TSTP Solution File: SEU675^2 by Vampire---4.9
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%------------------------------------------------------------------------------
% File : Vampire---4.9
% Problem : SEU675^2 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire %s %d THM
% Computer : n001.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 : Mon Jun 24 15:42:17 EDT 2024
% Result : Theorem 0.20s 0.39s
% Output : Refutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU675^2 : TPTP v8.2.0. Released v3.7.0.
% 0.03/0.12 % Command : run_vampire %s %d THM
% 0.12/0.33 % Computer : n001.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 21 12:15:09 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.20/0.35 This is a TH0_THM_EQU_NAR problem
% 0.20/0.35 Running higher-order theorem proving
% 0.20/0.35 Running /export/starexec/sandbox2/solver/bin/vampire_ho --cores 7 --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol /export/starexec/sandbox2/benchmark/theBenchmark.p -m 16384 -t 300
% 0.20/0.37 % (26862)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)
% 0.20/0.37 % (26861)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.20/0.37 % (26865)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)
% 0.20/0.37 % (26864)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.20/0.37 % (26863)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)
% 0.20/0.37 % (26866)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)
% 0.20/0.37 % (26864)Instruction limit reached!
% 0.20/0.37 % (26864)------------------------------
% 0.20/0.37 % (26864)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.20/0.37 % (26864)Termination reason: Unknown
% 0.20/0.37 % (26865)Instruction limit reached!
% 0.20/0.37 % (26865)------------------------------
% 0.20/0.37 % (26865)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.20/0.37 % (26864)Termination phase: Function definition elimination
% 0.20/0.37
% 0.20/0.37 % (26864)Memory used [KB]: 1023
% 0.20/0.37 % (26864)Time elapsed: 0.004 s
% 0.20/0.37 % (26864)Instructions burned: 3 (million)
% 0.20/0.37 % (26864)------------------------------
% 0.20/0.37 % (26864)------------------------------
% 0.20/0.37 % (26865)Termination reason: Unknown
% 0.20/0.37 % (26865)Termination phase: Saturation
% 0.20/0.37
% 0.20/0.37 % (26865)Memory used [KB]: 1023
% 0.20/0.37 % (26865)Time elapsed: 0.004 s
% 0.20/0.37 % (26865)Instructions burned: 3 (million)
% 0.20/0.37 % (26865)------------------------------
% 0.20/0.37 % (26865)------------------------------
% 0.20/0.38 % (26867)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.20/0.38 % (26862)Instruction limit reached!
% 0.20/0.38 % (26862)------------------------------
% 0.20/0.38 % (26862)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.20/0.38 % (26862)Termination reason: Unknown
% 0.20/0.38 % (26862)Termination phase: Saturation
% 0.20/0.38
% 0.20/0.38 % (26862)Memory used [KB]: 5500
% 0.20/0.38 % (26862)Time elapsed: 0.005 s
% 0.20/0.38 % (26862)Instructions burned: 4 (million)
% 0.20/0.38 % (26862)------------------------------
% 0.20/0.38 % (26862)------------------------------
% 0.20/0.38 % (26866)Refutation not found, incomplete strategy
% 0.20/0.38 % (26866)------------------------------
% 0.20/0.38 % (26866)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.20/0.38 % (26866)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.38
% 0.20/0.38
% 0.20/0.38 % (26866)Memory used [KB]: 5500
% 0.20/0.38 % (26866)Time elapsed: 0.005 s
% 0.20/0.38 % (26866)Instructions burned: 3 (million)
% 0.20/0.38 % (26866)------------------------------
% 0.20/0.38 % (26866)------------------------------
% 0.20/0.38 % (26867)First to succeed.
% 0.20/0.39 % (26867)Refutation found. Thanks to Tanya!
% 0.20/0.39 % SZS status Theorem for theBenchmark
% 0.20/0.39 % SZS output start Proof for theBenchmark
% 0.20/0.39 thf(func_def_0, type, in: $i > $i > $o).
% 0.20/0.39 thf(func_def_2, type, setadjoin: $i > $i > $i).
% 0.20/0.39 thf(func_def_3, type, powerset: $i > $i).
% 0.20/0.39 thf(func_def_4, type, dsetconstr: $i > ($i > $o) > $i).
% 0.20/0.39 thf(func_def_7, type, subset: $i > $i > $o).
% 0.20/0.39 thf(func_def_8, type, kpair: $i > $i > $i).
% 0.20/0.39 thf(func_def_9, type, cartprod: $i > $i > $i).
% 0.20/0.39 thf(func_def_10, type, singleton: $i > $o).
% 0.20/0.39 thf(func_def_11, type, ex1: $i > ($i > $o) > $o).
% 0.20/0.39 thf(func_def_12, type, breln: $i > $i > $i > $o).
% 0.20/0.39 thf(func_def_13, type, func: $i > $i > $i > $o).
% 0.20/0.39 thf(func_def_14, type, funcSet: $i > $i > $i).
% 0.20/0.39 thf(func_def_30, type, sK3: $i > $o).
% 0.20/0.39 thf(func_def_37, type, ph8: !>[X0: $tType]:(X0)).
% 0.20/0.39 thf(func_def_38, type, sK9: $i > $i).
% 0.20/0.39 thf(f114,plain,(
% 0.20/0.39 $false),
% 0.20/0.39 inference(avatar_sat_refutation,[],[f70,f75,f110,f113])).
% 0.20/0.39 thf(f113,plain,(
% 0.20/0.39 ~spl6_1),
% 0.20/0.39 inference(avatar_contradiction_clause,[],[f112])).
