0.03/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.03/0.13 % Command : tptp2X_and_run_prover9 %d %s 0.12/0.34 % Computer : n025.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 : 960 0.12/0.34 % WCLimit : 120 0.12/0.34 % DateTime : Tue Aug 9 04:39:56 EDT 2022 0.12/0.34 % CPUTime : 0.43/1.02 ============================== Prover9 =============================== 0.43/1.02 Prover9 (32) version 2009-11A, November 2009. 0.43/1.02 Process 8468 was started by sandbox2 on n025.cluster.edu, 0.43/1.02 Tue Aug 9 04:39:57 2022 0.43/1.02 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 960 -f /tmp/Prover9_8122_n025.cluster.edu". 0.43/1.02 ============================== end of head =========================== 0.43/1.02 0.43/1.02 ============================== INPUT ================================= 0.43/1.02 0.43/1.02 % Reading from file /tmp/Prover9_8122_n025.cluster.edu 0.43/1.02 0.43/1.02 set(prolog_style_variables). 0.43/1.02 set(auto2). 0.43/1.02 % set(auto2) -> set(auto). 0.43/1.02 % set(auto) -> set(auto_inference). 0.43/1.02 % set(auto) -> set(auto_setup). 0.43/1.02 % set(auto_setup) -> set(predicate_elim). 0.43/1.02 % set(auto_setup) -> assign(eq_defs, unfold). 0.43/1.02 % set(auto) -> set(auto_limits). 0.43/1.02 % set(auto_limits) -> assign(max_weight, "100.000"). 0.43/1.02 % set(auto_limits) -> assign(sos_limit, 20000). 0.43/1.02 % set(auto) -> set(auto_denials). 0.43/1.02 % set(auto) -> set(auto_process). 0.43/1.02 % set(auto2) -> assign(new_constants, 1). 0.43/1.02 % set(auto2) -> assign(fold_denial_max, 3). 0.43/1.02 % set(auto2) -> assign(max_weight, "200.000"). 0.43/1.02 % set(auto2) -> assign(max_hours, 1). 0.43/1.02 % assign(max_hours, 1) -> assign(max_seconds, 3600). 0.43/1.02 % set(auto2) -> assign(max_seconds, 0). 0.43/1.02 % set(auto2) -> assign(max_minutes, 5). 0.43/1.02 % assign(max_minutes, 5) -> assign(max_seconds, 300). 0.43/1.02 % set(auto2) -> set(sort_initial_sos). 0.43/1.02 % set(auto2) -> assign(sos_limit, -1). 0.43/1.02 % set(auto2) -> assign(lrs_ticks, 3000). 0.43/1.02 % set(auto2) -> assign(max_megs, 400). 0.43/1.02 % set(auto2) -> assign(stats, some). 0.43/1.02 % set(auto2) -> clear(echo_input). 0.43/1.02 % set(auto2) -> set(quiet). 0.43/1.02 % set(auto2) -> clear(print_initial_clauses). 0.43/1.02 % set(auto2) -> clear(print_given). 0.43/1.02 assign(lrs_ticks,-1). 0.43/1.02 assign(sos_limit,10000). 0.43/1.02 assign(order,kbo). 0.43/1.02 set(lex_order_vars). 0.43/1.02 clear(print_given). 0.43/1.02 0.43/1.02 % formulas(sos). % not echoed (45 formulas) 0.43/1.02 0.43/1.02 ============================== end of input ========================== 0.43/1.02 0.43/1.02 % From the command line: assign(max_seconds, 960). 0.43/1.02 0.43/1.02 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 0.43/1.02 0.43/1.02 % Formulas that are not ordinary clauses: 0.43/1.02 1 and_1 <-> (all X all Y is_a_theorem(implies(and(X,Y),X))) # label(and_1) # label(axiom) # label(non_clause). [assumption]. 0.43/1.02 2 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]. 0.43/1.02 3 (all X all Y is_a_theorem(implies(and(X,Y),Y))) <-> and_2 # label(and_2) # label(axiom) # label(non_clause). [assumption]. 0.43/1.02 4 (all X all Y all Z is_a_theorem(implies(implies(X,Z),implies(implies(Y,Z),implies(or(X,Y),Z))))) <-> or_3 # label(or_3) # label(axiom) # label(non_clause). [assumption]. 