0.00/0.04 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.00/0.08 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 180 THM 0.18/0.44 % Computer : n016.cluster.edu 0.18/0.44 % Model : x86_64 x86_64 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.18/0.44 % Memory : 8046.5625MB 0.18/0.44 % OS : Linux 6.8.0-71-generic 0.18/0.44 % CPULimit : 1440 0.18/0.44 % WCLimit : 180 0.18/0.44 % DateTime : Mon Jul 27 09:26:07 UTC 2026 0.18/0.44 % CPUTime : 0.18/0.44 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 180 THM 0.18/0.48 Running higher-order theorem proving 0.18/0.50 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 180 /export/starexec/sandbox2/benchmark/theBenchmark.p 0.26/0.57 % (1098499)Detected a higher-order problem, will run a greedy HOL sequence. 0.26/0.57 % (1098506)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3503745595:i=3:rtra=on:inj=on:ntd=on_1799 on theBenchmark for (1799ds/3Mi) 0.26/0.57 % (1098506)Instruction limit reached! 0.26/0.57 % (1098506)------------------------------ 0.26/0.57 % (1098506)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 0.26/0.57 % (1098506)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.26/0.57 % (1098506)CaDiCaL version: 2.1.3 0.26/0.57 % (1098506)Termination reason: Instruction limit 0.26/0.57 % (1098506)Termination phase: Saturation 0.26/0.57 % (1098506)Time elapsed: 0.003 s 0.26/0.57 % (1098506)Peak memory usage: 12 MB 0.26/0.57 % (1098506)Instructions burned: 5 (million) 0.26/0.57 % (1098510)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on 0.26/0.57 % (1098510)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on 0.26/0.57 % (1098504)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2317946125:s2a=on:i=87:rtra=on:ntd=on_1799 on theBenchmark for (1799ds/87Mi) 0.26/0.57 % (1098507)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=4286481410:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_1799 on theBenchmark for (1799ds/634Mi) 0.26/0.57 % (1098508)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1059005386:i=24:av=off:rtra=on_1799 on theBenchmark for (1799ds/24Mi) 0.26/0.57 % (1098509)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2574496860:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_1799 on theBenchmark for (1799ds/75Mi) 0.26/0.57 % (1098510)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=383811662:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_1799 on theBenchmark for (1799ds/157Mi) 0.26/0.57 % (1098505)lrs+10_16_si=on:nwc=1.5:random_seed=4262575660:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_1799 on theBenchmark for (1799ds/18Mi) 0.26/0.57 % (1098512)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=1371567897:i=2:hud=10:rtra=on_1799 on theBenchmark for (1799ds/2Mi) 0.26/0.57 % (1098507) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1098499-1098507"... 