TSTP Solution File: LCL859^1 by Vampire---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : LCL859^1 : TPTP v8.2.0. Bugfixed v5.0.0.
% 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 : n008.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 00:23:31 EDT 2024
% Result : Theorem 0.23s 0.42s
% Output : Refutation 0.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : LCL859^1 : TPTP v8.2.0. Bugfixed v5.0.0.
% 0.08/0.16 % 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
% 0.15/0.38 % Computer : n008.cluster.edu
% 0.15/0.38 % Model : x86_64 x86_64
% 0.15/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.38 % Memory : 8042.1875MB
% 0.15/0.38 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.38 % CPULimit : 300
% 0.15/0.38 % WCLimit : 300
% 0.15/0.38 % DateTime : Mon May 20 01:09:53 EDT 2024
% 0.15/0.38 % CPUTime :
% 0.15/0.38 This is a TH0_THM_EQU_NAR problem
% 0.15/0.38 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
% 0.23/0.40 % (352)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)
% 0.23/0.40 % (352)Instruction limit reached!
% 0.23/0.40 % (352)------------------------------
% 0.23/0.40 % (352)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.23/0.40 % (352)Termination reason: Unknown
% 0.23/0.40 % (352)Termination phase: shuffling
% 0.23/0.40
% 0.23/0.40 % (352)Memory used [KB]: 1023
% 0.23/0.40 % (352)Time elapsed: 0.003 s
% 0.23/0.40 % (352)Instructions burned: 3 (million)
% 0.23/0.40 % (352)------------------------------
% 0.23/0.40 % (352)------------------------------
% 0.23/0.40 % (346)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)
% 0.23/0.40 % (349)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)
% 0.23/0.40 % (345)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.23/0.40 % (349)Instruction limit reached!
% 0.23/0.40 % (349)------------------------------
% 0.23/0.40 % (349)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.23/0.40 % (349)Termination reason: Unknown
% 0.23/0.40 % (349)Termination phase: shuffling
% 0.23/0.40
% 0.23/0.40 % (349)Memory used [KB]: 1023
% 0.23/0.40 % (349)Time elapsed: 0.004 s
% 0.23/0.40 % (349)Instructions burned: 3 (million)
% 0.23/0.40 % (349)------------------------------
% 0.23/0.40 % (349)------------------------------
% 0.23/0.40 % (346)Instruction limit reached!
% 0.23/0.40 % (346)------------------------------
% 0.23/0.40 % (346)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.23/0.40 % (346)Termination reason: Unknown
% 0.23/0.40 % (346)Termination phase: Preprocessing 3
% 0.23/0.40
% 0.23/0.40 % (346)Memory used [KB]: 1023
% 0.23/0.40 % (346)Time elapsed: 0.004 s
% 0.23/0.40 % (346)Instructions burned: 5 (million)
% 0.23/0.40 % (346)------------------------------
% 0.23/0.40 % (346)------------------------------
% 0.23/0.40 % (348)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.23/0.40 % (348)Instruction limit reached!
% 0.23/0.40 % (348)------------------------------
% 0.23/0.40 % (348)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.23/0.40 % (348)Termination reason: Unknown
% 0.23/0.40 % (348)Termination phase: shuffling
% 0.23/0.40
% 0.23/0.40 % (348)Memory used [KB]: 1023
% 0.23/0.40 % (348)Time elapsed: 0.003 s
% 0.23/0.40 % (348)Instructions burned: 3 (million)
% 0.23/0.40 % (348)------------------------------
% 0.23/0.40 % (348)------------------------------
% 0.23/0.41 % (351)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.23/0.41 % (350)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)
% 0.23/0.41 % (347)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)
% 0.23/0.41 % (353)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 0.23/0.42 % (351)Instruction limit reached!
% 0.23/0.42 % (351)------------------------------
% 0.23/0.42 % (351)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.23/0.42 % (351)Termination reason: Unknown
% 0.23/0.42 % (351)Termination phase: Saturation
% 0.23/0.42
% 0.23/0.42 % (351)Memory used [KB]: 5628
% 0.23/0.42 % (351)Time elapsed: 0.011 s
% 0.23/0.42 % (351)Instructions burned: 19 (million)
% 0.23/0.42 % (355)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.23/0.42 % (351)------------------------------
% 0.23/0.42 % (351)------------------------------
% 0.23/0.42 % (354)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on theBenchmark for (2999ds/15Mi)
% 0.23/0.42 % (355)Instruction limit reached!
% 0.23/0.42 % (355)------------------------------
% 0.23/0.42 % (355)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.23/0.42 % (355)Termination reason: Unknown
% 0.23/0.42 % (355)Termination phase: shuffling
% 0.23/0.42
% 0.23/0.42 % (355)Memory used [KB]: 1023
% 0.23/0.42 % (355)Time elapsed: 0.003 s
% 0.23/0.42 % (355)Instructions burned: 3 (million)
% 0.23/0.42 % (355)------------------------------
% 0.23/0.42 % (355)------------------------------
% 0.23/0.42 % (345)First to succeed.
% 0.23/0.42 % (356)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on theBenchmark for (2999ds/1041Mi)
% 0.23/0.42 % (350)Also succeeded, but the first one will report.
% 0.23/0.42 % (347)Also succeeded, but the first one will report.
% 0.23/0.42 % (345)Refutation found. Thanks to Tanya!
% 0.23/0.42 % SZS status Theorem for theBenchmark
% 0.23/0.42 % SZS output start Proof for theBenchmark
% 0.23/0.42 thf(type_def_5, type, mu: $tType).
% 0.23/0.42 thf(func_def_0, type, mu: $tType).
% 0.23/0.42 thf(func_def_1, type, meq_ind: mu > mu > $i > $o).
% 0.23/0.42 thf(func_def_2, type, meq_prop: ($i > $o) > ($i > $o) > $i > $o).
% 0.23/0.42 thf(func_def_4, type, mnot: ($i > $o) > $i > $o).
% 0.23/0.42 thf(func_def_5, type, mor: ($i > $o) > ($i > $o) > $i > $o).
