TSTP Solution File: ITP156^1 by Satallax---3.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : ITP156^1 : 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 : n023.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 00:29:19 EDT 2022
% Result : Theorem 1.96s 2.21s
% Output : Proof 1.96s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : ITP156^1 : TPTP v8.1.0. Released v7.5.0.
% 0.03/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n023.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Fri Jun 3 02:43:10 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.96/2.21 % SZS status Theorem
% 1.96/2.21 % Mode: mode507:USE_SINE=true:SINE_TOLERANCE=3.0:SINE_GENERALITY_THRESHOLD=0:SINE_RANK_LIMIT=1.:SINE_DEPTH=1
% 1.96/2.21 % Inferences: 4
% 1.96/2.21 % SZS output start Proof
% 1.96/2.21 thf(ty_a, type, a : $tType).
% 1.96/2.21 thf(ty_product_prod_a_a, type, product_prod_a_a : $tType).
% 1.96/2.21 thf(ty_set_Product_prod_a_a, type, set_Product_prod_a_a : $tType).
% 1.96/2.21 thf(ty_real, type, real : $tType).
% 1.96/2.21 thf(ty_zero_zero_real, type, zero_zero_real : real).
% 1.96/2.21 thf(ty_real_V1035702895aleR_a, type, real_V1035702895aleR_a : (real>a>a)).
% 1.96/2.21 thf(ty_relation, type, relation : set_Product_prod_a_a).
% 1.96/2.21 thf(ty_member449909584od_a_a, type, member449909584od_a_a : (product_prod_a_a>set_Product_prod_a_a>$o)).
% 1.96/2.21 thf(ty_v, type, v : real).
% 1.96/2.21 thf(ty_plus_plus_a, type, plus_plus_a : (a>a>a)).
% 1.96/2.21 thf(ty_u, type, u : real).
% 1.96/2.21 thf(ty_y, type, y : a).
% 1.96/2.21 thf(ty_one_one_real, type, one_one_real : real).
% 1.96/2.21 thf(ty_x, type, x : a).
% 1.96/2.21 thf(ty_product_Pair_a_a, type, product_Pair_a_a : (a>a>product_prod_a_a)).
% 1.96/2.21 thf(sP1,plain,sP1 <=> (u = zero_zero_real),introduced(definition,[new_symbols(definition,[sP1])])).
% 1.96/2.21 thf(sP2,plain,sP2 <=> ((member449909584od_a_a @ ((product_Pair_a_a @ ((plus_plus_a @ ((real_V1035702895aleR_a @ u) @ x)) @ ((real_V1035702895aleR_a @ v) @ y))) @ y)) @ relation),introduced(definition,[new_symbols(definition,[sP2])])).
% 1.96/2.21 thf(conj_0,conjecture,sP2).
% 1.96/2.21 thf(h0,negated_conjecture,(~(sP2)),inference(assume_negation,[status(cth)],[conj_0])).
% 1.96/2.21 thf(h1,assumption,(~(sP1)),introduced(assumption,[])).
% 1.96/2.21 thf(h2,assumption,sP2,introduced(assumption,[])).
% 1.96/2.21 thf(h3,assumption,((~(sP1)) => (u = one_one_real)),introduced(assumption,[])).
% 1.96/2.21 thf(h4,assumption,sP1,introduced(assumption,[])).
% 1.96/2.21 thf(h5,assumption,(u = one_one_real),introduced(assumption,[])).
% 1.96/2.21 thf(1,plain,$false,inference(tab_conflict,[status(thm),assumptions([h4,h3,h1,h0])],[h4,h1])).
% 1.96/2.21 thf(pax8, axiom, (p8=>(fu)=(fone_one_real)), file('<stdin>', pax8)).
% 1.96/2.21 thf(pax28, axiom, (p28=>![X42:a, X43:a, X44:a]:((fplus_plus_a @ X42 @ X43)=(fplus_plus_a @ X42 @ X44)=>(X43)=(X44))), file('<stdin>', pax28)).
% 1.96/2.21 thf(pax22, axiom, (p22=>![X48:a]:(fplus_plus_a @ X48 @ fzero_zero_a)=(X48)), file('<stdin>', pax22)).
% 1.96/2.21 thf(pax50, axiom, (p50=>![X21:real, X22:real, X18:a]:(freal_V1035702895aleR_a @ (fplus_plus_real @ X21 @ X22) @ X18)=(fplus_plus_a @ (freal_V1035702895aleR_a @ X21 @ X18) @ (freal_V1035702895aleR_a @ X22 @ X18))), file('<stdin>', pax50)).
