TSTP Solution File: SWC090+1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SWC090+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n006.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 : 600s
% DateTime : Tue Jul 19 21:45:16 EDT 2022
% Result : Theorem 167.14s 167.39s
% Output : Refutation 167.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWC090+1 : TPTP v8.1.0. Released v2.4.0.
% 0.07/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.34 % Computer : n006.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sat Jun 11 22:27:27 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.45/1.11 ============================== Prover9 ===============================
% 0.45/1.11 Prover9 (32) version 2009-11A, November 2009.
% 0.45/1.11 Process 28450 was started by sandbox2 on n006.cluster.edu,
% 0.45/1.11 Sat Jun 11 22:27:28 2022
% 0.45/1.11 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_28297_n006.cluster.edu".
% 0.45/1.11 ============================== end of head ===========================
% 0.45/1.11
% 0.45/1.11 ============================== INPUT =================================
% 0.45/1.11
% 0.45/1.11 % Reading from file /tmp/Prover9_28297_n006.cluster.edu
% 0.45/1.11
% 0.45/1.11 set(prolog_style_variables).
% 0.45/1.11 set(auto2).
% 0.45/1.11 % set(auto2) -> set(auto).
% 0.45/1.11 % set(auto) -> set(auto_inference).
% 0.45/1.11 % set(auto) -> set(auto_setup).
% 0.45/1.11 % set(auto_setup) -> set(predicate_elim).
% 0.45/1.11 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.45/1.11 % set(auto) -> set(auto_limits).
% 0.45/1.11 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.45/1.11 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.45/1.11 % set(auto) -> set(auto_denials).
% 0.45/1.11 % set(auto) -> set(auto_process).
% 0.45/1.11 % set(auto2) -> assign(new_constants, 1).
% 0.45/1.11 % set(auto2) -> assign(fold_denial_max, 3).
% 0.45/1.11 % set(auto2) -> assign(max_weight, "200.000").
% 0.45/1.11 % set(auto2) -> assign(max_hours, 1).
% 0.45/1.11 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.45/1.11 % set(auto2) -> assign(max_seconds, 0).
% 0.45/1.11 % set(auto2) -> assign(max_minutes, 5).
% 0.45/1.11 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.45/1.11 % set(auto2) -> set(sort_initial_sos).
% 0.45/1.11 % set(auto2) -> assign(sos_limit, -1).
% 0.45/1.11 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.45/1.11 % set(auto2) -> assign(max_megs, 400).
% 0.45/1.11 % set(auto2) -> assign(stats, some).
% 0.45/1.11 % set(auto2) -> clear(echo_input).
% 0.45/1.11 % set(auto2) -> set(quiet).
% 0.45/1.11 % set(auto2) -> clear(print_initial_clauses).
% 0.45/1.11 % set(auto2) -> clear(print_given).
% 0.45/1.11 assign(lrs_ticks,-1).
% 0.45/1.11 assign(sos_limit,10000).
% 0.45/1.11 assign(order,kbo).
% 0.45/1.11 set(lex_order_vars).
% 0.45/1.11 clear(print_given).
% 0.45/1.11
% 0.45/1.11 % formulas(sos). % not echoed (96 formulas)
% 0.45/1.11
% 0.45/1.11 ============================== end of input ==========================
% 0.45/1.11
% 0.45/1.11 % From the command line: assign(max_seconds, 300).
% 0.45/1.11
% 0.45/1.11 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.45/1.11
% 0.45/1.11 % Formulas that are not ordinary clauses:
% 0.45/1.11 1 (all U (ssItem(U) -> (all V (ssItem(V) -> (neq(U,V) <-> U != V))))) # label(ax1) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.11 2 (exists U (ssItem(U) & (exists V (ssItem(V) & U != V)))) # label(ax2) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.11 3 (all U (ssList(U) -> (all V (ssItem(V) -> (memberP(U,V) <-> (exists W (ssList(W) & (exists X (ssList(X) & app(W,cons(V,X)) = U))))))))) # label(ax3) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.11 4 (all U (ssList(U) -> (singletonP(U) <-> (exists V (ssItem(V) & cons(V,nil) = U))))) # label(ax4) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.11 5 (all U (ssList(U) -> (all V (ssList(V) -> (frontsegP(U,V) <-> (exists W (ssList(W) & app(V,W) = U))))))) # label(ax5) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.11 6 (all U (ssList(U) -> (all V (ssList(V) -> (rearsegP(U,V) <-> (exists W (ssList(W) & app(W,V) = U))))))) # label(ax6) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.11 7 (all U (ssList(U) -> (all V (ssList(V) -> (segmentP(U,V) <-> (exists W (ssList(W) & (exists X (ssList(X) & app(app(W,V),X) = U))))))))) # label(ax7) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.11 8 (all U (ssList(U) -> (cyclefreeP(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)))))))))))))))) # label(ax8) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.11 9 (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(V,W) | leq(W,V))))))))))))))) # label(ax9) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.11 10 (all U (ssList(U) -> (strictorderP(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))))))))))))))) # label(ax10) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.11 11 (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) -> (app(app(X,cons(V,Y)),cons(W,Z)) = U -> leq(V,W))))))))))))))) # label(ax11) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.11 12 (all U (ssList(U) -> (strictorderedP(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))))))))))))))) # label(ax12) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.11 13 (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].
% 0.45/1.11 14 (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].
