TSTP Solution File: NUN076+2 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : NUN076+2 : TPTP v8.1.0. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n020.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 16:37:13 EDT 2022
% Result : Theorem 0.45s 1.05s
% Output : Refutation 0.45s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUN076+2 : TPTP v8.1.0. Released v7.3.0.
% 0.07/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.35 % Computer : n020.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Thu Jun 2 10:48:38 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.45/1.03 ============================== Prover9 ===============================
% 0.45/1.03 Prover9 (32) version 2009-11A, November 2009.
% 0.45/1.03 Process 29855 was started by sandbox2 on n020.cluster.edu,
% 0.45/1.03 Thu Jun 2 10:48:39 2022
% 0.45/1.03 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_29702_n020.cluster.edu".
% 0.45/1.03 ============================== end of head ===========================
% 0.45/1.03
% 0.45/1.03 ============================== INPUT =================================
% 0.45/1.03
% 0.45/1.03 % Reading from file /tmp/Prover9_29702_n020.cluster.edu
% 0.45/1.03
% 0.45/1.03 set(prolog_style_variables).
% 0.45/1.03 set(auto2).
% 0.45/1.03 % set(auto2) -> set(auto).
% 0.45/1.03 % set(auto) -> set(auto_inference).
% 0.45/1.03 % set(auto) -> set(auto_setup).
% 0.45/1.03 % set(auto_setup) -> set(predicate_elim).
% 0.45/1.03 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.45/1.03 % set(auto) -> set(auto_limits).
% 0.45/1.03 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.45/1.03 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.45/1.03 % set(auto) -> set(auto_denials).
% 0.45/1.03 % set(auto) -> set(auto_process).
% 0.45/1.03 % set(auto2) -> assign(new_constants, 1).
% 0.45/1.03 % set(auto2) -> assign(fold_denial_max, 3).
% 0.45/1.03 % set(auto2) -> assign(max_weight, "200.000").
% 0.45/1.03 % set(auto2) -> assign(max_hours, 1).
% 0.45/1.03 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.45/1.03 % set(auto2) -> assign(max_seconds, 0).
% 0.45/1.03 % set(auto2) -> assign(max_minutes, 5).
% 0.45/1.03 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.45/1.03 % set(auto2) -> set(sort_initial_sos).
% 0.45/1.03 % set(auto2) -> assign(sos_limit, -1).
% 0.45/1.03 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.45/1.03 % set(auto2) -> assign(max_megs, 400).
% 0.45/1.03 % set(auto2) -> assign(stats, some).
% 0.45/1.03 % set(auto2) -> clear(echo_input).
% 0.45/1.03 % set(auto2) -> set(quiet).
% 0.45/1.03 % set(auto2) -> clear(print_initial_clauses).
% 0.45/1.03 % set(auto2) -> clear(print_given).
% 0.45/1.03 assign(lrs_ticks,-1).
% 0.45/1.03 assign(sos_limit,10000).
% 0.45/1.03 assign(order,kbo).
% 0.45/1.03 set(lex_order_vars).
% 0.45/1.03 clear(print_given).
% 0.45/1.03
% 0.45/1.03 % formulas(sos). % not echoed (12 formulas)
% 0.45/1.03
% 0.45/1.03 ============================== end of input ==========================
% 0.45/1.03
% 0.45/1.03 % From the command line: assign(max_seconds, 300).
% 0.45/1.03
% 0.45/1.03 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.45/1.03
% 0.45/1.03 % Formulas that are not ordinary clauses:
% 0.45/1.03 1 (exists Y24 all X19 (-r1(X19) & X19 != Y24 | r1(X19) & X19 = Y24)) # label(axiom_1) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.03 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].
% 0.45/1.03 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].
% 0.45/1.03 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].
% 0.45/1.03 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].
% 0.45/1.03 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].
% 0.45/1.03 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].
% 0.45/1.03 8 (all X4 exists Y9 ((exists Y16 (r1(Y16) & r3(X4,Y16,Y9))) & Y9 = X4)) # label(axiom_4a) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.03 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].
% 0.45/1.03 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].
