0.00/0.11 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.11/0.12 % Command : tptp2X_and_run_prover9 %d %s 0.11/0.33 % Computer : n028.cluster.edu 0.11/0.33 % Model : x86_64 x86_64 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.11/0.33 % Memory : 8042.1875MB 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64 0.11/0.33 % CPULimit : 960 0.11/0.33 % DateTime : Thu Jul 2 15:25:53 EDT 2020 0.11/0.33 % CPUTime : 0.84/1.52 ============================== Prover9 =============================== 0.84/1.52 Prover9 (32) version 2009-11A, November 2009. 0.84/1.52 Process 1116 was started by sandbox2 on n028.cluster.edu, 0.84/1.52 Thu Jul 2 15:25:55 2020 0.84/1.52 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 960 -f /tmp/Prover9_892_n028.cluster.edu". 0.84/1.52 ============================== end of head =========================== 0.84/1.52 0.84/1.52 ============================== INPUT ================================= 0.84/1.52 0.84/1.52 % Reading from file /tmp/Prover9_892_n028.cluster.edu 0.84/1.52 0.84/1.52 set(prolog_style_variables). 0.84/1.52 set(auto2). 0.84/1.52 % set(auto2) -> set(auto). 0.84/1.52 % set(auto) -> set(auto_inference). 0.84/1.52 % set(auto) -> set(auto_setup). 0.84/1.52 % set(auto_setup) -> set(predicate_elim). 0.84/1.52 % set(auto_setup) -> assign(eq_defs, unfold). 0.84/1.52 % set(auto) -> set(auto_limits). 0.84/1.52 % set(auto_limits) -> assign(max_weight, "100.000"). 0.84/1.52 % set(auto_limits) -> assign(sos_limit, 20000). 0.84/1.52 % set(auto) -> set(auto_denials). 0.84/1.52 % set(auto) -> set(auto_process). 0.84/1.52 % set(auto2) -> assign(new_constants, 1). 0.84/1.52 % set(auto2) -> assign(fold_denial_max, 3). 0.84/1.52 % set(auto2) -> assign(max_weight, "200.000"). 0.84/1.52 % set(auto2) -> assign(max_hours, 1). 0.84/1.52 % assign(max_hours, 1) -> assign(max_seconds, 3600). 0.84/1.52 % set(auto2) -> assign(max_seconds, 0). 0.84/1.52 % set(auto2) -> assign(max_minutes, 5). 0.84/1.52 % assign(max_minutes, 5) -> assign(max_seconds, 300). 0.84/1.52 % set(auto2) -> set(sort_initial_sos). 0.84/1.52 % set(auto2) -> assign(sos_limit, -1). 0.84/1.52 % set(auto2) -> assign(lrs_ticks, 3000). 0.84/1.52 % set(auto2) -> assign(max_megs, 400). 0.84/1.52 % set(auto2) -> assign(stats, some). 0.84/1.52 % set(auto2) -> clear(echo_input). 0.84/1.52 % set(auto2) -> set(quiet). 0.84/1.52 % set(auto2) -> clear(print_initial_clauses). 0.84/1.52 % set(auto2) -> clear(print_given). 0.84/1.52 assign(lrs_ticks,-1). 0.84/1.52 assign(sos_limit,10000). 0.84/1.52 assign(order,kbo). 0.84/1.52 set(lex_order_vars). 0.84/1.52 clear(print_given). 