TSTP Solution File: ALG359-1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : ALG359-1 : 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 : n027.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 16:43:03 EDT 2023
% Result : Unsatisfiable 118.56s 15.55s
% Output : Proof 118.56s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ALG359-1 : 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
% 0.13/0.34 % Computer : n027.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 : Mon Aug 28 03:58:51 EDT 2023
% 0.13/0.34 % CPUTime :
% 118.56/15.55 Command-line arguments: --flip-ordering --lhs-weight 1 --depth-weight 60 --distributivity-heuristic
% 118.56/15.55
% 118.56/15.55 % SZS status Unsatisfiable
% 118.56/15.55
% 118.56/15.55 % SZS output start Proof
% 118.56/15.55 Take the following subset of the input axioms:
% 118.56/15.56 fof(cls_CHAINED_0, axiom, c_Power_Opower__class_Opower(c_NthRoot_Oroot(v_na____, c_RealVector_Onorm__class_Onorm(v_b, tc_Complex_Ocomplex)), v_na____, tc_RealDef_Oreal)=c_RealVector_Onorm__class_Onorm(v_b, tc_Complex_Ocomplex)).
% 118.56/15.56 fof(cls_complex__of__real__power_0, axiom, ![V_x, V_n]: c_Power_Opower__class_Opower(c_RealVector_Oof__real(V_x, tc_Complex_Ocomplex), V_n, tc_Complex_Ocomplex)=c_RealVector_Oof__real(c_Power_Opower__class_Opower(V_x, V_n, tc_RealDef_Oreal), tc_Complex_Ocomplex)).
% 118.56/15.56 fof(cls_conjecture_0, negated_conjecture, c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(v_v____, c_RealVector_Oof__real(c_NthRoot_Oroot(v_na____, c_RealVector_Onorm__class_Onorm(v_b, tc_Complex_Ocomplex)), tc_Complex_Ocomplex), tc_Complex_Ocomplex), v_na____, tc_Complex_Ocomplex)!=c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_v____, v_na____, tc_Complex_Ocomplex), c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex)).
% 118.56/15.56 fof(cls_power__divide_0, axiom, ![T_a, V_a, V_b, V_n2]: (~class_Ring__and__Field_Ofield(T_a) | (~class_Ring__and__Field_Odivision__by__zero(T_a) | c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(V_a, V_b, T_a), V_n2, T_a)=c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(V_a, V_n2, T_a), c_Power_Opower__class_Opower(V_b, V_n2, T_a), T_a)))).
% 118.56/15.56 fof(clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__by__zero, axiom, class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex)).
% 118.56/15.56 fof(clsarity_Complex__Ocomplex__Ring__and__Field_Ofield, axiom, class_Ring__and__Field_Ofield(tc_Complex_Ocomplex)).
% 118.56/15.56
% 118.56/15.56 Now clausify the problem and encode Horn clauses using encoding 3 of
% 118.56/15.56 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 118.56/15.56 We repeatedly replace C & s=t => u=v by the two clauses:
% 118.56/15.56 fresh(y, y, x1...xn) = u
% 118.56/15.56 C => fresh(s, t, x1...xn) = v
% 118.56/15.56 where fresh is a fresh function symbol and x1..xn are the free
% 118.56/15.56 variables of u and v.
% 118.56/15.56 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 118.56/15.56 input problem has no model of domain size 1).
% 118.56/15.56
% 118.56/15.56 The encoding turns the above axioms into the following unit equations and goals:
% 118.56/15.56
% 118.56/15.56 Axiom 1 (clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__by__zero): class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) = true2.
% 118.56/15.56 Axiom 2 (clsarity_Complex__Ocomplex__Ring__and__Field_Ofield): class_Ring__and__Field_Ofield(tc_Complex_Ocomplex) = true2.
% 118.56/15.56 Axiom 3 (cls_complex__of__real__power_0): c_Power_Opower__class_Opower(c_RealVector_Oof__real(X, tc_Complex_Ocomplex), Y, tc_Complex_Ocomplex) = c_RealVector_Oof__real(c_Power_Opower__class_Opower(X, Y, tc_RealDef_Oreal), tc_Complex_Ocomplex).
% 118.56/15.56 Axiom 4 (cls_power__divide_0): fresh780(X, X, Y, Z, W, V) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(Z, W, Y), V, Y).
% 118.56/15.56 Axiom 5 (cls_CHAINED_0): c_Power_Opower__class_Opower(c_NthRoot_Oroot(v_na____, c_RealVector_Onorm__class_Onorm(v_b, tc_Complex_Ocomplex)), v_na____, tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(v_b, tc_Complex_Ocomplex).
