%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GEO002-4 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n003.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 09:50:05 AM UTC 2026
% Result : Unsatisfiable 3.12s 0.82s
% Output : Proof 3.83s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO002-4 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n003.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sun Sep 27 06:31:10 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.12/0.82 Command-line arguments: --flatten --complete-subsets
% 3.12/0.82
% 3.12/0.82 % SZS status Unsatisfiable
% 3.12/0.82
% 3.83/0.92 % SZS output start Proof
% 3.83/0.92 Axiom 1 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 3.83/0.92 Axiom 2 (segment_construction1): between(X, Y, extension(X, Y, Z, W)) = true.
% 3.83/0.92 Axiom 3 (segment_construction2): equidistant(X, extension(Y, X, Z, W), Z, W) = true.
% 3.83/0.92 Axiom 4 (identity_for_equidistance): ifeq(equidistant(X, Y, Z, Z), true, equalish(X, Y), true) = true.
% 3.83/0.92 Axiom 5 (between_substitution3): ifeq(equalish(X, Y), true, ifeq(between(Z, W, X), true, between(Z, W, Y), true), true) = true.
% 3.83/0.92 Axiom 6 (transitivity_for_betweeness): ifeq(between(X, Y, Z), true, ifeq(between(W, X, Z), true, between(W, X, Y), true), true) = true.
% 3.83/0.92 Axiom 7 (outer_pasch2): ifeq(between(X, Y, Z), true, ifeq(between(W, V, Y), true, between(Z, V, outer_pasch(V, W, X, Z, Y)), true), true) = true.
% 3.83/0.93 Axiom 8 (outer_pasch1): ifeq(between(X, Y, Z), true, ifeq(between(W, V, Y), true, between(W, outer_pasch(V, W, X, Z, Y), X), true), true) = true.
% 3.83/0.93
% 3.83/0.93 Goal 1 (prove_a_between_a_and_b): between(a, a, b) = true.
% 3.83/0.93 Proof:
% 3.83/0.93 between(a, a, b)
% 3.83/0.93 = { by axiom 1 (ifeq_axiom) R->L }
% 3.83/0.93 ifeq(true, true, between(a, a, b), true)
% 3.83/0.93 = { by axiom 6 (transitivity_for_betweeness) R->L }
% 3.83/0.93 ifeq(ifeq(between(b, outer_pasch(a, b, b, a, a), b), true, ifeq(between(a, b, b), true, between(a, b, outer_pasch(a, b, b, a, a)), true), true), true, between(a, a, b), true)
% 3.83/0.93 = { by axiom 1 (ifeq_axiom) R->L }
% 3.83/0.93 ifeq(ifeq(between(b, outer_pasch(a, b, b, a, a), b), true, ifeq(ifeq(true, true, between(a, b, b), true), true, between(a, b, outer_pasch(a, b, b, a, a)), true), true), true, between(a, a, b), true)
% 3.83/0.93 = { by axiom 5 (between_substitution3) R->L }
% 3.83/0.94 ifeq(ifeq(between(b, outer_pasch(a, b, b, a, a), b), true, ifeq(ifeq(ifeq(equalish(b, extension(a, b, X, X)), true, ifeq(between(b, b, b), true, between(b, b, extension(a, b, X, X)), true), true), true, between(a, b, b), true), true, between(a, b, outer_pasch(a, b, b, a, a)), true), true), true, between(a, a, b), true)
% 3.83/0.94 = { by axiom 1 (ifeq_axiom) R->L }
% 3.83/0.94 ifeq(ifeq(between(b, outer_pasch(a, b, b, a, a), b), true, ifeq(ifeq(ifeq(equalish(b, extension(a, b, X, X)), true, ifeq(ifeq(true, true, between(b, b, b), true), true, between(b, b, extension(a, b, X, X)), true), true), true, between(a, b, b), true), true, between(a, b, outer_pasch(a, b, b, a, a)), true), true), true, between(a, a, b), true)
% 3.83/0.94 = { by axiom 2 (segment_construction1) R->L }
% 3.83/0.94 ifeq(ifeq(between(b, outer_pasch(a, b, b, a, a), b), true, ifeq(ifeq(ifeq(equalish(b, extension(a, b, X, X)), true, ifeq(ifeq(between(b, b, extension(b, b, Y, Z)), true, between(b, b, b), true), true, between(b, b, extension(a, b, X, X)), true), true), true, between(a, b, b), true), true, between(a, b, outer_pasch(a, b, b, a, a)), true), true), true, between(a, a, b), true)
% 3.83/0.94 = { by axiom 1 (ifeq_axiom) R->L }
% 3.83/0.94 ifeq(ifeq(between(b, outer_pasch(a, b, b, a, a), b), true, ifeq(ifeq(ifeq(equalish(b, extension(a, b, X, X)), true, ifeq(ifeq(true, true, ifeq(between(b, b, extension(b, b, Y, Z)), true, between(b, b, b), true), true), true, between(b, b, extension(a, b, X, X)), true), true), true, between(a, b, b), true), true, between(a, b, outer_pasch(a, b, b, a, a)), true), true), true, between(a, a, b), true)
