TSTP Solution File: SET741^4 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SET741^4 : TPTP v8.2.0. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% 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
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 21 03:13:04 EDT 2024
% Result : Theorem 0.20s 0.41s
% Output : Refutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SET741^4 : TPTP v8.2.0. Released v3.6.0.
% 0.07/0.14 % 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
% 0.14/0.35 % Computer : n020.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon May 20 12:08:08 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.35 This is a TH0_THM_EQU_NAR problem
% 0.14/0.35 Running vampire_ho --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol --cores 8 -m 12000 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.38 % (11734)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.14/0.38 % (11739)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 (2999ds/275Mi)
% 0.14/0.38 % (11738)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.14/0.39 % (11738)Instruction limit reached!
% 0.14/0.39 % (11738)------------------------------
% 0.14/0.39 % (11738)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.39 % (11738)Termination reason: Unknown
% 0.14/0.39 % (11738)Termination phase: Property scanning
% 0.14/0.39
% 0.14/0.39 % (11738)Memory used [KB]: 1023
% 0.14/0.39 % (11738)Time elapsed: 0.003 s
% 0.14/0.39 % (11738)Instructions burned: 3 (million)
% 0.14/0.39 % (11738)------------------------------
% 0.14/0.39 % (11738)------------------------------
% 0.14/0.39 % (11735)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.14/0.39 % (11741)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.14/0.39 % (11737)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.14/0.39 % (11736)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on theBenchmark for (2999ds/27Mi)
% 0.14/0.39 % (11737)Instruction limit reached!
% 0.14/0.39 % (11737)------------------------------
% 0.14/0.39 % (11737)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.39 % (11737)Termination reason: Unknown
% 0.14/0.39 % (11737)Termination phase: Property scanning
% 0.14/0.39
% 0.14/0.39 % (11737)Memory used [KB]: 895
% 0.14/0.39 % (11737)Time elapsed: 0.003 s
% 0.14/0.39 % (11737)Instructions burned: 2 (million)
% 0.14/0.39 % (11737)------------------------------
% 0.14/0.39 % (11737)------------------------------
% 0.14/0.39 % (11741)Instruction limit reached!
% 0.14/0.39 % (11741)------------------------------
% 0.14/0.39 % (11741)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.39 % (11741)Termination reason: Unknown
% 0.14/0.39 % (11741)Termination phase: Property scanning
% 0.14/0.39
% 0.14/0.39 % (11741)Memory used [KB]: 1023
% 0.14/0.39 % (11741)Time elapsed: 0.005 s
% 0.14/0.39 % (11741)Instructions burned: 3 (million)
% 0.14/0.39 % (11741)------------------------------
% 0.14/0.39 % (11741)------------------------------
% 0.14/0.39 % (11740)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.14/0.40 % (11740)Instruction limit reached!
% 0.14/0.40 % (11740)------------------------------
% 0.14/0.40 % (11740)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.40 % (11740)Termination reason: Unknown
% 0.14/0.40 % (11740)Termination phase: Saturation
% 0.14/0.40
% 0.14/0.40 % (11740)Memory used [KB]: 5628
% 0.14/0.40 % (11740)Time elapsed: 0.012 s
% 0.14/0.40 % (11740)Instructions burned: 19 (million)
% 0.14/0.40 % (11740)------------------------------
% 0.14/0.40 % (11740)------------------------------
% 0.14/0.40 % (11742)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 0.14/0.40 % (11735)Instruction limit reached!
% 0.14/0.40 % (11735)------------------------------
% 0.14/0.40 % (11735)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.40 % (11735)Termination reason: Unknown
% 0.14/0.40 % (11735)Termination phase: Saturation
% 0.14/0.40
% 0.14/0.40 % (11735)Memory used [KB]: 5500
% 0.14/0.40 % (11735)Time elapsed: 0.005 s
% 0.14/0.40 % (11735)Instructions burned: 5 (million)
% 0.14/0.40 % (11735)------------------------------
% 0.14/0.40 % (11735)------------------------------
% 0.14/0.40 % (11743)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on theBenchmark for (2999ds/15Mi)
% 0.14/0.40 % (11736)First to succeed.
% 0.14/0.40 % (11744)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.20/0.41 % (11744)Instruction limit reached!
