%------------------------------------------------------------------------------
% 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 : n028.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 06:24:09 AM UTC 2026
% Result : Unsatisfiable 0.12s 0.39s
% Output : Proof 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : MGT058-1 : TPTP v9.3.0. Released v2.4.0.
% 0.00/0.02 % Command : run_E %s %d THM
% 0.06/0.33 % Computer : n028.cluster.edu
% 0.06/0.33 % Model : x86_64 x86_64
% 0.06/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.33 % Memory : 8046.5625MB
% 0.06/0.33 % OS : Linux 6.8.0-71-generic
% 0.06/0.33 % CPULimit : 300
% 0.06/0.33 % WCLimit : 300
% 0.06/0.33 % DateTime : Mon Sep 7 13:34:49 UTC 2026
% 0.06/0.33 % CPUTime :
% 0.12/0.39 % SZS status Unsatisfiable
% 0.12/0.39 % SZS output start Proof
% 0.12/0.39 tff(smaller_or_equal_type, type, (
% 0.12/0.39 smaller_or_equal: ( $i * $i ) > $o)).
% 0.12/0.39 tff(zero_type, type, (
% 0.12/0.39 zero: $i)).
% 0.12/0.39 tff(sigma_type, type, (
% 0.12/0.39 sigma: $i)).
% 0.12/0.39 tff(age_type, type, (
% 0.12/0.39 age: ( $i * $i ) > $i)).
% 0.12/0.39 tff(sk4_type, type, (
% 0.12/0.39 sk4: $i)).
% 0.12/0.39 tff(sk3_type, type, (
% 0.12/0.39 sk3: $i)).
% 0.12/0.39 tff(greater_type, type, (
% 0.12/0.39 greater: ( $i * $i ) > $o)).
% 0.12/0.39 tff(smaller_type, type, (
% 0.12/0.39 smaller: ( $i * $i ) > $o)).
% 0.12/0.39 tff(positional_advantage_type, type, (
% 0.12/0.39 positional_advantage: ( $i * $i ) > $o)).
% 0.12/0.39 tff(tau_type, type, (
% 0.12/0.39 tau: $i)).
% 0.12/0.39 tff(greater_or_equal_type, type, (
% 0.12/0.39 greater_or_equal: ( $i * $i ) > $o)).
% 0.12/0.39 tff(robust_position_type, type, (
% 0.12/0.39 robust_position: $i > $o)).
% 0.12/0.39 tff(fragile_position_type, type, (
% 0.12/0.39 fragile_position: $i > $o)).
% 0.12/0.39 tff(1,plain,
% 0.12/0.39 ((age(sk3, sk4) = zero) <=> (age(sk3, sk4) = zero)),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(2,axiom,(age(sk3, sk4) = zero), file('/export/starexec/sandbox/benchmark/theBenchmark.p','lemma_10_43')).
% 0.12/0.39 tff(3,plain,
% 0.12/0.39 (age(sk3, sk4) = zero),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[2, 1])).
% 0.12/0.39 tff(4,plain,
% 0.12/0.39 (zero = age(sk3, sk4)),
% 0.12/0.39 inference(symmetry,[status(thm)],[3])).
% 0.12/0.39 tff(5,plain,
% 0.12/0.39 (smaller_or_equal(zero, sigma) <=> smaller_or_equal(age(sk3, sk4), sigma)),
% 0.12/0.39 inference(monotonicity,[status(thm)],[4])).
% 0.12/0.39 tff(6,plain,
% 0.12/0.39 (smaller_or_equal(age(sk3, sk4), sigma) <=> smaller_or_equal(zero, sigma)),
% 0.12/0.39 inference(symmetry,[status(thm)],[5])).
% 0.12/0.39 tff(7,plain,
% 0.12/0.39 ((~smaller_or_equal(age(sk3, sk4), sigma)) <=> (~smaller_or_equal(zero, sigma))),
% 0.12/0.39 inference(monotonicity,[status(thm)],[6])).
% 0.12/0.39 tff(8,plain,
% 0.12/0.39 (smaller_or_equal(zero, tau) <=> smaller_or_equal(age(sk3, sk4), tau)),
% 0.12/0.39 inference(monotonicity,[status(thm)],[4])).
% 0.12/0.39 tff(9,plain,
% 0.12/0.39 (smaller_or_equal(age(sk3, sk4), tau) <=> smaller_or_equal(zero, tau)),
% 0.12/0.39 inference(symmetry,[status(thm)],[8])).
