%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : ITP152^1 : 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 : n007.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 01:47:07 PM UTC 2025
% Result : Theorem 1.43s 1.65s
% Output : Proof 1.43s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.14 % Problem : ITP152^1 : TPTP v9.2.0. Released v7.5.0.
% 0.11/0.15 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.36 % Computer : n007.cluster.edu
% 0.13/0.36 % Model : x86_64 x86_64
% 0.13/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.36 % Memory : 8042.1875MB
% 0.13/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.36 % CPULimit : 300
% 0.13/0.36 % WCLimit : 300
% 0.13/0.36 % DateTime : Wed Oct 8 18:34:38 EDT 2025
% 0.13/0.36 % CPUTime :
% 1.43/1.65 % SZS status Theorem
% 1.43/1.65 % Mode: mode507:USE_SINE=true:SINE_TOLERANCE=3.0:SINE_GENERALITY_THRESHOLD=0:SINE_RANK_LIMIT=1.:SINE_DEPTH=1
% 1.43/1.65 % Inferences: 3
% 1.43/1.65 % SZS output start Proof
% 1.43/1.65 thf(ty_a, type, a : $tType).
% 1.43/1.65 thf(ty_product_prod_a_a, type, product_prod_a_a : $tType).
% 1.43/1.65 thf(ty_set_Product_prod_a_a, type, set_Product_prod_a_a : $tType).
% 1.43/1.65 thf(ty_relation, type, relation : set_Product_prod_a_a).
% 1.43/1.65 thf(ty_member449909584od_a_a, type, member449909584od_a_a : (product_prod_a_a>set_Product_prod_a_a>$o)).
% 1.43/1.65 thf(ty_y, type, y : a).
% 1.43/1.65 thf(ty_x, type, x : a).
% 1.43/1.65 thf(ty_product_Pair_a_a, type, product_Pair_a_a : (a>a>product_prod_a_a)).
% 1.43/1.65 thf(conj_3,conjecture,((~(((member449909584od_a_a @ ((product_Pair_a_a @ x) @ y)) @ relation))) => ((member449909584od_a_a @ ((product_Pair_a_a @ y) @ x)) @ relation))).
% 1.43/1.65 thf(h0,negated_conjecture,(~(((~(((member449909584od_a_a @ ((product_Pair_a_a @ x) @ y)) @ relation))) => ((member449909584od_a_a @ ((product_Pair_a_a @ y) @ x)) @ relation)))),inference(assume_negation,[status(cth)],[conj_3])).
% 1.43/1.65 thf(h1,assumption,(~(((member449909584od_a_a @ ((product_Pair_a_a @ x) @ y)) @ relation))),introduced(assumption,[])).
% 1.43/1.65 thf(h2,assumption,(~(((member449909584od_a_a @ ((product_Pair_a_a @ y) @ x)) @ relation))),introduced(assumption,[])).
% 1.43/1.65 thf(pax4, axiom, (p4=>![X59:a]:(fmember_a @ X59 @ fcarrier=>![X57:a]:(fmember_a @ X57 @ fcarrier=>(~(fmember449909584od_a_a @ (fproduct_Pair_a_a @ X59 @ X57) @ frelation)=>fmember449909584od_a_a @ (fproduct_Pair_a_a @ X57 @ X59) @ frelation)))), file('<stdin>', pax4)).
% 1.43/1.65 thf(pax54, axiom, (p54=>fmember_a @ fx @ fcarrier), file('<stdin>', pax54)).
% 1.43/1.65 thf(ax54, axiom, p4, file('<stdin>', ax54)).
% 1.43/1.65 thf(ax4, axiom, p54, file('<stdin>', ax4)).
% 1.43/1.65 thf(pax55, axiom, (p55=>fmember_a @ fy @ fcarrier), file('<stdin>', pax55)).
% 1.43/1.65 thf(nax57, axiom, (p57<=fmember449909584od_a_a @ (fproduct_Pair_a_a @ fy @ fx) @ frelation), file('<stdin>', nax57)).
% 1.43/1.65 thf(ax1, axiom, ~(p57), file('<stdin>', ax1)).
% 1.43/1.65 thf(nax58, axiom, (p58<=fmember449909584od_a_a @ (fproduct_Pair_a_a @ fx @ fy) @ frelation), file('<stdin>', nax58)).
% 1.43/1.65 thf(ax0, axiom, ~(p58), file('<stdin>', ax0)).
% 1.43/1.65 thf(ax3, axiom, p55, file('<stdin>', ax3)).
% 1.43/1.65 thf(c_0_10, plain, ![X282:a, X283:a]:(~p4|(~fmember_a @ X282 @ fcarrier|(~fmember_a @ X283 @ fcarrier|(fmember449909584od_a_a @ (fproduct_Pair_a_a @ X282 @ X283) @ frelation|fmember449909584od_a_a @ (fproduct_Pair_a_a @ X283 @ X282) @ frelation)))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[pax4])])])])).
% 1.43/1.65 thf(c_0_11, plain, (~p54|fmember_a @ fx @ fcarrier), inference(fof_nnf,[status(thm)],[pax54])).
