%------------------------------------------------------------------------------ % File : Prover9---1109a % Problem : SWX204+1 : TPTP v9.3.0. Released v9.3.0. % Transfm : none % Format : tptp:raw % Command : tptp2X_and_run_prover9 %d %s % Computer : n012.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 02:38:05 PM UTC 2026 % Result : Theorem 0.42s 0.70s % Output : Refutation 0.42s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.06 % Problem : SWX204+1 : TPTP v9.3.0. Released v9.3.0. % 0.00/0.07 % Command : tptp2X_and_run_prover9 %d %s % 0.09/0.25 % Computer : n012.cluster.edu % 0.09/0.25 % Model : x86_64 x86_64 % 0.09/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.09/0.25 % Memory : 8042.1875MB % 0.09/0.25 % OS : Linux 3.10.0-693.el7.x86_64 % 0.09/0.25 % CPULimit : 300 % 0.09/0.25 % WCLimit : 300 % 0.09/0.25 % DateTime : Wed Apr 29 00:50:45 EDT 2026 % 0.09/0.25 % CPUTime : % 0.42/0.70 ============================== Prover9 =============================== % 0.42/0.70 Prover9 (32) version 2009-11A, November 2009. % 0.42/0.70 Process 22852 was started by sandbox on n012.cluster.edu, % 0.42/0.70 Wed Apr 29 00:50:46 2026 % 0.42/0.70 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_22627_n012.cluster.edu". % 0.42/0.70 ============================== end of head =========================== % 0.42/0.70 % 0.42/0.70 ============================== INPUT ================================= % 0.42/0.70 % 0.42/0.70 % Reading from file /tmp/Prover9_22627_n012.cluster.edu % 0.42/0.70 % 0.42/0.70 set(prolog_style_variables). % 0.42/0.70 set(auto2). % 0.42/0.70 % set(auto2) -> set(auto). % 0.42/0.70 % set(auto) -> set(auto_inference). % 0.42/0.70 % set(auto) -> set(auto_setup). % 0.42/0.70 % set(auto_setup) -> set(predicate_elim). % 0.42/0.70 % set(auto_setup) -> assign(eq_defs, unfold). % 0.42/0.70 % set(auto) -> set(auto_limits). % 0.42/0.70 % set(auto_limits) -> assign(max_weight, "100.000"). % 0.42/0.70 % set(auto_limits) -> assign(sos_limit, 20000). % 0.42/0.70 % set(auto) -> set(auto_denials). % 0.42/0.70 % set(auto) -> set(auto_process). % 0.42/0.70 % set(auto2) -> assign(new_constants, 1). % 0.42/0.70 % set(auto2) -> assign(fold_denial_max, 3). % 0.42/0.70 % set(auto2) -> assign(max_weight, "200.000"). % 0.42/0.70 % set(auto2) -> assign(max_hours, 1). % 0.42/0.70 % assign(max_hours, 1) -> assign(max_seconds, 3600). % 0.42/0.70 % set(auto2) -> assign(max_seconds, 0). % 0.42/0.70 % set(auto2) -> assign(max_minutes, 5). % 0.42/0.70 % assign(max_minutes, 5) -> assign(max_seconds, 300). % 0.42/0.70 % set(auto2) -> set(sort_initial_sos). % 0.42/0.70 % set(auto2) -> assign(sos_limit, -1). % 0.42/0.70 % set(auto2) -> assign(lrs_ticks, 3000). % 0.42/0.70 % set(auto2) -> assign(max_megs, 400). % 0.42/0.70 % set(auto2) -> assign(stats, some). % 0.42/0.70 % set(auto2) -> clear(echo_input). % 0.42/0.70 % set(auto2) -> set(quiet). % 0.42/0.70 % set(auto2) -> clear(print_initial_clauses). % 0.42/0.70 % set(auto2) -> clear(print_given). % 0.42/0.70 assign(lrs_ticks,-1). % 0.42/0.70 assign(sos_limit,10000). % 0.42/0.70 assign(order,kbo). % 0.42/0.70 