%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : ITP145^1 : 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 : n020.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 01:47:06 PM UTC 2025
% Result : Theorem 3.08s 3.28s
% Output : Proof 3.08s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : ITP145^1 : TPTP v9.2.0. Released v7.5.0.
% 0.07/0.14 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.14/0.35 % Computer : n020.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Wed Oct 8 18:26:23 EDT 2025
% 0.14/0.36 % CPUTime :
% 3.08/3.28 % SZS status Theorem
% 3.08/3.28 % Mode: mode507:USE_SINE=true:SINE_TOLERANCE=3.0:SINE_GENERALITY_THRESHOLD=0:SINE_RANK_LIMIT=1.:SINE_DEPTH=1
% 3.08/3.28 % Inferences: 4
% 3.08/3.28 % SZS output start Proof
% 3.08/3.28 thf(conj_4,conjecture,((member1069318160_state @ ((produc1909270103_state @ ((produc1204172211_state @ ((cons_com @ c) @ nil_com)) @ s)) @ (f @ (suc @ n)))) @ (transi1302705790_state @ pHoare259243666_exec1))).
% 3.08/3.28 thf(h0,negated_conjecture,(~(((member1069318160_state @ ((produc1909270103_state @ ((produc1204172211_state @ ((cons_com @ c) @ nil_com)) @ s)) @ (f @ (suc @ n)))) @ (transi1302705790_state @ pHoare259243666_exec1)))),inference(assume_negation,[status(cth)],[conj_4])).
% 3.08/3.28 thf(pax22, axiom, (p22=>![X199:produc410756839_state, X197:set_Pr1165141447_state]:(fmember1069318160_state @ X199 @ X197=>fmember1069318160_state @ X199 @ (ftransi1302705790_state @ X197))), file('<stdin>', pax22)).
% 3.08/3.28 thf(pax167, axiom, (p167=>![X1:nat]:fmember1069318160_state @ (fproduc1909270103_state @ (ff @ X1) @ (ff @ (fsuc @ X1))) @ (ftransi1726587420_state @ fpHoare259243666_exec1)), file('<stdin>', pax167)).
% 3.08/3.28 thf(pax8, axiom, (p8=>![X216:set_Pr1165141447_state]:(ftransi1302705790_state @ (ftransi1726587420_state @ X216))=(ftransi1302705790_state @ X216)), file('<stdin>', pax8)).
% 3.08/3.28 thf(pax43, axiom, (p43=>![X186:produc2041926651_state, X187:produc2041926651_state, X188:set_Pr1165141447_state, X189:produc2041926651_state]:(fmember1069318160_state @ (fproduc1909270103_state @ X186 @ X187) @ X188=>(fmember1069318160_state @ (fproduc1909270103_state @ X187 @ X189) @ X188=>fmember1069318160_state @ (fproduc1909270103_state @ X186 @ X189) @ (ftransi1726587420_state @ X188)))), file('<stdin>', pax43)).
% 3.08/3.28 thf(ax150, axiom, p22, file('<stdin>', ax150)).
% 3.08/3.28 thf(ax5, axiom, p167, file('<stdin>', ax5)).
% 3.08/3.28 thf(ax164, axiom, p8, file('<stdin>', ax164)).
% 3.08/3.28 thf(pax7, axiom, (p7=>![X216:set_Pr1165141447_state]:(ftransi1726587420_state @ (ftransi1302705790_state @ X216))=(ftransi1302705790_state @ X216)), file('<stdin>', pax7)).
% 3.08/3.28 thf(pax166, axiom, (p166=>(ff @ fzero_zero_nat)=(fproduc1204172211_state @ (fcons_com @ fc @ fnil_com) @ fs)), file('<stdin>', pax166)).
% 3.08/3.28 thf(ax129, axiom, p43, file('<stdin>', ax129)).
% 3.08/3.28 thf(ax165, axiom, p7, file('<stdin>', ax165)).
