0, (~$less(X0,X1),~$less(X1,X0))),
% 2.76/1.16 inference(rectify,[],[f5])).
% 2.76/1.16 tff(f10,definition,(
% 2.76/1.16 ! [X0 : $int,X1 : $int] : (~max(X0,X1) = X0 => (~$less(X1,X0) <=> iG1(X0,X1))) & ! [X0 : $int,X1 : $int] : (max(X0,X1) = X0 => (iG1(X0,X1) <=> ~$less(X0,X1)))),
% 2.76/1.16 introduced(definition,[new_symbols(definition,[iG1])],[fool_ite_definition])).
% 2.76/1.16 tff(f11,plain,(
% 2.76/1.16 ~! [X1 : $int,X0 : $int] : iG1(X0,X1)),
% 2.76/1.16 inference(fool_elimination,[],[f9,f10])).
% 2.76/1.16 tff(f12,plain,(
% 2.76/1.16 ! [X0 : $int,X1 : $int] : (~max(X0,X1) = X0 => (~$less(X1,X0) <=> iG1(X0,X1))) & ! [X2 : $int,X3 : $int] : (max(X2,X3) = X2 => (iG1(X2,X3) <=> ~$less(X2,X3)))),
% 2.76/1.16 inference(rectify,[],[f10])).
% 2.76/1.16 tff(f13,plain,(
% 2.76/1.16 ! [X0 : $int,X1 : $int] : (max(X0,X1) != X0 => (~$less(X1,X0) <=> iG1(X0,X1))) & ! [X2 : $int,X3 : $int] : (max(X2,X3) = X2 => (iG1(X2,X3) <=> ~$less(X2,X3)))),
% 2.76/1.16 inference(flattening,[],[f12])).
% 2.76/1.16 tff(f14,plain,(
% 2.76/1.16 ! [X0 : $int,X1 : $int] : (~$less(X1,X0) => iG0(X0,X1) = X1) & ! [X2 : $int,X3 : $int] : ($less(X3,X2) => iG0(X2,X3) = X2)),
% 2.76/1.16 inference(rectify,[],[f7])).
% 2.76/1.16 tff(f15,plain,(
% 2.76/1.16 ! [X2 : $int,X3 : $int] : ($less(X3,X2) => iG0(X2,X3) = X2) & ! [X1 : $int,X0 : $int] : (~$less(X1,X0) => iG0(X0,X1) = X1)),
% 2.76/1.16 inference(flattening,[],[f14])).
% 2.76/1.16 tff(f16,plain,(
% 2.76/1.16 ! [X1 : $int,X0 : $int] : (max(X0,X1) = X0 | (~$less(X1,X0) <=> iG1(X0,X1))) & ! [X2 : $int,X3 : $int] : (max(X2,X3) != X2 | (iG1(X2,X3) <=> ~$less(X2,X3)))),
% 2.76/1.16 inference(ennf_transformation,[],[f13])).
% 2.76/1.16 tff(f17,plain,(
% 2.76/1.16 ? [X1 : $int,X0 : $int] : ~iG1(X0,X1)),
% 2.76/1.16 inference(ennf_transformation,[],[f11])).
% 2.76/1.16 tff(f18,plain,(
% 2.76/1.16 ! [X0 : $int,X1 : $int] : ($less(X1,X0) | iG0(X0,X1) = X1) & ! [X3 : $int,X2 : $int] : (~$less(X3,X2) | iG0(X2,X3) = X2)),
% 2.76/1.16 inference(ennf_transformation,[],[f15])).
% 2.76/1.16 tff(f19,plain,(
% 2.76/1.16 ! [X1 : $int,X0 : $int] : (max(X0,X1) = X0 | ((~$less(X1,X0) | ~iG1(X0,X1)) & (iG1(X0,X1) | $less(X1,X0)))) & ! [X2 : $int,X3 : $int] : (max(X2,X3) != X2 | ((iG1(X2,X3) | $less(X2,X3)) & (~$less(X2,X3) | ~iG1(X2,X3))))),
% 2.76/1.16 inference(nnf_transformation,[],[f16])).
% 2.76/1.16 tff(f20,plain,(
% 2.76/1.16 ! [X0 : $int,X1 : $int] : (max(X1,X0) = X1 | ((~$less(X0,X1) | ~iG1(X1,X0)) & (iG1(X1,X0) | $less(X0,X1)))) & ! [X2 : $int,X3 : $int] : (max(X2,X3) != X2 | ((iG1(X2,X3) | $less(X2,X3)) & (~$less(X2,X3) | ~iG1(X2,X3))))),
% 2.76/1.16 inference(rectify,[],[f19])).
% 2.76/1.16 tff(f21,plain,(
% 2.76/1.16 ? [X0 : $int,X1 : $int] : ~iG1(X1,X0)),
% 2.76/1.16 inference(rectify,[],[f17])).
% 2.76/1.16 tff(f22,plain,(
% 2.76/1.16 ~iG1(sK3,sK2)),
% 2.76/1.16 inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(X0,sK2),skolemize(X1,sK3)],[f21])).
% 2.76/1.16 tff(f23,plain,(
% 2.76/1.16 ! [X0 : $int,X1 : $int] : ($less(X1,X0) | iG0(X0,X1) = X1) & ! [X2 : $int,X3 : $int] : (~$less(X2,X3) | iG0(X3,X2) = X3)),
% 2.76/1.16 inference(rectify,[],[f18])).
% 2.76/1.16 tff(f25,plain,(
% 2.76/1.16 ( ! [X2 : $int,X3 : $int] : (iG1(X2,X3) | max(X2,X3) != X2 | $less(X2,X3)) )),
% 2.76/1.16 inference(cnf_transformation,[],[f20])).