% 0.20/0.39 thf(f112,plain,(
% 0.20/0.39 $false | ~spl6_1),
% 0.20/0.39 inference(trivial_inequality_removal,[],[f111])).
% 0.20/0.39 thf(f111,plain,(
% 0.20/0.39 ($true = $false) | ~spl6_1),
% 0.20/0.39 inference(backward_demodulation,[],[f80,f66])).
% 0.20/0.39 thf(f66,plain,(
% 0.20/0.39 ((subset @ sK0 @ (cartprod @ sK1 @ sK2)) = $false) | ~spl6_1),
% 0.20/0.39 inference(avatar_component_clause,[],[f64])).
% 0.20/0.39 thf(f64,plain,(
% 0.20/0.39 spl6_1 <=> ((subset @ sK0 @ (cartprod @ sK1 @ sK2)) = $false)),
% 0.20/0.39 introduced(avatar_definition,[new_symbols(naming,[spl6_1])])).
% 0.20/0.39 thf(f80,plain,(
% 0.20/0.39 ((subset @ sK0 @ (cartprod @ sK1 @ sK2)) = $true)),
% 0.20/0.39 inference(binary_proxy_clausification,[],[f78])).
% 0.20/0.39 thf(f78,plain,(
% 0.20/0.39 ($true = ((subset @ sK0 @ (cartprod @ sK1 @ sK2)) & (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK1) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (dsetconstr @ sK2 @ (^[Y2 : $i]: (in @ (kpair @ Y0 @ Y2) @ sK0)))) & ((setadjoin @ Y1 @ emptyset) = (dsetconstr @ sK2 @ (^[Y2 : $i]: (in @ (kpair @ Y0 @ Y2) @ sK0))))))))))))),
% 0.20/0.39 inference(beta_eta_normalization,[],[f77])).
% 0.20/0.39 thf(f77,plain,(
% 0.20/0.39 (((^[Y0 : $i]: ((subset @ Y0 @ (cartprod @ sK1 @ sK2)) & (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK1) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ sK2 @ (^[Y3 : $i]: (in @ (kpair @ Y1 @ Y3) @ Y0)))) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ sK2 @ (^[Y3 : $i]: (in @ (kpair @ Y1 @ Y3) @ Y0)))))))))))) @ sK0) = $true)),
% 0.20/0.39 inference(trivial_inequality_removal,[],[f76])).
% 0.20/0.39 thf(f76,plain,(
% 0.20/0.39 ($true != $true) | (((^[Y0 : $i]: ((subset @ Y0 @ (cartprod @ sK1 @ sK2)) & (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK1) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ sK2 @ (^[Y3 : $i]: (in @ (kpair @ Y1 @ Y3) @ Y0)))) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ sK2 @ (^[Y3 : $i]: (in @ (kpair @ Y1 @ Y3) @ Y0)))))))))))) @ sK0) = $true)),
% 0.20/0.39 inference(superposition,[],[f52,f50])).
% 0.20/0.39 thf(f50,plain,(
% 0.20/0.39 ((in @ sK0 @ (dsetconstr @ (powerset @ (cartprod @ sK1 @ sK2)) @ (^[Y0 : $i]: ((subset @ Y0 @ (cartprod @ sK1 @ sK2)) & (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK1) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ sK2 @ (^[Y3 : $i]: (in @ (kpair @ Y1 @ Y3) @ Y0)))) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ sK2 @ (^[Y3 : $i]: (in @ (kpair @ Y1 @ Y3) @ Y0)))))))))))))) = $true)),
% 0.20/0.39 inference(beta_eta_normalization,[],[f46])).
% 0.20/0.39 thf(f46,plain,(
% 0.20/0.39 ($true = (in @ sK0 @ ((^[Y0 : $i]: ((^[Y1 : $i]: (dsetconstr @ (powerset @ (cartprod @ Y0 @ Y1)) @ (^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: (((^[Y6 : $i]: ((^[Y7 : $i]: ((^[Y8 : $i]: (subset @ Y8 @ (cartprod @ Y6 @ Y7))))))) @ Y3 @ Y4 @ Y5) & (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y3) => ((^[Y7 : $i]: ((^[Y8 : $i > $o]: ((^[Y9 : $i]: (?? @ $i @ (^[Y10 : $i]: ((in @ Y10 @ Y9) & ((setadjoin @ Y10 @ emptyset) = Y9))))) @ (dsetconstr @ Y7 @ (^[Y9 : $i]: (Y8 @ Y9))))))) @ Y4 @ (^[Y7 : $i]: (in @ (kpair @ Y6 @ Y7) @ Y5)))))))))))) @ Y0 @ Y1 @ Y2)))))) @ sK1 @ sK2)))),
% 0.20/0.39 inference(definition_unfolding,[],[f33,f44])).
% 0.20/0.39 thf(f44,plain,(
% 0.20/0.39 (funcSet = (^[Y0 : $i]: ((^[Y1 : $i]: (dsetconstr @ (powerset @ (cartprod @ Y0 @ Y1)) @ (^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: (((^[Y6 : $i]: ((^[Y7 : $i]: ((^[Y8 : $i]: (subset @ Y8 @ (cartprod @ Y6 @ Y7))))))) @ Y3 @ Y4 @ Y5) & (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y3) => ((^[Y7 : $i]: ((^[Y8 : $i > $o]: ((^[Y9 : $i]: (?? @ $i @ (^[Y10 : $i]: ((in @ Y10 @ Y9) & ((setadjoin @ Y10 @ emptyset) = Y9))))) @ (dsetconstr @ Y7 @ (^[Y9 : $i]: (Y8 @ Y9))))))) @ Y4 @ (^[Y7 : $i]: (in @ (kpair @ Y6 @ Y7) @ Y5)))))))))))) @ Y0 @ Y1 @ Y2)))))))),
% 0.20/0.39 inference(definition_unfolding,[],[f40,f43])).