% 3.08/3.28 thf(pax168, axiom, (p168=>fmember1069318160_state @ (fproduc1909270103_state @ (fproduc1204172211_state @ (fcons_com @ fc @ fnil_com) @ fs) @ (ff @ fn)) @ (ftransi1302705790_state @ fpHoare259243666_exec1)), file('<stdin>', pax168)).
% 3.08/3.28 thf(ax6, axiom, p166, file('<stdin>', ax6)).
% 3.08/3.28 thf(nax169, axiom, (p169<=fmember1069318160_state @ (fproduc1909270103_state @ (fproduc1204172211_state @ (fcons_com @ fc @ fnil_com) @ fs) @ (ff @ (fsuc @ fn))) @ (ftransi1302705790_state @ fpHoare259243666_exec1)), file('<stdin>', nax169)).
% 3.08/3.28 thf(ax3, axiom, ~(p169), file('<stdin>', ax3)).
% 3.08/3.28 thf(ax4, axiom, p168, file('<stdin>', ax4)).
% 3.08/3.28 thf(c_0_16, plain, ![X907:produc410756839_state, X908:set_Pr1165141447_state]:(~p22|(~fmember1069318160_state @ X907 @ X908|fmember1069318160_state @ X907 @ (ftransi1302705790_state @ X908))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax22])])])).
% 3.08/3.28 thf(c_0_17, plain, ![X257:nat]:(~p167|fmember1069318160_state @ (fproduc1909270103_state @ (ff @ X257) @ (ff @ (fsuc @ X257))) @ (ftransi1726587420_state @ fpHoare259243666_exec1)), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax167])])])).
% 3.08/3.28 thf(c_0_18, plain, ![X967:set_Pr1165141447_state]:(~p8|(ftransi1302705790_state @ (ftransi1726587420_state @ X967))=(ftransi1302705790_state @ X967)), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax8])])])).
% 3.08/3.28 thf(c_0_19, plain, ![X803:produc2041926651_state, X804:produc2041926651_state, X805:set_Pr1165141447_state, X806:produc2041926651_state]:(~p43|(~fmember1069318160_state @ (fproduc1909270103_state @ X803 @ X804) @ X805|(~fmember1069318160_state @ (fproduc1909270103_state @ X804 @ X806) @ X805|fmember1069318160_state @ (fproduc1909270103_state @ X803 @ X806) @ (ftransi1726587420_state @ X805)))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax43])])])).
% 3.08/3.28 thf(c_0_20, plain, ![X132:produc410756839_state, X8:set_Pr1165141447_state]:(fmember1069318160_state @ X132 @ (ftransi1302705790_state @ X8)|~p22|~fmember1069318160_state @ X132 @ X8), inference(split_conjunct,[status(thm)],[c_0_16])).
% 3.08/3.28 thf(c_0_21, plain, p22, inference(split_conjunct,[status(thm)],[ax150])).
% 3.08/3.28 thf(c_0_22, plain, ![X1:nat]:(fmember1069318160_state @ (fproduc1909270103_state @ (ff @ X1) @ (ff @ (fsuc @ X1))) @ (ftransi1726587420_state @ fpHoare259243666_exec1)|~p167), inference(split_conjunct,[status(thm)],[c_0_17])).
% 3.08/3.28 thf(c_0_23, plain, p167, inference(split_conjunct,[status(thm)],[ax5])).
% 3.08/3.28 thf(c_0_24, plain, ![X8:set_Pr1165141447_state]:((ftransi1302705790_state @ (ftransi1726587420_state @ X8))=(ftransi1302705790_state @ X8)|~p8), inference(split_conjunct,[status(thm)],[c_0_18])).
% 3.08/3.28 thf(c_0_25, plain, p8, inference(split_conjunct,[status(thm)],[ax164])).
% 3.08/3.28 thf(c_0_26, plain, ![X969:set_Pr1165141447_state]:(~p7|(ftransi1726587420_state @ (ftransi1302705790_state @ X969))=(ftransi1302705790_state @ X969)), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax7])])])).
