TSTP Solution File: GRP644+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : GRP644+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 : n012.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 01:12:48 EDT 2023
% Result : Theorem 12.79s 2.57s
% Output : Proof 17.71s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP644+1 : TPTP v8.1.2. Released v3.4.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n012.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Aug 28 20:06:24 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.66 ________ _____
% 0.20/0.66 ___ __ \_________(_)________________________________
% 0.20/0.66 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.66 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.66 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.66
% 0.20/0.66 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.66 (2023-06-19)
% 0.20/0.66
% 0.20/0.66 (c) Philipp Rümmer, 2009-2023
% 0.20/0.66 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.66 Amanda Stjerna.
% 0.20/0.66 Free software under BSD-3-Clause.
% 0.20/0.66
% 0.20/0.66 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.66
% 0.20/0.66 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.20/0.68 Running up to 7 provers in parallel.
% 0.20/0.69 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.69 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.69 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.69 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.69 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.69 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.69 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.45/1.33 Prover 4: Preprocessing ...
% 3.45/1.33 Prover 1: Preprocessing ...
% 3.45/1.37 Prover 0: Preprocessing ...
% 3.45/1.37 Prover 6: Preprocessing ...
% 3.45/1.37 Prover 5: Preprocessing ...
% 3.45/1.37 Prover 2: Preprocessing ...
% 3.45/1.37 Prover 3: Preprocessing ...
% 7.66/1.91 Prover 5: Proving ...
% 7.66/1.91 Prover 1: Warning: ignoring some quantifiers
% 8.33/2.00 Prover 1: Constructing countermodel ...
% 8.33/2.02 Prover 2: Proving ...
% 8.33/2.06 Prover 6: Proving ...
% 8.33/2.07 Prover 3: Warning: ignoring some quantifiers
% 8.70/2.12 Prover 3: Constructing countermodel ...
% 11.87/2.48 Prover 4: Warning: ignoring some quantifiers
% 12.38/2.55 Prover 4: Constructing countermodel ...
% 12.38/2.56 Prover 3: proved (1877ms)
% 12.79/2.56
% 12.79/2.57 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 12.79/2.57
% 12.79/2.57 Prover 2: stopped
% 12.79/2.57 Prover 6: stopped
% 12.79/2.58 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 12.79/2.58 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 12.79/2.58 Prover 5: proved (1889ms)
% 12.79/2.58
% 12.79/2.58 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 12.79/2.58
% 12.79/2.59 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 12.79/2.59 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 12.79/2.64 Prover 8: Preprocessing ...
% 12.79/2.66 Prover 7: Preprocessing ...
% 12.79/2.67 Prover 10: Preprocessing ...
% 12.79/2.71 Prover 11: Preprocessing ...
% 12.79/2.76 Prover 0: Proving ...
% 12.79/2.76 Prover 0: stopped
% 13.70/2.77 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 13.70/2.81 Prover 10: Warning: ignoring some quantifiers
% 14.55/2.81 Prover 7: Warning: ignoring some quantifiers
% 14.55/2.83 Prover 13: Preprocessing ...
% 14.55/2.84 Prover 10: Constructing countermodel ...
% 14.55/2.84 Prover 7: Constructing countermodel ...
% 14.89/2.86 Prover 8: Warning: ignoring some quantifiers
% 14.89/2.90 Prover 8: Constructing countermodel ...
% 15.91/3.00 Prover 13: Warning: ignoring some quantifiers
% 15.91/3.02 Prover 13: Constructing countermodel ...
% 16.88/3.12 Prover 7: Found proof (size 44)
% 16.88/3.12 Prover 7: proved (550ms)
% 16.88/3.12 Prover 13: stopped
% 16.88/3.12 Prover 8: stopped
% 16.88/3.12 Prover 1: stopped
% 16.88/3.12 Prover 10: stopped
% 16.88/3.12 Prover 4: stopped
% 17.13/3.22 Prover 11: Warning: ignoring some quantifiers
% 17.51/3.24 Prover 11: Constructing countermodel ...