% 0.20/0.39 thf(f43,plain,(
% 0.20/0.39 (func = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: (subset @ Y5 @ (cartprod @ Y3 @ Y4))))))) @ Y0 @ Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((^[Y4 : $i]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: (?? @ $i @ (^[Y7 : $i]: ((in @ Y7 @ Y6) & ((setadjoin @ Y7 @ emptyset) = Y6))))) @ (dsetconstr @ Y4 @ (^[Y6 : $i]: (Y5 @ Y6))))))) @ Y1 @ (^[Y4 : $i]: (in @ (kpair @ Y3 @ Y4) @ Y2)))))))))))))),
% 0.20/0.39 inference(definition_unfolding,[],[f32,f31,f42])).
% 0.20/0.39 thf(f42,plain,(
% 0.20/0.39 (ex1 = (^[Y0 : $i]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) & ((setadjoin @ Y3 @ emptyset) = Y2))))) @ (dsetconstr @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))))))))),
% 0.20/0.39 inference(definition_unfolding,[],[f36,f41])).
% 0.20/0.39 thf(f41,plain,(
% 0.20/0.39 (singleton = (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & ((setadjoin @ Y1 @ emptyset) = Y0))))))),
% 0.20/0.39 inference(cnf_transformation,[],[f16])).
% 0.20/0.39 thf(f16,plain,(
% 0.20/0.39 (singleton = (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & ((setadjoin @ Y1 @ emptyset) = Y0))))))),
% 0.20/0.39 inference(fool_elimination,[],[f15])).
% 0.20/0.39 thf(f15,plain,(
% 0.20/0.39 (singleton = (^[X0 : $i] : (? [X1] : (((setadjoin @ X1 @ emptyset) = X0) & (in @ X1 @ X0)))))),
% 0.20/0.39 inference(rectify,[],[f2])).
% 0.20/0.39 thf(f2,axiom,(
% 0.20/0.39 (singleton = (^[X0 : $i] : (? [X2] : (((setadjoin @ X2 @ emptyset) = X0) & (in @ X2 @ X0)))))),
% 0.20/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton)).
% 0.20/0.39 thf(f36,plain,(
% 0.20/0.39 (ex1 = (^[Y0 : $i]: ((^[Y1 : $i > $o]: (singleton @ (dsetconstr @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))))))))),
% 0.20/0.39 inference(cnf_transformation,[],[f12])).
% 0.20/0.39 thf(f12,plain,(
% 0.20/0.39 (ex1 = (^[Y0 : $i]: ((^[Y1 : $i > $o]: (singleton @ (dsetconstr @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))))))))),
% 0.20/0.39 inference(fool_elimination,[],[f3])).
% 0.20/0.39 thf(f3,axiom,(
% 0.20/0.39 ((^[X0 : $i, X1 : $i > $o] : (singleton @ (dsetconstr @ X0 @ (^[X2 : $i] : (X1 @ X2))))) = ex1)),
% 0.20/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ex1)).
% 0.20/0.39 thf(f31,plain,(
% 0.20/0.39 (breln = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (subset @ Y2 @ (cartprod @ Y0 @ Y1))))))))),
% 0.20/0.39 inference(cnf_transformation,[],[f20])).
% 0.20/0.39 thf(f20,plain,(
% 0.20/0.39 (breln = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (subset @ Y2 @ (cartprod @ Y0 @ Y1))))))))),
% 0.20/0.39 inference(fool_elimination,[],[f19])).
% 0.20/0.39 thf(f19,plain,(
% 0.20/0.39 ((^[X0 : $i, X1 : $i, X2 : $i] : (subset @ X2 @ (cartprod @ X0 @ X1))) = breln)),
% 0.20/0.39 inference(rectify,[],[f4])).
% 0.20/0.39 thf(f4,axiom,(
% 0.20/0.39 ((^[X0 : $i, X4 : $i, X5 : $i] : (subset @ X5 @ (cartprod @ X0 @ X4))) = breln)),
% 0.20/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',breln)).
% 0.20/0.39 thf(f32,plain,(
% 0.20/0.39 (func = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((breln @ Y0 @ Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (ex1 @ Y1 @ (^[Y4 : $i]: (in @ (kpair @ Y3 @ Y4) @ Y2)))))))))))))),
% 0.20/0.39 inference(cnf_transformation,[],[f22])).
% 0.20/0.39 thf(f22,plain,(
% 0.20/0.39 (func = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((breln @ Y0 @ Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (ex1 @ Y1 @ (^[Y4 : $i]: (in @ (kpair @ Y3 @ Y4) @ Y2)))))))))))))),
% 0.20/0.39 inference(fool_elimination,[],[f21])).
% 0.20/0.39 thf(f21,plain,(
% 0.20/0.39 ((^[X0 : $i, X1 : $i, X2 : $i] : (! [X3] : ((in @ X3 @ X0) => (ex1 @ X1 @ (^[X4 : $i] : (in @ (kpair @ X3 @ X4) @ X2)))) & (breln @ X0 @ X1 @ X2))) = func)),
% 0.20/0.39 inference(rectify,[],[f5])).
% 0.20/0.39 thf(f5,axiom,(
% 0.20/0.39 ((^[X0 : $i, X4 : $i, X6 : $i] : (! [X2] : ((in @ X2 @ X0) => (ex1 @ X4 @ (^[X3 : $i] : (in @ (kpair @ X2 @ X3) @ X6)))) & (breln @ X0 @ X4 @ X6))) = func)),
% 0.20/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',func)).
