TSTP Solution File: SET753^4 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SET753^4 : 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 : n009.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 03:13:07 EDT 2024
% Result : Theorem 0.18s 0.37s
% Output : Refutation 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.01/0.11 % Problem : SET753^4 : TPTP v8.2.0. Released v3.6.0.
% 0.11/0.13 % 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
% 0.11/0.34 % Computer : n009.cluster.edu
% 0.11/0.34 % Model : x86_64 x86_64
% 0.11/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.34 % Memory : 8042.1875MB
% 0.11/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.34 % CPULimit : 300
% 0.11/0.34 % WCLimit : 300
% 0.11/0.34 % DateTime : Mon May 20 13:10:22 EDT 2024
% 0.18/0.34 % CPUTime :
% 0.18/0.34 This is a TH0_THM_EQU_NAR problem
% 0.18/0.34 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
% 0.18/0.36 % (23732)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.18/0.36 % (23728)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)
% 0.18/0.36 % (23730)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)
% 0.18/0.36 % (23729)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.18/0.36 % (23731)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)
% 0.18/0.36 % (23727)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)
% 0.18/0.36 % (23733)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)
% 0.18/0.36 % (23726)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.18/0.36 % (23729)Instruction limit reached!
% 0.18/0.36 % (23729)------------------------------
% 0.18/0.36 % (23729)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.36 % (23729)Termination reason: Unknown
% 0.18/0.36 % (23729)Termination phase: shuffling
% 0.18/0.36
% 0.18/0.36 % (23730)Instruction limit reached!
% 0.18/0.36 % (23730)------------------------------
% 0.18/0.36 % (23730)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.36 % (23730)Termination reason: Unknown
% 0.18/0.36 % (23730)Termination phase: shuffling
% 0.18/0.36
% 0.18/0.36 % (23730)Memory used [KB]: 1023
% 0.18/0.36 % (23730)Time elapsed: 0.003 s
% 0.18/0.36 % (23730)Instructions burned: 2 (million)
% 0.18/0.36 % (23730)------------------------------
% 0.18/0.36 % (23730)------------------------------
% 0.18/0.36 % (23729)Memory used [KB]: 1023
% 0.18/0.36 % (23729)Time elapsed: 0.003 s
% 0.18/0.36 % (23729)Instructions burned: 2 (million)
% 0.18/0.36 % (23729)------------------------------
% 0.18/0.36 % (23729)------------------------------
% 0.18/0.36 % (23733)Instruction limit reached!
% 0.18/0.36 % (23733)------------------------------
% 0.18/0.36 % (23733)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.36 % (23733)Termination reason: Unknown
% 0.18/0.36 % (23733)Termination phase: Property scanning
% 0.18/0.36
% 0.18/0.36 % (23733)Memory used [KB]: 1023
% 0.18/0.36 % (23733)Time elapsed: 0.004 s
% 0.18/0.36 % (23733)Instructions burned: 4 (million)
% 0.18/0.36 % (23733)------------------------------
% 0.18/0.36 % (23733)------------------------------
% 0.18/0.36 % (23727)Instruction limit reached!
% 0.18/0.36 % (23727)------------------------------
% 0.18/0.36 % (23727)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.36 % (23727)Termination reason: Unknown
% 0.18/0.36 % (23727)Termination phase: Function definition elimination
% 0.18/0.36
% 0.18/0.36 % (23727)Memory used [KB]: 1023
% 0.18/0.36 % (23727)Time elapsed: 0.005 s
% 0.18/0.36 % (23727)Instructions burned: 5 (million)
% 0.18/0.36 % (23727)------------------------------
% 0.18/0.36 % (23727)------------------------------
% 0.18/0.37 % (23731)First to succeed.
% 0.18/0.37 % (23726)Also succeeded, but the first one will report.
% 0.18/0.37 % (23728)Also succeeded, but the first one will report.
% 0.18/0.37 % (23731)Refutation found. Thanks to Tanya!
% 0.18/0.37 % SZS status Theorem for theBenchmark
% 0.18/0.37 % SZS output start Proof for theBenchmark
% 0.18/0.37 thf(func_def_0, type, in: $i > ($i > $o) > $o).
% 0.18/0.37 thf(func_def_2, type, is_a: $i > ($i > $o) > $o).
% 0.18/0.37 thf(func_def_3, type, emptyset: $i > $o).