% 1.43/1.65 thf(c_0_12, plain, ![X1:a, X2:a]:(fmember449909584od_a_a @ (fproduct_Pair_a_a @ X1 @ X2) @ frelation|fmember449909584od_a_a @ (fproduct_Pair_a_a @ X2 @ X1) @ frelation|~p4|~fmember_a @ X1 @ fcarrier|~fmember_a @ X2 @ fcarrier), inference(split_conjunct,[status(thm)],[c_0_10])).
% 1.43/1.65 thf(c_0_13, plain, p4, inference(split_conjunct,[status(thm)],[ax54])).
% 1.43/1.65 thf(c_0_14, plain, (fmember_a @ fx @ fcarrier|~p54), inference(split_conjunct,[status(thm)],[c_0_11])).
% 1.43/1.65 thf(c_0_15, plain, p54, inference(split_conjunct,[status(thm)],[ax4])).
% 1.43/1.65 thf(c_0_16, plain, (~p55|fmember_a @ fy @ fcarrier), inference(fof_nnf,[status(thm)],[pax55])).
% 1.43/1.65 thf(c_0_17, plain, (~fmember449909584od_a_a @ (fproduct_Pair_a_a @ fy @ fx) @ frelation|p57), inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax57])])).
% 1.43/1.65 thf(c_0_18, plain, ~p57, inference(fof_simplification,[status(thm)],[ax1])).
% 1.43/1.65 thf(c_0_19, plain, (~fmember449909584od_a_a @ (fproduct_Pair_a_a @ fx @ fy) @ frelation|p58), inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax58])])).
% 1.43/1.65 thf(c_0_20, plain, ~p58, inference(fof_simplification,[status(thm)],[ax0])).
% 1.43/1.65 thf(c_0_21, plain, ![X2:a, X1:a]:(fmember449909584od_a_a @ (fproduct_Pair_a_a @ X1 @ X2) @ frelation|fmember449909584od_a_a @ (fproduct_Pair_a_a @ X2 @ X1) @ frelation|~fmember_a @ X2 @ fcarrier|~fmember_a @ X1 @ fcarrier), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_12, c_0_13])])).
% 1.43/1.65 thf(c_0_22, plain, fmember_a @ fx @ fcarrier, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_14, c_0_15])])).
% 1.43/1.65 thf(c_0_23, plain, (fmember_a @ fy @ fcarrier|~p55), inference(split_conjunct,[status(thm)],[c_0_16])).
% 1.43/1.65 thf(c_0_24, plain, p55, inference(split_conjunct,[status(thm)],[ax3])).
% 1.43/1.65 thf(c_0_25, plain, (p57|~fmember449909584od_a_a @ (fproduct_Pair_a_a @ fy @ fx) @ frelation), inference(split_conjunct,[status(thm)],[c_0_17])).
% 1.43/1.65 thf(c_0_26, plain, ~p57, inference(split_conjunct,[status(thm)],[c_0_18])).
% 1.43/1.65 thf(c_0_27, plain, (p58|~fmember449909584od_a_a @ (fproduct_Pair_a_a @ fx @ fy) @ frelation), inference(split_conjunct,[status(thm)],[c_0_19])).
% 1.43/1.65 thf(c_0_28, plain, ~p58, inference(split_conjunct,[status(thm)],[c_0_20])).
% 1.43/1.65 thf(c_0_29, plain, ![X1:a]:(fmember449909584od_a_a @ (fproduct_Pair_a_a @ X1 @ fx) @ frelation|fmember449909584od_a_a @ (fproduct_Pair_a_a @ fx @ X1) @ frelation|~fmember_a @ X1 @ fcarrier), inference(spm,[status(thm)],[c_0_21, c_0_22])).
% 1.43/1.65 thf(c_0_30, plain, fmember_a @ fy @ fcarrier, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_23, c_0_24])])).
% 1.43/1.65 thf(c_0_31, plain, ~fmember449909584od_a_a @ (fproduct_Pair_a_a @ fy @ fx) @ frelation, inference(sr,[status(thm)],[c_0_25, c_0_26])).
% 1.43/1.65 thf(c_0_32, plain, ~fmember449909584od_a_a @ (fproduct_Pair_a_a @ fx @ fy) @ frelation, inference(sr,[status(thm)],[c_0_27, c_0_28])).
% 1.43/1.65 thf(c_0_33, plain, ($false), inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_29, c_0_30]), c_0_31]), c_0_32]), ['proof']).
% 1.43/1.65 thf(1,plain,$false,inference(eprover,[status(thm),assumptions([h1,h2,h0])],[])).
% 1.43/1.65 thf(2,plain,$false,inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,1,h1,h2])).
% 1.43/1.65 thf(0,theorem,((~(((member449909584od_a_a @ ((product_Pair_a_a @ x) @ y)) @ relation))) => ((member449909584od_a_a @ ((product_Pair_a_a @ y) @ x)) @ relation)),inference(contra,[status(thm),contra(discharge,[h0])],[2,h0])).
% 1.43/1.65 % SZS output end Proof
%------------------------------------------------------------------------------