%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SEU133+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 : n016.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 17:42:41 EDT 2023 % Result : Theorem 5.70s 1.52s % Output : Proof 6.57s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU133+1 : TPTP v8.1.2. Released v3.3.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.34 % Computer : n016.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 300 % 0.12/0.34 % DateTime : Wed Aug 23 17:02:22 EDT 2023 % 0.12/0.34 % 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 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 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 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 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 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 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 % 2.23/1.01 Prover 1: Preprocessing ... % 2.23/1.01 Prover 4: Preprocessing ... % 2.23/1.05 Prover 3: Preprocessing ... % 2.23/1.05 Prover 6: Preprocessing ... % 2.23/1.05 Prover 5: Preprocessing ... % 2.23/1.05 Prover 0: Preprocessing ... % 2.23/1.05 Prover 2: Preprocessing ... % 4.28/1.33 Prover 1: Warning: ignoring some quantifiers % 4.28/1.33 Prover 4: Warning: ignoring some quantifiers % 4.28/1.33 Prover 3: Warning: ignoring some quantifiers % 4.28/1.33 Prover 6: Proving ... % 4.28/1.34 Prover 2: Proving ... % 4.28/1.34 Prover 5: Proving ... % 4.28/1.34 Prover 1: Constructing countermodel ... % 4.28/1.34 Prover 3: Constructing countermodel ... % 4.28/1.35 Prover 4: Constructing countermodel ... % 4.28/1.36 Prover 0: Proving ... % 5.00/1.51 Prover 3: proved (878ms) % 5.00/1.51 % 5.70/1.52 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 5.70/1.52 % 5.70/1.52 Prover 6: stopped % 5.70/1.52 Prover 5: stopped % 5.74/1.53 Prover 2: stopped % 5.74/1.53 Prover 0: stopped % 5.74/1.53 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 5.74/1.53 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 5.74/1.53 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 5.74/1.53 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 5.74/1.54 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 5.74/1.55 Prover 7: Preprocessing ... % 5.74/1.55 Prover 8: Preprocessing ... % 5.74/1.56 Prover 10: Preprocessing ... % 5.74/1.57 Prover 11: Preprocessing ... % 5.74/1.57 Prover 1: Found proof (size 23) % 5.74/1.57 Prover 1: proved (944ms) % 5.74/1.57 Prover 4: stopped % 5.74/1.57 Prover 10: stopped % 5.74/1.58 Prover 13: Preprocessing ... % 5.74/1.59 Prover 7: stopped % 5.74/1.60 Prover 13: stopped % 6.22/1.61 Prover 11: stopped % 6.22/1.63 Prover 8: Warning: ignoring some quantifiers % 6.22/1.63 Prover 8: Constructing countermodel ... % 6.22/1.64 Prover 8: stopped % 6.22/1.64 % 6.22/1.64 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 6.22/1.64 % 6.22/1.64 % SZS output start Proof for theBenchmark % 6.22/1.65 Assumptions after simplification: % 6.22/1.65 --------------------------------- % 6.22/1.65 % 6.22/1.65 (d3_tarski) % 6.22/1.67 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2) % 6.22/1.67 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & in(v3, % 6.57/1.67 v1) = v4 & in(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 6.57/1.67 (subset(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ! [v2: $i] : ( ~ (in(v2, v0) % 6.57/1.67 = 0) | ~ $i(v2) | in(v2, v1) = 0)) % 6.57/1.67 % 6.57/1.67 (d4_xboole_0) % 6.57/1.68 ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~ % 6.57/1.68 (set_difference(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: % 6.57/1.68 $i] : ? [v5: any] : ? [v6: any] : ? [v7: any] : (in(v4, v2) = v7 & % 6.57/1.68 in(v4, v1) = v6 & in(v4, v0) = v5 & $i(v4) & ( ~ (v6 = 0) | ~ (v5 = 0) | % 6.57/1.68 v7 = 0) & (v5 = 0 | (v6 = 0 & ~ (v7 = 0))))) & ! [v0: $i] : ! [v1: % 6.57/1.68 $i] : ! [v2: $i] : ( ~ (set_difference(v0, v1) = v2) | ~ $i(v2) | ~ % 6.57/1.68 $i(v1) | ~ $i(v0) | ( ! [v3: $i] : ! [v4: any] : ( ~ (in(v3, v0) = v4) | % 6.57/1.68 ~ $i(v3) | ? [v5: any] : ? [v6: any] : (in(v3, v2) = v5 & in(v3, v1) = % 6.57/1.68 v6 & ( ~ (v5 = 0) | (v4 = 0 & ~ (v6 = 0))))) & ! [v3: $i] : ( ~ % 6.57/1.68 (in(v3, v0) = 0) | ~ $i(v3) | ? [v4: any] : ? [v5: any] : (in(v3, v2) % 6.57/1.68 = v5 & in(v3, v1) = v4 & (v5 = 0 | v4 = 0))))) % 6.57/1.68 % 6.57/1.68 (t36_xboole_1) % 6.57/1.68 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & % 6.57/1.68 set_difference(v0, v1) = v2 & subset(v2, v0) = v3 & $i(v2) & $i(v1) & % 6.57/1.68 $i(v0)) % 6.57/1.68 % 6.57/1.68 (function-axioms) % 6.57/1.69 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 6.57/1.69 (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0)) & ! [v0: % 6.57/1.69 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 6.57/1.69 : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0: % 6.57/1.69 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 6.57/1.69 : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0: % 6.57/1.69 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 6.57/1.69 ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) % 6.57/1.69 % 6.57/1.69 Further assumptions not needed in the proof: % 6.57/1.69 -------------------------------------------- % 6.57/1.69 antisymmetry_r2_hidden, dt_k1_xboole_0, dt_k4_xboole_0, fc1_xboole_0, % 6.57/1.69 rc1_xboole_0, rc2_xboole_0, reflexivity_r1_tarski, t3_boole, t4_boole, t6_boole, % 6.57/1.69 t7_boole, t8_boole % 6.57/1.69 % 6.57/1.69 Those formulas are unsatisfiable: % 6.57/1.69 --------------------------------- % 6.57/1.69 % 6.57/1.69 Begin of proof % 6.57/1.69 | % 6.57/1.69 | ALPHA: (d3_tarski) implies: % 6.57/1.69 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) % 6.57/1.69 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ % 6.57/1.69 | (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0 & $i(v3))) % 6.57/1.69 | % 6.57/1.69 | ALPHA: (d4_xboole_0) implies: % 6.57/1.69 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_difference(v0, v1) = % 6.57/1.69 | v2) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ( ! [v3: $i] : ! [v4: % 6.57/1.69 | any] : ( ~ (in(v3, v0) = v4) | ~ $i(v3) | ? [v5: any] : ? [v6: % 6.57/1.69 | any] : (in(v3, v2) = v5 & in(v3, v1) = v6 & ( ~ (v5 = 0) | (v4 % 6.57/1.69 | = 0 & ~ (v6 = 0))))) & ! [v3: $i] : ( ~ (in(v3, v0) = 0) % 6.57/1.69 | | ~ $i(v3) | ? [v4: any] : ? [v5: any] : (in(v3, v2) = v5 & % 6.57/1.69 | in(v3, v1) = v4 & (v5 = 0 | v4 = 0))))) % 6.57/1.69 | % 6.57/1.69 | ALPHA: (function-axioms) implies: % 6.57/1.69 | (3) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 6.57/1.69 | ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) % 6.57/1.69 | % 6.57/1.70 | DELTA: instantiating (t36_xboole_1) with fresh symbols all_18_0, all_18_1, % 6.57/1.70 | all_18_2, all_18_3 gives: % 6.57/1.70 | (4) ~ (all_18_0 = 0) & set_difference(all_18_3, all_18_2) = all_18_1 & % 6.57/1.70 | subset(all_18_1, all_18_3) = all_18_0 & $i(all_18_1) & $i(all_18_2) & % 6.57/1.70 | $i(all_18_3) % 6.57/1.70 | % 6.57/1.70 | ALPHA: (4) implies: % 6.57/1.70 | (5) ~ (all_18_0 = 0) % 6.57/1.70 | (6) $i(all_18_3) % 6.57/1.70 | (7) $i(all_18_2) % 6.57/1.70 | (8) $i(all_18_1) % 6.57/1.70 | (9) subset(all_18_1, all_18_3) = all_18_0 % 6.57/1.70 | (10) set_difference(all_18_3, all_18_2) = all_18_1 % 6.57/1.70 | % 6.57/1.70 | GROUND_INST: instantiating (1) with all_18_1, all_18_3, all_18_0, simplifying % 6.57/1.70 | with (6), (8), (9) gives: % 6.57/1.70 | (11) all_18_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0, % 6.57/1.70 | all_18_1) = 0 & in(v0, all_18_3) = v1 & $i(v0)) % 6.57/1.70 | % 6.57/1.70 | GROUND_INST: instantiating (2) with all_18_3, all_18_2, all_18_1, simplifying % 6.57/1.70 | with (6), (7), (8), (10) gives: % 6.57/1.70 | (12) ! [v0: $i] : ! [v1: any] : ( ~ (in(v0, all_18_3) = v1) | ~ $i(v0) | % 6.57/1.70 | ? [v2: any] : ? [v3: any] : (in(v0, all_18_1) = v2 & in(v0, % 6.57/1.70 | all_18_2) = v3 & ( ~ (v2 = 0) | (v1 = 0 & ~ (v3 = 0))))) & ! % 6.57/1.70 | [v0: $i] : ( ~ (in(v0, all_18_3) = 0) | ~ $i(v0) | ? [v1: any] : ? % 6.57/1.70 | [v2: any] : (in(v0, all_18_1) = v2 & in(v0, all_18_2) = v1 & (v2 = 0 % 6.57/1.70 | | v1 = 0))) % 6.57/1.70 | % 6.57/1.70 | ALPHA: (12) implies: % 6.57/1.70 | (13) ! [v0: $i] : ! [v1: any] : ( ~ (in(v0, all_18_3) = v1) | ~ $i(v0) | % 6.57/1.70 | ? [v2: any] : ? [v3: any] : (in(v0, all_18_1) = v2 & in(v0, % 6.57/1.70 | all_18_2) = v3 & ( ~ (v2 = 0) | (v1 = 0 & ~ (v3 = 0))))) % 6.57/1.70 | % 6.57/1.70 | BETA: splitting (11) gives: % 6.57/1.70 | % 6.57/1.70 | Case 1: % 6.57/1.70 | | % 6.57/1.70 | | (14) all_18_0 = 0 % 6.57/1.70 | | % 6.57/1.70 | | REDUCE: (5), (14) imply: % 6.57/1.70 | | (15) $false % 6.57/1.71 | | % 6.57/1.71 | | CLOSE: (15) is inconsistent. % 6.57/1.71 | | % 6.57/1.71 | Case 2: % 6.57/1.71 | | % 6.57/1.71 | | (16) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0, all_18_1) = 0 & % 6.57/1.71 | | in(v0, all_18_3) = v1 & $i(v0)) % 6.57/1.71 | | % 6.57/1.71 | | DELTA: instantiating (16) with fresh symbols all_33_0, all_33_1 gives: % 6.57/1.71 | | (17) ~ (all_33_0 = 0) & in(all_33_1, all_18_1) = 0 & in(all_33_1, % 6.57/1.71 | | all_18_3) = all_33_0 & $i(all_33_1) % 6.57/1.71 | | % 6.57/1.71 | | ALPHA: (17) implies: % 6.57/1.71 | | (18) ~ (all_33_0 = 0) % 6.57/1.71 | | (19) $i(all_33_1) % 6.57/1.71 | | (20) in(all_33_1, all_18_3) = all_33_0 % 6.57/1.71 | | (21) in(all_33_1, all_18_1) = 0 % 6.57/1.71 | | % 6.57/1.71 | | GROUND_INST: instantiating (13) with all_33_1, all_33_0, simplifying with % 6.57/1.71 | | (19), (20) gives: % 6.57/1.71 | | (22) ? [v0: any] : ? [v1: any] : (in(all_33_1, all_18_1) = v0 & % 6.57/1.71 | | in(all_33_1, all_18_2) = v1 & ( ~ (v0 = 0) | (all_33_0 = 0 & ~ % 6.57/1.71 | | (v1 = 0)))) % 6.57/1.71 | | % 6.57/1.71 | | DELTA: instantiating (22) with fresh symbols all_44_0, all_44_1 gives: % 6.57/1.71 | | (23) in(all_33_1, all_18_1) = all_44_1 & in(all_33_1, all_18_2) = % 6.57/1.71 | | all_44_0 & ( ~ (all_44_1 = 0) | (all_33_0 = 0 & ~ (all_44_0 = 0))) % 6.57/1.71 | | % 6.57/1.71 | | ALPHA: (23) implies: % 6.57/1.71 | | (24) in(all_33_1, all_18_1) = all_44_1 % 6.57/1.71 | | (25) ~ (all_44_1 = 0) | (all_33_0 = 0 & ~ (all_44_0 = 0)) % 6.57/1.71 | | % 6.57/1.71 | | BETA: splitting (25) gives: % 6.57/1.71 | | % 6.57/1.71 | | Case 1: % 6.57/1.71 | | | % 6.57/1.71 | | | (26) ~ (all_44_1 = 0) % 6.57/1.71 | | | % 6.57/1.71 | | | GROUND_INST: instantiating (3) with 0, all_44_1, all_18_1, all_33_1, % 6.57/1.71 | | | simplifying with (21), (24) gives: % 6.57/1.71 | | | (27) all_44_1 = 0 % 6.57/1.71 | | | % 6.57/1.71 | | | REDUCE: (26), (27) imply: % 6.57/1.71 | | | (28) $false % 6.57/1.71 | | | % 6.57/1.71 | | | CLOSE: (28) is inconsistent. % 6.57/1.71 | | | % 6.57/1.71 | | Case 2: % 6.57/1.71 | | | % 6.57/1.71 | | | (29) all_33_0 = 0 & ~ (all_44_0 = 0) % 6.57/1.71 | | | % 6.57/1.71 | | | ALPHA: (29) implies: % 6.57/1.71 | | | (30) all_33_0 = 0 % 6.57/1.71 | | | % 6.57/1.71 | | | REDUCE: (18), (30) imply: % 6.57/1.71 | | | (31) $false % 6.57/1.71 | | | % 6.57/1.71 | | | CLOSE: (31) is inconsistent. % 6.57/1.71 | | | % 6.57/1.71 | | End of split % 6.57/1.71 | | % 6.57/1.71 | End of split % 6.57/1.71 | % 6.57/1.71 End of proof % 6.57/1.71 % SZS output end Proof for theBenchmark % 6.57/1.71 % 6.57/1.71 1105ms %------------------------------------------------------------------------------