TSTP Solution File: COL121-2 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : COL121-2 : 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 : n020.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 18:32:15 EDT 2023
% Result : Unsatisfiable 0.23s 0.54s
% Output : Proof 0.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : COL121-2 : TPTP v8.1.2. Released v3.2.0.
% 0.15/0.15 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.15/0.37 % Computer : n020.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Sun Aug 27 05:19:14 EDT 2023
% 0.15/0.37 % CPUTime :
% 0.23/0.54 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.23/0.54
% 0.23/0.54 % SZS status Unsatisfiable
% 0.23/0.54
% 0.23/0.58 % SZS output start Proof
% 0.23/0.58 Take the following subset of the input axioms:
% 0.23/0.58 fof(cls_Comb_Odiamond__strip__lemmaE_0, axiom, ![V_r, T_a, V_x, V_y_H, V_y]: (~c_Comb_Odiamond(V_r, T_a) | (~c_in(c_Pair(V_x, V_y_H, T_a, T_a), V_r, tc_prod(T_a, T_a)) | (~c_in(c_Pair(V_x, V_y, T_a, T_a), c_Transitive__Closure_Ortrancl(V_r, T_a), tc_prod(T_a, T_a)) | c_in(c_Pair(V_y_H, c_Comb_Odiamond__strip__lemmaE__1(V_r, V_y, V_y_H, T_a), T_a, T_a), c_Transitive__Closure_Ortrancl(V_r, T_a), tc_prod(T_a, T_a)))))).
% 0.23/0.58 fof(cls_Comb_Odiamond__strip__lemmaE_1, axiom, ![V_r2, T_a2, V_x2, V_y_H2, V_y2]: (~c_Comb_Odiamond(V_r2, T_a2) | (~c_in(c_Pair(V_x2, V_y_H2, T_a2, T_a2), V_r2, tc_prod(T_a2, T_a2)) | (~c_in(c_Pair(V_x2, V_y2, T_a2, T_a2), c_Transitive__Closure_Ortrancl(V_r2, T_a2), tc_prod(T_a2, T_a2)) | c_in(c_Pair(V_y2, c_Comb_Odiamond__strip__lemmaE__1(V_r2, V_y2, V_y_H2, T_a2), T_a2, T_a2), V_r2, tc_prod(T_a2, T_a2)))))).
% 0.23/0.58 fof(cls_Transitive__Closure_Or__into__rtrancl_0, axiom, ![V_p, V_r2, T_a2]: (~c_in(V_p, V_r2, tc_prod(T_a2, T_a2)) | c_in(V_p, c_Transitive__Closure_Ortrancl(V_r2, T_a2), tc_prod(T_a2, T_a2)))).
% 0.23/0.58 fof(cls_Transitive__Closure_Ortrancl__trans_0, axiom, ![V_b, V_c, V_a, V_r2, T_a2]: (~c_in(c_Pair(V_b, V_c, T_a2, T_a2), c_Transitive__Closure_Ortrancl(V_r2, T_a2), tc_prod(T_a2, T_a2)) | (~c_in(c_Pair(V_a, V_b, T_a2, T_a2), c_Transitive__Closure_Ortrancl(V_r2, T_a2), tc_prod(T_a2, T_a2)) | c_in(c_Pair(V_a, V_c, T_a2, T_a2), c_Transitive__Closure_Ortrancl(V_r2, T_a2), tc_prod(T_a2, T_a2))))).
% 0.23/0.58 fof(cls_conjecture_0, negated_conjecture, c_Comb_Odiamond(v_r, t_a)).
% 0.23/0.58 fof(cls_conjecture_2, negated_conjecture, c_in(c_Pair(v_ya, v_z, t_a, t_a), v_r, tc_prod(t_a, t_a))).
% 0.23/0.58 fof(cls_conjecture_3, negated_conjecture, c_in(c_Pair(v_y, v_xaa, t_a, t_a), c_Transitive__Closure_Ortrancl(v_r, t_a), tc_prod(t_a, t_a))).
