TSTP Solution File: AGT037^2 by Vampire---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : AGT037^2 : TPTP v8.2.0. Released v5.2.0.
% 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 : n012.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 May 20 17:58:49 EDT 2024
% Result : Theorem 0.15s 0.38s
% Output : Refutation 0.15s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : AGT037^2 : TPTP v8.2.0. Released v5.2.0.
% 0.14/0.14 % 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
% 0.15/0.35 % Computer : n012.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Sat May 18 18:49:37 EDT 2024
% 0.15/0.35 % CPUTime :
% 0.15/0.35 This is a TH0_THM_EQU_NAR problem
% 0.15/0.35 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
% 0.15/0.37 % (21121)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.15/0.37 % (21122)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)
% 0.15/0.37 % (21123)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)
% 0.15/0.37 % (21124)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.15/0.37 % (21126)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)
% 0.15/0.37 % (21125)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)
% 0.15/0.37 % (21127)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.15/0.37 % (21128)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)
% 0.15/0.37 % (21124)Instruction limit reached!
% 0.15/0.37 % (21124)------------------------------
% 0.15/0.37 % (21124)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.37 % (21124)Termination reason: Unknown
% 0.15/0.37 % (21124)Termination phase: shuffling
% 0.15/0.37
% 0.15/0.37 % (21124)Memory used [KB]: 1023
% 0.15/0.37 % (21124)Time elapsed: 0.003 s
% 0.15/0.37 % (21124)Instructions burned: 2 (million)
% 0.15/0.37 % (21124)------------------------------
% 0.15/0.37 % (21124)------------------------------
% 0.15/0.37 % (21125)Instruction limit reached!
% 0.15/0.37 % (21125)------------------------------
% 0.15/0.37 % (21125)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.37 % (21125)Termination reason: Unknown
% 0.15/0.37 % (21125)Termination phase: shuffling
% 0.15/0.37
% 0.15/0.37 % (21125)Memory used [KB]: 1023
% 0.15/0.37 % (21125)Time elapsed: 0.003 s
% 0.15/0.37 % (21125)Instructions burned: 3 (million)
% 0.15/0.37 % (21125)------------------------------
% 0.15/0.37 % (21125)------------------------------
% 0.15/0.37 % (21128)Instruction limit reached!
% 0.15/0.37 % (21128)------------------------------
% 0.15/0.37 % (21128)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.37 % (21128)Termination reason: Unknown
% 0.15/0.37 % (21128)Termination phase: shuffling
% 0.15/0.37
% 0.15/0.37 % (21128)Memory used [KB]: 1023
% 0.15/0.37 % (21128)Time elapsed: 0.004 s
% 0.15/0.37 % (21128)Instructions burned: 3 (million)
% 0.15/0.37 % (21128)------------------------------
% 0.15/0.37 % (21128)------------------------------
% 0.15/0.38 % (21122)Instruction limit reached!
% 0.15/0.38 % (21122)------------------------------
% 0.15/0.38 % (21122)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.38 % (21122)Termination reason: Unknown
% 0.15/0.38 % (21122)Termination phase: Property scanning
% 0.15/0.38
% 0.15/0.38 % (21122)Memory used [KB]: 1151
% 0.15/0.38 % (21122)Time elapsed: 0.005 s
% 0.15/0.38 % (21122)Instructions burned: 5 (million)
% 0.15/0.38 % (21122)------------------------------
% 0.15/0.38 % (21122)------------------------------
% 0.15/0.38 % (21126)Refutation not found, incomplete strategy
% 0.15/0.38 % (21126)------------------------------
% 0.15/0.38 % (21126)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.38 % (21121)First to succeed.
% 0.15/0.38 % (21126)Termination reason: Refutation not found, incomplete strategy
% 0.15/0.38
% 0.15/0.38
% 0.15/0.38 % (21126)Memory used [KB]: 5628
% 0.15/0.38 % (21126)Time elapsed: 0.009 s
% 0.15/0.38 % (21126)Instructions burned: 13 (million)
% 0.15/0.38 % (21126)------------------------------
% 0.15/0.38 % (21126)------------------------------
% 0.15/0.38 % (21127)Instruction limit reached!
% 0.15/0.38 % (21127)------------------------------
% 0.15/0.38 % (21127)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.38 % (21127)Termination reason: Unknown
% 0.15/0.38 % (21127)Termination phase: Saturation
% 0.15/0.38
% 0.15/0.38 % (21127)Memory used [KB]: 5628
% 0.15/0.38 % (21127)Time elapsed: 0.011 s
% 0.15/0.38 % (21127)Instructions burned: 18 (million)
% 0.15/0.38 % (21127)------------------------------
% 0.15/0.38 % (21127)------------------------------
% 0.15/0.38 % (21121)Refutation found. Thanks to Tanya!
