TSTP Solution File: SWV684-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SWV684-1 : 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 : n019.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 : Thu Aug 31 23:05:53 EDT 2023
% Result : Unsatisfiable 175.66s 22.87s
% Output : Proof 175.66s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWV684-1 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.16/0.34 % Computer : n019.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Aug 29 10:31:43 EDT 2023
% 0.16/0.34 % CPUTime :
% 175.66/22.87 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 175.66/22.87
% 175.66/22.87 % SZS status Unsatisfiable
% 175.66/22.87
% 175.66/22.87 % SZS output start Proof
% 175.66/22.87 Take the following subset of the input axioms:
% 175.66/22.88 fof(cls_COMBB__def_0, axiom, ![T_a, T_b, T_c, V_P, V_Q, V_R]: hAPP(hAPP(hAPP(c_COMBB(T_b, T_a, T_c), V_P), V_Q), V_R)=hAPP(V_P, hAPP(V_Q, V_R))).
% 175.66/22.88 fof(cls_COMBC__def_0, axiom, ![T_a2, T_b2, T_c2, V_P2, V_Q2, V_R2]: hAPP(hAPP(hAPP(c_COMBC(T_b2, T_c2, T_a2), V_P2), V_Q2), V_R2)=hAPP(hAPP(V_P2, V_R2), V_Q2)).
% 175.66/22.88 fof(cls_COMBS__def_0, axiom, ![T_a2, T_b2, T_c2, V_P2, V_Q2, V_R2]: hAPP(hAPP(hAPP(c_COMBS(T_b2, T_c2, T_a2), V_P2), V_Q2), V_R2)=hAPP(hAPP(V_P2, V_R2), hAPP(V_Q2, V_R2))).
% 175.66/22.88 fof(cls_Suc__n__not__n_0, axiom, ![V_n]: hAPP(c_Suc, V_n)!=V_n).
% 175.66/22.88 fof(cls_Suc__neq__Zero_0, axiom, ![V_m]: hAPP(c_Suc, V_m)!=c_HOL_Ozero__class_Ozero(tc_nat)).
% 175.66/22.88 fof(cls_Zero__neq__Suc_0, axiom, ![V_m2]: c_HOL_Ozero__class_Ozero(tc_nat)!=hAPP(c_Suc, V_m2)).
% 175.66/22.88 fof(cls_gr__implies__not0_0, axiom, ![V_m2]: ~c_HOL_Oord__class_Oless(V_m2, c_HOL_Ozero__class_Ozero(tc_nat), tc_nat)).
% 175.66/22.88 fof(cls_less__not__refl_0, axiom, ![V_n2]: ~c_HOL_Oord__class_Oless(V_n2, V_n2, tc_nat)).
% 175.66/22.88 fof(cls_linorder__neq__iff_1, axiom, ![V_x, T_a2]: (~class_Orderings_Olinorder(T_a2) | ~c_HOL_Oord__class_Oless(V_x, V_x, T_a2))).
% 175.66/22.88 fof(cls_n__not__Suc__n_0, axiom, ![V_n2]: V_n2!=hAPP(c_Suc, V_n2)).
% 175.66/22.88 fof(cls_nat_Osimps_I2_J_0, axiom, ![V_nat_H]: c_HOL_Ozero__class_Ozero(tc_nat)!=hAPP(c_Suc, V_nat_H)).
% 175.66/22.88 fof(cls_nat_Osimps_I3_J_0, axiom, ![V_nat_H2]: hAPP(c_Suc, V_nat_H2)!=c_HOL_Ozero__class_Ozero(tc_nat)).
% 175.66/22.88 fof(cls_nat__less__le_1, axiom, ![V_x2]: ~c_HOL_Oord__class_Oless(V_x2, V_x2, tc_nat)).
% 175.66/22.88 fof(cls_not__add__less1_0, axiom, ![V_i, V_j]: ~c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat), V_i), V_j), V_i, tc_nat)).
% 175.66/22.88 fof(cls_not__add__less2_0, axiom, ![V_i2, V_j2]: ~c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat), V_j2), V_i2), V_i2, tc_nat)).
% 175.66/22.88 fof(cls_not__less0_0, axiom, ![V_n2]: ~c_HOL_Oord__class_Oless(V_n2, c_HOL_Ozero__class_Ozero(tc_nat), tc_nat)).
% 175.66/22.88 fof(cls_not__less__eq_1, axiom, ![V_m2, V_n2]: (~c_HOL_Oord__class_Oless(V_m2, V_n2, tc_nat) | ~c_HOL_Oord__class_Oless(V_n2, hAPP(c_Suc, V_m2), tc_nat))).
