TSTP Solution File: SWC380+1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SWC380+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 21:47:02 EDT 2022
% Result : Theorem 14.71s 15.03s
% Output : Refutation 14.71s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWC380+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 23:30:57 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.44/1.10 ============================== Prover9 ===============================
% 0.44/1.10 Prover9 (32) version 2009-11A, November 2009.
% 0.44/1.10 Process 18283 was started by sandbox on n006.cluster.edu,
% 0.44/1.10 Sat Jun 11 23:30:58 2022
% 0.44/1.10 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_18130_n006.cluster.edu".
% 0.44/1.10 ============================== end of head ===========================
% 0.44/1.10
% 0.44/1.10 ============================== INPUT =================================
% 0.44/1.10
% 0.44/1.10 % Reading from file /tmp/Prover9_18130_n006.cluster.edu
% 0.44/1.10
% 0.44/1.10 set(prolog_style_variables).
% 0.44/1.10 set(auto2).
% 0.44/1.10 % set(auto2) -> set(auto).
% 0.44/1.10 % set(auto) -> set(auto_inference).
% 0.44/1.10 % set(auto) -> set(auto_setup).
% 0.44/1.10 % set(auto_setup) -> set(predicate_elim).
% 0.44/1.10 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.44/1.10 % set(auto) -> set(auto_limits).
% 0.44/1.10 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.44/1.10 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.44/1.10 % set(auto) -> set(auto_denials).
% 0.44/1.10 % set(auto) -> set(auto_process).
% 0.44/1.10 % set(auto2) -> assign(new_constants, 1).
% 0.44/1.10 % set(auto2) -> assign(fold_denial_max, 3).
% 0.44/1.10 % set(auto2) -> assign(max_weight, "200.000").
% 0.44/1.10 % set(auto2) -> assign(max_hours, 1).
% 0.44/1.10 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.44/1.10 % set(auto2) -> assign(max_seconds, 0).
% 0.44/1.10 % set(auto2) -> assign(max_minutes, 5).
% 0.44/1.10 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.44/1.10 % set(auto2) -> set(sort_initial_sos).
% 0.44/1.10 % set(auto2) -> assign(sos_limit, -1).
% 0.44/1.10 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.44/1.10 % set(auto2) -> assign(max_megs, 400).
% 0.44/1.10 % set(auto2) -> assign(stats, some).
% 0.44/1.10 % set(auto2) -> clear(echo_input).
% 0.44/1.10 % set(auto2) -> set(quiet).
% 0.44/1.10 % set(auto2) -> clear(print_initial_clauses).
% 0.44/1.10 % set(auto2) -> clear(print_given).
% 0.44/1.10 assign(lrs_ticks,-1).
% 0.44/1.10 assign(sos_limit,10000).
% 0.44/1.10 assign(order,kbo).
% 0.44/1.10 set(lex_order_vars).
% 0.44/1.10 clear(print_given).
% 0.44/1.10
% 0.44/1.10 % formulas(sos). % not echoed (96 formulas)
% 0.44/1.10
% 0.44/1.10 ============================== end of input ==========================
% 0.44/1.10
% 0.44/1.10 % From the command line: assign(max_seconds, 300).
% 0.44/1.10
% 0.44/1.10 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.44/1.10
% 0.44/1.10 % Formulas that are not ordinary clauses:
% 0.44/1.10 1 (all U (ssItem(U) -> (all V (ssItem(V) -> (neq(U,V) <-> U != V))))) # label(ax1) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.10 2 (exists U (ssItem(U) & (exists V (ssItem(V) & U != V)))) # label(ax2) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.10 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].
% 0.44/1.10 4 (all U (ssList(U) -> (singletonP(U) <-> (exists V (ssItem(V) & cons(V,nil) = U))))) # label(ax4) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.10 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].
% 0.44/1.10 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].
% 0.44/1.10 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].
% 0.44/1.10 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].
% 0.44/1.10 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].
% 0.44/1.10 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].
% 0.44/1.10 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].
% 0.44/1.10 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].
% 0.44/1.10 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].
% 0.44/1.10 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].