% 0.12/0.39 tff(10,plain,
% 0.12/0.39 ((~smaller_or_equal(age(sk3, sk4), tau)) <=> (~smaller_or_equal(zero, tau))),
% 0.12/0.39 inference(monotonicity,[status(thm)],[9])).
% 0.12/0.39 tff(11,assumption,(~smaller_or_equal(age(sk3, sk4), tau)), introduced(assumption)).
% 0.12/0.39 tff(12,plain,
% 0.12/0.39 (~smaller_or_equal(zero, tau)),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.12/0.39 tff(13,plain,
% 0.12/0.39 (^[B: $i, A: $i] : refl(((~smaller(A, B)) | smaller_or_equal(A, B)) <=> ((~smaller(A, B)) | smaller_or_equal(A, B)))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(14,plain,
% 0.12/0.39 (![B: $i, A: $i] : ((~smaller(A, B)) | smaller_or_equal(A, B)) <=> ![B: $i, A: $i] : ((~smaller(A, B)) | smaller_or_equal(A, B))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[13])).
% 0.12/0.39 tff(15,plain,
% 0.12/0.39 (![B: $i, A: $i] : ((~smaller(A, B)) | smaller_or_equal(A, B)) <=> ![B: $i, A: $i] : ((~smaller(A, B)) | smaller_or_equal(A, B))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(16,axiom,(![B: $i, A: $i] : ((~smaller(A, B)) | smaller_or_equal(A, B))), file('/export/starexec/sandbox/benchmark/Axioms/MGT001-0.ax','definition_smaller_or_equal_2')).
% 0.12/0.39 tff(17,plain,
% 0.12/0.39 (![B: $i, A: $i] : ((~smaller(A, B)) | smaller_or_equal(A, B))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.12/0.39 tff(18,plain,(
% 0.12/0.39 ![B: $i, A: $i] : ((~smaller(A, B)) | smaller_or_equal(A, B))),
% 0.12/0.39 inference(skolemize,[status(sab)],[17])).
% 0.12/0.39 tff(19,plain,
% 0.12/0.39 (![B: $i, A: $i] : ((~smaller(A, B)) | smaller_or_equal(A, B))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.12/0.39 tff(20,plain,
% 0.12/0.39 (((~![B: $i, A: $i] : ((~smaller(A, B)) | smaller_or_equal(A, B))) | ((~smaller(zero, tau)) | smaller_or_equal(zero, tau))) <=> ((~![B: $i, A: $i] : ((~smaller(A, B)) | smaller_or_equal(A, B))) | (~smaller(zero, tau)) | smaller_or_equal(zero, tau))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(21,plain,
% 0.12/0.39 ((~![B: $i, A: $i] : ((~smaller(A, B)) | smaller_or_equal(A, B))) | ((~smaller(zero, tau)) | smaller_or_equal(zero, tau))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(22,plain,
% 0.12/0.39 ((~![B: $i, A: $i] : ((~smaller(A, B)) | smaller_or_equal(A, B))) | (~smaller(zero, tau)) | smaller_or_equal(zero, tau)),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.12/0.39 tff(23,plain,
% 0.12/0.39 ((~smaller(zero, tau)) | smaller_or_equal(zero, tau)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[22, 19])).
% 0.12/0.39 tff(24,plain,
% 0.12/0.39 (~smaller(zero, tau)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[23, 12])).
% 0.12/0.39 tff(25,plain,
% 0.12/0.39 (^[B: $i, A: $i] : refl(((~greater(A, B)) | smaller(B, A)) <=> ((~greater(A, B)) | smaller(B, A)))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(26,plain,
% 0.12/0.39 (![B: $i, A: $i] : ((~greater(A, B)) | smaller(B, A)) <=> ![B: $i, A: $i] : ((~greater(A, B)) | smaller(B, A))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[25])).
% 0.12/0.39 tff(27,plain,
% 0.12/0.39 (![B: $i, A: $i] : ((~greater(A, B)) | smaller(B, A)) <=> ![B: $i, A: $i] : ((~greater(A, B)) | smaller(B, A))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(28,axiom,(![B: $i, A: $i] : ((~greater(A, B)) | smaller(B, A))), file('/export/starexec/sandbox/benchmark/Axioms/MGT001-0.ax','definition_smaller_8')).
% 0.12/0.39 tff(29,plain,
% 0.12/0.39 (![B: $i, A: $i] : ((~greater(A, B)) | smaller(B, A))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.12/0.39 tff(30,plain,(
% 0.12/0.39 ![B: $i, A: $i] : ((~greater(A, B)) | smaller(B, A))),
% 0.12/0.39 inference(skolemize,[status(sab)],[29])).
