0.04/0.09 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.04/0.09 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s 0.08/0.29 % Computer : n006.cluster.edu 0.08/0.29 % Model : x86_64 x86_64 0.08/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.08/0.29 % Memory : 8042.1875MB 0.08/0.29 % OS : Linux 3.10.0-693.el7.x86_64 0.08/0.29 % CPULimit : 300 0.08/0.29 % WCLimit : 300 0.08/0.29 % DateTime : Fri Jul 5 04:28:09 EDT 2024 0.08/0.29 % CPUTime : 0.08/0.30 This is a THF_ problem 0.08/0.30 Running vampire_ho --cores 8 --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol -m 12000 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p 0.16/0.32 % (10667)lrs+10_1:2_cnfonf=off:hud=1:inj=on:i=36:si=on:rtra=on_0 on theBenchmark for (2999ds/36Mi) 0.16/0.32 % (10672)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi) 0.16/0.32 % (10666)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on theBenchmark for (2999ds/96Mi) 0.16/0.32 % (10668)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=34:si=on:rtra=on_0 on theBenchmark for (2999ds/34Mi) 0.16/0.32 % (10669)lrs+1002_1:1_au=on:s2a=on:s2agt=32:sgt=8:ss=axioms:i=385:si=on:rtra=on_0 on theBenchmark for (2999ds/385Mi) 0.16/0.32 % (10673)lrs+1002_1:14_au=on:bd=off:e2e=on:fde=unused:sac=on:sos=on:i=915:si=on:rtra=on_0 on theBenchmark for (2999ds/915Mi) 0.16/0.32 % (10670)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on theBenchmark for (2999ds/17Mi) 0.16/0.32 % (10671)ott+1010_1:1_cnfonf=lazy_gen:fe=off:kws=inv_arity:plsq=on:plsqc=1:plsqr=32,1:prag=on:sp=const_frequency:i=74:si=on:rtra=on_0 on theBenchmark for (2999ds/74Mi) 0.16/0.32 % (10672)Instruction limit reached! 0.16/0.32 % (10672)------------------------------ 0.16/0.32 % (10672)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.16/0.32 % (10672)Termination reason: Unknown 0.16/0.32 % (10672)Termination phase: Saturation 0.16/0.32 0.16/0.32 % (10672)Memory used [KB]: 5500 0.16/0.32 % (10672)Time elapsed: 0.004 s 0.16/0.32 % (10672)Instructions burned: 5 (million) 0.16/0.32 % (10672)------------------------------ 0.16/0.32 % (10672)------------------------------ 0.16/0.33 % (10670)Instruction limit reached! 0.16/0.33 % (10670)------------------------------ 0.16/0.33 % (10670)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.16/0.33 % (10670)Termination reason: Unknown 0.16/0.33 % (10670)Termination phase: Saturation 0.16/0.33 0.16/0.33 % (10670)Memory used [KB]: 5756 0.16/0.33 % (10670)Time elapsed: 0.012 s 0.16/0.33 % (10670)Instructions burned: 18 (million) 0.16/0.33 % (10670)------------------------------ 0.16/0.33 % (10670)------------------------------ 0.16/0.33 % (10674)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on theBenchmark for (2999ds/21Mi) 0.16/0.34 % (10668)Instruction limit reached! 0.16/0.34 % (10668)------------------------------ 0.16/0.34 % (10668)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.16/0.34 % (10668)Termination reason: Unknown 0.16/0.34 % (10668)Termination phase: Saturation 0.16/0.34 0.16/0.34 % (10668)Memory used [KB]: 5628 0.16/0.34 % (10668)Time elapsed: 0.021 s 0.16/0.34 % (10668)Instructions burned: 35 (million) 0.16/0.34 % (10668)------------------------------ 0.16/0.34 % (10668)------------------------------ 0.16/0.34 % (10667)Instruction limit reached! 0.16/0.34 % (10667)------------------------------ 0.16/0.34 % (10667)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.16/0.34 % (10667)Termination reason: Unknown 0.16/0.34 % (10667)Termination phase: Saturation 0.16/0.34 0.16/0.34 % (10667)Memory used [KB]: 5756 0.16/0.34 % (10667)Time elapsed: 0.022 s 0.16/0.34 % (10667)Instructions burned: 37 (million) 0.16/0.34 % (10667)------------------------------ 0.16/0.34 % (10667)------------------------------ 0.16/0.34 % (10675)lrs-3_1:1024_cbe=off:chr=on:tnu=1:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi) 0.16/0.35 % (10674)Instruction limit reached! 0.16/0.35 % (10674)------------------------------ 0.16/0.35 % (10674)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.16/0.35 % (10674)Termination reason: Unknown 0.16/0.35 % (10674)Termination phase: Saturation 0.16/0.35 0.16/0.35 % (10674)Memory used [KB]: 5628 0.16/0.35 % (10674)Time elapsed: 0.013 s 0.16/0.35 % (10674)Instructions burned: 21 (million) 0.16/0.35 % (10674)------------------------------ 0.16/0.35 % (10674)------------------------------ 0.16/0.35 % (10675)Instruction limit reached! 0.16/0.35 % (10675)------------------------------ 0.16/0.35 % (10675)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.16/0.35 % (10675)Termination reason: Unknown 0.16/0.35 % (10675)Termination phase: Saturation 0.16/0.35 0.16/0.35 % (10675)Memory used [KB]: 5500 0.16/0.35 % (10675)Time elapsed: 0.006 s 0.16/0.35 % (10675)Instructions burned: 8 (million) 0.16/0.35 % (10675)------------------------------ 0.16/0.35 % (10675)------------------------------ 0.16/0.35 % (10676)dis+2_1:1_bd=off:e2e=on:hud=1:nm=3:piset=or:prag=on:s2a=on:sp=const_max:i=1021:si=on:rtra=on_0 on theBenchmark for (2999ds/1021Mi) 0.16/0.35 % (10677)lrs-1004_1:1_au=on:bsd=on:cbe=off:cnfonf=off:fe=axiom:fsd=on:i=71:si=on:rtra=on_0 on theBenchmark for (2999ds/71Mi) 0.16/0.36 % (10671)Instruction limit reached! 0.16/0.36 % (10671)------------------------------ 0.16/0.36 % (10671)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.16/0.36 % (10671)Termination reason: Unknown 0.16/0.36 % (10671)Termination phase: Saturation 0.16/0.36 0.16/0.36 % (10671)Memory used [KB]: 5756 0.16/0.36 % (10671)Time elapsed: 0.040 s 0.16/0.36 % (10671)Instructions burned: 74 (million) 0.16/0.36 % (10671)------------------------------ 0.16/0.36 % (10671)------------------------------ 0.16/0.36 % (10678)lrs-1010_1:50_au=on:awrs=converge:awrsf=430:bet=on:cbe=off:cha=on:nm=20:sac=on:i=9:si=on:rtra=on_0 on theBenchmark for (2999ds/9Mi) 0.16/0.36 % (10679)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=1044:si=on:rtra=on_0 on theBenchmark for (2999ds/1044Mi) 0.16/0.36 % (10678)Instruction limit reached! 0.16/0.36 % (10678)------------------------------ 0.16/0.36 % (10678)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.16/0.36 % (10678)Termination reason: Unknown 0.16/0.36 % (10678)Termination phase: Saturation 0.16/0.36 0.16/0.36 % (10678)Memory used [KB]: 5500 0.16/0.36 % (10678)Time elapsed: 0.006 s 0.16/0.36 % (10678)Instructions burned: 9 (million) 0.16/0.36 % (10678)------------------------------ 0.16/0.36 % (10678)------------------------------ 0.16/0.37 % (10666)Instruction limit reached! 0.16/0.37 % (10666)------------------------------ 0.16/0.37 % (10666)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.16/0.37 % (10666)Termination reason: Unknown 0.16/0.37 % (10666)Termination phase: Saturation 0.16/0.37 0.16/0.37 % (10666)Memory used [KB]: 5884 0.16/0.37 % (10666)Time elapsed: 0.052 s 0.16/0.37 % (10666)Instructions burned: 97 (million) 0.16/0.37 % (10666)------------------------------ 0.16/0.37 % (10666)------------------------------ 0.16/0.37 % (10680)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=128:si=on:rtra=on_0 on theBenchmark for (2999ds/128Mi) 0.16/0.38 % (10681)lrs+21_1:1_cond=on:e2e=on:i=61:si=on:rtra=on_0 on theBenchmark for (2999ds/61Mi) 0.16/0.38 % (10682)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=14:si=on:rtra=on_0 on theBenchmark for (2999ds/14Mi) 0.16/0.39 % (10677)Instruction limit reached! 