0.10/0.11	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.10/0.12	% Command    : tptp2X_and_run_prover9 %d %s
0.12/0.33	% Computer   : n010.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   : 1200
0.12/0.33	% DateTime   : Tue Jul 13 14:26:51 EDT 2021
0.12/0.33	% CPUTime    : 
0.80/1.06	============================== Prover9 ===============================
0.80/1.06	Prover9 (32) version 2009-11A, November 2009.
0.80/1.06	Process 17792 was started by sandbox2 on n010.cluster.edu,
0.80/1.06	Tue Jul 13 14:26:52 2021
0.80/1.06	The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 1200 -f /tmp/Prover9_17599_n010.cluster.edu".
0.80/1.06	============================== end of head ===========================
0.80/1.06	
0.80/1.06	============================== INPUT =================================
0.80/1.06	
0.80/1.06	% Reading from file /tmp/Prover9_17599_n010.cluster.edu
0.80/1.06	
0.80/1.06	set(prolog_style_variables).
0.80/1.06	set(auto2).
0.80/1.06	    % set(auto2) -> set(auto).
0.80/1.06	    % set(auto) -> set(auto_inference).
0.80/1.06	    % set(auto) -> set(auto_setup).
0.80/1.06	    % set(auto_setup) -> set(predicate_elim).
0.80/1.06	    % set(auto_setup) -> assign(eq_defs, unfold).
0.80/1.06	    % set(auto) -> set(auto_limits).
0.80/1.06	    % set(auto_limits) -> assign(max_weight, "100.000").
0.80/1.06	    % set(auto_limits) -> assign(sos_limit, 20000).
0.80/1.06	    % set(auto) -> set(auto_denials).
0.80/1.06	    % set(auto) -> set(auto_process).
0.80/1.06	    % set(auto2) -> assign(new_constants, 1).
0.80/1.06	    % set(auto2) -> assign(fold_denial_max, 3).
0.80/1.06	    % set(auto2) -> assign(max_weight, "200.000").
0.80/1.06	    % set(auto2) -> assign(max_hours, 1).
0.80/1.06	    % assign(max_hours, 1) -> assign(max_seconds, 3600).
0.80/1.06	    % set(auto2) -> assign(max_seconds, 0).
0.80/1.06	    % set(auto2) -> assign(max_minutes, 5).
0.80/1.06	    % assign(max_minutes, 5) -> assign(max_seconds, 300).
0.80/1.06	    % set(auto2) -> set(sort_initial_sos).
0.80/1.06	    % set(auto2) -> assign(sos_limit, -1).
0.80/1.06	    % set(auto2) -> assign(lrs_ticks, 3000).
0.80/1.06	    % set(auto2) -> assign(max_megs, 400).
0.80/1.06	    % set(auto2) -> assign(stats, some).
0.80/1.06	    % set(auto2) -> clear(echo_input).
0.80/1.06	    % set(auto2) -> set(quiet).
0.80/1.06	    % set(auto2) -> clear(print_initial_clauses).
0.80/1.06	    % set(auto2) -> clear(print_given).
0.80/1.06	assign(lrs_ticks,-1).
0.80/1.06	assign(sos_limit,10000).
0.80/1.06	assign(order,kbo).
0.80/1.06	set(lex_order_vars).
0.80/1.06	clear(print_given).
0.80/1.06	
0.80/1.06	% formulas(sos).  % not echoed (8 formulas)
0.80/1.06	
0.80/1.06	============================== end of input ==========================
0.80/1.06	
0.80/1.06	% From the command line: assign(max_seconds, 1200).
0.80/1.06	
0.80/1.06	============================== PROCESS NON-CLAUSAL FORMULAS ==========
0.80/1.06	
0.80/1.06	% Formulas that are not ordinary clauses:
0.80/1.06	1 (all G all X all Y all Z (group_member(Y,G) & group_member(Z,G) & group_member(X,G) -> multiply(G,X,multiply(G,Y,Z)) = multiply(G,multiply(G,X,Y),Z))) # label(associativity) # label(axiom) # label(non_clause).  [assumption].