% 0.12/0.39 tff(31,plain,
% 0.12/0.39 (![B: $i, A: $i] : ((~greater(A, B)) | smaller(B, A))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[30, 26])).
% 0.12/0.39 tff(32,plain,
% 0.12/0.39 (((~![B: $i, A: $i] : ((~greater(A, B)) | smaller(B, A))) | ((~greater(tau, zero)) | smaller(zero, tau))) <=> ((~![B: $i, A: $i] : ((~greater(A, B)) | smaller(B, A))) | (~greater(tau, zero)) | smaller(zero, tau))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(33,plain,
% 0.12/0.39 ((~![B: $i, A: $i] : ((~greater(A, B)) | smaller(B, A))) | ((~greater(tau, zero)) | smaller(zero, tau))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(34,plain,
% 0.12/0.39 ((~![B: $i, A: $i] : ((~greater(A, B)) | smaller(B, A))) | (~greater(tau, zero)) | smaller(zero, tau)),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.12/0.39 tff(35,plain,
% 0.12/0.39 (~greater(tau, zero)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[34, 31, 24])).
% 0.12/0.39 tff(36,plain,
% 0.12/0.39 (greater_or_equal(tau, zero) <=> greater_or_equal(tau, zero)),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(37,axiom,(greater_or_equal(tau, zero)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','lemma_10_45')).
% 0.12/0.39 tff(38,plain,
% 0.12/0.39 (greater_or_equal(tau, zero)),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.12/0.39 tff(39,plain,
% 0.12/0.39 (^[B: $i, A: $i] : refl(((A = B) | greater(A, B) | (~greater_or_equal(A, B))) <=> ((A = B) | greater(A, B) | (~greater_or_equal(A, B))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(40,plain,
% 0.12/0.39 (![B: $i, A: $i] : ((A = B) | greater(A, B) | (~greater_or_equal(A, B))) <=> ![B: $i, A: $i] : ((A = B) | greater(A, B) | (~greater_or_equal(A, B)))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[39])).
% 0.12/0.39 tff(41,plain,
% 0.12/0.39 (![B: $i, A: $i] : ((A = B) | greater(A, B) | (~greater_or_equal(A, B))) <=> ![B: $i, A: $i] : ((A = B) | greater(A, B) | (~greater_or_equal(A, B)))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(42,plain,
% 0.12/0.39 (^[B: $i, A: $i] : rewrite((((~greater_or_equal(A, B)) | greater(A, B)) | (A = B)) <=> ((A = B) | greater(A, B) | (~greater_or_equal(A, B))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(43,plain,
% 0.12/0.39 (![B: $i, A: $i] : (((~greater_or_equal(A, B)) | greater(A, B)) | (A = B)) <=> ![B: $i, A: $i] : ((A = B) | greater(A, B) | (~greater_or_equal(A, B)))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[42])).
% 0.12/0.39 tff(44,axiom,(![B: $i, A: $i] : (((~greater_or_equal(A, B)) | greater(A, B)) | (A = B))), file('/export/starexec/sandbox/benchmark/Axioms/MGT001-0.ax','definition_greater_or_equal_4')).
% 0.12/0.39 tff(45,plain,
% 0.12/0.39 (![B: $i, A: $i] : ((A = B) | greater(A, B) | (~greater_or_equal(A, B)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.12/0.39 tff(46,plain,
% 0.12/0.39 (![B: $i, A: $i] : ((A = B) | greater(A, B) | (~greater_or_equal(A, B)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[45, 41])).
% 0.12/0.39 tff(47,plain,(
% 0.12/0.39 ![B: $i, A: $i] : ((A = B) | greater(A, B) | (~greater_or_equal(A, B)))),
% 0.12/0.39 inference(skolemize,[status(sab)],[46])).
% 0.12/0.39 tff(48,plain,
% 0.12/0.39 (![B: $i, A: $i] : ((A = B) | greater(A, B) | (~greater_or_equal(A, B)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[47, 40])).