% 0.15/0.38 % SZS status Theorem for theBenchmark
% 0.15/0.38 % SZS output start Proof for theBenchmark
% 0.15/0.38 thf(type_def_5, type, mu: $tType).
% 0.15/0.38 thf(func_def_0, type, mu: $tType).
% 0.15/0.38 thf(func_def_1, type, meq_ind: mu > mu > $i > $o).
% 0.15/0.38 thf(func_def_2, type, meq_prop: ($i > $o) > ($i > $o) > $i > $o).
% 0.15/0.38 thf(func_def_4, type, mnot: ($i > $o) > $i > $o).
% 0.15/0.38 thf(func_def_5, type, mor: ($i > $o) > ($i > $o) > $i > $o).
% 0.15/0.38 thf(func_def_6, type, mand: ($i > $o) > ($i > $o) > $i > $o).
% 0.15/0.38 thf(func_def_7, type, mimplies: ($i > $o) > ($i > $o) > $i > $o).
% 0.15/0.38 thf(func_def_8, type, mimplied: ($i > $o) > ($i > $o) > $i > $o).
% 0.15/0.38 thf(func_def_9, type, mequiv: ($i > $o) > ($i > $o) > $i > $o).
% 0.15/0.38 thf(func_def_10, type, mxor: ($i > $o) > ($i > $o) > $i > $o).
% 0.15/0.38 thf(func_def_11, type, mforall_ind: (mu > $i > $o) > $i > $o).
% 0.15/0.38 thf(func_def_12, type, mforall_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.15/0.38 thf(func_def_13, type, mexists_ind: (mu > $i > $o) > $i > $o).
% 0.15/0.38 thf(func_def_14, type, mexists_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.15/0.38 thf(func_def_15, type, mtrue: $i > $o).
% 0.15/0.38 thf(func_def_16, type, mfalse: $i > $o).
% 0.15/0.38 thf(func_def_17, type, mbox: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.15/0.38 thf(func_def_18, type, mdia: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.15/0.38 thf(func_def_19, type, mreflexive: ($i > $i > $o) > $o).
% 0.15/0.38 thf(func_def_20, type, msymmetric: ($i > $i > $o) > $o).
% 0.15/0.38 thf(func_def_21, type, mserial: ($i > $i > $o) > $o).
% 0.15/0.38 thf(func_def_22, type, mtransitive: ($i > $i > $o) > $o).
% 0.15/0.38 thf(func_def_23, type, meuclidean: ($i > $i > $o) > $o).
% 0.15/0.38 thf(func_def_24, type, mpartially_functional: ($i > $i > $o) > $o).
% 0.15/0.38 thf(func_def_25, type, mfunctional: ($i > $i > $o) > $o).
% 0.15/0.38 thf(func_def_26, type, mweakly_dense: ($i > $i > $o) > $o).
% 0.15/0.38 thf(func_def_27, type, mweakly_connected: ($i > $i > $o) > $o).
% 0.15/0.38 thf(func_def_28, type, mweakly_directed: ($i > $i > $o) > $o).
% 0.15/0.38 thf(func_def_29, type, mvalid: ($i > $o) > $o).
% 0.15/0.38 thf(func_def_30, type, minvalid: ($i > $o) > $o).
% 0.15/0.38 thf(func_def_31, type, msatisfiable: ($i > $o) > $o).
% 0.15/0.38 thf(func_def_32, type, mcountersatisfiable: ($i > $o) > $o).
% 0.15/0.38 thf(func_def_33, type, a1: $i > $i > $o).
% 0.15/0.38 thf(func_def_34, type, a2: $i > $i > $o).
% 0.15/0.38 thf(func_def_35, type, a3: $i > $i > $o).
% 0.15/0.38 thf(func_def_36, type, jan: mu).
% 0.15/0.38 thf(func_def_37, type, piotr: mu).
% 0.15/0.38 thf(func_def_38, type, cola: mu).
% 0.15/0.38 thf(func_def_39, type, pepsi: mu).
% 0.15/0.38 thf(func_def_40, type, beer: mu).
% 0.15/0.38 thf(func_def_41, type, likes: mu > mu > $i > $o).
% 0.15/0.38 thf(func_def_42, type, very_much_likes: mu > mu > $i > $o).
% 0.15/0.38 thf(func_def_43, type, possibly_likes: mu > mu > $i > $o).
% 0.15/0.38 thf(func_def_60, type, sK1: mu > $i > mu > $i).
% 0.15/0.38 thf(func_def_61, type, sK2: mu > $i > mu > $i).
% 0.15/0.38 thf(func_def_62, type, sK3: mu > $i > mu > $i).
% 0.15/0.38 thf(func_def_64, type, sK5: $i > $i).
% 0.15/0.38 thf(func_def_65, type, sK6: $i > $i).
