TSTP Solution File: LCL431-2 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LCL431-2 : 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 : n010.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 08:18:55 EDT 2023
% Result : Unsatisfiable 0.19s 0.38s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : LCL431-2 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.34 % Computer : n010.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Thu Aug 24 23:03:21 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.19/0.38 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.19/0.38
% 0.19/0.38 % SZS status Unsatisfiable
% 0.19/0.38
% 0.19/0.38 % SZS output start Proof
% 0.19/0.38 Take the following subset of the input axioms:
% 0.19/0.38 fof(cls_PropLog_Ocompleteness__0__lemma__dest_0, axiom, ![V_p, T_a, V_U, V_t0]: (~c_PropLog_Osat(c_emptyset, V_p, T_a) | c_in(V_p, c_PropLog_Othms(c_minus(c_PropLog_Ohyps(V_p, V_U, T_a), c_PropLog_Ohyps(V_p, V_t0, T_a), tc_set(tc_PropLog_Opl(T_a))), T_a), tc_PropLog_Opl(T_a)))).
% 0.19/0.38 fof(cls_Set_ODiff__cancel_0, axiom, ![V_A, T_a2]: c_minus(V_A, V_A, tc_set(T_a2))=c_emptyset).
% 0.19/0.38 fof(cls_conjecture_0, negated_conjecture, c_PropLog_Osat(c_emptyset, v_p, t_a)).
% 0.19/0.38 fof(cls_conjecture_1, negated_conjecture, ~c_in(v_p, c_PropLog_Othms(c_emptyset, t_a), tc_PropLog_Opl(t_a))).
% 0.19/0.38
% 0.19/0.38 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.19/0.38 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.19/0.38 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.19/0.38 fresh(y, y, x1...xn) = u
% 0.19/0.38 C => fresh(s, t, x1...xn) = v
% 0.19/0.38 where fresh is a fresh function symbol and x1..xn are the free
% 0.19/0.38 variables of u and v.
% 0.19/0.38 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.19/0.38 input problem has no model of domain size 1).
% 0.19/0.38
% 0.19/0.38 The encoding turns the above axioms into the following unit equations and goals:
% 0.19/0.38
% 0.19/0.38 Axiom 1 (cls_conjecture_0): c_PropLog_Osat(c_emptyset, v_p, t_a) = true.
% 0.19/0.38 Axiom 2 (cls_Set_ODiff__cancel_0): c_minus(X, X, tc_set(Y)) = c_emptyset.
% 0.19/0.38 Axiom 3 (cls_PropLog_Ocompleteness__0__lemma__dest_0): fresh(X, X, Y, Z, W, V) = true.
% 0.19/0.38 Axiom 4 (cls_PropLog_Ocompleteness__0__lemma__dest_0): fresh(c_PropLog_Osat(c_emptyset, X, Y), true, X, Y, Z, W) = c_in(X, c_PropLog_Othms(c_minus(c_PropLog_Ohyps(X, Z, Y), c_PropLog_Ohyps(X, W, Y), tc_set(tc_PropLog_Opl(Y))), Y), tc_PropLog_Opl(Y)).
% 0.19/0.38
% 0.19/0.38 Goal 1 (cls_conjecture_1): c_in(v_p, c_PropLog_Othms(c_emptyset, t_a), tc_PropLog_Opl(t_a)) = true.
% 0.19/0.38 Proof:
% 0.19/0.38 c_in(v_p, c_PropLog_Othms(c_emptyset, t_a), tc_PropLog_Opl(t_a))
% 0.19/0.38 = { by axiom 2 (cls_Set_ODiff__cancel_0) R->L }
% 0.19/0.38 c_in(v_p, c_PropLog_Othms(c_minus(c_PropLog_Ohyps(v_p, X, t_a), c_PropLog_Ohyps(v_p, X, t_a), tc_set(tc_PropLog_Opl(t_a))), t_a), tc_PropLog_Opl(t_a))
% 0.19/0.38 = { by axiom 4 (cls_PropLog_Ocompleteness__0__lemma__dest_0) R->L }
% 0.19/0.38 fresh(c_PropLog_Osat(c_emptyset, v_p, t_a), true, v_p, t_a, X, X)
% 0.19/0.38 = { by axiom 1 (cls_conjecture_0) }
% 0.19/0.38 fresh(true, true, v_p, t_a, X, X)
% 0.19/0.38 = { by axiom 3 (cls_PropLog_Ocompleteness__0__lemma__dest_0) }
% 0.19/0.38 true
% 0.19/0.38 % SZS output end Proof
% 0.19/0.39
% 0.19/0.39 RESULT: Unsatisfiable (the axioms are contradictory).
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