%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SEU371+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 : n031.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 17:44:20 EDT 2023 % Result : Theorem 59.35s 8.81s % Output : Proof 60.24s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.09 % Problem : SEU371+1 : TPTP v8.1.2. Released v3.3.0. % 0.00/0.10 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.08/0.29 % Computer : n031.cluster.edu % 0.08/0.29 % Model : x86_64 x86_64 % 0.08/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.08/0.29 % Memory : 8042.1875MB % 0.08/0.29 % OS : Linux 3.10.0-693.el7.x86_64 % 0.08/0.29 % CPULimit : 300 % 0.08/0.29 % WCLimit : 300 % 0.08/0.29 % DateTime : Wed Aug 23 15:06:35 EDT 2023 % 0.08/0.29 % CPUTime : % 0.13/0.55 ________ _____ % 0.13/0.55 ___ __ \_________(_)________________________________ % 0.13/0.55 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.13/0.55 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.13/0.55 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.13/0.55 % 0.13/0.55 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.13/0.55 (2023-06-19) % 0.13/0.55 % 0.13/0.55 (c) Philipp Rümmer, 2009-2023 % 0.13/0.55 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.13/0.55 Amanda Stjerna. % 0.13/0.55 Free software under BSD-3-Clause. % 0.13/0.55 % 0.13/0.55 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.13/0.55 % 0.13/0.55 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.13/0.57 Running up to 7 provers in parallel. % 0.13/0.58 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.13/0.58 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.13/0.58 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.13/0.58 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.13/0.58 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.13/0.58 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.13/0.58 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 5.62/1.57 Prover 4: Preprocessing ... % 5.62/1.57 Prover 1: Preprocessing ... % 6.21/1.62 Prover 2: Preprocessing ... % 6.21/1.62 Prover 6: Preprocessing ... % 6.21/1.62 Prover 3: Preprocessing ... % 6.21/1.62 Prover 0: Preprocessing ... % 6.21/1.62 Prover 5: Preprocessing ... % 17.14/3.17 Prover 1: Warning: ignoring some quantifiers % 18.42/3.29 Prover 5: Proving ... % 18.73/3.32 Prover 3: Warning: ignoring some quantifiers % 18.73/3.34 Prover 1: Constructing countermodel ... % 18.73/3.37 Prover 3: Constructing countermodel ... % 19.45/3.43 Prover 6: Proving ... % 19.45/3.53 Prover 2: Proving ... % 23.60/4.00 Prover 4: Warning: ignoring some quantifiers % 24.38/4.16 Prover 4: Constructing countermodel ... % 25.85/4.37 Prover 0: Proving ... % 31.56/5.08 Prover 3: gave up % 31.56/5.08 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 32.23/5.37 Prover 7: Preprocessing ... % 37.11/5.80 Prover 7: Warning: ignoring some quantifiers % 37.60/5.87 Prover 7: Constructing countermodel ... % 49.03/7.40 Prover 1: gave up % 49.20/7.41 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 50.77/7.75 Prover 8: Preprocessing ... % 54.39/8.15 Prover 8: Warning: ignoring some quantifiers % 55.24/8.20 Prover 8: Constructing countermodel ... % 59.35/8.79 Prover 7: Found proof (size 54) % 59.35/8.79 Prover 7: proved (3708ms) % 59.35/8.80 Prover 2: stopped % 59.35/8.80 Prover 0: stopped % 59.35/8.80 Prover 6: stopped % 59.35/8.80 Prover 5: stopped % 59.35/8.80 Prover 8: stopped % 59.35/8.81 Prover 4: stopped % 59.35/8.81 % 59.35/8.81 