%------------------------------------------------------------------------------ % File : Prover9---1109a % Problem : SWX186+1 : TPTP v9.3.0. Released v9.3.0. % Transfm : none % Format : tptp:raw % Command : tptp2X_and_run_prover9 %d %s % Computer : n004.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 02:38:02 PM UTC 2026 % Result : Theorem 0.42s 1.00s % Output : Refutation 0.42s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SWX186+1 : TPTP v9.3.0. Released v9.3.0. % 0.00/0.12 % Command : tptp2X_and_run_prover9 %d %s % 0.16/0.33 % Computer : n004.cluster.edu % 0.16/0.33 % Model : x86_64 x86_64 % 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.33 % Memory : 8042.1875MB % 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.33 % CPULimit : 300 % 0.16/0.33 % WCLimit : 300 % 0.16/0.33 % DateTime : Tue Apr 28 23:31:01 EDT 2026 % 0.16/0.33 % CPUTime : % 0.42/1.00 ============================== Prover9 =============================== % 0.42/1.00 Prover9 (32) version 2009-11A, November 2009. % 0.42/1.00 Process 3291 was started by sandbox on n004.cluster.edu, % 0.42/1.00 Tue Apr 28 23:31:02 2026 % 0.42/1.00 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_3138_n004.cluster.edu". % 0.42/1.00 ============================== end of head =========================== % 0.42/1.00 % 0.42/1.00 ============================== INPUT ================================= % 0.42/1.00 % 0.42/1.00 % Reading from file /tmp/Prover9_3138_n004.cluster.edu % 0.42/1.00 % 0.42/1.00 set(prolog_style_variables). % 0.42/1.00 set(auto2). % 0.42/1.00 % set(auto2) -> set(auto). % 0.42/1.00 % set(auto) -> set(auto_inference). % 0.42/1.00 % set(auto) -> set(auto_setup). % 0.42/1.00 % set(auto_setup) -> set(predicate_elim). % 0.42/1.00 % set(auto_setup) -> assign(eq_defs, unfold). % 0.42/1.00 % set(auto) -> set(auto_limits). % 0.42/1.00 % set(auto_limits) -> assign(max_weight, "100.000"). % 0.42/1.00 % set(auto_limits) -> assign(sos_limit, 20000). % 0.42/1.00 % set(auto) -> set(auto_denials). % 0.42/1.00 % set(auto) -> set(auto_process). % 0.42/1.00 % set(auto2) -> assign(new_constants, 1). % 0.42/1.00 % set(auto2) -> assign(fold_denial_max, 3). % 0.42/1.00 % set(auto2) -> assign(max_weight, "200.000"). % 0.42/1.00 % set(auto2) -> assign(max_hours, 1). % 0.42/1.00 % assign(max_hours, 1) -> assign(max_seconds, 3600). % 0.42/1.00 % set(auto2) -> assign(max_seconds, 0). % 0.42/1.00 % set(auto2) -> assign(max_minutes, 5). % 0.42/1.00 % assign(max_minutes, 5) -> assign(max_seconds, 300). % 0.42/1.00 % set(auto2) -> set(sort_initial_sos). % 0.42/1.00 % set(auto2) -> assign(sos_limit, -1). % 0.42/1.00 % set(auto2) -> assign(lrs_ticks, 3000). % 0.42/1.00 % set(auto2) -> assign(max_megs, 400). % 0.42/1.00 % set(auto2) -> assign(stats, some). % 0.42/1.00 % set(auto2) -> clear(echo_input). % 0.42/1.00 % set(auto2) -> set(quiet). % 0.42/1.00 % set(auto2) -> clear(print_initial_clauses). % 0.42/1.00 % set(auto2) -> clear(print_given). % 0.42/1.00 assign(lrs_ticks,-1). % 0.42/1.00 assign(sos_limit,10000). % 0.42/1.00 assign(order,kbo). % 0.42/1.00 set(lex_order_vars). % 0.42/1.00 clear(print_given). % 0.42/1.00 % 0.42/1.00 % formulas(sos). % not echoed (9 formulas) % 0.42/1.00 % 0.42/1.00 ============================== end of input ========================== % 0.42/1.00 % 0.42/1.00 % From the command line: assign(max_seconds, 300). % 0.42/1.00 % 0.42/1.00 ============================== PROCESS NON-CLAUSAL FORMULAS ========== % 0.42/1.00 % 0.42/1.00 % Formulas that are not ordinary clauses: % 0.42/1.00 1 (all X all X2 head(cons(X,X2)) = X) # label(axiom_001) # label(axiom) # label(non_clause). [assumption]. % 