% 175.66/22.88 fof(cls_not__less__iff__gr__or__eq_1, axiom, ![V_y, T_a2, V_x2]: (~class_Orderings_Olinorder(T_a2) | (~c_HOL_Oord__class_Oless(V_x2, V_y, T_a2) | ~c_HOL_Oord__class_Oless(V_y, V_x2, T_a2)))).
% 175.66/22.88 fof(cls_not__square__less__zero_0, axiom, ![V_a, T_a2]: (~class_Ring__and__Field_Oordered__ring__strict(T_a2) | ~c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a2), V_a), V_a), c_HOL_Ozero__class_Ozero(T_a2), T_a2))).
% 175.66/22.88 fof(cls_not__sum__squares__lt__zero_0, axiom, ![T_a2, V_x2, V_y2]: (~class_Ring__and__Field_Oordered__ring__strict(T_a2) | ~c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a2), hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a2), V_x2), V_x2)), hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a2), V_y2), V_y2)), c_HOL_Ozero__class_Ozero(T_a2), T_a2))).
% 175.66/22.88 fof(cls_of__nat__less__0__iff_0, axiom, ![T_a2, V_m2]: (~class_Ring__and__Field_Oordered__semidom(T_a2) | ~c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(V_m2, T_a2), c_HOL_Ozero__class_Ozero(T_a2), T_a2))).
% 175.66/22.88 fof(cls_order__less__asym_0, axiom, ![T_a2, V_x2, V_y2]: (~class_Orderings_Opreorder(T_a2) | (~c_HOL_Oord__class_Oless(V_y2, V_x2, T_a2) | ~c_HOL_Oord__class_Oless(V_x2, V_y2, T_a2)))).
% 175.66/22.88 fof(cls_order__less__asym_H_0, axiom, ![V_b, T_a2, V_a2]: (~class_Orderings_Opreorder(T_a2) | (~c_HOL_Oord__class_Oless(V_b, V_a2, T_a2) | ~c_HOL_Oord__class_Oless(V_a2, V_b, T_a2)))).
% 175.66/22.88 fof(cls_order__less__irrefl_0, axiom, ![T_a2, V_x2]: (~class_Orderings_Opreorder(T_a2) | ~c_HOL_Oord__class_Oless(V_x2, V_x2, T_a2))).
% 175.66/22.88 fof(cls_order__less__le_1, axiom, ![T_a2, V_x2]: (~class_Orderings_Oorder(T_a2) | ~c_HOL_Oord__class_Oless(V_x2, V_x2, T_a2))).
% 175.66/22.88 fof(cls_power__eq__0__iff_1, axiom, ![T_a2, V_a2]: (~class_Ring__and__Field_Ozero__neq__one(T_a2) | (~class_Ring__and__Field_Ono__zero__divisors(T_a2) | (~class_Ring__and__Field_Omult__zero(T_a2) | (~class_Power_Opower(T_a2) | hAPP(hAPP(c_Power_Opower__class_Opower(T_a2), V_a2), c_HOL_Ozero__class_Ozero(tc_nat))!=c_HOL_Ozero__class_Ozero(T_a2)))))).
% 175.66/22.88 fof(cls_sum__squares__gt__zero__iff_0, axiom, ![T_a2]: (~class_Ring__and__Field_Oordered__ring__strict(T_a2) | ~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a2), hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a2), hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a2), c_HOL_Ozero__class_Ozero(T_a2)), c_HOL_Ozero__class_Ozero(T_a2))), hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a2), c_HOL_Ozero__class_Ozero(T_a2)), c_HOL_Ozero__class_Ozero(T_a2))), T_a2))).
% 175.66/22.88 fof(cls_xt1_I9_J_0, axiom, ![T_a2, V_a2, V_b2]: (~class_Orderings_Oorder(T_a2) | (~c_HOL_Oord__class_Oless(V_a2, V_b2, T_a2) | ~c_HOL_Oord__class_Oless(V_b2, V_a2, T_a2)))).
% 175.66/22.88
% 175.66/22.88 Now clausify the problem and encode Horn clauses using encoding 3 of
% 175.66/22.88 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 175.66/22.88 We repeatedly replace C & s=t => u=v by the two clauses:
% 175.66/22.88 fresh(y, y, x1...xn) = u
% 175.66/22.88 C => fresh(s, t, x1...xn) = v
% 175.66/22.88 where fresh is a fresh function symbol and x1..xn are the free
% 175.66/22.88 variables of u and v.