% 3.83/0.94 = { by axiom 2 (segment_construction1) R->L }
% 3.83/0.94 ifeq(ifeq(between(b, outer_pasch(a, b, b, a, a), b), true, ifeq(ifeq(ifeq(equalish(b, extension(a, b, X, X)), true, ifeq(ifeq(between(b, b, extension(b, b, Y, Z)), true, ifeq(between(b, b, extension(b, b, Y, Z)), true, between(b, b, b), true), true), true, between(b, b, extension(a, b, X, X)), true), true), true, between(a, b, b), true), true, between(a, b, outer_pasch(a, b, b, a, a)), true), true), true, between(a, a, b), true)
% 3.83/0.94 = { by axiom 6 (transitivity_for_betweeness) }
% 3.83/0.94 ifeq(ifeq(between(b, outer_pasch(a, b, b, a, a), b), true, ifeq(ifeq(ifeq(equalish(b, extension(a, b, X, X)), true, ifeq(true, true, between(b, b, extension(a, b, X, X)), true), true), true, between(a, b, b), true), true, between(a, b, outer_pasch(a, b, b, a, a)), true), true), true, between(a, a, b), true)
% 3.83/0.94 = { by axiom 1 (ifeq_axiom) }
% 3.83/0.94 ifeq(ifeq(between(b, outer_pasch(a, b, b, a, a), b), true, ifeq(ifeq(ifeq(equalish(b, extension(a, b, X, X)), true, between(b, b, extension(a, b, X, X)), true), true, between(a, b, b), true), true, between(a, b, outer_pasch(a, b, b, a, a)), true), true), true, between(a, a, b), true)
% 3.83/0.94 = { by axiom 1 (ifeq_axiom) R->L }
% 3.83/0.94 ifeq(ifeq(between(b, outer_pasch(a, b, b, a, a), b), true, ifeq(ifeq(ifeq(ifeq(true, true, equalish(b, extension(a, b, X, X)), true), true, between(b, b, extension(a, b, X, X)), true), true, between(a, b, b), true), true, between(a, b, outer_pasch(a, b, b, a, a)), true), true), true, between(a, a, b), true)
% 3.83/0.94 = { by axiom 3 (segment_construction2) R->L }
% 3.83/0.94 ifeq(ifeq(between(b, outer_pasch(a, b, b, a, a), b), true, ifeq(ifeq(ifeq(ifeq(equidistant(b, extension(a, b, X, X), X, X), true, equalish(b, extension(a, b, X, X)), true), true, between(b, b, extension(a, b, X, X)), true), true, between(a, b, b), true), true, between(a, b, outer_pasch(a, b, b, a, a)), true), true), true, between(a, a, b), true)
% 3.83/0.94 = { by axiom 4 (identity_for_equidistance) }
% 3.83/0.94 ifeq(ifeq(between(b, outer_pasch(a, b, b, a, a), b), true, ifeq(ifeq(ifeq(true, true, between(b, b, extension(a, b, X, X)), true), true, between(a, b, b), true), true, between(a, b, outer_pasch(a, b, b, a, a)), true), true), true, between(a, a, b), true)
% 3.83/0.94 = { by axiom 1 (ifeq_axiom) }
% 3.83/0.94 ifeq(ifeq(between(b, outer_pasch(a, b, b, a, a), b), true, ifeq(ifeq(between(b, b, extension(a, b, X, X)), true, between(a, b, b), true), true, between(a, b, outer_pasch(a, b, b, a, a)), true), true), true, between(a, a, b), true)
% 3.83/0.94 = { by axiom 1 (ifeq_axiom) R->L }
% 3.83/0.94 ifeq(ifeq(between(b, outer_pasch(a, b, b, a, a), b), true, ifeq(ifeq(between(b, b, extension(a, b, X, X)), true, ifeq(true, true, between(a, b, b), true), true), true, between(a, b, outer_pasch(a, b, b, a, a)), true), true), true, between(a, a, b), true)
% 3.83/0.94 = { by axiom 2 (segment_construction1) R->L }
% 3.83/0.94 ifeq(ifeq(between(b, outer_pasch(a, b, b, a, a), b), true, ifeq(ifeq(between(b, b, extension(a, b, X, X)), true, ifeq(between(a, b, extension(a, b, X, X)), true, between(a, b, b), true), true), true, between(a, b, outer_pasch(a, b, b, a, a)), true), true), true, between(a, a, b), true)
% 3.83/0.94 = { by axiom 6 (transitivity_for_betweeness) }
% 3.83/0.94 ifeq(ifeq(between(b, outer_pasch(a, b, b, a, a), b), true, ifeq(true, true, between(a, b, outer_pasch(a, b, b, a, a)), true), true), true, between(a, a, b), true)
% 3.83/0.94 = { by axiom 1 (ifeq_axiom) }
% 3.83/0.94 ifeq(ifeq(between(b, outer_pasch(a, b, b, a, a), b), true, between(a, b, outer_pasch(a, b, b, a, a)), true), true, between(a, a, b), true)
% 3.83/0.94 = { by axiom 1 (ifeq_axiom) R->L }
% 3.83/0.94 ifeq(ifeq(ifeq(true, true, between(b, outer_pasch(a, b, b, a, a), b), true), true, between(a, b, outer_pasch(a, b, b, a, a)), true), true, between(a, a, b), true)
% 3.83/0.94 = { by axiom 6 (transitivity_for_betweeness) R->L }