% 2.76/1.16 tff(f26,plain,(
% 2.76/1.16 ( ! [X0 : $int,X1 : $int] : (max(X1,X0) = X1 | $less(X0,X1) | iG1(X1,X0)) )),
% 2.76/1.16 inference(cnf_transformation,[],[f20])).
% 2.76/1.16 tff(f28,plain,(
% 2.76/1.16 ~iG1(sK3,sK2)),
% 2.76/1.16 inference(cnf_transformation,[],[f22])).
% 2.76/1.16 tff(f29,plain,(
% 2.76/1.16 ( ! [X0 : $int,X1 : $int] : (iG0(X0,X1) = max(X1,X0)) )),
% 2.76/1.16 inference(cnf_transformation,[],[f8])).
% 2.76/1.16 tff(f30,plain,(
% 2.76/1.16 ( ! [X2 : $int,X3 : $int] : (~$less(X2,X3) | iG0(X3,X2) = X3) )),
% 2.76/1.16 inference(cnf_transformation,[],[f23])).
% 2.76/1.16 tff(f31,plain,(
% 2.76/1.16 ( ! [X0 : $int,X1 : $int] : ($less(X1,X0) | iG0(X0,X1) = X1) )),
% 2.76/1.16 inference(cnf_transformation,[],[f23])).
% 2.76/1.16 tff(f32,plain,(
% 2.76/1.16 ( ! [X0 : $int,X1 : $int] : (max(X1,X0) = X1 | $less(X1,X0)) )),
% 2.76/1.16 inference(definition_unfolding,[],[f31,f29])).
% 2.76/1.16 tff(f33,plain,(
% 2.76/1.16 ( ! [X2 : $int,X3 : $int] : (max(X2,X3) = X3 | ~$less(X2,X3)) )),
% 2.76/1.16 inference(definition_unfolding,[],[f30,f29])).
% 2.76/1.16 tff(f35,definition,(
% 2.76/1.16 spl4_1 <=> iG1(sK3,sK2)),
% 2.76/1.16 introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition])).
% 2.76/1.16 tff(f37,plain,(
% 2.76/1.16 ~iG1(sK3,sK2) | spl4_1),
% 2.76/1.16 inference(avatar_component_clause,[],[f35])).
% 2.76/1.16 tff(f38,plain,(
% 2.76/1.16 ~spl4_1),
% 2.76/1.16 inference(avatar_split_clause,[],[f28,f35])).
% 2.76/1.16 tff(f44,plain,(
% 2.76/1.16 ( ! [X2 : $int,X3 : $int] : (iG1(X2,X3) | $less(X2,X3)) )),
% 2.76/1.16 inference(forward_subsumption_resolution,[],[f25,f32])).
% 2.76/1.16 tff(f45,plain,(
% 2.76/1.16 $less(sK3,sK2) | spl4_1),
% 2.76/1.16 inference(resolution,[],[f44,f37])).
% 2.76/1.16 tff(f48,definition,(
% 2.76/1.16 spl4_2 <=> $less(sK3,sK2)),
% 2.76/1.16 introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition])).
% 2.76/1.16 tff(f51,plain,(
% 2.76/1.16 spl4_2 | spl4_1),
% 2.76/1.16 inference(avatar_split_clause,[],[f45,f35,f48])).
% 2.76/1.16 tff(f54,plain,(
% 2.76/1.16 ( ! [X0 : $int,X1 : $int] : (~$less(X0,X1) | $less(X1,X0) | iG1(X0,X1) | X0 = X1) )),
% 2.76/1.16 inference(superposition,[],[f33,f26])).
% 2.76/1.16 tff(f55,plain,(
% 2.76/1.16 ( ! [X0 : $int,X1 : $int] : (iG1(X0,X1) | X0 = X1 | $less(X1,X0)) )),
% 2.76/1.16 inference(forward_subsumption_resolution,[],[f54,f44])).
% 2.76/1.16 tff(f64,plain,(
% 2.76/1.16 sK3 = sK2 | $less(sK2,sK3) | spl4_1),
% 2.76/1.16 inference(resolution,[],[f55,f37])).
% 2.76/1.16 tff(f67,definition,(
% 2.76/1.16 spl4_3 <=> sK3 = sK2),
% 2.76/1.16 introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition])).
% 2.76/1.16 tff(f71,definition,(
% 2.76/1.16 spl4_4 <=> $less(sK2,sK3)),
% 2.76/1.16 introduced(definition,[new_symbols(definition,[spl4_4])],[avatar_definition])).
% 2.76/1.16 tff(f74,plain,(
% 2.76/1.16 spl4_3 | spl4_4 | spl4_1),
% 2.76/1.16 inference(avatar_split_clause,[],[f64,f35,f71,f67])).
% 2.76/1.16 tff(f75,plain,(
% 2.76/1.16 $false),
% 2.76/1.16 inference(avatar_smt_refutation,[],[f74,f51,f38])).
% 2.76/1.16 % SZS output end Proof for theBenchmark
% 2.76/1.16 % (4022930)------------------------------
% 2.76/1.16 % (4022930)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.76/1.16 % (4022930)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.76/1.16 % (4022930)CaDiCaL version: 2.1.3
% 2.76/1.16 % (4022930)Termination reason: Refutation
% 2.76/1.16 % (4022930)Time elapsed: 0.021 s
% 2.76/1.16 % (4022930)Peak memory usage: 116 MB
% 2.76/1.16 % (4022930)Instructions burned: 11 (million)
% 2.76/1.16 % (4022930)------------------------------
% 2.76/1.16 % (4022930)------------------------------
% 2.76/1.16 % (4022894)Success in time 0.296 s
% 2.76/1.16 % Vampire exiting
%------------------------------------------------------------------------------