TSTP Solution File: LCL498+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : LCL498+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n007.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 13:47:13 EDT 2022
% Result : Theorem 2.54s 2.84s
% Output : Refutation 2.54s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : LCL498+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.14 % Command : tptp2X_and_run_prover9 %d %s
% 0.14/0.35 % Computer : n007.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 : 600
% 0.14/0.35 % DateTime : Mon Jul 4 14:02:12 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.78/1.03 ============================== Prover9 ===============================
% 0.78/1.03 Prover9 (32) version 2009-11A, November 2009.
% 0.78/1.03 Process 30776 was started by sandbox2 on n007.cluster.edu,
% 0.78/1.03 Mon Jul 4 14:02:12 2022
% 0.78/1.03 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_30623_n007.cluster.edu".
% 0.78/1.03 ============================== end of head ===========================
% 0.78/1.03
% 0.78/1.03 ============================== INPUT =================================
% 0.78/1.03
% 0.78/1.03 % Reading from file /tmp/Prover9_30623_n007.cluster.edu
% 0.78/1.03
% 0.78/1.03 set(prolog_style_variables).
% 0.78/1.03 set(auto2).
% 0.78/1.03 % set(auto2) -> set(auto).
% 0.78/1.03 % set(auto) -> set(auto_inference).
% 0.78/1.03 % set(auto) -> set(auto_setup).
% 0.78/1.03 % set(auto_setup) -> set(predicate_elim).
% 0.78/1.03 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.78/1.03 % set(auto) -> set(auto_limits).
% 0.78/1.03 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.78/1.03 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.78/1.03 % set(auto) -> set(auto_denials).
% 0.78/1.03 % set(auto) -> set(auto_process).
% 0.78/1.03 % set(auto2) -> assign(new_constants, 1).
% 0.78/1.03 % set(auto2) -> assign(fold_denial_max, 3).
% 0.78/1.03 % set(auto2) -> assign(max_weight, "200.000").
% 0.78/1.03 % set(auto2) -> assign(max_hours, 1).
% 0.78/1.03 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.78/1.03 % set(auto2) -> assign(max_seconds, 0).
% 0.78/1.03 % set(auto2) -> assign(max_minutes, 5).
% 0.78/1.03 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.78/1.03 % set(auto2) -> set(sort_initial_sos).
% 0.78/1.03 % set(auto2) -> assign(sos_limit, -1).
% 0.78/1.03 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.78/1.03 % set(auto2) -> assign(max_megs, 400).
% 0.78/1.03 % set(auto2) -> assign(stats, some).
% 0.78/1.03 % set(auto2) -> clear(echo_input).
% 0.78/1.03 % set(auto2) -> set(quiet).
% 0.78/1.03 % set(auto2) -> clear(print_initial_clauses).
% 0.78/1.03 % set(auto2) -> clear(print_given).
% 0.78/1.03 assign(lrs_ticks,-1).
% 0.78/1.03 assign(sos_limit,10000).
% 0.78/1.03 assign(order,kbo).
% 0.78/1.03 set(lex_order_vars).
% 0.78/1.03 clear(print_given).
% 0.78/1.03
% 0.78/1.03 % formulas(sos). % not echoed (45 formulas)
% 0.78/1.03
% 0.78/1.03 ============================== end of input ==========================
% 0.78/1.03
% 0.78/1.03 % From the command line: assign(max_seconds, 300).
