TSTP Solution File: ITP155^1 by Satallax---3.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : ITP155^1 : 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 : n025.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 00:29:18 EDT 2022
% Result : Theorem 50.93s 50.91s
% Output : Proof 50.93s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : ITP155^1 : TPTP v8.1.0. Released v7.5.0.
% 0.10/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n025.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 : 600
% 0.12/0.33 % DateTime : Sat Jun 4 00:44:01 EDT 2022
% 0.12/0.33 % CPUTime :
% 50.93/50.91 % SZS status Theorem
% 50.93/50.91 % Mode: mode485:USE_SINE=true:SINE_TOLERANCE=1.2:SINE_GENERALITY_THRESHOLD=4:SINE_RANK_LIMIT=4.:SINE_DEPTH=0
% 50.93/50.91 % Inferences: 150
% 50.93/50.91 % SZS output start Proof
% 50.93/50.91 thf(conj_0,conjecture,((ord_less_eq_set_a @ (((prefer1676310729than_a @ x) @ carrier) @ relation)) @ (((prefer1676310729than_a @ y) @ carrier) @ relation))).
% 50.93/50.91 thf(h0,negated_conjecture,(~(((ord_less_eq_set_a @ (((prefer1676310729than_a @ x) @ carrier) @ relation)) @ (((prefer1676310729than_a @ y) @ carrier) @ relation)))),inference(assume_negation,[status(cth)],[conj_0])).
% 50.93/50.91 thf(pax77, axiom, (p77=>![X229:set_a, X230:set_a, X232:a]:(ford_less_eq_set_a @ X229 @ X230=>(fmember_a @ X232 @ X229=>fmember_a @ X232 @ X230))), file('<stdin>', pax77)).
% 50.93/50.91 thf(pax3, axiom, (p3=>fmember_a @ fx @ fcarrier), file('<stdin>', pax3)).
% 50.93/50.91 thf(pax6, axiom, (p6=>![X294:a, X295:a]:(~(ford_less_eq_set_a @ (fprefer1676310729than_a @ X294 @ fcarrier @ frelation) @ (fprefer1676310729than_a @ X295 @ fcarrier @ frelation))=>ford_less_eq_set_a @ (fprefer1676310729than_a @ X295 @ fcarrier @ frelation) @ (fprefer1676310729than_a @ X294 @ fcarrier @ frelation))), file('<stdin>', pax6)).
% 50.93/50.91 thf(nax1, axiom, (p1<=ford_less_eq_set_a @ (fprefer1676310729than_a @ fx @ fcarrier @ frelation) @ (fprefer1676310729than_a @ fy @ fcarrier @ frelation)), file('<stdin>', nax1)).
% 50.93/50.91 thf(ax2015, axiom, ~(p1), file('<stdin>', ax2015)).
% 50.93/50.91 thf(pax7, axiom, (p7=>![X294:a]:(fmember_a @ X294 @ fcarrier=>ford_less_eq_set_a @ (fprefer1676310729than_a @ X294 @ fcarrier @ frelation) @ fcarrier)), file('<stdin>', pax7)).
% 50.93/50.91 thf(ax1939, axiom, p77, file('<stdin>', ax1939)).
% 50.93/50.91 thf(ax2013, axiom, p3, file('<stdin>', ax2013)).
% 50.93/50.91 thf(pax84, axiom, (p84=>![X229:set_a]:ford_less_eq_set_a @ X229 @ X229), file('<stdin>', pax84)).
% 50.93/50.91 thf(pax134, axiom, (p134=>![X168:nat, X169:nat]:(ford_less_eq_nat @ X168 @ X169=>(ford_less_eq_nat @ X169 @ X168=>(X169)=(X168)))), file('<stdin>', pax134)).
% 50.93/50.91 thf(pax55, axiom, (p55=>![X263:set_a, X264:set_a]:(ffinite_finite_a @ X263=>(ford_less_eq_set_a @ X264 @ X263=>ford_less_eq_nat @ (ffinite_card_a @ X264) @ (ffinite_card_a @ X263)))), file('<stdin>', pax55)).
% 50.93/50.91 thf(nax225, axiom, (p225<=ford_less_eq_set_a @ (fprefer1676310729than_a @ fy @ fcarrier @ frelation) @ (fprefer1676310729than_a @ fx @ fcarrier @ frelation)), file('<stdin>', nax225)).
% 50.93/50.91 thf(ax2010, axiom, p6, file('<stdin>', ax2010)).
