TSTP Solution File: SWV824-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SWV824-1 : TPTP v8.1.2. Released v4.1.0.
% 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 : n017.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 23:06:25 EDT 2023
% Result : Unsatisfiable 39.06s 6.53s
% Output : Proof 39.06s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SWV824-1 : TPTP v8.1.2. Released v4.1.0.
% 0.06/0.13 % 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 : n017.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 : Tue Aug 29 05:00:43 EDT 2023
% 0.14/0.35 % CPUTime :
% 39.06/6.53 Command-line arguments: --no-flatten-goal
% 39.06/6.53
% 39.06/6.53 % SZS status Unsatisfiable
% 39.06/6.53
% 39.06/6.53 % SZS output start Proof
% 39.06/6.53 Take the following subset of the input axioms:
% 39.06/6.53 fof(cls_conjecture_0, negated_conjecture, v_fun1(v_x, v_xa)).
% 39.06/6.53 fof(cls_conjecture_1, negated_conjecture, c_Natural_Oevaln(v_com, v_xa, v_n, v_xb)).
% 39.06/6.53 fof(cls_conjecture_2, negated_conjecture, ~v_fun2(v_x, v_xb)).
% 39.06/6.53 fof(cls_conjecture_3, negated_conjecture, ![V_s, V_s_H, V_Z]: (v_fun2(V_Z, V_s_H) | (~c_Natural_Oevaln(v_com, V_s, c_Suc(v_n), V_s_H) | ~v_fun1(V_Z, V_s)))).
% 39.06/6.53 fof(cls_evaln__Suc_0, axiom, ![V_n, V_c, V_s2, V_s_H2]: (c_Natural_Oevaln(V_c, V_s2, c_Suc(V_n), V_s_H2) | ~c_Natural_Oevaln(V_c, V_s2, V_n, V_s_H2))).
% 39.06/6.53
% 39.06/6.53 Now clausify the problem and encode Horn clauses using encoding 3 of
% 39.06/6.54 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 39.06/6.54 We repeatedly replace C & s=t => u=v by the two clauses:
% 39.06/6.54 fresh(y, y, x1...xn) = u
% 39.06/6.54 C => fresh(s, t, x1...xn) = v
% 39.06/6.54 where fresh is a fresh function symbol and x1..xn are the free
% 39.06/6.54 variables of u and v.
% 39.06/6.54 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 39.06/6.54 input problem has no model of domain size 1).
% 39.06/6.54
% 39.06/6.54 The encoding turns the above axioms into the following unit equations and goals:
% 39.06/6.54
% 39.06/6.54 Axiom 1 (cls_conjecture_0): v_fun1(v_x, v_xa) = true2.
% 39.06/6.54 Axiom 2 (cls_conjecture_3): fresh455(X, X, Y, Z) = true2.
% 39.06/6.54 Axiom 3 (cls_conjecture_1): c_Natural_Oevaln(v_com, v_xa, v_n, v_xb) = true2.
% 39.06/6.54 Axiom 4 (cls_conjecture_3): fresh456(X, X, Y, Z, W) = v_fun2(Y, Z).
% 39.06/6.54 Axiom 5 (cls_evaln__Suc_0): fresh421(X, X, Y, Z, W, V) = true2.
% 39.06/6.54 Axiom 6 (cls_conjecture_3): fresh456(v_fun1(X, Y), true2, X, Z, Y) = fresh455(c_Natural_Oevaln(v_com, Y, c_Suc(v_n), Z), true2, X, Z).
% 39.06/6.54 Axiom 7 (cls_evaln__Suc_0): fresh421(c_Natural_Oevaln(X, Y, Z, W), true2, X, Y, Z, W) = c_Natural_Oevaln(X, Y, c_Suc(Z), W).
% 39.06/6.54
% 39.06/6.54 Goal 1 (cls_conjecture_2): v_fun2(v_x, v_xb) = true2.
% 39.06/6.54 Proof:
% 39.06/6.54 v_fun2(v_x, v_xb)
% 39.06/6.54 = { by axiom 4 (cls_conjecture_3) R->L }
% 39.06/6.54 fresh456(true2, true2, v_x, v_xb, v_xa)
% 39.06/6.54 = { by axiom 1 (cls_conjecture_0) R->L }
% 39.06/6.54 fresh456(v_fun1(v_x, v_xa), true2, v_x, v_xb, v_xa)
% 39.06/6.54 = { by axiom 6 (cls_conjecture_3) }
% 39.06/6.54 fresh455(c_Natural_Oevaln(v_com, v_xa, c_Suc(v_n), v_xb), true2, v_x, v_xb)
% 39.06/6.54 = { by axiom 7 (cls_evaln__Suc_0) R->L }
% 39.06/6.54 fresh455(fresh421(c_Natural_Oevaln(v_com, v_xa, v_n, v_xb), true2, v_com, v_xa, v_n, v_xb), true2, v_x, v_xb)
% 39.06/6.54 = { by axiom 3 (cls_conjecture_1) }
% 39.06/6.54 fresh455(fresh421(true2, true2, v_com, v_xa, v_n, v_xb), true2, v_x, v_xb)
% 39.06/6.54 = { by axiom 5 (cls_evaln__Suc_0) }
% 39.06/6.54 fresh455(true2, true2, v_x, v_xb)
% 39.06/6.54 = { by axiom 2 (cls_conjecture_3) }
% 39.06/6.54 true2
% 39.06/6.54 % SZS output end Proof
% 39.06/6.54
% 39.06/6.54 RESULT: Unsatisfiable (the axioms are contradictory).
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