%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LCL008-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 11:48:49 AM UTC 2026
% Result : Unsatisfiable 0.21s 0.54s
% Output : Proof 0.84s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : LCL008-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.42 % Computer : n010.cluster.edu
% 0.16/0.42 % Model : x86_64 x86_64
% 0.16/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.42 % Memory : 8046.5625MB
% 0.16/0.42 % OS : Linux 6.8.0-71-generic
% 0.16/0.42 % CPULimit : 300
% 0.16/0.42 % WCLimit : 300
% 0.16/0.42 % DateTime : Sun Sep 27 15:17:16 UTC 2026
% 0.16/0.42 % CPUTime :
% 0.16/0.42 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.54 Command-line arguments: --no-flatten-goal
% 0.21/0.54
% 0.21/0.54 % SZS status Unsatisfiable
% 0.21/0.54
% 0.21/0.61 % SZS output start Proof
% 0.21/0.61 Axiom 1 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 0.21/0.61 Axiom 2 (condensed_detachment): ifeq(is_a_theorem(equivalent(X, Y)), true, ifeq(is_a_theorem(X), true, is_a_theorem(Y), true), true) = true.
% 0.21/0.61 Axiom 3 (yql): is_a_theorem(equivalent(equivalent(X, Y), equivalent(equivalent(Z, Y), equivalent(X, Z)))) = true.
% 0.21/0.61
% 0.21/0.61 Goal 1 (prove_ec_4): is_a_theorem(equivalent(equivalent(a, b), equivalent(b, a))) = true.
% 0.21/0.61 Proof:
% 0.21/0.61 is_a_theorem(equivalent(equivalent(a, b), equivalent(b, a)))
% 0.21/0.61 = { by axiom 1 (ifeq_axiom) R->L }
% 0.21/0.61 ifeq(true, true, is_a_theorem(equivalent(equivalent(a, b), equivalent(b, a))), true)
% 0.21/0.61 = { by axiom 2 (condensed_detachment) R->L }
% 0.21/0.61 ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(b, b))), true, ifeq(is_a_theorem(equivalent(equivalent(b, b), equivalent(b, b))), true, is_a_theorem(equivalent(b, b)), true), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(b, a))), true)
% 0.21/0.61 = { by axiom 1 (ifeq_axiom) R->L }
% 0.21/0.61 ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(b, b))), true, ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(b, b), equivalent(b, b))), true), true, is_a_theorem(equivalent(b, b)), true), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(b, a))), true)
% 0.21/0.61 = { by axiom 2 (condensed_detachment) R->L }
% 0.21/0.62 ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(b, b))), true, ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(X, b), equivalent(b, X))), equivalent(equivalent(equivalent(b, b), equivalent(equivalent(X, b), equivalent(b, X))), equivalent(equivalent(b, b), equivalent(b, b))))), true, ifeq(is_a_theorem(equivalent(equivalent(b, b), equivalent(equivalent(X, b), equivalent(b, X)))), true, is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(X, b), equivalent(b, X))), equivalent(equivalent(b, b), equivalent(b, b)))), true), true), true, is_a_theorem(equivalent(equivalent(b, b), equivalent(b, b))), true), true, is_a_theorem(equivalent(b, b)), true), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(b, a))), true)
% 0.21/0.62 = { by axiom 3 (yql) }
% 0.21/0.62 ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(b, b))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(b, b), equivalent(equivalent(X, b), equivalent(b, X)))), true, is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(X, b), equivalent(b, X))), equivalent(equivalent(b, b), equivalent(b, b)))), true), true), true, is_a_theorem(equivalent(equivalent(b, b), equivalent(b, b))), true), true, is_a_theorem(equivalent(b, b)), true), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(b, a))), true)
% 0.21/0.62 = { by axiom 1 (ifeq_axiom) }
% 0.21/0.62 ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(b, b))), true, ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(b, b), equivalent(equivalent(X, b), equivalent(b, X)))), true, is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(X, b), equivalent(b, X))), equivalent(equivalent(b, b), equivalent(b, b)))), true), true, is_a_theorem(equivalent(equivalent(b, b), equivalent(b, b))), true), true, is_a_theorem(equivalent(b, b)), true), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(b, a))), true)
% 0.21/0.62 = { by axiom 3 (yql) }
% 0.84/0.62 ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(b, b))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(X, b), equivalent(b, X))), equivalent(equivalent(b, b), equivalent(b, b)))), true), true, is_a_theorem(equivalent(equivalent(b, b), equivalent(b, b))), true), true, is_a_theorem(equivalent(b, b)), true), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(b, a))), true)
% 0.84/0.62 = { by axiom 1 (ifeq_axiom) }
% 0.84/0.62 ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(b, b))), true, ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(X, b), equivalent(b, X))), equivalent(equivalent(b, b), equivalent(b, b)))), true, is_a_theorem(equivalent(equivalent(b, b), equivalent(b, b))), true), true, is_a_theorem(equivalent(b, b)), true), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(b, a))), true)
% 0.84/0.62 = { by axiom 1 (ifeq_axiom) R->L }
% 0.84/0.62 ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(b, b))), true, ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(X, b), equivalent(b, X))), equivalent(equivalent(b, b), equivalent(b, b)))), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(b, b), equivalent(b, b))), true), true), true, is_a_theorem(equivalent(b, b)), true), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(b, a))), true)
% 0.84/0.62 = { by axiom 3 (yql) R->L }
