%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : GRP620+1 : TPTP v8.1.2. Released v3.4.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n004.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 01:12:35 EDT 2023 % Result : Theorem 70.43s 10.07s % Output : Proof 93.95s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.09 % Problem : GRP620+1 : TPTP v8.1.2. Released v3.4.0. % 0.08/0.10 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.10/0.30 % Computer : n004.cluster.edu % 0.10/0.30 % Model : x86_64 x86_64 % 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.10/0.30 % Memory : 8042.1875MB % 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64 % 0.10/0.30 % CPULimit : 300 % 0.10/0.30 % WCLimit : 300 % 0.10/0.30 % DateTime : Mon Aug 28 21:49:37 EDT 2023 % 0.10/0.30 % CPUTime : % 0.14/0.58 ________ _____ % 0.14/0.58 ___ __ \_________(_)________________________________ % 0.14/0.58 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.14/0.58 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.14/0.58 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.14/0.58 % 0.14/0.58 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.14/0.58 (2023-06-19) % 0.14/0.58 % 0.14/0.58 (c) Philipp Rümmer, 2009-2023 % 0.14/0.58 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.14/0.58 Amanda Stjerna. % 0.14/0.58 Free software under BSD-3-Clause. % 0.14/0.58 % 0.14/0.58 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.14/0.58 % 0.14/0.58 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.14/0.60 Running up to 7 provers in parallel. % 0.14/0.61 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.14/0.61 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.14/0.61 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.14/0.61 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.14/0.61 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.14/0.61 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 0.14/0.61 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 3.82/1.32 Prover 4: Preprocessing ... % 3.82/1.34 Prover 1: Preprocessing ... % 3.82/1.37 Prover 2: Preprocessing ... % 3.82/1.37 Prover 6: Preprocessing ... % 3.82/1.37 Prover 0: Preprocessing ... % 3.82/1.37 Prover 3: Preprocessing ... % 4.63/1.38 Prover 5: Preprocessing ... % 12.93/2.60 Prover 1: Warning: ignoring some quantifiers % 13.52/2.62 Prover 5: Proving ... % 13.88/2.65 Prover 3: Warning: ignoring some quantifiers % 14.42/2.69 Prover 3: Constructing countermodel ... % 14.42/2.70 Prover 1: Constructing countermodel ... % 14.42/2.70 Prover 2: Proving ... % 15.18/2.81 Prover 6: Proving ... % 57.65/8.34 Prover 3: gave up % 57.76/8.36 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 58.63/8.52 Prover 7: Preprocessing ... % 61.57/8.89 Prover 7: Warning: ignoring some quantifiers % 62.24/8.95 Prover 7: Constructing countermodel ... % 70.43/10.04 Prover 5: proved (9425ms) % 70.43/10.07 % 70.43/10.07 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 70.43/10.07 % 70.43/10.07 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 70.43/10.08 Prover 6: stopped % 70.43/10.08 Prover 2: stopped % 70.43/10.09 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 70.43/10.09 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 72.18/10.28 Prover 8: Preprocessing ... % 72.18/10.29 Prover 11: Preprocessing ... % 73.36/10.40 Prover 10: Preprocessing ... % 75.31/10.68 Prover 10: Warning: ignoring some quantifiers % 75.31/10.69 Prover 8: Warning: ignoring some quantifiers % 75.31/10.72 Prover 10: Constructing countermodel ... % 75.31/10.72 Prover 8: Constructing countermodel ... % 79.94/11.30 Prover 4: Warning: ignoring some quantifiers % 79.94/11.50 Prover 4: Constructing countermodel ... % 85.38/11.98 Prover 10: Found proof (size 124) % 85.38/11.98 Prover 10: proved (1893ms) % 85.38/11.98 Prover 7: stopped % 85.38/11.98 Prover 8: stopped % 85.38/11.98 Prover 11: stopped % 85.38/11.99 Prover 1: stopped % 85.38/12.00 Prover 4: stopped % 92.88/13.75 Prover 0: Proving ... % 92.88/13.75 Prover 0: stopped % 92.88/13.75 % 92.88/13.75 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 92.88/13.75 % 92.88/13.77 % SZS output start Proof for theBenchmark % 92.88/13.78 Assumptions after simplification: % 92.88/13.78 --------------------------------- % 92.88/13.78 % 92.88/13.78 (cc1_fraenkel) % 92.88/13.79 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ m1_subset_1(v1, v0) | % 92.88/13.79 ~ v1_fraenkel(v0) | v1_funct_1(v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) % 92.88/13.79 | ~ $i(v0) | ~ m1_subset_1(v1, v0) | ~ v1_fraenkel(v0) | v1_relat_1(v1)) % 92.88/13.79 % 92.88/13.79 (d1_autgroup) % 93.20/13.84 ! [v0: $i] : ! [v1: $i] : ( ~ (k1_autgroup(v0) = v1) | ~ $i(v0) | ~ % 93.20/13.84 l1_group_1(v0) | ~ v4_group_1(v0) | ~ v3_group_1(v0) | ~ v1_group_1(v0) | % 93.20/13.84 v3_struct_0(v0) | ? [v2: $i] : (u1_struct_0(v0) = v2 & $i(v2) & ! [v3: $i] % 93.20/13.84 : (v3 = v1 | ~ $i(v3) | ~ m1_fraenkel(v3, v2, v2) | ? [v4: $i] : % 93.20/13.84 ($i(v4) & ((m2_relset_1(v4, v2, v2) & v1_group_6(v4, v0, v0) & % 93.20/13.84 v1_funct_2(v4, v2, v2) & v1_funct_1(v4) & ( ~ v3_group_6(v4, v0, % 93.20/13.84 v0) | ~ v2_funct_1(v4) | ~ r2_hidden(v4, v3)) & % 93.20/13.84 (r2_hidden(v4, v3) | (v3_group_6(v4, v0, v0) & v2_funct_1(v4)))) | % 93.20/13.84 (m2_fraenkel(v4, v2, v2, v3) & ( ~ m2_relset_1(v4, v2, v2) | ~ % 93.20/13.84 v1_group_6(v4, v0, v0) | ~ v1_funct_2(v4, v2, v2) | ~ % 93.20/13.84 v1_funct_1(v4)))))) & ! [v3: $i] : ( ~ $i(v3) | ~ $i(v1) | ~ % 93.20/13.84 m1_fraenkel(v1, v2, v2) | ~ v3_group_6(v3, v0, v0) | ~ m2_relset_1(v3, % 93.20/13.84 v2, v2) | ~ v1_group_6(v3, v0, v0) | ~ v2_funct_1(v3) | ~ % 93.20/13.84 v1_funct_2(v3, v2, v2) | ~ v1_funct_1(v3) | r2_hidden(v3, v1)) & ! % 93.20/13.84 [v3: $i] : ( ~ $i(v3) | ~ $i(v1) | ~ m1_fraenkel(v1, v2, v2) | ~ % 93.20/13.84 m2_relset_1(v3, v2, v2) | ~ v1_group_6(v3, v0, v0) | ~ v1_funct_2(v3, % 93.20/13.84 v2, v2) | ~ v1_funct_1(v3) | ~ r2_hidden(v3, v1) | v3_group_6(v3, % 93.20/13.84 v0, v0)) & ! [v3: $i] : ( ~ $i(v3) | ~ $i(v1) | ~ m1_fraenkel(v1, % 93.20/13.84 v2, v2) | ~ m2_relset_1(v3, v2, v2) | ~ v1_group_6(v3, v0, v0) | ~ % 93.20/13.84 v1_funct_2(v3, v2, v2) | ~ v1_funct_1(v3) | ~ r2_hidden(v3, v1) | % 93.20/13.84 v2_funct_1(v3)) & ! [v3: $i] : ( ~ $i(v3) | ~ $i(v1) | ~ % 93.20/13.84 m1_fraenkel(v1, v2, v2) | ~ m2_fraenkel(v3, v2, v2, v1) | % 93.20/13.84 m2_relset_1(v3, v2, v2)) & ! [v3: $i] : ( ~ $i(v3) | ~ $i(v1) | ~ % 93.20/13.84 m1_fraenkel(v1, v2, v2) | ~ m2_fraenkel(v3, v2, v2, v1) | % 93.20/13.84 v1_group_6(v3, v0, v0)) & ! [v3: $i] : ( ~ $i(v3) | ~ $i(v1) | ~ % 93.20/13.84 m1_fraenkel(v1, v2, v2) | ~ m2_fraenkel(v3, v2, v2, v1) | % 93.20/13.84 v1_funct_2(v3, v2, v2)) & ! [v3: $i] : ( ~ $i(v3) | ~ $i(v1) | ~ % 93.20/13.84 m1_fraenkel(v1, v2, v2) | ~ m2_fraenkel(v3, v2, v2, v1) | % 93.20/13.84 v1_funct_1(v3)))) % 93.20/13.84 % 93.20/13.84 (dt_k1_autgroup) % 93.20/13.84 ! [v0: $i] : ! [v1: $i] : ( ~ (k1_autgroup(v0) = v1) | ~ $i(v0) | ~ % 93.20/13.84 l1_group_1(v0) | ~ v4_group_1(v0) | ~ v3_group_1(v0) | ~ v1_group_1(v0) | % 93.20/13.84 v3_struct_0(v0) | ? [v2: $i] : (u1_struct_0(v0) = v2 & $i(v2) & % 93.20/13.84 m1_fraenkel(v1, v2, v2))) % 93.20/13.84 % 93.20/13.84 (dt_k2_funct_1) % 93.20/13.84 ! [v0: $i] : ! [v1: $i] : ( ~ (k2_funct_1(v0) = v1) | ~ $i(v0) | ~ % 93.20/13.84 v1_funct_1(v0) | ~ v1_relat_1(v0) | v1_funct_1(v1)) & ! [v0: $i] : ! [v1: % 93.20/13.84 $i] : ( ~ (k2_funct_1(v0) = v1) | ~ $i(v0) | ~ v1_funct_1(v0) | ~ % 93.20/13.84 v1_relat_1(v0) | v1_relat_1(v1)) % 93.20/13.84 % 93.20/13.84 (dt_l1_group_1) % 93.20/13.85 ! [v0: $i] : ( ~ $i(v0) | ~ l1_group_1(v0) | l1_struct_0(v0)) % 93.20/13.85 % 93.20/13.85 (dt_m1_fraenkel) % 93.20/13.85 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 93.20/13.85 ~ m1_fraenkel(v2, v0, v1) | ~ v1_xboole_0(v2)) & ! [v0: $i] : ! [v1: $i] % 93.20/13.85 : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ m1_fraenkel(v2, v0, % 93.20/13.85 v1) | v1_fraenkel(v2)) % 93.20/13.85 % 93.20/13.85 (dt_m2_fraenkel) % 93.20/13.85 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2) % 93.20/13.85 | ~ $i(v1) | ~ $i(v0) | ~ m1_fraenkel(v2, v0, v1) | ~ m2_fraenkel(v3, % 93.20/13.85 v0, v1, v2) | m2_relset_1(v3, v0, v1) | v1_xboole_0(v1)) & ! [v0: $i] : % 93.20/13.85 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | % 93.20/13.85 ~ $i(v0) | ~ m1_fraenkel(v2, v0, v1) | ~ m2_fraenkel(v3, v0, v1, v2) | % 93.20/13.85 v1_funct_2(v3, v0, v1) | v1_xboole_0(v1)) & ! [v0: $i] : ! [v1: $i] : ! % 93.20/13.85 [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 93.20/13.85 m1_fraenkel(v2, v0, v1) | ~ m2_fraenkel(v3, v0, v1, v2) | v1_xboole_0(v1) | % 93.20/13.85 v1_funct_1(v3)) % 93.20/13.85 % 93.20/13.85 (fc1_struct_0) % 93.20/13.85 ! [v0: $i] : ! [v1: $i] : ( ~ (u1_struct_0(v0) = v1) | ~ $i(v0) | ~ % 93.20/13.85 l1_struct_0(v0) | ~ v1_xboole_0(v1) | v3_struct_0(v0)) % 93.20/13.85 % 93.20/13.85 (redefinition_m2_fraenkel) % 93.20/13.85 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2) % 93.20/13.85 | ~ $i(v1) | ~ $i(v0) | ~ m1_fraenkel(v2, v0, v1) | ~ m1_subset_1(v3, % 93.20/13.85 v2) | v1_xboole_0(v1) | m2_fraenkel(v3, v0, v1, v2)) & ! [v0: $i] : ! % 93.20/13.85 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 93.20/13.85 $i(v0) | ~ m1_fraenkel(v2, v0, v1) | ~ m2_fraenkel(v3, v0, v1, v2) | % 93.20/13.85 v1_xboole_0(v1) | m1_subset_1(v3, v2)) % 93.20/13.85 % 93.20/13.85 (t1_subset) % 93.20/13.85 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ r2_hidden(v0, v1) | % 93.20/13.85 m1_subset_1(v0, v1)) % 93.20/13.85 % 93.20/13.85 (t2_subset) % 93.20/13.86 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ m1_subset_1(v0, v1) | % 93.20/13.86 v1_xboole_0(v1) | r2_hidden(v0, v1)) % 93.20/13.86 % 93.20/13.86 (t5_autgroup) % 93.20/13.86 ! [v0: $i] : ! [v1: $i] : ( ~ (k1_autgroup(v0) = v1) | ~ $i(v0) | ~ % 93.20/13.86 l1_group_1(v0) | ~ v4_group_1(v0) | ~ v3_group_1(v0) | ~ v1_group_1(v0) | % 93.20/13.86 v3_struct_0(v0) | ? [v2: $i] : (u1_struct_0(v0) = v2 & $i(v2) & ! [v3: $i] % 93.20/13.86 : ( ~ $i(v3) | ~ v4_group_6(v3, v0, v0) | ~ m2_relset_1(v3, v2, v2) | ~ % 93.20/13.86 v1_group_6(v3, v0, v0) | ~ v1_funct_2(v3, v2, v2) | ~ v1_funct_1(v3) | % 93.20/13.86 r2_hidden(v3, v1)) & ! [v3: $i] : ( ~ $i(v3) | ~ m2_relset_1(v3, v2, % 93.20/13.86 v2) | ~ v1_group_6(v3, v0, v0) | ~ v1_funct_2(v3, v2, v2) | ~ % 93.20/13.86 v1_funct_1(v3) | ~ r2_hidden(v3, v1) | v4_group_6(v3, v0, v0)))) % 93.20/13.86 % 93.20/13.86 (t6_autgroup) % 93.20/13.86 ! [v0: $i] : ! [v1: $i] : ( ~ (k1_autgroup(v0) = v1) | ~ $i(v0) | ~ % 93.20/13.86 l1_group_1(v0) | ~ v4_group_1(v0) | ~ v3_group_1(v0) | ~ v1_group_1(v0) | % 93.20/13.86 v3_struct_0(v0) | ? [v2: $i] : (u1_struct_0(v0) = v2 & $i(v2) & ! [v3: $i] % 93.20/13.86 : ! [v4: $i] : ( ~ (k2_funct_1(v3) = v4) | ~ $i(v3) | ~ m2_fraenkel(v3, % 93.20/13.86 v2, v2, v1) | m2_relset_1(v4, v2, v2)) & ! [v3: $i] : ! [v4: $i] : ( % 93.20/13.86 ~ (k2_funct_1(v3) = v4) | ~ $i(v3) | ~ m2_fraenkel(v3, v2, v2, v1) | % 93.20/13.86 v1_group_6(v4, v0, v0)) & ! [v3: $i] : ! [v4: $i] : ( ~ % 93.20/13.86 (k2_funct_1(v3) = v4) | ~ $i(v3) | ~ m2_fraenkel(v3, v2, v2, v1) | % 93.20/13.86 v1_funct_2(v4, v2, v2)) & ! [v3: $i] : ! [v4: $i] : ( ~ % 93.20/13.86 (k2_funct_1(v3) = v4) | ~ $i(v3) | ~ m2_fraenkel(v3, v2, v2, v1) | % 93.20/13.86 v1_funct_1(v4)))) % 93.20/13.86 % 93.20/13.86 (t73_group_6) % 93.20/13.87 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 93.20/13.87 $i] : ( ~ (k2_funct_1(v4) = v5) | ~ (u1_struct_0(v2) = v3) | ~ % 93.20/13.87 (u1_struct_0(v0) = v1) | ~ $i(v5) | ~ $i(v4) | ~ $i(v2) | ~ $i(v0) | ~ % 93.20/13.87 v4_group_6(v4, v2, v0) | ~ m2_relset_1(v5, v1, v3) | ~ m2_relset_1(v4, v3, % 93.20/13.87 v1) | ~ v1_group_6(v5, v0, v2) | ~ v1_group_6(v4, v2, v0) | ~ % 93.20/13.87 v1_funct_2(v5, v1, v3) | ~ v1_funct_2(v4, v3, v1) | ~ v1_funct_1(v5) | ~ % 93.20/13.87 v1_funct_1(v4) | ~ l1_group_1(v2) | ~ l1_group_1(v0) | ~ v4_group_1(v2) | % 93.20/13.87 ~ v4_group_1(v0) | ~ v3_group_1(v2) | ~ v3_group_1(v0) | v4_group_6(v5, % 93.20/13.87 v0, v2) | v3_struct_0(v2) | v3_struct_0(v0)) % 93.20/13.87 % 93.20/13.87 (t7_autgroup) % 93.20/13.87 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 93.20/13.87 (k2_funct_1(v3) = v4 & k1_autgroup(v0) = v2 & u1_struct_0(v0) = v1 & $i(v4) & % 93.20/13.87 $i(v3) & $i(v2) & $i(v1) & $i(v0) & m2_fraenkel(v3, v1, v1, v2) & % 93.20/13.87 l1_group_1(v0) & v4_group_1(v0) & v3_group_1(v0) & v1_group_1(v0) & ~ % 93.20/13.87 m2_fraenkel(v4, v1, v1, v2) & ~ v3_struct_0(v0)) % 93.20/13.87 % 93.20/13.87 (function-axioms) % 93.46/13.87 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 93.46/13.87 (k2_zfmisc_1(v3, v2) = v1) | ~ (k2_zfmisc_1(v3, v2) = v0)) & ! [v0: $i] : % 93.46/13.87 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (g1_group_1(v3, v2) = % 93.46/13.87 v1) | ~ (g1_group_1(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 93.46/13.87 $i] : (v1 = v0 | ~ (k2_funct_1(v2) = v1) | ~ (k2_funct_1(v2) = v0)) & ! % 93.46/13.87 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (k1_autgroup(v2) = v1) | % 93.46/13.87 ~ (k1_autgroup(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 93.46/13.87 v0 | ~ (k1_zfmisc_1(v2) = v1) | ~ (k1_zfmisc_1(v2) = v0)) & ! [v0: $i] : % 93.46/13.87 ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (u1_struct_0(v2) = v1) | ~ % 93.46/13.87 (u1_struct_0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 % 93.46/13.87 | ~ (u1_group_1(v2) = v1) | ~ (u1_group_1(v2) = v0)) % 93.46/13.87 % 93.46/13.87 Further assumptions not needed in the proof: % 93.46/13.87 -------------------------------------------- % 93.46/13.88 abstractness_v1_group_1, antisymmetry_r2_hidden, cc1_funct_1, cc1_funct_2, % 93.46/13.88 cc1_group_1, cc1_relset_1, cc2_funct_1, cc5_funct_2, cc6_funct_2, d12_group_6, % 93.46/13.88 d14_group_6, dt_g1_group_1, dt_k1_xboole_0, dt_k1_zfmisc_1, dt_k2_zfmisc_1, % 93.46/13.88 dt_l1_struct_0, dt_m1_relset_1, dt_m1_subset_1, dt_m2_relset_1, dt_u1_group_1, % 93.46/13.88 dt_u1_struct_0, existence_l1_group_1, existence_l1_struct_0, % 93.46/13.88 existence_m1_fraenkel, existence_m1_relset_1, existence_m1_subset_1, % 93.46/13.88 existence_m2_fraenkel, existence_m2_relset_1, fc1_group_1, fc1_xboole_0, % 93.46/13.88 free_g1_group_1, rc1_fraenkel, rc1_funct_1, rc1_funct_2, rc1_group_1, % 93.46/13.88 rc1_partfun1, rc1_xboole_0, rc2_funct_1, rc2_group_1, rc2_group_6, rc2_partfun1, % 93.46/13.88 rc2_xboole_0, rc3_funct_1, rc3_group_1, rc3_struct_0, rc5_struct_0, % 93.46/13.88 redefinition_m2_relset_1, reflexivity_r1_tarski, t3_subset, t4_subset, % 93.46/13.88 t5_subset, t6_boole, t7_boole, t8_boole % 93.46/13.88 % 93.46/13.88 Those formulas are unsatisfiable: % 93.46/13.88 --------------------------------- % 93.46/13.88 % 93.46/13.88 Begin of proof % 93.46/13.88 | % 93.46/13.88 | ALPHA: (cc1_fraenkel) implies: % 93.46/13.88 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ m1_subset_1(v1, % 93.46/13.88 | v0) | ~ v1_fraenkel(v0) | v1_relat_1(v1)) % 93.46/13.88 | % 93.46/13.88 | ALPHA: (dt_k2_funct_1) implies: % 93.46/13.88 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (k2_funct_1(v0) = v1) | ~ $i(v0) | ~ % 93.46/13.88 | v1_funct_1(v0) | ~ v1_relat_1(v0) | v1_funct_1(v1)) % 93.46/13.88 | % 93.46/13.88 | ALPHA: (dt_m1_fraenkel) implies: % 93.46/13.88 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ % 93.46/13.88 | $i(v0) | ~ m1_fraenkel(v2, v0, v1) | v1_fraenkel(v2)) % 93.46/13.88 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ % 93.46/13.88 | $i(v0) | ~ m1_fraenkel(v2, v0, v1) | ~ v1_xboole_0(v2)) % 93.46/13.88 | % 93.46/13.88 | ALPHA: (dt_m2_fraenkel) implies: % 93.46/13.88 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ % 93.46/13.88 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ m1_fraenkel(v2, v0, v1) | ~ % 93.46/13.88 | m2_fraenkel(v3, v0, v1, v2) | v1_xboole_0(v1) | v1_funct_1(v3)) % 93.46/13.89 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ % 93.46/13.89 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ m1_fraenkel(v2, v0, v1) | ~ % 93.46/13.89 | m2_fraenkel(v3, v0, v1, v2) | v1_funct_2(v3, v0, v1) | % 93.46/13.89 | v1_xboole_0(v1)) % 93.46/13.89 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ % 93.46/13.89 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ m1_fraenkel(v2, v0, v1) | ~ % 93.46/13.89 | m2_fraenkel(v3, v0, v1, v2) | m2_relset_1(v3, v0, v1) | % 93.46/13.89 | v1_xboole_0(v1)) % 93.46/13.89 | % 93.46/13.89 | ALPHA: (redefinition_m2_fraenkel) implies: % 93.46/13.89 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ % 93.46/13.89 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ m1_fraenkel(v2, v0, v1) | ~ % 93.46/13.89 | m2_fraenkel(v3, v0, v1, v2) | v1_xboole_0(v1) | m1_subset_1(v3, v2)) % 93.46/13.89 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ % 93.46/13.89 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ m1_fraenkel(v2, v0, v1) | ~ % 93.46/13.89 | m1_subset_1(v3, v2) | v1_xboole_0(v1) | m2_fraenkel(v3, v0, v1, v2)) % 93.46/13.89 | % 93.46/13.89 | ALPHA: (function-axioms) implies: % 93.46/13.89 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 93.46/13.89 | (u1_struct_0(v2) = v1) | ~ (u1_struct_0(v2) = v0)) % 93.46/13.89 | % 93.46/13.89 | DELTA: instantiating (t7_autgroup) with fresh symbols all_78_0, all_78_1, % 93.46/13.89 | all_78_2, all_78_3, all_78_4 gives: % 93.46/13.89 | (11) k2_funct_1(all_78_1) = all_78_0 & k1_autgroup(all_78_4) = all_78_2 & % 93.46/13.89 | u1_struct_0(all_78_4) = all_78_3 & $i(all_78_0) & $i(all_78_1) & % 93.46/13.89 | $i(all_78_2) & $i(all_78_3) & $i(all_78_4) & m2_fraenkel(all_78_1, % 93.46/13.89 | all_78_3, all_78_3, all_78_2) & l1_group_1(all_78_4) & % 93.46/13.89 | v4_group_1(all_78_4) & v3_group_1(all_78_4) & v1_group_1(all_78_4) & % 93.46/13.89 | ~ m2_fraenkel(all_78_0, all_78_3, all_78_3, all_78_2) & ~ % 93.46/13.89 | v3_struct_0(all_78_4) % 93.46/13.90 | % 93.46/13.90 | ALPHA: (11) implies: % 93.46/13.90 | (12) ~ v3_struct_0(all_78_4) % 93.46/13.90 | (13) ~ m2_fraenkel(all_78_0, all_78_3, all_78_3, all_78_2) % 93.46/13.90 | (14) v1_group_1(all_78_4) % 93.46/13.90 | (15) v3_group_1(all_78_4) % 93.46/13.90 | (16) v4_group_1(all_78_4) % 93.46/13.90 | (17) l1_group_1(all_78_4) % 93.46/13.90 | (18) m2_fraenkel(all_78_1, all_78_3, all_78_3, all_78_2) % 93.46/13.90 | (19) $i(all_78_4) % 93.46/13.90 | (20) $i(all_78_2) % 93.46/13.90 | (21) $i(all_78_1) % 93.46/13.90 | (22) $i(all_78_0) % 93.46/13.90 | (23) u1_struct_0(all_78_4) = all_78_3 % 93.46/13.90 | (24) k1_autgroup(all_78_4) = all_78_2 % 93.46/13.90 | (25) k2_funct_1(all_78_1) = all_78_0 % 93.46/13.90 | % 93.46/13.90 | GROUND_INST: instantiating (dt_l1_group_1) with all_78_4, simplifying with % 93.46/13.90 | (17), (19) gives: % 93.46/13.90 | (26) l1_struct_0(all_78_4) % 93.46/13.90 | % 93.46/13.90 | GROUND_INST: instantiating (dt_k1_autgroup) with all_78_4, all_78_2, % 93.46/13.90 | simplifying with (12), (14), (15), (16), (17), (19), (24) gives: % 93.46/13.90 | (27) ? [v0: $i] : (u1_struct_0(all_78_4) = v0 & $i(v0) & % 93.46/13.90 | m1_fraenkel(all_78_2, v0, v0)) % 93.46/13.90 | % 93.46/13.90 | GROUND_INST: instantiating (t6_autgroup) with all_78_4, all_78_2, simplifying % 93.46/13.90 | with (12), (14), (15), (16), (17), (19), (24) gives: % 93.46/13.91 | (28) ? [v0: $i] : (u1_struct_0(all_78_4) = v0 & $i(v0) & ! [v1: $i] : ! % 93.46/13.91 | [v2: $i] : ( ~ (k2_funct_1(v1) = v2) | ~ $i(v1) | ~ % 93.46/13.91 | m2_fraenkel(v1, v0, v0, all_78_2) | m2_relset_1(v2, v0, v0)) & ! % 93.46/13.91 | [v1: $i] : ! [v2: $i] : ( ~ (k2_funct_1(v1) = v2) | ~ $i(v1) | ~ % 93.46/13.91 | m2_fraenkel(v1, v0, v0, all_78_2) | v1_group_6(v2, all_78_4, % 93.46/13.91 | all_78_4)) & ! [v1: $i] : ! [v2: $i] : ( ~ (k2_funct_1(v1) = % 93.46/13.91 | v2) | ~ $i(v1) | ~ m2_fraenkel(v1, v0, v0, all_78_2) | % 93.46/13.91 | v1_funct_2(v2, v0, v0)) & ! [v1: $i] : ! [v2: $i] : ( ~ % 93.46/13.91 | (k2_funct_1(v1) = v2) | ~ $i(v1) | ~ m2_fraenkel(v1, v0, v0, % 93.46/13.91 | all_78_2) | v1_funct_1(v2))) % 93.46/13.91 | % 93.46/13.91 | GROUND_INST: instantiating (d1_autgroup) with all_78_4, all_78_2, simplifying % 93.46/13.91 | with (12), (14), (15), (16), (17), (19), (24) gives: % 93.46/13.92 | (29) ? [v0: $i] : (u1_struct_0(all_78_4) = v0 & $i(v0) & ! [v1: any] : % 93.46/13.92 | (v1 = all_78_2 | ~ $i(v1) | ~ m1_fraenkel(v1, v0, v0) | ? [v2: % 93.46/13.92 | $i] : ($i(v2) & ((m2_relset_1(v2, v0, v0) & v1_group_6(v2, % 93.46/13.92 | all_78_4, all_78_4) & v1_funct_2(v2, v0, v0) & % 93.46/13.92 | v1_funct_1(v2) & ( ~ v3_group_6(v2, all_78_4, all_78_4) | ~ % 93.46/13.92 | v2_funct_1(v2) | ~ r2_hidden(v2, v1)) & (r2_hidden(v2, % 93.46/13.92 | v1) | (v3_group_6(v2, all_78_4, all_78_4) & % 93.46/13.92 | v2_funct_1(v2)))) | (m2_fraenkel(v2, v0, v0, v1) & ( ~ % 93.46/13.92 | m2_relset_1(v2, v0, v0) | ~ v1_group_6(v2, all_78_4, % 93.46/13.92 | all_78_4) | ~ v1_funct_2(v2, v0, v0) | ~ % 93.46/13.92 | v1_funct_1(v2)))))) & ! [v1: $i] : ( ~ $i(v1) | ~ % 93.46/13.92 | $i(all_78_2) | ~ m1_fraenkel(all_78_2, v0, v0) | ~ % 93.46/13.92 | v3_group_6(v1, all_78_4, all_78_4) | ~ m2_relset_1(v1, v0, v0) | % 93.46/13.92 | ~ v1_group_6(v1, all_78_4, all_78_4) | ~ v2_funct_1(v1) | ~ % 93.46/13.92 | v1_funct_2(v1, v0, v0) | ~ v1_funct_1(v1) | r2_hidden(v1, % 93.46/13.92 | all_78_2)) & ! [v1: $i] : ( ~ $i(v1) | ~ $i(all_78_2) | ~ % 93.46/13.92 | m1_fraenkel(all_78_2, v0, v0) | ~ m2_relset_1(v1, v0, v0) | ~ % 93.46/13.92 | v1_group_6(v1, all_78_4, all_78_4) | ~ v1_funct_2(v1, v0, v0) | % 93.46/13.92 | ~ v1_funct_1(v1) | ~ r2_hidden(v1, all_78_2) | v3_group_6(v1, % 93.46/13.92 | all_78_4, all_78_4)) & ! [v1: $i] : ( ~ $i(v1) | ~ % 93.46/13.92 | $i(all_78_2) | ~ m1_fraenkel(all_78_2, v0, v0) | ~ % 93.46/13.92 | m2_relset_1(v1, v0, v0) | ~ v1_group_6(v1, all_78_4, all_78_4) | % 93.46/13.92 | ~ v1_funct_2(v1, v0, v0) | ~ v1_funct_1(v1) | ~ r2_hidden(v1, % 93.46/13.92 | all_78_2) | v2_funct_1(v1)) & ! [v1: $i] : ( ~ $i(v1) | ~ % 93.46/13.92 | $i(all_78_2) | ~ m1_fraenkel(all_78_2, v0, v0) | ~ % 93.46/13.92 | m2_fraenkel(v1, v0, v0, all_78_2) | m2_relset_1(v1, v0, v0)) & ! % 93.46/13.92 | [v1: $i] : ( ~ $i(v1) | ~ $i(all_78_2) | ~ m1_fraenkel(all_78_2, % 93.46/13.92 | v0, v0) | ~ m2_fraenkel(v1, v0, v0, all_78_2) | v1_group_6(v1, % 93.46/13.92 | all_78_4, all_78_4)) & ! [v1: $i] : ( ~ $i(v1) | ~ % 93.46/13.92 | $i(all_78_2) | ~ m1_fraenkel(all_78_2, v0, v0) | ~ % 93.46/13.92 | m2_fraenkel(v1, v0, v0, all_78_2) | v1_funct_2(v1, v0, v0)) & ! % 93.46/13.92 | [v1: $i] : ( ~ $i(v1) | ~ $i(all_78_2) | ~ m1_fraenkel(all_78_2, % 93.46/13.92 | v0, v0) | ~ m2_fraenkel(v1, v0, v0, all_78_2) | % 93.46/13.92 | v1_funct_1(v1))) % 93.46/13.92 | % 93.46/13.92 | GROUND_INST: instantiating (t5_autgroup) with all_78_4, all_78_2, simplifying % 93.46/13.92 | with (12), (14), (15), (16), (17), (19), (24) gives: % 93.46/13.92 | (30) ? [v0: $i] : (u1_struct_0(all_78_4) = v0 & $i(v0) & ! [v1: $i] : ( ~ % 93.46/13.92 | $i(v1) | ~ v4_group_6(v1, all_78_4, all_78_4) | ~ % 93.46/13.92 | m2_relset_1(v1, v0, v0) | ~ v1_group_6(v1, all_78_4, all_78_4) | % 93.46/13.92 | ~ v1_funct_2(v1, v0, v0) | ~ v1_funct_1(v1) | r2_hidden(v1, % 93.46/13.92 | all_78_2)) & ! [v1: $i] : ( ~ $i(v1) | ~ m2_relset_1(v1, v0, % 93.46/13.92 | v0) | ~ v1_group_6(v1, all_78_4, all_78_4) | ~ v1_funct_2(v1, % 93.46/13.92 | v0, v0) | ~ v1_funct_1(v1) | ~ r2_hidden(v1, all_78_2) | % 93.46/13.92 | v4_group_6(v1, all_78_4, all_78_4))) % 93.46/13.92 | % 93.46/13.92 | DELTA: instantiating (27) with fresh symbol all_86_0 gives: % 93.46/13.92 | (31) u1_struct_0(all_78_4) = all_86_0 & $i(all_86_0) & % 93.46/13.92 | m1_fraenkel(all_78_2, all_86_0, all_86_0) % 93.46/13.92 | % 93.46/13.92 | ALPHA: (31) implies: % 93.46/13.92 | (32) m1_fraenkel(all_78_2, all_86_0, all_86_0) % 93.46/13.92 | (33) $i(all_86_0) % 93.46/13.92 | (34) u1_struct_0(all_78_4) = all_86_0 % 93.46/13.92 | % 93.46/13.92 | DELTA: instantiating (30) with fresh symbol all_90_0 gives: % 93.46/13.93 | (35) u1_struct_0(all_78_4) = all_90_0 & $i(all_90_0) & ! [v0: $i] : ( ~ % 93.46/13.93 | $i(v0) | ~ v4_group_6(v0, all_78_4, all_78_4) | ~ m2_relset_1(v0, % 93.46/13.93 | all_90_0, all_90_0) | ~ v1_group_6(v0, all_78_4, all_78_4) | ~ % 93.46/13.93 | v1_funct_2(v0, all_90_0, all_90_0) | ~ v1_funct_1(v0) | % 93.46/13.93 | r2_hidden(v0, all_78_2)) & ! [v0: $i] : ( ~ $i(v0) | ~ % 93.46/13.93 | m2_relset_1(v0, all_90_0, all_90_0) | ~ v1_group_6(v0, all_78_4, % 93.46/13.93 | all_78_4) | ~ v1_funct_2(v0, all_90_0, all_90_0) | ~ % 93.46/13.93 | v1_funct_1(v0) | ~ r2_hidden(v0, all_78_2) | v4_group_6(v0, % 93.46/13.93 | all_78_4, all_78_4)) % 93.46/13.93 | % 93.46/13.93 | ALPHA: (35) implies: % 93.46/13.93 | (36) u1_struct_0(all_78_4) = all_90_0 % 93.46/13.93 | (37) ! [v0: $i] : ( ~ $i(v0) | ~ m2_relset_1(v0, all_90_0, all_90_0) | ~ % 93.46/13.93 | v1_group_6(v0, all_78_4, all_78_4) | ~ v1_funct_2(v0, all_90_0, % 93.46/13.93 | all_90_0) | ~ v1_funct_1(v0) | ~ r2_hidden(v0, all_78_2) | % 93.46/13.93 | v4_group_6(v0, all_78_4, all_78_4)) % 93.46/13.93 | (38) ! [v0: $i] : ( ~ $i(v0) | ~ v4_group_6(v0, all_78_4, all_78_4) | ~ % 93.46/13.93 | m2_relset_1(v0, all_90_0, all_90_0) | ~ v1_group_6(v0, all_78_4, % 93.46/13.93 | all_78_4) | ~ v1_funct_2(v0, all_90_0, all_90_0) | ~ % 93.46/13.93 | v1_funct_1(v0) | r2_hidden(v0, all_78_2)) % 93.46/13.93 | % 93.46/13.93 | DELTA: instantiating (28) with fresh symbol all_93_0 gives: % 93.46/13.93 | (39) u1_struct_0(all_78_4) = all_93_0 & $i(all_93_0) & ! [v0: $i] : ! % 93.46/13.93 | [v1: $i] : ( ~ (k2_funct_1(v0) = v1) | ~ $i(v0) | ~ m2_fraenkel(v0, % 93.46/13.93 | all_93_0, all_93_0, all_78_2) | m2_relset_1(v1, all_93_0, % 93.46/13.93 | all_93_0)) & ! [v0: $i] : ! [v1: $i] : ( ~ (k2_funct_1(v0) = v1) % 93.46/13.93 | | ~ $i(v0) | ~ m2_fraenkel(v0, all_93_0, all_93_0, all_78_2) | % 93.46/13.93 | v1_group_6(v1, all_78_4, all_78_4)) & ! [v0: $i] : ! [v1: $i] : ( % 93.46/13.93 | ~ (k2_funct_1(v0) = v1) | ~ $i(v0) | ~ m2_fraenkel(v0, all_93_0, % 93.46/13.93 | all_93_0, all_78_2) | v1_funct_2(v1, all_93_0, all_93_0)) & ! % 93.46/13.93 | [v0: $i] : ! [v1: $i] : ( ~ (k2_funct_1(v0) = v1) | ~ $i(v0) | ~ % 93.46/13.93 | m2_fraenkel(v0, all_93_0, all_93_0, all_78_2) | v1_funct_1(v1)) % 93.46/13.93 | % 93.46/13.93 | ALPHA: (39) implies: % 93.46/13.93 | (40) u1_struct_0(all_78_4) = all_93_0 % 93.46/13.93 | (41) ! [v0: $i] : ! [v1: $i] : ( ~ (k2_funct_1(v0) = v1) | ~ $i(v0) | ~ % 93.46/13.93 | m2_fraenkel(v0, all_93_0, all_93_0, all_78_2) | v1_funct_2(v1, % 93.46/13.93 | all_93_0, all_93_0)) % 93.46/13.93 | (42) ! [v0: $i] : ! [v1: $i] : ( ~ (k2_funct_1(v0) = v1) | ~ $i(v0) | ~ % 93.46/13.93 | m2_fraenkel(v0, all_93_0, all_93_0, all_78_2) | v1_group_6(v1, % 93.46/13.93 | all_78_4, all_78_4)) % 93.46/13.93 | (43) ! [v0: $i] : ! [v1: $i] : ( ~ (k2_funct_1(v0) = v1) | ~ $i(v0) | ~ % 93.46/13.93 | m2_fraenkel(v0, all_93_0, all_93_0, all_78_2) | m2_relset_1(v1, % 93.46/13.93 | all_93_0, all_93_0)) % 93.46/13.93 | % 93.46/13.93 | DELTA: instantiating (29) with fresh symbol all_96_0 gives: % 93.46/13.94 | (44) u1_struct_0(all_78_4) = all_96_0 & $i(all_96_0) & ! [v0: any] : (v0 = % 93.46/13.94 | all_78_2 | ~ $i(v0) | ~ m1_fraenkel(v0, all_96_0, all_96_0) | ? % 93.46/13.94 | [v1: $i] : ($i(v1) & ((m2_relset_1(v1, all_96_0, all_96_0) & % 93.46/13.94 | v1_group_6(v1, all_78_4, all_78_4) & v1_funct_2(v1, all_96_0, % 93.46/13.94 | all_96_0) & v1_funct_1(v1) & ( ~ v3_group_6(v1, all_78_4, % 93.46/13.94 | all_78_4) | ~ v2_funct_1(v1) | ~ r2_hidden(v1, v0)) & % 93.46/13.94 | (r2_hidden(v1, v0) | (v3_group_6(v1, all_78_4, all_78_4) & % 93.46/13.94 | v2_funct_1(v1)))) | (m2_fraenkel(v1, all_96_0, all_96_0, % 93.46/13.94 | v0) & ( ~ m2_relset_1(v1, all_96_0, all_96_0) | ~ % 93.46/13.94 | v1_group_6(v1, all_78_4, all_78_4) | ~ v1_funct_2(v1, % 93.46/13.94 | all_96_0, all_96_0) | ~ v1_funct_1(v1)))))) & ! [v0: $i] % 93.46/13.94 | : ( ~ $i(v0) | ~ $i(all_78_2) | ~ m1_fraenkel(all_78_2, all_96_0, % 93.46/13.94 | all_96_0) | ~ v3_group_6(v0, all_78_4, all_78_4) | ~ % 93.46/13.94 | m2_relset_1(v0, all_96_0, all_96_0) | ~ v1_group_6(v0, all_78_4, % 93.46/13.94 | all_78_4) | ~ v2_funct_1(v0) | ~ v1_funct_2(v0, all_96_0, % 93.46/13.94 | all_96_0) | ~ v1_funct_1(v0) | r2_hidden(v0, all_78_2)) & ! [v0: % 93.46/13.94 | $i] : ( ~ $i(v0) | ~ $i(all_78_2) | ~ m1_fraenkel(all_78_2, % 93.46/13.94 | all_96_0, all_96_0) | ~ m2_relset_1(v0, all_96_0, all_96_0) | ~ % 93.46/13.94 | v1_group_6(v0, all_78_4, all_78_4) | ~ v1_funct_2(v0, all_96_0, % 93.46/13.94 | all_96_0) | ~ v1_funct_1(v0) | ~ r2_hidden(v0, all_78_2) | % 93.46/13.94 | v3_group_6(v0, all_78_4, all_78_4)) & ! [v0: $i] : ( ~ $i(v0) | ~ % 93.46/13.94 | $i(all_78_2) | ~ m1_fraenkel(all_78_2, all_96_0, all_96_0) | ~ % 93.46/13.94 | m2_relset_1(v0, all_96_0, all_96_0) | ~ v1_group_6(v0, all_78_4, % 93.46/13.94 | all_78_4) | ~ v1_funct_2(v0, all_96_0, all_96_0) | ~ % 93.46/13.94 | v1_funct_1(v0) | ~ r2_hidden(v0, all_78_2) | v2_funct_1(v0)) & ! % 93.46/13.94 | [v0: $i] : ( ~ $i(v0) | ~ $i(all_78_2) | ~ m1_fraenkel(all_78_2, % 93.46/13.94 | all_96_0, all_96_0) | ~ m2_fraenkel(v0, all_96_0, all_96_0, % 93.46/13.94 | all_78_2) | m2_relset_1(v0, all_96_0, all_96_0)) & ! [v0: $i] : ( % 93.46/13.94 | ~ $i(v0) | ~ $i(all_78_2) | ~ m1_fraenkel(all_78_2, all_96_0, % 93.46/13.94 | all_96_0) | ~ m2_fraenkel(v0, all_96_0, all_96_0, all_78_2) | % 93.46/13.94 | v1_group_6(v0, all_78_4, all_78_4)) & ! [v0: $i] : ( ~ $i(v0) | ~ % 93.46/13.94 | $i(all_78_2) | ~ m1_fraenkel(all_78_2, all_96_0, all_96_0) | ~ % 93.46/13.94 | m2_fraenkel(v0, all_96_0, all_96_0, all_78_2) | v1_funct_2(v0, % 93.46/13.94 | all_96_0, all_96_0)) & ! [v0: $i] : ( ~ $i(v0) | ~ $i(all_78_2) % 93.46/13.94 | | ~ m1_fraenkel(all_78_2, all_96_0, all_96_0) | ~ m2_fraenkel(v0, % 93.46/13.94 | all_96_0, all_96_0, all_78_2) | v1_funct_1(v0)) % 93.46/13.94 | % 93.46/13.94 | ALPHA: (44) implies: % 93.46/13.94 | (45) u1_struct_0(all_78_4) = all_96_0 % 93.46/13.94 | (46) ! [v0: $i] : ( ~ $i(v0) | ~ $i(all_78_2) | ~ m1_fraenkel(all_78_2, % 93.46/13.94 | all_96_0, all_96_0) | ~ m2_fraenkel(v0, all_96_0, all_96_0, % 93.46/13.94 | all_78_2) | v1_group_6(v0, all_78_4, all_78_4)) % 93.46/13.94 | % 93.46/13.94 | GROUND_INST: instantiating (10) with all_78_3, all_90_0, all_78_4, simplifying % 93.46/13.94 | with (23), (36) gives: % 93.46/13.94 | (47) all_90_0 = all_78_3 % 93.46/13.94 | % 93.46/13.94 | GROUND_INST: instantiating (10) with all_90_0, all_93_0, all_78_4, simplifying % 93.46/13.94 | with (36), (40) gives: % 93.46/13.94 | (48) all_93_0 = all_90_0 % 93.46/13.94 | % 93.46/13.94 | GROUND_INST: instantiating (10) with all_93_0, all_96_0, all_78_4, simplifying % 93.46/13.94 | with (40), (45) gives: % 93.46/13.94 | (49) all_96_0 = all_93_0 % 93.46/13.95 | % 93.46/13.95 | GROUND_INST: instantiating (10) with all_86_0, all_96_0, all_78_4, simplifying % 93.46/13.95 | with (34), (45) gives: % 93.46/13.95 | (50) all_96_0 = all_86_0 % 93.46/13.95 | % 93.46/13.95 | COMBINE_EQS: (49), (50) imply: % 93.46/13.95 | (51) all_93_0 = all_86_0 % 93.46/13.95 | % 93.46/13.95 | SIMP: (51) implies: % 93.46/13.95 | (52) all_93_0 = all_86_0 % 93.46/13.95 | % 93.46/13.95 | COMBINE_EQS: (48), (52) imply: % 93.46/13.95 | (53) all_90_0 = all_86_0 % 93.46/13.95 | % 93.46/13.95 | SIMP: (53) implies: % 93.46/13.95 | (54) all_90_0 = all_86_0 % 93.46/13.95 | % 93.46/13.95 | COMBINE_EQS: (47), (54) imply: % 93.46/13.95 | (55) all_86_0 = all_78_3 % 93.46/13.95 | % 93.46/13.95 | SIMP: (55) implies: % 93.46/13.95 | (56) all_86_0 = all_78_3 % 93.46/13.95 | % 93.46/13.95 | COMBINE_EQS: (52), (56) imply: % 93.46/13.95 | (57) all_93_0 = all_78_3 % 93.46/13.95 | % 93.46/13.95 | COMBINE_EQS: (50), (56) imply: % 93.46/13.95 | (58) all_96_0 = all_78_3 % 93.46/13.95 | % 93.46/13.95 | REDUCE: (33), (56) imply: % 93.46/13.95 | (59) $i(all_78_3) % 93.46/13.95 | % 93.46/13.95 | REDUCE: (32), (56) imply: % 93.46/13.95 | (60) m1_fraenkel(all_78_2, all_78_3, all_78_3) % 93.46/13.95 | % 93.46/13.95 | GROUND_INST: instantiating (7) with all_78_3, all_78_3, all_78_2, all_78_1, % 93.46/13.95 | simplifying with (18), (20), (21), (59), (60) gives: % 93.46/13.95 | (61) m2_relset_1(all_78_1, all_78_3, all_78_3) | v1_xboole_0(all_78_3) % 