0.16/0.39 % (10677)------------------------------ 0.16/0.39 % (10677)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.16/0.39 % (10677)Termination reason: Unknown 0.16/0.39 % (10677)Termination phase: Saturation 0.16/0.39 0.16/0.39 % (10677)Memory used [KB]: 5756 0.16/0.39 % (10677)Time elapsed: 0.038 s 0.16/0.39 % (10677)Instructions burned: 71 (million) 0.16/0.39 % (10677)------------------------------ 0.16/0.39 % (10677)------------------------------ 0.16/0.39 % (10682)Instruction limit reached! 0.16/0.39 % (10682)------------------------------ 0.16/0.39 % (10682)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.16/0.39 % (10682)Termination reason: Unknown 0.16/0.39 % (10682)Termination phase: Saturation 0.16/0.39 0.16/0.39 % (10682)Memory used [KB]: 5500 0.16/0.39 % (10682)Time elapsed: 0.009 s 0.16/0.39 % (10682)Instructions burned: 14 (million) 0.16/0.39 % (10682)------------------------------ 0.16/0.39 % (10682)------------------------------ 0.16/0.40 % (10683)lrs+2_5:1_cnfonf=lazy_not_be_gen:hud=10:inj=on:ntd=on:tnu=1:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi) 0.16/0.40 % (10683)Instruction limit reached! 0.16/0.40 % (10683)------------------------------ 0.16/0.40 % (10683)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.16/0.40 % (10683)Termination reason: Unknown 0.16/0.40 % (10683)Termination phase: shuffling 0.16/0.40 0.16/0.40 % (10683)Memory used [KB]: 895 0.16/0.40 % (10683)Time elapsed: 0.002 s 0.16/0.40 % (10683)Instructions burned: 2 (million) 0.16/0.40 % (10683)------------------------------ 0.16/0.40 % (10683)------------------------------ 0.16/0.40 % (10684)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on theBenchmark for (2999ds/1041Mi) 0.16/0.40 % (10681)Instruction limit reached! 0.16/0.40 % (10681)------------------------------ 0.16/0.40 % (10681)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.16/0.40 % (10681)Termination reason: Unknown 0.16/0.40 % (10681)Termination phase: Saturation 0.16/0.40 0.16/0.40 % (10681)Memory used [KB]: 5756 0.16/0.40 % (10681)Time elapsed: 0.052 s 0.16/0.40 % (10681)Instructions burned: 62 (million) 0.16/0.40 % (10681)------------------------------ 0.16/0.40 % (10681)------------------------------ 0.16/0.41 % (10685)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on theBenchmark for (2998ds/11Mi) 0.16/0.42 % (10686)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on theBenchmark for (2998ds/140Mi) 0.16/0.42 % (10685)Instruction limit reached! 0.16/0.42 % (10685)------------------------------ 0.16/0.42 % (10685)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.16/0.42 % (10685)Termination reason: Unknown 0.16/0.42 % (10685)Termination phase: Saturation 0.16/0.42 0.16/0.42 % (10685)Memory used [KB]: 5500 0.16/0.42 % (10685)Time elapsed: 0.007 s 0.16/0.42 % (10685)Instructions burned: 12 (million) 0.16/0.42 % (10685)------------------------------ 0.16/0.42 % (10685)------------------------------ 0.16/0.42 % (10686)Refutation not found, incomplete strategy 0.16/0.42 % (10686)------------------------------ 0.16/0.42 % (10686)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.16/0.42 % (10686)Termination reason: Refutation not found, incomplete strategy 0.16/0.42 0.16/0.42 0.16/0.43 % (10686)Memory used [KB]: 5628 0.16/0.43 % (10686)Time elapsed: 0.009 s 0.16/0.43 % (10686)Instructions burned: 14 (million) 0.16/0.43 % (10686)------------------------------ 0.16/0.43 % (10686)------------------------------ 0.16/0.43 % (10680)Instruction limit reached! 0.16/0.43 % (10680)------------------------------ 0.16/0.43 % (10680)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.16/0.43 % (10680)Termination reason: Unknown 0.16/0.43 % (10680)Termination phase: Saturation 0.16/0.43 0.16/0.43 % (10680)Memory used [KB]: 6396 0.16/0.43 % (10680)Time elapsed: 0.064 s 0.16/0.43 % (10680)Instructions burned: 129 (million) 0.16/0.43 % (10680)------------------------------ 0.16/0.43 % (10680)------------------------------ 0.16/0.43 % (10687)dis+1002_1:1_bd=preordered:c=on:cbe=off:cnfonf=lazy_not_gen_be_off:hud=10:ixr=off:prag=on:i=26:si=on:rtra=on_0 on theBenchmark for (2998ds/26Mi) 0.16/0.44 % (10688)lrs+1002_1:4_au=on:av=off:bsr=on:cbe=off:nm=2:i=56:si=on:rtra=on_0 on theBenchmark for (2998ds/56Mi) 0.16/0.44 % (10687)Instruction limit reached! 0.16/0.44 % (10687)------------------------------ 0.16/0.44 % (10687)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.16/0.44 % (10687)Termination reason: Unknown 0.16/0.44 % (10687)Termination phase: Saturation 0.16/0.44 0.16/0.44 % (10687)Memory used [KB]: 5500 0.16/0.44 % (10687)Time elapsed: 0.013 s 0.16/0.44 % (10687)Instructions burned: 27 (million) 0.16/0.44 % (10687)------------------------------ 0.16/0.44 % (10687)------------------------------ 0.16/0.45 % (10689)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on theBenchmark for (2998ds/275Mi) 0.16/0.45 % (10684)First to succeed. 0.16/0.46 % (10690)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (2998ds/3Mi) 0.16/0.46 % (10690)Instruction limit reached! 0.16/0.46 % (10690)------------------------------ 0.16/0.46 % (10690)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.16/0.46 % (10690)Termination reason: Unknown 0.16/0.46 % (10690)Termination phase: Property scanning 0.16/0.46 0.16/0.46 % (10690)Memory used [KB]: 1023 0.16/0.46 % (10690)Time elapsed: 0.003 s 0.16/0.46 % (10690)Instructions burned: 3 (million) 0.16/0.46 % (10690)------------------------------ 0.16/0.46 % (10690)------------------------------ 0.16/0.46 % (10684)Refutation found. Thanks to Tanya! 0.16/0.46 % SZS status Theorem for theBenchmark 0.16/0.46 % SZS output start Proof for theBenchmark 0.16/0.46 thf(type_def_5, type, a: $tType). 0.16/0.46 thf(func_def_0, type, a: $tType). 0.16/0.46 thf(func_def_1, type, cP: a > a > a). 0.16/0.46 thf(func_def_2, type, cG: a > $o). 0.16/0.46 thf(func_def_3, type, cX: a > $o). 0.16/0.46 thf(func_def_4, type, cR: a > a). 0.16/0.46 thf(func_def_5, type, cL: a > a). 0.16/0.46 thf(func_def_6, type, cF: a > $o). 0.16/0.46 thf(func_def_7, type, cZ: a). 0.16/0.46 thf(func_def_24, type, ph1: !>[X0: $tType]:(X0)). 0.16/0.46 thf(func_def_25, type, sK2: a). 0.16/0.46 thf(func_def_26, type, sK3: a). 0.16/0.46 thf(func_def_27, type, sK4: a). 0.16/0.46 thf(func_def_28, type, sK5: a). 0.16/0.46 thf(func_def_29, type, sK6: a > $o). 0.16/0.46 thf(func_def_30, type, sK7: a). 0.16/0.46 thf(func_def_31, type, sK8: a). 0.16/0.46 thf(func_def_32, type, sK9: a > $o). 0.16/0.46 thf(func_def_33, type, sK10: a). 