0.80/1.06	2 (all G all X all Y (group_member(Y,G) & group_member(X,G) -> group_member(multiply(G,X,Y),G))) # label(total_function) # label(axiom) # label(non_clause).  [assumption].
0.80/1.06	3 (all G all X (left_zero(G,X) <-> group_member(X,G) & (all Y (group_member(Y,G) -> X = multiply(G,X,Y))))) # label(left_zero) # label(axiom) # label(non_clause).  [assumption].
0.80/1.06	4 (all X all Y (group_member(Y,f) & group_member(X,f) -> phi(multiply(f,X,Y)) = multiply(h,phi(X),phi(Y)))) # label(homomorphism2) # label(axiom) # label(non_clause).  [assumption].
0.80/1.06	5 (all X (group_member(X,f) -> group_member(phi(X),h))) # label(homomorphism1) # label(axiom) # label(non_clause).  [assumption].
0.80/1.06	6 (all X (group_member(X,h) -> (exists Y (X = phi(Y) & group_member(Y,f))))) # label(surjective) # label(axiom) # label(non_clause).  [assumption].
0.80/1.06	
0.80/1.06	============================== end of process non-clausal formulas ===
0.80/1.06	
0.80/1.06	============================== PROCESS INITIAL CLAUSES ===============
0.80/1.06	
0.80/1.06	============================== PREDICATE ELIMINATION =================
0.80/1.06	
0.80/1.06	============================== end predicate elimination =============
0.80/1.06	
0.80/1.06	Auto_denials:  (non-Horn, no changes).
0.80/1.06	
0.80/1.06	Term ordering decisions:
0.80/1.06	Function symbol KB weights:  f=1. h=1. f_left_zero=1. f1=1. phi=1. f2=1. multiply=1.
0.80/1.06	
0.80/1.06	============================== end of process initial clauses ========
0.80/1.06	
0.80/1.06	============================== CLAUSES FOR SEARCH ====================
0.80/1.06	
0.80/1.06	============================== end of clauses for search =============
0.80/1.06	
0.80/1.06	============================== SEARCH ================================
0.80/1.06	
0.80/1.06	% Starting search at 0.01 seconds.
0.80/1.06	
0.80/1.06	============================== PROOF =================================
0.80/1.06	% SZS status Theorem
0.80/1.06	% SZS output start Refutation
0.80/1.06	
0.80/1.06	% Proof 1 at 0.03 (+ 0.00) seconds.
0.80/1.06	% Length of proof is 25.
0.80/1.06	% Level of proof is 7.
0.80/1.06	% Maximum clause weight is 18.000.
0.80/1.06	% Given clauses 65.
0.80/1.06	
0.80/1.06	3 (all G all X (left_zero(G,X) <-> group_member(X,G) & (all Y (group_member(Y,G) -> X = multiply(G,X,Y))))) # label(left_zero) # label(axiom) # label(non_clause).  [assumption].
0.80/1.06	4 (all X all Y (group_member(Y,f) & group_member(X,f) -> phi(multiply(f,X,Y)) = multiply(h,phi(X),phi(Y)))) # label(homomorphism2) # label(axiom) # label(non_clause).  [assumption].
0.80/1.06	5 (all X (group_member(X,f) -> group_member(phi(X),h))) # label(homomorphism1) # label(axiom) # label(non_clause).  [assumption].
0.80/1.06	6 (all X (group_member(X,h) -> (exists Y (X = phi(Y) & group_member(Y,f))))) # label(surjective) # label(axiom) # label(non_clause).  [assumption].
0.80/1.06	7 left_zero(f,f_left_zero) # label(left_zero_for_f) # label(hypothesis).  [assumption].
0.80/1.06	8 -left_zero(h,phi(f_left_zero)) # label(prove_left_zero_h) # label(negated_conjecture).  [assumption].
0.80/1.06	9 -left_zero(A,B) | group_member(B,A) # label(left_zero) # label(axiom).  [clausify(3)].
