TSTP Solution File: SEU780^2 by Vampire---4.8
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%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SEU780^2 : TPTP v8.2.0. Released v3.7.0.
% 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 : n025.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 03:51:28 EDT 2024
% Result : Theorem 0.11s 0.35s
% Output : Refutation 0.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SEU780^2 : TPTP v8.2.0. Released v3.7.0.
% 0.10/0.12 % 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
% 0.11/0.32 % Computer : n025.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Sun May 19 17:05:52 EDT 2024
% 0.11/0.33 % CPUTime :
% 0.11/0.33 This is a TH0_THM_EQU_NAR problem
% 0.11/0.33 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
% 0.11/0.34 % (28737)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)
% 0.11/0.34 % (28742)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.11/0.34 % (28740)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)
% 0.11/0.34 % (28741)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)
% 0.11/0.34 % (28739)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.11/0.34 % (28736)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.11/0.34 % (28738)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)
% 0.11/0.34 % (28743)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)
% 0.11/0.35 % (28739)Instruction limit reached!
% 0.11/0.35 % (28739)------------------------------
% 0.11/0.35 % (28739)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.11/0.35 % (28739)Termination reason: Unknown
% 0.11/0.35 % (28739)Termination phase: Preprocessing 3
% 0.11/0.35 % (28740)Instruction limit reached!
% 0.11/0.35 % (28740)------------------------------
% 0.11/0.35 % (28740)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.11/0.35 % (28740)Termination reason: Unknown
% 0.11/0.35 % (28740)Termination phase: Property scanning
% 0.11/0.35
% 0.11/0.35 % (28740)Memory used [KB]: 1023
% 0.11/0.35 % (28740)Time elapsed: 0.003 s
% 0.11/0.35 % (28740)Instructions burned: 3 (million)
% 0.11/0.35 % (28740)------------------------------
% 0.11/0.35 % (28740)------------------------------
% 0.11/0.35
% 0.11/0.35 % (28739)Memory used [KB]: 1023
% 0.11/0.35 % (28739)Time elapsed: 0.003 s
% 0.11/0.35 % (28739)Instructions burned: 3 (million)
% 0.11/0.35 % (28739)------------------------------
% 0.11/0.35 % (28739)------------------------------
% 0.11/0.35 % (28737)Instruction limit reached!
% 0.11/0.35 % (28737)------------------------------
% 0.11/0.35 % (28737)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.11/0.35 % (28737)Termination reason: Unknown
% 0.11/0.35 % (28737)Termination phase: Saturation
% 0.11/0.35
% 0.11/0.35 % (28737)Memory used [KB]: 5500
% 0.11/0.35 % (28737)Time elapsed: 0.004 s
% 0.11/0.35 % (28737)Instructions burned: 4 (million)
% 0.11/0.35 % (28737)------------------------------
% 0.11/0.35 % (28737)------------------------------
% 0.11/0.35 % (28743)Instruction limit reached!
% 0.11/0.35 % (28743)------------------------------
% 0.11/0.35 % (28743)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.11/0.35 % (28743)Termination reason: Unknown
% 0.11/0.35 % (28743)Termination phase: Property scanning
% 0.11/0.35
% 0.11/0.35 % (28743)Memory used [KB]: 1023
% 0.11/0.35 % (28743)Time elapsed: 0.003 s
% 0.11/0.35 % (28743)Instructions burned: 4 (million)
% 0.11/0.35 % (28743)------------------------------
% 0.11/0.35 % (28743)------------------------------
% 0.11/0.35 % (28741)Refutation not found, incomplete strategy
% 0.11/0.35 % (28741)------------------------------
% 0.11/0.35 % (28741)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.11/0.35 % (28741)Termination reason: Refutation not found, incomplete strategy
% 0.11/0.35
% 0.11/0.35
% 0.11/0.35 % (28741)Memory used [KB]: 5500
% 0.11/0.35 % (28741)Time elapsed: 0.005 s
% 0.11/0.35 % (28741)Instructions burned: 4 (million)
% 0.11/0.35 % (28741)------------------------------
% 0.11/0.35 % (28741)------------------------------
% 0.11/0.35 % (28742)First to succeed.
