0.07/0.11 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.07/0.12 % Command : tptp2X_and_run_prover9 %d %s 0.11/0.33 % Computer : n014.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 % WCLimit : 120 0.11/0.33 % DateTime : Tue Aug 9 01:57:16 EDT 2022 0.11/0.33 % CPUTime : 0.41/1.05 ============================== Prover9 =============================== 0.41/1.05 Prover9 (32) version 2009-11A, November 2009. 0.41/1.05 Process 5938 was started by sandbox2 on n014.cluster.edu, 0.41/1.05 Tue Aug 9 01:57:17 2022 0.41/1.05 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 960 -f /tmp/Prover9_5755_n014.cluster.edu". 0.41/1.05 ============================== end of head =========================== 0.41/1.05 0.41/1.05 ============================== INPUT ================================= 0.41/1.05 0.41/1.05 % Reading from file /tmp/Prover9_5755_n014.cluster.edu 0.41/1.05 0.41/1.05 set(prolog_style_variables). 0.41/1.05 set(auto2). 0.41/1.05 % set(auto2) -> set(auto). 0.41/1.05 % set(auto) -> set(auto_inference). 0.41/1.05 % set(auto) -> set(auto_setup). 0.41/1.05 % set(auto_setup) -> set(predicate_elim). 0.41/1.05 % set(auto_setup) -> assign(eq_defs, unfold). 0.41/1.05 % set(auto) -> set(auto_limits). 0.41/1.05 % set(auto_limits) -> assign(max_weight, "100.000"). 0.41/1.05 % set(auto_limits) -> assign(sos_limit, 20000). 0.41/1.05 % set(auto) -> set(auto_denials). 0.41/1.05 % set(auto) -> set(auto_process). 0.41/1.05 % set(auto2) -> assign(new_constants, 1). 0.41/1.05 % set(auto2) -> assign(fold_denial_max, 3). 0.41/1.05 % set(auto2) -> assign(max_weight, "200.000"). 0.41/1.05 % set(auto2) -> assign(max_hours, 1). 0.41/1.05 % assign(max_hours, 1) -> assign(max_seconds, 3600). 0.41/1.05 % set(auto2) -> assign(max_seconds, 0). 0.41/1.05 % set(auto2) -> assign(max_minutes, 5). 0.41/1.05 % assign(max_minutes, 5) -> assign(max_seconds, 300). 0.41/1.05 % set(auto2) -> set(sort_initial_sos). 0.41/1.05 % set(auto2) -> assign(sos_limit, -1). 0.41/1.05 % set(auto2) -> assign(lrs_ticks, 3000). 0.41/1.05 % set(auto2) -> assign(max_megs, 400). 0.41/1.05 % set(auto2) -> assign(stats, some). 0.41/1.05 % set(auto2) -> clear(echo_input). 0.41/1.05 % set(auto2) -> set(quiet). 0.41/1.05 % set(auto2) -> clear(print_initial_clauses). 0.41/1.05 % set(auto2) -> clear(print_given). 0.41/1.05 assign(lrs_ticks,-1). 0.41/1.05 assign(sos_limit,10000). 0.41/1.05 assign(order,kbo). 0.41/1.05 set(lex_order_vars). 0.41/1.05 clear(print_given). 0.41/1.05 0.41/1.05 % formulas(sos). % not echoed (96 formulas) 0.41/1.05 0.41/1.05 ============================== end of input ========================== 0.41/1.05 0.41/1.05 % From the command line: assign(max_seconds, 960). 0.41/1.05 0.41/1.05 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 0.41/1.05 0.41/1.05 % Formulas that are not ordinary clauses: 0.41/1.05 1 (all U (ssItem(U) -> (all V (ssItem(V) -> (all W (ssList(W) -> (all X (ssList(X) -> (frontsegP(cons(U,W),cons(V,X)) <-> frontsegP(W,X) & V = U))))))))) # label(ax44) # label(axiom) # label(non_clause). [assumption]. 0.41/1.05 2 (all U (ssList(U) -> (all V (ssList(V) -> (all W (ssList(W) -> (frontsegP(U,V) -> frontsegP(app(U,W),V)))))))) # label(ax43) # label(axiom) # label(non_clause). [assumption]. 0.41/1.05 3 (all U (ssItem(U) -> -memberP(nil,U))) # label(ax38) # label(axiom) # label(non_clause). [assumption]. 0.41/1.05 4 (all U (ssList(U) -> (all V (ssList(V) -> (U != nil -> hd(app(U,V)) = hd(U)))))) # label(ax85) # label(axiom) # label(non_clause). [assumption]. 0.41/1.05 5 (all U (ssList(U) -> rearsegP(U,nil))) # label(ax51) # label(axiom) # label(non_clause). [assumption]. 0.41/1.05 6 (all U (ssList(U) -> app(nil,U) = U)) # label(ax28) # label(axiom) # label(non_clause). [assumption]. 0.41/1.05 7 (all U (ssList(U) -> (all V (ssList(V) -> (all W (ssList(W) -> (app(W,V) = app(U,V) -> W = U))))))) # label(ax79) # label(axiom) # label(non_clause). [assumption]. 0.41/1.05 8 (all U (ssItem(U) -> (all V (ssItem(V) -> (all W (ssItem(W) -> (geq(V,W) & geq(U,V) -> geq(U,W)))))))) # label(ax88) # label(axiom) # label(non_clause). [assumption]. 0.41/1.05 9 (all U (ssItem(U) -> (all V (ssItem(V) -> (all W (ssItem(W) -> (gt(U,V) & gt(V,W) -> gt(U,W)))))))) # label(ax95) # label(axiom) # label(non_clause). [assumption]. 0.41/1.05 10 (all U (ssList(U) -> (all V (ssList(V) -> (all W (ssItem(W) -> (all X (ssItem(X) -> (cons(X,V) = cons(W,U) -> X = W & U = V))))))))) # label(ax19) # label(axiom) # label(non_clause). [assumption]. 0.41/1.05 11 (all U (ssList(U) -> (all V (ssList(V) -> ((exists W ((exists X (U = app(app(W,V),X) & ssList(X))) & ssList(W))) <-> segmentP(U,V)))))) # label(ax7) # label(axiom) # label(non_clause). [assumption]. 0.41/1.05 12 (all U (ssItem(U) -> totalorderedP(cons(U,nil)))) # label(ax65) # label(axiom) # label(non_clause). [assumption]. 