%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : ITP154^1 : 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 : n011.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 2.25s 2.48s
% Output : Proof 2.25s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.15 % Problem : ITP154^1 : TPTP v9.2.0. Released v7.5.0.
% 0.07/0.16 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.38 % Computer : n011.cluster.edu
% 0.13/0.38 % Model : x86_64 x86_64
% 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38 % Memory : 8042.1875MB
% 0.13/0.38 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.38 % CPULimit : 300
% 0.13/0.38 % WCLimit : 300
% 0.13/0.38 % DateTime : Wed Oct 8 17:50:08 EDT 2025
% 0.13/0.38 % CPUTime :
% 2.25/2.48 % SZS status Theorem
% 2.25/2.48 % Mode: mode507:USE_SINE=true:SINE_TOLERANCE=3.0:SINE_GENERALITY_THRESHOLD=0:SINE_RANK_LIMIT=1.:SINE_DEPTH=1
% 2.25/2.48 % Inferences: 5
% 2.25/2.48 % SZS output start Proof
% 2.25/2.48 thf(ty_a, type, a : $tType).
% 2.25/2.48 thf(ty_set_a, type, set_a : $tType).
% 2.25/2.48 thf(ty_set_Product_prod_a_a, type, set_Product_prod_a_a : $tType).
% 2.25/2.48 thf(ty_relation, type, relation : set_Product_prod_a_a).
% 2.25/2.48 thf(ty_prefer1676310729than_a, type, prefer1676310729than_a : (a>set_a>set_Product_prod_a_a>set_a)).
% 2.25/2.48 thf(ty_ord_less_eq_set_a, type, ord_less_eq_set_a : (set_a>set_a>$o)).
% 2.25/2.48 thf(ty_carrier, type, carrier : set_a).
% 2.25/2.48 thf(ty_x, type, x : a).
% 2.25/2.48 thf(conj_0,conjecture,((~(((ord_less_eq_set_a @ (((prefer1676310729than_a @ x) @ carrier) @ relation)) @ (((prefer1676310729than_a @ x) @ carrier) @ relation)))) => ((ord_less_eq_set_a @ (((prefer1676310729than_a @ x) @ carrier) @ relation)) @ (((prefer1676310729than_a @ x) @ carrier) @ relation)))).
% 2.25/2.48 thf(h0,negated_conjecture,(~(((~(((ord_less_eq_set_a @ (((prefer1676310729than_a @ x) @ carrier) @ relation)) @ (((prefer1676310729than_a @ x) @ carrier) @ relation)))) => ((ord_less_eq_set_a @ (((prefer1676310729than_a @ x) @ carrier) @ relation)) @ (((prefer1676310729than_a @ x) @ carrier) @ relation))))),inference(assume_negation,[status(cth)],[conj_0])).
% 2.25/2.48 thf(h1,assumption,(~(((ord_less_eq_set_a @ (((prefer1676310729than_a @ x) @ carrier) @ relation)) @ (((prefer1676310729than_a @ x) @ carrier) @ relation)))),introduced(assumption,[])).
% 2.25/2.48 thf(pax37, axiom, (p37=>![X7:set_a]:ford_less_eq_set_a @ X7 @ X7), file('<stdin>', pax37)).
% 2.25/2.48 thf(nax67, axiom, (p67<=ford_less_eq_set_a @ (fprefer1676310729than_a @ fx @ fcarrier @ frelation) @ (fprefer1676310729than_a @ fx @ fcarrier @ frelation)), file('<stdin>', nax67)).
% 2.25/2.48 thf(ax37, axiom, p37, file('<stdin>', ax37)).
% 2.25/2.48 thf(ax7, axiom, ~(p67), file('<stdin>', ax7)).
% 2.25/2.48 thf(c_0_4, plain, ![X171:set_a]:(~p37|ford_less_eq_set_a @ X171 @ X171), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax37])])])).
% 2.25/2.48 thf(c_0_5, plain, (~ford_less_eq_set_a @ (fprefer1676310729than_a @ fx @ fcarrier @ frelation) @ (fprefer1676310729than_a @ fx @ fcarrier @ frelation)|p67), inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax67])])).
% 2.25/2.48 thf(c_0_6, plain, ![X1:set_a]:(ford_less_eq_set_a @ X1 @ X1|~p37), inference(split_conjunct,[status(thm)],[c_0_4])).
% 2.25/2.48 thf(c_0_7, plain, p37, inference(split_conjunct,[status(thm)],[ax37])).
% 2.25/2.48 thf(c_0_8, plain, ~p67, inference(fof_simplification,[status(thm)],[ax7])).
% 2.25/2.48 thf(c_0_9, plain, (p67|~ford_less_eq_set_a @ (fprefer1676310729than_a @ fx @ fcarrier @ frelation) @ (fprefer1676310729than_a @ fx @ fcarrier @ frelation)), inference(split_conjunct,[status(thm)],[c_0_5])).
% 2.25/2.48 thf(c_0_10, plain, ![X1:set_a]:ford_less_eq_set_a @ X1 @ X1, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_6, c_0_7])])).
% 2.25/2.48 thf(c_0_11, plain, ~p67, inference(split_conjunct,[status(thm)],[c_0_8])).
% 2.25/2.48 thf(c_0_12, plain, ($false), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_9, c_0_10])]), c_0_11]), ['proof']).
% 2.25/2.48 thf(1,plain,$false,inference(eprover,[status(thm),assumptions([h1,h1,h0])],[])).
% 2.25/2.48 thf(2,plain,$false,inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h1])],[h0,1,h1,h1])).
% 2.25/2.48 thf(0,theorem,((~(((ord_less_eq_set_a @ (((prefer1676310729than_a @ x) @ carrier) @ relation)) @ (((prefer1676310729than_a @ x) @ carrier) @ relation)))) => ((ord_less_eq_set_a @ (((prefer1676310729than_a @ x) @ carrier) @ relation)) @ (((prefer1676310729than_a @ x) @ carrier) @ relation))),inference(contra,[status(thm),contra(discharge,[h0])],[2,h0])).
% 2.25/2.48 % SZS output end Proof
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