%------------------------------------------------------------------------------ % File : Prover9---1109a % Problem : SWX222-1 : TPTP v9.3.0. Released v9.3.0. % Transfm : none % Format : tptp:raw % Command : tptp2X_and_run_prover9 %d %s % Computer : n031.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 02:38:07 PM UTC 2026 % Result : Unsatisfiable 0.70s 1.04s % Output : Refutation 0.70s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SWX222-1 : TPTP v9.3.0. Released v9.3.0. % 0.11/0.12 % Command : tptp2X_and_run_prover9 %d %s % 0.16/0.33 % Computer : n031.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 % 0.16/0.34 % CPULimit : 300 % 0.16/0.34 % WCLimit : 300 % 0.16/0.34 % DateTime : Wed Apr 29 02:11:47 EDT 2026 % 0.16/0.34 % CPUTime : % 0.70/1.04 ============================== Prover9 =============================== % 0.70/1.04 Prover9 (32) version 2009-11A, November 2009. % 0.70/1.04 Process 1434 was started by sandbox on n031.cluster.edu, % 0.70/1.04 Wed Apr 29 02:11:48 2026 % 0.70/1.04 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_1204_n031.cluster.edu". % 0.70/1.04 ============================== end of head =========================== % 0.70/1.04 % 0.70/1.04 ============================== INPUT ================================= % 0.70/1.04 % 0.70/1.04 % Reading from file /tmp/Prover9_1204_n031.cluster.edu % 0.70/1.04 % 0.70/1.04 set(prolog_style_variables). % 0.70/1.04 set(auto2). % 0.70/1.04 % set(auto2) -> set(auto). % 0.70/1.04 % set(auto) -> set(auto_inference). % 0.70/1.04 % set(auto) -> set(auto_setup). % 0.70/1.04 % set(auto_setup) -> set(predicate_elim). % 0.70/1.04 % set(auto_setup) -> assign(eq_defs, unfold). % 0.70/1.04 % set(auto) -> set(auto_limits). % 0.70/1.04 % set(auto_limits) -> assign(max_weight, "100.000"). % 0.70/1.04 % set(auto_limits) -> assign(sos_limit, 20000). % 0.70/1.04 % set(auto) -> set(auto_denials). % 0.70/1.04 % set(auto) -> set(auto_process). % 0.70/1.04 % set(auto2) -> assign(new_constants, 1). % 0.70/1.04 % set(auto2) -> assign(fold_denial_max, 3). % 0.70/1.04 % set(auto2) -> assign(max_weight, "200.000"). % 0.70/1.04 % set(auto2) -> assign(max_hours, 1). % 0.70/1.04 % assign(max_hours, 1) -> assign(max_seconds, 3600). % 0.70/1.04 % set(auto2) -> assign(max_seconds, 0). % 0.70/1.04 % set(auto2) -> assign(max_minutes, 5). % 0.70/1.04 % assign(max_minutes, 5) -> assign(max_seconds, 300). % 0.70/1.04 % set(auto2) -> set(sort_initial_sos). % 0.70/1.04 % set(auto2) -> assign(sos_limit, -1). % 0.70/1.04 % set(auto2) -> assign(lrs_ticks, 3000). % 0.70/1.04 % set(auto2) -> assign(max_megs, 400). % 0.70/1.04 % set(auto2) -> assign(stats, some). % 0.70/1.04 % set(auto2) -> clear(echo_input). % 0.70/1.04 % set(auto2) -> set(quiet). % 0.70/1.04 % set(auto2) -> clear(print_initial_clauses). % 0.70/1.04 % set(auto2) -> clear(print_given). % 0.70/1.04 assign(lrs_ticks,-1). % 0.70/1.04 assign(sos_limit,10000). % 0.70/1.04 assign(order,kbo). % 0.70/1.04 set(lex_order_vars). % 0.70/1.04 clear(print_given). % 0.70/1.04 % 0.70/1.04 % formulas(sos). % not echoed (56 formulas) % 0.70/1.04 % 0.70/1.04 ============================== end of input ========================== % 0.70/1.04 % 0.70/1.04 % From the command line: assign(max_seconds, 300). % 0.70/1.04 % 0.70/1.04 ============================== PROCESS NON-CLAUSAL FORMULAS ========== % 0.70/1.04 % 0.70/1.04 % Formulas that are not ordinary clauses: % 0.70/1.04 % 0.70/1.04 ============================== end of process non-clausal formulas === % 0.70/1.04 % 0.70/1.04 ============================== PROCESS INITIAL CLAUSES =============== % 0.70/1.04 % 0.70/1.04 ============================== PREDICATE ELIMINATION ================= % 0.70/1.04 % 0.70/1.04 ============================== end predicate elimination ============= % 0.70/1.04 % 0.70/1.04 Auto_denials: % 0.70/1.04 % copying label goal to answer in negative clause % 0.70/1.04 % 0.70/1.04 Term