0.26/0.57 % (1098512)Instruction limit reached! 0.26/0.57 % (1098512)------------------------------ 0.26/0.57 % (1098512)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 0.26/0.57 % (1098512)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.26/0.57 % (1098512)CaDiCaL version: 2.1.3 0.26/0.57 % (1098512)Termination reason: Instruction limit 0.26/0.57 % (1098512)Termination phase: Saturation 0.26/0.57 % (1098512)Time elapsed: 0.002 s 0.26/0.57 % (1098512)Peak memory usage: 12 MB 0.26/0.57 % (1098512)Instructions burned: 3 (million) 0.26/0.57 % (1098504) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1098499-1098504"... 0.26/0.57 % (1098509) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1098499-1098509"... 0.26/0.57 % (1098510)Refutation not found, incomplete strategy 0.26/0.57 % (1098510)------------------------------ 0.26/0.57 % (1098510)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 0.26/0.57 % (1098510)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.26/0.57 % (1098510)CaDiCaL version: 2.1.3 0.26/0.57 % (1098510)Termination reason: Refutation not found, incomplete strategy 0.26/0.57 % (1098510)Time elapsed: 0.012 s 0.26/0.57 % (1098510)Peak memory usage: 12 MB 0.26/0.57 % (1098510)Instructions burned: 11 (million) 0.26/0.57 % (1098507)...printing done. 0.26/0.57 % (1098510)------------------------------ 0.26/0.57 % (1098510)------------------------------ 0.26/0.57 % (1098504)...printing done. 0.26/0.57 % (1098507)Refutation found. Thanks to Tanya! 0.26/0.57 % SZS status Theorem for theBenchmark 0.26/0.57 % SZS output start Proof for theBenchmark 0.26/0.57 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType). 0.26/0.57 thf(func_def_3, type, sK0: ((($i > $o) > ($i > $o) > $o) > $i > $o)). 0.26/0.57 thf(func_def_4, type, sK1: ((($i > $o) > ($i > $o) > $o) > $i > $o)). 0.26/0.57 thf(func_def_5, type, sK2: ((($i > $o) > ($i > $o) > $o) > $i > $o)). 0.26/0.57 thf(func_def_6, type, sK3: ((($i > $o) > ($i > $o) > $o) > $i > $o)). 0.26/0.57 thf(func_def_7, type, vNOT: ($o > $o)). 0.26/0.57 thf(func_def_8, type, db0: !>[X0: $tType]:(X0)). 0.26/0.57 thf(func_def_9, type, db1: !>[X0: $tType]:(X0)). 0.26/0.57 thf(func_def_10, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))). 0.26/0.57 thf(func_def_11, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))). 0.26/0.57 thf(f1,conjecture,( 0.26/0.57 ? [X0 : (($i > $o) > ($i > $o) > $o)] : (? [X7 : ($i > $o),X6 : ($i > $o)] : (X0 @ X6 @ X7) & ! [X3 : ($i > $o),X5 : ($i > $o),X4 : ($i > $o)] : (((X0 @ X3 @ X4) & (X0 @ X4 @ X5)) => (X0 @ X3 @ X5)) & ! [X3 : ($i > $o)] : (X0 @ X3 @ X3) & ? [X1 : ($i > $o),X2 : ($i > $o)] : ~(X0 @ X1 @ X2))), 0.26/0.57 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM120_2_pme)). 