0.16/0.46 thf(f422,plain,( 0.16/0.46 $false), 0.16/0.46 inference(avatar_sat_refutation,[],[f39,f46,f50,f63,f98,f249,f255,f421])). 0.16/0.46 thf(f421,plain,( 0.16/0.46 ~spl0_1 | ~spl0_6), 0.16/0.46 inference(avatar_contradiction_clause,[],[f420])). 0.16/0.46 thf(f420,plain,( 0.16/0.46 $false | (~spl0_1 | ~spl0_6)), 0.16/0.46 inference(trivial_inequality_removal,[],[f419])). 0.16/0.46 thf(f419,plain,( 0.16/0.46 ($true = $false) | (~spl0_1 | ~spl0_6)), 0.16/0.46 inference(boolean_simplification,[],[f418])). 0.16/0.46 thf(f418,plain,( 0.16/0.46 ($true = (~ $true)) | (~spl0_1 | ~spl0_6)), 0.16/0.46 inference(forward_demodulation,[],[f416,f417])). 0.16/0.46 thf(f417,plain,( 0.16/0.46 ($true = (sK9 @ sK7)) | (~spl0_1 | ~spl0_6)), 0.16/0.46 inference(boolean_simplification,[],[f415])). 0.16/0.46 thf(f415,plain,( 0.16/0.46 ($true = ($true & (sK9 @ sK7))) | (~spl0_1 | ~spl0_6)), 0.16/0.46 inference(backward_demodulation,[],[f380,f413])). 0.16/0.46 thf(f413,plain,( 0.16/0.46 ($true = (!! @ a @ (^[Y0 : a]: ((sK9 @ Y0) => (sK9 @ (cL @ Y0)))))) | (~spl0_1 | ~spl0_6)), 0.16/0.46 inference(binary_proxy_clausification,[],[f380])). 0.16/0.46 thf(f380,plain,( 0.16/0.46 ($true = ((!! @ a @ (^[Y0 : a]: ((sK9 @ Y0) => (sK9 @ (cL @ Y0))))) & (sK9 @ sK7))) | (~spl0_1 | ~spl0_6)), 0.16/0.46 inference(binary_proxy_clausification,[],[f378])). 0.16/0.46 thf(f378,plain,( 0.16/0.46 ($false = (((!! @ a @ (^[Y0 : a]: ((sK9 @ Y0) => (sK9 @ (cL @ Y0))))) & (sK9 @ sK7)) => (?? @ a @ (^[Y0 : a]: ((sK9 @ Y0) & ((cR @ Y0) = sK8)))))) | (~spl0_1 | ~spl0_6)), 0.16/0.46 inference(beta_eta_normalization,[],[f375])). 0.16/0.46 thf(f375,plain,( 0.16/0.46 (((^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (Y0 @ (cL @ Y1))))) & (Y0 @ sK7)) => (?? @ a @ (^[Y1 : a]: ((Y0 @ Y1) & ((cR @ Y1) = sK8)))))) @ sK9) = $false) | (~spl0_1 | ~spl0_6)), 0.16/0.46 inference(sigma_clausification,[],[f368])). 0.16/0.46 thf(f368,plain,( 0.16/0.46 ($false = (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (Y0 @ (cL @ Y1))))) & (Y0 @ sK7)) => (?? @ a @ (^[Y1 : a]: ((Y0 @ Y1) & ((cR @ Y1) = sK8)))))))) | (~spl0_1 | ~spl0_6)), 0.16/0.46 inference(not_proxy_clausification,[],[f360])). 0.16/0.46 thf(f360,plain,( 0.16/0.46 ((~ (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (Y0 @ (cL @ Y1))))) & (Y0 @ sK7)) => (?? @ a @ (^[Y1 : a]: ((Y0 @ Y1) & ((cR @ Y1) = sK8)))))))) = $true) | (~spl0_1 | ~spl0_6)), 0.16/0.46 inference(boolean_simplification,[],[f359])). 0.16/0.46 thf(f359,plain,( 0.16/0.46 ($true = ((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (Y0 @ (cL @ Y1))))) & (Y0 @ sK7)) => (?? @ a @ (^[Y1 : a]: ((Y0 @ Y1) & ((cR @ Y1) = sK8))))))) => $false)) | (~spl0_1 | ~spl0_6)), 0.16/0.46 inference(superposition,[],[f305,f358])). 0.16/0.46 thf(f358,plain,( 0.16/0.46 ($false = (cX @ sK8)) | (~spl0_1 | ~spl0_6)), 0.16/0.46 inference(boolean_simplification,[],[f357])). 0.16/0.46 thf(f357,plain,( 0.16/0.46 (($true => (cX @ sK8)) = $false) | (~spl0_1 | ~spl0_6)), 0.16/0.46 inference(backward_demodulation,[],[f351,f356])). 0.16/0.46 thf(f356,plain,( 0.16/0.46 ((!! @ (a > $o) @ (^[Y0 : a > $o]: (((Y0 @ sK7) & (!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (Y0 @ (cL @ Y1)))))) => (?? @ a @ (^[Y1 : a]: ((Y0 @ Y1) & ((cR @ Y1) = sK8))))))) = $true) | (~spl0_1 | ~spl0_6)), 0.16/0.46 inference(binary_proxy_clausification,[],[f351])). 0.16/0.46 thf(f351,plain,( 0.16/0.46 ($false = ((!! @ (a > $o) @ (^[Y0 : a > $o]: (((Y0 @ sK7) & (!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (Y0 @ (cL @ Y1)))))) => (?? @ a @ (^[Y1 : a]: ((Y0 @ Y1) & ((cR @ Y1) = sK8))))))) => (cX @ sK8))) | (~spl0_1 | ~spl0_6)), 0.16/0.46 inference(beta_eta_normalization,[],[f348])). 0.16/0.46 thf(f348,plain,( 0.16/0.46 ($false = ((^[Y0 : a]: ((!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ sK7) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0))))))) => (cX @ Y0))) @ sK8)) | (~spl0_1 | ~spl0_6)), 0.16/0.46 inference(sigma_clausification,[],[f339])). 0.16/0.46 thf(f339,plain,( 0.16/0.46 ((!! @ a @ (^[Y0 : a]: ((!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ sK7) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0))))))) => (cX @ Y0)))) = $false) | (~spl0_1 | ~spl0_6)), 0.16/0.46 inference(boolean_simplification,[],[f338])). 0.16/0.46 thf(f338,plain,( 0.16/0.46 ($false = ($true & (!! @ a @ (^[Y0 : a]: ((!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ sK7) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0))))))) => (cX @ Y0)))))) | (~spl0_1 | ~spl0_6)), 0.16/0.46 inference(boolean_simplification,[],[f337])). 0.16/0.46 thf(f337,plain,( 0.16/0.46 ($false = (($true | (cF @ (cP @ sK7 @ sK2))) & (!! @ a @ (^[Y0 : a]: ((!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ sK7) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0))))))) => (cX @ Y0)))))) | (~spl0_1 | ~spl0_6)), 0.16/0.46 inference(superposition,[],[f325,f301])). 0.16/0.46 thf(f301,plain,( 0.16/0.46 ($true = (cG @ (cP @ sK7 @ sK2))) | ~spl0_6), 0.16/0.46 inference(binary_proxy_clausification,[],[f272])). 0.16/0.46 thf(f272,plain,( 0.16/0.46 ($true = ((cG @ (cP @ sK7 @ sK2)) & (!! @ a @ (^[Y0 : a]: ((!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ sK7)) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0))))))) => (cX @ Y0)))))) | ~spl0_6), 0.16/0.46 inference(beta_eta_normalization,[],[f271])). 0.16/0.46 thf(f271,plain,( 0.16/0.46 ($true = ((^[Y0 : a]: ((cG @ (cP @ Y0 @ sK2)) & (!! @ a @ (^[Y1 : a]: ((!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (Y2 @ (cL @ Y3))))) & (Y2 @ Y0)) => (?? @ a @ (^[Y3 : a]: ((Y2 @ Y3) & ((cR @ Y3) = Y1))))))) => (cX @ Y1)))))) @ sK7)) | ~spl0_6), 0.16/0.46 inference(sigma_clausification,[],[f62])). 0.16/0.46 thf(f62,plain,( 0.16/0.46 ($true = (?? @ a @ (^[Y0 : a]: ((cG @ (cP @ Y0 @ sK2)) & (!! @ a @ (^[Y1 : a]: ((!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (Y2 @ (cL @ Y3))))) & (Y2 @ Y0)) => (?? @ a @ (^[Y3 : a]: ((Y2 @ Y3) & ((cR @ Y3) = Y1))))))) => (cX @ Y1)))))))) | ~spl0_6), 0.16/0.46 inference(avatar_component_clause,[],[f61])). 0.16/0.46 thf(f61,plain,( 0.16/0.46 spl0_6 <=> ($true = (?? @ a @ (^[Y0 : a]: ((cG @ (cP @ Y0 @ sK2)) & (!! @ a @ (^[Y1 : a]: ((!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (Y2 @ (cL @ Y3))))) & (Y2 @ Y0)) => (?? @ a @ (^[Y3 : a]: ((Y2 @ Y3) & ((cR @ Y3) = Y1))))))) => (cX @ Y1))))))))), 0.16/0.46 introduced(avatar_definition,[new_symbols(naming,[spl0_6])])). 0.16/0.46 thf(f325,plain,( 0.16/0.46 ( ! [X1 : a] : (((((cG @ (cP @ X1 @ sK2)) | (cF @ (cP @ X1 @ sK2))) & (!! @ a @ (^[Y0 : a]: ((!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ X1) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0))))))) => (cX @ Y0))))) = $false)) ) | ~spl0_1), 0.16/0.46 inference(beta_eta_normalization,[],[f324])). 0.16/0.46 thf(f324,plain,( 0.16/0.46 ( ! [X1 : a] : ((((^[Y0 : a]: (((cG @ (cP @ Y0 @ sK2)) | (cF @ (cP @ Y0 @ sK2))) & (!! @ a @ (^[Y1 : a]: ((!! @ (a > $o) @ (^[Y2 : a > $o]: (((Y2 @ Y0) & (!