% 0.23/0.58 fof(cls_conjecture_4, negated_conjecture, ![V_U]: (c_in(c_Pair(v_ya, v_x(V_U), t_a, t_a), c_Transitive__Closure_Ortrancl(v_r, t_a), tc_prod(t_a, t_a)) | ~c_in(c_Pair(v_y, V_U, t_a, t_a), c_Transitive__Closure_Ortrancl(v_r, t_a), tc_prod(t_a, t_a)))).
% 0.23/0.58 fof(cls_conjecture_5, negated_conjecture, ![V_U2]: (c_in(c_Pair(V_U2, v_x(V_U2), t_a, t_a), c_Transitive__Closure_Ortrancl(v_r, t_a), tc_prod(t_a, t_a)) | ~c_in(c_Pair(v_y, V_U2, t_a, t_a), c_Transitive__Closure_Ortrancl(v_r, t_a), tc_prod(t_a, t_a)))).
% 0.23/0.58 fof(cls_conjecture_6, negated_conjecture, ![V_U2]: (~c_in(c_Pair(v_xaa, V_U2, t_a, t_a), c_Transitive__Closure_Ortrancl(v_r, t_a), tc_prod(t_a, t_a)) | ~c_in(c_Pair(v_z, V_U2, t_a, t_a), c_Transitive__Closure_Ortrancl(v_r, t_a), tc_prod(t_a, t_a)))).
% 0.23/0.58
% 0.23/0.58 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.23/0.58 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.23/0.58 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.23/0.58 fresh(y, y, x1...xn) = u
% 0.23/0.58 C => fresh(s, t, x1...xn) = v
% 0.23/0.58 where fresh is a fresh function symbol and x1..xn are the free
% 0.23/0.58 variables of u and v.
% 0.23/0.58 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.23/0.58 input problem has no model of domain size 1).
% 0.23/0.58
% 0.23/0.58 The encoding turns the above axioms into the following unit equations and goals:
% 0.23/0.58
% 0.23/0.58 Axiom 1 (cls_conjecture_0): c_Comb_Odiamond(v_r, t_a) = true2.
% 0.23/0.58 Axiom 2 (cls_conjecture_5): fresh(X, X, Y) = true2.
% 0.23/0.58 Axiom 3 (cls_conjecture_4): fresh2(X, X, Y) = true2.
% 0.23/0.58 Axiom 4 (cls_Transitive__Closure_Or__into__rtrancl_0): fresh5(X, X, Y, Z, W) = true2.
% 0.23/0.58 Axiom 5 (cls_Comb_Odiamond__strip__lemmaE_0): fresh11(X, X, Y, Z, W, V) = true2.
% 0.23/0.58 Axiom 6 (cls_Comb_Odiamond__strip__lemmaE_1): fresh9(X, X, Y, Z, W, V) = true2.
% 0.23/0.58 Axiom 7 (cls_Transitive__Closure_Ortrancl__trans_0): fresh3(X, X, Y, Z, W, V) = true2.
% 0.23/0.58 Axiom 8 (cls_Comb_Odiamond__strip__lemmaE_0): fresh10(X, X, Y, Z, W, V) = fresh11(c_Comb_Odiamond(Y, Z), true2, Y, Z, W, V).
% 0.23/0.58 Axiom 9 (cls_Comb_Odiamond__strip__lemmaE_1): fresh8(X, X, Y, Z, W, V) = fresh9(c_Comb_Odiamond(Y, Z), true2, Y, Z, W, V).
% 0.23/0.58 Axiom 10 (cls_conjecture_2): c_in(c_Pair(v_ya, v_z, t_a, t_a), v_r, tc_prod(t_a, t_a)) = true2.
% 0.23/0.58 Axiom 11 (cls_Transitive__Closure_Or__into__rtrancl_0): fresh5(c_in(X, Y, tc_prod(Z, Z)), true2, X, Y, Z) = c_in(X, c_Transitive__Closure_Ortrancl(Y, Z), tc_prod(Z, Z)).