% 0.44/1.10 15 (all U (ssList(U) -> (all V (ssList(V) -> (neq(U,V) <-> U != V))))) # label(ax15) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.10 16 (all U (ssList(U) -> (all V (ssItem(V) -> ssList(cons(V,U)))))) # label(ax16) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.10 17 (all U (ssList(U) -> (all V (ssItem(V) -> cons(V,U) != U)))) # label(ax18) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.10 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].
% 0.44/1.10 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].
% 0.44/1.10 20 (all U (ssList(U) -> (all V (ssItem(V) -> nil != cons(V,U))))) # label(ax21) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.10 21 (all U (ssList(U) -> (nil != U -> ssItem(hd(U))))) # label(ax22) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.10 22 (all U (ssList(U) -> (all V (ssItem(V) -> hd(cons(V,U)) = V)))) # label(ax23) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.10 23 (all U (ssList(U) -> (nil != U -> ssList(tl(U))))) # label(ax24) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.10 24 (all U (ssList(U) -> (all V (ssItem(V) -> tl(cons(V,U)) = U)))) # label(ax25) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.10 25 (all U (ssList(U) -> (all V (ssList(V) -> ssList(app(U,V)))))) # label(ax26) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.10 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].
% 0.44/1.10 27 (all U (ssList(U) -> app(nil,U) = U)) # label(ax28) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.10 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].
% 0.44/1.10 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].
% 0.44/1.10 30 (all U (ssItem(U) -> leq(U,U))) # label(ax31) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.10 31 (all U (ssItem(U) -> (all V (ssItem(V) -> (geq(U,V) <-> leq(V,U)))))) # label(ax32) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.10 32 (all U (ssItem(U) -> (all V (ssItem(V) -> (lt(U,V) -> -lt(V,U)))))) # label(ax33) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.10 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].
% 0.44/1.10 34 (all U (ssItem(U) -> (all V (ssItem(V) -> (gt(U,V) <-> lt(V,U)))))) # label(ax35) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.10 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].
% 0.44/1.10 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].
% 0.44/1.10 37 (all U (ssItem(U) -> -memberP(nil,U))) # label(ax38) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.10 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].
% 0.44/1.10 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].
% 0.44/1.10 40 (all U (ssList(U) -> frontsegP(U,U))) # label(ax42) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.10 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].
% 0.44/1.10 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].
% 0.44/1.10 43 (all U (ssList(U) -> frontsegP(U,nil))) # label(ax45) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.10 44 (all U (ssList(U) -> (frontsegP(nil,U) <-> nil = U))) # label(ax46) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.10 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].
% 0.44/1.10 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].
% 0.44/1.10 47 (all U (ssList(U) -> rearsegP(U,U))) # label(ax49) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.10 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].
% 0.44/1.10 49 (all U (ssList(U) -> rearsegP(U,nil))) # label(ax51) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.10 50 (all U (ssList(U) -> (rearsegP(nil,U) <-> nil = U))) # label(ax52) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.10 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].
% 0.44/1.10 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].
% 0.44/1.10 53 (all U (ssList(U) -> segmentP(U,U))) # label(ax55) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.10 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].
% 0.44/1.10 55 (all U (ssList(U) -> segmentP(U,nil))) # label(ax57) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.10 56 (all U (ssList(U) -> (segmentP(nil,U) <-> nil = U))) # label(ax58) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.10 57 (all U (ssItem(U) -> cyclefreeP(cons(U,nil)))) # label(ax59) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.10 58 (all U (ssItem(U) -> totalorderP(cons(U,nil)))) # label(ax61) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.10 59 (all U (ssItem(U) -> strictorderP(cons(U,nil)))) # label(ax63) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.10 60 (all U (ssItem(U) -> totalorderedP(cons(U,nil)))) # label(ax65) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.10 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].
% 0.44/1.10 62 (all U (ssItem(U) -> strictorderedP(cons(U,nil)))) # label(ax68) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.10 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].
% 0.44/1.10 64 (all U (ssItem(U) -> duplicatefreeP(cons(U,nil)))) # label(ax71) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.10 65 (all U (ssItem(U) -> equalelemsP(cons(U,nil)))) # label(ax73) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.10 66 (all U (ssList(U) -> (nil != U -> (exists V (ssItem(V) & hd(U) = V))))) # label(ax75) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.10 67 (all U (ssList(U) -> (nil != U -> (exists V (ssList(V) & tl(U) = V))))) # label(ax76) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.10 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].