% 0.15/0.38 thf(func_def_66, type, sK7: mu > $i > mu > $i).
% 0.15/0.38 thf(f479,plain,(
% 0.15/0.38 $false),
% 0.15/0.38 inference(trivial_inequality_removal,[],[f477])).
% 0.15/0.38 thf(f477,plain,(
% 0.15/0.38 ($false = $true)),
% 0.15/0.38 inference(superposition,[],[f476,f343])).
% 0.15/0.38 thf(f343,plain,(
% 0.15/0.38 ( ! [X1 : $i] : (($true = (a1 @ X1 @ (sK5 @ X1)))) )),
% 0.15/0.38 inference(not_proxy_clausification,[],[f340])).
% 0.15/0.38 thf(f340,plain,(
% 0.15/0.38 ( ! [X1 : $i] : (($false = (~ (a1 @ X1 @ (sK5 @ X1))))) )),
% 0.15/0.38 inference(binary_proxy_clausification,[],[f339])).
% 0.15/0.38 thf(f339,plain,(
% 0.15/0.38 ( ! [X1 : $i] : (($false = ((~ (likes @ piotr @ beer @ (sK5 @ X1))) | (~ (a1 @ X1 @ (sK5 @ X1)))))) )),
% 0.15/0.38 inference(beta_eta_normalization,[],[f338])).
% 0.15/0.38 thf(f338,plain,(
% 0.15/0.38 ( ! [X1 : $i] : (($false = ((^[Y0 : $i]: ((~ (likes @ piotr @ beer @ Y0)) | (~ (a1 @ X1 @ Y0)))) @ (sK5 @ X1)))) )),
% 0.15/0.38 inference(sigma_clausification,[],[f337])).
% 0.15/0.38 thf(f337,plain,(
% 0.15/0.38 ( ! [X1 : $i] : (($false = (!! @ $i @ (^[Y0 : $i]: ((~ (likes @ piotr @ beer @ Y0)) | (~ (a1 @ X1 @ Y0))))))) )),
% 0.15/0.38 inference(not_proxy_clausification,[],[f336])).
% 0.15/0.38 thf(f336,plain,(
% 0.15/0.38 ( ! [X1 : $i] : (($true = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (likes @ piotr @ beer @ Y0)) | (~ (a1 @ X1 @ Y0)))))))) )),
% 0.15/0.38 inference(beta_eta_normalization,[],[f335])).
% 0.15/0.38 thf(f335,plain,(
% 0.15/0.38 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (~ (!! @ $i @ (^[Y1 : $i]: ((~ (likes @ piotr @ beer @ Y1)) | (~ (a1 @ Y0 @ Y1))))))) @ X1))) )),
% 0.15/0.38 inference(pi_clausification,[],[f334])).
% 0.15/0.38 thf(f334,plain,(
% 0.15/0.38 ($true = (!! @ $i @ (^[Y0 : $i]: (~ (!! @ $i @ (^[Y1 : $i]: ((~ (likes @ piotr @ beer @ Y1)) | (~ (a1 @ Y0 @ Y1)))))))))),
% 0.15/0.38 inference(beta_eta_normalization,[],[f210])).
% 0.15/0.38 thf(f210,plain,(
% 0.15/0.38 ($true = ((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ ((^[Y2 : $i > $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5) | (~ (Y2 @ Y4 @ Y5)))))))))) @ Y0 @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y1)))))) @ a1 @ (likes @ piotr @ beer))))),
% 0.15/0.38 inference(definition_unfolding,[],[f157,f163,f208])).
% 0.15/0.38 thf(f208,plain,(
% 0.15/0.38 (mdia = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ ((^[Y2 : $i > $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5) | (~ (Y2 @ Y4 @ Y5)))))))))) @ Y0 @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y1)))))))),
% 0.15/0.38 inference(definition_unfolding,[],[f174,f196,f156,f196])).
% 0.15/0.38 thf(f156,plain,(
% 0.15/0.38 (mbox = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (Y0 @ Y2 @ Y3)))))))))))),
% 0.15/0.38 inference(cnf_transformation,[],[f132])).
% 0.15/0.38 thf(f132,plain,(
% 0.15/0.38 (mbox = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (Y0 @ Y2 @ Y3)))))))))))),
% 0.15/0.38 inference(fool_elimination,[],[f131])).
% 0.15/0.38 thf(f131,plain,(
% 0.15/0.38 ((^[X0 : $i > $i > $o, X1 : $i > $o, X2 : $i] : (! [X3] : (~(X0 @ X2 @ X3) | (X1 @ X3)))) = mbox)),
% 0.15/0.38 inference(rectify,[],[f16])).
