%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LCL025-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n014.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 11:48:51 AM UTC 2026
% Result : Unsatisfiable 4.60s 1.16s
% Output : Proof 7.75s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : LCL025-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.40 % Computer : n014.cluster.edu
% 0.16/0.40 % Model : x86_64 x86_64
% 0.16/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.40 % Memory : 8046.5625MB
% 0.16/0.40 % OS : Linux 6.8.0-71-generic
% 0.16/0.40 % CPULimit : 300
% 0.16/0.40 % WCLimit : 300
% 0.16/0.40 % DateTime : Sun Sep 27 15:17:46 UTC 2026
% 0.16/0.41 % CPUTime :
% 0.16/0.41 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.60/1.16 Command-line arguments: --no-flatten-goal
% 4.60/1.16
% 4.60/1.16 % SZS status Unsatisfiable
% 4.60/1.16
% 6.38/1.38 % SZS output start Proof
% 6.38/1.38 Axiom 1 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 6.38/1.38 Axiom 2 (c0_2): is_a_theorem(implies(X, implies(Y, X))) = true.
% 6.38/1.39 Axiom 3 (condensed_detachment): ifeq(is_a_theorem(implies(X, Y)), true, ifeq(is_a_theorem(X), true, is_a_theorem(Y), true), true) = true.
% 6.38/1.39 Axiom 4 (c0_6): is_a_theorem(implies(implies(X, implies(Y, Z)), implies(implies(X, Y), implies(X, Z)))) = true.
% 6.38/1.39
% 6.38/1.39 Goal 1 (prove_c0_1): is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))) = true.
% 6.38/1.39 Proof:
% 6.38/1.39 is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 6.38/1.39 = { by axiom 1 (ifeq_axiom) R->L }
% 6.38/1.39 ifeq(true, true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 6.38/1.39 = { by axiom 3 (condensed_detachment) R->L }
% 6.38/1.39 ifeq(ifeq(is_a_theorem(implies(implies(implies(b, c), implies(implies(a, b), implies(a, c))), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))))), true, ifeq(is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(a, c)))), true, is_a_theorem(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 6.38/1.39 = { by axiom 4 (c0_6) }
% 6.38/1.39 ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(a, c)))), true, is_a_theorem(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 6.38/1.40 = { by axiom 1 (ifeq_axiom) }
% 6.38/1.40 ifeq(ifeq(is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(a, c)))), true, is_a_theorem(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 6.38/1.40 = { by axiom 1 (ifeq_axiom) R->L }
% 6.38/1.40 ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(a, c)))), true), true, is_a_theorem(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 6.38/1.40 = { by axiom 3 (condensed_detachment) R->L }
% 6.38/1.40 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))), implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))))), true, ifeq(is_a_theorem(implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), true, is_a_theorem(implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(a, c)))), true), true, is_a_theorem(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 6.38/1.40 = { by axiom 2 (c0_2) }
% 6.38/1.40 ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), true, is_a_theorem(implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(a, c)))), true), true, is_a_theorem(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 6.38/1.40 = { by axiom 1 (ifeq_axiom) }
% 6.38/1.40 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), true, is_a_theorem(implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true), true, is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(a, c)))), true), true, is_a_theorem(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 6.38/1.40 = { by axiom 4 (c0_6) }
% 6.38/1.40 ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true), true, is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(a, c)))), true), true, is_a_theorem(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 6.38/1.40 = { by axiom 1 (ifeq_axiom) }
% 6.38/1.40 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true, is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(a, c)))), true), true, is_a_theorem(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 6.38/1.40 = { by axiom 1 (ifeq_axiom) R->L }
% 6.38/1.40 ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true, is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(a, c)))), true), true), true, is_a_theorem(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 7.08/1.40 = { by axiom 3 (condensed_detachment) R->L }
% 7.08/1.41 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), implies(implies(b, c), implies(a, implies(b, c)))), implies(implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), implies(implies(b, c), implies(implies(a, b), implies(a, c)))))), true, ifeq(is_a_theorem(implies(implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), implies(implies(b, c), implies(a, implies(b, c))))), true, is_a_theorem(implies(implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), implies(implies(b, c), implies(implies(a, b), implies(a, c))))), true), true), true, ifeq(is_a_theorem(implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true, is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(a, c)))), true), true), true, is_a_theorem(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 7.08/1.41 = { by axiom 1 (ifeq_axiom) R->L }
% 7.08/1.41 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), implies(implies(b, c), implies(a, implies(b, c)))), implies(implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), implies(implies(b, c), implies(implies(a, b), implies(a, c)))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), implies(implies(b, c), implies(a, implies(b, c))))), true), true, is_a_theorem(implies(implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), implies(implies(b, c), implies(implies(a, b), implies(a, c))))), true), true), true, ifeq(is_a_theorem(implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true, is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(a, c)))), true), true), true, is_a_theorem(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 7.08/1.41 = { by axiom 2 (c0_2) R->L }
% 7.08/1.41 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), implies(implies(b, c), implies(a, implies(b, c)))), implies(implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), implies(implies(b, c), implies(implies(a, b), implies(a, c)))))), true, ifeq(ifeq(is_a_theorem(implies(implies(b, c), implies(a, implies(b, c)))), true, is_a_theorem(implies(implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), implies(implies(b, c), implies(a, implies(b, c))))), true), true, is_a_theorem(implies(implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), implies(implies(b, c), implies(implies(a, b), implies(a, c))))), true), true), true, ifeq(is_a_theorem(implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true, is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(a, c)))), true), true), true, is_a_theorem(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 7.08/1.41 = { by axiom 1 (ifeq_axiom) R->L }
