TSTP Solution File: ITP356_1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : ITP001_1 : TPTP v8.1.2. Released v8.1.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n010.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 : Thu Aug 31 04:11:51 EDT 2023
% Result : Theorem 46.96s 7.07s
% Output : Proof 84.35s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : ITP001_1 : TPTP v8.1.2. Released v8.1.0.
% 0.06/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n010.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sun Aug 27 15:57:34 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.64 ________ _____
% 0.20/0.64 ___ __ \_________(_)________________________________
% 0.20/0.64 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.64 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.64 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.64
% 0.20/0.64 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.64 (2023-06-19)
% 0.20/0.64
% 0.20/0.64 (c) Philipp Rümmer, 2009-2023
% 0.20/0.64 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.64 Amanda Stjerna.
% 0.20/0.64 Free software under BSD-3-Clause.
% 0.20/0.64
% 0.20/0.64 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.64
% 0.20/0.64 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.20/0.66 Running up to 7 provers in parallel.
% 0.20/0.68 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.68 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.68 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.68 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.68 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.68 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.68 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 16.66/3.03 Prover 6: Preprocessing ...
% 17.15/3.11 Prover 3: Preprocessing ...
% 17.15/3.13 Prover 2: Preprocessing ...
% 17.15/3.15 Prover 4: Preprocessing ...
% 17.85/3.16 Prover 0: Preprocessing ...
% 17.85/3.18 Prover 5: Preprocessing ...
% 18.04/3.19 Prover 1: Preprocessing ...
% 41.70/6.32 Prover 3: Warning: ignoring some quantifiers
% 41.70/6.38 Prover 3: Constructing countermodel ...
% 42.33/6.47 Prover 1: Warning: ignoring some quantifiers
% 43.27/6.53 Prover 6: Proving ...
% 44.02/6.72 Prover 1: Constructing countermodel ...
% 45.14/6.84 Prover 4: Warning: ignoring some quantifiers
% 46.96/7.06 Prover 6: proved (6381ms)
% 46.96/7.07
% 46.96/7.07 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 46.96/7.07
% 46.96/7.08 Prover 3: stopped
% 46.96/7.08 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 46.96/7.09 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 48.28/7.19 Prover 4: Constructing countermodel ...
% 48.49/7.21 Prover 0: Proving ...
% 48.49/7.21 Prover 0: stopped
% 48.49/7.21 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 51.72/7.68 Prover 5: Proving ...
% 51.72/7.68 Prover 5: stopped
% 51.72/7.68 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 56.03/8.24 Prover 7: Preprocessing ...
% 57.34/8.40 Prover 8: Preprocessing ...
% 58.37/8.53 Prover 10: Preprocessing ...
% 60.69/8.85 Prover 11: Preprocessing ...
% 64.75/9.41 Prover 2: Proving ...
% 64.75/9.41 Prover 2: stopped
% 64.75/9.43 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 71.85/10.31 Prover 13: Preprocessing ...
% 71.85/10.31 Prover 10: Warning: ignoring some quantifiers
% 73.32/10.49 Prover 7: Warning: ignoring some quantifiers
% 73.32/10.50 Prover 10: Constructing countermodel ...
% 73.98/10.57 Prover 8: Warning: ignoring some quantifiers
% 75.37/10.77 Prover 7: Constructing countermodel ...
% 75.37/10.79 Prover 8: Constructing countermodel ...
% 79.37/11.29 Prover 1: Found proof (size 16)
% 79.37/11.29 Prover 1: proved (10621ms)
% 79.37/11.29 Prover 10: stopped
% 79.37/11.29 Prover 7: stopped
% 79.37/11.30 Prover 8: stopped
% 79.37/11.30 Prover 4: stopped
% 80.52/11.50 Prover 11: Warning: ignoring some quantifiers
% 81.48/11.66 Prover 11: Constructing countermodel ...
% 81.48/11.67 Prover 11: stopped
% 83.18/12.10 Prover 13: Warning: ignoring some quantifiers
% 83.79/12.24 Prover 13: Constructing countermodel ...
% 83.79/12.25 Prover 13: stopped
% 83.79/12.25
% 83.79/12.25 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 83.79/12.25
% 83.79/12.25 % SZS output start Proof for theBenchmark
% 84.13/12.30 Assumptions after simplification:
% 84.13/12.30 ---------------------------------
% 84.13/12.30
% 84.13/12.30 (axiom6)
% 84.27/12.33 A_ltln_list_a_ltln_list_list_fun$(subseqs$) & A_ltln_list_list$(nil$b) & !
