%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : ALG002-1 : TPTP v8.2.0. Released v1.0.0. % Transfm : none % Format : tptp:raw % Command : java -jar /export/starexec/sandbox/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 03:40:35 EDT 2024 % Result : Unsatisfiable 0.56s 0.90s % Output : CNFRefutation 0.56s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.13 % Problem : ALG002-1 : TPTP v8.2.0. Released v1.0.0. % 0.12/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s % 0.12/0.34 % Computer : n025.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 300 % 0.12/0.34 % DateTime : Wed Jun 19 15:58:39 EDT 2024 % 0.12/0.34 % CPUTime : % 0.54/0.58 start to proof:theBenchmark % 0.56/0.89 %------------------------------------------- % 0.56/0.89 % File :CSE---1.7 % 0.56/0.89 % Problem :theBenchmark % 0.56/0.89 % Transform :cnf % 0.56/0.89 % Format :tptp:raw % 0.56/0.89 % Command :java -jar mcs_scs.jar %d %s % 0.56/0.89 % 0.56/0.89 % Result :Theorem 0.280000s % 0.56/0.89 % Output :CNFRefutation 0.280000s % 0.56/0.89 %------------------------------------------- % 0.56/0.89 %-------------------------------------------------------------------------- % 0.56/0.89 % File : ALG002-1 : TPTP v8.2.0. Released v1.0.0. % 0.56/0.89 % Domain : General Algebra % 0.56/0.89 % Problem : In an ordered field, if X > 0 then X^-1 > 0 % 0.56/0.89 % Version : [FL+74] axioms. % 0.56/0.89 % English : % 0.56/0.89 % 0.56/0.89 % Refs : [FL+74] Fleisig et al. (1974), An Implementation of the Model % 0.56/0.89 % : [WM76] Wilson & Minker (1976), Resolution, Refinements, and S % 0.56/0.89 % Source : [SPRFN] % 0.56/0.89 % Names : Example 5 [FL+74] % 0.56/0.89 % : EX5-T? [WM76] % 0.56/0.89 % : ex5.lop [SETHEO] % 0.56/0.89 % : FEX5 [SPRFN] % 0.56/0.89 % 0.56/0.89 % Status : Unsatisfiable % 0.56/0.89 % Rating : 0.00 v8.1.0, 0.17 v7.0.0, 0.12 v6.3.0, 0.14 v6.2.0, 0.00 v2.0.0 % 0.56/0.89 % Syntax : Number of clauses : 14 ( 4 unt; 2 nHn; 11 RR) % 0.56/0.89 % Number of literals : 28 ( 0 equ; 15 neg) % 0.56/0.89 % Maximal clause size : 4 ( 2 avg) % 0.56/0.90 % Maximal term depth : 2 ( 1 avg) % 0.56/0.90 % Number of predicates : 2 ( 2 usr; 0 prp; 1-3 aty) % 0.56/0.90 % Number of functors : 5 ( 5 usr; 3 con; 0-1 aty) % 0.56/0.90 % Number of variables : 23 ( 1 sgn) % 0.56/0.90 % SPC : CNF_UNS_RFO_NEQ_NHN % 0.56/0.90 % 0.56/0.90 % Comments : % 0.56/0.90 %-------------------------------------------------------------------------- % 0.56/0.90 cnf(right_identity,axiom, % 0.56/0.90 product(X,multiplicative_identity,X) ). % 0.56/0.90 % 0.56/0.90 cnf(not_abelian,axiom, % 0.56/0.90 ~ product(multiplicative_identity,multiplicative_identity,additive_identity) ). % 