% 0.20/0.41 % (11744)------------------------------
% 0.20/0.41 % (11744)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.41 % (11744)Termination reason: Unknown
% 0.20/0.41 % (11744)Termination phase: Saturation
% 0.20/0.41
% 0.20/0.41 % (11744)Memory used [KB]: 1023
% 0.20/0.41 % (11744)Time elapsed: 0.004 s
% 0.20/0.41 % (11744)Instructions burned: 4 (million)
% 0.20/0.41 % (11744)------------------------------
% 0.20/0.41 % (11744)------------------------------
% 0.20/0.41 % (11734)Also succeeded, but the first one will report.
% 0.20/0.41 % (11736)Refutation found. Thanks to Tanya!
% 0.20/0.41 % SZS status Theorem for theBenchmark
% 0.20/0.41 % SZS output start Proof for theBenchmark
% 0.20/0.41 thf(func_def_0, type, fun_image: ($i > $i) > ($i > $o) > $i > $o).
% 0.20/0.41 thf(func_def_2, type, fun_composition: ($i > $i) > ($i > $i) > $i > $i).
% 0.20/0.41 thf(func_def_3, type, fun_inv_image: ($i > $i) > ($i > $o) > $i > $o).
% 0.20/0.41 thf(func_def_4, type, fun_injective: ($i > $i) > $o).
% 0.20/0.41 thf(func_def_5, type, fun_surjective: ($i > $i) > $o).
% 0.20/0.41 thf(func_def_6, type, fun_bijective: ($i > $i) > $o).
% 0.20/0.41 thf(func_def_7, type, fun_decreasing: ($i > $i) > ($i > $i > $o) > $o).
% 0.20/0.41 thf(func_def_8, type, fun_increasing: ($i > $i) > ($i > $i > $o) > $o).
% 0.20/0.41 thf(func_def_9, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 0.20/0.41 thf(func_def_22, type, sK0: $i > $i).
% 0.20/0.41 thf(func_def_23, type, sK1: $i > $i).
% 0.20/0.41 thf(func_def_24, type, sK2: $i > $i).
% 0.20/0.41 thf(func_def_26, type, sK4: $i > $i).
% 0.20/0.41 thf(func_def_30, type, sK8: $i > $i).
% 0.20/0.41 thf(f170,plain,(
% 0.20/0.41 $false),
% 0.20/0.41 inference(avatar_sat_refutation,[],[f96,f101,f149,f169])).
% 0.20/0.41 thf(f169,plain,(
% 0.20/0.41 ~spl3_1),
% 0.20/0.41 inference(avatar_contradiction_clause,[],[f168])).
% 0.20/0.41 thf(f168,plain,(
% 0.20/0.41 $false | ~spl3_1),
% 0.20/0.41 inference(equality_resolution,[],[f160])).
% 0.20/0.41 thf(f160,plain,(
% 0.20/0.41 ( ! [X0 : $i] : ((sK5 != X0)) ) | ~spl3_1),
% 0.20/0.41 inference(superposition,[],[f91,f109])).
% 0.20/0.41 thf(f109,plain,(
% 0.20/0.41 ( ! [X0 : $i] : (((sK0 @ (sK4 @ (sK1 @ (sK2 @ X0)))) = X0)) )),
% 0.20/0.41 inference(equality_resolution,[],[f103])).
% 0.20/0.41 thf(f103,plain,(
% 0.20/0.41 ( ! [X0 : $i,X1 : $i] : (((sK0 @ (sK1 @ (sK2 @ X1))) != (sK0 @ X0)) | ((sK0 @ (sK4 @ X0)) = X1)) )),
% 0.20/0.41 inference(superposition,[],[f88,f56])).
% 0.20/0.41 thf(f56,plain,(
% 0.20/0.41 ( ! [X1 : $i] : (((sK1 @ (sK2 @ (sK0 @ (sK4 @ X1)))) = X1)) )),
% 0.20/0.41 inference(equality_proxy_clausification,[],[f55])).
% 0.20/0.41 thf(f55,plain,(
% 0.20/0.41 ( ! [X1 : $i] : ((((sK1 @ (sK2 @ (sK0 @ (sK4 @ X1)))) = X1) = $true)) )),
% 0.20/0.41 inference(beta_eta_normalization,[],[f54])).
% 0.20/0.41 thf(f54,plain,(
% 0.20/0.41 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((sK1 @ (sK2 @ (sK0 @ Y0))) = X1)) @ (sK4 @ X1)))) )),
% 0.20/0.41 inference(sigma_clausification,[],[f53])).
