TSTP Solution File: NUN059+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : NUN059+1 : TPTP v8.1.0. Bugfixed v7.4.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n026.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 16:37:05 EDT 2022
% Result : Theorem 2.63s 2.98s
% Output : Refutation 2.63s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUN059+1 : TPTP v8.1.0. Bugfixed v7.4.0.
% 0.07/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.34 % Computer : n026.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % 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 07:59:42 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.74/1.02 ============================== Prover9 ===============================
% 0.74/1.02 Prover9 (32) version 2009-11A, November 2009.
% 0.74/1.02 Process 28564 was started by sandbox on n026.cluster.edu,
% 0.74/1.02 Thu Jun 2 07:59:43 2022
% 0.74/1.02 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_28402_n026.cluster.edu".
% 0.74/1.02 ============================== end of head ===========================
% 0.74/1.02
% 0.74/1.02 ============================== INPUT =================================
% 0.74/1.02
% 0.74/1.02 % Reading from file /tmp/Prover9_28402_n026.cluster.edu
% 0.74/1.02
% 0.74/1.02 set(prolog_style_variables).
% 0.74/1.02 set(auto2).
% 0.74/1.02 % set(auto2) -> set(auto).
% 0.74/1.02 % set(auto) -> set(auto_inference).
% 0.74/1.02 % set(auto) -> set(auto_setup).
% 0.74/1.02 % set(auto_setup) -> set(predicate_elim).
% 0.74/1.02 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.74/1.02 % set(auto) -> set(auto_limits).
% 0.74/1.02 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.74/1.02 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.74/1.02 % set(auto) -> set(auto_denials).
% 0.74/1.02 % set(auto) -> set(auto_process).
% 0.74/1.02 % set(auto2) -> assign(new_constants, 1).
% 0.74/1.02 % set(auto2) -> assign(fold_denial_max, 3).
% 0.74/1.02 % set(auto2) -> assign(max_weight, "200.000").
% 0.74/1.02 % set(auto2) -> assign(max_hours, 1).
% 0.74/1.02 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.74/1.02 % set(auto2) -> assign(max_seconds, 0).
% 0.74/1.02 % set(auto2) -> assign(max_minutes, 5).
% 0.74/1.02 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.74/1.02 % set(auto2) -> set(sort_initial_sos).
% 0.74/1.02 % set(auto2) -> assign(sos_limit, -1).
% 0.74/1.02 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.74/1.02 % set(auto2) -> assign(max_megs, 400).
% 0.74/1.02 % set(auto2) -> assign(stats, some).
% 0.74/1.02 % set(auto2) -> clear(echo_input).
% 0.74/1.02 % set(auto2) -> set(quiet).
% 0.74/1.02 % set(auto2) -> clear(print_initial_clauses).
% 0.74/1.02 % set(auto2) -> clear(print_given).
% 0.74/1.02 assign(lrs_ticks,-1).
% 0.74/1.02 assign(sos_limit,10000).
% 0.74/1.02 assign(order,kbo).
% 0.74/1.02 set(lex_order_vars).
% 0.74/1.02 clear(print_given).
% 0.74/1.02
% 0.74/1.02 % formulas(sos). % not echoed (19 formulas)
% 0.74/1.02
% 0.74/1.02 ============================== end of input ==========================
% 0.74/1.02
% 0.74/1.02 % From the command line: assign(max_seconds, 300).
% 0.74/1.02
% 0.74/1.02 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.74/1.02
% 0.74/1.02 % Formulas that are not ordinary clauses:
% 0.74/1.02 1 (exists Y24 all X19 (id(X19,Y24) & r1(X19) | -r1(X19) & -id(X19,Y24))) # label(axiom_1) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.02 2 (all X11 exists Y21 all X12 (id(X12,Y21) & r2(X11,X12) | -r2(X11,X12) & -id(X12,Y21))) # label(axiom_2) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.02 3 (all X13 all X14 exists Y22 all X15 (id(X15,Y22) & r3(X13,X14,X15) | -r3(X13,X14,X15) & -id(X15,Y22))) # label(axiom_3) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.02 4 (all X16 all X17 exists Y23 all X18 (id(X18,Y23) & r4(X16,X17,X18) | -r4(X16,X17,X18) & -id(X18,Y23))) # label(axiom_4) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.02 5 (all X20 id(X20,X20)) # label(axiom_5) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.02 6 (all X21 all X22 (-id(X21,X22) | id(X22,X21))) # label(axiom_6) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.02 7 (all X23 all X24 all X25 (-id(X23,X24) | id(X23,X25) | -id(X24,X25))) # label(axiom_7) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.02 8 (all X26 all X27 (-id(X26,X27) | -r1(X26) & -r1(X27) | r1(X26) & r1(X27))) # label(axiom_8) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.02 9 (all X28 all X29 all X30 all X31 (-id(X28,X30) | -id(X29,X31) | -r2(X28,X29) & -r2(X30,X31) | r2(X28,X29) & r2(X30,X31))) # label(axiom_9) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.02 10 (all X32 all X33 all X34 all X35 all X36 all X37 (-id(X32,X35) | -id(X33,X36) | -id(X34,X37) | -r3(X32,X33,X34) & -r3(X35,X36,X37) | r3(X32,X33,X34) & r3(X35,X36,X37))) # label(axiom_10) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.02 11 (all X38 all X39 all X40 all X41 all X42 all X43 (-id(X38,X41) | -id(X39,X42) | -id(X40,X43) | -r4(X38,X39,X40) & -r4(X41,X42,X43) | r4(X38,X39,X40) & r4(X41,X42,X43))) # label(axiom_11) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.02 12 (all X1 all X8 exists Y4 ((exists Y5 (id(Y5,Y4) & (exists Y15 (r2(X8,Y15) & r3(X1,Y15,Y5))))) & (exists Y7 (r2(Y7,Y4) & r3(X1,X8,Y7))))) # label(axiom_1a) # label(axiom) # label(non_clause). [assumption].