% 0.78/1.03
% 0.78/1.03 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.78/1.03
% 0.78/1.03 % Formulas that are not ordinary clauses:
% 0.78/1.03 1 modus_ponens <-> (all X all Y (is_a_theorem(X) & is_a_theorem(implies(X,Y)) -> is_a_theorem(Y))) # label(modus_ponens) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.03 2 substitution_of_equivalents <-> (all X all Y (is_a_theorem(equiv(X,Y)) -> X = Y)) # label(substitution_of_equivalents) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.03 3 modus_tollens <-> (all X all Y is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y)))) # label(modus_tollens) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.03 4 implies_1 <-> (all X all Y is_a_theorem(implies(X,implies(Y,X)))) # label(implies_1) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.03 5 implies_2 <-> (all X all Y is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y)))) # label(implies_2) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.03 6 implies_3 <-> (all X all Y all Z is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))))) # label(implies_3) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.03 7 and_1 <-> (all X all Y is_a_theorem(implies(and(X,Y),X))) # label(and_1) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.03 8 and_2 <-> (all X all Y is_a_theorem(implies(and(X,Y),Y))) # label(and_2) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.03 9 and_3 <-> (all X all Y is_a_theorem(implies(X,implies(Y,and(X,Y))))) # label(and_3) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.03 10 or_1 <-> (all X all Y is_a_theorem(implies(X,or(X,Y)))) # label(or_1) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.03 11 or_2 <-> (all X all Y is_a_theorem(implies(Y,or(X,Y)))) # label(or_2) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.03 12 or_3 <-> (all X all Y all Z is_a_theorem(implies(implies(X,Z),implies(implies(Y,Z),implies(or(X,Y),Z))))) # label(or_3) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.03 13 equivalence_1 <-> (all X all Y is_a_theorem(implies(equiv(X,Y),implies(X,Y)))) # label(equivalence_1) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.03 14 equivalence_2 <-> (all X all Y is_a_theorem(implies(equiv(X,Y),implies(Y,X)))) # label(equivalence_2) # label(axiom) # label(non_clause). [assumption].
% 1.72/1.99 15 equivalence_3 <-> (all X all Y is_a_theorem(implies(implies(X,Y),implies(implies(Y,X),equiv(X,Y))))) # label(equivalence_3) # label(axiom) # label(non_clause). [assumption].
% 1.72/1.99 16 kn1 <-> (all P is_a_theorem(implies(P,and(P,P)))) # label(kn1) # label(axiom) # label(non_clause). [assumption].
% 1.72/1.99 17 kn2 <-> (all P all Q is_a_theorem(implies(and(P,Q),P))) # label(kn2) # label(axiom) # label(non_clause). [assumption].
% 1.72/1.99 18 kn3 <-> (all P all Q all R is_a_theorem(implies(implies(P,Q),implies(not(and(Q,R)),not(and(R,P)))))) # label(kn3) # label(axiom) # label(non_clause). [assumption].
% 1.72/1.99 19 cn1 <-> (all P all Q all R is_a_theorem(implies(implies(P,Q),implies(implies(Q,R),implies(P,R))))) # label(cn1) # label(axiom) # label(non_clause). [assumption].
% 1.72/1.99 20 cn2 <-> (all P all Q is_a_theorem(implies(P,implies(not(P),Q)))) # label(cn2) # label(axiom) # label(non_clause). [assumption].
% 1.72/1.99 21 cn3 <-> (all P is_a_theorem(implies(implies(not(P),P),P))) # label(cn3) # label(axiom) # label(non_clause). [assumption].
% 1.72/1.99 22 r1 <-> (all P is_a_theorem(implies(or(P,P),P))) # label(r1) # label(axiom) # label(non_clause). [assumption].
% 1.72/1.99 23 r2 <-> (all P all Q is_a_theorem(implies(Q,or(P,Q)))) # label(r2) # label(axiom) # label(non_clause). [assumption].
% 1.72/1.99 24 r3 <-> (all P all Q is_a_theorem(implies(or(P,Q),or(Q,P)))) # label(r3) # label(axiom) # label(non_clause). [assumption].
% 1.72/1.99 25 r4 <-> (all P all Q all R is_a_theorem(implies(or(P,or(Q,R)),or(Q,or(P,R))))) # label(r4) # label(axiom) # label(non_clause). [assumption].
% 1.72/1.99 26 r5 <-> (all P all Q all R is_a_theorem(implies(implies(Q,R),implies(or(P,Q),or(P,R))))) # label(r5) # label(axiom) # label(non_clause). [assumption].
% 1.72/1.99 27 op_or -> (all X all Y or(X,Y) = not(and(not(X),not(Y)))) # label(op_or) # label(axiom) # label(non_clause). [assumption].
% 1.72/1.99 28 op_and -> (all X all Y and(X,Y) = not(or(not(X),not(Y)))) # label(op_and) # label(axiom) # label(non_clause). [assumption].
% 1.72/1.99 29 op_implies_and -> (all X all Y implies(X,Y) = not(and(X,not(Y)))) # label(op_implies_and) # label(axiom) # label(non_clause). [assumption].
