%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : ITP157^1 : TPTP v9.2.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n026.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 : Thu Oct 9 01:47:08 PM UTC 2025
% Result : Theorem 24.39s 24.54s
% Output : Proof 24.39s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ITP157^1 : TPTP v9.2.0. Released v7.5.0.
% 0.07/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n026.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Oct 8 18:23:23 EDT 2025
% 0.12/0.33 % CPUTime :
% 24.39/24.54 % SZS status Theorem
% 24.39/24.54 % Mode: mode485:USE_SINE=true:SINE_TOLERANCE=1.2:SINE_GENERALITY_THRESHOLD=4:SINE_RANK_LIMIT=4.:SINE_DEPTH=0
% 24.39/24.54 % Inferences: 1757
% 24.39/24.54 % SZS output start Proof
% 24.39/24.54 thf(conj_0,conjecture,((member449909584od_a_a @ ((product_Pair_a_a @ z) @ y)) @ pr)).
% 24.39/24.54 thf(h0,negated_conjecture,(~(((member449909584od_a_a @ ((product_Pair_a_a @ z) @ y)) @ pr))),inference(assume_negation,[status(cth)],[conj_0])).
% 24.39/24.54 thf(pax3, axiom, (p3=>![X96:a, X97:a, X98:set_a, X99:set_Product_prod_a_a]:(fmember_a @ X96 @ (fprefer161218362good_a @ X97 @ X98 @ X99)=>fmember449909584od_a_a @ (fproduct_Pair_a_a @ X96 @ X97) @ X99)), file('<stdin>', pax3)).
% 24.39/24.54 thf(pax2, axiom, (p2=>fmember_a @ fz @ (fprefer161218362good_a @ fy @ fb @ fpr)), file('<stdin>', pax2)).
% 24.39/24.54 thf(nax1, axiom, (p1<=fmember449909584od_a_a @ (fproduct_Pair_a_a @ fz @ fy) @ fpr), file('<stdin>', nax1)).
% 24.39/24.54 thf(ax2542, axiom, ~(p1), file('<stdin>', ax2542)).
% 24.39/24.54 thf(ax2540, axiom, p3, file('<stdin>', ax2540)).
% 24.39/24.54 thf(ax2541, axiom, p2, file('<stdin>', ax2541)).
% 24.39/24.54 thf(c_0_6, plain, ![X774:a, X775:a, X776:set_a, X777:set_Product_prod_a_a]:(~p3|(~fmember_a @ X774 @ (fprefer161218362good_a @ X775 @ X776 @ X777)|fmember449909584od_a_a @ (fproduct_Pair_a_a @ X774 @ X775) @ X777)), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax3])])])).
% 24.39/24.54 thf(c_0_7, plain, (~p2|fmember_a @ fz @ (fprefer161218362good_a @ fy @ fb @ fpr)), inference(fof_nnf,[status(thm)],[pax2])).
% 24.39/24.54 thf(c_0_8, plain, (~fmember449909584od_a_a @ (fproduct_Pair_a_a @ fz @ fy) @ fpr|p1), inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax1])])).
% 24.39/24.54 thf(c_0_9, plain, ~p1, inference(fof_simplification,[status(thm)],[ax2542])).
% 24.39/24.54 thf(c_0_10, plain, ![X1:a, X70:set_a, X3:a, X2:set_Product_prod_a_a]:(fmember449909584od_a_a @ (fproduct_Pair_a_a @ X1 @ X3) @ X2|~p3|~fmember_a @ X1 @ (fprefer161218362good_a @ X3 @ X70 @ X2)), inference(split_conjunct,[status(thm)],[c_0_6])).
% 24.39/24.54 thf(c_0_11, plain, p3, inference(split_conjunct,[status(thm)],[ax2540])).
% 24.39/24.54 thf(c_0_12, plain, (fmember_a @ fz @ (fprefer161218362good_a @ fy @ fb @ fpr)|~p2), inference(split_conjunct,[status(thm)],[c_0_7])).
% 24.39/24.54 thf(c_0_13, plain, p2, inference(split_conjunct,[status(thm)],[ax2541])).
% 24.39/24.54 thf(c_0_14, plain, (p1|~fmember449909584od_a_a @ (fproduct_Pair_a_a @ fz @ fy) @ fpr), inference(split_conjunct,[status(thm)],[c_0_8])).
% 24.39/24.54 thf(c_0_15, plain, ~p1, inference(split_conjunct,[status(thm)],[c_0_9])).
% 24.39/24.54 thf(c_0_16, plain, ![X1:a, X70:set_a, X3:a, X2:set_Product_prod_a_a]:(fmember449909584od_a_a @ (fproduct_Pair_a_a @ X1 @ X3) @ X2|~fmember_a @ X1 @ (fprefer161218362good_a @ X3 @ X70 @ X2)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_10, c_0_11])])).
% 24.39/24.54 thf(c_0_17, plain, fmember_a @ fz @ (fprefer161218362good_a @ fy @ fb @ fpr), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_12, c_0_13])])).
% 24.39/24.54 thf(c_0_18, plain, ~fmember449909584od_a_a @ (fproduct_Pair_a_a @ fz @ fy) @ fpr, inference(sr,[status(thm)],[c_0_14, c_0_15])).
% 24.39/24.54 thf(c_0_19, plain, ($false), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_16, c_0_17]), c_0_18]), ['proof']).
% 24.39/24.54 thf(1,plain,$false,inference(eprover,[status(thm),assumptions([h0])],[])).
% 24.39/24.54 thf(0,theorem,((member449909584od_a_a @ ((product_Pair_a_a @ z) @ y)) @ pr),inference(contra,[status(thm),contra(discharge,[h0])],[1,h0])).
% 24.39/24.54 % SZS output end Proof
%------------------------------------------------------------------------------