% 3.83/0.94 ifeq(ifeq(ifeq(ifeq(between(a, a, extension(b, a, W, W)), true, ifeq(between(b, a, extension(b, a, W, W)), true, between(b, a, a), true), true), true, between(b, outer_pasch(a, b, b, a, a), b), true), true, between(a, b, outer_pasch(a, b, b, a, a)), true), true, between(a, a, b), true)
% 3.83/0.94 = { by axiom 2 (segment_construction1) }
% 3.83/0.94 ifeq(ifeq(ifeq(ifeq(between(a, a, extension(b, a, W, W)), true, ifeq(true, true, between(b, a, a), true), true), true, between(b, outer_pasch(a, b, b, a, a), b), true), true, between(a, b, outer_pasch(a, b, b, a, a)), true), true, between(a, a, b), true)
% 3.83/0.94 = { by axiom 1 (ifeq_axiom) }
% 3.83/0.94 ifeq(ifeq(ifeq(ifeq(between(a, a, extension(b, a, W, W)), true, between(b, a, a), true), true, between(b, outer_pasch(a, b, b, a, a), b), true), true, between(a, b, outer_pasch(a, b, b, a, a)), true), true, between(a, a, b), true)
% 3.83/0.94 = { by axiom 1 (ifeq_axiom) R->L }
% 3.83/0.95 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, between(a, a, extension(b, a, W, W)), true), true, between(b, a, a), true), true, between(b, outer_pasch(a, b, b, a, a), b), true), true, between(a, b, outer_pasch(a, b, b, a, a)), true), true, between(a, a, b), true)
% 3.83/0.95 = { by axiom 4 (identity_for_equidistance) R->L }
% 3.83/0.95 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(equidistant(a, extension(b, a, W, W), W, W), true, equalish(a, extension(b, a, W, W)), true), true, between(a, a, extension(b, a, W, W)), true), true, between(b, a, a), true), true, between(b, outer_pasch(a, b, b, a, a), b), true), true, between(a, b, outer_pasch(a, b, b, a, a)), true), true, between(a, a, b), true)
% 3.83/0.95 = { by axiom 3 (segment_construction2) }
% 3.83/0.95 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, equalish(a, extension(b, a, W, W)), true), true, between(a, a, extension(b, a, W, W)), true), true, between(b, a, a), true), true, between(b, outer_pasch(a, b, b, a, a), b), true), true, between(a, b, outer_pasch(a, b, b, a, a)), true), true, between(a, a, b), true)
% 3.83/0.95 = { by axiom 1 (ifeq_axiom) }
% 3.83/0.95 ifeq(ifeq(ifeq(ifeq(ifeq(equalish(a, extension(b, a, W, W)), true, between(a, a, extension(b, a, W, W)), true), true, between(b, a, a), true), true, between(b, outer_pasch(a, b, b, a, a), b), true), true, between(a, b, outer_pasch(a, b, b, a, a)), true), true, between(a, a, b), true)
% 3.83/0.95 = { by axiom 1 (ifeq_axiom) R->L }
% 3.83/0.95 ifeq(ifeq(ifeq(ifeq(ifeq(equalish(a, extension(b, a, W, W)), true, ifeq(true, true, between(a, a, extension(b, a, W, W)), true), true), true, between(b, a, a), true), true, between(b, outer_pasch(a, b, b, a, a), b), true), true, between(a, b, outer_pasch(a, b, b, a, a)), true), true, between(a, a, b), true)
% 3.83/0.95 = { by axiom 6 (transitivity_for_betweeness) R->L }
% 3.83/0.95 ifeq(ifeq(ifeq(ifeq(ifeq(equalish(a, extension(b, a, W, W)), true, ifeq(ifeq(between(a, a, extension(a, a, V, U)), true, ifeq(between(a, a, extension(a, a, V, U)), true, between(a, a, a), true), true), true, between(a, a, extension(b, a, W, W)), true), true), true, between(b, a, a), true), true, between(b, outer_pasch(a, b, b, a, a), b), true), true, between(a, b, outer_pasch(a, b, b, a, a)), true), true, between(a, a, b), true)
% 3.83/0.95 = { by axiom 2 (segment_construction1) }
% 3.83/0.95 ifeq(ifeq(ifeq(ifeq(ifeq(equalish(a, extension(b, a, W, W)), true, ifeq(ifeq(true, true, ifeq(between(a, a, extension(a, a, V, U)), true, between(a, a, a), true), true), true, between(a, a, extension(b, a, W, W)), true), true), true, between(b, a, a), true), true, between(b, outer_pasch(a, b, b, a, a), b), true), true, between(a, b, outer_pasch(a, b, b, a, a)), true), true, between(a, a, b), true)
% 3.83/0.95 = { by axiom 1 (ifeq_axiom) }
% 3.83/0.95 ifeq(ifeq(ifeq(ifeq(ifeq(equalish(a, extension(b, a, W, W)), true, ifeq(ifeq(between(a, a, extension(a, a, V, U)), true, between(a, a, a), true), true, between(a, a, extension(b, a, W, W)), true), true), true, between(b, a, a), true), true, between(b, outer_pasch(a, b, b, a, a), b), true), true, between(a, b, outer_pasch(a, b, b, a, a)), true), true, between(a, a, b), true)
% 3.83/0.95 = { by axiom 2 (segment_construction1) }