0.41/1.05 13 (all U (ssItem(U) -> geq(U,U))) # label(ax89) # label(axiom) # label(non_clause). [assumption]. 0.41/1.05 14 (all U (ssList(U) -> (all V (ssList(V) -> ssList(app(U,V)))))) # label(ax26) # label(axiom) # label(non_clause). [assumption]. 0.41/1.05 15 (all U (ssList(U) -> (all V (ssItem(V) -> ssList(cons(V,U)))))) # label(ax16) # label(axiom) # label(non_clause). [assumption]. 0.41/1.05 16 (all U (ssItem(U) -> duplicatefreeP(cons(U,nil)))) # label(ax71) # label(axiom) # label(non_clause). [assumption]. 0.41/1.05 17 (all U (ssItem(U) -> totalorderP(cons(U,nil)))) # label(ax61) # label(axiom) # label(non_clause). [assumption]. 0.41/1.05 18 (all U (ssList(U) -> (all V (ssList(V) -> ((exists W (ssList(W) & app(V,W) = U)) <-> frontsegP(U,V)))))) # label(ax5) # label(axiom) # label(non_clause). [assumption]. 0.41/1.05 19 (all U (ssList(U) -> frontsegP(U,U))) # label(ax42) # label(axiom) # label(non_clause). [assumption]. 0.41/1.05 20 (all U (ssList(U) -> rearsegP(U,U))) # label(ax49) # label(axiom) # label(non_clause). [assumption]. 0.41/1.05 21 (all U (ssItem(U) -> (all V (ssItem(V) -> (all W (ssList(W) -> (memberP(cons(V,W),U) <-> memberP(W,U) | V = U))))))) # label(ax37) # label(axiom) # label(non_clause). [assumption]. 0.41/1.05 22 (all U (ssItem(U) -> strictorderP(cons(U,nil)))) # label(ax63) # label(axiom) # label(non_clause). [assumption]. 0.41/1.05 23 (all U (ssList(U) -> ((all V (ssItem(V) -> (all W (ssItem(W) -> (all X (ssList(X) -> (all Y (ssList(Y) -> (all Z (ssList(Z) -> (app(app(X,cons(V,Y)),cons(W,Z)) = U -> -(leq(V,W) & leq(W,V))))))))))))) <-> cyclefreeP(U)))) # label(ax8) # label(axiom) # label(non_clause). [assumption]. 0.41/1.05 24 (all U (ssList(U) -> (equalelemsP(U) <-> (all V (ssItem(V) -> (all W (ssItem(W) -> (all X (ssList(X) -> (all Y (ssList(Y) -> (app(X,cons(V,cons(W,Y))) = U -> V = W)))))))))))) # label(ax14) # label(axiom) # label(non_clause). [assumption]. 0.41/1.05 25 (all U (ssList(U) -> segmentP(U,U))) # label(ax55) # label(axiom) # label(non_clause). [assumption]. 0.41/1.05 26 (all U (ssList(U) -> (all V (ssList(V) -> (all W (ssList(W) -> (all X (ssList(X) -> (segmentP(U,V) -> segmentP(app(app(W,U),X),V)))))))))) # label(ax56) # label(axiom) # label(non_clause). [assumption]. 0.41/1.05 27 (all U (ssList(U) -> nil = U | (exists V ((exists W (cons(W,V) = U & ssItem(W))) & ssList(V))))) # label(ax20) # label(axiom) # label(non_clause). [assumption]. 0.41/1.05 28 (all U (ssList(U) -> ((all V (ssItem(V) -> (all W (ssItem(W) -> (all X (ssList(X) -> (all Y (ssList(Y) -> (all Z (ssList(Z) -> (app(app(X,cons(V,Y)),cons(W,Z)) = U -> lt(V,W)))))))))))) <-> strictorderedP(U)))) # label(ax12) # label(axiom) # label(non_clause). [assumption]. 0.41/1.05 29 (all U (ssItem(U) -> -lt(U,U))) # label(ax90) # label(axiom) # label(non_clause). [assumption]. 0.41/1.05 30 (all U (ssItem(U) -> (all V (ssList(V) -> (V != nil & strictorderedP(V) & lt(U,hd(V)) | V = nil <-> strictorderedP(cons(U,V))))))) # label(ax70) # label(axiom) # label(non_clause). [assumption]. 0.41/1.05 31 (all U (ssList(U) -> (nil != U -> ssItem(hd(U))))) # label(ax22) # label(axiom) # label(non_clause). [assumption]. 0.41/1.05 32 (all U (ssList(U) -> (U != nil -> ssList(tl(U))))) # label(ax24) # label(axiom) # label(non_clause). [assumption]. 0.41/1.05 33 (all U (ssList(U) -> (all V (ssList(V) -> (all W (ssList(W) -> (rearsegP(U,V) & rearsegP(V,W) -> rearsegP(U,W)))))))) # label(ax47) # label(axiom) # label(non_clause). [assumption]. 0.41/1.05 34 (all U (ssList(U) -> (all V (ssList(V) -> (all W (ssItem(W) -> cons(W,app(V,U)) = app(cons(W,V),U))))))) # label(ax27) # label(axiom) # label(non_clause). [assumption]. 0.41/1.05 35 (all U (ssList(U) -> (all V (ssList(V) -> (V != U <-> neq(U,V)))))) # label(ax15) # label(axiom) # label(non_clause). [assumption]. 0.41/1.05 36 (all U (ssItem(U) -> (all V (ssList(V) -> (V = nil | leq(U,hd(V)) & totalorderedP(V) & V != nil <-> totalorderedP(cons(U,V))))))) # label(ax67) # label(axiom) # label(non_clause). [assumption]. 0.41/1.05 37 (all U (ssList(U) -> ((all V (ssItem(V) -> (all W (ssItem(W) -> (all X (ssList(X) -> (all Y (ssList(Y) -> (all Z (ssList(Z) -> (app(app(X,cons(V,Y)),cons(W,Z)) = U -> lt(V,W) | lt(W,V)))))))))))) <-> strictorderP(U)))) # label(ax10) # label(axiom) # label(non_clause). [assumption]. 0.41/1.05 38 (all U (ssList(U) -> (nil != U -> (exists V (ssList(V) & V = tl(U)))))) # label(ax76) # label(axiom) # label(non_clause). [assumption]. 0.41/1.05 39 (all U (ssList(U) -> (nil != U -> cons(hd(U),tl(U)) = U))) # label(ax78) # label(axiom) # label(non_clause). [assumption]. 0.41/1.05 40 (all U (ssList(U) -> (U = nil <-> frontsegP(nil,U)))) # label(ax46) # label(axiom) # label(non_clause). [assumption]. 0.41/1.05 41 (all U (ssItem(U) -> (all V (ssItem(V) -> (neq(U,V) <-> U != V))))) # label(ax1) # label(axiom) # label(non_clause). [assumption]. 