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (Y2 @ (cL @ Y3)))))) => (?? @ a @ (^[Y3 : a]: ((Y2 @ Y3) & ((cR @ Y3) = Y1))))))) => (cX @ Y1)))))) @ X1) = $false)) ) | ~spl0_1), 0.16/0.46 inference(pi_clausification,[],[f35])). 0.16/0.46 thf(f35,plain,( 0.16/0.46 ((?? @ a @ (^[Y0 : a]: (((cG @ (cP @ Y0 @ sK2)) | (cF @ (cP @ Y0 @ sK2))) & (!! @ a @ (^[Y1 : a]: ((!! @ (a > $o) @ (^[Y2 : a > $o]: (((Y2 @ Y0) & (!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (Y2 @ (cL @ Y3)))))) => (?? @ a @ (^[Y3 : a]: ((Y2 @ Y3) & ((cR @ Y3) = Y1))))))) => (cX @ Y1))))))) = $false) | ~spl0_1), 0.16/0.46 inference(avatar_component_clause,[],[f34])). 0.16/0.46 thf(f34,plain,( 0.16/0.46 spl0_1 <=> ((?? @ a @ (^[Y0 : a]: (((cG @ (cP @ Y0 @ sK2)) | (cF @ (cP @ Y0 @ sK2))) & (!! @ a @ (^[Y1 : a]: ((!! @ (a > $o) @ (^[Y2 : a > $o]: (((Y2 @ Y0) & (!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (Y2 @ (cL @ Y3)))))) => (?? @ a @ (^[Y3 : a]: ((Y2 @ Y3) & ((cR @ Y3) = Y1))))))) => (cX @ Y1))))))) = $false)), 0.16/0.46 introduced(avatar_definition,[new_symbols(naming,[spl0_1])])). 0.16/0.46 thf(f305,plain,( 0.16/0.46 ( ! [X1 : a] : (($true = ((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (Y0 @ (cL @ Y1))))) & (Y0 @ sK7)) => (?? @ a @ (^[Y1 : a]: ((Y0 @ Y1) & ((cR @ Y1) = X1))))))) => (cX @ X1)))) ) | ~spl0_6), 0.16/0.46 inference(beta_eta_normalization,[],[f304])). 0.16/0.46 thf(f304,plain,( 0.16/0.46 ( ! [X1 : a] : (($true = ((^[Y0 : a]: ((!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ sK7)) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0))))))) => (cX @ Y0))) @ X1))) ) | ~spl0_6), 0.16/0.46 inference(pi_clausification,[],[f303])). 0.16/0.46 thf(f303,plain,( 0.16/0.46 ((!! @ a @ (^[Y0 : a]: ((!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ sK7)) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0))))))) => (cX @ Y0)))) = $true) | ~spl0_6), 0.16/0.46 inference(boolean_simplification,[],[f302])). 0.16/0.46 thf(f302,plain,( 0.16/0.46 (($true & (!! @ a @ (^[Y0 : a]: ((!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ sK7)) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0))))))) => (cX @ Y0))))) = $true) | ~spl0_6), 0.16/0.46 inference(backward_demodulation,[],[f272,f301])). 0.16/0.46 thf(f416,plain,( 0.16/0.46 ((~ (sK9 @ sK7)) = $true) | (~spl0_1 | ~spl0_6)), 0.16/0.46 inference(boolean_simplification,[],[f414])). 0.16/0.46 thf(f414,plain,( 0.16/0.46 ($true = (~ ((sK9 @ sK7) & $true))) | (~spl0_1 | ~spl0_6)), 0.16/0.46 inference(backward_demodulation,[],[f391,f413])). 0.16/0.46 thf(f391,plain,( 0.16/0.46 ($true = (~ ((sK9 @ sK7) & (!! @ a @ (^[Y0 : a]: ((sK9 @ Y0) => (sK9 @ (cL @ Y0)))))))) | (~spl0_1 | ~spl0_6)), 0.16/0.46 inference(boolean_simplification,[],[f390])). 0.16/0.46 thf(f390,plain,( 0.16/0.46 ($true = (((sK9 @ sK7) & (!! @ a @ (^[Y0 : a]: ((sK9 @ Y0) => (sK9 @ (cL @ Y0)))))) => $false)) | (~spl0_1 | ~spl0_6)), 0.16/0.46 inference(superposition,[],[f362,f379])). 0.16/0.46 thf(f379,plain,( 0.16/0.46 ((?? @ a @ (^[Y0 : a]: ((sK9 @ Y0) & ((cR @ Y0) = sK8)))) = $false) | (~spl0_1 | ~spl0_6)), 0.16/0.46 inference(binary_proxy_clausification,[],[f378])). 0.16/0.46 thf(f362,plain,( 0.16/0.46 ( ! [X1 : a > $o] : (($true = (((X1 @ sK7) & (!! @ a @ (^[Y0 : a]: ((X1 @ Y0) => (X1 @ (cL @ Y0)))))) => (?? @ a @ (^[Y0 : a]: ((X1 @ Y0) & ((cR @ Y0) = sK8))))))) ) | (~spl0_1 | ~spl0_6)), 0.16/0.46 inference(beta_eta_normalization,[],[f361])). 0.16/0.46 thf(f361,plain,( 0.16/0.46 ( ! [X1 : a > $o] : ((((^[Y0 : a > $o]: (((Y0 @ sK7) & (!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (Y0 @ (cL @ Y1)))))) => (?? @ a @ (^[Y1 : a]: ((Y0 @ Y1) & ((cR @ Y1) = sK8)))))) @ X1) = $true)) ) | (~spl0_1 | ~spl0_6)), 0.16/0.46 inference(pi_clausification,[],[f356])). 0.16/0.46 thf(f255,plain,( 0.16/0.46 spl0_8 | ~spl0_2 | ~spl0_4), 0.16/0.46 inference(avatar_split_clause,[],[f254,f44,f37,f132])). 0.16/0.46 thf(f132,plain,( 0.16/0.46 spl0_8 <=> ((cG @ (cP @ sK4 @ sK2)) = $true)), 0.16/0.46 introduced(avatar_definition,[new_symbols(naming,[spl0_8])])). 0.16/0.46 thf(f37,plain,( 0.16/0.46 spl0_2 <=> ($false = ((?? @ a @ (^[Y0 : a]: ((cG @ (cP @ Y0 @ sK2)) & (!! @ a @ (^[Y1 : a]: ((!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (Y2 @ (cL @ Y3))))) & (Y2 @ Y0)) => (?? @ a @ (^[Y3 : a]: ((Y2 @ Y3) & ((cR @ Y3) = Y1))))))) => (cX @ Y1))))))) | (?? @ a @ (^[Y0 : a]: ((!! @ a @ (^[Y1 : a]: ((!! @ (a > $o) @ (^[Y2 : a > $o]: (((Y2 @ Y0) & (!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (Y2 @ (cL @ Y3)))))) => (?? @ a @ (^[Y3 : a]: ((Y2 @ Y3) & ((cR @ Y3) = Y1))))))) => (cX @ Y1)))) & (cF @ (cP @ Y0 @ sK2)))))))), 0.16/0.46 introduced(avatar_definition,[new_symbols(naming,[spl0_2])])). 0.16/0.46 thf(f44,plain,( 0.16/0.46 spl0_4 <=> ($true = (?? @ a @ (^[Y0 : a]: (((cG @ (cP @ Y0 @ sK2)) | (cF @ (cP @ Y0 @ sK2))) & (!! @ a @ (^[Y1 : a]: ((!! @ (a > $o) @ (^[Y2 : a > $o]: (((Y2 @ Y0) & (!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (Y2 @ (cL @ Y3)))))) => (?? @ a @ (^[Y3 : a]: ((Y2 @ Y3) & ((cR @ Y3) = Y1))))))) => (cX @ Y1))))))))), 0.16/0.46 introduced(avatar_definition,[new_symbols(naming,[spl0_4])])). 0.16/0.46 thf(f254,plain,( 0.16/0.46 ((cG @ (cP @ sK4 @ sK2)) = $true) | (~spl0_2 | ~spl0_4)), 0.16/0.46 inference(boolean_simplification,[],[f253])). 0.16/0.46 thf(f253,plain,( 0.16/0.46 ($true = ((cG @ (cP @ sK4 @ sK2)) | $false)) | (~spl0_2 | ~spl0_4)), 0.16/0.46 inference(forward_demodulation,[],[f116,f149])). 0.16/0.46 thf(f149,plain,( 0.16/0.46 ($false = (cF @ (cP @ sK4 @ sK2))) | (~spl0_2 | ~spl0_4)), 0.16/0.46 inference(boolean_simplification,[],[f148])). 0.16/0.46 thf(f148,plain,( 0.16/0.46 (($true & (cF @ (cP @ sK4 @ sK2))) = $false) | (~spl0_2 | ~spl0_4)), 0.16/0.46 inference(superposition,[],[f142,f118])). 0.16/0.46 thf(f118,plain,( 0.16/0.46 ((!! @ a @ (^[Y0 : a]: ((!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ sK4) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0))))))) => (cX @ Y0)))) = $true) | ~spl0_4), 0.16/0.46 inference(boolean_simplification,[],[f117])). 0.16/0.46 thf(f117,plain,( 0.16/0.46 ($true = ($true & (!! @ a @ (^[Y0 : a]: ((!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ sK4) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0))))))) => (cX @ Y0)))))) | ~spl0_4), 0.16/0.46 inference(backward_demodulation,[],[f112,f116])). 0.16/0.46 thf(f112,plain,( 0.16/0.46 ($true = (((cG @ (cP @ sK4 @ sK2)) | (cF @ (cP @ sK4 @ sK2))) & (!! @ a @ (^[Y0 : a]: ((!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ sK4) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0))))))) => (cX @ Y0)))))) | ~spl0_4), 0.16/0.46 inference(beta_eta_normalization,[],[f111])). 0.16/0.46 thf(f111,plain,( 0.16/0.46 ($true = ((^[Y0 : a]: (((cG @ (cP @ Y0 @ sK2)) | (cF @ (cP @ Y0 @ sK2))) & (!! @ a @ (^[Y1 : a]: ((!! @ (a > $o) @ (^[Y2 : a > $o]: (((Y2 @ Y0) & (!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (Y2 @ (cL @ Y3)))))) => (?? @ a @ (^[Y3 : a]: ((Y2 @ Y3) & ((cR @ Y3) = Y1))))))) => (cX @ Y1)))))) @ sK4)) | ~spl0_4), 0.16/0.46 inference(sigma_clausification,[],[f45])). 