TSTP Solution File: ANA028-2 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : ANA028-2 : 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 : n021.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 : Wed Aug 30 17:21:08 EDT 2023
% Result : Unsatisfiable 0.20s 0.55s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : ANA028-2 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.18/0.35 % Computer : n021.cluster.edu
% 0.18/0.35 % Model : x86_64 x86_64
% 0.18/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.35 % Memory : 8042.1875MB
% 0.18/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.35 % CPULimit : 300
% 0.18/0.35 % WCLimit : 300
% 0.18/0.35 % DateTime : Fri Aug 25 18:15:11 EDT 2023
% 0.18/0.35 % CPUTime :
% 0.20/0.55 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 0.20/0.55
% 0.20/0.55 % SZS status Unsatisfiable
% 0.20/0.55
% 0.20/0.56 % SZS output start Proof
% 0.20/0.56 Take the following subset of the input axioms:
% 0.20/0.56 fof(cls_OrderedGroup_Ocomm__monoid__add__class_Oaxioms_0, axiom, ![T_a, V_y]: (~class_OrderedGroup_Ocomm__monoid__add(T_a) | c_plus(c_0, V_y, T_a)=V_y)).
% 0.20/0.56 fof(cls_OrderedGroup_Ocompare__rls__3_0, axiom, ![V_a, V_b, V_c, T_a2]: (~class_OrderedGroup_Oab__group__add(T_a2) | c_plus(c_minus(V_a, V_b, T_a2), V_c, T_a2)=c_minus(c_plus(V_a, V_c, T_a2), V_b, T_a2))).
% 0.20/0.56 fof(cls_OrderedGroup_Ocompare__rls__5_0, axiom, ![T_a2, V_a2, V_b2, V_c2]: (~class_OrderedGroup_Oab__group__add(T_a2) | c_minus(V_a2, c_minus(V_b2, V_c2, T_a2), T_a2)=c_minus(c_plus(V_a2, V_c2, T_a2), V_b2, T_a2))).
% 0.20/0.56 fof(cls_OrderedGroup_Ocompare__rls__8_1, axiom, ![T_a2, V_a2, V_b2, V_c2]: (~class_OrderedGroup_Opordered__ab__group__add(T_a2) | (~c_lessequals(V_a2, c_plus(V_c2, V_b2, T_a2), T_a2) | c_lessequals(c_minus(V_a2, V_b2, T_a2), V_c2, T_a2)))).
% 0.20/0.56 fof(cls_OrderedGroup_Odiff__self_0, axiom, ![T_a2, V_a2]: (~class_OrderedGroup_Oab__group__add(T_a2) | c_minus(V_a2, V_a2, T_a2)=c_0)).
% 0.20/0.56 fof(cls_conjecture_1, negated_conjecture, ![V_U]: c_lessequals(v_g(V_U), v_k(V_U), t_b)).
% 0.20/0.56 fof(cls_conjecture_3, negated_conjecture, ~c_lessequals(c_minus(v_f(v_x), v_k(v_x), t_b), c_minus(v_f(v_x), v_g(v_x), t_b), t_b)).
% 0.20/0.56 fof(clsrel_Ring__and__Field_Oordered__idom_23, axiom, ![T]: (~class_Ring__and__Field_Oordered__idom(T) | class_OrderedGroup_Ocomm__monoid__add(T))).
% 0.20/0.56 fof(clsrel_Ring__and__Field_Oordered__idom_4, axiom, ![T2]: (~class_Ring__and__Field_Oordered__idom(T2) | class_OrderedGroup_Oab__group__add(T2))).
% 0.20/0.56 fof(clsrel_Ring__and__Field_Oordered__idom_54, axiom, ![T2]: (~class_Ring__and__Field_Oordered__idom(T2) | class_OrderedGroup_Opordered__ab__group__add(T2))).
% 0.20/0.56 fof(tfree_tcs, negated_conjecture, class_Ring__and__Field_Oordered__idom(t_b)).
