TSTP Solution File: MGT058-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : MGT058-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n028.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 18 05:22:17 EDT 2022
% Result : Unsatisfiable 0.19s 0.40s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : MGT058-1 : TPTP v8.1.0. Released v2.4.0.
% 0.06/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n028.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Sep 2 03:05:07 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.19/0.40 % SZS status Unsatisfiable
% 0.19/0.40 % SZS output start Proof
% 0.19/0.40 tff(age_type, type, (
% 0.19/0.40 age: ( $i * $i ) > $i)).
% 0.19/0.40 tff(sk4_type, type, (
% 0.19/0.40 sk4: $i)).
% 0.19/0.40 tff(sk3_type, type, (
% 0.19/0.40 sk3: $i)).
% 0.19/0.40 tff(sigma_type, type, (
% 0.19/0.40 sigma: $i)).
% 0.19/0.40 tff(smaller_or_equal_type, type, (
% 0.19/0.40 smaller_or_equal: ( $i * $i ) > $o)).
% 0.19/0.40 tff(positional_advantage_type, type, (
% 0.19/0.40 positional_advantage: ( $i * $i ) > $o)).
% 0.19/0.40 tff(tau_type, type, (
% 0.19/0.40 tau: $i)).
% 0.19/0.40 tff(greater_type, type, (
% 0.19/0.40 greater: ( $i * $i ) > $o)).
% 0.19/0.40 tff(smaller_type, type, (
% 0.19/0.40 smaller: ( $i * $i ) > $o)).
% 0.19/0.40 tff(greater_or_equal_type, type, (
% 0.19/0.40 greater_or_equal: ( $i * $i ) > $o)).
% 0.19/0.40 tff(zero_type, type, (
% 0.19/0.40 zero: $i)).
% 0.19/0.40 tff(robust_position_type, type, (
% 0.19/0.40 robust_position: $i > $o)).
% 0.19/0.40 tff(fragile_position_type, type, (
% 0.19/0.40 fragile_position: $i > $o)).
% 0.19/0.40 tff(1,plain,
% 0.19/0.40 ((age(sk3, sk4) = sigma) <=> (sigma = age(sk3, sk4))),
% 0.19/0.40 inference(commutativity,[status(thm)],[])).
% 0.19/0.40 tff(2,plain,
% 0.19/0.40 ((~(age(sk3, sk4) = sigma)) <=> (~(sigma = age(sk3, sk4)))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[1])).
% 0.19/0.40 tff(3,plain,
% 0.19/0.40 ((age(sk3, sk4) = tau) <=> (tau = age(sk3, sk4))),
% 0.19/0.40 inference(commutativity,[status(thm)],[])).
% 0.19/0.40 tff(4,plain,
% 0.19/0.40 ((~(age(sk3, sk4) = tau)) <=> (~(tau = age(sk3, sk4)))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[3])).
% 0.19/0.40 tff(5,assumption,(~smaller_or_equal(age(sk3, sk4), tau)), introduced(assumption)).
% 0.19/0.40 tff(6,plain,
% 0.19/0.40 (^[B: $i, A: $i] : refl(((~(A = B)) | smaller_or_equal(A, B)) <=> ((~(A = B)) | smaller_or_equal(A, B)))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(7,plain,
% 0.19/0.40 (![B: $i, A: $i] : ((~(A = B)) | smaller_or_equal(A, B)) <=> ![B: $i, A: $i] : ((~(A = B)) | smaller_or_equal(A, B))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[6])).
% 0.19/0.40 tff(8,plain,
% 0.19/0.40 (![B: $i, A: $i] : ((~(A = B)) | smaller_or_equal(A, B)) <=> ![B: $i, A: $i] : ((~(A = B)) | smaller_or_equal(A, B))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(9,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')).
% 0.19/0.40 tff(10,plain,
% 0.19/0.40 (![B: $i, A: $i] : ((~(A = B)) | smaller_or_equal(A, B))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[9, 8])).
% 0.19/0.40 tff(11,plain,(
% 0.19/0.40 ![B: $i, A: $i] : ((~(A = B)) | smaller_or_equal(A, B))),
% 0.19/0.40 inference(skolemize,[status(sab)],[10])).
