TSTP Solution File: NUN060+2 by Prover9---1109a

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Prover9---1109a
% Problem  : NUN060+2 : TPTP v8.1.0. Released v7.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : tptp2X_and_run_prover9 %d %s

% Computer : n017.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 : Mon Jul 18 16:37:06 EDT 2022

% Result   : Theorem 0.73s 1.01s
% Output   : Refutation 0.73s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : NUN060+2 : TPTP v8.1.0. Released v7.3.0.
% 0.11/0.12  % Command  : tptp2X_and_run_prover9 %d %s
% 0.12/0.33  % Computer : n017.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.18/0.33  % WCLimit  : 600
% 0.18/0.33  % DateTime : Thu Jun  2 09:22:57 EDT 2022
% 0.18/0.33  % CPUTime  : 
% 0.43/0.98  ============================== Prover9 ===============================
% 0.43/0.98  Prover9 (32) version 2009-11A, November 2009.
% 0.43/0.98  Process 13021 was started by sandbox on n017.cluster.edu,
% 0.43/0.98  Thu Jun  2 09:22:58 2022
% 0.43/0.98  The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_12868_n017.cluster.edu".
% 0.43/0.98  ============================== end of head ===========================
% 0.43/0.98  
% 0.43/0.98  ============================== INPUT =================================
% 0.43/0.98  
% 0.43/0.98  % Reading from file /tmp/Prover9_12868_n017.cluster.edu
% 0.43/0.98  
% 0.43/0.98  set(prolog_style_variables).
% 0.43/0.98  set(auto2).
% 0.43/0.98      % set(auto2) -> set(auto).
% 0.43/0.98      % set(auto) -> set(auto_inference).
% 0.43/0.98      % set(auto) -> set(auto_setup).
% 0.43/0.98      % set(auto_setup) -> set(predicate_elim).
% 0.43/0.98      % set(auto_setup) -> assign(eq_defs, unfold).
% 0.43/0.98      % set(auto) -> set(auto_limits).
% 0.43/0.98      % set(auto_limits) -> assign(max_weight, "100.000").
% 0.43/0.98      % set(auto_limits) -> assign(sos_limit, 20000).
% 0.43/0.98      % set(auto) -> set(auto_denials).
% 0.43/0.98      % set(auto) -> set(auto_process).
% 0.43/0.98      % set(auto2) -> assign(new_constants, 1).
% 0.43/0.98      % set(auto2) -> assign(fold_denial_max, 3).
% 0.43/0.98      % set(auto2) -> assign(max_weight, "200.000").
% 0.43/0.98      % set(auto2) -> assign(max_hours, 1).
% 0.43/0.98      % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.43/0.98      % set(auto2) -> assign(max_seconds, 0).
% 0.43/0.98      % set(auto2) -> assign(max_minutes, 5).
% 0.43/0.98      % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.43/0.98      % set(auto2) -> set(sort_initial_sos).
% 0.43/0.98      % set(auto2) -> assign(sos_limit, -1).
% 0.43/0.98      % set(auto2) -> assign(lrs_ticks, 3000).
% 0.43/0.98      % set(auto2) -> assign(max_megs, 400).
% 0.43/0.98      % set(auto2) -> assign(stats, some).
% 0.43/0.98      % set(auto2) -> clear(echo_input).
% 0.43/0.98      % set(auto2) -> set(quiet).
% 0.43/0.98      % set(auto2) -> clear(print_initial_clauses).
% 0.43/0.98      % set(auto2) -> clear(print_given).
% 0.43/0.98  assign(lrs_ticks,-1).
% 0.43/0.98  assign(sos_limit,10000).
% 0.43/0.98  assign(order,kbo).
% 0.43/0.98  set(lex_order_vars).
% 0.43/0.98  clear(print_given).
% 0.43/0.98  
% 0.43/0.98  % formulas(sos).  % not echoed (12 formulas)
% 0.43/0.98  
% 0.43/0.98  ============================== end of input ==========================
% 0.43/0.98  
% 0.43/0.98  % From the command line: assign(max_seconds, 300).