% 0.44/1.10 69 (all U (ssList(U) -> (nil != U -> cons(hd(U),tl(U)) = U))) # label(ax78) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.10 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].
% 0.44/1.10 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].
% 0.44/1.10 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].
% 0.44/1.10 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].
% 0.44/1.10 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].
% 0.44/1.10 75 (all U (ssList(U) -> app(U,nil) = U)) # label(ax84) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.10 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].
% 0.44/1.10 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].
% 0.44/1.10 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].
% 0.44/1.10 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].
% 0.44/1.10 80 (all U (ssItem(U) -> geq(U,U))) # label(ax89) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.10 81 (all U (ssItem(U) -> -lt(U,U))) # label(ax90) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.10 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].
% 0.44/1.10 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].
% 0.44/1.10 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].
% 0.44/1.10 85 (all U (ssItem(U) -> (all V (ssItem(V) -> (gt(U,V) -> -gt(V,U)))))) # label(ax94) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.10 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].
% 0.44/1.10 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 (ssItem(Y) & cons(Y,nil) = U & memberP(V,Y))) | (all Z (ssItem(Z) -> (all X1 (ssList(X1) -> cons(Z,nil) != W | app(cons(Z,nil),X1) != X))))) & (-neq(V,nil) | neq(X,nil)))))))))) # label(co1) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.44/1.10
% 0.44/1.10 ============================== end of process non-clausal formulas ===
% 0.44/1.10
% 0.44/1.10 ============================== PROCESS INITIAL CLAUSES ===============
% 0.44/1.10
% 0.44/1.10 ============================== PREDICATE ELIMINATION =================
% 0.44/1.10 88 -ssList(A) | cyclefreeP(A) | ssItem(f8(A)) # label(ax8) # label(axiom). [clausify(8)].
% 0.44/1.10 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)].
% 0.44/1.12 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)].
% 0.44/1.12 90 -ssList(A) | cyclefreeP(A) | ssItem(f9(A)) # label(ax8) # label(axiom). [clausify(8)].
% 0.44/1.12 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)].
% 0.44/1.12 91 -ssList(A) | cyclefreeP(A) | ssList(f10(A)) # label(ax8) # label(axiom). [clausify(8)].
% 0.44/1.12 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)].
% 0.44/1.12 92 -ssList(A) | cyclefreeP(A) | ssList(f11(A)) # label(ax8) # label(axiom). [clausify(8)].
% 0.44/1.12 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)].
% 0.44/1.12 93 -ssList(A) | cyclefreeP(A) | ssList(f12(A)) # label(ax8) # label(axiom). [clausify(8)].
% 0.44/1.12 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)].
% 0.44/1.12 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)].
% 0.44/1.12 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)].
% 0.44/1.12 95 -ssList(A) | cyclefreeP(A) | leq(f8(A),f9(A)) # label(ax8) # label(axiom). [clausify(8)].
% 0.44/1.12 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)].
% 0.44/1.12 96 -ssList(A) | cyclefreeP(A) | leq(f9(A),f8(A)) # label(ax8) # label(axiom). [clausify(8)].
% 0.44/1.12 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)].
% 0.44/1.12 97 -ssItem(A) | cyclefreeP(cons(A,nil)) # label(ax59) # label(axiom). [clausify(57)].
% 0.44/1.12 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)].
% 0.44/1.12 98 cyclefreeP(nil) # label(ax60) # label(axiom). [assumption].
% 0.44/1.12 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)].
% 0.44/1.12 99 -ssList(A) | totalorderP(A) | ssItem(f13(A)) # label(ax9) # label(axiom). [clausify(9)].
% 0.44/1.12 100 -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)].
% 0.44/1.12 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)].
% 0.44/1.12 101 -ssList(A) | totalorderP(A) | ssItem(f14(A)) # label(ax9) # label(axiom). [clausify(9)].
% 0.44/1.12 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)].
% 0.44/1.12 102 -ssList(A) | totalorderP(A) | ssList(f15(A)) # label(ax9) # label(axiom). [clausify(9)].
