TSTP Solution File: ITP034^1 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : ITP034^1 : 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 : n018.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 00:28:50 EDT 2022
% Result : Theorem 1.51s 1.74s
% Output : Proof 1.51s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : ITP034^1 : 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 : n018.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 : Thu Jun 2 14:41:45 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.51/1.74 % SZS status Theorem
% 1.51/1.74 % Mode: mode507:USE_SINE=true:SINE_TOLERANCE=3.0:SINE_GENERALITY_THRESHOLD=0:SINE_RANK_LIMIT=1.:SINE_DEPTH=1
% 1.51/1.74 % Inferences: 12
% 1.51/1.74 % SZS output start Proof
% 1.51/1.74 thf(ty_a, type, a : $tType).
% 1.51/1.74 thf(ty_binary1439146945Tree_a, type, binary1439146945Tree_a : $tType).
% 1.51/1.74 thf(ty_int, type, int : $tType).
% 1.51/1.74 thf(ty_set_a, type, set_a : $tType).
% 1.51/1.74 thf(ty_h, type, h : (a>int)).
% 1.51/1.74 thf(ty_member_a, type, member_a : (a>set_a>$o)).
% 1.51/1.74 thf(ty_binary476621312_Tip_a, type, binary476621312_Tip_a : binary1439146945Tree_a).
% 1.51/1.74 thf(ty_binary1721989714Tree_a, type, binary1721989714Tree_a : ((a>int)>binary1439146945Tree_a>$o)).
% 1.51/1.74 thf(ty_binary339557810e_rm_a, type, binary339557810e_rm_a : ((a>int)>binary1439146945Tree_a>a)).
% 1.51/1.74 thf(ty_t2, type, t2 : binary1439146945Tree_a).
% 1.51/1.74 thf(ty_binary1217730267_wrm_a, type, binary1217730267_wrm_a : ((a>int)>binary1439146945Tree_a>binary1439146945Tree_a)).
% 1.51/1.74 thf(ty_t1, type, t1 : binary1439146945Tree_a).
% 1.51/1.74 thf(ty_ord_less_int, type, ord_less_int : (int>int>$o)).
% 1.51/1.74 thf(ty_binary945792244etOf_a, type, binary945792244etOf_a : (binary1439146945Tree_a>set_a)).
% 1.51/1.74 thf(sP1,plain,sP1 <=> ((binary1721989714Tree_a @ h) @ t2),introduced(definition,[new_symbols(definition,[sP1])])).
% 1.51/1.74 thf(sP2,plain,sP2 <=> (t2 = binary476621312_Tip_a),introduced(definition,[new_symbols(definition,[sP2])])).
% 1.51/1.74 thf(sP3,plain,sP3 <=> ((binary1721989714Tree_a @ h) @ t1),introduced(definition,[new_symbols(definition,[sP3])])).
% 1.51/1.74 thf(conj_0,conjecture,((ord_less_int @ (h @ l)) @ (h @ ((binary339557810e_rm_a @ h) @ (((binary717961607le_T_a @ t1) @ x) @ t2))))).
% 1.51/1.74 thf(h0,negated_conjecture,(~(((ord_less_int @ (h @ l)) @ (h @ ((binary339557810e_rm_a @ h) @ (((binary717961607le_T_a @ t1) @ x) @ t2)))))),inference(assume_negation,[status(cth)],[conj_0])).
% 1.51/1.74 thf(h1,assumption,((~(sP2)) => (~(sP1))),introduced(assumption,[])).
% 1.51/1.74 thf(h2,assumption,(![X1:a]:(((member_a @ X1) @ (binary945792244etOf_a @ ((binary1217730267_wrm_a @ h) @ t2))) => ((ord_less_int @ (h @ X1)) @ (h @ ((binary339557810e_rm_a @ h) @ t2))))),introduced(assumption,[])).
% 1.51/1.74 thf(h3,assumption,sP2,introduced(assumption,[])).
% 1.51/1.74 thf(h4,assumption,(~(sP1)),introduced(assumption,[])).
% 1.51/1.74 thf(h5,assumption,((~((t1 = binary476621312_Tip_a))) => (~(sP3))),introduced(assumption,[])).
% 1.51/1.74 thf(h6,assumption,(![X1:a]:(((member_a @ X1) @ (binary945792244etOf_a @ ((binary1217730267_wrm_a @ h) @ t1))) => ((ord_less_int @ (h @ X1)) @ (h @ ((binary339557810e_rm_a @ h) @ t1))))),introduced(assumption,[])).
