TSTP Solution File: LCL499+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : LCL499+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n017.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 0.95s 1.22s
% Output : Refutation 0.95s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : LCL499+1 : TPTP v8.1.0. Released v3.3.0.
% 0.11/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.11/0.33 % Computer : n017.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 600
% 0.11/0.33 % DateTime : Sat Jul 2 21:16:41 EDT 2022
% 0.11/0.33 % CPUTime :
% 0.74/1.00 ============================== Prover9 ===============================
% 0.74/1.00 Prover9 (32) version 2009-11A, November 2009.
% 0.74/1.00 Process 5008 was started by sandbox on n017.cluster.edu,
% 0.74/1.00 Sat Jul 2 21:16:41 2022
% 0.74/1.00 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_4854_n017.cluster.edu".
% 0.74/1.00 ============================== end of head ===========================
% 0.74/1.00
% 0.74/1.00 ============================== INPUT =================================
% 0.74/1.00
% 0.74/1.00 % Reading from file /tmp/Prover9_4854_n017.cluster.edu
% 0.74/1.00
% 0.74/1.00 set(prolog_style_variables).
% 0.74/1.00 set(auto2).
% 0.74/1.00 % set(auto2) -> set(auto).
% 0.74/1.00 % set(auto) -> set(auto_inference).
% 0.74/1.00 % set(auto) -> set(auto_setup).
% 0.74/1.00 % set(auto_setup) -> set(predicate_elim).
% 0.74/1.00 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.74/1.00 % set(auto) -> set(auto_limits).
% 0.74/1.00 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.74/1.00 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.74/1.00 % set(auto) -> set(auto_denials).
% 0.74/1.00 % set(auto) -> set(auto_process).
% 0.74/1.00 % set(auto2) -> assign(new_constants, 1).
% 0.74/1.00 % set(auto2) -> assign(fold_denial_max, 3).
% 0.74/1.00 % set(auto2) -> assign(max_weight, "200.000").
% 0.74/1.00 % set(auto2) -> assign(max_hours, 1).
% 0.74/1.00 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.74/1.00 % set(auto2) -> assign(max_seconds, 0).
% 0.74/1.00 % set(auto2) -> assign(max_minutes, 5).
% 0.74/1.00 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.74/1.00 % set(auto2) -> set(sort_initial_sos).
% 0.74/1.00 % set(auto2) -> assign(sos_limit, -1).
% 0.74/1.00 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.74/1.00 % set(auto2) -> assign(max_megs, 400).
% 0.74/1.00 % set(auto2) -> assign(stats, some).
% 0.74/1.00 % set(auto2) -> clear(echo_input).
% 0.74/1.00 % set(auto2) -> set(quiet).
% 0.74/1.00 % set(auto2) -> clear(print_initial_clauses).
% 0.74/1.00 % set(auto2) -> clear(print_given).
% 0.74/1.00 assign(lrs_ticks,-1).
% 0.74/1.00 assign(sos_limit,10000).
% 0.74/1.00 assign(order,kbo).
% 0.74/1.00 set(lex_order_vars).
% 0.74/1.00 clear(print_given).
% 0.74/1.00
% 0.74/1.00 % formulas(sos). % not echoed (45 formulas)
% 0.74/1.00
% 0.74/1.00 ============================== end of input ==========================
% 0.74/1.00
% 0.74/1.00 % From the command line: assign(max_seconds, 300).
% 0.74/1.00
% 0.74/1.00 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.74/1.00
% 0.74/1.00 % Formulas that are not ordinary clauses:
% 0.74/1.00 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].
% 0.74/1.00 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].
% 0.74/1.00 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].
% 0.74/1.00 4 implies_1 <-> (all X all Y is_a_theorem(implies(X,implies(Y,X)))) # label(implies_1) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.00 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].
% 0.74/1.00 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].
% 0.74/1.00 7 and_1 <-> (all X all Y is_a_theorem(implies(and(X,Y),X))) # label(and_1) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.00 8 and_2 <-> (all X all Y is_a_theorem(implies(and(X,Y),Y))) # label(and_2) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.00 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].
% 0.74/1.00 10 or_1 <-> (all X all Y is_a_theorem(implies(X,or(X,Y)))) # label(or_1) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.00 11 or_2 <-> (all X all Y is_a_theorem(implies(Y,or(X,Y)))) # label(or_2) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.00 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].