% 0.44/1.12 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)].
% 0.44/1.13 103 -ssList(A) | totalorderP(A) | ssList(f16(A)) # label(ax9) # label(axiom). [clausify(9)].
% 0.44/1.13 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)].
% 0.44/1.13 104 -ssList(A) | totalorderP(A) | ssList(f17(A)) # label(ax9) # label(axiom). [clausify(9)].
% 0.44/1.13 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)].
% 0.44/1.13 105 -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)].
% 0.44/1.13 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)].
% 0.44/1.13 106 -ssList(A) | totalorderP(A) | -leq(f13(A),f14(A)) # label(ax9) # label(axiom). [clausify(9)].
% 0.44/1.13 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)].
% 0.44/1.13 107 -ssList(A) | totalorderP(A) | -leq(f14(A),f13(A)) # label(ax9) # label(axiom). [clausify(9)].
% 0.44/1.13 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)].
% 0.44/1.13 108 -ssItem(A) | totalorderP(cons(A,nil)) # label(ax61) # label(axiom). [clausify(58)].
% 0.44/1.13 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) | leq(B,C) | leq(C,B). [resolve(108,b,100,b)].
% 0.44/1.13 109 totalorderP(nil) # label(ax62) # label(axiom). [assumption].
% 0.44/1.13 Derived: -ssList(nil) | -ssItem(A) | -ssItem(B) | -ssList(C) | -ssList(D) | -ssList(E) | app(app(C,cons(A,D)),cons(B,E)) != nil | leq(A,B) | leq(B,A). [resolve(109,a,100,b)].
% 0.44/1.13 110 -ssList(A) | strictorderP(A) | ssItem(f18(A)) # label(ax10) # label(axiom). [clausify(10)].
% 0.44/1.13 111 -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)].
% 0.44/1.13 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)].
% 0.44/1.13 112 -ssList(A) | strictorderP(A) | ssItem(f19(A)) # label(ax10) # label(axiom). [clausify(10)].
% 0.44/1.13 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)].
% 0.44/1.13 113 -ssList(A) | strictorderP(A) | ssList(f20(A)) # label(ax10) # label(axiom). [clausify(10)].
% 0.44/1.13 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)].
% 0.44/1.13 114 -ssList(A) | strictorderP(A) | ssList(f21(A)) # label(ax10) # label(axiom). [clausify(10)].
% 0.44/1.13 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)].
% 0.44/1.13 115 -ssList(A) | strictorderP(A) | ssList(f22(A)) # label(ax10) # label(axiom). [clausify(10)].
% 0.44/1.13 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)].
% 0.44/1.13 116 -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)].
% 0.44/1.13 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)].
% 0.44/1.16 117 -ssList(A) | strictorderP(A) | -lt(f18(A),f19(A)) # label(ax10) # label(axiom). [clausify(10)].
% 0.44/1.16 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)].
% 0.44/1.16 118 -ssList(A) | strictorderP(A) | -lt(f19(A),f18(A)) # label(ax10) # label(axiom). [clausify(10)].
% 0.44/1.16 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)].
% 0.44/1.16 119 -ssItem(A) | strictorderP(cons(A,nil)) # label(ax63) # label(axiom). [clausify(59)].
% 0.44/1.16 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)].
% 0.44/1.16 120 strictorderP(nil) # label(ax64) # label(axiom). [assumption].
% 0.44/1.16 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)].
% 0.44/1.16 121 -ssList(A) | duplicatefreeP(A) | ssItem(f33(A)) # label(ax13) # label(axiom). [clausify(13)].
% 0.44/1.16 122 -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)].
% 0.44/1.16 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)].
% 0.44/1.16 123 -ssList(A) | duplicatefreeP(A) | ssItem(f34(A)) # label(ax13) # label(axiom). [clausify(13)].
% 0.44/1.16 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)].
% 0.44/1.16 124 -ssList(A) | duplicatefreeP(A) | ssList(f35(A)) # label(ax13) # label(axiom). [clausify(13)].
% 0.44/1.16 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)].
% 0.44/1.16 125 -ssList(A) | duplicatefreeP(A) | ssList(f36(A)) # label(ax13) # label(axiom). [clausify(13)].