0.41/1.05 42 (all U (ssList(U) -> (all V (ssList(V) -> (frontsegP(U,V) & frontsegP(V,U) -> U = V))))) # label(ax41) # label(axiom) # label(non_clause). [assumption]. 0.41/1.05 43 (all U (ssItem(U) -> strictorderedP(cons(U,nil)))) # label(ax68) # label(axiom) # label(non_clause). [assumption]. 0.41/1.05 44 (all U (ssItem(U) -> (all V (ssItem(V) -> (geq(U,V) & geq(V,U) -> U = V))))) # label(ax87) # label(axiom) # label(non_clause). [assumption]. 0.41/1.05 45 (all U (ssList(U) -> (all V (ssItem(V) -> V = hd(cons(V,U)))))) # label(ax23) # label(axiom) # label(non_clause). [assumption]. 0.41/1.05 46 (all U (ssItem(U) -> (all V (ssItem(V) -> (lt(U,V) -> -lt(V,U)))))) # label(ax33) # label(axiom) # label(non_clause). [assumption]. 0.41/1.05 47 (all U (ssList(U) -> (all V (ssList(V) -> (rearsegP(V,U) & rearsegP(U,V) -> V = U))))) # label(ax48) # label(axiom) # label(non_clause). [assumption]. 0.41/1.05 48 (all U (ssList(U) -> (U != nil -> (exists V (hd(U) = V & ssItem(V)))))) # label(ax75) # label(axiom) # label(non_clause). [assumption]. 0.41/1.05 49 (all U (ssList(U) -> (all V (ssList(V) -> (all W (ssList(W) -> (frontsegP(V,W) & frontsegP(U,V) -> frontsegP(U,W)))))))) # label(ax40) # label(axiom) # label(non_clause). [assumption]. 0.41/1.05 50 (all U (ssList(U) -> (all V (ssItem(V) -> app(cons(V,nil),U) = cons(V,U))))) # label(ax81) # label(axiom) # label(non_clause). [assumption]. 0.41/1.05 51 (all U (ssList(U) -> (rearsegP(nil,U) <-> U = nil))) # label(ax52) # label(axiom) # label(non_clause). [assumption]. 0.41/1.05 52 (all U (ssItem(U) -> (all V (ssItem(V) -> (geq(U,V) <-> leq(V,U)))))) # label(ax32) # label(axiom) # label(non_clause). [assumption]. 0.41/1.05 53 (all U (ssList(U) -> (totalorderedP(U) <-> (all V (ssItem(V) -> (all W (ssItem(W) -> (all X (ssList(X) -> (all Y (ssList(Y) -> (all Z (ssList(Z) -> (U = app(app(X,cons(V,Y)),cons(W,Z)) -> leq(V,W))))))))))))))) # label(ax11) # label(axiom) # label(non_clause). [assumption]. 0.41/1.05 54 (all U (ssItem(U) -> (all V (ssItem(V) -> (leq(V,U) & leq(U,V) -> V = U))))) # label(ax29) # label(axiom) # label(non_clause). [assumption]. 0.41/1.05 55 (all U (ssList(U) -> (duplicatefreeP(U) <-> (all V (ssItem(V) -> (all W (ssItem(W) -> (all X (ssList(X) -> (all Y (ssList(Y) -> (all Z (ssList(Z) -> (app(app(X,cons(V,Y)),cons(W,Z)) = U -> V != W)))))))))))))) # label(ax13) # label(axiom) # label(non_clause). [assumption]. 0.41/1.05 56 (all U (ssItem(U) -> cyclefreeP(cons(U,nil)))) # label(ax59) # label(axiom) # label(non_clause). [assumption]. 0.41/1.05 57 (all U (ssList(U) -> (all V (ssList(V) -> (U != nil & tl(V) = tl(U) & hd(U) = hd(V) & nil != V -> V = U))))) # label(ax77) # label(axiom) # label(non_clause). [assumption]. 0.41/1.05 58 (all U (ssList(U) -> (all V (ssList(V) -> (all W (ssList(W) -> (rearsegP(U,V) -> rearsegP(app(W,U),V)))))))) # label(ax50) # label(axiom) # label(non_clause). [assumption]. 0.41/1.05 59 (all U (ssList(U) -> (segmentP(nil,U) <-> U = nil))) # label(ax58) # label(axiom) # label(non_clause). [assumption]. 0.41/1.05 60 (all U (ssList(U) -> (all V (ssList(V) -> (nil = V & U = nil <-> app(U,V) = nil))))) # label(ax83) # label(axiom) # label(non_clause). [assumption]. 0.41/1.05 61 (all U (ssList(U) -> (all V (ssItem(V) -> tl(cons(V,U)) = U)))) # label(ax25) # label(axiom) # label(non_clause). [assumption]. 0.41/1.05 62 (all U (ssList(U) -> U = app(U,nil))) # label(ax84) # label(axiom) # label(non_clause). [assumption]. 0.41/1.05 63 (all U (ssList(U) -> (all V (ssList(V) -> (all W (ssList(W) -> (app(V,W) = app(V,U) -> U = W))))))) # label(ax80) # label(axiom) # label(non_clause). [assumption]. 0.41/1.05 64 (all U (ssItem(U) -> leq(U,U))) # label(ax31) # label(axiom) # label(non_clause). [assumption]. 0.41/1.05 65 (all U (ssList(U) -> (all V (ssItem(V) -> cons(V,U) != U)))) # label(ax18) # label(axiom) # label(non_clause). [assumption]. 0.41/1.05 66 (all U (ssList(U) -> (all V (ssList(V) -> (segmentP(U,V) & segmentP(V,U) -> V = U))))) # label(ax54) # label(axiom) # label(non_clause). [assumption]. 0.41/1.05 67 (all U (ssList(U) -> (all V (ssList(V) -> (nil != U -> tl(app(U,V)) = app(tl(U),V)))))) # label(ax86) # label(axiom) # label(non_clause). [assumption]. 0.41/1.05 68 (all U (ssList(U) -> (all V (ssItem(V) -> cons(V,U) != nil)))) # label(ax21) # label(axiom) # label(non_clause). [assumption]. 0.41/1.05 69 (all U (ssItem(U) -> (all V (ssList(V) -> (all W (ssList(W) -> (memberP(W,U) | memberP(V,U) <-> memberP(app(V,W),U)))))))) # label(ax36) # label(axiom) # label(non_clause). [assumption]. 0.41/1.05 70 (all U (ssItem(U) -> equalelemsP(cons(U,nil)))) # label(ax73) # label(axiom) # label(non_clause). [assumption]. 0.41/1.05 71 (all U (ssList(U) -> frontsegP(U,nil))) # label(ax45) # label(axiom) # label(non_clause). [assumption]. 