% 0.20/0.41 thf(f53,plain,(
% 0.20/0.41 ( ! [X1 : $i] : (($true = (?? @ $i @ (^[Y0 : $i]: ((sK1 @ (sK2 @ (sK0 @ Y0))) = X1))))) )),
% 0.20/0.41 inference(beta_eta_normalization,[],[f52])).
% 0.20/0.41 thf(f52,plain,(
% 0.20/0.41 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((sK1 @ (sK2 @ (sK0 @ Y1))) = Y0)))) @ X1))) )),
% 0.20/0.41 inference(pi_clausification,[],[f51])).
% 0.20/0.41 thf(f51,plain,(
% 0.20/0.41 ($true = (!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((sK1 @ (sK2 @ (sK0 @ Y1))) = Y0))))))),
% 0.20/0.41 inference(beta_eta_normalization,[],[f50])).
% 0.20/0.41 thf(f50,plain,(
% 0.20/0.41 ($true = ((^[Y0 : $i > $i]: (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = Y1)))))) @ ((^[Y0 : $i > $i]: ((^[Y1 : $i > $i]: ((^[Y2 : $i]: (Y1 @ (Y0 @ Y2))))))) @ ((^[Y0 : $i > $i]: ((^[Y1 : $i > $i]: ((^[Y2 : $i]: (Y1 @ (Y0 @ Y2))))))) @ sK0 @ sK2) @ sK1)))),
% 0.20/0.41 inference(definition_unfolding,[],[f36,f35,f44,f44])).
% 0.20/0.41 thf(f44,plain,(
% 0.20/0.41 (fun_composition = (^[Y0 : $i > $i]: ((^[Y1 : $i > $i]: ((^[Y2 : $i]: (Y1 @ (Y0 @ Y2))))))))),
% 0.20/0.41 inference(cnf_transformation,[],[f23])).
% 0.20/0.41 thf(f23,plain,(
% 0.20/0.41 (fun_composition = (^[Y0 : $i > $i]: ((^[Y1 : $i > $i]: ((^[Y2 : $i]: (Y1 @ (Y0 @ Y2))))))))),
% 0.20/0.41 inference(fool_elimination,[],[f22])).
% 0.20/0.41 thf(f22,plain,(
% 0.20/0.41 ((^[X0 : $i > $i, X1 : $i > $i, X2 : $i] : (X1 @ (X0 @ X2))) = fun_composition)),
% 0.20/0.41 inference(rectify,[],[f2])).
% 0.20/0.41 thf(f2,axiom,(
% 0.20/0.41 ((^[X0 : $i > $i, X4 : $i > $i, X3 : $i] : (X4 @ (X0 @ X3))) = fun_composition)),
% 0.20/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fun_composition)).
% 0.20/0.41 thf(f35,plain,(
% 0.20/0.41 (fun_surjective = (^[Y0 : $i > $i]: (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = Y1)))))))),
% 0.20/0.41 inference(cnf_transformation,[],[f13])).
% 0.20/0.41 thf(f13,plain,(
% 0.20/0.41 (fun_surjective = (^[Y0 : $i > $i]: (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = Y1)))))))),
% 0.20/0.41 inference(fool_elimination,[],[f12])).
% 0.20/0.41 thf(f12,plain,(
% 0.20/0.41 ((^[X0 : $i > $i] : (! [X1] : ? [X2] : ((X0 @ X2) = X1))) = fun_surjective)),
% 0.20/0.41 inference(rectify,[],[f5])).
% 0.20/0.41 thf(f5,axiom,(
% 0.20/0.41 ((^[X0 : $i > $i] : (! [X2] : ? [X3] : ((X0 @ X3) = X2))) = fun_surjective)),
% 0.20/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fun_surjective)).
% 0.20/0.41 thf(f36,plain,(
% 0.20/0.41 ($true = (fun_surjective @ (fun_composition @ (fun_composition @ sK0 @ sK2) @ sK1)))),
% 0.20/0.41 inference(cnf_transformation,[],[f33])).
% 0.20/0.41 thf(f33,plain,(
% 0.20/0.41 ($true = (fun_injective @ (fun_composition @ (fun_composition @ sK2 @ sK1) @ sK0))) & ($true != (fun_bijective @ sK0)) & ($true = (fun_surjective @ (fun_composition @ (fun_composition @ sK1 @ sK0) @ sK2))) & ($true = (fun_surjective @ (fun_composition @ (fun_composition @ sK0 @ sK2) @ sK1)))),
% 0.20/0.41 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f31,f32])).