% 0.74/1.00 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].
% 0.74/1.00 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].
% 0.95/1.22 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].
% 0.95/1.22 16 kn1 <-> (all P is_a_theorem(implies(P,and(P,P)))) # label(kn1) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.22 17 kn2 <-> (all P all Q is_a_theorem(implies(and(P,Q),P))) # label(kn2) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.22 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].
% 0.95/1.22 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].
% 0.95/1.22 20 cn2 <-> (all P all Q is_a_theorem(implies(P,implies(not(P),Q)))) # label(cn2) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.22 21 cn3 <-> (all P is_a_theorem(implies(implies(not(P),P),P))) # label(cn3) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.22 22 r1 <-> (all P is_a_theorem(implies(or(P,P),P))) # label(r1) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.22 23 r2 <-> (all P all Q is_a_theorem(implies(Q,or(P,Q)))) # label(r2) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.22 24 r3 <-> (all P all Q is_a_theorem(implies(or(P,Q),or(Q,P)))) # label(r3) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.22 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].
% 0.95/1.22 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].
% 0.95/1.22 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].
% 0.95/1.22 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].
% 0.95/1.22 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].
% 0.95/1.22 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].
% 0.95/1.22 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].
% 0.95/1.22
% 0.95/1.22 ============================== end of process non-clausal formulas ===
% 0.95/1.22
% 0.95/1.22 ============================== PROCESS INITIAL CLAUSES ===============
% 0.95/1.22
% 0.95/1.22 ============================== PREDICATE ELIMINATION =================
% 0.95/1.22
% 0.95/1.22 ============================== end predicate elimination =============
% 0.95/1.22
% 0.95/1.22 Auto_denials: (non-Horn, no changes).
% 0.95/1.22
% 0.95/1.22 Term ordering decisions:
% 0.95/1.22
% 0.95/1.22 % Assigning unary symbol not kb_weight 0 and highest precedence (93).
% 0.95/1.22 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.
% 0.95/1.22
% 0.95/1.22 ============================== end of process initial clauses ========
% 0.95/1.22
% 0.95/1.22 ============================== CLAUSES FOR SEARCH ====================
% 0.95/1.22
% 0.95/1.22 ============================== end of clauses for search =============
% 0.95/1.22
% 0.95/1.22 ============================== SEARCH ================================
% 0.95/1.22
% 0.95/1.22 % Starting search at 0.02 seconds.
% 0.95/1.22
% 0.95/1.22 ============================== PROOF =================================
% 0.95/1.22 % SZS status Theorem
% 0.95/1.22 % SZS output start Refutation
% 0.95/1.22
% 0.95/1.22 % Proof 1 at 0.22 (+ 0.01) seconds.
% 0.95/1.22 % Length of proof is 64.
% 0.95/1.22 % Level of proof is 13.
% 0.95/1.22 % Maximum clause weight is 16.000.
% 0.95/1.22 % Given clauses 178.
% 0.95/1.22
% 0.95/1.22 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].
% 0.95/1.22 16 kn1 <-> (all P is_a_theorem(implies(P,and(P,P)))) # label(kn1) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.22 22 r1 <-> (all P is_a_theorem(implies(or(P,P),P))) # label(r1) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.22 23 r2 <-> (all P all Q is_a_theorem(implies(Q,or(P,Q)))) # label(r2) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.22 24 r3 <-> (all P all Q is_a_theorem(implies(or(P,Q),or(Q,P)))) # label(r3) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.22 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].
% 0.95/1.22 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].
% 0.95/1.22 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].
% 0.95/1.22 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].
% 0.95/1.22 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].
% 0.95/1.22 32 op_implies_or # label(principia_op_implies_or) # label(axiom). [assumption].
% 0.95/1.22 33 op_and # label(principia_op_and) # label(axiom). [assumption].
% 0.95/1.22 35 modus_ponens # label(principia_modus_ponens) # label(axiom). [assumption].
% 0.95/1.22 36 r1 # label(principia_r1) # label(axiom). [assumption].
% 0.95/1.22 37 r2 # label(principia_r2) # label(axiom). [assumption].