% 3.83/0.95 ifeq(ifeq(ifeq(ifeq(ifeq(equalish(a, extension(b, a, W, W)), true, ifeq(ifeq(true, true, between(a, a, a), true), true, between(a, a, extension(b, a, W, W)), true), true), true, between(b, a, a), true), true, between(b, outer_pasch(a, b, b, a, a), b), true), true, between(a, b, outer_pasch(a, b, b, a, a)), true), true, between(a, a, b), true)
% 3.83/0.95 = { by axiom 1 (ifeq_axiom) }
% 3.83/0.95 ifeq(ifeq(ifeq(ifeq(ifeq(equalish(a, extension(b, a, W, W)), true, ifeq(between(a, a, a), true, between(a, a, extension(b, a, W, W)), true), true), true, between(b, a, a), true), true, between(b, outer_pasch(a, b, b, a, a), b), true), true, between(a, b, outer_pasch(a, b, b, a, a)), true), true, between(a, a, b), true)
% 3.83/0.95 = { by axiom 5 (between_substitution3) }
% 3.83/0.95 ifeq(ifeq(ifeq(ifeq(true, true, between(b, a, a), true), true, between(b, outer_pasch(a, b, b, a, a), b), true), true, between(a, b, outer_pasch(a, b, b, a, a)), true), true, between(a, a, b), true)
% 3.83/0.95 = { by axiom 1 (ifeq_axiom) }
% 3.83/0.95 ifeq(ifeq(ifeq(between(b, a, a), true, between(b, outer_pasch(a, b, b, a, a), b), true), true, between(a, b, outer_pasch(a, b, b, a, a)), true), true, between(a, a, b), true)
% 3.83/0.95 = { by axiom 1 (ifeq_axiom) R->L }
% 3.83/0.95 ifeq(ifeq(ifeq(true, true, ifeq(between(b, a, a), true, between(b, outer_pasch(a, b, b, a, a), b), true), true), true, between(a, b, outer_pasch(a, b, b, a, a)), true), true, between(a, a, b), true)
% 3.83/0.95 = { by axiom 6 (transitivity_for_betweeness) R->L }
% 3.83/0.95 ifeq(ifeq(ifeq(ifeq(between(a, a, extension(b, a, T, T)), true, ifeq(between(b, a, extension(b, a, T, T)), true, between(b, a, a), true), true), true, ifeq(between(b, a, a), true, between(b, outer_pasch(a, b, b, a, a), b), true), true), true, between(a, b, outer_pasch(a, b, b, a, a)), true), true, between(a, a, b), true)
% 3.83/0.96 = { by axiom 2 (segment_construction1) }
% 3.83/0.96 ifeq(ifeq(ifeq(ifeq(between(a, a, extension(b, a, T, T)), true, ifeq(true, true, between(b, a, a), true), true), true, ifeq(between(b, a, a), true, between(b, outer_pasch(a, b, b, a, a), b), true), true), true, between(a, b, outer_pasch(a, b, b, a, a)), true), true, between(a, a, b), true)
% 3.83/0.96 = { by axiom 1 (ifeq_axiom) }
% 3.83/0.96 ifeq(ifeq(ifeq(ifeq(between(a, a, extension(b, a, T, T)), true, between(b, a, a), true), true, ifeq(between(b, a, a), true, between(b, outer_pasch(a, b, b, a, a), b), true), true), true, between(a, b, outer_pasch(a, b, b, a, a)), true), true, between(a, a, b), true)
% 3.83/0.96 = { by axiom 1 (ifeq_axiom) R->L }
% 3.83/0.96 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, between(a, a, extension(b, a, T, T)), true), true, between(b, a, a), true), true, ifeq(between(b, a, a), true, between(b, outer_pasch(a, b, b, a, a), b), true), true), true, between(a, b, outer_pasch(a, b, b, a, a)), true), true, between(a, a, b), true)
% 3.83/0.96 = { by axiom 4 (identity_for_equidistance) R->L }
% 3.83/0.96 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(equidistant(a, extension(b, a, T, T), T, T), true, equalish(a, extension(b, a, T, T)), true), true, between(a, a, extension(b, a, T, T)), true), true, between(b, a, a), true), true, ifeq(between(b, a, a), true, between(b, outer_pasch(a, b, b, a, a), b), true), true), true, between(a, b, outer_pasch(a, b, b, a, a)), true), true, between(a, a, b), true)
% 3.83/0.96 = { by axiom 3 (segment_construction2) }
% 3.83/0.96 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, equalish(a, extension(b, a, T, T)), true), true, between(a, a, extension(b, a, T, T)), true), true, between(b, a, a), true), true, ifeq(between(b, a, a), true, between(b, outer_pasch(a, b, b, a, a), b), true), true), true, between(a, b, outer_pasch(a, b, b, a, a)), true), true, between(a, a, b), true)
% 3.83/0.96 = { by axiom 1 (ifeq_axiom) }
% 3.83/0.96 ifeq(ifeq(ifeq(ifeq(ifeq(equalish(a, extension(b, a, T, T)), true, between(a, a, extension(b, a, T, T)), true), true, between(b, a, a), true), true, ifeq(between(b, a, a), true, between(b, outer_pasch(a, b, b, a, a), b), true), true), true, between(a, b, outer_pasch(a, b, b, a, a)), true), true, between(a, a, b), true)