% 84.27/12.33 [v0: A_ltln_list$] : ( ~ (fun_app$d(subseqs$, v0) = nil$b) | ~
% 84.27/12.33 A_ltln_list$(v0))
% 84.27/12.33
% 84.27/12.33 (axiom7)
% 84.27/12.34 A_ltln_list_a_ltln_list_prod_list$(nil$) & A_ltln_list_list$(nil$b) & ! [v0:
% 84.27/12.34 A_ltln_list_list$] : ! [v1: A_ltln_list_list$] : (v1 = nil$b | v0 = nil$b |
% 84.27/12.34 ~ (product$(v0, v1) = nil$) | ~ A_ltln_list_list$(v1) | ~
% 84.27/12.34 A_ltln_list_list$(v0))
% 84.27/12.34
% 84.27/12.34 (conjecture4)
% 84.35/12.34 A_ltln_list_a_ltln_list_prod_list$(nil$) &
% 84.35/12.34 A_ltln_list_a_ltln_list_list_fun$(subseqs$) & A_ltln$(phi$) &
% 84.35/12.34 A_ltln_a_ltln_list_fun$(subformulas_mu_list$) &
% 84.35/12.34 A_ltln_a_ltln_list_fun$(subformulas_nu_list$) & ? [v0: A_ltln_list$] : ?
% 84.35/12.34 [v1: A_ltln_list_list$] : ? [v2: A_ltln_list$] : ? [v3: A_ltln_list_list$] :
% 84.35/12.34 (fun_app$e(subformulas_mu_list$, phi$) = v0 & fun_app$e(subformulas_nu_list$,
% 84.35/12.34 phi$) = v2 & product$(v1, v3) = nil$ & fun_app$d(subseqs$, v2) = v3 &
% 84.35/12.34 fun_app$d(subseqs$, v0) = v1 & A_ltln_list_list$(v3) & A_ltln_list_list$(v1)
% 84.35/12.34 & A_ltln_list$(v2) & A_ltln_list$(v0))
% 84.35/12.34
% 84.35/12.34 Further assumptions not needed in the proof:
% 84.35/12.34 --------------------------------------------
% 84.35/12.34 axiom0, axiom1, axiom10, axiom100, axiom101, axiom102, axiom103, axiom104,
% 84.35/12.34 axiom105, axiom106, axiom107, axiom108, axiom109, axiom11, axiom110, axiom111,
% 84.35/12.34 axiom112, axiom113, axiom114, axiom115, axiom116, axiom117, axiom118, axiom119,
% 84.35/12.34 axiom12, axiom120, axiom121, axiom122, axiom123, axiom124, axiom125, axiom126,
% 84.35/12.34 axiom127, axiom128, axiom129, axiom13, axiom130, axiom131, axiom132, axiom133,
% 84.35/12.34 axiom134, axiom135, axiom136, axiom137, axiom138, axiom139, axiom14, axiom140,
% 84.35/12.34 axiom141, axiom142, axiom143, axiom144, axiom145, axiom146, axiom147, axiom148,
% 84.35/12.34 axiom149, axiom15, axiom150, axiom151, axiom152, axiom153, axiom154, axiom155,
% 84.35/12.34 axiom156, axiom157, axiom158, axiom159, axiom16, axiom160, axiom161, axiom162,
% 84.35/12.34 axiom163, axiom164, axiom165, axiom166, axiom167, axiom168, axiom169, axiom17,
% 84.35/12.35 axiom170, axiom171, axiom172, axiom173, axiom174, axiom175, axiom176, axiom177,
% 84.35/12.35 axiom178, axiom179, axiom18, axiom180, axiom181, axiom182, axiom183, axiom184,
% 84.35/12.35 axiom185, axiom186, axiom187, axiom188, axiom189, axiom19, axiom190, axiom191,
% 84.35/12.35 axiom192, axiom193, axiom194, axiom195, axiom196, axiom197, axiom198, axiom199,
% 84.35/12.35 axiom2, axiom20, axiom200, axiom201, axiom202, axiom203, axiom204, axiom205,
% 84.35/12.35 axiom206, axiom207, axiom208, axiom209, axiom21, axiom210, axiom211, axiom212,
% 84.35/12.35 axiom213, axiom214, axiom215, axiom216, axiom217, axiom218, axiom219, axiom22,
% 84.35/12.35 axiom220, axiom221, axiom222, axiom223, axiom224, axiom225, axiom226, axiom227,
% 84.35/12.35 axiom228, axiom229, axiom23, axiom230, axiom231, axiom232, axiom233, axiom234,