% 0.11/0.35 % (28736)Also succeeded, but the first one will report.
% 0.11/0.35 % (28742)Refutation found. Thanks to Tanya!
% 0.11/0.35 % SZS status Theorem for theBenchmark
% 0.11/0.35 % SZS output start Proof for theBenchmark
% 0.11/0.35 thf(func_def_0, type, in: $i > $i > $o).
% 0.11/0.35 thf(func_def_1, type, subset: $i > $i > $o).
% 0.11/0.35 thf(func_def_2, type, kpair: $i > $i > $i).
% 0.11/0.35 thf(func_def_3, type, cartprod: $i > $i > $i).
% 0.11/0.35 thf(func_def_4, type, breln: $i > $i > $i > $o).
% 0.11/0.35 thf(func_def_6, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
% 0.11/0.35 thf(func_def_8, type, breln1: $i > $i > $o).
% 0.11/0.35 thf(func_def_9, type, breln1compset: $i > $i > $i > $i).
% 0.11/0.35 thf(func_def_23, type, sK2: $i > $i > $o).
% 0.11/0.35 thf(func_def_33, type, ph11: !>[X0: $tType]:(X0)).
% 0.11/0.35 thf(f66,plain,(
% 0.11/0.35 $false),
% 0.11/0.35 inference(subsumption_resolution,[],[f65,f62])).
% 0.11/0.35 thf(f62,plain,(
% 0.11/0.35 ($true = (in @ sK12 @ sK5))),
% 0.11/0.35 inference(binary_proxy_clausification,[],[f60])).
% 0.11/0.35 thf(f60,plain,(
% 0.11/0.35 ($true = ((in @ sK12 @ sK5) & (in @ (kpair @ sK8 @ sK12) @ sK6)))),
% 0.11/0.35 inference(binary_proxy_clausification,[],[f58])).
% 0.11/0.35 thf(f58,plain,(
% 0.11/0.35 ($true = (((in @ sK12 @ sK5) & (in @ (kpair @ sK8 @ sK12) @ sK6)) & (in @ (kpair @ sK12 @ sK9) @ sK7)))),
% 0.11/0.35 inference(beta_eta_normalization,[],[f57])).
% 0.11/0.35 thf(f57,plain,(
% 0.11/0.35 ($true = ((^[Y0 : $i]: (((in @ Y0 @ sK5) & (in @ (kpair @ sK8 @ Y0) @ sK6)) & (in @ (kpair @ Y0 @ sK9) @ sK7))) @ sK12))),
% 0.11/0.35 inference(sigma_clausification,[],[f56])).
% 0.11/0.35 thf(f56,plain,(
% 0.11/0.35 ($true = (?? @ $i @ (^[Y0 : $i]: (((in @ Y0 @ sK5) & (in @ (kpair @ sK8 @ Y0) @ sK6)) & (in @ (kpair @ Y0 @ sK9) @ sK7)))))),
% 0.11/0.35 inference(beta_eta_normalization,[],[f55])).
% 0.11/0.35 thf(f55,plain,(
% 0.11/0.35 ($true = ((^[Y0 : $i]: ((^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (((in @ Y2 @ sK5) & (in @ (kpair @ Y0 @ Y2) @ sK6)) & (in @ (kpair @ Y2 @ Y1) @ sK7))))))) @ sK8 @ sK9))),
% 0.11/0.35 inference(trivial_inequality_removal,[],[f54])).