% 0.45/1.11 15 (all U (ssList(U) -> (all V (ssList(V) -> (neq(U,V) <-> U != V))))) # label(ax15) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.11 16 (all U (ssList(U) -> (all V (ssItem(V) -> ssList(cons(V,U)))))) # label(ax16) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.11 17 (all U (ssList(U) -> (all V (ssItem(V) -> cons(V,U) != U)))) # label(ax18) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.11 18 (all U (ssList(U) -> (all V (ssList(V) -> (all W (ssItem(W) -> (all X (ssItem(X) -> (cons(W,U) = cons(X,V) -> W = X & V = U))))))))) # label(ax19) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.11 19 (all U (ssList(U) -> nil = U | (exists V (ssList(V) & (exists W (ssItem(W) & cons(W,V) = U)))))) # label(ax20) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.11 20 (all U (ssList(U) -> (all V (ssItem(V) -> nil != cons(V,U))))) # label(ax21) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.11 21 (all U (ssList(U) -> (nil != U -> ssItem(hd(U))))) # label(ax22) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.11 22 (all U (ssList(U) -> (all V (ssItem(V) -> hd(cons(V,U)) = V)))) # label(ax23) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.11 23 (all U (ssList(U) -> (nil != U -> ssList(tl(U))))) # label(ax24) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.11 24 (all U (ssList(U) -> (all V (ssItem(V) -> tl(cons(V,U)) = U)))) # label(ax25) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.11 25 (all U (ssList(U) -> (all V (ssList(V) -> ssList(app(U,V)))))) # label(ax26) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.11 26 (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].
% 0.45/1.11 27 (all U (ssList(U) -> app(nil,U) = U)) # label(ax28) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.11 28 (all U (ssItem(U) -> (all V (ssItem(V) -> (leq(U,V) & leq(V,U) -> U = V))))) # label(ax29) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.11 29 (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].
% 0.45/1.11 30 (all U (ssItem(U) -> leq(U,U))) # label(ax31) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.11 31 (all U (ssItem(U) -> (all V (ssItem(V) -> (geq(U,V) <-> leq(V,U)))))) # label(ax32) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.11 32 (all U (ssItem(U) -> (all V (ssItem(V) -> (lt(U,V) -> -lt(V,U)))))) # label(ax33) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.11 33 (all U (ssItem(U) -> (all V (ssItem(V) -> (all W (ssItem(W) -> (lt(U,V) & lt(V,W) -> lt(U,W)))))))) # label(ax34) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.11 34 (all U (ssItem(U) -> (all V (ssItem(V) -> (gt(U,V) <-> lt(V,U)))))) # label(ax35) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.11 35 (all U (ssItem(U) -> (all V (ssList(V) -> (all W (ssList(W) -> (memberP(app(V,W),U) <-> memberP(V,U) | memberP(W,U)))))))) # label(ax36) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.11 36 (all U (ssItem(U) -> (all V (ssItem(V) -> (all W (ssList(W) -> (memberP(cons(V,W),U) <-> U = V | memberP(W,U)))))))) # label(ax37) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.11 37 (all U (ssItem(U) -> -memberP(nil,U))) # label(ax38) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.11 38 (all U (ssList(U) -> (all V (ssList(V) -> (all W (ssList(W) -> (frontsegP(U,V) & frontsegP(V,W) -> frontsegP(U,W)))))))) # label(ax40) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.11 39 (all U (ssList(U) -> (all V (ssList(V) -> (frontsegP(U,V) & frontsegP(V,U) -> U = V))))) # label(ax41) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.11 40 (all U (ssList(U) -> frontsegP(U,U))) # label(ax42) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.11 41 (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].
% 0.45/1.11 42 (all U (ssItem(U) -> (all V (ssItem(V) -> (all W (ssList(W) -> (all X (ssList(X) -> (frontsegP(cons(U,W),cons(V,X)) <-> U = V & frontsegP(W,X)))))))))) # label(ax44) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.11 43 (all U (ssList(U) -> frontsegP(U,nil))) # label(ax45) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.11 44 (all U (ssList(U) -> (frontsegP(nil,U) <-> nil = U))) # label(ax46) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.11 45 (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].
% 0.45/1.11 46 (all U (ssList(U) -> (all V (ssList(V) -> (rearsegP(U,V) & rearsegP(V,U) -> U = V))))) # label(ax48) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.11 47 (all U (ssList(U) -> rearsegP(U,U))) # label(ax49) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.11 48 (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].
% 0.45/1.11 49 (all U (ssList(U) -> rearsegP(U,nil))) # label(ax51) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.11 50 (all U (ssList(U) -> (rearsegP(nil,U) <-> nil = U))) # label(ax52) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.11 51 (all U (ssList(U) -> (all V (ssList(V) -> (all W (ssList(W) -> (segmentP(U,V) & segmentP(V,W) -> segmentP(U,W)))))))) # label(ax53) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.11 52 (all U (ssList(U) -> (all V (ssList(V) -> (segmentP(U,V) & segmentP(V,U) -> U = V))))) # label(ax54) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.11 53 (all U (ssList(U) -> segmentP(U,U))) # label(ax55) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.11 54 (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].
% 0.45/1.11 55 (all U (ssList(U) -> segmentP(U,nil))) # label(ax57) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.11 56 (all U (ssList(U) -> (segmentP(nil,U) <-> nil = U))) # label(ax58) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.11 57 (all U (ssItem(U) -> cyclefreeP(cons(U,nil)))) # label(ax59) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.11 58 (all U (ssItem(U) -> totalorderP(cons(U,nil)))) # label(ax61) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.11 59 (all U (ssItem(U) -> strictorderP(cons(U,nil)))) # label(ax63) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.11 60 (all U (ssItem(U) -> totalorderedP(cons(U,nil)))) # label(ax65) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.11 61 (all U (ssItem(U) -> (all V (ssList(V) -> (totalorderedP(cons(U,V)) <-> nil = V | nil != V & totalorderedP(V) & leq(U,hd(V))))))) # label(ax67) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.11 62 (all U (ssItem(U) -> strictorderedP(cons(U,nil)))) # label(ax68) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.11 63 (all U (ssItem(U) -> (all V (ssList(V) -> (strictorderedP(cons(U,V)) <-> nil = V | nil != V & strictorderedP(V) & lt(U,hd(V))))))) # label(ax70) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.11 64 (all U (ssItem(U) -> duplicatefreeP(cons(U,nil)))) # label(ax71) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.11 65 (all U (ssItem(U) -> equalelemsP(cons(U,nil)))) # label(ax73) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.11 66 (all U (ssList(U) -> (nil != U -> (exists V (ssItem(V) & hd(U) = V))))) # label(ax75) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.11 67 (all U (ssList(U) -> (nil != U -> (exists V (ssList(V) & tl(U) = V))))) # label(ax76) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.11 68 (all U (ssList(U) -> (all V (ssList(V) -> (nil != V & nil != U & hd(V) = hd(U) & tl(V) = tl(U) -> V = U))))) # label(ax77) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.11 69 (all U (ssList(U) -> (nil != U -> cons(hd(U),tl(U)) = U))) # label(ax78) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.11 70 (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].