0.84/1.52 0.84/1.52 % formulas(sos). % not echoed (50 formulas) 0.84/1.52 0.84/1.52 ============================== end of input ========================== 0.84/1.52 0.84/1.52 % From the command line: assign(max_seconds, 960). 0.84/1.52 0.84/1.52 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 0.84/1.52 0.84/1.52 % Formulas that are not ordinary clauses: 0.84/1.52 1 (all A all X (mem(X,A) -> X = ap(i(A),X))) # label(ibeta) # label(axiom) # label(non_clause). [assumption]. 0.84/1.52 2 (all Q (mem(Q,bool) -> (all R (mem(R,bool) -> ((p(Q) <-> p(R)) -> R = Q))))) # label(boolext) # label(axiom) # label(non_clause). [assumption]. 0.84/1.52 3 (all A (ne(A) -> (all B (ne(B) -> ne(arr(A,B)))))) # label(arr_ne) # label(axiom) # label(non_clause). [assumption]. 0.84/1.52 4 (all A all B all F (mem(F,arr(A,B)) -> (all G (mem(G,arr(A,B)) -> ((all X (mem(X,A) -> ap(F,X) = ap(G,X))) -> F = G))))) # label(funcext) # label(axiom) # label(non_clause). [assumption]. 0.84/1.52 5 (all A all Y all X (mem(X,A) -> Y = ap(k(A,Y),X))) # label(kbeta) # label(axiom) # label(non_clause). [assumption]. 0.84/1.52 6 (all A all B all F (mem(F,arr(A,B)) -> (all X (mem(X,A) -> mem(ap(F,X),B))))) # label(ap_tp) # label(axiom) # label(non_clause). [assumption]. 0.84/1.52 7 (all V0t (mem(V0t,bool) -> (p(V0t) <-> p(V0t)) & (p(V0t) <-> p(V0t)) & (p(V0t) & $F <-> $F) & (p(V0t) <-> p(V0t) & p(V0t)) & ($F <-> $F & p(V0t)))) # label(conj_thm_2Ebool_2EAND__CLAUSES) # label(axiom) # label(non_clause). [assumption]. 0.84/1.52 8 $T # label(conj_thm_2Ebool_2ETRUTH) # label(axiom) # label(non_clause). [assumption]. 0.84/1.52 9 (all A (ne(A) -> (all Q (mem(Q,arr(A,bool)) -> (p(ap(c_2Ebool_2E_21(A),Q)) <-> (all X (mem(X,A) -> p(ap(Q,X))))))))) # label(ax_all_p) # label(axiom) # label(non_clause). [assumption]. 0.84/1.52 10 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0e (mem(V0e,A_27b) -> (all V1f (mem(V1f,arr(A_27a,A_27b)) -> (all V2e (mem(V2e,ty_2Eoption_2Eoption(A_27a)) -> (all V5x (mem(V5x,A_27a) -> ap(c_2Eoption_2ETHE(A_27a),ap(c_2Eoption_2ESOME(A_27a),V5x)) = V5x)) & (all V6x (mem(V6x,A_27a) -> ap(c_2Eoption_2ESOME(A_27a),V6x) != c_2Eoption_2ENONE(A_27a))) & (all V8x (mem(V8x,A_27a) -> (p(ap(c_2Eoption_2EIS__SOME(A_27a),ap(c_2Eoption_2ESOME(A_27a),V8x))) <-> $T))) & (all V11x (mem(V11x,ty_2Eoption_2Eoption(A_27a)) -> (p(ap(c_2Eoption_2EIS__SOME(A_27a),V11x)) -> V11x = ap(c_2Eoption_2ESOME(A_27a),ap(c_2Eoption_2ETHE(A_27a),V11x))))) & (all V13x (mem(V13x,ty_2Eoption_2Eoption(A_27a)) -> V13x = ap(ap(ap(c_2Eoption_2Eoption__CASE(A_27a,ty_2Eoption_2Eoption(A_27a)),V13x),V13x),c_2Eoption_2ESOME(A_27a)))) & (all V16x (mem(V16x,ty_2Eoption_2Eoption(A_27a)) -> (p(ap(c_2Eoption_2EIS__SOME(A_27a),V16x)) -> V16x = ap(ap(ap(c_2Eoption_2Eoption__CASE(A_27a,ty_2Eoption_2Eoption(A_27a)),V16x),V2e),c_2Eoption_2ESOME(A_27a))))) & (all