0.03/0.12	% Problem  : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.03/0.13	% Command  : tptp2X_and_run_prover9 %d %s
0.14/0.34	% Computer : n010.cluster.edu
0.14/0.34	% Model    : x86_64 x86_64
0.14/0.34	% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.14/0.34	% Memory   : 8042.1875MB
0.14/0.34	% OS       : Linux 3.10.0-693.el7.x86_64
0.14/0.34	% CPULimit : 1440
0.14/0.34	% WCLimit  : 180
0.14/0.34	% DateTime : Mon Jul  3 04:29:54 EDT 2023
0.14/0.34	% CPUTime  : 
0.76/1.02	============================== Prover9 ===============================
0.76/1.02	Prover9 (32) version 2009-11A, November 2009.
0.76/1.02	Process 19189 was started by sandbox2 on n010.cluster.edu,
0.76/1.02	Mon Jul  3 04:29:55 2023
0.76/1.02	The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 1440 -f /tmp/Prover9_19029_n010.cluster.edu".
0.76/1.02	============================== end of head ===========================
0.76/1.02	
0.76/1.02	============================== INPUT =================================
0.76/1.02	
0.76/1.02	% Reading from file /tmp/Prover9_19029_n010.cluster.edu
0.76/1.02	
0.76/1.02	set(prolog_style_variables).
0.76/1.02	set(auto2).
0.76/1.02	    % set(auto2) -> set(auto).
0.76/1.02	    % set(auto) -> set(auto_inference).
0.76/1.02	    % set(auto) -> set(auto_setup).
0.76/1.02	    % set(auto_setup) -> set(predicate_elim).
0.76/1.02	    % set(auto_setup) -> assign(eq_defs, unfold).
0.76/1.02	    % set(auto) -> set(auto_limits).
0.76/1.02	    % set(auto_limits) -> assign(max_weight, "100.000").
0.76/1.02	    % set(auto_limits) -> assign(sos_limit, 20000).
0.76/1.02	    % set(auto) -> set(auto_denials).
0.76/1.02	    % set(auto) -> set(auto_process).
0.76/1.02	    % set(auto2) -> assign(new_constants, 1).
0.76/1.02	    % set(auto2) -> assign(fold_denial_max, 3).
0.76/1.02	    % set(auto2) -> assign(max_weight, "200.000").
0.76/1.02	    % set(auto2) -> assign(max_hours, 1).
0.76/1.02	    % assign(max_hours, 1) -> assign(max_seconds, 3600).
0.76/1.02	    % set(auto2) -> assign(max_seconds, 0).
0.76/1.02	    % set(auto2) -> assign(max_minutes, 5).
0.76/1.02	    % assign(max_minutes, 5) -> assign(max_seconds, 300).
0.76/1.02	    % set(auto2) -> set(sort_initial_sos).
0.76/1.02	    % set(auto2) -> assign(sos_limit, -1).
0.76/1.02	    % set(auto2) -> assign(lrs_ticks, 3000).
0.76/1.02	    % set(auto2) -> assign(max_megs, 400).
0.76/1.02	    % set(auto2) -> assign(stats, some).
0.76/1.02	    % set(auto2) -> clear(echo_input).
0.76/1.02	    % set(auto2) -> set(quiet).
0.76/1.02	    % set(auto2) -> clear(print_initial_clauses).
0.76/1.02	    % set(auto2) -> clear(print_given).
0.76/1.02	assign(lrs_ticks,-1).
0.76/1.02	assign(sos_limit,10000).
0.76/1.02	assign(order,kbo).
0.76/1.02	set(lex_order_vars).
0.76/1.02	clear(print_given).
0.76/1.02	
0.76/1.02	% formulas(sos).  % not echoed (12 formulas)
0.76/1.02	
0.76/1.02	============================== end of input ==========================
0.76/1.02	
0.76/1.02	% From the command line: assign(max_seconds, 1440).
0.76/1.02	
0.76/1.02	============================== PROCESS NON-CLAUSAL FORMULAS ==========
0.76/1.02	
0.76/1.02	% Formulas that are not ordinary clauses:
0.76/1.02	1 (all X1 all X8 exists Y4 ((exists Y7 (r2(Y7,Y4) & r3(X1,X8,Y7))) & (exists Y5 ((exists Y15 (r3(X1,Y15,Y5) & r2(X8,Y15))) & Y5 = Y4)))) # label(axiom_1a) # label(axiom) # label(non_clause).  [assumption].