% 0.45/1.03 11 (all X7 all Y10 ((all Y20 (-r1(Y20) | Y20 != Y10)) | -r2(X7,Y10))) # label(axiom_7a) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.03 12 -(exists Y1 exists Y2 exists Y3 ((exists Y4 (Y4 = Y1 & (exists Y6 (r4(Y6,Y2,Y4) & (exists Y7 (r2(Y7,Y6) & (exists Y8 (r1(Y8) & r2(Y8,Y7))))))))) & (exists Y5 (r3(Y2,Y3,Y5) & Y5 = Y1)))) # label(thereexistsanevennumber) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.45/1.03
% 0.45/1.03 ============================== end of process non-clausal formulas ===
% 0.45/1.03
% 0.45/1.03 ============================== PROCESS INITIAL CLAUSES ===============
% 0.45/1.03
% 0.45/1.03 ============================== PREDICATE ELIMINATION =================
% 0.45/1.03 13 -r1(A) | A != B | -r2(C,B) # label(axiom_7a) # label(axiom). [clausify(11)].
% 0.45/1.03 14 r1(f13(A)) # label(axiom_4a) # label(axiom). [clausify(8)].
% 0.45/1.03 15 r1(f15(A)) # label(axiom_5a) # label(axiom). [clausify(9)].
% 0.45/1.03 16 r1(f16(A)) # label(axiom_5a) # label(axiom). [clausify(9)].
% 0.45/1.03 17 r1(f17(A)) | f19(A) = A # label(axiom_6a) # label(axiom). [clausify(10)].
% 0.45/1.03 18 r1(f17(A)) | r2(f18(A),f19(A)) # label(axiom_6a) # label(axiom). [clausify(10)].
% 0.45/1.03 Derived: f13(A) != B | -r2(C,B). [resolve(13,a,14,a)].
% 0.45/1.03 Derived: f15(A) != B | -r2(C,B). [resolve(13,a,15,a)].
% 0.45/1.03 Derived: f16(A) != B | -r2(C,B). [resolve(13,a,16,a)].
% 0.45/1.03 Derived: f17(A) != B | -r2(C,B) | f19(A) = A. [resolve(13,a,17,a)].
% 0.45/1.03 Derived: f17(A) != B | -r2(C,B) | r2(f18(A),f19(A)). [resolve(13,a,18,a)].
% 0.45/1.03 19 A != B | -r4(C,D,B) | -r2(E,C) | -r1(F) | -r2(F,E) | -r3(D,V6,V7) | A != V7 # label(thereexistsanevennumber) # label(negated_conjecture). [clausify(12)].
% 0.45/1.03 Derived: A != B | -r4(C,D,B) | -r2(E,C) | -r2(f13(F),E) | -r3(D,V6,V7) | A != V7. [resolve(19,d,14,a)].
% 0.45/1.03 Derived: A != B | -r4(C,D,B) | -r2(E,C) | -r2(f15(F),E) | -r3(D,V6,V7) | A != V7. [resolve(19,d,15,a)].
% 0.45/1.03 Derived: A != B | -r4(C,D,B) | -r2(E,C) | -r2(f16(F),E) | -r3(D,V6,V7) | A != V7. [resolve(19,d,16,a)].
% 0.45/1.03 Derived: A != B | -r4(C,D,B) | -r2(E,C) | -r2(f17(F),E) | -r3(D,V6,V7) | A != V7 | f19(F) = F. [resolve(19,d,17,a)].
% 0.45/1.03 Derived: A != B | -r4(C,D,B) | -r2(E,C) | -r2(f17(F),E) | -r3(D,V6,V7) | A != V7 | r2(f18(F),f19(F)). [resolve(19,d,18,a)].
% 0.45/1.03 20 -r1(A) | A = c1 # label(axiom_1) # label(axiom). [clausify(1)].
% 0.45/1.03 Derived: f13(A) = c1. [resolve(20,a,14,a)].
% 0.45/1.03 Derived: f15(A) = c1. [resolve(20,a,15,a)].
% 0.45/1.03 Derived: f16(A) = c1. [resolve(20,a,16,a)].
% 0.45/1.03 Derived: f17(A) = c1 | f19(A) = A. [resolve(20,a,17,a)].
% 0.45/1.03 Derived: f17(A) = c1 | r2(f18(A),f19(A)). [resolve(20,a,18,a)].