% 0.20/0.39 thf(f40,plain,(
% 0.20/0.39 (funcSet = (^[Y0 : $i]: ((^[Y1 : $i]: (dsetconstr @ (powerset @ (cartprod @ Y0 @ Y1)) @ (^[Y2 : $i]: (func @ Y0 @ Y1 @ Y2)))))))),
% 0.20/0.39 inference(cnf_transformation,[],[f18])).
% 0.20/0.39 thf(f18,plain,(
% 0.20/0.39 (funcSet = (^[Y0 : $i]: ((^[Y1 : $i]: (dsetconstr @ (powerset @ (cartprod @ Y0 @ Y1)) @ (^[Y2 : $i]: (func @ Y0 @ Y1 @ Y2)))))))),
% 0.20/0.39 inference(fool_elimination,[],[f17])).
% 0.20/0.39 thf(f17,plain,(
% 0.20/0.39 (funcSet = (^[X0 : $i, X1 : $i] : (dsetconstr @ (powerset @ (cartprod @ X0 @ X1)) @ (^[X2 : $i] : (func @ X0 @ X1 @ X2)))))),
% 0.20/0.39 inference(rectify,[],[f6])).
% 0.20/0.39 thf(f6,axiom,(
% 0.20/0.39 (funcSet = (^[X0 : $i, X4 : $i] : (dsetconstr @ (powerset @ (cartprod @ X0 @ X4)) @ (^[X7 : $i] : (func @ X0 @ X4 @ X7)))))),
% 0.20/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',funcSet)).
% 0.20/0.39 thf(f33,plain,(
% 0.20/0.39 ((in @ sK0 @ (funcSet @ sK1 @ sK2)) = $true)),
% 0.20/0.39 inference(cnf_transformation,[],[f26])).
% 0.20/0.39 thf(f26,plain,(
% 0.20/0.39 (dsetconstrER = $true) & (($true != (func @ sK1 @ sK2 @ sK0)) & ((in @ sK0 @ (funcSet @ sK1 @ sK2)) = $true))),
% 0.20/0.39 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f23,f25])).
% 0.20/0.39 thf(f25,plain,(
% 0.20/0.39 ? [X0,X1,X2] : (($true != (func @ X1 @ X2 @ X0)) & ((in @ X0 @ (funcSet @ X1 @ X2)) = $true)) => (($true != (func @ sK1 @ sK2 @ sK0)) & ((in @ sK0 @ (funcSet @ sK1 @ sK2)) = $true))),
% 0.20/0.39 introduced(choice_axiom,[])).
% 0.20/0.39 thf(f23,plain,(
% 0.20/0.39 (dsetconstrER = $true) & ? [X0,X1,X2] : (($true != (func @ X1 @ X2 @ X0)) & ((in @ X0 @ (funcSet @ X1 @ X2)) = $true))),
% 0.20/0.39 inference(ennf_transformation,[],[f14])).
% 0.20/0.39 thf(f14,plain,(
% 0.20/0.39 ~((dsetconstrER = $true) => ! [X0,X1,X2] : (((in @ X0 @ (funcSet @ X1 @ X2)) = $true) => ($true = (func @ X1 @ X2 @ X0))))),
% 0.20/0.39 inference(fool_elimination,[],[f13])).
% 0.20/0.39 thf(f13,plain,(
% 0.20/0.39 ~(dsetconstrER => ! [X0,X1,X2] : ((in @ X0 @ (funcSet @ X1 @ X2)) => (func @ X1 @ X2 @ X0)))),
% 0.20/0.39 inference(rectify,[],[f8])).
% 0.20/0.39 thf(f8,negated_conjecture,(
% 0.20/0.39 ~(dsetconstrER => ! [X7,X0,X4] : ((in @ X7 @ (funcSet @ X0 @ X4)) => (func @ X0 @ X4 @ X7)))),
% 0.20/0.39 inference(negated_conjecture,[],[f7])).
% 0.20/0.39 thf(f7,conjecture,(
% 0.20/0.39 dsetconstrER => ! [X7,X0,X4] : ((in @ X7 @ (funcSet @ X0 @ X4)) => (func @ X0 @ X4 @ X7))),
% 0.20/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',infuncsetfunc)).
% 0.20/0.39 thf(f52,plain,(
% 0.20/0.39 ( ! [X2 : $i,X0 : $i > $o,X1 : $i] : (($true != (in @ X2 @ (dsetconstr @ X1 @ X0))) | ($true = (X0 @ X2))) )),
% 0.20/0.39 inference(beta_eta_normalization,[],[f51])).
% 0.20/0.39 thf(f51,plain,(
% 0.20/0.39 ( ! [X2 : $i,X0 : $i > $o,X1 : $i] : (((in @ X2 @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X0 @ Y0)))) != $true) | ($true = (X0 @ X2))) )),
% 0.20/0.39 inference(trivial_inequality_removal,[],[f47])).
% 0.20/0.39 thf(f47,plain,(
% 0.20/0.39 ( ! [X2 : $i,X0 : $i > $o,X1 : $i] : (($true != $true) | ((in @ X2 @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X0 @ Y0)))) != $true) | ($true = (X0 @ X2))) )),
% 0.20/0.39 inference(definition_unfolding,[],[f39,f35])).
% 0.20/0.39 thf(f35,plain,(
% 0.20/0.39 (dsetconstrER = $true)),
% 0.20/0.39 inference(cnf_transformation,[],[f26])).
