TSTP Solution File: LCL452+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : LCL452+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 13:46:55 EDT 2022
% Result : Theorem 0.44s 1.01s
% Output : Refutation 0.44s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : LCL452+1 : TPTP v8.1.0. Released v3.3.0.
% 0.11/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.34 % Computer : n007.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Mon Jul 4 23:23:42 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.44/1.01 ============================== Prover9 ===============================
% 0.44/1.01 Prover9 (32) version 2009-11A, November 2009.
% 0.44/1.01 Process 2794 was started by sandbox2 on n007.cluster.edu,
% 0.44/1.01 Mon Jul 4 23:23:43 2022
% 0.44/1.01 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_2640_n007.cluster.edu".
% 0.44/1.01 ============================== end of head ===========================
% 0.44/1.01
% 0.44/1.01 ============================== INPUT =================================
% 0.44/1.01
% 0.44/1.01 % Reading from file /tmp/Prover9_2640_n007.cluster.edu
% 0.44/1.01
% 0.44/1.01 set(prolog_style_variables).
% 0.44/1.01 set(auto2).
% 0.44/1.01 % set(auto2) -> set(auto).
% 0.44/1.01 % set(auto) -> set(auto_inference).
% 0.44/1.01 % set(auto) -> set(auto_setup).
% 0.44/1.01 % set(auto_setup) -> set(predicate_elim).
% 0.44/1.01 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.44/1.01 % set(auto) -> set(auto_limits).
% 0.44/1.01 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.44/1.01 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.44/1.01 % set(auto) -> set(auto_denials).
% 0.44/1.01 % set(auto) -> set(auto_process).
% 0.44/1.01 % set(auto2) -> assign(new_constants, 1).
% 0.44/1.01 % set(auto2) -> assign(fold_denial_max, 3).
% 0.44/1.01 % set(auto2) -> assign(max_weight, "200.000").
% 0.44/1.01 % set(auto2) -> assign(max_hours, 1).
% 0.44/1.01 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.44/1.01 % set(auto2) -> assign(max_seconds, 0).
% 0.44/1.01 % set(auto2) -> assign(max_minutes, 5).
% 0.44/1.01 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.44/1.01 % set(auto2) -> set(sort_initial_sos).
% 0.44/1.01 % set(auto2) -> assign(sos_limit, -1).
% 0.44/1.01 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.44/1.01 % set(auto2) -> assign(max_megs, 400).
% 0.44/1.01 % set(auto2) -> assign(stats, some).
% 0.44/1.01 % set(auto2) -> clear(echo_input).
% 0.44/1.01 % set(auto2) -> set(quiet).
% 0.44/1.01 % set(auto2) -> clear(print_initial_clauses).
% 0.44/1.01 % set(auto2) -> clear(print_given).
% 0.44/1.01 assign(lrs_ticks,-1).
% 0.44/1.01 assign(sos_limit,10000).
% 0.44/1.01 assign(order,kbo).
% 0.44/1.01 set(lex_order_vars).
% 0.44/1.01 clear(print_given).
% 0.44/1.01
% 0.44/1.01 % formulas(sos). % not echoed (53 formulas)
% 0.44/1.01
% 0.44/1.01 ============================== end of input ==========================
% 0.44/1.01
% 0.44/1.01 % From the command line: assign(max_seconds, 300).
% 0.44/1.01
% 0.44/1.01 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.44/1.01
% 0.44/1.01 % Formulas that are not ordinary clauses:
% 0.44/1.01 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].
% 0.44/1.01 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].
% 0.44/1.01 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].
% 0.44/1.01 4 implies_1 <-> (all X all Y is_a_theorem(implies(X,implies(Y,X)))) # label(implies_1) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 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].
% 0.44/1.01 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].
% 0.44/1.01 7 and_1 <-> (all X all Y is_a_theorem(implies(and(X,Y),X))) # label(and_1) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 8 and_2 <-> (all X all Y is_a_theorem(implies(and(X,Y),Y))) # label(and_2) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 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].
% 0.44/1.01 10 or_1 <-> (all X all Y is_a_theorem(implies(X,or(X,Y)))) # label(or_1) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 11 or_2 <-> (all X all Y is_a_theorem(implies(Y,or(X,Y)))) # label(or_2) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 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].
% 0.44/1.01 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].
% 0.44/1.01 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].
% 0.44/1.01 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].
% 0.44/1.01 16 kn1 <-> (all P is_a_theorem(implies(P,and(P,P)))) # label(kn1) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 17 kn2 <-> (all P all Q is_a_theorem(implies(and(P,Q),P))) # label(kn2) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 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].
% 0.44/1.01 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].
% 0.44/1.01 20 cn2 <-> (all P all Q is_a_theorem(implies(P,implies(not(P),Q)))) # label(cn2) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 21 cn3 <-> (all P is_a_theorem(implies(implies(not(P),P),P))) # label(cn3) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 22 r1 <-> (all P is_a_theorem(implies(or(P,P),P))) # label(r1) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 23 r2 <-> (all P all Q is_a_theorem(implies(Q,or(P,Q)))) # label(r2) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 24 r3 <-> (all P all Q is_a_theorem(implies(or(P,Q),or(Q,P)))) # label(r3) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 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].