% 0.12/0.39 tff(49,plain,
% 0.12/0.39 (((~![B: $i, A: $i] : ((A = B) | greater(A, B) | (~greater_or_equal(A, B)))) | ((tau = zero) | greater(tau, zero) | (~greater_or_equal(tau, zero)))) <=> ((~![B: $i, A: $i] : ((A = B) | greater(A, B) | (~greater_or_equal(A, B)))) | (tau = zero) | greater(tau, zero) | (~greater_or_equal(tau, zero)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(50,plain,
% 0.12/0.40 ((~![B: $i, A: $i] : ((A = B) | greater(A, B) | (~greater_or_equal(A, B)))) | ((tau = zero) | greater(tau, zero) | (~greater_or_equal(tau, zero)))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(51,plain,
% 0.12/0.40 ((~![B: $i, A: $i] : ((A = B) | greater(A, B) | (~greater_or_equal(A, B)))) | (tau = zero) | greater(tau, zero) | (~greater_or_equal(tau, zero))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.12/0.40 tff(52,plain,
% 0.12/0.40 ((tau = zero) | greater(tau, zero)),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[51, 48, 38])).
% 0.12/0.40 tff(53,plain,
% 0.12/0.40 (tau = zero),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[52, 35])).
% 0.12/0.40 tff(54,plain,
% 0.12/0.40 (zero = tau),
% 0.12/0.40 inference(symmetry,[status(thm)],[53])).
% 0.12/0.40 tff(55,plain,
% 0.12/0.40 (smaller_or_equal(zero, zero) <=> smaller_or_equal(age(sk3, sk4), tau)),
% 0.12/0.40 inference(monotonicity,[status(thm)],[4, 54])).
% 0.12/0.40 tff(56,plain,
% 0.12/0.40 (smaller_or_equal(age(sk3, sk4), tau) <=> smaller_or_equal(zero, zero)),
% 0.12/0.40 inference(symmetry,[status(thm)],[55])).
% 0.12/0.40 tff(57,plain,
% 0.12/0.40 ((~smaller_or_equal(age(sk3, sk4), tau)) <=> (~smaller_or_equal(zero, zero))),
% 0.12/0.40 inference(monotonicity,[status(thm)],[56])).
% 0.12/0.40 tff(58,plain,
% 0.12/0.40 (~smaller_or_equal(zero, zero)),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[11, 57])).
% 0.12/0.40 tff(59,plain,
% 0.12/0.40 (^[B: $i] : refl(smaller_or_equal(B, B) <=> smaller_or_equal(B, B))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(60,plain,
% 0.12/0.40 (![B: $i] : smaller_or_equal(B, B) <=> ![B: $i] : smaller_or_equal(B, B)),
% 0.12/0.40 inference(quant_intro,[status(thm)],[59])).
% 0.12/0.40 tff(61,plain,
% 0.12/0.40 (![B: $i] : smaller_or_equal(B, B) <=> ![B: $i] : smaller_or_equal(B, B)),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(62,plain,
% 0.12/0.40 (![B: $i, A: $i] : smaller_or_equal(B, B) <=> ![B: $i] : smaller_or_equal(B, B)),
% 0.12/0.40 inference(elim_unused_vars,[status(thm)],[])).
% 0.12/0.40 tff(63,plain,
% 0.12/0.40 (![B: $i, A: $i] : ((~(A = B)) | smaller_or_equal(A, B)) <=> ![B: $i, A: $i] : smaller_or_equal(B, B)),
% 0.12/0.40 inference(destructive_equality_resolution,[status(thm)],[])).
% 0.12/0.40 tff(64,plain,
% 0.12/0.40 (![B: $i, A: $i] : ((~(A = B)) | smaller_or_equal(A, B)) <=> ![B: $i] : smaller_or_equal(B, B)),
% 0.12/0.40 inference(transitivity,[status(thm)],[63, 62])).
% 0.12/0.40 tff(65,axiom,(![B: $i, A: $i] : ((~(A = B)) | smaller_or_equal(A, B))), file('/export/starexec/sandbox/benchmark/Axioms/MGT001-0.ax','definition_smaller_or_equal_3')).
% 0.12/0.40 tff(66,plain,
% 0.12/0.40 (![B: $i] : smaller_or_equal(B, B)),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.12/0.40 tff(67,plain,
% 0.12/0.40 (![B: $i] : smaller_or_equal(B, B)),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[66, 61])).
% 0.12/0.40 tff(68,plain,(
% 0.12/0.40 ![B: $i] : smaller_or_equal(B, B)),
% 0.12/0.40 inference(skolemize,[status(sab)],[67])).
% 0.12/0.40 tff(69,plain,
% 0.12/0.40 (![B: $i] : smaller_or_equal(B, B)),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[68, 60])).
% 0.12/0.40 tff(70,plain,
% 0.12/0.40 ((~![B: $i] : smaller_or_equal(B, B)) | smaller_or_equal(zero, zero)),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(71,plain,
% 0.12/0.40 (smaller_or_equal(zero, zero)),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[70, 69])).