0.76/1.02	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].
0.76/1.02	3 (all X4 exists Y9 (Y9 = X4 & (exists Y16 (r1(Y16) & r3(X4,Y16,Y9))))) # label(axiom_4a) # label(axiom) # label(non_clause).  [assumption].
0.76/1.02	4 (all X2 all X9 exists Y2 ((exists Y6 (r3(Y6,X2,Y2) & r4(X2,X9,Y6))) & (exists Y3 (Y3 = Y2 & (exists Y14 (r4(X2,Y14,Y3) & r2(X9,Y14))))))) # label(axiom_2a) # label(axiom) # label(non_clause).  [assumption].
0.76/1.02	5 (exists Y24 all X19 (r1(X19) & Y24 = X19 | Y24 != X19 & -r1(X19))) # label(axiom_1) # label(axiom) # label(non_clause).  [assumption].
0.76/1.02	6 (all X3 all X10 ((all Y12 ((all Y13 (Y13 != Y12 | -r2(X3,Y13))) | -r2(X10,Y12))) | X3 = X10)) # label(axiom_3a) # label(axiom) # label(non_clause).  [assumption].
0.76/1.02	7 (all X16 all X17 exists Y23 all X18 (-r4(X16,X17,X18) & Y23 != X18 | r4(X16,X17,X18) & X18 = Y23)) # label(axiom_4) # label(axiom) # label(non_clause).  [assumption].
0.76/1.02	8 (all X13 all X14 exists Y22 all X15 (r3(X13,X14,X15) & Y22 = X15 | X15 != Y22 & -r3(X13,X14,X15))) # label(axiom_3) # label(axiom) # label(non_clause).  [assumption].
0.76/1.02	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].
0.76/1.02	10 (all X6 ((exists Y1 exists Y11 (r2(Y1,Y11) & X6 = Y11)) | (exists Y19 (X6 = Y19 & r1(Y19))))) # label(axiom_6a) # label(axiom) # label(non_clause).  [assumption].
0.76/1.02	11 (all X7 all Y10 ((all Y20 (Y20 != Y10 | -r1(Y20))) | -r2(X7,Y10))) # label(axiom_7a) # label(axiom) # label(non_clause).  [assumption].
0.76/1.02	12 -(exists Y1 exists Y3 exists Y2 exists Y4 ((exists Y6 ((exists Y7 (r3(Y7,Y6,Y4) & r4(Y1,Y1,Y7))) & r4(Y3,Y3,Y6))) & (exists Y5 (r4(Y2,Y2,Y5) & Y4 = Y5)))) # label(fermattothepoweroftwo) # label(negated_conjecture) # label(non_clause).  [assumption].
0.76/1.02	
0.76/1.02	============================== end of process non-clausal formulas ===
0.76/1.02	
0.76/1.02	============================== PROCESS INITIAL CLAUSES ===============
0.76/1.02	
0.76/1.02	============================== PREDICATE ELIMINATION =================
0.76/1.02	13 A != B | -r1(A) | -r2(C,B) # label(axiom_7a) # label(axiom).  [clausify(11)].
0.76/1.02	14 r1(f7(A)) # label(axiom_4a) # label(axiom).  [clausify(3)].
0.76/1.02	15 r1(f15(A)) # label(axiom_5a) # label(axiom).  [clausify(9)].
0.76/1.02	16 r1(f16(A)) # label(axiom_5a) # label(axiom).  [clausify(9)].
0.76/1.02	17 f18(A) = A | r1(f19(A)) # label(axiom_6a) # label(axiom).  [clausify(10)].
0.76/1.02	18 r2(f17(A),f18(A)) | r1(f19(A)) # label(axiom_6a) # label(axiom).  [clausify(10)].
0.76/1.02	Derived: f7(A) != B | -r2(C,B).  [resolve(13,b,14,a)].
0.76/1.02	Derived: f15(A) != B | -r2(C,B).  [resolve(13,b,15,a)].
0.76/1.02	Derived: f16(A) != B | -r2(C,B).  [resolve(13,b,16,a)].
0.76/1.02	Derived: f19(A) != B | -r2(C,B) | f18(A) = A.  [resolve(13,b,17,b)].
0.76/1.02	Derived: f19(A) != B | -r2(C,B) | r2(f17(A),f18(A)).  [resolve(13,b,18,b)].