0.56/0.90 % 0.56/0.90 cnf(product_of_inverses1,axiom, % 0.56/0.90 ( ~ product(X,Y,Z) % 0.56/0.90 | product(additive_inverse(X),additive_inverse(Y),Z) ) ). % 0.56/0.90 % 0.56/0.90 cnf(product_of_inverses2,axiom, % 0.56/0.90 ( product(X,Y,Z) % 0.56/0.90 | ~ product(additive_inverse(X),additive_inverse(Y),Z) ) ). % 0.56/0.90 % 0.56/0.90 cnf(product_to_inverse,axiom, % 0.56/0.90 ( ~ product(X,Y,Z) % 0.56/0.90 | product(X,additive_inverse(Y),additive_inverse(Z)) ) ). % 0.56/0.90 % 0.56/0.90 cnf(inverse_and_identity,axiom, % 0.56/0.90 ( product(X,multiplicative_inverse(X),multiplicative_identity) % 0.56/0.90 | product(X,X,additive_identity) ) ). % 0.56/0.90 % 0.56/0.90 cnf(inverse_greater_than_0,axiom, % 0.56/0.90 ( ~ greater_than_0(X) % 0.56/0.90 | ~ greater_than_0(additive_inverse(X)) ) ). % 0.56/0.90 % 0.56/0.90 cnf(greater_than_0_square,axiom, % 0.56/0.90 ( ~ greater_than_0(X) % 0.56/0.90 | ~ product(X,X,additive_identity) ) ). % 0.56/0.90 % 0.56/0.90 cnf(commutativity_of_product,axiom, % 0.56/0.90 ( ~ product(X,Y,Z) % 0.56/0.90 | product(Y,X,Z) ) ). % 0.56/0.90 % 0.56/0.90 cnf(product_and_inverse,axiom, % 0.56/0.90 ( greater_than_0(X) % 0.56/0.90 | product(X,X,additive_identity) % 0.56/0.90 | greater_than_0(additive_inverse(X)) ) ). % 0.56/0.90 % 0.56/0.90 cnf(square_to_0,axiom, % 0.56/0.90 ( ~ product(Y,Z,X) % 0.56/0.90 | ~ product(Y,Y,additive_identity) % 0.56/0.90 | product(X,X,additive_identity) ) ). % 0.56/0.90 % 0.56/0.90 cnf(product_and_greater_than_0,axiom, % 0.56/0.90 ( ~ product(Y,Z,X) % 0.56/0.90 | ~ greater_than_0(Y) % 0.56/0.90 | ~ greater_than_0(Z) % 0.56/0.90 | greater_than_0(X) ) ). % 0.56/0.90 % 0.56/0.90 cnf(a_greater_than_0,hypothesis, % 0.56/0.90 greater_than_0(a) ). % 0.56/0.90 % 0.56/0.90 cnf(prove_a_inverse_greater_than_0,negated_conjecture, % 0.56/0.90 ~ greater_than_0(multiplicative_inverse(a)) ). % 0.56/0.90 % 0.56/0.90 %-------------------------------------------------------------------------- % 0.56/0.90 %------------------------------------------- % 0.56/0.90 % Proof found % 0.56/0.90 % SZS status Theorem for theBenchmark % 0.56/0.90 % SZS output start Proof % 0.56/0.90 %ClaNum:14(EqnAxiom:0) % 0.56/0.90 %VarNum:52(SingletonVarNum:23) % 0.56/0.90 %MaxLitNum:4 % 0.56/0.90 %MaxfuncDepth:1 % 0.56/0.90 %SharedTerms:7 % 0.56/0.90 %goalClause: 3 % 0.56/0.90 %singleGoalClaCount:1 % 0.56/0.90 [1]P1(a1) % 0.56/0.90 [4]~P2(a2,a2,a3) % 0.56/0.90 [3]~P1(f5(a1)) % 0.56/0.90 [2]P2(x21,a2,x21) % 0.56/0.90 [7]~P1(x71)+~P2(x71,x71,a3) % 0.56/0.90 [5]~P1(x51)+~P1(f4(x51)) % 0.56/0.90 [9]P2(x91,x91,a3)+P2(x91,f5(x91),a2) % 0.56/0.90 [10]~P2(x102,x101,x103)+P2(x101,x102,x103) % 