0.04/0.12	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.04/0.12	% Command    : tptp2X_and_run_prover9 %d %s
0.13/0.34	% Computer   : n027.cluster.edu
0.13/0.34	% Model      : x86_64 x86_64
0.13/0.34	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.13/0.34	% Memory     : 8042.1875MB
0.13/0.34	% OS         : Linux 3.10.0-693.el7.x86_64
0.13/0.34	% CPULimit   : 1200
0.13/0.34	% DateTime   : Tue Jul 13 10:33:25 EDT 2021
0.13/0.34	% CPUTime    : 
0.74/1.09	============================== Prover9 ===============================
0.74/1.09	Prover9 (32) version 2009-11A, November 2009.
0.74/1.09	Process 12945 was started by sandbox on n027.cluster.edu,
0.74/1.09	Tue Jul 13 10:33:26 2021
0.74/1.09	The command was "/export/starexec/sandbox/solver/bin/prover9 -t 1200 -f /tmp/Prover9_12719_n027.cluster.edu".
0.74/1.09	============================== end of head ===========================
0.74/1.09	
0.74/1.09	============================== INPUT =================================
0.74/1.09	
0.74/1.09	% Reading from file /tmp/Prover9_12719_n027.cluster.edu
0.74/1.09	
0.74/1.09	set(prolog_style_variables).
0.74/1.09	set(auto2).
0.74/1.09	    % set(auto2) -> set(auto).
0.74/1.09	    % set(auto) -> set(auto_inference).
0.74/1.09	    % set(auto) -> set(auto_setup).
0.74/1.09	    % set(auto_setup) -> set(predicate_elim).
0.74/1.09	    % set(auto_setup) -> assign(eq_defs, unfold).
0.74/1.09	    % set(auto) -> set(auto_limits).
0.74/1.09	    % set(auto_limits) -> assign(max_weight, "100.000").
0.74/1.09	    % set(auto_limits) -> assign(sos_limit, 20000).
0.74/1.09	    % set(auto) -> set(auto_denials).
0.74/1.09	    % set(auto) -> set(auto_process).
0.74/1.09	    % set(auto2) -> assign(new_constants, 1).
0.74/1.09	    % set(auto2) -> assign(fold_denial_max, 3).
0.74/1.09	    % set(auto2) -> assign(max_weight, "200.000").
0.74/1.09	    % set(auto2) -> assign(max_hours, 1).
0.74/1.09	    % assign(max_hours, 1) -> assign(max_seconds, 3600).
0.74/1.09	    % set(auto2) -> assign(max_seconds, 0).
0.74/1.09	    % set(auto2) -> assign(max_minutes, 5).
0.74/1.09	    % assign(max_minutes, 5) -> assign(max_seconds, 300).
0.74/1.09	    % set(auto2) -> set(sort_initial_sos).
0.74/1.09	    % set(auto2) -> assign(sos_limit, -1).
0.74/1.09	    % set(auto2) -> assign(lrs_ticks, 3000).
0.74/1.09	    % set(auto2) -> assign(max_megs, 400).
0.74/1.09	    % set(auto2) -> assign(stats, some).
0.74/1.09	    % set(auto2) -> clear(echo_input).
0.74/1.09	    % set(auto2) -> set(quiet).
0.74/1.09	    % set(auto2) -> clear(print_initial_clauses).
0.74/1.09	    % set(auto2) -> clear(print_given).
0.74/1.09	assign(lrs_ticks,-1).
0.74/1.09	assign(sos_limit,10000).
0.74/1.09	assign(order,kbo).
0.74/1.09	set(lex_order_vars).
0.74/1.09	clear(print_given).
0.74/1.09	
0.74/1.09	% formulas(sos).  % not echoed (5 formulas)
0.74/1.09	
0.74/1.09	============================== end of input ==========================
0.74/1.09	
0.74/1.09	% From the command line: assign(max_seconds, 1200).
0.74/1.09	
0.74/1.09	============================== PROCESS NON-CLAUSAL FORMULAS ==========
0.74/1.09	
0.74/1.09	% Formulas that are not ordinary clauses:
0.74/1.09	1 (all U (sorti1(U) -> (all V (sorti1(V) -> sorti1(op1(U,V)))))) # label(ax1) # label(axiom) # label(non_clause).  [assumption].
