TSTP Solution File: LAT271-2 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : LAT271-2 : 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 : n025.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 06:28:03 EDT 2023
% Result : Unsatisfiable 0.21s 0.40s
% 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
% 0.00/0.14 % Problem : LAT271-2 : TPTP v8.1.2. Released v3.2.0.
% 0.14/0.15 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.36 % Computer : n025.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Thu Aug 24 07:36:51 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.21/0.40 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.21/0.40
% 0.21/0.40 % SZS status Unsatisfiable
% 0.21/0.40
% 0.21/0.40 % SZS output start Proof
% 0.21/0.40 Take the following subset of the input axioms:
% 0.21/0.40 fof(cls_Tarski_O_91_124_AS1_A_60_61_Ainterval_Ar_Aa1_Ab1_59_Ax1_A_58_AS1_A_124_93_A_61_61_62_A_Ia1_M_Ax1_J_A_58_Ar_A_61_61_ATrue_0, axiom, ![V_x, V_S, T_a, V_r, V_a, V_b]: (~c_in(V_x, V_S, T_a) | (~c_lessequals(V_S, c_Tarski_Ointerval(V_r, V_a, V_b, T_a), tc_set(T_a)) | c_in(c_Pair(V_a, V_x, T_a, T_a), V_r, tc_prod(T_a, T_a))))).
% 0.21/0.40 fof(cls_conjecture_2, negated_conjecture, c_lessequals(v_S, c_Tarski_Ointerval(v_r, v_a, v_b, t_a), tc_set(t_a))).
% 0.21/0.40 fof(cls_conjecture_6, negated_conjecture, c_in(v_x, v_S, t_a)).
% 0.21/0.40 fof(cls_conjecture_7, negated_conjecture, ~c_in(c_Pair(v_a, v_x, t_a, t_a), v_r, tc_prod(t_a, t_a))).
% 0.21/0.40
% 0.21/0.40 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.21/0.40 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.21/0.40 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.21/0.40 fresh(y, y, x1...xn) = u
% 0.21/0.40 C => fresh(s, t, x1...xn) = v
% 0.21/0.40 where fresh is a fresh function symbol and x1..xn are the free
% 0.21/0.40 variables of u and v.
% 0.21/0.40 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.21/0.40 input problem has no model of domain size 1).
% 0.21/0.40
% 0.21/0.40 The encoding turns the above axioms into the following unit equations and goals:
% 0.21/0.40
% 0.21/0.40 Axiom 1 (cls_conjecture_6): c_in(v_x, v_S, t_a) = true.
% 0.21/0.40 Axiom 2 (cls_Tarski_O_91_124_AS1_A_60_61_Ainterval_Ar_Aa1_Ab1_59_Ax1_A_58_AS1_A_124_93_A_61_61_62_A_Ia1_M_Ax1_J_A_58_Ar_A_61_61_ATrue_0): fresh2(X, X, Y, Z, W, V) = true.
% 0.21/0.40 Axiom 3 (cls_conjecture_2): c_lessequals(v_S, c_Tarski_Ointerval(v_r, v_a, v_b, t_a), tc_set(t_a)) = true.
% 0.21/0.40 Axiom 4 (cls_Tarski_O_91_124_AS1_A_60_61_Ainterval_Ar_Aa1_Ab1_59_Ax1_A_58_AS1_A_124_93_A_61_61_62_A_Ia1_M_Ax1_J_A_58_Ar_A_61_61_ATrue_0): fresh(X, X, Y, Z, W, V, U, T) = c_in(c_Pair(U, Y, W, W), V, tc_prod(W, W)).
% 0.21/0.40 Axiom 5 (cls_Tarski_O_91_124_AS1_A_60_61_Ainterval_Ar_Aa1_Ab1_59_Ax1_A_58_AS1_A_124_93_A_61_61_62_A_Ia1_M_Ax1_J_A_58_Ar_A_61_61_ATrue_0): fresh(c_in(X, Y, Z), true, X, Y, Z, W, V, U) = fresh2(c_lessequals(Y, c_Tarski_Ointerval(W, V, U, Z), tc_set(Z)), true, X, Z, W, V).
% 0.21/0.40
% 0.21/0.40 Goal 1 (cls_conjecture_7): c_in(c_Pair(v_a, v_x, t_a, t_a), v_r, tc_prod(t_a, t_a)) = true.
% 0.21/0.40 Proof:
% 0.21/0.40 c_in(c_Pair(v_a, v_x, t_a, t_a), v_r, tc_prod(t_a, t_a))
% 0.21/0.40 = { by axiom 4 (cls_Tarski_O_91_124_AS1_A_60_61_Ainterval_Ar_Aa1_Ab1_59_Ax1_A_58_AS1_A_124_93_A_61_61_62_A_Ia1_M_Ax1_J_A_58_Ar_A_61_61_ATrue_0) R->L }
% 0.21/0.40 fresh(true, true, v_x, v_S, t_a, v_r, v_a, v_b)
% 0.21/0.40 = { by axiom 1 (cls_conjecture_6) R->L }
% 0.21/0.40 fresh(c_in(v_x, v_S, t_a), true, v_x, v_S, t_a, v_r, v_a, v_b)
% 0.21/0.40 = { by axiom 5 (cls_Tarski_O_91_124_AS1_A_60_61_Ainterval_Ar_Aa1_Ab1_59_Ax1_A_58_AS1_A_124_93_A_61_61_62_A_Ia1_M_Ax1_J_A_58_Ar_A_61_61_ATrue_0) }
% 0.21/0.40 fresh2(c_lessequals(v_S, c_Tarski_Ointerval(v_r, v_a, v_b, t_a), tc_set(t_a)), true, v_x, t_a, v_r, v_a)
% 0.21/0.40 = { by axiom 3 (cls_conjecture_2) }
% 0.21/0.40 fresh2(true, true, v_x, t_a, v_r, v_a)
% 0.21/0.40 = { by axiom 2 (cls_Tarski_O_91_124_AS1_A_60_61_Ainterval_Ar_Aa1_Ab1_59_Ax1_A_58_AS1_A_124_93_A_61_61_62_A_Ia1_M_Ax1_J_A_58_Ar_A_61_61_ATrue_0) }
% 0.21/0.40 true
% 0.21/0.40 % SZS output end Proof
% 0.21/0.40
% 0.21/0.41 RESULT: Unsatisfiable (the axioms are contradictory).
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