%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET926+1 : TPTP v8.1.2. Released v3.2.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n021.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 15:27:04 EDT 2023 % Result : Theorem 3.41s 1.48s % Output : Proof 4.87s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.14 % Problem : SET926+1 : TPTP v8.1.2. Released v3.2.0. % 0.00/0.15 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.15/0.36 % Computer : n021.cluster.edu % 0.15/0.36 % Model : x86_64 x86_64 % 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.36 % Memory : 8042.1875MB % 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.37 % CPULimit : 300 % 0.15/0.37 % WCLimit : 300 % 0.15/0.37 % DateTime : Sat Aug 26 11:45:57 EDT 2023 % 0.15/0.37 % 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 ... % 0.22/0.64 Running up to 7 provers in parallel. % 0.22/0.66 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.22/0.66 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.22/0.66 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 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 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 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 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 1.69/1.03 Prover 1: Preprocessing ... % 1.69/1.03 Prover 4: Preprocessing ... % 2.06/1.07 Prover 0: Preprocessing ... % 2.06/1.07 Prover 5: Preprocessing ... % 2.06/1.07 Prover 3: Preprocessing ... % 2.06/1.07 Prover 6: Preprocessing ... % 2.06/1.07 Prover 2: Preprocessing ... % 3.13/1.30 Prover 6: Constructing countermodel ... % 3.13/1.31 Prover 1: Constructing countermodel ... % 3.13/1.31 Prover 3: Constructing countermodel ... % 3.13/1.32 Prover 5: Proving ... % 3.13/1.32 Prover 2: Proving ... % 3.13/1.32 Prover 4: Constructing countermodel ... % 3.13/1.33 Prover 0: Proving ... % 3.41/1.46 Prover 3: proved (793ms) % 3.41/1.46 % 3.41/1.48 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 3.41/1.48 % 3.41/1.48 Prover 6: stopped % 3.41/1.48 Prover 2: stopped % 3.41/1.49 Prover 5: stopped % 3.41/1.49 Prover 0: stopped % 3.93/1.50 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 3.93/1.50 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 3.93/1.50 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 3.93/1.50 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 3.93/1.51 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 3.93/1.51 Prover 7: Preprocessing ... % 3.93/1.52 Prover 13: Preprocessing ... % 3.93/1.53 Prover 11: Preprocessing ... % 3.93/1.53 Prover 8: Preprocessing ... % 3.93/1.53 Prover 10: Preprocessing ... % 4.26/1.54 Prover 7: Constructing countermodel ... % 4.26/1.56 Prover 1: Found proof (size 19) % 4.26/1.56 Prover 1: proved (904ms) % 4.26/1.57 Prover 7: stopped % 4.44/1.58 Prover 4: Found proof (size 19) % 4.44/1.58 Prover 4: proved (909ms) % 4.44/1.58 Prover 8: Warning: ignoring some quantifiers % 4.44/1.58 Prover 8: Constructing countermodel ... % 4.44/1.58 Prover 13: Warning: ignoring some quantifiers % 4.44/1.59 Prover 8: stopped % 4.44/1.59 Prover 13: Constructing countermodel ... % 4.44/1.60 Prover 13: stopped % 4.44/1.60 Prover 10: Constructing countermodel ... % 4.44/1.60 Prover 10: stopped % 4.74/1.63 Prover 11: Constructing countermodel ... % 4.74/1.64 Prover 11: stopped % 4.74/1.64 % 4.74/1.64 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 4.74/1.64 % 4.74/1.64 % SZS output start Proof for theBenchmark % 4.74/1.64 Assumptions after simplification: % 4.74/1.64 --------------------------------- % 4.74/1.64 % 4.74/1.64 (l34_zfmisc_1) % 4.87/1.68 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v2 | ~ % 4.87/1.68 (singleton(v0) = v2) | ~ (set_difference(v2, v1) = v3) | ~ $i(v1) | ~ % 4.87/1.68 $i(v0) | in(v0, v1) = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 4.87/1.68 (singleton(v0) = v2) | ~ (set_difference(v2, v1) = v2) | ~ $i(v1) | ~ % 4.87/1.68 $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & in(v0, v1) = v3)) % 4.87/1.68 % 4.87/1.68 (l36_zfmisc_1) % 4.87/1.68 $i(empty_set) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = % 4.87/1.68 empty_set | ~ (singleton(v0) = v2) | ~ (set_difference(v2, v1) = v3) | ~ % 4.87/1.68 $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & in(v0, v1) = v4)) & ! % 4.87/1.68 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (singleton(v0) = v2) | ~ % 4.87/1.68 (set_difference(v2, v1) = empty_set) | ~ $i(v1) | ~ $i(v0) | in(v0, v1) = % 4.87/1.68 0) % 4.87/1.68 % 4.87/1.68 (t69_zfmisc_1) % 4.87/1.68 $i(empty_set) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ( ~ % 4.87/1.69 (v3 = v2) & ~ (v3 = empty_set) & singleton(v0) = v2 & set_difference(v2, % 4.87/1.69 v1) = v3 & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 4.87/1.69 % 4.87/1.69 (function-axioms) % 4.87/1.69 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 4.87/1.69 (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0)) & ! [v0: % 4.87/1.69 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 4.87/1.69 : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0: $i] : ! % 4.87/1.69 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ % 4.87/1.69 (singleton(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 4.87/1.69 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (empty(v2) = v1) | ~ % 4.87/1.69 (empty(v2) = v0)) % 4.87/1.69 % 4.87/1.69 Further assumptions not needed in the proof: % 4.87/1.69 -------------------------------------------- % 4.87/1.69 antisymmetry_r2_hidden, fc1_xboole_0, rc1_xboole_0, rc2_xboole_0 % 4.87/1.69 % 4.87/1.69 Those formulas are unsatisfiable: % 4.87/1.69 --------------------------------- % 4.87/1.69 % 4.87/1.69 Begin of proof % 4.87/1.69 | % 4.87/1.69 | ALPHA: (l34_zfmisc_1) implies: % 4.87/1.70 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v2 | ~ % 4.87/1.70 | (singleton(v0) = v2) | ~ (set_difference(v2, v1) = v3) | ~ $i(v1) | % 4.87/1.70 | ~ $i(v0) | in(v0, v1) = 0) % 4.87/1.70 | % 4.87/1.70 | ALPHA: (l36_zfmisc_1) implies: % 4.87/1.70 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = empty_set % 4.87/1.70 | | ~ (singleton(v0) = v2) | ~ (set_difference(v2, v1) = v3) | ~ % 4.87/1.70 | $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & in(v0, v1) = v4)) % 4.87/1.70 | % 4.87/1.70 | ALPHA: (t69_zfmisc_1) implies: % 4.87/1.70 | (3) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ( ~ (v3 = v2) & % 4.87/1.70 | ~ (v3 = empty_set) & singleton(v0) = v2 & set_difference(v2, v1) = % 4.87/1.70 | v3 & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 4.87/1.70 | % 4.87/1.70 | ALPHA: (function-axioms) implies: % 4.87/1.70 | (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 4.87/1.70 | ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) % 4.87/1.70 | % 4.87/1.70 | DELTA: instantiating (3) with fresh symbols all_11_0, all_11_1, all_11_2, % 4.87/1.70 | all_11_3 gives: % 4.87/1.71 | (5) ~ (all_11_0 = all_11_1) & ~ (all_11_0 = empty_set) & % 4.87/1.71 | singleton(all_11_3) = all_11_1 & set_difference(all_11_1, all_11_2) = % 4.87/1.71 | all_11_0 & $i(all_11_0) & $i(all_11_1) & $i(all_11_2) & $i(all_11_3) % 4.87/1.71 | % 4.87/1.71 | ALPHA: (5) implies: % 4.87/1.71 | (6) ~ (all_11_0 = empty_set) % 4.87/1.71 | (7) ~ (all_11_0 = all_11_1) % 4.87/1.71 | (8) $i(all_11_3) % 4.87/1.71 | (9) $i(all_11_2) % 4.87/1.71 | (10) set_difference(all_11_1, all_11_2) = all_11_0 % 4.87/1.71 | (11) singleton(all_11_3) = all_11_1 % 4.87/1.71 | % 4.87/1.71 | GROUND_INST: instantiating (1) with all_11_3, all_11_2, all_11_1, all_11_0, % 4.87/1.71 | simplifying with (8), (9), (10), (11) gives: % 4.87/1.71 | (12) all_11_0 = all_11_1 | in(all_11_3, all_11_2) = 0 % 4.87/1.71 | % 4.87/1.71 | GROUND_INST: instantiating (2) with all_11_3, all_11_2, all_11_1, all_11_0, % 4.87/1.71 | simplifying with (8), (9), (10), (11) gives: % 4.87/1.71 | (13) all_11_0 = empty_set | ? [v0: int] : ( ~ (v0 = 0) & in(all_11_3, % 4.87/1.71 | all_11_2) = v0) % 4.87/1.71 | % 4.87/1.71 | BETA: splitting (13) gives: % 4.87/1.71 | % 4.87/1.71 | Case 1: % 4.87/1.71 | | % 4.87/1.71 | | (14) all_11_0 = empty_set % 4.87/1.71 | | % 4.87/1.71 | | REDUCE: (6), (14) imply: % 4.87/1.71 | | (15) $false % 4.87/1.72 | | % 4.87/1.72 | | CLOSE: (15) is inconsistent. % 4.87/1.72 | | % 4.87/1.72 | Case 2: % 4.87/1.72 | | % 4.87/1.72 | | (16) ? [v0: int] : ( ~ (v0 = 0) & in(all_11_3, all_11_2) = v0) % 4.87/1.72 | | % 4.87/1.72 | | DELTA: instantiating (16) with fresh symbol all_20_0 gives: % 4.87/1.72 | | (17) ~ (all_20_0 = 0) & in(all_11_3, all_11_2) = all_20_0 % 4.87/1.72 | | % 4.87/1.72 | | ALPHA: (17) implies: % 4.87/1.72 | | (18) ~ (all_20_0 = 0) % 4.87/1.72 | | (19) in(all_11_3, all_11_2) = all_20_0 % 4.87/1.72 | | % 4.87/1.72 | | BETA: splitting (12) gives: % 4.87/1.72 | | % 4.87/1.72 | | Case 1: % 4.87/1.72 | | | % 4.87/1.72 | | | (20) in(all_11_3, all_11_2) = 0 % 4.87/1.72 | | | % 4.87/1.72 | | | GROUND_INST: instantiating (4) with 0, all_20_0, all_11_2, all_11_3, % 4.87/1.72 | | | simplifying with (19), (20) gives: % 4.87/1.72 | | | (21) all_20_0 = 0 % 4.87/1.72 | | | % 4.87/1.72 | | | REDUCE: (18), (21) imply: % 4.87/1.72 | | | (22) $false % 4.87/1.72 | | | % 4.87/1.72 | | | CLOSE: (22) is inconsistent. % 4.87/1.72 | | | % 4.87/1.72 | | Case 2: % 4.87/1.72 | | | % 4.87/1.72 | | | (23) all_11_0 = all_11_1 % 4.87/1.72 | | | % 4.87/1.72 | | | REDUCE: (7), (23) imply: % 4.87/1.72 | | | (24) $false % 4.87/1.72 | | | % 4.87/1.72 | | | CLOSE: (24) is inconsistent. % 4.87/1.72 | | | % 4.87/1.72 | | End of split % 4.87/1.72 | | % 4.87/1.72 | End of split % 4.87/1.72 | % 4.87/1.72 End of proof % 4.87/1.72 % SZS output end Proof for theBenchmark % 4.87/1.72 % 4.87/1.72 1093ms %------------------------------------------------------------------------------