%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SEU230+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 : n029.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 17:43:30 EDT 2023 % Result : Theorem 8.29s 1.87s % Output : Proof 10.93s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU230+1 : TPTP v8.1.2. Released v3.3.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.17/0.34 % Computer : n029.cluster.edu % 0.17/0.34 % Model : x86_64 x86_64 % 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.34 % Memory : 8042.1875MB % 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.34 % CPULimit : 300 % 0.17/0.34 % WCLimit : 300 % 0.17/0.34 % DateTime : Wed Aug 23 12:41:38 EDT 2023 % 0.17/0.34 % CPUTime : % 0.19/0.61 ________ _____ % 0.19/0.61 ___ __ \_________(_)________________________________ % 0.19/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 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/sandbox2/benchmark/theBenchmark.p ... % 0.19/0.62 Running up to 7 provers in parallel. % 0.19/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.44/1.03 Prover 1: Preprocessing ... % 2.44/1.03 Prover 4: Preprocessing ... % 2.94/1.07 Prover 6: Preprocessing ... % 2.94/1.07 Prover 5: Preprocessing ... % 2.94/1.07 Prover 2: Preprocessing ... % 2.94/1.07 Prover 3: Preprocessing ... % 2.94/1.07 Prover 0: Preprocessing ... % 5.03/1.45 Prover 1: Warning: ignoring some quantifiers % 5.62/1.48 Prover 4: Warning: ignoring some quantifiers % 5.62/1.48 Prover 3: Warning: ignoring some quantifiers % 5.62/1.49 Prover 6: Proving ... % 5.62/1.50 Prover 2: Proving ... % 5.62/1.50 Prover 1: Constructing countermodel ... % 5.62/1.50 Prover 3: Constructing countermodel ... % 5.62/1.50 Prover 5: Proving ... % 5.91/1.51 Prover 4: Constructing countermodel ... % 5.91/1.54 Prover 0: Proving ... % 7.74/1.77 Prover 3: gave up % 7.74/1.77 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 8.05/1.84 Prover 1: gave up % 8.05/1.84 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 8.29/1.85 Prover 7: Preprocessing ... % 8.29/1.87 Prover 8: Preprocessing ... % 8.29/1.87 Prover 0: proved (1245ms) % 8.29/1.87 % 8.29/1.87 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 8.29/1.87 % 8.29/1.87 Prover 5: stopped % 8.29/1.87 Prover 2: stopped % 8.29/1.87 Prover 6: stopped % 8.29/1.88 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 8.29/1.88 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 8.29/1.88 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 8.29/1.89 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 8.29/1.92 Prover 11: Preprocessing ... % 8.29/1.92 Prover 13: Preprocessing ... % 8.29/1.93 Prover 16: Preprocessing ... % 8.95/1.95 Prover 10: Preprocessing ... % 8.95/1.96 Prover 7: Warning: ignoring some quantifiers % 8.95/1.97 Prover 7: Constructing countermodel ... % 9.32/2.03 Prover 8: Warning: ignoring some quantifiers % 9.32/2.03 Prover 10: Warning: ignoring some quantifiers % 9.32/2.04 Prover 10: Constructing countermodel ... % 9.32/2.04 Prover 16: Warning: ignoring some quantifiers % 9.32/2.05 Prover 16: Constructing countermodel ... % 9.32/2.08 Prover 8: Constructing countermodel ... % 9.32/2.10 Prover 13: Warning: ignoring some quantifiers % 9.32/2.11 Prover 13: Constructing countermodel ... % 9.32/2.14 Prover 7: Found proof (size 14) % 9.32/2.14 Prover 7: proved (375ms) % 9.32/2.14 Prover 8: stopped % 9.32/2.15 