% 0.84/0.63 ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(b, b))), true, ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(X, b), equivalent(b, X))), equivalent(equivalent(b, b), equivalent(b, b)))), true, ifeq(is_a_theorem(equivalent(equivalent(b, b), equivalent(equivalent(X, b), equivalent(b, X)))), true, is_a_theorem(equivalent(equivalent(b, b), equivalent(b, b))), true), true), true, is_a_theorem(equivalent(b, b)), true), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(b, a))), true)
% 0.84/0.63 = { by axiom 2 (condensed_detachment) }
% 0.84/0.63 ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(b, b))), true, ifeq(true, true, is_a_theorem(equivalent(b, b)), true), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(b, a))), true)
% 0.84/0.63 = { by axiom 1 (ifeq_axiom) }
% 0.84/0.63 ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(b, b))), true, is_a_theorem(equivalent(b, b)), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(b, a))), true)
% 0.84/0.63 = { by axiom 1 (ifeq_axiom) R->L }
% 0.84/0.63 ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(b, b))), true), true, is_a_theorem(equivalent(b, b)), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(b, a))), true)
% 0.84/0.63 = { by axiom 2 (condensed_detachment) R->L }
% 0.84/0.63 ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(b, b), equivalent(b, b))), equivalent(equivalent(equivalent(b, b), equivalent(equivalent(b, b), equivalent(b, b))), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(b, b))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(b, b), equivalent(b, b)))), true, is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(b, b), equivalent(b, b))), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(b, b)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(b, b))), true), true, is_a_theorem(equivalent(b, b)), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(b, a))), true)
% 0.84/0.63 = { by axiom 3 (yql) }
% 0.84/0.63 ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(b, b), equivalent(b, b)))), true, is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(b, b), equivalent(b, b))), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(b, b)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(b, b))), true), true, is_a_theorem(equivalent(b, b)), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(b, a))), true)
% 0.84/0.63 = { by axiom 1 (ifeq_axiom) }
% 0.84/0.63 ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(b, b), equivalent(b, b)))), true, is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(b, b), equivalent(b, b))), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(b, b)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(b, b))), true), true, is_a_theorem(equivalent(b, b)), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(b, a))), true)
% 0.84/0.63 = { by axiom 1 (ifeq_axiom) R->L }
% 0.84/0.63 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(b, b), equivalent(b, b)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(b, b), equivalent(b, b))), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(b, b)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(b, b))), true), true, is_a_theorem(equivalent(b, b)), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(b, a))), true)
% 0.84/0.64 = { by axiom 2 (condensed_detachment) R->L }
% 0.84/0.64 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(Y, equivalent(b, b)), equivalent(equivalent(b, b), Y))), equivalent(equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(Y, equivalent(b, b)), equivalent(equivalent(b, b), Y))), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(b, b), equivalent(b, b)))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(Y, equivalent(b, b)), equivalent(equivalent(b, b), Y)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(Y, equivalent(b, b)), equivalent(equivalent(b, b), Y))), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(b, b), equivalent(b, b))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(b, b), equivalent(b, b)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(b, b), equivalent(b, b))), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(b, b)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(b, b))), true), true, is_a_theorem(equivalent(b, b)), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(b, a))), true)
% 0.84/0.64 = { by axiom 3 (yql) }
% 0.84/0.64 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(Y, equivalent(b, b)), equivalent(equivalent(b, b), Y)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(Y, equivalent(b, b)), equivalent(equivalent(b, b), Y))), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(b, b), equivalent(b, b))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(b, b), equivalent(b, b)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(b, b), equivalent(b, b))), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(b, b)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(b, b))), true), true, is_a_theorem(equivalent(b, b)), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(b, a))), true)
% 0.84/0.64 = { by axiom 1 (ifeq_axiom) }
% 0.84/0.64 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(Y, equivalent(b, b)), equivalent(equivalent(b, b), Y)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(Y, equivalent(b, b)), equivalent(equivalent(b, b), Y))), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(b, b), equivalent(b, b))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(b, b), equivalent(b, b)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(b, b), equivalent(b, b))), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(b, b)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(b, b))), true), true, is_a_theorem(equivalent(b, b)), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(b, a))), true)