0.41/1.05 72 (all U (ssList(U) -> (all V (ssList(V) -> ((exists W (U = app(W,V) & ssList(W))) <-> rearsegP(U,V)))))) # label(ax6) # label(axiom) # label(non_clause). [assumption]. 0.41/1.05 73 (all U (ssList(U) -> (totalorderP(U) <-> (all V (ssItem(V) -> (all W (ssItem(W) -> (all X (ssList(X) -> (all Y (ssList(Y) -> (all Z (ssList(Z) -> (app(app(X,cons(V,Y)),cons(W,Z)) = U -> leq(W,V) | leq(V,W))))))))))))))) # label(ax9) # label(axiom) # label(non_clause). [assumption]. 0.41/1.05 74 (all U (ssItem(U) -> (all V (ssItem(V) -> (all W (ssItem(W) -> (leq(U,V) & leq(V,W) -> leq(U,W)))))))) # label(ax30) # label(axiom) # label(non_clause). [assumption]. 0.41/1.05 75 (all U (ssItem(U) -> (all V (ssItem(V) -> (leq(U,V) & V != U <-> lt(U,V)))))) # label(ax93) # label(axiom) # label(non_clause). [assumption]. 0.41/1.05 76 (all U (ssItem(U) -> (all V (ssItem(V) -> (all W (ssItem(W) -> (leq(U,V) & lt(V,W) -> lt(U,W)))))))) # label(ax91) # label(axiom) # label(non_clause). [assumption]. 0.41/1.05 77 (all U (ssItem(U) -> (all V (ssItem(V) -> (gt(U,V) -> -gt(V,U)))))) # label(ax94) # label(axiom) # label(non_clause). [assumption]. 0.41/1.05 78 (exists U (ssItem(U) & (exists V (ssItem(V) & U != V)))) # label(ax2) # label(axiom) # label(non_clause). [assumption]. 0.41/1.05 79 (all U (ssItem(U) -> (all V (ssItem(V) -> (gt(U,V) <-> lt(V,U)))))) # label(ax35) # label(axiom) # label(non_clause). [assumption]. 0.41/1.05 80 (all U (ssList(U) -> (all V (ssItem(V) -> (memberP(U,V) <-> (exists W ((exists X (U = app(W,cons(V,X)) & ssList(X))) & ssList(W)))))))) # label(ax3) # label(axiom) # label(non_clause). [assumption]. 0.41/1.05 81 (all U (ssList(U) -> segmentP(U,nil))) # label(ax57) # label(axiom) # label(non_clause). [assumption]. 0.41/1.05 82 (all U (ssItem(U) -> (all V (ssItem(V) -> (all W (ssItem(W) -> (lt(V,W) & lt(U,V) -> lt(U,W)))))))) # label(ax34) # label(axiom) # label(non_clause). [assumption]. 0.41/1.05 83 (all U (ssItem(U) -> (all V (ssItem(V) -> (leq(U,V) -> V = U | lt(U,V)))))) # label(ax92) # label(axiom) # label(non_clause). [assumption]. 0.41/1.05 84 (all U (ssList(U) -> ((exists V (ssItem(V) & U = cons(V,nil))) <-> singletonP(U)))) # label(ax4) # label(axiom) # label(non_clause). [assumption]. 0.41/1.05 85 (all U (ssList(U) -> (all V (ssList(V) -> (all W (ssList(W) -> (segmentP(V,W) & segmentP(U,V) -> segmentP(U,W)))))))) # label(ax53) # label(axiom) # label(non_clause). [assumption]. 0.41/1.05 86 (all U (ssList(U) -> (all V (ssList(V) -> (all W (ssList(W) -> app(app(U,V),W) = app(U,app(V,W)))))))) # label(ax82) # label(axiom) # label(non_clause). [assumption]. 0.41/1.05 87 -(all U (ssList(U) -> (all V (ssList(V) -> (all W (ssList(W) -> (all X (ssList(X) -> (all Y (ssList(Y) -> -neq(Y,nil) | -segmentP(W,Y) | -segmentP(X,Y))) & (nil != W | X != nil) | nil = U | W != U | V != X | V != nil)))))))) # label(co1) # label(negated_conjecture) # label(non_clause). [assumption]. 0.41/1.05 0.41/1.05 ============================== end of process non-clausal formulas === 0.41/1.05 0.41/1.05 ============================== PROCESS INITIAL CLAUSES =============== 0.41/1.05 0.41/1.05 ============================== PREDICATE ELIMINATION ================= 0.41/1.05 88 -ssList(A) | -equalelemsP(A) | -ssItem(B) | -ssItem(C) | -ssList(D) | -ssList(E) | app(D,cons(B,cons(C,E))) != A | C = B # label(ax14) # label(axiom). [clausify(24)]. 0.41/1.05 89 equalelemsP(nil) # label(ax74) # label(axiom). [assumption]. 0.41/1.05 Derived: -ssList(nil) | -ssItem(A) | -ssItem(B) | -ssList(C) | -ssList(D) | app(C,cons(A,cons(B,D))) != nil | B = A. [resolve(88,b,89,a)]. 0.77/1.07 90 -ssList(A) | equalelemsP(A) | ssItem(f9(A)) # label(ax14) # label(axiom). [clausify(24)]. 0.77/1.07 Derived: -ssList(A) | ssItem(f9(A)) | -ssList(A) | -ssItem(B) | -ssItem(C) | -ssList(D) | -ssList(E) | app(D,cons(B,cons(C,E))) != A | C = B. [resolve(90,b,88,b)]. 0.77/1.07 91 -ssList(A) | equalelemsP(A) | ssItem(f10(A)) # label(ax14) # label(axiom). [clausify(24)]. 0.77/1.07 Derived: -ssList(A) | ssItem(f10(A)) | -ssList(A) | -ssItem(B) | -ssItem(C) | -ssList(D) | -ssList(E) | app(D,cons(B,cons(C,E))) != A | C = B. [resolve(91,b,88,b)]. 0.77/1.07 92 -ssList(A) | equalelemsP(A) | ssList(f11(A)) # label(ax14) # label(axiom). [clausify(24)]. 0.77/1.07 Derived: -ssList(A) | ssList(f11(A)) | -ssList(A) | -ssItem(B) | -ssItem(C) | -ssList(D) | -ssList(E) | app(D,cons(B,cons(C,E))) != A | C = B. [resolve(92,b,88,b)]. 0.77/1.07 93 -ssList(A) | equalelemsP(A) | ssList(f12(A)) # label(ax14) # label(axiom). [clausify(24)]. 0.77/1.07 Derived: -ssList(A) | ssList(f12(A)) | -ssList(A) | -ssItem(B) | -ssItem(C) | -ssList(D) | -ssList(E) | app(D,cons(B,cons(C,E))) != A | C = B. [resolve(93,b,88,b)]. 0.77/1.07 94 -ssList(A) | equalelemsP(A) | app(f11(A),cons(f9(A),cons(f10(A),f12(A)))) = A # label(ax14) # label(axiom). [clausify(24)]. 