TSTP Solution File: LCL456+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : LCL456+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %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 13:46:57 EDT 2022
% Result : Theorem 0.64s 1.05s
% Output : Refutation 0.64s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.10 % Problem : LCL456+1 : TPTP v8.1.0. Released v3.3.0.
% 0.10/0.11 % Command : tptp2X_and_run_prover9 %d %s
% 0.10/0.32 % Computer : n023.cluster.edu
% 0.10/0.32 % Model : x86_64 x86_64
% 0.10/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.32 % Memory : 8042.1875MB
% 0.10/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32 % CPULimit : 300
% 0.10/0.32 % WCLimit : 600
% 0.10/0.32 % DateTime : Sun Jul 3 19:38:13 EDT 2022
% 0.10/0.32 % CPUTime :
% 0.40/0.91 ============================== Prover9 ===============================
% 0.40/0.91 Prover9 (32) version 2009-11A, November 2009.
% 0.40/0.91 Process 15467 was started by sandbox on n023.cluster.edu,
% 0.40/0.91 Sun Jul 3 19:38:13 2022
% 0.40/0.91 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_15313_n023.cluster.edu".
% 0.40/0.91 ============================== end of head ===========================
% 0.40/0.91
% 0.40/0.91 ============================== INPUT =================================
% 0.40/0.91
% 0.40/0.91 % Reading from file /tmp/Prover9_15313_n023.cluster.edu
% 0.40/0.91
% 0.40/0.91 set(prolog_style_variables).
% 0.40/0.91 set(auto2).
% 0.40/0.91 % set(auto2) -> set(auto).
% 0.40/0.91 % set(auto) -> set(auto_inference).
% 0.40/0.91 % set(auto) -> set(auto_setup).
% 0.40/0.91 % set(auto_setup) -> set(predicate_elim).
% 0.40/0.91 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.40/0.91 % set(auto) -> set(auto_limits).
% 0.40/0.91 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.40/0.91 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.40/0.91 % set(auto) -> set(auto_denials).
% 0.40/0.91 % set(auto) -> set(auto_process).
% 0.40/0.91 % set(auto2) -> assign(new_constants, 1).
% 0.40/0.91 % set(auto2) -> assign(fold_denial_max, 3).
% 0.40/0.91 % set(auto2) -> assign(max_weight, "200.000").
% 0.40/0.91 % set(auto2) -> assign(max_hours, 1).
% 0.40/0.91 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.40/0.91 % set(auto2) -> assign(max_seconds, 0).
% 0.40/0.91 % set(auto2) -> assign(max_minutes, 5).
% 0.40/0.91 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.40/0.91 % set(auto2) -> set(sort_initial_sos).
% 0.40/0.91 % set(auto2) -> assign(sos_limit, -1).
% 0.40/0.91 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.40/0.91 % set(auto2) -> assign(max_megs, 400).
% 0.40/0.91 % set(auto2) -> assign(stats, some).
% 0.40/0.91 % set(auto2) -> clear(echo_input).
% 0.40/0.91 % set(auto2) -> set(quiet).
% 0.40/0.91 % set(auto2) -> clear(print_initial_clauses).
% 0.40/0.91 % set(auto2) -> clear(print_given).
% 0.40/0.91 assign(lrs_ticks,-1).
% 0.40/0.91 assign(sos_limit,10000).
% 0.40/0.91 assign(order,kbo).
% 0.40/0.91 set(lex_order_vars).
% 0.40/0.91 clear(print_given).
% 0.40/0.91
% 0.40/0.91 % formulas(sos). % not echoed (53 formulas)
% 0.40/0.91
% 0.40/0.91 ============================== end of input ==========================
% 0.40/0.91
% 0.40/0.91 % From the command line: assign(max_seconds, 300).
% 0.40/0.91
% 0.40/0.91 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.40/0.91
% 0.40/0.91 % Formulas that are not ordinary clauses:
% 0.40/0.91 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].
% 0.40/0.91 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].
% 0.40/0.91 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].
% 0.40/0.91 4 implies_1 <-> (all X all Y is_a_theorem(implies(X,implies(Y,X)))) # label(implies_1) # label(axiom) # label(non_clause). [assumption].
% 0.40/0.91 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].
% 0.40/0.91 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].
% 0.40/0.91 7 and_1 <-> (all X all Y is_a_theorem(implies(and(X,Y),X))) # label(and_1) # label(axiom) # label(non_clause). [assumption].
% 0.40/0.91 8 and_2 <-> (all X all Y is_a_theorem(implies(and(X,Y),Y))) # label(and_2) # label(axiom) # label(non_clause). [assumption].
% 0.40/0.91 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].
% 0.40/0.91 10 or_1 <-> (all X all Y is_a_theorem(implies(X,or(X,Y)))) # label(or_1) # label(axiom) # label(non_clause). [assumption].