0.43/1.02 5 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]. 0.43/1.02 6 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]. 0.43/1.02 7 kn2 <-> (all P all Q is_a_theorem(implies(and(P,Q),P))) # label(kn2) # label(axiom) # label(non_clause). [assumption]. 0.43/1.02 8 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]. 0.43/1.02 9 or_1 <-> (all X all Y is_a_theorem(implies(X,or(X,Y)))) # label(or_1) # label(axiom) # label(non_clause). [assumption]. 0.43/1.02 10 cn3 <-> (all P is_a_theorem(implies(implies(not(P),P),P))) # label(cn3) # label(axiom) # label(non_clause). [assumption]. 0.43/1.02 11 (all P all Q all R is_a_theorem(implies(implies(P,Q),implies(implies(Q,R),implies(P,R))))) <-> cn1 # label(cn1) # label(axiom) # label(non_clause). [assumption]. 0.43/1.02 12 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]. 0.43/1.02 13 substitution_of_equivalents <-> (all X all Y (is_a_theorem(equiv(X,Y)) -> Y = X)) # label(substitution_of_equivalents) # label(axiom) # label(non_clause). [assumption]. 0.43/1.02 14 (all P all Q all R is_a_theorem(implies(implies(Q,R),implies(or(P,Q),or(P,R))))) <-> r5 # label(r5) # label(axiom) # label(non_clause). [assumption]. 0.88/1.19 15 (all P all Q is_a_theorem(implies(Q,or(P,Q)))) <-> r2 # label(r2) # label(axiom) # label(non_clause). [assumption]. 0.88/1.19 16 or_2 <-> (all X all Y is_a_theorem(implies(Y,or(X,Y)))) # label(or_2) # label(axiom) # label(non_clause). [assumption]. 0.88/1.19 17 (all P all Q is_a_theorem(implies(P,implies(not(P),Q)))) <-> cn2 # label(cn2) # label(axiom) # label(non_clause). [assumption]. 0.88/1.19 18 (all X all Y is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y)))) <-> implies_2 # label(implies_2) # label(axiom) # label(non_clause). [assumption]. 0.88/1.19 19 r1 <-> (all P is_a_theorem(implies(or(P,P),P))) # label(r1) # label(axiom) # label(non_clause). [assumption]. 0.88/1.19 20 r3 <-> (all P all Q is_a_theorem(implies(or(P,Q),or(Q,P)))) # label(r3) # label(axiom) # label(non_clause). [assumption]. 0.88/1.19 21 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]. 0.88/1.19 22 (all P is_a_theorem(implies(P,and(P,P)))) <-> kn1 # label(kn1) # label(axiom) # label(non_clause). [assumption]. 0.88/1.19 23 (all X all Y is_a_theorem(implies(equiv(X,Y),implies(Y,X)))) <-> equivalence_2 # label(equivalence_2) # label(axiom) # label(non_clause). [assumption]. 0.88/1.19 24 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]. 0.88/1.19 25 (all X all Y is_a_theorem(implies(X,implies(Y,X)))) <-> implies_1 # label(implies_1) # label(axiom) # label(non_clause). [assumption]. 0.88/1.19 26 (all X all Y all Z is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))))) <-> implies_3 # label(implies_3) # label(axiom) # label(non_clause). [assumption]. 0.88/1.19 27 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]. 0.88/1.19 28 op_implies_or -> (all X all Y or(not(X),Y) = implies(X,Y)) # label(op_implies_or) # label(axiom) # label(non_clause). [assumption]. 0.88/1.19 29 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]. 0.88/1.19 30 op_or -> (all X all Y not(and(not(X),not(Y))) = or(X,Y)) # label(op_or) # label(axiom) # label(non_clause). [assumption]. 0.88/1.19 31 op_and -> (all X all Y and(X,Y) = not(or(not(X),not(Y)))) # label(op_and) # label(axiom) # label(non_clause). [assumption]. 