% 0.11/0.35 thf(f54,plain,(
% 0.11/0.35 ($true = ((^[Y0 : $i]: ((^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (((in @ Y2 @ sK5) & (in @ (kpair @ Y0 @ Y2) @ sK6)) & (in @ (kpair @ Y2 @ Y1) @ sK7))))))) @ sK8 @ sK9)) | ($true != $true)),
% 0.11/0.35 inference(superposition,[],[f50,f53])).
% 0.11/0.35 thf(f53,plain,(
% 0.11/0.35 ($true = (in @ (kpair @ sK8 @ sK9) @ (dpsetconstr @ sK5 @ sK5 @ (^[Y0 : $i]: ((^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (((in @ Y2 @ sK5) & (in @ (kpair @ Y0 @ Y2) @ sK6)) & (in @ (kpair @ Y2 @ Y1) @ sK7))))))))))),
% 0.11/0.35 inference(beta_eta_normalization,[],[f47])).
% 0.11/0.35 thf(f47,plain,(
% 0.11/0.35 ($true = (in @ (kpair @ sK8 @ sK9) @ ((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (dpsetconstr @ Y0 @ Y0 @ (^[Y3 : $i]: ((^[Y4 : $i]: (?? @ $i @ (^[Y5 : $i]: (((in @ Y5 @ Y0) & (in @ (kpair @ Y3 @ Y5) @ Y1)) & (in @ (kpair @ Y5 @ Y4) @ Y2))))))))))))) @ sK5 @ sK6 @ sK7)))),
% 0.11/0.35 inference(definition_unfolding,[],[f36,f40])).
% 0.11/0.35 thf(f40,plain,(
% 0.11/0.35 (breln1compset = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (dpsetconstr @ Y0 @ Y0 @ (^[Y3 : $i]: ((^[Y4 : $i]: (?? @ $i @ (^[Y5 : $i]: (((in @ Y5 @ Y0) & (in @ (kpair @ Y3 @ Y5) @ Y1)) & (in @ (kpair @ Y5 @ Y4) @ Y2))))))))))))))),
% 0.11/0.35 inference(cnf_transformation,[],[f14])).
% 0.11/0.35 thf(f14,plain,(
% 0.11/0.35 (breln1compset = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (dpsetconstr @ Y0 @ Y0 @ (^[Y3 : $i]: ((^[Y4 : $i]: (?? @ $i @ (^[Y5 : $i]: (((in @ Y5 @ Y0) & (in @ (kpair @ Y3 @ Y5) @ Y1)) & (in @ (kpair @ Y5 @ Y4) @ Y2))))))))))))))),
% 0.11/0.35 inference(fool_elimination,[],[f13])).
% 0.11/0.35 thf(f13,plain,(
% 0.11/0.35 ((^[X0 : $i, X1 : $i, X2 : $i] : (dpsetconstr @ X0 @ X0 @ (^[X3 : $i, X4 : $i] : (? [X5] : ((in @ (kpair @ X5 @ X4) @ X2) & (in @ (kpair @ X3 @ X5) @ X1) & (in @ X5 @ X0)))))) = breln1compset)),
% 0.11/0.35 inference(rectify,[],[f4])).
% 0.11/0.35 thf(f4,axiom,(
% 0.11/0.35 ((^[X0 : $i, X8 : $i, X9 : $i] : (dpsetconstr @ X0 @ X0 @ (^[X4 : $i, X5 : $i] : (? [X6] : ((in @ (kpair @ X6 @ X5) @ X9) & (in @ (kpair @ X4 @ X6) @ X8) & (in @ X6 @ X0)))))) = breln1compset)),
% 0.11/0.35 file('/export/starexec/sandbox/benchmark/theBenchmark.p',breln1compset)).
% 0.11/0.35 thf(f36,plain,(
% 0.11/0.35 ($true = (in @ (kpair @ sK8 @ sK9) @ (breln1compset @ sK5 @ sK6 @ sK7)))),
% 0.11/0.35 inference(cnf_transformation,[],[f28])).