0.16/0.46 thf(f45,plain,( 0.16/0.46 ($true = (?? @ a @ (^[Y0 : a]: (((cG @ (cP @ Y0 @ sK2)) | (cF @ (cP @ Y0 @ sK2))) & (!! @ a @ (^[Y1 : a]: ((!! @ (a > $o) @ (^[Y2 : a > $o]: (((Y2 @ Y0) & (!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (Y2 @ (cL @ Y3)))))) => (?? @ a @ (^[Y3 : a]: ((Y2 @ Y3) & ((cR @ Y3) = Y1))))))) => (cX @ Y1)))))))) | ~spl0_4), 0.16/0.46 inference(avatar_component_clause,[],[f44])). 0.16/0.46 thf(f142,plain,( 0.16/0.46 ( ! 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@ a @ (^[Y0 : a]: ((cG @ (cP @ Y0 @ sK2)) & (!! @ a @ (^[Y1 : a]: ((!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (Y2 @ (cL @ Y3))))) & (Y2 @ Y0)) => (?? @ a @ (^[Y3 : a]: ((Y2 @ Y3) & ((cR @ Y3) = Y1))))))) => (cX @ Y1)))))))) | ~spl0_2), 0.16/0.46 inference(binary_proxy_clausification,[],[f38])). 0.16/0.46 thf(f38,plain,( 0.16/0.46 ($false = ((?? @ a @ (^[Y0 : a]: ((cG @ (cP @ Y0 @ sK2)) & (!! @ a @ (^[Y1 : a]: ((!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (Y2 @ (cL @ Y3))))) & (Y2 @ Y0)) => (?? @ a @ (^[Y3 : a]: ((Y2 @ Y3) & ((cR @ Y3) = Y1))))))) => (cX @ Y1))))))) | (?? @ a @ (^[Y0 : a]: ((!! @ a @ (^[Y1 : a]: ((!! @ (a > $o) @ (^[Y2 : a > $o]: (((Y2 @ Y0) & (!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (Y2 @ (cL @ Y3)))))) => (?? @ a @ (^[Y3 : a]: ((Y2 @ Y3) & ((cR @ Y3) = Y1))))))) => (cX @ Y1)))) & (cF @ (cP @ Y0 @ sK2))))))) | ~spl0_2), 0.16/0.46 inference(avatar_component_clause,[],[f37])). 0.16/0.46 thf(f116,plain,( 0.16/0.46 (((cG @ (cP @ sK4 @ sK2)) | (cF @ (cP @ sK4 @ sK2))) = $true) | ~spl0_4), 0.16/0.46 inference(binary_proxy_clausification,[],[f112])). 0.16/0.46 thf(f249,plain,( 0.16/0.46 ~spl0_2 | ~spl0_4 | ~spl0_8), 0.16/0.46 inference(avatar_contradiction_clause,[],[f248])). 0.16/0.46 thf(f248,plain,( 0.16/0.46 $false | (~spl0_2 | ~spl0_4 | ~spl0_8)), 0.16/0.46 inference(trivial_inequality_removal,[],[f247])). 0.16/0.46 thf(f247,plain,( 0.16/0.46 ($true = $false) | (~spl0_2 | ~spl0_4 | ~spl0_8)), 0.16/0.46 inference(boolean_simplification,[],[f246])). 0.16/0.46 thf(f246,plain,( 0.16/0.46 ($true = (~ $true)) | (~spl0_2 | ~spl0_4 | ~spl0_8)), 0.16/0.46 inference(backward_demodulation,[],[f245,f244])). 0.16/0.46 thf(f244,plain,( 0.16/0.46 ($true = (!! @ a @ (^[Y0 : a]: ((sK6 @ Y0) => (sK6 @ (cL @ Y0)))))) | (~spl0_2 | ~spl0_4 | ~spl0_8)), 0.16/0.46 inference(boolean_simplification,[],[f243])). 0.16/0.46 thf(f243,plain,( 0.16/0.46 ($true = ($true & (!! @ a @ (^[Y0 : a]: ((sK6 @ Y0) => (sK6 @ (cL @ Y0))))))) | (~spl0_2 | ~spl0_4 | ~spl0_8)), 0.16/0.46 inference(backward_demodulation,[],[f218,f241])). 0.16/0.46 thf(f241,plain,( 0.16/0.46 ($true = (sK6 @ sK4)) | (~spl0_2 | ~spl0_4 | ~spl0_8)), 0.16/0.46 inference(binary_proxy_clausification,[],[f218])). 0.16/0.46 thf(f218,plain,( 0.16/0.46 ($true = ((sK6 @ sK4) & (!! @ a @ (^[Y0 : a]: ((sK6 @ Y0) => (sK6 @ (cL @ Y0))))))) | (~spl0_2 | ~spl0_4 | ~spl0_8)), 0.16/0.46 inference(binary_proxy_clausification,[],[f216])). 0.16/0.46 thf(f216,plain,( 0.16/0.46 ((((sK6 @ sK4) & (!! @ a @ (^[Y0 : a]: ((sK6 @ Y0) => (sK6 @ (cL @ Y0)))))) => (?? 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[X1 : a] : (($false = ((cG @ (cP @ X1 @ sK2)) & (!! @ a @ (^[Y0 : a]: ((!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ X1)) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0))))))) => (cX @ Y0))))))) ) | ~spl0_2), 0.16/0.46 inference(beta_eta_normalization,[],[f152])). 0.16/0.46 thf(f152,plain,( 0.16/0.46 ( ! [X1 : a] : ((((^[Y0 : a]: ((cG @ (cP @ Y0 @ sK2)) & (!! @ a @ (^[Y1 : a]: ((!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (Y2 @ (cL @ Y3))))) & (Y2 @ Y0)) => (?? @ a @ (^[Y3 : a]: ((Y2 @ Y3) & ((cR @ Y3) = Y1))))))) => (cX @ Y1)))))) @ X1) = $false)) ) | ~spl0_2), 0.16/0.46 inference(pi_clausification,[],[f138])). 0.16/0.46 thf(f125,plain,( 0.16/0.46 ( ! [X1 : a] : (($true = ((!! @ (a > $o) @ (^[Y0 : a > $o]: (((Y0 @ sK4) & (!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (Y0 @ (cL @ Y1)))))) => (?? @ a @ (^[Y1 : a]: ((Y0 @ Y1) & ((cR @ Y1) = X1))))))) => (cX @ X1)))) ) | ~spl0_4), 0.16/0.46 inference(beta_eta_normalization,[],[f124])). 0.16/0.46 thf(f124,plain,( 0.16/0.46 ( ! [X1 : a] : (($true = ((^[Y0 : a]: ((!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ sK4) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0))))))) => (cX @ Y0))) @ X1))) ) | ~spl0_4), 0.16/0.46 inference(pi_clausification,[],[f118])). 0.16/0.46 thf(f245,plain,( 0.16/0.46 ((~ (!! @ a @ (^[Y0 : a]: ((sK6 @ Y0) => (sK6 @ (cL @ Y0)))))) = $true) | (~spl0_2 | ~spl0_4 | ~spl0_8)), 0.16/0.46 inference(boolean_simplification,[],[f242])). 0.16/0.46 thf(f242,plain,( 0.16/0.46 ($true = (~ ((!! @ a @ (^[Y0 : a]: ((sK6 @ Y0) => (sK6 @ (cL @ Y0))))) & $true))) | (~spl0_2 | ~spl0_4 | ~spl0_8)), 0.16/0.46 inference(backward_demodulation,[],[f226,f241])). 0.16/0.46 thf(f226,plain,( 0.16/0.46 ($true = (~ ((!! @ a @ (^[Y0 : a]: ((sK6 @ Y0) => (sK6 @ (cL @ Y0))))) & (sK6 @ sK4)))) | (~spl0_2 | ~spl0_4 | ~spl0_8)), 0.16/0.46 inference(boolean_simplification,[],[f224])). 0.16/0.46 thf(f224,plain,( 0.16/0.46 ($true = (((!! @ a @ (^[Y0 : a]: ((sK6 @ Y0) => (sK6 @ (cL @ Y0))))) & (sK6 @ sK4)) => $false)) | (~spl0_2 | ~spl0_4 | ~spl0_8)), 0.16/0.46 inference(superposition,[],[f203,f217])). 0.16/0.46 thf(f217,plain,( 0.16/0.46 ((?? @ a @ (^[Y0 : a]: ((sK6 @ Y0) & ((cR @ Y0) = sK5)))) = $false) | (~spl0_2 | ~spl0_4 | ~spl0_8)), 0.16/0.46 inference(binary_proxy_clausification,[],[f216])). 0.16/0.46 thf(f203,plain,( 0.16/0.46 ( ! [X1 : a > $o] : (($true = (((!! @ a @ (^[Y0 : a]: ((X1 @ Y0) => (X1 @ (cL @ Y0))))) & (X1 @ sK4)) => (?? @ a @ (^[Y0 : a]: ((X1 @ Y0) & ((cR @ Y0) = sK5))))))) ) | (~spl0_2 | ~spl0_8)), 0.16/0.46 inference(beta_eta_normalization,[],[f202])). 0.16/0.46 thf(f202,plain,( 0.16/0.46 ( ! [X1 : a > $o] : ((((^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (Y0 @ (cL @ Y1))))) & (Y0 @ sK4)) => (?? @ a @ (^[Y1 : a]: ((Y0 @ Y1) & ((cR @ Y1) = sK5)))))) @ X1) = $true)) ) | (~spl0_2 | ~spl0_8)), 0.16/0.46 inference(pi_clausification,[],[f174])). 0.16/0.46 thf(f98,plain,( 0.16/0.46 ~spl0_1 | ~spl0_5), 0.16/0.46 inference(avatar_contradiction_clause,[],[f97])). 0.16/0.46 thf(f97,plain,( 0.16/0.46 $false | (~spl0_1 | ~spl0_5)), 0.16/0.46 inference(trivial_inequality_removal,[],[f96])). 0.16/0.46 thf(f96,plain,( 0.16/0.46 ($true = $false) | (~spl0_1 | ~spl0_5)), 0.16/0.46 inference(boolean_simplification,[],[f95])). 0.16/0.46 thf(f95,plain,( 0.16/0.46 (((cG @ (cP @ sK3 @ sK2)) | $true) = $false) | (~spl0_1 | ~spl0_5)), 0.16/0.46 inference(forward_demodulation,[],[f89,f76])). 0.16/0.46 thf(f76,plain,( 0.16/0.46 ($true = (cF @ (cP @ sK3 @ sK2))) | ~spl0_5), 0.16/0.46 inference(boolean_simplification,[],[f75])). 0.16/0.46 thf(f75,plain,( 0.16/0.46 ($true = ($true & (cF @ (cP @ sK3 @ sK2)))) | ~spl0_5), 0.16/0.46 inference(backward_demodulation,[],[f72,f74])). 0.16/0.46 thf(f74,plain,( 0.16/0.46 ($true = (!! @ a @ (^[Y0 : a]: ((!