% 17.51/3.26 Prover 11: stopped
% 17.51/3.26
% 17.51/3.26 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 17.51/3.26
% 17.51/3.27 % SZS output start Proof for theBenchmark
% 17.51/3.27 Assumptions after simplification:
% 17.51/3.27 ---------------------------------
% 17.51/3.27
% 17.51/3.27 (dt_k1_latsubgr)
% 17.71/3.30 ! [v0: $i] : ! [v1: $i] : ( ~ (k1_latsubgr(v0) = v1) | ~ $i(v0) | ~
% 17.71/3.30 l1_group_1(v0) | ~ v4_group_1(v0) | ~ v3_group_1(v0) | v1_funct_1(v1) |
% 17.71/3.30 v3_struct_0(v0)) & ! [v0: $i] : ! [v1: $i] : ( ~ (k1_latsubgr(v0) = v1) |
% 17.71/3.30 ~ $i(v0) | ~ l1_group_1(v0) | ~ v4_group_1(v0) | ~ v3_group_1(v0) |
% 17.71/3.30 v3_struct_0(v0) | ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : (k1_group_3(v0)
% 17.71/3.30 = v2 & k1_zfmisc_1(v3) = v4 & u1_struct_0(v0) = v3 & $i(v4) & $i(v3) &
% 17.71/3.30 $i(v2) & m2_relset_1(v1, v2, v4) & v1_funct_2(v1, v2, v4))) & ! [v0: $i]
% 17.71/3.30 : ! [v1: $i] : ( ~ (k1_group_3(v0) = v1) | ~ $i(v0) | ~ l1_group_1(v0) | ~
% 17.71/3.30 v4_group_1(v0) | ~ v3_group_1(v0) | v3_struct_0(v0) | ? [v2: $i] : ? [v3:
% 17.71/3.30 $i] : ? [v4: $i] : (k1_latsubgr(v0) = v2 & k1_zfmisc_1(v3) = v4 &
% 17.71/3.30 u1_struct_0(v0) = v3 & $i(v4) & $i(v3) & $i(v2) & m2_relset_1(v2, v1, v4)
% 17.71/3.30 & v1_funct_2(v2, v1, v4) & v1_funct_1(v2))) & ! [v0: $i] : ! [v1: $i] :
% 17.71/3.30 ( ~ (u1_struct_0(v0) = v1) | ~ $i(v0) | ~ l1_group_1(v0) | ~ v4_group_1(v0)
% 17.71/3.30 | ~ v3_group_1(v0) | v3_struct_0(v0) | ? [v2: $i] : ? [v3: $i] : ? [v4:
% 17.71/3.30 $i] : (k1_latsubgr(v0) = v2 & k1_group_3(v0) = v3 & k1_zfmisc_1(v1) = v4 &
% 17.71/3.30 $i(v4) & $i(v3) & $i(v2) & m2_relset_1(v2, v3, v4) & v1_funct_2(v2, v3,
% 17.71/3.30 v4) & v1_funct_1(v2)))
% 17.71/3.30
% 17.71/3.30 (dt_k3_group_1)
% 17.71/3.30 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (k3_group_1(v0, v1) = v2) | ~
% 17.71/3.30 $i(v1) | ~ $i(v0) | ~ l1_group_1(v0) | ~ v4_group_1(v0) | ~
% 17.71/3.30 v3_group_1(v0) | v3_struct_0(v0) | ? [v3: $i] : (u1_struct_0(v0) = v3 &
% 17.71/3.30 $i(v3) & ( ~ m1_subset_1(v1, v3) | m1_subset_1(v2, v3))))
% 17.71/3.30
% 17.71/3.30 (t18_latsubgr)
% 17.71/3.30 ! [v0: $i] : ! [v1: $i] : ( ~ (k1_latsubgr(v0) = v1) | ~ $i(v0) | ~
% 17.71/3.30 l1_group_1(v0) | ~ v4_group_1(v0) | ~ v3_group_1(v0) | v3_struct_0(v0) |
% 17.71/3.30 ? [v2: $i] : (u1_struct_0(v0) = v2 & $i(v2) & ! [v3: $i] : ! [v4: $i] : !
% 17.71/3.30 [v5: $i] : ( ~ (k1_funct_1(v1, v3) = v4) | ~ $i(v5) | ~ $i(v3) | ~
% 17.71/3.30 r1_rlvect_1(v3, v5) | ~ m1_subset_1(v5, v2) | ~ m1_group_2(v3, v0) |
% 17.71/3.30 ~ v1_group_1(v3) | r2_hidden(v5, v4)) & ! [v3: $i] : ! [v4: $i] : !