% 0.95/1.22 38 r3 # label(principia_r3) # label(axiom). [assumption].
% 0.95/1.22 39 r4 # label(principia_r4) # label(axiom). [assumption].
% 0.95/1.22 42 op_or # label(rosser_op_or) # label(axiom). [assumption].
% 0.95/1.22 43 op_implies_and # label(rosser_op_implies_and) # label(axiom). [assumption].
% 0.95/1.22 44 -kn1 # label(rosser_kn1) # label(negated_conjecture). [assumption].
% 0.95/1.22 55 kn1 | -is_a_theorem(implies(c33,and(c33,c33))) # label(kn1) # label(axiom). [clausify(16)].
% 0.95/1.22 56 -is_a_theorem(implies(c33,and(c33,c33))). [copy(55),unit_del(a,44)].
% 0.95/1.22 59 -r1 | is_a_theorem(implies(or(A,A),A)) # label(r1) # label(axiom). [clausify(22)].
% 0.95/1.22 60 is_a_theorem(implies(or(A,A),A)). [copy(59),unit_del(a,36)].
% 0.95/1.22 62 -r2 | is_a_theorem(implies(A,or(B,A))) # label(r2) # label(axiom). [clausify(23)].
% 0.95/1.22 63 is_a_theorem(implies(A,or(B,A))). [copy(62),unit_del(a,37)].
% 0.95/1.22 71 -modus_ponens | -is_a_theorem(A) | -is_a_theorem(implies(A,B)) | is_a_theorem(B) # label(modus_ponens) # label(axiom). [clausify(1)].
% 0.95/1.22 72 -is_a_theorem(A) | -is_a_theorem(implies(A,B)) | is_a_theorem(B). [copy(71),unit_del(a,35)].
% 0.95/1.22 79 -r3 | is_a_theorem(implies(or(A,B),or(B,A))) # label(r3) # label(axiom). [clausify(24)].
% 0.95/1.22 80 is_a_theorem(implies(or(A,B),or(B,A))). [copy(79),unit_del(a,38)].
% 0.95/1.22 82 -op_implies_or | or(not(A),B) = implies(A,B) # label(op_implies_or) # label(axiom). [clausify(30)].
% 0.95/1.22 83 or(not(A),B) = implies(A,B). [copy(82),unit_del(a,32)].
% 0.95/1.22 84 -op_implies_and | not(and(A,not(B))) = implies(A,B) # label(op_implies_and) # label(axiom). [clausify(29)].
% 0.95/1.22 85 not(and(A,not(B))) = implies(A,B). [copy(84),unit_del(a,43)].
% 0.95/1.22 90 -op_or | or(A,B) = not(and(not(A),not(B))) # label(op_or) # label(axiom). [clausify(27)].
% 0.95/1.22 91 or(A,B) = implies(not(A),B). [copy(90),rewrite([85(6)]),unit_del(a,42)].
% 0.95/1.22 92 -op_and | and(A,B) = not(or(not(A),not(B))) # label(op_and) # label(axiom). [clausify(28)].
% 0.95/1.22 93 not(implies(not(not(A)),not(B))) = and(A,B). [copy(92),rewrite([91(5)]),flip(b),unit_del(a,33)].
% 0.95/1.22 102 -r4 | is_a_theorem(implies(or(A,or(B,C)),or(B,or(A,C)))) # label(r4) # label(axiom). [clausify(25)].
% 0.95/1.22 103 is_a_theorem(implies(implies(not(A),implies(not(B),C)),implies(not(B),implies(not(A),C)))). [copy(102),rewrite([91(2),91(4),91(6),91(8)]),unit_del(a,39)].
% 0.95/1.22 115 implies(not(not(A)),B) = implies(A,B). [back_rewrite(83),rewrite([91(2)])].
% 0.95/1.22 116 is_a_theorem(implies(implies(not(A),B),implies(not(B),A))). [back_rewrite(80),rewrite([91(1),91(3)])].
% 0.95/1.22 117 is_a_theorem(implies(A,implies(not(B),A))). [back_rewrite(63),rewrite([91(1)])].
% 0.95/1.22 118 is_a_theorem(implies(implies(not(A),A),A)). [back_rewrite(60),rewrite([91(1)])].
