%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SEU219+1 : TPTP v8.1.2. Released v3.3.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n018.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 17:43:21 EDT 2023 % Result : Theorem 4.94s 1.44s % Output : Proof 7.62s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU219+1 : TPTP v8.1.2. Released v3.3.0. % 0.00/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.33 % Computer : n018.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 300 % 0.12/0.33 % DateTime : Wed Aug 23 17:50:56 EDT 2023 % 0.12/0.34 % CPUTime : % 0.19/0.60 ________ _____ % 0.19/0.60 ___ __ \_________(_)________________________________ % 0.19/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.61 % 0.19/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.61 (2023-06-19) % 0.19/0.61 % 0.19/0.61 (c) Philipp Rümmer, 2009-2023 % 0.19/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.61 Amanda Stjerna. % 0.19/0.61 Free software under BSD-3-Clause. % 0.19/0.61 % 0.19/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.61 % 0.19/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.19/0.62 Running up to 7 provers in parallel. % 0.19/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 1.79/0.98 Prover 1: Preprocessing ... % 1.79/0.98 Prover 4: Preprocessing ... % 2.27/1.02 Prover 2: Preprocessing ... % 2.27/1.02 Prover 3: Preprocessing ... % 2.27/1.02 Prover 6: Preprocessing ... % 2.27/1.02 Prover 0: Preprocessing ... % 2.27/1.02 Prover 5: Preprocessing ... % 3.81/1.25 Prover 3: Constructing countermodel ... % 3.81/1.26 Prover 1: Constructing countermodel ... % 3.81/1.27 Prover 6: Constructing countermodel ... % 4.30/1.28 Prover 5: Constructing countermodel ... % 4.30/1.29 Prover 2: Proving ... % 4.30/1.33 Prover 4: Constructing countermodel ... % 4.94/1.43 Prover 0: Proving ... % 4.94/1.44 Prover 3: proved (808ms) % 4.94/1.44 % 4.94/1.44 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 4.94/1.44 % 4.94/1.44 Prover 6: stopped % 4.94/1.44 Prover 5: stopped % 4.94/1.45 Prover 2: stopped % 4.94/1.45 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 4.94/1.45 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 4.94/1.45 Prover 0: stopped % 4.94/1.46 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 4.94/1.47 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 4.94/1.47 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 4.94/1.47 Prover 8: Preprocessing ... % 4.94/1.47 Prover 10: Preprocessing ... % 4.94/1.48 Prover 7: Preprocessing ... % 5.13/1.49 Prover 13: Preprocessing ... % 5.13/1.51 Prover 11: Preprocessing ... % 6.06/1.54 Prover 10: Constructing countermodel ... % 6.06/1.56 Prover 8: Warning: ignoring some quantifiers % 6.06/1.56 Prover 7: Constructing countermodel ... % 6.06/1.57 Prover 8: Constructing countermodel ... % 6.06/1.59 Prover 13: Constructing countermodel ... % 6.66/1.62 Prover 11: Constructing countermodel ... % 7.10/1.70 Prover 10: Found proof (size 27) % 7.10/1.70 Prover 10: proved (248ms) % 7.10/1.70 Prover 11: stopped % 7.10/1.70 Prover 13: stopped % 7.10/1.70 Prover 8: stopped % 7.10/1.70 Prover 1: stopped % 7.10/1.70 Prover 4: stopped % 7.10/1.71 Prover 