0.88/1.19 0.88/1.19 ============================== end of process non-clausal formulas === 0.88/1.19 0.88/1.19 ============================== PROCESS INITIAL CLAUSES =============== 0.88/1.19 0.88/1.19 ============================== PREDICATE ELIMINATION ================= 0.88/1.19 0.88/1.19 ============================== end predicate elimination ============= 0.88/1.19 0.88/1.19 Auto_denials: (non-Horn, no changes). 0.88/1.19 0.88/1.19 Term ordering decisions: 0.88/1.19 0.88/1.19 % Assigning unary symbol not kb_weight 0 and highest precedence (93). 0.88/1.19 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. 0.88/1.19 0.88/1.19 ============================== end of process initial clauses ======== 0.88/1.19 0.88/1.19 ============================== CLAUSES FOR SEARCH ==================== 0.88/1.19 0.88/1.19 ============================== end of clauses for search ============= 0.88/1.19 0.88/1.19 ============================== SEARCH ================================ 0.88/1.19 0.88/1.19 % Starting search at 0.02 seconds. 0.88/1.19 0.88/1.19 ============================== PROOF ================================= 0.88/1.19 % SZS status Theorem 0.88/1.19 % SZS output start Refutation 0.88/1.19 0.88/1.19 % Proof 1 at 0.18 (+ 0.01) seconds. 0.88/1.19 % Length of proof is 39. 0.88/1.19 % Level of proof is 7. 0.88/1.19 % Maximum clause weight is 24.000. 0.88/1.19 % Given clauses 160. 0.88/1.19 0.88/1.19 11 (all P all Q all R is_a_theorem(implies(implies(P,Q),implies(implies(Q,R),implies(P,R))))) <-> cn1 # label(cn1) # label(axiom) # label(non_clause). [assumption]. 0.88/1.19 14 (all P all Q all R is_a_theorem(implies(implies(Q,R),implies(or(P,Q),or(P,R))))) <-> r5 # label(r5) # label(axiom) # label(non_clause). [assumption]. 0.88/1.19 21 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]. 0.88/1.19 24 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]. 0.88/1.19 26 (all X all Y all Z is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))))) <-> implies_3 # label(implies_3) # label(axiom) # label(non_clause). [assumption]. 0.88/1.19 27 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]. 0.88/1.19 28 op_implies_or -> (all X all Y or(not(X),Y) = implies(X,Y)) # label(op_implies_or) # label(axiom) # label(non_clause). [assumption]. 0.88/1.19 30 op_or -> (all X all Y not(and(not(X),not(Y))) = or(X,Y)) # label(op_or) # label(axiom) # label(non_clause). [assumption]. 0.88/1.19 32 r4 # label(principia_r4) # label(axiom). [assumption]. 0.88/1.19 34 op_implies_or # label(principia_op_implies_or) # label(axiom). [assumption]. 0.88/1.19 35 modus_ponens # label(principia_modus_ponens) # label(axiom). [assumption]. 0.88/1.19 39 r5 # label(principia_r5) # label(axiom). [assumption]. 0.88/1.19 42 op_or # label(hilbert_op_or) # label(axiom). [assumption]. 0.88/1.19 43 op_implies_and # label(hilbert_op_implies_and) # label(axiom). [assumption]. 0.88/1.19 44 -implies_3 # label(hilbert_implies_3) # label(negated_conjecture). [assumption]. 0.88/1.19 79 -modus_ponens | -is_a_theorem(A) | -is_a_theorem(implies(A,B)) | is_a_theorem(B) # label(modus_ponens) # label(axiom). [clausify(24)]. 0.88/1.19 80 -is_a_theorem(A) | -is_a_theorem(implies(A,B)) | is_a_theorem(B). [copy(79),unit_del(a,35)]. 0.88/1.19 81 -op_implies_or | or(not(A),B) = implies(A,B) # label(op_implies_or) # label(axiom). [clausify(28)]. 