%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : TOP021+1 : TPTP v8.2.0. Released v3.1.0. % Transfm : none % Format : tptp:raw % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s % Computer : n006.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 : 300s % DateTime : Mon Jun 24 21:15:06 EDT 2024 % Result : Theorem 0.44s 0.63s % Output : CNFRefutation 0.56s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.13 % Problem : TOP021+1 : TPTP v8.2.0. Released v3.1.0. % 0.04/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s % 0.13/0.35 % Computer : n006.cluster.edu % 0.13/0.35 % Model : x86_64 x86_64 % 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.35 % Memory : 8042.1875MB % 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 300 % 0.13/0.35 % DateTime : Tue Jun 18 11:04:09 EDT 2024 % 0.13/0.35 % CPUTime : % 0.44/0.59 start to proof:theBenchmark % 0.44/0.63 %------------------------------------------- % 0.44/0.63 % File :CSE---1.7 % 0.44/0.63 % Problem :theBenchmark % 0.44/0.63 % Transform :cnf % 0.44/0.63 % Format :tptp:raw % 0.44/0.63 % Command :java -jar mcs_scs.jar %d %s % 0.44/0.63 % 0.44/0.63 % Result :Theorem 0.000000s % 0.44/0.63 % Output :CNFRefutation 0.000000s % 0.44/0.63 %------------------------------------------- % 0.44/0.63 %------------------------------------------------------------------------------ % 0.44/0.63 % File : TOP021+1 : TPTP v8.2.0. Released v3.1.0. % 0.44/0.63 % Domain : Topology % 0.44/0.63 % Problem : Locally compact tological space % 0.44/0.63 % Version : [Shu96] axioms : Especial. % 0.44/0.63 % English : % 0.44/0.63 % 0.44/0.63 % Refs : [Kel55] Kelley (1955), General Topology % 0.44/0.63 % : [Shu96] Shults (1996), Email to Geoff Sutcliffe % 0.44/0.63 % Source : [Shu96] % 0.44/0.63 % Names : % 0.44/0.63 % 0.44/0.63 % Status : Theorem % 0.44/0.63 % Rating : 0.00 v5.5.0, 0.04 v5.3.0, 0.13 v5.2.0, 0.07 v5.0.0, 0.05 v4.1.0, 0.06 v4.0.1, 0.05 v3.7.0, 0.00 v3.1.0 % 0.44/0.63 % Syntax : Number of formulae : 4 ( 2 unt; 0 def) % 0.44/0.63 % Number of atoms : 8 ( 0 equ) % 0.44/0.63 % Maximal formula atoms : 4 ( 2 avg) % 0.44/0.63 % Number of connectives : 4 ( 0 ~; 0 |; 2 &) % 0.44/0.63 % ( 0 <=>; 2 =>; 0 <=; 0 <~>) % 0.44/0.63 % Maximal formula depth : 7 ( 5 avg) % 0.44/0.63 % Maximal term depth : 2 ( 1 avg) % 0.44/0.63 % Number of predicates : 3 ( 3 usr; 0 prp; 1-3 aty) % 0.44/0.63 % Number of functors : 3 ( 3 usr; 0 con; 2-3 aty) % 0.44/0.63 % Number of variables : 13 ( 13 !; 0 ?) % 0.44/0.63 % SPC : FOF_THM_RFO_NEQ % 0.44/0.63 % 0.44/0.63 % Comments : % 0.44/0.63 %------------------------------------------------------------------------------ % 0.44/0.63 %----The statement on the top of page 90 of Kelley % 0.44/0.63 fof(kelley_p90a,axiom, % 0.44/0.63 ! [A,X,A1] : a_continuous_function_from_onto(the_projection_function(A,X,A1),the_product_top_space_over(X,A1),apply(X,A)) ). % 0.44/0.63 % 0.44/0.63 %----Theorem 2 in chapter 3 of Kelley % 0.44/0.63 fof(kelley_3_2,axiom, % 0.44/0.63 ! [A,X,A1,X1] : an_open_function_from_onto(the_projection_function(A,X,A1),the_product_top_space_over(X1,A1),apply(X1,A)) ). % 0.44/0.63 % 0.44/0.63 %----A statement near the bottom of page 147 of Kelley % 0.44/0.63 fof(kelley_p_147e,axiom, % 0.44/0.63 ! [F,A,B] : % 0.44/0.63 ( ( an_open_function_from_onto(F,A,B) % 0.44/0.63 & a_continuous_function_from_onto(F,A,B) % 0.44/0.63 & a_locally_compact_top_space(A) ) % 0.44/0.63 => a_locally_compact_top_space(B) ) ). % 0.44/0.63 % 0.44/0.63 %----The first half of Theorem 19 in Chapter 5 of Kelley % 0.44/0.63 fof(kelley_5_19a,conjecture, % 0.44/0.63 ! [X1,A1] : % 0.44/0.63 ( a_locally_compact_top_space(the_product_top_space_over(X1,A1)) % 0.44/0.63 => ! [A] : a_locally_compact_top_space(apply(X1,A)) ) ). % 0.44/0.63 % 0.44/0.63 %------------------------------------------------------------------------------ % 0.44/0.63 %------------------------------------------- % 0.44/0.63 % Proof found % 0.44/0.63 % SZS status Theorem for theBenchmark % 0.44/0.63 % SZS output start Proof % 0.44/0.63 %ClaNum:5(EqnAxiom:0) % 0.44/0.63 %VarNum:22(SingletonVarNum:10) % 0.44/0.63 %MaxLitNum:4 % 0.44/0.63 %MaxfuncDepth:1 % 0.44/0.63 %SharedTerms:7 % 0.44/0.63 %goalClause: 1 4 % 0.44/0.63 %singleGoalClaCount:2 % 0.44/0.63 [1]P1(f4(a1,a3)) % 0.56/0.63 [4]~P1(f2(a1,a5)) % 0.56/0.63 [2]P2(f6(x21,x22,x23),f4(x22,x23),f2(x22,x21)) % 0.56/0.63 [3]P3(f6(x31,x32,x33),f4(x34,x33),f2(x34,x31)) % 0.56/0.63 [5]~P3(x53,x52,x51)+P1(x51)+~P2(x53,x52,x51)+~P1(x52) % 0.56/0.63 %EqnAxiom % 0.56/0.63 % 0.56/0.63 %------------------------------------------- % 0.56/0.64 cnf(6,plain, % 0.56/0.64 ($false), % 0.56/0.64 inference(scs_inference,[],[3,4,2,1,5]), % 0.56/0.64 ['proof']). % 0.56/0.64 % SZS output end Proof % 0.56/0.64 % Total time :0.000000s %------------------------------------------------------------------------------