V17v (mem(V17v,A_27b) -> (all V18f (mem(V18f,arr(A_27a,A_27b)) -> V17v = ap(ap(ap(c_2Eoption_2Eoption__CASE(A_27a,A_27b),c_2Eoption_2ENONE(A_27a)),V17v),V18f))))) & (all V19x (mem(V19x,A_27a) -> (all V20v (mem(V20v,A_27b) -> (all V21f (mem(V21f,arr(A_27a,A_27b)) -> ap(V21f,V19x) = ap(ap(ap(c_2Eoption_2Eoption__CASE(A_27a,A_27b),ap(c_2Eoption_2ESOME(A_27a),V19x)),V20v),V21f))))))) & c_2Eoption_2ENONE(A_27a) = ap(c_2Eoption_2EOPTION__JOIN(A_27a),c_2Eoption_2ENONE(ty_2Eoption_2Eoption(A_27a))) & (all V25x (mem(V25x,ty_2Eoption_2Eoption(A_27a)) -> V25x = ap(c_2Eoption_2EOPTION__JOIN(A_27a),ap(c_2Eoption_2ESOME(ty_2Eoption_2Eoption(A_27a)),V25x)))) & (all V24f (mem(V24f,arr(A_27a,A_27b)) -> c_2Eoption_2ENONE(A_27b) = ap(ap(c_2Eoption_2EOPTION__MAP(A_27a,A_27b),V24f),c_2Eoption_2ENONE(A_27a)))) & (all V22f (mem(V22f,arr(A_27a,A_27b)) -> (all V23x (mem(V23x,A_27a) -> ap(ap(c_2Eoption_2EOPTION__MAP(A_27a,A_27b),V22f),ap(c_2Eoption_2ESOME(A_27a),V23x)) = ap(c_2Eoption_2ESOME(A_27b),ap(V22f,V23x)))))) & (all V15x (mem(V15x,ty_2Eoption_2Eoption(A_27a)) -> (p(ap(c_2Eoption_2EIS__SOME(A_27a),V15x)) -> ap(ap(ap(c_2Eoption_2Eoption__CASE(A_27a,A_27b),V15x),V0e),V1f) = ap(V1f,ap(c_2Eoption_2ETHE(A_27a),V15x))))) & (all V14x (mem(V14x,ty_2Eoption_2Eoption(A_27a)) -> (p(ap(c_2Eoption_2EIS__NONE(A_27a),V14x)) -> V0e = ap(ap(ap(c_2Eoption_2Eoption__CASE(A_27a,A_27b),V14x),V0e),V1f)))) & (all V12x (mem(V12x,ty_2Eoption_2Eoption(A_27a)) -> ap(ap(ap(c_2Eoption_2Eoption__CASE(A_27a,ty_2Eoption_2Eoption(A_27a)),V12x),c_2Eoption_2ENONE(A_27a)),c_2Eoption_2ESOME(A_27a)) = V12x)) & (all V10x (mem(V10x,ty_2Eoption_2Eoption(A_27a)) -> (V10x = c_2Eoption_2ENONE(A_27a) <-> -p(ap(c_2Eoption_2EIS__SOME(A_27a),V10x))))) & (all V9x (mem(V9x,ty_2Eoption_2Eoption(A_27a)) -> (c_2Eoption_2ENONE(A_27a) = V9x <-> p(ap(c_2Eoption_2EIS__NONE(A_27a),V9x))))) & (p(ap(c_2Eoption_2EIS__SOME(A_27a),c_2Eoption_2ENONE(A_27a))) <-> $F) & (all V7x (mem(V7x,A_27a) -> ap(c_2Eoption_2ESOME(A_27a),V7x) != c_2Eoption_2ENONE(A_27a))) & (all V3x (mem(V3x,A_27a) -> (all V4y (mem(V4y,A_27a) -> (ap(c_2Eoption_2ESOME(A_27a),V4y) = ap(c_2Eoption_2ESOME(A_27a),V3x) <-> V3x = V4y))))))))))))))) # label(conj_thm_2Eoption_2Eoption__CLAUSES) # label(axiom) # label(non_clause). [assumption]. 0.84/1.52 11 -$F <-> $T # label(conj_thm_2Ebool_2ENOT__CLAUSES_AndLHS) # label(axiom) # label(non_clause). [assumption]. 0.84/1.52 12 -$T <-> $F # label(conj_thm_2Ebool_2ENOT__CLAUSES_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 0.84/1.52 13 (all V0t (mem(V0t,bool) -> (--p(V0t) <-> p(V0t)))) # label(conj_thm_2Ebool_2ENOT__CLAUSES_AndRHS_AndRHS) # label(axiom) # label(non_clause). [assumption]. 