% 50.93/50.91 thf(pax103, axiom, (p103=>![X205:set_a, X206:set_a]:(ffinite_finite_a @ X205=>(ford_less_eq_set_a @ X206 @ X205=>ffinite_finite_a @ X206))), file('<stdin>', pax103)).
% 50.93/50.91 thf(ax2009, axiom, p7, file('<stdin>', ax2009)).
% 50.93/50.91 thf(ax1932, axiom, p84, file('<stdin>', ax1932)).
% 50.93/50.91 thf(pax9, axiom, (p9=>ffinite_finite_a @ fcarrier), file('<stdin>', pax9)).
% 50.93/50.91 thf(ax1882, axiom, p134, file('<stdin>', ax1882)).
% 50.93/50.91 thf(ax1961, axiom, p55, file('<stdin>', ax1961)).
% 50.93/50.91 thf(pax5, axiom, (p5=>ford_less_eq_nat @ (ffinite_card_a @ (fprefer1676310729than_a @ fx @ fcarrier @ frelation)) @ (ffinite_card_a @ (fprefer1676310729than_a @ fy @ fcarrier @ frelation))), file('<stdin>', pax5)).
% 50.93/50.91 thf(pax225, axiom, (p225=>ford_less_eq_set_a @ (fprefer1676310729than_a @ fy @ fcarrier @ frelation) @ (fprefer1676310729than_a @ fx @ fcarrier @ frelation)), file('<stdin>', pax225)).
% 50.93/50.91 thf(ax1913, axiom, p103, file('<stdin>', ax1913)).
% 50.93/50.91 thf(ax2007, axiom, p9, file('<stdin>', ax2007)).
% 50.93/50.91 thf(pax108, axiom, (p108=>![X196:set_a, X197:set_a]:(ffinite_finite_a @ X196=>(ford_less_eq_set_a @ X197 @ X196=>((ffinite_card_a @ X197)=(ffinite_card_a @ X196)=>(X197)=(X196))))), file('<stdin>', pax108)).
% 50.93/50.91 thf(ax2011, axiom, p5, file('<stdin>', ax2011)).
% 50.93/50.91 thf(ax1908, axiom, p108, file('<stdin>', ax1908)).
% 50.93/50.91 thf(c_0_26, plain, ![X8692:set_a, X8693:set_a, X8694:a]:(~p77|(~ford_less_eq_set_a @ X8692 @ X8693|(~fmember_a @ X8694 @ X8692|fmember_a @ X8694 @ X8693))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax77])])])).
% 50.93/50.91 thf(c_0_27, plain, (~p3|fmember_a @ fx @ fcarrier), inference(fof_nnf,[status(thm)],[pax3])).
% 50.93/50.91 thf(c_0_28, plain, ![X9000:a, X9001:a]:(~p6|(ford_less_eq_set_a @ (fprefer1676310729than_a @ X9000 @ fcarrier @ frelation) @ (fprefer1676310729than_a @ X9001 @ fcarrier @ frelation)|ford_less_eq_set_a @ (fprefer1676310729than_a @ X9001 @ fcarrier @ frelation) @ (fprefer1676310729than_a @ X9000 @ fcarrier @ frelation))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[pax6])])])])).
% 50.93/50.91 thf(c_0_29, plain, (~ford_less_eq_set_a @ (fprefer1676310729than_a @ fx @ fcarrier @ frelation) @ (fprefer1676310729than_a @ fy @ fcarrier @ frelation)|p1), inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax1])])).
% 50.93/50.91 thf(c_0_30, plain, ~p1, inference(fof_simplification,[status(thm)],[ax2015])).
% 50.93/50.91 thf(c_0_31, plain, ![X8998:a]:(~p7|(~fmember_a @ X8998 @ fcarrier|ford_less_eq_set_a @ (fprefer1676310729than_a @ X8998 @ fcarrier @ frelation) @ fcarrier)), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax7])])])).
% 50.93/50.91 thf(c_0_32, plain, ![X65:a, X2:set_a, X1:set_a]:(fmember_a @ X65 @ X2|~p77|~ford_less_eq_set_a @ X1 @ X2|~fmember_a @ X65 @ X1), inference(split_conjunct,[status(thm)],[c_0_26])).
% 50.93/50.91 thf(c_0_33, plain, p77, inference(split_conjunct,[status(thm)],[ax1939])).
% 50.93/50.91 thf(c_0_34, plain, (fmember_a @ fx @ fcarrier|~p3), inference(split_conjunct,[status(thm)],[c_0_27])).
% 50.93/50.91 thf(c_0_35, plain, p3, inference(split_conjunct,[status(thm)],[ax2013])).
