TSTP Solution File: SWW194+1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SWW194+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 : 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 : 300s
% DateTime : Fri Sep 1 00:54:23 EDT 2023
% Result : Theorem 155.11s 20.44s
% Output : Proof 155.60s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWW194+1 : TPTP v8.1.2. Released v5.2.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.34 % Computer : n026.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Sun Aug 27 17:51:19 EDT 2023
% 0.14/0.34 % CPUTime :
% 155.11/20.44 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 155.11/20.44
% 155.11/20.44 % SZS status Theorem
% 155.11/20.44
% 155.60/20.44 % SZS output start Proof
% 155.60/20.44 Take the following subset of the input axioms:
% 155.60/20.44 fof(arity_RealDef__Oreal__Groups_Omonoid__mult, axiom, class_Groups_Omonoid__mult(tc_RealDef_Oreal)).
% 155.60/20.44 fof(arity_RealDef__Oreal__Rings_Olinordered__idom, axiom, class_Rings_Olinordered__idom(tc_RealDef_Oreal)).
% 155.60/20.44 fof(conj_0, conjecture, c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, hAPP(hAPP(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)))), hAPP(hAPP(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)))))).
% 155.60/20.44 fof(fact__096abs_A_I2_A_K_Ax_J_A_060_061_A1_096, axiom, c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, hAPP(hAPP(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_Groups_Oone__class_Oone(tc_RealDef_Oreal))).
% 155.60/20.44 fof(fact_power2__abs, axiom, ![V_a, T_a]: (class_Rings_Olinordered__idom(T_a) => hAPP(hAPP(c_Power_Opower__class_Opower(T_a), c_Groups_Oabs__class_Oabs(T_a, V_a)), c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))=hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_a), c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))).
% 155.60/20.45 fof(fact_power__one, axiom, ![V_n, T_a2]: (class_Groups_Omonoid__mult(T_a2) => hAPP(hAPP(c_Power_Opower__class_Opower(T_a2), c_Groups_Oone__class_Oone(T_a2)), V_n)=c_Groups_Oone__class_Oone(T_a2))).
% 155.60/20.45 fof(fact_real__sqrt__abs, axiom, ![V_x]: c_NthRoot_Osqrt(hAPP(hAPP(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_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, V_x)).
% 155.60/20.45 fof(fact_real__sqrt__le__1__iff, axiom, ![V_xa_2]: (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_NthRoot_Osqrt(V_xa_2), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, V_xa_2, c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))).
% 155.60/20.45
% 155.60/20.45 Now clausify the problem and encode Horn clauses using encoding 3 of
% 155.60/20.45 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 155.60/20.45 We repeatedly replace C & s=t => u=v by the two clauses:
% 155.60/20.45 fresh(y, y, x1...xn) = u
% 155.60/20.45 C => fresh(s, t, x1...xn) = v
% 155.60/20.45 where fresh is a fresh function symbol and x1..xn are the free
% 155.60/20.45 variables of u and v.
% 155.60/20.45 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 155.60/20.45 input problem has no model of domain size 1).
% 155.60/20.45
% 155.60/20.45 The encoding turns the above axioms into the following unit equations and goals:
% 155.60/20.45
% 155.60/20.45 Axiom 1 (arity_RealDef__Oreal__Rings_Olinordered__idom): class_Rings_Olinordered__idom(tc_RealDef_Oreal) = true2.
% 155.60/20.45 Axiom 2 (arity_RealDef__Oreal__Groups_Omonoid__mult): class_Groups_Omonoid__mult(tc_RealDef_Oreal) = true2.
% 155.60/20.45 Axiom 3 (fact_real__sqrt__le__1__iff_1): fresh260(X, X, Y) = true2.
% 155.60/20.45 Axiom 4 (fact_power__one): fresh304(X, X, Y, Z) = c_Groups_Oone__class_Oone(Z).
% 155.60/20.45 Axiom 5 (fact_power__one): fresh304(class_Groups_Omonoid__mult(X), true2, Y, X) = hAPP(hAPP(c_Power_Opower__class_Opower(X), c_Groups_Oone__class_Oone(X)), Y).
