TSTP Solution File: ITP018+1 by Twee---2.5.0
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%------------------------------------------------------------------------------
% File : Twee---2.5.0
% Problem : ITP018+1 : TPTP v8.2.0. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : parallel-twee /export/starexec/sandbox2/benchmark/theBenchmark.p --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding
% Computer : n013.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 : Mon Jun 24 09:30:16 EDT 2024
% Result : Theorem 0.21s 0.49s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ITP018+1 : TPTP v8.2.0. Bugfixed v7.5.0.
% 0.07/0.12 % Command : parallel-twee /export/starexec/sandbox2/benchmark/theBenchmark.p --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding
% 0.12/0.33 % Computer : n013.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 : Wed Jun 19 03:18:54 EDT 2024
% 0.12/0.34 % CPUTime :
% 0.21/0.49 Command-line arguments: --random-mode --random-mode-goal-directed --no-flatten-goal --no-connectedness --no-ground-joining
% 0.21/0.49
% 0.21/0.49 % SZS status Theorem
% 0.21/0.49
% 0.21/0.49 % SZS output start Proof
% 0.21/0.49 Take the following subset of the input axioms:
% 0.21/0.49 fof(thm_2Ebinary__ieee_2Efloat__to__real__negate, axiom, ![A_27a, A_27b, V0x_2E0]: s(tyop_2Erealax_2Ereal, c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a, A_27b), c_2Ebinary__ieee_2Efloat__negate_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a, A_27b), V0x_2E0)))))=s(tyop_2Erealax_2Ereal, c_2Erealax_2Ereal__neg_2E1(s(tyop_2Erealax_2Ereal, c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a, A_27b), V0x_2E0)))))).
% 0.21/0.49 fof(thm_2Ebinary__ieee_2Eneg__ulp, conjecture, ![A_27t, A_27w]: s(tyop_2Erealax_2Ereal, c_2Erealax_2Ereal__neg_2E1(s(tyop_2Erealax_2Ereal, c_2Ebinary__ieee_2Eulp_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t, A_27w)), c_2Ebool_2Ethe__value_2E0)))))=s(tyop_2Erealax_2Ereal, c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t, A_27w), c_2Ebinary__ieee_2Efloat__negate_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t, A_27w), c_2Ebinary__ieee_2Efloat__plus__min_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t, A_27w)), c_2Ebool_2Ethe__value_2E0)))))))).
% 0.21/0.49 fof(thm_2Ebinary__ieee_2Eulp, axiom, ![A_27t2, A_27w2]: s(tyop_2Erealax_2Ereal, c_2Ebinary__ieee_2Eulp_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t2, A_27w2)), c_2Ebool_2Ethe__value_2E0)))=s(tyop_2Erealax_2Ereal, c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t2, A_27w2), c_2Ebinary__ieee_2Efloat__plus__min_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t2, A_27w2)), c_2Ebool_2Ethe__value_2E0)))))).
% 0.21/0.49
% 0.21/0.49 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.21/0.49 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.21/0.49 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.21/0.49 fresh(y, y, x1...xn) = u
% 0.21/0.49 C => fresh(s, t, x1...xn) = v
% 0.21/0.49 where fresh is a fresh function symbol and x1..xn are the free
% 0.21/0.49 variables of u and v.
% 0.21/0.49 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.21/0.49 input problem has no model of domain size 1).
% 0.21/0.49
% 0.21/0.49 The encoding turns the above axioms into the following unit equations and goals:
% 0.21/0.49
% 0.21/0.49 Axiom 1 (thm_2Ebinary__ieee_2Efloat__to__real__negate): s(tyop_2Erealax_2Ereal, c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(X, Y), c_2Ebinary__ieee_2Efloat__negate_2E1(s(tyop_2Ebinary__ieee_2Efloat(X, Y), Z))))) = s(tyop_2Erealax_2Ereal, c_2Erealax_2Ereal__neg_2E1(s(tyop_2Erealax_2Ereal, c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(X, Y), Z))))).
% 0.21/0.49 Axiom 2 (thm_2Ebinary__ieee_2Eulp): s(tyop_2Erealax_2Ereal, c_2Ebinary__ieee_2Eulp_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(X, Y)), c_2Ebool_2Ethe__value_2E0))) = s(tyop_2Erealax_2Ereal, c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(X, Y), c_2Ebinary__ieee_2Efloat__plus__min_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(X, Y)), c_2Ebool_2Ethe__value_2E0))))).
% 0.21/0.49
% 0.21/0.49 Goal 1 (thm_2Ebinary__ieee_2Eneg__ulp): s(tyop_2Erealax_2Ereal, c_2Erealax_2Ereal__neg_2E1(s(tyop_2Erealax_2Ereal, c_2Ebinary__ieee_2Eulp_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(a_27t, a_27w)), c_2Ebool_2Ethe__value_2E0))))) = s(tyop_2Erealax_2Ereal, c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(a_27t, a_27w), c_2Ebinary__ieee_2Efloat__negate_2E1(s(tyop_2Ebinary__ieee_2Efloat(a_27t, a_27w), c_2Ebinary__ieee_2Efloat__plus__min_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(a_27t, a_27w)), c_2Ebool_2Ethe__value_2E0))))))).
% 0.21/0.49 Proof:
% 0.21/0.49 s(tyop_2Erealax_2Ereal, c_2Erealax_2Ereal__neg_2E1(s(tyop_2Erealax_2Ereal, c_2Ebinary__ieee_2Eulp_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(a_27t, a_27w)), c_2Ebool_2Ethe__value_2E0)))))
% 0.21/0.49 = { by axiom 2 (thm_2Ebinary__ieee_2Eulp) }
% 0.21/0.49 s(tyop_2Erealax_2Ereal, c_2Erealax_2Ereal__neg_2E1(s(tyop_2Erealax_2Ereal, c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(a_27t, a_27w), c_2Ebinary__ieee_2Efloat__plus__min_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(a_27t, a_27w)), c_2Ebool_2Ethe__value_2E0)))))))
% 0.21/0.49 = { by axiom 1 (thm_2Ebinary__ieee_2Efloat__to__real__negate) R->L }
% 0.21/0.49 s(tyop_2Erealax_2Ereal, c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(a_27t, a_27w), c_2Ebinary__ieee_2Efloat__negate_2E1(s(tyop_2Ebinary__ieee_2Efloat(a_27t, a_27w), c_2Ebinary__ieee_2Efloat__plus__min_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(a_27t, a_27w)), c_2Ebool_2Ethe__value_2E0)))))))
% 0.21/0.49 % SZS output end Proof
% 0.21/0.49
% 0.21/0.49 RESULT: Theorem (the conjecture is true).
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