% 175.66/22.88 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 175.66/22.88 input problem has no model of domain size 1).
% 175.66/22.88
% 175.66/22.88 The encoding turns the above axioms into the following unit equations and goals:
% 175.66/22.88
% 175.66/22.88 Axiom 1 (cls_COMBS__def_0): hAPP(hAPP(hAPP(c_COMBS(X, Y, Z), W), V), U) = hAPP(hAPP(W, U), hAPP(V, U)).
% 175.66/22.88 Axiom 2 (cls_COMBC__def_0): hAPP(hAPP(hAPP(c_COMBC(X, Y, Z), W), V), U) = hAPP(hAPP(W, U), V).
% 175.66/22.88 Axiom 3 (cls_COMBB__def_0): hAPP(hAPP(hAPP(c_COMBB(X, Y, Z), W), V), U) = hAPP(W, hAPP(V, U)).
% 175.66/22.88
% 175.66/22.88 Goal 1 (cls_n__not__Suc__n_0): X = hAPP(c_Suc, X).
% 175.66/22.88 The goal is true when:
% 175.66/22.88 X = hAPP(hAPP(hAPP(c_COMBS(X, Y, Z), hAPP(c_COMBC(W, V, U), hAPP(c_COMBB(T, S, X2), c_Suc))), hAPP(c_COMBS(X, Y, Z), hAPP(c_COMBC(W, V, U), hAPP(c_COMBB(T, S, X2), c_Suc)))), hAPP(c_COMBS(X, Y, Z), hAPP(c_COMBC(W, V, U), hAPP(c_COMBB(T, S, X2), c_Suc))))
% 175.66/22.88
% 175.66/22.88 Proof:
% 175.66/22.88 hAPP(hAPP(hAPP(c_COMBS(X, Y, Z), hAPP(c_COMBC(W, V, U), hAPP(c_COMBB(T, S, X2), c_Suc))), hAPP(c_COMBS(X, Y, Z), hAPP(c_COMBC(W, V, U), hAPP(c_COMBB(T, S, X2), c_Suc)))), hAPP(c_COMBS(X, Y, Z), hAPP(c_COMBC(W, V, U), hAPP(c_COMBB(T, S, X2), c_Suc))))
% 175.66/22.88 = { by axiom 1 (cls_COMBS__def_0) }
% 175.66/22.88 hAPP(hAPP(hAPP(c_COMBC(W, V, U), hAPP(c_COMBB(T, S, X2), c_Suc)), hAPP(c_COMBS(X, Y, Z), hAPP(c_COMBC(W, V, U), hAPP(c_COMBB(T, S, X2), c_Suc)))), hAPP(hAPP(c_COMBS(X, Y, Z), hAPP(c_COMBC(W, V, U), hAPP(c_COMBB(T, S, X2), c_Suc))), hAPP(c_COMBS(X, Y, Z), hAPP(c_COMBC(W, V, U), hAPP(c_COMBB(T, S, X2), c_Suc)))))
% 175.66/22.88 = { by axiom 2 (cls_COMBC__def_0) }
% 175.66/22.88 hAPP(hAPP(hAPP(c_COMBB(T, S, X2), c_Suc), hAPP(hAPP(c_COMBS(X, Y, Z), hAPP(c_COMBC(W, V, U), hAPP(c_COMBB(T, S, X2), c_Suc))), hAPP(c_COMBS(X, Y, Z), hAPP(c_COMBC(W, V, U), hAPP(c_COMBB(T, S, X2), c_Suc))))), hAPP(c_COMBS(X, Y, Z), hAPP(c_COMBC(W, V, U), hAPP(c_COMBB(T, S, X2), c_Suc))))
% 175.66/22.88 = { by axiom 3 (cls_COMBB__def_0) }
% 175.66/22.88 hAPP(c_Suc, hAPP(hAPP(hAPP(c_COMBS(X, Y, Z), hAPP(c_COMBC(W, V, U), hAPP(c_COMBB(T, S, X2), c_Suc))), hAPP(c_COMBS(X, Y, Z), hAPP(c_COMBC(W, V, U), hAPP(c_COMBB(T, S, X2), c_Suc)))), hAPP(c_COMBS(X, Y, Z), hAPP(c_COMBC(W, V, U), hAPP(c_COMBB(T, S, X2), c_Suc)))))
% 175.66/22.88 % SZS output end Proof
% 175.66/22.88
% 175.66/22.88 RESULT: Unsatisfiable (the axioms are contradictory).
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