% 0.44/1.16 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)].
% 0.44/1.16 126 -ssList(A) | duplicatefreeP(A) | ssList(f37(A)) # label(ax13) # label(axiom). [clausify(13)].
% 0.44/1.16 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)].
% 0.44/1.16 127 -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)].
% 0.44/1.16 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)].
% 0.44/1.16 128 -ssList(A) | duplicatefreeP(A) | f34(A) = f33(A) # label(ax13) # label(axiom). [clausify(13)].
% 0.44/1.16 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)].
% 0.44/1.16 129 -ssItem(A) | duplicatefreeP(cons(A,nil)) # label(ax71) # label(axiom). [clausify(64)].
% 0.44/1.16 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)].
% 0.44/1.16 130 duplicatefreeP(nil) # label(ax72) # label(axiom). [assumption].
% 0.44/1.16 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)].
% 0.44/1.16 131 -ssList(A) | equalelemsP(A) | ssItem(f38(A)) # label(ax14) # label(axiom). [clausify(14)].
% 3.04/3.35 132 -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)].
% 3.04/3.35 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)].
% 3.04/3.35 133 -ssList(A) | equalelemsP(A) | ssItem(f39(A)) # label(ax14) # label(axiom). [clausify(14)].
% 3.04/3.35 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)].
% 3.04/3.35 134 -ssList(A) | equalelemsP(A) | ssList(f40(A)) # label(ax14) # label(axiom). [clausify(14)].
% 3.04/3.35 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)].
% 3.04/3.35 135 -ssList(A) | equalelemsP(A) | ssList(f41(A)) # label(ax14) # label(axiom). [clausify(14)].
% 3.04/3.35 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)].
% 3.04/3.35 136 -ssList(A) | equalelemsP(A) | app(f40(A),cons(f38(A),cons(f39(A),f41(A)))) = A # label(ax14) # label(axiom). [clausify(14)].
% 3.04/3.35 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)].
% 3.04/3.35 137 -ssList(A) | equalelemsP(A) | f39(A) != f38(A) # label(ax14) # label(axiom). [clausify(14)].
% 3.04/3.35 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)].
% 3.04/3.35 138 -ssItem(A) | equalelemsP(cons(A,nil)) # label(ax73) # label(axiom). [clausify(65)].
% 3.04/3.35 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)].
% 3.04/3.35 139 equalelemsP(nil) # label(ax74) # label(axiom). [assumption].
% 3.04/3.35 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)].
% 3.04/3.35
% 3.04/3.35 ============================== end predicate elimination =============
% 3.04/3.35
% 3.04/3.35 Auto_denials: (non-Horn, no changes).
% 3.04/3.35
% 3.04/3.35 Term ordering decisions:
% 3.04/3.35 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.
% 3.04/3.35
% 3.04/3.35 ============================== end of process initial clauses ========
% 3.04/3.35
% 3.04/3.35 ============================== CLAUSES FOR SEARCH ====================
% 3.04/3.35
% 3.04/3.35 ============================== end of clauses for search =============
% 3.04/3.35
% 3.04/3.35 ============================== SEARCH ================================
% 3.04/3.35
% 3.04/3.35 % Starting search at 0.45 seconds.
% 3.04/3.35
% 3.04/3.35 Low Water (keep): wt=40.000, iters=4245
% 3.04/3.35
% 3.04/3.35 Low Water (keep): wt=29.000, iters=3407
% 3.04/3.35
% 3.04/3.35 Low Water (keep): wt=28.000, iters=3437
% 3.04/3.35
% 3.04/3.35 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 38 (0.00 of 1.14 sec).
