%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET954+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 : n008.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 15:27:11 EDT 2023 % Result : Theorem 4.28s 1.30s % Output : Proof 5.62s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET954+1 : TPTP v8.1.2. Released v3.2.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.34 % Computer : n008.cluster.edu % 0.14/0.34 % Model : x86_64 x86_64 % 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.34 % Memory : 8042.1875MB % 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.34 % CPULimit : 300 % 0.14/0.34 % WCLimit : 300 % 0.14/0.34 % DateTime : Sat Aug 26 08:36:17 EDT 2023 % 0.20/0.34 % CPUTime : % 0.20/0.60 ________ _____ % 0.20/0.60 ___ __ \_________(_)________________________________ % 0.20/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.60 % 0.20/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.60 (2023-06-19) % 0.20/0.60 % 0.20/0.60 (c) Philipp Rümmer, 2009-2023 % 0.20/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.60 Amanda Stjerna. % 0.20/0.60 Free software under BSD-3-Clause. % 0.20/0.60 % 0.20/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.60 % 0.20/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.20/0.61 Running up to 7 provers in parallel. % 0.20/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.21/0.97 Prover 1: Preprocessing ... % 2.21/0.97 Prover 4: Preprocessing ... % 2.21/1.01 Prover 0: Preprocessing ... % 2.21/1.01 Prover 3: Preprocessing ... % 2.21/1.01 Prover 5: Preprocessing ... % 2.21/1.01 Prover 2: Preprocessing ... % 2.21/1.01 Prover 6: Preprocessing ... % 3.62/1.18 Prover 6: Constructing countermodel ... % 3.62/1.18 Prover 1: Constructing countermodel ... % 3.62/1.19 Prover 5: Proving ... % 3.62/1.20 Prover 4: Constructing countermodel ... % 3.62/1.20 Prover 3: Constructing countermodel ... % 3.62/1.21 Prover 2: Proving ... % 4.05/1.23 Prover 0: Proving ... % 4.28/1.30 Prover 3: proved (677ms) % 4.28/1.30 % 4.28/1.30 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 4.28/1.30 % 4.28/1.30 Prover 0: stopped % 4.28/1.30 Prover 2: stopped % 4.28/1.31 Prover 5: stopped % 4.28/1.31 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 4.28/1.31 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 4.28/1.31 Prover 6: stopped % 4.28/1.31 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 4.28/1.31 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 4.28/1.32 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 4.82/1.33 Prover 8: Preprocessing ... % 4.82/1.33 Prover 10: Preprocessing ... % 4.82/1.33 Prover 7: Preprocessing ... % 4.82/1.34 Prover 11: Preprocessing ... % 4.82/1.36 Prover 13: Preprocessing ... % 4.82/1.38 Prover 10: Constructing countermodel ... % 4.82/1.39 Prover 4: Found proof (size 19) % 4.82/1.39 Prover 4: proved (763ms) % 4.82/1.39 Prover 1: stopped % 4.82/1.39 Prover 10: stopped % 4.82/1.40 Prover 7: Constructing countermodel ... % 4.82/1.40 Prover 7: stopped % 4.82/1.40 Prover 11: Constructing countermodel ... % 4.82/1.41 Prover 11: stopped % 4.82/1.41 Prover 13: Warning: ignoring some quantifiers % 4.82/1.41 Prover 8: Warning: ignoring some quantifiers % 4.82/1.42 Prover 8: Constructing countermodel ... % 4.82/1.42 Prover 13: Constructing countermodel ... % 4.82/1.42 Prover 8: stopped % 4.82/1.42 Prover 13: stopped % 4.82/1.42 % 4.82/1.42 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 4.82/1.42 % 4.82/1.43 % SZS output start Proof for theBenchmark % 4.82/1.43 Assumptions after simplification: % 4.82/1.43 --------------------------------- % 4.82/1.43 % 4.82/1.43 (l55_zfmisc_1) % 4.82/1.46 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 4.82/1.46 $i] : ! [v6: int] : (v6 = 0 | ~ (cartesian_product2(v2, v3) = v5) | ~ % 4.82/1.46 (ordered_pair(v0, v1) = v4) | ~ (in(v4, v5) = v6) | ~ $i(v3) | ~ $i(v2) | % 4.82/1.46 ~ $i(v1) | ~ $i(v0) | ? [v7: any] : ? [v8: any] : (in(v1, v3) = v8 & % 4.82/1.46 in(v0, v2) = v7 & ( ~ (v8 = 0) | ~ (v7 = 0)))) & ! [v0: $i] : ! [v1: % 4.82/1.46 $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ % 4.82/1.46 (cartesian_product2(v2, v3) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ % 4.82/1.46 (in(v4, v5) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | (in(v1, % 4.82/1.47 v3) = 0 & in(v0, v2) = 0)) % 4.82/1.47 % 4.82/1.47 (t107_zfmisc_1) % 4.82/1.47 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 4.82/1.47 $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: int] : ( ~ (v8 = 0) & % 4.82/1.47 cartesian_product2(v3, v2) = v7 & cartesian_product2(v2, v3) = v5 & % 4.82/1.47 ordered_pair(v1, v0) = v6 & ordered_pair(v0, v1) = v4 & in(v6, v7) = v8 & % 4.82/1.47 in(v4, v5) = 0 & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & % 4.82/1.47 $i(v1) & $i(v0)) % 4.82/1.47 % 4.82/1.47 (function-axioms) % 4.82/1.47 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 4.82/1.47 (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) = v0)) & % 4.82/1.47 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 4.82/1.47 (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0)) & ! [v0: $i] % 4.82/1.47 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (unordered_pair(v3, % 4.82/1.47 v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0: % 4.82/1.47 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 4.82/1.47 : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0: % 4.82/1.47 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 4.82/1.47 ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 4.82/1.47 [v2: $i] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) % 4.82/1.47 % 4.82/1.47 Further assumptions not needed in the proof: % 4.82/1.47 -------------------------------------------- % 4.82/1.48 antisymmetry_r2_hidden, commutativity_k2_tarski, d5_tarski, fc1_zfmisc_1, % 4.82/1.48 rc1_xboole_0, rc2_xboole_0 % 4.82/1.48 % 4.82/1.48 Those formulas are unsatisfiable: % 4.82/1.48 --------------------------------- % 4.82/1.48 % 4.82/1.48 Begin of proof % 4.82/1.48 | % 4.82/1.48 | ALPHA: (l55_zfmisc_1) implies: % 4.82/1.48 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 4.82/1.48 | ! [v5: $i] : ( ~ (cartesian_product2(v2, v3) = v5) | ~ % 4.82/1.48 | (ordered_pair(v0, v1) = v4) | ~ (in(v4, v5) = 0) | ~ $i(v3) | ~ % 4.82/1.48 | $i(v2) | ~ $i(v1) | ~ $i(v0) | (in(v1, v3) = 0 & in(v0, v2) = 0)) % 4.82/1.48 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 4.82/1.48 | ! [v5: $i] : ! [v6: int] : (v6 = 0 | ~ (cartesian_product2(v2, v3) = % 4.82/1.48 | v5) | ~ (ordered_pair(v0, v1) = v4) | ~ (in(v4, v5) = v6) | ~ % 4.82/1.48 | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v7: any] : ? [v8: % 4.82/1.48 | any] : (in(v1, v3) = v8 & in(v0, v2) = v7 & ( ~ (v8 = 0) | ~ (v7 = % 4.82/1.48 | 0)))) % 4.82/1.48 | % 4.82/1.48 | ALPHA: (function-axioms) implies: % 4.82/1.49 | (3) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 4.82/1.49 | ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) % 4.82/1.49 | % 4.82/1.49 | DELTA: instantiating (t107_zfmisc_1) with fresh symbols all_12_0, all_12_1, % 4.82/1.49 | all_12_2, all_12_3, all_12_4, all_12_5, all_12_6, all_12_7, all_12_8 % 4.82/1.49 | gives: % 4.82/1.49 | (4) ~ (all_12_0 = 0) & cartesian_product2(all_12_5, all_12_6) = all_12_1 & % 4.82/1.49 | cartesian_product2(all_12_6, all_12_5) = all_12_3 & % 4.82/1.49 | ordered_pair(all_12_7, all_12_8) = all_12_2 & ordered_pair(all_12_8, % 4.82/1.49 | all_12_7) = all_12_4 & in(all_12_2, all_12_1) = all_12_0 & % 4.82/1.49 | in(all_12_4, all_12_3) = 0 & $i(all_12_1) & $i(all_12_2) & $i(all_12_3) % 4.82/1.49 | & $i(all_12_4) & $i(all_12_5) & $i(all_12_6) & $i(all_12_7) & % 4.82/1.49 | $i(all_12_8) % 4.82/1.49 | % 4.82/1.49 | ALPHA: (4) implies: % 5.62/1.49 | (5) ~ (all_12_0 = 0) % 5.62/1.49 | (6) $i(all_12_8) % 5.62/1.49 | (7) $i(all_12_7) % 5.62/1.49 | (8) $i(all_12_6) % 5.62/1.49 | (9) $i(all_12_5) % 5.62/1.49 | (10) in(all_12_4, all_12_3) = 0 % 5.62/1.49 | (11) in(all_12_2, all_12_1) = all_12_0 % 5.62/1.49 | (12) ordered_pair(all_12_8, all_12_7) = all_12_4 % 5.62/1.49 | (13) ordered_pair(all_12_7, all_12_8) = all_12_2 % 5.62/1.49 | (14) cartesian_product2(all_12_6, all_12_5) = all_12_3 % 5.62/1.49 | (15) cartesian_product2(all_12_5, all_12_6) = all_12_1 % 5.62/1.49 | % 5.62/1.49 | GROUND_INST: instantiating (1) with all_12_8, all_12_7, all_12_6, all_12_5, % 5.62/1.49 | all_12_4, all_12_3, simplifying with (6), (7), (8), (9), (10), % 5.62/1.49 | (12), (14) gives: % 5.62/1.50 | (16) in(all_12_7, all_12_5) = 0 & in(all_12_8, all_12_6) = 0 % 5.62/1.50 | % 5.62/1.50 | ALPHA: (16) implies: % 5.62/1.50 | (17) in(all_12_8, all_12_6) = 0 % 5.62/1.50 | (18) in(all_12_7, all_12_5) = 0 % 5.62/1.50 | % 5.62/1.50 | GROUND_INST: instantiating (2) with all_12_7, all_12_8, all_12_5, all_12_6, % 5.62/1.50 | all_12_2, all_12_1, all_12_0, simplifying with (6), (7), (8), % 5.62/1.50 | (9), (11), (13), (15) gives: % 5.62/1.50 | (19) all_12_0 = 0 | ? [v0: any] : ? [v1: any] : (in(all_12_7, all_12_5) = % 5.62/1.50 | v0 & in(all_12_8, all_12_6) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 5.62/1.50 | % 5.62/1.50 | BETA: splitting (19) gives: % 5.62/1.50 | % 5.62/1.50 | Case 1: % 5.62/1.50 | | % 5.62/1.50 | | (20) all_12_0 = 0 % 5.62/1.50 | | % 5.62/1.50 | | REDUCE: (5), (20) imply: % 5.62/1.50 | | (21) $false % 5.62/1.50 | | % 5.62/1.50 | | CLOSE: (21) is inconsistent. % 5.62/1.50 | | % 5.62/1.50 | Case 2: % 5.62/1.50 | | % 5.62/1.50 | | (22) ? [v0: any] : ? [v1: any] : (in(all_12_7, all_12_5) = v0 & % 5.62/1.50 | | in(all_12_8, all_12_6) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 5.62/1.50 | | % 5.62/1.50 | | DELTA: instantiating (22) with fresh symbols all_34_0, all_34_1 gives: % 5.62/1.50 | | (23) in(all_12_7, all_12_5) = all_34_1 & in(all_12_8, all_12_6) = % 5.62/1.50 | | all_34_0 & ( ~ (all_34_0 = 0) | ~ (all_34_1 = 0)) % 5.62/1.50 | | % 5.62/1.50 | | ALPHA: (23) implies: % 5.62/1.50 | | (24) in(all_12_8, all_12_6) = all_34_0 % 5.62/1.50 | | (25) in(all_12_7, all_12_5) = all_34_1 % 5.62/1.50 | | (26) ~ (all_34_0 = 0) | ~ (all_34_1 = 0) % 5.62/1.50 | | % 5.62/1.50 | | GROUND_INST: instantiating (3) with 0, all_34_0, all_12_6, all_12_8, % 5.62/1.50 | | simplifying with (17), (24) gives: % 5.62/1.50 | | (27) all_34_0 = 0 % 5.62/1.50 | | % 5.62/1.50 | | GROUND_INST: instantiating (3) with 0, all_34_1, all_12_5, all_12_7, % 5.62/1.50 | | simplifying with (18), (25) gives: % 5.62/1.50 | | (28) all_34_1 = 0 % 5.62/1.50 | | % 5.62/1.50 | | BETA: splitting (26) gives: % 5.62/1.50 | | % 5.62/1.50 | | Case 1: % 5.62/1.50 | | | % 5.62/1.50 | | | (29) ~ (all_34_0 = 0) % 5.62/1.50 | | | % 5.62/1.50 | | | REDUCE: (27), (29) imply: % 5.62/1.50 | | | (30) $false % 5.62/1.50 | | | % 5.62/1.50 | | | CLOSE: (30) is inconsistent. % 5.62/1.50 | | | % 5.62/1.50 | | Case 2: % 5.62/1.50 | | | % 5.62/1.50 | | | (31) ~ (all_34_1 = 0) % 5.62/1.50 | | | % 5.62/1.50 | | | REDUCE: (28), (31) imply: % 5.62/1.50 | | | (32) $false % 5.62/1.50 | | | % 5.62/1.50 | | | CLOSE: (32) is inconsistent. % 5.62/1.50 | | | % 5.62/1.50 | | End of split % 5.62/1.50 | | % 5.62/1.50 | End of split % 5.62/1.50 | % 5.62/1.50 End of proof % 5.62/1.51 % SZS output end Proof for theBenchmark % 5.62/1.51 % 5.62/1.51 903ms %------------------------------------------------------------------------------