% 0.20/0.56
% 0.20/0.56 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.20/0.56 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.20/0.56 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.20/0.56 fresh(y, y, x1...xn) = u
% 0.20/0.56 C => fresh(s, t, x1...xn) = v
% 0.20/0.56 where fresh is a fresh function symbol and x1..xn are the free
% 0.20/0.56 variables of u and v.
% 0.20/0.56 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.20/0.56 input problem has no model of domain size 1).
% 0.20/0.56
% 0.20/0.56 The encoding turns the above axioms into the following unit equations and goals:
% 0.20/0.56
% 0.20/0.56 Axiom 1 (tfree_tcs): class_Ring__and__Field_Oordered__idom(t_b) = true.
% 0.20/0.56 Axiom 2 (clsrel_Ring__and__Field_Oordered__idom_23): fresh4(X, X, Y) = true.
% 0.20/0.56 Axiom 3 (clsrel_Ring__and__Field_Oordered__idom_4): fresh3(X, X, Y) = true.
% 0.20/0.56 Axiom 4 (clsrel_Ring__and__Field_Oordered__idom_54): fresh2(X, X, Y) = true.
% 0.20/0.56 Axiom 5 (cls_OrderedGroup_Ocomm__monoid__add__class_Oaxioms_0): fresh(X, X, Y, Z) = Z.
% 0.20/0.56 Axiom 6 (cls_OrderedGroup_Odiff__self_0): fresh5(X, X, Y, Z) = c_0.
% 0.20/0.56 Axiom 7 (clsrel_Ring__and__Field_Oordered__idom_23): fresh4(class_Ring__and__Field_Oordered__idom(X), true, X) = class_OrderedGroup_Ocomm__monoid__add(X).
% 0.20/0.56 Axiom 8 (clsrel_Ring__and__Field_Oordered__idom_4): fresh3(class_Ring__and__Field_Oordered__idom(X), true, X) = class_OrderedGroup_Oab__group__add(X).
% 0.20/0.56 Axiom 9 (clsrel_Ring__and__Field_Oordered__idom_54): fresh2(class_Ring__and__Field_Oordered__idom(X), true, X) = class_OrderedGroup_Opordered__ab__group__add(X).
% 0.20/0.56 Axiom 10 (cls_conjecture_1): c_lessequals(v_g(X), v_k(X), t_b) = true.
% 0.20/0.56 Axiom 11 (cls_OrderedGroup_Ocomm__monoid__add__class_Oaxioms_0): fresh(class_OrderedGroup_Ocomm__monoid__add(X), true, X, Y) = c_plus(c_0, Y, X).
% 0.20/0.56 Axiom 12 (cls_OrderedGroup_Odiff__self_0): fresh5(class_OrderedGroup_Oab__group__add(X), true, X, Y) = c_minus(Y, Y, X).
% 0.20/0.56 Axiom 13 (cls_OrderedGroup_Ocompare__rls__3_0): fresh12(X, X, Y, Z, W, V) = c_minus(c_plus(Z, V, Y), W, Y).
% 0.20/0.56 Axiom 14 (cls_OrderedGroup_Ocompare__rls__5_0): fresh10(X, X, Y, Z, W, V) = c_minus(c_plus(Z, V, Y), W, Y).
% 0.20/0.56 Axiom 15 (cls_OrderedGroup_Ocompare__rls__8_1): fresh9(X, X, Y, Z, W, V) = c_lessequals(c_minus(Z, V, Y), W, Y).
% 0.20/0.56 Axiom 16 (cls_OrderedGroup_Ocompare__rls__8_1): fresh8(X, X, Y, Z, W, V) = true.
% 0.20/0.56 Axiom 17 (cls_OrderedGroup_Ocompare__rls__3_0): fresh12(class_OrderedGroup_Oab__group__add(X), true, X, Y, Z, W) = c_plus(c_minus(Y, Z, X), W, X).
% 0.20/0.56 Axiom 18 (cls_OrderedGroup_Ocompare__rls__5_0): fresh10(class_OrderedGroup_Oab__group__add(X), true, X, Y, Z, W) = c_minus(Y, c_minus(Z, W, X), X).
