%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : COL121-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 09:37:30 AM UTC 2026
% Result : Unsatisfiable 1.44s 0.45s
% Output : Proof 1.44s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL121-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.16 % Computer : n010.cluster.edu
% 0.08/0.16 % Model : x86_64 x86_64
% 0.08/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.16 % Memory : 8046.5625MB
% 0.08/0.16 % OS : Linux 6.8.0-71-generic
% 0.08/0.16 % CPULimit : 300
% 0.08/0.16 % WCLimit : 300
% 0.08/0.16 % DateTime : Mon Sep 28 21:41:32 UTC 2026
% 0.08/0.16 % CPUTime :
% 0.08/0.16 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.44/0.45 Command-line arguments: --no-flatten-goal
% 1.44/0.45
% 1.44/0.45 % SZS status Unsatisfiable
% 1.44/0.45
% 1.44/0.47 % SZS output start Proof
% 1.44/0.47 Axiom 1 (cls_conjecture_0): c_Comb_Odiamond(v_r, t_a) = true.
% 1.44/0.47 Axiom 2 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 1.44/0.47 Axiom 3 (cls_conjecture_2): c_in(c_Pair(v_ya, v_z, t_a, t_a), v_r, tc_prod(t_a, t_a)) = true.
% 1.44/0.47 Axiom 4 (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)) = true.
% 1.44/0.47 Axiom 5 (cls_Transitive__Closure_Or__into__rtrancl_0): ifeq(c_in(X, Y, tc_prod(Z, Z)), true, c_in(X, c_Transitive__Closure_Ortrancl(Y, Z), tc_prod(Z, Z)), true) = true.
% 1.44/0.47 Axiom 6 (cls_conjecture_5): ifeq(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)), true, 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)), true) = true.
% 1.44/0.47 Axiom 7 (cls_conjecture_4): ifeq(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)), true, 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)), true) = true.
% 1.44/0.47 Axiom 8 (cls_Transitive__Closure_Ortrancl__trans_0): ifeq(c_in(c_Pair(X, Y, Z, Z), c_Transitive__Closure_Ortrancl(W, Z), tc_prod(Z, Z)), true, ifeq(c_in(c_Pair(Y, V, Z, Z), c_Transitive__Closure_Ortrancl(W, Z), tc_prod(Z, Z)), true, c_in(c_Pair(X, V, Z, Z), c_Transitive__Closure_Ortrancl(W, Z), tc_prod(Z, Z)), true), true) = true.
% 1.44/0.47 Axiom 9 (cls_Comb_Odiamond__strip__lemmaE_1): ifeq(c_in(c_Pair(X, Y, Z, Z), c_Transitive__Closure_Ortrancl(W, Z), tc_prod(Z, Z)), true, ifeq(c_in(c_Pair(X, V, Z, Z), W, tc_prod(Z, Z)), true, ifeq(c_Comb_Odiamond(W, Z), true, c_in(c_Pair(Y, c_Comb_Odiamond__strip__lemmaE__1(W, Y, V, Z), Z, Z), W, tc_prod(Z, Z)), true), true), true) = true.
% 1.44/0.47 Axiom 10 (cls_Comb_Odiamond__strip__lemmaE_0): ifeq(c_in(c_Pair(X, Y, Z, Z), c_Transitive__Closure_Ortrancl(W, Z), tc_prod(Z, Z)), true, ifeq(c_in(c_Pair(X, V, Z, Z), W, tc_prod(Z, Z)), true, ifeq(c_Comb_Odiamond(W, Z), true, c_in(c_Pair(V, c_Comb_Odiamond__strip__lemmaE__1(W, Y, V, Z), Z, Z), c_Transitive__Closure_Ortrancl(W, Z), tc_prod(Z, Z)), true), true), true) = true.
% 1.44/0.47
% 1.44/0.48 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(true, true).
% 1.44/0.48 The goal is true when:
% 1.44/0.48 X = c_Comb_Odiamond__strip__lemmaE__1(v_r, v_x(v_xaa), v_z, t_a)
% 1.44/0.48
% 1.44/0.48 Proof:
% 1.44/0.48 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)))
% 1.44/0.48 = { by axiom 2 (ifeq_axiom) R->L }
% 1.44/0.48 tuple(ifeq(true, true, 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)), true), 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)))
% 1.44/0.48 = { by axiom 7 (cls_conjecture_4) R->L }
% 1.44/0.48 tuple(ifeq(ifeq(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)), true, 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)), true), true, 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)), true), 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)))
% 1.44/0.48 = { by axiom 4 (cls_conjecture_3) }
% 1.44/0.48 tuple(ifeq(ifeq(true, true, 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)), true), true, 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)), true), 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)))
% 1.44/0.48 = { by axiom 2 (ifeq_axiom) }
% 1.44/0.48 tuple(ifeq(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)), true, 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)), true), 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)))
% 1.44/0.48 = { by axiom 2 (ifeq_axiom) R->L }
% 1.44/0.48 tuple(ifeq(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)), true, ifeq(true, true, 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)), true), true), 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)))
% 1.44/0.48 = { by axiom 1 (cls_conjecture_0) R->L }
% 1.44/0.48 tuple(ifeq(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)), true, ifeq(c_Comb_Odiamond(v_r, t_a), true, 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)), true), true), 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)))
% 1.44/0.48 = { by axiom 2 (ifeq_axiom) R->L }
% 1.44/0.48 tuple(ifeq(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)), true, ifeq(true, true, ifeq(c_Comb_Odiamond(v_r, t_a), true, 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)), true), true), true), 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)))
% 1.44/0.48 = { by axiom 3 (cls_conjecture_2) R->L }
% 1.44/0.48 tuple(ifeq(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)), true, ifeq(c_in(c_Pair(v_ya, v_z, t_a, t_a), v_r, tc_prod(t_a, t_a)), true, ifeq(c_Comb_Odiamond(v_r, t_a), true, 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)), true), true), true), 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)))
% 1.44/0.48 = { by axiom 10 (cls_Comb_Odiamond__strip__lemmaE_0) }
% 1.44/0.48 tuple(true, 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)))
% 1.44/0.48 = { by axiom 2 (ifeq_axiom) R->L }
