TSTP Solution File: NUN084+2 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : NUN084+2 : TPTP v8.1.0. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n022.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 16:37:15 EDT 2022
% Result : Theorem 0.51s 0.88s
% Output : Refutation 0.51s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.07 % Problem : NUN084+2 : TPTP v8.1.0. Released v7.3.0.
% 0.00/0.07 % Command : tptp2X_and_run_prover9 %d %s
% 0.06/0.25 % Computer : n022.cluster.edu
% 0.06/0.25 % Model : x86_64 x86_64
% 0.06/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.25 % Memory : 8042.1875MB
% 0.06/0.25 % OS : Linux 3.10.0-693.el7.x86_64
% 0.06/0.25 % CPULimit : 300
% 0.06/0.25 % WCLimit : 600
% 0.06/0.25 % DateTime : Thu Jun 2 05:27:51 EDT 2022
% 0.06/0.25 % CPUTime :
% 0.51/0.81 ============================== Prover9 ===============================
% 0.51/0.81 Prover9 (32) version 2009-11A, November 2009.
% 0.51/0.81 Process 12732 was started by sandbox2 on n022.cluster.edu,
% 0.51/0.81 Thu Jun 2 05:27:52 2022
% 0.51/0.81 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_12578_n022.cluster.edu".
% 0.51/0.81 ============================== end of head ===========================
% 0.51/0.81
% 0.51/0.81 ============================== INPUT =================================
% 0.51/0.81
% 0.51/0.81 % Reading from file /tmp/Prover9_12578_n022.cluster.edu
% 0.51/0.81
% 0.51/0.81 set(prolog_style_variables).
% 0.51/0.81 set(auto2).
% 0.51/0.81 % set(auto2) -> set(auto).
% 0.51/0.81 % set(auto) -> set(auto_inference).
% 0.51/0.81 % set(auto) -> set(auto_setup).
% 0.51/0.81 % set(auto_setup) -> set(predicate_elim).
% 0.51/0.81 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.51/0.81 % set(auto) -> set(auto_limits).
% 0.51/0.81 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.51/0.81 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.51/0.81 % set(auto) -> set(auto_denials).
% 0.51/0.81 % set(auto) -> set(auto_process).
% 0.51/0.81 % set(auto2) -> assign(new_constants, 1).
% 0.51/0.81 % set(auto2) -> assign(fold_denial_max, 3).
% 0.51/0.81 % set(auto2) -> assign(max_weight, "200.000").
% 0.51/0.81 % set(auto2) -> assign(max_hours, 1).
% 0.51/0.81 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.51/0.81 % set(auto2) -> assign(max_seconds, 0).
% 0.51/0.81 % set(auto2) -> assign(max_minutes, 5).
% 0.51/0.81 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.51/0.81 % set(auto2) -> set(sort_initial_sos).
% 0.51/0.81 % set(auto2) -> assign(sos_limit, -1).
% 0.51/0.81 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.51/0.81 % set(auto2) -> assign(max_megs, 400).
% 0.51/0.81 % set(auto2) -> assign(stats, some).
% 0.51/0.81 % set(auto2) -> clear(echo_input).
% 0.51/0.81 % set(auto2) -> set(quiet).
% 0.51/0.81 % set(auto2) -> clear(print_initial_clauses).
% 0.51/0.81 % set(auto2) -> clear(print_given).
% 0.51/0.81 assign(lrs_ticks,-1).
% 0.51/0.81 assign(sos_limit,10000).
% 0.51/0.81 assign(order,kbo).
% 0.51/0.81 set(lex_order_vars).
% 0.51/0.81 clear(print_given).
% 0.51/0.81
% 0.51/0.81 % formulas(sos). % not echoed (12 formulas)
% 0.51/0.81
% 0.51/0.81 ============================== end of input ==========================
% 0.51/0.81
% 0.51/0.81 % From the command line: assign(max_seconds, 300).