% 0.20/0.56 Axiom 19 (cls_OrderedGroup_Ocompare__rls__8_1): fresh9(c_lessequals(X, c_plus(Y, Z, W), W), true, W, X, Y, Z) = fresh8(class_OrderedGroup_Opordered__ab__group__add(W), true, W, X, Y, Z).
% 0.20/0.56
% 0.20/0.56 Lemma 20: class_OrderedGroup_Oab__group__add(t_b) = true.
% 0.20/0.56 Proof:
% 0.20/0.56 class_OrderedGroup_Oab__group__add(t_b)
% 0.20/0.56 = { by axiom 8 (clsrel_Ring__and__Field_Oordered__idom_4) R->L }
% 0.20/0.56 fresh3(class_Ring__and__Field_Oordered__idom(t_b), true, t_b)
% 0.20/0.56 = { by axiom 1 (tfree_tcs) }
% 0.20/0.56 fresh3(true, true, t_b)
% 0.20/0.56 = { by axiom 3 (clsrel_Ring__and__Field_Oordered__idom_4) }
% 0.20/0.56 true
% 0.20/0.56
% 0.20/0.56 Lemma 21: c_plus(c_0, X, t_b) = X.
% 0.20/0.56 Proof:
% 0.20/0.56 c_plus(c_0, X, t_b)
% 0.20/0.56 = { by axiom 11 (cls_OrderedGroup_Ocomm__monoid__add__class_Oaxioms_0) R->L }
% 0.20/0.56 fresh(class_OrderedGroup_Ocomm__monoid__add(t_b), true, t_b, X)
% 0.20/0.56 = { by axiom 7 (clsrel_Ring__and__Field_Oordered__idom_23) R->L }
% 0.20/0.56 fresh(fresh4(class_Ring__and__Field_Oordered__idom(t_b), true, t_b), true, t_b, X)
% 0.20/0.56 = { by axiom 1 (tfree_tcs) }
% 0.20/0.56 fresh(fresh4(true, true, t_b), true, t_b, X)
% 0.20/0.56 = { by axiom 2 (clsrel_Ring__and__Field_Oordered__idom_23) }
% 0.20/0.56 fresh(true, true, t_b, X)
% 0.20/0.56 = { by axiom 5 (cls_OrderedGroup_Ocomm__monoid__add__class_Oaxioms_0) }
% 0.20/0.56 X
% 0.20/0.56
% 0.20/0.56 Lemma 22: c_minus(c_plus(X, Y, t_b), Z, t_b) = c_minus(X, c_minus(Z, Y, t_b), t_b).
% 0.20/0.56 Proof:
% 0.20/0.56 c_minus(c_plus(X, Y, t_b), Z, t_b)
% 0.20/0.56 = { by axiom 14 (cls_OrderedGroup_Ocompare__rls__5_0) R->L }
% 0.20/0.56 fresh10(true, true, t_b, X, Z, Y)
% 0.20/0.56 = { by lemma 20 R->L }
% 0.20/0.56 fresh10(class_OrderedGroup_Oab__group__add(t_b), true, t_b, X, Z, Y)
% 0.20/0.56 = { by axiom 18 (cls_OrderedGroup_Ocompare__rls__5_0) }
% 0.20/0.56 c_minus(X, c_minus(Z, Y, t_b), t_b)
% 0.20/0.56
% 0.20/0.56 Lemma 23: c_plus(c_minus(X, Y, t_b), Z, t_b) = c_minus(X, c_minus(Y, Z, t_b), t_b).