ordering decisions: % 0.70/1.04 Function symbol KB weights: bfalse=1. btrue=1. b=1. a=1. c=1. zero=1. nil=1. nothing=1. eq=1. eq3=1. arr=1. andb=1. eq2=1. index=1. cons=1. eq4=1. lam=1. nf=1. var=1. suc=1. notb=1. just=1. sat_synth_nf_k=1. app=1. tc=1. aux=1. % 0.70/1.04 % 0.70/1.04 ============================== end of process initial clauses ======== % 0.70/1.04 % 0.70/1.04 ============================== CLAUSES FOR SEARCH ==================== % 0.70/1.04 % 0.70/1.04 ============================== end of clauses for search ============= % 0.70/1.04 % 0.70/1.04 ============================== SEARCH ================================ % 0.70/1.04 % 0.70/1.04 % Starting search at 0.02 seconds. % 0.70/1.04 % 0.70/1.04 ============================== PROOF ================================= % 0.70/1.04 % SZS status Unsatisfiable % 0.70/1.04 % SZS output start Refutation % 0.70/1.04 % 0.70/1.04 % Proof 1 at 0.03 (+ 0.00) seconds: goal. % 0.70/1.04 % Length of proof is 18. % 0.70/1.04 % Level of proof is 4. % 0.70/1.04 % Maximum clause weight is 16.000. % 0.70/1.04 % Given clauses 75. % 0.70/1.04 % 0.70/1.04 1 notb(btrue) = bfalse # label(axiom_002) # label(axiom). [assumption]. % 0.70/1.04 4 andb(btrue,A) = A # label(axiom_007) # label(axiom). [assumption]. % 0.70/1.04 6 nf(var(A)) = btrue # label(axiom_013) # label(axiom). [assumption]. % 0.70/1.04 15 eq(A,A) = btrue # label(axiom_051) # label(axiom). [assumption]. % 0.70/1.04 18 eq4(A,A) = btrue # label(axiom_054) # label(axiom). [assumption]. % 0.70/1.04 19 nf(lam(A)) = nf(A) # label(axiom_012) # label(axiom). [assumption]. % 0.70/1.04 34 index(cons(A,B),zero) = just(A) # label(axiom_005) # label(axiom). [assumption]. % 0.70/1.04 44 aux(A,B,C,just(D)) = eq(D,B) # label(axiom_001) # label(axiom). [assumption]. % 0.70/1.04 48 tc(A,var(B),C) = aux(A,C,B,index(A,B)) # label(axiom_019) # label(axiom). [assumption]. % 0.70/1.04 49 aux(A,B,C,index(A,C)) = tc(A,var(C),B). [copy(48),flip(a)]. % 0.70/1.04 50 tc(A,lam(B),arr(C,D)) = tc(cons(C,A),B,D) # label(axiom_015) # label(axiom). [assumption]. % 0.70/1.04 51 sat_synth_nf_k(A) = notb(andb(nf(A),tc(nil,A,arr(a,arr(b,b))))) # label(axiom_020) # label(axiom). [assumption]. % 0.70/1.04 55 eq4(sat_synth_nf_k(A),bfalse) != btrue # label(goal) # label(negated_conjecture) # answer(goal). [assumption]. % 0.70/1.04 56 eq4(notb(andb(nf(A),tc(nil,A,arr(a,arr(b,b))))),bfalse) != btrue # answer(goal). [copy(55),rewrite([51(1)])]. % 0.70/1.04 66 tc(cons(A,B),var(zero),C) = eq(A,C). [para(34(a,1),49(a,1,4)),rewrite([44(4)]),flip(a)]. % 0.70/1.04 84 eq4(notb(andb(nf(A),tc(cons(a,nil),A,arr(b,b)))),bfalse) != btrue # answer(goal). [para(19(a,1),56(a,1,1,1,1)),rewrite([50(9)])]. % 0.70/1.04 159 eq4(notb(andb(nf(A),tc(cons(b,cons(a,nil)),A,b))),bfalse) != btrue # answer(goal). [para(19(a,1),84(a,1,1,1,1)),rewrite([50(9)])]. % 0.70/1.04 174 $F # answer(goal). [para(66(a,1),159(a,1,1,1,2)),rewrite([6(3),15(4),4(3),1(2),18(3)]),xx(a)]. % 0.70/1.04 % 0.70/1.04 % SZS output end Refutation % 0.70/1.04 ============================== end of proof ========================== % 0.70/1.04 % 0.70/1.04 ============================== STATISTICS ============================ % 0.70/1.04 % 0.70/1.04 Given=75. Generated=443. Kept=168. proofs=1. % 0.70/1.04 Usable=74. Sos=82. Demods=105. Limbo=3, Disabled=65. Hints=0. % 0.70/1.04 Megabytes=0.26. % 0.70/1.04 User_CPU=0.03, System_CPU=0.00, Wall_clock=0. % 0.70/1.04 % 0.70/1.04 ============================== end of statistics ===================== % 0.70/1.04 % 0.70/1.04 ============================== end of search ========================= % 0.70/1.04 % 0.70/1.04 THEOREM PROVED % 0.70/1.04 % SZS status Unsatisfiable % 0.70/1.04 % 0.70/1.04 Exiting with 1 proof. % 0.70/1.04 % 0.70/1.04 Process 1434 exit (max_proofs) Wed Apr 29 02:11:48 2026 % 0.70/1.04 Prover9 interrupted %------------------------------------------------------------------------------