% 0.18/0.37 thf(func_def_4, type, unord_pair: $i > $i > $i > $o).
% 0.18/0.37 thf(func_def_5, type, singleton: $i > $i > $o).
% 0.18/0.37 thf(func_def_6, type, union: ($i > $o) > ($i > $o) > $i > $o).
% 0.18/0.37 thf(func_def_7, type, excl_union: ($i > $o) > ($i > $o) > $i > $o).
% 0.18/0.37 thf(func_def_8, type, intersection: ($i > $o) > ($i > $o) > $i > $o).
% 0.18/0.37 thf(func_def_9, type, setminus: ($i > $o) > ($i > $o) > $i > $o).
% 0.18/0.37 thf(func_def_10, type, complement: ($i > $o) > $i > $o).
% 0.18/0.37 thf(func_def_11, type, disjoint: ($i > $o) > ($i > $o) > $o).
% 0.18/0.37 thf(func_def_12, type, subset: ($i > $o) > ($i > $o) > $o).
% 0.18/0.37 thf(func_def_13, type, meets: ($i > $o) > ($i > $o) > $o).
% 0.18/0.37 thf(func_def_14, type, misses: ($i > $o) > ($i > $o) > $o).
% 0.18/0.37 thf(func_def_15, type, fun_image: ($i > $i) > ($i > $o) > $i > $o).
% 0.18/0.37 thf(func_def_16, type, fun_composition: ($i > $i) > ($i > $i) > $i > $i).
% 0.18/0.37 thf(func_def_17, type, fun_inv_image: ($i > $i) > ($i > $o) > $i > $o).
% 0.18/0.37 thf(func_def_18, type, fun_injective: ($i > $i) > $o).
% 0.18/0.37 thf(func_def_19, type, fun_surjective: ($i > $i) > $o).
% 0.18/0.37 thf(func_def_20, type, fun_bijective: ($i > $i) > $o).
% 0.18/0.37 thf(func_def_21, type, fun_decreasing: ($i > $i) > ($i > $i > $o) > $o).
% 0.18/0.37 thf(func_def_22, type, fun_increasing: ($i > $i) > ($i > $i > $o) > $o).
% 0.18/0.37 thf(func_def_37, type, sK0: $i > $i).
% 0.18/0.37 thf(func_def_38, type, sK1: $i > $o).
% 0.18/0.37 thf(func_def_39, type, sK2: $i > $o).
% 0.18/0.37 thf(f122,plain,(
% 0.18/0.37 $false),
% 0.18/0.37 inference(avatar_sat_refutation,[],[f105,f113,f121])).
% 0.18/0.37 thf(f121,plain,(
% 0.18/0.37 ~spl3_1),
% 0.18/0.37 inference(avatar_contradiction_clause,[],[f120])).
% 0.18/0.37 thf(f120,plain,(
% 0.18/0.37 $false | ~spl3_1),
% 0.18/0.37 inference(subsumption_resolution,[],[f116,f87])).
% 0.18/0.37 thf(f87,plain,(
% 0.18/0.37 ((sK0 @ sK5) = sK4)),
% 0.18/0.37 inference(equality_proxy_clausification,[],[f86])).
% 0.18/0.37 thf(f86,plain,(
% 0.18/0.37 ($true = ((sK0 @ sK5) = sK4))),
% 0.18/0.37 inference(binary_proxy_clausification,[],[f84])).
% 0.18/0.37 thf(f84,plain,(
% 0.18/0.37 ($true = (((sK0 @ sK5) = sK4) & ((sK2 @ sK5) & (sK1 @ sK5))))),
% 0.18/0.37 inference(beta_eta_normalization,[],[f83])).
% 0.18/0.37 thf(f83,plain,(
% 0.18/0.37 ($true = ((^[Y0 : $i]: (((sK0 @ Y0) = sK4) & ((sK2 @ Y0) & (sK1 @ Y0)))) @ sK5))),
% 0.18/0.37 inference(sigma_clausification,[],[f82])).
% 0.18/0.37 thf(f82,plain,(
% 0.18/0.37 ((?? @ $i @ (^[Y0 : $i]: (((sK0 @ Y0) = sK4) & ((sK2 @ Y0) & (sK1 @ Y0))))) = $true)),
% 0.18/0.37 inference(binary_proxy_clausification,[],[f80])).