0.80/1.06	10 -group_member(A,f) | group_member(phi(A),h) # label(homomorphism1) # label(axiom).  [clausify(5)].
0.80/1.06	11 -group_member(A,h) | group_member(f2(A),f) # label(surjective) # label(axiom).  [clausify(6)].
0.80/1.06	12 -group_member(A,h) | phi(f2(A)) = A # label(surjective) # label(axiom).  [clausify(6)].
0.80/1.06	13 left_zero(A,B) | -group_member(B,A) | group_member(f1(A,B),A) # label(left_zero) # label(axiom).  [clausify(3)].
0.80/1.06	15 -left_zero(A,B) | -group_member(C,A) | multiply(A,B,C) = B # label(left_zero) # label(axiom).  [clausify(3)].
0.80/1.06	16 left_zero(A,B) | -group_member(B,A) | multiply(A,B,f1(A,B)) != B # label(left_zero) # label(axiom).  [clausify(3)].
0.80/1.06	17 -group_member(A,f) | -group_member(B,f) | phi(multiply(f,B,A)) = multiply(h,phi(B),phi(A)) # label(homomorphism2) # label(axiom).  [clausify(4)].
0.80/1.06	18 -group_member(A,f) | -group_member(B,f) | multiply(h,phi(B),phi(A)) = phi(multiply(f,B,A)).  [copy(17),flip(c)].
0.80/1.06	26 group_member(f_left_zero,f).  [resolve(9,a,7,a)].
0.80/1.06	27 -group_member(A,f) | multiply(f,f_left_zero,A) = f_left_zero.  [resolve(15,a,7,a)].
0.80/1.06	40 -group_member(A,f) | multiply(h,phi(f_left_zero),phi(A)) = phi(multiply(f,f_left_zero,A)).  [resolve(26,a,18,b)].
0.80/1.06	44 group_member(phi(f_left_zero),h).  [resolve(26,a,10,a)].
0.80/1.06	56 multiply(h,phi(f_left_zero),f1(h,phi(f_left_zero))) != phi(f_left_zero).  [resolve(44,a,16,b),unit_del(a,8)].
0.80/1.06	59 group_member(f1(h,phi(f_left_zero)),h).  [resolve(44,a,13,b),unit_del(a,8)].
0.80/1.06	113 phi(f2(f1(h,phi(f_left_zero)))) = f1(h,phi(f_left_zero)).  [resolve(59,a,12,a)].
0.80/1.06	114 group_member(f2(f1(h,phi(f_left_zero))),f).  [resolve(59,a,11,a)].
0.80/1.06	124 multiply(f,f_left_zero,f2(f1(h,phi(f_left_zero)))) = f_left_zero.  [resolve(114,a,27,a)].
0.80/1.06	599 $F.  [resolve(40,a,114,a),rewrite([113(9),124(16)]),unit_del(a,56)].
0.80/1.06	
0.80/1.06	% SZS output end Refutation
0.80/1.06	============================== end of proof ==========================
0.80/1.06	
0.80/1.06	============================== STATISTICS ============================
0.80/1.06	
0.80/1.06	Given=65. Generated=739. Kept=591. proofs=1.
0.80/1.06	Usable=64. Sos=459. Demods=95. Limbo=7, Disabled=73. Hints=0.
0.80/1.06	Megabytes=0.95.
0.80/1.06	User_CPU=0.03, System_CPU=0.00, Wall_clock=0.
0.80/1.06	
0.80/1.06	============================== end of statistics =====================
0.80/1.06	
0.80/1.06	============================== end of search =========================
0.80/1.06	
0.80/1.06	THEOREM PROVED
0.80/1.06	% SZS status Theorem
0.80/1.06	
0.80/1.06	Exiting with 1 proof.
0.80/1.06	
0.80/1.06	Process 17792 exit (max_proofs) Tue Jul 13 14:26:52 2021
0.80/1.06	Prover9 interrupted
0.80/1.06	EOF