% 0.45/1.03 21 A != c1 | r1(A) # label(axiom_1) # label(axiom). [clausify(1)].
% 0.45/1.03 Derived: A != c1 | A != B | -r2(C,B). [resolve(21,b,13,a)].
% 0.45/1.03 Derived: A != c1 | B != C | -r4(D,E,C) | -r2(F,D) | -r2(A,F) | -r3(E,V6,V7) | B != V7. [resolve(21,b,19,d)].
% 0.45/1.03 22 -r3(A,B,C) | C = f2(A,B) # label(axiom_3) # label(axiom). [clausify(3)].
% 0.45/1.03 23 r3(A,B,f7(A,B)) # label(axiom_1a) # label(axiom). [clausify(5)].
% 0.45/1.03 24 r3(A,f13(A),f12(A)) # label(axiom_4a) # label(axiom). [clausify(8)].
% 0.45/1.03 25 r3(A,f6(A,B),f5(A,B)) # label(axiom_1a) # label(axiom). [clausify(5)].
% 0.45/1.03 26 r3(f11(A,B),A,f8(A,B)) # label(axiom_2a) # label(axiom). [clausify(6)].
% 0.45/1.03 Derived: f7(A,B) = f2(A,B). [resolve(22,a,23,a)].
% 0.45/1.03 Derived: f12(A) = f2(A,f13(A)). [resolve(22,a,24,a)].
% 0.45/1.03 Derived: f5(A,B) = f2(A,f6(A,B)). [resolve(22,a,25,a)].
% 0.45/1.03 Derived: f8(A,B) = f2(f11(A,B),A). [resolve(22,a,26,a)].
% 0.45/1.03 27 A != f2(B,C) | r3(B,C,A) # label(axiom_3) # label(axiom). [clausify(3)].
% 0.45/1.03 28 A != B | -r4(C,D,B) | -r2(E,C) | -r2(f13(F),E) | -r3(D,V6,V7) | A != V7. [resolve(19,d,14,a)].
% 0.45/1.03 Derived: A != B | -r4(C,D,B) | -r2(E,C) | -r2(f13(F),E) | A != f7(D,V6). [resolve(28,e,23,a)].
% 0.45/1.03 Derived: A != B | -r4(C,D,B) | -r2(E,C) | -r2(f13(F),E) | A != f12(D). [resolve(28,e,24,a)].
% 0.45/1.03 Derived: A != B | -r4(C,D,B) | -r2(E,C) | -r2(f13(F),E) | A != f5(D,V6). [resolve(28,e,25,a)].
% 0.45/1.03 Derived: A != B | -r4(C,f11(D,E),B) | -r2(F,C) | -r2(f13(V6),F) | A != f8(D,E). [resolve(28,e,26,a)].
% 0.45/1.03 Derived: A != B | -r4(C,D,B) | -r2(E,C) | -r2(f13(F),E) | A != V6 | V6 != f2(D,V7). [resolve(28,e,27,b)].
% 0.45/1.03 29 A != B | -r4(C,D,B) | -r2(E,C) | -r2(f15(F),E) | -r3(D,V6,V7) | A != V7. [resolve(19,d,15,a)].
% 0.45/1.03 Derived: A != B | -r4(C,D,B) | -r2(E,C) | -r2(f15(F),E) | A != f7(D,V6). [resolve(29,e,23,a)].
% 0.45/1.03 Derived: A != B | -r4(C,D,B) | -r2(E,C) | -r2(f15(F),E) | A != f12(D). [resolve(29,e,24,a)].
% 0.45/1.03 Derived: A != B | -r4(C,D,B) | -r2(E,C) | -r2(f15(F),E) | A != f5(D,V6). [resolve(29,e,25,a)].
% 0.45/1.03 Derived: A != B | -r4(C,f11(D,E),B) | -r2(F,C) | -r2(f15(V6),F) | A != f8(D,E). [resolve(29,e,26,a)].
% 0.45/1.05 Derived: A != B | -r4(C,D,B) | -r2(E,C) | -r2(f15(F),E) | A != V6 | V6 != f2(D,V7). [resolve(29,e,27,b)].
