%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET916+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 : n011.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 15:27:01 EDT 2023 % Result : Theorem 7.57s 1.80s % Output : Proof 10.18s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : SET916+1 : TPTP v8.1.2. Released v3.2.0. % 0.00/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.35 % Computer : n011.cluster.edu % 0.13/0.35 % Model : x86_64 x86_64 % 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.35 % Memory : 8042.1875MB % 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 300 % 0.13/0.35 % DateTime : Sat Aug 26 16:08:39 EDT 2023 % 0.13/0.35 % CPUTime : % 0.21/0.62 ________ _____ % 0.21/0.62 ___ __ \_________(_)________________________________ % 0.21/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.21/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.21/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.21/0.62 % 0.21/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.21/0.62 (2023-06-19) % 0.21/0.62 % 0.21/0.62 (c) Philipp Rümmer, 2009-2023 % 0.21/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.21/0.62 Amanda Stjerna. % 0.21/0.62 Free software under BSD-3-Clause. % 0.21/0.62 % 0.21/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.21/0.62 % 0.21/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.21/0.63 Running up to 7 provers in parallel. % 0.21/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.21/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.21/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.21/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.21/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.21/0.66 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.21/0.66 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.13/1.04 Prover 1: Preprocessing ... % 2.13/1.04 Prover 4: Preprocessing ... % 2.62/1.09 Prover 5: Preprocessing ... % 2.62/1.09 Prover 3: Preprocessing ... % 2.62/1.09 Prover 2: Preprocessing ... % 2.62/1.09 Prover 0: Preprocessing ... % 2.62/1.09 Prover 6: Preprocessing ... % 4.77/1.39 Prover 6: Proving ... % 4.77/1.39 Prover 5: Proving ... % 4.77/1.39 Prover 3: Warning: ignoring some quantifiers % 4.77/1.39 Prover 1: Warning: ignoring some quantifiers % 4.77/1.40 Prover 3: Constructing countermodel ... % 4.77/1.41 Prover 1: Constructing countermodel ... % 4.77/1.43 Prover 4: Warning: ignoring some quantifiers % 4.77/1.44 Prover 2: Proving ... % 4.77/1.45 Prover 4: Constructing countermodel ... % 5.22/1.46 Prover 0: Proving ... % 7.00/1.74 Prover 3: gave up % 7.00/1.75 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 7.57/1.77 Prover 7: Preprocessing ... % 7.57/1.79 Prover 0: proved (1152ms) % 7.57/1.79 % 7.57/1.80 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 7.57/1.80 % 7.57/1.80 Prover 5: stopped % 7.57/1.80 Prover 2: stopped % 7.89/1.81 Prover 6: stopped % 7.89/1.82 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 7.89/1.82 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 7.89/1.82 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 7.89/1.82 Prover 7: Warning: ignoring some quantifiers % 