% 1.51/1.74 thf(h7,assumption,(t1 = binary476621312_Tip_a),introduced(assumption,[])).
% 1.51/1.74 thf(h8,assumption,(~(sP3)),introduced(assumption,[])).
% 1.51/1.74 thf(fact_2_t2nTip,axiom,(~(sP2))).
% 1.51/1.74 thf(1,plain,$false,inference(tab_conflict,[status(thm),assumptions([h7,h5,h3,h1,h0])],[h3,fact_2_t2nTip])).
% 1.51/1.74 thf(fact_7_s1,axiom,sP3).
% 1.51/1.74 thf(2,plain,$false,inference(tab_conflict,[status(thm),assumptions([h8,h5,h3,h1,h0])],[fact_7_s1,h8])).
% 1.51/1.74 thf(3,plain,$false,inference(tab_imp,[status(thm),assumptions([h5,h3,h1,h0]),tab_imp(discharge,[h7]),tab_imp(discharge,[h8])],[h5,1,2,h7,h8])).
% 1.51/1.74 thf(4,plain,$false,inference(tab_conflict,[status(thm),assumptions([h6,h3,h1,h0])],[h3,fact_2_t2nTip])).
% 1.51/1.74 thf(fact_35_h1,axiom,((~(((~((t1 = binary476621312_Tip_a))) => (~(sP3))))) => (![X1:a]:(((member_a @ X1) @ (binary945792244etOf_a @ ((binary1217730267_wrm_a @ h) @ t1))) => ((ord_less_int @ (h @ X1)) @ (h @ ((binary339557810e_rm_a @ h) @ t1))))))).
% 1.51/1.74 thf(5,plain,$false,inference(tab_imp,[status(thm),assumptions([h3,h1,h0]),tab_imp(discharge,[h5]),tab_imp(discharge,[h6])],[fact_35_h1,3,4,h5,h6])).
% 1.51/1.74 thf(fact_8_s2,axiom,sP1).
% 1.51/1.74 thf(6,plain,$false,inference(tab_conflict,[status(thm),assumptions([h7,h5,h4,h1,h0])],[fact_8_s2,h4])).
% 1.51/1.74 thf(7,plain,$false,inference(tab_conflict,[status(thm),assumptions([h8,h5,h4,h1,h0])],[fact_7_s1,h8])).
% 1.51/1.74 thf(8,plain,$false,inference(tab_imp,[status(thm),assumptions([h5,h4,h1,h0]),tab_imp(discharge,[h7]),tab_imp(discharge,[h8])],[h5,6,7,h7,h8])).
% 1.51/1.74 thf(9,plain,$false,inference(tab_conflict,[status(thm),assumptions([h6,h4,h1,h0])],[fact_8_s2,h4])).
% 1.51/1.74 thf(10,plain,$false,inference(tab_imp,[status(thm),assumptions([h4,h1,h0]),tab_imp(discharge,[h5]),tab_imp(discharge,[h6])],[fact_35_h1,8,9,h5,h6])).
% 1.51/1.74 thf(11,plain,$false,inference(tab_imp,[status(thm),assumptions([h1,h0]),tab_imp(discharge,[h3]),tab_imp(discharge,[h4])],[h1,5,10,h3,h4])).
% 1.51/1.74 thf(pax2, axiom, (p2=>(fbinary339557810e_rm_a @ fh @ (fbinary717961607le_T_a @ ft1 @ fx @ ft2))=(fbinary339557810e_rm_a @ fh @ ft2)), file('<stdin>', pax2)).
% 1.51/1.74 thf(pax1, axiom, (p1=>ford_less_int @ (fh @ fl) @ (fh @ (fbinary339557810e_rm_a @ fh @ ft2))), file('<stdin>', pax1)).
% 1.51/1.74 thf(nax45, axiom, (p45<=ford_less_int @ (fh @ fl) @ (fh @ (fbinary339557810e_rm_a @ fh @ (fbinary717961607le_T_a @ ft1 @ fx @ ft2)))), file('<stdin>', nax45)).
% 1.51/1.74 thf(ax49, axiom, p2, file('<stdin>', ax49)).
% 1.51/1.74 thf(ax50, axiom, p1, file('<stdin>', ax50)).
% 1.51/1.74 thf(ax7, axiom, ~(p45), file('<stdin>', ax7)).