% 0.40/0.91 11 or_2 <-> (all X all Y is_a_theorem(implies(Y,or(X,Y)))) # label(or_2) # label(axiom) # label(non_clause). [assumption].
% 0.40/0.91 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].
% 0.40/0.91 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].
% 0.40/0.91 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].
% 0.64/1.05 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].
% 0.64/1.05 16 kn1 <-> (all P is_a_theorem(implies(P,and(P,P)))) # label(kn1) # label(axiom) # label(non_clause). [assumption].
% 0.64/1.05 17 kn2 <-> (all P all Q is_a_theorem(implies(and(P,Q),P))) # label(kn2) # label(axiom) # label(non_clause). [assumption].
% 0.64/1.05 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].
% 0.64/1.05 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].
% 0.64/1.05 20 cn2 <-> (all P all Q is_a_theorem(implies(P,implies(not(P),Q)))) # label(cn2) # label(axiom) # label(non_clause). [assumption].
% 0.64/1.05 21 cn3 <-> (all P is_a_theorem(implies(implies(not(P),P),P))) # label(cn3) # label(axiom) # label(non_clause). [assumption].
% 0.64/1.05 22 r1 <-> (all P is_a_theorem(implies(or(P,P),P))) # label(r1) # label(axiom) # label(non_clause). [assumption].
% 0.64/1.05 23 r2 <-> (all P all Q is_a_theorem(implies(Q,or(P,Q)))) # label(r2) # label(axiom) # label(non_clause). [assumption].
% 0.64/1.05 24 r3 <-> (all P all Q is_a_theorem(implies(or(P,Q),or(Q,P)))) # label(r3) # label(axiom) # label(non_clause). [assumption].
% 0.64/1.05 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].
% 0.64/1.05 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].
% 0.64/1.05 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].
% 0.64/1.05 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].
% 0.64/1.05 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].
% 0.64/1.05 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].
% 0.64/1.05 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].
% 0.64/1.05
% 0.64/1.05 ============================== end of process non-clausal formulas ===
% 0.64/1.05
% 0.64/1.05 ============================== PROCESS INITIAL CLAUSES ===============
% 0.64/1.05
% 0.64/1.05 ============================== PREDICATE ELIMINATION =================
% 0.64/1.05
% 0.64/1.05 ============================== end predicate elimination =============
% 0.64/1.05
% 0.64/1.05 Auto_denials: (non-Horn, no changes).
% 0.64/1.05
% 0.64/1.05 Term ordering decisions:
% 0.64/1.05
% 0.64/1.05 % Assigning unary symbol not kb_weight 0 and highest precedence (93).
% 0.64/1.05 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.
% 0.64/1.05
% 0.64/1.05 ============================== end of process initial clauses ========
% 0.64/1.05
% 0.64/1.05 ============================== CLAUSES FOR SEARCH ====================
% 0.64/1.05
% 0.64/1.05 ============================== end of clauses for search =============
% 0.64/1.05
% 0.64/1.05 ============================== SEARCH ================================
% 0.64/1.05
% 0.64/1.05 % Starting search at 0.02 seconds.
% 0.64/1.05
% 0.64/1.05 ============================== PROOF =================================
% 0.64/1.05 % SZS status Theorem
% 0.64/1.05 % SZS output start Refutation
% 0.64/1.05
% 0.64/1.05 % Proof 1 at 0.14 (+ 0.01) seconds.
% 0.64/1.05 % Length of proof is 34.
% 0.64/1.05 % Level of proof is 7.
% 0.64/1.05 % Maximum clause weight is 17.000.
% 0.64/1.05 % Given clauses 130.
% 0.64/1.05
% 0.64/1.05 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].
% 0.64/1.05 4 implies_1 <-> (all X all Y is_a_theorem(implies(X,implies(Y,X)))) # label(implies_1) # label(axiom) # label(non_clause). [assumption].
% 0.64/1.05 10 or_1 <-> (all X all Y is_a_theorem(implies(X,or(X,Y)))) # label(or_1) # label(axiom) # label(non_clause). [assumption].
% 0.64/1.05 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].
% 0.64/1.05 24 r3 <-> (all P all Q is_a_theorem(implies(or(P,Q),or(Q,P)))) # label(r3) # label(axiom) # label(non_clause). [assumption].
% 0.64/1.05 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].
% 0.64/1.05 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].
% 0.64/1.05 32 op_or # label(hilbert_op_or) # label(axiom). [assumption].
% 0.64/1.05 33 op_implies_and # label(hilbert_op_implies_and) # label(axiom). [assumption].
% 0.64/1.05 35 modus_ponens # label(hilbert_modus_ponens) # label(axiom). [assumption].