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 59.35/8.81 % 59.35/8.81 % SZS output start Proof for theBenchmark % 59.35/8.82 Assumptions after simplification: % 59.35/8.83 --------------------------------- % 59.35/8.83 % 59.35/8.83 (d11_yellow_0) % 59.83/8.87 $i(empty_set) & ! [v0: $i] : ! [v1: $i] : ( ~ (join_on_relstr(v0, empty_set) % 59.83/8.87 = v1) | ~ $i(v0) | ~ rel_str(v0) | (bottom_of_relstr(v0) = v1 & $i(v1))) % 59.83/8.87 & ! [v0: $i] : ! [v1: $i] : ( ~ (bottom_of_relstr(v0) = v1) | ~ $i(v0) | ~ % 59.83/8.87 rel_str(v0) | (join_on_relstr(v0, empty_set) = v1 & $i(v1))) % 59.83/8.87 % 59.83/8.87 (d2_yellow_1) % 59.83/8.88 ! [v0: $i] : ! [v1: $i] : ( ~ (boole_POSet(v0) = v1) | ~ $i(v0) | ? [v2: % 59.83/8.88 $i] : (boole_lattice(v0) = v2 & poset_of_lattice(v2) = v1 & $i(v2) & % 59.83/8.88 $i(v1))) & ! [v0: $i] : ! [v1: $i] : ( ~ (boole_lattice(v0) = v1) | ~ % 59.83/8.88 $i(v0) | ? [v2: $i] : (boole_POSet(v0) = v2 & poset_of_lattice(v1) = v2 & % 59.83/8.88 $i(v2))) % 59.83/8.88 % 59.83/8.88 (dt_k1_lattice3) % 59.83/8.88 ! [v0: $i] : ! [v1: $i] : ( ~ (boole_lattice(v0) = v1) | ~ $i(v0) | % 59.98/8.88 strict_latt_str(v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ (boole_lattice(v0) = % 59.98/8.88 v1) | ~ $i(v0) | latt_str(v1)) % 59.98/8.88 % 59.98/8.88 (dt_k3_yellow_0) % 59.98/8.88 ! [v0: $i] : ! [v1: $i] : ( ~ (bottom_of_relstr(v0) = v1) | ~ $i(v0) | ~ % 59.98/8.88 rel_str(v0) | ? [v2: $i] : (the_carrier(v0) = v2 & $i(v2) & element(v1, % 59.98/8.88 v2))) & ! [v0: $i] : ! [v1: $i] : ( ~ (the_carrier(v0) = v1) | ~ % 59.98/8.88 $i(v0) | ~ rel_str(v0) | ? [v2: $i] : (bottom_of_relstr(v0) = v2 & $i(v2) % 59.98/8.88 & element(v2, v1))) % 59.98/8.88 % 59.98/8.88 (dt_k3_yellow_1) % 59.98/8.89 ! [v0: $i] : ! [v1: $i] : ( ~ (boole_POSet(v0) = v1) | ~ $i(v0) | % 59.98/8.89 strict_rel_str(v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ (boole_POSet(v0) = v1) % 59.98/8.89 | ~ $i(v0) | rel_str(v1)) % 59.98/8.89 % 59.98/8.89 (fc1_knaster) % 59.98/8.89 ! [v0: $i] : ! [v1: $i] : ( ~ (boole_lattice(v0) = v1) | ~ $i(v0) | ~ % 59.98/8.89 empty_carrier(v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ (boole_lattice(v0) = % 59.98/8.89 v1) | ~ $i(v0) | modular_lattstr(v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ % 59.98/8.89 (boole_lattice(v0) = v1) | ~ $i(v0) | complemented_lattstr(v1)) & ! [v0: % 59.98/8.89 $i] : ! [v1: $i] : ( ~ (boole_lattice(v0) = v1) | ~ $i(v0) | % 59.98/8.89 distributive_lattstr(v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ % 59.98/8.89 (boole_lattice(v0) = v1) | ~ $i(v0) | boolean_lattstr(v1)) & ! [v0: $i] : % 59.98/8.89 ! [v1: $i] : ( ~ (boole_lattice(v0) = v1) | ~ $i(v0) | bounded_lattstr(v1)) & % 59.98/8.89 ! [v0: $i] : ! [v1: $i] : ( ~ (boole_lattice(v0) = v1) | ~ $i(v0) | % 59.98/8.89 upper_bounded_semilattstr(v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ % 59.98/8.89 (boole_lattice(v0) = v1) | ~ $i(v0) | lower_bounded_semilattstr(v1)) & ! % 59.98/8.89 [v0: $i] : ! [v1: $i] : ( ~ (boole_lattice(v0) = v1) | ~ $i(v0) | % 59.98/8.89 join_absorbing(v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ (boole_lattice(v0) = % 59.98/8.89 v1) | ~ $i(v0) | meet_absorbing(v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ % 59.98/8.89 (boole_lattice(v0) = v1) | ~ $i(v0) | meet_associative(v1)) & ! [v0: $i] : % 59.98/8.89 ! [v1: $i] : ( ~ (boole_lattice(v0) = v1) | ~ $i(v0) | meet_commutative(v1)) % 59.98/8.89 & ! [v0: $i] : ! [v1: $i] : ( ~ (boole_lattice(v0) = v1) | ~ $i(v0) | % 59.98/8.89 