TSTP Solution File: SWV629-1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : SWV629-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% Computer : n017.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 : Thu Aug 31 23:05:41 EDT 2023
% Result : Unsatisfiable 6.74s 1.21s
% Output : Proof 6.74s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWV629-1 : TPTP v8.1.2. Released v4.1.0.
% 0.07/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.33 % Computer : n017.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Tue Aug 29 08:05:28 EDT 2023
% 0.13/0.33 % CPUTime :
% 6.74/1.21 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 6.74/1.21
% 6.74/1.21 % SZS status Unsatisfiable
% 6.74/1.21
% 6.74/1.21 % SZS output start Proof
% 6.74/1.21 Take the following subset of the input axioms:
% 6.74/1.21 fof(cls_conjecture_0, negated_conjecture, c_FFT__Mirabelle_Oroot(c_HOL_Oone__class_Oone(tc_nat))!=c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)).
% 6.74/1.21 fof(cls_power__one__right_0, axiom, ![T_a, V_a]: (~class_OrderedGroup_Omonoid__mult(T_a) | c_Power_Opower__class_Opower(V_a, c_HOL_Oone__class_Oone(tc_nat), T_a)=V_a)).
% 6.74/1.21 fof(cls_root__unity_0, axiom, ![V_n]: c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(V_n), V_n, tc_Complex_Ocomplex)=c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)).
% 6.74/1.21 fof(clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__mult, axiom, class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex)).
% 6.74/1.21
% 6.74/1.21 Now clausify the problem and encode Horn clauses using encoding 3 of
% 6.74/1.21 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 6.74/1.21 We repeatedly replace C & s=t => u=v by the two clauses:
% 6.74/1.21 fresh(y, y, x1...xn) = u
% 6.74/1.21 C => fresh(s, t, x1...xn) = v
% 6.74/1.21 where fresh is a fresh function symbol and x1..xn are the free
% 6.74/1.21 variables of u and v.
% 6.74/1.21 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 6.74/1.21 input problem has no model of domain size 1).
% 6.74/1.21
% 6.74/1.21 The encoding turns the above axioms into the following unit equations and goals:
% 6.74/1.21
% 6.74/1.21 Axiom 1 (clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__mult): class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex) = true2.
% 6.74/1.21 Axiom 2 (cls_root__unity_0): c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(X), X, tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex).
% 6.74/1.21 Axiom 3 (cls_power__one__right_0): fresh19(X, X, Y, Z) = Z.
% 6.74/1.21 Axiom 4 (cls_power__one__right_0): fresh19(class_OrderedGroup_Omonoid__mult(X), true2, X, Y) = c_Power_Opower__class_Opower(Y, c_HOL_Oone__class_Oone(tc_nat), X).
% 6.74/1.21
% 6.74/1.21 Goal 1 (cls_conjecture_0): c_FFT__Mirabelle_Oroot(c_HOL_Oone__class_Oone(tc_nat)) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex).
% 6.74/1.21 Proof:
% 6.74/1.21 c_FFT__Mirabelle_Oroot(c_HOL_Oone__class_Oone(tc_nat))
% 6.74/1.21 = { by axiom 3 (cls_power__one__right_0) R->L }
% 6.74/1.21 fresh19(true2, true2, tc_Complex_Ocomplex, c_FFT__Mirabelle_Oroot(c_HOL_Oone__class_Oone(tc_nat)))
% 6.74/1.21 = { by axiom 1 (clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__mult) R->L }
% 6.74/1.21 fresh19(class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex), true2, tc_Complex_Ocomplex, c_FFT__Mirabelle_Oroot(c_HOL_Oone__class_Oone(tc_nat)))
% 6.74/1.21 = { by axiom 4 (cls_power__one__right_0) }
% 6.74/1.21 c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Oone__class_Oone(tc_nat)), c_HOL_Oone__class_Oone(tc_nat), tc_Complex_Ocomplex)
% 6.74/1.21 = { by axiom 2 (cls_root__unity_0) }
% 6.74/1.21 c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)
% 6.74/1.21 % SZS output end Proof
% 6.74/1.21
% 6.74/1.21 RESULT: Unsatisfiable (the axioms are contradictory).
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