0.77/1.07 Derived: -ssList(A) | app(f11(A),cons(f9(A),cons(f10(A),f12(A)))) = A | -ssList(A) | -ssItem(B) | -ssItem(C) | -ssList(D) | -ssList(E) | app(D,cons(B,cons(C,E))) != A | C = B. [resolve(94,b,88,b)]. 0.77/1.07 95 -ssList(A) | equalelemsP(A) | f10(A) != f9(A) # label(ax14) # label(axiom). [clausify(24)]. 0.77/1.07 Derived: -ssList(A) | f10(A) != f9(A) | -ssList(A) | -ssItem(B) | -ssItem(C) | -ssList(D) | -ssList(E) | app(D,cons(B,cons(C,E))) != A | C = B. [resolve(95,b,88,b)]. 0.77/1.07 96 -ssItem(A) | equalelemsP(cons(A,nil)) # label(ax73) # label(axiom). [clausify(70)]. 0.77/1.07 Derived: -ssItem(A) | -ssList(cons(A,nil)) | -ssItem(B) | -ssItem(C) | -ssList(D) | -ssList(E) | app(D,cons(B,cons(C,E))) != cons(A,nil) | C = B. [resolve(96,b,88,b)]. 0.77/1.07 97 -ssList(A) | -duplicatefreeP(A) | -ssItem(B) | -ssItem(C) | -ssList(D) | -ssList(E) | -ssList(F) | app(app(D,cons(B,E)),cons(C,F)) != A | C != B # label(ax13) # label(axiom). [clausify(55)]. 0.77/1.07 98 -ssItem(A) | duplicatefreeP(cons(A,nil)) # label(ax71) # label(axiom). [clausify(16)]. 0.77/1.07 Derived: -ssList(cons(A,nil)) | -ssItem(B) | -ssItem(C) | -ssList(D) | -ssList(E) | -ssList(F) | app(app(D,cons(B,E)),cons(C,F)) != cons(A,nil) | C != B | -ssItem(A). [resolve(97,b,98,b)]. 0.77/1.07 99 -ssList(A) | duplicatefreeP(A) | ssItem(f32(A)) # label(ax13) # label(axiom). [clausify(55)]. 0.77/1.07 Derived: -ssList(A) | ssItem(f32(A)) | -ssList(A) | -ssItem(B) | -ssItem(C) | -ssList(D) | -ssList(E) | -ssList(F) | app(app(D,cons(B,E)),cons(C,F)) != A | C != B. [resolve(99,b,97,b)]. 0.77/1.07 100 -ssList(A) | duplicatefreeP(A) | ssItem(f33(A)) # label(ax13) # label(axiom). [clausify(55)]. 0.77/1.07 Derived: -ssList(A) | ssItem(f33(A)) | -ssList(A) | -ssItem(B) | -ssItem(C) | -ssList(D) | -ssList(E) | -ssList(F) | app(app(D,cons(B,E)),cons(C,F)) != A | C != B. [resolve(100,b,97,b)]. 0.77/1.07 101 -ssList(A) | duplicatefreeP(A) | ssList(f34(A)) # label(ax13) # label(axiom). [clausify(55)]. 0.77/1.07 Derived: -ssList(A) | ssList(f34(A)) | -ssList(A) | -ssItem(B) | -ssItem(C) | -ssList(D) | -ssList(E) | -ssList(F) | app(app(D,cons(B,E)),cons(C,F)) != A | C != B. [resolve(101,b,97,b)]. 0.77/1.07 102 -ssList(A) | duplicatefreeP(A) | ssList(f35(A)) # label(ax13) # label(axiom). [clausify(55)]. 0.77/1.07 Derived: -ssList(A) | ssList(f35(A)) | -ssList(A) | -ssItem(B) | -ssItem(C) | -ssList(D) | -ssList(E) | -ssList(F) | app(app(D,cons(B,E)),cons(C,F)) != A | C != B. [resolve(102,b,97,b)]. 0.77/1.07 103 -ssList(A) | duplicatefreeP(A) | ssList(f36(A)) # label(ax13) # label(axiom). [clausify(55)]. 0.77/1.07 Derived: -ssList(A) | ssList(f36(A)) | -ssList(A) | -ssItem(B) | -ssItem(C) | -ssList(D) | -ssList(E) | -ssList(F) | app(app(D,cons(B,E)),cons(C,F)) != A | C != B. [resolve(103,b,97,b)]. 0.77/1.07 104 -ssList(A) | duplicatefreeP(A) | app(app(f34(A),cons(f32(A),f35(A))),cons(f33(A),f36(A))) = A # label(ax13) # label(axiom). [clausify(55)]. 0.77/1.07 Derived: -ssList(A) | app(app(f34(A),cons(f32(A),f35(A))),cons(f33(A),f36(A))) = A | -ssList(A) | -ssItem(B) | -ssItem(C) | -ssList(D) | -ssList(E) | -ssList(F) | app(app(D,cons(B,E)),cons(C,F)) != A | C != B. [resolve(104,b,97,b)]. 0.81/1.08 105 -ssList(A) | duplicatefreeP(A) | f33(A) = f32(A) # label(ax13) # label(axiom). [clausify(55)]. 0.81/1.08 Derived: -ssList(A) | f33(A) = f32(A) | -ssList(A) | -ssItem(B) | -ssItem(C) | -ssList(D) | -ssList(E) | -ssList(F) | app(app(D,cons(B,E)),cons(C,F)) != A | C != B. [resolve(105,b,97,b)]. 0.81/1.08 106 duplicatefreeP(nil) # label(ax72) # label(axiom). [assumption]. 0.81/1.08 Derived: -ssList(nil) | -ssItem(A) | -ssItem(B) | -ssList(C) | -ssList(D) | -ssList(E) | app(app(C,cons(A,D)),cons(B,E)) != nil | B != A. [resolve(106,a,97,b)]. 0.81/1.08 107 -ssList(A) | -totalorderP(A) | -ssItem(B) | -ssItem(C) | -ssList(D) | -ssList(E) | -ssList(F) | app(app(D,cons(B,E)),cons(C,F)) != A | leq(C,B) | leq(B,C) # label(ax9) # label(axiom). [clausify(73)]. 0.81/1.08 108 -ssItem(A) | totalorderP(cons(A,nil)) # label(ax61) # label(axiom). [clausify(17)]. 0.81/1.08 109 totalorderP(nil) # label(ax62) # label(axiom). [assumption]. 0.81/1.08 Derived: -ssList(cons(A,nil)) | -ssItem(B) | -ssItem(C) | -ssList(D) | -ssList(E) | -ssList(F) | app(app(D,cons(B,E)),cons(C,F)) != cons(A,nil) | leq(C,B) | leq(B,C) | -ssItem(A). [resolve(107,b,108,b)]. 0.81/1.08 Derived: -ssList(nil) | -ssItem(A) | -ssItem(B) | -ssList(C) | -ssList(D) | -ssList(E) | app(app(C,cons(A,D)),cons(B,E)) != nil | leq(B,A) | leq(A,B). [resolve(107,b,109,a)]. 0.81/1.08 110 -ssList(A) | totalorderP(A) | ssItem(f38(A)) # label(ax9) # label(axiom). [clausify(73)]. 0.81/1.08 Derived: -ssList(A) | ssItem(f38(A)) | -ssList(A) | -ssItem(B) | -ssItem(C) | -ssList(D) | -ssList(E) | -ssList(F) | app(app(D,cons(B,E)),cons(C,F)) != A | leq(C,B) | leq(B,C). [resolve(110,b,107,b)]. 0.81/1.08 111 -ssList(A) | totalorderP(A) | ssItem(f39(A)) # label(ax9) # label(axiom). [clausify(73)]. 