% 0.20/0.56 Proof:
% 0.20/0.56 c_plus(c_minus(X, Y, t_b), Z, t_b)
% 0.20/0.56 = { by axiom 17 (cls_OrderedGroup_Ocompare__rls__3_0) R->L }
% 0.20/0.56 fresh12(class_OrderedGroup_Oab__group__add(t_b), true, t_b, X, Y, Z)
% 0.20/0.56 = { by lemma 20 }
% 0.20/0.56 fresh12(true, true, t_b, X, Y, Z)
% 0.20/0.56 = { by axiom 13 (cls_OrderedGroup_Ocompare__rls__3_0) }
% 0.20/0.56 c_minus(c_plus(X, Z, t_b), Y, t_b)
% 0.20/0.56 = { by lemma 22 }
% 0.20/0.56 c_minus(X, c_minus(Y, Z, t_b), t_b)
% 0.20/0.56
% 0.20/0.56 Lemma 24: c_minus(X, c_minus(X, Y, t_b), t_b) = Y.
% 0.20/0.56 Proof:
% 0.20/0.56 c_minus(X, c_minus(X, Y, t_b), t_b)
% 0.20/0.56 = { by lemma 23 R->L }
% 0.20/0.56 c_plus(c_minus(X, X, t_b), Y, t_b)
% 0.20/0.56 = { by axiom 12 (cls_OrderedGroup_Odiff__self_0) R->L }
% 0.20/0.56 c_plus(fresh5(class_OrderedGroup_Oab__group__add(t_b), true, t_b, X), Y, t_b)
% 0.20/0.56 = { by lemma 20 }
% 0.20/0.56 c_plus(fresh5(true, true, t_b, X), Y, t_b)
% 0.20/0.56 = { by axiom 6 (cls_OrderedGroup_Odiff__self_0) }
% 0.20/0.56 c_plus(c_0, Y, t_b)
% 0.20/0.56 = { by lemma 21 }
% 0.20/0.56 Y
% 0.20/0.56
% 0.20/0.56 Lemma 25: c_minus(c_0, c_minus(X, Y, t_b), t_b) = c_minus(Y, X, t_b).
% 0.20/0.56 Proof:
% 0.20/0.56 c_minus(c_0, c_minus(X, Y, t_b), t_b)
% 0.20/0.56 = { by lemma 22 R->L }
% 0.20/0.56 c_minus(c_plus(c_0, Y, t_b), X, t_b)
% 0.20/0.56 = { by lemma 21 }
% 0.20/0.57 c_minus(Y, X, t_b)
% 0.20/0.57
% 0.20/0.57 Lemma 26: c_minus(X, c_minus(Y, Z, t_b), t_b) = c_minus(Z, c_minus(Y, X, t_b), t_b).
% 0.20/0.57 Proof:
% 0.20/0.57 c_minus(X, c_minus(Y, Z, t_b), t_b)
% 0.20/0.57 = { by lemma 25 R->L }
% 0.20/0.57 c_minus(c_0, c_minus(c_minus(Y, Z, t_b), X, t_b), t_b)
% 0.20/0.57 = { by lemma 23 R->L }
% 0.20/0.57 c_plus(c_minus(c_0, c_minus(Y, Z, t_b), t_b), X, t_b)
% 0.20/0.57 = { by lemma 25 }
% 0.20/0.57 c_plus(c_minus(Z, Y, t_b), X, t_b)
% 0.20/0.57 = { by lemma 23 }
% 0.20/0.57 c_minus(Z, c_minus(Y, X, t_b), t_b)
% 0.20/0.57
% 0.20/0.57 Lemma 27: c_minus(c_minus(X, Y, t_b), X, t_b) = c_minus(c_0, Y, t_b).
% 0.20/0.57 Proof:
% 0.20/0.57 c_minus(c_minus(X, Y, t_b), X, t_b)
% 0.20/0.57 = { by lemma 25 R->L }
% 0.20/0.57 c_minus(c_0, c_minus(X, c_minus(X, Y, t_b), t_b), t_b)
% 0.20/0.57 = { by lemma 24 }
% 0.20/0.57 c_minus(c_0, Y, t_b)
% 0.20/0.57
% 0.20/0.57 Goal 1 (cls_conjecture_3): c_lessequals(c_minus(v_f(v_x), v_k(v_x), t_b), c_minus(v_f(v_x), v_g(v_x), t_b), t_b) = true.
