TSTP Solution File: SET764^4 by Vampire---4.9
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%------------------------------------------------------------------------------
% File : Vampire---4.9
% Problem : SET764^4 : TPTP v8.2.0. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire %s %d THM
% Computer : n021.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 14:53:34 EDT 2024
% Result : Theorem 0.11s 0.38s
% Output : Refutation 0.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET764^4 : TPTP v8.2.0. Released v3.6.0.
% 0.07/0.12 % Command : run_vampire %s %d THM
% 0.11/0.33 % Computer : n021.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Sun Jun 23 15:02:24 EDT 2024
% 0.11/0.33 % CPUTime :
% 0.11/0.35 This is a TH0_THM_EQU_NAR problem
% 0.11/0.35 Running higher-order theorem proving
% 0.11/0.35 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
% 0.11/0.36 % (24894)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)
% 0.11/0.37 % (24894)Instruction limit reached!
% 0.11/0.37 % (24894)------------------------------
% 0.11/0.37 % (24894)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.11/0.37 % (24894)Termination reason: Unknown
% 0.11/0.37 % (24894)Termination phase: Saturation
% 0.11/0.37
% 0.11/0.37 % (24894)Memory used [KB]: 5500
% 0.11/0.37 % (24894)Time elapsed: 0.003 s
% 0.11/0.37 % (24894)Instructions burned: 5 (million)
% 0.11/0.37 % (24894)------------------------------
% 0.11/0.37 % (24894)------------------------------
% 0.11/0.37 % (24893)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.11/0.37 % (24895)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)
% 0.11/0.37 % (24896)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.11/0.37 % (24897)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)
% 0.11/0.37 % (24898)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)
% 0.11/0.37 % (24899)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.11/0.37 % (24896)Instruction limit reached!
% 0.11/0.37 % (24896)------------------------------
% 0.11/0.37 % (24896)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.11/0.37 % (24896)Termination reason: Unknown
% 0.11/0.37 % (24896)Termination phase: shuffling
% 0.11/0.37
% 0.11/0.37 % (24896)Memory used [KB]: 1023
% 0.11/0.37 % (24896)Time elapsed: 0.003 s
% 0.11/0.37 % (24896)Instructions burned: 2 (million)
% 0.11/0.37 % (24896)------------------------------
% 0.11/0.37 % (24896)------------------------------
% 0.11/0.37 % (24897)Instruction limit reached!
% 0.11/0.37 % (24897)------------------------------
% 0.11/0.37 % (24897)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.11/0.37 % (24897)Termination reason: Unknown
% 0.11/0.37 % (24897)Termination phase: shuffling
% 0.11/0.37
% 0.11/0.37 % (24897)Memory used [KB]: 1023
% 0.11/0.37 % (24897)Time elapsed: 0.003 s
% 0.11/0.37 % (24897)Instructions burned: 2 (million)
% 0.11/0.37 % (24897)------------------------------
% 0.11/0.37 % (24897)------------------------------
% 0.11/0.37 % (24893)First to succeed.
% 0.11/0.38 % (24895)Also succeeded, but the first one will report.
% 0.11/0.38 % (24898)Refutation not found, incomplete strategy
% 0.11/0.38 % (24898)------------------------------
% 0.11/0.38 % (24898)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.11/0.38 % (24898)Termination reason: Refutation not found, incomplete strategy
% 0.11/0.38
% 0.11/0.38
% 0.11/0.38 % (24898)Memory used [KB]: 5628
% 0.11/0.38 % (24898)Time elapsed: 0.006 s
% 0.11/0.38 % (24898)Instructions burned: 5 (million)
% 0.11/0.38 % (24898)------------------------------
% 0.11/0.38 % (24898)------------------------------
% 0.11/0.38 % (24900)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)
% 0.11/0.38 % (24899)Also succeeded, but the first one will report.
% 0.11/0.38 % (24893)Refutation found. Thanks to Tanya!
% 0.11/0.38 % SZS status Theorem for theBenchmark
% 0.11/0.38 % SZS output start Proof for theBenchmark
% 0.11/0.38 thf(func_def_0, type, in: $i > ($i > $o) > $o).
% 0.11/0.38 thf(func_def_2, type, is_a: $i > ($i > $o) > $o).
