TSTP Solution File: LCL774-1 by SOS---2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : SOS---2.0
% Problem : LCL774-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : sos-script %s
% Computer : n016.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 14:32:49 EDT 2022
% Result : Unsatisfiable 0.12s 0.38s
% Output : Refutation 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : LCL774-1 : TPTP v8.1.0. Released v4.1.0.
% 0.06/0.12 % Command : sos-script %s
% 0.12/0.32 % Computer : n016.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 600
% 0.12/0.32 % DateTime : Sun Jul 3 20:24:01 EDT 2022
% 0.12/0.32 % CPUTime :
% 0.12/0.37 ----- Otter 3.2, August 2001 -----
% 0.12/0.37 The process was started by sandbox on n016.cluster.edu,
% 0.12/0.37 Sun Jul 3 20:24:01 2022
% 0.12/0.37 The command was "./sos". The process ID is 12514.
% 0.12/0.37
% 0.12/0.37 set(prolog_style_variables).
% 0.12/0.37 set(auto).
% 0.12/0.37 dependent: set(auto1).
% 0.12/0.37 dependent: set(process_input).
% 0.12/0.37 dependent: clear(print_kept).
% 0.12/0.37 dependent: clear(print_new_demod).
% 0.12/0.37 dependent: clear(print_back_demod).
% 0.12/0.37 dependent: clear(print_back_sub).
% 0.12/0.37 dependent: set(control_memory).
% 0.12/0.37 dependent: assign(max_mem, 12000).
% 0.12/0.37 dependent: assign(pick_given_ratio, 4).
% 0.12/0.37 dependent: assign(stats_level, 1).
% 0.12/0.37 dependent: assign(pick_semantic_ratio, 3).
% 0.12/0.37 dependent: assign(sos_limit, 5000).
% 0.12/0.37 dependent: assign(max_weight, 60).
% 0.12/0.37 clear(print_given).
% 0.12/0.37
% 0.12/0.37 list(usable).
% 0.12/0.37
% 0.12/0.37 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=5.
% 0.12/0.37
% 0.12/0.37 This ia a non-Horn set with equality. The strategy will be
% 0.12/0.37 Knuth-Bendix, ordered hyper_res, ur_res, factoring, and
% 0.12/0.37 unit deletion, with positive clauses in sos and nonpositive
% 0.12/0.37 clauses in usable.
% 0.12/0.37
% 0.12/0.37 dependent: set(knuth_bendix).
% 0.12/0.37 dependent: set(para_from).
% 0.12/0.37 dependent: set(para_into).
% 0.12/0.37 dependent: clear(para_from_right).
% 0.12/0.37 dependent: clear(para_into_right).
% 0.12/0.37 dependent: set(para_from_vars).
% 0.12/0.37 dependent: set(eq_units_both_ways).
% 0.12/0.37 dependent: set(dynamic_demod_all).
% 0.12/0.37 dependent: set(dynamic_demod).
% 0.12/0.37 dependent: set(order_eq).
% 0.12/0.37 dependent: set(back_demod).
% 0.12/0.37 dependent: set(lrpo).
% 0.12/0.37 dependent: set(hyper_res).
% 0.12/0.37 dependent: set(unit_deletion).
% 0.12/0.37 dependent: set(factor).
% 0.12/0.37
% 0.12/0.37 ------------> process usable:
% 0.12/0.37 Following clause subsumed by 1 during input processing: 0 [] {-} -class_Ring__and__Field_Ocomm__semiring__1(A)|c_HOL_Otimes__class_Otimes(B,C,A)=c_HOL_Otimes__class_Otimes(C,B,A).
% 0.12/0.37 Following clause subsumed by 4 during input processing: 0 [] {-} -class_Ring__and__Field_Oidom(A)| -class_Int_Onumber__ring(A)|c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A)=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,D,A),c_HOL_Otimes__class_Otimes(B,C,A),A).
% 0.12/0.37 Following clause subsumed by 6 during input processing: 0 [] {-} -class_Ring__and__Field_Oring(A)|c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(D,B,A),C,A),E,A),A)=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(D,C,A),E,A).
% 0.12/0.37 Following clause subsumed by 9 during input processing: 0 [] {-} c_HOL_Oord__class_Oless(A,c_HOL_Oplus__class_Oplus(B,C,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(A,B,tc_nat).
% 0.12/0.37 Following clause subsumed by 10 during input processing: 0 [] {-} c_HOL_Oord__class_Oless(A,c_HOL_Oplus__class_Oplus(B,C,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(A,C,tc_nat).
% 0.12/0.37 Following clause subsumed by 12 during input processing: 0 [] {-} -class_Ring__and__Field_Ocomm__semiring__1(A)|c_HOL_Oplus__class_Oplus(B,C,A)=c_HOL_Oplus__class_Oplus(C,B,A).
