%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : MGT058+1 : TPTP v9.3.0. Released v2.4.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : run_E %s %d THM
% Computer : n005.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 8 06:24:08 AM UTC 2026
% Result : Theorem 0.14s 0.41s
% Output : Proof 0.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT058+1 : TPTP v9.3.0. Released v2.4.0.
% 0.00/0.03 % Command : run_E %s %d THM
% 0.08/0.34 % Computer : n005.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 7 13:31:52 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.14/0.41 % SZS status Theorem
% 0.14/0.41 % SZS output start Proof
% 0.14/0.41 tff(smaller_or_equal_type, type, (
% 0.14/0.41 smaller_or_equal: ( $i * $i ) > $o)).
% 0.14/0.41 tff(sigma_type, type, (
% 0.14/0.41 sigma: $i)).
% 0.14/0.41 tff(zero_type, type, (
% 0.14/0.41 zero: $i)).
% 0.14/0.41 tff(age_type, type, (
% 0.14/0.41 age: ( $i * $i ) > $i)).
% 0.14/0.41 tff(tptp_fun_T0_3_type, type, (
% 0.14/0.41 tptp_fun_T0_3: $i)).
% 0.14/0.41 tff(tptp_fun_X_2_type, type, (
% 0.14/0.41 tptp_fun_X_2: $i)).
% 0.14/0.41 tff(greater_or_equal_type, type, (
% 0.14/0.41 greater_or_equal: ( $i * $i ) > $o)).
% 0.14/0.41 tff(tau_type, type, (
% 0.14/0.41 tau: $i)).
% 0.14/0.41 tff(organization_type, type, (
% 0.14/0.41 organization: $i > $o)).
% 0.14/0.41 tff(robust_position_type, type, (
% 0.14/0.41 robust_position: $i > $o)).
% 0.14/0.41 tff(fragile_position_type, type, (
% 0.14/0.41 fragile_position: $i > $o)).
% 0.14/0.41 tff(positional_advantage_type, type, (
% 0.14/0.41 positional_advantage: ( $i * $i ) > $o)).
% 0.14/0.41 tff(smaller_type, type, (
% 0.14/0.41 smaller: ( $i * $i ) > $o)).
% 0.14/0.41 tff(greater_type, type, (
% 0.14/0.41 greater: ( $i * $i ) > $o)).
% 0.14/0.41 tff(tptp_fun_T_1_type, type, (
% 0.14/0.41 tptp_fun_T_1: $i > $i)).
% 0.14/0.41 tff(tptp_fun_T_0_type, type, (
% 0.14/0.41 tptp_fun_T_0: $i > $i)).
% 0.14/0.41 tff(1,plain,
% 0.14/0.41 (((fragile_position(X!2) & robust_position(X!2)) & (organization(X!2) & (age(X!2, T0!3) = zero) & greater_or_equal(sigma, zero) & greater_or_equal(tau, zero))) <=> (fragile_position(X!2) & robust_position(X!2) & organization(X!2) & (age(X!2, T0!3) = zero) & greater_or_equal(sigma, zero) & greater_or_equal(tau, zero))),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(2,plain,
% 0.14/0.41 ((~![X: $i] : ((~(fragile_position(X) & robust_position(X))) | (~(organization(X) & ?[T0: $i] : (age(X, T0) = zero) & greater_or_equal(sigma, zero) & greater_or_equal(tau, zero))))) <=> (~![X: $i] : ((~(fragile_position(X) & robust_position(X))) | (~(organization(X) & ?[T0: $i] : (age(X, T0) = zero) & greater_or_equal(sigma, zero) & greater_or_equal(tau, zero)))))),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(3,plain,
% 0.14/0.41 ((~![X: $i] : ((((organization(X) & ?[T0: $i] : (age(X, T0) = zero)) & greater_or_equal(sigma, zero)) & greater_or_equal(tau, zero)) => (~(fragile_position(X) & robust_position(X))))) <=> (~![X: $i] : ((~(fragile_position(X) & robust_position(X))) | (~(organization(X) & ?[T0: $i] : (age(X, T0) = zero) & greater_or_equal(sigma, zero) & greater_or_equal(tau, zero)))))),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(4,axiom,(~![X: $i] : ((((organization(X) & ?[T0: $i] : (age(X, T0) = zero)) & greater_or_equal(sigma, zero)) & greater_or_equal(tau, zero)) => (~(fragile_position(X) & robust_position(X))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','lemma_10')).
% 0.14/0.41 tff(5,plain,
% 0.14/0.41 (~![X: $i] : ((~(fragile_position(X) & robust_position(X))) | (~(organization(X) & ?[T0: $i] : (age(X, T0) = zero) & greater_or_equal(sigma, zero) & greater_or_equal(tau, zero))))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.14/0.41 tff(6,plain,
% 0.14/0.41 (~![X: $i] : ((~(fragile_position(X) & robust_position(X))) | (~(organization(X) & ?[T0: $i] : (age(X, T0) = zero) & greater_or_equal(sigma, zero) & greater_or_equal(tau, zero))))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[5, 2])).
% 0.14/0.41 tff(7,plain,
% 0.14/0.41 (~![X: $i] : ((~(fragile_position(X) & robust_position(X))) | (~(organization(X) & ?[T0: $i] : (age(X, T0) = zero) & greater_or_equal(sigma, zero) & greater_or_equal(tau, zero))))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.14/0.41 tff(8,plain,
% 0.14/0.41 (~![X: $i] : ((~(fragile_position(X) & robust_position(X))) | (~(organization(X) & ?[T0: $i] : (age(X, T0) = zero) & greater_or_equal(sigma, zero) & greater_or_equal(tau, zero))))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[7, 2])).
% 0.14/0.41 tff(9,plain,
% 0.14/0.41 (fragile_position(X!2) & robust_position(X!2) & organization(X!2) & (age(X!2, T0!3) = zero) & greater_or_equal(sigma, zero) & greater_or_equal(tau, zero)),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[8, 1])).
% 0.14/0.41 tff(10,plain,
% 0.14/0.41 (age(X!2, T0!3) = zero),
% 0.14/0.41 inference(and_elim,[status(thm)],[9])).
% 0.14/0.41 tff(11,plain,
% 0.14/0.41 (zero = age(X!2, T0!3)),
% 0.14/0.41 inference(symmetry,[status(thm)],[10])).
% 0.14/0.41 tff(12,plain,
% 0.14/0.41 (smaller_or_equal(zero, sigma) <=> smaller_or_equal(age(X!2, T0!3), sigma)),
% 0.14/0.41 inference(monotonicity,[status(thm)],[11])).
% 0.14/0.41 tff(13,plain,
% 0.14/0.41 (smaller_or_equal(age(X!2, T0!3), sigma) <=> smaller_or_equal(zero, sigma)),
% 0.14/0.41 inference(symmetry,[status(thm)],[12])).
% 0.14/0.41 tff(14,plain,
% 0.14/0.41 ((~smaller_or_equal(age(X!2, T0!3), sigma)) <=> (~smaller_or_equal(zero, sigma))),
% 0.14/0.41 inference(monotonicity,[status(thm)],[13])).
% 0.14/0.41 tff(15,plain,
% 0.14/0.41 (smaller_or_equal(zero, tau) <=> smaller_or_equal(age(X!2, T0!3), tau)),
% 0.14/0.41 inference(monotonicity,[status(thm)],[11])).
% 0.14/0.41 tff(16,plain,
% 0.14/0.41 (smaller_or_equal(age(X!2, T0!3), tau) <=> smaller_or_equal(zero, tau)),
% 0.14/0.41 inference(symmetry,[status(thm)],[15])).
% 0.14/0.41 tff(17,plain,
% 0.14/0.41 ((~smaller_or_equal(age(X!2, T0!3), tau)) <=> (~smaller_or_equal(zero, tau))),
% 0.14/0.41 inference(monotonicity,[status(thm)],[16])).
% 0.14/0.41 tff(18,assumption,(~smaller_or_equal(age(X!2, T0!3), tau)), introduced(assumption)).
% 0.14/0.41 tff(19,plain,
% 0.14/0.41 (~smaller_or_equal(zero, tau)),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.14/0.41 tff(20,plain,
% 0.14/0.41 (^[X: $i, Y: $i] : refl((smaller_or_equal(X, Y) <=> ((X = Y) | smaller(X, Y))) <=> (smaller_or_equal(X, Y) <=> ((X = Y) | smaller(X, Y))))),
% 0.14/0.41 inference(bind,[status(th)],[])).
% 0.14/0.41 tff(21,plain,
% 0.14/0.41 (![X: $i, Y: $i] : (smaller_or_equal(X, Y) <=> ((X = Y) | smaller(X, Y))) <=> ![X: $i, Y: $i] : (smaller_or_equal(X, Y) <=> ((X = Y) | smaller(X, Y)))),
% 0.14/0.41 inference(quant_intro,[status(thm)],[20])).
% 0.14/0.41 tff(22,plain,
% 0.14/0.41 (![X: $i, Y: $i] : (smaller_or_equal(X, Y) <=> ((X = Y) | smaller(X, Y))) <=> ![X: $i, Y: $i] : (smaller_or_equal(X, Y) <=> ((X = Y) | smaller(X, Y)))),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(23,plain,
% 0.14/0.41 (^[X: $i, Y: $i] : rewrite((smaller_or_equal(X, Y) <=> (smaller(X, Y) | (X = Y))) <=> (smaller_or_equal(X, Y) <=> ((X = Y) | smaller(X, Y))))),
% 0.14/0.41 inference(bind,[status(th)],[])).
% 0.14/0.41 tff(24,plain,
% 0.14/0.41 (![X: $i, Y: $i] : (smaller_or_equal(X, Y) <=> (smaller(X, Y) | (X = Y))) <=> ![X: $i, Y: $i] : (smaller_or_equal(X, Y) <=> ((X = Y) | smaller(X, Y)))),
% 0.14/0.41 inference(quant_intro,[status(thm)],[23])).
% 0.14/0.41 tff(25,axiom,(![X: $i, Y: $i] : (smaller_or_equal(X, Y) <=> (smaller(X, Y) | (X = Y)))), file('/export/starexec/sandbox2/benchmark/Axioms/MGT001+0.ax','definition_smaller_or_equal')).
% 0.14/0.41 tff(26,plain,
% 0.14/0.41 (![X: $i, Y: $i] : (smaller_or_equal(X, Y) <=> ((X = Y) | smaller(X, Y)))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.14/0.41 tff(27,plain,
% 0.14/0.41 (![X: $i, Y: $i] : (smaller_or_equal(X, Y) <=> ((X = Y) | smaller(X, Y)))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[26, 22])).
% 0.14/0.41 tff(28,plain,(
% 0.14/0.41 ![X: $i, Y: $i] : (smaller_or_equal(X, Y) <=> ((X = Y) | smaller(X, Y)))),
% 0.14/0.41 inference(skolemize,[status(sab)],[27])).
% 0.14/0.41 tff(29,plain,
% 0.14/0.41 (![X: $i, Y: $i] : (smaller_or_equal(X, Y) <=> ((X = Y) | smaller(X, Y)))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[28, 21])).
% 0.14/0.41 tff(30,plain,
% 0.14/0.41 ((~![X: $i, Y: $i] : (smaller_or_equal(X, Y) <=> ((X = Y) | smaller(X, Y)))) | (smaller_or_equal(zero, tau) <=> ((zero = tau) | smaller(zero, tau)))),
% 0.14/0.41 inference(quant_inst,[status(thm)],[])).
% 0.14/0.41 tff(31,plain,
% 0.14/0.41 (smaller_or_equal(zero, tau) <=> ((zero = tau) | smaller(zero, tau))),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[30, 29])).
% 0.14/0.41 tff(32,plain,
% 0.14/0.41 (^[X: $i, Y: $i] : refl((smaller(X, Y) <=> greater(Y, X)) <=> (smaller(X, Y) <=> greater(Y, X)))),
% 0.14/0.41 inference(bind,[status(th)],[])).
% 0.14/0.41 tff(33,plain,
% 0.14/0.41 (![X: $i, Y: $i] : (smaller(X, Y) <=> greater(Y, X)) <=> ![X: $i, Y: $i] : (smaller(X, Y) <=> greater(Y, X))),
% 0.14/0.41 inference(quant_intro,[status(thm)],[32])).
% 0.14/0.41 tff(34,plain,
% 0.14/0.41 (![X: $i, Y: $i] : (smaller(X, Y) <=> greater(Y, X)) <=> ![X: $i, Y: $i] : (smaller(X, Y) <=> greater(Y, X))),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(35,axiom,(![X: $i, Y: $i] : (smaller(X, Y) <=> greater(Y, X))), file('/export/starexec/sandbox2/benchmark/Axioms/MGT001+0.ax','definition_smaller')).