0.26/0.57 thf(f2,negated_conjecture,( 0.26/0.57 ~ ? [X0 : (($i > $o) > ($i > $o) > $o)] : (? [X7 : ($i > $o),X6 : ($i > $o)] : (X0 @ X6 @ X7) & ! [X3 : ($i > $o),X5 : ($i > $o),X4 : ($i > $o)] : (((X0 @ X3 @ X4) & (X0 @ X4 @ X5)) => (X0 @ X3 @ X5)) & ! [X3 : ($i > $o)] : (X0 @ X3 @ X3) & ? [X1 : ($i > $o),X2 : ($i > $o)] : ~(X0 @ X1 @ X2))), 0.26/0.57 inference(negated_conjecture,[status(cth)],[f1])). 0.26/0.57 thf(f3,plain,( 0.26/0.57 ~ ? [X0 : (($i > $o) > ($i > $o) > $o)] : (? [X1 : ($i > $o),X2 : ($i > $o)] : (X0 @ X2 @ X1) & ! [X3 : ($i > $o),X4 : ($i > $o),X5 : ($i > $o)] : (((X0 @ X3 @ X5) & (X0 @ X5 @ X4)) => (X0 @ X3 @ X4)) & ! [X6 : ($i > $o)] : (X0 @ X6 @ X6) & ? [X7 : ($i > $o),X8 : ($i > $o)] : ~(X0 @ X7 @ X8))), 0.26/0.57 inference(rectify,[],[f2])). 0.26/0.57 thf(f4,plain,( 0.26/0.57 ~ ? [X0 : (($i > $o) > ($i > $o) > $o)] : (? [X2 : ($i > $o),X1 : ($i > $o)] : (((X0 @ X2 @ X1)) = $true) & ! [X3 : ($i > $o),X5 : ($i > $o),X4 : ($i > $o)] : (((((X0 @ X5 @ X4)) = $true) & (((X0 @ X3 @ X5)) = $true)) => (((X0 @ X3 @ X4)) = $true)) & ! [X6 : ($i > $o)] : (((X0 @ X6 @ X6)) = $true) & ? [X7 : ($i > $o),X8 : ($i > $o)] : ~ (((X0 @ X7 @ X8)) = $true))), 0.26/0.57 inference(fool_elimination,[],[f3])). 0.26/0.57 thf(f5,plain,( 0.26/0.57 ~ ? [X0 : (($i > $o) > ($i > $o) > $o)] : (! [X6 : ($i > $o)] : (((X0 @ X6 @ X6)) = $true) & ! [X3 : ($i > $o),X5 : ($i > $o),X4 : ($i > $o)] : (((((X0 @ X5 @ X4)) = $true) & (((X0 @ X3 @ X5)) = $true)) => (((X0 @ X3 @ X4)) = $true)) & ? [X7 : ($i > $o),X8 : ($i > $o)] : (((X0 @ X7 @ X8)) != $true) & ? [X2 : ($i > $o),X1 : ($i > $o)] : (((X0 @ X2 @ X1)) = $true))), 0.26/0.57 inference(flattening,[],[f4])). 0.26/0.57 thf(f6,plain,( 0.26/0.57 ! [X0 : (($i > $o) > ($i > $o) > $o)] : (? [X6 : ($i > $o)] : (((X0 @ X6 @ X6)) != $true) | ? [X3 : ($i > $o),X5 : ($i > $o),X4 : ($i > $o)] : ((((X0 @ X3 @ X4)) != $true) & ((((X0 @ X5 @ X4)) = $true) & (((X0 @ X3 @ X5)) = $true))) | ! [X8 : ($i > $o),X7 : ($i > $o)] : (((X0 @ X7 @ X8)) = $true) | ! [X1 : ($i > $o),X2 : ($i > $o)] : (((X0 @ X2 @ X1)) != $true))), 0.26/0.57 inference(ennf_transformation,[],[f5])). 0.26/0.57 thf(f7,plain,( 0.26/0.57 ! [X0 : (($i > $o) > ($i > $o) > $o)] : (! [X8 : ($i > $o),X7 : ($i > $o)] : (((X0 @ X7 @ X8)) = $true) | ? [X6 : ($i > $o)] : (((X0 @ X6 @ X6)) != $true) | ? [X5 : ($i > $o),X4 : ($i > $o),X3 : ($i > $o)] : ((((X0 @ X5 @ X4)) = $true) & (((X0 @ X3 @ X4)) != $true) & (((X0 @ X3 @ X5)) = $true)) | ! [X1 : ($i > $o),X2 : ($i > $o)] : (((X0 @ X2 @ X1)) != $true))), 0.26/0.57 inference(flattening,[],[f6])). 