TSTP Solution File: LCL440-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LCL440-1 : TPTP v8.1.2. Released v3.2.0.
% 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 : 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 : Thu Aug 31 08:18:58 EDT 2023
% Result : Unsatisfiable 43.71s 5.99s
% Output : Proof 43.71s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL440-1 : TPTP v8.1.2. Released v3.2.0.
% 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 : n013.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 : Fri Aug 25 07:12:02 EDT 2023
% 0.16/0.34 % CPUTime :
% 43.71/5.99 Command-line arguments: --no-flatten-goal
% 43.71/5.99
% 43.71/5.99 % SZS status Unsatisfiable
% 43.71/5.99
% 43.71/5.99 % SZS output start Proof
% 43.71/5.99 Take the following subset of the input axioms:
% 43.71/5.99 fof(cls_PropLog_Othms__I_0, axiom, ![T_a, V_p, V_H]: c_in(c_PropLog_Opl_Oop_A_N_62(V_p, V_p, T_a), c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a))).
% 43.71/5.99 fof(cls_conjecture_0, negated_conjecture, ~c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ofalse, c_PropLog_Opl_Ofalse, t_a), c_PropLog_Othms(c_emptyset, t_a), tc_PropLog_Opl(t_a))).
% 43.71/5.99
% 43.71/5.99 Now clausify the problem and encode Horn clauses using encoding 3 of
% 43.71/5.99 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 43.71/5.99 We repeatedly replace C & s=t => u=v by the two clauses:
% 43.71/5.99 fresh(y, y, x1...xn) = u
% 43.71/5.99 C => fresh(s, t, x1...xn) = v
% 43.71/5.99 where fresh is a fresh function symbol and x1..xn are the free
% 43.71/5.99 variables of u and v.
% 43.71/5.99 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 43.71/5.99 input problem has no model of domain size 1).
% 43.71/5.99
% 43.71/5.99 The encoding turns the above axioms into the following unit equations and goals:
% 43.71/5.99
% 43.71/5.99 Axiom 1 (cls_PropLog_Othms__I_0): c_in(c_PropLog_Opl_Oop_A_N_62(X, X, Y), c_PropLog_Othms(Z, Y), tc_PropLog_Opl(Y)) = true2.
% 43.71/5.99
% 43.71/5.99 Goal 1 (cls_conjecture_0): c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ofalse, c_PropLog_Opl_Ofalse, t_a), c_PropLog_Othms(c_emptyset, t_a), tc_PropLog_Opl(t_a)) = true2.
% 43.71/5.99 Proof:
% 43.71/5.99 c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ofalse, c_PropLog_Opl_Ofalse, t_a), c_PropLog_Othms(c_emptyset, t_a), tc_PropLog_Opl(t_a))
% 43.71/5.99 = { by axiom 1 (cls_PropLog_Othms__I_0) }
% 43.71/5.99 true2
% 43.71/5.99 % SZS output end Proof
% 43.71/5.99
% 43.71/5.99 RESULT: Unsatisfiable (the axioms are contradictory).
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