% 0.12/0.40 tff(72,plain,
% 0.12/0.40 ($false),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[71, 58])).
% 0.12/0.40 tff(73,plain,(smaller_or_equal(age(sk3, sk4), tau)), inference(lemma,lemma(discharge,[]))).
% 0.12/0.40 tff(74,plain,
% 0.12/0.40 (robust_position(sk3) <=> robust_position(sk3)),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(75,axiom,(robust_position(sk3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','lemma_10_47')).
% 0.12/0.40 tff(76,plain,
% 0.12/0.40 (robust_position(sk3)),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[75, 74])).
% 0.12/0.40 tff(77,plain,
% 0.12/0.40 (^[B: $i, A: $i] : refl(((~positional_advantage(A, B)) | (~smaller_or_equal(age(A, B), tau)) | (~robust_position(A))) <=> ((~positional_advantage(A, B)) | (~smaller_or_equal(age(A, B), tau)) | (~robust_position(A))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(78,plain,
% 0.12/0.40 (![B: $i, A: $i] : ((~positional_advantage(A, B)) | (~smaller_or_equal(age(A, B), tau)) | (~robust_position(A))) <=> ![B: $i, A: $i] : ((~positional_advantage(A, B)) | (~smaller_or_equal(age(A, B), tau)) | (~robust_position(A)))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[77])).
% 0.12/0.40 tff(79,plain,
% 0.12/0.40 (![B: $i, A: $i] : ((~positional_advantage(A, B)) | (~smaller_or_equal(age(A, B), tau)) | (~robust_position(A))) <=> ![B: $i, A: $i] : ((~positional_advantage(A, B)) | (~smaller_or_equal(age(A, B), tau)) | (~robust_position(A)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(80,plain,
% 0.12/0.40 (^[B: $i, A: $i] : rewrite((((~robust_position(A)) | (~smaller_or_equal(age(A, B), tau))) | (~positional_advantage(A, B))) <=> ((~positional_advantage(A, B)) | (~smaller_or_equal(age(A, B), tau)) | (~robust_position(A))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(81,plain,
% 0.12/0.40 (![B: $i, A: $i] : (((~robust_position(A)) | (~smaller_or_equal(age(A, B), tau))) | (~positional_advantage(A, B))) <=> ![B: $i, A: $i] : ((~positional_advantage(A, B)) | (~smaller_or_equal(age(A, B), tau)) | (~robust_position(A)))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[80])).
% 0.12/0.40 tff(82,axiom,(![B: $i, A: $i] : (((~robust_position(A)) | (~smaller_or_equal(age(A, B), tau))) | (~positional_advantage(A, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','definition_4_36')).
% 0.12/0.40 tff(83,plain,
% 0.12/0.40 (![B: $i, A: $i] : ((~positional_advantage(A, B)) | (~smaller_or_equal(age(A, B), tau)) | (~robust_position(A)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.12/0.40 tff(84,plain,
% 0.12/0.40 (![B: $i, A: $i] : ((~positional_advantage(A, B)) | (~smaller_or_equal(age(A, B), tau)) | (~robust_position(A)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[83, 79])).
% 0.12/0.40 tff(85,plain,(
% 0.12/0.40 ![B: $i, A: $i] : ((~positional_advantage(A, B)) | (~smaller_or_equal(age(A, B), tau)) | (~robust_position(A)))),
% 0.12/0.40 inference(skolemize,[status(sab)],[84])).
% 0.12/0.40 tff(86,plain,
% 0.12/0.40 (![B: $i, A: $i] : ((~positional_advantage(A, B)) | (~smaller_or_equal(age(A, B), tau)) | (~robust_position(A)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[85, 78])).