0.81/1.08 Derived: -ssList(A) | ssItem(f39(A)) | -ssList(A) | -ssItem(B) | -ssItem(C) | -ssList(D) | -ssList(E) | -ssList(F) | app(app(D,cons(B,E)),cons(C,F)) != A | leq(C,B) | leq(B,C). [resolve(111,b,107,b)]. 0.81/1.08 112 -ssList(A) | totalorderP(A) | ssList(f40(A)) # label(ax9) # label(axiom). [clausify(73)]. 0.81/1.08 Derived: -ssList(A) | ssList(f40(A)) | -ssList(A) | -ssItem(B) | -ssItem(C) | -ssList(D) | -ssList(E) | -ssList(F) | app(app(D,cons(B,E)),cons(C,F)) != A | leq(C,B) | leq(B,C). [resolve(112,b,107,b)]. 0.81/1.08 113 -ssList(A) | totalorderP(A) | ssList(f41(A)) # label(ax9) # label(axiom). [clausify(73)]. 0.81/1.08 Derived: -ssList(A) | ssList(f41(A)) | -ssList(A) | -ssItem(B) | -ssItem(C) | -ssList(D) | -ssList(E) | -ssList(F) | app(app(D,cons(B,E)),cons(C,F)) != A | leq(C,B) | leq(B,C). [resolve(113,b,107,b)]. 0.81/1.08 114 -ssList(A) | totalorderP(A) | ssList(f42(A)) # label(ax9) # label(axiom). [clausify(73)]. 0.81/1.08 Derived: -ssList(A) | ssList(f42(A)) | -ssList(A) | -ssItem(B) | -ssItem(C) | -ssList(D) | -ssList(E) | -ssList(F) | app(app(D,cons(B,E)),cons(C,F)) != A | leq(C,B) | leq(B,C). [resolve(114,b,107,b)]. 0.81/1.08 115 -ssList(A) | totalorderP(A) | app(app(f40(A),cons(f38(A),f41(A))),cons(f39(A),f42(A))) = A # label(ax9) # label(axiom). [clausify(73)]. 0.81/1.08 Derived: -ssList(A) | app(app(f40(A),cons(f38(A),f41(A))),cons(f39(A),f42(A))) = A | -ssList(A) | -ssItem(B) | -ssItem(C) | -ssList(D) | -ssList(E) | -ssList(F) | app(app(D,cons(B,E)),cons(C,F)) != A | leq(C,B) | leq(B,C). [resolve(115,b,107,b)]. 0.81/1.08 116 -ssList(A) | totalorderP(A) | -leq(f39(A),f38(A)) # label(ax9) # label(axiom). [clausify(73)]. 0.81/1.08 Derived: -ssList(A) | -leq(f39(A),f38(A)) | -ssList(A) | -ssItem(B) | -ssItem(C) | -ssList(D) | -ssList(E) | -ssList(F) | app(app(D,cons(B,E)),cons(C,F)) != A | leq(C,B) | leq(B,C). [resolve(116,b,107,b)]. 0.81/1.08 117 -ssList(A) | totalorderP(A) | -leq(f38(A),f39(A)) # label(ax9) # label(axiom). [clausify(73)]. 0.81/1.08 Derived: -ssList(A) | -leq(f38(A),f39(A)) | -ssList(A) | -ssItem(B) | -ssItem(C) | -ssList(D) | -ssList(E) | -ssList(F) | app(app(D,cons(B,E)),cons(C,F)) != A | leq(C,B) | leq(B,C). [resolve(117,b,107,b)]. 0.81/1.08 118 -ssList(A) | -ssItem(B) | -ssItem(C) | -ssList(D) | -ssList(E) | -ssList(F) | app(app(D,cons(B,E)),cons(C,F)) != A | lt(B,C) | lt(C,B) | -strictorderP(A) # label(ax10) # label(axiom). [clausify(37)]. 0.85/1.12 119 -ssItem(A) | strictorderP(cons(A,nil)) # label(ax63) # label(axiom). [clausify(22)]. 0.85/1.12 120 -ssList(A) | ssItem(f20(A)) | strictorderP(A) # label(ax10) # label(axiom). [clausify(37)]. 0.85/1.12 121 -ssList(A) | ssItem(f21(A)) | strictorderP(A) # label(ax10) # label(axiom). [clausify(37)]. 0.85/1.12 122 -ssList(A) | ssList(f22(A)) | strictorderP(A) # label(ax10) # label(axiom). [clausify(37)]. 0.85/1.12 123 -ssList(A) | ssList(f23(A)) | strictorderP(A) # label(ax10) # label(axiom). [clausify(37)]. 0.85/1.12 124 -ssList(A) | ssList(f24(A)) | strictorderP(A) # label(ax10) # label(axiom). [clausify(37)]. 0.85/1.12 125 -ssList(A) | app(app(f22(A),cons(f20(A),f23(A))),cons(f21(A),f24(A))) = A | strictorderP(A) # label(ax10) # label(axiom). [clausify(37)]. 0.85/1.12 126 -ssList(A) | -lt(f20(A),f21(A)) | strictorderP(A) # label(ax10) # label(axiom). [clausify(37)]. 0.85/1.12 127 -ssList(A) | -lt(f21(A),f20(A)) | strictorderP(A) # label(ax10) # label(axiom). [clausify(37)]. 0.85/1.12 Derived: -ssList(cons(A,nil)) | -ssItem(B) | -ssItem(C) | -ssList(D) | -ssList(E) | -ssList(F) | app(app(D,cons(B,E)),cons(C,F)) != cons(A,nil) | lt(B,C) | lt(C,B) | -ssItem(A). [resolve(118,j,119,b)]. 0.85/1.12 Derived: -ssList(A) | -ssItem(B) | -ssItem(C) | -ssList(D) | -ssList(E) | -ssList(F) | app(app(D,cons(B,E)),cons(C,F)) != A | lt(B,C) | lt(C,B) | -ssList(A) | ssItem(f20(A)). [resolve(118,j,120,c)]. 0.85/1.12 Derived: -ssList(A) | -ssItem(B) | -ssItem(C) | -ssList(D) | -ssList(E) | -ssList(F) | app(app(D,cons(B,E)),cons(C,F)) != A | lt(B,C) | lt(C,B) | -ssList(A) | ssItem(f21(A)). [resolve(118,j,121,c)]. 0.85/1.12 Derived: -ssList(A) | -ssItem(B) | -ssItem(C) | -ssList(D) | -ssList(E) | -ssList(F) | app(app(D,cons(B,E)),cons(C,F)) != A | lt(B,C) | lt(C,B) | -ssList(A) | ssList(f22(A)). [resolve(118,j,122,c)]. 0.85/1.12 Derived: -ssList(A) | -ssItem(B) | -ssItem(C) | -ssList(D) | -ssList(E) | -ssList(F) | app(app(D,cons(B,E)),cons(C,F)) != A | lt(B,C) | lt(C,B) | -ssList(A) | ssList(f23(A)). [resolve(118,j,123,c)]. 0.85/1.12 Derived: -ssList(A) | -ssItem(B) | -ssItem(C) | -ssList(D) | -ssList(E) | -ssList(F) | app(app(D,cons(B,E)),cons(C,F)) != A | lt(B,C) | lt(C,B) | -ssList(A) | ssList(f24(A)). [resolve(118,j,124,c)]. 