7.89/1.82 Prover 10: Preprocessing ... % 7.89/1.82 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 7.89/1.83 Prover 7: Constructing countermodel ... % 7.89/1.83 Prover 8: Preprocessing ... % 7.89/1.84 Prover 13: Preprocessing ... % 7.89/1.85 Prover 11: Preprocessing ... % 7.89/1.86 Prover 10: Warning: ignoring some quantifiers % 7.89/1.86 Prover 10: Constructing countermodel ... % 7.89/1.87 Prover 7: gave up % 7.89/1.88 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 7.89/1.89 Prover 16: Preprocessing ... % 7.89/1.90 Prover 10: gave up % 8.23/1.91 Prover 13: Warning: ignoring some quantifiers % 8.23/1.91 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 8.23/1.92 Prover 8: Warning: ignoring some quantifiers % 8.23/1.92 Prover 8: Constructing countermodel ... % 8.23/1.92 Prover 13: Constructing countermodel ... % 8.23/1.92 Prover 19: Preprocessing ... % 8.23/1.95 Prover 16: Warning: ignoring some quantifiers % 8.23/1.95 Prover 16: Constructing countermodel ... % 8.23/1.98 Prover 11: Warning: ignoring some quantifiers % 8.23/1.99 Prover 11: Constructing countermodel ... % 9.22/2.02 Prover 19: Warning: ignoring some quantifiers % 9.22/2.03 Prover 19: Constructing countermodel ... % 9.67/2.05 Prover 8: gave up % 9.70/2.08 Prover 13: gave up % 9.98/2.10 Prover 4: Found proof (size 36) % 9.98/2.10 Prover 4: proved (1451ms) % 9.98/2.10 Prover 19: stopped % 9.98/2.10 Prover 16: stopped % 9.98/2.10 Prover 11: stopped % 9.98/2.10 Prover 1: stopped % 9.98/2.11 % 9.98/2.11 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 9.98/2.11 % 9.98/2.12 % SZS output start Proof for theBenchmark % 9.98/2.12 Assumptions after simplification: % 9.98/2.12 --------------------------------- % 9.98/2.12 % 9.98/2.12 (commutativity_k2_tarski) % 10.18/2.16 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (unordered_pair(v1, v0) = v2) | % 10.18/2.16 ~ $i(v1) | ~ $i(v0) | (unordered_pair(v0, v1) = v2 & $i(v2))) & ! [v0: $i] % 10.18/2.16 : ! [v1: $i] : ! [v2: $i] : ( ~ (unordered_pair(v0, v1) = v2) | ~ $i(v1) | % 10.18/2.16 ~ $i(v0) | (unordered_pair(v1, v0) = v2 & $i(v2))) % 10.18/2.16 % 10.18/2.16 (d2_tarski) % 10.18/2.16 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v1 | v3 = v0 | % 10.18/2.16 ~ (unordered_pair(v0, v1) = v2) | ~ (in(v3, v2) = 0) | ~ $i(v3) | ~ % 10.18/2.16 $i(v2) | ~ $i(v1) | ~ $i(v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 10.18/2.16 ! [v3: int] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (in(v1, v2) = % 10.18/2.16 v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)) & ! [v0: $i] : ! [v1: $i] : ! % 10.18/2.16 [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ % 10.18/2.16 (in(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)) & ? [v0: $i] : ! % 10.18/2.16 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~ (unordered_pair(v1, v2) = % 10.18/2.16 v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : ? [v5: any] : % 10.18/2.16 (in(v4, v0) = v5 & $i(v4) & ( ~ (v5 = 0) | ( ~ (v4 = v2) & ~ (v4 = v1))) & % 10.18/2.17 (v5 = 0 | v4 = v2 | v4 = v1))) % 10.18/2.17 % 10.18/2.17 (d3_xboole_0) % 10.18/2.18 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 % 10.18/2.18 | ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v2) = v4) | ~ $i(v3) | % 10.18/2.18 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : (in(v3, v1) % 10.18/2.18 = v6 & in(v3, v0) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0)))) & ! [v0: $i] : ! % 10.18/2.18 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: any] : ( ~ % 10.18/2.18 (set_intersection2(v0, v1) = v2) | ~ (in(v3, v1) = v4) | ~ $i(v3) | ~ % 10.18/2.18 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : (in(v3, v2) = % 10.18/2.18 v5 & in(v3, v0) = v6 & ( ~ (v5 = 0) | (v6 = 0 & v4 = 0)))) & ! [v0: $i] : % 10.18/2.18 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: any] : ( ~ % 10.18/2.18 (set_intersection2(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ~ $i(v3) | ~ % 10.18/2.18 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : (in(v3, v2) = % 10.18/2.18 v5 & in(v3, v1) = v6 & ( ~ (v5 = 0) | (v6 = 0 & v4 = 0)))) & ! [v0: $i] : % 10.18/2.18 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (set_intersection2(v0, v1) = v2) % 10.18/2.18 | ~ (in(v3, v2) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 10.18/2.18 (in(v3, v1) = 0 & in(v3, v0) = 0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 10.18/2.18 : ! [v3: $i] : ( ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v1) = 0) | % 10.18/2.18 ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : % 10.18/2.18 (in(v3, v2) = v5 & in(v3, v0) = v4 & ( ~ (v4 = 0) | v5 = 0))) & ! [v0: $i] % 10.18/2.18 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (set_intersection2(v0, v1) = % 10.18/2.18 v2) | ~ (in(v3, v0) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) % 10.18/2.18 | ? [v4: any] : ? [v5: any] : (in(v3, v2) = v5 & in(v3, v1) = v4 & ( ~ (v4 % 10.18/2.18 = 0) | v5 = 0))) & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 10.18/2.18 $i] : (v3 = v0 | ~ (set_intersection2(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) % 10.18/2.18 | ~ $i(v0) | ? [v4: $i] : ? [v5: any] : ? [v6: any] : ? [v7: any] : % 10.18/2.18 (in(v4, v2) = v7 & in(v4, v1) = v6 & in(v4, v0) = v5 & $i(v4) & ( ~ (v7 = 0) % 10.18/2.18 | ~ (v6 = 0) | ~ (v5 = 0)) & (v5 = 0 | (v7 = 0 & v6 = 0)))) % 10.18/2.18 % 10.18/2.18 (t4_xboole_0) % 10.18/2.18 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 10.18/2.18 (set_intersection2(v0, v1) = v2) | ~ (in(v3, v2) = 0) | ~ $i(v3) | ~ % 10.18/2.18 $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & disjoint(v0, v1) = v4)) & % 10.18/2.18 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (disjoint(v0, v1) = % 10.18/2.18 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : % 10.18/2.18 (set_intersection2(v0, v1) = v3 & in(v4, v3) = 0 & $i(v4) & $i(v3))) & ! % 10.18/2.18 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_intersection2(v0, v1) = v2) | % 10.18/2.18 ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: $i] : ? [v5: int] : ($i(v4) & % 10.18/2.18 ((v5 = 0 & in(v4, v2) = 0) | (v3 = 0 & disjoint(v0, v1) = 0)))) & ! [v0: % 10.18/2.18 $i] : ! [v1: $i] : ( ~ (disjoint(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? % 10.18/2.18 [v2: $i] : (set_intersection2(v0, v1) = v2 & $i(v2) & ! [v3: $i] : ( ~ % 10.18/2.18 (in(v3, v2) = 