% 0.51/0.81
% 0.51/0.81 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.51/0.81
% 0.51/0.81 % Formulas that are not ordinary clauses:
% 0.51/0.81 1 (exists Y24 all X19 (-r1(X19) & X19 != Y24 | r1(X19) & X19 = Y24)) # label(axiom_1) # label(axiom) # label(non_clause). [assumption].
% 0.51/0.81 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].
% 0.51/0.81 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].
% 0.51/0.81 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].
% 0.51/0.81 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].
% 0.51/0.81 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].
% 0.51/0.81 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].
% 0.51/0.81 8 (all X4 exists Y9 ((exists Y16 (r1(Y16) & r3(X4,Y16,Y9))) & Y9 = X4)) # label(axiom_4a) # label(axiom) # label(non_clause). [assumption].
% 0.51/0.81 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].
% 0.51/0.81 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].
% 0.51/0.81 11 (all X7 all Y10 ((all Y20 (-r1(Y20) | Y20 != Y10)) | -r2(X7,Y10))) # label(axiom_7a) # label(axiom) # label(non_clause). [assumption].
% 0.51/0.81 12 -(exists Y1 exists Y2 exists Y3 (r4(Y1,Y2,Y3) & (exists Y4 (Y3 = Y4 & (exists Y5 (r2(Y5,Y4) & (exists Y6 (r1(Y6) & r2(Y6,Y5))))))))) # label(xtimesyeqtwo) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.51/0.81
% 0.51/0.81 ============================== end of process non-clausal formulas ===
% 0.51/0.81
% 0.51/0.81 ============================== PROCESS INITIAL CLAUSES ===============
% 0.51/0.81
% 0.51/0.81 ============================== PREDICATE ELIMINATION =================
% 0.51/0.81 13 -r1(A) | A != B | -r2(C,B) # label(axiom_7a) # label(axiom). [clausify(11)].
% 0.51/0.81 14 r1(f13(A)) # label(axiom_4a) # label(axiom). [clausify(8)].
% 0.51/0.81 15 r1(f15(A)) # label(axiom_5a) # label(axiom). [clausify(9)].
% 0.51/0.81 16 r1(f16(A)) # label(axiom_5a) # label(axiom). [clausify(9)].
% 0.51/0.81 17 r1(f17(A)) | f19(A) = A # label(axiom_6a) # label(axiom). [clausify(10)].
% 0.51/0.81 18 r1(f17(A)) | r2(f18(A),f19(A)) # label(axiom_6a) # label(axiom). [clausify(10)].
% 0.51/0.81 Derived: f13(A) != B | -r2(C,B). [resolve(13,a,14,a)].
% 0.51/0.81 Derived: f15(A) != B | -r2(C,B). [resolve(13,a,15,a)].
% 0.51/0.81 Derived: f16(A) != B | -r2(C,B). [resolve(13,a,16,a)].
% 0.51/0.81 Derived: f17(A) != B | -r2(C,B) | f19(A) = A. [resolve(13,a,17,a)].
% 0.51/0.81 Derived: f17(A) != B | -r2(C,B) | r2(f18(A),f19(A)). [resolve(13,a,18,a)].
% 0.51/0.81 19 -r4(A,B,C) | C != D | -r2(E,D) | -r1(F) | -r2(F,E) # label(xtimesyeqtwo) # label(negated_conjecture). [clausify(12)].
% 0.51/0.81 Derived: -r4(A,B,C) | C != D | -r2(E,D) | -r2(f13(F),E). [resolve(19,d,14,a)].
% 0.51/0.81 Derived: -r4(A,B,C) | C != D | -r2(E,D) | -r2(f15(F),E). [resolve(19,d,15,a)].
% 0.51/0.81 Derived: -r4(A,B,C) | C != D | -r2(E,D) | -r2(f16(F),E). [resolve(19,d,16,a)].
% 0.51/0.81 Derived: -r4(A,B,C) | C != D | -r2(E,D) | -r2(f17(F),E) | f19(F) = F. [resolve(19,d,17,a)].
% 0.51/0.81 Derived: -r4(A,B,C) | C != D | -r2(E,D) | -r2(f17(F),E) | r2(f18(F),f19(F)). [resolve(19,d,18,a)].