% 50.93/50.91 thf(c_0_36, plain, ![X8678:set_a]:(~p84|ford_less_eq_set_a @ X8678 @ X8678), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax84])])])).
% 50.93/50.91 thf(c_0_37, plain, ![X8508:nat, X8509:nat]:(~p134|(~ford_less_eq_nat @ X8508 @ X8509|(~ford_less_eq_nat @ X8509 @ X8508|(X8509)=(X8508)))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax134])])])).
% 50.93/50.91 thf(c_0_38, plain, ![X8762:set_a, X8763:set_a]:(~p55|(~ffinite_finite_a @ X8762|(~ford_less_eq_set_a @ X8763 @ X8762|ford_less_eq_nat @ (ffinite_card_a @ X8763) @ (ffinite_card_a @ X8762)))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax55])])])).
% 50.93/50.91 thf(c_0_39, plain, (~ford_less_eq_set_a @ (fprefer1676310729than_a @ fy @ fcarrier @ frelation) @ (fprefer1676310729than_a @ fx @ fcarrier @ frelation)|p225), inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax225])])).
% 50.93/50.91 thf(c_0_40, plain, ![X66:a, X65:a]:(ford_less_eq_set_a @ (fprefer1676310729than_a @ X65 @ fcarrier @ frelation) @ (fprefer1676310729than_a @ X66 @ fcarrier @ frelation)|ford_less_eq_set_a @ (fprefer1676310729than_a @ X66 @ fcarrier @ frelation) @ (fprefer1676310729than_a @ X65 @ fcarrier @ frelation)|~p6), inference(split_conjunct,[status(thm)],[c_0_28])).
% 50.93/50.91 thf(c_0_41, plain, p6, inference(split_conjunct,[status(thm)],[ax2010])).
% 50.93/50.91 thf(c_0_42, plain, (p1|~ford_less_eq_set_a @ (fprefer1676310729than_a @ fx @ fcarrier @ frelation) @ (fprefer1676310729than_a @ fy @ fcarrier @ frelation)), inference(split_conjunct,[status(thm)],[c_0_29])).
% 50.93/50.91 thf(c_0_43, plain, ~p1, inference(split_conjunct,[status(thm)],[c_0_30])).
% 50.93/50.91 thf(c_0_44, plain, ![X8614:set_a, X8615:set_a]:(~p103|(~ffinite_finite_a @ X8614|(~ford_less_eq_set_a @ X8615 @ X8614|ffinite_finite_a @ X8615))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax103])])])).
% 50.93/50.91 thf(c_0_45, plain, ![X65:a]:(ford_less_eq_set_a @ (fprefer1676310729than_a @ X65 @ fcarrier @ frelation) @ fcarrier|~p7|~fmember_a @ X65 @ fcarrier), inference(split_conjunct,[status(thm)],[c_0_31])).
% 50.93/50.91 thf(c_0_46, plain, p7, inference(split_conjunct,[status(thm)],[ax2009])).
% 50.93/50.91 thf(c_0_47, plain, ![X65:a, X2:set_a, X1:set_a]:(fmember_a @ X65 @ X1|~fmember_a @ X65 @ X2|~ford_less_eq_set_a @ X2 @ X1), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_32, c_0_33])])).
% 50.93/50.91 thf(c_0_48, plain, fmember_a @ fx @ fcarrier, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_34, c_0_35])])).
% 50.93/50.91 thf(c_0_49, plain, ![X1:set_a]:(ford_less_eq_set_a @ X1 @ X1|~p84), inference(split_conjunct,[status(thm)],[c_0_36])).
% 50.93/50.91 thf(c_0_50, plain, p84, inference(split_conjunct,[status(thm)],[ax1932])).
% 50.93/50.91 thf(c_0_51, plain, (~p9|ffinite_finite_a @ fcarrier), inference(fof_nnf,[status(thm)],[pax9])).
% 50.93/50.91 thf(c_0_52, plain, ![X80:nat, X71:nat]:((X80)=(X71)|~p134|~ford_less_eq_nat @ X71 @ X80|~ford_less_eq_nat @ X80 @ X71), inference(split_conjunct,[status(thm)],[c_0_37])).
% 50.93/50.91 thf(c_0_53, plain, p134, inference(split_conjunct,[status(thm)],[ax1882])).
% 50.93/50.91 thf(c_0_54, plain, ![X2:set_a, X1:set_a]:(ford_less_eq_nat @ (ffinite_card_a @ X2) @ (ffinite_card_a @ X1)|~p55|~ffinite_finite_a @ X1|~ford_less_eq_set_a @ X2 @ X1), inference(split_conjunct,[status(thm)],[c_0_38])).