% 1.51/1.74 thf(c_0_6, plain, (~p2|(fbinary339557810e_rm_a @ fh @ (fbinary717961607le_T_a @ ft1 @ fx @ ft2))=(fbinary339557810e_rm_a @ fh @ ft2)), inference(fof_nnf,[status(thm)],[pax2])).
% 1.51/1.74 thf(c_0_7, plain, (~p1|ford_less_int @ (fh @ fl) @ (fh @ (fbinary339557810e_rm_a @ fh @ ft2))), inference(fof_nnf,[status(thm)],[pax1])).
% 1.51/1.74 thf(c_0_8, plain, (~ford_less_int @ (fh @ fl) @ (fh @ (fbinary339557810e_rm_a @ fh @ (fbinary717961607le_T_a @ ft1 @ fx @ ft2)))|p45), inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax45])])).
% 1.51/1.74 thf(c_0_9, plain, ((fbinary339557810e_rm_a @ fh @ (fbinary717961607le_T_a @ ft1 @ fx @ ft2))=(fbinary339557810e_rm_a @ fh @ ft2)|~p2), inference(split_conjunct,[status(thm)],[c_0_6])).
% 1.51/1.74 thf(c_0_10, plain, p2, inference(split_conjunct,[status(thm)],[ax49])).
% 1.51/1.74 thf(c_0_11, plain, (ford_less_int @ (fh @ fl) @ (fh @ (fbinary339557810e_rm_a @ fh @ ft2))|~p1), inference(split_conjunct,[status(thm)],[c_0_7])).
% 1.51/1.74 thf(c_0_12, plain, p1, inference(split_conjunct,[status(thm)],[ax50])).
% 1.51/1.74 thf(c_0_13, plain, ~p45, inference(fof_simplification,[status(thm)],[ax7])).
% 1.51/1.74 thf(c_0_14, plain, (p45|~ford_less_int @ (fh @ fl) @ (fh @ (fbinary339557810e_rm_a @ fh @ (fbinary717961607le_T_a @ ft1 @ fx @ ft2)))), inference(split_conjunct,[status(thm)],[c_0_8])).
% 1.51/1.74 thf(c_0_15, plain, (fbinary339557810e_rm_a @ fh @ (fbinary717961607le_T_a @ ft1 @ fx @ ft2))=(fbinary339557810e_rm_a @ fh @ ft2), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_9, c_0_10])])).
% 1.51/1.74 thf(c_0_16, plain, ford_less_int @ (fh @ fl) @ (fh @ (fbinary339557810e_rm_a @ fh @ ft2)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_11, c_0_12])])).
% 1.51/1.74 thf(c_0_17, plain, ~p45, inference(split_conjunct,[status(thm)],[c_0_13])).
% 1.51/1.74 thf(c_0_18, plain, ($false), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_14, c_0_15]), c_0_16])]), c_0_17]), ['proof']).
% 1.51/1.74 thf(12,plain,$false,inference(eprover,[status(thm),assumptions([h7,h5,h2,h0])],[])).
% 1.51/1.74 thf(13,plain,$false,inference(tab_conflict,[status(thm),assumptions([h8,h5,h2,h0])],[fact_7_s1,h8])).
% 1.51/1.74 thf(14,plain,$false,inference(tab_imp,[status(thm),assumptions([h5,h2,h0]),tab_imp(discharge,[h7]),tab_imp(discharge,[h8])],[h5,12,13,h7,h8])).
% 1.51/1.74 thf(nax45, axiom, (p45<=ford_less_int @ (fh @ fl) @ (fh @ (fbinary339557810e_rm_a @ fh @ (fbinary717961607le_T_a @ ft1 @ fx @ ft2)))), file('<stdin>', nax45)).
% 1.51/1.74 thf(ax25, axiom, ~(p45), file('<stdin>', ax25)).
% 1.51/1.74 thf(pax2, axiom, (p2=>(fbinary339557810e_rm_a @ fh @ (fbinary717961607le_T_a @ ft1 @ fx @ ft2))=(fbinary339557810e_rm_a @ fh @ ft2)), file('<stdin>', pax2)).
% 1.51/1.74 thf(pax1, axiom, (p1=>ford_less_int @ (fh @ fl) @ (fh @ (fbinary339557810e_rm_a @ fh @ ft2))), file('<stdin>', pax1)).
% 1.51/1.74 thf(ax67, axiom, p2, file('<stdin>', ax67)).
% 1.51/1.74 thf(ax68, axiom, p1, file('<stdin>', ax68)).