% 0.18/0.37 thf(f80,plain,(
% 0.18/0.37 (((?? @ $i @ (^[Y0 : $i]: (((sK0 @ Y0) = sK4) & ((sK2 @ Y0) & (sK1 @ Y0))))) => ((?? @ $i @ (^[Y0 : $i]: (((sK0 @ Y0) = sK4) & (sK2 @ Y0)))) & (?? @ $i @ (^[Y0 : $i]: (((sK0 @ Y0) = sK4) & (sK1 @ Y0)))))) = $false)),
% 0.18/0.37 inference(beta_eta_normalization,[],[f79])).
% 0.18/0.37 thf(f79,plain,(
% 0.18/0.37 (((^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (((sK0 @ Y1) = Y0) & ((sK2 @ Y1) & (sK1 @ Y1))))) => ((?? @ $i @ (^[Y1 : $i]: (((sK0 @ Y1) = Y0) & (sK2 @ Y1)))) & (?? @ $i @ (^[Y1 : $i]: (((sK0 @ Y1) = Y0) & (sK1 @ Y1))))))) @ sK4) = $false)),
% 0.18/0.37 inference(sigma_clausification,[],[f78])).
% 0.18/0.37 thf(f78,plain,(
% 0.18/0.37 ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (((sK0 @ Y1) = Y0) & ((sK2 @ Y1) & (sK1 @ Y1))))) => ((?? @ $i @ (^[Y1 : $i]: (((sK0 @ Y1) = Y0) & (sK2 @ Y1)))) & (?? @ $i @ (^[Y1 : $i]: (((sK0 @ Y1) = Y0) & (sK1 @ Y1)))))))) != $true)),
% 0.18/0.37 inference(beta_eta_normalization,[],[f77])).
% 0.18/0.37 thf(f77,plain,(
% 0.18/0.37 (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 @ Y2))))))) @ ((^[Y0 : $i > $i]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: (((Y0 @ Y3) = Y2) & (Y1 @ Y3))))))))) @ sK0 @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ Y2))))))) @ sK1 @ sK2)) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ Y2))))))) @ ((^[Y0 : $i > $i]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: (((Y0 @ Y3) = Y2) & (Y1 @ Y3))))))))) @ sK0 @ sK1) @ ((^[Y0 : $i > $i]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: (((Y0 @ Y3) = Y2) & (Y1 @ Y3))))))))) @ sK0 @ sK2))) != $true)),
% 0.18/0.37 inference(definition_unfolding,[],[f73,f74,f72,f75,f75,f72,f72])).
% 0.18/0.37 thf(f75,plain,(
% 0.18/0.37 (intersection = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ Y2))))))))),
% 0.18/0.37 inference(cnf_transformation,[],[f29])).
% 0.18/0.37 thf(f29,plain,(
% 0.18/0.37 (intersection = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ Y2))))))))),
% 0.18/0.37 inference(fool_elimination,[],[f28])).
% 0.18/0.37 thf(f28,plain,(
% 0.18/0.37 (intersection = (^[X0 : $i > $o, X1 : $i > $o, X2 : $i] : ((X0 @ X2) & (X1 @ X2))))),
% 0.18/0.37 inference(rectify,[],[f8])).
% 0.18/0.37 thf(f8,axiom,(
% 0.18/0.37 (intersection = (^[X0 : $i > $o, X2 : $i > $o, X3 : $i] : ((X0 @ X3) & (X2 @ X3))))),
% 0.18/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection)).
% 0.18/0.37 thf(f72,plain,(
% 0.18/0.37 (fun_image = (^[Y0 : $i > $i]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: (((Y0 @ Y3) = Y2) & (Y1 @ Y3))))))))))),
% 0.18/0.37 inference(cnf_transformation,[],[f52])).
% 0.18/0.37 thf(f52,plain,(
% 0.18/0.37 (fun_image = (^[Y0 : $i > $i]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: (((Y0 @ Y3) = Y2) & (Y1 @ Y3))))))))))),
% 0.18/0.37 inference(fool_elimination,[],[f51])).
% 0.18/0.37 thf(f51,plain,(
% 0.18/0.37 ((^[X0 : $i > $i, X1 : $i > $o, X2 : $i] : (? [X3] : ((X1 @ X3) & ((X0 @ X3) = X2)))) = fun_image)),
% 0.18/0.37 inference(rectify,[],[f15])).