% 0.20/0.41 thf(f32,plain,(
% 0.20/0.41 ? [X0 : $i > $i,X1 : $i > $i,X2 : $i > $i] : (($true = (fun_injective @ (fun_composition @ (fun_composition @ X2 @ X1) @ X0))) & ($true != (fun_bijective @ X0)) & ((fun_surjective @ (fun_composition @ (fun_composition @ X1 @ X0) @ X2)) = $true) & ($true = (fun_surjective @ (fun_composition @ (fun_composition @ X0 @ X2) @ X1)))) => (($true = (fun_injective @ (fun_composition @ (fun_composition @ sK2 @ sK1) @ sK0))) & ($true != (fun_bijective @ sK0)) & ($true = (fun_surjective @ (fun_composition @ (fun_composition @ sK1 @ sK0) @ sK2))) & ($true = (fun_surjective @ (fun_composition @ (fun_composition @ sK0 @ sK2) @ sK1))))),
% 0.20/0.41 introduced(choice_axiom,[])).
% 0.20/0.41 thf(f31,plain,(
% 0.20/0.41 ? [X0 : $i > $i,X1 : $i > $i,X2 : $i > $i] : (($true = (fun_injective @ (fun_composition @ (fun_composition @ X2 @ X1) @ X0))) & ($true != (fun_bijective @ X0)) & ((fun_surjective @ (fun_composition @ (fun_composition @ X1 @ X0) @ X2)) = $true) & ($true = (fun_surjective @ (fun_composition @ (fun_composition @ X0 @ X2) @ X1))))),
% 0.20/0.41 inference(flattening,[],[f30])).
% 0.20/0.41 thf(f30,plain,(
% 0.20/0.41 ? [X0 : $i > $i,X1 : $i > $i,X2 : $i > $i] : (($true != (fun_bijective @ X0)) & (((fun_surjective @ (fun_composition @ (fun_composition @ X1 @ X0) @ X2)) = $true) & ($true = (fun_surjective @ (fun_composition @ (fun_composition @ X0 @ X2) @ X1))) & ($true = (fun_injective @ (fun_composition @ (fun_composition @ X2 @ X1) @ X0)))))),
% 0.20/0.41 inference(ennf_transformation,[],[f19])).
% 0.20/0.41 thf(f19,plain,(
% 0.20/0.41 ~! [X0 : $i > $i,X1 : $i > $i,X2 : $i > $i] : ((((fun_surjective @ (fun_composition @ (fun_composition @ X1 @ X0) @ X2)) = $true) & ($true = (fun_surjective @ (fun_composition @ (fun_composition @ X0 @ X2) @ X1))) & ($true = (fun_injective @ (fun_composition @ (fun_composition @ X2 @ X1) @ X0)))) => ($true = (fun_bijective @ X0)))),
% 0.20/0.41 inference(fool_elimination,[],[f18])).
% 0.20/0.41 thf(f18,plain,(
% 0.20/0.41 ~! [X0 : $i > $i,X1 : $i > $i,X2 : $i > $i] : (((fun_injective @ (fun_composition @ (fun_composition @ X2 @ X1) @ X0)) & (fun_surjective @ (fun_composition @ (fun_composition @ X1 @ X0) @ X2)) & (fun_surjective @ (fun_composition @ (fun_composition @ X0 @ X2) @ X1))) => (fun_bijective @ X0))),
% 0.20/0.41 inference(rectify,[],[f10])).
% 0.20/0.41 thf(f10,negated_conjecture,(
% 0.20/0.41 ~! [X7 : $i > $i,X4 : $i > $i,X0 : $i > $i] : (((fun_injective @ (fun_composition @ (fun_composition @ X0 @ X4) @ X7)) & (fun_surjective @ (fun_composition @ (fun_composition @ X4 @ X7) @ X0)) & (fun_surjective @ (fun_composition @ (fun_composition @ X7 @ X0) @ X4))) => (fun_bijective @ X7))),
% 0.20/0.41 inference(negated_conjecture,[],[f9])).
% 0.20/0.41 thf(f9,conjecture,(
% 0.20/0.41 ! [X7 : $i > $i,X4 : $i > $i,X0 : $i > $i] : (((fun_injective @ (fun_composition @ (fun_composition @ X0 @ X4) @ X7)) & (fun_surjective @ (fun_composition @ (fun_composition @ X4 @ X7) @ X0)) & (fun_surjective @ (fun_composition @ (fun_composition @ X7 @ X0) @ X4))) => (fun_bijective @ X7))),
% 0.20/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm)).