% 1.72/1.99 30 op_implies_or -> (all X all Y implies(X,Y) = or(not(X),Y)) # label(op_implies_or) # label(axiom) # label(non_clause). [assumption].
% 1.72/1.99 31 op_equiv -> (all X all Y equiv(X,Y) = and(implies(X,Y),implies(Y,X))) # label(op_equiv) # label(axiom) # label(non_clause). [assumption].
% 1.72/1.99
% 1.72/1.99 ============================== end of process non-clausal formulas ===
% 1.72/1.99
% 1.72/1.99 ============================== PROCESS INITIAL CLAUSES ===============
% 1.72/1.99
% 1.72/1.99 ============================== PREDICATE ELIMINATION =================
% 1.72/1.99
% 1.72/1.99 ============================== end predicate elimination =============
% 1.72/1.99
% 1.72/1.99 Auto_denials: (non-Horn, no changes).
% 1.72/1.99
% 1.72/1.99 Term ordering decisions:
% 1.72/1.99
% 1.72/1.99 % Assigning unary symbol not kb_weight 0 and highest precedence (94).
% 1.72/1.99 Function symbol KB weights: c1=1. c2=1. c3=1. c4=1. c5=1. c6=1. c7=1. c8=1. c9=1. c10=1. c11=1. c12=1. c13=1. c14=1. c15=1. c16=1. c17=1. c18=1. c19=1. c20=1. c21=1. c22=1. c23=1. c24=1. c25=1. c26=1. c27=1. c28=1. c29=1. c30=1. c31=1. c32=1. c33=1. c34=1. c35=1. c36=1. c37=1. c38=1. c39=1. c40=1. c41=1. c42=1. c43=1. c44=1. c45=1. c46=1. c47=1. c48=1. c49=1. c50=1. c51=1. c52=1. c53=1. c54=1. c55=1. implies=1. or=1. and=1. equiv=1. not=0.
% 1.72/1.99
% 1.72/1.99 ============================== end of process initial clauses ========
% 1.72/1.99
% 1.72/1.99 ============================== CLAUSES FOR SEARCH ====================
% 1.72/1.99
% 1.72/1.99 ============================== end of clauses for search =============
% 1.72/1.99
% 1.72/1.99 ============================== SEARCH ================================
% 1.72/1.99
% 1.72/1.99 % Starting search at 0.02 seconds.
% 1.72/1.99
% 1.72/1.99 Low Water (keep): wt=23.000, iters=3357
% 1.72/1.99
% 1.72/1.99 Low Water (keep): wt=22.000, iters=3502
% 1.72/1.99
% 1.72/1.99 Low Water (keep): wt=20.000, iters=3361
% 1.72/1.99
% 1.72/1.99 Low Water (keep): wt=19.000, iters=3341
% 1.72/1.99
% 1.72/1.99 Low Water (keep): wt=18.000, iters=3342
% 1.72/1.99
% 1.72/1.99 Low Water (keep): wt=17.000, iters=3444
% 1.72/1.99
% 1.72/1.99 Low Water (keep): wt=16.000, iters=3405
% 1.72/1.99
% 1.72/1.99 Low Water (keep): wt=15.000, iters=3335
% 1.72/1.99
% 1.72/1.99 Low Water (displace): id=2785, wt=45.000
% 1.72/1.99
% 1.72/1.99 Low Water (displace): id=1182, wt=37.000
% 2.54/2.84
% 2.54/2.84 Low Water (displace): id=11423, wt=14.000
% 2.54/2.84
% 2.54/2.84 Low Water (displace): id=11902, wt=13.000
% 2.54/2.84
% 2.54/2.84 Low Water (displace): id=14048, wt=12.000
% 2.54/2.84
% 2.54/2.84 Low Water (displace): id=14070, wt=11.000
% 2.54/2.84
% 2.54/2.84 Low Water (displace): id=14145, wt=10.000
% 2.54/2.84
% 2.54/2.84 Low Water (keep): wt=14.000, iters=3375
% 2.54/2.84
% 2.54/2.84 ============================== PROOF =================================
% 2.54/2.84 % SZS status Theorem
% 2.54/2.84 % SZS output start Refutation
% 2.54/2.84
% 2.54/2.84 % Proof 1 at 1.75 (+ 0.06) seconds.