0.26/0.57 thf(f8,plain,( 0.26/0.57 ! [X0 : (($i > $o) > ($i > $o) > $o)] : (! [X1 : ($i > $o),X2 : ($i > $o)] : (((X0 @ X2 @ X1)) = $true) | ? [X3 : ($i > $o)] : (((X0 @ X3 @ X3)) != $true) | ? [X4 : ($i > $o),X5 : ($i > $o),X6 : ($i > $o)] : ((((X0 @ X4 @ X5)) = $true) & (((X0 @ X6 @ X5)) != $true) & ($true = ((X0 @ X6 @ X4)))) | ! [X7 : ($i > $o),X8 : ($i > $o)] : (((X0 @ X8 @ X7)) != $true))), 0.26/0.57 inference(rectify,[],[f7])). 0.26/0.57 thf(f9,plain,( 0.26/0.57 ! [X0 : (($i > $o) > ($i > $o) > $o)] : (! [X1 : ($i > $o),X2 : ($i > $o)] : (((X0 @ X2 @ X1)) = $true) | (((X0 @ (sK0 @ X0) @ (sK0 @ X0))) != $true) | ((((X0 @ (sK1 @ X0) @ (sK2 @ X0))) = $true) & ($true != ((X0 @ (sK3 @ X0) @ (sK2 @ X0)))) & ($true = ((X0 @ (sK3 @ X0) @ (sK1 @ X0))))) | ! [X7 : ($i > $o),X8 : ($i > $o)] : (((X0 @ X8 @ X7)) != $true))), 0.26/0.58 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP,vAPP,vAPP]),skolemize(X6,sK3 @ X0),skolemize(X6,sK3 @ X0),skolemize(X6,sK3 @ X0),skolemize(X6,sK3 @ X0)],[f8])). 0.26/0.58 thf(f10,plain,( 0.26/0.58 ( ! [X2 : ($i > $o),X0 : (($i > $o) > ($i > $o) > $o),X1 : ($i > $o),X8 : ($i > $o),X7 : ($i > $o)] : (($true = ((X0 @ (sK3 @ X0) @ (sK1 @ X0)))) | (((X0 @ X2 @ X1)) = $true) | (((X0 @ (sK0 @ X0) @ (sK0 @ X0))) != $true) | (((X0 @ X8 @ X7)) != $true)) )), 0.26/0.58 inference(cnf_transformation,[],[f9])). 0.26/0.58 thf(f11,plain,( 0.26/0.58 ( ! [X2 : ($i > $o),X0 : (($i > $o) > ($i > $o) > $o),X1 : ($i > $o),X8 : ($i > $o),X7 : ($i > $o)] : (($true != ((X0 @ (sK3 @ X0) @ (sK2 @ X0)))) | (((X0 @ X2 @ X1)) = $true) | (((X0 @ (sK0 @ X0) @ (sK0 @ X0))) != $true) | (((X0 @ X8 @ X7)) != $true)) )), 0.26/0.58 inference(cnf_transformation,[],[f9])). 0.26/0.58 thf(f12,plain,( 0.26/0.58 ( ! [X2 : ($i > $o),X0 : (($i > $o) > ($i > $o) > $o),X1 : ($i > $o),X8 : ($i > $o),X7 : ($i > $o)] : ((((X0 @ (sK1 @ X0) @ (sK2 @ X0))) = $true) | (((X0 @ (sK0 @ X0) @ (sK0 @ X0))) != $true) | (((X0 @ X2 @ X1)) = $true) | (((X0 @ X8 @ X7)) != $true)) )), 0.26/0.58 inference(cnf_transformation,[],[f9])). 0.26/0.58 thf(f14,plain,( 0.26/0.58 ( ! [X2 : ($i > $o),X1 : ($i > $o),X8 : ($i > $o),X7 : ($i > $o)] : (((((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))) @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1))))) @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1))))))) = $true) | ((((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))) @ X2 @ X1)) = $true) | ((((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))) @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1))))) @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1))))))) != $true) | ($true != (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))) @ X8 @ X7)))) )), 0.26/0.58 inference(primitive_instantiation,[],[f10])). 