% 0.19/0.40 tff(12,plain,
% 0.19/0.40 (![B: $i, A: $i] : ((~(A = B)) | smaller_or_equal(A, B))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[11, 7])).
% 0.19/0.40 tff(13,plain,
% 0.19/0.40 (((~![B: $i, A: $i] : ((~(A = B)) | smaller_or_equal(A, B))) | ((~(age(sk3, sk4) = tau)) | smaller_or_equal(age(sk3, sk4), tau))) <=> ((~![B: $i, A: $i] : ((~(A = B)) | smaller_or_equal(A, B))) | (~(age(sk3, sk4) = tau)) | smaller_or_equal(age(sk3, sk4), tau))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(14,plain,
% 0.19/0.40 ((~![B: $i, A: $i] : ((~(A = B)) | smaller_or_equal(A, B))) | ((~(age(sk3, sk4) = tau)) | smaller_or_equal(age(sk3, sk4), tau))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(15,plain,
% 0.19/0.40 ((~![B: $i, A: $i] : ((~(A = B)) | smaller_or_equal(A, B))) | (~(age(sk3, sk4) = tau)) | smaller_or_equal(age(sk3, sk4), tau)),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.19/0.40 tff(16,plain,
% 0.19/0.40 (~(age(sk3, sk4) = tau)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[15, 12, 5])).
% 0.19/0.40 tff(17,plain,
% 0.19/0.40 (~(tau = age(sk3, sk4))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[16, 4])).
% 0.19/0.40 tff(18,plain,
% 0.19/0.40 (^[B: $i, A: $i] : refl(((~smaller(A, B)) | smaller_or_equal(A, B)) <=> ((~smaller(A, B)) | smaller_or_equal(A, B)))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(19,plain,
% 0.19/0.40 (![B: $i, A: $i] : ((~smaller(A, B)) | smaller_or_equal(A, B)) <=> ![B: $i, A: $i] : ((~smaller(A, B)) | smaller_or_equal(A, B))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[18])).
% 0.19/0.40 tff(20,plain,
% 0.19/0.40 (![B: $i, A: $i] : ((~smaller(A, B)) | smaller_or_equal(A, B)) <=> ![B: $i, A: $i] : ((~smaller(A, B)) | smaller_or_equal(A, B))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(21,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')).
% 0.19/0.40 tff(22,plain,
% 0.19/0.40 (![B: $i, A: $i] : ((~smaller(A, B)) | smaller_or_equal(A, B))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.19/0.41 tff(23,plain,(
% 0.19/0.41 ![B: $i, A: $i] : ((~smaller(A, B)) | smaller_or_equal(A, B))),
% 0.19/0.41 inference(skolemize,[status(sab)],[22])).
% 0.19/0.41 tff(24,plain,
% 0.19/0.41 (![B: $i, A: $i] : ((~smaller(A, B)) | smaller_or_equal(A, B))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[23, 19])).
% 0.19/0.41 tff(25,plain,
% 0.19/0.41 (((~![B: $i, A: $i] : ((~smaller(A, B)) | smaller_or_equal(A, B))) | ((~smaller(age(sk3, sk4), tau)) | smaller_or_equal(age(sk3, sk4), tau))) <=> ((~![B: $i, A: $i] : ((~smaller(A, B)) | smaller_or_equal(A, B))) | (~smaller(age(sk3, sk4), tau)) | smaller_or_equal(age(sk3, sk4), tau))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(26,plain,
% 0.19/0.41 ((~![B: $i, A: $i] : ((~smaller(A, B)) | smaller_or_equal(A, B))) | ((~smaller(age(sk3, sk4), tau)) | smaller_or_equal(age(sk3, sk4), tau))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(27,plain,
% 0.19/0.41 ((~![B: $i, A: $i] : ((~smaller(A, B)) | smaller_or_equal(A, B))) | (~smaller(age(sk3, sk4), tau)) | smaller_or_equal(age(sk3, sk4), tau)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.19/0.41 tff(28,plain,
% 0.19/0.41 (~smaller(age(sk3, sk4), tau)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[27, 24, 5])).