% 0.23/0.42 thf(func_def_6, type, mand: ($i > $o) > ($i > $o) > $i > $o).
% 0.23/0.42 thf(func_def_7, type, mimplies: ($i > $o) > ($i > $o) > $i > $o).
% 0.23/0.42 thf(func_def_8, type, mimplied: ($i > $o) > ($i > $o) > $i > $o).
% 0.23/0.42 thf(func_def_9, type, mequiv: ($i > $o) > ($i > $o) > $i > $o).
% 0.23/0.42 thf(func_def_10, type, mxor: ($i > $o) > ($i > $o) > $i > $o).
% 0.23/0.42 thf(func_def_11, type, mforall_ind: (mu > $i > $o) > $i > $o).
% 0.23/0.42 thf(func_def_12, type, mforall_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.23/0.42 thf(func_def_13, type, mexists_ind: (mu > $i > $o) > $i > $o).
% 0.23/0.42 thf(func_def_14, type, mexists_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.23/0.42 thf(func_def_15, type, mtrue: $i > $o).
% 0.23/0.42 thf(func_def_16, type, mfalse: $i > $o).
% 0.23/0.42 thf(func_def_17, type, mbox: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.23/0.42 thf(func_def_18, type, mdia: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.23/0.42 thf(func_def_19, type, mreflexive: ($i > $i > $o) > $o).
% 0.23/0.42 thf(func_def_20, type, msymmetric: ($i > $i > $o) > $o).
% 0.23/0.42 thf(func_def_21, type, mserial: ($i > $i > $o) > $o).
% 0.23/0.42 thf(func_def_22, type, mtransitive: ($i > $i > $o) > $o).
% 0.23/0.42 thf(func_def_23, type, meuclidean: ($i > $i > $o) > $o).
% 0.23/0.42 thf(func_def_24, type, mpartially_functional: ($i > $i > $o) > $o).
% 0.23/0.42 thf(func_def_25, type, mfunctional: ($i > $i > $o) > $o).
% 0.23/0.42 thf(func_def_26, type, mweakly_dense: ($i > $i > $o) > $o).
% 0.23/0.42 thf(func_def_27, type, mweakly_connected: ($i > $i > $o) > $o).
% 0.23/0.42 thf(func_def_28, type, mweakly_directed: ($i > $i > $o) > $o).
% 0.23/0.42 thf(func_def_29, type, mvalid: ($i > $o) > $o).
% 0.23/0.42 thf(func_def_30, type, minvalid: ($i > $o) > $o).
% 0.23/0.42 thf(func_def_31, type, msatisfiable: ($i > $o) > $o).
% 0.23/0.42 thf(func_def_32, type, mcountersatisfiable: ($i > $o) > $o).
% 0.23/0.42 thf(func_def_48, type, sK0: $i > $i > $o).
% 0.23/0.42 thf(f425,plain,(
% 0.23/0.42 $false),
% 0.23/0.42 inference(avatar_sat_refutation,[],[f252,f257,f262,f271,f276,f281,f316,f350,f359,f424])).
% 0.23/0.42 thf(f424,plain,(
% 0.23/0.42 ~spl1_2 | ~spl1_4 | ~spl1_5),
% 0.23/0.42 inference(avatar_contradiction_clause,[],[f423])).
% 0.23/0.42 thf(f423,plain,(
% 0.23/0.42 $false | (~spl1_2 | ~spl1_4 | ~spl1_5)),
% 0.23/0.42 inference(trivial_inequality_removal,[],[f418])).
% 0.23/0.42 thf(f418,plain,(
% 0.23/0.42 ($false = $true) | (~spl1_2 | ~spl1_4 | ~spl1_5)),
% 0.23/0.42 inference(superposition,[],[f261,f415])).
% 0.23/0.42 thf(f415,plain,(
% 0.23/0.42 ((sK0 @ sK5 @ sK9) = $false) | (~spl1_2 | ~spl1_4)),
% 0.23/0.42 inference(trivial_inequality_removal,[],[f408])).
% 0.23/0.42 thf(f408,plain,(
% 0.23/0.42 ((sK0 @ sK5 @ sK9) = $false) | ($false = $true) | (~spl1_2 | ~spl1_4)),
% 0.23/0.42 inference(superposition,[],[f378,f247])).
% 0.23/0.42 thf(f247,plain,(
% 0.23/0.42 ($false = (sK0 @ sK8 @ sK9)) | ~spl1_2),
% 0.23/0.42 inference(avatar_component_clause,[],[f245])).
% 0.23/0.42 thf(f245,plain,(
% 0.23/0.42 spl1_2 <=> ($false = (sK0 @ sK8 @ sK9))),
% 0.23/0.42 introduced(avatar_definition,[new_symbols(naming,[spl1_2])])).
% 0.23/0.42 thf(f378,plain,(
% 0.23/0.42 ( ! [X0 : $i] : (((sK0 @ sK8 @ X0) = $true) | ((sK0 @ sK5 @ X0) = $false)) ) | ~spl1_4),
% 0.23/0.42 inference(trivial_inequality_removal,[],[f376])).
% 0.23/0.42 thf(f376,plain,(
% 0.23/0.42 ( ! [X0 : $i] : (((sK0 @ sK5 @ X0) = $false) | ((sK0 @ sK8 @ X0) = $true) | ($false = $true)) ) | ~spl1_4),
% 0.23/0.42 inference(superposition,[],[f207,f256])).
% 0.23/0.42 thf(f256,plain,(
% 0.23/0.42 ($true = (sK0 @ sK5 @ sK8)) | ~spl1_4),
% 0.23/0.42 inference(avatar_component_clause,[],[f254])).
% 0.23/0.42 thf(f254,plain,(
% 0.23/0.42 spl1_4 <=> ($true = (sK0 @ sK5 @ sK8))),
% 0.23/0.42 introduced(avatar_definition,[new_symbols(naming,[spl1_4])])).
