TSTP Solution File: SWW174+1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : SWW174+1 : TPTP v8.1.2. Released v5.2.0.
% 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 : n002.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 : Fri Sep 1 00:54:20 EDT 2023
% Result : Theorem 145.42s 18.83s
% Output : Proof 145.42s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SWW174+1 : TPTP v8.1.2. Released v5.2.0.
% 0.12/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.35 % Computer : n002.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sun Aug 27 23:06:19 EDT 2023
% 0.14/0.35 % CPUTime :
% 145.42/18.83 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 145.42/18.83
% 145.42/18.83 % SZS status Theorem
% 145.42/18.83
% 145.42/18.84 % SZS output start Proof
% 145.42/18.84 Take the following subset of the input axioms:
% 145.42/18.84 fof(arity_RealDef__Oreal__Groups_Omonoid__mult, axiom, class_Groups_Omonoid__mult(tc_RealDef_Oreal)).
% 145.42/18.84 fof(conj_0, conjecture, c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal, c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))=c_NthRoot_Osqrt(c_Power_Opower__class_Opower(tc_RealDef_Oreal, c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal, c_Int_OBit0(c_Int_OBit1(c_Int_OPls))), c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))).
% 145.42/18.84 fof(fact_four__x__squared, axiom, ![V_x]: c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal, c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal, c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), c_Power_Opower__class_Opower(tc_RealDef_Oreal, V_x, c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))=c_Power_Opower__class_Opower(tc_RealDef_Oreal, c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal, c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal, c_Int_OBit0(c_Int_OBit1(c_Int_OPls))), V_x), c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))).
% 145.42/18.84 fof(fact_power__one, axiom, ![T_a, V_n]: (class_Groups_Omonoid__mult(T_a) => c_Power_Opower__class_Opower(T_a, c_Groups_Oone__class_Oone(T_a), V_n)=c_Groups_Oone__class_Oone(T_a))).
% 145.42/18.84 fof(fact_real__mult__1, axiom, ![V_z]: c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal), V_z)=V_z).
% 145.42/18.84 fof(fact_real__mult__commute, axiom, ![V_w, V_z2]: c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal, V_z2, V_w)=c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal, V_w, V_z2)).
% 145.42/18.84
% 145.42/18.84 Now clausify the problem and encode Horn clauses using encoding 3 of
% 145.42/18.84 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 145.42/18.84 We repeatedly replace C & s=t => u=v by the two clauses:
% 145.42/18.84 fresh(y, y, x1...xn) = u
% 145.42/18.84 C => fresh(s, t, x1...xn) = v
% 145.42/18.84 where fresh is a fresh function symbol and x1..xn are the free
% 145.42/18.84 variables of u and v.
% 145.42/18.84 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 145.42/18.84 input problem has no model of domain size 1).
% 145.42/18.84
% 145.42/18.84 The encoding turns the above axioms into the following unit equations and goals:
% 145.42/18.84
% 145.42/18.84 Axiom 1 (arity_RealDef__Oreal__Groups_Omonoid__mult): class_Groups_Omonoid__mult(tc_RealDef_Oreal) = true2.
% 145.42/18.84 Axiom 2 (fact_real__mult__commute): c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal, X, Y) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal, Y, X).
% 145.42/18.84 Axiom 3 (fact_real__mult__1): c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal), X) = X.
% 145.42/18.84 Axiom 4 (fact_power__one): fresh322(X, X, Y, Z) = c_Groups_Oone__class_Oone(Z).
% 145.42/18.84 Axiom 5 (fact_power__one): fresh322(class_Groups_Omonoid__mult(X), true2, Y, X) = c_Power_Opower__class_Opower(X, c_Groups_Oone__class_Oone(X), Y).
% 145.42/18.84 Axiom 6 (fact_four__x__squared): c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal, c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal, c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), c_Power_Opower__class_Opower(tc_RealDef_Oreal, X, c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Power_Opower__class_Opower(tc_RealDef_Oreal, c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal, c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal, c_Int_OBit0(c_Int_OBit1(c_Int_OPls))), X), c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))).
% 145.42/18.84
% 145.42/18.84 Lemma 7: c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal, X, c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = X.
% 145.42/18.84 Proof:
% 145.42/18.84 c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal, X, c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
% 145.42/18.84 = { by axiom 2 (fact_real__mult__commute) R->L }
% 145.42/18.84 c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal), X)
% 145.42/18.84 = { by axiom 3 (fact_real__mult__1) }
% 145.42/18.84 X
% 145.42/18.84
% 145.42/18.84 Goal 1 (conj_0): c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal, c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_NthRoot_Osqrt(c_Power_Opower__class_Opower(tc_RealDef_Oreal, c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal, c_Int_OBit0(c_Int_OBit1(c_Int_OPls))), c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))).
% 145.42/18.84 Proof:
% 145.42/18.84 c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal, c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
% 145.42/18.84 = { by lemma 7 R->L }
% 145.42/18.84 c_NthRoot_Osqrt(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal, c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal, c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
% 145.42/18.84 = { by axiom 4 (fact_power__one) R->L }
% 145.42/18.84 c_NthRoot_Osqrt(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal, c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal, c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), fresh322(true2, true2, c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, c_Int_OBit0(c_Int_OBit1(c_Int_OPls))), tc_RealDef_Oreal)))
% 145.42/18.84 = { by axiom 1 (arity_RealDef__Oreal__Groups_Omonoid__mult) R->L }
% 145.42/18.84 c_NthRoot_Osqrt(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal, c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal, c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), fresh322(class_Groups_Omonoid__mult(tc_RealDef_Oreal), true2, c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, c_Int_OBit0(c_Int_OBit1(c_Int_OPls))), tc_RealDef_Oreal)))
% 145.42/18.84 = { by axiom 5 (fact_power__one) }
% 145.42/18.84 c_NthRoot_Osqrt(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal, c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal, c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), c_Power_Opower__class_Opower(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal), c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
% 145.42/18.84 = { by axiom 6 (fact_four__x__squared) }
% 145.42/18.84 c_NthRoot_Osqrt(c_Power_Opower__class_Opower(tc_RealDef_Oreal, c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal, c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal, c_Int_OBit0(c_Int_OBit1(c_Int_OPls))), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
% 145.42/18.84 = { by lemma 7 }
% 145.42/18.84 c_NthRoot_Osqrt(c_Power_Opower__class_Opower(tc_RealDef_Oreal, c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal, c_Int_OBit0(c_Int_OBit1(c_Int_OPls))), c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
% 145.42/18.84 % SZS output end Proof
% 145.42/18.84
% 145.42/18.84 RESULT: Theorem (the conjecture is true).
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