% 0.45/1.11 71 (all U (ssList(U) -> (all V (ssList(V) -> (all W (ssList(W) -> (app(V,W) = app(V,U) -> W = U))))))) # label(ax80) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.11 72 (all U (ssList(U) -> (all V (ssItem(V) -> cons(V,U) = app(cons(V,nil),U))))) # label(ax81) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.11 73 (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].
% 0.45/1.11 74 (all U (ssList(U) -> (all V (ssList(V) -> (nil = app(U,V) <-> nil = V & nil = U))))) # label(ax83) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.11 75 (all U (ssList(U) -> app(U,nil) = U)) # label(ax84) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.11 76 (all U (ssList(U) -> (all V (ssList(V) -> (nil != U -> hd(app(U,V)) = hd(U)))))) # label(ax85) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.11 77 (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].
% 0.45/1.11 78 (all U (ssItem(U) -> (all V (ssItem(V) -> (geq(U,V) & geq(V,U) -> U = V))))) # label(ax87) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.11 79 (all U (ssItem(U) -> (all V (ssItem(V) -> (all W (ssItem(W) -> (geq(U,V) & geq(V,W) -> geq(U,W)))))))) # label(ax88) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.11 80 (all U (ssItem(U) -> geq(U,U))) # label(ax89) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.11 81 (all U (ssItem(U) -> -lt(U,U))) # label(ax90) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.11 82 (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].
% 0.45/1.11 83 (all U (ssItem(U) -> (all V (ssItem(V) -> (leq(U,V) -> U = V | lt(U,V)))))) # label(ax92) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.11 84 (all U (ssItem(U) -> (all V (ssItem(V) -> (lt(U,V) <-> U != V & leq(U,V)))))) # label(ax93) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.11 85 (all U (ssItem(U) -> (all V (ssItem(V) -> (gt(U,V) -> -gt(V,U)))))) # label(ax94) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.11 86 (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].
% 0.45/1.11 87 -(all U (ssList(U) -> (all V (ssList(V) -> (all W (ssList(W) -> (all X (ssList(X) -> V != X | U != W | -neq(V,nil) | (exists Y (ssList(Y) & neq(Y,nil) & segmentP(V,Y) & segmentP(U,Y))) | (all Z (ssList(Z) -> (all X1 (ssList(X1) -> app(Z,X1) != X | app(X1,Z) != W)))))))))))) # label(co1) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.45/1.11
% 0.45/1.11 ============================== end of process non-clausal formulas ===
% 0.45/1.11
% 0.45/1.11 ============================== PROCESS INITIAL CLAUSES ===============
% 0.45/1.11
% 0.45/1.11 ============================== PREDICATE ELIMINATION =================
% 0.45/1.11 88 -ssList(A) | cyclefreeP(A) | ssItem(f8(A)) # label(ax8) # label(axiom). [clausify(8)].
% 0.45/1.11 89 -ssList(A) | -cyclefreeP(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) # label(ax8) # label(axiom). [clausify(8)].
% 0.45/1.12 Derived: -ssList(A) | ssItem(f8(A)) | -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). [resolve(88,b,89,b)].
% 0.45/1.12 90 -ssList(A) | cyclefreeP(A) | ssItem(f9(A)) # label(ax8) # label(axiom). [clausify(8)].
% 0.45/1.12 Derived: -ssList(A) | ssItem(f9(A)) | -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). [resolve(90,b,89,b)].
% 0.45/1.12 91 -ssList(A) | cyclefreeP(A) | ssList(f10(A)) # label(ax8) # label(axiom). [clausify(8)].
% 0.45/1.12 Derived: -ssList(A) | ssList(f10(A)) | -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). [resolve(91,b,89,b)].
% 0.45/1.12 92 -ssList(A) | cyclefreeP(A) | ssList(f11(A)) # label(ax8) # label(axiom). [clausify(8)].
% 0.45/1.12 Derived: -ssList(A) | ssList(f11(A)) | -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). [resolve(92,b,89,b)].
% 0.45/1.12 93 -ssList(A) | cyclefreeP(A) | ssList(f12(A)) # label(ax8) # label(axiom). [clausify(8)].
% 0.45/1.12 Derived: -ssList(A) | ssList(f12(A)) | -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). [resolve(93,b,89,b)].
% 0.45/1.12 94 -ssList(A) | cyclefreeP(A) | app(app(f10(A),cons(f8(A),f11(A))),cons(f9(A),f12(A))) = A # label(ax8) # label(axiom). [clausify(8)].
% 0.45/1.12 Derived: -ssList(A) | app(app(f10(A),cons(f8(A),f11(A))),cons(f9(A),f12(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(B,C) | -leq(C,B). [resolve(94,b,89,b)].
% 0.45/1.12 95 -ssList(A) | cyclefreeP(A) | leq(f8(A),f9(A)) # label(ax8) # label(axiom). [clausify(8)].
% 0.45/1.12 Derived: -ssList(A) | leq(f8(A),f9(A)) | -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). [resolve(95,b,89,b)].
% 0.45/1.12 96 -ssList(A) | cyclefreeP(A) | leq(f9(A),f8(A)) # label(ax8) # label(axiom). [clausify(8)].