% 0.23/0.58 Axiom 12 (cls_Transitive__Closure_Ortrancl__trans_0): fresh4(X, X, Y, Z, W, V, U) = c_in(c_Pair(U, Z, W, W), c_Transitive__Closure_Ortrancl(V, W), tc_prod(W, W)).
% 0.23/0.58 Axiom 13 (cls_conjecture_3): c_in(c_Pair(v_y, v_xaa, t_a, t_a), c_Transitive__Closure_Ortrancl(v_r, t_a), tc_prod(t_a, t_a)) = true2.
% 0.23/0.58 Axiom 14 (cls_Comb_Odiamond__strip__lemmaE_1): fresh6(X, X, Y, Z, W, V, U) = c_in(c_Pair(U, c_Comb_Odiamond__strip__lemmaE__1(Y, U, V, Z), Z, Z), Y, tc_prod(Z, Z)).
% 0.23/0.59 Axiom 15 (cls_conjecture_5): fresh(c_in(c_Pair(v_y, X, t_a, t_a), c_Transitive__Closure_Ortrancl(v_r, t_a), tc_prod(t_a, t_a)), true2, X) = c_in(c_Pair(X, v_x(X), t_a, t_a), c_Transitive__Closure_Ortrancl(v_r, t_a), tc_prod(t_a, t_a)).
% 0.23/0.59 Axiom 16 (cls_conjecture_4): fresh2(c_in(c_Pair(v_y, X, t_a, t_a), c_Transitive__Closure_Ortrancl(v_r, t_a), tc_prod(t_a, t_a)), true2, X) = c_in(c_Pair(v_ya, v_x(X), t_a, t_a), c_Transitive__Closure_Ortrancl(v_r, t_a), tc_prod(t_a, t_a)).
% 0.23/0.59 Axiom 17 (cls_Comb_Odiamond__strip__lemmaE_0): fresh7(X, X, Y, Z, W, V, U) = c_in(c_Pair(V, c_Comb_Odiamond__strip__lemmaE__1(Y, U, V, Z), Z, Z), c_Transitive__Closure_Ortrancl(Y, Z), tc_prod(Z, Z)).
% 0.23/0.59 Axiom 18 (cls_Comb_Odiamond__strip__lemmaE_0): fresh7(c_in(c_Pair(X, Y, Z, Z), c_Transitive__Closure_Ortrancl(W, Z), tc_prod(Z, Z)), true2, W, Z, X, V, Y) = fresh10(c_in(c_Pair(X, V, Z, Z), W, tc_prod(Z, Z)), true2, W, Z, V, Y).
% 0.23/0.59 Axiom 19 (cls_Comb_Odiamond__strip__lemmaE_1): fresh6(c_in(c_Pair(X, Y, Z, Z), c_Transitive__Closure_Ortrancl(W, Z), tc_prod(Z, Z)), true2, W, Z, X, V, Y) = fresh8(c_in(c_Pair(X, V, Z, Z), W, tc_prod(Z, Z)), true2, W, Z, V, Y).
% 0.23/0.59 Axiom 20 (cls_Transitive__Closure_Ortrancl__trans_0): fresh4(c_in(c_Pair(X, Y, Z, Z), c_Transitive__Closure_Ortrancl(W, Z), tc_prod(Z, Z)), true2, Y, V, Z, W, X) = fresh3(c_in(c_Pair(Y, V, Z, Z), c_Transitive__Closure_Ortrancl(W, Z), tc_prod(Z, Z)), true2, V, Z, W, X).
% 0.23/0.59
% 0.23/0.59 Lemma 21: fresh4(X, X, Y, v_xaa, t_a, v_r, v_y) = true2.
% 0.23/0.59 Proof:
% 0.23/0.59 fresh4(X, X, Y, v_xaa, t_a, v_r, v_y)
% 0.23/0.59 = { by axiom 12 (cls_Transitive__Closure_Ortrancl__trans_0) }
% 0.23/0.59 c_in(c_Pair(v_y, v_xaa, t_a, t_a), c_Transitive__Closure_Ortrancl(v_r, t_a), tc_prod(t_a, t_a))
% 0.23/0.59 = { by axiom 13 (cls_conjecture_3) }
% 0.23/0.59 true2
% 0.23/0.59
% 0.23/0.59 Lemma 22: fresh4(X, X, Y, v_x(v_xaa), t_a, v_r, v_ya) = true2.
