%------------------------------------------------------------------------------ % 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 : n019.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 04:11:46 EDT 2023 % Result : Theorem 90.34s 12.84s % Output : Proof 130.69s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : ITP001_1 : TPTP v8.1.2. Released v8.1.0. % 0.00/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.18/0.36 % Computer : n019.cluster.edu % 0.18/0.36 % Model : x86_64 x86_64 % 0.18/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.18/0.36 % Memory : 8042.1875MB % 0.18/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.21/0.36 % CPULimit : 300 % 0.21/0.36 % WCLimit : 300 % 0.21/0.36 % DateTime : Sun Aug 27 16:49:13 EDT 2023 % 0.21/0.36 % CPUTime : % 0.22/0.63 ________ _____ % 0.22/0.63 ___ __ \_________(_)________________________________ % 0.22/0.63 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.22/0.63 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.22/0.63 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.22/0.63 % 0.22/0.63 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.22/0.63 (2023-06-19) % 0.22/0.63 % 0.22/0.63 (c) Philipp Rümmer, 2009-2023 % 0.22/0.63 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.22/0.63 Amanda Stjerna. % 0.22/0.63 Free software under BSD-3-Clause. % 0.22/0.63 % 0.22/0.63 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.22/0.63 % 0.22/0.63 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.22/0.65 Running up to 7 provers in parallel. % 0.22/0.67 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.22/0.67 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.22/0.67 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.22/0.67 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.22/0.67 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.22/0.67 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.22/0.67 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.42/1.10 Prover 2: Warning: Problem contains reals, using incomplete axiomatisation % 2.42/1.10 Prover 4: Warning: Problem contains reals, using incomplete axiomatisation % 2.42/1.11 Prover 0: Warning: Problem contains reals, using incomplete axiomatisation % 2.42/1.11 Prover 5: Warning: Problem contains reals, using incomplete axiomatisation % 2.42/1.11 Prover 1: Warning: Problem contains reals, using incomplete axiomatisation % 2.42/1.11 Prover 3: Warning: Problem contains reals, using incomplete axiomatisation % 2.42/1.11 Prover 6: Warning: Problem contains reals, using incomplete axiomatisation % 13.88/2.71 Prover 5: Preprocessing ... % 13.88/2.72 Prover 4: Preprocessing ... % 14.50/2.75 Prover 1: Preprocessing ... % 14.50/2.77 Prover 2: Preprocessing ... % 14.50/2.77 Prover 3: Preprocessing ... % 14.50/2.78 Prover 0: Preprocessing ... % 14.50/2.80 Prover 6: Preprocessing ... % 37.30/5.82 Prover 1: Warning: ignoring some quantifiers % 37.30/5.89 Prover 3: Warning: ignoring some quantifiers % 38.37/5.99 Prover 3: Constructing countermodel ... % 38.37/6.00 Prover 1: Constructing countermodel ... % 38.81/6.01 Prover 6: Proving ... % 39.20/6.10 Prover 4: Warning: ignoring some quantifiers % 40.66/6.26 Prover 