% 7.08/1.42 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), implies(implies(b, c), implies(a, implies(b, c)))), implies(implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), implies(implies(b, c), implies(implies(a, b), implies(a, c)))))), true, ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(b, c), implies(a, implies(b, c)))), true, is_a_theorem(implies(implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), implies(implies(b, c), implies(a, implies(b, c))))), true), true), true, is_a_theorem(implies(implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), implies(implies(b, c), implies(implies(a, b), implies(a, c))))), true), true), true, ifeq(is_a_theorem(implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true, is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(a, c)))), true), true), true, is_a_theorem(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 7.08/1.42 = { by axiom 2 (c0_2) R->L }
% 7.08/1.42 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), implies(implies(b, c), implies(a, implies(b, c)))), implies(implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), implies(implies(b, c), implies(implies(a, b), implies(a, c)))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(b, c), implies(a, implies(b, c))), implies(implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), implies(implies(b, c), implies(a, implies(b, c)))))), true, ifeq(is_a_theorem(implies(implies(b, c), implies(a, implies(b, c)))), true, is_a_theorem(implies(implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), implies(implies(b, c), implies(a, implies(b, c))))), true), true), true, is_a_theorem(implies(implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), implies(implies(b, c), implies(implies(a, b), implies(a, c))))), true), true), true, ifeq(is_a_theorem(implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true, is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(a, c)))), true), true), true, is_a_theorem(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 7.08/1.42 = { by axiom 3 (condensed_detachment) }
% 7.08/1.42 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), implies(implies(b, c), implies(a, implies(b, c)))), implies(implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), implies(implies(b, c), implies(implies(a, b), implies(a, c)))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), implies(implies(b, c), implies(implies(a, b), implies(a, c))))), true), true), true, ifeq(is_a_theorem(implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true, is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(a, c)))), true), true), true, is_a_theorem(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 7.08/1.42 = { by axiom 1 (ifeq_axiom) }
% 7.08/1.42 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), implies(implies(b, c), implies(a, implies(b, c)))), implies(implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), implies(implies(b, c), implies(implies(a, b), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), implies(implies(b, c), implies(implies(a, b), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true, is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(a, c)))), true), true), true, is_a_theorem(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 7.08/1.42 = { by axiom 1 (ifeq_axiom) R->L }
% 7.08/1.43 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), implies(implies(b, c), implies(a, implies(b, c)))), implies(implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), implies(implies(b, c), implies(implies(a, b), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), implies(implies(b, c), implies(implies(a, b), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true, is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(a, c)))), true), true), true, is_a_theorem(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 7.08/1.43 = { by axiom 4 (c0_6) R->L }
% 7.08/1.43 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), implies(implies(implies(b, c), implies(a, implies(b, c))), implies(implies(b, c), implies(implies(a, b), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), implies(implies(b, c), implies(a, implies(b, c)))), implies(implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), implies(implies(b, c), implies(implies(a, b), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), implies(implies(b, c), implies(implies(a, b), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true, is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(a, c)))), true), true), true, is_a_theorem(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 7.08/1.43 = { by axiom 1 (ifeq_axiom) R->L }
% 7.08/1.43 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), implies(implies(implies(b, c), implies(a, implies(b, c))), implies(implies(b, c), implies(implies(a, b), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), implies(implies(b, c), implies(a, implies(b, c)))), implies(implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), implies(implies(b, c), implies(implies(a, b), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), implies(implies(b, c), implies(implies(a, b), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true, is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(a, c)))), true), true), true, is_a_theorem(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 7.08/1.43 = { by axiom 4 (c0_6) R->L }
% 7.08/1.43 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), implies(implies(implies(b, c), implies(a, implies(b, c))), implies(implies(b, c), implies(implies(a, b), implies(a, c))))), implies(implies(implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), implies(implies(b, c), implies(a, implies(b, c)))), implies(implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), implies(implies(b, c), implies(implies(a, b), implies(a, c))))))), true, ifeq(is_a_theorem(implies(implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), implies(implies(implies(b, c), implies(a, implies(b, c))), implies(implies(b, c), implies(implies(a, b), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), implies(implies(b, c), implies(a, implies(b, c)))), implies(implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), implies(implies(b, c), implies(implies(a, b), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), implies(implies(b, c), implies(implies(a, b), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true, is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(a, c)))), true), true), true, is_a_theorem(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 7.08/1.43 = { by axiom 3 (condensed_detachment) }