% 118.56/15.56 Axiom 6 (cls_power__divide_0): fresh779(X, X, Y, Z, W, V) = fresh780(class_Ring__and__Field_Odivision__by__zero(Y), true2, Y, Z, W, V).
% 118.56/15.56 Axiom 7 (cls_power__divide_0): fresh779(class_Ring__and__Field_Ofield(X), true2, X, Y, Z, W) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(Y, W, X), c_Power_Opower__class_Opower(Z, W, X), X).
% 118.56/15.56
% 118.56/15.56 Goal 1 (cls_conjecture_0): c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(v_v____, c_RealVector_Oof__real(c_NthRoot_Oroot(v_na____, c_RealVector_Onorm__class_Onorm(v_b, tc_Complex_Ocomplex)), tc_Complex_Ocomplex), tc_Complex_Ocomplex), v_na____, tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_v____, v_na____, tc_Complex_Ocomplex), c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex).
% 118.56/15.56 Proof:
% 118.56/15.56 c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(v_v____, c_RealVector_Oof__real(c_NthRoot_Oroot(v_na____, c_RealVector_Onorm__class_Onorm(v_b, tc_Complex_Ocomplex)), tc_Complex_Ocomplex), tc_Complex_Ocomplex), v_na____, tc_Complex_Ocomplex)
% 118.56/15.56 = { by axiom 4 (cls_power__divide_0) R->L }
% 118.56/15.56 fresh780(true2, true2, tc_Complex_Ocomplex, v_v____, c_RealVector_Oof__real(c_NthRoot_Oroot(v_na____, c_RealVector_Onorm__class_Onorm(v_b, tc_Complex_Ocomplex)), tc_Complex_Ocomplex), v_na____)
% 118.56/15.56 = { by axiom 1 (clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__by__zero) R->L }
% 118.56/15.56 fresh780(class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex), true2, tc_Complex_Ocomplex, v_v____, c_RealVector_Oof__real(c_NthRoot_Oroot(v_na____, c_RealVector_Onorm__class_Onorm(v_b, tc_Complex_Ocomplex)), tc_Complex_Ocomplex), v_na____)
% 118.56/15.56 = { by axiom 6 (cls_power__divide_0) R->L }
% 118.56/15.56 fresh779(true2, true2, tc_Complex_Ocomplex, v_v____, c_RealVector_Oof__real(c_NthRoot_Oroot(v_na____, c_RealVector_Onorm__class_Onorm(v_b, tc_Complex_Ocomplex)), tc_Complex_Ocomplex), v_na____)
% 118.56/15.56 = { by axiom 2 (clsarity_Complex__Ocomplex__Ring__and__Field_Ofield) R->L }
% 118.56/15.56 fresh779(class_Ring__and__Field_Ofield(tc_Complex_Ocomplex), true2, tc_Complex_Ocomplex, v_v____, c_RealVector_Oof__real(c_NthRoot_Oroot(v_na____, c_RealVector_Onorm__class_Onorm(v_b, tc_Complex_Ocomplex)), tc_Complex_Ocomplex), v_na____)
% 118.56/15.56 = { by axiom 7 (cls_power__divide_0) }
% 118.56/15.56 c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_v____, v_na____, tc_Complex_Ocomplex), c_Power_Opower__class_Opower(c_RealVector_Oof__real(c_NthRoot_Oroot(v_na____, c_RealVector_Onorm__class_Onorm(v_b, tc_Complex_Ocomplex)), tc_Complex_Ocomplex), v_na____, tc_Complex_Ocomplex), tc_Complex_Ocomplex)
% 118.56/15.56 = { by axiom 3 (cls_complex__of__real__power_0) }
% 118.56/15.56 c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_v____, v_na____, tc_Complex_Ocomplex), c_RealVector_Oof__real(c_Power_Opower__class_Opower(c_NthRoot_Oroot(v_na____, c_RealVector_Onorm__class_Onorm(v_b, tc_Complex_Ocomplex)), v_na____, tc_RealDef_Oreal), tc_Complex_Ocomplex), tc_Complex_Ocomplex)
% 118.56/15.56 = { by axiom 5 (cls_CHAINED_0) }
% 118.56/15.56 c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_v____, v_na____, tc_Complex_Ocomplex), c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex)
% 118.56/15.56 % SZS output end Proof
% 118.56/15.56
% 118.56/15.56 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------