% 0.15/0.38 thf(f16,axiom,(
% 0.15/0.38 ((^[X6 : $i > $i > $o, X3 : $i > $o, X2 : $i] : (! [X7] : (~(X6 @ X2 @ X7) | (X3 @ X7)))) = mbox)),
% 0.15/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mbox)).
% 0.15/0.38 thf(f196,plain,(
% 0.15/0.38 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.15/0.38 inference(cnf_transformation,[],[f130])).
% 0.15/0.38 thf(f130,plain,(
% 0.15/0.38 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.15/0.38 inference(fool_elimination,[],[f129])).
% 0.15/0.38 thf(f129,plain,(
% 0.15/0.38 (mnot = (^[X0 : $i > $o, X1 : $i] : (~(X0 @ X1))))),
% 0.15/0.38 inference(rectify,[],[f3])).
% 0.15/0.38 thf(f3,axiom,(
% 0.15/0.38 (mnot = (^[X3 : $i > $o, X2 : $i] : (~(X3 @ X2))))),
% 0.15/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mnot)).
% 0.15/0.38 thf(f174,plain,(
% 0.15/0.38 (mdia = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: (mnot @ (mbox @ Y0 @ (mnot @ Y1)))))))),
% 0.15/0.38 inference(cnf_transformation,[],[f68])).
% 0.15/0.38 thf(f68,plain,(
% 0.15/0.38 (mdia = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: (mnot @ (mbox @ Y0 @ (mnot @ Y1)))))))),
% 0.15/0.38 inference(fool_elimination,[],[f67])).
% 0.15/0.38 thf(f67,plain,(
% 0.15/0.38 (mdia = (^[X0 : $i > $i > $o, X1 : $i > $o] : (mnot @ (mbox @ X0 @ (mnot @ X1)))))),
% 0.15/0.38 inference(rectify,[],[f17])).
% 0.15/0.38 thf(f17,axiom,(
% 0.15/0.38 (mdia = (^[X6 : $i > $i > $o, X3 : $i > $o] : (mnot @ (mbox @ X6 @ (mnot @ X3)))))),
% 0.15/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mdia)).
% 0.15/0.38 thf(f163,plain,(
% 0.15/0.38 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.15/0.38 inference(cnf_transformation,[],[f102])).
% 0.15/0.38 thf(f102,plain,(
% 0.15/0.38 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.15/0.38 inference(fool_elimination,[],[f101])).
% 0.15/0.38 thf(f101,plain,(
% 0.15/0.38 ((^[X0 : $i > $o] : (! [X1] : (X0 @ X1))) = mvalid)),
% 0.15/0.38 inference(rectify,[],[f28])).
% 0.15/0.38 thf(f28,axiom,(
% 0.15/0.38 ((^[X3 : $i > $o] : (! [X2] : (X3 @ X2))) = mvalid)),
% 0.15/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mvalid)).
% 0.15/0.38 thf(f157,plain,(
% 0.15/0.38 ((mvalid @ (mdia @ a1 @ (likes @ piotr @ beer))) = $true)),
% 0.15/0.38 inference(cnf_transformation,[],[f108])).
% 0.15/0.38 thf(f108,plain,(
% 0.15/0.38 ((mvalid @ (mdia @ a1 @ (likes @ piotr @ beer))) = $true)),
% 0.15/0.38 inference(fool_elimination,[],[f107])).
% 0.15/0.38 thf(f107,plain,(
% 0.15/0.38 (mvalid @ (mdia @ a1 @ (likes @ piotr @ beer)))),
% 0.15/0.38 inference(rectify,[],[f43])).
% 0.15/0.38 thf(f43,axiom,(
% 0.15/0.38 (mvalid @ (mdia @ a1 @ (likes @ piotr @ beer)))),
% 0.15/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_a3_3)).
% 0.15/0.38 thf(f476,plain,(
% 0.15/0.38 ( ! [X0 : $i] : (($false = (a1 @ sK4 @ X0))) )),
% 0.15/0.38 inference(trivial_inequality_removal,[],[f473])).
% 0.15/0.38 thf(f473,plain,(
% 0.15/0.38 ( ! [X0 : $i] : (($false = (a1 @ sK4 @ X0)) | ($false != $false)) )),
% 0.15/0.38 inference(equality_factoring,[],[f462])).
% 0.15/0.38 thf(f462,plain,(
% 0.15/0.38 ( ! [X0 : $i,X1 : $i] : (($false = (a1 @ sK4 @ X0)) | ($false = (a1 @ X1 @ X0))) )),
% 0.15/0.38 inference(trivial_inequality_removal,[],[f457])).
% 0.15/0.38 thf(f457,plain,(
% 0.15/0.38 ( ! [X0 : $i,X1 : $i] : (($false = (a1 @ sK4 @ X0)) | ($false = $true) | ($false = (a1 @ X1 @ X0))) )),
% 0.15/0.38 inference(superposition,[],[f436,f454])).