% 0.11/0.35 thf(f28,plain,(
% 0.11/0.35 (dpsetconstrER = $true) & (($true = (breln1 @ sK5 @ sK6)) & (((! [X5] : (($true != (in @ X5 @ sK5)) | ($true != (in @ (kpair @ X5 @ sK9) @ sK7)) | ($true != (in @ (kpair @ sK8 @ X5) @ sK6))) & ($true = (in @ (kpair @ sK8 @ sK9) @ (breln1compset @ sK5 @ sK6 @ sK7))) & ($true = (in @ sK9 @ sK5))) & ($true = (in @ sK8 @ sK5))) & ($true = (breln1 @ sK5 @ sK7))))),
% 0.11/0.35 inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6,sK7,sK8,sK9])],[f18,f27,f26,f25,f24])).
% 0.11/0.35 thf(f24,plain,(
% 0.11/0.35 ? [X0,X1] : (($true = (breln1 @ X0 @ X1)) & ? [X2] : (? [X3] : (? [X4] : (! [X5] : (((in @ X5 @ X0) != $true) | ($true != (in @ (kpair @ X5 @ X4) @ X2)) | ($true != (in @ (kpair @ X3 @ X5) @ X1))) & ($true = (in @ (kpair @ X3 @ X4) @ (breln1compset @ X0 @ X1 @ X2))) & ((in @ X4 @ X0) = $true)) & ($true = (in @ X3 @ X0))) & ($true = (breln1 @ X0 @ X2)))) => (($true = (breln1 @ sK5 @ sK6)) & ? [X2] : (? [X3] : (? [X4] : (! [X5] : (($true != (in @ X5 @ sK5)) | ($true != (in @ (kpair @ X5 @ X4) @ X2)) | ($true != (in @ (kpair @ X3 @ X5) @ sK6))) & ($true = (in @ (kpair @ X3 @ X4) @ (breln1compset @ sK5 @ sK6 @ X2))) & ($true = (in @ X4 @ sK5))) & ($true = (in @ X3 @ sK5))) & ($true = (breln1 @ sK5 @ X2))))),
% 0.11/0.35 introduced(choice_axiom,[])).
% 0.11/0.35 thf(f25,plain,(
% 0.11/0.35 ? [X2] : (? [X3] : (? [X4] : (! [X5] : (($true != (in @ X5 @ sK5)) | ($true != (in @ (kpair @ X5 @ X4) @ X2)) | ($true != (in @ (kpair @ X3 @ X5) @ sK6))) & ($true = (in @ (kpair @ X3 @ X4) @ (breln1compset @ sK5 @ sK6 @ X2))) & ($true = (in @ X4 @ sK5))) & ($true = (in @ X3 @ sK5))) & ($true = (breln1 @ sK5 @ X2))) => (? [X3] : (? [X4] : (! [X5] : (($true != (in @ X5 @ sK5)) | ($true != (in @ (kpair @ X5 @ X4) @ sK7)) | ($true != (in @ (kpair @ X3 @ X5) @ sK6))) & ($true = (in @ (kpair @ X3 @ X4) @ (breln1compset @ sK5 @ sK6 @ sK7))) & ($true = (in @ X4 @ sK5))) & ($true = (in @ X3 @ sK5))) & ($true = (breln1 @ sK5 @ sK7)))),
% 0.11/0.35 introduced(choice_axiom,[])).
% 0.11/0.35 thf(f26,plain,(
% 0.11/0.35 ? [X3] : (? [X4] : (! [X5] : (($true != (in @ X5 @ sK5)) | ($true != (in @ (kpair @ X5 @ X4) @ sK7)) | ($true != (in @ (kpair @ X3 @ X5) @ sK6))) & ($true = (in @ (kpair @ X3 @ X4) @ (breln1compset @ sK5 @ sK6 @ sK7))) & ($true = (in @ X4 @ sK5))) & ($true = (in @ X3 @ sK5))) => (? [X4] : (! [X5] : (($true != (in @ X5 @ sK5)) | ($true != (in @ (kpair @ X5 @ X4) @ sK7)) | ($true != (in @ (kpair @ sK8 @ X5) @ sK6))) & ($true = (in @ (kpair @ sK8 @ X4) @ (breln1compset @ sK5 @ sK6 @ sK7))) & ($true = (in @ X4 @ sK5))) & ($true = (in @ sK8 @ sK5)))),
% 0.11/0.35 introduced(choice_axiom,[])).