% 0.45/1.05 30 A != B | -r4(C,D,B) | -r2(E,C) | -r2(f16(F),E) | -r3(D,V6,V7) | A != V7. [resolve(19,d,16,a)].
% 0.45/1.05 Derived: A != B | -r4(C,D,B) | -r2(E,C) | -r2(f16(F),E) | A != f7(D,V6). [resolve(30,e,23,a)].
% 0.45/1.05 Derived: A != B | -r4(C,D,B) | -r2(E,C) | -r2(f16(F),E) | A != f12(D). [resolve(30,e,24,a)].
% 0.45/1.05 Derived: A != B | -r4(C,D,B) | -r2(E,C) | -r2(f16(F),E) | A != f5(D,V6). [resolve(30,e,25,a)].
% 0.45/1.05 Derived: A != B | -r4(C,f11(D,E),B) | -r2(F,C) | -r2(f16(V6),F) | A != f8(D,E). [resolve(30,e,26,a)].
% 0.45/1.05 Derived: A != B | -r4(C,D,B) | -r2(E,C) | -r2(f16(F),E) | A != V6 | V6 != f2(D,V7). [resolve(30,e,27,b)].
% 0.45/1.05 31 A != B | -r4(C,D,B) | -r2(E,C) | -r2(f17(F),E) | -r3(D,V6,V7) | A != V7 | f19(F) = F. [resolve(19,d,17,a)].
% 0.45/1.05 Derived: A != B | -r4(C,D,B) | -r2(E,C) | -r2(f17(F),E) | A != f7(D,V6) | f19(F) = F. [resolve(31,e,23,a)].
% 0.45/1.05 Derived: A != B | -r4(C,D,B) | -r2(E,C) | -r2(f17(F),E) | A != f12(D) | f19(F) = F. [resolve(31,e,24,a)].
% 0.45/1.05 Derived: A != B | -r4(C,D,B) | -r2(E,C) | -r2(f17(F),E) | A != f5(D,V6) | f19(F) = F. [resolve(31,e,25,a)].
% 0.45/1.05 Derived: A != B | -r4(C,f11(D,E),B) | -r2(F,C) | -r2(f17(V6),F) | A != f8(D,E) | f19(V6) = V6. [resolve(31,e,26,a)].
% 0.45/1.05 Derived: A != B | -r4(C,D,B) | -r2(E,C) | -r2(f17(F),E) | A != V6 | f19(F) = F | V6 != f2(D,V7). [resolve(31,e,27,b)].
% 0.45/1.05 32 A != B | -r4(C,D,B) | -r2(E,C) | -r2(f17(F),E) | -r3(D,V6,V7) | A != V7 | r2(f18(F),f19(F)). [resolve(19,d,18,a)].
% 0.45/1.05 Derived: A != B | -r4(C,D,B) | -r2(E,C) | -r2(f17(F),E) | A != f7(D,V6) | r2(f18(F),f19(F)). [resolve(32,e,23,a)].
% 0.45/1.05 Derived: A != B | -r4(C,D,B) | -r2(E,C) | -r2(f17(F),E) | A != f12(D) | r2(f18(F),f19(F)). [resolve(32,e,24,a)].
% 0.45/1.05 Derived: A != B | -r4(C,D,B) | -r2(E,C) | -r2(f17(F),E) | A != f5(D,V6) | r2(f18(F),f19(F)). [resolve(32,e,25,a)].
% 0.45/1.05 Derived: A != B | -r4(C,f11(D,E),B) | -r2(F,C) | -r2(f17(V6),F) | A != f8(D,E) | r2(f18(V6),f19(V6)). [resolve(32,e,26,a)].
% 0.45/1.05 Derived: A != B | -r4(C,D,B) | -r2(E,C) | -r2(f17(F),E) | A != V6 | r2(f18(F),f19(F)) | V6 != f2(D,V7). [resolve(32,e,27,b)].
% 0.45/1.05 33 A != c1 | B != C | -r4(D,E,C) | -r2(F,D) | -r2(A,F) | -r3(E,V6,V7) | B != V7. [resolve(21,b,19,d)].
% 0.45/1.05 Derived: A != c1 | B != C | -r4(D,E,C) | -r2(F,D) | -r2(A,F) | B != f7(E,V6). [resolve(33,f,23,a)].