7: Found proof (size 24) % 7.10/1.71 Prover 7: proved (263ms) % 7.10/1.71 % 7.10/1.71 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 7.10/1.71 % 7.10/1.71 % SZS output start Proof for theBenchmark % 7.10/1.71 Assumptions after simplification: % 7.10/1.71 --------------------------------- % 7.10/1.71 % 7.10/1.71 (d9_funct_1) % 7.10/1.74 ! [v0: $i] : ! [v1: $i] : ( ~ (function_inverse(v0) = v1) | ~ $i(v0) | ~ % 7.10/1.74 one_to_one(v0) | ~ function(v0) | ~ relation(v0) | (relation_inverse(v0) = % 7.10/1.74 v1 & $i(v1))) % 7.10/1.74 % 7.10/1.74 (dt_k2_funct_1) % 7.10/1.74 ! [v0: $i] : ! [v1: $i] : ( ~ (function_inverse(v0) = v1) | ~ $i(v0) | ~ % 7.10/1.74 function(v0) | ~ relation(v0) | function(v1)) & ! [v0: $i] : ! [v1: $i] : % 7.10/1.74 ( ~ (function_inverse(v0) = v1) | ~ $i(v0) | ~ function(v0) | ~ % 7.10/1.74 relation(v0) | relation(v1)) % 7.10/1.74 % 7.10/1.74 (involutiveness_k4_relat_1) % 7.10/1.75 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_inverse(v0) = v1) | ~ $i(v0) | ~ % 7.10/1.75 relation(v0) | relation_inverse(v1) = v0) % 7.10/1.75 % 7.10/1.75 (t37_relat_1) % 7.10/1.75 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) | ~ % 7.10/1.75 relation(v0) | ? [v2: $i] : ? [v3: $i] : (relation_dom(v2) = v1 & % 7.10/1.75 relation_dom(v0) = v3 & relation_rng(v2) = v3 & relation_inverse(v0) = v2 % 7.10/1.75 & $i(v3) & $i(v2) & $i(v1))) % 7.10/1.75 % 7.10/1.75 (t55_funct_1) % 7.10/1.75 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 7.10/1.75 $i] : (function_inverse(v0) = v2 & $i(v2) & $i(v0) & one_to_one(v0) & % 7.10/1.75 function(v0) & relation(v0) & (( ~ (v5 = v4) & relation_dom(v0) = v4 & % 7.10/1.75 relation_rng(v2) = v5 & $i(v5) & $i(v4)) | ( ~ (v3 = v1) & % 7.10/1.75 relation_dom(v2) = v3 & relation_rng(v0) = v1 & $i(v3) & $i(v1)))) % 7.10/1.75 % 7.10/1.75 (function-axioms) % 7.10/1.76 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (relation_dom(v2) = % 7.10/1.76 v1) | ~ (relation_dom(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 7.10/1.76 $i] : (v1 = v0 | ~ (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0)) & % 7.10/1.76 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (function_inverse(v2) = % 7.10/1.76 v1) | ~ (function_inverse(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 7.10/1.76 [v2: $i] : (v1 = v0 | ~ (relation_inverse(v2) = v1) | ~ % 7.10/1.76 (relation_inverse(v2) = v0)) % 7.10/1.76 % 7.10/1.76 Further assumptions not needed in the proof: % 7.10/1.76 -------------------------------------------- % 7.10/1.76 dt_k1_relat_1, dt_k2_relat_1, dt_k4_relat_1, fc3_funct_1, rc1_funct_1, % 7.10/1.76 rc3_funct_1 % 7.10/1.76 % 7.10/1.76 Those formulas are unsatisfiable: % 7.10/1.76 --------------------------------- % 7.10/1.76 % 7.10/1.76 Begin of proof % 7.10/1.76 | % 7.10/1.76 | ALPHA: (dt_k2_funct_1) implies: % 7.10/1.76 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (function_inverse(v0) = v1) | ~ $i(v0) % 7.10/1.76 | | ~ function(v0) | ~ relation(v0) | relation(v1)) % 7.10/1.76 | % 7.10/1.76 | ALPHA: (function-axioms) implies: % 7.10/1.76 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 7.10/1.76 | (relation_inverse(v2) = v1) | ~ (relation_inverse(v2) = v0)) % 