% 3.83/0.96 = { by axiom 1 (ifeq_axiom) R->L }
% 3.83/0.96 ifeq(ifeq(ifeq(ifeq(ifeq(equalish(a, extension(b, a, T, T)), true, ifeq(true, true, between(a, a, extension(b, a, T, T)), true), true), true, between(b, a, a), true), true, ifeq(between(b, a, a), true, between(b, outer_pasch(a, b, b, a, a), b), true), true), true, between(a, b, outer_pasch(a, b, b, a, a)), true), true, between(a, a, b), true)
% 3.83/0.96 = { by axiom 6 (transitivity_for_betweeness) R->L }
% 3.83/0.96 ifeq(ifeq(ifeq(ifeq(ifeq(equalish(a, extension(b, a, T, T)), true, ifeq(ifeq(between(a, a, extension(a, a, S, X2)), true, ifeq(between(a, a, extension(a, a, S, X2)), true, between(a, a, a), true), true), true, between(a, a, extension(b, a, T, T)), true), true), true, between(b, a, a), true), true, ifeq(between(b, a, a), true, between(b, outer_pasch(a, b, b, a, a), b), true), true), true, between(a, b, outer_pasch(a, b, b, a, a)), true), true, between(a, a, b), true)
% 3.83/0.96 = { by axiom 2 (segment_construction1) }
% 3.83/0.96 ifeq(ifeq(ifeq(ifeq(ifeq(equalish(a, extension(b, a, T, T)), true, ifeq(ifeq(true, true, ifeq(between(a, a, extension(a, a, S, X2)), true, between(a, a, a), true), true), true, between(a, a, extension(b, a, T, T)), true), true), true, between(b, a, a), true), true, ifeq(between(b, a, a), true, between(b, outer_pasch(a, b, b, a, a), b), true), true), true, between(a, b, outer_pasch(a, b, b, a, a)), true), true, between(a, a, b), true)
% 3.83/0.96 = { by axiom 1 (ifeq_axiom) }
% 3.83/0.96 ifeq(ifeq(ifeq(ifeq(ifeq(equalish(a, extension(b, a, T, T)), true, ifeq(ifeq(between(a, a, extension(a, a, S, X2)), true, between(a, a, a), true), true, between(a, a, extension(b, a, T, T)), true), true), true, between(b, a, a), true), true, ifeq(between(b, a, a), true, between(b, outer_pasch(a, b, b, a, a), b), true), true), true, between(a, b, outer_pasch(a, b, b, a, a)), true), true, between(a, a, b), true)
% 3.83/0.96 = { by axiom 2 (segment_construction1) }
% 3.83/0.96 ifeq(ifeq(ifeq(ifeq(ifeq(equalish(a, extension(b, a, T, T)), true, ifeq(ifeq(true, true, between(a, a, a), true), true, between(a, a, extension(b, a, T, T)), true), true), true, between(b, a, a), true), true, ifeq(between(b, a, a), true, between(b, outer_pasch(a, b, b, a, a), b), true), true), true, between(a, b, outer_pasch(a, b, b, a, a)), true), true, between(a, a, b), true)
% 3.83/0.96 = { by axiom 1 (ifeq_axiom) }
% 3.83/0.96 ifeq(ifeq(ifeq(ifeq(ifeq(equalish(a, extension(b, a, T, T)), true, ifeq(between(a, a, a), true, between(a, a, extension(b, a, T, T)), true), true), true, between(b, a, a), true), true, ifeq(between(b, a, a), true, between(b, outer_pasch(a, b, b, a, a), b), true), true), true, between(a, b, outer_pasch(a, b, b, a, a)), true), true, between(a, a, b), true)
% 3.83/0.96 = { by axiom 5 (between_substitution3) }
% 3.83/0.96 ifeq(ifeq(ifeq(ifeq(true, true, between(b, a, a), true), true, ifeq(between(b, a, a), true, between(b, outer_pasch(a, b, b, a, a), b), true), true), true, between(a, b, outer_pasch(a, b, b, a, a)), true), true, between(a, a, b), true)
% 3.83/0.96 = { by axiom 1 (ifeq_axiom) }
% 3.83/0.96 ifeq(ifeq(ifeq(between(b, a, a), true, ifeq(between(b, a, a), true, between(b, outer_pasch(a, b, b, a, a), b), true), true), true, between(a, b, outer_pasch(a, b, b, a, a)), true), true, between(a, a, b), true)
% 3.83/0.96 = { by axiom 8 (outer_pasch1) }
% 3.83/0.96 ifeq(ifeq(true, true, between(a, b, outer_pasch(a, b, b, a, a)), true), true, between(a, a, b), true)
% 3.83/0.96 = { by axiom 1 (ifeq_axiom) }
% 3.83/0.96 ifeq(between(a, b, outer_pasch(a, b, b, a, a)), true, between(a, a, b), true)
% 3.83/0.96 = { by axiom 1 (ifeq_axiom) R->L }
% 3.83/0.96 ifeq(between(a, b, outer_pasch(a, b, b, a, a)), true, ifeq(true, true, between(a, a, b), true), true)
% 3.83/0.96 = { by axiom 7 (outer_pasch2) R->L }
% 3.83/0.96 ifeq(between(a, b, outer_pasch(a, b, b, a, a)), true, ifeq(ifeq(between(b, a, a), true, ifeq(between(b, a, a), true, between(a, a, outer_pasch(a, b, b, a, a)), true), true), true, between(a, a, b), true), true)