% 0.19/0.41 tff(29,plain,
% 0.19/0.41 (^[B: $i, A: $i] : refl(((~greater(A, B)) | smaller(B, A)) <=> ((~greater(A, B)) | smaller(B, A)))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(30,plain,
% 0.19/0.41 (![B: $i, A: $i] : ((~greater(A, B)) | smaller(B, A)) <=> ![B: $i, A: $i] : ((~greater(A, B)) | smaller(B, A))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[29])).
% 0.19/0.41 tff(31,plain,
% 0.19/0.41 (![B: $i, A: $i] : ((~greater(A, B)) | smaller(B, A)) <=> ![B: $i, A: $i] : ((~greater(A, B)) | smaller(B, A))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(32,axiom,(![B: $i, A: $i] : ((~greater(A, B)) | smaller(B, A))), file('/export/starexec/sandbox/benchmark/Axioms/MGT001-0.ax','definition_smaller_8')).
% 0.19/0.41 tff(33,plain,
% 0.19/0.41 (![B: $i, A: $i] : ((~greater(A, B)) | smaller(B, A))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.19/0.41 tff(34,plain,(
% 0.19/0.41 ![B: $i, A: $i] : ((~greater(A, B)) | smaller(B, A))),
% 0.19/0.41 inference(skolemize,[status(sab)],[33])).
% 0.19/0.41 tff(35,plain,
% 0.19/0.41 (![B: $i, A: $i] : ((~greater(A, B)) | smaller(B, A))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[34, 30])).
% 0.19/0.41 tff(36,plain,
% 0.19/0.41 (((~![B: $i, A: $i] : ((~greater(A, B)) | smaller(B, A))) | ((~greater(tau, age(sk3, sk4))) | smaller(age(sk3, sk4), tau))) <=> ((~![B: $i, A: $i] : ((~greater(A, B)) | smaller(B, A))) | (~greater(tau, age(sk3, sk4))) | smaller(age(sk3, sk4), tau))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(37,plain,
% 0.19/0.41 ((~![B: $i, A: $i] : ((~greater(A, B)) | smaller(B, A))) | ((~greater(tau, age(sk3, sk4))) | smaller(age(sk3, sk4), tau))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(38,plain,
% 0.19/0.41 ((~![B: $i, A: $i] : ((~greater(A, B)) | smaller(B, A))) | (~greater(tau, age(sk3, sk4))) | smaller(age(sk3, sk4), tau)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.19/0.41 tff(39,plain,
% 0.19/0.41 (~greater(tau, age(sk3, sk4))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[38, 35, 28])).
% 0.19/0.41 tff(40,plain,
% 0.19/0.41 (greater_or_equal(tau, zero) <=> greater_or_equal(tau, age(sk3, sk4))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(41,plain,
% 0.19/0.41 (greater_or_equal(tau, zero) <=> greater_or_equal(tau, zero)),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(42,axiom,(greater_or_equal(tau, zero)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','lemma_10_45')).
% 0.19/0.41 tff(43,plain,
% 0.19/0.41 (greater_or_equal(tau, zero)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.19/0.41 tff(44,plain,
% 0.19/0.41 (greater_or_equal(tau, age(sk3, sk4))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[43, 40])).
% 0.19/0.41 tff(45,plain,
% 0.19/0.41 (^[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))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(46,plain,
% 0.19/0.41 (![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)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[45])).
% 0.19/0.41 tff(47,plain,
% 0.19/0.41 (![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)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(48,plain,
% 0.19/0.41 (^[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))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(49,plain,
% 0.19/0.41 (![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)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[48])).
% 0.19/0.41 tff(50,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')).
% 0.19/0.41 tff(51,plain,
% 0.19/0.41 (![B: $i, A: $i] : ((A = B) | greater(A, B) | (~greater_or_equal(A, B)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.19/0.41 tff(52,plain,
% 0.19/0.41 (![B: $i, A: $i] : ((A = B) | greater(A, B) | (~greater_or_equal(A, B)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[51, 47])).
% 0.19/0.41 tff(53,plain,(
% 0.19/0.41 ![B: $i, A: $i] : ((A = B) | greater(A, B) | (~greater_or_equal(A, B)))),
% 0.19/0.41 inference(skolemize,[status(sab)],[52])).
% 0.19/0.41 tff(54,plain,
% 0.19/0.41 (![B: $i, A: $i] : ((A = B) | greater(A, B) | (~greater_or_equal(A, B)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[53, 46])).