4: Constructing countermodel ... % 41.41/6.39 Prover 5: Proving ... % 43.64/6.65 Prover 0: Proving ... % 48.77/7.38 Prover 2: Proving ... % 90.34/12.84 Prover 6: proved (12168ms) % 90.34/12.84 % 90.34/12.84 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 90.34/12.84 % 90.34/12.84 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 90.34/12.84 Prover 3: stopped % 90.34/12.85 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 90.34/12.86 Prover 5: stopped % 90.34/12.86 Prover 2: stopped % 90.34/12.86 Prover 0: stopped % 90.99/12.88 Prover 8: Warning: Problem contains reals, using incomplete axiomatisation % 90.99/12.88 Prover 7: Warning: Problem contains reals, using incomplete axiomatisation % 90.99/12.88 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 90.99/12.88 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 90.99/12.88 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 90.99/12.90 Prover 10: Warning: Problem contains reals, using incomplete axiomatisation % 90.99/12.90 Prover 11: Warning: Problem contains reals, using incomplete axiomatisation % 90.99/12.91 Prover 13: Warning: Problem contains reals, using incomplete axiomatisation % 98.01/13.83 Prover 7: Preprocessing ... % 98.01/13.84 Prover 10: Preprocessing ... % 98.01/13.86 Prover 8: Preprocessing ... % 98.56/13.87 Prover 11: Preprocessing ... % 99.07/13.93 Prover 13: Preprocessing ... % 105.60/14.91 Prover 8: Warning: ignoring some quantifiers % 105.60/14.99 Prover 10: Warning: ignoring some quantifiers % 107.36/15.04 Prover 11: Warning: ignoring some quantifiers % 107.36/15.04 Prover 8: Constructing countermodel ... % 107.52/15.05 Prover 7: Warning: ignoring some quantifiers % 107.62/15.09 Prover 10: Constructing countermodel ... % 108.01/15.11 Prover 13: Warning: ignoring some quantifiers % 108.01/15.12 Prover 11: Constructing countermodel ... % 108.01/15.14 Prover 7: Constructing countermodel ... % 108.31/15.19 Prover 13: Constructing countermodel ... % 114.74/16.01 Prover 1: stopped % 114.74/16.02 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 114.74/16.03 Prover 16: Warning: Problem contains reals, using incomplete axiomatisation % 118.79/16.59 Prover 16: Preprocessing ... % 121.74/16.96 Prover 13: stopped % 121.74/16.97 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 121.74/16.97 Prover 19: Warning: Problem contains reals, using incomplete axiomatisation % 126.02/17.53 Prover 16: Warning: ignoring some quantifiers % 126.44/17.54 Prover 19: Preprocessing ... % 126.58/17.61 Prover 16: Constructing countermodel ... % 127.48/17.69 Prover 10: Found proof (size 9) % 127.48/17.70 Prover 10: proved (4823ms) % 127.48/17.70 Prover 16: stopped % 127.48/17.70 Prover 11: stopped % 127.48/17.70 Prover 8: stopped % 127.48/17.71 Prover 7: stopped % 127.48/17.71 Prover 4: stopped % 130.10/18.25 Prover 19: Warning: ignoring some quantifiers % 130.33/18.31 Prover 19: Constructing countermodel ... % 130.33/18.31 Prover 19: stopped % 130.33/18.32 % 130.33/18.32 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 130.33/18.32 % 130.33/18.33 % SZS output start Proof for theBenchmark % 130.62/18.36 Assumptions after simplification: % 130.62/18.36 --------------------------------- % 