% 0.23/0.42 thf(f207,plain,(
% 0.23/0.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (sK0 @ X1 @ X2)) | ((sK0 @ X2 @ X3) = $true) | ((sK0 @ X1 @ X3) = $false)) )),
% 0.23/0.42 inference(binary_proxy_clausification,[],[f206])).
% 0.23/0.42 thf(f206,plain,(
% 0.23/0.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((sK0 @ X2 @ X3) = $true) | ($false = ((sK0 @ X1 @ X3) & (sK0 @ X1 @ X2)))) )),
% 0.23/0.42 inference(binary_proxy_clausification,[],[f205])).
% 0.23/0.42 thf(f205,plain,(
% 0.23/0.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((sK0 @ X1 @ X3) & (sK0 @ X1 @ X2)) => (sK0 @ X2 @ X3)))) )),
% 0.23/0.42 inference(beta_eta_normalization,[],[f204])).
% 0.23/0.42 thf(f204,plain,(
% 0.23/0.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((^[Y0 : $i]: (((sK0 @ X1 @ Y0) & (sK0 @ X1 @ X2)) => (sK0 @ X2 @ Y0))) @ X3) = $true)) )),
% 0.23/0.42 inference(pi_clausification,[],[f203])).
% 0.23/0.42 thf(f203,plain,(
% 0.23/0.42 ( ! [X2 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: (((sK0 @ X1 @ Y0) & (sK0 @ X1 @ X2)) => (sK0 @ X2 @ Y0)))) = $true)) )),
% 0.23/0.42 inference(beta_eta_normalization,[],[f202])).
% 0.23/0.42 thf(f202,plain,(
% 0.23/0.42 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((sK0 @ X1 @ Y1) & (sK0 @ X1 @ Y0)) => (sK0 @ Y0 @ Y1))))) @ X2) = $true)) )),
% 0.23/0.42 inference(pi_clausification,[],[f201])).
% 0.23/0.42 thf(f201,plain,(
% 0.23/0.42 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((sK0 @ X1 @ Y1) & (sK0 @ X1 @ Y0)) => (sK0 @ Y0 @ Y1)))))) = $true)) )),
% 0.23/0.42 inference(beta_eta_normalization,[],[f200])).
% 0.23/0.42 thf(f200,plain,(
% 0.23/0.42 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK0 @ Y0 @ Y2) & (sK0 @ Y0 @ Y1)) => (sK0 @ Y1 @ Y2))))))) @ X1))) )),
% 0.23/0.42 inference(pi_clausification,[],[f199])).
% 0.23/0.42 thf(f199,plain,(
% 0.23/0.42 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK0 @ Y0 @ Y2) & (sK0 @ Y0 @ Y1)) => (sK0 @ Y1 @ Y2)))))))) = $true)),
% 0.23/0.42 inference(beta_eta_normalization,[],[f198])).
% 0.23/0.42 thf(f198,plain,(
% 0.23/0.42 ($true = ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y1 @ Y2)) => (Y0 @ Y2 @ Y3))))))))) @ sK0))),
% 0.23/0.42 inference(duplicate_literal_removal,[],[f150])).
% 0.23/0.42 thf(f150,plain,(
% 0.23/0.42 ($true = ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y1 @ Y2)) => (Y0 @ Y2 @ Y3))))))))) @ sK0)) | ($true = ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y1 @ Y2)) => (Y0 @ Y2 @ Y3))))))))) @ sK0))),
% 0.23/0.42 inference(definition_unfolding,[],[f108,f135,f135])).
% 0.23/0.42 thf(f135,plain,(
% 0.23/0.42 (meuclidean = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y1 @ Y2)) => (Y0 @ Y2 @ Y3))))))))))),
% 0.23/0.42 inference(cnf_transformation,[],[f56])).
% 0.23/0.42 thf(f56,plain,(
% 0.23/0.42 (meuclidean = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y1 @ Y2)) => (Y0 @ Y2 @ Y3))))))))))),
% 0.23/0.42 inference(fool_elimination,[],[f55])).
% 0.23/0.42 thf(f55,plain,(
% 0.23/0.42 ((^[X0 : $i > $i > $o] : (! [X1,X2,X3] : (((X0 @ X3 @ X2) & (X0 @ X3 @ X1)) => (X0 @ X2 @ X1)))) = meuclidean)),
% 0.23/0.42 inference(rectify,[],[f22])).
% 0.23/0.42 thf(f22,axiom,(
% 0.23/0.42 ((^[X6 : $i > $i > $o] : (! [X10,X9,X8] : (((X6 @ X8 @ X9) & (X6 @ X8 @ X10)) => (X6 @ X9 @ X10)))) = meuclidean)),
% 0.23/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p',meuclidean)).
% 0.23/0.42 thf(f108,plain,(
% 0.23/0.42 ((meuclidean @ sK0) = $true) | ((meuclidean @ sK0) = $true)),
% 0.23/0.42 inference(cnf_transformation,[],[f99])).
% 0.23/0.42 thf(f99,plain,(
% 0.23/0.42 (((mreflexive @ sK0) != $true) | ((meuclidean @ sK0) != $true) | ((msymmetric @ sK0) != $true) | ((meuclidean @ sK0) != $true) | ((mreflexive @ sK0) != $true)) & ((((mreflexive @ sK0) = $true) & ((meuclidean @ sK0) = $true) & ((msymmetric @ sK0) = $true)) | (((meuclidean @ sK0) = $true) & ((mreflexive @ sK0) = $true)))),
% 0.23/0.42 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f97,f98])).
% 0.23/0.42 thf(f98,plain,(
% 0.23/0.42 ? [X0 : $i > $i > $o] : ((((mreflexive @ X0) != $true) | ((meuclidean @ X0) != $true) | ((msymmetric @ X0) != $true) | ((meuclidean @ X0) != $true) | ((mreflexive @ X0) != $true)) & ((((mreflexive @ X0) = $true) & ((meuclidean @ X0) = $true) & ((msymmetric @ X0) = $true)) | (((meuclidean @ X0) = $true) & ((mreflexive @ X0) = $true)))) => ((((mreflexive @ sK0) != $true) | ((meuclidean @ sK0) != $true) | ((msymmetric @ sK0) != $true) | ((meuclidean @ sK0) != $true) | ((mreflexive @ sK0) != $true)) & ((((mreflexive @ sK0) = $true) & ((meuclidean @ sK0) = $true) & ((msymmetric @ sK0) = $true)) | (((meuclidean @ sK0) = $true) & ((mreflexive @ sK0) = $true))))),
% 0.23/0.42 introduced(choice_axiom,[])).