0.85/1.12 Derived: -ssList(A) | -ssItem(B) | -ssItem(C) | -ssList(D) | -ssList(E) | -ssList(F) | app(app(D,cons(B,E)),cons(C,F)) != A | lt(B,C) | lt(C,B) | -ssList(A) | app(app(f22(A),cons(f20(A),f23(A))),cons(f21(A),f24(A))) = A. [resolve(118,j,125,c)]. 0.85/1.12 Derived: -ssList(A) | -ssItem(B) | -ssItem(C) | -ssList(D) | -ssList(E) | -ssList(F) | app(app(D,cons(B,E)),cons(C,F)) != A | lt(B,C) | lt(C,B) | -ssList(A) | -lt(f20(A),f21(A)). [resolve(118,j,126,c)]. 0.85/1.12 Derived: -ssList(A) | -ssItem(B) | -ssItem(C) | -ssList(D) | -ssList(E) | -ssList(F) | app(app(D,cons(B,E)),cons(C,F)) != A | lt(B,C) | lt(C,B) | -ssList(A) | -lt(f21(A),f20(A)). [resolve(118,j,127,c)]. 0.85/1.12 128 strictorderP(nil) # label(ax64) # label(axiom). [assumption]. 0.85/1.12 Derived: -ssList(nil) | -ssItem(A) | -ssItem(B) | -ssList(C) | -ssList(D) | -ssList(E) | app(app(C,cons(A,D)),cons(B,E)) != nil | lt(A,B) | lt(B,A). [resolve(128,a,118,j)]. 0.85/1.12 129 -ssList(A) | -ssItem(B) | -ssItem(C) | -ssList(D) | -ssList(E) | -ssList(F) | app(app(D,cons(B,E)),cons(C,F)) != A | -leq(B,C) | -leq(C,B) | -cyclefreeP(A) # label(ax8) # label(axiom). [clausify(23)]. 0.85/1.12 130 -ssList(A) | ssItem(f4(A)) | cyclefreeP(A) # label(ax8) # label(axiom). [clausify(23)]. 0.85/1.12 131 -ssList(A) | ssItem(f5(A)) | cyclefreeP(A) # label(ax8) # label(axiom). [clausify(23)]. 0.85/1.12 132 -ssList(A) | ssList(f6(A)) | cyclefreeP(A) # label(ax8) # label(axiom). [clausify(23)]. 0.85/1.12 133 -ssList(A) | ssList(f7(A)) | cyclefreeP(A) # label(ax8) # label(axiom). [clausify(23)]. 0.85/1.12 134 -ssList(A) | ssList(f8(A)) | cyclefreeP(A) # label(ax8) # label(axiom). [clausify(23)]. 0.85/1.12 135 -ssList(A) | app(app(f6(A),cons(f4(A),f7(A))),cons(f5(A),f8(A))) = A | cyclefreeP(A) # label(ax8) # label(axiom). [clausify(23)]. 0.85/1.12 136 -ssList(A) | leq(f4(A),f5(A)) | cyclefreeP(A) # label(ax8) # label(axiom). [clausify(23)]. 0.85/1.12 137 -ssList(A) | leq(f5(A),f4(A)) | cyclefreeP(A) # label(ax8) # label(axiom). [clausify(23)]. 0.85/1.12 Derived: -ssList(A) | -ssItem(B) | -ssItem(C) | -ssList(D) | -ssList(E) | -ssList(F) | app(app(D,cons(B,E)),cons(C,F)) != A | -leq(B,C) | -leq(C,B) | -ssList(A) | ssItem(f4(A)). [resolve(129,j,130,c)]. 1.60/1.92 Derived: -ssList(A) | -ssItem(B) | -ssItem(C) | -ssList(D) | -ssList(E) | -ssList(F) | app(app(D,cons(B,E)),cons(C,F)) != A | -leq(B,C) | -leq(C,B) | -ssList(A) | ssItem(f5(A)). [resolve(129,j,131,c)]. 1.60/1.92 Derived: -ssList(A) | -ssItem(B) | -ssItem(C) | -ssList(D) | -ssList(E) | -ssList(F) | app(app(D,cons(B,E)),cons(C,F)) != A | -leq(B,C) | -leq(C,B) | -ssList(A) | ssList(f6(A)). [resolve(129,j,132,c)]. 1.60/1.92 Derived: -ssList(A) | -ssItem(B) | -ssItem(C) | -ssList(D) | -ssList(E) | -ssList(F) | app(app(D,cons(B,E)),cons(C,F)) != A | -leq(B,C) | -leq(C,B) | -ssList(A) | ssList(f7(A)). [resolve(129,j,133,c)]. 1.60/1.92 Derived: -ssList(A) | -ssItem(B) | -ssItem(C) | -ssList(D) | -ssList(E) | -ssList(F) | app(app(D,cons(B,E)),cons(C,F)) != A | -leq(B,C) | -leq(C,B) | -ssList(A) | ssList(f8(A)). [resolve(129,j,134,c)]. 1.60/1.92 Derived: -ssList(A) | -ssItem(B) | -ssItem(C) | -ssList(D) | -ssList(E) | -ssList(F) | app(app(D,cons(B,E)),cons(C,F)) != A | -leq(B,C) | -leq(C,B) | -ssList(A) | app(app(f6(A),cons(f4(A),f7(A))),cons(f5(A),f8(A))) = A. [resolve(129,j,135,c)]. 1.60/1.92 Derived: -ssList(A) | -ssItem(B) | -ssItem(C) | -ssList(D) | -ssList(E) | -ssList(F) | app(app(D,cons(B,E)),cons(C,F)) != A | -leq(B,C) | -leq(C,B) | -ssList(A) | leq(f4(A),f5(A)). [resolve(129,j,136,c)]. 1.60/1.92 Derived: -ssList(A) | -ssItem(B) | -ssItem(C) | -ssList(D) | -ssList(E) | -ssList(F) | app(app(D,cons(B,E)),cons(C,F)) != A | -leq(B,C) | -leq(C,B) | -ssList(A) | leq(f5(A),f4(A)). [resolve(129,j,137,c)]. 1.60/1.92 138 cyclefreeP(nil) # label(ax60) # label(axiom). [assumption]. 1.60/1.92 Derived: -ssList(nil) | -ssItem(A) | -ssItem(B) | -ssList(C) | -ssList(D) | -ssList(E) | app(app(C,cons(A,D)),cons(B,E)) != nil | -leq(A,B) | -leq(B,A). [resolve(138,a,129,j)]. 1.60/1.92 139 -ssItem(A) | cyclefreeP(cons(A,nil)) # label(ax59) # label(axiom). [clausify(56)]. 1.60/1.92 Derived: -ssItem(A) | -ssList(cons(A,nil)) | -ssItem(B) | -ssItem(C) | -ssList(D) | -ssList(E) | -ssList(F) | app(app(D,cons(B,E)),cons(C,F)) != cons(A,nil) | -leq(B,C) | -leq(C,B). [resolve(139,b,129,j)]. 1.60/1.92 140 -ssList(A) | -ssList(B) | B != A | -neq(A,B) # label(ax15) # label(axiom). [clausify(35)]. 1.60/1.92 141 -ssList(A) | -ssList(B) | B = A | neq(A,B) # label(ax15) # label(axiom). [clausify(35)]. 1.60/1.92 142 -ssItem(A) | -ssItem(B) | -neq(A,B) | B != A # label(ax1) # label(axiom). [clausify(41)]. 1.60/1.92 143 -ssItem(A) | -ssItem(B) | neq(A,B) | B = A # label(ax1) # label(axiom). [clausify(41)]. 1.60/1.92 144 neq(c7,nil) | nil = c5 # label(co1) # label(negated_conjecture). [clausify(87)]. 1.60/1.92 Derived: nil = c5 | -ssList(c7) | -ssList(nil) | nil != c7. [resolve(144,a,140,d)]. 