0.26/0.58 thf(f26,plain,( 0.26/0.58 ( ! [X2 : ($i > $o),X1 : ($i > $o),X8 : ($i > $o),X7 : ($i > $o)] : (((((sK3 @ =) = (sK1 @ =))) = $true) | (((X2 = X1)) = $true) | ((((sK0 @ =) = (sK0 @ =))) != $true) | (((X8 = X7)) != $true)) )), 0.26/0.58 inference(beta-eta_normalization,[],[f14])). 0.26/0.58 thf(f27,plain,( 0.26/0.58 ( ! [X2 : ($i > $o),X1 : ($i > $o),X8 : ($i > $o),X7 : ($i > $o)] : ((((X8 = X7)) != $true) | (((X2 = X1)) = $true) | (((sK3 @ =)) = ((sK1 @ =))) | ((((sK0 @ =) = (sK0 @ =))) != $true)) )), 0.26/0.58 inference(equality_proxy_clausification,[],[f26])). 0.26/0.58 thf(f28,plain,( 0.26/0.58 ( ! [X2 : ($i > $o),X1 : ($i > $o),X8 : ($i > $o),X7 : ($i > $o)] : ((X7 != X8) | ((((sK0 @ =) = (sK0 @ =))) != $true) | (((sK3 @ =)) = ((sK1 @ =))) | (((X2 = X1)) = $true)) )), 0.26/0.58 inference(equality_proxy_clausification,[],[f27])). 0.26/0.58 thf(f29,plain,( 0.26/0.58 ( ! [X2 : ($i > $o),X1 : ($i > $o),X8 : ($i > $o),X7 : ($i > $o)] : ((((sK0 @ =)) != ((sK0 @ =))) | (X7 != X8) | (((sK3 @ =)) = ((sK1 @ =))) | (((X2 = X1)) = $true)) )), 0.26/0.58 inference(equality_proxy_clausification,[],[f28])). 0.26/0.58 thf(f30,plain,( 0.26/0.58 ( ! [X2 : ($i > $o),X1 : ($i > $o),X8 : ($i > $o),X7 : ($i > $o)] : ((((sK3 @ =)) = ((sK1 @ =))) | (X1 = X2) | (((sK0 @ =)) != ((sK0 @ =))) | (X7 != X8)) )), 0.26/0.58 inference(equality_proxy_clausification,[],[f29])). 0.26/0.58 thf(f31,plain,( 0.26/0.58 ( ! [X2 : ($i > $o),X1 : ($i > $o),X8 : ($i > $o),X7 : ($i > $o)] : ((X7 != X8) | (X1 = X2) | (((sK3 @ =)) = ((sK1 @ =)))) )), 0.26/0.58 inference(trivial_inequality_removal,[],[f30])). 0.26/0.58 thf(f46,definition,( 0.26/0.58 spl4_1 <=> ! [X2 : ($i > $o),X1 : ($i > $o)] : (X1 = X2)), 0.26/0.58 introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition])). 0.26/0.58 thf(f47,plain,( 0.26/0.58 ( ! [X2 : ($i > $o),X1 : ($i > $o)] : ((X1 = X2)) ) | ~spl4_1), 0.26/0.58 inference(avatar_component_clause,[],[f46])). 0.26/0.58 thf(f49,definition,( 0.26/0.58 spl4_2 <=> (((sK3 @ =)) = ((sK1 @ =)))), 0.26/0.58 introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition])). 0.26/0.58 thf(f51,plain,( 0.26/0.58 (((sK3 @ =)) = ((sK1 @ =))) | ~spl4_2), 0.26/0.58 inference(avatar_component_clause,[],[f49])). 0.26/0.58 thf(f53,definition,( 0.26/0.58 spl4_3 <=> ! [X8 : ($i > $o),X7 : ($i > $o)] : (X7 != X8)), 0.26/0.58 introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition])). 0.26/0.58 thf(f54,plain,( 0.26/0.58 ( ! [X8 : ($i > $o),X7 : ($i > $o)] : ((X7 != X8)) ) | ~spl4_3), 0.26/0.58 inference(avatar_component_clause,[],[f53])). 0.26/0.58 thf(f55,plain,( 0.26/0.58 spl4_1 | spl4_2 | spl4_3), 0.26/0.58 inference(avatar_split_clause,[],[f31,f53,f49,f46])). 