TSTP Solution File: FLD018-1 by SPASS---3.9
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% File : SPASS---3.9
% Problem : FLD018-1 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n026.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 02:28:18 EDT 2022
% Result : Unsatisfiable 0.18s 0.42s
% Output : Refutation 0.18s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : FLD018-1 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.11/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n026.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon Jun 6 23:13:16 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.42
% 0.18/0.42 SPASS V 3.9
% 0.18/0.42 SPASS beiseite: Proof found.
% 0.18/0.42 % SZS status Theorem
% 0.18/0.42 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.42 SPASS derived 121 clauses, backtracked 0 clauses, performed 0 splits and kept 94 clauses.
% 0.18/0.42 SPASS allocated 75771 KBytes.
% 0.18/0.42 SPASS spent 0:00:00.07 on the problem.
% 0.18/0.42 0:00:00.03 for the input.
% 0.18/0.42 0:00:00.00 for the FLOTTER CNF translation.
% 0.18/0.42 0:00:00.00 for inferences.
% 0.18/0.42 0:00:00.00 for the backtracking.
% 0.18/0.42 0:00:00.01 for the reduction.
% 0.18/0.42
% 0.18/0.42
% 0.18/0.42 Here is a proof with depth 3, length 17 :
% 0.18/0.42 % SZS output start Refutation
% 0.18/0.42 1[0:Inp] || -> defined(a)*.
% 0.18/0.42 2[0:Inp] || -> equalish(a,additive_identity)*l.
% 0.18/0.42 3[0:Inp] || equalish(additive_inverse(a),additive_identity)*l -> .
% 0.18/0.42 5[0:Inp] defined(u) || -> equalish(add(additive_identity,u),u)*l.
% 0.18/0.42 6[0:Inp] defined(u) || -> equalish(add(u,additive_inverse(u)),additive_identity)*l.
% 0.18/0.42 15[0:Inp] defined(u) || -> defined(additive_inverse(u))*.
% 0.18/0.42 25[0:Inp] || equalish(u,v)* -> equalish(v,u).
% 0.18/0.42 26[0:Inp] || equalish(u,v)* equalish(v,w)* -> equalish(u,w)*.
% 0.18/0.42 27[0:Inp] defined(u) || equalish(v,w) -> equalish(add(v,u),add(w,u))*.
% 0.18/0.42 33[0:Res:2.0,27.1] defined(u) || -> equalish(add(a,u),add(additive_identity,u))*l.
% 0.18/0.42 37[0:Res:25.1,3.0] || equalish(additive_identity,additive_inverse(a))*r -> .
% 0.18/0.42 48[0:Res:6.1,25.0] defined(u) || -> equalish(additive_identity,add(u,additive_inverse(u)))*r.
% 0.18/0.42 177[0:OCh:26.1,26.0,48.1,33.1] defined(a) defined(additive_inverse(a)) || -> equalish(additive_identity,add(additive_identity,additive_inverse(a)))*r.
% 0.18/0.42 180[0:SSi:177.1,177.0,15.0,1.0,1.1] || -> equalish(additive_identity,add(additive_identity,additive_inverse(a)))*r.
% 0.18/0.42 204[0:OCh:26.1,26.0,180.0,5.1] defined(additive_inverse(a)) || -> equalish(additive_identity,additive_inverse(a))*r.
% 0.18/0.42 206[0:SSi:204.0,15.0,1.1] || -> equalish(additive_identity,additive_inverse(a))*r.
% 0.18/0.42 207[0:MRR:206.0,37.0] || -> .
% 0.18/0.42 % SZS output end Refutation
% 0.18/0.42 Formulae used in the proof : a_is_defined a_equals_additive_identity_2 additive_inverse_not_equal_to_additive_identity_3 existence_of_identity_addition existence_of_inverse_addition well_definedness_of_additive_inverse symmetry_of_equality transitivity_of_equality compatibility_of_equality_and_addition
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