TSTP Solution File: SWW178+1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : SWW178+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 : n023.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 00:54:21 EDT 2023
% Result : Theorem 109.38s 14.12s
% Output : Proof 109.38s
% 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 : SWW178+1 : TPTP v8.1.2. Released v5.2.0.
% 0.07/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.34 % Computer : n023.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sun Aug 27 18:43:56 EDT 2023
% 0.13/0.34 % CPUTime :
% 109.38/14.12 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 109.38/14.12
% 109.38/14.12 % SZS status Theorem
% 109.38/14.12
% 109.38/14.13 % SZS output start Proof
% 109.38/14.13 Take the following subset of the input axioms:
% 109.38/14.13 fof(arity_Complex__Ocomplex__Groups_Ogroup__add, axiom, class_Groups_Ogroup__add(tc_Complex_Ocomplex)).
% 109.38/14.13 fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__vector, axiom, class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex)).
% 109.38/14.13 fof(conj_0, conjecture, c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_w), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, v_w, v_z)), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_z)))).
% 109.38/14.13 fof(fact_add__diff__cancel, axiom, ![T_a, V_b, V_a]: (class_Groups_Ogroup__add(T_a) => c_Groups_Ominus__class_Ominus(T_a, c_Groups_Oplus__class_Oplus(T_a, V_a, V_b), V_b)=V_a)).
% 109.38/14.13 fof(fact_norm__triangle__ineq4, axiom, ![T_a2, V_b2, V_a2]: (class_RealVector_Oreal__normed__vector(T_a2) => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(T_a2, c_Groups_Ominus__class_Ominus(T_a2, V_a2, V_b2)), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(T_a2, V_a2), c_RealVector_Onorm__class_Onorm(T_a2, V_b2))))).
% 109.38/14.13
% 109.38/14.13 Now clausify the problem and encode Horn clauses using encoding 3 of
% 109.38/14.13 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 109.38/14.13 We repeatedly replace C & s=t => u=v by the two clauses:
% 109.38/14.13 fresh(y, y, x1...xn) = u
% 109.38/14.13 C => fresh(s, t, x1...xn) = v
% 109.38/14.13 where fresh is a fresh function symbol and x1..xn are the free
% 109.38/14.13 variables of u and v.
% 109.38/14.13 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 109.38/14.13 input problem has no model of domain size 1).
% 109.38/14.13
% 109.38/14.13 The encoding turns the above axioms into the following unit equations and goals:
% 109.38/14.13
% 109.38/14.13 Axiom 1 (arity_Complex__Ocomplex__RealVector_Oreal__normed__vector): class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex) = true2.
% 109.38/14.13 Axiom 2 (arity_Complex__Ocomplex__Groups_Ogroup__add): class_Groups_Ogroup__add(tc_Complex_Ocomplex) = true2.
% 109.38/14.13 Axiom 3 (fact_norm__triangle__ineq4): fresh384(X, X, Y, Z, W) = true2.
% 109.38/14.13 Axiom 4 (fact_add__diff__cancel): fresh149(X, X, Y, Z, W) = Z.
% 109.38/14.13 Axiom 5 (fact_add__diff__cancel): fresh149(class_Groups_Ogroup__add(X), true2, Y, Z, X) = c_Groups_Ominus__class_Ominus(X, c_Groups_Oplus__class_Oplus(X, Z, Y), Y).
% 109.38/14.13 Axiom 6 (fact_norm__triangle__ineq4): fresh384(class_RealVector_Oreal__normed__vector(X), true2, Y, Z, X) = c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(X, c_Groups_Ominus__class_Ominus(X, Z, Y)), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(X, Z), c_RealVector_Onorm__class_Onorm(X, Y))).
% 109.38/14.13
% 109.38/14.13 Goal 1 (conj_0): c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_w), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, v_w, v_z)), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_z))) = true2.
% 109.38/14.13 Proof:
% 109.38/14.13 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_w), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, v_w, v_z)), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_z)))
% 109.38/14.13 = { by axiom 4 (fact_add__diff__cancel) R->L }
% 109.38/14.13 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, fresh149(true2, true2, v_z, v_w, tc_Complex_Ocomplex)), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, v_w, v_z)), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_z)))
% 109.38/14.13 = { by axiom 2 (arity_Complex__Ocomplex__Groups_Ogroup__add) R->L }
% 109.38/14.13 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, fresh149(class_Groups_Ogroup__add(tc_Complex_Ocomplex), true2, v_z, v_w, tc_Complex_Ocomplex)), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, v_w, v_z)), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_z)))
% 109.38/14.13 = { by axiom 5 (fact_add__diff__cancel) }
% 109.38/14.13 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, v_w, v_z), v_z)), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, v_w, v_z)), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_z)))
% 109.38/14.13 = { by axiom 6 (fact_norm__triangle__ineq4) R->L }
% 109.38/14.13 fresh384(class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex), true2, v_z, c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, v_w, v_z), tc_Complex_Ocomplex)
% 109.38/14.13 = { by axiom 1 (arity_Complex__Ocomplex__RealVector_Oreal__normed__vector) }
% 109.38/14.13 fresh384(true2, true2, v_z, c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, v_w, v_z), tc_Complex_Ocomplex)
% 109.38/14.13 = { by axiom 3 (fact_norm__triangle__ineq4) }
% 109.38/14.13 true2
% 109.38/14.13 % SZS output end Proof
% 109.38/14.13
% 109.38/14.13 RESULT: Theorem (the conjecture is true).
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