0.74/1.09	2 -(exists U ((all V (sorti2(V) -> op2(V,V) = U)) & sorti2(U))) # label(ax4) # label(axiom) # label(non_clause).  [assumption].
0.74/1.09	3 (exists U (sorti1(U) & (all V (sorti1(V) -> op1(V,V) = U)))) # label(ax3) # label(axiom) # label(non_clause).  [assumption].
0.74/1.09	4 (all U (sorti2(U) -> (all V (sorti2(V) -> sorti2(op2(U,V)))))) # label(ax2) # label(axiom) # label(non_clause).  [assumption].
0.74/1.09	5 -((all U (sorti1(U) -> sorti2(h(U)))) & (all V (sorti2(V) -> sorti1(j(V)))) -> -((all W (sorti1(W) -> (all X (sorti1(X) -> h(op1(W,X)) = op2(h(W),h(X)))))) & (all X1 (sorti2(X1) -> X1 = h(j(X1)))) & (all X2 (sorti1(X2) -> j(h(X2)) = X2)) & (all Y (sorti2(Y) -> (all Z (sorti2(Z) -> j(op2(Y,Z)) = op1(j(Y),j(Z)))))))) # label(co1) # label(negated_conjecture) # label(non_clause).  [assumption].
0.74/1.09	
0.74/1.09	============================== end of process non-clausal formulas ===
0.74/1.09	
0.74/1.09	============================== PROCESS INITIAL CLAUSES ===============
0.74/1.09	
0.74/1.09	============================== PREDICATE ELIMINATION =================
0.74/1.09	
0.74/1.09	============================== end predicate elimination =============
0.74/1.09	
0.74/1.09	Auto_denials:
0.74/1.09	  % copying label ax4 to answer in negative clause
0.74/1.09	
0.74/1.09	Term ordering decisions:
0.74/1.09	Function symbol KB weights:  c1=1. op1=1. op2=1. h=1. j=1. f1=1.
0.74/1.09	
0.74/1.09	============================== end of process initial clauses ========
0.74/1.09	
0.74/1.09	============================== CLAUSES FOR SEARCH ====================
0.74/1.09	
0.74/1.09	============================== end of clauses for search =============
0.74/1.09	
0.74/1.09	============================== SEARCH ================================
0.74/1.09	
0.74/1.09	% Starting search at 0.01 seconds.
0.74/1.09	
0.74/1.09	============================== PROOF =================================
0.74/1.09	% SZS status Theorem
0.74/1.09	% SZS output start Refutation
0.74/1.09	
0.74/1.09	% Proof 1 at 0.01 (+ 0.00) seconds: ax4.
0.74/1.09	% Length of proof is 23.
0.74/1.09	% Level of proof is 6.
0.74/1.09	% Maximum clause weight is 18.000.
0.74/1.09	% Given clauses 18.
0.74/1.09	
0.74/1.09	2 -(exists U ((all V (sorti2(V) -> op2(V,V) = U)) & sorti2(U))) # label(ax4) # label(axiom) # label(non_clause).  [assumption].
0.74/1.09	3 (exists U (sorti1(U) & (all V (sorti1(V) -> op1(V,V) = U)))) # label(ax3) # label(axiom) # label(non_clause).  [assumption].
0.74/1.09	5 -((all U (sorti1(U) -> sorti2(h(U)))) & (all V (sorti2(V) -> sorti1(j(V)))) -> -((all W (sorti1(W) -> (all X (sorti1(X) -> h(op1(W,X)) = op2(h(W),h(X)))))) & (all X1 (sorti2(X1) -> X1 = h(j(X1)))) & (all X2 (sorti1(X2) -> j(h(X2)) = X2)) & (all Y (sorti2(Y) -> (all Z (sorti2(Z) -> j(op2(Y,Z)) = op1(j(Y),j(Z)))))))) # label(co1) # label(negated_conjecture) # label(non_clause).  [assumption].