% 0.11/0.35 thf(f27,plain,(
% 0.11/0.35 ? [X4] : (! [X5] : (($true != (in @ X5 @ sK5)) | ($true != (in @ (kpair @ X5 @ X4) @ sK7)) | ($true != (in @ (kpair @ sK8 @ X5) @ sK6))) & ($true = (in @ (kpair @ sK8 @ X4) @ (breln1compset @ sK5 @ sK6 @ sK7))) & ($true = (in @ X4 @ sK5))) => (! [X5] : (($true != (in @ X5 @ sK5)) | ($true != (in @ (kpair @ X5 @ sK9) @ sK7)) | ($true != (in @ (kpair @ sK8 @ X5) @ sK6))) & ($true = (in @ (kpair @ sK8 @ sK9) @ (breln1compset @ sK5 @ sK6 @ sK7))) & ($true = (in @ sK9 @ sK5)))),
% 0.11/0.35 introduced(choice_axiom,[])).
% 0.11/0.35 thf(f18,plain,(
% 0.11/0.35 (dpsetconstrER = $true) & ? [X0,X1] : (($true = (breln1 @ X0 @ X1)) & ? [X2] : (? [X3] : (? [X4] : (! [X5] : (((in @ X5 @ X0) != $true) | ($true != (in @ (kpair @ X5 @ X4) @ X2)) | ($true != (in @ (kpair @ X3 @ X5) @ X1))) & ($true = (in @ (kpair @ X3 @ X4) @ (breln1compset @ X0 @ X1 @ X2))) & ((in @ X4 @ X0) = $true)) & ($true = (in @ X3 @ X0))) & ($true = (breln1 @ X0 @ X2))))),
% 0.11/0.35 inference(flattening,[],[f17])).
% 0.11/0.35 thf(f17,plain,(
% 0.11/0.35 ? [X0,X1] : (? [X2] : (? [X3] : (? [X4] : ((! [X5] : (((in @ X5 @ X0) != $true) | ($true != (in @ (kpair @ X5 @ X4) @ X2)) | ($true != (in @ (kpair @ X3 @ X5) @ X1))) & ($true = (in @ (kpair @ X3 @ X4) @ (breln1compset @ X0 @ X1 @ X2)))) & ((in @ X4 @ X0) = $true)) & ($true = (in @ X3 @ X0))) & ($true = (breln1 @ X0 @ X2))) & ($true = (breln1 @ X0 @ X1))) & (dpsetconstrER = $true)),
% 0.11/0.35 inference(ennf_transformation,[],[f10])).
% 0.11/0.35 thf(f10,plain,(
% 0.11/0.35 ~((dpsetconstrER = $true) => ! [X0,X1] : (($true = (breln1 @ X0 @ X1)) => ! [X2] : (($true = (breln1 @ X0 @ X2)) => ! [X3] : (($true = (in @ X3 @ X0)) => ! [X4] : (((in @ X4 @ X0) = $true) => (($true = (in @ (kpair @ X3 @ X4) @ (breln1compset @ X0 @ X1 @ X2))) => ? [X5] : (($true = (in @ (kpair @ X3 @ X5) @ X1)) & ((in @ X5 @ X0) = $true) & ($true = (in @ (kpair @ X5 @ X4) @ X2)))))))))),
% 0.11/0.35 inference(fool_elimination,[],[f9])).