% 0.45/1.12 Derived: -ssList(A) | leq(f9(A),f8(A)) | -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). [resolve(96,b,89,b)].
% 0.45/1.12 97 -ssItem(A) | cyclefreeP(cons(A,nil)) # label(ax59) # label(axiom). [clausify(57)].
% 0.45/1.12 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(97,b,89,b)].
% 0.45/1.12 98 cyclefreeP(nil) # label(ax60) # label(axiom). [assumption].
% 0.45/1.12 Derived: -ssList(nil) | -ssItem(A) | -ssItem(B) | -ssList(C) | -ssList(D) | -ssList(E) | app(app(C,cons(A,D)),cons(B,E)) != nil | -leq(A,B) | -leq(B,A). [resolve(98,a,89,b)].
% 0.45/1.12 99 -ssList(A) | totalorderP(A) | ssItem(f13(A)) # label(ax9) # label(axiom). [clausify(9)].
% 0.45/1.12 100 -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(B,C) | leq(C,B) # label(ax9) # label(axiom). [clausify(9)].
% 0.45/1.12 Derived: -ssList(A) | ssItem(f13(A)) | -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). [resolve(99,b,100,b)].
% 0.45/1.12 101 -ssList(A) | totalorderP(A) | ssItem(f14(A)) # label(ax9) # label(axiom). [clausify(9)].
% 0.45/1.12 Derived: -ssList(A) | ssItem(f14(A)) | -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). [resolve(101,b,100,b)].
% 0.45/1.12 102 -ssList(A) | totalorderP(A) | ssList(f15(A)) # label(ax9) # label(axiom). [clausify(9)].
% 0.45/1.12 Derived: -ssList(A) | ssList(f15(A)) | -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). [resolve(102,b,100,b)].
% 0.45/1.12 103 -ssList(A) | totalorderP(A) | ssList(f16(A)) # label(ax9) # label(axiom). [clausify(9)].
% 0.45/1.12 Derived: -ssList(A) | ssList(f16(A)) | -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). [resolve(103,b,100,b)].
% 0.45/1.12 104 -ssList(A) | totalorderP(A) | ssList(f17(A)) # label(ax9) # label(axiom). [clausify(9)].
% 0.45/1.12 Derived: -ssList(A) | ssList(f17(A)) | -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). [resolve(104,b,100,b)].
% 0.45/1.12 105 -ssList(A) | totalorderP(A) | app(app(f15(A),cons(f13(A),f16(A))),cons(f14(A),f17(A))) = A # label(ax9) # label(axiom). [clausify(9)].
% 0.45/1.12 Derived: -ssList(A) | app(app(f15(A),cons(f13(A),f16(A))),cons(f14(A),f17(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(B,C) | leq(C,B). [resolve(105,b,100,b)].
% 0.45/1.12 106 -ssList(A) | totalorderP(A) | -leq(f13(A),f14(A)) # label(ax9) # label(axiom). [clausify(9)].
% 0.45/1.12 Derived: -ssList(A) | -leq(f13(A),f14(A)) | -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). [resolve(106,b,100,b)].
% 0.45/1.12 107 -ssList(A) | totalorderP(A) | -leq(f14(A),f13(A)) # label(ax9) # label(axiom). [clausify(9)].
% 0.45/1.12 Derived: -ssList(A) | -leq(f14(A),f13(A)) | -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). [resolve(107,b,100,b)].
% 0.45/1.12 108 -ssItem(A) | totalorderP(cons(A,nil)) # label(ax61) # label(axiom). [clausify(58)].
% 0.45/1.12 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(108,b,100,b)].
% 0.45/1.12 109 totalorderP(nil) # label(ax62) # label(axiom). [assumption].
% 0.45/1.12 Derived: -ssList(nil) | -ssItem(A) | -ssItem(B) | -ssList(C) | -ssList(D) | -ssList(E) | app(app(C,cons(A,D)),cons(B,E)) != nil | leq(A,B) | leq(B,A). [resolve(109,a,100,b)].
% 0.45/1.12 110 -ssList(A) | strictorderP(A) | ssItem(f18(A)) # label(ax10) # label(axiom). [clausify(10)].
% 0.45/1.12 111 -ssList(A) | -strictorderP(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) # label(ax10) # label(axiom). [clausify(10)].
% 0.45/1.12 Derived: -ssList(A) | ssItem(f18(A)) | -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). [resolve(110,b,111,b)].
% 0.45/1.12 112 -ssList(A) | strictorderP(A) | ssItem(f19(A)) # label(ax10) # label(axiom). [clausify(10)].
% 0.45/1.12 Derived: -ssList(A) | ssItem(f19(A)) | -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). [resolve(112,b,111,b)].
% 0.45/1.12 113 -ssList(A) | strictorderP(A) | ssList(f20(A)) # label(ax10) # label(axiom). [clausify(10)].
% 0.45/1.12 Derived: -ssList(A) | ssList(f20(A)) | -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). [resolve(113,b,111,b)].
% 0.45/1.12 114 -ssList(A) | strictorderP(A) | ssList(f21(A)) # label(ax10) # label(axiom). [clausify(10)].
% 0.45/1.12 Derived: -ssList(A) | ssList(f21(A)) | -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). [resolve(114,b,111,b)].
% 0.45/1.12 115 -ssList(A) | strictorderP(A) | ssList(f22(A)) # label(ax10) # label(axiom). [clausify(10)].
% 0.45/1.12 Derived: -ssList(A) | ssList(f22(A)) | -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). [resolve(115,b,111,b)].
% 0.45/1.12 116 -ssList(A) | strictorderP(A) | app(app(f20(A),cons(f18(A),f21(A))),cons(f19(A),f22(A))) = A # label(ax10) # label(axiom). [clausify(10)].
% 0.45/1.12 Derived: -ssList(A) | app(app(f20(A),cons(f18(A),f21(A))),cons(f19(A),f22(A))) = A | -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). [resolve(116,b,111,b)].