% 0.84/0.64 = { by axiom 3 (yql) }
% 0.84/0.64 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(Y, equivalent(b, b)), equivalent(equivalent(b, b), Y))), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(b, b), equivalent(b, b))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(b, b), equivalent(b, b)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(b, b), equivalent(b, b))), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(b, b)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(b, b))), true), true, is_a_theorem(equivalent(b, b)), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(b, a))), true)
% 0.84/0.64 = { by axiom 1 (ifeq_axiom) }
% 0.84/0.65 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(Y, equivalent(b, b)), equivalent(equivalent(b, b), Y))), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(b, b), equivalent(b, b))))), true, is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(b, b), equivalent(b, b)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(b, b), equivalent(b, b))), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(b, b)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(b, b))), true), true, is_a_theorem(equivalent(b, b)), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(b, a))), true)
% 0.84/0.65 = { by axiom 1 (ifeq_axiom) R->L }
% 0.84/0.65 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(Y, equivalent(b, b)), equivalent(equivalent(b, b), Y))), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(b, b), equivalent(b, b))))), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(b, b), equivalent(b, b)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(b, b), equivalent(b, b))), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(b, b)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(b, b))), true), true, is_a_theorem(equivalent(b, b)), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(b, a))), true)
% 0.84/0.65 = { by axiom 3 (yql) R->L }
% 0.84/0.65 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(Y, equivalent(b, b)), equivalent(equivalent(b, b), Y))), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(b, b), equivalent(b, b))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(Y, equivalent(b, b)), equivalent(equivalent(b, b), Y)))), true, is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(b, b), equivalent(b, b)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(b, b), equivalent(b, b))), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(b, b)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(b, b))), true), true, is_a_theorem(equivalent(b, b)), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(b, a))), true)
% 0.84/0.65 = { by axiom 2 (condensed_detachment) }
% 0.84/0.65 ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(b, b), equivalent(b, b))), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(b, b)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(b, b))), true), true, is_a_theorem(equivalent(b, b)), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(b, a))), true)
% 0.84/0.65 = { by axiom 1 (ifeq_axiom) }
% 0.84/0.65 ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(b, b), equivalent(b, b))), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(b, b)))), true, is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(b, b))), true), true, is_a_theorem(equivalent(b, b)), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(b, a))), true)
% 0.84/0.65 = { by axiom 1 (ifeq_axiom) R->L }
% 0.84/0.65 ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(b, b), equivalent(b, b))), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(b, b)))), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(b, b))), true), true), true, is_a_theorem(equivalent(b, b)), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(b, a))), true)
% 0.84/0.65 = { by axiom 3 (yql) R->L }
% 0.84/0.65 ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(b, b), equivalent(b, b))), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(b, b)))), true, ifeq(is_a_theorem(equivalent(equivalent(b, b), equivalent(equivalent(b, b), equivalent(b, b)))), true, is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(b, b))), true), true), true, is_a_theorem(equivalent(b, b)), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(b, a))), true)
% 0.84/0.65 = { by axiom 2 (condensed_detachment) }
% 0.84/0.65 ifeq(ifeq(true, true, is_a_theorem(equivalent(b, b)), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(b, a))), true)
% 0.84/0.65 = { by axiom 1 (ifeq_axiom) }
% 0.84/0.65 ifeq(is_a_theorem(equivalent(b, b)), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(b, a))), true)
% 0.84/0.65 = { by axiom 1 (ifeq_axiom) R->L }
% 0.84/0.65 ifeq(true, true, ifeq(is_a_theorem(equivalent(b, b)), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(b, a))), true), true)
% 0.84/0.65 = { by axiom 3 (yql) R->L }
% 0.84/0.65 ifeq(is_a_theorem(equivalent(equivalent(b, b), equivalent(equivalent(a, b), equivalent(b, a)))), true, ifeq(is_a_theorem(equivalent(b, b)), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(b, a))), true), true)
% 0.84/0.66 = { by axiom 2 (condensed_detachment) }
% 0.84/0.66 true
% 0.84/0.66 % SZS output end Proof
% 0.84/0.66
% 0.84/0.66 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------