% 0.20/0.39 thf(f39,plain,(
% 0.20/0.39 ( ! [X2 : $i,X0 : $i > $o,X1 : $i] : (($true = (X0 @ X2)) | ((in @ X2 @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X0 @ Y0)))) != $true) | (dsetconstrER != $true)) )),
% 0.20/0.39 inference(cnf_transformation,[],[f30])).
% 0.20/0.39 thf(f30,plain,(
% 0.20/0.39 (! [X0 : $i > $o,X1,X2] : (($true = (X0 @ X2)) | ((in @ X2 @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X0 @ Y0)))) != $true)) | (dsetconstrER != $true)) & ((dsetconstrER = $true) | (((sK3 @ sK5) != $true) & ($true = (in @ sK5 @ (dsetconstr @ sK4 @ (^[Y0 : $i]: (sK3 @ Y0)))))))),
% 0.20/0.39 inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5])],[f28,f29])).
% 0.20/0.39 thf(f29,plain,(
% 0.20/0.39 ? [X3 : $i > $o,X4,X5] : (((X3 @ X5) != $true) & ((in @ X5 @ (dsetconstr @ X4 @ (^[Y0 : $i]: (X3 @ Y0)))) = $true)) => (((sK3 @ sK5) != $true) & ($true = (in @ sK5 @ (dsetconstr @ sK4 @ (^[Y0 : $i]: (sK3 @ Y0))))))),
% 0.20/0.39 introduced(choice_axiom,[])).
% 0.20/0.39 thf(f28,plain,(
% 0.20/0.39 (! [X0 : $i > $o,X1,X2] : (($true = (X0 @ X2)) | ((in @ X2 @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X0 @ Y0)))) != $true)) | (dsetconstrER != $true)) & ((dsetconstrER = $true) | ? [X3 : $i > $o,X4,X5] : (((X3 @ X5) != $true) & ((in @ X5 @ (dsetconstr @ X4 @ (^[Y0 : $i]: (X3 @ Y0)))) = $true)))),
% 0.20/0.39 inference(rectify,[],[f27])).
% 0.20/0.39 thf(f27,plain,(
% 0.20/0.39 (! [X0 : $i > $o,X1,X2] : (($true = (X0 @ X2)) | ((in @ X2 @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X0 @ Y0)))) != $true)) | (dsetconstrER != $true)) & ((dsetconstrER = $true) | ? [X0 : $i > $o,X1,X2] : (($true != (X0 @ X2)) & ((in @ X2 @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X0 @ Y0)))) = $true)))),
% 0.20/0.39 inference(nnf_transformation,[],[f24])).
% 0.20/0.39 thf(f24,plain,(
% 0.20/0.39 ! [X0 : $i > $o,X1,X2] : (($true = (X0 @ X2)) | ((in @ X2 @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X0 @ Y0)))) != $true)) <=> (dsetconstrER = $true)),
% 0.20/0.39 inference(ennf_transformation,[],[f11])).
% 0.20/0.39 thf(f11,plain,(
% 0.20/0.39 ! [X0 : $i > $o,X1,X2] : (((in @ X2 @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X0 @ Y0)))) = $true) => ($true = (X0 @ X2))) <=> (dsetconstrER = $true)),
% 0.20/0.39 inference(fool_elimination,[],[f10])).
% 0.20/0.39 thf(f10,plain,(
% 0.20/0.39 (! [X0 : $i > $o,X1,X2] : ((in @ X2 @ (dsetconstr @ X1 @ (^[X3 : $i] : (X0 @ X3)))) => (X0 @ X2)) = dsetconstrER)),
% 0.20/0.39 inference(rectify,[],[f1])).
% 0.20/0.39 thf(f1,axiom,(
% 0.20/0.39 (! [X1 : $i > $o,X0,X2] : ((in @ X2 @ (dsetconstr @ X0 @ (^[X3 : $i] : (X1 @ X3)))) => (X1 @ X2)) = dsetconstrER)),
% 0.20/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dsetconstrER)).
% 0.20/0.39 thf(f110,plain,(
% 0.20/0.39 ~spl6_2 | ~spl6_3),
% 0.20/0.39 inference(avatar_contradiction_clause,[],[f109])).
% 0.20/0.39 thf(f109,plain,(
% 0.20/0.39 $false | (~spl6_2 | ~spl6_3)),
% 0.20/0.39 inference(trivial_inequality_removal,[],[f108])).
% 0.20/0.39 thf(f108,plain,(
% 0.20/0.39 ($true = $false) | (~spl6_2 | ~spl6_3)),
% 0.20/0.39 inference(backward_demodulation,[],[f100,f107])).
% 0.20/0.39 thf(f107,plain,(
% 0.20/0.39 ((in @ (sK9 @ sK7) @ (setadjoin @ (sK9 @ sK7) @ emptyset)) = $false) | (~spl6_2 | ~spl6_3)),
% 0.20/0.39 inference(equality_resolution,[],[f106])).
% 0.20/0.39 thf(f106,plain,(
% 0.20/0.39 ( ! [X0 : $i] : (((setadjoin @ (sK9 @ sK7) @ emptyset) != (setadjoin @ X0 @ emptyset)) | ($false = (in @ X0 @ (setadjoin @ (sK9 @ sK7) @ emptyset)))) ) | (~spl6_2 | ~spl6_3)),
% 0.20/0.39 inference(superposition,[],[f101,f99])).
% 0.20/0.39 thf(f99,plain,(
% 0.20/0.39 ((setadjoin @ (sK9 @ sK7) @ emptyset) = (dsetconstr @ sK2 @ (^[Y0 : $i]: (in @ (kpair @ sK7 @ Y0) @ sK0)))) | ~spl6_3),
% 0.20/0.39 inference(trivial_inequality_removal,[],[f97])).