% 0.45/1.13 117 -ssList(A) | strictorderP(A) | -lt(f18(A),f19(A)) # label(ax10) # label(axiom). [clausify(10)].
% 0.45/1.13 Derived: -ssList(A) | -lt(f18(A),f19(A)) | -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). [resolve(117,b,111,b)].
% 0.45/1.13 118 -ssList(A) | strictorderP(A) | -lt(f19(A),f18(A)) # label(ax10) # label(axiom). [clausify(10)].
% 0.45/1.13 Derived: -ssList(A) | -lt(f19(A),f18(A)) | -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). [resolve(118,b,111,b)].
% 0.45/1.13 119 -ssItem(A) | strictorderP(cons(A,nil)) # label(ax63) # label(axiom). [clausify(59)].
% 0.45/1.13 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) | lt(B,C) | lt(C,B). [resolve(119,b,111,b)].
% 0.45/1.13 120 strictorderP(nil) # label(ax64) # label(axiom). [assumption].
% 0.45/1.13 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(120,a,111,b)].
% 0.45/1.13 121 -ssList(A) | duplicatefreeP(A) | ssItem(f33(A)) # label(ax13) # label(axiom). [clausify(13)].
% 0.45/1.13 122 -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(13)].
% 0.45/1.13 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(121,b,122,b)].
% 0.45/1.13 123 -ssList(A) | duplicatefreeP(A) | ssItem(f34(A)) # label(ax13) # label(axiom). [clausify(13)].
% 0.45/1.13 Derived: -ssList(A) | ssItem(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(123,b,122,b)].
% 0.45/1.13 124 -ssList(A) | duplicatefreeP(A) | ssList(f35(A)) # label(ax13) # label(axiom). [clausify(13)].
% 0.45/1.13 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(124,b,122,b)].
% 0.45/1.13 125 -ssList(A) | duplicatefreeP(A) | ssList(f36(A)) # label(ax13) # label(axiom). [clausify(13)].
% 0.45/1.13 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(125,b,122,b)].
% 0.45/1.13 126 -ssList(A) | duplicatefreeP(A) | ssList(f37(A)) # label(ax13) # label(axiom). [clausify(13)].
% 0.45/1.13 Derived: -ssList(A) | ssList(f37(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(126,b,122,b)].
% 0.45/1.13 127 -ssList(A) | duplicatefreeP(A) | app(app(f35(A),cons(f33(A),f36(A))),cons(f34(A),f37(A))) = A # label(ax13) # label(axiom). [clausify(13)].
% 0.45/1.13 Derived: -ssList(A) | app(app(f35(A),cons(f33(A),f36(A))),cons(f34(A),f37(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(127,b,122,b)].
% 0.45/1.13 128 -ssList(A) | duplicatefreeP(A) | f34(A) = f33(A) # label(ax13) # label(axiom). [clausify(13)].
% 0.45/1.13 Derived: -ssList(A) | f34(A) = 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(128,b,122,b)].
% 0.45/1.13 129 -ssItem(A) | duplicatefreeP(cons(A,nil)) # label(ax71) # label(axiom). [clausify(64)].
% 0.45/1.13 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) | C != B. [resolve(129,b,122,b)].
% 0.45/1.13 130 duplicatefreeP(nil) # label(ax72) # label(axiom). [assumption].
% 0.45/1.13 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(130,a,122,b)].
% 0.45/1.13 131 -ssList(A) | equalelemsP(A) | ssItem(f38(A)) # label(ax14) # label(axiom). [clausify(14)].
% 2.84/3.16 132 -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(14)].
% 2.84/3.16 Derived: -ssList(A) | ssItem(f38(A)) | -ssList(A) | -ssItem(B) | -ssItem(C) | -ssList(D) | -ssList(E) | app(D,cons(B,cons(C,E))) != A | C = B. [resolve(131,b,132,b)].
% 2.84/3.16 133 -ssList(A) | equalelemsP(A) | ssItem(f39(A)) # label(ax14) # label(axiom). [clausify(14)].
% 2.84/3.16 Derived: -ssList(A) | ssItem(f39(A)) | -ssList(A) | -ssItem(B) | -ssItem(C) | -ssList(D) | -ssList(E) | app(D,cons(B,cons(C,E))) != A | C = B. [resolve(133,b,132,b)].
% 2.84/3.16 134 -ssList(A) | equalelemsP(A) | ssList(f40(A)) # label(ax14) # label(axiom). [clausify(14)].
% 2.84/3.16 Derived: -ssList(A) | ssList(f40(A)) | -ssList(A) | -ssItem(B) | -ssItem(C) | -ssList(D) | -ssList(E) | app(D,cons(B,cons(C,E))) != A | C = B. [resolve(134,b,132,b)].
% 2.84/3.16 135 -ssList(A) | equalelemsP(A) | ssList(f41(A)) # label(ax14) # label(axiom). [clausify(14)].
% 2.84/3.16 Derived: -ssList(A) | ssList(f41(A)) | -ssList(A) | -ssItem(B) | -ssItem(C) | -ssList(D) | -ssList(E) | app(D,cons(B,cons(C,E))) != A | C = B. [resolve(135,b,132,b)].
% 2.84/3.16 136 -ssList(A) | equalelemsP(A) | app(f40(A),cons(f38(A),cons(f39(A),f41(A)))) = A # label(ax14) # label(axiom). [clausify(14)].
% 2.84/3.16 Derived: -ssList(A) | app(f40(A),cons(f38(A),cons(f39(A),f41(A)))) = A | -ssList(A) | -ssItem(B) | -ssItem(C) | -ssList(D) | -ssList(E) | app(D,cons(B,cons(C,E))) != A | C = B. [resolve(136,b,132,b)].
% 2.84/3.16 137 -ssList(A) | equalelemsP(A) | f39(A) != f38(A) # label(ax14) # label(axiom). [clausify(14)].