% 0.51/0.81 20 -r1(A) | A = c1 # label(axiom_1) # label(axiom). [clausify(1)].
% 0.51/0.81 Derived: f13(A) = c1. [resolve(20,a,14,a)].
% 0.51/0.81 Derived: f15(A) = c1. [resolve(20,a,15,a)].
% 0.51/0.81 Derived: f16(A) = c1. [resolve(20,a,16,a)].
% 0.51/0.81 Derived: f17(A) = c1 | f19(A) = A. [resolve(20,a,17,a)].
% 0.51/0.81 Derived: f17(A) = c1 | r2(f18(A),f19(A)). [resolve(20,a,18,a)].
% 0.51/0.81 21 A != c1 | r1(A) # label(axiom_1) # label(axiom). [clausify(1)].
% 0.51/0.81 Derived: A != c1 | A != B | -r2(C,B). [resolve(21,b,13,a)].
% 0.51/0.81 Derived: A != c1 | -r4(B,C,D) | D != E | -r2(F,E) | -r2(A,F). [resolve(21,b,19,d)].
% 0.51/0.81 22 -r3(A,B,C) | C = f2(A,B) # label(axiom_3) # label(axiom). [clausify(3)].
% 0.51/0.81 23 r3(A,B,f7(A,B)) # label(axiom_1a) # label(axiom). [clausify(5)].
% 0.51/0.81 24 r3(A,f13(A),f12(A)) # label(axiom_4a) # label(axiom). [clausify(8)].
% 0.51/0.81 25 r3(A,f6(A,B),f5(A,B)) # label(axiom_1a) # label(axiom). [clausify(5)].
% 0.51/0.81 26 r3(f11(A,B),A,f8(A,B)) # label(axiom_2a) # label(axiom). [clausify(6)].
% 0.51/0.81 Derived: f7(A,B) = f2(A,B). [resolve(22,a,23,a)].
% 0.51/0.81 Derived: f12(A) = f2(A,f13(A)). [resolve(22,a,24,a)].
% 0.51/0.81 Derived: f5(A,B) = f2(A,f6(A,B)). [resolve(22,a,25,a)].
% 0.51/0.81 Derived: f8(A,B) = f2(f11(A,B),A). [resolve(22,a,26,a)].
% 0.51/0.81 27 A != f2(B,C) | r3(B,C,A) # label(axiom_3) # label(axiom). [clausify(3)].
% 0.51/0.81 28 -r4(A,B,C) | C = f3(A,B) # label(axiom_4) # label(axiom). [clausify(4)].
% 0.51/0.81 29 r4(A,B,f11(A,B)) # label(axiom_2a) # label(axiom). [clausify(6)].
% 0.51/0.81 30 r4(A,f15(A),f14(A)) # label(axiom_5a) # label(axiom). [clausify(9)].
% 0.51/0.81 31 r4(A,f10(A,B),f9(A,B)) # label(axiom_2a) # label(axiom). [clausify(6)].
% 0.51/0.81 Derived: f11(A,B) = f3(A,B). [resolve(28,a,29,a)].
% 0.51/0.81 Derived: f14(A) = f3(A,f15(A)). [resolve(28,a,30,a)].
% 0.51/0.81 Derived: f9(A,B) = f3(A,f10(A,B)). [resolve(28,a,31,a)].
% 0.51/0.81 32 A != f3(B,C) | r4(B,C,A) # label(axiom_4) # label(axiom). [clausify(4)].
% 0.51/0.81 33 -r4(A,B,C) | C != D | -r2(E,D) | -r2(f13(F),E). [resolve(19,d,14,a)].
% 0.51/0.81 Derived: f11(A,B) != C | -r2(D,C) | -r2(f13(E),D). [resolve(33,a,29,a)].
% 0.51/0.81 Derived: f14(A) != B | -r2(C,B) | -r2(f13(D),C). [resolve(33,a,30,a)].
% 0.51/0.81 Derived: f9(A,B) != C | -r2(D,C) | -r2(f13(E),D). [resolve(33,a,31,a)].