% 0.20/0.41 thf(f88,plain,(
% 0.20/0.41 ( ! [X2 : $i,X1 : $i] : (((sK0 @ (sK1 @ (sK2 @ X2))) != (sK0 @ (sK1 @ (sK2 @ X1)))) | (X1 = X2)) )),
% 0.20/0.41 inference(equality_proxy_clausification,[],[f87])).
% 0.20/0.41 thf(f87,plain,(
% 0.20/0.41 ( ! [X2 : $i,X1 : $i] : ((((sK0 @ (sK1 @ (sK2 @ X1))) = (sK0 @ (sK1 @ (sK2 @ X2)))) = $false) | (X1 = X2)) )),
% 0.20/0.41 inference(equality_proxy_clausification,[],[f86])).
% 0.20/0.41 thf(f86,plain,(
% 0.20/0.41 ( ! [X2 : $i,X1 : $i] : (((X2 = X1) = $true) | (((sK0 @ (sK1 @ (sK2 @ X1))) = (sK0 @ (sK1 @ (sK2 @ X2)))) = $false)) )),
% 0.20/0.41 inference(binary_proxy_clausification,[],[f85])).
% 0.20/0.41 thf(f85,plain,(
% 0.20/0.41 ( ! [X2 : $i,X1 : $i] : (((((sK0 @ (sK1 @ (sK2 @ X1))) = (sK0 @ (sK1 @ (sK2 @ X2)))) => (X2 = X1)) = $true)) )),
% 0.20/0.41 inference(beta_eta_normalization,[],[f84])).
% 0.20/0.41 thf(f84,plain,(
% 0.20/0.41 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (((sK0 @ (sK1 @ (sK2 @ X1))) = (sK0 @ (sK1 @ (sK2 @ Y0)))) => (Y0 = X1))) @ X2))) )),
% 0.20/0.41 inference(pi_clausification,[],[f83])).
% 0.20/0.41 thf(f83,plain,(
% 0.20/0.41 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: (((sK0 @ (sK1 @ (sK2 @ X1))) = (sK0 @ (sK1 @ (sK2 @ Y0)))) => (Y0 = X1)))) = $true)) )),
% 0.20/0.41 inference(beta_eta_normalization,[],[f82])).
% 0.20/0.41 thf(f82,plain,(
% 0.20/0.41 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((sK0 @ (sK1 @ (sK2 @ Y0))) = (sK0 @ (sK1 @ (sK2 @ Y1)))) => (Y1 = Y0))))) @ X1) = $true)) )),
% 0.20/0.41 inference(pi_clausification,[],[f81])).
% 0.20/0.41 thf(f81,plain,(
% 0.20/0.41 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((sK0 @ (sK1 @ (sK2 @ Y0))) = (sK0 @ (sK1 @ (sK2 @ Y1)))) => (Y1 = Y0)))))))),
% 0.20/0.41 inference(beta_eta_normalization,[],[f47])).
% 0.20/0.41 thf(f47,plain,(
% 0.20/0.41 ($true = ((^[Y0 : $i > $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((Y0 @ Y1) = (Y0 @ Y2)) => (Y2 = Y1))))))) @ ((^[Y0 : $i > $i]: ((^[Y1 : $i > $i]: ((^[Y2 : $i]: (Y1 @ (Y0 @ Y2))))))) @ ((^[Y0 : $i > $i]: ((^[Y1 : $i > $i]: ((^[Y2 : $i]: (Y1 @ (Y0 @ Y2))))))) @ sK2 @ sK1) @ sK0)))),
% 0.20/0.41 inference(definition_unfolding,[],[f39,f41,f44,f44])).
% 0.20/0.41 thf(f41,plain,(
% 0.20/0.41 (fun_injective = (^[Y0 : $i > $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((Y0 @ Y1) = (Y0 @ Y2)) => (Y2 = Y1))))))))),
% 0.20/0.41 inference(cnf_transformation,[],[f29])).
% 0.20/0.41 thf(f29,plain,(
% 0.20/0.41 (fun_injective = (^[Y0 : $i > $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((Y0 @ Y1) = (Y0 @ Y2)) => (Y2 = Y1))))))))),
% 0.20/0.41 inference(fool_elimination,[],[f28])).