% 0.45/1.05 Derived: A != c1 | B != C | -r4(D,E,C) | -r2(F,D) | -r2(A,F) | B != f12(E). [resolve(33,f,24,a)].
% 0.45/1.05 Derived: A != c1 | B != C | -r4(D,E,C) | -r2(F,D) | -r2(A,F) | B != f5(E,V6). [resolve(33,f,25,a)].
% 0.45/1.05 Derived: A != c1 | B != C | -r4(D,f11(E,F),C) | -r2(V6,D) | -r2(A,V6) | B != f8(E,F). [resolve(33,f,26,a)].
% 0.45/1.05 Derived: A != c1 | B != C | -r4(D,E,C) | -r2(F,D) | -r2(A,F) | B != V6 | V6 != f2(E,V7). [resolve(33,f,27,b)].
% 0.45/1.05
% 0.45/1.05 ============================== end predicate elimination =============
% 0.45/1.05
% 0.45/1.05 Auto_denials: (non-Horn, no changes).
% 0.45/1.05
% 0.45/1.05 Term ordering decisions:
% 0.45/1.05 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.
% 0.45/1.05
% 0.45/1.05 ============================== end of process initial clauses ========
% 0.45/1.05
% 0.45/1.05 ============================== CLAUSES FOR SEARCH ====================
% 0.45/1.05
% 0.45/1.05 ============================== end of clauses for search =============
% 0.45/1.05
% 0.45/1.05 ============================== SEARCH ================================
% 0.45/1.05
% 0.45/1.05 % Starting search at 0.01 seconds.
% 0.45/1.05
% 0.45/1.05 ============================== PROOF =================================
% 0.45/1.05 % SZS status Theorem
% 0.45/1.05 % SZS output start Refutation
% 0.45/1.05
% 0.45/1.05 % Proof 1 at 0.03 (+ 0.00) seconds.
% 0.45/1.05 % Length of proof is 38.
% 0.45/1.05 % Level of proof is 7.
% 0.45/1.05 % Maximum clause weight is 21.000.
% 0.45/1.05 % Given clauses 53.
% 0.45/1.05
% 0.45/1.05 1 (exists Y24 all X19 (-r1(X19) & X19 != Y24 | r1(X19) & X19 = Y24)) # label(axiom_1) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.05 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].
% 0.45/1.05 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].
% 0.45/1.05 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].
% 0.45/1.05 8 (all X4 exists Y9 ((exists Y16 (r1(Y16) & r3(X4,Y16,Y9))) & Y9 = X4)) # label(axiom_4a) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.05 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].
% 0.45/1.05 12 -(exists Y1 exists Y2 exists Y3 ((exists Y4 (Y4 = Y1 & (exists Y6 (r4(Y6,Y2,Y4) & (exists Y7 (r2(Y7,Y6) & (exists Y8 (r1(Y8) & r2(Y8,Y7))))))))) & (exists Y5 (r3(Y2,Y3,Y5) & Y5 = Y1)))) # label(thereexistsanevennumber) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.45/1.05 14 r1(f13(A)) # label(axiom_4a) # label(axiom). [clausify(8)].
% 0.45/1.05 15 r1(f15(A)) # label(axiom_5a) # label(axiom). [clausify(9)].
% 0.45/1.05 16 r1(f16(A)) # label(axiom_5a) # label(axiom). [clausify(9)].
% 0.45/1.05 19 A != B | -r4(C,D,B) | -r2(E,C) | -r1(F) | -r2(F,E) | -r3(D,V6,V7) | A != V7 # label(thereexistsanevennumber) # label(negated_conjecture). [clausify(12)].
% 0.45/1.05 20 -r1(A) | A = c1 # label(axiom_1) # label(axiom). [clausify(1)].
% 0.45/1.05 22 -r3(A,B,C) | C = f2(A,B) # label(axiom_3) # label(axiom). [clausify(3)].
% 0.45/1.05 23 r3(A,B,f7(A,B)) # label(axiom_1a) # label(axiom). [clausify(5)].
% 0.45/1.05 24 r3(A,f13(A),f12(A)) # label(axiom_4a) # label(axiom). [clausify(8)].