% 0.18/0.37 thf(f15,axiom,(
% 0.18/0.37 ((^[X4 : $i > $i, X5 : $i > $o, X2 : $i] : (? [X0] : ((X5 @ X0) & ((X4 @ X0) = X2)))) = fun_image)),
% 0.18/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fun_image)).
% 0.18/0.37 thf(f74,plain,(
% 0.18/0.37 (subset = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 @ Y2))))))))),
% 0.18/0.37 inference(cnf_transformation,[],[f63])).
% 0.18/0.37 thf(f63,plain,(
% 0.18/0.37 (subset = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 @ Y2))))))))),
% 0.18/0.37 inference(fool_elimination,[],[f62])).
% 0.18/0.37 thf(f62,plain,(
% 0.18/0.37 ((^[X0 : $i > $o, X1 : $i > $o] : (! [X2] : ((X0 @ X2) => (X1 @ X2)))) = subset)),
% 0.18/0.37 inference(rectify,[],[f12])).
% 0.18/0.37 thf(f12,axiom,(
% 0.18/0.37 ((^[X0 : $i > $o, X2 : $i > $o] : (! [X3] : ((X0 @ X3) => (X2 @ X3)))) = subset)),
% 0.18/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset)).
% 0.18/0.37 thf(f73,plain,(
% 0.18/0.37 ($true != (subset @ (fun_image @ sK0 @ (intersection @ sK1 @ sK2)) @ (intersection @ (fun_image @ sK0 @ sK1) @ (fun_image @ sK0 @ sK2))))),
% 0.18/0.37 inference(cnf_transformation,[],[f71])).
% 0.18/0.37 thf(f71,plain,(
% 0.18/0.37 ($true != (subset @ (fun_image @ sK0 @ (intersection @ sK1 @ sK2)) @ (intersection @ (fun_image @ sK0 @ sK1) @ (fun_image @ sK0 @ sK2))))),
% 0.18/0.37 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f69,f70])).
% 0.18/0.37 thf(f70,plain,(
% 0.18/0.37 ? [X0 : $i > $i,X1 : $i > $o,X2 : $i > $o] : ((subset @ (fun_image @ X0 @ (intersection @ X1 @ X2)) @ (intersection @ (fun_image @ X0 @ X1) @ (fun_image @ X0 @ X2))) != $true) => ($true != (subset @ (fun_image @ sK0 @ (intersection @ sK1 @ sK2)) @ (intersection @ (fun_image @ sK0 @ sK1) @ (fun_image @ sK0 @ sK2))))),
% 0.18/0.37 introduced(choice_axiom,[])).
% 0.18/0.37 thf(f69,plain,(
% 0.18/0.37 ? [X0 : $i > $i,X1 : $i > $o,X2 : $i > $o] : ((subset @ (fun_image @ X0 @ (intersection @ X1 @ X2)) @ (intersection @ (fun_image @ X0 @ X1) @ (fun_image @ X0 @ X2))) != $true)),
% 0.18/0.37 inference(ennf_transformation,[],[f31])).
% 0.18/0.37 thf(f31,plain,(
% 0.18/0.37 ~! [X0 : $i > $i,X1 : $i > $o,X2 : $i > $o] : ((subset @ (fun_image @ X0 @ (intersection @ X1 @ X2)) @ (intersection @ (fun_image @ X0 @ X1) @ (fun_image @ X0 @ X2))) = $true)),
% 0.18/0.37 inference(fool_elimination,[],[f30])).
% 0.18/0.37 thf(f30,plain,(
% 0.18/0.37 ~! [X0 : $i > $i,X1 : $i > $o,X2 : $i > $o] : (subset @ (fun_image @ X0 @ (intersection @ X1 @ X2)) @ (intersection @ (fun_image @ X0 @ X1) @ (fun_image @ X0 @ X2)))),
% 0.18/0.37 inference(rectify,[],[f24])).
% 0.18/0.37 thf(f24,negated_conjecture,(
% 0.18/0.37 ~! [X4 : $i > $i,X0 : $i > $o,X2 : $i > $o] : (subset @ (fun_image @ X4 @ (intersection @ X0 @ X2)) @ (intersection @ (fun_image @ X4 @ X0) @ (fun_image @ X4 @ X2)))),
% 0.18/0.37 inference(negated_conjecture,[],[f23])).