% 0.23/0.42 thf(f97,plain,(
% 0.23/0.42 ? [X0 : $i > $i > $o] : ((((mreflexive @ X0) != $true) | ((meuclidean @ X0) != $true) | ((msymmetric @ X0) != $true) | ((meuclidean @ X0) != $true) | ((mreflexive @ X0) != $true)) & ((((mreflexive @ X0) = $true) & ((meuclidean @ X0) = $true) & ((msymmetric @ X0) = $true)) | (((meuclidean @ X0) = $true) & ((mreflexive @ X0) = $true))))),
% 0.23/0.42 inference(flattening,[],[f96])).
% 0.23/0.42 thf(f96,plain,(
% 0.23/0.42 ? [X0 : $i > $i > $o] : (((((mreflexive @ X0) != $true) | ((meuclidean @ X0) != $true) | ((msymmetric @ X0) != $true)) | (((meuclidean @ X0) != $true) | ((mreflexive @ X0) != $true))) & ((((mreflexive @ X0) = $true) & ((meuclidean @ X0) = $true) & ((msymmetric @ X0) = $true)) | (((meuclidean @ X0) = $true) & ((mreflexive @ X0) = $true))))),
% 0.23/0.42 inference(nnf_transformation,[],[f95])).
% 0.23/0.42 thf(f95,plain,(
% 0.23/0.42 ? [X0 : $i > $i > $o] : ((((meuclidean @ X0) = $true) & ((mreflexive @ X0) = $true)) <~> (((mreflexive @ X0) = $true) & ((meuclidean @ X0) = $true) & ((msymmetric @ X0) = $true)))),
% 0.23/0.42 inference(ennf_transformation,[],[f84])).
% 0.23/0.42 thf(f84,plain,(
% 0.23/0.42 ~! [X0 : $i > $i > $o] : ((((meuclidean @ X0) = $true) & ((mreflexive @ X0) = $true)) <=> (((mreflexive @ X0) = $true) & ((meuclidean @ X0) = $true) & ((msymmetric @ X0) = $true)))),
% 0.23/0.42 inference(fool_elimination,[],[f83])).
% 0.23/0.42 thf(f83,plain,(
% 0.23/0.42 ~! [X0 : $i > $i > $o] : (((msymmetric @ X0) & (mreflexive @ X0) & (meuclidean @ X0)) <=> ((meuclidean @ X0) & (mreflexive @ X0)))),
% 0.23/0.42 inference(rectify,[],[f33])).
% 0.23/0.42 thf(f33,negated_conjecture,(
% 0.23/0.42 ~! [X6 : $i > $i > $o] : (((msymmetric @ X6) & (mreflexive @ X6) & (meuclidean @ X6)) <=> ((meuclidean @ X6) & (mreflexive @ X6)))),
% 0.23/0.42 inference(negated_conjecture,[],[f32])).
% 0.23/0.42 thf(f32,conjecture,(
% 0.23/0.42 ! [X6 : $i > $i > $o] : (((msymmetric @ X6) & (mreflexive @ X6) & (meuclidean @ X6)) <=> ((meuclidean @ X6) & (mreflexive @ X6)))),
% 0.23/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj)).
% 0.23/0.42 thf(f261,plain,(
% 0.23/0.42 ((sK0 @ sK5 @ sK9) = $true) | ~spl1_5),
% 0.23/0.42 inference(avatar_component_clause,[],[f259])).
% 0.23/0.42 thf(f259,plain,(
% 0.23/0.42 spl1_5 <=> ((sK0 @ sK5 @ sK9) = $true)),
% 0.23/0.42 introduced(avatar_definition,[new_symbols(naming,[spl1_5])])).
% 0.23/0.42 thf(f359,plain,(
% 0.23/0.42 ~spl1_1),
% 0.23/0.42 inference(avatar_contradiction_clause,[],[f358])).
% 0.23/0.42 thf(f358,plain,(
% 0.23/0.42 $false | ~spl1_1),
% 0.23/0.42 inference(trivial_inequality_removal,[],[f354])).
% 0.23/0.42 thf(f354,plain,(
% 0.23/0.42 ($false = $true) | ~spl1_1),
% 0.23/0.42 inference(superposition,[],[f239,f243])).
% 0.23/0.42 thf(f243,plain,(
% 0.23/0.42 ((sK0 @ sK3 @ sK3) = $false) | ~spl1_1),
% 0.23/0.42 inference(avatar_component_clause,[],[f241])).
% 0.23/0.42 thf(f241,plain,(
% 0.23/0.42 spl1_1 <=> ((sK0 @ sK3 @ sK3) = $false)),
% 0.23/0.42 introduced(avatar_definition,[new_symbols(naming,[spl1_1])])).
% 0.23/0.42 thf(f239,plain,(
% 0.23/0.42 ( ! [X1 : $i] : (($true = (sK0 @ X1 @ X1))) )),
% 0.23/0.42 inference(beta_eta_normalization,[],[f238])).
% 0.23/0.42 thf(f238,plain,(
% 0.23/0.42 ( ! [X1 : $i] : ((((^[Y0 : $i]: (sK0 @ Y0 @ Y0)) @ X1) = $true)) )),
% 0.23/0.42 inference(pi_clausification,[],[f237])).
% 0.23/0.42 thf(f237,plain,(
% 0.23/0.42 ((!! @ $i @ (^[Y0 : $i]: (sK0 @ Y0 @ Y0))) = $true)),
% 0.23/0.42 inference(beta_eta_normalization,[],[f236])).
% 0.23/0.42 thf(f236,plain,(
% 0.23/0.42 (((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))) @ sK0) = $true)),
% 0.23/0.42 inference(duplicate_literal_removal,[],[f149])).