% 7.08/1.43 ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), implies(implies(b, c), implies(implies(a, b), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true, is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(a, c)))), true), true), true, is_a_theorem(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 7.08/1.43 = { by axiom 1 (ifeq_axiom) }
% 7.08/1.43 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), implies(implies(b, c), implies(implies(a, b), implies(a, c))))), true, ifeq(is_a_theorem(implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true, is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(a, c)))), true), true), true, is_a_theorem(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 7.08/1.43 = { by axiom 3 (condensed_detachment) }
% 7.08/1.43 ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 7.08/1.44 = { by axiom 1 (ifeq_axiom) }
% 7.08/1.44 ifeq(is_a_theorem(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 7.08/1.44 = { by axiom 1 (ifeq_axiom) R->L }
% 7.08/1.44 ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 7.08/1.44 = { by axiom 3 (condensed_detachment) R->L }
% 7.08/1.44 ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 7.08/1.45 = { by axiom 1 (ifeq_axiom) R->L }
% 7.08/1.45 ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 7.08/1.45 = { by axiom 3 (condensed_detachment) R->L }
% 7.08/1.46 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 7.08/1.46 = { by axiom 4 (c0_6) }
% 7.08/1.46 ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 7.08/1.47 = { by axiom 1 (ifeq_axiom) }
% 7.08/1.47 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 7.08/1.48 = { by axiom 4 (c0_6) }
% 7.08/1.48 ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 7.08/1.48 = { by axiom 1 (ifeq_axiom) }
% 7.08/1.49 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, is_a_theorem(implies(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 7.08/1.50 = { by axiom 1 (ifeq_axiom) R->L }
% 7.08/1.50 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 7.75/1.50 = { by axiom 3 (condensed_detachment) R->L }
% 7.75/1.51 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 7.75/1.51 = { by axiom 2 (c0_2) }
% 7.75/1.52 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 7.75/1.52 = { by axiom 1 (ifeq_axiom) }
% 7.75/1.52 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 7.75/1.52 = { by axiom 2 (c0_2) }
% 7.75/1.53 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 7.75/1.53 = { by axiom 1 (ifeq_axiom) }
% 7.75/1.54 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))))))), true, is_a_theorem(implies(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 7.75/1.54 = { by axiom 3 (condensed_detachment) }
% 7.75/1.54 ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 7.75/1.54 = { by axiom 1 (ifeq_axiom) }
% 7.75/1.54 ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 7.75/1.54 = { by axiom 1 (ifeq_axiom) R->L }
% 7.75/1.55 ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 7.75/1.55 = { by axiom 3 (condensed_detachment) R->L }
% 7.75/1.55 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, b)))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, b))))), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 7.75/1.56 = { by axiom 1 (ifeq_axiom) R->L }
% 7.75/1.56 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, b)))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 7.75/1.56 = { by axiom 2 (c0_2) R->L }
% 7.75/1.56 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, b)))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, ifeq(ifeq(is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, b)))), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 7.75/1.57 = { by axiom 1 (ifeq_axiom) R->L }
% 7.75/1.57 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, b)))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, b)))), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 7.75/1.57 = { by axiom 2 (c0_2) R->L }
% 7.75/1.57 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, b)))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(b, c), implies(a, b))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, b)))))), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, b)))), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 7.75/1.57 = { by axiom 3 (condensed_detachment) }
% 7.75/1.57 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, b)))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 7.75/1.58 = { by axiom 1 (ifeq_axiom) }
% 7.75/1.58 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, b)))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 7.75/1.58 = { by axiom 1 (ifeq_axiom) R->L }
% 7.75/1.58 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, b)))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 7.75/1.58 = { by axiom 4 (c0_6) R->L }
% 7.75/1.58 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, b))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, b)))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 7.75/1.58 = { by axiom 1 (ifeq_axiom) R->L }
% 7.75/1.59 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, b))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, b)))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 7.75/1.59 = { by axiom 4 (c0_6) R->L }
% 7.75/1.59 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, b))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, b)))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, b))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, b)))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 7.75/1.59 = { by axiom 3 (condensed_detachment) }
% 7.75/1.59 ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 7.75/1.59 = { by axiom 1 (ifeq_axiom) }
% 7.75/1.59 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 7.75/1.59 = { by axiom 1 (ifeq_axiom) R->L }
% 7.75/1.59 ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 7.75/1.60 = { by axiom 2 (c0_2) R->L }
% 7.75/1.60 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 7.75/1.60 = { by axiom 3 (condensed_detachment) }
% 7.75/1.60 ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 7.75/1.60 = { by axiom 1 (ifeq_axiom) }
% 7.75/1.60 ifeq(is_a_theorem(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, ifeq(is_a_theorem(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 7.75/1.60 = { by axiom 3 (condensed_detachment) }
% 7.75/1.60 true
% 7.75/1.60 % SZS output end Proof
% 7.75/1.60
% 7.75/1.60 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------