% 0.44/1.01 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].
% 0.44/1.01 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].
% 0.44/1.01 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].
% 0.44/1.01 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].
% 0.44/1.01 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].
% 0.44/1.01 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].
% 0.44/1.01
% 0.44/1.01 ============================== end of process non-clausal formulas ===
% 0.44/1.01
% 0.44/1.01 ============================== PROCESS INITIAL CLAUSES ===============
% 0.44/1.01
% 0.44/1.01 ============================== PREDICATE ELIMINATION =================
% 0.44/1.01
% 0.44/1.01 ============================== end predicate elimination =============
% 0.44/1.01
% 0.44/1.01 Auto_denials: (non-Horn, no changes).
% 0.44/1.01
% 0.44/1.01 Term ordering decisions:
% 0.44/1.01
% 0.44/1.01 % Assigning unary symbol not kb_weight 0 and highest precedence (94).
% 0.44/1.01 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.
% 0.44/1.01
% 0.44/1.01 ============================== PROOF =================================
% 0.44/1.01 % SZS status Theorem
% 0.44/1.01 % SZS output start Refutation
% 0.44/1.01
% 0.44/1.01 % Proof 1 at 0.02 (+ 0.00) seconds.
% 0.44/1.01 % Length of proof is 18.
% 0.44/1.01 % Level of proof is 5.
% 0.44/1.01 % Maximum clause weight is 9.000.
% 0.44/1.01 % Given clauses 0.
% 0.44/1.01
% 0.44/1.01 10 or_1 <-> (all X all Y is_a_theorem(implies(X,or(X,Y)))) # label(or_1) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 20 cn2 <-> (all P all Q is_a_theorem(implies(P,implies(not(P),Q)))) # label(cn2) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 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].
% 0.44/1.01 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].
% 0.44/1.01 32 op_or # label(hilbert_op_or) # label(axiom). [assumption].
% 0.44/1.01 33 op_implies_and # label(hilbert_op_implies_and) # label(axiom). [assumption].
% 0.44/1.01 43 or_1 # label(hilbert_or_1) # label(axiom). [assumption].
% 0.44/1.01 51 -cn2 # label(luka_cn2) # label(negated_conjecture). [assumption].
% 0.44/1.01 61 -or_1 | is_a_theorem(implies(A,or(A,B))) # label(or_1) # label(axiom). [clausify(10)].
% 0.44/1.01 62 is_a_theorem(implies(A,or(A,B))). [copy(61),unit_del(a,43)].
% 0.44/1.01 77 cn2 | -is_a_theorem(implies(c42,implies(not(c42),c43))) # label(cn2) # label(axiom). [clausify(20)].
% 0.44/1.01 78 -is_a_theorem(implies(c42,implies(not(c42),c43))). [copy(77),unit_del(a,51)].
% 0.44/1.01 95 -op_implies_and | not(and(A,not(B))) = implies(A,B) # label(op_implies_and) # label(axiom). [clausify(29)].
% 0.44/1.01 96 not(and(A,not(B))) = implies(A,B). [copy(95),unit_del(a,33)].
% 0.44/1.01 103 -op_or | or(A,B) = not(and(not(A),not(B))) # label(op_or) # label(axiom). [clausify(27)].
% 0.44/1.01 104 or(A,B) = implies(not(A),B). [copy(103),rewrite([96(6)]),unit_del(a,32)].
% 0.44/1.01 135 is_a_theorem(implies(A,implies(not(A),B))). [back_rewrite(62),rewrite([104(1)])].
% 0.44/1.01 136 $F. [resolve(135,a,78,a)].
% 0.44/1.01
% 0.44/1.01 % SZS output end Refutation
% 0.44/1.01 ============================== end of proof ==========================
% 0.44/1.01
% 0.44/1.01 ============================== STATISTICS ============================
% 0.44/1.01
% 0.44/1.01 Given=0. Generated=89. Kept=64. proofs=1.
% 0.44/1.01 Usable=0. Sos=38. Demods=3. Limbo=18, Disabled=89. Hints=0.
% 0.44/1.01 Megabytes=0.17.
% 0.44/1.01 User_CPU=0.02, System_CPU=0.00, Wall_clock=0.
% 0.44/1.01
% 0.44/1.01 ============================== end of statistics =====================
% 0.44/1.01
% 0.44/1.01 ============================== end of search =========================
% 0.44/1.01
% 0.44/1.01 THEOREM PROVED
% 0.44/1.01 % SZS status Theorem
% 0.44/1.01
% 0.44/1.01 Exiting with 1 proof.
% 0.44/1.01
% 0.44/1.01 Process 2794 exit (max_proofs) Mon Jul 4 23:23:43 2022
% 0.44/1.01 Prover9 interrupted
%------------------------------------------------------------------------------