set(lex_order_vars). % 0.42/0.70 clear(print_given). % 0.42/0.70 % 0.42/0.70 % formulas(sos). % not echoed (7 formulas) % 0.42/0.70 % 0.42/0.70 ============================== end of input ========================== % 0.42/0.70 % 0.42/0.70 % From the command line: assign(max_seconds, 300). % 0.42/0.70 % 0.42/0.70 ============================== PROCESS NON-CLAUSAL FORMULAS ========== % 0.42/0.70 % 0.42/0.70 % Formulas that are not ordinary clauses: % 0.42/0.70 1 (all X proj1S(s(X)) = X) # label(axiom_001) # label(axiom) # label(non_clause). [assumption]. % 0.42/0.70 2 (all X z != s(X)) # label(axiom_002) # label(axiom) # label(non_clause). [assumption]. % 0.42/0.70 3 (all Y x2(z,Y) = Y) # label(axiom_003) # label(axiom) # label(non_clause). [assumption]. % 0.42/0.70 4 (all Y all N x2(s(N),Y) = s(x2(N,Y))) # label(axiom_004) # label(axiom) # label(non_clause). [assumption]. % 0.42/0.70 5 (all Y x22(z,Y) = z) # label(axiom_005) # label(axiom) # label(non_clause). [assumption]. % 0.42/0.70 6 (all Y all N x22(s(N),Y) = x2(Y,x22(N,Y))) # label(axiom_006) # label(axiom) # label(non_clause). [assumption]. % 0.42/0.70 7 -(exists X x22(X,X) != X) # label(goal_007) # label(negated_conjecture) # label(non_clause). [assumption]. % 0.42/0.70 % 0.42/0.70 ============================== end of process non-clausal formulas === % 0.42/0.70 % 0.42/0.70 ============================== PROCESS INITIAL CLAUSES =============== % 0.42/0.70 % 0.42/0.70 ============================== PREDICATE ELIMINATION ================= % 0.42/0.70 % 0.42/0.70 ============================== end predicate elimination ============= % 0.42/0.70 % 0.42/0.70 Auto_denials: % 0.42/0.70 % copying label axiom_002 to answer in negative clause % 0.42/0.70 % 0.42/0.70 Term ordering decisions: % 0.42/0.70 Function symbol KB weights: z=1. x2=1. x22=1. s=1. proj1S=1. % 0.42/0.70 % 0.42/0.70 ============================== end of process initial clauses ======== % 0.42/0.70 % 0.42/0.70 ============================== CLAUSES FOR SEARCH ==================== % 0.42/0.70 % 0.42/0.70 ============================== end of clauses for search ============= % 0.42/0.70 % 0.42/0.70 ============================== SEARCH ================================ % 0.42/0.70 % 0.42/0.70 % Starting search at 0.01 seconds. % 0.42/0.70 % 0.42/0.70 ============================== PROOF ================================= % 0.42/0.70 % SZS status Theorem % 0.42/0.70 % SZS output start Refutation % 0.42/0.70 % 0.42/0.70 % Proof 1 at 0.01 (+ 0.00) seconds: axiom_002. % 0.42/0.70 % Length of proof is 29. % 0.42/0.70 % Level of proof is 10. % 0.42/0.70 % Maximum clause weight is 13.000. % 0.42/0.70 % Given clauses 26. % 0.42/0.70 % 0.42/0.70 1 (all X proj1S(s(X)) = X) # label(axiom_001) # label(axiom) # label(non_clause). [assumption]. % 0.42/0.70 2 (all X z != s(X)) # label(axiom_002) # label(axiom) # label(non_clause). [assumption]. % 0.42/0.70 3 (all Y x2(z,Y) = Y) # label(axiom_003) # label(axiom) # label(non_clause). [assumption]. % 0.42/0.70 4 (all Y all N x2(s(N),Y) = s(x2(N,Y))) # label(axiom_004) # label(axiom) # label(non_clause). [assumption]. % 