TSTP Solution File: ALG434-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : ALG434-1 : 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 : n018.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 : Wed Aug 30 16:43:17 EDT 2023
% Result : Unsatisfiable 12.91s 1.99s
% Output : Proof 12.91s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : ALG434-1 : TPTP v8.1.2. Released v4.1.0.
% 0.11/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.33 % Computer : n018.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Aug 28 03:14:46 EDT 2023
% 0.12/0.34 % CPUTime :
% 12.91/1.99 Command-line arguments: --no-flatten-goal
% 12.91/1.99
% 12.91/1.99 % SZS status Unsatisfiable
% 12.91/1.99
% 12.91/2.00 % SZS output start Proof
% 12.91/2.00 Take the following subset of the input axioms:
% 12.91/2.00 fof(cls_conjecture_0, negated_conjecture, ~c_Ring__and__Field_Odvd__class_Odvd(v_p, c_Polynomial_Osmult(v_a, v_q, tc_Complex_Ocomplex), tc_Polynomial_Opoly(tc_Complex_Ocomplex))).
% 12.91/2.00 fof(cls_dvd__smult_0, axiom, ![T_a, V_p, V_q, V_a]: (~class_Ring__and__Field_Ocomm__semiring__1(T_a) | (c_Ring__and__Field_Odvd__class_Odvd(V_p, c_Polynomial_Osmult(V_a, V_q, T_a), tc_Polynomial_Opoly(T_a)) | ~c_Ring__and__Field_Odvd__class_Odvd(V_p, V_q, tc_Polynomial_Opoly(T_a))))).
% 12.91/2.00 fof(cls_pq_0, axiom, c_Ring__and__Field_Odvd__class_Odvd(v_p, v_q, tc_Polynomial_Opoly(tc_Complex_Ocomplex))).
% 12.91/2.00 fof(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1, axiom, class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex)).
% 12.91/2.00
% 12.91/2.00 Now clausify the problem and encode Horn clauses using encoding 3 of
% 12.91/2.00 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 12.91/2.00 We repeatedly replace C & s=t => u=v by the two clauses:
% 12.91/2.00 fresh(y, y, x1...xn) = u
% 12.91/2.00 C => fresh(s, t, x1...xn) = v
% 12.91/2.00 where fresh is a fresh function symbol and x1..xn are the free
% 12.91/2.00 variables of u and v.
% 12.91/2.00 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 12.91/2.00 input problem has no model of domain size 1).
% 12.91/2.00
% 12.91/2.00 The encoding turns the above axioms into the following unit equations and goals:
% 12.91/2.00
% 12.91/2.00 Axiom 1 (clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1): class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex) = true2.
% 12.91/2.00 Axiom 2 (cls_pq_0): c_Ring__and__Field_Odvd__class_Odvd(v_p, v_q, tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = true2.
% 12.91/2.00 Axiom 3 (cls_dvd__smult_0): fresh306(X, X, Y, Z, W, V) = true2.
% 12.91/2.00 Axiom 4 (cls_dvd__smult_0): fresh307(X, X, Y, Z, W, V) = c_Ring__and__Field_Odvd__class_Odvd(Z, c_Polynomial_Osmult(W, V, Y), tc_Polynomial_Opoly(Y)).
% 12.91/2.00 Axiom 5 (cls_dvd__smult_0): fresh307(class_Ring__and__Field_Ocomm__semiring__1(X), true2, X, Y, Z, W) = fresh306(c_Ring__and__Field_Odvd__class_Odvd(Y, W, tc_Polynomial_Opoly(X)), true2, X, Y, Z, W).
% 12.91/2.00
% 12.91/2.00 Goal 1 (cls_conjecture_0): c_Ring__and__Field_Odvd__class_Odvd(v_p, c_Polynomial_Osmult(v_a, v_q, tc_Complex_Ocomplex), tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = true2.
% 12.91/2.00 Proof:
% 12.91/2.00 c_Ring__and__Field_Odvd__class_Odvd(v_p, c_Polynomial_Osmult(v_a, v_q, tc_Complex_Ocomplex), tc_Polynomial_Opoly(tc_Complex_Ocomplex))
% 12.91/2.00 = { by axiom 4 (cls_dvd__smult_0) R->L }
% 12.91/2.00 fresh307(true2, true2, tc_Complex_Ocomplex, v_p, v_a, v_q)
% 12.91/2.00 = { by axiom 1 (clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1) R->L }
% 12.91/2.00 fresh307(class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex), true2, tc_Complex_Ocomplex, v_p, v_a, v_q)
% 12.91/2.00 = { by axiom 5 (cls_dvd__smult_0) }
% 12.91/2.00 fresh306(c_Ring__and__Field_Odvd__class_Odvd(v_p, v_q, tc_Polynomial_Opoly(tc_Complex_Ocomplex)), true2, tc_Complex_Ocomplex, v_p, v_a, v_q)
% 12.91/2.00 = { by axiom 2 (cls_pq_0) }
% 12.91/2.00 fresh306(true2, true2, tc_Complex_Ocomplex, v_p, v_a, v_q)
% 12.91/2.00 = { by axiom 3 (cls_dvd__smult_0) }
% 12.91/2.00 true2
% 12.91/2.00 % SZS output end Proof
% 12.91/2.00
% 12.91/2.00 RESULT: Unsatisfiable (the axioms are contradictory).
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