% 2.54/2.84 % Length of proof is 47.
% 2.54/2.84 % Level of proof is 13.
% 2.54/2.84 % Maximum clause weight is 13.000.
% 2.54/2.84 % Given clauses 734.
% 2.54/2.84
% 2.54/2.84 1 modus_ponens <-> (all X all Y (is_a_theorem(X) & is_a_theorem(implies(X,Y)) -> is_a_theorem(Y))) # label(modus_ponens) # label(axiom) # label(non_clause). [assumption].
% 2.54/2.84 21 cn3 <-> (all P is_a_theorem(implies(implies(not(P),P),P))) # label(cn3) # label(axiom) # label(non_clause). [assumption].
% 2.54/2.84 22 r1 <-> (all P is_a_theorem(implies(or(P,P),P))) # label(r1) # label(axiom) # label(non_clause). [assumption].
% 2.54/2.84 23 r2 <-> (all P all Q is_a_theorem(implies(Q,or(P,Q)))) # label(r2) # label(axiom) # label(non_clause). [assumption].
% 2.54/2.84 24 r3 <-> (all P all Q is_a_theorem(implies(or(P,Q),or(Q,P)))) # label(r3) # label(axiom) # label(non_clause). [assumption].
% 2.54/2.84 26 r5 <-> (all P all Q all R is_a_theorem(implies(implies(Q,R),implies(or(P,Q),or(P,R))))) # label(r5) # label(axiom) # label(non_clause). [assumption].
% 2.54/2.84 30 op_implies_or -> (all X all Y implies(X,Y) = or(not(X),Y)) # label(op_implies_or) # label(axiom) # label(non_clause). [assumption].
% 2.54/2.84 32 op_implies_or # label(principia_op_implies_or) # label(axiom). [assumption].
% 2.54/2.84 35 modus_ponens # label(principia_modus_ponens) # label(axiom). [assumption].
% 2.54/2.84 36 r1 # label(principia_r1) # label(axiom). [assumption].
% 2.54/2.84 37 r2 # label(principia_r2) # label(axiom). [assumption].
% 2.54/2.84 38 r3 # label(principia_r3) # label(axiom). [assumption].
% 2.54/2.84 40 r5 # label(principia_r5) # label(axiom). [assumption].
% 2.54/2.84 44 -cn3 # label(luka_cn3) # label(negated_conjecture). [assumption].
% 2.54/2.84 59 -r1 | is_a_theorem(implies(or(A,A),A)) # label(r1) # label(axiom). [clausify(22)].
% 2.54/2.84 60 is_a_theorem(implies(or(A,A),A)). [copy(59),unit_del(a,36)].
% 2.54/2.84 62 -r2 | is_a_theorem(implies(A,or(B,A))) # label(r2) # label(axiom). [clausify(23)].
% 2.54/2.84 63 is_a_theorem(implies(A,or(B,A))). [copy(62),unit_del(a,37)].
% 2.54/2.84 69 cn3 | -is_a_theorem(implies(implies(not(c44),c44),c44)) # label(cn3) # label(axiom). [clausify(21)].
% 2.54/2.84 70 -is_a_theorem(implies(implies(not(c44),c44),c44)). [copy(69),unit_del(a,44)].
% 2.54/2.84 71 -modus_ponens | -is_a_theorem(A) | -is_a_theorem(implies(A,B)) | is_a_theorem(B) # label(modus_ponens) # label(axiom). [clausify(1)].
% 2.54/2.84 72 -is_a_theorem(A) | -is_a_theorem(implies(A,B)) | is_a_theorem(B). [copy(71),unit_del(a,35)].
% 2.54/2.84 79 -r3 | is_a_theorem(implies(or(A,B),or(B,A))) # label(r3) # label(axiom). [clausify(24)].
% 2.54/2.84 80 is_a_theorem(implies(or(A,B),or(B,A))). [copy(79),unit_del(a,38)].
% 2.54/2.84 82 -op_implies_or | or(not(A),B) = implies(A,B) # label(op_implies_or) # label(axiom). [clausify(30)].
% 2.54/2.84 83 or(not(A),B) = implies(A,B). [copy(82),unit_del(a,32)].
% 2.54/2.84 104 -r5 | is_a_theorem(implies(implies(A,B),implies(or(C,A),or(C,B)))) # label(r5) # label(axiom). [clausify(26)].
