%------------------------------------------------------------------------------ % File : Prover9---1109a % Problem : SWX200+1 : TPTP v9.3.0. Released v9.3.0. % Transfm : none % Format : tptp:raw % Command : tptp2X_and_run_prover9 %d %s % Computer : n015.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 : 300s % DateTime : Wed Apr 29 02:38:04 PM UTC 2026 % Result : Theorem 0.43s 0.99s % Output : Refutation 0.43s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.11 % Problem : SWX200+1 : TPTP v9.3.0. Released v9.3.0. % 0.00/0.12 % Command : tptp2X_and_run_prover9 %d %s % 0.15/0.33 % Computer : n015.cluster.edu % 0.15/0.33 % Model : x86_64 x86_64 % 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.33 % Memory : 8042.1875MB % 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.33 % CPULimit : 300 % 0.15/0.33 % WCLimit : 300 % 0.15/0.33 % DateTime : Wed Apr 29 00:34:46 EDT 2026 % 0.15/0.33 % CPUTime : % 0.43/0.99 ============================== Prover9 =============================== % 0.43/0.99 Prover9 (32) version 2009-11A, November 2009. % 0.43/0.99 Process 30293 was started by sandbox2 on n015.cluster.edu, % 0.43/0.99 Wed Apr 29 00:34:47 2026 % 0.43/0.99 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_30140_n015.cluster.edu". % 0.43/0.99 ============================== end of head =========================== % 0.43/0.99 % 0.43/0.99 ============================== INPUT ================================= % 0.43/0.99 % 0.43/0.99 % Reading from file /tmp/Prover9_30140_n015.cluster.edu % 0.43/0.99 % 0.43/0.99 set(prolog_style_variables). % 0.43/0.99 set(auto2). % 0.43/0.99 % set(auto2) -> set(auto). % 0.43/0.99 % set(auto) -> set(auto_inference). % 0.43/0.99 % set(auto) -> set(auto_setup). % 0.43/0.99 % set(auto_setup) -> set(predicate_elim). % 0.43/0.99 % set(auto_setup) -> assign(eq_defs, unfold). % 0.43/0.99 % set(auto) -> set(auto_limits). % 0.43/0.99 % set(auto_limits) -> assign(max_weight, "100.000"). % 0.43/0.99 % set(auto_limits) -> assign(sos_limit, 20000). % 0.43/0.99 % set(auto) -> set(auto_denials). % 0.43/0.99 % set(auto) -> set(auto_process). % 0.43/0.99 % set(auto2) -> assign(new_constants, 1). % 0.43/0.99 % set(auto2) -> assign(fold_denial_max, 3). % 0.43/0.99 % set(auto2) -> assign(max_weight, "200.000"). % 0.43/0.99 % set(auto2) -> assign(max_hours, 1). % 0.43/0.99 % assign(max_hours, 1) -> assign(max_seconds, 3600). % 0.43/0.99 % set(auto2) -> assign(max_seconds, 0). % 0.43/0.99 % set(auto2) -> assign(max_minutes, 5). % 0.43/0.99 % assign(max_minutes, 5) -> assign(max_seconds, 300). % 0.43/0.99 % set(auto2) -> set(sort_initial_sos). % 0.43/0.99 % set(auto2) -> assign(sos_limit, -1). % 0.43/0.99 % set(auto2) -> assign(lrs_ticks, 3000). % 0.43/0.99 % set(auto2) -> assign(max_megs, 400). % 0.43/0.99 % set(auto2) -> assign(stats, some). % 0.43/0.99 % set(auto2) -> clear(echo_input). % 0.43/0.99 % set(auto2) -> set(quiet). % 0.43/0.99 % set(auto2) -> clear(print_initial_clauses). % 0.43/0.99 % set(auto2) -> clear(print_given). % 0.43/0.99 assign(lrs_ticks,-1). % 0.43/0.99 assign(sos_limit,10000). % 0.43/0.99 assign(order,kbo). % 0.43/0.99 