% 1.96/2.21 thf(pax10, axiom, (p10=>(fplus_plus_real @ fu @ fv)=(fone_one_real)), file('<stdin>', pax10)).
% 1.96/2.21 thf(ax53, axiom, p8, file('<stdin>', ax53)).
% 1.96/2.21 thf(pax41, axiom, (p41=>![X32:a]:(freal_V1035702895aleR_a @ fone_one_real @ X32)=(X32)), file('<stdin>', pax41)).
% 1.96/2.21 thf(ax32, axiom, p28, file('<stdin>', ax32)).
% 1.96/2.21 thf(ax38, axiom, p22, file('<stdin>', ax38)).
% 1.96/2.21 thf(ax10, axiom, p50, file('<stdin>', ax10)).
% 1.96/2.21 thf(ax50, axiom, p10, file('<stdin>', ax50)).
% 1.96/2.21 thf(ax19, axiom, p41, file('<stdin>', ax19)).
% 1.96/2.21 thf(nax54, axiom, (p54<=fmember449909584od_a_a @ (fproduct_Pair_a_a @ (fplus_plus_a @ (freal_V1035702895aleR_a @ fu @ fx) @ (freal_V1035702895aleR_a @ fv @ fy)) @ fy) @ frelation), file('<stdin>', nax54)).
% 1.96/2.21 thf(ax6, axiom, ~(p54), file('<stdin>', ax6)).
% 1.96/2.21 thf(pax6, axiom, (p6=>fmember449909584od_a_a @ (fproduct_Pair_a_a @ fx @ fy) @ frelation), file('<stdin>', pax6)).
% 1.96/2.21 thf(ax54, axiom, p6, file('<stdin>', ax54)).
% 1.96/2.21 thf(c_0_16, plain, (~p8|(fu)=(fone_one_real)), inference(fof_nnf,[status(thm)],[pax8])).
% 1.96/2.21 thf(c_0_17, plain, ![X217:a, X218:a, X219:a]:(~p28|((fplus_plus_a @ X217 @ X218)!=(fplus_plus_a @ X217 @ X219)|(X218)=(X219))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax28])])])).
% 1.96/2.21 thf(c_0_18, plain, ![X241:a]:(~p22|(fplus_plus_a @ X241 @ fzero_zero_a)=(X241)), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax22])])])).
% 1.96/2.21 thf(c_0_19, plain, ![X125:real, X126:real, X127:a]:(~p50|(freal_V1035702895aleR_a @ (fplus_plus_real @ X125 @ X126) @ X127)=(fplus_plus_a @ (freal_V1035702895aleR_a @ X125 @ X127) @ (freal_V1035702895aleR_a @ X126 @ X127))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax50])])])).
% 1.96/2.21 thf(c_0_20, plain, (~p10|(fplus_plus_real @ fu @ fv)=(fone_one_real)), inference(fof_nnf,[status(thm)],[pax10])).
% 1.96/2.21 thf(c_0_21, plain, ((fu)=(fone_one_real)|~p8), inference(split_conjunct,[status(thm)],[c_0_16])).
% 1.96/2.21 thf(c_0_22, plain, p8, inference(split_conjunct,[status(thm)],[ax53])).
% 1.96/2.21 thf(c_0_23, plain, ![X161:a]:(~p41|(freal_V1035702895aleR_a @ fone_one_real @ X161)=(X161)), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax41])])])).
% 1.96/2.21 thf(c_0_24, plain, ![X1:a, X2:a, X7:a]:((X2)=(X7)|~p28|(fplus_plus_a @ X1 @ X2)!=(fplus_plus_a @ X1 @ X7)), inference(split_conjunct,[status(thm)],[c_0_17])).
% 1.96/2.21 thf(c_0_25, plain, p28, inference(split_conjunct,[status(thm)],[ax32])).
% 1.96/2.21 thf(c_0_26, plain, ![X1:a]:((fplus_plus_a @ X1 @ fzero_zero_a)=(X1)|~p22), inference(split_conjunct,[status(thm)],[c_0_18])).
% 1.96/2.21 thf(c_0_27, plain, p22, inference(split_conjunct,[status(thm)],[ax38])).