% 3.04/3.35
% 3.04/3.35 Low Water (keep): wt=26.000, iters=3340
% 3.04/3.35
% 3.04/3.35 Low Water (keep): wt=25.000, iters=3344
% 3.04/3.35
% 3.04/3.35 Low Water (keep): wt=24.000, iters=3411
% 3.04/3.35
% 3.04/3.35 Low Water (keep): wt=23.000, iters=3540
% 3.04/3.35
% 3.04/3.35 Low Water (keep): wt=22.000, iters=3461
% 3.04/3.35
% 3.04/3.35 Low Water (keep): wt=21.000, iters=3436
% 3.04/3.35
% 3.04/3.35 Low Water (keep): wt=20.000, iters=3397
% 3.04/3.35
% 3.04/3.35 Low Water (keep): wt=19.000, iters=3339
% 3.04/3.35
% 3.04/3.35 Low Water (keep): wt=18.000, iters=3395
% 3.04/3.35
% 3.04/3.35 Low Water (keep): wt=17.000, iters=3433
% 3.04/3.35
% 3.04/3.35 Low Water (keep): wt=16.000, iters=3393
% 3.04/3.35
% 3.04/3.35 Low Water (displace): id=3472, wt=43.000
% 3.04/3.35
% 3.04/3.35 Low Water (displace): id=3511, wt=41.000
% 3.04/3.35
% 3.04/3.35 Low Water (displace): id=3571, wt=39.000
% 3.04/3.35
% 3.04/3.35 Low Water (keep): wt=15.000, iters=3378
% 3.04/3.35
% 3.04/3.35 Low Water (displace): id=3493, wt=38.000
% 3.04/3.35
% 3.04/3.35 Low Water (displace): id=3598, wt=37.000
% 3.04/3.35
% 3.04/3.35 Low Water (displace): id=3550, wt=36.000
% 14.71/15.03
% 14.71/15.03 Low Water (displace): id=3595, wt=34.000
% 14.71/15.03
% 14.71/15.03 Low Water (keep): wt=14.000, iters=3353
% 14.71/15.03
% 14.71/15.03 Low Water (displace): id=3906, wt=33.000
% 14.71/15.03
% 14.71/15.03 Low Water (displace): id=3601, wt=32.000
% 14.71/15.03
% 14.71/15.03 Low Water (displace): id=3938, wt=31.000
% 14.71/15.03
% 14.71/15.03 Low Water (displace): id=3337, wt=30.000
% 14.71/15.03
% 14.71/15.03 Low Water (displace): id=13491, wt=12.000
% 14.71/15.03
% 14.71/15.03 Low Water (displace): id=13496, wt=11.000
% 14.71/15.03
% 14.71/15.03 Low Water (displace): id=13519, wt=10.000
% 14.71/15.03
% 14.71/15.03 Low Water (displace): id=14419, wt=9.000
% 14.71/15.03
% 14.71/15.03 Low Water (keep): wt=13.000, iters=3335
% 14.71/15.03
% 14.71/15.03 Low Water (displace): id=21353, wt=8.000
% 14.71/15.03
% 14.71/15.03 Low Water (keep): wt=12.000, iters=3342
% 14.71/15.03
% 14.71/15.03 Low Water (displace): id=23773, wt=7.000
% 14.71/15.03
% 14.71/15.03 Low Water (keep): wt=11.000, iters=3333
% 14.71/15.03
% 14.71/15.03 Low Water (displace): id=28053, wt=6.000
% 14.71/15.03
% 14.71/15.03 Low Water (keep): wt=10.000, iters=3333
% 14.71/15.03
% 14.71/15.03 ============================== PROOF =================================
% 14.71/15.03 % SZS status Theorem
% 14.71/15.03 % SZS output start Refutation
% 14.71/15.03
% 14.71/15.03 % Proof 1 at 13.71 (+ 0.24) seconds.
% 14.71/15.03 % Length of proof is 24.
% 14.71/15.03 % Level of proof is 6.
% 14.71/15.03 % Maximum clause weight is 14.000.
% 14.71/15.03 % Given clauses 4073.
% 14.71/15.03
% 14.71/15.03 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].
% 14.71/15.04 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].
% 14.71/15.04 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 (ssItem(Y) & cons(Y,nil) = U & memberP(V,Y))) | (all Z (ssItem(Z) -> (all X1 (ssList(X1) -> cons(Z,nil) != W | app(cons(Z,nil),X1) != X))))) & (-neq(V,nil) | neq(X,nil)))))))))) # label(co1) # label(negated_conjecture) # label(non_clause). [assumption].
% 14.71/15.04 209 -ssItem(A) | -ssItem(B) | -ssList(C) | memberP(cons(B,C),A) | B != A # label(ax37) # label(axiom). [clausify(36)].