% 0.43/0.98  
% 0.43/0.98  ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.43/0.98  
% 0.43/0.98  % Formulas that are not ordinary clauses:
% 0.43/0.98  1 (exists Y24 all X19 (-r1(X19) & X19 != Y24 | r1(X19) & X19 = Y24)) # label(axiom_1) # label(axiom) # label(non_clause).  [assumption].
% 0.43/0.98  2 (all X11 exists Y21 all X12 (-r2(X11,X12) & X12 != Y21 | r2(X11,X12) & X12 = Y21)) # label(axiom_2) # label(axiom) # label(non_clause).  [assumption].
% 0.43/0.98  3 (all X13 all X14 exists Y22 all X15 (-r3(X13,X14,X15) & X15 != Y22 | r3(X13,X14,X15) & X15 = Y22)) # label(axiom_3) # label(axiom) # label(non_clause).  [assumption].
% 0.43/0.98  4 (all X16 all X17 exists Y23 all X18 (-r4(X16,X17,X18) & X18 != Y23 | r4(X16,X17,X18) & X18 = Y23)) # label(axiom_4) # label(axiom) # label(non_clause).  [assumption].
% 0.43/0.98  5 (all X1 all X8 exists Y4 ((exists Y5 ((exists Y15 (r2(X8,Y15) & r3(X1,Y15,Y5))) & Y5 = Y4)) & (exists Y7 (r2(Y7,Y4) & r3(X1,X8,Y7))))) # label(axiom_1a) # label(axiom) # label(non_clause).  [assumption].
% 0.43/0.98  6 (all X2 all X9 exists Y2 ((exists Y3 ((exists Y14 (r2(X9,Y14) & r4(X2,Y14,Y3))) & Y3 = Y2)) & (exists Y6 (r3(Y6,X2,Y2) & r4(X2,X9,Y6))))) # label(axiom_2a) # label(axiom) # label(non_clause).  [assumption].
% 0.43/0.98  7 (all X3 all X10 ((all Y12 ((all Y13 (-r2(X3,Y13) | Y13 != Y12)) | -r2(X10,Y12))) | X3 = X10)) # label(axiom_3a) # label(axiom) # label(non_clause).  [assumption].
% 0.43/0.98  8 (all X4 exists Y9 ((exists Y16 (r1(Y16) & r3(X4,Y16,Y9))) & Y9 = X4)) # label(axiom_4a) # label(axiom) # label(non_clause).  [assumption].
% 0.43/0.98  9 (all X5 exists Y8 ((exists Y17 (r1(Y17) & r4(X5,Y17,Y8))) & (exists Y18 (r1(Y18) & Y8 = Y18)))) # label(axiom_5a) # label(axiom) # label(non_clause).  [assumption].
% 0.43/0.98  10 (all X6 ((exists Y19 (r1(Y19) & X6 = Y19)) | (exists Y1 exists Y11 (r2(Y1,Y11) & X6 = Y11)))) # label(axiom_6a) # label(axiom) # label(non_clause).  [assumption].
% 0.43/0.98  11 (all X7 all Y10 ((all Y20 (-r1(Y20) | Y20 != Y10)) | -r2(X7,Y10))) # label(axiom_7a) # label(axiom) # label(non_clause).  [assumption].
% 0.43/0.98  12 -(exists Y1 exists Y2 exists Y3 (Y3 = Y1 & (exists Y4 (r3(Y2,Y4,Y3) & (exists Y5 (r2(Y5,Y4) & (exists Y6 (r2(Y6,Y5) & (exists Y7 (r2(Y7,Y6) & (exists Y8 (r1(Y8) & r2(Y8,Y7))))))))))))) # label(greq4) # label(negated_conjecture) # label(non_clause).  [assumption].
% 0.43/0.98  
% 0.43/0.98  ============================== end of process non-clausal formulas ===
% 0.43/0.98  
% 0.43/0.98  ============================== PROCESS INITIAL CLAUSES ===============
% 0.43/0.98  
% 0.43/0.98  ============================== PREDICATE ELIMINATION =================
% 0.43/0.98  13 -r1(A) | A != B | -r2(C,B) # label(axiom_7a) # label(axiom).  [clausify(11)].
% 0.43/0.98  14 r1(f13(A)) # label(axiom_4a) # label(axiom).  [clausify(8)].