% 0.18/0.37 thf(f23,conjecture,(
% 0.18/0.37 ! [X4 : $i > $i,X0 : $i > $o,X2 : $i > $o] : (subset @ (fun_image @ X4 @ (intersection @ X0 @ X2)) @ (intersection @ (fun_image @ X4 @ X0) @ (fun_image @ X4 @ X2)))),
% 0.18/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm)).
% 0.18/0.37 thf(f116,plain,(
% 0.18/0.37 ((sK0 @ sK5) != sK4) | ~spl3_1),
% 0.18/0.37 inference(trivial_inequality_removal,[],[f115])).
% 0.18/0.37 thf(f115,plain,(
% 0.18/0.37 ($true = $false) | ((sK0 @ sK5) != sK4) | ~spl3_1),
% 0.18/0.37 inference(superposition,[],[f88,f101])).
% 0.18/0.37 thf(f101,plain,(
% 0.18/0.37 ( ! [X2 : $i] : (((sK1 @ X2) = $false) | ((sK0 @ X2) != sK4)) ) | ~spl3_1),
% 0.18/0.37 inference(avatar_component_clause,[],[f100])).
% 0.18/0.37 thf(f100,plain,(
% 0.18/0.37 spl3_1 <=> ! [X2] : (((sK1 @ X2) = $false) | ((sK0 @ X2) != sK4))),
% 0.18/0.37 introduced(avatar_definition,[new_symbols(naming,[spl3_1])])).
% 0.18/0.37 thf(f88,plain,(
% 0.18/0.37 ($true = (sK1 @ sK5))),
% 0.18/0.37 inference(binary_proxy_clausification,[],[f85])).
% 0.18/0.37 thf(f85,plain,(
% 0.18/0.37 ($true = ((sK2 @ sK5) & (sK1 @ sK5)))),
% 0.18/0.37 inference(binary_proxy_clausification,[],[f84])).
% 0.18/0.37 thf(f113,plain,(
% 0.18/0.37 ~spl3_2),
% 0.18/0.37 inference(avatar_contradiction_clause,[],[f112])).
% 0.18/0.37 thf(f112,plain,(
% 0.18/0.37 $false | ~spl3_2),
% 0.18/0.37 inference(subsumption_resolution,[],[f108,f87])).
% 0.18/0.37 thf(f108,plain,(
% 0.18/0.37 ((sK0 @ sK5) != sK4) | ~spl3_2),
% 0.18/0.37 inference(trivial_inequality_removal,[],[f107])).
% 0.18/0.37 thf(f107,plain,(
% 0.18/0.37 ((sK0 @ sK5) != sK4) | ($true = $false) | ~spl3_2),
% 0.18/0.37 inference(superposition,[],[f104,f89])).
% 0.18/0.37 thf(f89,plain,(
% 0.18/0.37 ((sK2 @ sK5) = $true)),
% 0.18/0.37 inference(binary_proxy_clausification,[],[f85])).
% 0.18/0.37 thf(f104,plain,(
% 0.18/0.37 ( ! [X1 : $i] : (((sK2 @ X1) = $false) | ((sK0 @ X1) != sK4)) ) | ~spl3_2),
% 0.18/0.37 inference(avatar_component_clause,[],[f103])).
% 0.18/0.37 thf(f103,plain,(
% 0.18/0.37 spl3_2 <=> ! [X1] : (((sK2 @ X1) = $false) | ((sK0 @ X1) != sK4))),
% 0.18/0.37 introduced(avatar_definition,[new_symbols(naming,[spl3_2])])).
% 0.18/0.37 thf(f105,plain,(
% 0.18/0.37 spl3_1 | spl3_2),
% 0.18/0.37 inference(avatar_split_clause,[],[f98,f103,f100])).
% 0.18/0.37 thf(f98,plain,(
% 0.18/0.37 ( ! [X2 : $i,X1 : $i] : (((sK2 @ X1) = $false) | ((sK0 @ X1) != sK4) | ((sK1 @ X2) = $false) | ((sK0 @ X2) != sK4)) )),
% 0.18/0.37 inference(equality_proxy_clausification,[],[f97])).
% 0.18/0.37 thf(f97,plain,(
% 0.18/0.37 ( ! [X2 : $i,X1 : $i] : (((sK0 @ X1) != sK4) | (((sK0 @ X2) = sK4) = $false) | ((sK1 @ X2) = $false) | ((sK2 @ X1) = $false)) )),
% 0.18/0.37 inference(binary_proxy_clausification,[],[f96])).