% 0.14/0.41 tff(36,plain,
% 0.14/0.41 (![X: $i, Y: $i] : (smaller(X, Y) <=> greater(Y, X))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.14/0.41 tff(37,plain,(
% 0.14/0.41 ![X: $i, Y: $i] : (smaller(X, Y) <=> greater(Y, X))),
% 0.14/0.41 inference(skolemize,[status(sab)],[36])).
% 0.14/0.41 tff(38,plain,
% 0.14/0.41 (![X: $i, Y: $i] : (smaller(X, Y) <=> greater(Y, X))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[37, 33])).
% 0.14/0.41 tff(39,plain,
% 0.14/0.41 ((~![X: $i, Y: $i] : (smaller(X, Y) <=> greater(Y, X))) | (smaller(zero, tau) <=> greater(tau, zero))),
% 0.14/0.41 inference(quant_inst,[status(thm)],[])).
% 0.14/0.41 tff(40,plain,
% 0.14/0.41 (smaller(zero, tau) <=> greater(tau, zero)),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[39, 38])).
% 0.14/0.41 tff(41,plain,
% 0.14/0.41 ((zero = tau) <=> (tau = zero)),
% 0.14/0.41 inference(commutativity,[status(thm)],[])).
% 0.14/0.41 tff(42,plain,
% 0.14/0.41 ((~(zero = tau)) <=> (~(tau = zero))),
% 0.14/0.41 inference(monotonicity,[status(thm)],[41])).
% 0.14/0.41 tff(43,assumption,(~((zero = tau) | smaller(zero, tau))), introduced(assumption)).
% 0.14/0.41 tff(44,plain,
% 0.14/0.41 (((zero = tau) | smaller(zero, tau)) | (~(zero = tau))),
% 0.14/0.41 inference(tautology,[status(thm)],[])).
% 0.14/0.41 tff(45,plain,
% 0.14/0.41 (~(zero = tau)),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[44, 43])).
% 0.14/0.41 tff(46,plain,
% 0.14/0.41 (~(tau = zero)),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[45, 42])).
% 0.14/0.41 tff(47,plain,
% 0.14/0.41 (^[X: $i, Y: $i] : refl((greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y))) <=> (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y))))),
% 0.14/0.41 inference(bind,[status(th)],[])).
% 0.14/0.41 tff(48,plain,
% 0.14/0.41 (![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y))) <=> ![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y)))),
% 0.14/0.41 inference(quant_intro,[status(thm)],[47])).
% 0.14/0.41 tff(49,plain,
% 0.14/0.41 (![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y))) <=> ![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y)))),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(50,plain,
% 0.14/0.41 (^[X: $i, Y: $i] : rewrite((greater_or_equal(X, Y) <=> (greater(X, Y) | (X = Y))) <=> (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y))))),
% 0.14/0.41 inference(bind,[status(th)],[])).
% 0.14/0.41 tff(51,plain,
% 0.14/0.41 (![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> (greater(X, Y) | (X = Y))) <=> ![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y)))),
% 0.14/0.41 inference(quant_intro,[status(thm)],[50])).
% 0.14/0.41 tff(52,axiom,(![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> (greater(X, Y) | (X = Y)))), file('/export/starexec/sandbox2/benchmark/Axioms/MGT001+0.ax','definition_greater_or_equal')).
% 0.14/0.41 tff(53,plain,
% 0.14/0.41 (![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y)))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.14/0.41 tff(54,plain,
% 0.14/0.41 (![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y)))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[53, 49])).
% 0.14/0.41 tff(55,plain,(
% 0.14/0.41 ![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y)))),
% 0.14/0.41 inference(skolemize,[status(sab)],[54])).
% 0.14/0.41 tff(56,plain,
% 0.14/0.41 (![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y)))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[55, 48])).
% 0.14/0.41 tff(57,plain,
% 0.14/0.41 ((~![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y)))) | (greater_or_equal(tau, zero) <=> ((tau = zero) | greater(tau, zero)))),
% 0.14/0.41 inference(quant_inst,[status(thm)],[])).
% 0.14/0.41 tff(58,plain,
% 0.14/0.41 (greater_or_equal(tau, zero) <=> ((tau = zero) | greater(tau, zero))),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[57, 56])).
% 0.14/0.41 tff(59,plain,
% 0.14/0.41 (greater_or_equal(tau, zero)),
% 0.14/0.41 inference(and_elim,[status(thm)],[9])).
% 0.14/0.41 tff(60,plain,
% 0.14/0.41 ((~(greater_or_equal(tau, zero) <=> ((tau = zero) | greater(tau, zero)))) | (~greater_or_equal(tau, zero)) | ((tau = zero) | greater(tau, zero))),
% 0.14/0.41 inference(tautology,[status(thm)],[])).
% 0.14/0.41 tff(61,plain,
% 0.14/0.41 ((~(greater_or_equal(tau, zero) <=> ((tau = zero) | greater(tau, zero)))) | ((tau = zero) | greater(tau, zero))),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[60, 59])).
% 0.14/0.41 tff(62,plain,
% 0.14/0.41 ((tau = zero) | greater(tau, zero)),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[61, 58])).
% 0.14/0.41 tff(63,plain,
% 0.14/0.41 ((~((tau = zero) | greater(tau, zero))) | (tau = zero) | greater(tau, zero)),
% 0.14/0.41 inference(tautology,[status(thm)],[])).
% 0.14/0.41 tff(64,plain,
% 0.14/0.41 ((tau = zero) | greater(tau, zero)),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[63, 62])).
% 0.14/0.41 tff(65,plain,
% 0.14/0.41 (greater(tau, zero)),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[64, 46])).
% 0.14/0.41 tff(66,plain,
% 0.14/0.41 (((zero = tau) | smaller(zero, tau)) | (~smaller(zero, tau))),
% 0.14/0.41 inference(tautology,[status(thm)],[])).
% 0.14/0.41 tff(67,plain,
% 0.14/0.41 (~smaller(zero, tau)),
% 0.14/0.42 inference(unit_resolution,[status(thm)],[66, 43])).
% 0.14/0.42 tff(68,plain,
% 0.14/0.42 ((~(smaller(zero, tau) <=> greater(tau, zero))) | smaller(zero, tau) | (~greater(tau, zero))),
% 0.14/0.42 inference(tautology,[status(thm)],[])).
% 0.14/0.42 tff(69,plain,
% 0.14/0.42 ((~(smaller(zero, tau) <=> greater(tau, zero))) | (~greater(tau, zero))),
% 0.14/0.42 inference(unit_resolution,[status(thm)],[68, 67])).
% 0.14/0.42 tff(70,plain,
% 0.14/0.42 ($false),
% 0.14/0.42 inference(unit_resolution,[status(thm)],[69, 65, 40])).
% 0.14/0.42 tff(71,plain,((zero = tau) | smaller(zero, tau)), inference(lemma,lemma(discharge,[]))).
% 0.14/0.42 tff(72,plain,
% 0.14/0.42 ((~(smaller_or_equal(zero, tau) <=> ((zero = tau) | smaller(zero, tau)))) | smaller_or_equal(zero, tau) | (~((zero = tau) | smaller(zero, tau)))),
% 0.14/0.42 inference(tautology,[status(thm)],[])).
% 0.14/0.42 tff(73,plain,
% 0.14/0.42 ((~(smaller_or_equal(zero, tau) <=> ((zero = tau) | smaller(zero, tau)))) | smaller_or_equal(zero, tau)),
% 0.14/0.42 inference(unit_resolution,[status(thm)],[72, 71])).
% 0.14/0.42 tff(74,plain,
% 0.14/0.42 (smaller_or_equal(zero, tau)),
% 0.14/0.42 inference(unit_resolution,[status(thm)],[73, 31])).
% 0.14/0.42 tff(75,plain,
% 0.14/0.42 ($false),
% 0.14/0.42 inference(unit_resolution,[status(thm)],[74, 19])).
% 0.14/0.42 tff(76,plain,(smaller_or_equal(age(X!2, T0!3), tau)), inference(lemma,lemma(discharge,[]))).
% 0.14/0.42 tff(77,plain,
% 0.14/0.42 (^[X: $i] : rewrite((~((~((~robust_position(X)) | ![T: $i] : (~((~((~positional_advantage(X, T)) | (~smaller_or_equal(age(X, T), tau)))) | (~((~greater(age(X, T), tau)) | positional_advantage(X, T))))))) | (~(robust_position(X) | (~((~positional_advantage(X, tptp_fun_T_1(X))) | (~smaller_or_equal(age(X, tptp_fun_T_1(X)), tau)))) | (~((~greater(age(X, tptp_fun_T_1(X)), tau)) | positional_advantage(X, tptp_fun_T_1(X)))))))) <=> (~((~(robust_position(X) | (~((~positional_advantage(X, tptp_fun_T_1(X))) | (~smaller_or_equal(age(X, tptp_fun_T_1(X)), tau)))) | (~((~greater(age(X, tptp_fun_T_1(X)), tau)) | positional_advantage(X, tptp_fun_T_1(X)))))) | (~((~robust_position(X)) | ![T: $i] : (~((~((~positional_advantage(X, T)) | (~smaller_or_equal(age(X, T), tau)))) | (~((~greater(age(X, T), tau)) | positional_advantage(X, T))))))))))),
% 0.14/0.42 inference(bind,[status(th)],[])).
% 0.14/0.42 tff(78,plain,
% 0.14/0.42 (![X: $i] : (~((~((~robust_position(X)) | ![T: $i] : (~((~((~positional_advantage(X, T)) | (~smaller_or_equal(age(X, T), tau)))) | (~((~greater(age(X, T), tau)) | positional_advantage(X, T))))))) | (~(robust_position(X) | (~((~positional_advantage(X, tptp_fun_T_1(X))) | (~smaller_or_equal(age(X, tptp_fun_T_1(X)), tau)))) | (~((~greater(age(X, tptp_fun_T_1(X)), tau)) | positional_advantage(X, tptp_fun_T_1(X)))))))) <=> ![X: $i] : (~((~(robust_position(X) | (~((~positional_advantage(X, tptp_fun_T_1(X))) | (~smaller_or_equal(age(X, tptp_fun_T_1(X)), tau)))) | (~((~greater(age(X, tptp_fun_T_1(X)), tau)) | positional_advantage(X, tptp_fun_T_1(X)))))) | (~((~robust_position(X)) | ![T: $i] : (~((~((~positional_advantage(X, T)) | (~smaller_or_equal(age(X, T), tau)))) | (~((~greater(age(X, T), tau)) | positional_advantage(X, T)))))))))),
% 0.14/0.42 inference(quant_intro,[status(thm)],[77])).
% 0.14/0.42 tff(79,plain,
% 0.14/0.42 (^[X: $i] : refl((~((~((~robust_position(X)) | ![T: $i] : (~((~((~positional_advantage(X, T)) | (~smaller_or_equal(age(X, T), tau)))) | (~((~greater(age(X, T), tau)) | positional_advantage(X, T))))))) | (~(robust_position(X) | (~((~positional_advantage(X, tptp_fun_T_1(X))) | (~smaller_or_equal(age(X, tptp_fun_T_1(X)), tau)))) | (~((~greater(age(X, tptp_fun_T_1(X)), tau)) | positional_advantage(X, tptp_fun_T_1(X)))))))) <=> (~((~((~robust_position(X)) | ![T: $i] : (~((~((~positional_advantage(X, T)) | (~smaller_or_equal(age(X, T), tau)))) | (~((~greater(age(X, T), tau)) | positional_advantage(X, T))))))) | (~(robust_position(X) | (~((~positional_advantage(X, tptp_fun_T_1(X))) | (~smaller_or_equal(age(X, tptp_fun_T_1(X)), tau)))) | (~((~greater(age(X, tptp_fun_T_1(X)), tau)) | positional_advantage(X, tptp_fun_T_1(X)))))))))),
% 0.14/0.42 inference(bind,[status(th)],[])).
% 0.14/0.42 tff(80,plain,
% 0.14/0.42 (![X: $i] : (~((~((~robust_position(X)) | ![T: $i] : (~((~((~positional_advantage(X, T)) | (~smaller_or_equal(age(X, T), tau)))) | (~((~greater(age(X, T), tau)) | positional_advantage(X, T))))))) | (~(robust_position(X) | (~((~positional_advantage(X, tptp_fun_T_1(X))) | (~smaller_or_equal(age(X, tptp_fun_T_1(X)), tau)))) | (~((~greater(age(X, tptp_fun_T_1(X)), tau)) | positional_advantage(X, tptp_fun_T_1(X)))))))) <=> ![X: $i] : (~((~((~robust_position(X)) | ![T: $i] : (~((~((~positional_advantage(X, T)) | (~smaller_or_equal(age(X, T), tau)))) | (~((~greater(age(X, T), tau)) | positional_advantage(X, T))))))) | (~(robust_position(X) | (~((~positional_advantage(X, tptp_fun_T_1(X))) | (~smaller_or_equal(age(X, tptp_fun_T_1(X)), tau)))) | (~((~greater(age(X, tptp_fun_T_1(X)), tau)) | positional_advantage(X, tptp_fun_T_1(X))))))))),
% 0.14/0.42 inference(quant_intro,[status(thm)],[79])).