% 0.43/0.98  15 r1(f15(A)) # label(axiom_5a) # label(axiom).  [clausify(9)].
% 0.43/0.98  16 r1(f16(A)) # label(axiom_5a) # label(axiom).  [clausify(9)].
% 0.43/0.98  17 r1(f17(A)) | f19(A) = A # label(axiom_6a) # label(axiom).  [clausify(10)].
% 0.43/0.98  18 r1(f17(A)) | r2(f18(A),f19(A)) # label(axiom_6a) # label(axiom).  [clausify(10)].
% 0.43/0.98  Derived: f13(A) != B | -r2(C,B).  [resolve(13,a,14,a)].
% 0.43/0.98  Derived: f15(A) != B | -r2(C,B).  [resolve(13,a,15,a)].
% 0.43/0.98  Derived: f16(A) != B | -r2(C,B).  [resolve(13,a,16,a)].
% 0.43/0.98  Derived: f17(A) != B | -r2(C,B) | f19(A) = A.  [resolve(13,a,17,a)].
% 0.43/0.98  Derived: f17(A) != B | -r2(C,B) | r2(f18(A),f19(A)).  [resolve(13,a,18,a)].
% 0.43/0.98  19 A != B | -r3(C,D,B) | -r2(E,D) | -r2(F,E) | -r2(V6,F) | -r1(V7) | -r2(V7,V6) # label(greq4) # label(negated_conjecture).  [clausify(12)].
% 0.43/0.98  Derived: A != B | -r3(C,D,B) | -r2(E,D) | -r2(F,E) | -r2(V6,F) | -r2(f13(V7),V6).  [resolve(19,f,14,a)].
% 0.43/0.98  Derived: A != B | -r3(C,D,B) | -r2(E,D) | -r2(F,E) | -r2(V6,F) | -r2(f15(V7),V6).  [resolve(19,f,15,a)].
% 0.43/0.98  Derived: A != B | -r3(C,D,B) | -r2(E,D) | -r2(F,E) | -r2(V6,F) | -r2(f16(V7),V6).  [resolve(19,f,16,a)].
% 0.43/0.98  Derived: A != B | -r3(C,D,B) | -r2(E,D) | -r2(F,E) | -r2(V6,F) | -r2(f17(V7),V6) | f19(V7) = V7.  [resolve(19,f,17,a)].
% 0.43/0.98  Derived: A != B | -r3(C,D,B) | -r2(E,D) | -r2(F,E) | -r2(V6,F) | -r2(f17(V7),V6) | r2(f18(V7),f19(V7)).  [resolve(19,f,18,a)].
% 0.43/0.98  20 -r1(A) | A = c1 # label(axiom_1) # label(axiom).  [clausify(1)].
% 0.43/0.98  Derived: f13(A) = c1.  [resolve(20,a,14,a)].
% 0.43/0.98  Derived: f15(A) = c1.  [resolve(20,a,15,a)].
% 0.43/0.98  Derived: f16(A) = c1.  [resolve(20,a,16,a)].
% 0.43/0.98  Derived: f17(A) = c1 | f19(A) = A.  [resolve(20,a,17,a)].
% 0.43/0.98  Derived: f17(A) = c1 | r2(f18(A),f19(A)).  [resolve(20,a,18,a)].
% 0.43/0.98  21 A != c1 | r1(A) # label(axiom_1) # label(axiom).  [clausify(1)].
% 0.43/0.98  Derived: A != c1 | A != B | -r2(C,B).  [resolve(21,b,13,a)].
% 0.43/0.98  Derived: A != c1 | B != C | -r3(D,E,C) | -r2(F,E) | -r2(V6,F) | -r2(V7,V6) | -r2(A,V7).  [resolve(21,b,19,f)].
% 0.43/0.98  22 -r3(A,B,C) | C = f2(A,B) # label(axiom_3) # label(axiom).  [clausify(3)].
% 0.43/0.98  23 r3(A,B,f7(A,B)) # label(axiom_1a) # label(axiom).  [clausify(5)].
% 0.43/0.98  24 r3(A,f13(A),f12(A)) # label(axiom_4a) # label(axiom).  [clausify(8)].