join_associative(v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ (boole_lattice(v0) = % 59.98/8.89 v1) | ~ $i(v0) | join_commutative(v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ % 59.98/8.89 (boole_lattice(v0) = v1) | ~ $i(v0) | complete_latt_str(v1)) & ! [v0: $i] % 59.98/8.89 : ! [v1: $i] : ( ~ (boole_lattice(v0) = v1) | ~ $i(v0) | lattice(v1)) & ! % 59.98/8.89 [v0: $i] : ! [v1: $i] : ( ~ (boole_lattice(v0) = v1) | ~ $i(v0) | % 59.98/8.89 strict_latt_str(v1)) % 59.98/8.89 % 59.98/8.89 (fc3_lattice3) % 59.98/8.90 ! [v0: $i] : ! [v1: $i] : ( ~ (boole_lattice(v0) = v1) | ~ $i(v0) | ~ % 59.98/8.90 empty_carrier(v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ (boole_lattice(v0) = % 59.98/8.90 v1) | ~ $i(v0) | modular_lattstr(v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ % 59.98/8.90 (boole_lattice(v0) = v1) | ~ $i(v0) | complemented_lattstr(v1)) & ! [v0: % 59.98/8.90 $i] : ! [v1: $i] : ( ~ (boole_lattice(v0) = v1) | ~ $i(v0) | % 59.98/8.90 distributive_lattstr(v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ % 59.98/8.90 (boole_lattice(v0) = v1) | ~ $i(v0) | boolean_lattstr(v1)) & ! [v0: $i] : % 59.98/8.90 ! [v1: $i] : ( ~ (boole_lattice(v0) = v1) | ~ $i(v0) | bounded_lattstr(v1)) & % 59.98/8.90 ! [v0: $i] : ! [v1: $i] : ( ~ (boole_lattice(v0) = v1) | ~ $i(v0) | % 59.98/8.90 upper_bounded_semilattstr(v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ % 59.98/8.90 (boole_lattice(v0) = v1) | ~ $i(v0) | lower_bounded_semilattstr(v1)) & ! % 59.98/8.90 [v0: $i] : ! [v1: $i] : ( ~ (boole_lattice(v0) = v1) | ~ $i(v0) | % 59.98/8.90 join_absorbing(v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ (boole_lattice(v0) = % 59.98/8.90 v1) | ~ $i(v0) | meet_absorbing(v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ % 59.98/8.90 (boole_lattice(v0) = v1) | ~ $i(v0) | meet_associative(v1)) & ! [v0: $i] : % 59.98/8.90 ! [v1: $i] : ( ~ (boole_lattice(v0) = v1) | ~ $i(v0) | meet_commutative(v1)) % 59.98/8.90 & ! [v0: $i] : ! [v1: $i] : ( ~ (boole_lattice(v0) = v1) | ~ $i(v0) | % 59.98/8.90 join_associative(v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ (boole_lattice(v0) = % 59.98/8.90 v1) | ~ $i(v0) | join_commutative(v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ % 59.98/8.90 (boole_lattice(v0) = v1) | ~ $i(v0) | lattice(v1)) & ! [v0: $i] : ! [v1: % 59.98/8.90 $i] : ( ~ (boole_lattice(v0) = v1) | ~ $i(v0) | strict_latt_str(v1)) % 59.98/8.90 % 59.98/8.90 (rc1_xboole_0) % 59.98/8.90 ? [v0: $i] : ($i(v0) & empty(v0)) % 59.98/8.90 % 59.98/8.90 (t18_yellow_1) % 59.98/8.90 $i(empty_set) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v2 = empty_set) % 59.98/8.90 & boole_POSet(v0) = v1 & bottom_of_relstr(v1) = v2 & $i(v2) & $i(v1) & % 59.98/8.90 $i(v0)) % 59.98/8.90 % 59.98/8.90 (t29_yellow_0) % 59.98/8.91 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 59.98/8.91 (meet_on_relstr(v1, v2) = v3) | ~ (poset_of_lattice(v0) = v1) | ~ $i(v2) | % 59.98/8.91 ~ $i(v0) | ~ complete_latt_str(v0) | ~ lattice(v0) | ~ latt_str(v0) | % 59.98/8.91 empty_carrier(v0) | (meet_of_latt_set(v0, v2) = v3 & $i(v3))) & ! [v0: $i] % 59.98/8.91 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (poset_of_lattice(v0) = v1) | % 59.98/8.91 ~ (meet_of_latt_set(v0, v2) = v3) | ~ $i(v2) | ~ $i(v0) | ~ % 59.98/8.91 complete_latt_str(v0) | ~ lattice(v0) | ~ latt_str(v0) | empty_carrier(v0) % 59.98/8.91 | (meet_on_relstr(v1, v2) = v3 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ! % 59.98/8.91 [v2: $i] : ! [v3: $i] : ( ~ (poset_of_lattice(v0) = v1) | ~ % 59.98/8.91 (join_of_latt_set(v0, v2) = v3) | ~ $i(v2) | ~ $i(v0) | ~ % 59.98/8.91 complete_latt_str(v0) | ~ lattice(v0) | ~ latt_str(v0) | empty_carrier(v0) % 59.98/8.91 | (join_on_relstr(v1, v2) = v3 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ! % 59.98/8.91 [v2: $i] : ! [v3: $i] : ( ~ (poset_of_lattice(v0) = v1) | ~ % 59.98/8.91 (join_on_relstr(v1, v2) = v3) | ~ $i(v2) | ~ $i(v0) | ~ % 59.98/8.91 complete_latt_str(v0) | ~ lattice(v0) | ~ latt_str(v0) | empty_carrier(v0) % 59.98/8.91 | (join_of_latt_set(v0, v2) = v3 & $i(v3))) % 59.98/8.91 % 59.98/8.91 (t3_lattice3) % 59.98/8.91 $i(empty_set) & ! [v0: $i] : ! [v1: $i] : ( ~ (boole_lattice(v0) = v1) | ~ % 59.98/8.91 $i(v0) | bottom_of_semilattstr(v1) = empty_set) & ! [v0: $i] : ! [v1: $i] % 59.98/8.91 : ( ~ (boole_lattice(v0) = v1) | ~ $i(v0) | lower_bounded_semilattstr(v1)) % 59.98/8.91 % 59.98/8.91 (t50_lattice3) % 59.98/8.91 $i(empty_set) & ! [v0: $i] : ! [v1: $i] : ( ~ (bottom_of_semilattstr(v0) = % 59.98/8.91 v1) | ~ $i(v0) | ~ complete_latt_str(v0) | ~ lattice(v0) | ~ % 59.98/8.91 latt_str(v0) | lower_bounded_semilattstr(v0) | empty_carrier(v0)) & ! [v0: % 59.98/8.91 $i] : ! [v1: $i] : ( ~ (bottom_of_semilattstr(v0) = v1) | ~ $i(v0) | ~ % 59.98/8.91 complete_latt_str(v0) | ~ lattice(v0) | ~ latt_str(v0) | empty_carrier(v0) % 59.98/8.91 | (join_of_latt_set(v0, empty_set) = v1 & $i(v1))) & ! [v0: $i] : ! [v1: % 59.98/8.91 $i] : ( ~ (join_of_latt_set(v0, empty_set) = v1) | ~ $i(v0) | ~ % 59.98/8.91 complete_latt_str(v0) | ~ lattice(v0) | ~ latt_str(v0) | % 59.98/8.91 lower_bounded_semilattstr(v0) | empty_carrier(v0)) & ! [v0: $i] : ! [v1: % 59.98/8.91 $i] : ( ~ (join_of_latt_set(v0, empty_set) = v1) | ~ $i(v0) | ~ % 59.98/8.91 complete_latt_str(v0) | ~ lattice(v0) | ~ latt_str(v0) | empty_carrier(v0) % 59.98/8.91 | (bottom_of_semilattstr(v0) = v1 & $i(v1))) % 59.98/8.91 % 59.98/8.91 (t6_boole) % 59.98/8.91 $i(empty_set) & ! [v0: $i] : (v0 = empty_set | ~ $i(v0) | ~ empty(v0)) % 59.98/8.91 % 59.98/8.91 (function-axioms) % 59.98/8.92 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 % 59.98/8.92 | ~ (latt_str_of(v4, v3, v2) = v1) | ~ (latt_str_of(v4, v3, v2) = v0)) & % 59.98/8.92 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 59.98/8.92 (meet_on_relstr(v3, v2) = v1) | ~ (meet_on_relstr(v3, v2) = v0)) & ! [v0: % 59.98/8.92 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 59.98/8.92 (meet_of_latt_set(v3, v2) = v1) | ~ (meet_of_latt_set(v3, v2) = v0)) & ! % 59.98/8.92 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 59.98/8.92 (a_2_2_lattice3(v3, v2) = v1) | ~ (a_2_2_lattice3(v3, v2) = v0)) & ! [v0: % 59.98/8.92 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 59.98/8.92 (join_of_latt_set(v3, v2) = v1) | ~ (join_of_latt_set(v3, v2) = v0)) & ! % 59.98/8.92 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 59.98/8.92 (join_on_relstr(v3, v2) = v1) | ~ (join_on_relstr(v3, v2) = v0)) & ! [v0: % 59.98/8.92 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 59.98/8.92 (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) = v0)) & % 59.98/8.92 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 59.98/8.92 (rel_str_of(v3, v2) = v1) | ~ (rel_str_of(v3, v2) = v0)) & ! [v0: $i] : ! % 59.98/8.92 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (relation_of_lattice(v2) = v1) | ~ % 59.98/8.92 (relation_of_lattice(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 59.98/8.92 (v1 = v0 | ~ (bottom_of_semilattstr(v2) = v1) | ~ (bottom_of_semilattstr(v2) % 