% 0.11/0.35 thf(f9,plain,(
% 0.11/0.35 ~(dpsetconstrER => ! [X0,X1] : ((breln1 @ X0 @ X1) => ! [X2] : ((breln1 @ X0 @ X2) => ! [X3] : ((in @ X3 @ X0) => ! [X4] : ((in @ X4 @ X0) => ((in @ (kpair @ X3 @ X4) @ (breln1compset @ X0 @ X1 @ X2)) => ? [X5] : ((in @ (kpair @ X5 @ X4) @ X2) & (in @ (kpair @ X3 @ X5) @ X1) & (in @ X5 @ X0))))))))),
% 0.11/0.35 inference(rectify,[],[f6])).
% 0.11/0.35 thf(f6,negated_conjecture,(
% 0.11/0.35 ~(dpsetconstrER => ! [X0,X8] : ((breln1 @ X0 @ X8) => ! [X9] : ((breln1 @ X0 @ X9) => ! [X4] : ((in @ X4 @ X0) => ! [X5] : ((in @ X5 @ X0) => ((in @ (kpair @ X4 @ X5) @ (breln1compset @ X0 @ X8 @ X9)) => ? [X6] : ((in @ (kpair @ X6 @ X5) @ X9) & (in @ (kpair @ X4 @ X6) @ X8) & (in @ X6 @ X0))))))))),
% 0.11/0.35 inference(negated_conjecture,[],[f5])).
% 0.11/0.35 thf(f5,conjecture,(
% 0.11/0.35 dpsetconstrER => ! [X0,X8] : ((breln1 @ X0 @ X8) => ! [X9] : ((breln1 @ X0 @ X9) => ! [X4] : ((in @ X4 @ X0) => ! [X5] : ((in @ X5 @ X0) => ((in @ (kpair @ X4 @ X5) @ (breln1compset @ X0 @ X8 @ X9)) => ? [X6] : ((in @ (kpair @ X6 @ X5) @ X9) & (in @ (kpair @ X4 @ X6) @ X8) & (in @ X6 @ X0)))))))),
% 0.11/0.35 file('/export/starexec/sandbox/benchmark/theBenchmark.p',breln1compE)).
% 0.11/0.35 thf(f50,plain,(
% 0.11/0.35 ( ! [X2 : $i > $i > $o,X3 : $i,X0 : $i,X1 : $i,X4 : $i] : (((in @ (kpair @ X1 @ X4) @ (dpsetconstr @ X0 @ X3 @ X2)) != $true) | ($true = (X2 @ X1 @ X4))) )),
% 0.11/0.35 inference(beta_eta_normalization,[],[f49])).
% 0.11/0.35 thf(f49,plain,(
% 0.11/0.35 ( ! [X2 : $i > $i > $o,X3 : $i,X0 : $i,X1 : $i,X4 : $i] : (((in @ (kpair @ X1 @ X4) @ (dpsetconstr @ X0 @ X3 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X2 @ Y0 @ Y1)))))) != $true) | ($true = (X2 @ X1 @ X4))) )),
% 0.11/0.35 inference(trivial_inequality_removal,[],[f43])).
% 0.11/0.35 thf(f43,plain,(
% 0.11/0.35 ( ! [X2 : $i > $i > $o,X3 : $i,X0 : $i,X1 : $i,X4 : $i] : (($true != $true) | ((in @ (kpair @ X1 @ X4) @ (dpsetconstr @ X0 @ X3 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X2 @ Y0 @ Y1)))))) != $true) | ($true = (X2 @ X1 @ X4))) )),
% 0.11/0.35 inference(definition_unfolding,[],[f32,f39])).
% 0.11/0.35 thf(f39,plain,(
% 0.11/0.35 (dpsetconstrER = $true)),
% 0.11/0.35 inference(cnf_transformation,[],[f28])).