% 0.43/0.98  25 r3(A,f6(A,B),f5(A,B)) # label(axiom_1a) # label(axiom).  [clausify(5)].
% 0.43/0.98  26 r3(f11(A,B),A,f8(A,B)) # label(axiom_2a) # label(axiom).  [clausify(6)].
% 0.43/0.98  Derived: f7(A,B) = f2(A,B).  [resolve(22,a,23,a)].
% 0.43/0.98  Derived: f12(A) = f2(A,f13(A)).  [resolve(22,a,24,a)].
% 0.43/0.98  Derived: f5(A,B) = f2(A,f6(A,B)).  [resolve(22,a,25,a)].
% 0.43/0.98  Derived: f8(A,B) = f2(f11(A,B),A).  [resolve(22,a,26,a)].
% 0.43/0.98  27 A != f2(B,C) | r3(B,C,A) # label(axiom_3) # label(axiom).  [clausify(3)].
% 0.43/0.98  28 A != B | -r3(C,D,B) | -r2(E,D) | -r2(F,E) | -r2(V6,F) | -r2(f13(V7),V6).  [resolve(19,f,14,a)].
% 0.43/0.98  Derived: A != f7(B,C) | -r2(D,C) | -r2(E,D) | -r2(F,E) | -r2(f13(V6),F).  [resolve(28,b,23,a)].
% 0.43/0.98  Derived: A != f12(B) | -r2(C,f13(B)) | -r2(D,C) | -r2(E,D) | -r2(f13(F),E).  [resolve(28,b,24,a)].
% 0.43/0.98  Derived: A != f5(B,C) | -r2(D,f6(B,C)) | -r2(E,D) | -r2(F,E) | -r2(f13(V6),F).  [resolve(28,b,25,a)].
% 0.43/0.98  Derived: A != f8(B,C) | -r2(D,B) | -r2(E,D) | -r2(F,E) | -r2(f13(V6),F).  [resolve(28,b,26,a)].
% 0.43/0.98  Derived: A != B | -r2(C,D) | -r2(E,C) | -r2(F,E) | -r2(f13(V6),F) | B != f2(V7,D).  [resolve(28,b,27,b)].
% 0.43/0.98  29 A != B | -r3(C,D,B) | -r2(E,D) | -r2(F,E) | -r2(V6,F) | -r2(f15(V7),V6).  [resolve(19,f,15,a)].
% 0.43/0.98  Derived: A != f7(B,C) | -r2(D,C) | -r2(E,D) | -r2(F,E) | -r2(f15(V6),F).  [resolve(29,b,23,a)].
% 0.43/0.98  Derived: A != f12(B) | -r2(C,f13(B)) | -r2(D,C) | -r2(E,D) | -r2(f15(F),E).  [resolve(29,b,24,a)].
% 0.43/0.98  Derived: A != f5(B,C) | -r2(D,f6(B,C)) | -r2(E,D) | -r2(F,E) | -r2(f15(V6),F).  [resolve(29,b,25,a)].
% 0.43/0.98  Derived: A != f8(B,C) | -r2(D,B) | -r2(E,D) | -r2(F,E) | -r2(f15(V6),F).  [resolve(29,b,26,a)].
% 0.73/1.01  Derived: A != B | -r2(C,D) | -r2(E,C) | -r2(F,E) | -r2(f15(V6),F) | B != f2(V7,D).  [resolve(29,b,27,b)].
% 0.73/1.01  30 A != B | -r3(C,D,B) | -r2(E,D) | -r2(F,E) | -r2(V6,F) | -r2(f16(V7),V6).  [resolve(19,f,16,a)].
% 0.73/1.01  Derived: A != f7(B,C) | -r2(D,C) | -r2(E,D) | -r2(F,E) | -r2(f16(V6),F).  [resolve(30,b,23,a)].
% 0.73/1.01  Derived: A != f12(B) | -r2(C,f13(B)) | -r2(D,C) | -r2(E,D) | -r2(f16(F),E).  [resolve(30,b,24,a)].
% 0.73/1.01  Derived: A != f5(B,C) | -r2(D,f6(B,C)) | -r2(E,D) | -r2(F,E) | -r2(f16(V6),F).  [resolve(30,b,25,a)].