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ sK3) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0))))))) => (cX @ Y0))))) | ~spl0_5), 0.16/0.46 inference(binary_proxy_clausification,[],[f72])). 0.16/0.46 thf(f72,plain,( 0.16/0.46 ($true = ((!! @ a @ (^[Y0 : a]: ((!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ sK3) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0))))))) => (cX @ Y0)))) & (cF @ (cP @ sK3 @ sK2)))) | ~spl0_5), 0.16/0.46 inference(beta_eta_normalization,[],[f71])). 0.16/0.46 thf(f71,plain,( 0.16/0.46 ($true = ((^[Y0 : a]: ((!! @ a @ (^[Y1 : a]: ((!! @ (a > $o) @ (^[Y2 : a > $o]: (((Y2 @ Y0) & (!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (Y2 @ (cL @ Y3)))))) => (?? @ a @ (^[Y3 : a]: ((Y2 @ Y3) & ((cR @ Y3) = Y1))))))) => (cX @ Y1)))) & (cF @ (cP @ Y0 @ sK2)))) @ sK3)) | ~spl0_5), 0.16/0.46 inference(sigma_clausification,[],[f59])). 0.16/0.46 thf(f59,plain,( 0.16/0.46 ((?? @ a @ (^[Y0 : a]: ((!! @ a @ (^[Y1 : a]: ((!! @ (a > $o) @ (^[Y2 : a > $o]: (((Y2 @ Y0) & (!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (Y2 @ (cL @ Y3)))))) => (?? @ a @ (^[Y3 : a]: ((Y2 @ Y3) & ((cR @ Y3) = Y1))))))) => (cX @ Y1)))) & (cF @ (cP @ Y0 @ sK2))))) = $true) | ~spl0_5), 0.16/0.46 inference(avatar_component_clause,[],[f58])). 0.16/0.46 thf(f58,plain,( 0.16/0.46 spl0_5 <=> ((?? @ a @ (^[Y0 : a]: ((!! @ a @ (^[Y1 : a]: ((!! @ (a > $o) @ (^[Y2 : a > $o]: (((Y2 @ Y0) & (!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (Y2 @ (cL @ Y3)))))) => (?? @ a @ (^[Y3 : a]: ((Y2 @ Y3) & ((cR @ Y3) = Y1))))))) => (cX @ Y1)))) & (cF @ (cP @ Y0 @ sK2))))) = $true)), 0.16/0.46 introduced(avatar_definition,[new_symbols(naming,[spl0_5])])). 0.16/0.46 thf(f89,plain,( 0.16/0.46 ($false = ((cG @ (cP @ sK3 @ sK2)) | (cF @ (cP @ sK3 @ sK2)))) | (~spl0_1 | ~spl0_5)), 0.16/0.46 inference(boolean_simplification,[],[f87])). 0.16/0.46 thf(f87,plain,( 0.16/0.46 ((((cG @ (cP @ sK3 @ sK2)) | (cF @ (cP @ sK3 @ sK2))) & $true) = $false) | (~spl0_1 | ~spl0_5)), 0.16/0.46 inference(superposition,[],[f81,f74])). 0.16/0.46 thf(f81,plain,( 0.16/0.46 ( ! [X1 : a] : (((((cG @ (cP @ X1 @ sK2)) | (cF @ (cP @ X1 @ sK2))) & (!! @ a @ (^[Y0 : a]: ((!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ X1) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0))))))) => (cX @ Y0))))) = $false)) ) | ~spl0_1), 0.16/0.46 inference(beta_eta_normalization,[],[f80])). 0.16/0.46 thf(f80,plain,( 0.16/0.46 ( ! [X1 : a] : ((((^[Y0 : a]: (((cG @ (cP @ Y0 @ sK2)) | (cF @ (cP @ Y0 @ sK2))) & (!! @ a @ (^[Y1 : a]: ((!! @ (a > $o) @ (^[Y2 : a > $o]: (((Y2 @ Y0) & (!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (Y2 @ (cL @ Y3)))))) => (?? @ a @ (^[Y3 : a]: ((Y2 @ Y3) & ((cR @ Y3) = Y1))))))) => (cX @ Y1)))))) @ X1) = $false)) ) | ~spl0_1), 0.16/0.46 inference(pi_clausification,[],[f35])). 0.16/0.46 thf(f63,plain,( 0.16/0.46 spl0_5 | spl0_6 | ~spl0_1), 0.16/0.46 inference(avatar_split_clause,[],[f56,f34,f61,f58])). 0.16/0.46 thf(f56,plain,( 0.16/0.46 ($true = (?? @ a @ (^[Y0 : a]: ((cG @ (cP @ Y0 @ sK2)) & (!! @ a @ (^[Y1 : a]: ((!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (Y2 @ (cL @ Y3))))) & (Y2 @ Y0)) => (?? @ a @ (^[Y3 : a]: ((Y2 @ Y3) & ((cR @ Y3) = Y1))))))) => (cX @ Y1)))))))) | ((?? @ a @ (^[Y0 : a]: ((!! @ a @ (^[Y1 : a]: ((!! @ (a > $o) @ (^[Y2 : a > $o]: (((Y2 @ Y0) & (!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (Y2 @ (cL @ Y3)))))) => (?? @ a @ (^[Y3 : a]: ((Y2 @ Y3) & ((cR @ Y3) = Y1))))))) => (cX @ Y1)))) & (cF @ (cP @ Y0 @ sK2))))) = $true) | ~spl0_1), 0.16/0.46 inference(binary_proxy_clausification,[],[f51])). 0.16/0.46 thf(f51,plain,( 0.16/0.46 ($false != ((?? @ a @ (^[Y0 : a]: ((cG @ (cP @ Y0 @ sK2)) & (!! @ a @ (^[Y1 : a]: ((!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (Y2 @ (cL @ Y3))))) & (Y2 @ Y0)) => (?? @ a @ (^[Y3 : a]: ((Y2 @ Y3) & ((cR @ Y3) = Y1))))))) => (cX @ Y1))))))) | (?? @ a @ (^[Y0 : a]: ((!! @ a @ (^[Y1 : a]: ((!! @ (a > $o) @ (^[Y2 : a > $o]: (((Y2 @ Y0) & (!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (Y2 @ (cL @ Y3)))))) => (?? @ a @ (^[Y3 : a]: ((Y2 @ Y3) & ((cR @ Y3) = Y1))))))) => (cX @ Y1)))) & (cF @ (cP @ Y0 @ sK2))))))) | ~spl0_1), 0.16/0.46 inference(backward_demodulation,[],[f20,f35])). 0.16/0.46 thf(f20,plain,( 0.16/0.46 ((?? @ a @ (^[Y0 : a]: (((cG @ (cP @ Y0 @ sK2)) | (cF @ (cP @ Y0 @ sK2))) & (!! @ a @ (^[Y1 : a]: ((!! @ (a > $o) @ (^[Y2 : a > $o]: (((Y2 @ Y0) & (!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (Y2 @ (cL @ Y3)))))) => (?? @ a @ (^[Y3 : a]: ((Y2 @ Y3) & ((cR @ Y3) = Y1))))))) => (cX @ Y1))))))) != ((?? @ a @ (^[Y0 : a]: ((cG @ (cP @ Y0 @ sK2)) & (!! @ a @ (^[Y1 : a]: ((!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (Y2 @ (cL @ Y3))))) & (Y2 @ Y0)) => (?? @ a @ (^[Y3 : a]: ((Y2 @ Y3) & ((cR @ Y3) = Y1))))))) => (cX @ Y1))))))) | (?? @ a @ (^[Y0 : a]: ((!! @ a @ (^[Y1 : a]: ((!! @ (a > $o) @ (^[Y2 : a > $o]: (((Y2 @ Y0) & (!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (Y2 @ (cL @ Y3)))))) => (?? @ a @ (^[Y3 : a]: ((Y2 @ Y3) & ((cR @ Y3) = Y1))))))) => (cX @ Y1)))) & (cF @ (cP @ Y0 @ sK2)))))))), 0.16/0.46 inference(beta_eta_normalization,[],[f19])). 0.16/0.46 thf(f19,plain,( 0.16/0.46 (((^[Y0 : a]: (?? @ a @ (^[Y1 : a]: (((cG @ (cP @ Y1 @ Y0)) | (cF @ (cP @ Y1 @ Y0))) & (!! @ a @ (^[Y2 : a]: ((!! @ (a > $o) @ (^[Y3 : a > $o]: (((Y3 @ Y1) & (!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4)))))) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2))))))) => (cX @ Y2)))))))) @ sK2) != ((^[Y0 : a]: ((?? @ a @ (^[Y1 : a]: ((cG @ (cP @ Y1 @ Y0)) & (!! @ a @ (^[Y2 : a]: ((!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4))))) & (Y3 @ Y1)) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2))))))) => (cX @ Y2))))))) | (?? @ a @ (^[Y1 : a]: ((!! @ a @ (^[Y2 : a]: ((!! @ (a > $o) @ (^[Y3 : a > $o]: (((Y3 @ Y1) & (!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4)))))) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2))))))) => (cX @ Y2)))) & (cF @ (cP @ Y1 @ Y0))))))) @ sK2))), 0.16/0.46 inference(negative_extensionality,[],[f14])). 0.16/0.46 thf(f14,plain,( 0.16/0.46 ((^[Y0 : a]: (?? @ a @ (^[Y1 : a]: (((cG @ (cP @ Y1 @ Y0)) | (cF @ (cP @ Y1 @ Y0))) & (!! @ a @ (^[Y2 : a]: ((!! @ (a > $o) @ (^[Y3 : a > $o]: (((Y3 @ Y1) & (!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4)))))) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2))))))) => (cX @ Y2)))))))) != (^[Y0 : a]: ((?? @ a @ (^[Y1 : a]: ((cG @ (cP @ Y1 @ Y0)) & (!! @ a @ (^[Y2 : a]: ((!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4))))) & (Y3 @ Y1)) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2))))))) => (cX @ Y2))))))) | (?? @ a @ (^[Y1 : a]: ((!! @ a @ (^[Y2 : a]: ((!! @ (a > $o) @ (^[Y3 : a > $o]: (((Y3 @ Y1) & (!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4)))))) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2))))))) => (cX @ Y2)))) & (cF @ (cP @ Y1 @ Y0))))))))), 0.16/0.46 inference(equality_proxy_clausification,[],[f13])). 