% 0.15/0.38 thf(f454,plain,(
% 0.15/0.38 ( ! [X0 : $i] : (($false = (likes @ jan @ cola @ X0)) | ($false = (a1 @ sK4 @ X0))) )),
% 0.15/0.38 inference(trivial_inequality_removal,[],[f452])).
% 0.15/0.38 thf(f452,plain,(
% 0.15/0.38 ( ! [X0 : $i] : (($false = $true) | ($false = (likes @ jan @ cola @ X0)) | ($false = (a1 @ sK4 @ X0))) )),
% 0.15/0.38 inference(superposition,[],[f301,f315])).
% 0.15/0.38 thf(f315,plain,(
% 0.15/0.38 ( ! [X2 : mu,X3 : mu,X1 : $i,X4 : $i] : (($true = (possibly_likes @ X2 @ X3 @ X1)) | ($false = (a1 @ X1 @ X4)) | ((likes @ X2 @ X3 @ X4) = $false)) )),
% 0.15/0.38 inference(not_proxy_clausification,[],[f314])).
% 0.15/0.38 thf(f314,plain,(
% 0.15/0.38 ( ! [X2 : mu,X3 : mu,X1 : $i,X4 : $i] : (($true = (possibly_likes @ X2 @ X3 @ X1)) | ($false = (a1 @ X1 @ X4)) | ($true = (~ (likes @ X2 @ X3 @ X4)))) )),
% 0.15/0.38 inference(not_proxy_clausification,[],[f313])).
% 0.15/0.38 thf(f313,plain,(
% 0.15/0.38 ( ! [X2 : mu,X3 : mu,X1 : $i,X4 : $i] : (($true = (possibly_likes @ X2 @ X3 @ X1)) | ($true = (~ (a1 @ X1 @ X4))) | ($true = (~ (likes @ X2 @ X3 @ X4)))) )),
% 0.15/0.38 inference(binary_proxy_clausification,[],[f312])).
% 0.15/0.38 thf(f312,plain,(
% 0.15/0.38 ( ! [X2 : mu,X3 : mu,X1 : $i,X4 : $i] : (($true = (possibly_likes @ X2 @ X3 @ X1)) | (((~ (likes @ X2 @ X3 @ X4)) | (~ (a1 @ X1 @ X4))) = $true)) )),
% 0.15/0.38 inference(beta_eta_normalization,[],[f311])).
% 0.15/0.38 thf(f311,plain,(
% 0.15/0.38 ( ! [X2 : mu,X3 : mu,X1 : $i,X4 : $i] : (($true = (possibly_likes @ X2 @ X3 @ X1)) | ($true = ((^[Y0 : $i]: ((~ (likes @ X2 @ X3 @ Y0)) | (~ (a1 @ X1 @ Y0)))) @ X4))) )),
% 0.15/0.38 inference(pi_clausification,[],[f310])).
% 0.15/0.38 thf(f310,plain,(
% 0.15/0.38 ( ! [X2 : mu,X3 : mu,X1 : $i] : (($true = (possibly_likes @ X2 @ X3 @ X1)) | ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (likes @ X2 @ X3 @ Y0)) | (~ (a1 @ X1 @ Y0))))))) )),
% 0.15/0.38 inference(binary_proxy_clausification,[],[f309])).
% 0.15/0.38 thf(f309,plain,(
% 0.15/0.38 ( ! [X2 : mu,X3 : mu,X1 : $i] : ((((possibly_likes @ X2 @ X3 @ X1) | (!! @ $i @ (^[Y0 : $i]: ((~ (likes @ X2 @ X3 @ Y0)) | (~ (a1 @ X1 @ Y0)))))) = $true)) )),
% 0.15/0.38 inference(beta_eta_normalization,[],[f308])).
% 0.15/0.38 thf(f308,plain,(
% 0.15/0.38 ( ! [X2 : mu,X3 : mu,X1 : $i] : (($true = ((^[Y0 : mu]: ((possibly_likes @ X2 @ Y0 @ X1) | (!! @ $i @ (^[Y1 : $i]: ((~ (likes @ X2 @ Y0 @ Y1)) | (~ (a1 @ X1 @ Y1))))))) @ X3))) )),
% 0.15/0.38 inference(pi_clausification,[],[f307])).
% 0.15/0.38 thf(f307,plain,(
% 0.15/0.38 ( ! [X2 : mu,X1 : $i] : (($true = (!! @ mu @ (^[Y0 : mu]: ((possibly_likes @ X2 @ Y0 @ X1) | (!! @ $i @ (^[Y1 : $i]: ((~ (likes @ X2 @ Y0 @ Y1)) | (~ (a1 @ X1 @ Y1)))))))))) )),
% 0.15/0.38 inference(beta_eta_normalization,[],[f306])).
