TSTP Solution File: SET826-1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : SET826-1 : 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 : 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 15:33:22 EDT 2023
% Result : Unsatisfiable 85.26s 11.29s
% Output : Proof 85.26s
% 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 : SET826-1 : TPTP v8.1.2. Released v3.2.0.
% 0.12/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.34 % Computer : n010.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Aug 26 11:14:50 EDT 2023
% 0.13/0.34 % CPUTime :
% 85.26/11.29 Command-line arguments: --flip-ordering --lhs-weight 1 --depth-weight 60 --distributivity-heuristic
% 85.26/11.29
% 85.26/11.29 % SZS status Unsatisfiable
% 85.26/11.29
% 85.26/11.29 % SZS output start Proof
% 85.26/11.29 Take the following subset of the input axioms:
% 85.26/11.29 fof(cls_Set_OsubsetD_0, axiom, ![T_a, V_A, V_B, V_c]: (~c_in(V_c, V_A, T_a) | (~c_lessequals(V_A, V_B, tc_set(T_a)) | c_in(V_c, V_B, T_a)))).
% 85.26/11.29 fof(cls_conjecture_0, negated_conjecture, c_in(v_x, v_V, t_a)).
% 85.26/11.29 fof(cls_conjecture_1, negated_conjecture, c_lessequals(v_V, v_Y, tc_set(t_a))).
% 85.26/11.29 fof(cls_conjecture_3, negated_conjecture, ~c_in(v_x, v_Y, t_a)).
% 85.26/11.29
% 85.26/11.29 Now clausify the problem and encode Horn clauses using encoding 3 of
% 85.26/11.29 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 85.26/11.29 We repeatedly replace C & s=t => u=v by the two clauses:
% 85.26/11.29 fresh(y, y, x1...xn) = u
% 85.26/11.29 C => fresh(s, t, x1...xn) = v
% 85.26/11.29 where fresh is a fresh function symbol and x1..xn are the free
% 85.26/11.29 variables of u and v.
% 85.26/11.29 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 85.26/11.29 input problem has no model of domain size 1).
% 85.26/11.29
% 85.26/11.29 The encoding turns the above axioms into the following unit equations and goals:
% 85.26/11.29
% 85.26/11.29 Axiom 1 (cls_conjecture_0): c_in(v_x, v_V, t_a) = true2.
% 85.26/11.29 Axiom 2 (cls_conjecture_1): c_lessequals(v_V, v_Y, tc_set(t_a)) = true2.
% 85.26/11.29 Axiom 3 (cls_Set_OsubsetD_0): fresh985(X, X, Y, Z, W) = true2.
% 85.26/11.29 Axiom 4 (cls_Set_OsubsetD_0): fresh986(X, X, Y, Z, W, V) = c_in(Y, V, W).
% 85.26/11.29 Axiom 5 (cls_Set_OsubsetD_0): fresh986(c_lessequals(X, Y, tc_set(Z)), true2, W, X, Z, Y) = fresh985(c_in(W, X, Z), true2, W, Z, Y).
% 85.26/11.29
% 85.26/11.29 Goal 1 (cls_conjecture_3): c_in(v_x, v_Y, t_a) = true2.
% 85.26/11.29 Proof:
% 85.26/11.29 c_in(v_x, v_Y, t_a)
% 85.26/11.29 = { by axiom 4 (cls_Set_OsubsetD_0) R->L }
% 85.26/11.29 fresh986(true2, true2, v_x, v_V, t_a, v_Y)
% 85.26/11.29 = { by axiom 2 (cls_conjecture_1) R->L }
% 85.26/11.29 fresh986(c_lessequals(v_V, v_Y, tc_set(t_a)), true2, v_x, v_V, t_a, v_Y)
% 85.26/11.29 = { by axiom 5 (cls_Set_OsubsetD_0) }
% 85.26/11.29 fresh985(c_in(v_x, v_V, t_a), true2, v_x, t_a, v_Y)
% 85.26/11.29 = { by axiom 1 (cls_conjecture_0) }
% 85.26/11.29 fresh985(true2, true2, v_x, t_a, v_Y)
% 85.26/11.29 = { by axiom 3 (cls_Set_OsubsetD_0) }
% 85.26/11.29 true2
% 85.26/11.29 % SZS output end Proof
% 85.26/11.29
% 85.26/11.29 RESULT: Unsatisfiable (the axioms are contradictory).
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