% 0.19/0.41 tff(55,plain,
% 0.19/0.41 (((~![B: $i, A: $i] : ((A = B) | greater(A, B) | (~greater_or_equal(A, B)))) | ((tau = age(sk3, sk4)) | greater(tau, age(sk3, sk4)) | (~greater_or_equal(tau, age(sk3, sk4))))) <=> ((~![B: $i, A: $i] : ((A = B) | greater(A, B) | (~greater_or_equal(A, B)))) | (tau = age(sk3, sk4)) | greater(tau, age(sk3, sk4)) | (~greater_or_equal(tau, age(sk3, sk4))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(56,plain,
% 0.19/0.41 ((~![B: $i, A: $i] : ((A = B) | greater(A, B) | (~greater_or_equal(A, B)))) | ((tau = age(sk3, sk4)) | greater(tau, age(sk3, sk4)) | (~greater_or_equal(tau, age(sk3, sk4))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(57,plain,
% 0.19/0.41 ((~![B: $i, A: $i] : ((A = B) | greater(A, B) | (~greater_or_equal(A, B)))) | (tau = age(sk3, sk4)) | greater(tau, age(sk3, sk4)) | (~greater_or_equal(tau, age(sk3, sk4)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.19/0.41 tff(58,plain,
% 0.19/0.41 ((tau = age(sk3, sk4)) | greater(tau, age(sk3, sk4))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[57, 54, 44])).
% 0.19/0.41 tff(59,plain,
% 0.19/0.41 ($false),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[58, 39, 17])).
% 0.19/0.41 tff(60,plain,(smaller_or_equal(age(sk3, sk4), tau)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.41 tff(61,plain,
% 0.19/0.41 (robust_position(sk3) <=> robust_position(sk3)),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(62,axiom,(robust_position(sk3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','lemma_10_47')).
% 0.19/0.41 tff(63,plain,
% 0.19/0.41 (robust_position(sk3)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.19/0.41 tff(64,plain,
% 0.19/0.41 (^[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))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(65,plain,
% 0.19/0.41 (![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)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[64])).
% 0.19/0.41 tff(66,plain,
% 0.19/0.41 (![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)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(67,plain,
% 0.19/0.41 (^[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))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(68,plain,
% 0.19/0.41 (![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)))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[67])).
% 0.19/0.42 tff(69,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')).
% 0.19/0.42 tff(70,plain,
% 0.19/0.42 (![B: $i, A: $i] : ((~positional_advantage(A, B)) | (~smaller_or_equal(age(A, B), tau)) | (~robust_position(A)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.19/0.42 tff(71,plain,
% 0.19/0.42 (![B: $i, A: $i] : ((~positional_advantage(A, B)) | (~smaller_or_equal(age(A, B), tau)) | (~robust_position(A)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[70, 66])).
% 0.19/0.42 tff(72,plain,(
% 0.19/0.42 ![B: $i, A: $i] : ((~positional_advantage(A, B)) | (~smaller_or_equal(age(A, B), tau)) | (~robust_position(A)))),
% 0.19/0.42 inference(skolemize,[status(sab)],[71])).
% 0.19/0.42 tff(73,plain,
% 0.19/0.42 (![B: $i, A: $i] : ((~positional_advantage(A, B)) | (~smaller_or_equal(age(A, B), tau)) | (~robust_position(A)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[72, 65])).
% 0.19/0.42 tff(74,plain,
% 0.19/0.42 (((~![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)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(75,plain,
% 0.19/0.42 (((~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)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(76,plain,
% 0.19/0.42 (((~![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))))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[75])).
% 0.19/0.42 tff(77,plain,
% 0.19/0.42 (((~![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)))),
% 0.19/0.42 inference(transitivity,[status(thm)],[76, 74])).
% 0.19/0.42 tff(78,plain,
% 0.19/0.42 ((~![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)))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(79,plain,
% 0.19/0.42 ((~![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))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.19/0.42 tff(80,plain,
% 0.19/0.42 ((~positional_advantage(sk3, sk4)) | (~smaller_or_equal(age(sk3, sk4), tau))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[79, 73, 63])).
% 0.19/0.42 tff(81,plain,
% 0.19/0.42 (~positional_advantage(sk3, sk4)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[80, 60])).