% 0.15/0.38 thf(f306,plain,(
% 0.15/0.38 ( ! [X2 : mu,X1 : $i] : (($true = ((^[Y0 : mu]: (!! @ mu @ (^[Y1 : mu]: ((possibly_likes @ Y0 @ Y1 @ X1) | (!! @ $i @ (^[Y2 : $i]: ((~ (likes @ Y0 @ Y1 @ Y2)) | (~ (a1 @ X1 @ Y2))))))))) @ X2))) )),
% 0.15/0.38 inference(pi_clausification,[],[f305])).
% 0.15/0.38 thf(f305,plain,(
% 0.15/0.38 ( ! [X1 : $i] : (((!! @ mu @ (^[Y0 : mu]: (!! @ mu @ (^[Y1 : mu]: ((possibly_likes @ Y0 @ Y1 @ X1) | (!! @ $i @ (^[Y2 : $i]: ((~ (likes @ Y0 @ Y1 @ Y2)) | (~ (a1 @ X1 @ Y2)))))))))) = $true)) )),
% 0.15/0.38 inference(beta_eta_normalization,[],[f304])).
% 0.15/0.38 thf(f304,plain,(
% 0.15/0.38 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ mu @ (^[Y1 : mu]: (!! @ mu @ (^[Y2 : mu]: ((possibly_likes @ Y1 @ Y2 @ Y0) | (!! @ $i @ (^[Y3 : $i]: ((~ (likes @ Y1 @ Y2 @ Y3)) | (~ (a1 @ Y0 @ Y3))))))))))) @ X1))) )),
% 0.15/0.38 inference(pi_clausification,[],[f303])).
% 0.15/0.38 thf(f303,plain,(
% 0.15/0.38 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ mu @ (^[Y1 : mu]: (!! @ mu @ (^[Y2 : mu]: ((possibly_likes @ Y1 @ Y2 @ Y0) | (!! @ $i @ (^[Y3 : $i]: ((~ (likes @ Y1 @ Y2 @ Y3)) | (~ (a1 @ Y0 @ Y3)))))))))))))),
% 0.15/0.38 inference(boolean_simplification,[],[f302])).
% 0.15/0.38 thf(f302,plain,(
% 0.15/0.38 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ mu @ (^[Y1 : mu]: (!! @ mu @ (^[Y2 : mu]: ((possibly_likes @ Y1 @ Y2 @ Y0) | (~ (~ (!! @ $i @ (^[Y3 : $i]: ((~ (likes @ Y1 @ Y2 @ Y3)) | (~ (a1 @ Y0 @ Y3)))))))))))))))),
% 0.15/0.38 inference(beta_eta_normalization,[],[f224])).
% 0.15/0.38 thf(f224,plain,(
% 0.15/0.38 ($true = ((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : mu > $i > $o]: ((^[Y1 : $i]: (!! @ mu @ (^[Y2 : mu]: (Y0 @ Y2 @ Y1)))))) @ (^[Y0 : mu]: ((^[Y1 : mu > $i > $o]: ((^[Y2 : $i]: (!! @ mu @ (^[Y3 : mu]: (Y1 @ Y3 @ Y2)))))) @ (^[Y1 : mu]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y5 @ Y6) | (Y4 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ ((^[Y2 : $i > $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ ((^[Y4 : $i > $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y5 @ Y7) | (~ (Y4 @ Y6 @ Y7)))))))))) @ Y2 @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y3)))))) @ a1 @ (likes @ Y0 @ Y1)) @ (possibly_likes @ Y0 @ Y1))))))))),
% 0.15/0.38 inference(definition_unfolding,[],[f187,f163,f166,f166,f201,f208])).
% 0.15/0.38 thf(f201,plain,(
% 0.15/0.38 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y3 @ Y4) | (Y2 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ Y1)))))),
% 0.15/0.38 inference(definition_unfolding,[],[f152,f195,f196])).
% 0.15/0.38 thf(f195,plain,(
% 0.15/0.38 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))))),
% 0.15/0.38 inference(cnf_transformation,[],[f122])).
% 0.15/0.38 thf(f122,plain,(
% 0.15/0.38 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))))),
% 0.15/0.38 inference(fool_elimination,[],[f121])).
% 0.15/0.38 thf(f121,plain,(
% 0.15/0.38 ((^[X0 : $i > $o, X1 : $i > $o, X2 : $i] : ((X0 @ X2) | (X1 @ X2))) = mor)),
% 0.15/0.38 inference(rectify,[],[f4])).
% 0.15/0.38 thf(f4,axiom,(
% 0.15/0.38 ((^[X3 : $i > $o, X4 : $i > $o, X2 : $i] : ((X3 @ X2) | (X4 @ X2))) = mor)),
% 0.15/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mor)).