0.16/0.46 thf(f13,plain,( 0.16/0.46 (((^[Y0 : a]: ((?? @ a @ (^[Y1 : a]: ((cG @ (cP @ Y1 @ Y0)) & (!! @ a @ (^[Y2 : a]: ((!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4))))) & (Y3 @ Y1)) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2))))))) => (cX @ Y2))))))) | (?? @ a @ (^[Y1 : a]: ((!! @ a @ (^[Y2 : a]: ((!! @ (a > $o) @ (^[Y3 : a > $o]: (((Y3 @ Y1) & (!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4)))))) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2))))))) => (cX @ Y2)))) & (cF @ (cP @ Y1 @ Y0))))))) = (^[Y0 : a]: (?? @ a @ (^[Y1 : a]: (((cG @ (cP @ Y1 @ Y0)) | (cF @ (cP @ Y1 @ Y0))) & (!! @ a @ (^[Y2 : a]: ((!! @ (a > $o) @ (^[Y3 : a > $o]: (((Y3 @ Y1) & (!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4)))))) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2))))))) => (cX @ Y2))))))))) = $false)), 0.16/0.46 inference(boolean_simplification,[],[f12])). 0.16/0.46 thf(f12,plain,( 0.16/0.46 ($false = ($true => ((^[Y0 : a]: ((?? @ a @ (^[Y1 : a]: ((cG @ (cP @ Y1 @ Y0)) & (!! @ a @ (^[Y2 : a]: ((!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4))))) & (Y3 @ Y1)) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2))))))) => (cX @ Y2))))))) | (?? @ a @ (^[Y1 : a]: ((!! @ a @ (^[Y2 : a]: ((!! @ (a > $o) @ (^[Y3 : a > $o]: (((Y3 @ Y1) & (!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4)))))) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2))))))) => (cX @ Y2)))) & (cF @ (cP @ Y1 @ Y0))))))) = (^[Y0 : a]: (?? @ a @ (^[Y1 : a]: (((cG @ (cP @ Y1 @ Y0)) | (cF @ (cP @ Y1 @ Y0))) & (!! @ a @ (^[Y2 : a]: ((!! @ (a > $o) @ (^[Y3 : a > $o]: (((Y3 @ Y1) & (!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4)))))) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2))))))) => (cX @ Y2)))))))))))), 0.16/0.46 inference(backward_demodulation,[],[f7,f11])). 0.16/0.46 thf(f11,plain,( 0.16/0.46 ($true = ((((((!! @ a @ (^[Y0 : a]: ((~ (cZ = Y0)) = ((cP @ (cL @ Y0) @ (cR @ Y0)) = Y0)))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((cR @ (cP @ Y0 @ Y1)) = Y1)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((cL @ (cP @ Y1 @ Y0)) = Y1)))))) & (cZ = (cL @ cZ))) & (cZ = (cR @ cZ))) & (!! @ (a > $o) @ (^[Y0 : a > $o]: ((?? @ a @ (^[Y1 : a]: ((Y0 @ Y1) & (!! @ a @ (^[Y2 : a]: ((Y0 @ Y2) => (Y0 @ (cL @ Y2)))))))) => (Y0 @ cZ))))))), 0.16/0.46 inference(binary_proxy_clausification,[],[f7])). 0.16/0.46 thf(f7,plain,( 0.16/0.46 ($false = (((((((!! @ a @ (^[Y0 : a]: ((~ (cZ = Y0)) = ((cP @ (cL @ Y0) @ (cR @ Y0)) = Y0)))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((cR @ (cP @ Y0 @ Y1)) = Y1)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((cL @ (cP @ Y1 @ Y0)) = Y1)))))) & (cZ = (cL @ cZ))) & (cZ = (cR @ cZ))) & (!! @ (a > $o) @ (^[Y0 : a > $o]: ((?? @ a @ (^[Y1 : a]: ((Y0 @ Y1) & (!! @ a @ (^[Y2 : a]: ((Y0 @ Y2) => (Y0 @ (cL @ Y2)))))))) => (Y0 @ cZ))))) => ((^[Y0 : a]: ((?? @ a @ (^[Y1 : a]: ((cG @ (cP @ Y1 @ Y0)) & (!! @ a @ (^[Y2 : a]: ((!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4))))) & (Y3 @ Y1)) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2))))))) => (cX @ Y2))))))) | (?? @ a @ (^[Y1 : a]: ((!! @ a @ (^[Y2 : a]: ((!! @ (a > $o) @ (^[Y3 : a > $o]: (((Y3 @ Y1) & (!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4)))))) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2))))))) => (cX @ Y2)))) & (cF @ (cP @ Y1 @ Y0))))))) = (^[Y0 : a]: (?? @ a @ (^[Y1 : a]: (((cG @ (cP @ Y1 @ Y0)) | (cF @ (cP @ Y1 @ Y0))) & (!! @ a @ (^[Y2 : a]: ((!! @ (a > $o) @ (^[Y3 : a > $o]: (((Y3 @ Y1) & (!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4)))))) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2))))))) => (cX @ Y2)))))))))))), 0.16/0.46 inference(not_proxy_clausification,[],[f6])). 0.16/0.46 thf(f6,plain,( 0.16/0.46 ($true = (~ (((((((!! @ a @ (^[Y0 : a]: ((~ (cZ = Y0)) = ((cP @ (cL @ Y0) @ (cR @ Y0)) = Y0)))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((cR @ (cP @ Y0 @ Y1)) = Y1)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((cL @ (cP @ Y1 @ Y0)) = Y1)))))) & (cZ = (cL @ cZ))) & (cZ = (cR @ cZ))) & (!! @ (a > $o) @ (^[Y0 : a > $o]: ((?? @ a @ (^[Y1 : a]: ((Y0 @ Y1) & (!! @ a @ (^[Y2 : a]: ((Y0 @ Y2) => (Y0 @ (cL @ Y2)))))))) => (Y0 @ cZ))))) => ((^[Y0 : a]: ((?? @ a @ (^[Y1 : a]: ((cG @ (cP @ Y1 @ Y0)) & (!! @ a @ (^[Y2 : a]: ((!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4))))) & (Y3 @ Y1)) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2))))))) => (cX @ Y2))))))) | (?? @ a @ (^[Y1 : a]: ((!! @ a @ (^[Y2 : a]: ((!! @ (a > $o) @ (^[Y3 : a > $o]: (((Y3 @ Y1) & (!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4)))))) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2))))))) => (cX @ Y2)))) & (cF @ (cP @ Y1 @ Y0))))))) = (^[Y0 : a]: (?? @ a @ (^[Y1 : a]: (((cG @ (cP @ Y1 @ Y0)) | (cF @ (cP @ Y1 @ Y0))) & (!! @ a @ (^[Y2 : a]: ((!! @ (a > $o) @ (^[Y3 : a > $o]: (((Y3 @ Y1) & (!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4)))))) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2))))))) => (cX @ Y2))))))))))))), 0.16/0.46 inference(cnf_transformation,[],[f5])). 0.16/0.46 thf(f5,plain,( 0.16/0.46 ($true = (~ (((((((!! @ a @ (^[Y0 : a]: ((~ (cZ = Y0)) = ((cP @ (cL @ Y0) @ (cR @ Y0)) = Y0)))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((cR @ (cP @ Y0 @ Y1)) = Y1)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((cL @ (cP @ Y1 @ Y0)) = Y1)))))) & (cZ = (cL @ cZ))) & (cZ = (cR @ cZ))) & (!! @ (a > $o) @ (^[Y0 : a > $o]: ((?? @ a @ (^[Y1 : a]: ((Y0 @ Y1) & (!! @ a @ (^[Y2 : a]: ((Y0 @ Y2) => (Y0 @ (cL @ Y2)))))))) => (Y0 @ cZ))))) => ((^[Y0 : a]: ((?? @ a @ (^[Y1 : a]: ((cG @ (cP @ Y1 @ Y0)) & (!! @ a @ (^[Y2 : a]: ((!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4))))) & (Y3 @ Y1)) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2))))))) => (cX @ Y2))))))) | (?? @ a @ (^[Y1 : a]: ((!! @ a @ (^[Y2 : a]: ((!! @ (a > $o) @ (^[Y3 : a > $o]: (((Y3 @ Y1) & (!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4)))))) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2))))))) => (cX @ Y2)))) & (cF @ (cP @ Y1 @ Y0))))))) = (^[Y0 : a]: (?? @ a @ (^[Y1 : a]: (((cG @ (cP @ Y1 @ Y0)) | (cF @ (cP @ Y1 @ Y0))) & (!! @ a @ (^[Y2 : a]: ((!! @ (a > $o) @ (^[Y3 : a > $o]: (((Y3 @ Y1) & (!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4)))))) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2))))))) => (cX @ Y2))))))))))))), 0.16/0.46 inference(fool_elimination,[],[f4])). 0.16/0.46 thf(f4,plain,( 0.16/0.46 ~((! [X0 : a > $o] : (? [X1 : a] : (! [X2 : a] : ((X0 @ X2) => (X0 @ (cL @ X2))) & (X0 @ X1)) => (X0 @ cZ)) & (cZ = (cR @ cZ)) & (cZ = (cL @ cZ)) & ! [X3 : a,X4 : a] : ((cL @ (cP @ X3 @ X4)) = X3) & ! [X5 : a,X6 : a] : ((cR @ (cP @ X6 @ X5)) = X5) & ! [X7 : a] : ((cZ != X7) <=> ((cP @ (cL @ X7) @ (cR @ X7)) = X7))) => ((^[X8 : a] : (? [X9 : a] : ((cF @ (cP @ X9 @ X8)) & ! [X10 : a] : (! [X11 : a > $o] : ((! [X12 : a] : ((X11 @ X12) => (X11 @ (cL @ X12))) & (X11 @ X9)) => ? [X13 : a] : (((cR @ X13) = X10) & (X11 @ X13))) => (cX @ X10))) | ? [X14 : a] : (! [X15 : a] : (! [X16 : a > $o] : (((X16 @ X14) & ! [X17 : a] : ((X16 @ X17) => (X16 @ (cL @ X17)))) => ? [X18 : a] : (((cR @ X18) = X15) & (X16 @ X18))) => (cX @ X15)) & (cG @ (cP @ X14 @ X8))))) = (^[X19 : a] : (? [X20 : a] : (! [X21 : a] : (! [X22 : a > $o] : ((! [X23 : a] : ((X22 @ X23) => (X22 @ (cL @ X23))) & (X22 @ X20)) => ? [X24 : a] : (((cR @ X24) = X21) & (X22 @ X24))) => (cX @ X21)) & ((cF @ (cP @ X20 @ X19)) | (cG @ (cP @ X20 @ X19))))))))), 0.16/0.46 inference(rectify,[],[f2])). 