TSTP Solution File: NUN071+2 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : NUN071+2 : TPTP v8.1.0. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n018.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 16:37:12 EDT 2022
% Result : Theorem 0.73s 1.03s
% Output : Refutation 0.73s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUN071+2 : TPTP v8.1.0. Released v7.3.0.
% 0.07/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n018.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
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Thu Jun 2 04:24:00 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.43/1.00 ============================== Prover9 ===============================
% 0.43/1.00 Prover9 (32) version 2009-11A, November 2009.
% 0.43/1.00 Process 3938 was started by sandbox2 on n018.cluster.edu,
% 0.43/1.00 Thu Jun 2 04:24:00 2022
% 0.43/1.00 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_3785_n018.cluster.edu".
% 0.43/1.00 ============================== end of head ===========================
% 0.43/1.00
% 0.43/1.00 ============================== INPUT =================================
% 0.43/1.00
% 0.43/1.00 % Reading from file /tmp/Prover9_3785_n018.cluster.edu
% 0.43/1.00
% 0.43/1.00 set(prolog_style_variables).
% 0.43/1.00 set(auto2).
% 0.43/1.00 % set(auto2) -> set(auto).
% 0.43/1.00 % set(auto) -> set(auto_inference).
% 0.43/1.00 % set(auto) -> set(auto_setup).
% 0.43/1.00 % set(auto_setup) -> set(predicate_elim).
% 0.43/1.00 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.43/1.00 % set(auto) -> set(auto_limits).
% 0.43/1.00 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.43/1.00 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.43/1.00 % set(auto) -> set(auto_denials).
% 0.43/1.00 % set(auto) -> set(auto_process).
% 0.43/1.00 % set(auto2) -> assign(new_constants, 1).
% 0.43/1.00 % set(auto2) -> assign(fold_denial_max, 3).
% 0.43/1.00 % set(auto2) -> assign(max_weight, "200.000").
% 0.43/1.00 % set(auto2) -> assign(max_hours, 1).
% 0.43/1.00 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.43/1.00 % set(auto2) -> assign(max_seconds, 0).
% 0.43/1.00 % set(auto2) -> assign(max_minutes, 5).
% 0.43/1.00 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.43/1.00 % set(auto2) -> set(sort_initial_sos).
% 0.43/1.00 % set(auto2) -> assign(sos_limit, -1).
% 0.43/1.00 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.43/1.00 % set(auto2) -> assign(max_megs, 400).
% 0.43/1.00 % set(auto2) -> assign(stats, some).
% 0.43/1.00 % set(auto2) -> clear(echo_input).
% 0.43/1.00 % set(auto2) -> set(quiet).
% 0.43/1.00 % set(auto2) -> clear(print_initial_clauses).
% 0.43/1.00 % set(auto2) -> clear(print_given).
% 0.43/1.00 assign(lrs_ticks,-1).
% 0.43/1.00 assign(sos_limit,10000).
% 0.43/1.00 assign(order,kbo).
% 0.43/1.00 set(lex_order_vars).
% 0.43/1.00 clear(print_given).
% 0.43/1.00
% 0.43/1.00 % formulas(sos). % not echoed (12 formulas)
% 0.43/1.00
% 0.43/1.00 ============================== end of input ==========================
% 0.43/1.00
% 0.43/1.00 % From the command line: assign(max_seconds, 300).
% 0.43/1.00
% 0.43/1.00 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.43/1.00
% 0.43/1.00 % Formulas that are not ordinary clauses:
% 0.43/1.00 1 (exists Y24 all X19 (-r1(X19) & X19 != Y24 | r1(X19) & X19 = Y24)) # label(axiom_1) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 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].
% 0.43/1.00 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].
% 0.43/1.00 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].
% 0.43/1.00 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].
% 0.43/1.00 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].
% 0.43/1.00 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].
% 0.43/1.00 8 (all X4 exists Y9 ((exists Y16 (r1(Y16) & r3(X4,Y16,Y9))) & Y9 = X4)) # label(axiom_4a) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 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].
% 0.43/1.00 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].