% 0.51/0.81 Derived: A != B | -r2(C,B) | -r2(f13(D),C) | A != f3(E,F). [resolve(33,a,32,b)].
% 0.51/0.81 34 -r4(A,B,C) | C != D | -r2(E,D) | -r2(f15(F),E). [resolve(19,d,15,a)].
% 0.51/0.81 Derived: f11(A,B) != C | -r2(D,C) | -r2(f15(E),D). [resolve(34,a,29,a)].
% 0.51/0.81 Derived: f14(A) != B | -r2(C,B) | -r2(f15(D),C). [resolve(34,a,30,a)].
% 0.51/0.81 Derived: f9(A,B) != C | -r2(D,C) | -r2(f15(E),D). [resolve(34,a,31,a)].
% 0.51/0.81 Derived: A != B | -r2(C,B) | -r2(f15(D),C) | A != f3(E,F). [resolve(34,a,32,b)].
% 0.51/0.88 35 -r4(A,B,C) | C != D | -r2(E,D) | -r2(f16(F),E). [resolve(19,d,16,a)].
% 0.51/0.88 Derived: f11(A,B) != C | -r2(D,C) | -r2(f16(E),D). [resolve(35,a,29,a)].
% 0.51/0.88 Derived: f14(A) != B | -r2(C,B) | -r2(f16(D),C). [resolve(35,a,30,a)].
% 0.51/0.88 Derived: f9(A,B) != C | -r2(D,C) | -r2(f16(E),D). [resolve(35,a,31,a)].
% 0.51/0.88 Derived: A != B | -r2(C,B) | -r2(f16(D),C) | A != f3(E,F). [resolve(35,a,32,b)].
% 0.51/0.88 36 -r4(A,B,C) | C != D | -r2(E,D) | -r2(f17(F),E) | f19(F) = F. [resolve(19,d,17,a)].
% 0.51/0.88 Derived: f11(A,B) != C | -r2(D,C) | -r2(f17(E),D) | f19(E) = E. [resolve(36,a,29,a)].
% 0.51/0.88 Derived: f14(A) != B | -r2(C,B) | -r2(f17(D),C) | f19(D) = D. [resolve(36,a,30,a)].
% 0.51/0.88 Derived: f9(A,B) != C | -r2(D,C) | -r2(f17(E),D) | f19(E) = E. [resolve(36,a,31,a)].
% 0.51/0.88 Derived: A != B | -r2(C,B) | -r2(f17(D),C) | f19(D) = D | A != f3(E,F). [resolve(36,a,32,b)].
% 0.51/0.88 37 -r4(A,B,C) | C != D | -r2(E,D) | -r2(f17(F),E) | r2(f18(F),f19(F)). [resolve(19,d,18,a)].
% 0.51/0.88 Derived: f11(A,B) != C | -r2(D,C) | -r2(f17(E),D) | r2(f18(E),f19(E)). [resolve(37,a,29,a)].
% 0.51/0.88 Derived: f14(A) != B | -r2(C,B) | -r2(f17(D),C) | r2(f18(D),f19(D)). [resolve(37,a,30,a)].
% 0.51/0.88 Derived: f9(A,B) != C | -r2(D,C) | -r2(f17(E),D) | r2(f18(E),f19(E)). [resolve(37,a,31,a)].
% 0.51/0.88 Derived: A != B | -r2(C,B) | -r2(f17(D),C) | r2(f18(D),f19(D)) | A != f3(E,F). [resolve(37,a,32,b)].
% 0.51/0.88 38 A != c1 | -r4(B,C,D) | D != E | -r2(F,E) | -r2(A,F). [resolve(21,b,19,d)].
% 0.51/0.88 Derived: A != c1 | f11(B,C) != D | -r2(E,D) | -r2(A,E). [resolve(38,b,29,a)].
% 0.51/0.88 Derived: A != c1 | f14(B) != C | -r2(D,C) | -r2(A,D). [resolve(38,b,30,a)].
% 0.51/0.88 Derived: A != c1 | f9(B,C) != D | -r2(E,D) | -r2(A,E). [resolve(38,b,31,a)].