% 0.14/0.42 tff(81,plain,
% 0.14/0.42 (^[X: $i] : rewrite((~((~((~robust_position(X)) | ![T: $i] : (~((~((~positional_advantage(X, T)) | (~smaller_or_equal(age(X, T), tau)))) | (~((~greater(age(X, T), tau)) | positional_advantage(X, T))))))) | (~(robust_position(X) | (~((~positional_advantage(X, tptp_fun_T_1(X))) | (~smaller_or_equal(age(X, tptp_fun_T_1(X)), tau)))) | (~((~greater(age(X, tptp_fun_T_1(X)), tau)) | positional_advantage(X, tptp_fun_T_1(X)))))))) <=> (~((~((~robust_position(X)) | ![T: $i] : (~((~((~positional_advantage(X, T)) | (~smaller_or_equal(age(X, T), tau)))) | (~((~greater(age(X, T), tau)) | positional_advantage(X, T))))))) | (~(robust_position(X) | (~((~positional_advantage(X, tptp_fun_T_1(X))) | (~smaller_or_equal(age(X, tptp_fun_T_1(X)), tau)))) | (~((~greater(age(X, tptp_fun_T_1(X)), tau)) | positional_advantage(X, tptp_fun_T_1(X)))))))))),
% 0.14/0.42 inference(bind,[status(th)],[])).
% 0.14/0.42 tff(82,plain,
% 0.14/0.42 (![X: $i] : (~((~((~robust_position(X)) | ![T: $i] : (~((~((~positional_advantage(X, T)) | (~smaller_or_equal(age(X, T), tau)))) | (~((~greater(age(X, T), tau)) | positional_advantage(X, T))))))) | (~(robust_position(X) | (~((~positional_advantage(X, tptp_fun_T_1(X))) | (~smaller_or_equal(age(X, tptp_fun_T_1(X)), tau)))) | (~((~greater(age(X, tptp_fun_T_1(X)), tau)) | positional_advantage(X, tptp_fun_T_1(X)))))))) <=> ![X: $i] : (~((~((~robust_position(X)) | ![T: $i] : (~((~((~positional_advantage(X, T)) | (~smaller_or_equal(age(X, T), tau)))) | (~((~greater(age(X, T), tau)) | positional_advantage(X, T))))))) | (~(robust_position(X) | (~((~positional_advantage(X, tptp_fun_T_1(X))) | (~smaller_or_equal(age(X, tptp_fun_T_1(X)), tau)))) | (~((~greater(age(X, tptp_fun_T_1(X)), tau)) | positional_advantage(X, tptp_fun_T_1(X))))))))),
% 0.14/0.42 inference(quant_intro,[status(thm)],[81])).
% 0.14/0.42 tff(83,plain,
% 0.14/0.42 (![X: $i] : (~((~((~robust_position(X)) | ![T: $i] : (~((~((~positional_advantage(X, T)) | (~smaller_or_equal(age(X, T), tau)))) | (~((~greater(age(X, T), tau)) | positional_advantage(X, T))))))) | (~(robust_position(X) | (~((~positional_advantage(X, tptp_fun_T_1(X))) | (~smaller_or_equal(age(X, tptp_fun_T_1(X)), tau)))) | (~((~greater(age(X, tptp_fun_T_1(X)), tau)) | positional_advantage(X, tptp_fun_T_1(X)))))))) <=> ![X: $i] : (~((~((~robust_position(X)) | ![T: $i] : (~((~((~positional_advantage(X, T)) | (~smaller_or_equal(age(X, T), tau)))) | (~((~greater(age(X, T), tau)) | positional_advantage(X, T))))))) | (~(robust_position(X) | (~((~positional_advantage(X, tptp_fun_T_1(X))) | (~smaller_or_equal(age(X, tptp_fun_T_1(X)), tau)))) | (~((~greater(age(X, tptp_fun_T_1(X)), tau)) | positional_advantage(X, tptp_fun_T_1(X))))))))),
% 0.14/0.42 inference(transitivity,[status(thm)],[82, 80])).
% 0.14/0.42 tff(84,plain,
% 0.14/0.42 (^[X: $i] : trans(monotonicity(rewrite(((~robust_position(X)) | ![T: $i] : (((~positional_advantage(X, T)) | (~smaller_or_equal(age(X, T), tau))) & ((~greater(age(X, T), tau)) | positional_advantage(X, T)))) <=> ((~robust_position(X)) | ![T: $i] : (~((~((~positional_advantage(X, T)) | (~smaller_or_equal(age(X, T), tau)))) | (~((~greater(age(X, T), tau)) | positional_advantage(X, T))))))), trans(monotonicity(trans(monotonicity(rewrite((((~positional_advantage(X, tptp_fun_T_1(X))) | (~smaller_or_equal(age(X, tptp_fun_T_1(X)), tau))) & ((~greater(age(X, tptp_fun_T_1(X)), tau)) | positional_advantage(X, tptp_fun_T_1(X)))) <=> (~((~((~positional_advantage(X, tptp_fun_T_1(X))) | (~smaller_or_equal(age(X, tptp_fun_T_1(X)), tau)))) | (~((~greater(age(X, tptp_fun_T_1(X)), tau)) | positional_advantage(X, tptp_fun_T_1(X))))))), ((~(((~positional_advantage(X, tptp_fun_T_1(X))) | (~smaller_or_equal(age(X, tptp_fun_T_1(X)), tau))) & ((~greater(age(X, tptp_fun_T_1(X)), tau)) | positional_advantage(X, tptp_fun_T_1(X))))) <=> (~(~((~((~positional_advantage(X, tptp_fun_T_1(X))) | (~smaller_or_equal(age(X, tptp_fun_T_1(X)), tau)))) | (~((~greater(age(X, tptp_fun_T_1(X)), tau)) | positional_advantage(X, tptp_fun_T_1(X))))))))), rewrite((~(~((~((~positional_advantage(X, tptp_fun_T_1(X))) | (~smaller_or_equal(age(X, tptp_fun_T_1(X)), tau)))) | (~((~greater(age(X, tptp_fun_T_1(X)), tau)) | positional_advantage(X, tptp_fun_T_1(X))))))) <=> ((~((~positional_advantage(X, tptp_fun_T_1(X))) | (~smaller_or_equal(age(X, tptp_fun_T_1(X)), tau)))) | (~((~greater(age(X, tptp_fun_T_1(X)), tau)) | positional_advantage(X, tptp_fun_T_1(X)))))), ((~(((~positional_advantage(X, tptp_fun_T_1(X))) | (~smaller_or_equal(age(X, tptp_fun_T_1(X)), tau))) & ((~greater(age(X, tptp_fun_T_1(X)), tau)) | positional_advantage(X, tptp_fun_T_1(X))))) <=> ((~((~positional_advantage(X, tptp_fun_T_1(X))) | (~smaller_or_equal(age(X, tptp_fun_T_1(X)), tau)))) | (~((~greater(age(X, tptp_fun_T_1(X)), tau)) | positional_advantage(X, tptp_fun_T_1(X))))))), ((robust_position(X) | (~(((~positional_advantage(X, tptp_fun_T_1(X))) | (~smaller_or_equal(age(X, tptp_fun_T_1(X)), tau))) & ((~greater(age(X, tptp_fun_T_1(X)), tau)) | positional_advantage(X, tptp_fun_T_1(X)))))) <=> (robust_position(X) | ((~((~positional_advantage(X, tptp_fun_T_1(X))) | (~smaller_or_equal(age(X, tptp_fun_T_1(X)), tau)))) | (~((~greater(age(X, tptp_fun_T_1(X)), tau)) | positional_advantage(X, tptp_fun_T_1(X)))))))), rewrite((robust_position(X) | ((~((~positional_advantage(X, tptp_fun_T_1(X))) | (~smaller_or_equal(age(X, tptp_fun_T_1(X)), tau)))) | (~((~greater(age(X, tptp_fun_T_1(X)), tau)) | positional_advantage(X, tptp_fun_T_1(X)))))) <=> (robust_position(X) | (~((~positional_advantage(X, tptp_fun_T_1(X))) | (~smaller_or_equal(age(X, tptp_fun_T_1(X)), tau)))) | (~((~greater(age(X, tptp_fun_T_1(X)), tau)) | positional_advantage(X, tptp_fun_T_1(X)))))), ((robust_position(X) | (~(((~positional_advantage(X, tptp_fun_T_1(X))) | (~smaller_or_equal(age(X, tptp_fun_T_1(X)), tau))) & ((~greater(age(X, tptp_fun_T_1(X)), tau)) | positional_advantage(X, tptp_fun_T_1(X)))))) <=> (robust_position(X) | (~((~positional_advantage(X, tptp_fun_T_1(X))) | (~smaller_or_equal(age(X, tptp_fun_T_1(X)), tau)))) | (~((~greater(age(X, tptp_fun_T_1(X)), tau)) | positional_advantage(X, tptp_fun_T_1(X))))))), ((((~robust_position(X)) | ![T: $i] : (((~positional_advantage(X, T)) | (~smaller_or_equal(age(X, T), tau))) & ((~greater(age(X, T), tau)) | positional_advantage(X, T)))) & (robust_position(X) | (~(((~positional_advantage(X, tptp_fun_T_1(X))) | (~smaller_or_equal(age(X, tptp_fun_T_1(X)), tau))) & ((~greater(age(X, tptp_fun_T_1(X)), tau)) | positional_advantage(X, tptp_fun_T_1(X))))))) <=> (((~robust_position(X)) | ![T: $i] : (~((~((~positional_advantage(X, T)) | (~smaller_or_equal(age(X, T), tau)))) | (~((~greater(age(X, T), tau)) | positional_advantage(X, T)))))) & (robust_position(X) | (~((~positional_advantage(X, tptp_fun_T_1(X))) | (~smaller_or_equal(age(X, tptp_fun_T_1(X)), tau)))) | (~((~greater(age(X, tptp_fun_T_1(X)), tau)) | positional_advantage(X, tptp_fun_T_1(X)))))))), rewrite((((~robust_position(X)) | ![T: $i] : (~((~((~positional_advantage(X, T)) | (~smaller_or_equal(age(X, T), tau)))) | (~((~greater(age(X, T), tau)) | positional_advantage(X, T)))))) & (robust_position(X) | (~((~positional_advantage(X, tptp_fun_T_1(X))) | (~smaller_or_equal(age(X, tptp_fun_T_1(X)), tau)))) | (~((~greater(age(X, tptp_fun_T_1(X)), tau)) | positional_advantage(X, tptp_fun_T_1(X)))))) <=> (~((~((~robust_position(X)) | ![T: $i] : (~((~((~positional_advantage(X, T)) | (~smaller_or_equal(age(X, T), tau)))) | (~((~greater(age(X, T), tau)) | positional_advantage(X, T))))))) | (~(robust_position(X) | (~((~positional_advantage(X, tptp_fun_T_1(X))) | (~smaller_or_equal(age(X, tptp_fun_T_1(X)), tau)))) | (~((~greater(age(X, tptp_fun_T_1(X)), tau)) | positional_advantage(X, tptp_fun_T_1(X))))))))), ((((~robust_position(X)) | ![T: $i] : (((~positional_advantage(X, T)) | (~smaller_or_equal(age(X, T), tau))) & ((~greater(age(X, T), tau)) | positional_advantage(X, T)))) & (robust_position(X) | (~(((~positional_advantage(X, tptp_fun_T_1(X))) | (~smaller_or_equal(age(X, tptp_fun_T_1(X)), tau))) & ((~greater(age(X, tptp_fun_T_1(X)), tau)) | positional_advantage(X, tptp_fun_T_1(X))))))) <=> (~((~((~robust_position(X)) | ![T: $i] : (~((~((~positional_advantage(X, T)) | (~smaller_or_equal(age(X, T), tau)))) | (~((~greater(age(X, T), tau)) | positional_advantage(X, T))))))) | (~(robust_position(X) | (~((~positional_advantage(X, tptp_fun_T_1(X))) | (~smaller_or_equal(age(X, tptp_fun_T_1(X)), tau)))) | (~((~greater(age(X, tptp_fun_T_1(X)), tau)) | positional_advantage(X, tptp_fun_T_1(X))))))))))),
% 0.14/0.42 inference(bind,[status(th)],[])).