% 0.23/0.42 thf(f149,plain,(
% 0.23/0.42 (((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))) @ sK0) = $true) | (((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))) @ sK0) = $true)),
% 0.23/0.42 inference(definition_unfolding,[],[f109,f129,f129])).
% 0.23/0.42 thf(f129,plain,(
% 0.23/0.42 (mreflexive = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))))),
% 0.23/0.42 inference(cnf_transformation,[],[f60])).
% 0.23/0.42 thf(f60,plain,(
% 0.23/0.42 (mreflexive = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))))),
% 0.23/0.42 inference(fool_elimination,[],[f59])).
% 0.23/0.42 thf(f59,plain,(
% 0.23/0.42 (mreflexive = (^[X0 : $i > $i > $o] : (! [X1] : (X0 @ X1 @ X1))))),
% 0.23/0.42 inference(rectify,[],[f18])).
% 0.23/0.42 thf(f18,axiom,(
% 0.23/0.42 (mreflexive = (^[X6 : $i > $i > $o] : (! [X8] : (X6 @ X8 @ X8))))),
% 0.23/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mreflexive)).
% 0.23/0.42 thf(f109,plain,(
% 0.23/0.42 ((mreflexive @ sK0) = $true) | ((mreflexive @ sK0) = $true)),
% 0.23/0.42 inference(cnf_transformation,[],[f99])).
% 0.23/0.42 thf(f350,plain,(
% 0.23/0.42 ~spl1_7 | ~spl1_8 | ~spl1_9),
% 0.23/0.42 inference(avatar_contradiction_clause,[],[f349])).
% 0.23/0.42 thf(f349,plain,(
% 0.23/0.42 $false | (~spl1_7 | ~spl1_8 | ~spl1_9)),
% 0.23/0.42 inference(trivial_inequality_removal,[],[f345])).
% 0.23/0.42 thf(f345,plain,(
% 0.23/0.42 ($false = $true) | (~spl1_7 | ~spl1_8 | ~spl1_9)),
% 0.23/0.42 inference(superposition,[],[f280,f341])).
% 0.23/0.42 thf(f341,plain,(
% 0.23/0.42 ((sK0 @ sK5 @ sK7) = $false) | (~spl1_7 | ~spl1_8)),
% 0.23/0.42 inference(trivial_inequality_removal,[],[f337])).
% 0.23/0.42 thf(f337,plain,(
% 0.23/0.42 ($false = $true) | ((sK0 @ sK5 @ sK7) = $false) | (~spl1_7 | ~spl1_8)),
% 0.23/0.42 inference(superposition,[],[f270,f326])).
% 0.23/0.42 thf(f326,plain,(
% 0.23/0.42 ( ! [X0 : $i] : (((sK0 @ sK6 @ X0) = $true) | ((sK0 @ sK5 @ X0) = $false)) ) | ~spl1_8),
% 0.23/0.42 inference(trivial_inequality_removal,[],[f324])).
% 0.23/0.42 thf(f324,plain,(
% 0.23/0.42 ( ! [X0 : $i] : (($false = $true) | ((sK0 @ sK6 @ X0) = $true) | ((sK0 @ sK5 @ X0) = $false)) ) | ~spl1_8),
% 0.23/0.42 inference(superposition,[],[f207,f275])).
% 0.23/0.42 thf(f275,plain,(
% 0.23/0.42 ((sK0 @ sK5 @ sK6) = $true) | ~spl1_8),
% 0.23/0.42 inference(avatar_component_clause,[],[f273])).
% 0.23/0.42 thf(f273,plain,(
% 0.23/0.42 spl1_8 <=> ((sK0 @ sK5 @ sK6) = $true)),
% 0.23/0.42 introduced(avatar_definition,[new_symbols(naming,[spl1_8])])).
% 0.23/0.42 thf(f270,plain,(
% 0.23/0.42 ((sK0 @ sK6 @ sK7) = $false) | ~spl1_7),
% 0.23/0.42 inference(avatar_component_clause,[],[f268])).
% 0.23/0.42 thf(f268,plain,(
% 0.23/0.42 spl1_7 <=> ((sK0 @ sK6 @ sK7) = $false)),
% 0.23/0.42 introduced(avatar_definition,[new_symbols(naming,[spl1_7])])).
% 0.23/0.42 thf(f280,plain,(
% 0.23/0.42 ((sK0 @ sK5 @ sK7) = $true) | ~spl1_9),
% 0.23/0.42 inference(avatar_component_clause,[],[f278])).
% 0.23/0.42 thf(f278,plain,(
% 0.23/0.42 spl1_9 <=> ((sK0 @ sK5 @ sK7) = $true)),
% 0.23/0.42 introduced(avatar_definition,[new_symbols(naming,[spl1_9])])).
% 0.23/0.42 thf(f316,plain,(
% 0.23/0.42 ~spl1_3 | ~spl1_6),
% 0.23/0.42 inference(avatar_contradiction_clause,[],[f315])).
% 0.23/0.42 thf(f315,plain,(
% 0.23/0.42 $false | (~spl1_3 | ~spl1_6)),
% 0.23/0.42 inference(trivial_inequality_removal,[],[f310])).
% 0.23/0.42 thf(f310,plain,(
% 0.23/0.42 ($false = $true) | (~spl1_3 | ~spl1_6)),
% 0.23/0.42 inference(superposition,[],[f239,f306])).
% 0.23/0.42 thf(f306,plain,(
% 0.23/0.42 ($false = (sK0 @ sK2 @ sK2)) | (~spl1_3 | ~spl1_6)),
% 0.23/0.42 inference(trivial_inequality_removal,[],[f302])).
% 0.23/0.42 thf(f302,plain,(
% 0.23/0.42 ($false = $true) | ($false = (sK0 @ sK2 @ sK2)) | (~spl1_3 | ~spl1_6)),
% 0.23/0.42 inference(superposition,[],[f251,f291])).