% 0.11/0.38 thf(func_def_3, type, emptyset: $i > $o).
% 0.11/0.38 thf(func_def_4, type, unord_pair: $i > $i > $i > $o).
% 0.11/0.38 thf(func_def_5, type, singleton: $i > $i > $o).
% 0.11/0.38 thf(func_def_6, type, union: ($i > $o) > ($i > $o) > $i > $o).
% 0.11/0.38 thf(func_def_7, type, excl_union: ($i > $o) > ($i > $o) > $i > $o).
% 0.11/0.38 thf(func_def_8, type, intersection: ($i > $o) > ($i > $o) > $i > $o).
% 0.11/0.38 thf(func_def_9, type, setminus: ($i > $o) > ($i > $o) > $i > $o).
% 0.11/0.38 thf(func_def_10, type, complement: ($i > $o) > $i > $o).
% 0.11/0.38 thf(func_def_11, type, disjoint: ($i > $o) > ($i > $o) > $o).
% 0.11/0.38 thf(func_def_12, type, subset: ($i > $o) > ($i > $o) > $o).
% 0.11/0.38 thf(func_def_13, type, meets: ($i > $o) > ($i > $o) > $o).
% 0.11/0.38 thf(func_def_14, type, misses: ($i > $o) > ($i > $o) > $o).
% 0.11/0.38 thf(func_def_15, type, fun_image: ($i > $i) > ($i > $o) > $i > $o).
% 0.11/0.38 thf(func_def_16, type, fun_composition: ($i > $i) > ($i > $i) > $i > $i).
% 0.11/0.38 thf(func_def_17, type, fun_inv_image: ($i > $i) > ($i > $o) > $i > $o).
% 0.11/0.38 thf(func_def_18, type, fun_injective: ($i > $i) > $o).
% 0.11/0.38 thf(func_def_19, type, fun_surjective: ($i > $i) > $o).
% 0.11/0.38 thf(func_def_20, type, fun_bijective: ($i > $i) > $o).
% 0.11/0.38 thf(func_def_21, type, fun_decreasing: ($i > $i) > ($i > $i > $o) > $o).
% 0.11/0.38 thf(func_def_22, type, fun_increasing: ($i > $i) > ($i > $i > $o) > $o).
% 0.11/0.38 thf(func_def_37, type, sK0: $i > $i).
% 0.11/0.38 thf(func_def_39, type, ph2: !>[X0: $tType]:(X0)).
% 0.11/0.38 thf(f103,plain,(
% 0.11/0.38 $false),
% 0.11/0.38 inference(trivial_inequality_removal,[],[f102])).
% 0.11/0.38 thf(f102,plain,(
% 0.11/0.38 ($true = $false)),
% 0.11/0.38 inference(beta_eta_normalization,[],[f101])).
% 0.11/0.38 thf(f101,plain,(
% 0.11/0.38 (((^[Y0 : $i]: ($false)) @ sK4) = $true)),
% 0.11/0.38 inference(sigma_clausification,[],[f100])).
% 0.11/0.38 thf(f100,plain,(
% 0.11/0.38 ((?? @ $i @ (^[Y0 : $i]: ($false))) != $false)),
% 0.11/0.38 inference(beta_eta_normalization,[],[f99])).
% 0.11/0.38 thf(f99,plain,(
% 0.11/0.38 (((^[Y0 : $i]: ($false)) @ sK3) != ((^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ($false)))) @ sK3))),
% 0.11/0.38 inference(negative_extensionality,[],[f98])).
% 0.11/0.38 thf(f98,plain,(
% 0.11/0.38 ((^[Y0 : $i]: ($false)) != (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ($false)))))),
% 0.11/0.38 inference(boolean_simplification,[],[f97])).
% 0.11/0.38 thf(f97,plain,(
% 0.11/0.38 ((^[Y0 : $i]: ($false)) != (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ($false & ((sK0 @ Y0) = Y1))))))),
% 0.11/0.38 inference(beta_eta_normalization,[],[f96])).
% 0.11/0.38 thf(f96,plain,(
% 0.11/0.38 ((^[Y0 : $i]: ($false)) != ((^[Y0 : $i > $i]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) & ((Y0 @ Y2) = Y3))))))))) @ sK0 @ (^[Y0 : $i]: ($false))))),
% 0.11/0.38 inference(definition_unfolding,[],[f82,f76,f83,f76])).