% 50.93/50.91 thf(c_0_55, plain, p55, inference(split_conjunct,[status(thm)],[ax1961])).
% 50.93/50.91 thf(c_0_56, plain, (~p5|ford_less_eq_nat @ (ffinite_card_a @ (fprefer1676310729than_a @ fx @ fcarrier @ frelation)) @ (ffinite_card_a @ (fprefer1676310729than_a @ fy @ fcarrier @ frelation))), inference(fof_nnf,[status(thm)],[pax5])).
% 50.93/50.91 thf(c_0_57, plain, (~p225|ford_less_eq_set_a @ (fprefer1676310729than_a @ fy @ fcarrier @ frelation) @ (fprefer1676310729than_a @ fx @ fcarrier @ frelation)), inference(fof_nnf,[status(thm)],[pax225])).
% 50.93/50.91 thf(c_0_58, plain, (p225|~ford_less_eq_set_a @ (fprefer1676310729than_a @ fy @ fcarrier @ frelation) @ (fprefer1676310729than_a @ fx @ fcarrier @ frelation)), inference(split_conjunct,[status(thm)],[c_0_39])).
% 50.93/50.91 thf(c_0_59, plain, ![X66:a, X65:a]:(ford_less_eq_set_a @ (fprefer1676310729than_a @ X65 @ fcarrier @ frelation) @ (fprefer1676310729than_a @ X66 @ fcarrier @ frelation)|ford_less_eq_set_a @ (fprefer1676310729than_a @ X66 @ fcarrier @ frelation) @ (fprefer1676310729than_a @ X65 @ fcarrier @ frelation)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_40, c_0_41])])).
% 50.93/50.91 thf(c_0_60, plain, ~ford_less_eq_set_a @ (fprefer1676310729than_a @ fx @ fcarrier @ frelation) @ (fprefer1676310729than_a @ fy @ fcarrier @ frelation), inference(sr,[status(thm)],[c_0_42, c_0_43])).
% 50.93/50.91 thf(c_0_61, plain, ![X2:set_a, X1:set_a]:(ffinite_finite_a @ X2|~p103|~ffinite_finite_a @ X1|~ford_less_eq_set_a @ X2 @ X1), inference(split_conjunct,[status(thm)],[c_0_44])).
% 50.93/50.91 thf(c_0_62, plain, p103, inference(split_conjunct,[status(thm)],[ax1913])).
% 50.93/50.91 thf(c_0_63, plain, ![X65:a]:(ford_less_eq_set_a @ (fprefer1676310729than_a @ X65 @ fcarrier @ frelation) @ fcarrier|~fmember_a @ X65 @ fcarrier), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_45, c_0_46])])).
% 50.93/50.91 thf(c_0_64, plain, ![X1:set_a]:(fmember_a @ fx @ X1|~ford_less_eq_set_a @ fcarrier @ X1), inference(spm,[status(thm)],[c_0_47, c_0_48])).
% 50.93/50.91 thf(c_0_65, plain, ![X1:set_a]:ford_less_eq_set_a @ X1 @ X1, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_49, c_0_50])])).
% 50.93/50.91 thf(c_0_66, plain, (ffinite_finite_a @ fcarrier|~p9), inference(split_conjunct,[status(thm)],[c_0_51])).
% 50.93/50.91 thf(c_0_67, plain, p9, inference(split_conjunct,[status(thm)],[ax2007])).
% 50.93/50.91 thf(c_0_68, plain, ![X8590:set_a, X8591:set_a]:(~p108|(~ffinite_finite_a @ X8590|(~ford_less_eq_set_a @ X8591 @ X8590|((ffinite_card_a @ X8591)!=(ffinite_card_a @ X8590)|(X8591)=(X8590))))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax108])])])).
% 50.93/50.91 thf(c_0_69, plain, ![X71:nat, X80:nat]:((X71)=(X80)|~ford_less_eq_nat @ X80 @ X71|~ford_less_eq_nat @ X71 @ X80), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_52, c_0_53])])).
% 50.93/50.91 thf(c_0_70, plain, ![X1:set_a, X2:set_a]:(ford_less_eq_nat @ (ffinite_card_a @ X1) @ (ffinite_card_a @ X2)|~ford_less_eq_set_a @ X1 @ X2|~ffinite_finite_a @ X2), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_54, c_0_55])])).
% 50.93/50.91 thf(c_0_71, plain, (ford_less_eq_nat @ (ffinite_card_a @ (fprefer1676310729than_a @ fx @ fcarrier @ frelation)) @ (ffinite_card_a @ (fprefer1676310729than_a @ fy @ fcarrier @ frelation))|~p5), inference(split_conjunct,[status(thm)],[c_0_56])).
