TSTP Solution File: NUN069+2 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : NUN069+2 : TPTP v8.1.0. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n021.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 16:37:11 EDT 2022
% Result : Theorem 0.75s 1.00s
% Output : Refutation 0.75s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : NUN069+2 : TPTP v8.1.0. Released v7.3.0.
% 0.06/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n021.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
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Thu Jun 2 04:49:01 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.75/1.00 ============================== Prover9 ===============================
% 0.75/1.00 Prover9 (32) version 2009-11A, November 2009.
% 0.75/1.00 Process 19665 was started by sandbox2 on n021.cluster.edu,
% 0.75/1.00 Thu Jun 2 04:49:02 2022
% 0.75/1.00 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_19512_n021.cluster.edu".
% 0.75/1.00 ============================== end of head ===========================
% 0.75/1.00
% 0.75/1.00 ============================== INPUT =================================
% 0.75/1.00
% 0.75/1.00 % Reading from file /tmp/Prover9_19512_n021.cluster.edu
% 0.75/1.00
% 0.75/1.00 set(prolog_style_variables).
% 0.75/1.00 set(auto2).
% 0.75/1.00 % set(auto2) -> set(auto).
% 0.75/1.00 % set(auto) -> set(auto_inference).
% 0.75/1.00 % set(auto) -> set(auto_setup).
% 0.75/1.00 % set(auto_setup) -> set(predicate_elim).
% 0.75/1.00 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.75/1.00 % set(auto) -> set(auto_limits).
% 0.75/1.00 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.75/1.00 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.75/1.00 % set(auto) -> set(auto_denials).
% 0.75/1.00 % set(auto) -> set(auto_process).
% 0.75/1.00 % set(auto2) -> assign(new_constants, 1).
% 0.75/1.00 % set(auto2) -> assign(fold_denial_max, 3).
% 0.75/1.00 % set(auto2) -> assign(max_weight, "200.000").
% 0.75/1.00 % set(auto2) -> assign(max_hours, 1).
% 0.75/1.00 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.75/1.00 % set(auto2) -> assign(max_seconds, 0).
% 0.75/1.00 % set(auto2) -> assign(max_minutes, 5).
% 0.75/1.00 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.75/1.00 % set(auto2) -> set(sort_initial_sos).
% 0.75/1.00 % set(auto2) -> assign(sos_limit, -1).
% 0.75/1.00 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.75/1.00 % set(auto2) -> assign(max_megs, 400).
% 0.75/1.00 % set(auto2) -> assign(stats, some).
% 0.75/1.00 % set(auto2) -> clear(echo_input).
% 0.75/1.00 % set(auto2) -> set(quiet).
% 0.75/1.00 % set(auto2) -> clear(print_initial_clauses).
% 0.75/1.00 % set(auto2) -> clear(print_given).
% 0.75/1.00 assign(lrs_ticks,-1).
% 0.75/1.00 assign(sos_limit,10000).
% 0.75/1.00 assign(order,kbo).
% 0.75/1.00 set(lex_order_vars).
% 0.75/1.00 clear(print_given).
% 0.75/1.00
% 0.75/1.00 % formulas(sos). % not echoed (12 formulas)
% 0.75/1.00
% 0.75/1.00 ============================== end of input ==========================
% 0.75/1.00
% 0.75/1.00 % From the command line: assign(max_seconds, 300).
% 0.75/1.00
% 0.75/1.00 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.75/1.00
% 0.75/1.00 % Formulas that are not ordinary clauses:
% 0.75/1.00 1 (exists Y24 all X19 (-r1(X19) & X19 != Y24 | r1(X19) & X19 = Y24)) # label(axiom_1) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.00 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].
% 0.75/1.00 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].
% 0.75/1.00 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].
% 0.75/1.00 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].
% 0.75/1.00 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].
% 0.75/1.00 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].
% 0.75/1.00 8 (all X4 exists Y9 ((exists Y16 (r1(Y16) & r3(X4,Y16,Y9))) & Y9 = X4)) # label(axiom_4a) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.00 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].
% 0.75/1.00 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].