% 0.51/0.88 Derived: A != c1 | B != C | -r2(D,C) | -r2(A,D) | B != f3(E,F). [resolve(38,b,32,b)].
% 0.51/0.88
% 0.51/0.88 ============================== end predicate elimination =============
% 0.51/0.88
% 0.51/0.88 Auto_denials: (non-Horn, no changes).
% 0.51/0.88
% 0.51/0.88 Term ordering decisions:
% 0.51/0.88 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.
% 0.51/0.88
% 0.51/0.88 ============================== end of process initial clauses ========
% 0.51/0.88
% 0.51/0.88 ============================== CLAUSES FOR SEARCH ====================
% 0.51/0.88
% 0.51/0.88 ============================== end of clauses for search =============
% 0.51/0.88
% 0.51/0.88 ============================== SEARCH ================================
% 0.51/0.88
% 0.51/0.88 % Starting search at 0.02 seconds.
% 0.51/0.88
% 0.51/0.88 ============================== PROOF =================================
% 0.51/0.88 % SZS status Theorem
% 0.51/0.88 % SZS output start Refutation
% 0.51/0.88
% 0.51/0.88 % Proof 1 at 0.09 (+ 0.00) seconds.
% 0.51/0.88 % Length of proof is 76.
% 0.51/0.88 % Level of proof is 10.
% 0.51/0.88 % Maximum clause weight is 17.000.
% 0.51/0.88 % Given clauses 83.
% 0.51/0.88
% 0.51/0.88 1 (exists Y24 all X19 (-r1(X19) & X19 != Y24 | r1(X19) & X19 = Y24)) # label(axiom_1) # label(axiom) # label(non_clause). [assumption].
% 0.51/0.88 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].
% 0.51/0.88 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].
% 0.51/0.88 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].
% 0.51/0.88 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].
% 0.51/0.88 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].
% 0.51/0.88 8 (all X4 exists Y9 ((exists Y16 (r1(Y16) & r3(X4,Y16,Y9))) & Y9 = X4)) # label(axiom_4a) # label(axiom) # label(non_clause). [assumption].
% 0.51/0.88 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].
% 0.51/0.88 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].
% 0.51/0.89 11 (all X7 all Y10 ((all Y20 (-r1(Y20) | Y20 != Y10)) | -r2(X7,Y10))) # label(axiom_7a) # label(axiom) # label(non_clause). [assumption].
% 0.51/0.89 12 -(exists Y1 exists Y2 exists Y3 (r4(Y1,Y2,Y3) & (exists Y4 (Y3 = Y4 & (exists Y5 (r2(Y5,Y4) & (exists Y6 (r1(Y6) & r2(Y6,Y5))))))))) # label(xtimesyeqtwo) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.51/0.89 13 -r1(A) | A != B | -r2(C,B) # label(axiom_7a) # label(axiom). [clausify(11)].
% 0.51/0.89 14 r1(f13(A)) # label(axiom_4a) # label(axiom). [clausify(8)].
% 0.51/0.89 15 r1(f15(A)) # label(axiom_5a) # label(axiom). [clausify(9)].
% 0.51/0.89 16 r1(f16(A)) # label(axiom_5a) # label(axiom). [clausify(9)].
% 0.51/0.89 19 -r4(A,B,C) | C != D | -r2(E,D) | -r1(F) | -r2(F,E) # label(xtimesyeqtwo) # label(negated_conjecture). [clausify(12)].
% 0.51/0.89 20 -r1(A) | A = c1 # label(axiom_1) # label(axiom). [clausify(1)].
% 0.51/0.89 21 A != c1 | r1(A) # label(axiom_1) # label(axiom). [clausify(1)].
% 0.51/0.89 22 -r3(A,B,C) | C = f2(A,B) # label(axiom_3) # label(axiom). [clausify(3)].
% 0.51/0.89 23 r3(A,B,f7(A,B)) # label(axiom_1a) # label(axiom). [clausify(5)].
% 0.51/0.89 24 r3(A,f13(A),f12(A)) # label(axiom_4a) # label(axiom). [clausify(8)].
