TSTP Solution File: LCL441-1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : LCL441-1 : 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 : n018.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 46.02s 6.24s
% Output : Proof 46.02s
% 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 : LCL441-1 : 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
% 0.13/0.35 % Computer : n018.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Thu Aug 24 19:25:58 EDT 2023
% 0.13/0.35 % CPUTime :
% 46.02/6.24 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 46.02/6.24
% 46.02/6.24 % SZS status Unsatisfiable
% 46.02/6.24
% 46.02/6.25 % SZS output start Proof
% 46.02/6.25 Take the following subset of the input axioms:
% 46.02/6.25 fof(cls_PropLog_Othms_OH_0, axiom, ![T_a, V_p, V_H]: (~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)))).
% 46.02/6.25 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)).
% 46.02/6.25 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))).
% 46.02/6.25
% 46.02/6.25 Now clausify the problem and encode Horn clauses using encoding 3 of
% 46.02/6.25 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 46.02/6.25 We repeatedly replace C & s=t => u=v by the two clauses:
% 46.02/6.25 fresh(y, y, x1...xn) = u
% 46.02/6.25 C => fresh(s, t, x1...xn) = v
% 46.02/6.25 where fresh is a fresh function symbol and x1..xn are the free
% 46.02/6.25 variables of u and v.
% 46.02/6.25 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 46.02/6.25 input problem has no model of domain size 1).
% 46.02/6.25
% 46.02/6.25 The encoding turns the above axioms into the following unit equations and goals:
% 46.02/6.25
% 46.02/6.25 Axiom 1 (cls_Set_OinsertCI_1): c_in(X, c_insert(X, Y, Z), Z) = true2.
% 46.02/6.25 Axiom 2 (cls_PropLog_Othms_OH_0): fresh1071(X, X, Y, Z, W) = true2.
% 46.02/6.25 Axiom 3 (cls_PropLog_Othms_OH_0): fresh1071(c_in(X, Y, tc_PropLog_Opl(Z)), true2, X, Y, Z) = c_in(X, c_PropLog_Othms(Y, Z), tc_PropLog_Opl(Z)).
% 46.02/6.25
% 46.02/6.25 Lemma 4: c_in(X, c_PropLog_Othms(c_insert(X, Y, tc_PropLog_Opl(Z)), Z), tc_PropLog_Opl(Z)) = true2.
% 46.02/6.25 Proof:
% 46.02/6.25 c_in(X, c_PropLog_Othms(c_insert(X, Y, tc_PropLog_Opl(Z)), Z), tc_PropLog_Opl(Z))
% 46.02/6.25 = { by axiom 3 (cls_PropLog_Othms_OH_0) R->L }
% 46.02/6.25 fresh1071(c_in(X, c_insert(X, Y, tc_PropLog_Opl(Z)), tc_PropLog_Opl(Z)), true2, X, c_insert(X, Y, tc_PropLog_Opl(Z)), Z)
% 46.02/6.25 = { by axiom 1 (cls_Set_OinsertCI_1) }
% 46.02/6.25 fresh1071(true2, true2, X, c_insert(X, Y, tc_PropLog_Opl(Z)), Z)
% 46.02/6.25 = { by axiom 2 (cls_PropLog_Othms_OH_0) }
% 46.02/6.25 true2
% 46.02/6.25
% 46.02/6.25 Goal 1 (cls_conjecture_3): tuple(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)), 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))) = tuple(true2, true2).
% 46.02/6.25 Proof:
% 46.02/6.25 tuple(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)), 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)))
% 46.02/6.25 = { by lemma 4 }
% 46.02/6.25 tuple(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)), true2)
% 46.02/6.25 = { by lemma 4 }
% 46.02/6.25 tuple(true2, true2)
% 46.02/6.25 % SZS output end Proof
% 46.02/6.25
% 46.02/6.25 RESULT: Unsatisfiable (the axioms are contradictory).
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