0.42/0.70 5 (all Y x22(z,Y) = z) # label(axiom_005) # label(axiom) # label(non_clause). [assumption]. % 0.42/0.70 6 (all Y all N x22(s(N),Y) = x2(Y,x22(N,Y))) # label(axiom_006) # label(axiom) # label(non_clause). [assumption]. % 0.42/0.70 7 -(exists X x22(X,X) != X) # label(goal_007) # label(negated_conjecture) # label(non_clause). [assumption]. % 0.42/0.70 8 proj1S(s(A)) = A # label(axiom_001) # label(axiom). [clausify(1)]. % 0.42/0.70 9 x2(z,A) = A # label(axiom_003) # label(axiom). [clausify(3)]. % 0.42/0.70 10 x22(z,A) = z # label(axiom_005) # label(axiom). [clausify(5)]. % 0.42/0.70 11 x22(A,A) = A # label(goal_007) # label(negated_conjecture). [clausify(7)]. % 0.42/0.70 12 x2(s(A),B) = s(x2(A,B)) # label(axiom_004) # label(axiom). [clausify(4)]. % 0.42/0.70 13 s(x2(A,B)) = x2(s(A),B). [copy(12),flip(a)]. % 0.42/0.70 14 x22(s(A),B) = x2(B,x22(A,B)) # label(axiom_006) # label(axiom). [clausify(6)]. % 0.42/0.70 15 x2(A,x22(B,A)) = x22(s(B),A). [copy(14),flip(a)]. % 0.42/0.70 16 s(A) != z # label(axiom_002) # label(axiom) # answer(axiom_002). [clausify(2)]. % 0.42/0.70 17 proj1S(x2(s(A),B)) = x2(A,B). [para(13(a,1),8(a,1,1))]. % 0.42/0.70 18 x2(s(z),A) = s(A). [para(9(a,1),13(a,1,1)),flip(a)]. % 0.42/0.70 20 x22(s(z),A) = x2(A,z). [para(10(a,1),15(a,1,2)),flip(a)]. % 0.42/0.70 24 proj1S(x2(x2(s(A),B),C)) = x2(x2(A,B),C). [para(13(a,1),17(a,1,1,1))]. % 0.42/0.70 35 x2(s(s(z)),A) = s(s(A)). [para(18(a,1),13(a,1,1)),flip(a)]. % 0.42/0.70 38 x22(s(s(z)),A) = x2(A,x2(A,z)). [para(20(a,1),15(a,1,2)),flip(a)]. % 0.42/0.70 54 x2(s(s(s(z))),A) = s(s(s(A))). [para(35(a,1),13(a,1,1)),flip(a)]. % 0.42/0.70 71 s(s(s(s(z)))) = s(s(z)). [para(38(a,1),11(a,1)),rewrite([35(8),35(7)])]. % 0.42/0.70 75 s(s(s(z))) = s(z). [para(71(a,1),8(a,1,1)),rewrite([8(4)]),flip(a)]. % 0.42/0.70 78 s(s(s(A))) = s(A). [back_rewrite(54),rewrite([75(4),18(3)]),flip(a)]. % 0.42/0.70 82 x2(s(s(A)),B) = x2(A,B). [para(35(a,1),24(a,2,1)),rewrite([78(4),18(3),17(3)]),flip(a)]. % 0.42/0.70 88 s(s(A)) = A. [back_rewrite(35),rewrite([82(4),9(2)]),flip(a)]. % 0.42/0.70 89 $F # answer(axiom_002). [resolve(88,a,16,a)]. % 0.42/0.70 % 0.42/0.70 % SZS output end Refutation % 0.42/0.70 ============================== end of proof ========================== % 0.42/0.70 % 0.42/0.70 ============================== STATISTICS ============================ % 0.42/0.70 % 0.42/0.70 Given=26. Generated=264. Kept=79. proofs=1. % 0.42/0.70 Usable=24. Sos=40. Demods=34. Limbo=6, Disabled=15. Hints=0. % 0.42/0.70 Megabytes=0.11. % 0.42/0.70 User_CPU=0.01, System_CPU=0.00, Wall_clock=0. % 0.42/0.70 % 0.42/0.70 ============================== end of statistics ===================== % 0.42/0.70 % 0.42/0.70 ============================== end of search ========================= % 0.42/0.70 % 0.42/0.70 THEOREM PROVED % 0.42/0.70 % SZS status Theorem % 0.42/0.70 % 0.42/0.70 Exiting with 1 proof. % 0.42/0.70 % 0.42/0.70 Process 22852 exit (max_proofs) Wed Apr 29 00:50:46 2026 % 0.42/0.70 Prover9 interrupted %------------------------------------------------------------------------------