% 0.12/0.37 Following clause subsumed by 21 during input processing: 0 [flip.1] {-} c_HOL_Oplus__class_Oplus(A,B,tc_nat)!=A|B=c_HOL_Ozero__class_Ozero(tc_nat).
% 0.12/0.37 Following clause subsumed by 23 during input processing: 0 [] {-} -class_OrderedGroup_Ogroup__add(A)|c_HOL_Ominus__class_Ominus(B,B,A)=c_HOL_Ozero__class_Ozero(A).
% 0.12/0.37 Following clause subsumed by 26 during input processing: 0 [] {-} c_HOL_Otimes__class_Otimes(A,B,tc_nat)!=c_HOL_Otimes__class_Otimes(A,C,tc_nat)|A=c_HOL_Ozero__class_Ozero(tc_nat)|B=C.
% 0.12/0.37 Following clause subsumed by 38 during input processing: 0 [flip.2] {-} -class_Ring__and__Field_Ocomm__semiring__1(A)|c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(B,C,A),D,A)=c_HOL_Oplus__class_Oplus(B,c_HOL_Oplus__class_Oplus(C,D,A),A).
% 0.12/0.37 Following clause subsumed by 38 during input processing: 0 [] {-} -class_Ring__and__Field_Ocomm__semiring__1(A)|c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(B,C,A),D,A)=c_HOL_Oplus__class_Oplus(B,c_HOL_Oplus__class_Oplus(C,D,A),A).
% 0.12/0.37 Following clause subsumed by 66 during input processing: 0 [] {-} c_HOL_Oplus__class_Oplus(A,B,tc_nat)!=c_HOL_Oplus__class_Oplus(A,C,tc_nat)|B=C.
% 0.12/0.38 Following clause subsumed by 83 during input processing: 0 [] {-} c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,B,tc_nat),c_HOL_Otimes__class_Otimes(A,C,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat)| -c_HOL_Oord__class_Oless(B,C,tc_nat).
% 0.12/0.38 Following clause subsumed by 82 during input processing: 0 [] {-} c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,B,tc_nat),c_HOL_Otimes__class_Otimes(C,B,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat)| -c_HOL_Oord__class_Oless(A,C,tc_nat).
% 0.12/0.38 Following clause subsumed by 83 during input processing: 0 [] {-} c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,B,tc_nat),c_HOL_Otimes__class_Otimes(A,C,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(B,C,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat).
% 0.12/0.38 Following clause subsumed by 86 during input processing: 0 [] {-} -class_Ring__and__Field_Oordered__ring__strict(A)|c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A)| -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A)| -c_HOL_Oord__class_Oless(D,C,A).
% 0.12/0.38 Following clause subsumed by 88 during input processing: 0 [] {-} -class_Ring__and__Field_Oordered__ring__strict(A)|c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A)| -c_HOL_Oord__class_Oless(C,D,A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A).
% 0.12/0.38 Following clause subsumed by 86 during input processing: 0 [] {-} -class_Ring__and__Field_Oordered__ring__strict(A)|c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A)| -c_HOL_Oord__class_Oless(D,C,A)| -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A).
% 0.12/0.38 Following clause subsumed by 90 during input processing: 0 [] {-} -class_Ring__and__Field_Oordered__ring__strict(A)|c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,C,A),A)| -c_HOL_Oord__class_Oless(D,B,A)| -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(A),A).
% 0.12/0.38 Following clause subsumed by 96 during input processing: 0 [] {-} -class_Ring__and__Field_Ocomm__semiring__1(A)|c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(A),B,A)=B.
% 0.12/0.38 Following clause subsumed by 10 during input processing: 0 [] {-} c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(A,B,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat).
% 0.12/0.38 Following clause subsumed by 9 during input processing: 0 [] {-} c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(A,B,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat).
% 0.12/0.38 Following clause subsumed by 36 during input processing: 0 [] {-} -class_Ring__and__Field_Ono__zero__divisors(A)|c_HOL_Otimes__class_Otimes(B,C,A)!=c_HOL_Ozero__class_Ozero(A)|B=c_HOL_Ozero__class_Ozero(A)|C=c_HOL_Ozero__class_Ozero(A).
% 0.12/0.38 Following clause subsumed by 122 during input processing: 0 [] {-} -class_Ring__and__Field_Oidom(A)| -class_Int_Onumber__ring(A)|c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,E,A),A)!=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,E,A),c_HOL_Otimes__class_Otimes(D,C,A),A)|C=E|B=D.
% 0.12/0.38 Following clause subsumed by 123 during input processing: 0 [] {-} c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,B,tc_nat),c_HOL_Otimes__class_Otimes(C,D,tc_nat),tc_nat)!=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,D,tc_nat),c_HOL_Otimes__class_Otimes(C,B,tc_nat),tc_nat)|B=D|A=C.