% 0.20/0.39 thf(f97,plain,(
% 0.20/0.39 ($true = $false) | ((setadjoin @ (sK9 @ sK7) @ emptyset) = (dsetconstr @ sK2 @ (^[Y0 : $i]: (in @ (kpair @ sK7 @ Y0) @ sK0)))) | ~spl6_3),
% 0.20/0.39 inference(superposition,[],[f74,f88])).
% 0.20/0.39 thf(f88,plain,(
% 0.20/0.39 ( ! [X1 : $i] : (((in @ X1 @ sK1) = $false) | ((dsetconstr @ sK2 @ (^[Y0 : $i]: (in @ (kpair @ X1 @ Y0) @ sK0))) = (setadjoin @ (sK9 @ X1) @ emptyset))) )),
% 0.20/0.39 inference(equality_proxy_clausification,[],[f86])).
% 0.20/0.39 thf(f86,plain,(
% 0.20/0.39 ( ! [X1 : $i] : ((((setadjoin @ (sK9 @ X1) @ emptyset) = (dsetconstr @ sK2 @ (^[Y0 : $i]: (in @ (kpair @ X1 @ Y0) @ sK0)))) = $true) | ((in @ X1 @ sK1) = $false)) )),
% 0.20/0.39 inference(binary_proxy_clausification,[],[f85])).
% 0.20/0.39 thf(f85,plain,(
% 0.20/0.39 ( ! [X1 : $i] : (((in @ X1 @ sK1) = $false) | (((in @ (sK9 @ X1) @ (dsetconstr @ sK2 @ (^[Y0 : $i]: (in @ (kpair @ X1 @ Y0) @ sK0)))) & ((setadjoin @ (sK9 @ X1) @ emptyset) = (dsetconstr @ sK2 @ (^[Y0 : $i]: (in @ (kpair @ X1 @ Y0) @ sK0))))) = $true)) )),
% 0.20/0.39 inference(beta_eta_normalization,[],[f84])).
% 0.20/0.39 thf(f84,plain,(
% 0.20/0.39 ( ! [X1 : $i] : (((in @ X1 @ sK1) = $false) | (((^[Y0 : $i]: ((in @ Y0 @ (dsetconstr @ sK2 @ (^[Y1 : $i]: (in @ (kpair @ X1 @ Y1) @ sK0)))) & ((setadjoin @ Y0 @ emptyset) = (dsetconstr @ sK2 @ (^[Y1 : $i]: (in @ (kpair @ X1 @ Y1) @ sK0)))))) @ (sK9 @ X1)) = $true)) )),
% 0.20/0.39 inference(sigma_clausification,[],[f83])).
% 0.20/0.39 thf(f83,plain,(
% 0.20/0.39 ( ! [X1 : $i] : (((in @ X1 @ sK1) = $false) | ((?? @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (dsetconstr @ sK2 @ (^[Y1 : $i]: (in @ (kpair @ X1 @ Y1) @ sK0)))) & ((setadjoin @ Y0 @ emptyset) = (dsetconstr @ sK2 @ (^[Y1 : $i]: (in @ (kpair @ X1 @ Y1) @ sK0))))))) = $true)) )),
% 0.20/0.39 inference(binary_proxy_clausification,[],[f82])).
% 0.20/0.39 thf(f82,plain,(
% 0.20/0.39 ( ! [X1 : $i] : ((((in @ X1 @ sK1) => (?? @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (dsetconstr @ sK2 @ (^[Y1 : $i]: (in @ (kpair @ X1 @ Y1) @ sK0)))) & ((setadjoin @ Y0 @ emptyset) = (dsetconstr @ sK2 @ (^[Y1 : $i]: (in @ (kpair @ X1 @ Y1) @ sK0)))))))) = $true)) )),
% 0.20/0.39 inference(beta_eta_normalization,[],[f81])).
% 0.20/0.39 thf(f81,plain,(
% 0.20/0.39 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((in @ Y0 @ sK1) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (dsetconstr @ sK2 @ (^[Y2 : $i]: (in @ (kpair @ Y0 @ Y2) @ sK0)))) & ((setadjoin @ Y1 @ emptyset) = (dsetconstr @ sK2 @ (^[Y2 : $i]: (in @ (kpair @ Y0 @ Y2) @ sK0))))))))) @ X1) = $true)) )),
% 0.20/0.39 inference(pi_clausification,[],[f79])).
% 0.20/0.39 thf(f79,plain,(
% 0.20/0.39 ($true = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK1) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (dsetconstr @ sK2 @ (^[Y2 : $i]: (in @ (kpair @ Y0 @ Y2) @ sK0)))) & ((setadjoin @ Y1 @ emptyset) = (dsetconstr @ sK2 @ (^[Y2 : $i]: (in @ (kpair @ Y0 @ Y2) @ sK0)))))))))))),
% 0.20/0.39 inference(binary_proxy_clausification,[],[f78])).
% 0.20/0.39 thf(f74,plain,(
% 0.20/0.39 ($true = (in @ sK7 @ sK1)) | ~spl6_3),
% 0.20/0.39 inference(avatar_component_clause,[],[f72])).
% 0.20/0.39 thf(f72,plain,(
% 0.20/0.39 spl6_3 <=> ($true = (in @ sK7 @ sK1))),
% 0.20/0.39 introduced(avatar_definition,[new_symbols(naming,[spl6_3])])).