0.76/1.02	19 r1(A) | A != c1 # label(axiom_1) # label(axiom).  [clausify(5)].
0.76/1.02	Derived: A != c1 | A != B | -r2(C,B).  [resolve(19,a,13,b)].
0.76/1.02	20 A = c1 | -r1(A) # label(axiom_1) # label(axiom).  [clausify(5)].
0.76/1.02	Derived: f7(A) = c1.  [resolve(20,b,14,a)].
0.76/1.02	Derived: f15(A) = c1.  [resolve(20,b,15,a)].
0.76/1.02	Derived: f16(A) = c1.  [resolve(20,b,16,a)].
0.76/1.02	Derived: f19(A) = c1 | f18(A) = A.  [resolve(20,b,17,b)].
0.76/1.02	Derived: f19(A) = c1 | r2(f17(A),f18(A)).  [resolve(20,b,18,b)].
0.76/1.02	21 -r3(A,B,C) | -r4(D,D,A) | -r4(E,E,B) | -r4(F,F,V6) | V6 != C # label(fermattothepoweroftwo) # label(negated_conjecture).  [clausify(12)].
0.76/1.02	22 r3(A,B,f2(A,B)) # label(axiom_1a) # label(axiom).  [clausify(1)].
0.76/1.02	23 r3(A,f7(A),f6(A)) # label(axiom_4a) # label(axiom).  [clausify(3)].
0.76/1.02	24 r3(A,f4(A,B),f3(A,B)) # label(axiom_1a) # label(axiom).  [clausify(1)].
0.76/1.02	25 r3(f9(A,B),A,f8(A,B)) # label(axiom_2a) # label(axiom).  [clausify(4)].
0.76/1.02	Derived: -r4(A,A,B) | -r4(C,C,D) | -r4(E,E,F) | F != f2(B,D).  [resolve(21,a,22,a)].
0.76/1.02	Derived: -r4(A,A,B) | -r4(C,C,f7(B)) | -r4(D,D,E) | E != f6(B).  [resolve(21,a,23,a)].
0.76/1.02	Derived: -r4(A,A,B) | -r4(C,C,f4(B,D)) | -r4(E,E,F) | F != f3(B,D).  [resolve(21,a,24,a)].
0.76/1.02	Derived: -r4(A,A,f9(B,C)) | -r4(D,D,B) | -r4(E,E,F) | F != f8(B,C).  [resolve(21,a,25,a)].
0.76/1.02	26 r3(A,B,C) | C != f13(A,B) # label(axiom_3) # label(axiom).  [clausify(8)].
0.76/1.02	Derived: A != f13(B,C) | -r4(D,D,B) | -r4(E,E,C) | -r4(F,F,V6) | V6 != A.  [resolve(26,a,21,a)].
0.76/1.02	27 A = f13(B,C) | -r3(B,C,A) # label(axiom_3) # label(axiom).  [clausify(8)].
0.76/1.02	Derived: f2(A,B) = f13(A,B).  [resolve(27,b,22,a)].
0.76/1.02	Derived: f6(A) = f13(A,f7(A)).  [resolve(27,b,23,a)].
0.76/1.02	Derived: f3(A,B) = f13(A,f4(A,B)).  [resolve(27,b,24,a)].
0.76/1.02	Derived: f8(A,B) = f13(f9(A,B),A).  [resolve(27,b,25,a)].
0.76/1.02	
0.76/1.02	============================== end predicate elimination =============
0.76/1.02	
0.76/1.02	Auto_denials:  (non-Horn, no changes).
0.76/1.02	
0.76/1.02	Term ordering decisions:
0.76/1.02	Function symbol KB weights:  c1=1. f1=1. f2=1. f3=1. f4=1. f8=1. f9=1. f10=1. f11=1. f12=1. f13=1. f5=1. f6=1. f7=1. f14=1. f15=1. f16=1. f17=1. f18=1. f19=1.
0.76/1.02	
0.76/1.02	============================== PROOF =================================
0.76/1.02	% SZS status Theorem
0.76/1.02	% SZS output start Refutation
0.76/1.02	
0.76/1.02	% Proof 1 at 0.01 (+ 0.00) seconds.
0.76/1.02	% Length of proof is 23.
0.76/1.02	% Level of proof is 6.
0.76/1.02	% Maximum clause weight is 15.000.
0.76/1.02	% Given clauses 0.