% 0.20/0.41 thf(f28,plain,(
% 0.20/0.41 ((^[X0 : $i > $i] : (! [X1,X2] : (((X0 @ X2) = (X0 @ X1)) => (X1 = X2)))) = fun_injective)),
% 0.20/0.41 inference(rectify,[],[f4])).
% 0.20/0.41 thf(f4,axiom,(
% 0.20/0.41 ((^[X0 : $i > $i] : (! [X3,X2] : (((X0 @ X3) = (X0 @ X2)) => (X2 = X3)))) = fun_injective)),
% 0.20/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fun_injective)).
% 0.20/0.41 thf(f39,plain,(
% 0.20/0.41 ($true = (fun_injective @ (fun_composition @ (fun_composition @ sK2 @ sK1) @ sK0)))),
% 0.20/0.41 inference(cnf_transformation,[],[f33])).
% 0.20/0.41 thf(f91,plain,(
% 0.20/0.41 ( ! [X1 : $i] : ((sK5 != (sK0 @ X1))) ) | ~spl3_1),
% 0.20/0.41 inference(avatar_component_clause,[],[f90])).
% 0.20/0.41 thf(f90,plain,(
% 0.20/0.41 spl3_1 <=> ! [X1] : (sK5 != (sK0 @ X1))),
% 0.20/0.41 introduced(avatar_definition,[new_symbols(naming,[spl3_1])])).
% 0.20/0.41 thf(f149,plain,(
% 0.20/0.41 spl3_2 | ~spl3_3),
% 0.20/0.41 inference(avatar_split_clause,[],[f148,f98,f93])).
% 0.20/0.41 thf(f93,plain,(
% 0.20/0.41 spl3_2 <=> (sK7 = sK6)),
% 0.20/0.41 introduced(avatar_definition,[new_symbols(naming,[spl3_2])])).
% 0.20/0.41 thf(f98,plain,(
% 0.20/0.41 spl3_3 <=> ((sK0 @ sK7) = (sK0 @ sK6))),
% 0.20/0.41 introduced(avatar_definition,[new_symbols(naming,[spl3_3])])).
% 0.20/0.41 thf(f148,plain,(
% 0.20/0.41 (sK7 = sK6) | ~spl3_3),
% 0.20/0.41 inference(forward_demodulation,[],[f143,f56])).
% 0.20/0.41 thf(f143,plain,(
% 0.20/0.41 (sK7 = (sK1 @ (sK2 @ (sK0 @ (sK4 @ sK6))))) | ~spl3_3),
% 0.20/0.41 inference(superposition,[],[f56,f136])).
% 0.20/0.41 thf(f136,plain,(
% 0.20/0.41 ((sK0 @ (sK4 @ sK7)) = (sK0 @ (sK4 @ sK6))) | ~spl3_3),
% 0.20/0.41 inference(equality_resolution,[],[f118])).
% 0.20/0.41 thf(f118,plain,(
% 0.20/0.41 ( ! [X0 : $i] : (((sK0 @ sK6) != (sK0 @ X0)) | ((sK0 @ (sK4 @ sK7)) = (sK0 @ (sK4 @ X0)))) ) | ~spl3_3),
% 0.20/0.41 inference(superposition,[],[f108,f100])).
% 0.20/0.41 thf(f100,plain,(
% 0.20/0.41 ((sK0 @ sK7) = (sK0 @ sK6)) | ~spl3_3),
% 0.20/0.41 inference(avatar_component_clause,[],[f98])).
% 0.20/0.41 thf(f108,plain,(
% 0.20/0.41 ( ! [X0 : $i,X1 : $i] : (((sK0 @ X0) != (sK0 @ X1)) | ((sK0 @ (sK4 @ X1)) = (sK0 @ (sK4 @ X0)))) )),
% 0.20/0.41 inference(superposition,[],[f103,f56])).
% 0.20/0.41 thf(f101,plain,(
% 0.20/0.41 spl3_3 | spl3_1),
% 0.20/0.41 inference(avatar_split_clause,[],[f70,f90,f98])).
% 0.20/0.41 thf(f70,plain,(
% 0.20/0.41 ( ! [X1 : $i] : ((sK5 != (sK0 @ X1)) | ((sK0 @ sK7) = (sK0 @ sK6))) )),
% 0.20/0.41 inference(equality_proxy_clausification,[],[f69])).