130.62/18.36 % 130.62/18.36 (axiom2) % 130.62/18.36 A_n_vec_m_vec$(a$) & A_n_vec_m_vec$(b$) & equivalent_matrices$(a$, b$) % 130.62/18.36 % 130.62/18.36 (axiom8) % 130.69/18.37 ! [v0: A_n_vec_m_vec$] : ! [v1: A_n_vec_m_vec$] : ! [v2: A_m_vec_m_vec$] : % 130.69/18.37 ! [v3: A_n_vec_n_vec$] : ! [v4: A_m_vec_m_vec$] : ! [v5: A_n_vec_m_vec$] : ( % 130.69/18.37 ~ (matrix_inv$(v2) = v4) | ~ (matrix_matrix_mult$a(v4, v0) = v5) | ~ % 130.69/18.37 (matrix_matrix_mult$(v5, v3) = v1) | ~ A_n_vec_m_vec$(v1) | ~ % 130.69/18.37 A_n_vec_m_vec$(v0) | ~ A_n_vec_n_vec$(v3) | ~ A_m_vec_m_vec$(v2) | ~ % 130.69/18.37 invertible$(v2) | ~ invertible$a(v3) | equivalent_matrices$(v0, v1)) & ! % 130.69/18.37 [v0: A_n_vec_m_vec$] : ! [v1: A_n_vec_m_vec$] : ( ~ A_n_vec_m_vec$(v1) | ~ % 130.69/18.37 A_n_vec_m_vec$(v0) | ~ equivalent_matrices$(v0, v1) | ? [v2: % 130.69/18.37 A_m_vec_m_vec$] : ? [v3: A_n_vec_n_vec$] : ? [v4: A_m_vec_m_vec$] : ? % 130.69/18.37 [v5: A_n_vec_m_vec$] : (matrix_inv$(v2) = v4 & matrix_matrix_mult$a(v4, v0) % 130.69/18.37 = v5 & matrix_matrix_mult$(v5, v3) = v1 & A_n_vec_m_vec$(v5) & % 130.69/18.37 A_n_vec_n_vec$(v3) & A_m_vec_m_vec$(v4) & A_m_vec_m_vec$(v2) & % 130.69/18.37 invertible$(v2) & invertible$a(v3))) % 130.69/18.37 % 130.69/18.37 (conjecture0) % 130.69/18.37 ~ thesis$ % 130.69/18.37 % 130.69/18.37 (hypothesis1) % 130.69/18.37 A_n_vec_m_vec$(a$) & A_n_vec_m_vec$(b$) & ! [v0: A_m_vec_m_vec$] : ! [v1: % 130.69/18.37 A_n_vec_n_vec$] : ! [v2: A_m_vec_m_vec$] : ! [v3: A_n_vec_m_vec$] : ( ~ % 130.69/18.37 (matrix_inv$(v0) = v2) | ~ (matrix_matrix_mult$a(v2, a$) = v3) | ~ % 130.69/18.37 (matrix_matrix_mult$(v3, v1) = b$) | ~ A_n_vec_n_vec$(v1) | ~ % 130.69/18.37 A_m_vec_m_vec$(v0) | ~ invertible$(v0) | ~ invertible$a(v1) | thesis$) % 130.69/18.37 % 130.69/18.37 Further assumptions not needed in the proof: % 130.69/18.37 -------------------------------------------- % 130.69/18.38 axiom10, axiom100, axiom101, axiom102, axiom103, axiom104, axiom105, axiom106, % 130.69/18.38 axiom107, axiom108, axiom109, axiom11, axiom110, axiom111, axiom112, axiom113, % 130.69/18.38 axiom114, axiom115, axiom116, axiom117, axiom118, axiom119, axiom12, axiom120, % 130.69/18.38 axiom121, axiom122, axiom123, axiom124, axiom125, axiom126, axiom127, axiom128, % 130.69/18.38 axiom129, axiom13, axiom130, axiom131, axiom132, axiom133, axiom134, axiom135, % 130.69/18.38 axiom136, axiom137, axiom138, axiom139, axiom14, axiom140, axiom141, axiom142, % 130.69/18.38 axiom143, axiom144, axiom145, axiom146, axiom147, axiom148, axiom149, axiom15, % 130.69/18.38 axiom150, axiom151, axiom152, axiom153, axiom154, axiom155, axiom156, axiom157, % 130.69/18.38 axiom158, axiom159, axiom16, axiom160, axiom161, axiom162, axiom163, axiom164, % 130.69/18.38 axiom165, axiom166, axiom167, axiom168, axiom169, axiom17, axiom170, axiom171, % 130.69/18.38 axiom172, axiom173, axiom174, axiom175, axiom176, axiom177, axiom178, axiom179, % 130.69/18.38 axiom18, axiom180, axiom181, axiom182, axiom183, axiom184, axiom185, axiom186, % 130.69/18.38 axiom187, axiom188, axiom189, axiom19, axiom190, axiom191, axiom192, axiom193, % 130.69/18.38 axiom194, axiom195, axiom196, axiom197, axiom198, axiom199, axiom20, axiom200, % 