0.76/1.02	
0.76/1.02	3 (all X4 exists Y9 (Y9 = X4 & (exists Y16 (r1(Y16) & r3(X4,Y16,Y9))))) # label(axiom_4a) # label(axiom) # label(non_clause).  [assumption].
0.76/1.02	5 (exists Y24 all X19 (r1(X19) & Y24 = X19 | Y24 != X19 & -r1(X19))) # label(axiom_1) # label(axiom) # label(non_clause).  [assumption].
0.76/1.02	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].
0.76/1.02	12 -(exists Y1 exists Y3 exists Y2 exists Y4 ((exists Y6 ((exists Y7 (r3(Y7,Y6,Y4) & r4(Y1,Y1,Y7))) & r4(Y3,Y3,Y6))) & (exists Y5 (r4(Y2,Y2,Y5) & Y4 = Y5)))) # label(fermattothepoweroftwo) # label(negated_conjecture) # label(non_clause).  [assumption].
0.76/1.02	14 r1(f7(A)) # label(axiom_4a) # label(axiom).  [clausify(3)].
0.76/1.02	15 r1(f15(A)) # label(axiom_5a) # label(axiom).  [clausify(9)].
0.76/1.02	16 r1(f16(A)) # label(axiom_5a) # label(axiom).  [clausify(9)].
0.76/1.02	20 A = c1 | -r1(A) # label(axiom_1) # label(axiom).  [clausify(5)].
0.76/1.02	21 -r3(A,B,C) | -r4(D,D,A) | -r4(E,E,B) | -r4(F,F,V6) | V6 != C # label(fermattothepoweroftwo) # label(negated_conjecture).  [clausify(12)].
0.76/1.02	23 r3(A,f7(A),f6(A)) # label(axiom_4a) # label(axiom).  [clausify(3)].
0.76/1.02	28 f6(A) = A # label(axiom_4a) # label(axiom).  [clausify(3)].
0.76/1.02	31 f16(A) = f14(A) # label(axiom_5a) # label(axiom).  [clausify(9)].
0.76/1.02	33 r4(A,f15(A),f14(A)) # label(axiom_5a) # label(axiom).  [clausify(9)].
0.76/1.02	58 f7(A) = c1.  [resolve(20,b,14,a)].
0.76/1.02	59 f15(A) = c1.  [resolve(20,b,15,a)].
0.76/1.02	60 f16(A) = c1.  [resolve(20,b,16,a)].
0.76/1.02	61 f14(A) = c1.  [copy(60),rewrite([31(1)])].
0.76/1.02	66 -r4(A,A,B) | -r4(C,C,f7(B)) | -r4(D,D,E) | E != f6(B).  [resolve(21,a,23,a)].
0.76/1.02	67 -r4(A,A,B) | -r4(C,C,c1) | -r4(D,D,E) | E != B.  [copy(66),rewrite([58(2),28(5)])].
0.76/1.02	82 r4(A,c1,c1).  [back_rewrite(33),rewrite([59(1),61(2)])].
0.76/1.02	87 -r4(A,A,c1) | -r4(B,B,C) | c1 != C.  [factor(67,a,b),flip(c)].
0.76/1.02	100 -r4(A,A,c1).  [factor(87,a,b),xx(b)].
0.76/1.02	101 $F.  [resolve(100,a,82,a)].
0.76/1.02	
0.76/1.02	% SZS output end Refutation
0.76/1.02	============================== end of proof ==========================
0.76/1.02	
0.76/1.02	============================== STATISTICS ============================
0.76/1.02	
0.76/1.02	Given=0. Generated=67. Kept=58. proofs=1.
0.76/1.02	Usable=0. Sos=34. Demods=11. Limbo=13, Disabled=62. Hints=0.
0.76/1.02	Megabytes=0.11.
0.76/1.02	User_CPU=0.01, System_CPU=0.00, Wall_clock=0.
0.76/1.02	
0.76/1.02	============================== end of statistics =====================
0.76/1.02	
0.76/1.02	============================== end of search =========================
0.76/1.02	
0.76/1.02	THEOREM PROVED
0.76/1.02	% SZS status Theorem
0.76/1.02	
0.76/1.02	Exiting with 1 proof.
0.76/1.02	
0.76/1.02	Process 19189 exit (max_proofs) Mon Jul  3 04:29:55 2023
0.76/1.02	Prover9 interrupted
0.76/1.02	EOF