% 0.20/0.39 thf(f101,plain,(
% 0.20/0.39 ( ! [X1 : $i] : (((setadjoin @ X1 @ emptyset) != (dsetconstr @ sK2 @ (^[Y0 : $i]: (in @ (kpair @ sK7 @ Y0) @ sK0)))) | ($false = (in @ X1 @ (setadjoin @ (sK9 @ sK7) @ emptyset)))) ) | (~spl6_2 | ~spl6_3)),
% 0.20/0.39 inference(backward_demodulation,[],[f69,f99])).
% 0.20/0.39 thf(f69,plain,(
% 0.20/0.39 ( ! [X1 : $i] : (((setadjoin @ X1 @ emptyset) != (dsetconstr @ sK2 @ (^[Y0 : $i]: (in @ (kpair @ sK7 @ Y0) @ sK0)))) | ($false = (in @ X1 @ (dsetconstr @ sK2 @ (^[Y0 : $i]: (in @ (kpair @ sK7 @ Y0) @ sK0)))))) ) | ~spl6_2),
% 0.20/0.39 inference(avatar_component_clause,[],[f68])).
% 0.20/0.39 thf(f68,plain,(
% 0.20/0.39 spl6_2 <=> ! [X1] : (($false = (in @ X1 @ (dsetconstr @ sK2 @ (^[Y0 : $i]: (in @ (kpair @ sK7 @ Y0) @ sK0))))) | ((setadjoin @ X1 @ emptyset) != (dsetconstr @ sK2 @ (^[Y0 : $i]: (in @ (kpair @ sK7 @ Y0) @ sK0)))))),
% 0.20/0.39 introduced(avatar_definition,[new_symbols(naming,[spl6_2])])).
% 0.20/0.39 thf(f100,plain,(
% 0.20/0.39 ((in @ (sK9 @ sK7) @ (setadjoin @ (sK9 @ sK7) @ emptyset)) = $true) | ~spl6_3),
% 0.20/0.39 inference(backward_demodulation,[],[f92,f99])).
% 0.20/0.39 thf(f92,plain,(
% 0.20/0.39 ((in @ (sK9 @ sK7) @ (dsetconstr @ sK2 @ (^[Y0 : $i]: (in @ (kpair @ sK7 @ Y0) @ sK0)))) = $true) | ~spl6_3),
% 0.20/0.39 inference(trivial_inequality_removal,[],[f90])).
% 0.20/0.39 thf(f90,plain,(
% 0.20/0.39 ((in @ (sK9 @ sK7) @ (dsetconstr @ sK2 @ (^[Y0 : $i]: (in @ (kpair @ sK7 @ Y0) @ sK0)))) = $true) | ($true = $false) | ~spl6_3),
% 0.20/0.39 inference(superposition,[],[f74,f87])).
% 0.20/0.39 thf(f87,plain,(
% 0.20/0.39 ( ! [X1 : $i] : (((in @ X1 @ sK1) = $false) | ($true = (in @ (sK9 @ X1) @ (dsetconstr @ sK2 @ (^[Y0 : $i]: (in @ (kpair @ X1 @ Y0) @ sK0)))))) )),
% 0.20/0.39 inference(binary_proxy_clausification,[],[f85])).
% 0.20/0.39 thf(f75,plain,(
% 0.20/0.39 spl6_3 | spl6_1),
% 0.20/0.39 inference(avatar_split_clause,[],[f58,f64,f72])).
% 0.20/0.39 thf(f58,plain,(
% 0.20/0.39 ($true = (in @ sK7 @ sK1)) | ((subset @ sK0 @ (cartprod @ sK1 @ sK2)) = $false)),
% 0.20/0.39 inference(binary_proxy_clausification,[],[f56])).
% 0.20/0.39 thf(f56,plain,(
% 0.20/0.39 (((in @ sK7 @ sK1) => (?? @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (dsetconstr @ sK2 @ (^[Y1 : $i]: (in @ (kpair @ sK7 @ Y1) @ sK0)))) & ((setadjoin @ Y0 @ emptyset) = (dsetconstr @ sK2 @ (^[Y1 : $i]: (in @ (kpair @ sK7 @ Y1) @ sK0)))))))) = $false) | ((subset @ sK0 @ (cartprod @ sK1 @ sK2)) = $false)),
% 0.20/0.39 inference(beta_eta_normalization,[],[f55])).
% 0.20/0.39 thf(f55,plain,(
% 0.20/0.39 ($false = ((^[Y0 : $i]: ((in @ Y0 @ sK1) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (dsetconstr @ sK2 @ (^[Y2 : $i]: (in @ (kpair @ Y0 @ Y2) @ sK0)))) & ((setadjoin @ Y1 @ emptyset) = (dsetconstr @ sK2 @ (^[Y2 : $i]: (in @ (kpair @ Y0 @ Y2) @ sK0))))))))) @ sK7)) | ((subset @ sK0 @ (cartprod @ sK1 @ sK2)) = $false)),
% 0.20/0.39 inference(sigma_clausification,[],[f54])).
% 0.20/0.39 thf(f54,plain,(
% 0.20/0.39 ((subset @ sK0 @ (cartprod @ sK1 @ sK2)) = $false) | ($false = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK1) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (dsetconstr @ sK2 @ (^[Y2 : $i]: (in @ (kpair @ Y0 @ Y2) @ sK0)))) & ((setadjoin @ Y1 @ emptyset) = (dsetconstr @ sK2 @ (^[Y2 : $i]: (in @ (kpair @ Y0 @ Y2) @ sK0)))))))))))),
% 0.20/0.39 inference(binary_proxy_clausification,[],[f53])).