0.42/1.00 2 (all X all X2 tail(cons(X,X2)) = X2) # label(axiom_002) # label(axiom) # label(non_clause). [assumption]. % 0.42/1.00 3 (all X all X2 nil != cons(X,X2)) # label(axiom_003) # label(axiom) # label(non_clause). [assumption]. % 0.42/1.00 4 (all X proj1S(s(X)) = X) # label(axiom_004) # label(axiom) # label(non_clause). [assumption]. % 0.42/1.00 5 (all X s(X) != z) # label(axiom_005) # label(axiom) # label(non_clause). [assumption]. % 0.42/1.00 6 (all Z drop(s(Z),nil) = nil) # label(axiom_006) # label(axiom) # label(non_clause). [assumption]. % 0.42/1.00 7 (all Z all X2 all X3 drop(s(Z),cons(X2,X3)) = drop(Z,X3)) # label(axiom_007) # label(axiom) # label(non_clause). [assumption]. % 0.42/1.00 8 (all Y drop(z,Y) = Y) # label(axiom_008) # label(axiom) # label(non_clause). [assumption]. % 0.42/1.00 9 -(exists N exists Xs exists Ys -(drop(N,Xs) = drop(N,Ys) -> Xs = Ys)) # label(goal_009) # label(negated_conjecture) # label(non_clause). [assumption]. % 0.42/1.00 % 0.42/1.00 ============================== end of process non-clausal formulas === % 0.42/1.00 % 0.42/1.00 ============================== PROCESS INITIAL CLAUSES =============== % 0.42/1.00 % 0.42/1.00 ============================== PREDICATE ELIMINATION ================= % 0.42/1.00 % 0.42/1.00 ============================== end predicate elimination ============= % 0.42/1.00 % 0.42/1.00 Auto_denials: % 0.42/1.00 % copying label axiom_005 to answer in negative clause % 0.42/1.00 % copying label axiom_003 to answer in negative clause % 0.42/1.00 % assign(max_proofs, 2). % (Horn set with more than one neg. clause) % 0.42/1.00 % 0.42/1.00 Term ordering decisions: % 0.42/1.00 Function symbol KB weights: nil=1. z=1. drop=1. cons=1. s=1. head=1. proj1S=1. tail=1. % 0.42/1.00 % 0.42/1.00 ============================== end of process initial clauses ======== % 0.42/1.00 % 0.42/1.00 ============================== CLAUSES FOR SEARCH ==================== % 0.42/1.00 % 0.42/1.00 ============================== end of clauses for search ============= % 0.42/1.00 % 0.42/1.00 ============================== SEARCH ================================ % 0.42/1.00 % 0.42/1.00 % Starting search at 0.01 seconds. % 0.42/1.00 % 0.42/1.00 ============================== PROOF ================================= % 0.42/1.00 % SZS status Theorem % 0.42/1.00 % SZS output start Refutation % 0.42/1.00 % 0.42/1.00 % Proof 1 at 0.01 (+ 0.00) seconds: axiom_003. % 0.42/1.00 % Length of proof is 11. % 0.42/1.00 % Level of proof is 4. % 0.42/1.00 % Maximum clause weight is 10.000. % 0.42/1.00 % Given clauses 10. % 0.42/1.00 % 0.42/1.00 3 (all X all X2 nil != cons(X,X2)) # label(axiom_003) # label(axiom) # label(non_clause). [assumption]. % 0.42/1.00 6 (all Z drop(s(Z),nil) = nil) # label(axiom_006) # label(axiom) # label(non_clause). [assumption]. % 0.42/1.00 7 (all Z all X2 all X3 drop(s(Z),cons(X2,X3)) = drop(Z,X3)) # label(axiom_007) # label(axiom) # label(non_clause). [assumption]. % 0.42/1.00 9 -(exists N exists Xs exists Ys -(drop(N,Xs) = drop(N,Ys) -> Xs = Ys)) # label(goal_009) # label(negated_conjecture) # label(non_clause). [assumption]. % 0.42/1.00 14 drop(s(A),nil) = nil # label(axiom_006) # label(axiom). [clausify(6)]. % 0.42/1.00 15 drop(s(A),cons(B,C)) = drop(A,C) # label(axiom_007) # label(axiom). [clausify(7)]. % 0.42/1.00 17 cons(A,B) != nil # label(axiom_003) # label(axiom) # answer(axiom_003). [clausify(3)]. % 0.42/1.00 18 drop(A,B) != drop(A,C) | B = C # label(goal_009) # label(negated_conjecture). [clausify(9)]. % 0.42/1.00 19 