TSTP Solution File: SWV616-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SWV616-1 : 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 : n032.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 23:05:37 EDT 2023
% Result : Unsatisfiable 107.13s 14.10s
% Output : Proof 107.13s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.09 % Problem : SWV616-1 : TPTP v8.1.2. Released v4.1.0.
% 0.06/0.10 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.10/0.29 % Computer : n032.cluster.edu
% 0.10/0.29 % Model : x86_64 x86_64
% 0.10/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.29 % Memory : 8042.1875MB
% 0.10/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.29 % CPULimit : 300
% 0.10/0.29 % WCLimit : 300
% 0.10/0.29 % DateTime : Tue Aug 29 10:03:46 EDT 2023
% 0.10/0.29 % CPUTime :
% 107.13/14.10 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 107.13/14.10
% 107.13/14.10 % SZS status Unsatisfiable
% 107.13/14.10
% 107.13/14.11 % SZS output start Proof
% 107.13/14.11 Take the following subset of the input axioms:
% 107.13/14.11 fof(cls_class__semiring_Opwr__pwr_0, axiom, ![T_a, V_x, V_q, V_p]: (~class_Ring__and__Field_Ocomm__semiring__1(T_a) | c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(V_x, V_p, T_a), V_q, T_a)=c_Power_Opower__class_Opower(V_x, c_HOL_Otimes__class_Otimes(V_p, V_q, tc_nat), T_a))).
% 107.13/14.11 fof(cls_conjecture_0, negated_conjecture, c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n), v_k, tc_Complex_Ocomplex), v_n, tc_Complex_Ocomplex), c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n), v_k, tc_Complex_Ocomplex), c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex)!=c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n), v_n, tc_Complex_Ocomplex), v_k, tc_Complex_Ocomplex), c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n), v_k, tc_Complex_Ocomplex), c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex)).
% 107.13/14.11 fof(cls_nat__mult__commute_0, axiom, ![V_m, V_n]: c_HOL_Otimes__class_Otimes(V_m, V_n, tc_nat)=c_HOL_Otimes__class_Otimes(V_n, V_m, tc_nat)).
% 107.13/14.11 fof(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1, axiom, class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex)).
% 107.13/14.11
% 107.13/14.11 Now clausify the problem and encode Horn clauses using encoding 3 of
% 107.13/14.11 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 107.13/14.11 We repeatedly replace C & s=t => u=v by the two clauses:
% 107.13/14.11 fresh(y, y, x1...xn) = u
% 107.13/14.11 C => fresh(s, t, x1...xn) = v
% 107.13/14.11 where fresh is a fresh function symbol and x1..xn are the free
% 107.13/14.11 variables of u and v.
% 107.13/14.11 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 107.13/14.11 input problem has no model of domain size 1).
% 107.13/14.11
% 107.13/14.11 The encoding turns the above axioms into the following unit equations and goals:
% 107.13/14.11
% 107.13/14.11 Axiom 1 (clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1): class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex) = true2.
% 107.13/14.11 Axiom 2 (cls_nat__mult__commute_0): c_HOL_Otimes__class_Otimes(X, Y, tc_nat) = c_HOL_Otimes__class_Otimes(Y, X, tc_nat).
% 107.13/14.11 Axiom 3 (cls_class__semiring_Opwr__pwr_0): fresh719(X, X, Y, Z, W, V) = c_Power_Opower__class_Opower(Z, c_HOL_Otimes__class_Otimes(W, V, tc_nat), Y).
% 107.13/14.11 Axiom 4 (cls_class__semiring_Opwr__pwr_0): fresh719(class_Ring__and__Field_Ocomm__semiring__1(X), true2, X, Y, Z, W) = c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(Y, Z, X), W, X).
% 107.13/14.11
% 107.13/14.11 Lemma 5: c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(X, Y, tc_Complex_Ocomplex), Z, tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(X, c_HOL_Otimes__class_Otimes(Y, Z, tc_nat), tc_Complex_Ocomplex).
% 107.13/14.11 Proof:
% 107.13/14.11 c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(X, Y, tc_Complex_Ocomplex), Z, tc_Complex_Ocomplex)
% 107.13/14.11 = { by axiom 4 (cls_class__semiring_Opwr__pwr_0) R->L }
% 107.13/14.11 fresh719(class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex), true2, tc_Complex_Ocomplex, X, Y, Z)
% 107.13/14.11 = { by axiom 1 (clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1) }
% 107.13/14.11 fresh719(true2, true2, tc_Complex_Ocomplex, X, Y, Z)
% 107.13/14.11 = { by axiom 3 (cls_class__semiring_Opwr__pwr_0) }
% 107.13/14.11 c_Power_Opower__class_Opower(X, c_HOL_Otimes__class_Otimes(Y, Z, tc_nat), tc_Complex_Ocomplex)
% 107.13/14.11
% 107.13/14.11 Goal 1 (cls_conjecture_0): c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n), v_k, tc_Complex_Ocomplex), v_n, tc_Complex_Ocomplex), c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n), v_k, tc_Complex_Ocomplex), c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n), v_n, tc_Complex_Ocomplex), v_k, tc_Complex_Ocomplex), c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n), v_k, tc_Complex_Ocomplex), c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex).
% 107.13/14.11 Proof:
% 107.13/14.11 c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n), v_k, tc_Complex_Ocomplex), v_n, tc_Complex_Ocomplex), c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n), v_k, tc_Complex_Ocomplex), c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex)
% 107.13/14.11 = { by lemma 5 }
% 107.13/14.12 c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n), c_HOL_Otimes__class_Otimes(v_k, v_n, tc_nat), tc_Complex_Ocomplex), c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n), v_k, tc_Complex_Ocomplex), c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex)
% 107.13/14.12 = { by axiom 2 (cls_nat__mult__commute_0) }
% 107.13/14.12 c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n), c_HOL_Otimes__class_Otimes(v_n, v_k, tc_nat), tc_Complex_Ocomplex), c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n), v_k, tc_Complex_Ocomplex), c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex)
% 107.13/14.12 = { by lemma 5 R->L }
% 107.13/14.12 c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n), v_n, tc_Complex_Ocomplex), v_k, tc_Complex_Ocomplex), c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n), v_k, tc_Complex_Ocomplex), c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex)
% 107.13/14.12 % SZS output end Proof
% 107.13/14.12
% 107.13/14.12 RESULT: Unsatisfiable (the axioms are contradictory).
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