TSTP Solution File: ITP175^1 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : ITP175^1 : TPTP v8.1.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n027.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 : 600s
% DateTime : Sun Jul 17 00:29:23 EDT 2022
% Result : Theorem 2.33s 2.55s
% Output : Proof 2.33s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : ITP175^1 : TPTP v8.1.0. Released v7.5.0.
% 0.14/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.14/0.34 % Computer : n027.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Fri Jun 3 09:28:20 EDT 2022
% 0.14/0.35 % CPUTime :
% 2.33/2.55 % SZS status Theorem
% 2.33/2.55 % Mode: mode507:USE_SINE=true:SINE_TOLERANCE=3.0:SINE_GENERALITY_THRESHOLD=0:SINE_RANK_LIMIT=1.:SINE_DEPTH=1
% 2.33/2.55 % Inferences: 2
% 2.33/2.55 % SZS output start Proof
% 2.33/2.55 thf(ty_a, type, a : $tType).
% 2.33/2.55 thf(ty_set_b, type, set_b : $tType).
% 2.33/2.55 thf(ty_product_prod_b_b, type, product_prod_b_b : $tType).
% 2.33/2.55 thf(ty_b, type, b : $tType).
% 2.33/2.55 thf(ty_labeled_graph_a_b, type, labeled_graph_a_b : $tType).
% 2.33/2.55 thf(ty_set_Product_prod_b_b, type, set_Product_prod_b_b : $tType).
% 2.33/2.55 thf(ty_labeled_vertices_a_b, type, labeled_vertices_a_b : (labeled_graph_a_b>set_b)).
% 2.33/2.55 thf(ty_getRel_a_b, type, getRel_a_b : (a>labeled_graph_a_b>set_Product_prod_b_b)).
% 2.33/2.55 thf(ty_i, type, i : a).
% 2.33/2.55 thf(ty_member1285940496od_b_b, type, member1285940496od_b_b : (product_prod_b_b>set_Product_prod_b_b>$o)).
% 2.33/2.55 thf(ty_product_Pair_b_b, type, product_Pair_b_b : (b>b>product_prod_b_b)).
% 2.33/2.55 thf(ty_refl_on_b, type, refl_on_b : (set_b>set_Product_prod_b_b>$o)).
% 2.33/2.55 thf(ty_trans_b, type, trans_b : (set_Product_prod_b_b>$o)).
% 2.33/2.55 thf(ty_g, type, g : labeled_graph_a_b).
% 2.33/2.55 thf(conj_0,conjecture,((member1285940496od_b_b @ ((product_Pair_b_b @ z) @ y)) @ ((getRel_a_b @ i) @ g))).
% 2.33/2.55 thf(h0,negated_conjecture,(~(((member1285940496od_b_b @ ((product_Pair_b_b @ z) @ y)) @ ((getRel_a_b @ i) @ g)))),inference(assume_negation,[status(cth)],[conj_0])).
% 2.33/2.55 thf(h1,assumption,(~((((refl_on_b @ (labeled_vertices_a_b @ g)) @ ((getRel_a_b @ i) @ g)) => (~((![X1:b]:(![X2:b]:(((member1285940496od_b_b @ ((product_Pair_b_b @ X1) @ X2)) @ ((getRel_a_b @ i) @ g)) => ((member1285940496od_b_b @ ((product_Pair_b_b @ X2) @ X1)) @ ((getRel_a_b @ i) @ g)))))))))),introduced(assumption,[])).
% 2.33/2.55 thf(h2,assumption,(trans_b @ ((getRel_a_b @ i) @ g)),introduced(assumption,[])).
% 2.33/2.55 thf(h3,assumption,((refl_on_b @ (labeled_vertices_a_b @ g)) @ ((getRel_a_b @ i) @ g)),introduced(assumption,[])).
% 2.33/2.55 thf(h4,assumption,(![X1:b]:(![X2:b]:(((member1285940496od_b_b @ ((product_Pair_b_b @ X1) @ X2)) @ ((getRel_a_b @ i) @ g)) => ((member1285940496od_b_b @ ((product_Pair_b_b @ X2) @ X1)) @ ((getRel_a_b @ i) @ g))))),introduced(assumption,[])).
% 2.33/2.55 thf(pax2, axiom, (p2=>![X58:b, X56:b]:(fmember1285940496od_b_b @ (fproduct_Pair_b_b @ X58 @ X56) @ (fgetRel_a_b @ fi @ fg)=>fmember1285940496od_b_b @ (fproduct_Pair_b_b @ X56 @ X58) @ (fgetRel_a_b @ fi @ fg))), file('<stdin>', pax2)).
% 2.33/2.55 thf(pax4, axiom, (p4=>fmember1285940496od_b_b @ (fproduct_Pair_b_b @ fy @ fz) @ (fgetRel_a_b @ fi @ fg)), file('<stdin>', pax4)).
% 2.33/2.55 thf(nax51, axiom, (p51<=fmember1285940496od_b_b @ (fproduct_Pair_b_b @ fz @ fy) @ (fgetRel_a_b @ fi @ fg)), file('<stdin>', nax51)).
% 2.33/2.55 thf(ax0, axiom, ~(p51), file('<stdin>', ax0)).
% 2.33/2.55 thf(ax49, axiom, p2, file('<stdin>', ax49)).
% 2.33/2.55 thf(ax47, axiom, p4, file('<stdin>', ax47)).
% 2.33/2.55 thf(c_0_6, plain, ![X235:b, X236:b]:(~p2|(~fmember1285940496od_b_b @ (fproduct_Pair_b_b @ X235 @ X236) @ (fgetRel_a_b @ fi @ fg)|fmember1285940496od_b_b @ (fproduct_Pair_b_b @ X236 @ X235) @ (fgetRel_a_b @ fi @ fg))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax2])])])).