59.98/8.92 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 59.98/8.92 (boole_POSet(v2) = v1) | ~ (boole_POSet(v2) = v0)) & ! [v0: $i] : ! [v1: % 59.98/8.92 $i] : ! [v2: $i] : (v1 = v0 | ~ (boole_lattice(v2) = v1) | ~ % 59.98/8.92 (boole_lattice(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 59.98/8.92 v0 | ~ (poset_of_lattice(v2) = v1) | ~ (poset_of_lattice(v2) = v0)) & ! % 59.98/8.92 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (k2_lattice3(v2) = v1) | % 59.98/8.92 ~ (k2_lattice3(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 59.98/8.92 v0 | ~ (bottom_of_relstr(v2) = v1) | ~ (bottom_of_relstr(v2) = v0)) & ! % 59.98/8.92 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ % 59.98/8.92 (powerset(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | % 59.98/8.92 ~ (the_L_meet(v2) = v1) | ~ (the_L_meet(v2) = v0)) & ! [v0: $i] : ! [v1: % 59.98/8.92 $i] : ! [v2: $i] : (v1 = v0 | ~ (the_L_join(v2) = v1) | ~ (the_L_join(v2) % 59.98/8.92 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 59.98/8.92 (the_InternalRel(v2) = v1) | ~ (the_InternalRel(v2) = v0)) & ! [v0: $i] : % 59.98/8.92 ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (the_carrier(v2) = v1) | ~ % 59.98/8.92 (the_carrier(v2) = v0)) % 59.98/8.92 % 59.98/8.92 Further assumptions not needed in the proof: % 59.98/8.92 -------------------------------------------- % 59.98/8.92 abstractness_v1_orders_2, abstractness_v3_lattices, antisymmetry_r2_hidden, % 59.98/8.92 cc1_knaster, cc1_lattice3, cc1_lattices, cc1_relset_1, cc1_yellow_0, % 59.98/8.92 cc2_lattice3, cc2_lattices, cc3_lattices, cc3_yellow_0, cc4_lattices, % 59.98/8.92 cc4_yellow_0, cc5_lattices, cc5_yellow_0, cc6_lattices, cc7_lattices, % 59.98/8.92 d22_lattice3, d2_lattice3, dt_g1_orders_2, dt_g3_lattices, dt_k15_lattice3, % 59.98/8.92 dt_k16_lattice3, dt_k1_xboole_0, dt_k1_yellow_0, dt_k1_zfmisc_1, dt_k2_lattice3, % 59.98/8.92 dt_k2_yellow_0, dt_k2_zfmisc_1, dt_k3_lattice3, dt_k5_lattices, dt_k9_filter_1, % 59.98/8.92 dt_l1_lattices, dt_l1_orders_2, dt_l1_struct_0, dt_l2_lattices, dt_l3_lattices, % 59.98/8.92 dt_m1_relset_1, dt_m1_subset_1, dt_m2_relset_1, dt_u1_lattices, dt_u1_orders_2, % 59.98/8.92 dt_u1_struct_0, dt_u2_lattices, existence_l1_lattices, existence_l1_orders_2, % 59.98/8.92 existence_l1_struct_0, existence_l2_lattices, existence_l3_lattices, % 59.98/8.92 existence_m1_relset_1, existence_m1_subset_1, existence_m2_relset_1, % 59.98/8.92 fc1_lattice3, fc1_orders_2, fc1_struct_0, fc1_subset_1, fc1_xboole_0, % 59.98/8.92 fc1_yellow_1, fc2_lattice3, fc2_orders_2, fc2_yellow_1, fc3_lattices, % 59.98/8.92 fc3_orders_2, fc3_yellow_1, fc4_lattice3, fc4_subset_1, fc4_yellow_1, % 59.98/8.92 fc7_yellow_1, fc8_yellow_1, fraenkel_a_2_2_lattice3, free_g1_orders_2, % 59.98/8.92 free_g3_lattices, rc10_lattices, rc11_lattices, rc12_lattices, rc13_lattices, % 59.98/8.92 rc1_lattice3, rc1_orders_2, rc1_subset_1, rc2_lattice3, rc2_orders_2, % 59.98/8.92 rc2_partfun1, rc2_subset_1, rc2_xboole_0, rc2_yellow_0, rc3_lattices, % 59.98/8.92 rc3_struct_0, rc5_struct_0, rc6_lattices, rc9_lattices, % 59.98/8.92 redefinition_k2_lattice3, redefinition_m2_relset_1, reflexivity_r1_tarski, % 59.98/8.92 t1_subset, t2_subset, t2_tarski, t3_subset, t4_subset, t5_subset, t7_boole, % 59.98/8.92 t8_boole % 59.98/8.92 % 59.98/8.92 Those formulas are unsatisfiable: % 59.98/8.92 --------------------------------- % 59.98/8.92 % 59.98/8.92 Begin of proof % 59.98/8.93 | % 59.98/8.93 | ALPHA: (d11_yellow_0) implies: % 59.98/8.93 