% 0.20/0.57 Proof:
% 0.20/0.57 c_lessequals(c_minus(v_f(v_x), v_k(v_x), t_b), c_minus(v_f(v_x), v_g(v_x), t_b), t_b)
% 0.20/0.57 = { by lemma 24 R->L }
% 0.20/0.57 c_lessequals(c_minus(c_minus(v_f(v_x), v_g(v_x), t_b), c_minus(c_minus(v_f(v_x), v_g(v_x), t_b), c_minus(v_f(v_x), v_k(v_x), t_b), t_b), t_b), c_minus(v_f(v_x), v_g(v_x), t_b), t_b)
% 0.20/0.57 = { by lemma 23 R->L }
% 0.20/0.57 c_lessequals(c_minus(c_minus(v_f(v_x), v_g(v_x), t_b), c_plus(c_minus(c_minus(v_f(v_x), v_g(v_x), t_b), v_f(v_x), t_b), v_k(v_x), t_b), t_b), c_minus(v_f(v_x), v_g(v_x), t_b), t_b)
% 0.20/0.57 = { by lemma 27 }
% 0.20/0.57 c_lessequals(c_minus(c_minus(v_f(v_x), v_g(v_x), t_b), c_plus(c_minus(c_0, v_g(v_x), t_b), v_k(v_x), t_b), t_b), c_minus(v_f(v_x), v_g(v_x), t_b), t_b)
% 0.20/0.57 = { by lemma 23 }
% 0.20/0.57 c_lessequals(c_minus(c_minus(v_f(v_x), v_g(v_x), t_b), c_minus(c_0, c_minus(v_g(v_x), v_k(v_x), t_b), t_b), t_b), c_minus(v_f(v_x), v_g(v_x), t_b), t_b)
% 0.20/0.57 = { by lemma 25 }
% 0.20/0.57 c_lessequals(c_minus(c_minus(v_f(v_x), v_g(v_x), t_b), c_minus(v_k(v_x), v_g(v_x), t_b), t_b), c_minus(v_f(v_x), v_g(v_x), t_b), t_b)
% 0.20/0.57 = { by lemma 26 R->L }
% 0.20/0.57 c_lessequals(c_minus(v_g(v_x), c_minus(v_k(v_x), c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b), c_minus(v_f(v_x), v_g(v_x), t_b), t_b)
% 0.20/0.57 = { by lemma 26 R->L }
% 0.20/0.57 c_lessequals(c_minus(v_g(v_x), c_minus(v_g(v_x), c_minus(v_f(v_x), v_k(v_x), t_b), t_b), t_b), c_minus(v_f(v_x), v_g(v_x), t_b), t_b)
% 0.20/0.57 = { by axiom 15 (cls_OrderedGroup_Ocompare__rls__8_1) R->L }
% 0.20/0.57 fresh9(true, true, t_b, v_g(v_x), c_minus(v_f(v_x), v_g(v_x), t_b), c_minus(v_g(v_x), c_minus(v_f(v_x), v_k(v_x), t_b), t_b))
% 0.20/0.57 = { by lemma 26 }
% 0.20/0.57 fresh9(true, true, t_b, v_g(v_x), c_minus(v_f(v_x), v_g(v_x), t_b), c_minus(v_k(v_x), c_minus(v_f(v_x), v_g(v_x), t_b), t_b))
% 0.20/0.57 = { by axiom 10 (cls_conjecture_1) R->L }
% 0.20/0.57 fresh9(c_lessequals(v_g(v_x), v_k(v_x), t_b), true, t_b, v_g(v_x), c_minus(v_f(v_x), v_g(v_x), t_b), c_minus(v_k(v_x), c_minus(v_f(v_x), v_g(v_x), t_b), t_b))
% 0.20/0.57 = { by lemma 24 R->L }
% 0.20/0.57 fresh9(c_lessequals(v_g(v_x), c_minus(c_minus(v_k(v_x), c_minus(v_f(v_x), v_g(v_x), t_b), t_b), c_minus(c_minus(v_k(v_x), c_minus(v_f(v_x), v_g(v_x), t_b), t_b), v_k(v_x), t_b), t_b), t_b), true, t_b, v_g(v_x), c_minus(v_f(v_x), v_g(v_x), t_b), c_minus(v_k(v_x), c_minus(v_f(v_x), v_g(v_x), t_b), t_b))