% 0.43/1.00 11 (all X7 all Y10 ((all Y20 (-r1(Y20) | Y20 != Y10)) | -r2(X7,Y10))) # label(axiom_7a) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 12 -(exists Y1 ((exists Y2 (r4(Y2,Y2,Y1) & (exists Y4 (r1(Y4) & r2(Y4,Y2))))) & (exists Y3 (Y1 = Y3 & (exists Y5 (r1(Y5) & r2(Y5,Y3))))))) # label(onetimesoneeqone) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.73/1.03
% 0.73/1.03 ============================== end of process non-clausal formulas ===
% 0.73/1.03
% 0.73/1.03 ============================== PROCESS INITIAL CLAUSES ===============
% 0.73/1.03
% 0.73/1.03 ============================== PREDICATE ELIMINATION =================
% 0.73/1.03 13 -r3(A,B,C) | C = f2(A,B) # label(axiom_3) # label(axiom). [clausify(3)].
% 0.73/1.03 14 r3(A,B,f7(A,B)) # label(axiom_1a) # label(axiom). [clausify(5)].
% 0.73/1.03 15 r3(A,f13(A),f12(A)) # label(axiom_4a) # label(axiom). [clausify(8)].
% 0.73/1.03 16 r3(A,f6(A,B),f5(A,B)) # label(axiom_1a) # label(axiom). [clausify(5)].
% 0.73/1.03 17 r3(f11(A,B),A,f8(A,B)) # label(axiom_2a) # label(axiom). [clausify(6)].
% 0.73/1.03 Derived: f7(A,B) = f2(A,B). [resolve(13,a,14,a)].
% 0.73/1.03 Derived: f12(A) = f2(A,f13(A)). [resolve(13,a,15,a)].
% 0.73/1.03 Derived: f5(A,B) = f2(A,f6(A,B)). [resolve(13,a,16,a)].
% 0.73/1.03 Derived: f8(A,B) = f2(f11(A,B),A). [resolve(13,a,17,a)].
% 0.73/1.03 18 A != f2(B,C) | r3(B,C,A) # label(axiom_3) # label(axiom). [clausify(3)].
% 0.73/1.03
% 0.73/1.03 ============================== end predicate elimination =============
% 0.73/1.03
% 0.73/1.03 Auto_denials: (non-Horn, no changes).
% 0.73/1.03
% 0.73/1.03 Term ordering decisions:
% 0.73/1.03 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.
% 0.73/1.03
% 0.73/1.03 ============================== end of process initial clauses ========
% 0.73/1.03
% 0.73/1.03 ============================== CLAUSES FOR SEARCH ====================
% 0.73/1.03
% 0.73/1.03 ============================== end of clauses for search =============
% 0.73/1.03
% 0.73/1.03 ============================== SEARCH ================================
% 0.73/1.03
% 0.73/1.03 % Starting search at 0.01 seconds.
% 0.73/1.03
% 0.73/1.03 ============================== PROOF =================================
% 0.73/1.03 % SZS status Theorem
% 0.73/1.03 % SZS output start Refutation
% 0.73/1.03
% 0.73/1.03 % Proof 1 at 0.04 (+ 0.00) seconds.
% 0.73/1.03 % Length of proof is 63.
% 0.73/1.03 % Level of proof is 7.
% 0.73/1.03 % Maximum clause weight is 17.000.
% 0.73/1.03 % Given clauses 90.
% 0.73/1.03
% 0.73/1.03 1 (exists Y24 all X19 (-r1(X19) & X19 != Y24 | r1(X19) & X19 = Y24)) # label(axiom_1) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.03 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].
% 0.73/1.03 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].
% 0.73/1.03 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].
% 0.73/1.03 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].
% 0.73/1.03 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].
% 0.73/1.03 8 (all X4 exists Y9 ((exists Y16 (r1(Y16) & r3(X4,Y16,Y9))) & Y9 = X4)) # label(axiom_4a) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.03 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].