% 2.54/2.84 105 is_a_theorem(implies(implies(A,B),implies(or(C,A),or(C,B)))). [copy(104),unit_del(a,40)].
% 2.54/2.84 117 -is_a_theorem(or(A,B)) | is_a_theorem(or(B,A)). [resolve(80,a,72,b)].
% 2.54/2.84 122 is_a_theorem(implies(or(A,not(B)),implies(B,A))). [para(83(a,1),80(a,1,2))].
% 2.54/2.84 137 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(or(C,A),or(C,B))). [resolve(105,a,72,b)].
% 2.54/2.84 185 -is_a_theorem(implies(A,B)) | is_a_theorem(or(B,not(A))). [para(83(a,1),117(a,1))].
% 2.54/2.84 513 -is_a_theorem(or(A,not(B))) | is_a_theorem(implies(B,A)). [resolve(122,a,72,b)].
% 2.54/2.84 527 -is_a_theorem(or(c44,not(implies(not(c44),c44)))). [ur(72,b,122,a,c,70,a)].
% 2.54/2.84 1123 -is_a_theorem(implies(A,not(B))) | is_a_theorem(implies(B,not(A))). [para(83(a,1),513(a,1))].
% 2.54/2.84 4246 is_a_theorem(implies(or(A,or(B,B)),or(A,B))). [resolve(137,a,60,a)].
% 2.54/2.84 5651 -is_a_theorem(or(A,or(B,B))) | is_a_theorem(or(A,B)). [resolve(4246,a,72,b)].
% 2.54/2.84 6304 -is_a_theorem(implies(A,or(B,B))) | is_a_theorem(implies(A,B)). [para(83(a,1),5651(a,1)),rewrite([83(5)])].
% 2.54/2.84 7373 is_a_theorem(implies(A,A)). [resolve(6304,a,63,a)].
% 2.54/2.84 7385 is_a_theorem(implies(A,not(not(A)))). [resolve(7373,a,1123,a)].
% 2.54/2.84 7386 is_a_theorem(or(A,not(A))). [resolve(7373,a,185,a)].
% 2.54/2.84 7718 -is_a_theorem(implies(or(A,not(A)),or(c44,not(implies(not(c44),c44))))). [ur(72,a,7386,a,c,527,a)].
% 2.54/2.84 8319 is_a_theorem(implies(or(A,B),or(A,not(not(B))))). [resolve(7385,a,137,a)].
% 2.54/2.84 17178 is_a_theorem(implies(implies(not(A),A),not(not(A)))). [resolve(8319,a,6304,a),rewrite([83(3)])].
% 2.54/2.84 17212 is_a_theorem(implies(not(A),not(implies(not(A),A)))). [resolve(17178,a,1123,a)].
% 2.54/2.84 17306 is_a_theorem(implies(or(A,not(B)),or(A,not(implies(not(B),B))))). [resolve(17212,a,137,a)].
% 2.54/2.84 17307 $F. [resolve(17306,a,7718,a)].
% 2.54/2.84
% 2.54/2.84 % SZS output end Refutation
% 2.54/2.84 ============================== end of proof ==========================
% 2.54/2.84
% 2.54/2.84 ============================== STATISTICS ============================
% 2.54/2.84
% 2.54/2.84 Given=734. Generated=108382. Kept=17258. proofs=1.
% 2.54/2.84 Usable=704. Sos=9999. Demods=11. Limbo=15, Disabled=6613. Hints=0.
% 2.54/2.84 Megabytes=12.06.
% 2.54/2.84 User_CPU=1.75, System_CPU=0.06, Wall_clock=2.
% 2.54/2.84
% 2.54/2.84 ============================== end of statistics =====================
% 2.54/2.84
% 2.54/2.84 ============================== end of search =========================
% 2.54/2.84
% 2.54/2.84 THEOREM PROVED
% 2.54/2.84 % SZS status Theorem
% 2.54/2.84
% 2.54/2.84 Exiting with 1 proof.
% 2.54/2.84
% 2.54/2.84 Process 30776 exit (max_proofs) Mon Jul 4 14:02:14 2022
% 2.54/2.84 Prover9 interrupted
%------------------------------------------------------------------------------