% 0.64/1.05 37 implies_1 # label(hilbert_implies_1) # label(axiom). [assumption].
% 0.64/1.05 43 or_1 # label(hilbert_or_1) # label(axiom). [assumption].
% 0.64/1.05 45 or_3 # label(hilbert_or_3) # label(axiom). [assumption].
% 0.64/1.05 52 -r3 # label(principia_r3) # label(negated_conjecture). [assumption].
% 0.64/1.05 53 -implies_1 | is_a_theorem(implies(A,implies(B,A))) # label(implies_1) # label(axiom). [clausify(4)].
% 0.64/1.05 54 is_a_theorem(implies(A,implies(B,A))). [copy(53),unit_del(a,37)].
% 0.64/1.05 62 -or_1 | is_a_theorem(implies(A,or(A,B))) # label(or_1) # label(axiom). [clausify(10)].
% 0.64/1.05 63 is_a_theorem(implies(A,or(A,B))). [copy(62),unit_del(a,43)].
% 0.64/1.05 82 -modus_ponens | -is_a_theorem(A) | -is_a_theorem(implies(A,B)) | is_a_theorem(B) # label(modus_ponens) # label(axiom). [clausify(1)].
% 0.64/1.05 83 -is_a_theorem(A) | -is_a_theorem(implies(A,B)) | is_a_theorem(B). [copy(82),unit_del(a,35)].
% 0.64/1.05 93 r3 | -is_a_theorem(implies(or(c48,c49),or(c49,c48))) # label(r3) # label(axiom). [clausify(24)].
% 0.64/1.05 94 -is_a_theorem(implies(or(c48,c49),or(c49,c48))). [copy(93),unit_del(a,52)].
% 0.64/1.05 97 -op_implies_and | not(and(A,not(B))) = implies(A,B) # label(op_implies_and) # label(axiom). [clausify(29)].
% 0.64/1.05 98 not(and(A,not(B))) = implies(A,B). [copy(97),unit_del(a,33)].
% 0.64/1.05 105 -op_or | or(A,B) = not(and(not(A),not(B))) # label(op_or) # label(axiom). [clausify(27)].
% 0.64/1.05 106 or(A,B) = implies(not(A),B). [copy(105),rewrite([98(6)]),unit_del(a,32)].
% 0.64/1.05 127 -or_3 | is_a_theorem(implies(implies(A,B),implies(implies(C,B),implies(or(A,C),B)))) # label(or_3) # label(axiom). [clausify(12)].
% 0.64/1.05 128 is_a_theorem(implies(implies(A,B),implies(implies(C,B),implies(implies(not(A),C),B)))). [copy(127),rewrite([106(4)]),unit_del(a,45)].
% 0.64/1.05 133 -is_a_theorem(implies(implies(not(c48),c49),implies(not(c49),c48))). [back_rewrite(94),rewrite([106(3),106(7)])].
% 0.64/1.05 136 is_a_theorem(implies(A,implies(not(A),B))). [back_rewrite(63),rewrite([106(1)])].
% 0.64/1.05 152 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(implies(C,B),implies(implies(not(A),C),B))). [resolve(128,a,83,b)].
% 0.64/1.05 189 -is_a_theorem(implies(implies(A,implies(not(A),B)),implies(implies(not(c48),c49),implies(not(c49),c48)))). [ur(83,a,136,a,c,133,a)].
% 0.64/1.05 1645 is_a_theorem(implies(implies(A,implies(B,C)),implies(implies(not(C),A),implies(B,C)))). [resolve(152,a,54,a)].
% 0.64/1.05 1646 $F. [resolve(1645,a,189,a)].
% 0.64/1.05
% 0.64/1.05 % SZS output end Refutation
% 0.64/1.05 ============================== end of proof ==========================
% 0.64/1.05
% 0.64/1.05 ============================== STATISTICS ============================
% 0.64/1.05
% 0.64/1.05 Given=130. Generated=2109. Kept=1573. proofs=1.
% 0.64/1.05 Usable=126. Sos=1403. Demods=19. Limbo=21, Disabled=104. Hints=0.
% 0.64/1.05 Megabytes=1.28.
% 0.64/1.05 User_CPU=0.14, System_CPU=0.01, Wall_clock=0.
% 0.64/1.05
% 0.64/1.05 ============================== end of statistics =====================
% 0.64/1.05
% 0.64/1.05 ============================== end of search =========================
% 0.64/1.05
% 0.64/1.05 THEOREM PROVED
% 0.64/1.05 % SZS status Theorem
% 0.64/1.05
% 0.64/1.05 Exiting with 1 proof.
% 0.64/1.05
% 0.64/1.05 Process 15467 exit (max_proofs) Sun Jul 3 19:38:13 2022
% 0.64/1.05 Prover9 interrupted
%------------------------------------------------------------------------------