set(lex_order_vars). % 0.43/0.99 clear(print_given). % 0.43/0.99 % 0.43/0.99 % formulas(sos). % not echoed (16 formulas) % 0.43/0.99 % 0.43/0.99 ============================== end of input ========================== % 0.43/0.99 % 0.43/0.99 % From the command line: assign(max_seconds, 300). % 0.43/0.99 % 0.43/0.99 ============================== PROCESS NON-CLAUSAL FORMULAS ========== % 0.43/0.99 % 0.43/0.99 % Formulas that are not ordinary clauses: % 0.43/0.99 1 (all X all X2 head(cons(X,X2)) = X) # label(axiom_001) # label(axiom) # label(non_clause). [assumption]. % 0.43/0.99 2 (all X all X2 tail(cons(X,X2)) = X2) # label(axiom_002) # label(axiom) # label(non_clause). [assumption]. % 0.43/0.99 3 (all X all X2 nil != cons(X,X2)) # label(axiom_003) # label(axiom) # label(non_clause). [assumption]. % 0.43/0.99 4 (all X proj1S(s(X)) = X) # label(axiom_004) # label(axiom) # label(non_clause). [assumption]. % 0.43/0.99 5 (all X z != s(X)) # label(axiom_005) # label(axiom) # label(non_clause). [assumption]. % 0.43/0.99 6 (all Y leqNat(z,Y)) # label(axiom_006) # label(axiom) # label(non_clause). [assumption]. % 0.43/0.99 7 (all Z -leqNat(s(Z),z)) # label(axiom_007) # label(axiom) # label(non_clause). [assumption]. % 0.43/0.99 8 (all Z all M (leqNat(s(Z),s(M)) <-> leqNat(Z,M))) # label(axiom_008) # label(axiom) # label(non_clause). [assumption]. % 0.43/0.99 9 (all Y merge(nil,Y) = Y) # label(axiom_009) # label(axiom) # label(non_clause). [assumption]. % 0.43/0.99 10 (all Z all Xs merge(cons(Z,Xs),nil) = cons(Z,Xs)) # label(axiom_010) # label(axiom) # label(non_clause). [assumption]. % 0.43/0.99 11 (all Z all Xs all Y2 all Ys (leqNat(Z,Y2) -> merge(cons(Z,Xs),cons(Y2,Ys)) = cons(Z,merge(Xs,cons(Y2,Ys))))) # label(axiom_011) # label(axiom) # label(non_clause). [assumption]. % 0.43/0.99 12 (all Z all Xs all Y2 all Ys (-leqNat(Z,Y2) -> merge(cons(Z,Xs),cons(Y2,Ys)) = cons(Y2,merge(cons(Z,Xs),Ys)))) # label(axiom_012) # label(axiom) # label(non_clause). [assumption]. % 0.43/0.99 13 (all Y ord(cons(Y,nil))) # label(axiom_014) # label(axiom) # label(non_clause). [assumption]. % 0.43/0.99 14 (all Y all Y2 all Xs (ord(cons(Y,cons(Y2,Xs))) <-> leqNat(Y,Y2) & ord(cons(Y2,Xs)))) # label(axiom_015) # label(axiom) # label(non_clause). [assumption]. % 0.43/0.99 15 -(exists Xs exists Ys -(ord(Xs) -> (-ord(Ys) -> ord(merge(Xs,Ys))))) # label(goal_016) # label(negated_conjecture) # label(non_clause). [assumption]. % 0.43/0.99 % 0.43/0.99 ============================== end of process non-clausal formulas === % 0.43/0.99 % 0.43/0.99 ============================== PROCESS INITIAL CLAUSES =============== % 0.43/0.99 % 0.43/0.99 ============================== PREDICATE ELIMINATION ================= % 0.43/0.99 % 0.43/0.99 ============================== end predicate elimination ============= % 0.43/0.99 % 0.43/0.99 Auto_denials: (non-Horn, no changes). % 0.43/0.99 % 0.43/0.99 Term ordering decisions: % 0.43/0.99 Function symbol KB weights: nil=1. z=1. cons=1. merge=1. s=1. head=1. proj1S=1. tail=1. % 0.43/0.99 % 0.43/0.99 ============================== end of process initial clauses ======== % 0.43/0.99 % 0.43/0.99 ============================== CLAUSES FOR SEARCH ==================== % 0.43/0.99 % 0.43/0.99 ============================== end of clauses for search ============= % 0.43/0.99 % 0.43/0.99 ============================== SEARCH ================================ % 0.43/0.99 % 0.43/0.99 % Starting search at 0.01 seconds. % 0.43/0.99 % 0.43/0.99 ============================== PROOF ================================= % 0.43/0.99 % SZS status Theorem % 0.43/0.99 % SZS output start Refutation % 0.43/0.99 % 0.43/0.99 % Proof 1 at 0.01 (+ 0.00) seconds. % 0.43/0.99 % Length of proof is 15. % 0.43/0.99 % Level of proof is 4. % 0.43/0.99 % Maximum clause weight is 9.000. % 0.43/0.99 % Given clauses 15. % 0.43/0.99 % 0.43/0.99 7 (all Z -leqNat(s(Z),z)) # label(axiom_007) # label(axiom) # label(non_clause). [assumption]. % 0.43/0.99 8 (all Z all M (leqNat(s(Z),s(M)) <-> leqNat(Z,M))) # label(axiom_008) # label(axiom) # label(non_clause). [assumption]. % 0.43/0.99 9 (all Y merge(nil,Y) = Y) # label(axiom_009) # label(axiom) # label(non_clause). [assumption]. % 0.43/0.99 14 (all Y all Y2 all Xs (ord(cons(Y,cons(Y2,Xs))) <-> leqNat(Y,Y2) & ord(cons(Y2,Xs)))) # label(axiom_015) # label(axiom) # label(non_clause). [assumption]. % 0.43/0.99 15 -(exists Xs exists Ys -(ord(Xs) -> (-ord(Ys) -> ord(merge(Xs,Ys))))) # label(goal_016) # label(negated_conjecture) # label(non_clause). [assumption]. % 0.43/0.99 16 ord(nil) # label(axiom_013) # label(axiom). [assumption]. % 0.43/0.99 20 merge(nil,A) = A # label(axiom_009) # label(axiom). [clausify(9)]. % 0.43/0.99 26 -leqNat(s(A),z) # label(axiom_007) # label(axiom). [clausify(7)]. % 0.43/0.99 28 -leqNat(s(A),s(B)) | leqNat(A,B) # label(axiom_008) # label(axiom). [clausify(8)]. % 0.43/0.99 30 -ord(A) | ord(B) | ord(merge(A,B)) # label(goal_016) # label(negated_conjecture). [clausify(15)]. % 0.43/0.99 31 -ord(cons(A,cons(B,C))) | leqNat(A,B) # label(axiom_015) # label(axiom). [clausify(14)]. % 0.43/0.99 37 -leqNat(s(s(A)),s(z)). [ur(28,b,26,a)]. % 0.43/0.99 41 ord(A). [resolve(30,a,16,a),rewrite([20(3)]),merge(b)]. % 0.43/0.99 42 leqNat(A,B). [back_unit_del(31),unit_del(a,41)]. % 0.43/0.99 43 $F. [resolve(42,a,37,a)]. % 0.43/0.99 % 0.43/0.99 % SZS output end Refutation % 0.43/0.99 ============================== end of proof ========================== % 0.43/0.99 % 0.43/0.99 ============================== STATISTICS ============================ % 0.43/0.99 % 0.43/0.99 Given=15. Generated=32. Kept=27. proofs=1. % 0.43/0.99 Usable=12. Sos=6. Demods=6. Limbo=1, Disabled=26. Hints=0. % 0.43/0.99 Megabytes=0.07. % 0.43/0.99 User_CPU=0.01, System_CPU=0.00, Wall_clock=0. % 0.43/0.99 % 0.43/0.99 ============================== end of statistics ===================== % 0.43/0.99 % 0.43/0.99 ============================== end of search ========================= % 0.43/0.99 % 0.43/0.99 THEOREM PROVED % 0.43/0.99 % SZS status Theorem % 0.43/0.99 % 0.43/0.99 Exiting with 1 proof. % 0.43/0.99 % 0.43/0.99 Process 30293 exit (max_proofs) Wed Apr 29 00:34:47 2026 % 0.43/0.99 Prover9 interrupted %------------------------------------------------------------------------------