% 0.11/0.35 thf(f32,plain,(
% 0.11/0.35 ( ! [X2 : $i > $i > $o,X3 : $i,X0 : $i,X1 : $i,X4 : $i] : (((in @ (kpair @ X1 @ X4) @ (dpsetconstr @ X0 @ X3 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X2 @ Y0 @ Y1)))))) != $true) | ($true = (X2 @ X1 @ X4)) | (dpsetconstrER != $true)) )),
% 0.11/0.35 inference(cnf_transformation,[],[f23])).
% 0.11/0.35 thf(f23,plain,(
% 0.11/0.35 (! [X0,X1,X2 : $i > $i > $o,X3,X4] : (((in @ (kpair @ X1 @ X4) @ (dpsetconstr @ X0 @ X3 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X2 @ Y0 @ Y1)))))) != $true) | ($true = (X2 @ X1 @ X4))) | (dpsetconstrER != $true)) & ((dpsetconstrER = $true) | (($true = (in @ (kpair @ sK1 @ sK4) @ (dpsetconstr @ sK0 @ sK3 @ (^[Y0 : $i]: ((^[Y1 : $i]: (sK2 @ Y0 @ Y1))))))) & ($true != (sK2 @ sK1 @ sK4))))),
% 0.11/0.35 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4])],[f21,f22])).
% 0.11/0.35 thf(f22,plain,(
% 0.11/0.35 ? [X5,X6,X7 : $i > $i > $o,X8,X9] : (($true = (in @ (kpair @ X6 @ X9) @ (dpsetconstr @ X5 @ X8 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X7 @ Y0 @ Y1))))))) & ($true != (X7 @ X6 @ X9))) => (($true = (in @ (kpair @ sK1 @ sK4) @ (dpsetconstr @ sK0 @ sK3 @ (^[Y0 : $i]: ((^[Y1 : $i]: (sK2 @ Y0 @ Y1))))))) & ($true != (sK2 @ sK1 @ sK4)))),
% 0.11/0.35 introduced(choice_axiom,[])).
% 0.11/0.35 thf(f21,plain,(
% 0.11/0.35 (! [X0,X1,X2 : $i > $i > $o,X3,X4] : (((in @ (kpair @ X1 @ X4) @ (dpsetconstr @ X0 @ X3 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X2 @ Y0 @ Y1)))))) != $true) | ($true = (X2 @ X1 @ X4))) | (dpsetconstrER != $true)) & ((dpsetconstrER = $true) | ? [X5,X6,X7 : $i > $i > $o,X8,X9] : (($true = (in @ (kpair @ X6 @ X9) @ (dpsetconstr @ X5 @ X8 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X7 @ Y0 @ Y1))))))) & ($true != (X7 @ X6 @ X9))))),
% 0.11/0.35 inference(rectify,[],[f20])).
% 0.11/0.35 thf(f20,plain,(
% 0.11/0.35 (! [X0,X1,X2 : $i > $i > $o,X3,X4] : (((in @ (kpair @ X1 @ X4) @ (dpsetconstr @ X0 @ X3 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X2 @ Y0 @ Y1)))))) != $true) | ($true = (X2 @ X1 @ X4))) | (dpsetconstrER != $true)) & ((dpsetconstrER = $true) | ? [X0,X1,X2 : $i > $i > $o,X3,X4] : (((in @ (kpair @ X1 @ X4) @ (dpsetconstr @ X0 @ X3 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X2 @ Y0 @ Y1)))))) = $true) & ($true != (X2 @ X1 @ X4))))),
% 0.11/0.35 inference(nnf_transformation,[],[f19])).
% 0.11/0.35 thf(f19,plain,(
% 0.11/0.35 ! [X0,X1,X2 : $i > $i > $o,X3,X4] : (((in @ (kpair @ X1 @ X4) @ (dpsetconstr @ X0 @ X3 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X2 @ Y0 @ Y1)))))) != $true) | ($true = (X2 @ X1 @ X4))) <=> (dpsetconstrER = $true)),
% 0.11/0.35 inference(ennf_transformation,[],[f16])).