% 0.23/0.42 thf(f291,plain,(
% 0.23/0.42 ( ! [X0 : $i] : (($true = (sK0 @ sK4 @ X0)) | ($false = (sK0 @ sK2 @ X0))) ) | ~spl1_6),
% 0.23/0.42 inference(trivial_inequality_removal,[],[f285])).
% 0.23/0.42 thf(f285,plain,(
% 0.23/0.42 ( ! [X0 : $i] : (($false = (sK0 @ sK2 @ X0)) | ($false = $true) | ($true = (sK0 @ sK4 @ X0))) ) | ~spl1_6),
% 0.23/0.42 inference(superposition,[],[f266,f207])).
% 0.23/0.42 thf(f266,plain,(
% 0.23/0.42 ((sK0 @ sK2 @ sK4) = $true) | ~spl1_6),
% 0.23/0.42 inference(avatar_component_clause,[],[f264])).
% 0.23/0.42 thf(f264,plain,(
% 0.23/0.42 spl1_6 <=> ((sK0 @ sK2 @ sK4) = $true)),
% 0.23/0.42 introduced(avatar_definition,[new_symbols(naming,[spl1_6])])).
% 0.23/0.42 thf(f251,plain,(
% 0.23/0.42 ((sK0 @ sK4 @ sK2) = $false) | ~spl1_3),
% 0.23/0.42 inference(avatar_component_clause,[],[f249])).
% 0.23/0.42 thf(f249,plain,(
% 0.23/0.42 spl1_3 <=> ((sK0 @ sK4 @ sK2) = $false)),
% 0.23/0.42 introduced(avatar_definition,[new_symbols(naming,[spl1_3])])).
% 0.23/0.42 thf(f281,plain,(
% 0.23/0.42 spl1_6 | spl1_1 | spl1_9),
% 0.23/0.42 inference(avatar_split_clause,[],[f227,f278,f241,f264])).
% 0.23/0.42 thf(f227,plain,(
% 0.23/0.42 ((sK0 @ sK2 @ sK4) = $true) | ((sK0 @ sK5 @ sK7) = $true) | ((sK0 @ sK3 @ sK3) = $false)),
% 0.23/0.43 inference(binary_proxy_clausification,[],[f225])).
% 0.23/0.43 thf(f225,plain,(
% 0.23/0.43 ((sK0 @ sK2 @ sK4) = $true) | ((sK0 @ sK3 @ sK3) = $false) | (((sK0 @ sK5 @ sK7) & (sK0 @ sK5 @ sK6)) = $true)),
% 0.23/0.43 inference(binary_proxy_clausification,[],[f223])).
% 0.23/0.43 thf(f223,plain,(
% 0.23/0.43 ($false = (((sK0 @ sK5 @ sK7) & (sK0 @ sK5 @ sK6)) => (sK0 @ sK6 @ sK7))) | ((sK0 @ sK2 @ sK4) = $true) | ((sK0 @ sK3 @ sK3) = $false)),
% 0.23/0.43 inference(beta_eta_normalization,[],[f222])).
% 0.23/0.43 thf(f222,plain,(
% 0.23/0.43 ((sK0 @ sK2 @ sK4) = $true) | ((sK0 @ sK3 @ sK3) = $false) | (((^[Y0 : $i]: (((sK0 @ sK5 @ Y0) & (sK0 @ sK5 @ sK6)) => (sK0 @ sK6 @ Y0))) @ sK7) = $false)),
% 0.23/0.43 inference(sigma_clausification,[],[f221])).
% 0.23/0.43 thf(f221,plain,(
% 0.23/0.43 ((!! @ $i @ (^[Y0 : $i]: (((sK0 @ sK5 @ Y0) & (sK0 @ sK5 @ sK6)) => (sK0 @ sK6 @ Y0)))) = $false) | ((sK0 @ sK3 @ sK3) = $false) | ((sK0 @ sK2 @ sK4) = $true)),
% 0.23/0.43 inference(beta_eta_normalization,[],[f220])).
% 0.23/0.43 thf(f220,plain,(
% 0.23/0.43 ((sK0 @ sK2 @ sK4) = $true) | ((sK0 @ sK3 @ sK3) = $false) | (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((sK0 @ sK5 @ Y1) & (sK0 @ sK5 @ Y0)) => (sK0 @ Y0 @ Y1))))) @ sK6) = $false)),
% 0.23/0.43 inference(sigma_clausification,[],[f219])).
% 0.23/0.43 thf(f219,plain,(
% 0.23/0.43 ((sK0 @ sK2 @ sK4) = $true) | ((sK0 @ sK3 @ sK3) = $false) | ($false = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((sK0 @ sK5 @ Y1) & (sK0 @ sK5 @ Y0)) => (sK0 @ Y0 @ Y1)))))))),
% 0.23/0.43 inference(binary_proxy_clausification,[],[f217])).
% 0.23/0.43 thf(f217,plain,(
% 0.23/0.43 ($false = ((sK0 @ sK2 @ sK4) => (sK0 @ sK4 @ sK2))) | ((sK0 @ sK3 @ sK3) = $false) | ($false = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((sK0 @ sK5 @ Y1) & (sK0 @ sK5 @ Y0)) => (sK0 @ Y0 @ Y1)))))))),
% 0.23/0.43 inference(beta_eta_normalization,[],[f216])).
% 0.23/0.43 thf(f216,plain,(
% 0.23/0.43 ($false = ((sK0 @ sK2 @ sK4) => (sK0 @ sK4 @ sK2))) | (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK0 @ Y0 @ Y2) & (sK0 @ Y0 @ Y1)) => (sK0 @ Y1 @ Y2))))))) @ sK5) = $false) | ((sK0 @ sK3 @ sK3) = $false)),
% 0.23/0.43 inference(sigma_clausification,[],[f215])).
% 0.23/0.43 thf(f215,plain,(
% 0.23/0.43 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK0 @ Y0 @ Y2) & (sK0 @ Y0 @ Y1)) => (sK0 @ Y1 @ Y2)))))))) != $true) | ((sK0 @ sK3 @ sK3) = $false) | ($false = ((sK0 @ sK2 @ sK4) => (sK0 @ sK4 @ sK2)))),
% 0.23/0.43 inference(beta_eta_normalization,[],[f214])).