% 0.23/0.59 Proof:
% 0.23/0.59 fresh4(X, X, Y, v_x(v_xaa), t_a, v_r, v_ya)
% 0.23/0.59 = { by axiom 12 (cls_Transitive__Closure_Ortrancl__trans_0) }
% 0.23/0.59 c_in(c_Pair(v_ya, v_x(v_xaa), t_a, t_a), c_Transitive__Closure_Ortrancl(v_r, t_a), tc_prod(t_a, t_a))
% 0.23/0.59 = { by axiom 16 (cls_conjecture_4) R->L }
% 0.23/0.59 fresh2(c_in(c_Pair(v_y, v_xaa, t_a, t_a), c_Transitive__Closure_Ortrancl(v_r, t_a), tc_prod(t_a, t_a)), true2, v_xaa)
% 0.23/0.59 = { by axiom 12 (cls_Transitive__Closure_Ortrancl__trans_0) R->L }
% 0.23/0.59 fresh2(fresh4(Z, Z, W, v_xaa, t_a, v_r, v_y), true2, v_xaa)
% 0.23/0.59 = { by lemma 21 }
% 0.23/0.59 fresh2(true2, true2, v_xaa)
% 0.23/0.59 = { by axiom 3 (cls_conjecture_4) }
% 0.23/0.59 true2
% 0.23/0.59
% 0.23/0.59 Goal 1 (cls_conjecture_6): tuple(c_in(c_Pair(v_z, X, t_a, t_a), c_Transitive__Closure_Ortrancl(v_r, t_a), tc_prod(t_a, t_a)), c_in(c_Pair(v_xaa, X, t_a, t_a), c_Transitive__Closure_Ortrancl(v_r, t_a), tc_prod(t_a, t_a))) = tuple(true2, true2).
% 0.23/0.59 The goal is true when:
% 0.23/0.59 X = c_Comb_Odiamond__strip__lemmaE__1(v_r, v_x(v_xaa), v_z, t_a)
% 0.23/0.59
% 0.23/0.59 Proof:
% 0.23/0.59 tuple(c_in(c_Pair(v_z, c_Comb_Odiamond__strip__lemmaE__1(v_r, v_x(v_xaa), v_z, t_a), t_a, t_a), c_Transitive__Closure_Ortrancl(v_r, t_a), tc_prod(t_a, t_a)), c_in(c_Pair(v_xaa, c_Comb_Odiamond__strip__lemmaE__1(v_r, v_x(v_xaa), v_z, t_a), t_a, t_a), c_Transitive__Closure_Ortrancl(v_r, t_a), tc_prod(t_a, t_a)))
% 0.23/0.59 = { by axiom 12 (cls_Transitive__Closure_Ortrancl__trans_0) R->L }
% 0.23/0.59 tuple(fresh4(T, T, S, c_Comb_Odiamond__strip__lemmaE__1(v_r, v_x(v_xaa), v_z, t_a), t_a, v_r, v_z), c_in(c_Pair(v_xaa, c_Comb_Odiamond__strip__lemmaE__1(v_r, v_x(v_xaa), v_z, t_a), t_a, t_a), c_Transitive__Closure_Ortrancl(v_r, t_a), tc_prod(t_a, t_a)))
% 0.23/0.59 = { by axiom 12 (cls_Transitive__Closure_Ortrancl__trans_0) R->L }
% 0.23/0.59 tuple(fresh4(T, T, S, c_Comb_Odiamond__strip__lemmaE__1(v_r, v_x(v_xaa), v_z, t_a), t_a, v_r, v_z), fresh4(true2, true2, v_x(v_xaa), c_Comb_Odiamond__strip__lemmaE__1(v_r, v_x(v_xaa), v_z, t_a), t_a, v_r, v_xaa))
% 0.23/0.59 = { by axiom 12 (cls_Transitive__Closure_Ortrancl__trans_0) }