0.26/0.58 thf(f66,plain,( 0.26/0.58 ( ! [X2 : ($i > $o),X1 : ($i > $o),X8 : ($i > $o),X7 : ($i > $o)] : (((((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))) @ X2 @ X1)) = $true) | ($true != (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))) @ X8 @ X7))) | ((((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))) @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1))))) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1))))))) != $true) | ((((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))) @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1))))) @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1))))))) != $true)) )), 0.26/0.58 inference(primitive_instantiation,[],[f11])). 0.26/0.58 thf(f73,plain,( 0.26/0.58 ( ! [X2 : ($i > $o),X1 : ($i > $o),X8 : ($i > $o),X7 : ($i > $o)] : (($true != (((sK3 @ =) = (sK2 @ =)))) | (((X8 = X7)) != $true) | ((((sK0 @ =) = (sK0 @ =))) != $true) | (((X2 = X1)) = $true)) )), 0.26/0.58 inference(beta-eta_normalization,[],[f66])). 0.26/0.58 thf(f74,plain,( 0.26/0.58 ( ! [X2 : ($i > $o),X1 : ($i > $o),X8 : ($i > $o),X7 : ($i > $o)] : ((((X8 = X7)) != $true) | (((sK3 @ =)) != ((sK2 @ =))) | ((((sK0 @ =) = (sK0 @ =))) != $true) | (((X2 = X1)) = $true)) )), 0.26/0.58 inference(equality_proxy_clausification,[],[f73])). 0.26/0.58 thf(f75,plain,( 0.26/0.58 ( ! [X2 : ($i > $o),X1 : ($i > $o),X8 : ($i > $o),X7 : ($i > $o)] : (((((sK0 @ =) = (sK0 @ =))) != $true) | (((X2 = X1)) = $true) | (((sK3 @ =)) != ((sK2 @ =))) | (X7 != X8)) )), 0.26/0.58 inference(equality_proxy_clausification,[],[f74])). 0.26/0.58 thf(f76,plain,( 0.26/0.58 ( ! [X2 : ($i > $o),X1 : ($i > $o),X8 : ($i > $o),X7 : ($i > $o)] : ((((X2 = X1)) = $true) | (((sK3 @ =)) != ((sK2 @ =))) | (X7 != X8) | (((sK0 @ =)) != ((sK0 @ =)))) )), 0.26/0.58 inference(equality_proxy_clausification,[],[f75])). 0.26/0.58 thf(f77,plain,( 0.26/0.58 ( ! [X2 : ($i > $o),X1 : ($i > $o),X8 : ($i > $o),X7 : ($i > $o)] : ((((sK3 @ =)) != ((sK2 @ =))) | (X7 != X8) | (X1 = X2) | (((sK0 @ =)) != ((sK0 @ =)))) )), 0.26/0.58 inference(equality_proxy_clausification,[],[f76])). 0.26/0.58 thf(f78,plain,( 0.26/0.58 ( ! [X2 : ($i > $o),X1 : ($i > $o),X8 : ($i > $o),X7 : ($i > $o)] : ((((sK3 @ =)) != ((sK2 @ =))) | (X1 = X2) | (X7 != X8)) )), 0.26/0.58 inference(trivial_inequality_removal,[],[f77])). 0.26/0.58 thf(f104,plain,( 0.26/0.58 ( ! [X2 : ($i > $o),X1 : ($i > $o),X8 : ($i > $o),X7 : ($i > $o)] : ((((sK1 @ =)) != ((sK2 @ =))) | (X7 != X8) | (X1 = X2)) ) | ~spl4_2), 0.26/0.58 inference(forward_demodulation,[],[f78,f51])). 0.26/0.58 thf(f106,definition,( 0.26/0.58 spl4_4 <=> (((sK1 @ =)) = ((sK2 @ =)))), 0.26/0.58 introduced(definition,[new_symbols(definition,[spl4_4])],[avatar_definition])). 0.26/0.58 thf(f110,plain,( 0.26/0.58 spl4_1 | ~spl4_4 | spl4_3 | ~spl4_2), 0.26/0.58 inference(avatar_split_clause,[],[f104,f49,f53,f106,f46])). 