% 0.18/0.37 thf(f96,plain,(
% 0.18/0.37 ( ! [X2 : $i,X1 : $i] : (((sK2 @ X1) = $false) | ((((sK0 @ X2) = sK4) & (sK1 @ X2)) = $false) | ((sK0 @ X1) != sK4)) )),
% 0.18/0.37 inference(beta_eta_normalization,[],[f95])).
% 0.18/0.37 thf(f95,plain,(
% 0.18/0.37 ( ! [X2 : $i,X1 : $i] : (((sK0 @ X1) != sK4) | (((^[Y0 : $i]: (((sK0 @ Y0) = sK4) & (sK1 @ Y0))) @ X2) = $false) | ((sK2 @ X1) = $false)) )),
% 0.18/0.37 inference(pi_clausification,[],[f94])).
% 0.18/0.37 thf(f94,plain,(
% 0.18/0.37 ( ! [X1 : $i] : (((?? @ $i @ (^[Y0 : $i]: (((sK0 @ Y0) = sK4) & (sK1 @ Y0)))) = $false) | ((sK0 @ X1) != sK4) | ((sK2 @ X1) = $false)) )),
% 0.18/0.37 inference(equality_proxy_clausification,[],[f93])).
% 0.18/0.37 thf(f93,plain,(
% 0.18/0.37 ( ! [X1 : $i] : ((((sK0 @ X1) = sK4) = $false) | ((?? @ $i @ (^[Y0 : $i]: (((sK0 @ Y0) = sK4) & (sK1 @ Y0)))) = $false) | ((sK2 @ X1) = $false)) )),
% 0.18/0.37 inference(binary_proxy_clausification,[],[f92])).
% 0.18/0.37 thf(f92,plain,(
% 0.18/0.37 ( ! [X1 : $i] : (((((sK0 @ X1) = sK4) & (sK2 @ X1)) = $false) | ((?? @ $i @ (^[Y0 : $i]: (((sK0 @ Y0) = sK4) & (sK1 @ Y0)))) = $false)) )),
% 0.18/0.37 inference(beta_eta_normalization,[],[f91])).
% 0.18/0.37 thf(f91,plain,(
% 0.18/0.37 ( ! [X1 : $i] : ((((^[Y0 : $i]: (((sK0 @ Y0) = sK4) & (sK2 @ Y0))) @ X1) = $false) | ((?? @ $i @ (^[Y0 : $i]: (((sK0 @ Y0) = sK4) & (sK1 @ Y0)))) = $false)) )),
% 0.18/0.37 inference(pi_clausification,[],[f90])).
% 0.18/0.37 thf(f90,plain,(
% 0.18/0.37 ((?? @ $i @ (^[Y0 : $i]: (((sK0 @ Y0) = sK4) & (sK2 @ Y0)))) = $false) | ((?? @ $i @ (^[Y0 : $i]: (((sK0 @ Y0) = sK4) & (sK1 @ Y0)))) = $false)),
% 0.18/0.37 inference(binary_proxy_clausification,[],[f81])).
% 0.18/0.37 thf(f81,plain,(
% 0.18/0.37 (((?? @ $i @ (^[Y0 : $i]: (((sK0 @ Y0) = sK4) & (sK2 @ Y0)))) & (?? @ $i @ (^[Y0 : $i]: (((sK0 @ Y0) = sK4) & (sK1 @ Y0))))) = $false)),
% 0.18/0.37 inference(binary_proxy_clausification,[],[f80])).
% 0.18/0.37 % SZS output end Proof for theBenchmark
% 0.18/0.37 % (23731)------------------------------
% 0.18/0.37 % (23731)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.37 % (23731)Termination reason: Refutation
% 0.18/0.37
% 0.18/0.37 % (23731)Memory used [KB]: 5628
% 0.18/0.37 % (23731)Time elapsed: 0.009 s
% 0.18/0.37 % (23731)Instructions burned: 7 (million)
% 0.18/0.37 % (23731)------------------------------
% 0.18/0.37 % (23731)------------------------------
% 0.18/0.37 % (23725)Success in time 0.013 s
% 0.18/0.37 % Vampire---4.8 exiting
%------------------------------------------------------------------------------