% 0.23/0.59 tuple(c_in(c_Pair(v_z, c_Comb_Odiamond__strip__lemmaE__1(v_r, v_x(v_xaa), v_z, t_a), t_a, t_a), c_Transitive__Closure_Ortrancl(v_r, t_a), tc_prod(t_a, t_a)), fresh4(true2, true2, v_x(v_xaa), c_Comb_Odiamond__strip__lemmaE__1(v_r, v_x(v_xaa), v_z, t_a), t_a, v_r, v_xaa))
% 0.23/0.59 = { by axiom 2 (cls_conjecture_5) R->L }
% 0.23/0.59 tuple(c_in(c_Pair(v_z, c_Comb_Odiamond__strip__lemmaE__1(v_r, v_x(v_xaa), v_z, t_a), t_a, t_a), c_Transitive__Closure_Ortrancl(v_r, t_a), tc_prod(t_a, t_a)), fresh4(fresh(true2, true2, v_xaa), true2, v_x(v_xaa), c_Comb_Odiamond__strip__lemmaE__1(v_r, v_x(v_xaa), v_z, t_a), t_a, v_r, v_xaa))
% 0.23/0.59 = { by lemma 21 R->L }
% 0.23/0.59 tuple(c_in(c_Pair(v_z, c_Comb_Odiamond__strip__lemmaE__1(v_r, v_x(v_xaa), v_z, t_a), t_a, t_a), c_Transitive__Closure_Ortrancl(v_r, t_a), tc_prod(t_a, t_a)), fresh4(fresh(fresh4(V, V, U, v_xaa, t_a, v_r, v_y), true2, v_xaa), true2, v_x(v_xaa), c_Comb_Odiamond__strip__lemmaE__1(v_r, v_x(v_xaa), v_z, t_a), t_a, v_r, v_xaa))
% 0.23/0.59 = { by axiom 12 (cls_Transitive__Closure_Ortrancl__trans_0) }
% 0.23/0.59 tuple(c_in(c_Pair(v_z, c_Comb_Odiamond__strip__lemmaE__1(v_r, v_x(v_xaa), v_z, t_a), t_a, t_a), c_Transitive__Closure_Ortrancl(v_r, t_a), tc_prod(t_a, t_a)), fresh4(fresh(c_in(c_Pair(v_y, v_xaa, t_a, t_a), c_Transitive__Closure_Ortrancl(v_r, t_a), tc_prod(t_a, t_a)), true2, v_xaa), true2, v_x(v_xaa), c_Comb_Odiamond__strip__lemmaE__1(v_r, v_x(v_xaa), v_z, t_a), t_a, v_r, v_xaa))
% 0.23/0.59 = { by axiom 15 (cls_conjecture_5) }
% 0.23/0.59 tuple(c_in(c_Pair(v_z, c_Comb_Odiamond__strip__lemmaE__1(v_r, v_x(v_xaa), v_z, t_a), t_a, t_a), c_Transitive__Closure_Ortrancl(v_r, t_a), tc_prod(t_a, t_a)), fresh4(c_in(c_Pair(v_xaa, v_x(v_xaa), t_a, t_a), c_Transitive__Closure_Ortrancl(v_r, t_a), tc_prod(t_a, t_a)), true2, v_x(v_xaa), c_Comb_Odiamond__strip__lemmaE__1(v_r, v_x(v_xaa), v_z, t_a), t_a, v_r, v_xaa))
% 0.23/0.59 = { by axiom 20 (cls_Transitive__Closure_Ortrancl__trans_0) }
% 0.23/0.59 tuple(c_in(c_Pair(v_z, c_Comb_Odiamond__strip__lemmaE__1(v_r, v_x(v_xaa), v_z, t_a), t_a, t_a), c_Transitive__Closure_Ortrancl(v_r, t_a), tc_prod(t_a, t_a)), fresh3(c_in(c_Pair(v_x(v_xaa), c_Comb_Odiamond__strip__lemmaE__1(v_r, v_x(v_xaa), v_z, t_a), t_a, t_a), c_Transitive__Closure_Ortrancl(v_r, t_a), tc_prod(t_a, t_a)), true2, c_Comb_Odiamond__strip__lemmaE__1(v_r, v_x(v_xaa), v_z, t_a), t_a, v_r, v_xaa))
