TSTP Solution File: LCL441-2 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : LCL441-2 : 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 : 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 08:18:59 EDT 2023
% Result : Unsatisfiable 0.10s 0.31s
% Output : Proof 0.10s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08 % Problem : LCL441-2 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.09 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.10/0.28 % Computer : n032.cluster.edu
% 0.10/0.28 % Model : x86_64 x86_64
% 0.10/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.28 % Memory : 8042.1875MB
% 0.10/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.28 % CPULimit : 300
% 0.10/0.28 % WCLimit : 300
% 0.10/0.28 % DateTime : Fri Aug 25 00:16:42 EDT 2023
% 0.10/0.29 % CPUTime :
% 0.10/0.31 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.10/0.31
% 0.10/0.31 % SZS status Unsatisfiable
% 0.10/0.31
% 0.10/0.31 % SZS output start Proof
% 0.10/0.31 Take the following subset of the input axioms:
% 0.10/0.31 fof(cls_PropLog_Othms_OH_0, axiom, ![V_p, V_H, T_a]: (~c_in(V_p, V_H, tc_PropLog_Opl(T_a)) | c_in(V_p, c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a)))).
% 0.10/0.31 fof(cls_Set_OinsertCI_1, axiom, ![V_x, V_B, T_a2]: c_in(V_x, c_insert(V_x, V_B, T_a2), T_a2)).
% 0.10/0.31 fof(cls_conjecture_3, negated_conjecture, ~c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_a, t_a), c_PropLog_Opl_Ofalse, t_a), c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_a, t_a), c_PropLog_Opl_Ofalse, t_a), c_emptyset, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)) | ~c_in(c_PropLog_Opl_Ovar(v_a, t_a), c_PropLog_Othms(c_insert(c_PropLog_Opl_Ovar(v_a, t_a), c_emptyset, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a))).
% 0.10/0.31
% 0.10/0.31 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.10/0.31 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.10/0.31 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.10/0.31 fresh(y, y, x1...xn) = u
% 0.10/0.31 C => fresh(s, t, x1...xn) = v
% 0.10/0.31 where fresh is a fresh function symbol and x1..xn are the free
% 0.10/0.31 variables of u and v.
% 0.10/0.31 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.10/0.31 input problem has no model of domain size 1).
% 0.10/0.31
% 0.10/0.31 The encoding turns the above axioms into the following unit equations and goals:
% 0.10/0.31
% 0.10/0.31 Axiom 1 (cls_PropLog_Othms_OH_0): fresh(X, X, Y, Z, W) = true.
% 0.10/0.31 Axiom 2 (cls_Set_OinsertCI_1): c_in(X, c_insert(X, Y, Z), Z) = true.
% 0.10/0.31 Axiom 3 (cls_PropLog_Othms_OH_0): fresh(c_in(X, Y, tc_PropLog_Opl(Z)), true, X, Y, Z) = c_in(X, c_PropLog_Othms(Y, Z), tc_PropLog_Opl(Z)).
% 0.10/0.31
% 0.10/0.31 Lemma 4: c_in(X, c_PropLog_Othms(c_insert(X, Y, tc_PropLog_Opl(Z)), Z), tc_PropLog_Opl(Z)) = true.
% 0.10/0.31 Proof:
% 0.10/0.31 c_in(X, c_PropLog_Othms(c_insert(X, Y, tc_PropLog_Opl(Z)), Z), tc_PropLog_Opl(Z))
% 0.10/0.31 = { by axiom 3 (cls_PropLog_Othms_OH_0) R->L }
% 0.10/0.31 fresh(c_in(X, c_insert(X, Y, tc_PropLog_Opl(Z)), tc_PropLog_Opl(Z)), true, X, c_insert(X, Y, tc_PropLog_Opl(Z)), Z)
% 0.10/0.31 = { by axiom 2 (cls_Set_OinsertCI_1) }
% 0.10/0.31 fresh(true, true, X, c_insert(X, Y, tc_PropLog_Opl(Z)), Z)
% 0.10/0.31 = { by axiom 1 (cls_PropLog_Othms_OH_0) }
% 0.10/0.31 true
% 0.10/0.31
% 0.10/0.31 Goal 1 (cls_conjecture_3): tuple(c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_a, t_a), c_PropLog_Opl_Ofalse, t_a), c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_a, t_a), c_PropLog_Opl_Ofalse, t_a), c_emptyset, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)), c_in(c_PropLog_Opl_Ovar(v_a, t_a), c_PropLog_Othms(c_insert(c_PropLog_Opl_Ovar(v_a, t_a), c_emptyset, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a))) = tuple(true, true).
% 0.10/0.31 Proof:
% 0.10/0.31 tuple(c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_a, t_a), c_PropLog_Opl_Ofalse, t_a), c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_a, t_a), c_PropLog_Opl_Ofalse, t_a), c_emptyset, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)), c_in(c_PropLog_Opl_Ovar(v_a, t_a), c_PropLog_Othms(c_insert(c_PropLog_Opl_Ovar(v_a, t_a), c_emptyset, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)))
% 0.10/0.31 = { by lemma 4 }
% 0.10/0.31 tuple(true, c_in(c_PropLog_Opl_Ovar(v_a, t_a), c_PropLog_Othms(c_insert(c_PropLog_Opl_Ovar(v_a, t_a), c_emptyset, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)))
% 0.10/0.31 = { by lemma 4 }
% 0.10/0.31 tuple(true, true)
% 0.10/0.31 % SZS output end Proof
% 0.10/0.31
% 0.10/0.31 RESULT: Unsatisfiable (the axioms are contradictory).
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