% 0.15/0.38 thf(f152,plain,(
% 0.15/0.38 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.15/0.38 inference(cnf_transformation,[],[f140])).
% 0.15/0.38 thf(f140,plain,(
% 0.15/0.38 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.15/0.38 inference(fool_elimination,[],[f139])).
% 0.15/0.38 thf(f139,plain,(
% 0.15/0.38 (mimplies = (^[X0 : $i > $o, X1 : $i > $o] : (mor @ (mnot @ X0) @ X1)))),
% 0.15/0.38 inference(rectify,[],[f6])).
% 0.15/0.38 thf(f6,axiom,(
% 0.15/0.38 (mimplies = (^[X3 : $i > $o, X4 : $i > $o] : (mor @ (mnot @ X3) @ X4)))),
% 0.15/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mimplies)).
% 0.15/0.38 thf(f166,plain,(
% 0.15/0.38 (mforall_ind = (^[Y0 : mu > $i > $o]: ((^[Y1 : $i]: (!! @ mu @ (^[Y2 : mu]: (Y0 @ Y2 @ Y1)))))))),
% 0.15/0.38 inference(cnf_transformation,[],[f82])).
% 0.15/0.38 thf(f82,plain,(
% 0.15/0.38 (mforall_ind = (^[Y0 : mu > $i > $o]: ((^[Y1 : $i]: (!! @ mu @ (^[Y2 : mu]: (Y0 @ Y2 @ Y1)))))))),
% 0.15/0.38 inference(fool_elimination,[],[f81])).
% 0.15/0.38 thf(f81,plain,(
% 0.15/0.38 ((^[X0 : mu > $i > $o, X1 : $i] : (! [X2 : mu] : (X0 @ X2 @ X1))) = mforall_ind)),
% 0.15/0.38 inference(rectify,[],[f10])).
% 0.15/0.38 thf(f10,axiom,(
% 0.15/0.38 ((^[X3 : mu > $i > $o, X2 : $i] : (! [X0 : mu] : (X3 @ X0 @ X2))) = mforall_ind)),
% 0.15/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mforall_ind)).
% 0.15/0.38 thf(f187,plain,(
% 0.15/0.38 ($true = (mvalid @ (mforall_ind @ (^[Y0 : mu]: (mforall_ind @ (^[Y1 : mu]: (mimplies @ (mdia @ a1 @ (likes @ Y0 @ Y1)) @ (possibly_likes @ Y0 @ Y1))))))))),
% 0.15/0.38 inference(cnf_transformation,[],[f96])).
% 0.15/0.38 thf(f96,plain,(
% 0.15/0.38 ($true = (mvalid @ (mforall_ind @ (^[Y0 : mu]: (mforall_ind @ (^[Y1 : mu]: (mimplies @ (mdia @ a1 @ (likes @ Y0 @ Y1)) @ (possibly_likes @ Y0 @ Y1))))))))),
% 0.15/0.38 inference(fool_elimination,[],[f95])).
% 0.15/0.38 thf(f95,plain,(
% 0.15/0.38 (mvalid @ (mforall_ind @ (^[X0 : mu] : (mforall_ind @ (^[X1 : mu] : (mimplies @ (mdia @ a1 @ (likes @ X0 @ X1)) @ (possibly_likes @ X0 @ X1)))))))),
% 0.15/0.38 inference(rectify,[],[f47])).
% 0.15/0.38 thf(f47,axiom,(
% 0.15/0.38 (mvalid @ (mforall_ind @ (^[X0 : mu] : (mforall_ind @ (^[X1 : mu] : (mimplies @ (mdia @ a1 @ (likes @ X0 @ X1)) @ (possibly_likes @ X0 @ X1)))))))),
% 0.15/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_user_communication_3)).
% 0.15/0.38 thf(f301,plain,(
% 0.15/0.38 ($false = (possibly_likes @ jan @ cola @ sK4))),
% 0.15/0.38 inference(sigma_clausification,[],[f300])).
% 0.15/0.38 thf(f300,plain,(
% 0.15/0.38 ((!! @ $i @ (possibly_likes @ jan @ cola)) != $true)),
% 0.15/0.38 inference(beta_eta_normalization,[],[f222])).
% 0.15/0.38 thf(f222,plain,(
% 0.15/0.38 ($true != ((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ (possibly_likes @ jan @ cola)))),
% 0.15/0.38 inference(definition_unfolding,[],[f181,f163])).
% 0.15/0.38 thf(f181,plain,(
% 0.15/0.38 ((mvalid @ (possibly_likes @ jan @ cola)) != $true)),
% 0.15/0.38 inference(cnf_transformation,[],[f149])).
% 0.15/0.38 thf(f149,plain,(
% 0.15/0.38 ((mvalid @ (possibly_likes @ jan @ cola)) != $true)),
% 0.15/0.38 inference(flattening,[],[f138])).