% 0.11/0.38 thf(f83,plain,(
% 0.11/0.38 (fun_inv_image = (^[Y0 : $i > $i]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) & ((Y0 @ Y2) = Y3))))))))))),
% 0.11/0.38 inference(cnf_transformation,[],[f42])).
% 0.11/0.38 thf(f42,plain,(
% 0.11/0.38 (fun_inv_image = (^[Y0 : $i > $i]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) & ((Y0 @ Y2) = Y3))))))))))),
% 0.11/0.38 inference(fool_elimination,[],[f41])).
% 0.11/0.38 thf(f41,plain,(
% 0.11/0.38 (fun_inv_image = (^[X0 : $i > $i, X1 : $i > $o, X2 : $i] : (? [X3] : (((X0 @ X2) = X3) & (X1 @ X3)))))),
% 0.11/0.38 inference(rectify,[],[f17])).
% 0.11/0.38 thf(f17,axiom,(
% 0.11/0.38 (fun_inv_image = (^[X4 : $i > $i, X7 : $i > $o, X0 : $i] : (? [X2] : (((X4 @ X0) = X2) & (X7 @ X2)))))),
% 0.11/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fun_inv_image)).
% 0.11/0.38 thf(f76,plain,(
% 0.11/0.38 (emptyset = (^[Y0 : $i]: ($false)))),
% 0.11/0.38 inference(cnf_transformation,[],[f28])).
% 0.11/0.38 thf(f28,plain,(
% 0.11/0.38 (emptyset = (^[Y0 : $i]: ($false)))),
% 0.11/0.38 inference(fool_elimination,[],[f3])).
% 0.11/0.38 thf(f3,axiom,(
% 0.11/0.38 ((^[X0 : $i] : ($false)) = emptyset)),
% 0.11/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyset)).
% 0.11/0.38 thf(f82,plain,(
% 0.11/0.38 (emptyset != (fun_inv_image @ sK0 @ emptyset))),
% 0.11/0.38 inference(cnf_transformation,[],[f70])).
% 0.11/0.38 thf(f70,plain,(
% 0.11/0.38 (emptyset != (fun_inv_image @ sK0 @ emptyset))),
% 0.11/0.38 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f68,f69])).
% 0.11/0.38 thf(f69,plain,(
% 0.11/0.38 ? [X0 : $i > $i] : (emptyset != (fun_inv_image @ X0 @ emptyset)) => (emptyset != (fun_inv_image @ sK0 @ emptyset))),
% 0.11/0.38 introduced(choice_axiom,[])).
% 0.11/0.38 thf(f68,plain,(
% 0.11/0.38 ? [X0 : $i > $i] : (emptyset != (fun_inv_image @ X0 @ emptyset))),
% 0.11/0.38 inference(ennf_transformation,[],[f67])).
% 0.11/0.38 thf(f67,plain,(
% 0.11/0.38 ~! [X0 : $i > $i] : (emptyset = (fun_inv_image @ X0 @ emptyset))),
% 0.11/0.38 inference(rectify,[],[f24])).
% 0.11/0.38 thf(f24,negated_conjecture,(
% 0.11/0.38 ~! [X4 : $i > $i] : (emptyset = (fun_inv_image @ X4 @ emptyset))),
% 0.11/0.38 inference(negated_conjecture,[],[f23])).
% 0.11/0.38 thf(f23,conjecture,(
% 0.11/0.38 ! [X4 : $i > $i] : (emptyset = (fun_inv_image @ X4 @ emptyset))),
% 0.11/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm)).
% 0.11/0.38 % SZS output end Proof for theBenchmark
% 0.11/0.38 % (24893)------------------------------
% 0.11/0.38 % (24893)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.11/0.38 % (24893)Termination reason: Refutation
% 0.11/0.38
% 0.11/0.38 % (24893)Memory used [KB]: 5500
% 0.11/0.38 % (24893)Time elapsed: 0.006 s
% 0.11/0.38 % (24893)Instructions burned: 5 (million)
% 0.11/0.38 % (24893)------------------------------
% 0.11/0.38 % (24893)------------------------------
% 0.11/0.38 % (24892)Success in time 0.022 s
%------------------------------------------------------------------------------