0.84/1.52 14 (all V0t1 (mem(V0t1,bool) -> (all V1t2 (mem(V1t2,bool) -> ((p(V0t1) -> p(V1t2)) -> ((p(V1t2) -> p(V0t1)) -> (p(V1t2) <-> p(V0t1)))))))) # label(conj_thm_2Ebool_2EIMP__ANTISYM__AX) # label(axiom) # label(non_clause). [assumption]. 0.84/1.52 15 (all Q (mem(Q,bool) -> (all R (mem(R,bool) -> (p(R) & p(Q) <-> p(ap(ap(c_2Ebool_2E_2F_5C,Q),R))))))) # label(ax_and_p) # label(axiom) # label(non_clause). [assumption]. 0.84/1.52 16 (all A_27a (ne(A_27a) -> mem(c_2Eoption_2EIS__SOME(A_27a),arr(ty_2Eoption_2Eoption(A_27a),bool)))) # label(mem_c_2Eoption_2EIS__SOME) # label(axiom) # label(non_clause). [assumption]. 0.84/1.52 17 (all A_27a (ne(A_27a) -> mem(c_2Eoption_2EOPTION__JOIN(A_27a),arr(ty_2Eoption_2Eoption(ty_2Eoption_2Eoption(A_27a)),ty_2Eoption_2Eoption(A_27a))))) # label(mem_c_2Eoption_2EOPTION__JOIN) # label(axiom) # label(non_clause). [assumption]. 0.84/1.52 18 (all A_27a (ne(A_27a) -> (all V0t (mem(V0t,bool) -> ((exists V1x (mem(V1x,A_27a) & p(V0t))) <-> p(V0t)))))) # label(conj_thm_2Ebool_2EEXISTS__SIMP) # label(axiom) # label(non_clause). [assumption]. 0.84/1.53 19 (all A_27a (ne(A_27a) -> mem(c_2Emin_2E_3D(A_27a),arr(A_27a,arr(A_27a,bool))))) # label(mem_c_2Emin_2E_3D) # label(axiom) # label(non_clause). [assumption]. 0.84/1.53 20 (all A_27a (ne(A_27a) -> mem(c_2Eoption_2EIS__NONE(A_27a),arr(ty_2Eoption_2Eoption(A_27a),bool)))) # label(mem_c_2Eoption_2EIS__NONE) # label(axiom) # label(non_clause). [assumption]. 0.84/1.53 21 (all A (ne(A) -> (all X (mem(X,A) -> (all Y (mem(Y,A) -> (p(ap(ap(c_2Emin_2E_3D(A),X),Y)) <-> X = Y))))))) # label(ax_eq_p) # label(axiom) # label(non_clause). [assumption]. 0.84/1.53 22 (all V0t (mem(V0t,bool) -> (($T <-> p(V0t)) <-> p(V0t)) & (-p(V0t) <-> (p(V0t) <-> $F)) & (($F <-> p(V0t)) <-> -p(V0t)) & (p(V0t) <-> ($T <-> p(V0t))))) # label(conj_thm_2Ebool_2EEQ__CLAUSES) # label(axiom) # label(non_clause). [assumption]. 0.84/1.53 23 (all A0 (ne(A0) -> ne(ty_2Eoption_2Eoption(A0)))) # label(ne_ty_2Eoption_2Eoption) # label(axiom) # label(non_clause). [assumption]. 0.84/1.53 24 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27b,bool))) -> (all V1x (mem(V1x,ty_2Eoption_2Eoption(A_27a)) -> (all V2y (mem(V2y,ty_2Eoption_2Eoption(A_27b)) -> (p(ap(ap(ap(c_2Eoption_2EOPTREL(A_27a,A_27b),V0R),V1x),V2y)) <-> V1x = c_2Eoption_2ENONE(A_27a) & c_2Eoption_2ENONE(A_27b) = V2y | (exists V3x0 ((exists V4y0 (mem(V4y0,A_27b) & ap(c_2Eoption_2ESOME(A_27a),V3x0) = V1x & p(ap(ap(V0R,V3x0),V4y0)) & V2y = ap(c_2Eoption_2ESOME(A_27b),V4y0))) & mem(V3x0,A_27a)))))))))))))) # label(ax_thm_2Eoption_2EOPTREL__def) # label(axiom) # label(non_clause). [assumption]. 