% 0.75/1.00 11 (all X7 all Y10 ((all Y20 (-r1(Y20) | Y20 != Y10)) | -r2(X7,Y10))) # label(axiom_7a) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.00 12 -(exists Y1 (Y1 = Y1 & (exists Y2 (r1(Y2) & r2(Y2,Y1))))) # label(oneeqone) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.75/1.00
% 0.75/1.00 ============================== end of process non-clausal formulas ===
% 0.75/1.00
% 0.75/1.00 ============================== PROCESS INITIAL CLAUSES ===============
% 0.75/1.00
% 0.75/1.00 ============================== PREDICATE ELIMINATION =================
% 0.75/1.00 13 -r1(A) | A != B | -r2(C,B) # label(axiom_7a) # label(axiom). [clausify(11)].
% 0.75/1.00 14 r1(f13(A)) # label(axiom_4a) # label(axiom). [clausify(8)].
% 0.75/1.00 15 r1(f15(A)) # label(axiom_5a) # label(axiom). [clausify(9)].
% 0.75/1.00 16 r1(f16(A)) # label(axiom_5a) # label(axiom). [clausify(9)].
% 0.75/1.00 17 r1(f17(A)) | f19(A) = A # label(axiom_6a) # label(axiom). [clausify(10)].
% 0.75/1.00 18 r1(f17(A)) | r2(f18(A),f19(A)) # label(axiom_6a) # label(axiom). [clausify(10)].
% 0.75/1.00 Derived: f13(A) != B | -r2(C,B). [resolve(13,a,14,a)].
% 0.75/1.00 Derived: f15(A) != B | -r2(C,B). [resolve(13,a,15,a)].
% 0.75/1.00 Derived: f16(A) != B | -r2(C,B). [resolve(13,a,16,a)].
% 0.75/1.00 Derived: f17(A) != B | -r2(C,B) | f19(A) = A. [resolve(13,a,17,a)].
% 0.75/1.00 Derived: f17(A) != B | -r2(C,B) | r2(f18(A),f19(A)). [resolve(13,a,18,a)].
% 0.75/1.00 19 A != A | -r1(B) | -r2(B,A) # label(oneeqone) # label(negated_conjecture). [clausify(12)].
% 0.75/1.00 Derived: A != A | -r2(f13(B),A). [resolve(19,b,14,a)].
% 0.75/1.00 Derived: A != A | -r2(f15(B),A). [resolve(19,b,15,a)].
% 0.75/1.00 Derived: A != A | -r2(f16(B),A). [resolve(19,b,16,a)].
% 0.75/1.00 Derived: A != A | -r2(f17(B),A) | f19(B) = B. [resolve(19,b,17,a)].
% 0.75/1.00 Derived: A != A | -r2(f17(B),A) | r2(f18(B),f19(B)). [resolve(19,b,18,a)].
% 0.75/1.00 20 -r1(A) | A = c1 # label(axiom_1) # label(axiom). [clausify(1)].
% 0.75/1.00 Derived: f13(A) = c1. [resolve(20,a,14,a)].
% 0.75/1.00 Derived: f15(A) = c1. [resolve(20,a,15,a)].
% 0.75/1.00 Derived: f16(A) = c1. [resolve(20,a,16,a)].
% 0.75/1.00 Derived: f17(A) = c1 | f19(A) = A. [resolve(20,a,17,a)].
% 0.75/1.00 Derived: f17(A) = c1 | r2(f18(A),f19(A)). [resolve(20,a,18,a)].
% 0.75/1.00 21 A != c1 | r1(A) # label(axiom_1) # label(axiom). [clausify(1)].
% 0.75/1.00 Derived: A != c1 | A != B | -r2(C,B). [resolve(21,b,13,a)].
% 0.75/1.00 Derived: A != c1 | B != B | -r2(A,B). [resolve(21,b,19,b)].
% 0.75/1.00 22 -r3(A,B,C) | C = f2(A,B) # label(axiom_3) # label(axiom). [clausify(3)].
% 0.75/1.00 23 r3(A,B,f7(A,B)) # label(axiom_1a) # label(axiom). [clausify(5)].
% 0.75/1.00 24 r3(A,f13(A),f12(A)) # label(axiom_4a) # label(axiom). [clausify(8)].
% 0.75/1.00 25 r3(A,f6(A,B),f5(A,B)) # label(axiom_1a) # label(axiom). [clausify(5)].
% 0.75/1.00 26 r3(f11(A,B),A,f8(A,B)) # label(axiom_2a) # label(axiom). [clausify(6)].
% 0.75/1.00 Derived: f7(A,B) = f2(A,B). [resolve(22,a,23,a)].
% 0.75/1.00 Derived: f12(A) = f2(A,f13(A)). [resolve(22,a,24,a)].
% 0.75/1.00 Derived: f5(A,B) = f2(A,f6(A,B)). [resolve(22,a,25,a)].