% 0.23/0.59 = { by axiom 11 (cls_Transitive__Closure_Or__into__rtrancl_0) R->L }
% 0.23/0.59 tuple(c_in(c_Pair(v_z, c_Comb_Odiamond__strip__lemmaE__1(v_r, v_x(v_xaa), v_z, t_a), t_a, t_a), c_Transitive__Closure_Ortrancl(v_r, t_a), tc_prod(t_a, t_a)), fresh3(fresh5(c_in(c_Pair(v_x(v_xaa), c_Comb_Odiamond__strip__lemmaE__1(v_r, v_x(v_xaa), v_z, t_a), t_a, t_a), v_r, tc_prod(t_a, t_a)), true2, c_Pair(v_x(v_xaa), c_Comb_Odiamond__strip__lemmaE__1(v_r, v_x(v_xaa), v_z, t_a), t_a, t_a), v_r, t_a), true2, c_Comb_Odiamond__strip__lemmaE__1(v_r, v_x(v_xaa), v_z, t_a), t_a, v_r, v_xaa))
% 0.23/0.59 = { by axiom 14 (cls_Comb_Odiamond__strip__lemmaE_1) R->L }
% 0.23/0.59 tuple(c_in(c_Pair(v_z, c_Comb_Odiamond__strip__lemmaE__1(v_r, v_x(v_xaa), v_z, t_a), t_a, t_a), c_Transitive__Closure_Ortrancl(v_r, t_a), tc_prod(t_a, t_a)), fresh3(fresh5(fresh6(true2, true2, v_r, t_a, v_ya, v_z, v_x(v_xaa)), true2, c_Pair(v_x(v_xaa), c_Comb_Odiamond__strip__lemmaE__1(v_r, v_x(v_xaa), v_z, t_a), t_a, t_a), v_r, t_a), true2, c_Comb_Odiamond__strip__lemmaE__1(v_r, v_x(v_xaa), v_z, t_a), t_a, v_r, v_xaa))
% 0.23/0.59 = { by lemma 22 R->L }
% 0.23/0.59 tuple(c_in(c_Pair(v_z, c_Comb_Odiamond__strip__lemmaE__1(v_r, v_x(v_xaa), v_z, t_a), t_a, t_a), c_Transitive__Closure_Ortrancl(v_r, t_a), tc_prod(t_a, t_a)), fresh3(fresh5(fresh6(fresh4(Z, Z, W, v_x(v_xaa), t_a, v_r, v_ya), true2, v_r, t_a, v_ya, v_z, v_x(v_xaa)), true2, c_Pair(v_x(v_xaa), c_Comb_Odiamond__strip__lemmaE__1(v_r, v_x(v_xaa), v_z, t_a), t_a, t_a), v_r, t_a), true2, c_Comb_Odiamond__strip__lemmaE__1(v_r, v_x(v_xaa), v_z, t_a), t_a, v_r, v_xaa))
% 0.23/0.59 = { by axiom 12 (cls_Transitive__Closure_Ortrancl__trans_0) }
% 0.23/0.59 tuple(c_in(c_Pair(v_z, c_Comb_Odiamond__strip__lemmaE__1(v_r, v_x(v_xaa), v_z, t_a), t_a, t_a), c_Transitive__Closure_Ortrancl(v_r, t_a), tc_prod(t_a, t_a)), fresh3(fresh5(fresh6(c_in(c_Pair(v_ya, v_x(v_xaa), t_a, t_a), c_Transitive__Closure_Ortrancl(v_r, t_a), tc_prod(t_a, t_a)), true2, v_r, t_a, v_ya, v_z, v_x(v_xaa)), true2, c_Pair(v_x(v_xaa), c_Comb_Odiamond__strip__lemmaE__1(v_r, v_x(v_xaa), v_z, t_a), t_a, t_a), v_r, t_a), true2, c_Comb_Odiamond__strip__lemmaE__1(v_r, v_x(v_xaa), v_z, t_a), t_a, v_r, v_xaa))