0.84/1.53 25 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Eoption_2EOPTREL(A_27a,A_27b),arr(arr(A_27a,arr(A_27b,bool)),arr(ty_2Eoption_2Eoption(A_27a),arr(ty_2Eoption_2Eoption(A_27b),bool)))))))) # label(mem_c_2Eoption_2EOPTREL) # label(axiom) # label(non_clause). [assumption]. 0.84/1.53 26 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> (V0x = V0x <-> $T))))) # label(conj_thm_2Ebool_2EREFL__CLAUSE) # label(axiom) # label(non_clause). [assumption]. 0.84/1.53 27 (all V0t (mem(V0t,bool) -> ($F -> p(V0t)))) # label(conj_thm_2Ebool_2EFALSITY) # label(axiom) # label(non_clause). [assumption]. 0.84/1.53 28 (all V0t (mem(V0t,bool) -> (p(V0t) <-> p(V0t)) & (p(V0t) <-> p(V0t)) & (p(V0t) | p(V0t) <-> p(V0t)) & (p(V0t) | $T <-> $T) & (p(V0t) | $T <-> $T))) # label(conj_thm_2Ebool_2EOR__CLAUSES) # label(axiom) # label(non_clause). [assumption]. 0.84/1.53 29 (all A_27a (ne(A_27a) -> mem(c_2Eoption_2ETHE(A_27a),arr(ty_2Eoption_2Eoption(A_27a),A_27a)))) # label(mem_c_2Eoption_2ETHE) # label(axiom) # label(non_clause). [assumption]. 0.84/1.53 30 (all Q (mem(Q,bool) -> (-p(Q) <-> p(ap(c_2Ebool_2E_7E,Q))))) # label(ax_neg_p) # label(axiom) # label(non_clause). [assumption]. 0.84/1.53 31 (all A_27a (ne(A_27a) -> mem(c_2Ebool_2E_3F(A_27a),arr(arr(A_27a,bool),bool)))) # label(mem_c_2Ebool_2E_3F) # label(axiom) # label(non_clause). [assumption]. 0.84/1.53 32 (all A_27a (ne(A_27a) -> mem(c_2Eoption_2ENONE(A_27a),ty_2Eoption_2Eoption(A_27a)))) # label(mem_c_2Eoption_2ENONE) # label(axiom) # label(non_clause). [assumption]. 0.84/1.53 33 (all A_27a (ne(A_27a) -> mem(c_2Eoption_2ESOME(A_27a),arr(A_27a,ty_2Eoption_2Eoption(A_27a))))) # label(mem_c_2Eoption_2ESOME) # label(axiom) # label(non_clause). [assumption]. 0.84/1.53 34 (all Q (mem(Q,bool) -> (all R (mem(R,bool) -> ((p(Q) -> p(R)) <-> p(ap(ap(c_2Emin_2E_3D_3D_3E,Q),R))))))) # label(ax_imp_p) # label(axiom) # label(non_clause). [assumption]. 0.84/1.53 35 (all A_27a (ne(A_27a) -> mem(c_2Ebool_2E_21(A_27a),arr(arr(A_27a,bool),bool)))) # label(mem_c_2Ebool_2E_21) # label(axiom) # label(non_clause). [assumption]. 0.84/1.53 36 (all A (ne(A) -> (all Q (mem(Q,arr(A,bool)) -> (p(ap(c_2Ebool_2E_3F(A),Q)) <-> (exists X (mem(X,A) & p(ap(Q,X))))))))) # label(ax_ex_p) # label(axiom) # label(non_clause). [assumption]. 0.84/1.53 37 (all Q (mem(Q,bool) -> (all R (mem(R,bool) -> (p(ap(ap(c_2Ebool_2E_5C_2F,Q),R)) <-> p(Q) | p(R)))))) # label(ax_or_p) # label(axiom) # label(non_clause). [assumption]. 0.84/1.53 38 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Eoption_2Eoption__CASE(A_27a,A_27b),arr(ty_2Eoption_2Eoption(A_27a),arr(A_27b,arr(arr(A_27a,A_27b),A_27b)))))))) # label(mem_c_2Eoption_2Eoption_Alarm clock 119.14/120.05 Prover9 interrupted 119.14/120.05 EOF