% 3.08/3.28 thf(c_0_27, plain, (~p166|(ff @ fzero_zero_nat)=(fproduc1204172211_state @ (fcons_com @ fc @ fnil_com) @ fs)), inference(fof_nnf,[status(thm)],[pax166])).
% 3.08/3.28 thf(c_0_28, plain, ![X10:produc2041926651_state, X13:produc2041926651_state, X12:produc2041926651_state, X8:set_Pr1165141447_state]:(fmember1069318160_state @ (fproduc1909270103_state @ X10 @ X13) @ (ftransi1726587420_state @ X8)|~p43|~fmember1069318160_state @ (fproduc1909270103_state @ X10 @ X12) @ X8|~fmember1069318160_state @ (fproduc1909270103_state @ X12 @ X13) @ X8), inference(split_conjunct,[status(thm)],[c_0_19])).
% 3.08/3.28 thf(c_0_29, plain, p43, inference(split_conjunct,[status(thm)],[ax129])).
% 3.08/3.28 thf(c_0_30, plain, ![X132:produc410756839_state, X8:set_Pr1165141447_state]:(fmember1069318160_state @ X132 @ (ftransi1302705790_state @ X8)|~fmember1069318160_state @ X132 @ X8), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_20, c_0_21])])).
% 3.08/3.28 thf(c_0_31, plain, ![X1:nat]:fmember1069318160_state @ (fproduc1909270103_state @ (ff @ X1) @ (ff @ (fsuc @ X1))) @ (ftransi1726587420_state @ fpHoare259243666_exec1), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_22, c_0_23])])).
% 3.08/3.28 thf(c_0_32, plain, ![X8:set_Pr1165141447_state]:(ftransi1302705790_state @ (ftransi1726587420_state @ X8))=(ftransi1302705790_state @ X8), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_24, c_0_25])])).
% 3.08/3.28 thf(c_0_33, plain, ![X8:set_Pr1165141447_state]:((ftransi1726587420_state @ (ftransi1302705790_state @ X8))=(ftransi1302705790_state @ X8)|~p7), inference(split_conjunct,[status(thm)],[c_0_26])).
% 3.08/3.28 thf(c_0_34, plain, p7, inference(split_conjunct,[status(thm)],[ax165])).
% 3.08/3.28 thf(c_0_35, plain, (~p168|fmember1069318160_state @ (fproduc1909270103_state @ (fproduc1204172211_state @ (fcons_com @ fc @ fnil_com) @ fs) @ (ff @ fn)) @ (ftransi1302705790_state @ fpHoare259243666_exec1)), inference(fof_nnf,[status(thm)],[pax168])).
% 3.08/3.28 thf(c_0_36, plain, ((ff @ fzero_zero_nat)=(fproduc1204172211_state @ (fcons_com @ fc @ fnil_com) @ fs)|~p166), inference(split_conjunct,[status(thm)],[c_0_27])).
% 3.08/3.28 thf(c_0_37, plain, p166, inference(split_conjunct,[status(thm)],[ax6])).
% 3.08/3.28 thf(c_0_38, plain, (~fmember1069318160_state @ (fproduc1909270103_state @ (fproduc1204172211_state @ (fcons_com @ fc @ fnil_com) @ fs) @ (ff @ (fsuc @ fn))) @ (ftransi1302705790_state @ fpHoare259243666_exec1)|p169), inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax169])])).
% 3.08/3.28 thf(c_0_39, plain, ~p169, inference(fof_simplification,[status(thm)],[ax3])).
% 3.08/3.28 thf(c_0_40, plain, ![X10:produc2041926651_state, X13:produc2041926651_state, X12:produc2041926651_state, X8:set_Pr1165141447_state]:(fmember1069318160_state @ (fproduc1909270103_state @ X10 @ X12) @ (ftransi1726587420_state @ X8)|~fmember1069318160_state @ (fproduc1909270103_state @ X13 @ X12) @ X8|~fmember1069318160_state @ (fproduc1909270103_state @ X10 @ X13) @ X8), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_28, c_0_29])])).
