TSTP Solution File: LCL436-2 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LCL436-2 : 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 : n007.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 08:18:57 EDT 2023
% Result : Unsatisfiable 0.21s 0.39s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : LCL436-2 : TPTP v8.1.2. Released v3.2.0.
% 0.11/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.35 % Computer : n007.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri Aug 25 05:54:55 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.39 Command-line arguments: --no-flatten-goal
% 0.21/0.39
% 0.21/0.39 % SZS status Unsatisfiable
% 0.21/0.39
% 0.21/0.39 % SZS output start Proof
% 0.21/0.39 Take the following subset of the input axioms:
% 0.21/0.39 fof(cls_PropLog_Othms_OS_0, axiom, ![V_p, V_q, V_r, T_a, V_H]: c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(V_p, c_PropLog_Opl_Oop_A_N_62(V_q, V_r, T_a), T_a), c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(V_p, V_q, T_a), c_PropLog_Opl_Oop_A_N_62(V_p, V_r, T_a), T_a), T_a), c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a))).
% 0.21/0.39 fof(cls_PropLog_Oweaken__right_0, axiom, ![V_p2, V_q2, T_a2, V_H2]: (~c_in(V_q2, c_PropLog_Othms(V_H2, T_a2), tc_PropLog_Opl(T_a2)) | c_in(c_PropLog_Opl_Oop_A_N_62(V_p2, V_q2, T_a2), c_PropLog_Othms(V_H2, T_a2), tc_PropLog_Opl(T_a2)))).
% 0.21/0.39 fof(cls_conjecture_0, negated_conjecture, ~c_in(c_PropLog_Opl_Oop_A_N_62(v_p, c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_pa, c_PropLog_Opl_Oop_A_N_62(v_q, v_r, t_a), t_a), c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_pa, v_q, t_a), c_PropLog_Opl_Oop_A_N_62(v_pa, v_r, t_a), t_a), t_a), t_a), c_PropLog_Othms(v_H, t_a), tc_PropLog_Opl(t_a))).
% 0.21/0.39
% 0.21/0.39 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.21/0.39 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.21/0.39 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.21/0.39 fresh(y, y, x1...xn) = u
% 0.21/0.39 C => fresh(s, t, x1...xn) = v
% 0.21/0.39 where fresh is a fresh function symbol and x1..xn are the free
% 0.21/0.39 variables of u and v.
% 0.21/0.39 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.21/0.39 input problem has no model of domain size 1).
% 0.21/0.39
% 0.21/0.39 The encoding turns the above axioms into the following unit equations and goals:
% 0.21/0.39
% 0.21/0.39 Axiom 1 (cls_PropLog_Oweaken__right_0): fresh(X, X, Y, Z, W, V) = true.
% 0.21/0.39 Axiom 2 (cls_PropLog_Oweaken__right_0): fresh(c_in(X, c_PropLog_Othms(Y, Z), tc_PropLog_Opl(Z)), true, X, Y, Z, W) = c_in(c_PropLog_Opl_Oop_A_N_62(W, X, Z), c_PropLog_Othms(Y, Z), tc_PropLog_Opl(Z)).
% 0.21/0.39 Axiom 3 (cls_PropLog_Othms_OS_0): c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(X, c_PropLog_Opl_Oop_A_N_62(Y, Z, W), W), c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(X, Y, W), c_PropLog_Opl_Oop_A_N_62(X, Z, W), W), W), c_PropLog_Othms(V, W), tc_PropLog_Opl(W)) = true.
% 0.21/0.39
% 0.21/0.39 Goal 1 (cls_conjecture_0): c_in(c_PropLog_Opl_Oop_A_N_62(v_p, c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_pa, c_PropLog_Opl_Oop_A_N_62(v_q, v_r, t_a), t_a), c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_pa, v_q, t_a), c_PropLog_Opl_Oop_A_N_62(v_pa, v_r, t_a), t_a), t_a), t_a), c_PropLog_Othms(v_H, t_a), tc_PropLog_Opl(t_a)) = true.
% 0.21/0.39 Proof:
% 0.21/0.39 c_in(c_PropLog_Opl_Oop_A_N_62(v_p, c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_pa, c_PropLog_Opl_Oop_A_N_62(v_q, v_r, t_a), t_a), c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_pa, v_q, t_a), c_PropLog_Opl_Oop_A_N_62(v_pa, v_r, t_a), t_a), t_a), t_a), c_PropLog_Othms(v_H, t_a), tc_PropLog_Opl(t_a))
% 0.21/0.39 = { by axiom 2 (cls_PropLog_Oweaken__right_0) R->L }
% 0.21/0.39 fresh(c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_pa, c_PropLog_Opl_Oop_A_N_62(v_q, v_r, t_a), t_a), c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_pa, v_q, t_a), c_PropLog_Opl_Oop_A_N_62(v_pa, v_r, t_a), t_a), t_a), c_PropLog_Othms(v_H, t_a), tc_PropLog_Opl(t_a)), true, c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_pa, c_PropLog_Opl_Oop_A_N_62(v_q, v_r, t_a), t_a), c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_pa, v_q, t_a), c_PropLog_Opl_Oop_A_N_62(v_pa, v_r, t_a), t_a), t_a), v_H, t_a, v_p)
% 0.21/0.39 = { by axiom 3 (cls_PropLog_Othms_OS_0) }
% 0.21/0.39 fresh(true, true, c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_pa, c_PropLog_Opl_Oop_A_N_62(v_q, v_r, t_a), t_a), c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_pa, v_q, t_a), c_PropLog_Opl_Oop_A_N_62(v_pa, v_r, t_a), t_a), t_a), v_H, t_a, v_p)
% 0.21/0.39 = { by axiom 1 (cls_PropLog_Oweaken__right_0) }
% 0.21/0.39 true
% 0.21/0.39 % SZS output end Proof
% 0.21/0.39
% 0.21/0.39 RESULT: Unsatisfiable (the axioms are contradictory).
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