% 84.35/12.35 axiom235, axiom236, axiom237, axiom238, axiom239, axiom24, axiom240, axiom241,
% 84.35/12.35 axiom242, axiom243, axiom244, axiom245, axiom246, axiom247, axiom248, axiom249,
% 84.35/12.35 axiom25, axiom250, axiom251, axiom252, axiom253, axiom254, axiom255, axiom256,
% 84.35/12.35 axiom257, axiom258, axiom259, axiom26, axiom260, axiom261, axiom262, axiom263,
% 84.35/12.35 axiom264, axiom265, axiom266, axiom267, axiom268, axiom269, axiom27, axiom270,
% 84.35/12.35 axiom271, axiom272, axiom273, axiom274, axiom275, axiom276, axiom277, axiom278,
% 84.35/12.35 axiom279, axiom28, axiom280, axiom281, axiom282, axiom283, axiom284, axiom285,
% 84.35/12.35 axiom286, axiom287, axiom288, axiom289, axiom29, axiom290, axiom291, axiom292,
% 84.35/12.35 axiom293, axiom294, axiom295, axiom296, axiom297, axiom298, axiom299, axiom3,
% 84.35/12.35 axiom30, axiom300, axiom301, axiom302, axiom303, axiom304, axiom305, axiom306,
% 84.35/12.35 axiom307, axiom308, axiom309, axiom31, axiom310, axiom311, axiom312, axiom313,
% 84.35/12.35 axiom314, axiom315, axiom316, axiom317, axiom318, axiom319, axiom32, axiom320,
% 84.35/12.35 axiom321, axiom322, axiom323, axiom324, axiom325, axiom326, axiom327, axiom328,
% 84.35/12.35 axiom329, axiom33, axiom330, axiom331, axiom332, axiom333, axiom334, axiom335,
% 84.35/12.35 axiom336, axiom337, axiom338, axiom339, axiom34, axiom340, axiom341, axiom342,
% 84.35/12.35 axiom343, axiom344, axiom345, axiom346, axiom347, axiom348, axiom349, axiom35,
% 84.35/12.35 axiom350, axiom351, axiom352, axiom353, axiom354, axiom355, axiom356, axiom357,
% 84.35/12.35 axiom358, axiom359, axiom36, axiom360, axiom361, axiom362, axiom363, axiom364,
% 84.35/12.35 axiom365, axiom366, axiom367, axiom368, axiom369, axiom37, axiom370, axiom371,
% 84.35/12.35 axiom372, axiom373, axiom374, axiom375, axiom376, axiom377, axiom378, axiom379,
% 84.35/12.35 axiom38, axiom380, axiom381, axiom382, axiom383, axiom384, axiom385, axiom386,
% 84.35/12.35 axiom387, axiom388, axiom389, axiom39, axiom390, axiom391, axiom392, axiom393,
% 84.35/12.35 axiom394, axiom395, axiom396, axiom397, axiom398, axiom399, axiom40, axiom400,
% 84.35/12.35 axiom401, axiom402, axiom403, axiom404, axiom405, axiom406, axiom407, axiom408,
% 84.35/12.35 axiom409, axiom41, axiom410, axiom411, axiom412, axiom413, axiom414, axiom415,
% 84.35/12.35 axiom416, axiom417, axiom418, axiom419, axiom42, axiom420, axiom421, axiom422,
% 84.35/12.35 axiom423, axiom424, axiom425, axiom426, axiom427, axiom428, axiom429, axiom43,
% 84.35/12.35 axiom430, axiom431, axiom432, axiom433, axiom434, axiom435, axiom436, axiom437,
% 84.35/12.35 axiom438, axiom439, axiom44, axiom440, axiom441, axiom442, axiom443, axiom444,
% 84.35/12.35 axiom445, axiom446, axiom447, axiom448, axiom449, axiom45, axiom450, axiom451,
% 84.35/12.35 axiom452, axiom453, axiom454, axiom455, axiom456, axiom457, axiom458, axiom459,
% 84.35/12.35 axiom46, axiom460, axiom461, axiom462, axiom463, axiom464, axiom465, axiom466,
% 84.35/12.35 axiom467, axiom468, axiom469, axiom47, axiom470, axiom471, axiom472, axiom473,