7.53/1.76 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 7.53/1.76 | (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0)) % 7.53/1.76 | % 7.53/1.76 | DELTA: instantiating (t55_funct_1) with fresh symbols all_13_0, all_13_1, % 7.53/1.76 | all_13_2, all_13_3, all_13_4, all_13_5 gives: % 7.53/1.77 | (4) function_inverse(all_13_5) = all_13_3 & $i(all_13_3) & $i(all_13_5) & % 7.53/1.77 | one_to_one(all_13_5) & function(all_13_5) & relation(all_13_5) & (( ~ % 7.53/1.77 | (all_13_0 = all_13_1) & relation_dom(all_13_5) = all_13_1 & % 7.53/1.77 | relation_rng(all_13_3) = all_13_0 & $i(all_13_0) & $i(all_13_1)) | % 7.53/1.77 | ( ~ (all_13_2 = all_13_4) & relation_dom(all_13_3) = all_13_2 & % 7.53/1.77 | relation_rng(all_13_5) = all_13_4 & $i(all_13_2) & $i(all_13_4))) % 7.53/1.77 | % 7.53/1.77 | ALPHA: (4) implies: % 7.53/1.77 | (5) relation(all_13_5) % 7.53/1.77 | (6) function(all_13_5) % 7.53/1.77 | (7) one_to_one(all_13_5) % 7.53/1.77 | (8) $i(all_13_5) % 7.53/1.77 | (9) function_inverse(all_13_5) = all_13_3 % 7.53/1.77 | (10) ( ~ (all_13_0 = all_13_1) & relation_dom(all_13_5) = all_13_1 & % 7.53/1.77 | relation_rng(all_13_3) = all_13_0 & $i(all_13_0) & $i(all_13_1)) | ( % 7.53/1.77 | ~ (all_13_2 = all_13_4) & relation_dom(all_13_3) = all_13_2 & % 7.53/1.77 | relation_rng(all_13_5) = all_13_4 & $i(all_13_2) & $i(all_13_4)) % 7.53/1.77 | % 7.53/1.77 | GROUND_INST: instantiating (d9_funct_1) with all_13_5, all_13_3, simplifying % 7.53/1.77 | with (5), (6), (7), (8), (9) gives: % 7.53/1.77 | (11) relation_inverse(all_13_5) = all_13_3 & $i(all_13_3) % 7.53/1.77 | % 7.53/1.77 | ALPHA: (11) implies: % 7.53/1.77 | (12) $i(all_13_3) % 7.53/1.77 | (13) relation_inverse(all_13_5) = all_13_3 % 7.53/1.77 | % 7.53/1.77 | GROUND_INST: instantiating (1) with all_13_5, all_13_3, simplifying with (5), % 7.53/1.77 | (6), (8), (9) gives: % 7.53/1.77 | (14) relation(all_13_3) % 7.53/1.77 | % 7.53/1.77 | GROUND_INST: instantiating (involutiveness_k4_relat_1) with all_13_5, % 7.53/1.77 | all_13_3, simplifying with (5), (8), (13) gives: % 7.53/1.77 | (15) relation_inverse(all_13_3) = all_13_5 % 7.53/1.77 | % 7.53/1.77 | BETA: splitting (10) gives: % 7.53/1.77 | % 7.53/1.77 | Case 1: % 7.53/1.77 | | % 7.53/1.77 | | (16) ~ (all_13_0 = all_13_1) & relation_dom(all_13_5) = all_13_1 & % 7.53/1.77 | | relation_rng(all_13_3) = all_13_0 & $i(all_13_0) & $i(all_13_1) % 7.53/1.77 | | % 7.53/1.77 | | ALPHA: (16) implies: % 7.53/1.77 | | (17) ~ (all_13_0 = all_13_1) % 7.53/1.77 | | (18) relation_rng(all_13_3) = all_13_0 % 7.53/1.77 | | (19) relation_dom(all_13_5) = all_13_1 % 7.53/1.77 | | % 7.53/1.77 | | GROUND_INST: instantiating (t37_relat_1) with all_13_3, all_13_0, % 7.53/1.77 | | simplifying with (12), (14), (18) gives: % 7.53/1.78 | | (20) ? [v0: $i] : ? [v1: $i] : (relation_dom(v0) = all_13_0 & % 7.53/1.78 | | relation_dom(all_13_3) = v1 & relation_rng(v0) = v1 & % 7.53/1.78 | | relation_inverse(all_13_3) = v0 & $i(v1) & $i(v0) & $i(all_13_0)) % 7.53/1.78 | | % 7.53/1.78 | | DELTA: instantiating (20) with fresh symbols all_39_0, all_39_1 gives: % 7.53/1.78 | | (21) relation_dom(all_39_1) = all_13_0 & relation_dom(all_13_3) = % 7.53/1.78 | | all_39_0 & relation_rng(all_39_1) = all_39_0 & % 7.53/1.78 | | relation_inverse(all_13_3) = all_39_1 & $i(all_39_0) & $i(all_39_1) % 7.53/1.78 | | & $i(all_13_0) % 7.53/1.78 | | % 7.53/1.78 | | ALPHA: (21) implies: % 7.53/1.78 | | (22) relation_inverse(all_13_3) = all_39_1 % 7.53/1.78 | | (23) relation_dom(all_39_1) = all_13_0 % 7.53/1.78 | | % 7.53/1.78 | | GROUND_INST: instantiating (2) with all_13_5, all_39_1, all_13_3, % 7.53/1.78 | | simplifying with (15), (22) gives: % 7.53/1.78 | | (24) all_39_1 = all_13_5 % 7.53/1.78 | | % 7.53/1.78 | | REDUCE: (23), (24) imply: % 7.53/1.78 | | (25) relation_dom(all_13_5) = all_13_0 % 7.53/1.78 | | % 7.53/1.78 | | GROUND_INST: instantiating (3) with all_13_1, all_13_0, all_13_5, % 7.53/1.78 | | simplifying with (19), (25) gives: % 7.53/1.78 | | (26) all_13_0 = all_13_1 % 7.53/1.78 | | % 7.53/1.78 | | REDUCE: (17), (26) imply: % 7.53/1.78 | | (27) $false % 7.62/1.78 | | % 7.62/1.78 | | CLOSE: (27) is inconsistent. % 7.62/1.78 | | % 7.62/1.78 | Case 2: % 7.62/1.78 | | % 7.62/1.78 | | (28) ~ (all_13_2 = all_13_4) & relation_dom(all_13_3) = all_13_2 & % 7.62/1.78 | | relation_rng(all_13_5) = all_13_4 & $i(all_13_2) & $i(all_13_4) % 7.62/1.78 | | % 7.62/1.78 | | ALPHA: (28) implies: % 7.62/1.78 | | (29) ~ (all_13_2 = all_13_4) % 7.62/1.79 | | (30) relation_rng(all_13_5) = all_13_4 % 7.62/1.79 | | (31) relation_dom(all_13_3) = all_13_2 % 7.62/1.79 | | % 7.62/1.79 | | GROUND_INST: instantiating (t37_relat_1) with all_13_5, all_13_4, % 7.62/1.79 | | simplifying with (5), (8), (30) gives: % 7.62/1.79 | | (32) ? [v0: $i] : ? [v1: $i] : (relation_dom(v0) = all_13_4 & % 7.62/1.79 | | relation_dom(all_13_5) = v1 & relation_rng(v0) = v1 & % 7.62/1.79 | | relation_inverse(all_13_5) = v0 & $i(v1) & $i(v0) & $i(all_13_4)) % 7.62/1.79 | | % 7.62/1.79 | | DELTA: instantiating (32) with fresh symbols all_39_0, all_39_1 gives: % 7.62/1.79 | | (33) relation_dom(all_39_1) = all_13_4 & relation_dom(all_13_5) = % 7.62/1.79 | | all_39_0 & relation_rng(all_39_1) = all_39_0 & % 7.62/1.79 | | relation_inverse(all_13_5) = all_39_1 & $i(all_39_0) & $i(all_39_1) % 7.62/1.79 | | & $i(all_13_4) % 7.62/1.79 | | % 7.62/1.79 | | ALPHA: (33) implies: % 7.62/1.79 | | (34) relation_inverse(all_13_5) = all_39_1 % 7.62/1.79 | | (35) relation_dom(all_39_1) = all_13_4 % 7.62/1.79 | | % 7.62/1.79 | | GROUND_INST: instantiating (2) with all_13_3, all_39_1, all_13_5, % 7.62/1.79 | | simplifying with (13), (34) gives: % 7.62/1.79 | | (36) all_39_1 = all_13_3 % 7.62/1.79 | | % 7.62/1.79 | | REDUCE: (35), (36) imply: % 7.62/1.79 | | (37) relation_dom(all_13_3) = all_13_4 % 7.62/1.79 | | % 7.62/1.79 | | GROUND_INST: instantiating (3) with all_13_2, all_13_4, all_13_3, % 7.62/1.79 | | simplifying with (31), (37) gives: % 7.62/1.79 | | (38) all_13_2 = all_13_4 % 7.62/1.79 | | % 7.62/1.79 | | REDUCE: (29), (38) imply: % 7.62/1.79 | | (39) $false % 7.62/1.79 | | % 7.62/1.79 | | CLOSE: (39) is inconsistent. % 7.62/1.79 | | % 7.62/1.79 | End of split % 7.62/1.79 | % 7.62/1.79 End of proof % 7.62/1.79 % SZS output end Proof for theBenchmark % 7.62/1.79 % 7.62/1.79 1185ms %------------------------------------------------------------------------------