% 0.19/0.42 tff(82,plain,
% 0.19/0.42 (fragile_position(sk3) <=> fragile_position(sk3)),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(83,axiom,(fragile_position(sk3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','lemma_10_46')).
% 0.19/0.42 tff(84,plain,
% 0.19/0.42 (fragile_position(sk3)),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.19/0.42 tff(85,plain,
% 0.19/0.42 (^[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))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(86,plain,
% 0.19/0.42 (![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)))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[85])).
% 0.19/0.42 tff(87,plain,
% 0.19/0.42 (![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)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(88,plain,
% 0.19/0.42 (^[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))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(89,plain,
% 0.19/0.42 (![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)))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[88])).
% 0.19/0.42 tff(90,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')).
% 0.19/0.42 tff(91,plain,
% 0.19/0.42 (![B: $i, A: $i] : (positional_advantage(A, B) | (~smaller_or_equal(age(A, B), sigma)) | (~fragile_position(A)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[90, 89])).
% 0.19/0.42 tff(92,plain,
% 0.19/0.42 (![B: $i, A: $i] : (positional_advantage(A, B) | (~smaller_or_equal(age(A, B), sigma)) | (~fragile_position(A)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[91, 87])).
% 0.19/0.42 tff(93,plain,(
% 0.19/0.42 ![B: $i, A: $i] : (positional_advantage(A, B) | (~smaller_or_equal(age(A, B), sigma)) | (~fragile_position(A)))),
% 0.19/0.42 inference(skolemize,[status(sab)],[92])).
% 0.19/0.42 tff(94,plain,
% 0.19/0.42 (![B: $i, A: $i] : (positional_advantage(A, B) | (~smaller_or_equal(age(A, B), sigma)) | (~fragile_position(A)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[93, 86])).
% 0.19/0.42 tff(95,plain,
% 0.19/0.42 (((~![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)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(96,plain,
% 0.19/0.42 ((~![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)))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(97,plain,
% 0.19/0.42 ((~![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))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[96, 95])).
% 0.19/0.42 tff(98,plain,
% 0.19/0.42 (positional_advantage(sk3, sk4) | (~smaller_or_equal(age(sk3, sk4), sigma))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[97, 94, 84])).
% 0.19/0.42 tff(99,plain,
% 0.19/0.42 (~smaller_or_equal(age(sk3, sk4), sigma)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[98, 81])).
% 0.19/0.42 tff(100,plain,
% 0.19/0.42 (((~![B: $i, A: $i] : ((~(A = B)) | smaller_or_equal(A, B))) | ((~(age(sk3, sk4) = sigma)) | smaller_or_equal(age(sk3, sk4), sigma))) <=> ((~![B: $i, A: $i] : ((~(A = B)) | smaller_or_equal(A, B))) | (~(age(sk3, sk4) = sigma)) | smaller_or_equal(age(sk3, sk4), sigma))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(101,plain,
% 0.19/0.43 ((~![B: $i, A: $i] : ((~(A = B)) | smaller_or_equal(A, B))) | ((~(age(sk3, sk4) = sigma)) | smaller_or_equal(age(sk3, sk4), sigma))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(102,plain,
% 0.19/0.43 ((~![B: $i, A: $i] : ((~(A = B)) | smaller_or_equal(A, B))) | (~(age(sk3, sk4) = sigma)) | smaller_or_equal(age(sk3, sk4), sigma)),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[101, 100])).
% 0.19/0.43 tff(103,plain,
% 0.19/0.43 (~(age(sk3, sk4) = sigma)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[102, 12, 99])).
% 0.19/0.43 tff(104,plain,
% 0.19/0.43 (~(sigma = age(sk3, sk4))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[103, 2])).