0.56/0.90 [11]~P2(x111,x112,x113)+P2(x111,f4(x112),f4(x113)) % 0.56/0.90 [12]~P2(x121,x122,x123)+P2(f4(x121),f4(x122),x123) % 0.56/0.90 [13]P2(x131,x132,x133)+~P2(f4(x131),f4(x132),x133) % 0.56/0.90 [6]P1(x61)+P2(x61,x61,a3)+P1(f4(x61)) % 0.56/0.90 [14]~P2(x142,x143,x141)+~P2(x142,x142,a3)+P2(x141,x141,a3) % 0.56/0.90 [8]~P2(x83,x82,x81)+P1(x81)+~P1(x82)+~P1(x83) % 0.56/0.90 %EqnAxiom % 0.56/0.90 % 0.56/0.90 %------------------------------------------- % 0.56/0.90 cnf(22,plain, % 0.56/0.90 (~P2(f4(a1),f4(a1),a3)), % 0.56/0.90 inference(scs_inference,[],[1,13,7])). % 0.56/0.90 cnf(23,plain, % 0.56/0.90 (~P2(a1,a1,a3)), % 0.56/0.90 inference(scs_inference,[],[22,12])). % 0.56/0.90 cnf(25,plain, % 0.56/0.90 (~P2(x251,x251,a3)+~P2(f4(x251),f4(x252),a1)), % 0.56/0.90 inference(scs_inference,[],[23,14,13])). % 0.56/0.90 cnf(26,plain, % 0.56/0.90 (~P2(f4(x261),f4(x262),a1)+P2(x261,f5(x261),a2)), % 0.56/0.90 inference(scs_inference,[],[25,9])). % 0.56/0.90 cnf(27,plain, % 0.56/0.90 (P2(f5(x271),x271,a2)+~P2(f4(x271),f4(x272),a1)), % 0.56/0.90 inference(scs_inference,[],[26,10])). % 0.56/0.90 cnf(28,plain, % 0.56/0.90 (P2(f5(x281),f4(x281),f4(a2))+~P2(f4(x281),f4(x282),a1)), % 0.56/0.90 inference(scs_inference,[],[27,11])). % 0.56/0.90 cnf(30,plain, % 0.56/0.90 (P1(f4(f4(a1)))), % 0.56/0.90 inference(scs_inference,[],[1,22,5,6])). % 0.56/0.90 cnf(31,plain, % 0.56/0.90 (~P1(f4(a1))), % 0.56/0.90 inference(scs_inference,[],[30,5])). % 0.56/0.90 cnf(39,plain, % 0.56/0.90 (P2(f5(a1),a1,a2)), % 0.56/0.90 inference(scs_inference,[],[23,10,9])). % 0.56/0.90 cnf(58,plain, % 0.56/0.90 (P2(a1,f4(f5(a1)),f4(a2))), % 0.56/0.90 inference(scs_inference,[],[39,10,11])). % 0.56/0.90 cnf(70,plain, % 0.56/0.90 (P2(f4(a2),f4(x701),x701)), % 0.56/0.90 inference(scs_inference,[],[2,10,12])). % 0.56/0.90 cnf(72,plain, % 0.56/0.90 (P2(f4(a2),f4(x721),x721)), % 0.56/0.90 inference(rename_variables,[],[70])). % 0.56/0.90 cnf(74,plain, % 0.56/0.90 (P2(a2,x741,x741)), % 0.56/0.90 inference(scs_inference,[],[70,72,28,13])). % 0.56/0.90 cnf(82,plain, % 0.56/0.90 (P2(x821,f4(a2),f4(x821))), % 0.56/0.90 inference(scs_inference,[],[74,10,11])). % 0.56/0.90 cnf(83,plain, % 0.56/0.90 (~P1(f4(a2))), % 0.56/0.90 inference(scs_inference,[],[31,82,1,8])). % 0.56/0.90 cnf(115,plain, % 0.56/0.90 (P2(f5(a1),f5(a1),a3)), % 0.56/0.90 inference(scs_inference,[],[58,3,83,1,8,6])). % 0.56/0.90 cnf(182,plain, % 0.56/0.90 ($false), % 0.56/0.90 inference(scs_inference,[],[4,115,39,14]), % 0.56/0.90 ['proof']). % 0.56/0.90 % SZS output end Proof % 0.56/0.90 % Total time :0.280000s %------------------------------------------------------------------------------