%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : TOP022+1 : TPTP v8.2.0. Released v3.1.0. % Transfm : none % Format : tptp:raw % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s % Computer : n025.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 0.43s 0.60s % Output : CNFRefutation 0.43s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : TOP022+1 : TPTP v8.2.0. Released v3.1.0. % 0.06/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s % 0.11/0.33 % Computer : n025.cluster.edu % 0.11/0.33 % Model : x86_64 x86_64 % 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.11/0.33 % Memory : 8042.1875MB % 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.11/0.33 % CPULimit : 300 % 0.11/0.33 % WCLimit : 300 % 0.11/0.33 % DateTime : Tue Jun 18 11:22:39 EDT 2024 % 0.11/0.34 % CPUTime : % 0.43/0.58 start to proof:theBenchmark % 0.43/0.60 %------------------------------------------- % 0.43/0.60 % File :CSE---1.7 % 0.43/0.60 % Problem :theBenchmark % 0.43/0.60 % Transform :cnf % 0.43/0.60 % Format :tptp:raw % 0.43/0.60 % Command :java -jar mcs_scs.jar %d %s % 0.43/0.60 % 0.43/0.60 % Result :Theorem 0.000000s % 0.43/0.60 % Output :CNFRefutation 0.000000s % 0.43/0.60 %------------------------------------------- % 0.43/0.60 %------------------------------------------------------------------------------ % 0.43/0.60 % File : TOP022+1 : TPTP v8.2.0. Released v3.1.0. % 0.43/0.60 % Domain : Topology (Homotopy theory) % 0.43/0.60 % Problem : Homotopy groups % 0.43/0.60 % Version : [Shu96] axioms : Especial. % 0.43/0.60 % English : % 0.43/0.60 % 0.43/0.60 % Refs : [Mun75] Munkres (1975), Topology: A First Course % 0.43/0.60 % : [Shu96] Shults (1996), Email to Geoff Sutcliffe % 0.43/0.60 % Source : [Shu96] % 0.43/0.60 % Names : % 0.43/0.60 % 0.43/0.60 % Status : Theorem % 0.43/0.60 % Rating : 0.00 v8.2.0, 0.07 v8.1.0, 0.00 v6.1.0, 0.04 v6.0.0, 0.25 v5.5.0, 0.04 v5.3.0, 0.09 v5.2.0, 0.00 v3.1.0 % 0.43/0.60 % Syntax : Number of formulae : 4 ( 0 unt; 0 def) % 0.43/0.60 % Number of atoms : 12 ( 0 equ) % 0.43/0.60 % Maximal formula atoms : 4 ( 3 avg) % 0.43/0.60 % Number of connectives : 8 ( 0 ~; 0 |; 3 &) % 0.43/0.60 % ( 2 <=>; 3 =>; 0 <=; 0 <~>) % 0.43/0.60 % Maximal formula depth : 7 ( 6 avg) % 0.43/0.60 % Maximal term depth : 2 ( 1 avg) % 0.43/0.60 % Number of predicates : 5 ( 5 usr; 0 prp; 1-4 aty) % 0.43/0.60 % Number of functors : 2 ( 2 usr; 0 con; 1-2 aty) % 0.43/0.60 % Number of variables : 14 ( 12 !; 2 ?) % 0.43/0.60 % SPC : FOF_THM_RFO_NEQ % 0.43/0.60 % 0.43/0.60 % Comments : % 0.43/0.60 %------------------------------------------------------------------------------ % 0.43/0.60 %----What it means to be isomorphic % 0.43/0.60 fof(isomorphic_groups_defn,axiom, % 0.43/0.60 ! [A,B] : % 0.43/0.60 ( isomorphic_groups(A,B) % 0.43/0.60 <=> ? [F] : a_group_isomorphism_from_to(F,A,B) ) ). % 0.43/0.60 % 0.43/0.60 %----The definition of path connectedness % 0.43/0.60 fof(path_connected_defn,axiom, % 0.43/0.60 ! [X,X0,X1] : % 0.43/0.60 ( path_connected(X) % 0.43/0.60 <=> ( ( a_member_of(X0,X) % 0.43/0.60 & a_member_of(X1,X) ) % 0.43/0.60 => ? [P] : a_path_from_to_in(P,X0,X1,X) ) ) ). % 0.43/0.60 % 0.43/0.60 %----Theorem 2.1 in Chapter 8 of Munkres % 0.43/0.60 fof(m_8_2_1,axiom, % 0.43/0.60 ! [A,X0,X1,X] : % 0.43/0.60 ( a_path_from_to_in(A,X0,X1,X) % 0.43/0.60 => a_group_isomorphism_from_to(alpha_hat(A),first_homotop_grp(X,X0),first_homotop_grp(X,X1)) ) ). % 0.43/0.60 % 0.43/0.60 fof(m_8_2_2,conjecture, % 0.43/0.60 ! [X,X0,X1] : % 0.43/0.60 ( ( path_connected(X) % 0.43/0.60 & a_member_of(X0,X) % 0.43/0.60 & a_member_of(X1,X) ) % 0.43/0.60 => isomorphic_groups(first_homotop_grp(X,X0),first_homotop_grp(X,X1)) ) ). % 0.43/0.60 % 0.43/0.60 %------------------------------------------------------------------------------ % 0.43/0.60 %------------------------------------------- % 0.43/0.60 % Proof found % 0.43/0.60 % SZS status Theorem for theBenchmark % 0.43/0.60 % SZS output start Proof % 0.43/0.60 %ClaNum:11(EqnAxiom:0) % 0.43/0.60 %VarNum:39(SingletonVarNum:18) % 0.43/0.60 %MaxLitNum:4 % 0.43/0.60 %MaxfuncDepth:1 % 0.43/0.60 %SharedTerms:9 % 0.43/0.60 %goalClause: 1 2 3 4 % 0.43/0.60 %singleGoalClaCount:4 % 0.43/0.60 [1]P1(a1) % 0.43/0.60 [2]P2(a5,a1) % 0.43/0.60 [3]P2(a6,a1) % 0.43/0.60 [4]~P4(f7(a1,a5),f7(a1,a6)) % 0.43/0.60 [6]P1(x61)+P2(x62,x61) % 0.43/0.60 [8]~P4(x81,x82)+P3(f2(x81,x82),x81,x82) % 0.43/0.60 [7]P4(x71,x72)+~P3(x73,x71,x72) % 0.43/0.60 [9]P1(x91)+~P5(x92,x93,x94,x91) % 0.43/0.60 [11]~P5(x111,x113,x114,x112)+P3(f3(x111),f7(x112,x113),f7(x112,x114)) % 0.43/0.60 [10]~P1(x101)+~P2(x103,x101)+~P2(x102,x101)+P5(f4(x101,x102,x103),x102,x103,x101) % 0.43/0.60 %EqnAxiom % 0.43/0.60 % 0.43/0.60 %------------------------------------------- % 0.43/0.61 cnf(16,plain, % 0.43/0.61 ($false), % 0.43/0.61 inference(scs_inference,[],[1,2,3,4,7,11,10]), % 0.43/0.61 ['proof']). % 0.43/0.61 % SZS output end Proof % 0.43/0.61 % Total time :0.000000s %------------------------------------------------------------------------------