0.74/1.09	6 sorti1(c1) # label(ax3) # label(axiom).  [clausify(3)].
0.74/1.09	7 op2(f1(A),f1(A)) != A | -sorti2(A) # label(ax4) # label(axiom) # answer(ax4).  [clausify(2)].
0.74/1.09	8 sorti2(f1(A)) | -sorti2(A) # label(ax4) # label(axiom).  [clausify(2)].
0.74/1.09	9 -sorti1(A) | sorti2(h(A)) # label(co1) # label(negated_conjecture).  [clausify(5)].
0.74/1.09	10 -sorti2(A) | sorti1(j(A)) # label(co1) # label(negated_conjecture).  [clausify(5)].
0.74/1.09	11 -sorti1(A) | op1(A,A) = c1 # label(ax3) # label(axiom).  [clausify(3)].
0.74/1.09	12 -sorti2(A) | h(j(A)) = A # label(co1) # label(negated_conjecture).  [clausify(5)].
0.74/1.09	16 -sorti1(A) | -sorti1(B) | h(op1(A,B)) = op2(h(A),h(B)) # label(co1) # label(negated_conjecture).  [clausify(5)].
0.74/1.09	17 -sorti1(A) | -sorti1(B) | op2(h(A),h(B)) = h(op1(A,B)).  [copy(16),flip(c)].
0.74/1.09	18 -sorti2(A) | -sorti2(B) | j(op2(A,B)) = op1(j(A),j(B)) # label(co1) # label(negated_conjecture).  [clausify(5)].
0.74/1.09	19 -sorti2(A) | -sorti2(B) | op1(j(A),j(B)) = j(op2(A,B)).  [copy(18),flip(c)].
0.74/1.09	20 sorti2(h(c1)).  [hyper(9,a,6,a)].
0.74/1.09	24 sorti2(f1(h(c1))).  [hyper(8,b,20,a)].
0.74/1.09	25 op2(f1(h(c1)),f1(h(c1))) != h(c1) # answer(ax4).  [ur(7,b,20,a)].
0.74/1.09	26 op1(j(f1(h(c1))),j(f1(h(c1)))) = j(op2(f1(h(c1)),f1(h(c1)))).  [hyper(19,a,24,a,b,24,a)].
0.74/1.09	32 h(j(f1(h(c1)))) = f1(h(c1)).  [hyper(12,a,24,a)].
0.74/1.09	33 sorti1(j(f1(h(c1)))).  [hyper(10,a,24,a)].
0.74/1.09	36 h(j(op2(f1(h(c1)),f1(h(c1))))) = op2(f1(h(c1)),f1(h(c1))).  [hyper(17,a,33,a,b,33,a),rewrite([32(5),32(8),26(16)]),flip(a)].
0.74/1.09	42 j(op2(f1(h(c1)),f1(h(c1)))) = c1.  [hyper(11,a,33,a),rewrite([26(9)])].
0.74/1.09	43 $F # answer(ax4).  [back_rewrite(36),rewrite([42(8)]),flip(a),unit_del(a,25)].
0.74/1.09	
0.74/1.09	% SZS output end Refutation
0.74/1.09	============================== end of proof ==========================
0.74/1.09	
0.74/1.09	============================== STATISTICS ============================
0.74/1.09	
0.74/1.09	Given=18. Generated=52. Kept=35. proofs=1.
0.74/1.09	Usable=18. Sos=14. Demods=10. Limbo=1, Disabled=14. Hints=0.
0.74/1.09	Megabytes=0.08.
0.74/1.09	User_CPU=0.01, System_CPU=0.00, Wall_clock=0.
0.74/1.09	
0.74/1.09	============================== end of statistics =====================
0.74/1.09	
0.74/1.09	============================== end of search =========================
0.74/1.09	
0.74/1.09	THEOREM PROVED
0.74/1.09	% SZS status Theorem
0.74/1.09	
0.74/1.09	Exiting with 1 proof.
0.74/1.09	
0.74/1.09	Process 12945 exit (max_proofs) Tue Jul 13 10:33:26 2021
0.74/1.09	Prover9 interrupted
0.74/1.09	EOF