% 1.96/2.21 thf(c_0_28, plain, ![X4:real, X3:real, X1:a]:((freal_V1035702895aleR_a @ (fplus_plus_real @ X3 @ X4) @ X1)=(fplus_plus_a @ (freal_V1035702895aleR_a @ X3 @ X1) @ (freal_V1035702895aleR_a @ X4 @ X1))|~p50), inference(split_conjunct,[status(thm)],[c_0_19])).
% 1.96/2.21 thf(c_0_29, plain, p50, inference(split_conjunct,[status(thm)],[ax10])).
% 1.96/2.21 thf(c_0_30, plain, ((fplus_plus_real @ fu @ fv)=(fone_one_real)|~p10), inference(split_conjunct,[status(thm)],[c_0_20])).
% 1.96/2.21 thf(c_0_31, plain, (fone_one_real)=(fu), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_21, c_0_22])])).
% 1.96/2.21 thf(c_0_32, plain, p10, inference(split_conjunct,[status(thm)],[ax50])).
% 1.96/2.21 thf(c_0_33, plain, ![X1:a]:((freal_V1035702895aleR_a @ fone_one_real @ X1)=(X1)|~p41), inference(split_conjunct,[status(thm)],[c_0_23])).
% 1.96/2.21 thf(c_0_34, plain, p41, inference(split_conjunct,[status(thm)],[ax19])).
% 1.96/2.21 thf(c_0_35, plain, (~fmember449909584od_a_a @ (fproduct_Pair_a_a @ (fplus_plus_a @ (freal_V1035702895aleR_a @ fu @ fx) @ (freal_V1035702895aleR_a @ fv @ fy)) @ fy) @ frelation|p54), inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax54])])).
% 1.96/2.21 thf(c_0_36, plain, ~p54, inference(fof_simplification,[status(thm)],[ax6])).
% 1.96/2.21 thf(c_0_37, plain, ![X1:a, X7:a, X2:a]:((X1)=(X2)|(fplus_plus_a @ X7 @ X1)!=(fplus_plus_a @ X7 @ X2)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_24, c_0_25])])).
% 1.96/2.21 thf(c_0_38, plain, ![X1:a]:(fplus_plus_a @ X1 @ fzero_zero_a)=(X1), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_26, c_0_27])])).
% 1.96/2.21 thf(c_0_39, plain, ![X4:real, X3:real, X1:a]:(freal_V1035702895aleR_a @ (fplus_plus_real @ X3 @ X4) @ X1)=(fplus_plus_a @ (freal_V1035702895aleR_a @ X3 @ X1) @ (freal_V1035702895aleR_a @ X4 @ X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_28, c_0_29])])).
% 1.96/2.21 thf(c_0_40, plain, (fplus_plus_real @ fu @ fv)=(fu), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_30, c_0_31]), c_0_32])])).
% 1.96/2.21 thf(c_0_41, plain, ![X1:a]:(freal_V1035702895aleR_a @ fu @ X1)=(X1), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_33, c_0_31]), c_0_34])])).
% 1.96/2.21 thf(c_0_42, plain, (~p6|fmember449909584od_a_a @ (fproduct_Pair_a_a @ fx @ fy) @ frelation), inference(fof_nnf,[status(thm)],[pax6])).
% 1.96/2.21 thf(c_0_43, plain, (p54|~fmember449909584od_a_a @ (fproduct_Pair_a_a @ (fplus_plus_a @ (freal_V1035702895aleR_a @ fu @ fx) @ (freal_V1035702895aleR_a @ fv @ fy)) @ fy) @ frelation), inference(split_conjunct,[status(thm)],[c_0_35])).
% 1.96/2.21 thf(c_0_44, plain, ~p54, inference(split_conjunct,[status(thm)],[c_0_36])).
% 1.96/2.21 thf(c_0_45, plain, ![X1:a, X2:a]:((X1)=(fzero_zero_a)|(fplus_plus_a @ X2 @ X1)!=(X2)), inference(spm,[status(thm)],[c_0_37, c_0_38])).
% 1.96/2.21 thf(c_0_46, plain, ![X1:a]:(fplus_plus_a @ X1 @ (freal_V1035702895aleR_a @ fv @ X1))=(X1), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39, c_0_40]), c_0_41]), c_0_41])).
% 1.96/2.21 thf(c_0_47, plain, (fmember449909584od_a_a @ (fproduct_Pair_a_a @ fx @ fy) @ frelation|~p6), inference(split_conjunct,[status(thm)],[c_0_42])).