% 1.51/1.74 thf(c_0_6, plain, (~ford_less_int @ (fh @ fl) @ (fh @ (fbinary339557810e_rm_a @ fh @ (fbinary717961607le_T_a @ ft1 @ fx @ ft2)))|p45), inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax45])])).
% 1.51/1.74 thf(c_0_7, plain, ~p45, inference(fof_simplification,[status(thm)],[ax25])).
% 1.51/1.74 thf(c_0_8, plain, (~p2|(fbinary339557810e_rm_a @ fh @ (fbinary717961607le_T_a @ ft1 @ fx @ ft2))=(fbinary339557810e_rm_a @ fh @ ft2)), inference(fof_nnf,[status(thm)],[pax2])).
% 1.51/1.74 thf(c_0_9, plain, (~p1|ford_less_int @ (fh @ fl) @ (fh @ (fbinary339557810e_rm_a @ fh @ ft2))), inference(fof_nnf,[status(thm)],[pax1])).
% 1.51/1.74 thf(c_0_10, plain, (p45|~ford_less_int @ (fh @ fl) @ (fh @ (fbinary339557810e_rm_a @ fh @ (fbinary717961607le_T_a @ ft1 @ fx @ ft2)))), inference(split_conjunct,[status(thm)],[c_0_6])).
% 1.51/1.74 thf(c_0_11, plain, ~p45, inference(split_conjunct,[status(thm)],[c_0_7])).
% 1.51/1.74 thf(c_0_12, plain, ((fbinary339557810e_rm_a @ fh @ (fbinary717961607le_T_a @ ft1 @ fx @ ft2))=(fbinary339557810e_rm_a @ fh @ ft2)|~p2), inference(split_conjunct,[status(thm)],[c_0_8])).
% 1.51/1.74 thf(c_0_13, plain, p2, inference(split_conjunct,[status(thm)],[ax67])).
% 1.51/1.74 thf(c_0_14, plain, (ford_less_int @ (fh @ fl) @ (fh @ (fbinary339557810e_rm_a @ fh @ ft2))|~p1), inference(split_conjunct,[status(thm)],[c_0_9])).
% 1.51/1.74 thf(c_0_15, plain, p1, inference(split_conjunct,[status(thm)],[ax68])).
% 1.51/1.74 thf(c_0_16, plain, ~ford_less_int @ (fh @ fl) @ (fh @ (fbinary339557810e_rm_a @ fh @ (fbinary717961607le_T_a @ ft1 @ fx @ ft2))), inference(sr,[status(thm)],[c_0_10, c_0_11])).
% 1.51/1.74 thf(c_0_17, plain, (fbinary339557810e_rm_a @ fh @ (fbinary717961607le_T_a @ ft1 @ fx @ ft2))=(fbinary339557810e_rm_a @ fh @ ft2), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_12, c_0_13])])).
% 1.51/1.74 thf(c_0_18, plain, ford_less_int @ (fh @ fl) @ (fh @ (fbinary339557810e_rm_a @ fh @ ft2)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_14, c_0_15])])).
% 1.51/1.74 thf(c_0_19, plain, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_16, c_0_17]), c_0_18])]), ['proof']).
% 1.51/1.74 thf(15,plain,$false,inference(eprover,[status(thm),assumptions([h6,h2,h0])],[])).
% 1.51/1.74 thf(16,plain,$false,inference(tab_imp,[status(thm),assumptions([h2,h0]),tab_imp(discharge,[h5]),tab_imp(discharge,[h6])],[fact_35_h1,14,15,h5,h6])).
% 1.51/1.74 thf(fact_36_h2,axiom,((~(((~(sP2)) => (~(sP1))))) => (![X1:a]:(((member_a @ X1) @ (binary945792244etOf_a @ ((binary1217730267_wrm_a @ h) @ t2))) => ((ord_less_int @ (h @ X1)) @ (h @ ((binary339557810e_rm_a @ h) @ t2))))))).
% 1.51/1.74 thf(17,plain,$false,inference(tab_imp,[status(thm),assumptions([h0]),tab_imp(discharge,[h1]),tab_imp(discharge,[h2])],[fact_36_h2,11,16,h1,h2])).
% 1.51/1.74 thf(0,theorem,((ord_less_int @ (h @ l)) @ (h @ ((binary339557810e_rm_a @ h) @ (((binary717961607le_T_a @ t1) @ x) @ t2)))),inference(contra,[status(thm),contra(discharge,[h0])],[17,h0])).
% 1.51/1.74 % SZS output end Proof
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