% 0.20/0.41 thf(f69,plain,(
% 0.20/0.41 ( ! [X1 : $i] : (($false = ((sK0 @ X1) = sK5)) | ((sK0 @ sK7) = (sK0 @ sK6))) )),
% 0.20/0.41 inference(equality_proxy_clausification,[],[f68])).
% 0.20/0.41 thf(f68,plain,(
% 0.20/0.41 ( ! [X1 : $i] : (($true = ((sK0 @ sK6) = (sK0 @ sK7))) | ($false = ((sK0 @ X1) = sK5))) )),
% 0.20/0.41 inference(beta_eta_normalization,[],[f67])).
% 0.20/0.41 thf(f67,plain,(
% 0.20/0.41 ( ! [X1 : $i] : (($false = ((^[Y0 : $i]: ((sK0 @ Y0) = sK5)) @ X1)) | ($true = ((sK0 @ sK6) = (sK0 @ sK7)))) )),
% 0.20/0.41 inference(pi_clausification,[],[f66])).
% 0.20/0.41 thf(f66,plain,(
% 0.20/0.41 ($false = (?? @ $i @ (^[Y0 : $i]: ((sK0 @ Y0) = sK5)))) | ($true = ((sK0 @ sK6) = (sK0 @ sK7)))),
% 0.20/0.41 inference(binary_proxy_clausification,[],[f64])).
% 0.20/0.41 thf(f64,plain,(
% 0.20/0.41 ((((sK0 @ sK6) = (sK0 @ sK7)) => (sK7 = sK6)) = $false) | ($false = (?? @ $i @ (^[Y0 : $i]: ((sK0 @ Y0) = sK5))))),
% 0.20/0.41 inference(beta_eta_normalization,[],[f63])).
% 0.20/0.41 thf(f63,plain,(
% 0.20/0.41 (((^[Y0 : $i]: (((sK0 @ sK6) = (sK0 @ Y0)) => (Y0 = sK6))) @ sK7) = $false) | ($false = (?? @ $i @ (^[Y0 : $i]: ((sK0 @ Y0) = sK5))))),
% 0.20/0.41 inference(sigma_clausification,[],[f62])).
% 0.20/0.41 thf(f62,plain,(
% 0.20/0.41 ((!! @ $i @ (^[Y0 : $i]: (((sK0 @ sK6) = (sK0 @ Y0)) => (Y0 = sK6)))) = $false) | ($false = (?? @ $i @ (^[Y0 : $i]: ((sK0 @ Y0) = sK5))))),
% 0.20/0.41 inference(beta_eta_normalization,[],[f61])).
% 0.20/0.41 thf(f61,plain,(
% 0.20/0.41 ($false = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((sK0 @ Y0) = (sK0 @ Y1)) => (Y1 = Y0))))) @ sK6)) | ($false = (?? @ $i @ (^[Y0 : $i]: ((sK0 @ Y0) = sK5))))),
% 0.20/0.41 inference(sigma_clausification,[],[f60])).
% 0.20/0.41 thf(f60,plain,(
% 0.20/0.41 ($false = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((sK0 @ Y0) = (sK0 @ Y1)) => (Y1 = Y0))))))) | ($false = (?? @ $i @ (^[Y0 : $i]: ((sK0 @ Y0) = sK5))))),
% 0.20/0.41 inference(beta_eta_normalization,[],[f59])).
% 0.20/0.41 thf(f59,plain,(
% 0.20/0.41 ($false = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((sK0 @ Y0) = (sK0 @ Y1)) => (Y1 = Y0))))))) | (((^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((sK0 @ Y1) = Y0)))) @ sK5) = $false)),
% 0.20/0.41 inference(sigma_clausification,[],[f58])).
% 0.20/0.41 thf(f58,plain,(
% 0.20/0.41 ($false = (!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((sK0 @ Y1) = Y0)))))) | ($false = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((sK0 @ Y0) = (sK0 @ Y1)) => (Y1 = Y0)))))))),
% 0.20/0.41 inference(binary_proxy_clausification,[],[f57])).
% 0.20/0.41 thf(f57,plain,(
% 0.20/0.41 (((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((sK0 @ Y1) = Y0))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((sK0 @ Y0) = (sK0 @ Y1)) => (Y1 = Y0))))))) != $true)),
% 0.20/0.41 inference(beta_eta_normalization,[],[f48])).