drop(A,cons(B,C)) != drop(A,nil) # answer(axiom_003). [ur(18,b,17,a)]. % 0.42/1.00 24 drop(A,B) != nil # answer(axiom_003). [para(14(a,1),19(a,2)),rewrite([15(3)])]. % 0.42/1.00 25 $F # answer(axiom_003). [resolve(24,a,14,a)]. % 0.42/1.00 % 0.42/1.00 % SZS output end Refutation % 0.42/1.00 ============================== end of proof ========================== % 0.42/1.00 % Redundant proof: 26 $F # answer(axiom_003). [resolve(24,a,11,a)]. % 0.42/1.00 % 0.42/1.00 % Disable descendants (x means already disabled): % 0.42/1.00 17 19 23 24 % 0.42/1.00 % 0.42/1.00 ============================== PROOF ================================= % 0.42/1.00 % SZS status Theorem % 0.42/1.00 % SZS output start Refutation % 0.42/1.00 % 0.42/1.00 % Proof 2 at 0.01 (+ 0.00) seconds: axiom_005. % 0.42/1.00 % Length of proof is 17. % 0.42/1.00 % Level of proof is 7. % 0.42/1.00 % Maximum clause weight is 24.000. % 0.42/1.00 % Given clauses 16. % 0.42/1.00 % 0.42/1.00 1 (all X all X2 head(cons(X,X2)) = X) # label(axiom_001) # label(axiom) # label(non_clause). [assumption]. % 0.42/1.00 5 (all X s(X) != z) # label(axiom_005) # label(axiom) # label(non_clause). [assumption]. % 0.42/1.00 7 (all Z all X2 all X3 drop(s(Z),cons(X2,X3)) = drop(Z,X3)) # label(axiom_007) # label(axiom) # label(non_clause). [assumption]. % 0.42/1.00 9 -(exists N exists Xs exists Ys -(drop(N,Xs) = drop(N,Ys) -> Xs = Ys)) # label(goal_009) # label(negated_conjecture) # label(non_clause). [assumption]. % 0.42/1.00 12 head(cons(A,B)) = A # label(axiom_001) # label(axiom). [clausify(1)]. % 0.42/1.00 15 drop(s(A),cons(B,C)) = drop(A,C) # label(axiom_007) # label(axiom). [clausify(7)]. % 0.42/1.00 16 s(A) != z # label(axiom_005) # label(axiom) # answer(axiom_005). [clausify(5)]. % 0.42/1.00 18 drop(A,B) != drop(A,C) | B = C # label(goal_009) # label(negated_conjecture). [clausify(9)]. % 0.42/1.00 20 drop(A,s(B)) != drop(A,z) # answer(axiom_005). [ur(18,b,16,a)]. % 0.42/1.00 22 drop(s(A),B) != drop(A,C) | cons(D,C) = B. [para(15(a,1),18(a,1)),flip(a)]. % 0.42/1.00 27 drop(A,drop(B,s(C))) != drop(A,drop(B,z)) # answer(axiom_005). [ur(18,b,20,a)]. % 0.42/1.00 28 drop(A,drop(B,drop(C,s(D)))) != drop(A,drop(B,drop(C,z))) # answer(axiom_005). [ur(18,b,27,a)]. % 0.42/1.00 29 drop(A,drop(B,drop(C,drop(D,s(E))))) != drop(A,drop(B,drop(C,drop(D,z)))) # answer(axiom_005). [ur(18,b,28,a)]. % 0.42/1.00 30 drop(A,drop(B,drop(C,drop(D,drop(E,s(F)))))) != drop(A,drop(B,drop(C,drop(D,drop(E,z))))) # answer(axiom_005). [ur(18,b,29,a)]. % 0.42/1.00 31 cons(A,B) = cons(C,B). [hyper(22,a,15,a)]. % 0.42/1.00 38 A = B. [para(31(a,1),12(a,1,1)),rewrite([12(2)])]. % 0.42/1.00 39 $F # answer(axiom_005). [resolve(38,a,30,a)]. % 0.42/1.00 % 0.42/1.00 % SZS output end Refutation % 0.42/1.00 ============================== end of proof ========================== % 0.42/1.00 % 0.42/1.00 ============================== STATISTICS ============================ % 0.42/1.00 % 0.42/1.00 Given=16. Generated=74. Kept=27. proofs=2. % 0.42/1.00 Usable=14. Sos=7. Demods=7. Limbo=0, Disabled=14. Hints=0. % 0.42/1.00 Megabytes=0.06. % 0.42/1.00 User_CPU=0.01, System_CPU=0.00, Wall_clock=0. % 0.42/1.00 % 0.42/1.00 ============================== end of statistics ===================== % 0.42/1.00 % 0.42/1.00 ============================== end of search ========================= % 0.42/1.00 % 0.42/1.00 THEOREM PROVED % 0.42/1.00 % SZS status Theorem % 0.42/1.00 % 0.42/1.00 Exiting with 2 proofs. % 0.42/1.00 % 0.42/1.00 Process 3291 exit (max_proofs) Tue Apr 28 23:31:02 2026 % 0.42/1.00 Prover9 interrupted %------------------------------------------------------------------------------