% 2.63/2.98 13 (all X2 all X9 exists Y2 ((exists Y3 (id(Y3,Y2) & (exists Y14 (r2(X9,Y14) & r4(X2,Y14,Y3))))) & (exists Y6 (r3(Y6,X2,Y2) & r4(X2,X9,Y6))))) # label(axiom_2a) # label(axiom) # label(non_clause). [assumption].
% 2.63/2.98 14 (all X3 all X10 ((all Y12 ((all Y13 (-id(Y13,Y12) | -r2(X3,Y13))) | -r2(X10,Y12))) | id(X3,X10))) # label(axiom_3a) # label(axiom) # label(non_clause). [assumption].
% 2.63/2.98 15 (all X4 exists Y9 (id(Y9,X4) & (exists Y16 (r1(Y16) & r3(X4,Y16,Y9))))) # label(axiom_4a) # label(axiom) # label(non_clause). [assumption].
% 2.63/2.98 16 (all X5 exists Y8 ((exists Y17 (r1(Y17) & r4(X5,Y17,Y8))) & (exists Y18 (id(Y8,Y18) & r1(Y18))))) # label(axiom_5a) # label(axiom) # label(non_clause). [assumption].
% 2.63/2.98 17 (all X6 ((exists Y19 (id(X6,Y19) & r1(Y19))) | (exists Y1 exists Y11 (id(X6,Y11) & r2(Y1,Y11))))) # label(axiom_6a) # label(axiom) # label(non_clause). [assumption].
% 2.63/2.98 18 (all X7 all Y10 ((all Y20 (-id(Y20,Y10) | -r1(Y20))) | -r2(X7,Y10))) # label(axiom_7a) # label(axiom) # label(non_clause). [assumption].
% 2.63/2.98 19 -(exists Y1 exists Y3 exists Y2 exists Y4 ((exists Y5 (id(Y4,Y5) & r4(Y2,Y2,Y5))) & (exists Y6 (r4(Y3,Y3,Y6) & (exists Y7 (r4(Y1,Y1,Y7) & r3(Y7,Y6,Y4))))))) # label(fermattothepoweroftwoid) # label(negated_conjecture) # label(non_clause). [assumption].
% 2.63/2.98
% 2.63/2.98 ============================== end of process non-clausal formulas ===
% 2.63/2.98
% 2.63/2.98 ============================== PROCESS INITIAL CLAUSES ===============
% 2.63/2.98
% 2.63/2.98 ============================== PREDICATE ELIMINATION =================
% 2.63/2.98
% 2.63/2.98 ============================== end predicate elimination =============
% 2.63/2.98
% 2.63/2.98 Auto_denials: (non-Horn, no changes).
% 2.63/2.98
% 2.63/2.98 Term ordering decisions:
% 2.63/2.98 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.
% 2.63/2.98
% 2.63/2.98 ============================== end of process initial clauses ========
% 2.63/2.98
% 2.63/2.98 ============================== CLAUSES FOR SEARCH ====================
% 2.63/2.98
% 2.63/2.98 ============================== end of clauses for search =============
% 2.63/2.98
% 2.63/2.98 ============================== SEARCH ================================
% 2.63/2.98
% 2.63/2.98 % Starting search at 0.02 seconds.