% 3.83/0.96 = { by axiom 1 (ifeq_axiom) R->L }
% 3.83/0.96 ifeq(between(a, b, outer_pasch(a, b, b, a, a)), true, ifeq(ifeq(ifeq(true, true, between(b, a, a), true), true, ifeq(between(b, a, a), true, between(a, a, outer_pasch(a, b, b, a, a)), true), true), true, between(a, a, b), true), true)
% 3.83/0.96 = { by axiom 5 (between_substitution3) R->L }
% 3.83/0.96 ifeq(between(a, b, outer_pasch(a, b, b, a, a)), true, ifeq(ifeq(ifeq(ifeq(equalish(a, extension(b, a, Y2, Y2)), true, ifeq(between(a, a, a), true, between(a, a, extension(b, a, Y2, Y2)), true), true), true, between(b, a, a), true), true, ifeq(between(b, a, a), true, between(a, a, outer_pasch(a, b, b, a, a)), true), true), true, between(a, a, b), true), true)
% 3.83/0.96 = { by axiom 1 (ifeq_axiom) R->L }
% 3.83/0.96 ifeq(between(a, b, outer_pasch(a, b, b, a, a)), true, ifeq(ifeq(ifeq(ifeq(equalish(a, extension(b, a, Y2, Y2)), true, ifeq(ifeq(true, true, between(a, a, a), true), true, between(a, a, extension(b, a, Y2, Y2)), true), true), true, between(b, a, a), true), true, ifeq(between(b, a, a), true, between(a, a, outer_pasch(a, b, b, a, a)), true), true), true, between(a, a, b), true), true)
% 3.83/0.96 = { by axiom 2 (segment_construction1) R->L }
% 3.83/0.97 ifeq(between(a, b, outer_pasch(a, b, b, a, a)), true, ifeq(ifeq(ifeq(ifeq(equalish(a, extension(b, a, Y2, Y2)), true, ifeq(ifeq(between(a, a, extension(a, a, Z2, W2)), true, between(a, a, a), true), true, between(a, a, extension(b, a, Y2, Y2)), true), true), true, between(b, a, a), true), true, ifeq(between(b, a, a), true, between(a, a, outer_pasch(a, b, b, a, a)), true), true), true, between(a, a, b), true), true)
% 3.83/0.97 = { by axiom 1 (ifeq_axiom) R->L }
% 3.83/0.97 ifeq(between(a, b, outer_pasch(a, b, b, a, a)), true, ifeq(ifeq(ifeq(ifeq(equalish(a, extension(b, a, Y2, Y2)), true, ifeq(ifeq(true, true, ifeq(between(a, a, extension(a, a, Z2, W2)), true, between(a, a, a), true), true), true, between(a, a, extension(b, a, Y2, Y2)), true), true), true, between(b, a, a), true), true, ifeq(between(b, a, a), true, between(a, a, outer_pasch(a, b, b, a, a)), true), true), true, between(a, a, b), true), true)
% 3.83/0.97 = { by axiom 2 (segment_construction1) R->L }
% 3.83/0.97 ifeq(between(a, b, outer_pasch(a, b, b, a, a)), true, ifeq(ifeq(ifeq(ifeq(equalish(a, extension(b, a, Y2, Y2)), true, ifeq(ifeq(between(a, a, extension(a, a, Z2, W2)), true, ifeq(between(a, a, extension(a, a, Z2, W2)), true, between(a, a, a), true), true), true, between(a, a, extension(b, a, Y2, Y2)), true), true), true, between(b, a, a), true), true, ifeq(between(b, a, a), true, between(a, a, outer_pasch(a, b, b, a, a)), true), true), true, between(a, a, b), true), true)
% 3.83/0.97 = { by axiom 6 (transitivity_for_betweeness) }
% 3.83/0.97 ifeq(between(a, b, outer_pasch(a, b, b, a, a)), true, ifeq(ifeq(ifeq(ifeq(equalish(a, extension(b, a, Y2, Y2)), true, ifeq(true, true, between(a, a, extension(b, a, Y2, Y2)), true), true), true, between(b, a, a), true), true, ifeq(between(b, a, a), true, between(a, a, outer_pasch(a, b, b, a, a)), true), true), true, between(a, a, b), true), true)
% 3.83/0.97 = { by axiom 1 (ifeq_axiom) }
% 3.83/0.97 ifeq(between(a, b, outer_pasch(a, b, b, a, a)), true, ifeq(ifeq(ifeq(ifeq(equalish(a, extension(b, a, Y2, Y2)), true, between(a, a, extension(b, a, Y2, Y2)), true), true, between(b, a, a), true), true, ifeq(between(b, a, a), true, between(a, a, outer_pasch(a, b, b, a, a)), true), true), true, between(a, a, b), true), true)
% 3.83/0.97 = { by axiom 1 (ifeq_axiom) R->L }
% 3.83/0.97 ifeq(between(a, b, outer_pasch(a, b, b, a, a)), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, equalish(a, extension(b, a, Y2, Y2)), true), true, between(a, a, extension(b, a, Y2, Y2)), true), true, between(b, a, a), true), true, ifeq(between(b, a, a), true, between(a, a, outer_pasch(a, b, b, a, a)), true), true), true, between(a, a, b), true), true)
% 3.83/0.97 = { by axiom 3 (segment_construction2) R->L }