% 0.14/0.42 tff(85,plain,
% 0.14/0.42 (![X: $i] : (((~robust_position(X)) | ![T: $i] : (((~positional_advantage(X, T)) | (~smaller_or_equal(age(X, T), tau))) & ((~greater(age(X, T), tau)) | positional_advantage(X, T)))) & (robust_position(X) | (~(((~positional_advantage(X, tptp_fun_T_1(X))) | (~smaller_or_equal(age(X, tptp_fun_T_1(X)), tau))) & ((~greater(age(X, tptp_fun_T_1(X)), tau)) | positional_advantage(X, tptp_fun_T_1(X))))))) <=> ![X: $i] : (~((~((~robust_position(X)) | ![T: $i] : (~((~((~positional_advantage(X, T)) | (~smaller_or_equal(age(X, T), tau)))) | (~((~greater(age(X, T), tau)) | positional_advantage(X, T))))))) | (~(robust_position(X) | (~((~positional_advantage(X, tptp_fun_T_1(X))) | (~smaller_or_equal(age(X, tptp_fun_T_1(X)), tau)))) | (~((~greater(age(X, tptp_fun_T_1(X)), tau)) | positional_advantage(X, tptp_fun_T_1(X))))))))),
% 0.14/0.42 inference(quant_intro,[status(thm)],[84])).
% 0.14/0.42 tff(86,plain,
% 0.14/0.42 (![X: $i] : (robust_position(X) <=> ![T: $i] : (((~positional_advantage(X, T)) | (~smaller_or_equal(age(X, T), tau))) & ((~greater(age(X, T), tau)) | positional_advantage(X, T)))) <=> ![X: $i] : (robust_position(X) <=> ![T: $i] : (((~positional_advantage(X, T)) | (~smaller_or_equal(age(X, T), tau))) & ((~greater(age(X, T), tau)) | positional_advantage(X, T))))),
% 0.14/0.42 inference(rewrite,[status(thm)],[])).
% 0.14/0.42 tff(87,plain,
% 0.14/0.42 (^[X: $i] : rewrite((robust_position(X) <=> ![T: $i] : ((smaller_or_equal(age(X, T), tau) => (~positional_advantage(X, T))) & (greater(age(X, T), tau) => positional_advantage(X, T)))) <=> (robust_position(X) <=> ![T: $i] : (((~positional_advantage(X, T)) | (~smaller_or_equal(age(X, T), tau))) & ((~greater(age(X, T), tau)) | positional_advantage(X, T)))))),
% 0.14/0.42 inference(bind,[status(th)],[])).
% 0.14/0.42 tff(88,plain,
% 0.14/0.42 (![X: $i] : (robust_position(X) <=> ![T: $i] : ((smaller_or_equal(age(X, T), tau) => (~positional_advantage(X, T))) & (greater(age(X, T), tau) => positional_advantage(X, T)))) <=> ![X: $i] : (robust_position(X) <=> ![T: $i] : (((~positional_advantage(X, T)) | (~smaller_or_equal(age(X, T), tau))) & ((~greater(age(X, T), tau)) | positional_advantage(X, T))))),
% 0.14/0.42 inference(quant_intro,[status(thm)],[87])).
% 0.14/0.42 tff(89,axiom,(![X: $i] : (robust_position(X) <=> ![T: $i] : ((smaller_or_equal(age(X, T), tau) => (~positional_advantage(X, T))) & (greater(age(X, T), tau) => positional_advantage(X, T))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','definition_4')).
% 0.14/0.42 tff(90,plain,
% 0.14/0.42 (![X: $i] : (robust_position(X) <=> ![T: $i] : (((~positional_advantage(X, T)) | (~smaller_or_equal(age(X, T), tau))) & ((~greater(age(X, T), tau)) | positional_advantage(X, T))))),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[89, 88])).
% 0.14/0.42 tff(91,plain,
% 0.14/0.42 (![X: $i] : (robust_position(X) <=> ![T: $i] : (((~positional_advantage(X, T)) | (~smaller_or_equal(age(X, T), tau))) & ((~greater(age(X, T), tau)) | positional_advantage(X, T))))),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[90, 86])).
% 0.14/0.42 tff(92,plain,(
% 0.14/0.42 ![X: $i] : (((~robust_position(X)) | ![T: $i] : (((~positional_advantage(X, T)) | (~smaller_or_equal(age(X, T), tau))) & ((~greater(age(X, T), tau)) | positional_advantage(X, T)))) & (robust_position(X) | (~(((~positional_advantage(X, tptp_fun_T_1(X))) | (~smaller_or_equal(age(X, tptp_fun_T_1(X)), tau))) & ((~greater(age(X, tptp_fun_T_1(X)), tau)) | positional_advantage(X, tptp_fun_T_1(X)))))))),
% 0.14/0.42 inference(skolemize,[status(sab)],[91])).
% 0.14/0.42 tff(93,plain,
% 0.14/0.42 (![X: $i] : (~((~((~robust_position(X)) | ![T: $i] : (~((~((~positional_advantage(X, T)) | (~smaller_or_equal(age(X, T), tau)))) | (~((~greater(age(X, T), tau)) | positional_advantage(X, T))))))) | (~(robust_position(X) | (~((~positional_advantage(X, tptp_fun_T_1(X))) | (~smaller_or_equal(age(X, tptp_fun_T_1(X)), tau)))) | (~((~greater(age(X, tptp_fun_T_1(X)), tau)) | positional_advantage(X, tptp_fun_T_1(X))))))))),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[92, 85])).
% 0.14/0.42 tff(94,plain,
% 0.14/0.42 (![X: $i] : (~((~((~robust_position(X)) | ![T: $i] : (~((~((~positional_advantage(X, T)) | (~smaller_or_equal(age(X, T), tau)))) | (~((~greater(age(X, T), tau)) | positional_advantage(X, T))))))) | (~(robust_position(X) | (~((~positional_advantage(X, tptp_fun_T_1(X))) | (~smaller_or_equal(age(X, tptp_fun_T_1(X)), tau)))) | (~((~greater(age(X, tptp_fun_T_1(X)), tau)) | positional_advantage(X, tptp_fun_T_1(X))))))))),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[93, 83])).
% 0.14/0.42 tff(95,plain,
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% 0.14/0.42 inference(modus_ponens,[status(thm)],[94, 78])).
% 0.14/0.42 tff(96,plain,
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% 0.14/0.42 inference(quant_inst,[status(thm)],[])).
% 0.14/0.42 tff(97,plain,
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% 0.14/0.42 inference(unit_resolution,[status(thm)],[96, 95])).
% 0.14/0.42 tff(98,plain,
% 0.14/0.42 (((~(robust_position(X!2) | (~((~positional_advantage(X!2, tptp_fun_T_1(X!2))) | (~smaller_or_equal(age(X!2, tptp_fun_T_1(X!2)), tau)))) | (~((~greater(age(X!2, tptp_fun_T_1(X!2)), tau)) | positional_advantage(X!2, tptp_fun_T_1(X!2)))))) | (~((~robust_position(X!2)) | ![T: $i] : (~((~((~positional_advantage(X!2, T)) | (~smaller_or_equal(age(X!2, T), tau)))) | (~((~greater(age(X!2, T), tau)) | positional_advantage(X!2, T)))))))) | ((~robust_position(X!2)) | ![T: $i] : (~((~((~positional_advantage(X!2, T)) | (~smaller_or_equal(age(X!2, T), tau)))) | (~((~greater(age(X!2, T), tau)) | positional_advantage(X!2, T))))))),
% 0.14/0.42 inference(tautology,[status(thm)],[])).
% 0.14/0.42 tff(99,plain,
% 0.14/0.42 ((~robust_position(X!2)) | ![T: $i] : (~((~((~positional_advantage(X!2, T)) | (~smaller_or_equal(age(X!2, T), tau)))) | (~((~greater(age(X!2, T), tau)) | positional_advantage(X!2, T)))))),
% 0.14/0.42 inference(unit_resolution,[status(thm)],[98, 97])).
% 0.14/0.42 tff(100,plain,
% 0.14/0.42 (robust_position(X!2)),
% 0.14/0.42 inference(and_elim,[status(thm)],[9])).
% 0.14/0.42 tff(101,plain,
% 0.14/0.42 ((~((~robust_position(X!2)) | ![T: $i] : (~((~((~positional_advantage(X!2, T)) | (~smaller_or_equal(age(X!2, T), tau)))) | (~((~greater(age(X!2, T), tau)) | positional_advantage(X!2, T))))))) | (~robust_position(X!2)) | ![T: $i] : (~((~((~positional_advantage(X!2, T)) | (~smaller_or_equal(age(X!2, T), tau)))) | (~((~greater(age(X!2, T), tau)) | positional_advantage(X!2, T)))))),
% 0.14/0.42 inference(tautology,[status(thm)],[])).
% 0.14/0.42 tff(102,plain,
% 0.14/0.42 ((~((~robust_position(X!2)) | ![T: $i] : (~((~((~positional_advantage(X!2, T)) | (~smaller_or_equal(age(X!2, T), tau)))) | (~((~greater(age(X!2, T), tau)) | positional_advantage(X!2, T))))))) | ![T: $i] : (~((~((~positional_advantage(X!2, T)) | (~smaller_or_equal(age(X!2, T), tau)))) | (~((~greater(age(X!2, T), tau)) | positional_advantage(X!2, T)))))),
% 0.14/0.42 inference(unit_resolution,[status(thm)],[101, 100])).
% 0.14/0.42 tff(103,plain,
% 0.14/0.42 (![T: $i] : (~((~((~positional_advantage(X!2, T)) | (~smaller_or_equal(age(X!2, T), tau)))) | (~((~greater(age(X!2, T), tau)) | positional_advantage(X!2, T)))))),
% 0.14/0.42 inference(unit_resolution,[status(thm)],[102, 99])).
% 0.14/0.42 tff(104,plain,
% 0.14/0.42 ((~![T: $i] : (~((~((~positional_advantage(X!2, T)) | (~smaller_or_equal(age(X!2, T), tau)))) | (~((~greater(age(X!2, T), tau)) | positional_advantage(X!2, T)))))) | (~((~((~positional_advantage(X!2, T0!3)) | (~smaller_or_equal(age(X!2, T0!3), tau)))) | (~((~greater(age(X!2, T0!3), tau)) | positional_advantage(X!2, T0!3)))))),
% 0.14/0.42 inference(quant_inst,[status(thm)],[])).
% 0.14/0.42 tff(105,plain,
% 0.14/0.42 (~((~((~positional_advantage(X!2, T0!3)) | (~smaller_or_equal(age(X!2, T0!3), tau)))) | (~((~greater(age(X!2, T0!3), tau)) | positional_advantage(X!2, T0!3))))),
% 0.14/0.42 inference(unit_resolution,[status(thm)],[104, 103])).
% 0.14/0.42 tff(106,plain,
% 0.14/0.42 (((~((~positional_advantage(X!2, T0!3)) | (~smaller_or_equal(age(X!2, T0!3), tau)))) | (~((~greater(age(X!2, T0!3), tau)) | positional_advantage(X!2, T0!3)))) | ((~positional_advantage(X!2, T0!3)) | (~smaller_or_equal(age(X!2, T0!3), tau)))),
% 0.14/0.42 inference(tautology,[status(thm)],[])).
% 0.14/0.42 tff(107,plain,
% 0.14/0.42 ((~positional_advantage(X!2, T0!3)) | (~smaller_or_equal(age(X!2, T0!3), tau))),
% 0.14/0.42 inference(unit_resolution,[status(thm)],[106, 105])).
% 0.14/0.42 tff(108,plain,
% 0.14/0.42 ((~((~positional_advantage(X!2, T0!3)) | (~smaller_or_equal(age(X!2, T0!3), tau)))) | (~positional_advantage(X!2, T0!3)) | (~smaller_or_equal(age(X!2, T0!3), tau))),
% 0.14/0.42 inference(tautology,[status(thm)],[])).
% 0.14/0.42 tff(109,plain,
% 0.14/0.42 ((~positional_advantage(X!2, T0!3)) | (~smaller_or_equal(age(X!2, T0!3), tau))),
% 0.14/0.42 inference(unit_resolution,[status(thm)],[108, 107])).
% 0.14/0.42 tff(110,plain,
% 0.14/0.42 (~positional_advantage(X!2, T0!3)),
% 0.14/0.42 inference(unit_resolution,[status(thm)],[109, 76])).