0) | ~ $i(v3)))) % 10.18/2.18 % 10.18/2.18 (t57_zfmisc_1) % 10.18/2.18 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ? [v4: int] : ? % 10.18/2.18 [v5: $i] : ? [v6: int] : ( ~ (v6 = 0) & ~ (v4 = 0) & ~ (v3 = 0) & % 10.18/2.18 disjoint(v5, v1) = v6 & unordered_pair(v0, v2) = v5 & in(v2, v1) = v4 & % 10.18/2.18 in(v0, v1) = v3 & $i(v5) & $i(v2) & $i(v1) & $i(v0)) % 10.18/2.18 % 10.18/2.18 (function-axioms) % 10.18/2.18 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 10.18/2.18 [v3: $i] : (v1 = v0 | ~ (disjoint(v3, v2) = v1) | ~ (disjoint(v3, v2) = v0)) % 10.18/2.18 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 10.18/2.18 (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0)) & ! % 10.18/2.18 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 10.18/2.18 (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0: % 10.18/2.18 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 10.18/2.18 : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0: % 10.18/2.18 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 10.18/2.18 ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) % 10.18/2.18 % 10.18/2.18 Further assumptions not needed in the proof: % 10.18/2.18 -------------------------------------------- % 10.18/2.18 antisymmetry_r2_hidden, commutativity_k3_xboole_0, idempotence_k3_xboole_0, % 10.18/2.18 rc1_xboole_0, rc2_xboole_0, symmetry_r1_xboole_0 % 10.18/2.18 % 10.18/2.18 Those formulas are unsatisfiable: % 10.18/2.18 --------------------------------- % 10.18/2.18 % 10.18/2.18 Begin of proof % 10.18/2.18 | % 10.18/2.19 | ALPHA: (commutativity_k2_tarski) implies: % 10.18/2.19 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (unordered_pair(v1, v0) = % 10.18/2.19 | v2) | ~ $i(v1) | ~ $i(v0) | (unordered_pair(v0, v1) = v2 & % 10.18/2.19 | $i(v2))) % 10.18/2.19 | % 10.18/2.19 | ALPHA: (d2_tarski) implies: % 10.18/2.19 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v1 | v3 = % 10.18/2.19 | v0 | ~ (unordered_pair(v0, v1) = v2) | ~ (in(v3, v2) = 0) | ~ % 10.18/2.19 | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)) % 10.18/2.19 | % 10.18/2.19 | ALPHA: (d3_xboole_0) implies: % 10.18/2.19 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 10.18/2.19 | (set_intersection2(v0, v1) = v2) | ~ (in(v3, v2) = 0) | ~ $i(v3) | % 10.18/2.19 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | (in(v3, v1) = 0 & in(v3, v0) = 0)) % 10.18/2.19 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: any] : % 10.18/2.19 | ( ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v1) = v4) | ~ $i(v3) % 10.18/2.19 | | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : % 10.18/2.19 | (in(v3, v2) = v5 & in(v3, v0) = v6 & ( ~ (v5 = 0) | (v6 = 0 & v4 = % 10.18/2.19 | 0)))) % 10.18/2.19 | % 10.18/2.19 | ALPHA: (t4_xboole_0) implies: % 10.18/2.19 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (disjoint(v0, % 10.18/2.19 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : % 10.18/2.19 | (set_intersection2(v0, v1) = v3 & in(v4, v3) = 0 & $i(v4) & $i(v3))) % 10.18/2.19 | % 10.18/2.19 | ALPHA: (function-axioms) implies: % 10.18/2.19 | (6) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 10.18/2.19 | ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) % 10.18/2.19 | % 10.18/2.19 | DELTA: instantiating (t57_zfmisc_1) with fresh symbols all_15_0, all_15_1, % 10.18/2.19 | all_15_2, all_15_3, all_15_4, all_15_5, all_15_6 gives: % 10.18/2.19 | (7) ~ (all_15_0 = 0) & ~ (all_15_2 = 0) & ~ (all_15_3 = 0) & % 10.18/2.19 | disjoint(all_15_1, all_15_5) = all_15_0 & unordered_pair(all_15_6, % 10.18/2.19 | all_15_4) = all_15_1 & in(all_15_4, all_15_5) = all_15_2 & % 10.18/2.19 | in(all_15_6, all_15_5) = all_15_3 & $i(all_15_1) & $i(all_15_4) & % 10.18/2.19 | $i(all_15_5) & $i(all_15_6) % 10.18/2.19 | % 10.18/2.19 | ALPHA: (7) implies: % 10.18/2.19 | (8) ~ (all_15_3 = 0) % 10.18/2.19 | (9) ~ (all_15_2 = 0) % 10.18/2.19 | (10) ~ (all_15_0 = 0) % 10.18/2.19 | (11) $i(all_15_6) % 10.18/2.19 | (12) $i(all_15_5) % 10.18/2.19 | (13) $i(all_15_4) % 10.18/2.19 | (14) in(all_15_6, all_15_5) = all_15_3 % 10.18/2.19 | (15) in(all_15_4, all_15_5) = all_15_2 % 10.18/2.19 | (16) unordered_pair(all_15_6, all_15_4) = all_15_1 % 10.18/2.19 | (17) disjoint(all_15_1, all_15_5) = all_15_0 % 10.18/2.19 | % 10.18/2.20 | GROUND_INST: instantiating (1) with all_15_4, all_15_6, all_15_1, simplifying % 10.18/2.20 | with (11), (13), (16) gives: % 10.18/2.20 | (18) unordered_pair(all_15_4, all_15_6) = all_15_1 & $i(all_15_1) % 10.18/2.20 | % 10.18/2.20 | ALPHA: (18) implies: % 10.18/2.20 | (19) $i(all_15_1) % 10.18/2.20 | % 10.18/2.20 | GROUND_INST: instantiating (5) with all_15_1, all_15_5, all_15_0, simplifying % 10.18/2.20 | with (12), (17), (19) gives: % 10.18/2.20 | (20) all_15_0 = 0 | ? [v0: $i] : ? [v1: $i] : % 10.18/2.20 | (set_intersection2(all_15_1, all_15_5) = v0 & in(v1, v0) = 0 & $i(v1) % 10.18/2.20 | & $i(v0)) % 10.18/2.20 | % 10.18/2.20 | BETA: splitting (20) gives: % 10.18/2.20 | % 10.18/2.20 | Case 1: % 10.18/2.20 | | % 10.18/2.20 | | (21) all_15_0 = 0 % 10.18/2.20 | | % 10.18/2.20 | | REDUCE: (10), (21) imply: % 10.18/2.20 | | (22) $false % 10.18/2.20 | | % 10.18/2.20 | | CLOSE: (22) is inconsistent. % 10.18/2.20 | | % 10.18/2.20 | Case 2: % 10.18/2.20 | | % 10.18/2.20 | | (23) ? [v0: $i] : ? [v1: $i] : (set_intersection2(all_15_1, all_15_5) = % 10.18/2.20 | | v0 & in(v1, v0) = 0 & $i(v1) & $i(v0)) % 10.18/2.20 | | % 10.18/2.20 | | DELTA: instantiating (23) with fresh symbols all_31_0, all_31_1 gives: % 10.18/2.20 | | (24) set_intersection2(all_15_1, all_15_5) = all_31_1 & in(all_31_0, % 10.18/2.20 | | all_31_1) = 0 & $i(all_31_0) & $i(all_31_1) % 10.18/2.20 | | % 10.18/2.20 | | ALPHA: (24) implies: % 10.18/2.20 | | (25) $i(all_31_1) % 10.18/2.20 | | (26) $i(all_31_0) % 10.18/2.20 | | (27) in(all_31_0, all_31_1) = 0 % 10.18/2.20 | | (28) set_intersection2(all_15_1, all_15_5) = all_31_1 % 10.18/2.20 | | % 10.18/2.20 | | GROUND_INST: instantiating (4) with all_15_1, all_15_5, all_31_1, all_15_6, % 10.18/2.20 | | all_15_3, simplifying with (11), (12), (14), (19), (25), (28) % 10.18/2.20 | | gives: % 10.18/2.20 | | (29) ? [v0: any] : ? [v1: any] : (in(all_15_6, all_31_1) = v0 & % 10.18/2.20 | | in(all_15_6, all_15_1) = v1 & ( ~ (v0 = 0) | (v1 = 0 & all_15_3 = % 10.18/2.20 | | 0))) % 10.18/2.20 | | % 10.18/2.20 | | GROUND_INST: instantiating (3) with all_15_1, all_15_5, all_31_1, all_31_0, % 10.18/2.20 | | simplifying with (12), (19), (25), (26), (27), (28) gives: % 10.18/2.20 | | (30) in(all_31_0, all_15_1) = 0 & in(all_31_0, all_15_5) = 0 % 10.18/2.20 | | % 10.18/2.20 | | ALPHA: (30) implies: % 10.18/2.20 | | (31) in(all_31_0, all_15_5) = 0 % 10.18/2.20 | | (32) in(all_31_0, all_15_1) = 0 % 10.18/2.20 | | % 10.18/2.20 | | DELTA: instantiating (29) with fresh symbols all_46_0, all_46_1 gives: % 10.18/2.20 | | (33) in(all_15_6, all_31_1) = all_46_1 & in(all_15_6, all_15_1) = % 10.18/2.20 | | all_46_0 & ( ~ (all_46_1 = 0) | (all_46_0 = 0 & all_15_3 = 0)) % 10.18/2.20 | | % 10.18/2.20 | | ALPHA: (33) implies: % 10.18/2.20 | | (34) ~ (all_46_1 = 0) | (all_46_0 = 0 & all_15_3 = 0) % 10.18/2.20 | | % 10.18/2.20 | | BETA: splitting (34) gives: % 10.18/2.20 | | % 10.18/2.20 | | Case 1: % 10.18/2.20 | | | % 10.18/2.20 | | | % 10.18/2.20 | | | GROUND_INST: instantiating (2) with all_15_6, all_15_4, all_15_1, % 10.18/2.21 | | | all_31_0, simplifying with (11), (13), (16), (19), (26), (32) % 10.18/2.21 | | | gives: % 10.18/2.21 | | | (35) all_31_0 = all_15_4 | all_31_0 = all_15_6 % 10.18/2.21 | | | % 10.18/2.21 | | | BETA: splitting (35) gives: % 10.18/2.21 | | | % 10.18/2.21 | | | Case 1: % 10.18/2.21 | | | | % 10.18/2.21 | | | | (36) all_31_0 = all_15_4 % 10.18/2.21 | | | | % 10.18/2.21 | | | | REDUCE: (31), (36) imply: % 10.18/2.21 | | | | (37) in(all_15_4, all_15_5) = 0 % 10.18/2.21 | | | | % 10.18/2.21 | | | | GROUND_INST: instantiating (6) with all_15_2, 0, all_15_5, all_15_4, % 10.18/2.21 | | | | simplifying with (15), (37) gives: % 10.18/2.21 | | | | (38) all_15_2 = 0 % 10.18/2.21 | | | | % 10.18/2.21 | | | | REDUCE: (9), (38) imply: % 10.18/2.21 | | | | (39) $false % 10.18/2.21 | | | | % 10.18/2.21 | | | | CLOSE: (39) is inconsistent. % 10.18/2.21 | | | | % 10.18/2.21 | | | Case 2: % 10.18/2.21 | | | | % 10.18/2.21 | | | | (40) all_31_0 = all_15_6 % 10.18/2.21 | | | | % 10.18/2.21 | | | | REDUCE: (31), (40) imply: % 10.18/2.21 | | | | (41) in(all_15_6, all_15_5) = 0 % 10.18/2.21 | | | | % 10.18/2.21 | | | | GROUND_INST: instantiating (6) with all_15_3, 0, all_15_5, all_15_6, % 10.18/2.21 | | | | simplifying with (14), (41) gives: % 10.18/2.21 | | | | (42) all_15_3 = 0 % 10.18/2.21 | | | | % 10.18/2.21 | | | | REDUCE: (8), (42) imply: % 10.18/2.21 | | | | (43) $false % 10.18/2.21 | | | | % 10.18/2.21 | | | | CLOSE: (43) is inconsistent. % 10.18/2.21 | | | | % 10.18/2.21 | | | End of split % 10.18/2.21 | | | % 10.18/2.21 | | Case 2: % 10.18/2.21 | | | % 10.18/2.21 | | | (44) all_46_0 = 0 & all_15_3 = 0 % 10.18/2.21 | | | % 10.18/2.21 | | | ALPHA: (44) implies: % 10.18/2.21 | | | (45) all_15_3 = 0 % 10.18/2.21 | | | % 10.18/2.21 | | | REDUCE: (8), (45) imply: % 10.18/2.21 | | | (46) $false % 10.18/2.21 | | | % 10.18/2.21 | | | CLOSE: (46) is inconsistent. % 10.18/2.21 | | | % 10.18/2.21 | | End of split % 10.18/2.21 | | % 10.18/2.21 | End of split % 10.18/2.21 | % 10.18/2.21 End of proof % 10.18/2.21 % SZS output end Proof for theBenchmark % 10.18/2.21 % 10.18/2.21 1587ms %------------------------------------------------------------------------------