% 0.95/1.22 121 not(implies(A,not(B))) = and(A,B). [back_rewrite(93),rewrite([115(4)])].
% 0.95/1.22 124 not(and(A,implies(B,C))) = implies(A,and(B,not(C))). [para(85(a,1),85(a,1,1,2))].
% 0.95/1.22 125 -is_a_theorem(implies(not(A),implies(not(B),C))) | is_a_theorem(implies(not(B),implies(not(A),C))). [resolve(103,a,72,b)].
% 0.95/1.22 132 -is_a_theorem(not(not(A))) | -is_a_theorem(implies(A,B)) | is_a_theorem(B). [para(115(a,1),72(b,1))].
% 0.95/1.22 142 is_a_theorem(implies(implies(implies(A,B),C),implies(not(C),and(A,not(B))))). [para(85(a,1),116(a,1,1,1))].
% 0.95/1.22 150 is_a_theorem(implies(A,implies(B,A))). [para(115(a,1),117(a,1,2))].
% 0.95/1.22 153 -is_a_theorem(implies(not(A),A)) | is_a_theorem(A). [resolve(118,a,72,b)].
% 0.95/1.22 157 is_a_theorem(implies(implies(A,not(A)),not(A))). [para(115(a,1),118(a,1,1))].
% 0.95/1.22 165 not(implies(A,and(B,C))) = and(A,implies(B,not(C))). [para(121(a,1),121(a,1,1,2))].
% 0.95/1.22 198 is_a_theorem(implies(A,implies(B,not(not(A))))). [para(115(a,1),150(a,1))].
% 0.95/1.22 202 is_a_theorem(implies(not(A),implies(not(B),not(B)))). [resolve(125,a,150,a)].
% 0.95/1.22 245 -is_a_theorem(A) | is_a_theorem(implies(B,not(not(A)))). [resolve(198,a,72,b)].
% 0.95/1.22 402 is_a_theorem(implies(not(A),not(A))). [resolve(202,a,153,a)].
% 0.95/1.22 443 is_a_theorem(implies(A,not(not(A)))). [para(115(a,1),402(a,1))].
% 0.95/1.22 445 is_a_theorem(implies(A,implies(B,B))). [resolve(443,a,245,a),rewrite([121(4),85(3)])].
% 0.95/1.22 471 is_a_theorem(implies(A,A)). [resolve(445,a,153,a)].
% 0.95/1.22 606 -is_a_theorem(implies(c33,and(c33,not(not(c33))))). [ur(132,b,471,a,c,56,a),rewrite([165(6),124(7)])].
% 0.95/1.22 658 -is_a_theorem(implies(implies(implies(A,not(A)),not(A)),implies(c33,and(c33,not(not(c33)))))). [ur(72,a,157,a,c,606,a)].
% 0.95/1.22 2231 is_a_theorem(implies(implies(implies(A,B),not(C)),implies(C,and(A,not(B))))). [para(115(a,1),142(a,1,2))].
% 0.95/1.22 2232 $F. [resolve(2231,a,658,a)].
% 0.95/1.22
% 0.95/1.22 % SZS output end Refutation
% 0.95/1.22 ============================== end of proof ==========================
% 0.95/1.22
% 0.95/1.22 ============================== STATISTICS ============================
% 0.95/1.22
% 0.95/1.22 Given=178. Generated=4207. Kept=2180. proofs=1.
% 0.95/1.22 Usable=153. Sos=1811. Demods=42. Limbo=54, Disabled=235. Hints=0.
% 0.95/1.22 Megabytes=2.16.
% 0.95/1.22 User_CPU=0.22, System_CPU=0.01, Wall_clock=0.
% 0.95/1.22
% 0.95/1.22 ============================== end of statistics =====================
% 0.95/1.22
% 0.95/1.22 ============================== end of search =========================
% 0.95/1.22
% 0.95/1.22 THEOREM PROVED
% 0.95/1.22 % SZS status Theorem
% 0.95/1.22
% 0.95/1.22 Exiting with 1 proof.
% 0.95/1.22
% 0.95/1.22 Process 5008 exit (max_proofs) Sat Jul 2 21:16:41 2022
% 0.95/1.22 Prover9 interrupted
%------------------------------------------------------------------------------