% 0.45/1.05 27 A != f2(B,C) | r3(B,C,A) # label(axiom_3) # label(axiom). [clausify(3)].
% 0.45/1.05 28 A != B | -r4(C,D,B) | -r2(E,C) | -r2(f13(F),E) | -r3(D,V6,V7) | A != V7. [resolve(19,d,14,a)].
% 0.45/1.05 34 f12(A) = A # label(axiom_4a) # label(axiom). [clausify(8)].
% 0.45/1.05 37 f16(A) = f14(A) # label(axiom_5a) # label(axiom). [clausify(9)].
% 0.45/1.05 39 r4(A,f15(A),f14(A)) # label(axiom_5a) # label(axiom). [clausify(9)].
% 0.45/1.05 41 r2(f7(A,B),f4(A,B)) # label(axiom_1a) # label(axiom). [clausify(5)].
% 0.45/1.05 49 A != f1(B) | r2(B,A) # label(axiom_2) # label(axiom). [clausify(2)].
% 0.45/1.05 50 f1(A) != B | r2(A,B). [copy(49),flip(a)].
% 0.45/1.05 62 f13(A) = c1. [resolve(20,a,14,a)].
% 0.45/1.05 63 f15(A) = c1. [resolve(20,a,15,a)].
% 0.45/1.05 64 f16(A) = c1. [resolve(20,a,16,a)].
% 0.45/1.05 65 f14(A) = c1. [copy(64),rewrite([37(1)])].
% 0.45/1.05 70 f7(A,B) = f2(A,B). [resolve(22,a,23,a)].
% 0.45/1.05 71 f12(A) = f2(A,f13(A)). [resolve(22,a,24,a)].
% 0.45/1.05 72 f2(A,c1) = A. [copy(71),rewrite([34(1),62(1)]),flip(a)].
% 0.45/1.05 83 A != B | -r4(C,D,B) | -r2(E,C) | -r2(f13(F),E) | A != V6 | V6 != f2(D,V7). [resolve(28,e,27,b)].
% 0.45/1.05 84 A != B | -r4(C,D,B) | -r2(E,C) | -r2(c1,E) | A != F | f2(D,V6) != F. [copy(83),rewrite([62(4)]),flip(f)].
% 0.45/1.05 123 r4(A,c1,c1). [back_rewrite(39),rewrite([63(1),65(2)])].
% 0.45/1.05 124 f16(A) = c1. [back_rewrite(37),rewrite([65(2)])].
% 0.45/1.05 126 r2(f2(A,B),f4(A,B)). [back_rewrite(41),rewrite([70(1)])].
% 0.45/1.05 225 -r2(c1,f2(A,B)). [ur(84,a,124,a,b,123,a,c,126,a,e,124,a,f,72,a)].
% 0.45/1.05 238 f2(A,B) != f1(c1). [ur(50,b,225,a),flip(a)].
% 0.45/1.05 239 $F. [resolve(238,a,72,a)].
% 0.45/1.05
% 0.45/1.05 % SZS output end Refutation
% 0.45/1.05 ============================== end of proof ==========================
% 0.45/1.05
% 0.45/1.05 ============================== STATISTICS ============================
% 0.45/1.05
% 0.45/1.05 Given=53. Generated=361. Kept=165. proofs=1.
% 0.45/1.05 Usable=28. Sos=47. Demods=17. Limbo=0, Disabled=172. Hints=0.
% 0.45/1.05 Megabytes=0.23.
% 0.45/1.05 User_CPU=0.03, System_CPU=0.00, Wall_clock=0.
% 0.45/1.05
% 0.45/1.05 ============================== end of statistics =====================
% 0.45/1.05
% 0.45/1.05 ============================== end of search =========================
% 0.45/1.05
% 0.45/1.05 THEOREM PROVED
% 0.45/1.05 % SZS status Theorem
% 0.45/1.05
% 0.45/1.05 Exiting with 1 proof.
% 0.45/1.05
% 0.45/1.05 Process 29855 exit (max_proofs) Thu Jun 2 10:48:39 2022
% 0.45/1.05 Prover9 interrupted
%------------------------------------------------------------------------------