% 0.14/0.42 tff(111,plain,
% 0.14/0.42 (^[X: $i] : rewrite((~((~((~fragile_position(X)) | ![T: $i] : (~((~((~smaller_or_equal(age(X, T), sigma)) | positional_advantage(X, T))) | (~((~positional_advantage(X, T)) | (~greater(age(X, T), sigma)))))))) | (~(fragile_position(X) | (~((~smaller_or_equal(age(X, tptp_fun_T_0(X)), sigma)) | positional_advantage(X, tptp_fun_T_0(X)))) | (~((~positional_advantage(X, tptp_fun_T_0(X))) | (~greater(age(X, tptp_fun_T_0(X)), sigma)))))))) <=> (~((~(fragile_position(X) | (~((~smaller_or_equal(age(X, tptp_fun_T_0(X)), sigma)) | positional_advantage(X, tptp_fun_T_0(X)))) | (~((~positional_advantage(X, tptp_fun_T_0(X))) | (~greater(age(X, tptp_fun_T_0(X)), sigma)))))) | (~((~fragile_position(X)) | ![T: $i] : (~((~((~smaller_or_equal(age(X, T), sigma)) | positional_advantage(X, T))) | (~((~positional_advantage(X, T)) | (~greater(age(X, T), sigma)))))))))))),
% 0.14/0.42 inference(bind,[status(th)],[])).
% 0.14/0.42 tff(112,plain,
% 0.14/0.42 (![X: $i] : (~((~((~fragile_position(X)) | ![T: $i] : (~((~((~smaller_or_equal(age(X, T), sigma)) | positional_advantage(X, T))) | (~((~positional_advantage(X, T)) | (~greater(age(X, T), sigma)))))))) | (~(fragile_position(X) | (~((~smaller_or_equal(age(X, tptp_fun_T_0(X)), sigma)) | positional_advantage(X, tptp_fun_T_0(X)))) | (~((~positional_advantage(X, tptp_fun_T_0(X))) | (~greater(age(X, tptp_fun_T_0(X)), sigma)))))))) <=> ![X: $i] : (~((~(fragile_position(X) | (~((~smaller_or_equal(age(X, tptp_fun_T_0(X)), sigma)) | positional_advantage(X, tptp_fun_T_0(X)))) | (~((~positional_advantage(X, tptp_fun_T_0(X))) | (~greater(age(X, tptp_fun_T_0(X)), sigma)))))) | (~((~fragile_position(X)) | ![T: $i] : (~((~((~smaller_or_equal(age(X, T), sigma)) | positional_advantage(X, T))) | (~((~positional_advantage(X, T)) | (~greater(age(X, T), sigma))))))))))),
% 0.14/0.43 inference(quant_intro,[status(thm)],[111])).
% 0.14/0.43 tff(113,plain,
% 0.14/0.43 (^[X: $i] : refl((~((~((~fragile_position(X)) | ![T: $i] : (~((~((~smaller_or_equal(age(X, T), sigma)) | positional_advantage(X, T))) | (~((~positional_advantage(X, T)) | (~greater(age(X, T), sigma)))))))) | (~(fragile_position(X) | (~((~smaller_or_equal(age(X, tptp_fun_T_0(X)), sigma)) | positional_advantage(X, tptp_fun_T_0(X)))) | (~((~positional_advantage(X, tptp_fun_T_0(X))) | (~greater(age(X, tptp_fun_T_0(X)), sigma)))))))) <=> (~((~((~fragile_position(X)) | ![T: $i] : (~((~((~smaller_or_equal(age(X, T), sigma)) | positional_advantage(X, T))) | (~((~positional_advantage(X, T)) | (~greater(age(X, T), sigma)))))))) | (~(fragile_position(X) | (~((~smaller_or_equal(age(X, tptp_fun_T_0(X)), sigma)) | positional_advantage(X, tptp_fun_T_0(X)))) | (~((~positional_advantage(X, tptp_fun_T_0(X))) | (~greater(age(X, tptp_fun_T_0(X)), sigma)))))))))),
% 0.14/0.43 inference(bind,[status(th)],[])).
% 0.14/0.43 tff(114,plain,
% 0.14/0.43 (![X: $i] : (~((~((~fragile_position(X)) | ![T: $i] : (~((~((~smaller_or_equal(age(X, T), sigma)) | positional_advantage(X, T))) | (~((~positional_advantage(X, T)) | (~greater(age(X, T), sigma)))))))) | (~(fragile_position(X) | (~((~smaller_or_equal(age(X, tptp_fun_T_0(X)), sigma)) | positional_advantage(X, tptp_fun_T_0(X)))) | (~((~positional_advantage(X, tptp_fun_T_0(X))) | (~greater(age(X, tptp_fun_T_0(X)), sigma)))))))) <=> ![X: $i] : (~((~((~fragile_position(X)) | ![T: $i] : (~((~((~smaller_or_equal(age(X, T), sigma)) | positional_advantage(X, T))) | (~((~positional_advantage(X, T)) | (~greater(age(X, T), sigma)))))))) | (~(fragile_position(X) | (~((~smaller_or_equal(age(X, tptp_fun_T_0(X)), sigma)) | positional_advantage(X, tptp_fun_T_0(X)))) | (~((~positional_advantage(X, tptp_fun_T_0(X))) | (~greater(age(X, tptp_fun_T_0(X)), sigma))))))))),
% 0.14/0.43 inference(quant_intro,[status(thm)],[113])).
% 0.14/0.43 tff(115,plain,
% 0.14/0.43 (^[X: $i] : rewrite((~((~((~fragile_position(X)) | ![T: $i] : (~((~((~smaller_or_equal(age(X, T), sigma)) | positional_advantage(X, T))) | (~((~positional_advantage(X, T)) | (~greater(age(X, T), sigma)))))))) | (~(fragile_position(X) | (~((~smaller_or_equal(age(X, tptp_fun_T_0(X)), sigma)) | positional_advantage(X, tptp_fun_T_0(X)))) | (~((~positional_advantage(X, tptp_fun_T_0(X))) | (~greater(age(X, tptp_fun_T_0(X)), sigma)))))))) <=> (~((~((~fragile_position(X)) | ![T: $i] : (~((~((~smaller_or_equal(age(X, T), sigma)) | positional_advantage(X, T))) | (~((~positional_advantage(X, T)) | (~greater(age(X, T), sigma)))))))) | (~(fragile_position(X) | (~((~smaller_or_equal(age(X, tptp_fun_T_0(X)), sigma)) | positional_advantage(X, tptp_fun_T_0(X)))) | (~((~positional_advantage(X, tptp_fun_T_0(X))) | (~greater(age(X, tptp_fun_T_0(X)), sigma)))))))))),
% 0.14/0.43 inference(bind,[status(th)],[])).
% 0.14/0.43 tff(116,plain,
% 0.14/0.43 (![X: $i] : (~((~((~fragile_position(X)) | ![T: $i] : (~((~((~smaller_or_equal(age(X, T), sigma)) | positional_advantage(X, T))) | (~((~positional_advantage(X, T)) | (~greater(age(X, T), sigma)))))))) | (~(fragile_position(X) | (~((~smaller_or_equal(age(X, tptp_fun_T_0(X)), sigma)) | positional_advantage(X, tptp_fun_T_0(X)))) | (~((~positional_advantage(X, tptp_fun_T_0(X))) | (~greater(age(X, tptp_fun_T_0(X)), sigma)))))))) <=> ![X: $i] : (~((~((~fragile_position(X)) | ![T: $i] : (~((~((~smaller_or_equal(age(X, T), sigma)) | positional_advantage(X, T))) | (~((~positional_advantage(X, T)) | (~greater(age(X, T), sigma)))))))) | (~(fragile_position(X) | (~((~smaller_or_equal(age(X, tptp_fun_T_0(X)), sigma)) | positional_advantage(X, tptp_fun_T_0(X)))) | (~((~positional_advantage(X, tptp_fun_T_0(X))) | (~greater(age(X, tptp_fun_T_0(X)), sigma))))))))),
% 0.14/0.43 inference(quant_intro,[status(thm)],[115])).
% 0.14/0.43 tff(117,plain,
% 0.14/0.43 (![X: $i] : (~((~((~fragile_position(X)) | ![T: $i] : (~((~((~smaller_or_equal(age(X, T), sigma)) | positional_advantage(X, T))) | (~((~positional_advantage(X, T)) | (~greater(age(X, T), sigma)))))))) | (~(fragile_position(X) | (~((~smaller_or_equal(age(X, tptp_fun_T_0(X)), sigma)) | positional_advantage(X, tptp_fun_T_0(X)))) | (~((~positional_advantage(X, tptp_fun_T_0(X))) | (~greater(age(X, tptp_fun_T_0(X)), sigma)))))))) <=> ![X: $i] : (~((~((~fragile_position(X)) | ![T: $i] : (~((~((~smaller_or_equal(age(X, T), sigma)) | positional_advantage(X, T))) | (~((~positional_advantage(X, T)) | (~greater(age(X, T), sigma)))))))) | (~(fragile_position(X) | (~((~smaller_or_equal(age(X, tptp_fun_T_0(X)), sigma)) | positional_advantage(X, tptp_fun_T_0(X)))) | (~((~positional_advantage(X, tptp_fun_T_0(X))) | (~greater(age(X, tptp_fun_T_0(X)), sigma))))))))),
% 0.14/0.43 inference(transitivity,[status(thm)],[116, 114])).