% 0.12/0.40 tff(87,plain,
% 0.12/0.40 (((~![B: $i, A: $i] : ((~positional_advantage(A, B)) | (~smaller_or_equal(age(A, B), tau)) | (~robust_position(A)))) | ((~robust_position(sk3)) | (~positional_advantage(sk3, sk4)) | (~smaller_or_equal(age(sk3, sk4), tau)))) <=> ((~![B: $i, A: $i] : ((~positional_advantage(A, B)) | (~smaller_or_equal(age(A, B), tau)) | (~robust_position(A)))) | (~robust_position(sk3)) | (~positional_advantage(sk3, sk4)) | (~smaller_or_equal(age(sk3, sk4), tau)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(88,plain,
% 0.12/0.40 (((~positional_advantage(sk3, sk4)) | (~smaller_or_equal(age(sk3, sk4), tau)) | (~robust_position(sk3))) <=> ((~robust_position(sk3)) | (~positional_advantage(sk3, sk4)) | (~smaller_or_equal(age(sk3, sk4), tau)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(89,plain,
% 0.12/0.40 (((~![B: $i, A: $i] : ((~positional_advantage(A, B)) | (~smaller_or_equal(age(A, B), tau)) | (~robust_position(A)))) | ((~positional_advantage(sk3, sk4)) | (~smaller_or_equal(age(sk3, sk4), tau)) | (~robust_position(sk3)))) <=> ((~![B: $i, A: $i] : ((~positional_advantage(A, B)) | (~smaller_or_equal(age(A, B), tau)) | (~robust_position(A)))) | ((~robust_position(sk3)) | (~positional_advantage(sk3, sk4)) | (~smaller_or_equal(age(sk3, sk4), tau))))),
% 0.12/0.40 inference(monotonicity,[status(thm)],[88])).
% 0.12/0.40 tff(90,plain,
% 0.12/0.40 (((~![B: $i, A: $i] : ((~positional_advantage(A, B)) | (~smaller_or_equal(age(A, B), tau)) | (~robust_position(A)))) | ((~positional_advantage(sk3, sk4)) | (~smaller_or_equal(age(sk3, sk4), tau)) | (~robust_position(sk3)))) <=> ((~![B: $i, A: $i] : ((~positional_advantage(A, B)) | (~smaller_or_equal(age(A, B), tau)) | (~robust_position(A)))) | (~robust_position(sk3)) | (~positional_advantage(sk3, sk4)) | (~smaller_or_equal(age(sk3, sk4), tau)))),
% 0.12/0.40 inference(transitivity,[status(thm)],[89, 87])).
% 0.12/0.40 tff(91,plain,
% 0.12/0.40 ((~![B: $i, A: $i] : ((~positional_advantage(A, B)) | (~smaller_or_equal(age(A, B), tau)) | (~robust_position(A)))) | ((~positional_advantage(sk3, sk4)) | (~smaller_or_equal(age(sk3, sk4), tau)) | (~robust_position(sk3)))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(92,plain,
% 0.12/0.40 ((~![B: $i, A: $i] : ((~positional_advantage(A, B)) | (~smaller_or_equal(age(A, B), tau)) | (~robust_position(A)))) | (~robust_position(sk3)) | (~positional_advantage(sk3, sk4)) | (~smaller_or_equal(age(sk3, sk4), tau))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[91, 90])).
% 0.12/0.40 tff(93,plain,
% 0.12/0.40 ((~positional_advantage(sk3, sk4)) | (~smaller_or_equal(age(sk3, sk4), tau))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[92, 86, 76])).
% 0.12/0.40 tff(94,plain,
% 0.12/0.40 (~positional_advantage(sk3, sk4)),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[93, 73])).
% 0.12/0.40 tff(95,plain,
% 0.12/0.40 (fragile_position(sk3) <=> fragile_position(sk3)),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(96,axiom,(fragile_position(sk3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','lemma_10_46')).
% 0.12/0.40 tff(97,plain,
% 0.12/0.40 (fragile_position(sk3)),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[96, 95])).
% 0.12/0.40 tff(98,plain,
% 0.12/0.40 (^[B: $i, A: $i] : refl((positional_advantage(A, B) | (~smaller_or_equal(age(A, B), sigma)) | (~fragile_position(A))) <=> (positional_advantage(A, B) | (~smaller_or_equal(age(A, B), sigma)) | (~fragile_position(A))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(99,plain,
% 0.12/0.40 (![B: $i, A: $i] : (positional_advantage(A, B) | (~smaller_or_equal(age(A, B), sigma)) | (~fragile_position(A))) <=> ![B: $i, A: $i] : (positional_advantage(A, B) | (~smaller_or_equal(age(A, B), sigma)) | (~fragile_position(A)))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[98])).