% 0.73/1.01  Derived: A != f8(B,C) | -r2(D,B) | -r2(E,D) | -r2(F,E) | -r2(f16(V6),F).  [resolve(30,b,26,a)].
% 0.73/1.01  Derived: A != B | -r2(C,D) | -r2(E,C) | -r2(F,E) | -r2(f16(V6),F) | B != f2(V7,D).  [resolve(30,b,27,b)].
% 0.73/1.01  31 A != B | -r3(C,D,B) | -r2(E,D) | -r2(F,E) | -r2(V6,F) | -r2(f17(V7),V6) | f19(V7) = V7.  [resolve(19,f,17,a)].
% 0.73/1.01  Derived: A != f7(B,C) | -r2(D,C) | -r2(E,D) | -r2(F,E) | -r2(f17(V6),F) | f19(V6) = V6.  [resolve(31,b,23,a)].
% 0.73/1.01  Derived: A != f12(B) | -r2(C,f13(B)) | -r2(D,C) | -r2(E,D) | -r2(f17(F),E) | f19(F) = F.  [resolve(31,b,24,a)].
% 0.73/1.01  Derived: A != f5(B,C) | -r2(D,f6(B,C)) | -r2(E,D) | -r2(F,E) | -r2(f17(V6),F) | f19(V6) = V6.  [resolve(31,b,25,a)].
% 0.73/1.01  Derived: A != f8(B,C) | -r2(D,B) | -r2(E,D) | -r2(F,E) | -r2(f17(V6),F) | f19(V6) = V6.  [resolve(31,b,26,a)].
% 0.73/1.01  Derived: A != B | -r2(C,D) | -r2(E,C) | -r2(F,E) | -r2(f17(V6),F) | f19(V6) = V6 | B != f2(V7,D).  [resolve(31,b,27,b)].
% 0.73/1.01  32 A != B | -r3(C,D,B) | -r2(E,D) | -r2(F,E) | -r2(V6,F) | -r2(f17(V7),V6) | r2(f18(V7),f19(V7)).  [resolve(19,f,18,a)].
% 0.73/1.01  Derived: A != f7(B,C) | -r2(D,C) | -r2(E,D) | -r2(F,E) | -r2(f17(V6),F) | r2(f18(V6),f19(V6)).  [resolve(32,b,23,a)].
% 0.73/1.01  Derived: A != f12(B) | -r2(C,f13(B)) | -r2(D,C) | -r2(E,D) | -r2(f17(F),E) | r2(f18(F),f19(F)).  [resolve(32,b,24,a)].
% 0.73/1.01  Derived: A != f5(B,C) | -r2(D,f6(B,C)) | -r2(E,D) | -r2(F,E) | -r2(f17(V6),F) | r2(f18(V6),f19(V6)).  [resolve(32,b,25,a)].
% 0.73/1.01  Derived: A != f8(B,C) | -r2(D,B) | -r2(E,D) | -r2(F,E) | -r2(f17(V6),F) | r2(f18(V6),f19(V6)).  [resolve(32,b,26,a)].
% 0.73/1.01  Derived: A != B | -r2(C,D) | -r2(E,C) | -r2(F,E) | -r2(f17(V6),F) | r2(f18(V6),f19(V6)) | B != f2(V7,D).  [resolve(32,b,27,b)].
% 0.73/1.01  33 A != c1 | B != C | -r3(D,E,C) | -r2(F,E) | -r2(V6,F) | -r2(V7,V6) | -r2(A,V7).  [resolve(21,b,19,f)].
% 0.73/1.01  Derived: A != c1 | B != f7(C,D) | -r2(E,D) | -r2(F,E) | -r2(V6,F) | -r2(A,V6).  [resolve(33,c,23,a)].
% 0.73/1.01  Derived: A != c1 | B != f12(C) | -r2(D,f13(C)) | -r2(E,D) | -r2(F,E) | -r2(A,F).  [resolve(33,c,24,a)].
% 0.73/1.01  Derived: A != c1 | B != f5(C,D) | -r2(E,f6(C,D)) | -r2(F,E) | -r2(V6,F) | -r2(A,V6).  [resolve(33,c,25,a)].
