%------------------------------------------------------------------------------ % File : SPASS---3.9 % Problem : FLD023-1 : TPTP v8.1.0. Bugfixed v2.1.0. % 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 02:28:20 EDT 2022 % Result : Unsatisfiable 0.19s 0.42s % Output : Refutation 0.19s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : FLD023-1 : TPTP v8.1.0. Bugfixed v2.1.0. % 0.03/0.13 % 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 : Mon Jun 6 22:06:34 EDT 2022 % 0.13/0.34 % CPUTime : % 0.19/0.42 % 0.19/0.42 SPASS V 3.9 % 0.19/0.42 SPASS beiseite: Proof found. % 0.19/0.42 % SZS status Theorem % 0.19/0.42 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p % 0.19/0.42 SPASS derived 55 clauses, backtracked 0 clauses, performed 0 splits and kept 62 clauses. % 0.19/0.42 SPASS allocated 75695 KBytes. % 0.19/0.42 SPASS spent 0:00:00.06 on the problem. % 0.19/0.42 0:00:00.04 for the input. % 0.19/0.42 0:00:00.00 for the FLOTTER CNF translation. % 0.19/0.42 0:00:00.00 for inferences. % 0.19/0.42 0:00:00.00 for the backtracking. % 0.19/0.42 0:00:00.01 for the reduction. % 0.19/0.42 % 0.19/0.42 % 0.19/0.42 Here is a proof with depth 2, length 13 : % 0.19/0.42 % SZS output start Refutation % 0.19/0.42 1[0:Inp] || -> defined(a)*. % 0.19/0.42 3[0:Inp] || -> equalish(a,b)*l. % 0.19/0.42 4[0:Inp] || equalish(additive_identity,add(b,additive_inverse(a)))*r -> . % 0.19/0.42 7[0:Inp] defined(u) || -> equalish(add(u,additive_inverse(u)),additive_identity)*l. % 0.19/0.42 16[0:Inp] defined(u) || -> defined(additive_inverse(u))*. % 0.19/0.42 26[0:Inp] || equalish(u,v)* -> equalish(v,u). % 0.19/0.42 27[0:Inp] || equalish(u,v)* equalish(v,w)* -> equalish(u,w)*. % 0.19/0.42 28[0:Inp] defined(u) || equalish(v,w) -> equalish(add(v,u),add(w,u))*. % 0.19/0.42 34[0:Res:3.0,28.1] defined(u) || -> equalish(add(a,u),add(b,u))*l. % 0.19/0.42 53[0:Res:7.1,26.0] defined(u) || -> equalish(additive_identity,add(u,additive_inverse(u)))*r. % 0.19/0.42 107[0:OCh:27.1,27.0,53.1,34.1] defined(a) defined(additive_inverse(a)) || -> equalish(additive_identity,add(b,additive_inverse(a)))*r. % 0.19/0.42 110[0:SSi:107.1,107.0,16.0,1.0,1.1] || -> equalish(additive_identity,add(b,additive_inverse(a)))*r. % 0.19/0.42 111[0:MRR:110.0,4.0] || -> . % 0.19/0.42 % SZS output end Refutation % 0.19/0.42 Formulae used in the proof : a_is_defined a_equals_b_3 additive_identity_not_equal_to_add_4 existence_of_inverse_addition well_definedness_of_additive_inverse symmetry_of_equality transitivity_of_equality compatibility_of_equality_and_addition % 0.19/0.42 %------------------------------------------------------------------------------