% 0.12/0.40 tff(100,plain,
% 0.12/0.40 (![B: $i, A: $i] : (positional_advantage(A, B) | (~smaller_or_equal(age(A, B), sigma)) | (~fragile_position(A))) <=> ![B: $i, A: $i] : (positional_advantage(A, B) | (~smaller_or_equal(age(A, B), sigma)) | (~fragile_position(A)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(101,plain,
% 0.12/0.40 (^[B: $i, A: $i] : rewrite((((~fragile_position(A)) | (~smaller_or_equal(age(A, B), sigma))) | positional_advantage(A, B)) <=> (positional_advantage(A, B) | (~smaller_or_equal(age(A, B), sigma)) | (~fragile_position(A))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(102,plain,
% 0.12/0.40 (![B: $i, A: $i] : (((~fragile_position(A)) | (~smaller_or_equal(age(A, B), sigma))) | positional_advantage(A, B)) <=> ![B: $i, A: $i] : (positional_advantage(A, B) | (~smaller_or_equal(age(A, B), sigma)) | (~fragile_position(A)))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[101])).
% 0.12/0.40 tff(103,axiom,(![B: $i, A: $i] : (((~fragile_position(A)) | (~smaller_or_equal(age(A, B), sigma))) | positional_advantage(A, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','definition_3_30')).
% 0.12/0.40 tff(104,plain,
% 0.12/0.40 (![B: $i, A: $i] : (positional_advantage(A, B) | (~smaller_or_equal(age(A, B), sigma)) | (~fragile_position(A)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.12/0.40 tff(105,plain,
% 0.12/0.40 (![B: $i, A: $i] : (positional_advantage(A, B) | (~smaller_or_equal(age(A, B), sigma)) | (~fragile_position(A)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[104, 100])).
% 0.12/0.40 tff(106,plain,(
% 0.12/0.40 ![B: $i, A: $i] : (positional_advantage(A, B) | (~smaller_or_equal(age(A, B), sigma)) | (~fragile_position(A)))),
% 0.12/0.40 inference(skolemize,[status(sab)],[105])).
% 0.12/0.40 tff(107,plain,
% 0.12/0.40 (![B: $i, A: $i] : (positional_advantage(A, B) | (~smaller_or_equal(age(A, B), sigma)) | (~fragile_position(A)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[106, 99])).
% 0.12/0.40 tff(108,plain,
% 0.12/0.40 (((~![B: $i, A: $i] : (positional_advantage(A, B) | (~smaller_or_equal(age(A, B), sigma)) | (~fragile_position(A)))) | (positional_advantage(sk3, sk4) | (~smaller_or_equal(age(sk3, sk4), sigma)) | (~fragile_position(sk3)))) <=> ((~![B: $i, A: $i] : (positional_advantage(A, B) | (~smaller_or_equal(age(A, B), sigma)) | (~fragile_position(A)))) | positional_advantage(sk3, sk4) | (~smaller_or_equal(age(sk3, sk4), sigma)) | (~fragile_position(sk3)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(109,plain,
% 0.12/0.40 ((~![B: $i, A: $i] : (positional_advantage(A, B) | (~smaller_or_equal(age(A, B), sigma)) | (~fragile_position(A)))) | (positional_advantage(sk3, sk4) | (~smaller_or_equal(age(sk3, sk4), sigma)) | (~fragile_position(sk3)))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(110,plain,
% 0.12/0.40 ((~![B: $i, A: $i] : (positional_advantage(A, B) | (~smaller_or_equal(age(A, B), sigma)) | (~fragile_position(A)))) | positional_advantage(sk3, sk4) | (~smaller_or_equal(age(sk3, sk4), sigma)) | (~fragile_position(sk3))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[109, 108])).
% 0.12/0.40 tff(111,plain,
% 0.12/0.40 (positional_advantage(sk3, sk4) | (~smaller_or_equal(age(sk3, sk4), sigma))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[110, 107, 97])).
% 0.12/0.40 tff(112,plain,
% 0.12/0.40 (~smaller_or_equal(age(sk3, sk4), sigma)),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[111, 94])).
% 0.12/0.40 tff(113,plain,
% 0.12/0.40 (~smaller_or_equal(zero, sigma)),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[112, 7])).
% 0.12/0.40 tff(114,plain,
% 0.12/0.40 (((~![B: $i, A: $i] : ((~smaller(A, B)) | smaller_or_equal(A, B))) | ((~smaller(zero, sigma)) | smaller_or_equal(zero, sigma))) <=> ((~![B: $i, A: $i] : ((~smaller(A, B)) | smaller_or_equal(A, B))) | (~smaller(zero, sigma)) | smaller_or_equal(zero, sigma))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(115,plain,
% 0.12/0.40 ((~![B: $i, A: $i] : ((~smaller(A, B)) | smaller_or_equal(A, B))) | ((~smaller(zero, sigma)) | smaller_or_equal(zero, sigma))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(116,plain,
% 0.12/0.40 ((~![B: $i, A: $i] : ((~smaller(A, B)) | smaller_or_equal(A, B))) | (~smaller(zero, sigma)) | smaller_or_equal(zero, sigma)),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[115, 114])).