% 1.96/2.21 thf(c_0_48, plain, p6, inference(split_conjunct,[status(thm)],[ax54])).
% 1.96/2.21 thf(c_0_49, plain, ~fmember449909584od_a_a @ (fproduct_Pair_a_a @ (fplus_plus_a @ fx @ (freal_V1035702895aleR_a @ fv @ fy)) @ fy) @ frelation, inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_43, c_0_41]), c_0_44])).
% 1.96/2.21 thf(c_0_50, plain, ![X1:a]:(freal_V1035702895aleR_a @ fv @ X1)=(fzero_zero_a), inference(spm,[status(thm)],[c_0_45, c_0_46])).
% 1.96/2.21 thf(c_0_51, plain, fmember449909584od_a_a @ (fproduct_Pair_a_a @ fx @ fy) @ frelation, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_47, c_0_48])])).
% 1.96/2.21 thf(c_0_52, plain, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_49, c_0_50]), c_0_38]), c_0_51])]), ['proof']).
% 1.96/2.21 thf(2,plain,$false,inference(eprover,[status(thm),assumptions([h5,h3,h1,h0])],[])).
% 1.96/2.21 thf(3,plain,$false,inference(tab_imp,[status(thm),assumptions([h3,h1,h0]),tab_imp(discharge,[h4]),tab_imp(discharge,[h5])],[h3,1,2,h4,h5])).
% 1.96/2.21 thf(4,plain,$false,inference(tab_conflict,[status(thm),assumptions([h2,h1,h0])],[h2,h0])).
% 1.96/2.21 thf(fact_6__092_060open_062u_A_092_060noteq_062_A0_A_092_060and_062_Au_A_092_060noteq_062_A1_A_092_060longrightarrow_062_Au_A_K_092_060_094sub_062R_Ax_A_L_Av_A_K_092_060_094sub_062R_Ay_A_092_060succeq_062_Ay_092_060close_062,axiom,((~(((~(sP1)) => (u = one_one_real)))) => sP2)).
% 1.96/2.21 thf(5,plain,$false,inference(tab_imp,[status(thm),assumptions([h1,h0]),tab_imp(discharge,[h3]),tab_imp(discharge,[h2])],[fact_6__092_060open_062u_A_092_060noteq_062_A0_A_092_060and_062_Au_A_092_060noteq_062_A1_A_092_060longrightarrow_062_Au_A_K_092_060_094sub_062R_Ax_A_L_Av_A_K_092_060_094sub_062R_Ay_A_092_060succeq_062_Ay_092_060close_062,3,4,h3,h2])).
% 1.96/2.21 thf(6,plain,$false,inference(tab_conflict,[status(thm),assumptions([h4,h3,h2,h0])],[h2,h0])).
% 1.96/2.21 thf(7,plain,$false,inference(tab_conflict,[status(thm),assumptions([h5,h3,h2,h0])],[h2,h0])).
% 1.96/2.21 thf(8,plain,$false,inference(tab_imp,[status(thm),assumptions([h3,h2,h0]),tab_imp(discharge,[h4]),tab_imp(discharge,[h5])],[h3,6,7,h4,h5])).
% 1.96/2.21 thf(9,plain,$false,inference(tab_conflict,[status(thm),assumptions([h2,h2,h0])],[h2,h0])).
% 1.96/2.21 thf(10,plain,$false,inference(tab_imp,[status(thm),assumptions([h2,h0]),tab_imp(discharge,[h3]),tab_imp(discharge,[h2])],[fact_6__092_060open_062u_A_092_060noteq_062_A0_A_092_060and_062_Au_A_092_060noteq_062_A1_A_092_060longrightarrow_062_Au_A_K_092_060_094sub_062R_Ax_A_L_Av_A_K_092_060_094sub_062R_Ay_A_092_060succeq_062_Ay_092_060close_062,8,9,h3,h2])).
% 1.96/2.21 thf(fact_7_u__0,axiom,(sP1 => sP2)).
% 1.96/2.21 thf(11,plain,$false,inference(tab_imp,[status(thm),assumptions([h0]),tab_imp(discharge,[h1]),tab_imp(discharge,[h2])],[fact_7_u__0,5,10,h1,h2])).
% 1.96/2.21 thf(0,theorem,sP2,inference(contra,[status(thm),contra(discharge,[h0])],[11,h0])).
% 1.96/2.21 % SZS output end Proof
%------------------------------------------------------------------------------