% 0.73/1.03 12 -(exists Y1 ((exists Y2 (r4(Y2,Y2,Y1) & (exists Y4 (r1(Y4) & r2(Y4,Y2))))) & (exists Y3 (Y1 = Y3 & (exists Y5 (r1(Y5) & r2(Y5,Y3))))))) # label(onetimesoneeqone) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.73/1.03 13 -r3(A,B,C) | C = f2(A,B) # label(axiom_3) # label(axiom). [clausify(3)].
% 0.73/1.03 14 r3(A,B,f7(A,B)) # label(axiom_1a) # label(axiom). [clausify(5)].
% 0.73/1.03 15 r3(A,f13(A),f12(A)) # label(axiom_4a) # label(axiom). [clausify(8)].
% 0.73/1.03 16 r3(A,f6(A,B),f5(A,B)) # label(axiom_1a) # label(axiom). [clausify(5)].
% 0.73/1.03 17 r3(f11(A,B),A,f8(A,B)) # label(axiom_2a) # label(axiom). [clausify(6)].
% 0.73/1.03 19 r1(f13(A)) # label(axiom_4a) # label(axiom). [clausify(8)].
% 0.73/1.03 20 r1(f15(A)) # label(axiom_5a) # label(axiom). [clausify(9)].
% 0.73/1.03 21 r1(f16(A)) # label(axiom_5a) # label(axiom). [clausify(9)].
% 0.73/1.03 22 f12(A) = A # label(axiom_4a) # label(axiom). [clausify(8)].
% 0.73/1.03 23 r2(A,f6(B,A)) # label(axiom_1a) # label(axiom). [clausify(5)].
% 0.73/1.03 24 r2(A,f10(B,A)) # label(axiom_2a) # label(axiom). [clausify(6)].
% 0.73/1.03 25 f16(A) = f14(A) # label(axiom_5a) # label(axiom). [clausify(9)].
% 0.73/1.03 26 r4(A,B,f11(A,B)) # label(axiom_2a) # label(axiom). [clausify(6)].
% 0.73/1.03 27 r4(A,f15(A),f14(A)) # label(axiom_5a) # label(axiom). [clausify(9)].
% 0.73/1.03 28 f5(A,B) = f4(A,B) # label(axiom_1a) # label(axiom). [clausify(5)].
% 0.73/1.03 29 r2(f7(A,B),f4(A,B)) # label(axiom_1a) # label(axiom). [clausify(5)].
% 0.73/1.03 30 f9(A,B) = f8(A,B) # label(axiom_2a) # label(axiom). [clausify(6)].
% 0.73/1.03 32 r4(A,f10(A,B),f9(A,B)) # label(axiom_2a) # label(axiom). [clausify(6)].
% 0.73/1.03 33 r4(A,f10(A,B),f8(A,B)). [copy(32),rewrite([30(2)])].
% 0.73/1.03 38 -r4(A,A,B) | -r1(C) | -r2(C,A) | B != D | -r1(E) | -r2(E,D) # label(onetimesoneeqone) # label(negated_conjecture). [clausify(12)].
% 0.73/1.03 39 -r1(A) | A = c1 # label(axiom_1) # label(axiom). [clausify(1)].
% 0.73/1.03 40 -r1(A) | c1 = A. [copy(39),flip(b)].
% 0.73/1.03 43 -r2(A,B) | B = f1(A) # label(axiom_2) # label(axiom). [clausify(2)].
% 0.73/1.03 44 -r2(A,B) | f1(A) = B. [copy(43),flip(b)].
% 0.73/1.03 47 -r4(A,B,C) | C = f3(A,B) # label(axiom_4) # label(axiom). [clausify(4)].
% 0.73/1.03 48 -r4(A,B,C) | f3(A,B) = C. [copy(47),flip(b)].
% 0.73/1.03 52 f7(A,B) = f2(A,B). [resolve(13,a,14,a)].
% 0.73/1.03 53 f12(A) = f2(A,f13(A)). [resolve(13,a,15,a)].
% 0.73/1.03 54 f2(A,f13(A)) = A. [copy(53),rewrite([22(1)]),flip(a)].
% 0.73/1.03 55 f5(A,B) = f2(A,f6(A,B)). [resolve(13,a,16,a)].