% 84.35/12.35 axiom474, axiom475, axiom476, axiom477, axiom478, axiom479, axiom48, axiom480,
% 84.35/12.35 axiom481, axiom482, axiom483, axiom484, axiom485, axiom486, axiom487, axiom488,
% 84.35/12.35 axiom489, axiom49, axiom490, axiom491, axiom492, axiom493, axiom494, axiom495,
% 84.35/12.35 axiom496, axiom497, axiom498, axiom499, axiom5, axiom50, axiom500, axiom501,
% 84.35/12.35 axiom502, axiom503, axiom504, axiom505, axiom506, axiom507, axiom508, axiom509,
% 84.35/12.35 axiom51, axiom510, axiom511, axiom512, axiom513, axiom514, axiom515, axiom516,
% 84.35/12.35 axiom517, axiom518, axiom519, axiom52, axiom520, axiom521, axiom522, axiom523,
% 84.35/12.35 axiom524, axiom525, axiom526, axiom527, axiom528, axiom529, axiom53, axiom530,
% 84.35/12.35 axiom531, axiom532, axiom533, axiom534, axiom535, axiom536, axiom537, axiom538,
% 84.35/12.35 axiom539, axiom54, axiom540, axiom541, axiom542, axiom543, axiom544, axiom545,
% 84.35/12.35 axiom546, axiom547, axiom548, axiom549, axiom55, axiom550, axiom551, axiom552,
% 84.35/12.35 axiom553, axiom554, axiom555, axiom556, axiom557, axiom558, axiom559, axiom56,
% 84.35/12.35 axiom560, axiom561, axiom562, axiom563, axiom564, axiom565, axiom566, axiom567,
% 84.35/12.35 axiom568, axiom569, axiom57, axiom570, axiom571, axiom572, axiom573, axiom574,
% 84.35/12.35 axiom575, axiom576, axiom577, axiom578, axiom579, axiom58, axiom580, axiom581,
% 84.35/12.35 axiom582, axiom583, axiom584, axiom585, axiom586, axiom587, axiom588, axiom589,
% 84.35/12.35 axiom59, axiom590, axiom591, axiom592, axiom593, axiom594, axiom595, axiom596,
% 84.35/12.35 axiom597, axiom598, axiom599, axiom60, axiom600, axiom601, axiom602, axiom603,
% 84.35/12.35 axiom604, axiom605, axiom606, axiom607, axiom608, axiom609, axiom61, axiom610,
% 84.35/12.35 axiom611, axiom612, axiom613, axiom614, axiom615, axiom616, axiom617, axiom618,
% 84.35/12.35 axiom619, axiom62, axiom620, axiom621, axiom622, axiom623, axiom624, axiom625,
% 84.35/12.35 axiom626, axiom627, axiom628, axiom629, axiom63, axiom630, axiom631, axiom632,
% 84.35/12.35 axiom633, axiom634, axiom635, axiom636, axiom637, axiom638, axiom639, axiom64,
% 84.35/12.35 axiom640, axiom641, axiom642, axiom65, axiom66, axiom67, axiom68, axiom69,
% 84.35/12.35 axiom70, axiom71, axiom72, axiom73, axiom74, axiom75, axiom76, axiom77, axiom78,
% 84.35/12.35 axiom79, axiom8, axiom80, axiom81, axiom82, axiom83, axiom84, axiom85, axiom86,
% 84.35/12.35 axiom87, axiom88, axiom89, axiom9, axiom90, axiom91, axiom92, axiom93, axiom94,
% 84.35/12.35 axiom95, axiom96, axiom97, axiom98, axiom99
% 84.35/12.35
% 84.35/12.35 Those formulas are unsatisfiable:
% 84.35/12.35 ---------------------------------
% 84.35/12.35
% 84.35/12.35 Begin of proof
% 84.35/12.35 |
% 84.35/12.35 | ALPHA: (axiom6) implies:
% 84.35/12.35 | (1) ! [v0: A_ltln_list$] : ( ~ (fun_app$d(subseqs$, v0) = nil$b) | ~
% 84.35/12.35 | A_ltln_list$(v0))
% 84.35/12.35 |
% 84.35/12.35 | ALPHA: (axiom7) implies:
% 84.35/12.35 | (2) ! [v0: A_ltln_list_list$] : ! [v1: A_ltln_list_list$] : (v1 = nil$b |