% 2.63/2.98
% 2.63/2.98 Low Water (keep): wt=15.000, iters=4743
% 2.63/2.98
% 2.63/2.98 Low Water (keep): wt=14.000, iters=4324
% 2.63/2.98
% 2.63/2.98 Low Water (keep): wt=13.000, iters=3496
% 2.63/2.98
% 2.63/2.98 Low Water (keep): wt=10.000, iters=3838
% 2.63/2.98
% 2.63/2.98 ============================== PROOF =================================
% 2.63/2.98 % SZS status Theorem
% 2.63/2.98 % SZS output start Refutation
% 2.63/2.98
% 2.63/2.98 % Proof 1 at 1.95 (+ 0.02) seconds.
% 2.63/2.98 % Length of proof is 48.
% 2.63/2.98 % Level of proof is 8.
% 2.63/2.98 % Maximum clause weight is 19.000.
% 2.63/2.98 % Given clauses 256.
% 2.63/2.98
% 2.63/2.98 1 (exists Y24 all X19 (id(X19,Y24) & r1(X19) | -r1(X19) & -id(X19,Y24))) # label(axiom_1) # label(axiom) # label(non_clause). [assumption].
% 2.63/2.98 5 (all X20 id(X20,X20)) # label(axiom_5) # label(axiom) # label(non_clause). [assumption].
% 2.63/2.98 6 (all X21 all X22 (-id(X21,X22) | id(X22,X21))) # label(axiom_6) # label(axiom) # label(non_clause). [assumption].
% 2.63/2.98 8 (all X26 all X27 (-id(X26,X27) | -r1(X26) & -r1(X27) | r1(X26) & r1(X27))) # label(axiom_8) # label(axiom) # label(non_clause). [assumption].
% 2.63/2.98 11 (all X38 all X39 all X40 all X41 all X42 all X43 (-id(X38,X41) | -id(X39,X42) | -id(X40,X43) | -r4(X38,X39,X40) & -r4(X41,X42,X43) | r4(X38,X39,X40) & r4(X41,X42,X43))) # label(axiom_11) # label(axiom) # label(non_clause). [assumption].
% 2.63/2.98 13 (all X2 all X9 exists Y2 ((exists Y3 (id(Y3,Y2) & (exists Y14 (r2(X9,Y14) & r4(X2,Y14,Y3))))) & (exists Y6 (r3(Y6,X2,Y2) & r4(X2,X9,Y6))))) # label(axiom_2a) # label(axiom) # label(non_clause). [assumption].
% 2.63/2.98 15 (all X4 exists Y9 (id(Y9,X4) & (exists Y16 (r1(Y16) & r3(X4,Y16,Y9))))) # label(axiom_4a) # label(axiom) # label(non_clause). [assumption].
% 2.63/2.98 16 (all X5 exists Y8 ((exists Y17 (r1(Y17) & r4(X5,Y17,Y8))) & (exists Y18 (id(Y8,Y18) & r1(Y18))))) # label(axiom_5a) # label(axiom) # label(non_clause). [assumption].
% 2.63/2.98 17 (all X6 ((exists Y19 (id(X6,Y19) & r1(Y19))) | (exists Y1 exists Y11 (id(X6,Y11) & r2(Y1,Y11))))) # label(axiom_6a) # label(axiom) # label(non_clause). [assumption].
% 2.63/2.98 18 (all X7 all Y10 ((all Y20 (-id(Y20,Y10) | -r1(Y20))) | -r2(X7,Y10))) # label(axiom_7a) # label(axiom) # label(non_clause). [assumption].
% 2.63/2.98 19 -(exists Y1 exists Y3 exists Y2 exists Y4 ((exists Y5 (id(Y4,Y5) & r4(Y2,Y2,Y5))) & (exists Y6 (r4(Y3,Y3,Y6) & (exists Y7 (r4(Y1,Y1,Y7) & r3(Y7,Y6,Y4))))))) # label(fermattothepoweroftwoid) # label(negated_conjecture) # label(non_clause). [assumption].
% 2.63/2.98 20 id(A,A) # label(axiom_5) # label(axiom). [clausify(5)].
% 2.63/2.98 21 r1(f13(A)) # label(axiom_4a) # label(axiom). [clausify(15)].
% 2.63/2.98 22 r1(f15(A)) # label(axiom_5a) # label(axiom). [clausify(16)].
% 2.63/2.98 23 r1(f16(A)) # label(axiom_5a) # label(axiom). [clausify(16)].
% 2.63/2.98 24 id(f12(A),A) # label(axiom_4a) # label(axiom). [clausify(15)].
% 2.63/2.98 27 id(f14(A),f16(A)) # label(axiom_5a) # label(axiom). [clausify(16)].
% 2.63/2.98 29 r4(A,B,f11(A,B)) # label(axiom_2a) # label(axiom). [clausify(13)].
% 2.63/2.98 30 r3(A,f13(A),f12(A)) # label(axiom_4a) # label(axiom). [clausify(15)].
% 2.63/2.98 31 r4(A,f15(A),f14(A)) # label(axiom_5a) # label(axiom). [clausify(16)].