% 3.83/0.97 ifeq(between(a, b, outer_pasch(a, b, b, a, a)), true, ifeq(ifeq(ifeq(ifeq(ifeq(equidistant(a, extension(b, a, Y2, Y2), Y2, Y2), true, equalish(a, extension(b, a, Y2, Y2)), true), true, between(a, a, extension(b, a, Y2, Y2)), true), true, between(b, a, a), true), true, ifeq(between(b, a, a), true, between(a, a, outer_pasch(a, b, b, a, a)), true), true), true, between(a, a, b), true), true)
% 3.83/0.97 = { by axiom 4 (identity_for_equidistance) }
% 3.83/0.97 ifeq(between(a, b, outer_pasch(a, b, b, a, a)), true, ifeq(ifeq(ifeq(ifeq(true, true, between(a, a, extension(b, a, Y2, Y2)), true), true, between(b, a, a), true), true, ifeq(between(b, a, a), true, between(a, a, outer_pasch(a, b, b, a, a)), true), true), true, between(a, a, b), true), true)
% 3.83/0.97 = { by axiom 1 (ifeq_axiom) }
% 3.83/0.97 ifeq(between(a, b, outer_pasch(a, b, b, a, a)), true, ifeq(ifeq(ifeq(between(a, a, extension(b, a, Y2, Y2)), true, between(b, a, a), true), true, ifeq(between(b, a, a), true, between(a, a, outer_pasch(a, b, b, a, a)), true), true), true, between(a, a, b), true), true)
% 3.83/0.97 = { by axiom 1 (ifeq_axiom) R->L }
% 3.83/0.97 ifeq(between(a, b, outer_pasch(a, b, b, a, a)), true, ifeq(ifeq(ifeq(between(a, a, extension(b, a, Y2, Y2)), true, ifeq(true, true, between(b, a, a), true), true), true, ifeq(between(b, a, a), true, between(a, a, outer_pasch(a, b, b, a, a)), true), true), true, between(a, a, b), true), true)
% 3.83/0.97 = { by axiom 2 (segment_construction1) R->L }
% 3.83/0.97 ifeq(between(a, b, outer_pasch(a, b, b, a, a)), true, ifeq(ifeq(ifeq(between(a, a, extension(b, a, Y2, Y2)), true, ifeq(between(b, a, extension(b, a, Y2, Y2)), true, between(b, a, a), true), true), true, ifeq(between(b, a, a), true, between(a, a, outer_pasch(a, b, b, a, a)), true), true), true, between(a, a, b), true), true)
% 3.83/0.97 = { by axiom 6 (transitivity_for_betweeness) }
% 3.83/0.97 ifeq(between(a, b, outer_pasch(a, b, b, a, a)), true, ifeq(ifeq(true, true, ifeq(between(b, a, a), true, between(a, a, outer_pasch(a, b, b, a, a)), true), true), true, between(a, a, b), true), true)
% 3.83/0.97 = { by axiom 1 (ifeq_axiom) }
% 3.83/0.97 ifeq(between(a, b, outer_pasch(a, b, b, a, a)), true, ifeq(ifeq(between(b, a, a), true, between(a, a, outer_pasch(a, b, b, a, a)), true), true, between(a, a, b), true), true)
% 3.83/0.97 = { by axiom 1 (ifeq_axiom) R->L }
% 3.83/0.97 ifeq(between(a, b, outer_pasch(a, b, b, a, a)), true, ifeq(ifeq(ifeq(true, true, between(b, a, a), true), true, between(a, a, outer_pasch(a, b, b, a, a)), true), true, between(a, a, b), true), true)
% 3.83/0.97 = { by axiom 5 (between_substitution3) R->L }
% 3.83/0.97 ifeq(between(a, b, outer_pasch(a, b, b, a, a)), true, ifeq(ifeq(ifeq(ifeq(equalish(a, extension(b, a, V2, V2)), true, ifeq(between(a, a, a), true, between(a, a, extension(b, a, V2, V2)), true), true), true, between(b, a, a), true), true, between(a, a, outer_pasch(a, b, b, a, a)), true), true, between(a, a, b), true), true)
% 3.83/0.97 = { by axiom 1 (ifeq_axiom) R->L }
% 3.83/0.97 ifeq(between(a, b, outer_pasch(a, b, b, a, a)), true, ifeq(ifeq(ifeq(ifeq(equalish(a, extension(b, a, V2, V2)), true, ifeq(ifeq(true, true, between(a, a, a), true), true, between(a, a, extension(b, a, V2, V2)), true), true), true, between(b, a, a), true), true, between(a, a, outer_pasch(a, b, b, a, a)), true), true, between(a, a, b), true), true)
% 3.83/0.97 = { by axiom 2 (segment_construction1) R->L }
% 3.83/0.97 ifeq(between(a, b, outer_pasch(a, b, b, a, a)), true, ifeq(ifeq(ifeq(ifeq(equalish(a, extension(b, a, V2, V2)), true, ifeq(ifeq(between(a, a, extension(a, a, U2, T2)), true, between(a, a, a), true), true, between(a, a, extension(b, a, V2, V2)), true), true), true, between(b, a, a), true), true, between(a, a, outer_pasch(a, b, b, a, a)), true), true, between(a, a, b), true), true)
% 3.83/0.97 = { by axiom 1 (ifeq_axiom) R->L }
% 3.83/0.97 ifeq(between(a, b, outer_pasch(a, b, b, a, a)), true, ifeq(ifeq(ifeq(ifeq(equalish(a, extension(b, a, V2, V2)), true, ifeq(ifeq(true, true, ifeq(between(a, a, extension(a, a, U2, T2)), true, between(a, a, a), true), true), true, between(a, a, extension(b, a, V2, V2)), true), true), true, between(b, a, a), true), true, between(a, a, outer_pasch(a, b, b, a, a)), true), true, between(a, a, b), true), true)