% 84.35/12.35 | v0 = nil$b | ~ (product$(v0, v1) = nil$) | ~ A_ltln_list_list$(v1)
% 84.35/12.35 | | ~ A_ltln_list_list$(v0))
% 84.35/12.35 |
% 84.35/12.35 | ALPHA: (conjecture4) implies:
% 84.35/12.36 | (3) ? [v0: A_ltln_list$] : ? [v1: A_ltln_list_list$] : ? [v2:
% 84.35/12.36 | A_ltln_list$] : ? [v3: A_ltln_list_list$] :
% 84.35/12.36 | (fun_app$e(subformulas_mu_list$, phi$) = v0 &
% 84.35/12.36 | fun_app$e(subformulas_nu_list$, phi$) = v2 & product$(v1, v3) = nil$
% 84.35/12.36 | & fun_app$d(subseqs$, v2) = v3 & fun_app$d(subseqs$, v0) = v1 &
% 84.35/12.36 | A_ltln_list_list$(v3) & A_ltln_list_list$(v1) & A_ltln_list$(v2) &
% 84.35/12.36 | A_ltln_list$(v0))
% 84.35/12.36 |
% 84.35/12.36 | DELTA: instantiating (3) with fresh symbols all_875_0, all_875_1, all_875_2,
% 84.35/12.36 | all_875_3 gives:
% 84.35/12.36 | (4) fun_app$e(subformulas_mu_list$, phi$) = all_875_3 &
% 84.35/12.36 | fun_app$e(subformulas_nu_list$, phi$) = all_875_1 & product$(all_875_2,
% 84.35/12.36 | all_875_0) = nil$ & fun_app$d(subseqs$, all_875_1) = all_875_0 &
% 84.35/12.36 | fun_app$d(subseqs$, all_875_3) = all_875_2 &
% 84.35/12.36 | A_ltln_list_list$(all_875_0) & A_ltln_list_list$(all_875_2) &
% 84.35/12.36 | A_ltln_list$(all_875_1) & A_ltln_list$(all_875_3)
% 84.35/12.36 |
% 84.35/12.36 | ALPHA: (4) implies:
% 84.35/12.36 | (5) A_ltln_list$(all_875_3)
% 84.35/12.36 | (6) A_ltln_list$(all_875_1)
% 84.35/12.36 | (7) A_ltln_list_list$(all_875_2)
% 84.35/12.36 | (8) A_ltln_list_list$(all_875_0)
% 84.35/12.36 | (9) fun_app$d(subseqs$, all_875_3) = all_875_2
% 84.35/12.36 | (10) fun_app$d(subseqs$, all_875_1) = all_875_0
% 84.35/12.36 | (11) product$(all_875_2, all_875_0) = nil$
% 84.35/12.36 |
% 84.35/12.36 | GROUND_INST: instantiating (2) with all_875_2, all_875_0, simplifying with
% 84.35/12.36 | (7), (8), (11) gives:
% 84.35/12.37 | (12) all_875_0 = nil$b | all_875_2 = nil$b
% 84.35/12.37 |
% 84.35/12.37 | BETA: splitting (12) gives:
% 84.35/12.37 |
% 84.35/12.37 | Case 1:
% 84.35/12.37 | |
% 84.35/12.37 | | (13) all_875_0 = nil$b
% 84.35/12.37 | |
% 84.35/12.37 | | REDUCE: (10), (13) imply:
% 84.35/12.37 | | (14) fun_app$d(subseqs$, all_875_1) = nil$b
% 84.35/12.37 | |
% 84.35/12.37 | | GROUND_INST: instantiating (1) with all_875_1, simplifying with (6), (14)
% 84.35/12.37 | | gives:
% 84.35/12.37 | | (15) $false
% 84.35/12.37 | |
% 84.35/12.37 | | CLOSE: (15) is inconsistent.
% 84.35/12.37 | |
% 84.35/12.37 | Case 2:
% 84.35/12.37 | |
% 84.35/12.37 | | (16) all_875_2 = nil$b
% 84.35/12.37 | |
% 84.35/12.37 | | REDUCE: (9), (16) imply:
% 84.35/12.37 | | (17) fun_app$d(subseqs$, all_875_3) = nil$b
% 84.35/12.37 | |
% 84.35/12.37 | | GROUND_INST: instantiating (1) with all_875_3, simplifying with (5), (17)
% 84.35/12.37 | | gives:
% 84.35/12.37 | | (18) $false
% 84.35/12.37 | |
% 84.35/12.37 | | CLOSE: (18) is inconsistent.
% 84.35/12.37 | |
% 84.35/12.37 | End of split
% 84.35/12.37 |
% 84.35/12.37 End of proof
% 84.35/12.37 % SZS output end Proof for theBenchmark
% 84.35/12.37
% 84.35/12.37 11727ms
%------------------------------------------------------------------------------