130.69/18.38 axiom201, axiom202, axiom203, axiom204, axiom205, axiom206, axiom207, axiom208, % 130.69/18.38 axiom209, axiom21, axiom210, axiom211, axiom212, axiom213, axiom214, axiom215, % 130.69/18.38 axiom216, axiom217, axiom218, axiom219, axiom22, axiom220, axiom221, axiom222, % 130.69/18.38 axiom223, axiom224, axiom225, axiom226, axiom227, axiom228, axiom229, axiom23, % 130.69/18.38 axiom230, axiom231, axiom232, axiom233, axiom234, axiom235, axiom236, axiom237, % 130.69/18.38 axiom238, axiom239, axiom24, axiom240, axiom241, axiom242, axiom243, axiom244, % 130.69/18.38 axiom245, axiom246, axiom247, axiom248, axiom249, axiom25, axiom250, axiom251, % 130.69/18.38 axiom252, axiom253, axiom254, axiom255, axiom256, axiom257, axiom258, axiom259, % 130.69/18.38 axiom26, axiom260, axiom261, axiom262, axiom263, axiom264, axiom265, axiom266, % 130.69/18.38 axiom267, axiom268, axiom269, axiom27, axiom270, axiom271, axiom272, axiom273, % 130.69/18.38 axiom274, axiom275, axiom276, axiom277, axiom278, axiom279, axiom28, axiom280, % 130.69/18.38 axiom281, axiom282, axiom283, axiom284, axiom285, axiom286, axiom287, axiom288, % 130.69/18.38 axiom289, axiom29, axiom290, axiom291, axiom292, axiom293, axiom294, axiom295, % 130.69/18.38 axiom296, axiom297, axiom298, axiom299, axiom3, axiom30, axiom300, axiom301, % 130.69/18.38 axiom302, axiom303, axiom304, axiom305, axiom306, axiom307, axiom308, axiom309, % 130.69/18.38 axiom31, axiom310, axiom311, axiom312, axiom313, axiom314, axiom315, axiom316, % 130.69/18.38 axiom317, axiom318, axiom319, axiom32, axiom320, axiom321, axiom322, axiom323, % 130.69/18.38 axiom324, axiom325, axiom326, axiom327, axiom328, axiom329, axiom33, axiom330, % 130.69/18.38 axiom331, axiom332, axiom333, axiom334, axiom335, axiom336, axiom337, axiom338, % 130.69/18.38 axiom339, axiom34, axiom340, axiom341, axiom342, axiom343, axiom344, axiom345, % 130.69/18.38 axiom346, axiom347, axiom348, axiom349, axiom35, axiom350, axiom351, axiom352, % 130.69/18.38 axiom353, axiom354, axiom355, axiom356, axiom357, axiom358, axiom359, axiom36, % 130.69/18.38 axiom360, axiom361, axiom362, axiom363, axiom364, axiom365, axiom366, axiom367, % 130.69/18.38 axiom368, axiom369, axiom37, axiom370, axiom371, axiom372, axiom373, axiom374, % 130.69/18.38 axiom375, axiom376, axiom377, axiom378, axiom379, axiom38, axiom380, axiom381, % 130.69/18.38 axiom382, axiom383, axiom384, axiom385, axiom386, axiom387, axiom388, axiom389, % 130.69/18.38 axiom39, axiom390, axiom391, axiom392, axiom393, axiom394, axiom395, axiom396, % 130.69/18.38 axiom397, axiom398, axiom399, axiom4, axiom40, axiom400, axiom401, axiom402, % 130.69/18.38 axiom403, axiom404, axiom405, axiom406, axiom407, axiom408, axiom409, axiom41, % 130.69/18.38 axiom410, axiom411, axiom412, axiom413, axiom414, axiom415, axiom416, axiom417, % 130.69/18.38 axiom418, axiom419, axiom42, axiom420, axiom421, axiom422, axiom423, axiom424, % 130.69/18.38 axiom425, axiom426, axiom427, axiom428, axiom429, axiom43, axiom430, axiom431, % 130.69/18.38 axiom432, axiom433, axiom434, axiom435, axiom436, axiom437, axiom438, axiom439, % 130.69/18.38 axiom44, axiom440, axiom441, axiom442, axiom443, axiom444, axiom445, axiom446, % 