% 2.84/3.16 Derived: -ssList(A) | f39(A) != f38(A) | -ssList(A) | -ssItem(B) | -ssItem(C) | -ssList(D) | -ssList(E) | app(D,cons(B,cons(C,E))) != A | C = B. [resolve(137,b,132,b)].
% 2.84/3.16 138 -ssItem(A) | equalelemsP(cons(A,nil)) # label(ax73) # label(axiom). [clausify(65)].
% 2.84/3.16 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(138,b,132,b)].
% 2.84/3.16 139 equalelemsP(nil) # label(ax74) # label(axiom). [assumption].
% 2.84/3.16 Derived: -ssList(nil) | -ssItem(A) | -ssItem(B) | -ssList(C) | -ssList(D) | app(C,cons(A,cons(B,D))) != nil | B = A. [resolve(139,a,132,b)].
% 2.84/3.16
% 2.84/3.16 ============================== end predicate elimination =============
% 2.84/3.16
% 2.84/3.16 Auto_denials: (non-Horn, no changes).
% 2.84/3.16
% 2.84/3.16 Term ordering decisions:
% 2.84/3.16 Function symbol KB weights: nil=1. c1=1. c2=1. c3=1. c4=1. c5=1. c6=1. c7=1. c8=1. cons=1. app=1. f1=1. f2=1. f4=1. f5=1. f6=1. f7=1. hd=1. tl=1. f3=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. f37=1. f38=1. f39=1. f40=1. f41=1. f42=1. f43=1. f44=1. f45=1.
% 2.84/3.16
% 2.84/3.16 ============================== end of process initial clauses ========
% 2.84/3.16
% 2.84/3.16 ============================== CLAUSES FOR SEARCH ====================
% 2.84/3.16
% 2.84/3.16 ============================== end of clauses for search =============
% 2.84/3.16
% 2.84/3.16 ============================== SEARCH ================================
% 2.84/3.16
% 2.84/3.16 % Starting search at 0.28 seconds.
% 2.84/3.16
% 2.84/3.16 Low Water (keep): wt=41.000, iters=3737
% 2.84/3.16
% 2.84/3.16 Low Water (keep): wt=33.000, iters=3480
% 2.84/3.16
% 2.84/3.16 Low Water (keep): wt=31.000, iters=3334
% 2.84/3.16
% 2.84/3.16 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 37 (0.00 of 0.78 sec).
% 2.84/3.16
% 2.84/3.16 Low Water (keep): wt=30.000, iters=3569
% 2.84/3.16
% 2.84/3.16 Low Water (keep): wt=29.000, iters=3525
% 2.84/3.16
% 2.84/3.16 Low Water (keep): wt=28.000, iters=3348
% 2.84/3.16
% 2.84/3.16 Low Water (keep): wt=26.000, iters=3476
% 2.84/3.16
% 2.84/3.16 Low Water (keep): wt=23.000, iters=3450
% 2.84/3.16
% 2.84/3.16 Low Water (keep): wt=22.000, iters=3389
% 2.84/3.16
% 2.84/3.16 Low Water (keep): wt=21.000, iters=3350
% 2.84/3.16
% 2.84/3.16 Low Water (keep): wt=20.000, iters=3429
% 2.84/3.16
% 2.84/3.16 Low Water (keep): wt=19.000, iters=3398
% 2.84/3.16
% 2.84/3.16 Low Water (keep): wt=18.000, iters=3443
% 2.84/3.16
% 2.84/3.16 Low Water (keep): wt=17.000, iters=3388
% 2.84/3.16
% 2.84/3.16 Low Water (keep): wt=16.000, iters=3343
% 2.84/3.16
% 2.84/3.16 Low Water (keep): wt=14.000, iters=3370
% 2.84/3.16
% 2.84/3.16 Low Water (keep): wt=13.000, iters=3355
% 2.84/3.16
% 2.84/3.16 Low Water (keep): wt=12.000, iters=3390
% 2.84/3.16
% 2.84/3.16 Low Water (displace): id=3053, wt=43.000
% 2.84/3.16
% 2.84/3.16 Low Water (displace): id=3079, wt=41.000
% 2.84/3.16
% 2.84/3.16 Low Water (displace): id=13334, wt=11.000
% 2.84/3.16
% 2.84/3.16 Low Water (keep): wt=11.000, iters=3341
% 167.14/167.39
% 167.14/167.39 Low Water (displace): id=14136, wt=10.000
% 167.14/167.39
% 167.14/167.39 Low Water (displace): id=14308, wt=9.000
% 167.14/167.39
% 167.14/167.39 Low Water (displace): id=19279, wt=8.000
% 167.14/167.39
% 167.14/167.39 Low Water (keep): wt=10.000, iters=3345
% 167.14/167.39
% 167.14/167.39 Low Water (displace): id=21195, wt=7.000
% 167.14/167.39
% 167.14/167.39 Low Water (displace): id=25909, wt=6.000
% 167.14/167.39
% 167.14/167.39 Low Water (keep): wt=9.000, iters=3336
% 167.14/167.39
% 167.14/167.39 ============================== PROOF =================================
% 167.14/167.39 % SZS status Theorem
% 167.14/167.39 % SZS output start Refutation
% 167.14/167.39
% 167.14/167.39 % Proof 1 at 159.55 (+ 6.76) seconds.
% 167.14/167.39 % Length of proof is 73.
% 167.14/167.39 % Level of proof is 8.
% 167.14/167.39 % Maximum clause weight is 18.000.
% 167.14/167.39 % Given clauses 21065.
% 167.14/167.39
% 167.14/167.39 5 (all U (ssList(U) -> (all V (ssList(V) -> (frontsegP(U,V) <-> (exists W (ssList(W) & app(V,W) = U))))))) # label(ax5) # label(axiom) # label(non_clause). [assumption].
% 167.14/167.39 6 (all U (ssList(U) -> (all V (ssList(V) -> (rearsegP(U,V) <-> (exists W (ssList(W) & app(W,V) = U))))))) # label(ax6) # label(axiom) # label(non_clause). [assumption].
