TSTP Solution File: FLD031-1 by SPASS---3.9
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% File : SPASS---3.9
% Problem : FLD031-1 : 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 02:28:23 EDT 2022
% Result : Unsatisfiable 0.07s 0.31s
% Output : Refutation 0.07s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.07 % Problem : FLD031-1 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.06/0.07 % Command : run_spass %d %s
% 0.07/0.26 % Computer : n029.cluster.edu
% 0.07/0.26 % Model : x86_64 x86_64
% 0.07/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.26 % Memory : 8042.1875MB
% 0.07/0.26 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.26 % CPULimit : 300
% 0.07/0.26 % WCLimit : 600
% 0.07/0.26 % DateTime : Mon Jun 6 18:30:19 EDT 2022
% 0.07/0.26 % CPUTime :
% 0.07/0.31
% 0.07/0.31 SPASS V 3.9
% 0.07/0.31 SPASS beiseite: Proof found.
% 0.07/0.31 % SZS status Theorem
% 0.07/0.31 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.31 SPASS derived 38 clauses, backtracked 0 clauses, performed 0 splits and kept 60 clauses.
% 0.07/0.31 SPASS allocated 75666 KBytes.
% 0.07/0.31 SPASS spent 0:00:00.04 on the problem.
% 0.07/0.31 0:00:00.02 for the input.
% 0.07/0.31 0:00:00.00 for the FLOTTER CNF translation.
% 0.07/0.31 0:00:00.00 for inferences.
% 0.07/0.31 0:00:00.00 for the backtracking.
% 0.07/0.31 0:00:00.00 for the reduction.
% 0.07/0.31
% 0.07/0.31
% 0.07/0.31 Here is a proof with depth 4, length 22 :
% 0.07/0.31 % SZS output start Refutation
% 0.07/0.31 1[0:Inp] || -> defined(a)*.
% 0.07/0.31 2[0:Inp] || -> equalish(a,multiplicative_identity)*l.
% 0.07/0.31 3[0:Inp] || equalish(a,additive_identity)*l -> .
% 0.07/0.31 4[0:Inp] || equalish(multiplicative_inverse(a),multiplicative_identity)*l -> .
% 0.07/0.31 10[0:Inp] defined(u) || -> equalish(multiply(multiplicative_identity,u),u)*l.
% 0.07/0.31 11[0:Inp] defined(u) || -> equalish(u,additive_identity) equalish(multiply(u,multiplicative_inverse(u)),multiplicative_identity)*l.
% 0.07/0.31 19[0:Inp] defined(u) || -> defined(multiplicative_inverse(u))* equalish(u,additive_identity).
% 0.07/0.31 26[0:Inp] || equalish(u,v)* -> equalish(v,u).
% 0.07/0.31 27[0:Inp] || equalish(u,v)* equalish(v,w)* -> equalish(u,w)*.
% 0.07/0.31 29[0:Inp] defined(u) || equalish(v,w) -> equalish(multiply(v,u),multiply(w,u))*.
% 0.07/0.31 33[0:Res:2.0,29.1] defined(u) || -> equalish(multiply(a,u),multiply(multiplicative_identity,u))*l.
% 0.07/0.31 36[0:Res:11.2,3.0] defined(a) || -> equalish(multiply(a,multiplicative_inverse(a)),multiplicative_identity)*l.
% 0.07/0.31 37[0:Res:19.2,3.0] defined(a) || -> defined(multiplicative_inverse(a))*.
% 0.07/0.31 40[0:Res:26.1,4.0] || equalish(multiplicative_identity,multiplicative_inverse(a))*r -> .
% 0.07/0.31 42[0:MRR:37.0,1.0] || -> defined(multiplicative_inverse(a))*.
% 0.07/0.31 43[0:MRR:36.0,1.0] || -> equalish(multiply(a,multiplicative_inverse(a)),multiplicative_identity)*l.
% 0.07/0.31 56[0:Res:43.0,26.0] || -> equalish(multiplicative_identity,multiply(a,multiplicative_inverse(a)))*r.
% 0.07/0.31 75[0:OCh:27.1,27.0,56.0,33.1] defined(multiplicative_inverse(a)) || -> equalish(multiplicative_identity,multiply(multiplicative_identity,multiplicative_inverse(a)))*r.
% 0.07/0.31 77[0:SSi:75.0,42.0] || -> equalish(multiplicative_identity,multiply(multiplicative_identity,multiplicative_inverse(a)))*r.
% 0.07/0.31 79[0:OCh:27.1,27.0,77.0,10.1] defined(multiplicative_inverse(a)) || -> equalish(multiplicative_identity,multiplicative_inverse(a))*r.
% 0.07/0.31 81[0:SSi:79.0,42.0] || -> equalish(multiplicative_identity,multiplicative_inverse(a))*r.
% 0.07/0.31 82[0:MRR:81.0,40.0] || -> .
% 0.07/0.31 % SZS output end Refutation
% 0.07/0.31 Formulae used in the proof : a_is_defined a_equals_multiplicative_identity_2 a_not_equal_to_additive_identity_3 multiplicative_inverses_not_equal existence_of_identity_multiplication existence_of_inverse_multiplication well_definedness_of_multiplicative_inverse symmetry_of_equality transitivity_of_equality compatibility_of_equality_and_multiplication
% 0.07/0.31
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