0.88/1.19 82 or(not(A),B) = implies(A,B). [copy(81),unit_del(a,34)]. 0.88/1.19 83 -op_implies_and | not(and(A,not(B))) = implies(A,B) # label(op_implies_and) # label(axiom). [clausify(27)]. 0.88/1.19 84 not(and(A,not(B))) = implies(A,B). [copy(83),unit_del(a,43)]. 0.88/1.19 89 -op_or | or(A,B) = not(and(not(A),not(B))) # label(op_or) # label(axiom). [clausify(30)]. 0.88/1.19 90 or(A,B) = implies(not(A),B). [copy(89),rewrite([84(6)]),unit_del(a,42)]. 0.88/1.19 97 -is_a_theorem(implies(implies(c22,c23),implies(implies(c23,c24),implies(c22,c24)))) | cn1 # label(cn1) # label(axiom). [clausify(11)]. 0.88/1.19 98 is_a_theorem(implies(implies(A,B),implies(implies(B,C),implies(A,C)))) | -cn1 # label(cn1) # label(axiom). [clausify(11)]. 0.88/1.19 100 is_a_theorem(implies(implies(A,B),implies(or(C,A),or(C,B)))) | -r5 # label(r5) # label(axiom). [clausify(14)]. 0.88/1.19 101 is_a_theorem(implies(implies(A,B),implies(implies(not(C),A),implies(not(C),B)))). [copy(100),rewrite([90(2),90(4)]),unit_del(b,39)]. 0.88/1.19 102 -r4 | is_a_theorem(implies(or(A,or(B,C)),or(B,or(A,C)))) # label(r4) # label(axiom). [clausify(21)]. 0.88/1.19 103 is_a_theorem(implies(implies(not(A),implies(not(B),C)),implies(not(B),implies(not(A),C)))). [copy(102),rewrite([90(2),90(4),90(6),90(8)]),unit_del(a,32)]. 0.88/1.19 105 -is_a_theorem(implies(implies(c53,c54),implies(implies(c54,c55),implies(c53,c55)))) | implies_3 # label(implies_3) # label(axiom). [clausify(26)]. 0.88/1.19 106 -is_a_theorem(implies(implies(c53,c54),implies(implies(c54,c55),implies(c53,c55)))). [copy(105),unit_del(b,44)]. 0.88/1.19 113 implies(not(not(A)),B) = implies(A,B). [back_rewrite(82),rewrite([90(2)])]. 0.88/1.19 127 -cn1. [ur(98,a,106,a)]. 0.88/1.19 130 -is_a_theorem(implies(implies(c22,c23),implies(implies(c23,c24),implies(c22,c24)))). [back_unit_del(97),unit_del(b,127)]. 0.88/1.19 136 is_a_theorem(implies(implies(A,B),implies(implies(C,A),implies(C,B)))). [para(113(a,1),101(a,1,2,1)),rewrite([113(5)])]. 0.88/1.19 137 is_a_theorem(implies(implies(not(A),implies(B,C)),implies(B,implies(not(A),C)))). [para(113(a,1),103(a,1,1,2)),rewrite([113(8)])]. 0.88/1.19 1322 -is_a_theorem(implies(implies(implies(A,B),implies(implies(C,A),implies(C,B))),implies(implies(c22,c23),implies(implies(c23,c24),implies(c22,c24))))). [ur(80,a,136,a,c,130,a)]. 0.88/1.19 1563 is_a_theorem(implies(implies(implies(A,B),implies(C,D)),implies(C,implies(implies(A,B),D)))). [para(84(a,1),137(a,1,1,1)),rewrite([84(6)])]. 0.88/1.19 1564 $F. [resolve(1563,a,1322,a)]. 0.88/1.19 0.88/1.19 % SZS output end Refutation 0.88/1.19 ============================== end of proof ========================== 0.88/1.19 0.88/1.19 ============================== STATISTICS ============================ 0.88/1.19 0.88/1.19 Given=160. Generated=2862. Kept=1512. proofs=1. 0.88/1.19 Usable=134. Sos=1194. Demods=42. Limbo=45, Disabled=212. Hints=0. 0.88/1.19 Megabytes=1.49. 0.88/1.19 User_CPU=0.18, System_CPU=0.01, Wall_clock=0. 0.88/1.19 0.88/1.19 ============================== end of statistics ===================== 0.88/1.19 0.88/1.19 ============================== end of search ========================= 0.88/1.19 0.88/1.19 THEOREM PROVED 0.88/1.19 % SZS status Theorem 0.88/1.19 0.88/1.19 Exiting with 1 proof. 0.88/1.19 0.88/1.19 Process 8468 exit (max_proofs) Tue Aug 9 04:39:57 2022 0.88/1.19 Prover9 interrupted 0.88/1.19 EOF