% 0.23/0.43 thf(f214,plain,(
% 0.23/0.43 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK0 @ Y0 @ Y2) & (sK0 @ Y0 @ Y1)) => (sK0 @ Y1 @ Y2)))))))) != $true) | ((sK0 @ sK3 @ sK3) = $false) | ($false = ((^[Y0 : $i]: ((sK0 @ sK2 @ Y0) => (sK0 @ Y0 @ sK2))) @ sK4))),
% 0.23/0.43 inference(sigma_clausification,[],[f213])).
% 0.23/0.43 thf(f213,plain,(
% 0.23/0.43 ($false = (!! @ $i @ (^[Y0 : $i]: ((sK0 @ sK2 @ Y0) => (sK0 @ Y0 @ sK2))))) | ((sK0 @ sK3 @ sK3) = $false) | ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK0 @ Y0 @ Y2) & (sK0 @ Y0 @ Y1)) => (sK0 @ Y1 @ Y2)))))))) != $true)),
% 0.23/0.43 inference(beta_eta_normalization,[],[f212])).
% 0.23/0.43 thf(f212,plain,(
% 0.23/0.43 ($false = ((^[Y0 : $i]: (sK0 @ Y0 @ Y0)) @ sK3)) | ($false = (!! @ $i @ (^[Y0 : $i]: ((sK0 @ sK2 @ Y0) => (sK0 @ Y0 @ sK2))))) | ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK0 @ Y0 @ Y2) & (sK0 @ Y0 @ Y1)) => (sK0 @ Y1 @ Y2)))))))) != $true)),
% 0.23/0.43 inference(sigma_clausification,[],[f211])).
% 0.23/0.43 thf(f211,plain,(
% 0.23/0.43 ((!! @ $i @ (^[Y0 : $i]: (sK0 @ Y0 @ Y0))) != $true) | ($false = (!! @ $i @ (^[Y0 : $i]: ((sK0 @ sK2 @ Y0) => (sK0 @ Y0 @ sK2))))) | ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK0 @ Y0 @ Y2) & (sK0 @ Y0 @ Y1)) => (sK0 @ Y1 @ Y2)))))))) != $true)),
% 0.23/0.43 inference(beta_eta_normalization,[],[f210])).
% 0.23/0.43 thf(f210,plain,(
% 0.23/0.43 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK0 @ Y0 @ Y2) & (sK0 @ Y0 @ Y1)) => (sK0 @ Y1 @ Y2)))))))) != $true) | ((!! @ $i @ (^[Y0 : $i]: (sK0 @ Y0 @ Y0))) != $true) | ($false = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK0 @ Y0 @ Y1) => (sK0 @ Y1 @ Y0))))) @ sK2))),
% 0.23/0.43 inference(sigma_clausification,[],[f209])).
% 0.23/0.43 thf(f209,plain,(
% 0.23/0.43 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK0 @ Y0 @ Y1) => (sK0 @ Y1 @ Y0)))))) != $true) | ((!! @ $i @ (^[Y0 : $i]: (sK0 @ Y0 @ Y0))) != $true) | ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK0 @ Y0 @ Y2) & (sK0 @ Y0 @ Y1)) => (sK0 @ Y1 @ Y2)))))))) != $true)),
% 0.23/0.43 inference(beta_eta_normalization,[],[f208])).
% 0.23/0.43 thf(f208,plain,(
% 0.23/0.43 (((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1 @ Y2) => (Y0 @ Y2 @ Y1))))))) @ sK0) != $true) | ($true != ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y1 @ Y2)) => (Y0 @ Y2 @ Y3))))))))) @ sK0)) | (((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))) @ sK0) != $true)),
% 0.23/0.43 inference(duplicate_literal_removal,[],[f147])).
% 0.23/0.43 thf(f147,plain,(
% 0.23/0.43 ($true != ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y1 @ Y2)) => (Y0 @ Y2 @ Y3))))))))) @ sK0)) | (((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))) @ sK0) != $true) | (((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))) @ sK0) != $true) | (((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1 @ Y2) => (Y0 @ Y2 @ Y1))))))) @ sK0) != $true) | ($true != ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y1 @ Y2)) => (Y0 @ Y2 @ Y3))))))))) @ sK0))),
% 0.23/0.43 inference(definition_unfolding,[],[f111,f129,f135,f121,f135,f129])).
% 0.23/0.43 thf(f121,plain,(
% 0.23/0.43 (msymmetric = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1 @ Y2) => (Y0 @ Y2 @ Y1))))))))),
% 0.23/0.43 inference(cnf_transformation,[],[f78])).
% 0.23/0.43 thf(f78,plain,(
% 0.23/0.43 (msymmetric = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1 @ Y2) => (Y0 @ Y2 @ Y1))))))))),
% 0.23/0.43 inference(fool_elimination,[],[f77])).
% 0.23/0.43 thf(f77,plain,(
% 0.23/0.43 ((^[X0 : $i > $i > $o] : (! [X1,X2] : ((X0 @ X2 @ X1) => (X0 @ X1 @ X2)))) = msymmetric)),
% 0.23/0.43 inference(rectify,[],[f19])).
% 0.23/0.43 thf(f19,axiom,(
% 0.23/0.43 ((^[X6 : $i > $i > $o] : (! [X9,X8] : ((X6 @ X8 @ X9) => (X6 @ X9 @ X8)))) = msymmetric)),
% 0.23/0.43 file('/export/starexec/sandbox/benchmark/theBenchmark.p',msymmetric)).
% 0.23/0.43 thf(f111,plain,(
% 0.23/0.43 ((mreflexive @ sK0) != $true) | ((meuclidean @ sK0) != $true) | ((msymmetric @ sK0) != $true) | ((meuclidean @ sK0) != $true) | ((mreflexive @ sK0) != $true)),
% 0.23/0.43 inference(cnf_transformation,[],[f99])).