% 0.12/0.38 Following clause subsumed by 127 during input processing: 0 [] {-} -class_Ring__and__Field_Ocomm__semiring__1(A)|c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),B,A)=c_HOL_Ozero__class_Ozero(A).
% 0.12/0.38 Following clause subsumed by 145 during input processing: 0 [] {-} -class_Ring__and__Field_Oordered__semiring__strict(A)|c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Ozero__class_Ozero(A),A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A)| -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A).
% 0.12/0.38 Following clause subsumed by 182 during input processing: 0 [flip.2] {-} -class_Ring__and__Field_Ocomm__semiring__1(A)|c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(B,C,A),D,A)=c_HOL_Otimes__class_Otimes(B,c_HOL_Otimes__class_Otimes(C,D,A),A).
% 0.12/0.38 Following clause subsumed by 182 during input processing: 0 [flip.2] {-} -class_Ring__and__Field_Ocomm__semiring__1(A)|c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(B,C,A),D,A)=c_HOL_Otimes__class_Otimes(B,c_HOL_Otimes__class_Otimes(C,D,A),A).
% 0.12/0.38 Following clause subsumed by 95 during input processing: 0 [] {-} -class_Ring__and__Field_Ocomm__semiring__1(A)|c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(B,C,A),D,A)=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,D,A),c_HOL_Otimes__class_Otimes(C,D,A),A).
% 0.12/0.38 Following clause subsumed by 186 during input processing: 0 [] {-} -class_Orderings_Opreorder(A)| -c_HOL_Oord__class_Oless(B,C,A)| -c_HOL_Oord__class_Oless(C,B,A).
% 0.12/0.38 Following clause subsumed by 194 during input processing: 0 [] {-} c_Suc(A)!=A.
% 0.12/0.38 Following clause subsumed by 201 during input processing: 0 [] {-} c_Suc(A)!=c_HOL_Ozero__class_Ozero(tc_nat).
% 0.12/0.38 Following clause subsumed by 202 during input processing: 0 [] {-} -class_Orderings_Olinorder(A)|c_HOL_Oord__class_Oless(B,C,A)|C=B|c_HOL_Oord__class_Oless(C,B,A).
% 0.12/0.38 Following clause subsumed by 202 during input processing: 0 [] {-} -class_Orderings_Olinorder(A)|c_HOL_Oord__class_Oless(B,C,A)|c_HOL_Oord__class_Oless(C,B,A)|C=B.
% 0.12/0.38 Following clause subsumed by 202 during input processing: 0 [] {-} -class_Orderings_Olinorder(A)|B=C|c_HOL_Oord__class_Oless(C,B,A)|c_HOL_Oord__class_Oless(B,C,A).
% 0.12/0.38 Following clause subsumed by 207 during input processing: 0 [] {-} -c_HOL_Oord__class_Oless(A,A,tc_nat).
% 0.12/0.38 Following clause subsumed by 210 during input processing: 0 [] {-} A=B|c_HOL_Oord__class_Oless(A,B,tc_nat)| -c_HOL_Oord__class_Oless(A,c_Suc(B),tc_nat).
% 0.12/0.38 Following clause subsumed by 212 during input processing: 0 [] {-} c_Suc(A)!=c_Suc(B)|A=B.
% 0.12/0.38 Following clause subsumed by 201 during input processing: 0 [flip.1] {-} c_Suc(A)!=c_HOL_Ozero__class_Ozero(tc_nat).
% 0.12/0.38 Following clause subsumed by 201 during input processing: 0 [flip.1] {-} c_Suc(A)!=c_HOL_Ozero__class_Ozero(tc_nat).
% 0.12/0.38 Following clause subsumed by 221 during input processing: 0 [] {-} -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat).
% 0.12/0.38 Following clause subsumed by 225 during input processing: 0 [] {-} c_HOL_Oord__class_Oless(c_Suc(A),c_Suc(B),tc_nat)| -c_HOL_Oord__class_Oless(A,B,tc_nat).
% 0.12/0.38 142 back subsumes 84.
% 0.12/0.38 142 back subsumes 65.
% 0.12/0.38 182 back subsumes 125.
% 0.12/0.38 183 back subsumes 126.
% 0.12/0.38 207 back subsumes 197.
% 0.12/0.38 Following clause subsumed by 247 during input processing: 0 [copy,237,flip.1] {-} c_Lambda_OdB_OVar(A)!=c_Lambda_OdB_OAbs(B).
% 0.12/0.38 Following clause subsumed by 240 during input processing: 0 [copy,238,flip.1] {-} c_Lambda_OdB_OAbs(A)!=c_Lambda_OdB_OApp(B,C).
% 0.12/0.38 Following clause subsumed by 238 during input processing: 0 [copy,240,flip.1] {-} c_Lambda_OdB_OApp(A,B)!=c_Lambda_OdB_OAbs(C).