% 0.75/1.00 Derived: f8(A,B) = f2(f11(A,B),A). [resolve(22,a,26,a)].
% 0.75/1.00 27 A != f2(B,C) | r3(B,C,A) # label(axiom_3) # label(axiom). [clausify(3)].
% 0.75/1.00 28 -r4(A,B,C) | C = f3(A,B) # label(axiom_4) # label(axiom). [clausify(4)].
% 0.75/1.00 29 r4(A,B,f11(A,B)) # label(axiom_2a) # label(axiom). [clausify(6)].
% 0.75/1.00 30 r4(A,f15(A),f14(A)) # label(axiom_5a) # label(axiom). [clausify(9)].
% 0.75/1.00 31 r4(A,f10(A,B),f9(A,B)) # label(axiom_2a) # label(axiom). [clausify(6)].
% 0.75/1.00 Derived: f11(A,B) = f3(A,B). [resolve(28,a,29,a)].
% 0.75/1.00 Derived: f14(A) = f3(A,f15(A)). [resolve(28,a,30,a)].
% 0.75/1.00 Derived: f9(A,B) = f3(A,f10(A,B)). [resolve(28,a,31,a)].
% 0.75/1.00 32 A != f3(B,C) | r4(B,C,A) # label(axiom_4) # label(axiom). [clausify(4)].
% 0.75/1.00
% 0.75/1.00 ============================== end predicate elimination =============
% 0.75/1.00
% 0.75/1.00 Auto_denials: (non-Horn, no changes).
% 0.75/1.00
% 0.75/1.00 Term ordering decisions:
% 0.75/1.00 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.
% 0.75/1.00
% 0.75/1.00 ============================== PROOF =================================
% 0.75/1.00 % SZS status Theorem
% 0.75/1.00 % SZS output start Refutation
% 0.75/1.00
% 0.75/1.00 % Proof 1 at 0.02 (+ 0.00) seconds.
% 0.75/1.00 % Length of proof is 9.
% 0.75/1.00 % Level of proof is 4.
% 0.75/1.00 % Maximum clause weight is 5.000.
% 0.75/1.00 % Given clauses 0.
% 0.75/1.00
% 0.75/1.00 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].
% 0.75/1.00 8 (all X4 exists Y9 ((exists Y16 (r1(Y16) & r3(X4,Y16,Y9))) & Y9 = X4)) # label(axiom_4a) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.00 12 -(exists Y1 (Y1 = Y1 & (exists Y2 (r1(Y2) & r2(Y2,Y1))))) # label(oneeqone) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.75/1.00 14 r1(f13(A)) # label(axiom_4a) # label(axiom). [clausify(8)].
% 0.75/1.00 19 A != A | -r1(B) | -r2(B,A) # label(oneeqone) # label(negated_conjecture). [clausify(12)].
% 0.75/1.00 35 r2(A,f10(B,A)) # label(axiom_2a) # label(axiom). [clausify(6)].
% 0.75/1.00 53 A != A | -r2(f13(B),A). [resolve(19,b,14,a)].
% 0.75/1.00 54 -r2(f13(A),B). [copy(53),xx(a)].
% 0.75/1.00 55 $F. [resolve(54,a,35,a)].
% 0.75/1.00
% 0.75/1.00 % SZS output end Refutation
% 0.75/1.00 ============================== end of proof ==========================
% 0.75/1.00
% 0.75/1.00 ============================== STATISTICS ============================
% 0.75/1.00
% 0.75/1.00 Given=0. Generated=18. Kept=18. proofs=1.
% 0.75/1.00 Usable=0. Sos=0. Demods=4. Limbo=17, Disabled=38. Hints=0.
% 0.75/1.00 Megabytes=0.07.
% 0.75/1.00 User_CPU=0.02, System_CPU=0.00, Wall_clock=0.
% 0.75/1.00
% 0.75/1.00 ============================== end of statistics =====================
% 0.75/1.00
% 0.75/1.00 ============================== end of search =========================
% 0.75/1.00
% 0.75/1.00 THEOREM PROVED
% 0.75/1.00 % SZS status Theorem
% 0.75/1.00
% 0.75/1.00 Exiting with 1 proof.
% 0.75/1.00
% 0.75/1.00 Process 19665 exit (max_proofs) Thu Jun 2 04:49:02 2022
% 0.75/1.00 Prover9 interrupted
%------------------------------------------------------------------------------