% 2.33/2.55 thf(c_0_7, plain, (~p4|fmember1285940496od_b_b @ (fproduct_Pair_b_b @ fy @ fz) @ (fgetRel_a_b @ fi @ fg)), inference(fof_nnf,[status(thm)],[pax4])).
% 2.33/2.55 thf(c_0_8, plain, (~fmember1285940496od_b_b @ (fproduct_Pair_b_b @ fz @ fy) @ (fgetRel_a_b @ fi @ fg)|p51), inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax51])])).
% 2.33/2.55 thf(c_0_9, plain, ~p51, inference(fof_simplification,[status(thm)],[ax0])).
% 2.33/2.55 thf(c_0_10, plain, ![X4:b, X5:b]:(fmember1285940496od_b_b @ (fproduct_Pair_b_b @ X5 @ X4) @ (fgetRel_a_b @ fi @ fg)|~p2|~fmember1285940496od_b_b @ (fproduct_Pair_b_b @ X4 @ X5) @ (fgetRel_a_b @ fi @ fg)), inference(split_conjunct,[status(thm)],[c_0_6])).
% 2.33/2.55 thf(c_0_11, plain, p2, inference(split_conjunct,[status(thm)],[ax49])).
% 2.33/2.55 thf(c_0_12, plain, (fmember1285940496od_b_b @ (fproduct_Pair_b_b @ fy @ fz) @ (fgetRel_a_b @ fi @ fg)|~p4), inference(split_conjunct,[status(thm)],[c_0_7])).
% 2.33/2.55 thf(c_0_13, plain, p4, inference(split_conjunct,[status(thm)],[ax47])).
% 2.33/2.55 thf(c_0_14, plain, (p51|~fmember1285940496od_b_b @ (fproduct_Pair_b_b @ fz @ fy) @ (fgetRel_a_b @ fi @ fg)), inference(split_conjunct,[status(thm)],[c_0_8])).
% 2.33/2.55 thf(c_0_15, plain, ~p51, inference(split_conjunct,[status(thm)],[c_0_9])).
% 2.33/2.55 thf(c_0_16, plain, ![X5:b, X4:b]:(fmember1285940496od_b_b @ (fproduct_Pair_b_b @ X4 @ X5) @ (fgetRel_a_b @ fi @ fg)|~fmember1285940496od_b_b @ (fproduct_Pair_b_b @ X5 @ X4) @ (fgetRel_a_b @ fi @ fg)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_10, c_0_11])])).
% 2.33/2.55 thf(c_0_17, plain, fmember1285940496od_b_b @ (fproduct_Pair_b_b @ fy @ fz) @ (fgetRel_a_b @ fi @ fg), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_12, c_0_13])])).
% 2.33/2.55 thf(c_0_18, plain, ~fmember1285940496od_b_b @ (fproduct_Pair_b_b @ fz @ fy) @ (fgetRel_a_b @ fi @ fg), inference(sr,[status(thm)],[c_0_14, c_0_15])).
% 2.33/2.55 thf(c_0_19, plain, ($false), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_16, c_0_17]), c_0_18]), ['proof']).
% 2.33/2.55 thf(1,plain,$false,inference(eprover,[status(thm),assumptions([h3,h4,h1,h2,h0])],[])).
% 2.33/2.55 thf(2,plain,$false,inference(tab_negimp,[status(thm),assumptions([h1,h2,h0]),tab_negimp(discharge,[h3,h4])],[h1,1,h3,h4])).
% 2.33/2.55 thf(fact_0__092_060open_062refl__on_A_Ivertices_AG_J_A_IgetRel_AI_AG_J_A_092_060and_062_A_I_092_060forall_062x_Ay_O_A_Ix_M_Ay_J_A_092_060in_062_AgetRel_AI_AG_A_092_060longrightarrow_062_A_Iy_M_Ax_J_A_092_060in_062_AgetRel_AI_AG_J_A_092_060and_062_Atrans_A_IgetRel_AI_AG_J_092_060close_062,axiom,(~(((~((((refl_on_b @ (labeled_vertices_a_b @ g)) @ ((getRel_a_b @ i) @ g)) => (~((![X1:b]:(![X2:b]:(((member1285940496od_b_b @ ((product_Pair_b_b @ X1) @ X2)) @ ((getRel_a_b @ i) @ g)) => ((member1285940496od_b_b @ ((product_Pair_b_b @ X2) @ X1)) @ ((getRel_a_b @ i) @ g)))))))))) => (~((trans_b @ ((getRel_a_b @ i) @ g)))))))).
% 2.33/2.55 thf(3,plain,$false,inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[fact_0__092_060open_062refl__on_A_Ivertices_AG_J_A_IgetRel_AI_AG_J_A_092_060and_062_A_I_092_060forall_062x_Ay_O_A_Ix_M_Ay_J_A_092_060in_062_AgetRel_AI_AG_A_092_060longrightarrow_062_A_Iy_M_Ax_J_A_092_060in_062_AgetRel_AI_AG_J_A_092_060and_062_Atrans_A_IgetRel_AI_AG_J_092_060close_062,2,h1,h2])).
% 2.33/2.55 thf(0,theorem,((member1285940496od_b_b @ ((product_Pair_b_b @ z) @ y)) @ ((getRel_a_b @ i) @ g)),inference(contra,[status(thm),contra(discharge,[h0])],[3,h0])).
% 2.33/2.55 % SZS output end Proof
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