% 167.14/167.39 7 (all U (ssList(U) -> (all V (ssList(V) -> (segmentP(U,V) <-> (exists W (ssList(W) & (exists X (ssList(X) & app(app(W,V),X) = U))))))))) # label(ax7) # label(axiom) # label(non_clause). [assumption].
% 167.14/167.39 15 (all U (ssList(U) -> (all V (ssList(V) -> (neq(U,V) <-> U != V))))) # label(ax15) # label(axiom) # label(non_clause). [assumption].
% 167.14/167.39 27 (all U (ssList(U) -> app(nil,U) = U)) # label(ax28) # label(axiom) # label(non_clause). [assumption].
% 167.14/167.39 40 (all U (ssList(U) -> frontsegP(U,U))) # label(ax42) # label(axiom) # label(non_clause). [assumption].
% 167.14/167.39 47 (all U (ssList(U) -> rearsegP(U,U))) # label(ax49) # label(axiom) # label(non_clause). [assumption].
% 167.14/167.39 53 (all U (ssList(U) -> segmentP(U,U))) # label(ax55) # label(axiom) # label(non_clause). [assumption].
% 167.14/167.39 54 (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].
% 167.14/167.39 73 (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].
% 167.14/167.39 75 (all U (ssList(U) -> app(U,nil) = U)) # label(ax84) # label(axiom) # label(non_clause). [assumption].
% 167.14/167.39 87 -(all U (ssList(U) -> (all V (ssList(V) -> (all W (ssList(W) -> (all X (ssList(X) -> V != X | U != W | -neq(V,nil) | (exists Y (ssList(Y) & neq(Y,nil) & segmentP(V,Y) & segmentP(U,Y))) | (all Z (ssList(Z) -> (all X1 (ssList(X1) -> app(Z,X1) != X | app(X1,Z) != W)))))))))))) # label(co1) # label(negated_conjecture) # label(non_clause). [assumption].
% 167.14/167.39 152 -ssList(A) | -ssList(B) | -frontsegP(A,B) | ssList(f4(A,B)) # label(ax5) # label(axiom). [clausify(5)].
% 167.14/167.39 153 -ssList(A) | -ssList(B) | -frontsegP(A,B) | app(B,f4(A,B)) = A # label(ax5) # label(axiom). [clausify(5)].
% 167.14/167.39 155 -ssList(A) | -ssList(B) | -rearsegP(A,B) | ssList(f5(A,B)) # label(ax6) # label(axiom). [clausify(6)].
% 167.14/167.39 156 -ssList(A) | -ssList(B) | -rearsegP(A,B) | app(f5(A,B),B) = A # label(ax6) # label(axiom). [clausify(6)].
% 167.14/167.39 161 -ssList(A) | -ssList(B) | segmentP(A,B) | -ssList(C) | -ssList(D) | app(app(C,B),D) != A # label(ax7) # label(axiom). [clausify(7)].
% 167.14/167.39 179 -ssList(A) | -ssList(B) | neq(A,B) | B = A # label(ax15) # label(axiom). [clausify(15)].
% 167.14/167.39 181 ssList(nil) # label(ax17) # label(axiom). [assumption].
% 167.14/167.39 195 -ssList(A) | app(nil,A) = A # label(ax28) # label(axiom). [clausify(27)].
% 167.14/167.39 215 -ssList(A) | frontsegP(A,A) # label(ax42) # label(axiom). [clausify(40)].
% 167.14/167.39 225 -ssList(A) | rearsegP(A,A) # label(ax49) # label(axiom). [clausify(47)].
% 167.14/167.39 232 -ssList(A) | segmentP(A,A) # label(ax55) # label(axiom). [clausify(53)].
% 167.14/167.39 233 -ssList(A) | -ssList(B) | -ssList(C) | -ssList(D) | -segmentP(A,B) | segmentP(app(app(C,A),D),B) # label(ax56) # label(axiom). [clausify(54)].
% 167.14/167.39 260 -ssList(A) | -ssList(B) | -ssList(C) | app(app(A,B),C) = app(A,app(B,C)) # label(ax82) # label(axiom). [clausify(73)].
% 167.14/167.39 264 -ssList(A) | app(A,nil) = A # label(ax84) # label(axiom). [clausify(75)].
% 167.14/167.39 277 ssList(c3) # label(co1) # label(negated_conjecture). [clausify(87)].
% 167.14/167.39 278 ssList(c4) # label(co1) # label(negated_conjecture). [clausify(87)].
% 167.14/167.39 281 c6 = c4 # label(co1) # label(negated_conjecture). [clausify(87)].
% 167.14/167.39 282 c5 = c3 # label(co1) # label(negated_conjecture). [clausify(87)].
% 167.14/167.39 283 neq(c4,nil) # label(co1) # label(negated_conjecture). [clausify(87)].
% 167.14/167.39 284 -ssList(A) | -neq(A,nil) | -segmentP(c4,A) | -segmentP(c3,A) # label(co1) # label(negated_conjecture). [clausify(87)].
% 167.14/167.39 285 ssList(c7) # label(co1) # label(negated_conjecture). [clausify(87)].
% 167.14/167.39 286 ssList(c8) # label(co1) # label(negated_conjecture). [clausify(87)].
% 167.14/167.39 287 app(c7,c8) = c6 # label(co1) # label(negated_conjecture). [clausify(87)].
% 167.14/167.39 288 app(c7,c8) = c4. [copy(287),rewrite([281(4)])].
% 167.14/167.39 289 app(c8,c7) = c5 # label(co1) # label(negated_conjecture). [clausify(87)].
% 167.14/167.39 290 app(c8,c7) = c3. [copy(289),rewrite([282(4)])].
% 167.14/167.39 384 -ssList(A) | -frontsegP(A,A) | ssList(f4(A,A)). [factor(152,a,b)].