% 0.14/0.43 tff(118,plain,
% 0.14/0.43 (^[X: $i] : trans(monotonicity(rewrite(((~fragile_position(X)) | ![T: $i] : (((~smaller_or_equal(age(X, T), sigma)) | positional_advantage(X, T)) & ((~positional_advantage(X, T)) | (~greater(age(X, T), sigma))))) <=> ((~fragile_position(X)) | ![T: $i] : (~((~((~smaller_or_equal(age(X, T), sigma)) | positional_advantage(X, T))) | (~((~positional_advantage(X, T)) | (~greater(age(X, T), sigma)))))))), trans(monotonicity(trans(monotonicity(rewrite((((~smaller_or_equal(age(X, tptp_fun_T_0(X)), sigma)) | positional_advantage(X, tptp_fun_T_0(X))) & ((~positional_advantage(X, tptp_fun_T_0(X))) | (~greater(age(X, tptp_fun_T_0(X)), sigma)))) <=> (~((~((~smaller_or_equal(age(X, tptp_fun_T_0(X)), sigma)) | positional_advantage(X, tptp_fun_T_0(X)))) | (~((~positional_advantage(X, tptp_fun_T_0(X))) | (~greater(age(X, tptp_fun_T_0(X)), sigma))))))), ((~(((~smaller_or_equal(age(X, tptp_fun_T_0(X)), sigma)) | positional_advantage(X, tptp_fun_T_0(X))) & ((~positional_advantage(X, tptp_fun_T_0(X))) | (~greater(age(X, tptp_fun_T_0(X)), sigma))))) <=> (~(~((~((~smaller_or_equal(age(X, tptp_fun_T_0(X)), sigma)) | positional_advantage(X, tptp_fun_T_0(X)))) | (~((~positional_advantage(X, tptp_fun_T_0(X))) | (~greater(age(X, tptp_fun_T_0(X)), sigma))))))))), rewrite((~(~((~((~smaller_or_equal(age(X, tptp_fun_T_0(X)), sigma)) | positional_advantage(X, tptp_fun_T_0(X)))) | (~((~positional_advantage(X, tptp_fun_T_0(X))) | (~greater(age(X, tptp_fun_T_0(X)), sigma))))))) <=> ((~((~smaller_or_equal(age(X, tptp_fun_T_0(X)), sigma)) | positional_advantage(X, tptp_fun_T_0(X)))) | (~((~positional_advantage(X, tptp_fun_T_0(X))) | (~greater(age(X, tptp_fun_T_0(X)), sigma)))))), ((~(((~smaller_or_equal(age(X, tptp_fun_T_0(X)), sigma)) | positional_advantage(X, tptp_fun_T_0(X))) & ((~positional_advantage(X, tptp_fun_T_0(X))) | (~greater(age(X, tptp_fun_T_0(X)), sigma))))) <=> ((~((~smaller_or_equal(age(X, tptp_fun_T_0(X)), sigma)) | positional_advantage(X, tptp_fun_T_0(X)))) | (~((~positional_advantage(X, tptp_fun_T_0(X))) | (~greater(age(X, tptp_fun_T_0(X)), sigma))))))), ((fragile_position(X) | (~(((~smaller_or_equal(age(X, tptp_fun_T_0(X)), sigma)) | positional_advantage(X, tptp_fun_T_0(X))) & ((~positional_advantage(X, tptp_fun_T_0(X))) | (~greater(age(X, tptp_fun_T_0(X)), sigma)))))) <=> (fragile_position(X) | ((~((~smaller_or_equal(age(X, tptp_fun_T_0(X)), sigma)) | positional_advantage(X, tptp_fun_T_0(X)))) | (~((~positional_advantage(X, tptp_fun_T_0(X))) | (~greater(age(X, tptp_fun_T_0(X)), sigma)))))))), rewrite((fragile_position(X) | ((~((~smaller_or_equal(age(X, tptp_fun_T_0(X)), sigma)) | positional_advantage(X, tptp_fun_T_0(X)))) | (~((~positional_advantage(X, tptp_fun_T_0(X))) | (~greater(age(X, tptp_fun_T_0(X)), sigma)))))) <=> (fragile_position(X) | (~((~smaller_or_equal(age(X, tptp_fun_T_0(X)), sigma)) | positional_advantage(X, tptp_fun_T_0(X)))) | (~((~positional_advantage(X, tptp_fun_T_0(X))) | (~greater(age(X, tptp_fun_T_0(X)), sigma)))))), ((fragile_position(X) | (~(((~smaller_or_equal(age(X, tptp_fun_T_0(X)), sigma)) | positional_advantage(X, tptp_fun_T_0(X))) & ((~positional_advantage(X, tptp_fun_T_0(X))) | (~greater(age(X, tptp_fun_T_0(X)), sigma)))))) <=> (fragile_position(X) | (~((~smaller_or_equal(age(X, tptp_fun_T_0(X)), sigma)) | positional_advantage(X, tptp_fun_T_0(X)))) | (~((~positional_advantage(X, tptp_fun_T_0(X))) | (~greater(age(X, tptp_fun_T_0(X)), sigma))))))), ((((~fragile_position(X)) | ![T: $i] : (((~smaller_or_equal(age(X, T), sigma)) | positional_advantage(X, T)) & ((~positional_advantage(X, T)) | (~greater(age(X, T), sigma))))) & (fragile_position(X) | (~(((~smaller_or_equal(age(X, tptp_fun_T_0(X)), sigma)) | positional_advantage(X, tptp_fun_T_0(X))) & ((~positional_advantage(X, tptp_fun_T_0(X))) | (~greater(age(X, tptp_fun_T_0(X)), sigma))))))) <=> (((~fragile_position(X)) | ![T: $i] : (~((~((~smaller_or_equal(age(X, T), sigma)) | positional_advantage(X, T))) | (~((~positional_advantage(X, T)) | (~greater(age(X, T), sigma))))))) & (fragile_position(X) | (~((~smaller_or_equal(age(X, tptp_fun_T_0(X)), sigma)) | positional_advantage(X, tptp_fun_T_0(X)))) | (~((~positional_advantage(X, tptp_fun_T_0(X))) | (~greater(age(X, tptp_fun_T_0(X)), sigma)))))))), rewrite((((~fragile_position(X)) | ![T: $i] : (~((~((~smaller_or_equal(age(X, T), sigma)) | positional_advantage(X, T))) | (~((~positional_advantage(X, T)) | (~greater(age(X, T), sigma))))))) & (fragile_position(X) | (~((~smaller_or_equal(age(X, tptp_fun_T_0(X)), sigma)) | positional_advantage(X, tptp_fun_T_0(X)))) | (~((~positional_advantage(X, tptp_fun_T_0(X))) | (~greater(age(X, tptp_fun_T_0(X)), sigma)))))) <=> (~((~((~fragile_position(X)) | ![T: $i] : (~((~((~smaller_or_equal(age(X, T), sigma)) | positional_advantage(X, T))) | (~((~positional_advantage(X, T)) | (~greater(age(X, T), sigma)))))))) | (~(fragile_position(X) | (~((~smaller_or_equal(age(X, tptp_fun_T_0(X)), sigma)) | positional_advantage(X, tptp_fun_T_0(X)))) | (~((~positional_advantage(X, tptp_fun_T_0(X))) | (~greater(age(X, tptp_fun_T_0(X)), sigma))))))))), ((((~fragile_position(X)) | ![T: $i] : (((~smaller_or_equal(age(X, T), sigma)) | positional_advantage(X, T)) & ((~positional_advantage(X, T)) | (~greater(age(X, T), sigma))))) & (fragile_position(X) | (~(((~smaller_or_equal(age(X, tptp_fun_T_0(X)), sigma)) | positional_advantage(X, tptp_fun_T_0(X))) & ((~positional_advantage(X, tptp_fun_T_0(X))) | (~greater(age(X, tptp_fun_T_0(X)), sigma))))))) <=> (~((~((~fragile_position(X)) | ![T: $i] : (~((~((~smaller_or_equal(age(X, T), sigma)) | positional_advantage(X, T))) | (~((~positional_advantage(X, T)) | (~greater(age(X, T), sigma)))))))) | (~(fragile_position(X) | (~((~smaller_or_equal(age(X, tptp_fun_T_0(X)), sigma)) | positional_advantage(X, tptp_fun_T_0(X)))) | (~((~positional_advantage(X, tptp_fun_T_0(X))) | (~greater(age(X, tptp_fun_T_0(X)), sigma))))))))))),
% 0.14/0.43 inference(bind,[status(th)],[])).
% 0.14/0.43 tff(119,plain,
% 0.14/0.43 (![X: $i] : (((~fragile_position(X)) | ![T: $i] : (((~smaller_or_equal(age(X, T), sigma)) | positional_advantage(X, T)) & ((~positional_advantage(X, T)) | (~greater(age(X, T), sigma))))) & (fragile_position(X) | (~(((~smaller_or_equal(age(X, tptp_fun_T_0(X)), sigma)) | positional_advantage(X, tptp_fun_T_0(X))) & ((~positional_advantage(X, tptp_fun_T_0(X))) | (~greater(age(X, tptp_fun_T_0(X)), sigma))))))) <=> ![X: $i] : (~((~((~fragile_position(X)) | ![T: $i] : (~((~((~smaller_or_equal(age(X, T), sigma)) | positional_advantage(X, T))) | (~((~positional_advantage(X, T)) | (~greater(age(X, T), sigma)))))))) | (~(fragile_position(X) | (~((~smaller_or_equal(age(X, tptp_fun_T_0(X)), sigma)) | positional_advantage(X, tptp_fun_T_0(X)))) | (~((~positional_advantage(X, tptp_fun_T_0(X))) | (~greater(age(X, tptp_fun_T_0(X)), sigma))))))))),
% 0.14/0.43 inference(quant_intro,[status(thm)],[118])).
% 0.14/0.43 tff(120,plain,
% 0.14/0.43 (![X: $i] : (fragile_position(X) <=> ![T: $i] : (((~smaller_or_equal(age(X, T), sigma)) | positional_advantage(X, T)) & ((~positional_advantage(X, T)) | (~greater(age(X, T), sigma))))) <=> ![X: $i] : (fragile_position(X) <=> ![T: $i] : (((~smaller_or_equal(age(X, T), sigma)) | positional_advantage(X, T)) & ((~positional_advantage(X, T)) | (~greater(age(X, T), sigma)))))),
% 0.14/0.43 inference(rewrite,[status(thm)],[])).
% 0.14/0.43 tff(121,plain,
% 0.14/0.43 (^[X: $i] : rewrite((fragile_position(X) <=> ![T: $i] : ((smaller_or_equal(age(X, T), sigma) => positional_advantage(X, T)) & (greater(age(X, T), sigma) => (~positional_advantage(X, T))))) <=> (fragile_position(X) <=> ![T: $i] : (((~smaller_or_equal(age(X, T), sigma)) | positional_advantage(X, T)) & ((~positional_advantage(X, T)) | (~greater(age(X, T), sigma))))))),
% 0.14/0.43 inference(bind,[status(th)],[])).
% 0.14/0.43 tff(122,plain,
% 0.14/0.43 (![X: $i] : (fragile_position(X) <=> ![T: $i] : ((smaller_or_equal(age(X, T), sigma) => positional_advantage(X, T)) & (greater(age(X, T), sigma) => (~positional_advantage(X, T))))) <=> ![X: $i] : (fragile_position(X) <=> ![T: $i] : (((~smaller_or_equal(age(X, T), sigma)) | positional_advantage(X, T)) & ((~positional_advantage(X, T)) | (~greater(age(X, T), sigma)))))),
% 0.14/0.43 inference(quant_intro,[status(thm)],[121])).
% 0.14/0.43 tff(123,axiom,(![X: $i] : (fragile_position(X) <=> ![T: $i] : ((smaller_or_equal(age(X, T), sigma) => positional_advantage(X, T)) & (greater(age(X, T), sigma) => (~positional_advantage(X, T)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','definition_3')).
% 0.14/0.43 tff(124,plain,
% 0.14/0.43 (![X: $i] : (fragile_position(X) <=> ![T: $i] : (((~smaller_or_equal(age(X, T), sigma)) | positional_advantage(X, T)) & ((~positional_advantage(X, T)) | (~greater(age(X, T), sigma)))))),
% 0.14/0.43 inference(modus_ponens,[status(thm)],[123, 122])).
% 0.14/0.43 tff(125,plain,
% 0.14/0.43 (![X: $i] : (fragile_position(X) <=> ![T: $i] : (((~smaller_or_equal(age(X, T), sigma)) | positional_advantage(X, T)) & ((~positional_advantage(X, T)) | (~greater(age(X, T), sigma)))))),
% 0.14/0.43 inference(modus_ponens,[status(thm)],[124, 120])).
% 0.14/0.43 tff(126,plain,(
% 0.14/0.43 ![X: $i] : (((~fragile_position(X)) | ![T: $i] : (((~smaller_or_equal(age(X, T), sigma)) | positional_advantage(X, T)) & ((~positional_advantage(X, T)) | (~greater(age(X, T), sigma))))) & (fragile_position(X) | (~(((~smaller_or_equal(age(X, tptp_fun_T_0(X)), sigma)) | positional_advantage(X, tptp_fun_T_0(X))) & ((~positional_advantage(X, tptp_fun_T_0(X))) | (~greater(age(X, tptp_fun_T_0(X)), sigma)))))))),
% 0.14/0.43 inference(skolemize,[status(sab)],[125])).
% 0.14/0.43 tff(127,plain,
% 0.14/0.43 (![X: $i] : (~((~((~fragile_position(X)) | ![T: $i] : (~((~((~smaller_or_equal(age(X, T), sigma)) | positional_advantage(X, T))) | (~((~positional_advantage(X, T)) | (~greater(age(X, T), sigma)))))))) | (~(fragile_position(X) | (~((~smaller_or_equal(age(X, tptp_fun_T_0(X)), sigma)) | positional_advantage(X, tptp_fun_T_0(X)))) | (~((~positional_advantage(X, tptp_fun_T_0(X))) | (~greater(age(X, tptp_fun_T_0(X)), sigma))))))))),
% 0.14/0.43 inference(modus_ponens,[status(thm)],[126, 119])).
% 0.14/0.43 tff(128,plain,
% 0.14/0.43 (![X: $i] : (~((~((~fragile_position(X)) | ![T: $i] : (~((~((~smaller_or_equal(age(X, T), sigma)) | positional_advantage(X, T))) | (~((~positional_advantage(X, T)) | (~greater(age(X, T), sigma)))))))) | (~(fragile_position(X) | (~((~smaller_or_equal(age(X, tptp_fun_T_0(X)), sigma)) | positional_advantage(X, tptp_fun_T_0(X)))) | (~((~positional_advantage(X, tptp_fun_T_0(X))) | (~greater(age(X, tptp_fun_T_0(X)), sigma))))))))),
% 0.14/0.43 inference(modus_ponens,[status(thm)],[127, 117])).
% 0.14/0.43 tff(129,plain,
% 0.14/0.43 (![X: $i] : (~((~(fragile_position(X) | (~((~smaller_or_equal(age(X, tptp_fun_T_0(X)), sigma)) | positional_advantage(X, tptp_fun_T_0(X)))) | (~((~positional_advantage(X, tptp_fun_T_0(X))) | (~greater(age(X, tptp_fun_T_0(X)), sigma)))))) | (~((~fragile_position(X)) | ![T: $i] : (~((~((~smaller_or_equal(age(X, T), sigma)) | positional_advantage(X, T))) | (~((~positional_advantage(X, T)) | (~greater(age(X, T), sigma))))))))))),
% 0.14/0.43 inference(modus_ponens,[status(thm)],[128, 112])).