% 0.20/0.41 thf(f48,plain,(
% 0.20/0.41 ($true != ((^[Y0 : $i > $i]: (((^[Y1 : $i > $i]: (!! @ $i @ (^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) = Y2)))))) @ Y0) & ((^[Y1 : $i > $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y1 @ Y2) = (Y1 @ Y3)) => (Y3 = Y2))))))) @ Y0))) @ sK0))),
% 0.20/0.41 inference(definition_unfolding,[],[f38,f46])).
% 0.20/0.41 thf(f46,plain,(
% 0.20/0.41 (fun_bijective = (^[Y0 : $i > $i]: (((^[Y1 : $i > $i]: (!! @ $i @ (^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) = Y2)))))) @ Y0) & ((^[Y1 : $i > $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y1 @ Y2) = (Y1 @ Y3)) => (Y3 = Y2))))))) @ Y0))))),
% 0.20/0.41 inference(definition_unfolding,[],[f43,f35,f41])).
% 0.20/0.41 thf(f43,plain,(
% 0.20/0.41 (fun_bijective = (^[Y0 : $i > $i]: ((fun_surjective @ Y0) & (fun_injective @ Y0))))),
% 0.20/0.41 inference(cnf_transformation,[],[f25])).
% 0.20/0.41 thf(f25,plain,(
% 0.20/0.41 (fun_bijective = (^[Y0 : $i > $i]: ((fun_surjective @ Y0) & (fun_injective @ Y0))))),
% 0.20/0.41 inference(fool_elimination,[],[f24])).
% 0.20/0.41 thf(f24,plain,(
% 0.20/0.41 (fun_bijective = (^[X0 : $i > $i] : ((fun_injective @ X0) & (fun_surjective @ X0))))),
% 0.20/0.41 inference(rectify,[],[f6])).
% 0.20/0.41 thf(f6,axiom,(
% 0.20/0.41 (fun_bijective = (^[X0 : $i > $i] : ((fun_injective @ X0) & (fun_surjective @ X0))))),
% 0.20/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fun_bijective)).
% 0.20/0.41 thf(f38,plain,(
% 0.20/0.41 ($true != (fun_bijective @ sK0))),
% 0.20/0.41 inference(cnf_transformation,[],[f33])).
% 0.20/0.41 thf(f96,plain,(
% 0.20/0.41 spl3_1 | ~spl3_2),
% 0.20/0.41 inference(avatar_split_clause,[],[f74,f93,f90])).
% 0.20/0.41 thf(f74,plain,(
% 0.20/0.41 ( ! [X1 : $i] : ((sK7 != sK6) | (sK5 != (sK0 @ X1))) )),
% 0.20/0.41 inference(equality_proxy_clausification,[],[f73])).
% 0.20/0.41 thf(f73,plain,(
% 0.20/0.41 ( ! [X1 : $i] : (($false = ((sK0 @ X1) = sK5)) | (sK7 != sK6)) )),
% 0.20/0.41 inference(beta_eta_normalization,[],[f72])).
% 0.20/0.41 thf(f72,plain,(
% 0.20/0.41 ( ! [X1 : $i] : (($false = ((^[Y0 : $i]: ((sK0 @ Y0) = sK5)) @ X1)) | (sK7 != sK6)) )),
% 0.20/0.41 inference(pi_clausification,[],[f71])).
% 0.20/0.41 thf(f71,plain,(
% 0.20/0.41 ($false = (?? @ $i @ (^[Y0 : $i]: ((sK0 @ Y0) = sK5)))) | (sK7 != sK6)),
% 0.20/0.41 inference(equality_proxy_clausification,[],[f65])).
% 0.20/0.41 thf(f65,plain,(
% 0.20/0.41 ((sK7 = sK6) = $false) | ($false = (?? @ $i @ (^[Y0 : $i]: ((sK0 @ Y0) = sK5))))),
% 0.20/0.41 inference(binary_proxy_clausification,[],[f64])).
% 0.20/0.41 % SZS output end Proof for theBenchmark
% 0.20/0.41 % (11736)------------------------------
% 0.20/0.41 % (11736)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.41 % (11736)Termination reason: Refutation
% 0.20/0.41
% 0.20/0.41 % (11736)Memory used [KB]: 5628
% 0.20/0.41 % (11736)Time elapsed: 0.019 s
% 0.20/0.41 % (11736)Instructions burned: 22 (million)
% 0.20/0.41 % (11736)------------------------------
% 0.20/0.41 % (11736)------------------------------
% 0.20/0.41 % (11733)Success in time 0.044 s
% 0.20/0.41 % Vampire---4.8 exiting
%------------------------------------------------------------------------------