% 0.73/1.01  Derived: A != c1 | B != f8(C,D) | -r2(E,C) | -r2(F,E) | -r2(V6,F) | -r2(A,V6).  [resolve(33,c,26,a)].
% 0.73/1.01  Derived: A != c1 | B != C | -r2(D,E) | -r2(F,D) | -r2(V6,F) | -r2(A,V6) | C != f2(V7,E).  [resolve(33,c,27,b)].
% 0.73/1.01  34 -r4(A,B,C) | C = f3(A,B) # label(axiom_4) # label(axiom).  [clausify(4)].
% 0.73/1.01  35 r4(A,B,f11(A,B)) # label(axiom_2a) # label(axiom).  [clausify(6)].
% 0.73/1.01  36 r4(A,f15(A),f14(A)) # label(axiom_5a) # label(axiom).  [clausify(9)].
% 0.73/1.01  37 r4(A,f10(A,B),f9(A,B)) # label(axiom_2a) # label(axiom).  [clausify(6)].
% 0.73/1.01  Derived: f11(A,B) = f3(A,B).  [resolve(34,a,35,a)].
% 0.73/1.01  Derived: f14(A) = f3(A,f15(A)).  [resolve(34,a,36,a)].
% 0.73/1.01  Derived: f9(A,B) = f3(A,f10(A,B)).  [resolve(34,a,37,a)].
% 0.73/1.01  38 A != f3(B,C) | r4(B,C,A) # label(axiom_4) # label(axiom).  [clausify(4)].
% 0.73/1.01  
% 0.73/1.01  ============================== end predicate elimination =============
% 0.73/1.01  
% 0.73/1.01  Auto_denials:  (non-Horn, no changes).
% 0.73/1.01  
% 0.73/1.01  Term ordering decisions:
% 0.73/1.01  Function symbol KB weights:  c1=1. f2=1. f3=1. f4=1. f5=1. f6=1. f7=1. f8=1. f9=1. f10=1. f11=1. f1=1. f12=1. f13=1. f14=1. f15=1. f16=1. f17=1. f18=1. f19=1.
% 0.73/1.01  
% 0.73/1.01  ============================== end of process initial clauses ========
% 0.73/1.01  
% 0.73/1.01  ============================== CLAUSES FOR SEARCH ====================
% 0.73/1.01  
% 0.73/1.01  ============================== end of clauses for search =============
% 0.73/1.01  
% 0.73/1.01  ============================== SEARCH ================================
% 0.73/1.01  
% 0.73/1.01  % Starting search at 0.02 seconds.
% 0.73/1.01  
% 0.73/1.01  ============================== PROOF =================================
% 0.73/1.01  % SZS status Theorem
% 0.73/1.01  % SZS output start Refutation
% 0.73/1.01  
% 0.73/1.01  % Proof 1 at 0.04 (+ 0.00) seconds.
% 0.73/1.01  % Length of proof is 20.
% 0.73/1.01  % Level of proof is 5.
% 0.73/1.01  % Maximum clause weight is 15.000.
% 0.73/1.01  % Given clauses 53.
% 0.73/1.01  
% 0.73/1.01  1 (exists Y24 all X19 (-r1(X19) & X19 != Y24 | r1(X19) & X19 = Y24)) # label(axiom_1) # label(axiom) # label(non_clause).  [assumption].
% 0.73/1.01  2 (all X11 exists Y21 all X12 (-r2(X11,X12) & X12 != Y21 | r2(X11,X12) & X12 = Y21)) # label(axiom_2) # label(axiom) # label(non_clause).  [assumption].
% 0.73/1.01  3 (all X13 all X14 exists Y22 all X15 (-r3(X13,X14,X15) & X15 != Y22 | r3(X13,X14,X15) & X15 = Y22)) # label(axiom_3) # label(axiom) # label(non_clause).  [assumption].
% 0.73/1.01  5 (all X1 all X8 exists Y4 ((exists Y5 ((exists Y15 (r2(X8,Y15) & r3(X1,Y15,Y5))) & Y5 = Y4)) & (exists Y7 (r2(Y7,Y4) & r3(X1,X8,Y7))))) # label(axiom_1a) # label(axiom) # label(non_clause).  [assumption].