% 167.14/167.39 385 -ssList(A) | -frontsegP(A,A) | app(A,f4(A,A)) = A. [factor(153,a,b)].
% 167.14/167.39 388 -ssList(A) | -rearsegP(A,A) | ssList(f5(A,A)). [factor(155,a,b)].
% 167.14/167.39 389 -ssList(A) | -rearsegP(A,A) | app(f5(A,A),A) = A. [factor(156,a,b)].
% 167.14/167.39 432 -ssList(A) | -ssList(B) | -ssList(C) | -segmentP(A,A) | segmentP(app(app(B,A),C),A). [factor(233,a,b)].
% 167.14/167.39 1636 -ssList(A) | neq(A,nil) | nil = A. [resolve(181,a,179,b)].
% 167.14/167.39 1759 frontsegP(c3,c3). [resolve(277,a,215,a)].
% 167.14/167.39 1760 app(nil,c3) = c3. [resolve(277,a,195,a)].
% 167.14/167.39 1785 -ssList(A) | segmentP(c3,A) | -ssList(B) | -ssList(C) | app(app(B,A),C) != c3. [resolve(277,a,161,a)].
% 167.14/167.39 1817 app(c4,nil) = c4. [resolve(278,a,264,a)].
% 167.14/167.39 1839 segmentP(c4,c4). [resolve(278,a,232,a)].
% 167.14/167.39 1846 app(nil,c4) = c4. [resolve(278,a,195,a)].
% 167.14/167.39 1915 -segmentP(c3,c4). [resolve(284,b,283,a),unit_del(a,278),unit_del(b,1839)].
% 167.14/167.39 1942 segmentP(c7,c7). [resolve(285,a,232,a)].
% 167.14/167.39 1945 rearsegP(c7,c7). [resolve(285,a,225,a)].
% 167.14/167.39 2014 -ssList(A) | -ssList(B) | app(app(A,c8),B) = app(A,app(c8,B)). [resolve(286,a,260,b)].
% 167.14/167.39 2068 -ssList(A) | app(app(A,c8),A) = app(A,app(c8,A)). [factor(2014,a,b)].
% 167.14/167.39 5123 app(c3,f4(c3,c3)) = c3. [resolve(1759,a,385,b),unit_del(a,277)].
% 167.14/167.39 5124 ssList(f4(c3,c3)). [resolve(1759,a,384,b),unit_del(a,277)].
% 167.14/167.39 7042 -ssList(A) | -ssList(B) | segmentP(app(app(A,c7),B),c7). [resolve(1942,a,432,d),unit_del(a,285)].
% 167.14/167.39 7054 app(f5(c7,c7),c7) = c7. [resolve(1945,a,389,b),unit_del(a,285)].
% 167.14/167.39 7055 ssList(f5(c7,c7)). [resolve(1945,a,388,b),unit_del(a,285)].
% 167.14/167.39 10283 neq(c7,nil) | c7 = nil. [resolve(1636,a,285,a),flip(b)].
% 167.14/167.39 26209 -ssList(A) | -ssList(B) | app(app(A,c4),B) != c3. [resolve(1785,a,278,a),unit_del(a,1915)].
% 167.14/167.39 26210 -ssList(A) | app(app(A,c4),A) != c3. [factor(26209,a,b)].
% 167.14/167.39 27883 c7 = nil | -segmentP(c4,c7) | -segmentP(c3,c7). [resolve(10283,a,284,b),unit_del(b,285)].
% 167.14/167.39 65477 c4 != c3. [resolve(26210,a,181,a),rewrite([1846(3),1817(3)])].
% 167.14/167.39 69466 app(c7,c3) = app(c4,c7). [resolve(2068,a,285,a),rewrite([288(3),290(7)]),flip(a)].
% 167.14/167.39 344877 -ssList(A) | segmentP(app(c7,A),c7). [resolve(7042,a,7055,a),rewrite([7054(6)])].
% 167.14/167.39 344878 -ssList(A) | segmentP(app(c3,A),c7). [resolve(7042,a,286,a),rewrite([290(4)])].
% 167.14/167.39 345034 segmentP(c4,c7). [resolve(344877,a,286,a),rewrite([288(3)])].
% 167.14/167.39 345036 c7 = nil | -segmentP(c3,c7). [back_unit_del(27883),unit_del(b,345034)].
% 167.14/167.39 348692 segmentP(c3,c7). [resolve(344878,a,5124,a),rewrite([5123(5)])].
% 167.14/167.39 348707 c7 = nil. [back_unit_del(345036),unit_del(b,348692)].
% 167.14/167.39 350016 $F. [back_rewrite(69466),rewrite([348707(1),1760(3),348707(3),1817(4)]),flip(a),unit_del(a,65477)].
% 167.14/167.39
% 167.14/167.39 % SZS output end Refutation
% 167.14/167.39 ============================== end of proof ==========================
% 167.14/167.39
% 167.14/167.39 ============================== STATISTICS ============================
% 167.14/167.39
% 167.14/167.39 Given=21065. Generated=12820913. Kept=349830. proofs=1.
% 167.14/167.39 Usable=14039. Sos=7164. Demods=544. Limbo=1309, Disabled=327565. Hints=0.
% 167.14/167.39 Megabytes=209.60.
% 167.14/167.39 User_CPU=159.55, System_CPU=6.76, Wall_clock=166.
% 167.14/167.39
% 167.14/167.39 ============================== end of statistics =====================
% 167.14/167.39
% 167.14/167.39 ============================== end of search =========================
% 167.14/167.39
% 167.14/167.39 THEOREM PROVED
% 167.14/167.39 % SZS status Theorem
% 167.14/167.39
% 167.14/167.39 Exiting with 1 proof.
% 167.14/167.39
% 167.14/167.39 Process 28450 exit (max_proofs) Sat Jun 11 22:30:14 2022
% 167.14/167.39 Prover9 interrupted
%------------------------------------------------------------------------------