0.26/0.58 thf(f111,plain,( 0.26/0.58 ( ! [X2 : ($i > $o),X1 : ($i > $o),X8 : ($i > $o),X7 : ($i > $o)] : (((((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))) @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1))))) @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1))))))) != $true) | ($true = (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))) @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1))))) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))))))) | ($true != (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))) @ X8 @ X7))) | ((((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))) @ X2 @ X1)) = $true)) )), 0.26/0.58 inference(primitive_instantiation,[],[f12])). 0.26/0.58 thf(f136,plain,( 0.26/0.58 ( ! [X2 : ($i > $o),X1 : ($i > $o),X8 : ($i > $o),X7 : ($i > $o)] : (((((sK0 @ =) = (sK0 @ =))) != $true) | (((X8 = X7)) != $true) | ($true = (((sK1 @ =) = (sK2 @ =)))) | (((X2 = X1)) = $true)) )), 0.26/0.58 inference(beta-eta_normalization,[],[f111])). 0.26/0.58 thf(f137,plain,( 0.26/0.58 ( ! [X2 : ($i > $o),X1 : ($i > $o),X8 : ($i > $o),X7 : ($i > $o)] : ((((X8 = X7)) != $true) | ($true = (((sK1 @ =) = (sK2 @ =)))) | (((X2 = X1)) = $true) | (((sK0 @ =)) != ((sK0 @ =)))) )), 0.26/0.58 inference(equality_proxy_clausification,[],[f136])). 0.26/0.58 thf(f138,plain,( 0.26/0.58 ( ! [X2 : ($i > $o),X1 : ($i > $o),X8 : ($i > $o),X7 : ($i > $o)] : (($true = (((sK1 @ =) = (sK2 @ =)))) | (X7 != X8) | (((X2 = X1)) = $true) | (((sK0 @ =)) != ((sK0 @ =)))) )), 0.26/0.58 inference(equality_proxy_clausification,[],[f137])). 0.26/0.58 thf(f139,plain,( 0.26/0.58 ( ! [X2 : ($i > $o),X1 : ($i > $o),X8 : ($i > $o),X7 : ($i > $o)] : ((X7 != X8) | (((sK0 @ =)) != ((sK0 @ =))) | (((sK1 @ =)) = ((sK2 @ =))) | (((X2 = X1)) = $true)) )), 0.26/0.58 inference(equality_proxy_clausification,[],[f138])). 0.26/0.58 thf(f140,plain,( 0.26/0.58 ( ! [X2 : ($i > $o),X1 : ($i > $o),X8 : ($i > $o),X7 : ($i > $o)] : ((X7 != X8) | (((sK1 @ =)) = ((sK2 @ =))) | (((sK0 @ =)) != ((sK0 @ =))) | (X1 = X2)) )), 0.26/0.58 inference(equality_proxy_clausification,[],[f139])). 0.26/0.58 thf(f141,plain,( 0.26/0.58 ( ! [X2 : ($i > $o),X1 : ($i > $o),X8 : ($i > $o),X7 : ($i > $o)] : ((X7 != X8) | (((sK1 @ =)) = ((sK2 @ =))) | (X1 = X2)) )), 0.26/0.58 inference(trivial_inequality_removal,[],[f140])). 0.26/0.58 thf(f142,plain,( 0.26/0.58 spl4_1 | spl4_3 | spl4_4), 0.26/0.58 inference(avatar_split_clause,[],[f141,f106,f53,f46])). 0.26/0.58 thf(f143,plain,( 0.26/0.58 ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $o)] : ((((X1 @ X3)) = ((X2 @ X3)))) ) | ~spl4_1), 0.26/0.58 inference(argument_congruence,[],[f47])). 