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (bottom_of_relstr(v0) = v1) | ~ $i(v0) % 59.98/8.93 | | ~ rel_str(v0) | (join_on_relstr(v0, empty_set) = v1 & $i(v1))) % 59.98/8.93 | % 59.98/8.93 | ALPHA: (d2_yellow_1) implies: % 59.98/8.93 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (boole_POSet(v0) = v1) | ~ $i(v0) | ? % 59.98/8.93 | [v2: $i] : (boole_lattice(v0) = v2 & poset_of_lattice(v2) = v1 & % 59.98/8.93 | $i(v2) & $i(v1))) % 59.98/8.93 | % 59.98/8.93 | ALPHA: (dt_k1_lattice3) implies: % 59.98/8.93 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ (boole_lattice(v0) = v1) | ~ $i(v0) | % 59.98/8.93 | latt_str(v1)) % 59.98/8.93 | % 59.98/8.93 | ALPHA: (dt_k3_yellow_0) implies: % 59.98/8.93 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ (bottom_of_relstr(v0) = v1) | ~ $i(v0) % 59.98/8.93 | | ~ rel_str(v0) | ? [v2: $i] : (the_carrier(v0) = v2 & $i(v2) & % 59.98/8.93 | element(v1, v2))) % 59.98/8.93 | % 59.98/8.93 | ALPHA: (dt_k3_yellow_1) implies: % 59.98/8.93 | (5) ! [v0: $i] : ! [v1: $i] : ( ~ (boole_POSet(v0) = v1) | ~ $i(v0) | % 59.98/8.93 | rel_str(v1)) % 59.98/8.93 | % 59.98/8.93 | ALPHA: (fc1_knaster) implies: % 59.98/8.93 | (6) ! [v0: $i] : ! [v1: $i] : ( ~ (boole_lattice(v0) = v1) | ~ $i(v0) | % 59.98/8.93 | complete_latt_str(v1)) % 59.98/8.93 | % 59.98/8.93 | ALPHA: (fc3_lattice3) implies: % 59.98/8.93 | (7) ! [v0: $i] : ! [v1: $i] : ( ~ (boole_lattice(v0) = v1) | ~ $i(v0) | % 59.98/8.93 | lattice(v1)) % 59.98/8.93 | (8) ! [v0: $i] : ! [v1: $i] : ( ~ (boole_lattice(v0) = v1) | ~ $i(v0) | % 59.98/8.93 | ~ empty_carrier(v1)) % 59.98/8.93 | % 59.98/8.93 | ALPHA: (t29_yellow_0) implies: % 60.24/8.93 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 60.24/8.93 | (poset_of_lattice(v0) = v1) | ~ (join_on_relstr(v1, v2) = v3) | ~ % 60.24/8.93 | $i(v2) | ~ $i(v0) | ~ complete_latt_str(v0) | ~ lattice(v0) | ~ % 60.24/8.93 | latt_str(v0) | empty_carrier(v0) | (join_of_latt_set(v0, v2) = v3 & % 60.24/8.94 | $i(v3))) % 60.24/8.94 | % 60.24/8.94 | ALPHA: (t3_lattice3) implies: % 60.24/8.94 | (10) ! [v0: $i] : ! [v1: $i] : ( ~ (boole_lattice(v0) = v1) | ~ $i(v0) | % 60.24/8.94 | bottom_of_semilattstr(v1) = empty_set) % 60.24/8.94 | % 60.24/8.94 | ALPHA: (t50_lattice3) implies: % 60.24/8.94 | (11) ! [v0: $i] : ! [v1: $i] : ( ~ (bottom_of_semilattstr(v0) = v1) | ~ % 60.24/8.94 | $i(v0) | ~ complete_latt_str(v0) | ~ lattice(v0) | ~ latt_str(v0) % 60.24/8.94 | | empty_carrier(v0) | (join_of_latt_set(v0, empty_set) = v1 & % 60.24/8.94 | $i(v1))) % 60.24/8.94 | % 60.24/8.94 | ALPHA: (t6_boole) implies: % 60.24/8.94 | (12) ! [v0: $i] : (v0 = empty_set | ~ $i(v0) | ~ empty(v0)) % 60.24/8.94 | % 60.24/8.94 | ALPHA: (t18_yellow_1) implies: % 60.24/8.94 | (13) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v2 = empty_set) & % 60.24/8.94 | boole_POSet(v0) = v1 & bottom_of_relstr(v1) = v2 & $i(v2) & $i(v1) & % 60.24/8.94 | $i(v0)) % 60.24/8.94 | % 60.24/8.94 | ALPHA: (function-axioms) implies: % 60.24/8.94 | (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 60.24/8.94 | (join_of_latt_set(v3, v2) = v1) | ~ (join_of_latt_set(v3, v2) = % 60.24/8.94 | v0)) % 60.24/8.94 | % 60.24/8.94 | DELTA: instantiating (rc1_xboole_0) with fresh symbol all_96_0 gives: % 60.24/8.94 | (15) $i(all_96_0) & empty(all_96_0) % 60.24/8.94 | % 60.24/8.94 | ALPHA: (15) implies: % 60.24/8.94 | (16) empty(all_96_0) % 60.24/8.94 | (17) $i(all_96_0) % 60.24/8.94 | % 60.24/8.94 | DELTA: instantiating (13) with fresh symbols all_109_0, all_109_1, all_109_2 % 60.24/8.94 | gives: % 60.24/8.94 | (18) ~ (all_109_0 = empty_set) & boole_POSet(all_109_2) = all_109_1 & % 60.24/8.94 | bottom_of_relstr(all_109_1) = all_109_0 & $i(all_109_0) & % 60.24/8.94 | $i(all_109_1) & $i(all_109_2) % 60.24/8.94 | % 60.24/8.94 | ALPHA: (18) implies: % 60.24/8.94 | (19) ~ (all_109_0 = empty_set) % 60.24/8.94 | (20) $i(all_109_2) % 60.24/8.94 | (21) $i(all_109_1) % 60.24/8.94 | (22) bottom_of_relstr(all_109_1) = all_109_0 % 60.24/8.94 | (23) boole_POSet(all_109_2) = all_109_1 % 60.24/8.94 | % 60.24/8.94 | GROUND_INST: instantiating (12) with all_96_0, simplifying with (16), (17) % 60.24/8.94 | gives: % 60.24/8.94 | (24) all_96_0 = empty_set % 60.24/8.94 | % 60.24/8.95 | GROUND_INST: instantiating (4) with all_109_1, all_109_0, simplifying with % 60.24/8.95 | (21), (22) gives: % 60.24/8.95 | (25) ~ rel_str(all_109_1) | ? [v0: $i] : (the_carrier(all_109_1) = v0 & % 60.24/8.95 | $i(v0) & element(all_109_0, v0)) % 60.24/8.95 | % 60.24/8.95 | GROUND_INST: instantiating (1) with all_109_1, all_109_0, simplifying with % 60.24/8.95 | (21), (22) gives: % 60.24/8.95 | (26) ~ rel_str(all_109_1) | (join_on_relstr(all_109_1, empty_set) = % 60.24/8.95 | all_109_0 & $i(all_109_0)) % 60.24/8.95 | % 60.24/8.95 | GROUND_INST: instantiating (5) with all_109_2, all_109_1, simplifying with % 60.24/8.95 | (20), (23) gives: % 60.24/8.95 | (27) rel_str(all_109_1) % 60.24/8.95 | % 60.24/8.95 | GROUND_INST: instantiating (2) with all_109_2, all_109_1, simplifying with % 60.24/8.95 | (20), (23) gives: % 60.24/8.95 | (28) ? [v0: $i] : (boole_lattice(all_109_2) = v0 & poset_of_lattice(v0) = % 60.24/8.95 | all_109_1 & $i(v0) & $i(all_109_1)) % 60.24/8.95 | % 60.24/8.95 | DELTA: instantiating (28) with fresh symbol all_143_0 gives: % 60.24/8.95 | (29) boole_lattice(all_109_2) = all_143_0 & poset_of_lattice(all_143_0) = % 60.24/8.95 | all_109_1 & $i(all_143_0) & $i(all_109_1) % 60.24/8.95 | % 60.24/8.95 | ALPHA: (29) implies: % 60.24/8.95 | (30) $i(all_143_0) % 60.24/8.95 | (31) poset_of_lattice(all_143_0) = all_109_1 % 60.24/8.95 | (32) boole_lattice(all_109_2) = all_143_0 % 60.24/8.95 | % 60.24/8.95 | REDUCE: (17), (24) imply: % 60.24/8.95 | (33) $i(empty_set) % 60.24/8.95 | % 60.24/8.95 | BETA: splitting (26) gives: % 60.24/8.95 | % 60.24/8.95 | Case 1: % 60.24/8.95 | | % 60.24/8.95 | | (34) ~ rel_str(all_109_1) % 60.24/8.95 | | % 60.24/8.95 | | PRED_UNIFY: (27), (34) imply: % 60.24/8.95 | | (35) $false % 60.24/8.95 | | % 60.24/8.95 | | CLOSE: (35) is inconsistent. % 60.24/8.95 | | % 60.24/8.95 | Case 2: % 60.24/8.95 | | % 60.24/8.95 | | (36) join_on_relstr(all_109_1, empty_set) = all_109_0 & $i(all_109_0) % 60.24/8.95 | | % 60.24/8.95 | | ALPHA: (36) implies: % 60.24/8.95 | | (37) join_on_relstr(all_109_1, empty_set) = all_109_0 % 60.24/8.95 | | % 60.24/8.95 | | BETA: splitting (25) gives: % 60.24/8.95 | | % 60.24/8.95 | | Case 1: % 60.24/8.95 | | | % 60.24/8.95 | | | (38) ~ rel_str(all_109_1) % 60.24/8.95 | | | % 60.24/8.95 | | | PRED_UNIFY: (27), (38) imply: % 60.24/8.95 | | | (39) $false % 60.24/8.95 | | | % 60.24/8.95 | | | CLOSE: (39) is inconsistent. % 60.24/8.95 | | | % 60.24/8.95 | | Case 2: % 60.24/8.95 | | | % 60.24/8.95 | | | % 60.24/8.95 | | | GROUND_INST: instantiating (10) with all_109_2, all_143_0, simplifying % 60.24/8.95 | | | with (20), (32) gives: % 60.24/8.95 | | | (40) bottom_of_semilattstr(all_143_0) = empty_set % 60.24/8.95 | | | % 60.24/8.95 | | | GROUND_INST: instantiating (6) with all_109_2, all_143_0, simplifying with % 60.24/8.95 | | | (20), (32) gives: % 60.24/8.95 | | | (41) complete_latt_str(all_143_0) % 60.24/8.95 | | | % 60.24/8.96 | | | GROUND_INST: instantiating (7) with all_109_2, all_143_0, simplifying with % 60.24/8.96 | | | (20), (32) gives: % 60.24/8.96 | | | (42) lattice(all_143_0) % 60.24/8.96 | | | % 60.24/8.96 | | | GROUND_INST: instantiating (3) with all_109_2, all_143_0, simplifying with % 60.24/8.96 | | | (20), (32) gives: % 60.24/8.96 | | | (43) latt_str(all_143_0) % 60.24/8.96 | | | % 60.24/8.96 | | | GROUND_INST: instantiating (9) with all_143_0, all_109_1, empty_set, % 60.24/8.96 | | | all_109_0, simplifying with (30), (31), (33), (37), (41), % 60.24/8.96 | | | (42), (43) gives: % 60.24/8.96 | | | (44) empty_carrier(all_143_0) | (join_of_latt_set(all_143_0, empty_set) % 60.24/8.96 | | | = all_109_0 & $i(all_109_0)) % 60.24/8.96 | | | % 60.24/8.96 | | | GROUND_INST: instantiating (11) with all_143_0, empty_set, simplifying % 60.24/8.96 | | | with (30), (40), (41), (42), (43) gives: % 60.24/8.96 | | | (45) empty_carrier(all_143_0) | (join_of_latt_set(all_143_0, empty_set) % 60.24/8.96 | | | = empty_set & $i(empty_set)) % 60.24/8.96 | | | % 60.24/8.96 | | | BETA: splitting (45) gives: % 60.24/8.96 | | | % 60.24/8.96 | | | Case 1: % 60.24/8.96 | | | | % 60.24/8.96 | | | | (46) empty_carrier(all_143_0) % 60.24/8.96 | | | | % 60.24/8.96 | | | | GROUND_INST: instantiating (8) with all_109_2, all_143_0, simplifying % 60.24/8.96 | | | | with (20), (32), (46) gives: % 60.24/8.96 | | | | (47) $false % 60.24/8.96 | | | | % 60.24/8.96 | | | | CLOSE: (47) is inconsistent. % 60.24/8.96 | | | | % 60.24/8.96 | | | Case 2: % 60.24/8.96 | | | | % 60.24/8.96 | | | | (48) join_of_latt_set(all_143_0, empty_set) = empty_set & % 60.24/8.96 | | | | $i(empty_set) % 60.24/8.96 | | | | % 60.24/8.96 | | | | ALPHA: (48) implies: % 60.24/8.96 | | | | (49) join_of_latt_set(all_143_0, empty_set) = empty_set % 60.24/8.96 | | | | % 60.24/8.96 | | | | BETA: splitting (44) gives: % 60.24/8.96 | | | | % 60.24/8.96 | | | | Case 1: % 60.24/8.96 | | | | | % 60.24/8.96 | | | | | (50) empty_carrier(all_143_0) % 60.24/8.96 | | | | | % 60.24/8.96 | | | | | GROUND_INST: instantiating (8) with all_109_2, all_143_0, simplifying % 60.24/8.96 | | | | | with (20), (32), (50) gives: % 60.24/8.96 | | | | | (51) $false % 60.24/8.96 | | | | | % 60.24/8.96 | | | | | CLOSE: (51) is inconsistent. % 60.24/8.96 | | | | | % 60.24/8.96 | | | | Case 2: % 60.24/8.96 | | | | | % 60.24/8.96 | | | | | (52) join_of_latt_set(all_143_0, empty_set) = all_109_0 & % 60.24/8.96 | | | | | $i(all_109_0) % 60.24/8.96 | | | | | % 60.24/8.96 | | | | | ALPHA: (52) implies: % 60.24/8.96 | | | | | (53) join_of_latt_set(all_143_0, empty_set) = all_109_0 % 60.24/8.96 | | | | | % 60.24/8.96 | | | | | GROUND_INST: instantiating (14) with empty_set, all_109_0, empty_set, % 60.24/8.96 | | | | | all_143_0, simplifying with (49), (53) gives: % 60.24/8.96 | | | | | (54) all_109_0 = empty_set % 60.24/8.96 | | | | | % 60.24/8.96 | | | | | REDUCE: (19), (54) imply: % 60.24/8.96 | | | | | (55) $false % 60.24/8.96 | | | | | % 60.24/8.96 | | | | | CLOSE: (55) is inconsistent. % 60.24/8.96 | | | | | % 60.24/8.96 | | | | End of split % 60.24/8.96 | | | | % 60.24/8.96 | | | End of split % 60.24/8.96 | | | % 60.24/8.96 | | End of split % 60.24/8.96 | | % 60.24/8.96 | End of split % 60.24/8.96 | % 60.24/8.96 End of proof % 60.24/8.96 % SZS output end Proof for theBenchmark % 60.24/8.96 % 60.24/8.96 8412ms %------------------------------------------------------------------------------