93.46/13.95 | % 93.46/13.95 | GROUND_INST: instantiating (6) with all_78_3, all_78_3, all_78_2, all_78_1, % 93.46/13.95 | simplifying with (18), (20), (21), (59), (60) gives: % 93.46/13.95 | (62) v1_funct_2(all_78_1, all_78_3, all_78_3) | v1_xboole_0(all_78_3) % 93.46/13.95 | % 93.46/13.95 | GROUND_INST: instantiating (5) with all_78_3, all_78_3, all_78_2, all_78_1, % 93.46/13.95 | simplifying with (18), (20), (21), (59), (60) gives: % 93.83/13.95 | (63) v1_xboole_0(all_78_3) | v1_funct_1(all_78_1) % 93.83/13.95 | % 93.83/13.95 | GROUND_INST: instantiating (8) with all_78_3, all_78_3, all_78_2, all_78_1, % 93.83/13.95 | simplifying with (18), (20), (21), (59), (60) gives: % 93.83/13.95 | (64) v1_xboole_0(all_78_3) | m1_subset_1(all_78_1, all_78_2) % 93.83/13.95 | % 93.83/13.95 | GROUND_INST: instantiating (3) with all_78_3, all_78_3, all_78_2, simplifying % 93.83/13.95 | with (20), (59), (60) gives: % 93.83/13.95 | (65) v1_fraenkel(all_78_2) % 93.83/13.95 | % 93.83/13.95 | BETA: splitting (61) gives: % 93.83/13.95 | % 93.83/13.95 | Case 1: % 93.83/13.95 | | % 93.83/13.95 | | (66) m2_relset_1(all_78_1, all_78_3, all_78_3) % 93.83/13.95 | | % 93.83/13.95 | | BETA: splitting (64) gives: % 93.83/13.95 | | % 93.83/13.95 | | Case 1: % 93.83/13.95 | | | % 93.83/13.95 | | | (67) v1_xboole_0(all_78_3) % 93.83/13.95 | | | % 93.83/13.95 | | | GROUND_INST: instantiating (fc1_struct_0) with all_78_4, all_78_3, % 93.83/13.95 | | | simplifying with (12), (19), (23), (26), (67) gives: % 93.83/13.95 | | | (68) $false % 93.83/13.95 | | | % 93.83/13.95 | | | CLOSE: (68) is inconsistent. % 93.83/13.95 | | | % 93.83/13.95 | | Case 2: % 93.83/13.95 | | | % 93.83/13.95 | | | (69) m1_subset_1(all_78_1, all_78_2) % 93.83/13.95 | | | % 93.83/13.95 | | | BETA: splitting (63) gives: % 93.83/13.95 | | | % 93.83/13.95 | | | Case 1: % 93.83/13.95 | | | | % 93.83/13.96 | | | | (70) v1_xboole_0(all_78_3) % 93.83/13.96 | | | | % 93.83/13.96 | | | | GROUND_INST: instantiating (fc1_struct_0) with all_78_4, all_78_3, % 93.83/13.96 | | | | simplifying with (12), (19), (23), (26), (70) gives: % 93.83/13.96 | | | | (71) $false % 93.83/13.96 | | | | % 93.83/13.96 | | | | CLOSE: (71) is inconsistent. % 93.83/13.96 | | | | % 93.83/13.96 | | | Case 2: % 93.83/13.96 | | | | % 93.83/13.96 | | | | (72) ~ v1_xboole_0(all_78_3) % 93.83/13.96 | | | | (73) v1_funct_1(all_78_1) % 93.83/13.96 | | | | % 93.83/13.96 | | | | BETA: splitting (62) gives: % 93.83/13.96 | | | | % 93.83/13.96 | | | | Case 1: % 93.83/13.96 | | | | | % 93.83/13.96 | | | | | (74) v1_funct_2(all_78_1, all_78_3, all_78_3) % 93.83/13.96 | | | | | % 93.83/13.96 | | | | | GROUND_INST: instantiating (1) with all_78_2, all_78_1, simplifying % 93.83/13.96 | | | | | with (20), (21), (65), (69) gives: % 93.83/13.96 | | | | | (75) v1_relat_1(all_78_1) % 93.83/13.96 | | | | | % 93.83/13.96 | | | | | GROUND_INST: instantiating (t2_subset) with all_78_1, all_78_2, % 93.83/13.96 | | | | | simplifying with (20), (21), (69) gives: % 93.83/13.96 | | | | | (76) v1_xboole_0(all_78_2) | r2_hidden(all_78_1, all_78_2) % 93.83/13.96 | | | | | % 93.83/13.96 | | | | | GROUND_INST: instantiating (2) with all_78_1, all_78_0, simplifying % 93.83/13.96 | | | | | with (21), (25), (73), (75) gives: % 93.83/13.96 | | | | | (77) v1_funct_1(all_78_0) % 93.83/13.96 | | | | | % 93.83/13.96 | | | | | BETA: splitting (76) gives: % 93.83/13.96 | | | | | % 93.83/13.96 | | | | | Case 1: % 93.83/13.96 | | | | | | % 93.83/13.96 | | | | | | (78) v1_xboole_0(all_78_2) % 93.83/13.96 | | | | | | % 93.83/13.96 | | | | | | GROUND_INST: instantiating (4) with all_78_3, all_78_3, all_78_2, % 93.83/13.96 | | | | | | simplifying with (20), (59), (60), (78) gives: % 93.83/13.96 | | | | | | (79) $false % 93.83/13.96 | | | | | | % 93.83/13.96 | | | | | | CLOSE: (79) is inconsistent. % 93.83/13.96 | | | | | | % 93.83/13.96 | | | | | Case 2: % 93.83/13.96 | | | | | | % 93.83/13.96 | | | | | | (80) r2_hidden(all_78_1, all_78_2) % 93.83/13.96 | | | | | | % 93.83/13.96 | | | | | | GROUND_INST: instantiating (43) with all_78_1, all_78_0, simplifying % 93.83/13.96 | | | | | | with (21), (25) gives: % 93.83/13.96 | | | | | | (81) ~ m2_fraenkel(all_78_1, all_93_0, all_93_0, all_78_2) | % 93.83/13.96 | | | | | | m2_relset_1(all_78_0, all_93_0, all_93_0) % 93.83/13.96 | | | | | | % 93.83/13.96 | | | | | | GROUND_INST: instantiating (42) with all_78_1, all_78_0, simplifying % 93.83/13.96 | | | | | | with (21), (25) gives: % 93.83/13.96 | | | | | | (82) ~ m2_fraenkel(all_78_1, all_93_0, all_93_0, all_78_2) | % 93.83/13.96 | | | | | | v1_group_6(all_78_0, all_78_4, all_78_4) % 93.83/13.96 | | | | | | % 93.83/13.96 | | | | | | GROUND_INST: instantiating (41) with all_78_1, all_78_0, simplifying % 93.83/13.96 | | | | | | with (21), (25) gives: % 93.83/13.96 | | | | | | (83) ~ m2_fraenkel(all_78_1, all_93_0, all_93_0, all_78_2) | % 93.83/13.96 | | | | | | v1_funct_2(all_78_0, all_93_0, all_93_0) % 93.83/13.96 | | | | | | % 93.83/13.96 | | | | | | GROUND_INST: instantiating (46) with all_78_1, simplifying with % 93.83/13.96 | | | | | | (20), (21) gives: % 93.83/13.96 | | | | | | (84) ~ m1_fraenkel(all_78_2, all_96_0, all_96_0) | ~ % 93.83/13.96 | | | | | | m2_fraenkel(all_78_1, all_96_0, all_96_0, all_78_2) | % 93.83/13.96 | | | | | | v1_group_6(all_78_1, all_78_4, all_78_4) % 93.83/13.96 | | | | | | % 93.83/13.96 | | | | | | BETA: splitting (83) gives: % 93.83/13.96 | | | | | | % 93.83/13.96 | | | | | | Case 1: % 93.83/13.96 | | | | | | | % 93.83/13.96 | | | | | | | (85) ~ m2_fraenkel(all_78_1, all_93_0, all_93_0, all_78_2) % 93.83/13.96 | | | | | | | % 93.83/13.96 | | | | | | | REDUCE: (57), (85) imply: % 93.83/13.96 | | | | | | | (86) ~ m2_fraenkel(all_78_1, all_78_3, all_78_3, all_78_2) % 93.83/13.96 | | | | | | | % 93.83/13.96 | | | | | | | PRED_UNIFY: (18), (86) imply: % 93.83/13.96 | | | | | | | (87) $false % 93.83/13.96 | | | | | | | % 93.83/13.96 | | | | | | | CLOSE: (87) is inconsistent. % 93.83/13.96 | | | | | | | % 93.83/13.96 | | | | | | Case 2: % 93.83/13.96 | | | | | | | % 93.83/13.96 | | | | | | | (88) m2_fraenkel(all_78_1, all_93_0, all_93_0, all_78_2) % 93.83/13.96 | | | | | | | (89) v1_funct_2(all_78_0, all_93_0, all_93_0) % 93.83/13.96 | | | | | | | % 93.83/13.96 | | | | | | | REDUCE: (57), (89) imply: % 93.83/13.96 | | | | | | | (90) v1_funct_2(all_78_0, all_78_3, all_78_3) % 93.83/13.96 | | | | | | | % 93.83/13.96 | | | | | | | BETA: splitting (82) gives: % 93.83/13.96 | | | | | | | % 93.83/13.96 | | | | | | | Case 1: % 93.83/13.96 | | | | | | | | % 93.83/13.96 | | | | | | | | (91) ~ m2_fraenkel(all_78_1, all_93_0, all_93_0, all_78_2) % 93.83/13.96 | | | | | | | | % 93.83/13.96 | | | | | | | | REDUCE: (57), (91) imply: % 93.83/13.96 | | | | | | | | (92) ~ m2_fraenkel(all_78_1, all_78_3, all_78_3, all_78_2) % 93.83/13.96 | | | | | | | | % 93.83/13.96 | | | | | | | | PRED_UNIFY: (18), (92) imply: % 93.83/13.96 | | | | | | | | (93) $false % 93.83/13.96 | | | | | | | | % 93.83/13.96 | | | | | | | | CLOSE: (93) is inconsistent. % 93.83/13.96 | | | | | | | | % 93.83/13.96 | | | | | | | Case 2: % 93.83/13.96 | | | | | | | | % 93.83/13.96 | | | | | | | | (94) v1_group_6(all_78_0, all_78_4, all_78_4) % 93.83/13.96 | | | | | | | | % 93.83/13.96 | | | | | | | | BETA: splitting (84) gives: % 93.83/13.96 | | | | | | | | % 93.83/13.96 | | | | | | | | Case 1: % 93.83/13.96 | | | | | | | | | % 93.83/13.96 | | | | | | | | | (95) ~ m1_fraenkel(all_78_2, all_96_0, all_96_0) % 93.83/13.96 | | | | | | | | | % 93.83/13.96 | | | | | | | | | REDUCE: (58), (95) imply: % 93.83/13.96 | | | | | | | | | (96) ~ m1_fraenkel(all_78_2, all_78_3, all_78_3) % 93.83/13.96 | | | | | | | | | % 93.83/13.96 | | | | | | | | | PRED_UNIFY: (60), (96) imply: % 93.83/13.96 | | | | | | | | | (97) $false % 93.83/13.96 | | | | | | | | | % 93.83/13.96 | | | | | | | | | CLOSE: (97) is inconsistent. % 93.83/13.96 | | | | | | | | | % 93.83/13.96 | | | | | | | | Case 2: % 93.83/13.96 | | | | | | | | | % 93.83/13.97 | | | | | | | | | (98) m1_fraenkel(all_78_2, all_96_0, all_96_0) % 93.83/13.97 | | | | | | | | | (99) ~ m2_fraenkel(all_78_1, all_96_0, all_96_0, all_78_2) % 93.83/13.97 | | | | | | | | | | v1_group_6(all_78_1, all_78_4, all_78_4) % 93.83/13.97 | | | | | | | | | % 93.83/13.97 | | | | | | | | | BETA: splitting (99) gives: % 93.83/13.97 | | | | | | | | | % 93.83/13.97 | | | | | | | | | Case 1: % 93.83/13.97 | | | | | | | | | | % 93.83/13.97 | | | | | | | | | | (100) ~ m2_fraenkel(all_78_1, all_96_0, all_96_0, % 93.83/13.97 | | | | | | | | | | all_78_2) % 93.83/13.97 | | | | | | | | | | % 93.83/13.97 | | | | | | | | | | REDUCE: (58), (100) imply: % 93.83/13.97 | | | | | | | | | | (101) ~ m2_fraenkel(all_78_1, all_78_3, all_78_3, % 93.83/13.97 | | | | | | | | | | all_78_2) % 93.83/13.97 | | | | | | | | | | % 93.83/13.97 | | | | | | | | | | PRED_UNIFY: (18), (101) imply: % 93.83/13.97 | | | | | | | | | | (102) $false % 93.83/13.97 | | | | | | | | | | % 93.83/13.97 | | | | | | | | | | CLOSE: (102) is inconsistent. % 93.83/13.97 | | | | | | | | | | % 93.83/13.97 | | | | | | | | | Case 2: % 93.83/13.97 | | | | | | | | | | % 93.83/13.97 | | | | | | | | | | (103) m2_fraenkel(all_78_1, all_96_0, all_96_0, all_78_2) % 93.83/13.97 | | | | | | | | | | (104) v1_group_6(all_78_1, all_78_4, all_78_4) % 93.83/13.97 | | | | | | | | | | % 93.83/13.97 | | | | | | | | | | BETA: splitting (81) gives: % 93.83/13.97 | | | | | | | | | | % 93.83/13.97 | | | | | | | | | | Case 1: % 93.83/13.97 | | | | | | | | | | | % 93.83/13.97 | | | | | | | | | | | (105) ~ m2_fraenkel(all_78_1, all_93_0, all_93_0, % 93.83/13.97 | | | | | | | | | | | all_78_2) % 93.83/13.97 | | | | | | | | | | | % 93.83/13.97 | | | | | | | | | | | REDUCE: (57), (105) imply: % 93.83/13.97 | | | | | | | | | | | (106) ~ m2_fraenkel(all_78_1, all_78_3, all_78_3, % 93.83/13.97 | | | | | | | | | | | all_78_2) % 93.83/13.97 | | | | | | | | | | | % 93.83/13.97 | | | | | | | | | | | PRED_UNIFY: (18), (106) imply: % 93.83/13.97 | | | | | | | | | | | (107) $false % 93.83/13.97 | | | | | | | | | | | % 93.83/13.97 | | | | | | | | | | | CLOSE: (107) is inconsistent. % 93.83/13.97 | | | | | | | | | | | % 93.83/13.97 | | | | | | | | | | Case 2: % 93.83/13.97 | | | | | | | | | | | % 93.83/13.97 | | | | | | | | | | | (108) m2_relset_1(all_78_0, all_93_0, all_93_0) % 93.83/13.97 | | | | | | | | | | | % 93.83/13.97 | | | | | | | | | | | REDUCE: (57), (108) imply: % 93.83/13.97 | | | | | | | | | | | (109) m2_relset_1(all_78_0, all_78_3, all_78_3) % 93.83/13.97 | | | | | | | | | | | % 93.83/13.97 | | | | | | | | | | | GROUND_INST: instantiating (37) with all_78_1, simplifying with % 93.83/13.97 | | | | | | | | | | | (21), (73), (80), (104) gives: % 93.83/13.97 | | | | | | | | | | | (110) ~ m2_relset_1(all_78_1, all_90_0, all_90_0) | ~ % 93.83/13.97 | | | | | | | | | | | v1_funct_2(all_78_1, all_90_0, all_90_0) | % 93.83/13.97 | | | | | | | | | | | v4_group_6(all_78_1, all_78_4, all_78_4) % 93.83/13.97 | | | | | | | | | | | % 93.83/13.97 | | | | | | | | | | | BETA: splitting (110) gives: % 93.83/13.97 | | | | | | | | | | | % 93.83/13.97 | | | | | | | | | | | Case 1: % 93.83/13.97 | | | | | | | | | | | | % 93.83/13.97 | | | | | | | | | | | | (111) ~ m2_relset_1(all_78_1, all_90_0, all_90_0) % 93.83/13.97 | | | | | | | | | | | | % 93.83/13.97 | | | | | | | | | | | | REDUCE: (47), (111) imply: % 93.83/13.97 | | | | | | | | | | | | (112) ~ m2_relset_1(all_78_1, all_78_3, all_78_3) % 93.83/13.97 | | | | | | | | | | | | % 93.83/13.97 | | | | | | | | | | | | PRED_UNIFY: (66), (112) imply: % 93.83/13.97 | | | | | | | | | | | | (113) $false % 93.83/13.97 | | | | | | | | | | | | % 93.83/13.97 | | | | | | | | | | | | CLOSE: (113) is inconsistent. % 93.83/13.97 | | | | | | | | | | | | % 93.83/13.97 | | | | | | | | | | | Case 2: % 93.83/13.97 | | | | | | | | | | | | % 93.83/13.97 | | | | | | | | | | | | (114) m2_relset_1(all_78_1, all_90_0, all_90_0) % 93.83/13.97 | | | | | | | | | | | | (115) ~ v1_funct_2(all_78_1, all_90_0, all_90_0) | % 93.83/13.97 | | | | | | | | | | | | v4_group_6(all_78_1, all_78_4, all_78_4) % 93.83/13.97 | | | | | | | | | | | | % 93.83/13.97 | | | | | | | | | | | | BETA: splitting (115) gives: % 93.83/13.97 | | | | | | | | | | | | % 93.83/13.97 | | | | | | | | | | | | Case 1: % 93.83/13.97 | | | | | | | | | | | | | % 93.83/13.97 | | | | | | | | | | | | | (116) ~ v1_funct_2(all_78_1, all_90_0, all_90_0) % 93.83/13.97 | | | | | | | | | | | | | % 93.83/13.97 | | | | | | | | | | | | | REDUCE: (47), (116) imply: % 93.83/13.97 | | | | | | | | | | | | | (117) ~ v1_funct_2(all_78_1, all_78_3, all_78_3) % 93.83/13.97 | | | | | | | | | | | | | % 93.83/13.97 | | | | | | | | | | | | | PRED_UNIFY: (74), (117) imply: % 93.83/13.97 | | | | | | | | | | | | | (118) $false % 93.83/13.97 | | | | | | | | | | | | | % 93.83/13.97 | | | | | | | | | | | | | CLOSE: (118) is inconsistent. % 93.83/13.97 | | | | | | | | | | | | | % 93.83/13.97 | | | | | | | | | | | | Case 2: % 93.83/13.97 | | | | | | | | | | | | | % 93.83/13.97 | | | | | | | | | | | | | (119) v1_funct_2(all_78_1, all_90_0, all_90_0) % 93.83/13.97 | | | | | | | | | | | | | (120) v4_group_6(all_78_1, all_78_4, all_78_4) % 93.83/13.97 | | | | | | | | | | | | | % 93.83/13.97 | | | | | | | | | | | | | GROUND_INST: instantiating (t73_group_6) with all_78_4, % 93.83/13.97 | | | | | | | | | | | | | all_78_3, all_78_4, all_78_3, all_78_1, all_78_0, % 93.83/13.97 | | | | | | | | | | | | | simplifying with (12), (15), (16), (17), (19), % 93.83/13.97 | | | | | | | | | | | | | (21), (22), (23), (25), (66), (73), (74), (77), % 93.83/13.97 | | | | | | | | | | | | | (90), (94), (104), (109), (120) gives: % 93.83/13.97 | | | | | | | | | | | | | (121) v4_group_6(all_78_0, all_78_4, all_78_4) % 93.83/13.97 | | | | | | | | | | | | | % 93.83/13.97 | | | | | | | | | | | | | GROUND_INST: instantiating (38) with all_78_0, simplifying with % 93.83/13.97 | | | | | | | | | | | | | (22), (77), (94), (121) gives: % 93.83/13.97 | | | | | | | | | | | | | (122) ~ m2_relset_1(all_78_0, all_90_0, all_90_0) | ~ % 93.83/13.97 | | | | | | | | | | | | | v1_funct_2(all_78_0, all_90_0, all_90_0) | % 93.83/13.97 | | | | | | | | | | | | | r2_hidden(all_78_0, all_78_2) % 93.83/13.97 | | | | | | | | | | | | | % 93.83/13.97 | | | | | | | | | | | | | BETA: splitting (122) gives: % 93.83/13.97 | | | | | | | | | | | | | % 93.83/13.97 | | | | | | | | | | | | | Case 1: % 93.83/13.97 | | | | | | | | | | | | | | % 93.83/13.97 | | | | | | | | | | | | | | (123) ~ m2_relset_1(all_78_0, all_90_0, all_90_0) % 93.83/13.97 | | | | | | | | | | | | | | % 93.83/13.97 | | | | | | | | | | | | | | REDUCE: (47), (123) imply: % 93.83/13.97 | | | | | | | | | | | | | | (124) ~ m2_relset_1(all_78_0, all_78_3, all_78_3) % 93.83/13.97 | | | | | | | | | | | | | | % 93.83/13.97 | | | | | | | | | | | | | | PRED_UNIFY: (109), (124) imply: % 93.83/13.97 | | | | | | | | | | | | | | (125) $false % 93.83/13.97 | | | | | | | | | | | | | | % 93.83/13.97 | | | | | | | | | | | | | | CLOSE: (125) is inconsistent. % 93.83/13.97 | | | | | | | | | | | | | | % 93.83/13.97 | | | | | | | | | | | | | Case 2: % 93.83/13.97 | | | | | | | | | | | | | | % 93.83/13.98 | | | | | | | | | | | | | | (126) ~ v1_funct_2(all_78_0, all_90_0, all_90_0) | % 93.83/13.98 | | | | | | | | | | | | | | r2_hidden(all_78_0, all_78_2) % 93.83/13.98 | | | | | | | | | | | | | | % 93.83/13.98 | | | | | | | | | | | | | | BETA: splitting (126) gives: % 93.83/13.98 | | | | | | | | | | | | | | % 93.83/13.98 | | | | | | | | | | | | | | Case 1: % 93.83/13.98 | | | | | | | | | | | | | | | % 93.83/13.98 | | | | | | | | | | | | | | | (127) ~ v1_funct_2(all_78_0, all_90_0, all_90_0) % 93.83/13.98 | | | | | | | | | | | | | | | % 93.83/13.98 | | | | | | | | | | | | | | | REDUCE: (47), (127) imply: % 93.83/13.98 | | | | | | | | | | | | | | | (128) ~ v1_funct_2(all_78_0, all_78_3, all_78_3) % 93.83/13.98 | | | | | | | | | | | | | | | % 93.83/13.98 | | | | | | | | | | | | | | | PRED_UNIFY: (90), (128) imply: % 93.83/13.98 | | | | | | | | | | | | | | | (129) $false % 93.83/13.98 | | | | | | | | | | | | | | | % 93.83/13.98 | | | | | | | | | | | | | | | CLOSE: (129) is inconsistent. % 93.83/13.98 | | | | | | | | | | | | | | | % 93.83/13.98 | | | | | | | | | | | | | | Case 2: % 93.83/13.98 | | | | | | | | | | | | | | | % 93.83/13.98 | | | | | | | | | | | | | | | (130) r2_hidden(all_78_0, all_78_2) % 93.83/13.98 | | | | | | | | | | | | | | | % 93.83/13.98 | | | | | | | | | | | | | | | GROUND_INST: instantiating (t1_subset) with all_78_0, all_78_2, % 93.83/13.98 | | | | | | | | | | | | | | | simplifying with (20), (22), (130) gives: % 93.83/13.98 | | | | | | | | | | | | | | | (131) m1_subset_1(all_78_0, all_78_2) % 93.83/13.98 | | | | | | | | | | | | | | | % 93.83/13.98 | | | | | | | | | | | | | | | GROUND_INST: instantiating (9) with all_78_3, all_78_3, % 93.83/13.98 | | | | | | | | | | | | | | | all_78_2, all_78_0, simplifying with (13), (20), % 93.83/13.98 | | | | | | | | | | | | | | | (22), (59), (60), (72), (131) gives: % 93.95/13.98 | | | | | | | | | | | | | | | (132) $false % 93.95/13.98 | | | | | | | | | | | | | | | % 93.95/13.98 | | | | | | | | | | | | | | | CLOSE: (132) is inconsistent. % 93.95/13.98 | | | | | | | | | | | | | | | % 93.95/13.98 | | | | | | | | | | | | | | End of split % 93.95/13.98 | | | | | | | | | | | | | | % 93.95/13.98 | | | | | | | | | | | | | End of split % 93.95/13.98 | | | | | | | | | | | | | % 93.95/13.98 | | | | | | | | | | | | End of split % 93.95/13.98 | | | | | | | | | | | | % 93.95/13.98 | | | | | | | | | | | End of split % 93.95/13.98 | | | | | | | | | | | % 93.95/13.98 | | | | | | | | | | End of split % 93.95/13.98 | | | | | | | | | | % 93.95/13.98 | | | | | | | | | End of split % 93.95/13.98 | | | | | | | | | % 93.95/13.98 | | | | | | | | End of split % 93.95/13.98 | | | | | | | | % 93.95/13.98 | | | | | | | End of split % 93.95/13.98 | | | | | | | % 93.95/13.98 | | | | | | End of split % 93.95/13.98 | | | | | | % 93.95/13.98 | | | | | End of split % 93.95/13.98 | | | | | % 93.95/13.98 | | | | Case 2: % 93.95/13.98 | | | | | % 93.95/13.98 | | | | | (133) v1_xboole_0(all_78_3) % 93.95/13.98 | | | | | % 93.95/13.98 | | | | | GROUND_INST: instantiating (fc1_struct_0) with all_78_4, all_78_3, % 93.95/13.98 | | | | | simplifying with (12), (19), (23), (26), (133) gives: % 93.95/13.98 | | | | | (134) $false % 93.95/13.98 | | | | | % 93.95/13.98 | | | | | CLOSE: (134) is inconsistent. % 93.95/13.98 | | | | | % 93.95/13.98 | | | | End of split % 93.95/13.98 | | | | % 93.95/13.98 | | | End of split % 93.95/13.98 | | | % 93.95/13.98 | | End of split % 93.95/13.98 | | % 93.95/13.98 | Case 2: % 93.95/13.98 | | % 93.95/13.98 | | (135) v1_xboole_0(all_78_3) % 93.95/13.98 | | % 93.95/13.98 | | GROUND_INST: instantiating (fc1_struct_0) with all_78_4, all_78_3, % 93.95/13.98 | | simplifying with (12), (19), (23), (26), (135) gives: % 93.95/13.98 | | (136) $false % 93.95/13.98 | | % 93.95/13.98 | | CLOSE: (136) is inconsistent. % 93.95/13.98 | | % 93.95/13.98 | End of split % 93.95/13.98 | % 93.95/13.98 End of proof % 93.95/13.98 % SZS output end Proof for theBenchmark % 93.95/13.98 % 93.95/13.98 13395ms %------------------------------------------------------------------------------