% 0.23/0.59 = { by axiom 19 (cls_Comb_Odiamond__strip__lemmaE_1) }
% 0.23/0.59 tuple(c_in(c_Pair(v_z, c_Comb_Odiamond__strip__lemmaE__1(v_r, v_x(v_xaa), v_z, t_a), t_a, t_a), c_Transitive__Closure_Ortrancl(v_r, t_a), tc_prod(t_a, t_a)), fresh3(fresh5(fresh8(c_in(c_Pair(v_ya, v_z, t_a, t_a), v_r, tc_prod(t_a, t_a)), true2, v_r, t_a, v_z, v_x(v_xaa)), true2, c_Pair(v_x(v_xaa), c_Comb_Odiamond__strip__lemmaE__1(v_r, v_x(v_xaa), v_z, t_a), t_a, t_a), v_r, t_a), true2, c_Comb_Odiamond__strip__lemmaE__1(v_r, v_x(v_xaa), v_z, t_a), t_a, v_r, v_xaa))
% 0.23/0.59 = { by axiom 10 (cls_conjecture_2) }
% 0.23/0.59 tuple(c_in(c_Pair(v_z, c_Comb_Odiamond__strip__lemmaE__1(v_r, v_x(v_xaa), v_z, t_a), t_a, t_a), c_Transitive__Closure_Ortrancl(v_r, t_a), tc_prod(t_a, t_a)), fresh3(fresh5(fresh8(true2, true2, v_r, t_a, v_z, v_x(v_xaa)), true2, c_Pair(v_x(v_xaa), c_Comb_Odiamond__strip__lemmaE__1(v_r, v_x(v_xaa), v_z, t_a), t_a, t_a), v_r, t_a), true2, c_Comb_Odiamond__strip__lemmaE__1(v_r, v_x(v_xaa), v_z, t_a), t_a, v_r, v_xaa))
% 0.23/0.59 = { by axiom 9 (cls_Comb_Odiamond__strip__lemmaE_1) }
% 0.23/0.59 tuple(c_in(c_Pair(v_z, c_Comb_Odiamond__strip__lemmaE__1(v_r, v_x(v_xaa), v_z, t_a), t_a, t_a), c_Transitive__Closure_Ortrancl(v_r, t_a), tc_prod(t_a, t_a)), fresh3(fresh5(fresh9(c_Comb_Odiamond(v_r, t_a), true2, v_r, t_a, v_z, v_x(v_xaa)), true2, c_Pair(v_x(v_xaa), c_Comb_Odiamond__strip__lemmaE__1(v_r, v_x(v_xaa), v_z, t_a), t_a, t_a), v_r, t_a), true2, c_Comb_Odiamond__strip__lemmaE__1(v_r, v_x(v_xaa), v_z, t_a), t_a, v_r, v_xaa))
% 0.23/0.59 = { by axiom 1 (cls_conjecture_0) }
% 0.23/0.59 tuple(c_in(c_Pair(v_z, c_Comb_Odiamond__strip__lemmaE__1(v_r, v_x(v_xaa), v_z, t_a), t_a, t_a), c_Transitive__Closure_Ortrancl(v_r, t_a), tc_prod(t_a, t_a)), fresh3(fresh5(fresh9(true2, true2, v_r, t_a, v_z, v_x(v_xaa)), true2, c_Pair(v_x(v_xaa), c_Comb_Odiamond__strip__lemmaE__1(v_r, v_x(v_xaa), v_z, t_a), t_a, t_a), v_r, t_a), true2, c_Comb_Odiamond__strip__lemmaE__1(v_r, v_x(v_xaa), v_z, t_a), t_a, v_r, v_xaa))
% 0.23/0.59 = { by axiom 6 (cls_Comb_Odiamond__strip__lemmaE_1) }