% 155.60/20.45 Axiom 6 (fact_power2__abs): fresh330(X, X, Y, Z) = hAPP(hAPP(c_Power_Opower__class_Opower(Z), Y), c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))).
% 155.60/20.45 Axiom 7 (fact_real__sqrt__le__1__iff_1): fresh260(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_NthRoot_Osqrt(X), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), true2, X) = c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, X, c_Groups_Oone__class_Oone(tc_RealDef_Oreal)).
% 155.60/20.45 Axiom 8 (fact_power2__abs): fresh330(class_Rings_Olinordered__idom(X), true2, Y, X) = hAPP(hAPP(c_Power_Opower__class_Opower(X), c_Groups_Oabs__class_Oabs(X, Y)), c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))).
% 155.60/20.45 Axiom 9 (fact_real__sqrt__abs): c_NthRoot_Osqrt(hAPP(hAPP(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_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, X).
% 155.60/20.45 Axiom 10 (fact__096abs_A_I2_A_K_Ax_J_A_060_061_A1_096): c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, hAPP(hAPP(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_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = true2.
% 155.60/20.45
% 155.60/20.45 Goal 1 (conj_0): c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, hAPP(hAPP(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)))), hAPP(hAPP(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))))) = true2.
% 155.60/20.45 Proof:
% 155.60/20.45 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, hAPP(hAPP(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)))), hAPP(hAPP(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)))))
% 155.60/20.45 = { by axiom 5 (fact_power__one) R->L }
% 155.60/20.45 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, hAPP(hAPP(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)))), fresh304(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))
% 155.60/20.45 = { by axiom 2 (arity_RealDef__Oreal__Groups_Omonoid__mult) }
% 155.60/20.45 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, hAPP(hAPP(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)))), fresh304(true2, true2, c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, c_Int_OBit0(c_Int_OBit1(c_Int_OPls))), tc_RealDef_Oreal))
% 155.60/20.45 = { by axiom 4 (fact_power__one) }
% 155.60/20.45 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, hAPP(hAPP(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)))), c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
% 155.60/20.45 = { by axiom 7 (fact_real__sqrt__le__1__iff_1) R->L }
% 155.60/20.45 fresh260(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_NthRoot_Osqrt(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, hAPP(hAPP(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))))), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), true2, hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, hAPP(hAPP(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)))))
% 155.60/20.45 = { by axiom 8 (fact_power2__abs) R->L }
% 155.60/20.45 fresh260(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_NthRoot_Osqrt(fresh330(class_Rings_Olinordered__idom(tc_RealDef_Oreal), true2, hAPP(hAPP(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____), tc_RealDef_Oreal)), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), true2, hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, hAPP(hAPP(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)))))
% 155.60/20.45 = { by axiom 1 (arity_RealDef__Oreal__Rings_Olinordered__idom) }
% 155.60/20.45 fresh260(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_NthRoot_Osqrt(fresh330(true2, true2, hAPP(hAPP(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____), tc_RealDef_Oreal)), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), true2, hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, hAPP(hAPP(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)))))
% 155.60/20.45 = { by axiom 6 (fact_power2__abs) }
% 155.60/20.45 fresh260(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_NthRoot_Osqrt(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), hAPP(hAPP(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))))), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), true2, hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, hAPP(hAPP(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)))))
% 155.60/20.45 = { by axiom 9 (fact_real__sqrt__abs) }
% 155.60/20.45 fresh260(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, hAPP(hAPP(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_Groups_Oone__class_Oone(tc_RealDef_Oreal)), true2, hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, hAPP(hAPP(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)))))
% 155.60/20.45 = { by axiom 10 (fact__096abs_A_I2_A_K_Ax_J_A_060_061_A1_096) }
% 155.60/20.45 fresh260(true2, true2, hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, hAPP(hAPP(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)))))
% 155.60/20.45 = { by axiom 3 (fact_real__sqrt__le__1__iff_1) }
% 155.60/20.45 true2
% 155.60/20.45 % SZS output end Proof
% 155.60/20.45
% 155.60/20.45 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------