% 0.12/0.40 tff(117,plain,
% 0.12/0.40 ((~smaller(zero, sigma)) | smaller_or_equal(zero, sigma)),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[116, 19])).
% 0.12/0.40 tff(118,plain,
% 0.12/0.40 (~smaller(zero, sigma)),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[117, 113])).
% 0.12/0.40 tff(119,plain,
% 0.12/0.40 (((~![B: $i, A: $i] : ((~greater(A, B)) | smaller(B, A))) | ((~greater(sigma, zero)) | smaller(zero, sigma))) <=> ((~![B: $i, A: $i] : ((~greater(A, B)) | smaller(B, A))) | (~greater(sigma, zero)) | smaller(zero, sigma))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(120,plain,
% 0.12/0.40 ((~![B: $i, A: $i] : ((~greater(A, B)) | smaller(B, A))) | ((~greater(sigma, zero)) | smaller(zero, sigma))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(121,plain,
% 0.12/0.40 ((~![B: $i, A: $i] : ((~greater(A, B)) | smaller(B, A))) | (~greater(sigma, zero)) | smaller(zero, sigma)),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[120, 119])).
% 0.12/0.40 tff(122,plain,
% 0.12/0.40 (~greater(sigma, zero)),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[121, 31, 118])).
% 0.12/0.40 tff(123,plain,
% 0.12/0.40 (greater_or_equal(sigma, zero) <=> greater_or_equal(sigma, zero)),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(124,axiom,(greater_or_equal(sigma, zero)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','lemma_10_44')).
% 0.12/0.40 tff(125,plain,
% 0.12/0.40 (greater_or_equal(sigma, zero)),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[124, 123])).
% 0.12/0.40 tff(126,plain,
% 0.12/0.40 (((~![B: $i, A: $i] : ((A = B) | greater(A, B) | (~greater_or_equal(A, B)))) | ((sigma = zero) | greater(sigma, zero) | (~greater_or_equal(sigma, zero)))) <=> ((~![B: $i, A: $i] : ((A = B) | greater(A, B) | (~greater_or_equal(A, B)))) | (sigma = zero) | greater(sigma, zero) | (~greater_or_equal(sigma, zero)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(127,plain,
% 0.12/0.40 ((~![B: $i, A: $i] : ((A = B) | greater(A, B) | (~greater_or_equal(A, B)))) | ((sigma = zero) | greater(sigma, zero) | (~greater_or_equal(sigma, zero)))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(128,plain,
% 0.12/0.40 ((~![B: $i, A: $i] : ((A = B) | greater(A, B) | (~greater_or_equal(A, B)))) | (sigma = zero) | greater(sigma, zero) | (~greater_or_equal(sigma, zero))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[127, 126])).
% 0.12/0.40 tff(129,plain,
% 0.12/0.40 ((sigma = zero) | greater(sigma, zero)),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[128, 48, 125])).
% 0.12/0.40 tff(130,plain,
% 0.12/0.40 (sigma = zero),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[129, 122])).
% 0.12/0.40 tff(131,plain,
% 0.12/0.40 (zero = sigma),
% 0.12/0.40 inference(symmetry,[status(thm)],[130])).
% 0.12/0.40 tff(132,plain,
% 0.12/0.40 (smaller_or_equal(zero, zero) <=> smaller_or_equal(age(sk3, sk4), sigma)),
% 0.12/0.40 inference(monotonicity,[status(thm)],[4, 131])).
% 0.12/0.40 tff(133,plain,
% 0.12/0.41 (smaller_or_equal(age(sk3, sk4), sigma) <=> smaller_or_equal(zero, zero)),
% 0.12/0.41 inference(symmetry,[status(thm)],[132])).
% 0.12/0.41 tff(134,plain,
% 0.12/0.41 ((~smaller_or_equal(age(sk3, sk4), sigma)) <=> (~smaller_or_equal(zero, zero))),
% 0.12/0.41 inference(monotonicity,[status(thm)],[133])).
% 0.12/0.41 tff(135,plain,
% 0.12/0.41 (~smaller_or_equal(zero, zero)),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[112, 134])).
% 0.12/0.41 tff(136,plain,
% 0.12/0.41 ($false),
% 0.12/0.41 inference(unit_resolution,[status(thm)],[71, 135])).
% 0.12/0.41 % SZS output end Proof
% 0.12/0.41 % E exiting
%------------------------------------------------------------------------------