% 0.23/0.43 thf(f276,plain,(
% 0.23/0.43 spl1_8 | spl1_1 | spl1_6),
% 0.23/0.43 inference(avatar_split_clause,[],[f226,f264,f241,f273])).
% 0.23/0.43 thf(f226,plain,(
% 0.23/0.43 ((sK0 @ sK3 @ sK3) = $false) | ((sK0 @ sK5 @ sK6) = $true) | ((sK0 @ sK2 @ sK4) = $true)),
% 0.23/0.43 inference(binary_proxy_clausification,[],[f225])).
% 0.23/0.43 thf(f271,plain,(
% 0.23/0.43 spl1_1 | spl1_6 | spl1_7),
% 0.23/0.43 inference(avatar_split_clause,[],[f224,f268,f264,f241])).
% 0.23/0.43 thf(f224,plain,(
% 0.23/0.43 ((sK0 @ sK2 @ sK4) = $true) | ((sK0 @ sK6 @ sK7) = $false) | ((sK0 @ sK3 @ sK3) = $false)),
% 0.23/0.43 inference(binary_proxy_clausification,[],[f223])).
% 0.23/0.43 thf(f262,plain,(
% 0.23/0.43 spl1_5 | spl1_3 | spl1_1),
% 0.23/0.43 inference(avatar_split_clause,[],[f235,f241,f249,f259])).
% 0.23/0.43 thf(f235,plain,(
% 0.23/0.43 ((sK0 @ sK5 @ sK9) = $true) | ((sK0 @ sK4 @ sK2) = $false) | ((sK0 @ sK3 @ sK3) = $false)),
% 0.23/0.43 inference(binary_proxy_clausification,[],[f233])).
% 0.23/0.43 thf(f233,plain,(
% 0.23/0.43 ((sK0 @ sK4 @ sK2) = $false) | ((sK0 @ sK3 @ sK3) = $false) | (((sK0 @ sK5 @ sK9) & (sK0 @ sK5 @ sK8)) = $true)),
% 0.23/0.43 inference(binary_proxy_clausification,[],[f231])).
% 0.23/0.43 thf(f231,plain,(
% 0.23/0.43 ((sK0 @ sK3 @ sK3) = $false) | ($false = (((sK0 @ sK5 @ sK9) & (sK0 @ sK5 @ sK8)) => (sK0 @ sK8 @ sK9))) | ((sK0 @ sK4 @ sK2) = $false)),
% 0.23/0.43 inference(beta_eta_normalization,[],[f230])).
% 0.23/0.43 thf(f230,plain,(
% 0.23/0.43 ($false = ((^[Y0 : $i]: (((sK0 @ sK5 @ Y0) & (sK0 @ sK5 @ sK8)) => (sK0 @ sK8 @ Y0))) @ sK9)) | ((sK0 @ sK3 @ sK3) = $false) | ((sK0 @ sK4 @ sK2) = $false)),
% 0.23/0.43 inference(sigma_clausification,[],[f229])).
% 0.23/0.43 thf(f229,plain,(
% 0.23/0.43 ((sK0 @ sK4 @ sK2) = $false) | ((sK0 @ sK3 @ sK3) = $false) | ($false = (!! @ $i @ (^[Y0 : $i]: (((sK0 @ sK5 @ Y0) & (sK0 @ sK5 @ sK8)) => (sK0 @ sK8 @ Y0)))))),
% 0.23/0.43 inference(beta_eta_normalization,[],[f228])).
% 0.23/0.43 thf(f228,plain,(
% 0.23/0.43 ((sK0 @ sK4 @ sK2) = $false) | ((sK0 @ sK3 @ sK3) = $false) | ($false = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((sK0 @ sK5 @ Y1) & (sK0 @ sK5 @ Y0)) => (sK0 @ Y0 @ Y1))))) @ sK8))),
% 0.23/0.43 inference(sigma_clausification,[],[f218])).
% 0.23/0.43 thf(f218,plain,(
% 0.23/0.43 ((sK0 @ sK4 @ sK2) = $false) | ((sK0 @ sK3 @ sK3) = $false) | ($false = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((sK0 @ sK5 @ Y1) & (sK0 @ sK5 @ Y0)) => (sK0 @ Y0 @ Y1)))))))),
% 0.23/0.43 inference(binary_proxy_clausification,[],[f217])).
% 0.23/0.43 thf(f257,plain,(
% 0.23/0.43 spl1_1 | spl1_3 | spl1_4),
% 0.23/0.43 inference(avatar_split_clause,[],[f234,f254,f249,f241])).
% 0.23/0.43 thf(f234,plain,(
% 0.23/0.43 ((sK0 @ sK3 @ sK3) = $false) | ($true = (sK0 @ sK5 @ sK8)) | ((sK0 @ sK4 @ sK2) = $false)),
% 0.23/0.43 inference(binary_proxy_clausification,[],[f233])).
% 0.23/0.43 thf(f252,plain,(
% 0.23/0.43 spl1_1 | spl1_2 | spl1_3),
% 0.23/0.43 inference(avatar_split_clause,[],[f232,f249,f245,f241])).
% 0.23/0.43 thf(f232,plain,(
% 0.23/0.43 ((sK0 @ sK4 @ sK2) = $false) | ($false = (sK0 @ sK8 @ sK9)) | ((sK0 @ sK3 @ sK3) = $false)),
% 0.23/0.43 inference(binary_proxy_clausification,[],[f231])).
% 0.23/0.43 % SZS output end Proof for theBenchmark
% 0.23/0.43 % (345)------------------------------
% 0.23/0.43 % (345)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.23/0.43 % (345)Termination reason: Refutation
% 0.23/0.43
% 0.23/0.43 % (345)Memory used [KB]: 5756
% 0.23/0.43 % (345)Time elapsed: 0.023 s
% 0.23/0.43 % (345)Instructions burned: 27 (million)
% 0.23/0.43 % (345)------------------------------
% 0.23/0.43 % (345)------------------------------
% 0.23/0.43 % (344)Success in time 0.035 s
% 0.23/0.43 % Vampire---4.8 exiting
%------------------------------------------------------------------------------