Prover 16: stopped % 9.32/2.15 Prover 13: stopped % 9.32/2.15 Prover 10: gave up % 9.32/2.15 Prover 4: stopped % 9.32/2.16 Prover 11: Warning: ignoring some quantifiers % 10.58/2.17 Prover 11: Constructing countermodel ... % 10.58/2.18 Prover 11: stopped % 10.58/2.18 % 10.58/2.18 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 10.58/2.18 % 10.64/2.18 % SZS output start Proof for theBenchmark % 10.64/2.19 Assumptions after simplification: % 10.64/2.19 --------------------------------- % 10.64/2.19 % 10.64/2.19 (commutativity_k2_xboole_0) % 10.64/2.21 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_union2(v1, v0) = v2) | ~ % 10.64/2.21 $i(v1) | ~ $i(v0) | (set_union2(v0, v1) = v2 & $i(v2))) & ! [v0: $i] : ! % 10.64/2.21 [v1: $i] : ! [v2: $i] : ( ~ (set_union2(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) % 10.64/2.21 | (set_union2(v1, v0) = v2 & $i(v2))) % 10.64/2.21 % 10.64/2.21 (d1_ordinal1) % 10.64/2.22 ! [v0: $i] : ! [v1: $i] : ( ~ (succ(v0) = v1) | ~ $i(v0) | ? [v2: $i] : % 10.64/2.22 (singleton(v0) = v2 & set_union2(v0, v2) = v1 & $i(v2) & $i(v1))) & ! [v0: % 10.64/2.22 $i] : ! [v1: $i] : ( ~ (singleton(v0) = v1) | ~ $i(v0) | ? [v2: $i] : % 10.64/2.22 (succ(v0) = v2 & set_union2(v0, v1) = v2 & $i(v2))) % 10.64/2.22 % 10.64/2.22 (d1_tarski) % 10.64/2.22 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ (singleton(v0) = v1) | % 10.64/2.22 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ in(v2, v1)) & ? [v0: $i] : ! [v1: % 10.64/2.22 $i] : ! [v2: $i] : (v2 = v0 | ~ (singleton(v1) = v2) | ~ $i(v1) | ~ % 10.64/2.22 $i(v0) | ? [v3: $i] : ($i(v3) & ( ~ (v3 = v1) | ~ in(v1, v0)) & (v3 = v1 | % 10.64/2.22 in(v3, v0)))) & ! [v0: $i] : ! [v1: $i] : ( ~ (singleton(v0) = v1) | % 10.64/2.22 ~ $i(v1) | ~ $i(v0) | in(v0, v1)) % 10.64/2.22 % 10.64/2.22 (d2_xboole_0) % 10.86/2.23 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (set_union2(v0, % 10.86/2.23 v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ in(v3, % 10.86/2.23 v2) | in(v3, v1) | in(v3, v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 10.86/2.23 ! [v3: $i] : ( ~ (set_union2(v0, v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~ % 10.86/2.23 $i(v1) | ~ $i(v0) | ~ in(v3, v1) | in(v3, v2)) & ! [v0: $i] : ! [v1: $i] % 10.86/2.23 : ! [v2: $i] : ! [v3: $i] : ( ~ (set_union2(v0, v1) = v2) | ~ $i(v3) | ~ % 10.86/2.23 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ in(v3, v0) | in(v3, v2)) & ? [v0: $i] : % 10.86/2.23 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~ (set_union2(v1, v2) = % 10.86/2.23 v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : ($i(v4) & ( ~ % 10.86/2.23 in(v4, v0) | ( ~ in(v4, v2) & ~ in(v4, v1))) & (in(v4, v2) | in(v4, v1) % 10.86/2.23 | in(v4, v0)))) % 10.86/2.23 % 10.86/2.23 (t10_ordinal1) % 10.86/2.23 ? [v0: $i] : ? [v1: $i] : (succ(v0) = v1 & $i(v1) & $i(v0) & ~ in(v0, v1)) % 10.86/2.23 % 10.86/2.23 Further assumptions not needed in the proof: % 10.86/2.23 -------------------------------------------- % 10.86/2.23 antisymmetry_r2_hidden, cc1_funct_1, cc1_relat_1, cc2_funct_1, dt_k1_ordinal1, % 10.86/2.23 dt_k1_tarski, dt_k1_xboole_0, dt_k2_xboole_0, dt_m1_subset_1, % 10.86/2.23 existence_m1_subset_1, fc12_relat_1, fc1_ordinal1, fc1_xboole_0, fc2_relat_1, % 10.86/2.23 fc2_xboole_0, fc3_xboole_0, fc4_relat_1, idempotence_k2_xboole_0, rc1_funct_1, % 10.86/2.23 