% 0.23/0.59 tuple(c_in(c_Pair(v_z, c_Comb_Odiamond__strip__lemmaE__1(v_r, v_x(v_xaa), v_z, t_a), t_a, t_a), c_Transitive__Closure_Ortrancl(v_r, t_a), tc_prod(t_a, t_a)), fresh3(fresh5(true2, true2, c_Pair(v_x(v_xaa), c_Comb_Odiamond__strip__lemmaE__1(v_r, v_x(v_xaa), v_z, t_a), t_a, t_a), v_r, t_a), true2, c_Comb_Odiamond__strip__lemmaE__1(v_r, v_x(v_xaa), v_z, t_a), t_a, v_r, v_xaa))
% 0.23/0.59 = { by axiom 4 (cls_Transitive__Closure_Or__into__rtrancl_0) }
% 0.23/0.59 tuple(c_in(c_Pair(v_z, c_Comb_Odiamond__strip__lemmaE__1(v_r, v_x(v_xaa), v_z, t_a), t_a, t_a), c_Transitive__Closure_Ortrancl(v_r, t_a), tc_prod(t_a, t_a)), fresh3(true2, true2, c_Comb_Odiamond__strip__lemmaE__1(v_r, v_x(v_xaa), v_z, t_a), t_a, v_r, v_xaa))
% 0.23/0.59 = { by axiom 7 (cls_Transitive__Closure_Ortrancl__trans_0) }
% 0.23/0.59 tuple(c_in(c_Pair(v_z, c_Comb_Odiamond__strip__lemmaE__1(v_r, v_x(v_xaa), v_z, t_a), t_a, t_a), c_Transitive__Closure_Ortrancl(v_r, t_a), tc_prod(t_a, t_a)), true2)
% 0.23/0.59 = { by axiom 17 (cls_Comb_Odiamond__strip__lemmaE_0) R->L }
% 0.23/0.59 tuple(fresh7(true2, true2, v_r, t_a, v_ya, v_z, v_x(v_xaa)), true2)
% 0.23/0.59 = { by lemma 22 R->L }
% 0.23/0.59 tuple(fresh7(fresh4(X, X, Y, v_x(v_xaa), t_a, v_r, v_ya), true2, v_r, t_a, v_ya, v_z, v_x(v_xaa)), true2)
% 0.23/0.59 = { by axiom 12 (cls_Transitive__Closure_Ortrancl__trans_0) }
% 0.23/0.59 tuple(fresh7(c_in(c_Pair(v_ya, v_x(v_xaa), t_a, t_a), c_Transitive__Closure_Ortrancl(v_r, t_a), tc_prod(t_a, t_a)), true2, v_r, t_a, v_ya, v_z, v_x(v_xaa)), true2)
% 0.23/0.59 = { by axiom 18 (cls_Comb_Odiamond__strip__lemmaE_0) }
% 0.23/0.59 tuple(fresh10(c_in(c_Pair(v_ya, v_z, t_a, t_a), v_r, tc_prod(t_a, t_a)), true2, v_r, t_a, v_z, v_x(v_xaa)), true2)
% 0.23/0.59 = { by axiom 10 (cls_conjecture_2) }
% 0.23/0.59 tuple(fresh10(true2, true2, v_r, t_a, v_z, v_x(v_xaa)), true2)
% 0.23/0.59 = { by axiom 8 (cls_Comb_Odiamond__strip__lemmaE_0) }
% 0.23/0.59 tuple(fresh11(c_Comb_Odiamond(v_r, t_a), true2, v_r, t_a, v_z, v_x(v_xaa)), true2)
% 0.23/0.59 = { by axiom 1 (cls_conjecture_0) }
% 0.23/0.59 tuple(fresh11(true2, true2, v_r, t_a, v_z, v_x(v_xaa)), true2)
% 0.23/0.59 = { by axiom 5 (cls_Comb_Odiamond__strip__lemmaE_0) }
% 0.23/0.59 tuple(true2, true2)
% 0.23/0.59 % SZS output end Proof
% 0.23/0.59
% 0.23/0.59 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------