% 14.71/15.04 259 -ssList(A) | -ssItem(B) | app(cons(B,nil),A) = cons(B,A) # label(ax81) # label(axiom). [clausify(72)].
% 14.71/15.04 281 c6 = c4 # label(co1) # label(negated_conjecture). [clausify(87)].
% 14.71/15.04 282 c5 = c3 # label(co1) # label(negated_conjecture). [clausify(87)].
% 14.71/15.04 283 neq(c4,nil) # label(co1) # label(negated_conjecture). [clausify(87)].
% 14.71/15.04 284 -ssItem(A) | cons(A,nil) != c3 | -memberP(c4,A) | -neq(c6,nil) # label(co1) # label(negated_conjecture). [clausify(87)].
% 14.71/15.04 285 -ssItem(A) | cons(A,nil) != c3 | -memberP(c4,A). [copy(284),rewrite([281(8)]),unit_del(d,283)].
% 14.71/15.04 286 ssItem(c7) | -neq(c6,nil) # label(co1) # label(negated_conjecture). [clausify(87)].
% 14.71/15.04 287 ssItem(c7). [copy(286),rewrite([281(3)]),unit_del(b,283)].
% 14.71/15.04 288 ssList(c8) | -neq(c6,nil) # label(co1) # label(negated_conjecture). [clausify(87)].
% 14.71/15.04 289 ssList(c8). [copy(288),rewrite([281(3)]),unit_del(b,283)].
% 14.71/15.04 290 cons(c7,nil) = c5 | -neq(c6,nil) # label(co1) # label(negated_conjecture). [clausify(87)].
% 14.71/15.04 291 cons(c7,nil) = c3. [copy(290),rewrite([282(4),281(6)]),unit_del(b,283)].
% 14.71/15.04 292 app(cons(c7,nil),c8) = c6 | -neq(c6,nil) # label(co1) # label(negated_conjecture). [clausify(87)].
% 14.71/15.04 293 app(c3,c8) = c4. [copy(292),rewrite([291(3),281(4),281(6)]),unit_del(b,283)].
% 14.71/15.04 424 -ssItem(A) | -ssList(B) | memberP(cons(A,B),A). [factor(209,a,b),xx(d)].
% 14.71/15.04 1919 -ssList(A) | app(c3,A) = cons(c7,A). [resolve(287,a,259,b),rewrite([291(4)])].
% 14.71/15.04 4976 -ssList(A) | memberP(cons(c7,A),c7). [resolve(424,a,287,a)].
% 14.71/15.04 45120 cons(c7,c8) = c4. [resolve(1919,a,289,a),rewrite([293(3)]),flip(a)].
% 14.71/15.04 72096 memberP(c4,c7). [resolve(4976,a,289,a),rewrite([45120(3)])].
% 14.71/15.04 72100 $F. [resolve(72096,a,285,c),rewrite([291(5)]),xx(b),unit_del(a,287)].
% 14.71/15.04
% 14.71/15.04 % SZS output end Refutation
% 14.71/15.04 ============================== end of proof ==========================
% 14.71/15.04
% 14.71/15.04 ============================== STATISTICS ============================
% 14.71/15.04
% 14.71/15.04 Given=4073. Generated=447782. Kept=71911. proofs=1.
% 14.71/15.04 Usable=3593. Sos=9994. Demods=662. Limbo=0, Disabled=58571. Hints=0.
% 14.71/15.04 Megabytes=54.82.
% 14.71/15.04 User_CPU=13.71, System_CPU=0.24, Wall_clock=14.
% 14.71/15.04
% 14.71/15.04 ============================== end of statistics =====================
% 14.71/15.04
% 14.71/15.04 ============================== end of search =========================
% 14.71/15.04
% 14.71/15.04 THEOREM PROVED
% 14.71/15.04 % SZS status Theorem
% 14.71/15.04
% 14.71/15.04 Exiting with 1 proof.
% 14.71/15.04
% 14.71/15.04 Process 18283 exit (max_proofs) Sat Jun 11 23:31:12 2022
% 14.71/15.04 Prover9 interrupted
%------------------------------------------------------------------------------