% 0.14/0.43 tff(130,plain,
% 0.14/0.43 (((~![X: $i] : (~((~(fragile_position(X) | (~((~smaller_or_equal(age(X, tptp_fun_T_0(X)), sigma)) | positional_advantage(X, tptp_fun_T_0(X)))) | (~((~positional_advantage(X, tptp_fun_T_0(X))) | (~greater(age(X, tptp_fun_T_0(X)), sigma)))))) | (~((~fragile_position(X)) | ![T: $i] : (~((~((~smaller_or_equal(age(X, T), sigma)) | positional_advantage(X, T))) | (~((~positional_advantage(X, T)) | (~greater(age(X, T), sigma))))))))))) | (~((~(fragile_position(X!2) | (~((~positional_advantage(X!2, tptp_fun_T_0(X!2))) | (~greater(age(X!2, tptp_fun_T_0(X!2)), sigma)))) | (~((~smaller_or_equal(age(X!2, tptp_fun_T_0(X!2)), sigma)) | positional_advantage(X!2, tptp_fun_T_0(X!2)))))) | (~((~fragile_position(X!2)) | ![T: $i] : (~((~((~smaller_or_equal(age(X!2, T), sigma)) | positional_advantage(X!2, T))) | (~((~positional_advantage(X!2, T)) | (~greater(age(X!2, T), sigma))))))))))) <=> ((~![X: $i] : (~((~(fragile_position(X) | (~((~smaller_or_equal(age(X, tptp_fun_T_0(X)), sigma)) | positional_advantage(X, tptp_fun_T_0(X)))) | (~((~positional_advantage(X, tptp_fun_T_0(X))) | (~greater(age(X, tptp_fun_T_0(X)), sigma)))))) | (~((~fragile_position(X)) | ![T: $i] : (~((~((~smaller_or_equal(age(X, T), sigma)) | positional_advantage(X, T))) | (~((~positional_advantage(X, T)) | (~greater(age(X, T), sigma))))))))))) | (~((~(fragile_position(X!2) | (~((~positional_advantage(X!2, tptp_fun_T_0(X!2))) | (~greater(age(X!2, tptp_fun_T_0(X!2)), sigma)))) | (~((~smaller_or_equal(age(X!2, tptp_fun_T_0(X!2)), sigma)) | positional_advantage(X!2, tptp_fun_T_0(X!2)))))) | (~((~fragile_position(X!2)) | ![T: $i] : (~((~((~smaller_or_equal(age(X!2, T), sigma)) | positional_advantage(X!2, T))) | (~((~positional_advantage(X!2, T)) | (~greater(age(X!2, T), sigma)))))))))))),
% 0.14/0.43 inference(rewrite,[status(thm)],[])).
% 0.14/0.43 tff(131,plain,
% 0.14/0.43 ((~((~(fragile_position(X!2) | (~((~smaller_or_equal(age(X!2, tptp_fun_T_0(X!2)), sigma)) | positional_advantage(X!2, tptp_fun_T_0(X!2)))) | (~((~positional_advantage(X!2, tptp_fun_T_0(X!2))) | (~greater(age(X!2, tptp_fun_T_0(X!2)), sigma)))))) | (~((~fragile_position(X!2)) | ![T: $i] : (~((~((~smaller_or_equal(age(X!2, T), sigma)) | positional_advantage(X!2, T))) | (~((~positional_advantage(X!2, T)) | (~greater(age(X!2, T), sigma)))))))))) <=> (~((~(fragile_position(X!2) | (~((~positional_advantage(X!2, tptp_fun_T_0(X!2))) | (~greater(age(X!2, tptp_fun_T_0(X!2)), sigma)))) | (~((~smaller_or_equal(age(X!2, tptp_fun_T_0(X!2)), sigma)) | positional_advantage(X!2, tptp_fun_T_0(X!2)))))) | (~((~fragile_position(X!2)) | ![T: $i] : (~((~((~smaller_or_equal(age(X!2, T), sigma)) | positional_advantage(X!2, T))) | (~((~positional_advantage(X!2, T)) | (~greater(age(X!2, T), sigma))))))))))),
% 0.14/0.43 inference(rewrite,[status(thm)],[])).
% 0.14/0.43 tff(132,plain,
% 0.14/0.43 (((~![X: $i] : (~((~(fragile_position(X) | (~((~smaller_or_equal(age(X, tptp_fun_T_0(X)), sigma)) | positional_advantage(X, tptp_fun_T_0(X)))) | (~((~positional_advantage(X, tptp_fun_T_0(X))) | (~greater(age(X, tptp_fun_T_0(X)), sigma)))))) | (~((~fragile_position(X)) | ![T: $i] : (~((~((~smaller_or_equal(age(X, T), sigma)) | positional_advantage(X, T))) | (~((~positional_advantage(X, T)) | (~greater(age(X, T), sigma))))))))))) | (~((~(fragile_position(X!2) | (~((~smaller_or_equal(age(X!2, tptp_fun_T_0(X!2)), sigma)) | positional_advantage(X!2, tptp_fun_T_0(X!2)))) | (~((~positional_advantage(X!2, tptp_fun_T_0(X!2))) | (~greater(age(X!2, tptp_fun_T_0(X!2)), sigma)))))) | (~((~fragile_position(X!2)) | ![T: $i] : (~((~((~smaller_or_equal(age(X!2, T), sigma)) | positional_advantage(X!2, T))) | (~((~positional_advantage(X!2, T)) | (~greater(age(X!2, T), sigma))))))))))) <=> ((~![X: $i] : (~((~(fragile_position(X) | (~((~smaller_or_equal(age(X, tptp_fun_T_0(X)), sigma)) | positional_advantage(X, tptp_fun_T_0(X)))) | (~((~positional_advantage(X, tptp_fun_T_0(X))) | (~greater(age(X, tptp_fun_T_0(X)), sigma)))))) | (~((~fragile_position(X)) | ![T: $i] : (~((~((~smaller_or_equal(age(X, T), sigma)) | positional_advantage(X, T))) | (~((~positional_advantage(X, T)) | (~greater(age(X, T), sigma))))))))))) | (~((~(fragile_position(X!2) | (~((~positional_advantage(X!2, tptp_fun_T_0(X!2))) | (~greater(age(X!2, tptp_fun_T_0(X!2)), sigma)))) | (~((~smaller_or_equal(age(X!2, tptp_fun_T_0(X!2)), sigma)) | positional_advantage(X!2, tptp_fun_T_0(X!2)))))) | (~((~fragile_position(X!2)) | ![T: $i] : (~((~((~smaller_or_equal(age(X!2, T), sigma)) | positional_advantage(X!2, T))) | (~((~positional_advantage(X!2, T)) | (~greater(age(X!2, T), sigma)))))))))))),
% 0.14/0.44 inference(monotonicity,[status(thm)],[131])).
% 0.14/0.44 tff(133,plain,
% 0.14/0.44 (((~![X: $i] : (~((~(fragile_position(X) | (~((~smaller_or_equal(age(X, tptp_fun_T_0(X)), sigma)) | positional_advantage(X, tptp_fun_T_0(X)))) | (~((~positional_advantage(X, tptp_fun_T_0(X))) | (~greater(age(X, tptp_fun_T_0(X)), sigma)))))) | (~((~fragile_position(X)) | ![T: $i] : (~((~((~smaller_or_equal(age(X, T), sigma)) | positional_advantage(X, T))) | (~((~positional_advantage(X, T)) | (~greater(age(X, T), sigma))))))))))) | (~((~(fragile_position(X!2) | (~((~smaller_or_equal(age(X!2, tptp_fun_T_0(X!2)), sigma)) | positional_advantage(X!2, tptp_fun_T_0(X!2)))) | (~((~positional_advantage(X!2, tptp_fun_T_0(X!2))) | (~greater(age(X!2, tptp_fun_T_0(X!2)), sigma)))))) | (~((~fragile_position(X!2)) | ![T: $i] : (~((~((~smaller_or_equal(age(X!2, T), sigma)) | positional_advantage(X!2, T))) | (~((~positional_advantage(X!2, T)) | (~greater(age(X!2, T), sigma))))))))))) <=> ((~![X: $i] : (~((~(fragile_position(X) | (~((~smaller_or_equal(age(X, tptp_fun_T_0(X)), sigma)) | positional_advantage(X, tptp_fun_T_0(X)))) | (~((~positional_advantage(X, tptp_fun_T_0(X))) | (~greater(age(X, tptp_fun_T_0(X)), sigma)))))) | (~((~fragile_position(X)) | ![T: $i] : (~((~((~smaller_or_equal(age(X, T), sigma)) | positional_advantage(X, T))) | (~((~positional_advantage(X, T)) | (~greater(age(X, T), sigma))))))))))) | (~((~(fragile_position(X!2) | (~((~positional_advantage(X!2, tptp_fun_T_0(X!2))) | (~greater(age(X!2, tptp_fun_T_0(X!2)), sigma)))) | (~((~smaller_or_equal(age(X!2, tptp_fun_T_0(X!2)), sigma)) | positional_advantage(X!2, tptp_fun_T_0(X!2)))))) | (~((~fragile_position(X!2)) | ![T: $i] : (~((~((~smaller_or_equal(age(X!2, T), sigma)) | positional_advantage(X!2, T))) | (~((~positional_advantage(X!2, T)) | (~greater(age(X!2, T), sigma)))))))))))),
% 0.14/0.44 inference(transitivity,[status(thm)],[132, 130])).
% 0.14/0.44 tff(134,plain,
% 0.14/0.44 ((~![X: $i] : (~((~(fragile_position(X) | (~((~smaller_or_equal(age(X, tptp_fun_T_0(X)), sigma)) | positional_advantage(X, tptp_fun_T_0(X)))) | (~((~positional_advantage(X, tptp_fun_T_0(X))) | (~greater(age(X, tptp_fun_T_0(X)), sigma)))))) | (~((~fragile_position(X)) | ![T: $i] : (~((~((~smaller_or_equal(age(X, T), sigma)) | positional_advantage(X, T))) | (~((~positional_advantage(X, T)) | (~greater(age(X, T), sigma))))))))))) | (~((~(fragile_position(X!2) | (~((~smaller_or_equal(age(X!2, tptp_fun_T_0(X!2)), sigma)) | positional_advantage(X!2, tptp_fun_T_0(X!2)))) | (~((~positional_advantage(X!2, tptp_fun_T_0(X!2))) | (~greater(age(X!2, tptp_fun_T_0(X!2)), sigma)))))) | (~((~fragile_position(X!2)) | ![T: $i] : (~((~((~smaller_or_equal(age(X!2, T), sigma)) | positional_advantage(X!2, T))) | (~((~positional_advantage(X!2, T)) | (~greater(age(X!2, T), sigma))))))))))),
% 0.14/0.44 inference(quant_inst,[status(thm)],[])).
% 0.14/0.44 tff(135,plain,
% 0.14/0.44 ((~![X: $i] : (~((~(fragile_position(X) | (~((~smaller_or_equal(age(X, tptp_fun_T_0(X)), sigma)) | positional_advantage(X, tptp_fun_T_0(X)))) | (~((~positional_advantage(X, tptp_fun_T_0(X))) | (~greater(age(X, tptp_fun_T_0(X)), sigma)))))) | (~((~fragile_position(X)) | ![T: $i] : (~((~((~smaller_or_equal(age(X, T), sigma)) | positional_advantage(X, T))) | (~((~positional_advantage(X, T)) | (~greater(age(X, T), sigma))))))))))) | (~((~(fragile_position(X!2) | (~((~positional_advantage(X!2, tptp_fun_T_0(X!2))) | (~greater(age(X!2, tptp_fun_T_0(X!2)), sigma)))) | (~((~smaller_or_equal(age(X!2, tptp_fun_T_0(X!2)), sigma)) | positional_advantage(X!2, tptp_fun_T_0(X!2)))))) | (~((~fragile_position(X!2)) | ![T: $i] : (~((~((~smaller_or_equal(age(X!2, T), sigma)) | positional_advantage(X!2, T))) | (~((~positional_advantage(X!2, T)) | (~greater(age(X!2, T), sigma))))))))))),
% 0.14/0.44 inference(modus_ponens,[status(thm)],[134, 133])).
% 0.14/0.44 tff(136,plain,
% 0.14/0.44 (~((~(fragile_position(X!2) | (~((~positional_advantage(X!2, tptp_fun_T_0(X!2))) | (~greater(age(X!2, tptp_fun_T_0(X!2)), sigma)))) | (~((~smaller_or_equal(age(X!2, tptp_fun_T_0(X!2)), sigma)) | positional_advantage(X!2, tptp_fun_T_0(X!2)))))) | (~((~fragile_position(X!2)) | ![T: $i] : (~((~((~smaller_or_equal(age(X!2, T), sigma)) | positional_advantage(X!2, T))) | (~((~positional_advantage(X!2, T)) | (~greater(age(X!2, T), sigma)))))))))),
% 0.14/0.44 inference(unit_resolution,[status(thm)],[135, 129])).