% 0.19/0.43 tff(105,plain,
% 0.19/0.43 (((~![B: $i, A: $i] : ((~smaller(A, B)) | smaller_or_equal(A, B))) | ((~smaller(age(sk3, sk4), sigma)) | smaller_or_equal(age(sk3, sk4), sigma))) <=> ((~![B: $i, A: $i] : ((~smaller(A, B)) | smaller_or_equal(A, B))) | (~smaller(age(sk3, sk4), sigma)) | smaller_or_equal(age(sk3, sk4), sigma))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(106,plain,
% 0.19/0.43 ((~![B: $i, A: $i] : ((~smaller(A, B)) | smaller_or_equal(A, B))) | ((~smaller(age(sk3, sk4), sigma)) | smaller_or_equal(age(sk3, sk4), sigma))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(107,plain,
% 0.19/0.43 ((~![B: $i, A: $i] : ((~smaller(A, B)) | smaller_or_equal(A, B))) | (~smaller(age(sk3, sk4), sigma)) | smaller_or_equal(age(sk3, sk4), sigma)),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[106, 105])).
% 0.19/0.43 tff(108,plain,
% 0.19/0.43 (~smaller(age(sk3, sk4), sigma)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[107, 24, 99])).
% 0.19/0.43 tff(109,plain,
% 0.19/0.43 (((~![B: $i, A: $i] : ((~greater(A, B)) | smaller(B, A))) | ((~greater(sigma, age(sk3, sk4))) | smaller(age(sk3, sk4), sigma))) <=> ((~![B: $i, A: $i] : ((~greater(A, B)) | smaller(B, A))) | (~greater(sigma, age(sk3, sk4))) | smaller(age(sk3, sk4), sigma))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(110,plain,
% 0.19/0.43 ((~![B: $i, A: $i] : ((~greater(A, B)) | smaller(B, A))) | ((~greater(sigma, age(sk3, sk4))) | smaller(age(sk3, sk4), sigma))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(111,plain,
% 0.19/0.43 ((~![B: $i, A: $i] : ((~greater(A, B)) | smaller(B, A))) | (~greater(sigma, age(sk3, sk4))) | smaller(age(sk3, sk4), sigma)),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[110, 109])).
% 0.19/0.43 tff(112,plain,
% 0.19/0.43 (~greater(sigma, age(sk3, sk4))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[111, 35, 108])).
% 0.19/0.43 tff(113,plain,
% 0.19/0.43 (greater_or_equal(sigma, zero) <=> greater_or_equal(sigma, age(sk3, sk4))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(114,plain,
% 0.19/0.43 (greater_or_equal(sigma, zero) <=> greater_or_equal(sigma, zero)),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(115,axiom,(greater_or_equal(sigma, zero)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','lemma_10_44')).
% 0.19/0.43 tff(116,plain,
% 0.19/0.43 (greater_or_equal(sigma, zero)),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[115, 114])).
% 0.19/0.43 tff(117,plain,
% 0.19/0.43 (greater_or_equal(sigma, age(sk3, sk4))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[116, 113])).
% 0.19/0.43 tff(118,plain,
% 0.19/0.43 (((~![B: $i, A: $i] : ((A = B) | greater(A, B) | (~greater_or_equal(A, B)))) | ((sigma = age(sk3, sk4)) | greater(sigma, age(sk3, sk4)) | (~greater_or_equal(sigma, age(sk3, sk4))))) <=> ((~![B: $i, A: $i] : ((A = B) | greater(A, B) | (~greater_or_equal(A, B)))) | (sigma = age(sk3, sk4)) | greater(sigma, age(sk3, sk4)) | (~greater_or_equal(sigma, age(sk3, sk4))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(119,plain,
% 0.19/0.43 ((~![B: $i, A: $i] : ((A = B) | greater(A, B) | (~greater_or_equal(A, B)))) | ((sigma = age(sk3, sk4)) | greater(sigma, age(sk3, sk4)) | (~greater_or_equal(sigma, age(sk3, sk4))))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(120,plain,
% 0.19/0.43 ((~![B: $i, A: $i] : ((A = B) | greater(A, B) | (~greater_or_equal(A, B)))) | (sigma = age(sk3, sk4)) | greater(sigma, age(sk3, sk4)) | (~greater_or_equal(sigma, age(sk3, sk4)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[119, 118])).
% 0.19/0.43 tff(121,plain,
% 0.19/0.43 ((sigma = age(sk3, sk4)) | greater(sigma, age(sk3, sk4))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[120, 54, 117])).
% 0.19/0.43 tff(122,plain,
% 0.19/0.43 ($false),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[121, 112, 104])).
% 0.19/0.43 % SZS output end Proof
%------------------------------------------------------------------------------