% 0.73/1.03 56 f2(A,f6(A,B)) = f4(A,B). [copy(55),rewrite([28(1)]),flip(a)].
% 0.73/1.03 57 f8(A,B) = f2(f11(A,B),A). [resolve(13,a,17,a)].
% 0.73/1.03 58 r1(f14(A)). [back_rewrite(21),rewrite([25(1)])].
% 0.73/1.03 60 -r4(A,A,B) | -r1(C) | -r2(C,A) | B != A. [factor(38,c,f),merge(e)].
% 0.73/1.03 61 r2(f2(A,B),f4(A,B)). [back_rewrite(29),rewrite([52(1)])].
% 0.73/1.03 62 r4(A,f10(A,B),f2(f11(A,B),A)). [back_rewrite(33),rewrite([57(2)])].
% 0.73/1.03 122 f15(A) = c1. [resolve(40,a,20,a),flip(a)].
% 0.73/1.03 123 f13(A) = c1. [resolve(40,a,19,a),flip(a)].
% 0.73/1.03 137 r4(A,c1,f14(A)). [back_rewrite(27),rewrite([122(1)])].
% 0.73/1.03 138 r1(c1). [back_rewrite(20),rewrite([122(1)])].
% 0.73/1.03 139 f2(A,c1) = A. [back_rewrite(54),rewrite([123(1)])].
% 0.73/1.03 143 f10(A,B) = f1(B). [resolve(44,a,24,a),flip(a)].
% 0.73/1.03 144 f6(A,B) = f1(B). [resolve(44,a,23,a),flip(a)].
% 0.73/1.03 151 r4(A,f1(B),f2(f11(A,B),A)). [back_rewrite(62),rewrite([143(1)])].
% 0.73/1.03 152 r2(A,f1(A)). [back_rewrite(24),rewrite([143(1)])].
% 0.73/1.03 153 f2(A,f1(B)) = f4(A,B). [back_rewrite(56),rewrite([144(1)])].
% 0.73/1.03 155 f11(A,B) = f3(A,B). [resolve(48,a,26,a),flip(a)].
% 0.73/1.03 156 r4(A,f1(B),f2(f3(A,B),A)). [back_rewrite(151),rewrite([155(2)])].
% 0.73/1.03 168 f14(A) = c1. [resolve(58,a,40,a),flip(a)].
% 0.73/1.03 169 r4(A,c1,c1). [back_rewrite(137),rewrite([168(2)])].
% 0.73/1.03 192 f3(A,c1) = c1. [resolve(169,a,48,a)].
% 0.73/1.03 198 r2(A,f4(A,c1)). [para(139(a,1),61(a,1))].
% 0.73/1.03 202 f4(A,c1) = f1(A). [resolve(198,a,44,a),flip(a)].
% 0.73/1.03 273 $F. [ur(60,a,156,a,b,138,a,c,152,a),rewrite([192(4),153(4),202(3)]),xx(a)].
% 0.73/1.03
% 0.73/1.03 % SZS output end Refutation
% 0.73/1.03 ============================== end of proof ==========================
% 0.73/1.03
% 0.73/1.03 ============================== STATISTICS ============================
% 0.73/1.03
% 0.73/1.03 Given=90. Generated=1066. Kept=245. proofs=1.
% 0.73/1.03 Usable=75. Sos=64. Demods=22. Limbo=4, Disabled=138. Hints=0.
% 0.73/1.03 Megabytes=0.25.
% 0.73/1.03 User_CPU=0.04, System_CPU=0.00, Wall_clock=0.
% 0.73/1.03
% 0.73/1.03 ============================== end of statistics =====================
% 0.73/1.03
% 0.73/1.03 ============================== end of search =========================
% 0.73/1.03
% 0.73/1.03 THEOREM PROVED
% 0.73/1.03 % SZS status Theorem
% 0.73/1.03
% 0.73/1.03 Exiting with 1 proof.
% 0.73/1.03
% 0.73/1.03 Process 3938 exit (max_proofs) Thu Jun 2 04:24:00 2022
% 0.73/1.03 Prover9 interrupted
%------------------------------------------------------------------------------