0.16/0.46 thf(f2,negated_conjecture,( 0.16/0.46 ~((! [X3 : a > $o] : (? [X2 : a] : (! [X4 : a] : ((X3 @ X4) => (X3 @ (cL @ X4))) & (X3 @ X2)) => (X3 @ cZ)) & (cZ = (cR @ cZ)) & (cZ = (cL @ cZ)) & ! [X0 : a,X1 : a] : ((cL @ (cP @ X0 @ X1)) = X0) & ! [X1 : a,X0 : a] : ((cR @ (cP @ X0 @ X1)) = X1) & ! [X2 : a] : ((cZ != X2) <=> ((cP @ (cL @ X2) @ (cR @ X2)) = X2))) => ((^[X7 : a] : (? [X0 : a] : ((cF @ (cP @ X0 @ X7)) & ! [X8 : a] : (! [X3 : a > $o] : ((! [X9 : a] : ((X3 @ X9) => (X3 @ (cL @ X9))) & (X3 @ X0)) => ? [X6 : a] : (((cR @ X6) = X8) & (X3 @ X6))) => (cX @ X8))) | ? [X0 : a] : (! [X10 : a] : (! [X3 : a > $o] : (((X3 @ X0) & ! [X9 : a] : ((X3 @ X9) => (X3 @ (cL @ X9)))) => ? [X6 : a] : (((cR @ X6) = X10) & (X3 @ X6))) => (cX @ X10)) & (cG @ (cP @ X0 @ X7))))) = (^[X1 : a] : (? [X0 : a] : (! [X5 : a] : (! [X3 : a > $o] : ((! [X7 : a] : ((X3 @ X7) => (X3 @ (cL @ X7))) & (X3 @ X0)) => ? [X6 : a] : (((cR @ X6) = X5) & (X3 @ X6))) => (cX @ X5)) & ((cF @ (cP @ X0 @ X1)) | (cG @ (cP @ X0 @ X1))))))))), 0.16/0.46 inference(negated_conjecture,[],[f1])). 0.16/0.46 thf(f1,conjecture,( 0.16/0.46 (! [X3 : a > $o] : (? [X2 : a] : (! [X4 : a] : ((X3 @ X4) => (X3 @ (cL @ X4))) & (X3 @ X2)) => (X3 @ cZ)) & (cZ = (cR @ cZ)) & (cZ = (cL @ cZ)) & ! [X0 : a,X1 : a] : ((cL @ (cP @ X0 @ X1)) = X0) & ! [X1 : a,X0 : a] : ((cR @ (cP @ X0 @ X1)) = X1) & ! [X2 : a] : ((cZ != X2) <=> ((cP @ (cL @ X2) @ (cR @ X2)) = X2))) => ((^[X7 : a] : (? [X0 : a] : ((cF @ (cP @ X0 @ X7)) & ! [X8 : a] : (! [X3 : a > $o] : ((! [X9 : a] : ((X3 @ X9) => (X3 @ (cL @ X9))) & (X3 @ X0)) => ? [X6 : a] : (((cR @ X6) = X8) & (X3 @ X6))) => (cX @ X8))) | ? [X0 : a] : (! [X10 : a] : (! [X3 : a > $o] : (((X3 @ X0) & ! [X9 : a] : ((X3 @ X9) => (X3 @ (cL @ X9)))) => ? [X6 : a] : (((cR @ X6) = X10) & (X3 @ X6))) => (cX @ X10)) & (cG @ (cP @ X0 @ X7))))) = (^[X1 : a] : (? [X0 : a] : (! [X5 : a] : (! [X3 : a > $o] : ((! [X7 : a] : ((X3 @ X7) => (X3 @ (cL @ X7))) & (X3 @ X0)) => ? [X6 : a] : (((cR @ X6) = X5) & (X3 @ X6))) => (cX @ X5)) & ((cF @ (cP @ X0 @ X1)) | (cG @ (cP @ X0 @ X1)))))))), 0.16/0.46 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cPU_X2310A_pme)). 0.16/0.46 thf(f50,plain,( 0.16/0.46 ~spl0_2 | ~spl0_3), 0.16/0.46 inference(avatar_contradiction_clause,[],[f49])). 0.16/0.46 thf(f49,plain,( 0.16/0.46 $false | (~spl0_2 | ~spl0_3)), 0.16/0.46 inference(trivial_inequality_removal,[],[f48])). 0.16/0.46 thf(f48,plain,( 0.16/0.46 ($true = $false) | (~spl0_2 | ~spl0_3)), 0.16/0.46 inference(forward_demodulation,[],[f42,f38])). 0.16/0.46 thf(f42,plain,( 0.16/0.46 ($true = ((?? @ a @ (^[Y0 : a]: ((cG @ (cP @ Y0 @ sK2)) & (!! @ a @ (^[Y1 : a]: ((!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (Y2 @ (cL @ Y3))))) & (Y2 @ Y0)) => (?? @ a @ (^[Y3 : a]: ((Y2 @ Y3) & ((cR @ Y3) = Y1))))))) => (cX @ Y1))))))) | (?? @ a @ (^[Y0 : a]: ((!! @ a @ (^[Y1 : a]: ((!! @ (a > $o) @ (^[Y2 : a > $o]: (((Y2 @ Y0) & (!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (Y2 @ (cL @ Y3)))))) => (?? @ a @ (^[Y3 : a]: ((Y2 @ Y3) & ((cR @ Y3) = Y1))))))) => (cX @ Y1)))) & (cF @ (cP @ Y0 @ sK2))))))) | ~spl0_3), 0.16/0.46 inference(avatar_component_clause,[],[f41])). 0.16/0.46 thf(f41,plain,( 0.16/0.46 spl0_3 <=> ($true = ((?? @ a @ (^[Y0 : a]: ((cG @ (cP @ Y0 @ sK2)) & (!! @ a @ (^[Y1 : a]: ((!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (Y2 @ (cL @ Y3))))) & (Y2 @ Y0)) => (?? @ a @ (^[Y3 : a]: ((Y2 @ Y3) & ((cR @ Y3) = Y1))))))) => (cX @ Y1))))))) | (?? @ a @ (^[Y0 : a]: ((!! @ a @ (^[Y1 : a]: ((!! @ (a > $o) @ (^[Y2 : a > $o]: (((Y2 @ Y0) & (!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (Y2 @ (cL @ Y3)))))) => (?? @ a @ (^[Y3 : a]: ((Y2 @ Y3) & ((cR @ Y3) = Y1))))))) => (cX @ Y1)))) & (cF @ (cP @ Y0 @ sK2)))))))), 0.16/0.46 introduced(avatar_definition,[new_symbols(naming,[spl0_3])])). 0.16/0.46 thf(f46,plain,( 0.16/0.46 spl0_3 | spl0_4), 0.16/0.46 inference(avatar_split_clause,[],[f31,f44,f41])). 0.16/0.46 thf(f31,plain,( 0.16/0.46 ($true = (?? @ a @ (^[Y0 : a]: (((cG @ (cP @ Y0 @ sK2)) | (cF @ (cP @ Y0 @ sK2))) & (!! @ a @ (^[Y1 : a]: ((!! @ (a > $o) @ (^[Y2 : a > $o]: (((Y2 @ Y0) & (!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (Y2 @ (cL @ Y3)))))) => (?? @ a @ (^[Y3 : a]: ((Y2 @ Y3) & ((cR @ Y3) = Y1))))))) => (cX @ Y1)))))))) | ($true = ((?? @ a @ (^[Y0 : a]: ((cG @ (cP @ Y0 @ sK2)) & (!! @ a @ (^[Y1 : a]: ((!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (Y2 @ (cL @ Y3))))) & (Y2 @ Y0)) => (?? @ a @ (^[Y3 : a]: ((Y2 @ Y3) & ((cR @ Y3) = Y1))))))) => (cX @ Y1))))))) | (?? @ a @ (^[Y0 : a]: ((!! @ a @ (^[Y1 : a]: ((!! @ (a > $o) @ (^[Y2 : a > $o]: (((Y2 @ Y0) & (!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (Y2 @ (cL @ Y3)))))) => (?? @ a @ (^[Y3 : a]: ((Y2 @ Y3) & ((cR @ Y3) = Y1))))))) => (cX @ Y1)))) & (cF @ (cP @ Y0 @ sK2)))))))), 0.16/0.46 inference(binary_proxy_clausification,[],[f20])). 0.16/0.46 thf(f39,plain,( 0.16/0.46 spl0_1 | spl0_2), 0.16/0.46 inference(avatar_split_clause,[],[f32,f37,f34])). 0.16/0.46 thf(f32,plain,( 0.16/0.46 ($false = ((?? @ a @ (^[Y0 : a]: ((cG @ (cP @ Y0 @ sK2)) & (!! @ a @ (^[Y1 : a]: ((!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (Y2 @ (cL @ Y3))))) & (Y2 @ Y0)) => (?? @ a @ (^[Y3 : a]: ((Y2 @ Y3) & ((cR @ Y3) = Y1))))))) => (cX @ Y1))))))) | (?? @ a @ (^[Y0 : a]: ((!! @ a @ (^[Y1 : a]: ((!! @ (a > $o) @ (^[Y2 : a > $o]: (((Y2 @ Y0) & (!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (Y2 @ (cL @ Y3)))))) => (?? @ a @ (^[Y3 : a]: ((Y2 @ Y3) & ((cR @ Y3) = Y1))))))) => (cX @ Y1)))) & (cF @ (cP @ Y0 @ sK2))))))) | ((?? @ a @ (^[Y0 : a]: (((cG @ (cP @ Y0 @ sK2)) | (cF @ (cP @ Y0 @ sK2))) & (!! @ a @ (^[Y1 : a]: ((!! @ (a > $o) @ (^[Y2 : a > $o]: (((Y2 @ Y0) & (!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (Y2 @ (cL @ Y3)))))) => (?? @ a @ (^[Y3 : a]: ((Y2 @ Y3) & ((cR @ Y3) = Y1))))))) => (cX @ Y1))))))) = $false)), 0.16/0.46 inference(binary_proxy_clausification,[],[f20])). 0.16/0.46 % SZS output end Proof for theBenchmark 0.16/0.46 % (10684)------------------------------ 0.16/0.46 % (10684)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.16/0.46 % (10684)Termination reason: Refutation 0.16/0.46 0.16/0.46 % (10684)Memory used [KB]: 6012 0.16/0.46 % (10684)Time elapsed: 0.061 s 0.16/0.46 % (10684)Instructions burned: 100 (million) 0.16/0.46 % (10684)------------------------------ 0.16/0.46 % (10684)------------------------------ 0.16/0.46 % (10665)Success in time 0.158 s 0.16/0.46 % Vampire---4.8 exiting 0.16/0.46 EOF