rc1_relat_1, rc1_xboole_0, rc2_funct_1, rc2_relat_1, rc2_xboole_0, rc3_funct_1, % 10.86/2.23 rc3_relat_1, rc4_funct_1, t1_boole, t1_subset, t2_subset, t6_boole, t7_boole, % 10.86/2.23 t8_boole % 10.86/2.23 % 10.86/2.23 Those formulas are unsatisfiable: % 10.86/2.23 --------------------------------- % 10.86/2.23 % 10.86/2.23 Begin of proof % 10.86/2.23 | % 10.86/2.23 | ALPHA: (commutativity_k2_xboole_0) implies: % 10.86/2.23 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_union2(v1, v0) = v2) % 10.86/2.23 | | ~ $i(v1) | ~ $i(v0) | (set_union2(v0, v1) = v2 & $i(v2))) % 10.86/2.23 | % 10.86/2.23 | ALPHA: (d1_ordinal1) implies: % 10.86/2.23 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (succ(v0) = v1) | ~ $i(v0) | ? [v2: % 10.86/2.23 | $i] : (singleton(v0) = v2 & set_union2(v0, v2) = v1 & $i(v2) & % 10.86/2.23 | $i(v1))) % 10.86/2.23 | % 10.86/2.23 | ALPHA: (d1_tarski) implies: % 10.86/2.23 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ (singleton(v0) = v1) | ~ $i(v1) | ~ % 10.86/2.23 | $i(v0) | in(v0, v1)) % 10.86/2.23 | % 10.86/2.23 | ALPHA: (d2_xboole_0) implies: % 10.86/2.24 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 10.86/2.24 | (set_union2(v0, v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 10.86/2.24 | $i(v0) | ~ in(v3, v0) | in(v3, v2)) % 10.86/2.24 | % 10.86/2.24 | DELTA: instantiating (t10_ordinal1) with fresh symbols all_38_0, all_38_1 % 10.86/2.24 | gives: % 10.86/2.24 | (5) succ(all_38_1) = all_38_0 & $i(all_38_0) & $i(all_38_1) & ~ % 10.86/2.24 | in(all_38_1, all_38_0) % 10.86/2.24 | % 10.86/2.24 | ALPHA: (5) implies: % 10.86/2.24 | (6) ~ in(all_38_1, all_38_0) % 10.86/2.24 | (7) $i(all_38_1) % 10.86/2.24 | (8) succ(all_38_1) = all_38_0 % 10.86/2.24 | % 10.86/2.24 | GROUND_INST: instantiating (2) with all_38_1, all_38_0, simplifying with (7), % 10.86/2.24 | (8) gives: % 10.86/2.24 | (9) ? [v0: $i] : (singleton(all_38_1) = v0 & set_union2(all_38_1, v0) = % 10.86/2.24 | all_38_0 & $i(v0) & $i(all_38_0)) % 10.86/2.24 | % 10.86/2.24 | DELTA: instantiating (9) with fresh symbol all_58_0 gives: % 10.86/2.24 | (10) singleton(all_38_1) = all_58_0 & set_union2(all_38_1, all_58_0) = % 10.86/2.24 | all_38_0 & $i(all_58_0) & $i(all_38_0) % 10.86/2.24 | % 10.86/2.24 | ALPHA: (10) implies: % 10.93/2.24 | (11) $i(all_58_0) % 10.93/2.24 | (12) set_union2(all_38_1, all_58_0) = all_38_0 % 10.93/2.24 | (13) singleton(all_38_1) = all_58_0 % 10.93/2.24 | % 10.93/2.24 | GROUND_INST: instantiating (1) with all_58_0, all_38_1, all_38_0, simplifying % 10.93/2.24 | with (7), (11), (12) gives: % 10.93/2.24 | (14) set_union2(all_58_0, all_38_1) = all_38_0 & $i(all_38_0) % 10.93/2.24 | % 10.93/2.24 | ALPHA: (14) implies: % 10.93/2.24 | (15) $i(all_38_0) % 10.93/2.24 | (16) set_union2(all_58_0, all_38_1) = all_38_0 % 10.93/2.24 | % 10.93/2.24 | GROUND_INST: instantiating (3) with all_38_1, all_58_0, simplifying with (7), % 10.93/2.24 | (11), (13) gives: % 10.93/2.24 | (17) in(all_38_1, all_58_0) % 10.93/2.24 | % 10.93/2.24 | GROUND_INST: instantiating (4) with all_58_0, all_38_1, all_38_0, all_38_1, % 10.93/2.24 | simplifying with (6), (7), (11), (15), (16), (17) gives: % 10.93/2.24 | (18) $false % 10.93/2.25 | % 10.93/2.25 | CLOSE: (18) is inconsistent. % 10.93/2.25 | % 10.93/2.25 End of proof % 10.93/2.25 % SZS output end Proof for theBenchmark % 10.93/2.25 % 10.93/2.25 1637ms %------------------------------------------------------------------------------