% 0.14/0.44 tff(137,plain,
% 0.14/0.44 (((~(fragile_position(X!2) | (~((~positional_advantage(X!2, tptp_fun_T_0(X!2))) | (~greater(age(X!2, tptp_fun_T_0(X!2)), sigma)))) | (~((~smaller_or_equal(age(X!2, tptp_fun_T_0(X!2)), sigma)) | positional_advantage(X!2, tptp_fun_T_0(X!2)))))) | (~((~fragile_position(X!2)) | ![T: $i] : (~((~((~smaller_or_equal(age(X!2, T), sigma)) | positional_advantage(X!2, T))) | (~((~positional_advantage(X!2, T)) | (~greater(age(X!2, T), sigma))))))))) | ((~fragile_position(X!2)) | ![T: $i] : (~((~((~smaller_or_equal(age(X!2, T), sigma)) | positional_advantage(X!2, T))) | (~((~positional_advantage(X!2, T)) | (~greater(age(X!2, T), sigma)))))))),
% 0.14/0.44 inference(tautology,[status(thm)],[])).
% 0.14/0.44 tff(138,plain,
% 0.14/0.44 ((~fragile_position(X!2)) | ![T: $i] : (~((~((~smaller_or_equal(age(X!2, T), sigma)) | positional_advantage(X!2, T))) | (~((~positional_advantage(X!2, T)) | (~greater(age(X!2, T), sigma))))))),
% 0.14/0.44 inference(unit_resolution,[status(thm)],[137, 136])).
% 0.14/0.44 tff(139,plain,
% 0.14/0.44 (fragile_position(X!2)),
% 0.14/0.44 inference(and_elim,[status(thm)],[9])).
% 0.14/0.44 tff(140,plain,
% 0.14/0.44 ((~((~fragile_position(X!2)) | ![T: $i] : (~((~((~smaller_or_equal(age(X!2, T), sigma)) | positional_advantage(X!2, T))) | (~((~positional_advantage(X!2, T)) | (~greater(age(X!2, T), sigma)))))))) | (~fragile_position(X!2)) | ![T: $i] : (~((~((~smaller_or_equal(age(X!2, T), sigma)) | positional_advantage(X!2, T))) | (~((~positional_advantage(X!2, T)) | (~greater(age(X!2, T), sigma))))))),
% 0.14/0.44 inference(tautology,[status(thm)],[])).
% 0.14/0.44 tff(141,plain,
% 0.14/0.44 ((~((~fragile_position(X!2)) | ![T: $i] : (~((~((~smaller_or_equal(age(X!2, T), sigma)) | positional_advantage(X!2, T))) | (~((~positional_advantage(X!2, T)) | (~greater(age(X!2, T), sigma)))))))) | ![T: $i] : (~((~((~smaller_or_equal(age(X!2, T), sigma)) | positional_advantage(X!2, T))) | (~((~positional_advantage(X!2, T)) | (~greater(age(X!2, T), sigma))))))),
% 0.14/0.44 inference(unit_resolution,[status(thm)],[140, 139])).
% 0.14/0.44 tff(142,plain,
% 0.14/0.44 (![T: $i] : (~((~((~smaller_or_equal(age(X!2, T), sigma)) | positional_advantage(X!2, T))) | (~((~positional_advantage(X!2, T)) | (~greater(age(X!2, T), sigma))))))),
% 0.14/0.44 inference(unit_resolution,[status(thm)],[141, 138])).
% 0.14/0.44 tff(143,plain,
% 0.14/0.44 ((~![T: $i] : (~((~((~smaller_or_equal(age(X!2, T), sigma)) | positional_advantage(X!2, T))) | (~((~positional_advantage(X!2, T)) | (~greater(age(X!2, T), sigma))))))) | (~((~((~smaller_or_equal(age(X!2, T0!3), sigma)) | positional_advantage(X!2, T0!3))) | (~((~positional_advantage(X!2, T0!3)) | (~greater(age(X!2, T0!3), sigma))))))),
% 0.14/0.44 inference(quant_inst,[status(thm)],[])).
% 0.14/0.44 tff(144,plain,
% 0.14/0.44 (~((~((~smaller_or_equal(age(X!2, T0!3), sigma)) | positional_advantage(X!2, T0!3))) | (~((~positional_advantage(X!2, T0!3)) | (~greater(age(X!2, T0!3), sigma)))))),
% 0.14/0.44 inference(unit_resolution,[status(thm)],[143, 142])).
% 0.14/0.44 tff(145,plain,
% 0.14/0.44 (((~((~smaller_or_equal(age(X!2, T0!3), sigma)) | positional_advantage(X!2, T0!3))) | (~((~positional_advantage(X!2, T0!3)) | (~greater(age(X!2, T0!3), sigma))))) | ((~smaller_or_equal(age(X!2, T0!3), sigma)) | positional_advantage(X!2, T0!3))),
% 0.14/0.44 inference(tautology,[status(thm)],[])).
% 0.14/0.44 tff(146,plain,
% 0.14/0.44 ((~smaller_or_equal(age(X!2, T0!3), sigma)) | positional_advantage(X!2, T0!3)),
% 0.14/0.44 inference(unit_resolution,[status(thm)],[145, 144])).
% 0.14/0.44 tff(147,plain,
% 0.14/0.44 ((~((~smaller_or_equal(age(X!2, T0!3), sigma)) | positional_advantage(X!2, T0!3))) | (~smaller_or_equal(age(X!2, T0!3), sigma)) | positional_advantage(X!2, T0!3)),
% 0.14/0.44 inference(tautology,[status(thm)],[])).
% 0.14/0.44 tff(148,plain,
% 0.14/0.44 ((~smaller_or_equal(age(X!2, T0!3), sigma)) | positional_advantage(X!2, T0!3)),
% 0.14/0.44 inference(unit_resolution,[status(thm)],[147, 146])).
% 0.14/0.44 tff(149,plain,
% 0.14/0.44 (~smaller_or_equal(age(X!2, T0!3), sigma)),
% 0.14/0.44 inference(unit_resolution,[status(thm)],[148, 110])).
% 0.14/0.44 tff(150,plain,
% 0.14/0.44 (~smaller_or_equal(zero, sigma)),
% 0.14/0.44 inference(modus_ponens,[status(thm)],[149, 14])).
% 0.14/0.44 tff(151,plain,
% 0.14/0.44 ((~![X: $i, Y: $i] : (smaller_or_equal(X, Y) <=> ((X = Y) | smaller(X, Y)))) | (smaller_or_equal(zero, sigma) <=> ((zero = sigma) | smaller(zero, sigma)))),
% 0.14/0.44 inference(quant_inst,[status(thm)],[])).
% 0.14/0.44 tff(152,plain,
% 0.14/0.44 (smaller_or_equal(zero, sigma) <=> ((zero = sigma) | smaller(zero, sigma))),
% 0.14/0.44 inference(unit_resolution,[status(thm)],[151, 29])).
% 0.14/0.44 tff(153,plain,
% 0.14/0.44 ((~![X: $i, Y: $i] : (smaller(X, Y) <=> greater(Y, X))) | (smaller(zero, sigma) <=> greater(sigma, zero))),
% 0.14/0.44 inference(quant_inst,[status(thm)],[])).
% 0.14/0.44 tff(154,plain,
% 0.14/0.44 (smaller(zero, sigma) <=> greater(sigma, zero)),
% 0.14/0.44 inference(unit_resolution,[status(thm)],[153, 38])).
% 0.14/0.44 tff(155,plain,
% 0.14/0.44 ((zero = sigma) <=> (sigma = zero)),
% 0.14/0.44 inference(commutativity,[status(thm)],[])).
% 0.14/0.44 tff(156,plain,
% 0.14/0.44 ((~(zero = sigma)) <=> (~(sigma = zero))),
% 0.14/0.44 inference(monotonicity,[status(thm)],[155])).
% 0.14/0.44 tff(157,assumption,(~((zero = sigma) | smaller(zero, sigma))), introduced(assumption)).
% 0.14/0.44 tff(158,plain,
% 0.14/0.44 (((zero = sigma) | smaller(zero, sigma)) | (~(zero = sigma))),
% 0.14/0.44 inference(tautology,[status(thm)],[])).
% 0.14/0.44 tff(159,plain,
% 0.14/0.44 (~(zero = sigma)),
% 0.14/0.44 inference(unit_resolution,[status(thm)],[158, 157])).
% 0.14/0.44 tff(160,plain,
% 0.14/0.44 (~(sigma = zero)),
% 0.14/0.44 inference(modus_ponens,[status(thm)],[159, 156])).
% 0.14/0.44 tff(161,plain,
% 0.14/0.44 ((~![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y)))) | (greater_or_equal(sigma, zero) <=> ((sigma = zero) | greater(sigma, zero)))),
% 0.14/0.44 inference(quant_inst,[status(thm)],[])).
% 0.14/0.44 tff(162,plain,
% 0.14/0.44 (greater_or_equal(sigma, zero) <=> ((sigma = zero) | greater(sigma, zero))),
% 0.14/0.44 inference(unit_resolution,[status(thm)],[161, 56])).
% 0.14/0.44 tff(163,plain,
% 0.14/0.44 (greater_or_equal(sigma, zero)),
% 0.14/0.44 inference(and_elim,[status(thm)],[9])).
% 0.14/0.44 tff(164,plain,
% 0.14/0.44 ((~(greater_or_equal(sigma, zero) <=> ((sigma = zero) | greater(sigma, zero)))) | (~greater_or_equal(sigma, zero)) | ((sigma = zero) | greater(sigma, zero))),
% 0.14/0.44 inference(tautology,[status(thm)],[])).
% 0.14/0.44 tff(165,plain,
% 0.14/0.44 ((~(greater_or_equal(sigma, zero) <=> ((sigma = zero) | greater(sigma, zero)))) | ((sigma = zero) | greater(sigma, zero))),
% 0.14/0.44 inference(unit_resolution,[status(thm)],[164, 163])).
% 0.14/0.44 tff(166,plain,
% 0.14/0.44 ((sigma = zero) | greater(sigma, zero)),
% 0.14/0.44 inference(unit_resolution,[status(thm)],[165, 162])).
% 0.14/0.44 tff(167,plain,
% 0.14/0.44 ((~((sigma = zero) | greater(sigma, zero))) | (sigma = zero) | greater(sigma, zero)),
% 0.14/0.44 inference(tautology,[status(thm)],[])).
% 0.14/0.44 tff(168,plain,
% 0.14/0.44 ((sigma = zero) | greater(sigma, zero)),
% 0.14/0.44 inference(unit_resolution,[status(thm)],[167, 166])).
% 0.14/0.44 tff(169,plain,
% 0.14/0.44 (greater(sigma, zero)),
% 0.14/0.44 inference(unit_resolution,[status(thm)],[168, 160])).
% 0.14/0.44 tff(170,plain,
% 0.14/0.44 (((zero = sigma) | smaller(zero, sigma)) | (~smaller(zero, sigma))),
% 0.14/0.44 inference(tautology,[status(thm)],[])).
% 0.14/0.44 tff(171,plain,
% 0.14/0.44 (~smaller(zero, sigma)),
% 0.14/0.44 inference(unit_resolution,[status(thm)],[170, 157])).
% 0.14/0.44 tff(172,plain,
% 0.14/0.44 ((~(smaller(zero, sigma) <=> greater(sigma, zero))) | smaller(zero, sigma) | (~greater(sigma, zero))),
% 0.14/0.44 inference(tautology,[status(thm)],[])).
% 0.14/0.44 tff(173,plain,
% 0.14/0.44 ((~(smaller(zero, sigma) <=> greater(sigma, zero))) | (~greater(sigma, zero))),
% 0.14/0.44 inference(unit_resolution,[status(thm)],[172, 171])).
% 0.14/0.44 tff(174,plain,
% 0.14/0.44 ($false),
% 0.14/0.44 inference(unit_resolution,[status(thm)],[173, 169, 154])).
% 0.14/0.44 tff(175,plain,((zero = sigma) | smaller(zero, sigma)), inference(lemma,lemma(discharge,[]))).
% 0.14/0.44 tff(176,plain,
% 0.14/0.44 ((~(smaller_or_equal(zero, sigma) <=> ((zero = sigma) | smaller(zero, sigma)))) | smaller_or_equal(zero, sigma) | (~((zero = sigma) | smaller(zero, sigma)))),
% 0.14/0.44 inference(tautology,[status(thm)],[])).
% 0.14/0.44 tff(177,plain,
% 0.14/0.44 ((~(smaller_or_equal(zero, sigma) <=> ((zero = sigma) | smaller(zero, sigma)))) | smaller_or_equal(zero, sigma)),
% 0.14/0.44 inference(unit_resolution,[status(thm)],[176, 175])).
% 0.14/0.44 tff(178,plain,
% 0.14/0.44 (smaller_or_equal(zero, sigma)),
% 0.14/0.44 inference(unit_resolution,[status(thm)],[177, 152])).
% 0.14/0.44 tff(179,plain,
% 0.14/0.44 ($false),
% 0.14/0.44 inference(unit_resolution,[status(thm)],[178, 150])).
% 0.14/0.44 % SZS output end Proof
% 0.14/0.45 % E exiting
%------------------------------------------------------------------------------