% 0.12/0.38 Following clause subsumed by 251 during input processing: 0 [copy,245,flip.1] {-} c_Lambda_OdB_OApp(A,B)!=c_Lambda_OdB_OVar(C).
% 0.12/0.38 Following clause subsumed by 237 during input processing: 0 [copy,247,flip.1] {-} c_Lambda_OdB_OAbs(A)!=c_Lambda_OdB_OVar(B).
% 0.12/0.38 Following clause subsumed by 245 during input processing: 0 [copy,251,flip.1] {-} c_Lambda_OdB_OVar(A)!=c_Lambda_OdB_OApp(B,C).
% 0.12/0.38
% 0.12/0.38 ------------> process sos:
% 0.12/0.38 Following clause subsumed by 303 during input processing: 0 [] {-} c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,B,tc_nat),c_HOL_Otimes__class_Otimes(A,C,tc_nat),tc_nat)=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,C,tc_nat),c_HOL_Otimes__class_Otimes(A,B,tc_nat),tc_nat).
% 0.12/0.38 Following clause subsumed by 312 during input processing: 0 [demod,308] {-} c_HOL_Oord__class_Oless(A,c_HOL_Oplus__class_Oplus(A,c_Suc(B),tc_nat),tc_nat).
% 0.12/0.38 Following clause subsumed by 310 during input processing: 0 [] {-} c_HOL_Oplus__class_Oplus(c_Suc(A),B,tc_nat)=c_HOL_Oplus__class_Oplus(A,c_Suc(B),tc_nat).
% 0.12/0.38 Following clause subsumed by 350 during input processing: 0 [demod,346] {-} c_Su
% 0.12/0.38 -------- PROOF --------
% 0.12/0.38 % SZS status Unsatisfiable
% 0.12/0.38 % SZS output start Refutation
% 0.12/0.38 c(c_HOL_Ozero__class_Ozero(tc_nat))=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)).
% 0.12/0.38 Following clause subsumed by 350 during input processing: 0 [demod,365,365] {-} c_HOL_Ozero__class_Ozero(tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 0.12/0.38 Following clause subsumed by 350 during input processing: 0 [demod,367,367] {-} c_HOL_Ozero__class_Ozero(tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 0.12/0.38 Following clause subsumed by 350 during input processing: 0 [demod,348] {-} c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)).
% 0.12/0.38 Following clause subsumed by 378 during input processing: 0 [] {-} c_HOL_Oord__class_Oless(A,c_Suc(A),tc_nat).
% 0.12/0.38 Following clause subsumed by 379 during input processing: 0 [] {-} c_HOL_Oord__class_Oless(A,B,tc_nat)|c_HOL_Oord__class_Oless(B,A,tc_nat)|B=A.
% 0.12/0.38 Following clause subsumed by 378 during input processing: 0 [] {-} c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat).
% 0.12/0.38 Following clause subsumed by 381 during input processing: 0 [] {-} c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(A),tc_nat).
% 0.12/0.38 Following clause subsumed by 378 during input processing: 0 [unit_del,207] {-} c_HOL_Oord__class_Oless(A,c_Suc(A),tc_nat).
% 0.12/0.38 Following clause subsumed by 350 during input processing: 0 [demod,390] {-} B=B.
% 0.12/0.38
% 0.12/0.38 ----> UNIT CONFLICT at 0.02 sec ----> 402 [binary,401.1,252.1] {-} $F.
% 0.12/0.38
% 0.12/0.38 Length of proof is 0. Level of proof is 0.
% 0.12/0.38
% 0.12/0.38 ---------------- PROOF ----------------
% 0.12/0.38 % SZS status Unsatisfiable
% 0.12/0.38 % SZS output start Refutation
% 0.12/0.38
% 0.12/0.38 252 [] {-} -c_InductTermi_OIT(c_Lambda_OdB_OVar(v_i)).
% 0.12/0.38 401 [] {-} c_InductTermi_OIT(c_Lambda_OdB_OVar(A)).
% 0.12/0.38 402 [binary,401.1,252.1] {-} $F.
% 0.12/0.38
% 0.12/0.38 % SZS output end Refutation
% 0.12/0.38 ------------ end of proof -------------
% 0.12/0.38
% 0.12/0.38
% 0.12/0.38 Search stopped by max_proofs option.
% 0.12/0.38
% 0.12/0.38
% 0.12/0.38 Search stopped by max_proofs option.
% 0.12/0.38
% 0.12/0.38 ============ end of search ============
% 0.12/0.38
% 0.12/0.38 That finishes the proof of the theorem.
% 0.12/0.38
% 0.12/0.38 Process 12514 finished Sun Jul 3 20:24:01 2022
%------------------------------------------------------------------------------