% 0.51/0.89 25 r3(A,f6(A,B),f5(A,B)) # label(axiom_1a) # label(axiom). [clausify(5)].
% 0.51/0.89 26 r3(f11(A,B),A,f8(A,B)) # label(axiom_2a) # label(axiom). [clausify(6)].
% 0.51/0.89 28 -r4(A,B,C) | C = f3(A,B) # label(axiom_4) # label(axiom). [clausify(4)].
% 0.51/0.89 29 r4(A,B,f11(A,B)) # label(axiom_2a) # label(axiom). [clausify(6)].
% 0.51/0.89 30 r4(A,f15(A),f14(A)) # label(axiom_5a) # label(axiom). [clausify(9)].
% 0.51/0.89 31 r4(A,f10(A,B),f9(A,B)) # label(axiom_2a) # label(axiom). [clausify(6)].
% 0.51/0.89 32 A != f3(B,C) | r4(B,C,A) # label(axiom_4) # label(axiom). [clausify(4)].
% 0.51/0.89 38 A != c1 | -r4(B,C,D) | D != E | -r2(F,E) | -r2(A,F). [resolve(21,b,19,d)].
% 0.51/0.89 39 f12(A) = A # label(axiom_4a) # label(axiom). [clausify(8)].
% 0.51/0.89 40 r2(A,f6(B,A)) # label(axiom_1a) # label(axiom). [clausify(5)].
% 0.51/0.89 41 r2(A,f10(B,A)) # label(axiom_2a) # label(axiom). [clausify(6)].
% 0.51/0.89 42 f16(A) = f14(A) # label(axiom_5a) # label(axiom). [clausify(9)].
% 0.51/0.89 43 f5(A,B) = f4(A,B) # label(axiom_1a) # label(axiom). [clausify(5)].
% 0.51/0.89 44 r2(f7(A,B),f4(A,B)) # label(axiom_1a) # label(axiom). [clausify(5)].
% 0.51/0.89 45 f9(A,B) = f8(A,B) # label(axiom_2a) # label(axiom). [clausify(6)].
% 0.51/0.89 46 f17(A) = A | f19(A) = A # label(axiom_6a) # label(axiom). [clausify(10)].
% 0.51/0.89 47 f17(A) = A | r2(f18(A),f19(A)) # label(axiom_6a) # label(axiom). [clausify(10)].
% 0.51/0.89 48 -r2(A,B) | B = f1(A) # label(axiom_2) # label(axiom). [clausify(2)].
% 0.51/0.89 49 -r2(A,B) | f1(A) = B. [copy(48),flip(b)].
% 0.51/0.89 50 A != f1(B) | r2(B,A) # label(axiom_2) # label(axiom). [clausify(2)].
% 0.51/0.89 51 f1(A) != B | r2(A,B). [copy(50),flip(a)].
% 0.51/0.89 59 f13(A) = c1. [resolve(20,a,14,a)].
% 0.51/0.89 60 f15(A) = c1. [resolve(20,a,15,a)].
% 0.51/0.89 61 f16(A) = c1. [resolve(20,a,16,a)].
% 0.51/0.89 62 f14(A) = c1. [copy(61),rewrite([42(1)])].
% 0.51/0.89 65 A != c1 | A != B | -r2(C,B). [resolve(21,b,13,a)].
% 0.51/0.89 66 c1 != A | A != B | -r2(C,B). [copy(65),flip(a)].
% 0.51/0.89 67 f7(A,B) = f2(A,B). [resolve(22,a,23,a)].
% 0.51/0.89 68 f12(A) = f2(A,f13(A)). [resolve(22,a,24,a)].
% 0.51/0.89 69 f2(A,c1) = A. [copy(68),rewrite([39(1),59(1)]),flip(a)].
% 0.51/0.89 70 f5(A,B) = f2(A,f6(A,B)). [resolve(22,a,25,a)].
% 0.51/0.89 71 f2(A,f6(A,B)) = f4(A,B). [copy(70),rewrite([43(1)]),flip(a)].