% 50.93/50.91 thf(c_0_72, plain, p5, inference(split_conjunct,[status(thm)],[ax2011])).
% 50.93/50.91 thf(c_0_73, plain, (ford_less_eq_set_a @ (fprefer1676310729than_a @ fy @ fcarrier @ frelation) @ (fprefer1676310729than_a @ fx @ fcarrier @ frelation)|~p225), inference(split_conjunct,[status(thm)],[c_0_57])).
% 50.93/50.91 thf(c_0_74, plain, p225, inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_58, c_0_59]), c_0_60])).
% 50.93/50.91 thf(c_0_75, plain, ![X1:set_a, X2:set_a]:(ffinite_finite_a @ X1|~ford_less_eq_set_a @ X1 @ X2|~ffinite_finite_a @ X2), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_61, c_0_62])])).
% 50.93/50.91 thf(c_0_76, plain, ford_less_eq_set_a @ (fprefer1676310729than_a @ fx @ fcarrier @ frelation) @ fcarrier, inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63, c_0_64]), c_0_65])])).
% 50.93/50.91 thf(c_0_77, plain, ffinite_finite_a @ fcarrier, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_66, c_0_67])])).
% 50.93/50.91 thf(c_0_78, plain, ![X2:set_a, X1:set_a]:((X2)=(X1)|~p108|~ffinite_finite_a @ X1|~ford_less_eq_set_a @ X2 @ X1|(ffinite_card_a @ X2)!=(ffinite_card_a @ X1)), inference(split_conjunct,[status(thm)],[c_0_68])).
% 50.93/50.91 thf(c_0_79, plain, p108, inference(split_conjunct,[status(thm)],[ax1908])).
% 50.93/50.91 thf(c_0_80, plain, ![X2:set_a, X1:set_a]:((ffinite_card_a @ X1)=(ffinite_card_a @ X2)|~ford_less_eq_nat @ (ffinite_card_a @ X1) @ (ffinite_card_a @ X2)|~ford_less_eq_set_a @ X2 @ X1|~ffinite_finite_a @ X1), inference(spm,[status(thm)],[c_0_69, c_0_70])).
% 50.93/50.91 thf(c_0_81, plain, ford_less_eq_nat @ (ffinite_card_a @ (fprefer1676310729than_a @ fx @ fcarrier @ frelation)) @ (ffinite_card_a @ (fprefer1676310729than_a @ fy @ fcarrier @ frelation)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_71, c_0_72])])).
% 50.93/50.91 thf(c_0_82, plain, ford_less_eq_set_a @ (fprefer1676310729than_a @ fy @ fcarrier @ frelation) @ (fprefer1676310729than_a @ fx @ fcarrier @ frelation), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_73, c_0_74])])).
% 50.93/50.91 thf(c_0_83, plain, ffinite_finite_a @ (fprefer1676310729than_a @ fx @ fcarrier @ frelation), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75, c_0_76]), c_0_77])])).
% 50.93/50.91 thf(c_0_84, plain, ![X2:set_a, X1:set_a]:((X1)=(X2)|(ffinite_card_a @ X1)!=(ffinite_card_a @ X2)|~ford_less_eq_set_a @ X2 @ X1|~ffinite_finite_a @ X1), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_78, c_0_79])])).
% 50.93/50.91 thf(c_0_85, plain, (ffinite_card_a @ (fprefer1676310729than_a @ fy @ fcarrier @ frelation))=(ffinite_card_a @ (fprefer1676310729than_a @ fx @ fcarrier @ frelation)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80, c_0_81]), c_0_82]), c_0_83])])).
% 50.93/50.91 thf(c_0_86, plain, (fprefer1676310729than_a @ fy @ fcarrier @ frelation)=(fprefer1676310729than_a @ fx @ fcarrier @ frelation), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84, c_0_82]), c_0_83])]), c_0_85])])).
% 50.93/50.91 thf(c_0_87, plain, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_60, c_0_86]), c_0_65])]), ['proof']).
% 50.93/50.91 thf(1,plain,$false,inference(eprover,[status(thm),assumptions([h0])],[])).
% 50.93/50.91 thf(0,theorem,((ord_less_eq_set_a @ (((prefer1676310729than_a @ x) @ carrier) @ relation)) @ (((prefer1676310729than_a @ y) @ carrier) @ relation)),inference(contra,[status(thm),contra(discharge,[h0])],[1,h0])).
% 50.93/50.91 % SZS output end Proof
%------------------------------------------------------------------------------