0.26/0.58 thf(f144,plain,( 0.26/0.58 ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $o)] : ((((X2 @ X3)) = $false) | (((X1 @ X3)) = $true)) ) | ~spl4_1), 0.26/0.58 inference(iff_proxy_clausification,[],[f143])). 0.26/0.58 thf(f146,plain,( 0.26/0.58 ( ! [X3 : $i,X1 : ($i > $o)] : (((((^[Y0 : $i]: ($true)) @ X3)) = $false) | (((X1 @ X3)) = $true)) ) | ~spl4_1), 0.26/0.58 inference(primitive_instantiation,[],[f144])). 0.26/0.58 thf(f153,plain,( 0.26/0.58 ( ! [X3 : $i,X1 : ($i > $o)] : (($true = $false) | (((X1 @ X3)) = $true)) ) | ~spl4_1), 0.26/0.58 inference(beta-eta_normalization,[],[f146])). 0.26/0.58 thf(f154,plain,( 0.26/0.58 ( ! [X3 : $i,X1 : ($i > $o)] : ((((X1 @ X3)) = $true)) ) | ~spl4_1), 0.26/0.58 inference(trivial_inequality_removal,[],[f153])). 0.26/0.58 thf(f160,plain,( 0.26/0.58 ( ! [X3 : $i] : (((((^[Y0 : $i]: ($false)) @ X3)) = $true)) ) | ~spl4_1), 0.26/0.58 inference(primitive_instantiation,[],[f154])). 0.26/0.58 thf(f170,plain,( 0.26/0.58 ($true = $false) | ~spl4_1), 0.26/0.58 inference(beta-eta_normalization,[],[f160])). 0.26/0.58 thf(f171,plain,( 0.26/0.58 $false | ~spl4_1), 0.26/0.58 inference(trivial_inequality_removal,[],[f170])). 0.26/0.58 thf(f172,plain,( 0.26/0.58 ~spl4_1), 0.26/0.58 inference(avatar_contradiction_clause,[],[f171])). 0.26/0.58 thf(f176,plain,( 0.26/0.58 $false | ~spl4_3), 0.26/0.58 inference(flex-flex_simplification,[],[f54])). 0.26/0.58 thf(f177,plain,( 0.26/0.58 ~spl4_3), 0.26/0.58 inference(avatar_contradiction_clause,[],[f176])). 0.26/0.58 cnf(s1, plain, spl4_1 | spl4_2 | spl4_3, inference(sat_conversion,[],[f55])). 0.26/0.58 cnf(s3, plain, spl4_1 | ~spl4_2 | spl4_3 | ~spl4_4, inference(sat_conversion,[],[f110])). 0.26/0.58 cnf(s4, plain, spl4_1 | spl4_3 | spl4_4, inference(sat_conversion,[],[f142])). 0.26/0.58 cnf(s5, plain, ~spl4_1, inference(sat_conversion,[],[f172])). 0.26/0.58 cnf(s6, plain, ~spl4_3, inference(sat_conversion,[],[f177])). 0.26/0.58 cnf(s7, plain, spl4_4, inference(rat,[],[s4,s6,s5])). 0.26/0.58 cnf(s8, plain, ~spl4_2, inference(rat,[],[s3,s7,s6,s5])). 0.26/0.58 cnf(s9, plain, $false, inference(rat,[],[s1,s6,s8,s5])). 0.26/0.58 thf(f178,plain,( 0.26/0.58 $false), 0.26/0.58 inference(avatar_sat_refutation,[],[s9])). 0.26/0.58 % SZS output end Proof for theBenchmark 0.26/0.58 % (1098507)------------------------------ 0.26/0.58 % (1098507)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 0.26/0.58 % (1098507)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.26/0.58 % (1098507)CaDiCaL version: 2.1.3 0.26/0.58 % (1098507)Termination reason: Refutation 0.26/0.58 % (1098507)Time elapsed: 0.012 s 0.26/0.58 % (1098507)Peak memory usage: 13 MB 0.26/0.58 % (1098507)Instructions burned: 11 (million) 0.26/0.58 % (1098499)Success in time 0.059 s 0.26/0.58 % Vampire exiting 0.26/0.58 EOF