%------------------------------------------------------------------------------ % File : SPASS---3.9 % Problem : HEN010-2 : TPTP v8.1.0. Released v1.0.0. % Transfm : none % Format : tptp % Command : run_spass %d %s % Computer : n029.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 : 600s % DateTime : Sat Jul 16 13:03:12 EDT 2022 % Result : Unsatisfiable 1.50s 1.69s % Output : Refutation 1.50s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : HEN010-2 : TPTP v8.1.0. Released v1.0.0. % 0.06/0.13 % Command : run_spass %d %s % 0.13/0.34 % Computer : n029.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 : 300 % 0.13/0.34 % WCLimit : 600 % 0.13/0.34 % DateTime : Fri Jul 1 14:31:39 EDT 2022 % 0.13/0.34 % CPUTime : % 1.50/1.69 % 1.50/1.69 SPASS V 3.9 % 1.50/1.69 SPASS beiseite: Proof found. % 1.50/1.69 % SZS status Theorem % 1.50/1.69 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p % 1.50/1.69 SPASS derived 8326 clauses, backtracked 0 clauses, performed 0 splits and kept 1542 clauses. % 1.50/1.69 SPASS allocated 69478 KBytes. % 1.50/1.69 SPASS spent 0:00:01.25 on the problem. % 1.50/1.69 0:00:00.03 for the input. % 1.50/1.69 0:00:00.00 for the FLOTTER CNF translation. % 1.50/1.69 0:00:00.10 for inferences. % 1.50/1.69 0:00:00.00 for the backtracking. % 1.50/1.69 0:00:01.08 for the reduction. % 1.50/1.69 % 1.50/1.69 % 1.50/1.69 Here is a proof with depth 6, length 24 : % 1.50/1.69 % SZS output start Refutation % 1.50/1.69 3[0:Inp] || -> quotient(u,u,zero)*. % 1.50/1.69 4[0:Inp] || -> quotient(u,zero,u)*. % 1.50/1.69 9[0:Inp] || quotient(identity,u,v)*+ quotient(identity,w,u)* quotient(identity,x,w)* -> equal(w,v)*. % 1.50/1.69 10[0:Inp] || -> quotient(identity,a,idQa)*. % 1.50/1.69 11[0:Inp] || -> quotient(identity,idQa,idQ_idQa)*. % 1.50/1.69 12[0:Inp] || -> quotient(idQa,idQ_idQa,idQa_Q__idQ_idQa)*. % 1.50/1.69 13[0:Inp] || equal(idQa_Q__idQ_idQa,idQa)** -> . % 1.50/1.69 16[0:Inp] || quotient(u,v,w)* -> less_equal(w,u). % 1.50/1.69 17[0:Inp] || quotient(u,v,w)*+ quotient(x,y,z)* quotient(x1,v,x)* quotient(x2,v,y)* quotient(x1,x2,u)* -> less_equal(z,w)*. % 1.50/1.69 19[0:Inp] || less_equal(u,v)*+ less_equal(v,u)* -> equal(v,u). % 1.50/1.69 21[0:Inp] || -> quotient(u,v,divide(u,v))*. % 1.50/1.69 25[0:Res:19.2,13.0] || less_equal(idQa,idQa_Q__idQ_idQa) less_equal(idQa_Q__idQ_idQa,idQa)*l -> . % 1.50/1.69 37[0:Res:12.0,16.0] || -> less_equal(idQa_Q__idQ_idQa,idQa)*l. % 1.50/1.69 46[0:MRR:25.1,37.0] || less_equal(idQa,idQa_Q__idQ_idQa)*r -> . % 1.50/1.69 72[0:Res:21.0,9.0] || quotient(identity,u,v)*+ quotient(identity,w,u)* -> equal(u,divide(identity,v)). % 1.50/1.69 229[0:Res:12.0,17.0] || quotient(u,v,w)*+ quotient(x,idQ_idQa,u)* quotient(y,idQ_idQa,v)* quotient(x,y,idQa)* -> less_equal(w,idQa_Q__idQ_idQa). % 1.50/1.69 340[0:Res:11.0,72.0] || quotient(identity,u,idQa)* -> equal(divide(identity,idQ_idQa),idQa). % 1.50/1.69 353[0:Res:10.0,340.0] || -> equal(divide(identity,idQ_idQa),idQa)**. % 1.50/1.69 354[0:SpR:353.0,21.0] || -> quotient(identity,idQ_idQa,idQa)*. % 1.50/1.69 2995[0:Res:4.0,229.0] || quotient(u,idQ_idQa,v)*+ quotient(w,idQ_idQa,zero)* quotient(u,w,idQa)* -> less_equal(v,idQa_Q__idQ_idQa). % 1.50/1.69 10957[0:Res:354.0,2995.0] || quotient(u,idQ_idQa,zero)* quotient(identity,u,idQa)* -> less_equal(idQa,idQa_Q__idQ_idQa). % 1.50/1.69 10969[0:MRR:10957.2,46.0] || quotient(u,idQ_idQa,zero)*+ quotient(identity,u,idQa)* -> . % 1.50/1.69 10973[0:Res:3.0,10969.0] || quotient(identity,idQ_idQa,idQa)* -> . % 1.50/1.69 10980[0:MRR:10973.0,354.0] || -> . % 1.50/1.69 % SZS output end Refutation % 1.50/1.69 Formulae used in the proof : x_divide_x_is_zero x_divde_zero_is_x one_inversion_equals_three identity_divide_a identity_divide_idQa identity_divide_idQ_idQa prove_idQa_equals_idQa_Q__idQ_idQa divisor_existence quotient_property less_equal_and_equal closure % 1.50/1.69 %------------------------------------------------------------------------------