% 3.08/3.28 thf(c_0_41, plain, ![X1:nat]:fmember1069318160_state @ (fproduc1909270103_state @ (ff @ X1) @ (ff @ (fsuc @ X1))) @ (ftransi1302705790_state @ fpHoare259243666_exec1), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30, c_0_31]), c_0_32])).
% 3.08/3.28 thf(c_0_42, plain, ![X8:set_Pr1165141447_state]:(ftransi1726587420_state @ (ftransi1302705790_state @ X8))=(ftransi1302705790_state @ X8), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_33, c_0_34])])).
% 3.08/3.28 thf(c_0_43, plain, (fmember1069318160_state @ (fproduc1909270103_state @ (fproduc1204172211_state @ (fcons_com @ fc @ fnil_com) @ fs) @ (ff @ fn)) @ (ftransi1302705790_state @ fpHoare259243666_exec1)|~p168), inference(split_conjunct,[status(thm)],[c_0_35])).
% 3.08/3.28 thf(c_0_44, plain, (fproduc1204172211_state @ (fcons_com @ fc @ fnil_com) @ fs)=(ff @ fzero_zero_nat), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_36, c_0_37])])).
% 3.08/3.28 thf(c_0_45, plain, p168, inference(split_conjunct,[status(thm)],[ax4])).
% 3.08/3.28 thf(c_0_46, plain, (p169|~fmember1069318160_state @ (fproduc1909270103_state @ (fproduc1204172211_state @ (fcons_com @ fc @ fnil_com) @ fs) @ (ff @ (fsuc @ fn))) @ (ftransi1302705790_state @ fpHoare259243666_exec1)), inference(split_conjunct,[status(thm)],[c_0_38])).
% 3.08/3.28 thf(c_0_47, plain, ~p169, inference(split_conjunct,[status(thm)],[c_0_39])).
% 3.08/3.28 thf(c_0_48, plain, ![X10:produc2041926651_state, X1:nat]:(fmember1069318160_state @ (fproduc1909270103_state @ X10 @ (ff @ (fsuc @ X1))) @ (ftransi1302705790_state @ fpHoare259243666_exec1)|~fmember1069318160_state @ (fproduc1909270103_state @ X10 @ (ff @ X1)) @ (ftransi1302705790_state @ fpHoare259243666_exec1)), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40, c_0_41]), c_0_42])).
% 3.08/3.28 thf(c_0_49, plain, fmember1069318160_state @ (fproduc1909270103_state @ (ff @ fzero_zero_nat) @ (ff @ fn)) @ (ftransi1302705790_state @ fpHoare259243666_exec1), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_43, c_0_44]), c_0_45])])).
% 3.08/3.28 thf(c_0_50, plain, ~fmember1069318160_state @ (fproduc1909270103_state @ (ff @ fzero_zero_nat) @ (ff @ (fsuc @ fn))) @ (ftransi1302705790_state @ fpHoare259243666_exec1), inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_46, c_0_44]), c_0_47])).
% 3.08/3.28 thf(c_0_51, plain, ($false), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_48, c_0_49]), c_0_50]), ['proof']).
% 3.08/3.28 thf(1,plain,$false,inference(eprover,[status(thm),assumptions([h0])],[])).
% 3.08/3.28 thf(0,theorem,((member1069318160_state @ ((produc1909270103_state @ ((produc1204172211_state @ ((cons_com @ c) @ nil_com)) @ s)) @ (f @ (suc @ n)))) @ (transi1302705790_state @ pHoare259243666_exec1)),inference(contra,[status(thm),contra(discharge,[h0])],[1,h0])).
% 3.08/3.28 % SZS output end Proof
%------------------------------------------------------------------------------