% 0.51/0.89 72 f8(A,B) = f2(f11(A,B),A). [resolve(22,a,26,a)].
% 0.51/0.89 73 f11(A,B) = f3(A,B). [resolve(28,a,29,a)].
% 0.51/0.89 74 f14(A) = f3(A,f15(A)). [resolve(28,a,30,a)].
% 0.51/0.89 75 f3(A,c1) = c1. [copy(74),rewrite([62(1),60(2)]),flip(a)].
% 0.51/0.89 76 f9(A,B) = f3(A,f10(A,B)). [resolve(28,a,31,a)].
% 0.51/0.89 77 f3(A,f10(A,B)) = f2(f3(A,B),A). [copy(76),rewrite([45(1),72(1),73(1)]),flip(a)].
% 0.51/0.89 116 A != c1 | B != C | -r2(D,C) | -r2(A,D) | B != f3(E,F). [resolve(38,b,32,b)].
% 0.51/0.89 117 c1 != A | B != C | -r2(D,C) | -r2(A,D) | f3(E,F) != B. [copy(116),flip(a),flip(e)].
% 0.51/0.89 120 -r2(A,c1). [factor(66,a,b),xx(a)].
% 0.51/0.89 121 r2(f2(A,B),f4(A,B)). [back_rewrite(44),rewrite([67(1)])].
% 0.51/0.89 137 f17(A) = A | r2(f18(A),A). [para(46(b,1),47(b,2)),merge(b)].
% 0.51/0.89 139 f10(A,B) = f1(B). [resolve(49,a,41,a),flip(a)].
% 0.51/0.89 140 f6(A,B) = f1(B). [resolve(49,a,40,a),flip(a)].
% 0.51/0.89 141 f2(f3(A,B),A) = f3(A,f1(B)). [back_rewrite(77),rewrite([139(1)]),flip(a)].
% 0.51/0.89 143 f2(A,f1(B)) = f4(A,B). [back_rewrite(71),rewrite([140(1)])].
% 0.51/0.89 200 r2(A,f4(A,c1)). [para(69(a,1),121(a,1))].
% 0.51/0.89 207 f17(c1) = c1. [resolve(137,b,120,a)].
% 0.51/0.89 279 f4(A,c1) = f1(A). [resolve(200,a,49,a),flip(a)].
% 0.51/0.89 286 -r2(c1,f2(f3(f1(A),B),A)). [ur(117,a,207,a(flip),b,143,a,c,121,a,e,141,a(flip)),rewrite([207(2)])].
% 0.51/0.89 351 -r2(c1,f2(c1,A)). [para(75(a,1),286(a,2,1))].
% 0.51/0.89 389 -r2(c1,f4(c1,A)). [para(143(a,1),351(a,2))].
% 0.51/0.89 390 f4(c1,A) != f1(c1). [ur(51,b,389,a),flip(a)].
% 0.51/0.89 391 $F. [resolve(390,a,279,a)].
% 0.51/0.89
% 0.51/0.89 % SZS output end Refutation
% 0.51/0.89 ============================== end of proof ==========================
% 0.51/0.89
% 0.51/0.89 ============================== STATISTICS ============================
% 0.51/0.89
% 0.51/0.89 Given=83. Generated=2580. Kept=319. proofs=1.
% 0.51/0.89 Usable=77. Sos=187. Demods=25. Limbo=0, Disabled=134. Hints=0.
% 0.51/0.89 Megabytes=0.35.
% 0.51/0.89 User_CPU=0.09, System_CPU=0.00, Wall_clock=0.
% 0.51/0.89
% 0.51/0.89 ============================== end of statistics =====================
% 0.51/0.89
% 0.51/0.89 ============================== end of search =========================
% 0.51/0.89
% 0.51/0.89 THEOREM PROVED
% 0.51/0.89 % SZS status Theorem
% 0.51/0.89
% 0.51/0.89 Exiting with 1 proof.
% 0.51/0.89
% 0.51/0.89 Process 12732 exit (max_proofs) Thu Jun 2 05:27:52 2022
% 0.51/0.89 Prover9 interrupted
%------------------------------------------------------------------------------