% 2.63/2.98 35 r1(f17(A)) | id(A,f19(A)) # label(axiom_6a) # label(axiom). [clausify(17)].
% 2.63/2.98 40 r1(f17(A)) | r2(f18(A),f19(A)) # label(axiom_6a) # label(axiom). [clausify(17)].
% 2.63/2.98 42 -id(A,B) | -r1(A) | -r2(C,B) # label(axiom_7a) # label(axiom). [clausify(18)].
% 2.63/2.98 43 -id(A,B) | -r4(C,C,B) | -r4(D,D,E) | -r4(F,F,V6) | -r3(V6,E,A) # label(fermattothepoweroftwoid) # label(negated_conjecture). [clausify(19)].
% 2.63/2.98 44 id(A,c1) | -r1(A) # label(axiom_1) # label(axiom). [clausify(1)].
% 2.63/2.98 45 r1(A) | -id(A,c1) # label(axiom_1) # label(axiom). [clausify(1)].
% 2.63/2.98 46 -id(A,B) | id(B,A) # label(axiom_6) # label(axiom). [clausify(6)].
% 2.63/2.98 50 -id(A,B) | -r1(B) | r1(A) # label(axiom_8) # label(axiom). [clausify(8)].
% 2.63/2.98 62 -id(A,B) | -id(C,D) | -id(E,F) | -r4(B,D,F) | r4(A,C,E) # label(axiom_11) # label(axiom). [clausify(11)].
% 2.63/2.98 77 -id(A,B) | -id(C,D) | -r4(B,B,D) | r4(A,A,C). [factor(62,a,b)].
% 2.63/2.98 86 -id(A,f19(B)) | -r1(A) | r1(f17(B)). [resolve(42,c,40,b)].
% 2.63/2.98 116 -r4(A,A,f13(f11(B,B))). [ur(43,a,24,a,b,29,a,d,29,a,e,30,a)].
% 2.63/2.98 123 id(f15(A),c1). [resolve(44,b,22,a)].
% 2.63/2.98 124 id(f13(A),c1). [resolve(44,b,21,a)].
% 2.63/2.98 126 r1(c1). [resolve(45,b,20,a)].
% 2.63/2.98 147 r1(f14(A)). [resolve(50,a,27,a),unit_del(a,23)].
% 2.63/2.98 148 -r1(A) | r1(f12(A)). [resolve(50,a,24,a)].
% 2.63/2.98 252 id(f14(A),c1). [resolve(147,a,44,b)].
% 2.63/2.98 265 -r1(A) | r1(f17(A)). [resolve(86,a,35,b),merge(c)].
% 2.63/2.98 295 id(c1,f15(A)). [resolve(123,a,46,a)].
% 2.63/2.98 345 id(c1,f14(A)). [resolve(252,a,46,a)].
% 2.63/2.98 758 r1(f17(c1)). [resolve(265,a,126,a)].
% 2.63/2.98 764 r1(f12(f17(c1))). [resolve(758,a,148,a)].
% 2.63/2.98 1092 id(f12(f17(c1)),c1). [resolve(764,a,44,b)].
% 2.63/2.98 2686 id(c1,f12(f17(c1))). [resolve(1092,a,46,a)].
% 2.63/2.98 5216 -r4(A,A,c1). [ur(77,a,24,a,b,124,a,d,116,a)].
% 2.63/2.98 7974 -id(c1,A). [ur(62,b,295,a,c,345,a,d,31,a,e,5216,a)].
% 2.63/2.98 7975 $F. [resolve(7974,a,2686,a)].
% 2.63/2.98
% 2.63/2.98 % SZS output end Refutation
% 2.63/2.98 ============================== end of proof ==========================
% 2.63/2.98
% 2.63/2.98 ============================== STATISTICS ============================
% 2.63/2.98
% 2.63/2.98 Given=256. Generated=34274. Kept=7955. proofs=1.
% 2.63/2.98 Usable=256. Sos=6791. Demods=0. Limbo=684, Disabled=266. Hints=0.
% 2.63/2.98 Megabytes=4.47.
% 2.63/2.98 User_CPU=1.95, System_CPU=0.02, Wall_clock=2.
% 2.63/2.98
% 2.63/2.98 ============================== end of statistics =====================
% 2.63/2.98
% 2.63/2.98 ============================== end of search =========================
% 2.63/2.98
% 2.63/2.98 THEOREM PROVED
% 2.63/2.98 % SZS status Theorem
% 2.63/2.98
% 2.63/2.98 Exiting with 1 proof.
% 2.63/2.98
% 2.63/2.98 Process 28564 exit (max_proofs) Thu Jun 2 07:59:45 2022
% 2.63/2.98 Prover9 interrupted
%------------------------------------------------------------------------------