% 0.20/0.57 = { by lemma 27 }
% 0.20/0.57 fresh9(c_lessequals(v_g(v_x), c_minus(c_minus(v_k(v_x), c_minus(v_f(v_x), v_g(v_x), t_b), t_b), c_minus(c_0, c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b), t_b), true, t_b, v_g(v_x), c_minus(v_f(v_x), v_g(v_x), t_b), c_minus(v_k(v_x), c_minus(v_f(v_x), v_g(v_x), t_b), t_b))
% 0.20/0.57 = { by lemma 25 }
% 0.20/0.57 fresh9(c_lessequals(v_g(v_x), c_minus(c_minus(v_k(v_x), c_minus(v_f(v_x), v_g(v_x), t_b), t_b), c_minus(v_g(v_x), v_f(v_x), t_b), t_b), t_b), true, t_b, v_g(v_x), c_minus(v_f(v_x), v_g(v_x), t_b), c_minus(v_k(v_x), c_minus(v_f(v_x), v_g(v_x), t_b), t_b))
% 0.20/0.57 = { by lemma 26 R->L }
% 0.20/0.57 fresh9(c_lessequals(v_g(v_x), c_minus(v_f(v_x), c_minus(v_g(v_x), c_minus(v_k(v_x), c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b), t_b), t_b), true, t_b, v_g(v_x), c_minus(v_f(v_x), v_g(v_x), t_b), c_minus(v_k(v_x), c_minus(v_f(v_x), v_g(v_x), t_b), t_b))
% 0.20/0.57 = { by lemma 23 R->L }
% 0.20/0.57 fresh9(c_lessequals(v_g(v_x), c_plus(c_minus(v_f(v_x), v_g(v_x), t_b), c_minus(v_k(v_x), c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b), t_b), true, t_b, v_g(v_x), c_minus(v_f(v_x), v_g(v_x), t_b), c_minus(v_k(v_x), c_minus(v_f(v_x), v_g(v_x), t_b), t_b))
% 0.20/0.57 = { by axiom 19 (cls_OrderedGroup_Ocompare__rls__8_1) }
% 0.20/0.57 fresh8(class_OrderedGroup_Opordered__ab__group__add(t_b), true, t_b, v_g(v_x), c_minus(v_f(v_x), v_g(v_x), t_b), c_minus(v_k(v_x), c_minus(v_f(v_x), v_g(v_x), t_b), t_b))
% 0.20/0.57 = { by axiom 9 (clsrel_Ring__and__Field_Oordered__idom_54) R->L }
% 0.20/0.57 fresh8(fresh2(class_Ring__and__Field_Oordered__idom(t_b), true, t_b), true, t_b, v_g(v_x), c_minus(v_f(v_x), v_g(v_x), t_b), c_minus(v_k(v_x), c_minus(v_f(v_x), v_g(v_x), t_b), t_b))
% 0.20/0.57 = { by axiom 1 (tfree_tcs) }
% 0.20/0.57 fresh8(fresh2(true, true, t_b), true, t_b, v_g(v_x), c_minus(v_f(v_x), v_g(v_x), t_b), c_minus(v_k(v_x), c_minus(v_f(v_x), v_g(v_x), t_b), t_b))
% 0.20/0.57 = { by axiom 4 (clsrel_Ring__and__Field_Oordered__idom_54) }
% 0.20/0.57 fresh8(true, true, t_b, v_g(v_x), c_minus(v_f(v_x), v_g(v_x), t_b), c_minus(v_k(v_x), c_minus(v_f(v_x), v_g(v_x), t_b), t_b))
% 0.20/0.57 = { by axiom 16 (cls_OrderedGroup_Ocompare__rls__8_1) }
% 0.20/0.57 true
% 0.20/0.57 % SZS output end Proof
% 0.20/0.57
% 0.20/0.57 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------