% 1.44/0.48 tuple(true, ifeq(true, true, 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)), true))
% 1.44/0.48 = { by axiom 5 (cls_Transitive__Closure_Or__into__rtrancl_0) R->L }
% 1.44/0.48 tuple(true, ifeq(ifeq(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)), true, 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)), true), true, 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)), true))
% 1.44/0.48 = { by axiom 2 (ifeq_axiom) R->L }
% 1.44/0.48 tuple(true, ifeq(ifeq(ifeq(true, true, 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)), true), true, 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)), true), true, 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)), true))
% 1.44/0.48 = { by axiom 3 (cls_conjecture_2) R->L }
% 1.44/0.48 tuple(true, ifeq(ifeq(ifeq(c_in(c_Pair(v_ya, v_z, t_a, t_a), v_r, tc_prod(t_a, t_a)), true, 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)), true), true, 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)), true), true, 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)), true))
% 1.44/0.48 = { by axiom 2 (ifeq_axiom) R->L }
% 1.44/0.48 tuple(true, ifeq(ifeq(ifeq(c_in(c_Pair(v_ya, v_z, t_a, t_a), v_r, tc_prod(t_a, t_a)), true, ifeq(true, true, 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)), true), true), true, 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)), true), true, 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)), true))
% 1.44/0.48 = { by axiom 1 (cls_conjecture_0) R->L }
% 1.44/0.48 tuple(true, ifeq(ifeq(ifeq(c_in(c_Pair(v_ya, v_z, t_a, t_a), v_r, tc_prod(t_a, t_a)), true, ifeq(c_Comb_Odiamond(v_r, t_a), true, 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)), true), true), true, 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)), true), true, 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)), true))
% 1.44/0.48 = { by axiom 2 (ifeq_axiom) R->L }
% 1.44/0.48 tuple(true, ifeq(ifeq(ifeq(true, true, ifeq(c_in(c_Pair(v_ya, v_z, t_a, t_a), v_r, tc_prod(t_a, t_a)), true, ifeq(c_Comb_Odiamond(v_r, t_a), true, 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)), true), true), true), true, 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)), true), true, 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)), true))
% 1.44/0.48 = { by axiom 7 (cls_conjecture_4) R->L }
% 1.44/0.48 tuple(true, ifeq(ifeq(ifeq(ifeq(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)), true, 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)), true), true, ifeq(c_in(c_Pair(v_ya, v_z, t_a, t_a), v_r, tc_prod(t_a, t_a)), true, ifeq(c_Comb_Odiamond(v_r, t_a), true, 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)), true), true), true), true, 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)), true), true, 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)), true))
% 1.44/0.48 = { by axiom 4 (cls_conjecture_3) }
% 1.44/0.48 tuple(true, ifeq(ifeq(ifeq(ifeq(true, true, 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)), true), true, ifeq(c_in(c_Pair(v_ya, v_z, t_a, t_a), v_r, tc_prod(t_a, t_a)), true, ifeq(c_Comb_Odiamond(v_r, t_a), true, 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)), true), true), true), true, 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)), true), true, 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)), true))
% 1.44/0.48 = { by axiom 2 (ifeq_axiom) }
% 1.44/0.48 tuple(true, ifeq(ifeq(ifeq(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)), true, ifeq(c_in(c_Pair(v_ya, v_z, t_a, t_a), v_r, tc_prod(t_a, t_a)), true, ifeq(c_Comb_Odiamond(v_r, t_a), true, 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)), true), true), true), true, 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)), true), true, 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)), true))
% 1.44/0.48 = { by axiom 9 (cls_Comb_Odiamond__strip__lemmaE_1) }
% 1.44/0.49 tuple(true, ifeq(ifeq(true, true, 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)), true), true, 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)), true))
% 1.44/0.49 = { by axiom 2 (ifeq_axiom) }
% 1.44/0.49 tuple(true, ifeq(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)), true, 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)), true))
% 1.44/0.49 = { by axiom 2 (ifeq_axiom) R->L }
% 1.44/0.49 tuple(true, ifeq(true, true, ifeq(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)), true, 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)), true), true))
% 1.44/0.49 = { by axiom 6 (cls_conjecture_5) R->L }
% 1.44/0.49 tuple(true, ifeq(ifeq(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)), true, 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)), true), true, ifeq(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)), true, 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)), true), true))
% 1.44/0.49 = { by axiom 4 (cls_conjecture_3) }
% 1.44/0.49 tuple(true, ifeq(ifeq(true, true, 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)), true), true, ifeq(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)), true, 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)), true), true))
% 1.44/0.49 = { by axiom 2 (ifeq_axiom) }
% 1.44/0.49 tuple(true, ifeq(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)), true, ifeq(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)), true, 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)), true), true))
% 1.44/0.49 = { by axiom 8 (cls_Transitive__Closure_Ortrancl__trans_0) }
% 1.44/0.49 tuple(true, true)
% 1.44/0.49 % SZS output end Proof
% 1.44/0.49
% 1.44/0.49 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------