130.69/18.38 axiom447, axiom448, axiom449, axiom45, axiom450, axiom451, axiom452, axiom453, % 130.69/18.38 axiom454, axiom455, axiom456, axiom457, axiom458, axiom459, axiom46, axiom460, % 130.69/18.38 axiom461, axiom462, axiom463, axiom464, axiom465, axiom466, axiom467, axiom468, % 130.69/18.38 axiom469, axiom47, axiom470, axiom471, axiom472, axiom473, axiom474, axiom475, % 130.69/18.38 axiom476, axiom477, axiom478, axiom479, axiom48, axiom480, axiom481, axiom482, % 130.69/18.38 axiom483, axiom484, axiom485, axiom486, axiom487, axiom488, axiom489, axiom49, % 130.69/18.38 axiom490, axiom491, axiom492, axiom493, axiom494, axiom495, axiom496, axiom497, % 130.69/18.38 axiom498, axiom499, axiom5, axiom50, axiom500, axiom501, axiom502, axiom503, % 130.69/18.38 axiom504, axiom505, axiom506, axiom507, axiom508, axiom509, axiom51, axiom510, % 130.69/18.38 axiom511, axiom512, axiom513, axiom514, axiom515, axiom516, axiom517, axiom518, % 130.69/18.38 axiom519, axiom52, axiom520, axiom521, axiom522, axiom523, axiom524, axiom525, % 130.69/18.38 axiom526, axiom527, axiom528, axiom529, axiom53, axiom530, axiom531, axiom532, % 130.69/18.38 axiom533, axiom534, axiom535, axiom536, axiom537, axiom538, axiom539, axiom54, % 130.69/18.38 axiom540, axiom541, axiom542, axiom543, axiom544, axiom545, axiom546, axiom547, % 130.69/18.38 axiom548, axiom549, axiom55, axiom550, axiom551, axiom552, axiom553, axiom554, % 130.69/18.38 axiom555, axiom556, axiom557, axiom558, axiom559, axiom56, axiom560, axiom561, % 130.69/18.38 axiom562, axiom563, axiom564, axiom565, axiom566, axiom567, axiom568, axiom569, % 130.69/18.38 axiom57, axiom570, axiom571, axiom572, axiom573, axiom574, axiom575, axiom576, % 130.69/18.38 axiom577, axiom578, axiom579, axiom58, axiom580, axiom581, axiom582, axiom583, % 130.69/18.38 axiom584, axiom585, axiom586, axiom587, axiom588, axiom589, axiom59, axiom590, % 130.69/18.38 axiom591, axiom592, axiom593, axiom594, axiom595, axiom596, axiom597, axiom598, % 130.69/18.38 axiom599, axiom6, axiom60, axiom600, axiom601, axiom602, axiom603, axiom604, % 130.69/18.38 axiom605, axiom606, axiom607, axiom608, axiom609, axiom61, axiom610, axiom611, % 130.69/18.38 axiom612, axiom613, axiom614, axiom615, axiom616, axiom617, axiom618, axiom619, % 130.69/18.38 axiom62, axiom620, axiom621, axiom622, axiom623, axiom624, axiom625, axiom626, % 130.69/18.38 axiom627, axiom628, axiom629, axiom63, axiom630, axiom631, axiom632, axiom633, % 130.69/18.38 axiom634, axiom635, axiom636, axiom64, axiom65, axiom66, axiom67, axiom68, % 130.69/18.38 axiom69, axiom7, axiom70, axiom71, axiom72, axiom73, axiom74, axiom75, axiom76, % 130.69/18.38 axiom77, axiom78, axiom79, axiom80, axiom81, axiom82, axiom83, axiom84, axiom85, % 130.69/18.38 axiom86, axiom87, axiom88, axiom89, axiom9, axiom90, axiom91, axiom92, axiom93, % 130.69/18.38 axiom94, axiom95, axiom96, axiom97, axiom98, axiom99, formula_638, formula_639 % 130.69/18.38 % 130.69/18.38 Those formulas are unsatisfiable: % 130.69/18.38 --------------------------------- % 130.69/18.38 % 130.69/18.38 Begin of proof % 130.69/18.38 | % 130.69/18.38 | ALPHA: (hypothesis1) implies: % 130.69/18.38 | (1) ! [v0: A_m_vec_m_vec$] : ! [v1: A_n_vec_n_vec$] : ! [v2: % 130.69/18.38 | A_m_vec_m_vec$] : ! [v3: A_n_vec_m_vec$] : ( ~ (matrix_inv$(v0) = % 130.69/18.38 | v2) | ~ (matrix_matrix_mult$a(v2, a$) = v3) | ~ % 130.69/18.38 | (matrix_matrix_mult$(v3, v1) = b$) | ~ A_n_vec_n_vec$(v1) | ~ % 130.69/18.38 | A_m_vec_m_vec$(v0) | ~ invertible$(v0) | ~ invertible$a(v1) | % 130.69/18.38 | thesis$) % 130.69/18.38 | % 130.69/18.38 | ALPHA: (axiom2) implies: % 130.69/18.38 | (2) equivalent_matrices$(a$, b$) % 130.69/18.38 | (3) A_n_vec_m_vec$(b$) % 130.69/18.38 | (4) A_n_vec_m_vec$(a$) % 130.69/18.38 | % 130.69/18.38 | ALPHA: (axiom8) implies: % 130.69/18.38 | (5) ! [v0: A_n_vec_m_vec$] : ! [v1: A_n_vec_m_vec$] : ( ~ % 130.69/18.38 | A_n_vec_m_vec$(v1) | ~ A_n_vec_m_vec$(v0) | ~ % 130.69/18.38 | equivalent_matrices$(v0, v1) | ? [v2: A_m_vec_m_vec$] : ? [v3: % 130.69/18.38 | A_n_vec_n_vec$] : ? [v4: A_m_vec_m_vec$] : ? [v5: A_n_vec_m_vec$] % 130.69/18.38 | : (matrix_inv$(v2) = v4 & matrix_matrix_mult$a(v4, v0) = v5 & % 130.69/18.38 | matrix_matrix_mult$(v5, v3) = v1 & A_n_vec_m_vec$(v5) & % 130.69/18.38 | A_n_vec_n_vec$(v3) & A_m_vec_m_vec$(v4) & A_m_vec_m_vec$(v2) & % 130.69/18.38 | invertible$(v2) & invertible$a(v3))) % 130.69/18.38 | % 130.69/18.38 | GROUND_INST: instantiating (5) with a$, b$, simplifying with (2), (3), (4) % 130.69/18.38 | gives: % 130.69/18.39 | (6) ? [v0: A_m_vec_m_vec$] : ? [v1: A_n_vec_n_vec$] : ? [v2: % 130.69/18.39 | A_m_vec_m_vec$] : ? [v3: A_n_vec_m_vec$] : (matrix_inv$(v0) = v2 & % 130.69/18.39 | matrix_matrix_mult$a(v2, a$) = v3 & matrix_matrix_mult$(v3, v1) = b$ % 130.69/18.39 | & A_n_vec_m_vec$(v3) & A_n_vec_n_vec$(v1) & A_m_vec_m_vec$(v2) & % 130.69/18.39 | A_m_vec_m_vec$(v0) & invertible$(v0) & invertible$a(v1)) % 130.69/18.39 | % 130.69/18.39 | DELTA: instantiating (6) with fresh symbols all_814_0, all_814_1, all_814_2, % 130.69/18.39 | all_814_3 gives: % 130.69/18.39 | (7) matrix_inv$(all_814_3) = all_814_1 & matrix_matrix_mult$a(all_814_1, % 130.69/18.39 | a$) = all_814_0 & matrix_matrix_mult$(all_814_0, all_814_2) = b$ & % 130.69/18.39 | A_n_vec_m_vec$(all_814_0) & A_n_vec_n_vec$(all_814_2) & % 130.69/18.39 | A_m_vec_m_vec$(all_814_1) & A_m_vec_m_vec$(all_814_3) & % 130.69/18.39 | invertible$(all_814_3) & invertible$a(all_814_2) % 130.69/18.39 | % 130.69/18.39 | ALPHA: (7) implies: % 130.69/18.39 | (8) invertible$a(all_814_2) % 130.69/18.39 | (9) invertible$(all_814_3) % 130.69/18.39 | (10) A_m_vec_m_vec$(all_814_3) % 130.69/18.39 | (11) A_n_vec_n_vec$(all_814_2) % 130.69/18.39 | (12) matrix_matrix_mult$(all_814_0, all_814_2) = b$ % 130.69/18.39 | (13) matrix_matrix_mult$a(all_814_1, a$) = all_814_0 % 130.69/18.39 | (14) matrix_inv$(all_814_3) = all_814_1 % 130.69/18.39 | % 130.69/18.39 | GROUND_INST: instantiating (1) with all_814_3, all_814_2, all_814_1, % 130.69/18.39 | all_814_0, simplifying with (8), (9), (10), (11), (12), (13), % 130.69/18.39 | (14), (conjecture0) gives: % 130.69/18.39 | (15) $false % 130.69/18.39 | % 130.69/18.39 | CLOSE: (15) is inconsistent. % 130.69/18.39 | % 130.69/18.39 End of proof % 130.69/18.39 % SZS output end Proof for theBenchmark % 130.69/18.39 % 130.69/18.39 17755ms %------------------------------------------------------------------------------