TSTP Solution File: SWW238+1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SWW238+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 : n001.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 00:54:29 EDT 2023
% Result : Theorem 171.46s 22.34s
% Output : Proof 171.46s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWW238+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
% 0.14/0.35 % Computer : n001.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 18:37:48 EDT 2023
% 0.14/0.35 % CPUTime :
% 171.46/22.34 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 171.46/22.34
% 171.46/22.34 % SZS status Theorem
% 171.46/22.34
% 171.46/22.35 % SZS output start Proof
% 171.46/22.35 Take the following subset of the input axioms:
% 171.46/22.36 fof(arity_Complex__Ocomplex__Rings_Ocomm__semiring__1, axiom, class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex)).
% 171.46/22.36 fof(arity_RealDef__Oreal__Rings_Ocomm__semiring__1, axiom, class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal)).
% 171.46/22.36 fof(conj_0, conjecture, c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), v_z____), v_c____)), 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_aa____, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), v_z____), v_c____))), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_aa____)))).
% 171.46/22.36 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J, axiom, ![T_a, V_a, V_c]: (class_Rings_Ocomm__semiring__1(T_a) => c_Groups_Oplus__class_Oplus(T_a, V_a, V_c)=c_Groups_Oplus__class_Oplus(T_a, V_c, V_a))).
% 171.46/22.36 fof(fact_complex__mod__triangle__sub, axiom, ![V_z, V_w]: 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)))).
% 171.46/22.36
% 171.46/22.36 Now clausify the problem and encode Horn clauses using encoding 3 of
% 171.46/22.36 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 171.46/22.36 We repeatedly replace C & s=t => u=v by the two clauses:
% 171.46/22.36 fresh(y, y, x1...xn) = u
% 171.46/22.36 C => fresh(s, t, x1...xn) = v
% 171.46/22.36 where fresh is a fresh function symbol and x1..xn are the free
% 171.46/22.36 variables of u and v.
% 171.46/22.36 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 171.46/22.36 input problem has no model of domain size 1).
% 171.46/22.36
% 171.46/22.36 The encoding turns the above axioms into the following unit equations and goals:
% 171.46/22.36
% 171.46/22.36 Axiom 1 (arity_RealDef__Oreal__Rings_Ocomm__semiring__1): class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal) = true2.
% 171.46/22.36 Axiom 2 (arity_Complex__Ocomplex__Rings_Ocomm__semiring__1): class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex) = true2.
% 171.46/22.36 Axiom 3 (fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J): fresh942(X, X, Y, Z, W) = c_Groups_Oplus__class_Oplus(W, Y, Z).
% 171.46/22.36 Axiom 4 (fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J): fresh942(class_Rings_Ocomm__semiring__1(X), true2, Y, Z, X) = c_Groups_Oplus__class_Oplus(X, Z, Y).
% 171.46/22.36 Axiom 5 (fact_complex__mod__triangle__sub): c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, X), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, X, Y)), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, Y))) = true2.
% 171.46/22.36
% 171.46/22.36 Lemma 6: c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, X, Y) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, Y, X).
% 171.46/22.36 Proof:
% 171.46/22.36 c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, X, Y)
% 171.46/22.36 = { by axiom 4 (fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) R->L }
% 171.46/22.36 fresh942(class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal), true2, Y, X, tc_RealDef_Oreal)
% 171.46/22.36 = { by axiom 1 (arity_RealDef__Oreal__Rings_Ocomm__semiring__1) }
% 171.46/22.36 fresh942(true2, true2, Y, X, tc_RealDef_Oreal)
% 171.46/22.36 = { by axiom 3 (fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) }
% 171.46/22.36 c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, Y, X)
% 171.46/22.36
% 171.46/22.36 Goal 1 (conj_0): c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), v_z____), v_c____)), 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_aa____, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), v_z____), v_c____))), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_aa____))) = true2.
% 171.46/22.36 Proof:
% 171.46/22.36 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), v_z____), v_c____)), 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_aa____, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), v_z____), v_c____))), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_aa____)))
% 171.46/22.36 = { by lemma 6 R->L }
% 171.46/22.36 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), v_z____), v_c____)), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_aa____), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, v_aa____, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), v_z____), v_c____)))))
% 171.46/22.36 = { by axiom 3 (fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) R->L }
% 171.46/22.36 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), v_z____), v_c____)), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_aa____), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, fresh942(true2, true2, v_aa____, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), v_z____), v_c____), tc_Complex_Ocomplex))))
% 171.46/22.36 = { by axiom 2 (arity_Complex__Ocomplex__Rings_Ocomm__semiring__1) R->L }
% 171.46/22.36 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), v_z____), v_c____)), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_aa____), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, fresh942(class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex), true2, v_aa____, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), v_z____), v_c____), tc_Complex_Ocomplex))))
% 171.46/22.36 = { by axiom 4 (fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) }
% 171.46/22.36 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), v_z____), v_c____)), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_aa____), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), v_z____), v_c____), v_aa____))))
% 171.46/22.36 = { by lemma 6 R->L }
% 171.46/22.36 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), v_z____), v_c____)), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), v_z____), v_c____), v_aa____)), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_aa____)))
% 171.46/22.36 = { by axiom 5 (fact_complex__mod__triangle__sub) }
% 171.46/22.36 true2
% 171.46/22.36 % SZS output end Proof
% 171.46/22.36
% 171.46/22.36 RESULT: Theorem (the conjecture is true).
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