1.60/1.92 Derived: nil = c5 | -ssItem(c7) | -ssItem(nil) | nil != c7. [resolve(144,a,142,c)]. 1.60/1.92 145 neq(c7,nil) | nil = c6 # label(co1) # label(negated_conjecture). [clausify(87)]. 1.60/1.92 Derived: nil = c6 | -ssList(c7) | -ssList(nil) | nil != c7. [resolve(145,a,140,d)]. 1.60/1.92 Derived: nil = c6 | -ssItem(c7) | -ssItem(nil) | nil != c7. [resolve(145,a,142,c)]. 1.60/1.92 1.60/1.92 ============================== end predicate elimination ============= 1.60/1.92 1.60/1.92 Auto_denials: (non-Horn, no changes). 1.60/1.92 1.60/1.92 Term ordering decisions: 1.60/1.92 Function symbol KB weights: nil=1. c1=1. c2=1. c3=1. c4=1. c5=1. c6=1. c7=1. cons=1. app=1. f1=1. f2=1. f3=1. f37=1. f43=1. f44=1. hd=1. tl=1. f4=1. f5=1. f6=1. f7=1. f8=1. f9=1. f10=1. f11=1. f12=1. f13=1. f14=1. f15=1. f16=1. f17=1. f18=1. f19=1. f20=1. f21=1. f22=1. f23=1. f24=1. f25=1. f26=1. f27=1. f28=1. f29=1. f30=1. f31=1. f32=1. f33=1. f34=1. f35=1. f36=1. f38=1. f39=1. f40=1. f41=1. f42=1. f45=1. 1.60/1.92 1.60/1.92 ============================== end of process initial clauses ======== 1.60/1.92 1.60/1.92 ============================== CLAUSES FOR SEARCH ==================== 1.60/1.92 1.60/1.92 ============================== end of clauses for search ============= 1.60/1.92 1.60/1.92 ============================== SEARCH ================================ 1.60/1.92 1.60/1.92 % Starting search at 0.51 seconds. 1.60/1.92 1.60/1.92 ============================== PROOF ================================= 1.60/1.92 % SZS status Theorem 1.60/1.92 % SZS output start Refutation 1.60/1.92 1.60/1.92 % Proof 1 at 0.88 (+ 0.01) seconds. 1.60/1.92 % Length of proof is 23. 1.60/1.92 % Level of proof is 5. 1.60/1.92 % Maximum clause weight is 8.000. 1.60/1.92 % Given clauses 249. 1.60/1.92 1.60/1.92 35 (all U (ssList(U) -> (all V (ssList(V) -> (V != U <-> neq(U,V)))))) # label(ax15) # label(axiom) # label(non_clause). [assumption]. 1.60/1.92 59 (all U (ssList(U) -> (segmentP(nil,U) <-> U = nil))) # label(ax58) # label(axiom) # label(non_clause). [assumption]. 1.60/1.92 87 -(all U (ssList(U) -> (all V (ssList(V) -> (all W (ssList(W) -> (all X (ssList(X) -> (all Y (ssList(Y) -> -neq(Y,nil) | -segmentP(W,Y) | -segmentP(X,Y))) & (nil != W | X != nil) | nil = U | W != U | V != X | V != nil)))))))) # label(co1) # label(negated_conjecture) # label(non_clause). [assumption]. 1.60/1.92 140 -ssList(A) | -ssList(B) | B != A | -neq(A,B) # label(ax15) # label(axiom). [clausify(35)]. 1.60/1.92 144 neq(c7,nil) | nil = c5 # label(co1) # label(negated_conjecture). [clausify(87)]. 1.60/1.92 173 ssList(nil) # label(ax17) # label(axiom). [assumption]. 1.60/1.92 236 -ssList(A) | -segmentP(nil,A) | nil = A # label(ax58) # label(axiom). [clausify(59)]. 1.60/1.92 283 ssList(c7) | nil = c5 # label(co1) # label(negated_conjecture). [clausify(87)]. 1.60/1.92 284 ssList(c7) | c5 = nil. [copy(283),flip(b)]. 1.60/1.92 291 segmentP(c6,c7) | nil = c5 # label(co1) # label(negated_conjecture). [clausify(87)]. 1.60/1.92 292 segmentP(c6,c7) | c5 = nil. [copy(291),flip(b)]. 1.60/1.92 295 nil != c3 # label(co1) # label(negated_conjecture). [clausify(87)]. 1.60/1.92 296 c3 != nil. [copy(295),flip(a)]. 1.60/1.92 297 c5 = c3 # label(co1) # label(negated_conjecture). [clausify(87)]. 1.60/1.92 298 c6 = c4 # label(co1) # label(negated_conjecture). [clausify(87)]. 1.60/1.92 299 nil = c4 # label(co1) # label(negated_conjecture). [clausify(87)]. 1.60/1.92 300 c4 = nil. [copy(299),flip(a)]. 1.60/1.92 390 nil = c5 | -ssList(c7) | -ssList(nil) | nil != c7. [resolve(144,a,140,d)]. 1.60/1.92 391 -ssList(c7) | c7 != nil. [copy(390),rewrite([297(2)]),flip(a),flip(d),unit_del(a,296),unit_del(c,173)]. 1.60/1.92 465 segmentP(nil,c7). [back_rewrite(292),rewrite([298(1),300(1),297(4)]),unit_del(b,296)]. 1.60/1.92 467 ssList(c7). [back_rewrite(284),rewrite([297(3)]),unit_del(b,296)]. 1.60/1.92 785 c7 != nil. [back_unit_del(391),unit_del(a,467)]. 1.60/1.92 3867 $F. [resolve(465,a,236,b),flip(b),unit_del(a,467),unit_del(b,785)]. 1.60/1.92 1.60/1.92 % SZS output end Refutation 1.60/1.92 ============================== end of proof ========================== 1.60/1.92 1.60/1.92 ============================== STATISTICS ============================ 1.60/1.92 1.60/1.92 Given=249. Generated=10062. Kept=3665. proofs=1. 1.60/1.92 Usable=249. Sos=3383. Demods=12. Limbo=8, Disabled=280. Hints=0. 1.60/1.92 Megabytes=6.05. 1.60/1.92 User_CPU=0.88, System_CPU=0.01, Wall_clock=0. 1.60/1.92 1.60/1.92 ============================== end of statistics ===================== 1.60/1.92 1.60/1.92 ============================== end of search ========================= 1.60/1.92 1.60/1.92 THEOREM PROVED 1.60/1.92 % SZS status Theorem 1.60/1.92 1.60/1.92 Exiting with 1 proof. 1.60/1.92 1.60/1.92 Process 5938 exit (max_proofs) Tue Aug 9 01:57:17 2022 1.60/1.92 Prover9 interrupted 1.60/1.92 EOF