% 0.11/0.35 thf(f16,plain,(
% 0.11/0.35 (dpsetconstrER = $true) <=> ! [X0,X1,X2 : $i > $i > $o,X3,X4] : (((in @ (kpair @ X1 @ X4) @ (dpsetconstr @ X0 @ X3 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X2 @ Y0 @ Y1)))))) = $true) => ($true = (X2 @ X1 @ X4)))),
% 0.11/0.35 inference(fool_elimination,[],[f15])).
% 0.11/0.35 thf(f15,plain,(
% 0.11/0.35 (! [X0,X1,X2 : $i > $i > $o,X3,X4] : ((in @ (kpair @ X1 @ X4) @ (dpsetconstr @ X0 @ X3 @ (^[X5 : $i, X6 : $i] : (X2 @ X5 @ X6)))) => (X2 @ X1 @ X4)) = dpsetconstrER)),
% 0.11/0.35 inference(rectify,[],[f2])).
% 0.11/0.35 thf(f2,axiom,(
% 0.11/0.35 (! [X0,X4,X3 : $i > $i > $o,X1,X5] : ((in @ (kpair @ X4 @ X5) @ (dpsetconstr @ X0 @ X1 @ (^[X6 : $i, X7 : $i] : (X3 @ X6 @ X7)))) => (X3 @ X4 @ X5)) = dpsetconstrER)),
% 0.11/0.35 file('/export/starexec/sandbox/benchmark/theBenchmark.p',dpsetconstrER)).
% 0.11/0.35 thf(f65,plain,(
% 0.11/0.35 ($true != (in @ sK12 @ sK5))),
% 0.11/0.35 inference(subsumption_resolution,[],[f64,f59])).
% 0.11/0.35 thf(f59,plain,(
% 0.11/0.35 ($true = (in @ (kpair @ sK12 @ sK9) @ sK7))),
% 0.11/0.35 inference(binary_proxy_clausification,[],[f58])).
% 0.11/0.35 thf(f64,plain,(
% 0.11/0.35 ($true != (in @ (kpair @ sK12 @ sK9) @ sK7)) | ($true != (in @ sK12 @ sK5))),
% 0.11/0.35 inference(trivial_inequality_removal,[],[f63])).
% 0.11/0.35 thf(f63,plain,(
% 0.11/0.35 ($true != (in @ sK12 @ sK5)) | ($true != (in @ (kpair @ sK12 @ sK9) @ sK7)) | ($true != $true)),
% 0.11/0.35 inference(superposition,[],[f37,f61])).
% 0.11/0.35 thf(f61,plain,(
% 0.11/0.35 ($true = (in @ (kpair @ sK8 @ sK12) @ sK6))),
% 0.11/0.35 inference(binary_proxy_clausification,[],[f60])).
% 0.11/0.35 thf(f37,plain,(
% 0.11/0.35 ( ! [X5 : $i] : (($true != (in @ (kpair @ sK8 @ X5) @ sK6)) | ($true != (in @ (kpair @ X5 @ sK9) @ sK7)) | ($true != (in @ X5 @ sK5))) )),
% 0.11/0.35 inference(cnf_transformation,[],[f28])).
% 0.11/0.35 % SZS output end Proof for theBenchmark
% 0.11/0.35 % (28742)------------------------------
% 0.11/0.35 % (28742)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.11/0.35 % (28742)Termination reason: Refutation
% 0.11/0.35
% 0.11/0.35 % (28742)Memory used [KB]: 5628
% 0.11/0.35 % (28742)Time elapsed: 0.009 s
% 0.11/0.35 % (28742)Instructions burned: 8 (million)
% 0.11/0.35 % (28742)------------------------------
% 0.11/0.35 % (28742)------------------------------
% 0.11/0.35 % (28735)Success in time 0.01 s
% 0.11/0.35 % Vampire---4.8 exiting
%------------------------------------------------------------------------------