% 0.15/0.38 thf(f138,plain,(
% 0.15/0.38 ~((mvalid @ (possibly_likes @ jan @ cola)) = $true)),
% 0.15/0.38 inference(fool_elimination,[],[f137])).
% 0.15/0.38 thf(f137,plain,(
% 0.15/0.38 ~(mvalid @ (possibly_likes @ jan @ cola))),
% 0.15/0.38 inference(rectify,[],[f51])).
% 0.15/0.38 thf(f51,negated_conjecture,(
% 0.15/0.38 ~(mvalid @ (possibly_likes @ jan @ cola))),
% 0.15/0.38 inference(negated_conjecture,[],[f50])).
% 0.15/0.38 thf(f50,conjecture,(
% 0.15/0.38 (mvalid @ (possibly_likes @ jan @ cola))),
% 0.15/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj)).
% 0.15/0.38 thf(f436,plain,(
% 0.15/0.38 ( ! [X2 : $i,X1 : $i] : (((likes @ jan @ cola @ X2) = $true) | ($false = (a1 @ X1 @ X2))) )),
% 0.15/0.38 inference(not_proxy_clausification,[],[f435])).
% 0.15/0.38 thf(f435,plain,(
% 0.15/0.38 ( ! [X2 : $i,X1 : $i] : (((likes @ jan @ cola @ X2) = $true) | ($true = (~ (a1 @ X1 @ X2)))) )),
% 0.15/0.38 inference(binary_proxy_clausification,[],[f434])).
% 0.15/0.38 thf(f434,plain,(
% 0.15/0.38 ( ! [X2 : $i,X1 : $i] : (($true = ((likes @ jan @ cola @ X2) | (~ (a1 @ X1 @ X2))))) )),
% 0.15/0.38 inference(beta_eta_normalization,[],[f433])).
% 0.15/0.38 thf(f433,plain,(
% 0.15/0.38 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((likes @ jan @ cola @ Y0) | (~ (a1 @ X1 @ Y0)))) @ X2))) )),
% 0.15/0.38 inference(pi_clausification,[],[f432])).
% 0.15/0.38 thf(f432,plain,(
% 0.15/0.38 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((likes @ jan @ cola @ Y0) | (~ (a1 @ X1 @ Y0))))))) )),
% 0.15/0.38 inference(beta_eta_normalization,[],[f431])).
% 0.15/0.38 thf(f431,plain,(
% 0.15/0.38 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((likes @ jan @ cola @ Y1) | (~ (a1 @ Y0 @ Y1)))))) @ X1))) )),
% 0.15/0.38 inference(pi_clausification,[],[f430])).
% 0.15/0.38 thf(f430,plain,(
% 0.15/0.38 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((likes @ jan @ cola @ Y1) | (~ (a1 @ Y0 @ Y1))))))))),
% 0.15/0.38 inference(beta_eta_normalization,[],[f211])).
% 0.15/0.38 thf(f211,plain,(
% 0.15/0.38 ($true = ((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (Y0 @ Y2 @ Y3)))))))))) @ a1 @ (likes @ jan @ cola))))),
% 0.15/0.38 inference(definition_unfolding,[],[f158,f163,f156])).
% 0.15/0.38 thf(f158,plain,(
% 0.15/0.38 ((mvalid @ (mbox @ a1 @ (likes @ jan @ cola))) = $true)),
% 0.15/0.38 inference(cnf_transformation,[],[f86])).
% 0.15/0.38 thf(f86,plain,(
% 0.15/0.38 ((mvalid @ (mbox @ a1 @ (likes @ jan @ cola))) = $true)),
% 0.15/0.38 inference(fool_elimination,[],[f85])).
% 0.15/0.38 thf(f85,plain,(
% 0.15/0.38 (mvalid @ (mbox @ a1 @ (likes @ jan @ cola)))),
% 0.15/0.38 inference(rectify,[],[f32])).
% 0.15/0.38 thf(f32,axiom,(
% 0.15/0.38 (mvalid @ (mbox @ a1 @ (likes @ jan @ cola)))),
% 0.15/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_a1_1)).
% 0.15/0.38 % SZS output end Proof for theBenchmark
% 0.15/0.38 % (21121)------------------------------
% 0.15/0.38 % (21121)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.38 % (21121)Termination reason: Refutation
% 0.15/0.38
% 0.15/0.38 % (21121)Memory used [KB]: 6012
% 0.15/0.38 % (21121)Time elapsed: 0.016 s
% 0.15/0.38 % (21121)Instructions burned: 47 (million)
% 0.15/0.38 % (21121)------------------------------
% 0.15/0.38 % (21121)------------------------------
% 0.15/0.38 % (21120)Success in time 0.012 s
% 0.15/0.38 % Vampire---4.8 exiting
%------------------------------------------------------------------------------