% 3.83/0.97 = { by axiom 2 (segment_construction1) R->L }
% 3.83/0.97 ifeq(between(a, b, outer_pasch(a, b, b, a, a)), true, ifeq(ifeq(ifeq(ifeq(equalish(a, extension(b, a, V2, V2)), true, ifeq(ifeq(between(a, a, extension(a, a, U2, T2)), true, ifeq(between(a, a, extension(a, a, U2, T2)), true, between(a, a, a), true), true), true, between(a, a, extension(b, a, V2, V2)), true), true), true, between(b, a, a), true), true, between(a, a, outer_pasch(a, b, b, a, a)), true), true, between(a, a, b), true), true)
% 3.83/0.97 = { by axiom 6 (transitivity_for_betweeness) }
% 3.83/0.97 ifeq(between(a, b, outer_pasch(a, b, b, a, a)), true, ifeq(ifeq(ifeq(ifeq(equalish(a, extension(b, a, V2, V2)), true, ifeq(true, true, between(a, a, extension(b, a, V2, V2)), true), true), true, between(b, a, a), true), true, between(a, a, outer_pasch(a, b, b, a, a)), true), true, between(a, a, b), true), true)
% 3.83/0.97 = { by axiom 1 (ifeq_axiom) }
% 3.83/0.97 ifeq(between(a, b, outer_pasch(a, b, b, a, a)), true, ifeq(ifeq(ifeq(ifeq(equalish(a, extension(b, a, V2, V2)), true, between(a, a, extension(b, a, V2, V2)), true), true, between(b, a, a), true), true, between(a, a, outer_pasch(a, b, b, a, a)), true), true, between(a, a, b), true), true)
% 3.83/0.97 = { by axiom 1 (ifeq_axiom) R->L }
% 3.83/0.97 ifeq(between(a, b, outer_pasch(a, b, b, a, a)), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, equalish(a, extension(b, a, V2, V2)), true), true, between(a, a, extension(b, a, V2, V2)), true), true, between(b, a, a), true), true, between(a, a, outer_pasch(a, b, b, a, a)), true), true, between(a, a, b), true), true)
% 3.83/0.97 = { by axiom 3 (segment_construction2) R->L }
% 3.83/0.97 ifeq(between(a, b, outer_pasch(a, b, b, a, a)), true, ifeq(ifeq(ifeq(ifeq(ifeq(equidistant(a, extension(b, a, V2, V2), V2, V2), true, equalish(a, extension(b, a, V2, V2)), true), true, between(a, a, extension(b, a, V2, V2)), true), true, between(b, a, a), true), true, between(a, a, outer_pasch(a, b, b, a, a)), true), true, between(a, a, b), true), true)
% 3.83/0.97 = { by axiom 4 (identity_for_equidistance) }
% 3.83/0.97 ifeq(between(a, b, outer_pasch(a, b, b, a, a)), true, ifeq(ifeq(ifeq(ifeq(true, true, between(a, a, extension(b, a, V2, V2)), true), true, between(b, a, a), true), true, between(a, a, outer_pasch(a, b, b, a, a)), true), true, between(a, a, b), true), true)
% 3.83/0.97 = { by axiom 1 (ifeq_axiom) }
% 3.83/0.97 ifeq(between(a, b, outer_pasch(a, b, b, a, a)), true, ifeq(ifeq(ifeq(between(a, a, extension(b, a, V2, V2)), true, between(b, a, a), true), true, between(a, a, outer_pasch(a, b, b, a, a)), true), true, between(a, a, b), true), true)
% 3.83/0.97 = { by axiom 1 (ifeq_axiom) R->L }
% 3.83/0.97 ifeq(between(a, b, outer_pasch(a, b, b, a, a)), true, ifeq(ifeq(ifeq(between(a, a, extension(b, a, V2, V2)), true, ifeq(true, true, between(b, a, a), true), true), true, between(a, a, outer_pasch(a, b, b, a, a)), true), true, between(a, a, b), true), true)
% 3.83/0.97 = { by axiom 2 (segment_construction1) R->L }
% 3.83/0.97 ifeq(between(a, b, outer_pasch(a, b, b, a, a)), true, ifeq(ifeq(ifeq(between(a, a, extension(b, a, V2, V2)), true, ifeq(between(b, a, extension(b, a, V2, V2)), true, between(b, a, a), true), true), true, between(a, a, outer_pasch(a, b, b, a, a)), true), true, between(a, a, b), true), true)
% 3.83/0.98 = { by axiom 6 (transitivity_for_betweeness) }
% 3.83/0.98 ifeq(between(a, b, outer_pasch(a, b, b, a, a)), true, ifeq(ifeq(true, true, between(a, a, outer_pasch(a, b, b, a, a)), true), true, between(a, a, b), true), true)
% 3.83/0.98 = { by axiom 1 (ifeq_axiom) }
% 3.83/0.98 ifeq(between(a, b, outer_pasch(a, b, b, a, a)), true, ifeq(between(a, a, outer_pasch(a, b, b, a, a)), true, between(a, a, b), true), true)
% 3.83/0.98 = { by axiom 6 (transitivity_for_betweeness) }
% 3.83/0.98 true
% 3.83/0.98 % SZS output end Proof
% 3.83/0.98
% 3.83/0.98 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------