% 0.73/1.01  6 (all X2 all X9 exists Y2 ((exists Y3 ((exists Y14 (r2(X9,Y14) & r4(X2,Y14,Y3))) & Y3 = Y2)) & (exists Y6 (r3(Y6,X2,Y2) & r4(X2,X9,Y6))))) # label(axiom_2a) # label(axiom) # label(non_clause).  [assumption].
% 0.73/1.01  12 -(exists Y1 exists Y2 exists Y3 (Y3 = Y1 & (exists Y4 (r3(Y2,Y4,Y3) & (exists Y5 (r2(Y5,Y4) & (exists Y6 (r2(Y6,Y5) & (exists Y7 (r2(Y7,Y6) & (exists Y8 (r1(Y8) & r2(Y8,Y7))))))))))))) # label(greq4) # label(negated_conjecture) # label(non_clause).  [assumption].
% 0.73/1.01  19 A != B | -r3(C,D,B) | -r2(E,D) | -r2(F,E) | -r2(V6,F) | -r1(V7) | -r2(V7,V6) # label(greq4) # label(negated_conjecture).  [clausify(12)].
% 0.73/1.01  21 A != c1 | r1(A) # label(axiom_1) # label(axiom).  [clausify(1)].
% 0.73/1.01  22 -r3(A,B,C) | C = f2(A,B) # label(axiom_3) # label(axiom).  [clausify(3)].
% 0.73/1.01  23 r3(A,B,f7(A,B)) # label(axiom_1a) # label(axiom).  [clausify(5)].
% 0.73/1.01  33 A != c1 | B != C | -r3(D,E,C) | -r2(F,E) | -r2(V6,F) | -r2(V7,V6) | -r2(A,V7).  [resolve(21,b,19,f)].
% 0.73/1.01  41 r2(A,f10(B,A)) # label(axiom_2a) # label(axiom).  [clausify(6)].
% 0.73/1.01  48 -r2(A,B) | B = f1(A) # label(axiom_2) # label(axiom).  [clausify(2)].
% 0.73/1.01  49 -r2(A,B) | f1(A) = B.  [copy(48),flip(b)].
% 0.73/1.01  67 f7(A,B) = f2(A,B).  [resolve(22,a,23,a)].
% 0.73/1.01  101 A != c1 | B != f7(C,D) | -r2(E,D) | -r2(F,E) | -r2(V6,F) | -r2(A,V6).  [resolve(33,c,23,a)].
% 0.73/1.01  102 c1 != A | -r2(B,C) | -r2(D,B) | -r2(E,D) | -r2(A,E).  [copy(101),rewrite([67(3)]),flip(a),flip(b),xx(b)].
% 0.73/1.01  138 f10(A,B) = f1(B).  [resolve(49,a,41,a),flip(a)].
% 0.73/1.01  141 r2(A,f1(A)).  [back_rewrite(41),rewrite([138(1)])].
% 0.73/1.01  360 $F.  [ur(102,b,141,a,c,141,a,d,141,a,e,141,a),xx(a)].
% 0.73/1.01  
% 0.73/1.01  % SZS output end Refutation
% 0.73/1.01  ============================== end of proof ==========================
% 0.73/1.01  
% 0.73/1.01  ============================== STATISTICS ============================
% 0.73/1.01  
% 0.73/1.01  Given=53. Generated=651. Kept=282. proofs=1.
% 0.73/1.01  Usable=51. Sos=159. Demods=18. Limbo=55, Disabled=103. Hints=0.
% 0.73/1.01  Megabytes=0.31.
% 0.73/1.01  User_CPU=0.04, System_CPU=0.00, Wall_clock=0.
% 0.73/1.01  
% 0.73/1.01  ============================== end of statistics =====================
% 0.73/1.01  
% 0.73/1.01  ============================== end of search =========================
% 0.73/1.01  
% 0.73/1.01  THEOREM PROVED
% 0.73/1.01  % SZS status Theorem
% 0.73/1.01  
% 0.73/1.01  Exiting with 1 proof.
% 0.73/1.01  
% 0.73/1.01  Process 13021 exit (max_proofs) Thu Jun  2 09:22:58 2022
% 0.73/1.01  Prover9 interrupted
%------------------------------------------------------------------------------