% 0.20/0.39 thf(f53,plain,(
% 0.20/0.39 ($true != ((subset @ sK0 @ (cartprod @ sK1 @ sK2)) & (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK1) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (dsetconstr @ sK2 @ (^[Y2 : $i]: (in @ (kpair @ Y0 @ Y2) @ sK0)))) & ((setadjoin @ Y1 @ emptyset) = (dsetconstr @ sK2 @ (^[Y2 : $i]: (in @ (kpair @ Y0 @ Y2) @ sK0))))))))))))),
% 0.20/0.39 inference(beta_eta_normalization,[],[f45])).
% 0.20/0.39 thf(f45,plain,(
% 0.20/0.39 ($true != ((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: (subset @ Y5 @ (cartprod @ Y3 @ Y4))))))) @ Y0 @ Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((^[Y4 : $i]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: (?? @ $i @ (^[Y7 : $i]: ((in @ Y7 @ Y6) & ((setadjoin @ Y7 @ emptyset) = Y6))))) @ (dsetconstr @ Y4 @ (^[Y6 : $i]: (Y5 @ Y6))))))) @ Y1 @ (^[Y4 : $i]: (in @ (kpair @ Y3 @ Y4) @ Y2)))))))))))) @ sK1 @ sK2 @ sK0))),
% 0.20/0.39 inference(definition_unfolding,[],[f34,f43])).
% 0.20/0.39 thf(f34,plain,(
% 0.20/0.39 ($true != (func @ sK1 @ sK2 @ sK0))),
% 0.20/0.39 inference(cnf_transformation,[],[f26])).
% 0.20/0.39 thf(f70,plain,(
% 0.20/0.39 spl6_1 | spl6_2),
% 0.20/0.39 inference(avatar_split_clause,[],[f62,f68,f64])).
% 0.20/0.39 thf(f62,plain,(
% 0.20/0.39 ( ! [X1 : $i] : (((subset @ sK0 @ (cartprod @ sK1 @ sK2)) = $false) | ($false = (in @ X1 @ (dsetconstr @ sK2 @ (^[Y0 : $i]: (in @ (kpair @ sK7 @ Y0) @ sK0))))) | ((setadjoin @ X1 @ emptyset) != (dsetconstr @ sK2 @ (^[Y0 : $i]: (in @ (kpair @ sK7 @ Y0) @ sK0))))) )),
% 0.20/0.39 inference(equality_proxy_clausification,[],[f61])).
% 0.20/0.39 thf(f61,plain,(
% 0.20/0.39 ( ! [X1 : $i] : (($false = (in @ X1 @ (dsetconstr @ sK2 @ (^[Y0 : $i]: (in @ (kpair @ sK7 @ Y0) @ sK0))))) | (((setadjoin @ X1 @ emptyset) = (dsetconstr @ sK2 @ (^[Y0 : $i]: (in @ (kpair @ sK7 @ Y0) @ sK0)))) = $false) | ((subset @ sK0 @ (cartprod @ sK1 @ sK2)) = $false)) )),
% 0.20/0.39 inference(binary_proxy_clausification,[],[f60])).
% 0.20/0.39 thf(f60,plain,(
% 0.20/0.39 ( ! [X1 : $i] : (((subset @ sK0 @ (cartprod @ sK1 @ sK2)) = $false) | (((in @ X1 @ (dsetconstr @ sK2 @ (^[Y0 : $i]: (in @ (kpair @ sK7 @ Y0) @ sK0)))) & ((setadjoin @ X1 @ emptyset) = (dsetconstr @ sK2 @ (^[Y0 : $i]: (in @ (kpair @ sK7 @ Y0) @ sK0))))) = $false)) )),
% 0.20/0.39 inference(beta_eta_normalization,[],[f59])).
% 0.20/0.39 thf(f59,plain,(
% 0.20/0.39 ( ! [X1 : $i] : (((subset @ sK0 @ (cartprod @ sK1 @ sK2)) = $false) | (((^[Y0 : $i]: ((in @ Y0 @ (dsetconstr @ sK2 @ (^[Y1 : $i]: (in @ (kpair @ sK7 @ Y1) @ sK0)))) & ((setadjoin @ Y0 @ emptyset) = (dsetconstr @ sK2 @ (^[Y1 : $i]: (in @ (kpair @ sK7 @ Y1) @ sK0)))))) @ X1) = $false)) )),
% 0.20/0.39 inference(pi_clausification,[],[f57])).
% 0.20/0.39 thf(f57,plain,(
% 0.20/0.39 ((?? @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (dsetconstr @ sK2 @ (^[Y1 : $i]: (in @ (kpair @ sK7 @ Y1) @ sK0)))) & ((setadjoin @ Y0 @ emptyset) = (dsetconstr @ sK2 @ (^[Y1 : $i]: (in @ (kpair @ sK7 @ Y1) @ sK0))))))) = $false) | ((subset @ sK0 @ (cartprod @ sK1 @ sK2)) = $false)),
% 0.20/0.39 inference(binary_proxy_clausification,[],[f56])).
% 0.20/0.39 % SZS output end Proof for theBenchmark
% 0.20/0.39 % (26867)------------------------------
% 0.20/0.39 % (26867)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.20/0.39 % (26867)Termination reason: Refutation
% 0.20/0.39
% 0.20/0.39 % (26867)Memory used [KB]: 5628
% 0.20/0.39 % (26867)Time elapsed: 0.015 s
% 0.20/0.39 % (26867)Instructions burned: 12 (million)
% 0.20/0.39 % (26867)------------------------------
% 0.20/0.39 % (26867)------------------------------
% 0.20/0.39 % (26860)Success in time 0.018 s
%------------------------------------------------------------------------------