% 17.71/3.30 [v5: $i] : ( ~ (k1_funct_1(v1, v3) = v4) | ~ $i(v5) | ~ $i(v3) | ~
% 17.71/3.31 r2_hidden(v5, v4) | ~ m1_subset_1(v5, v2) | ~ m1_group_2(v3, v0) | ~
% 17.71/3.31 v1_group_1(v3) | r1_rlvect_1(v3, v5)))) & ! [v0: $i] : ! [v1: $i] : (
% 17.71/3.31 ~ (u1_struct_0(v0) = v1) | ~ $i(v0) | ~ l1_group_1(v0) | ~ v4_group_1(v0)
% 17.71/3.31 | ~ v3_group_1(v0) | v3_struct_0(v0) | ? [v2: $i] : (k1_latsubgr(v0) = v2
% 17.71/3.31 & $i(v2) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (k1_funct_1(v2,
% 17.71/3.31 v3) = v4) | ~ $i(v5) | ~ $i(v3) | ~ r1_rlvect_1(v3, v5) | ~
% 17.71/3.31 m1_subset_1(v5, v1) | ~ m1_group_2(v3, v0) | ~ v1_group_1(v3) |
% 17.71/3.31 r2_hidden(v5, v4)) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~
% 17.71/3.31 (k1_funct_1(v2, v3) = v4) | ~ $i(v5) | ~ $i(v3) | ~ r2_hidden(v5, v4)
% 17.71/3.31 | ~ m1_subset_1(v5, v1) | ~ m1_group_2(v3, v0) | ~ v1_group_1(v3) |
% 17.71/3.31 r1_rlvect_1(v3, v5))))
% 17.71/3.31
% 17.71/3.31 (t22_latsubgr)
% 17.71/3.31 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5:
% 17.71/3.31 $i] : ? [v6: $i] : (k1_funct_1(v2, v3) = v4 & k3_group_1(v0, v5) = v6 &
% 17.71/3.31 k1_latsubgr(v0) = v2 & u1_struct_0(v0) = v1 & $i(v6) & $i(v5) & $i(v4) &
% 17.71/3.31 $i(v3) & $i(v2) & $i(v1) & $i(v0) & r2_hidden(v5, v4) & m1_subset_1(v5, v1)
% 17.71/3.31 & m1_group_2(v3, v0) & v1_group_1(v3) & l1_group_1(v0) & v4_group_1(v0) &
% 17.71/3.31 v3_group_1(v0) & ~ r2_hidden(v6, v4) & ~ v3_struct_0(v0))
% 17.71/3.31
% 17.71/3.31 (t60_group_2)
% 17.71/3.31 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 17.71/3.31 (k3_group_1(v0, v2) = v3) | ~ (u1_struct_0(v0) = v1) | ~ $i(v4) | ~
% 17.71/3.31 $i(v2) | ~ $i(v0) | ~ r1_rlvect_1(v4, v2) | ~ m1_subset_1(v2, v1) | ~
% 17.71/3.31 m1_group_2(v4, v0) | ~ l1_group_1(v0) | ~ v4_group_1(v0) | ~
% 17.71/3.31 v3_group_1(v0) | r1_rlvect_1(v4, v3) | v3_struct_0(v0))
% 17.71/3.31
% 17.71/3.31 (function-axioms)
% 17.71/3.31 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 17.71/3.31 (k1_funct_1(v3, v2) = v1) | ~ (k1_funct_1(v3, v2) = v0)) & ! [v0: $i] : !
% 17.71/3.31 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (k3_group_1(v3, v2) = v1)
% 17.71/3.31 | ~ (k3_group_1(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 17.71/3.31 ! [v3: $i] : (v1 = v0 | ~ (k2_zfmisc_1(v3, v2) = v1) | ~ (k2_zfmisc_1(v3,
% 17.71/3.31 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1
% 17.71/3.31 = v0 | ~ (g1_group_1(v3, v2) = v1) | ~ (g1_group_1(v3, v2) = v0)) & !
% 17.71/3.31 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (k1_latsubgr(v2) = v1) |
% 17.71/3.31 ~ (k1_latsubgr(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 17.71/3.31 v0 | ~ (k1_group_3(v2) = v1) | ~ (k1_group_3(v2) = v0)) & ! [v0: $i] : !
% 17.71/3.31 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (k1_zfmisc_1(v2) = v1) | ~
% 17.71/3.31 (k1_zfmisc_1(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0
% 17.71/3.31 | ~ (u1_group_1(v2) = v1) | ~ (u1_group_1(v2) = v0)) & ! [v0: $i] : !
% 17.71/3.31 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (u1_struct_0(v2) = v1) | ~
% 17.71/3.31 (u1_struct_0(v2) = v0))
% 17.71/3.31
% 17.71/3.31 Further assumptions not needed in the proof:
% 17.71/3.31 --------------------------------------------
% 17.71/3.31 abstractness_v1_group_1, antisymmetry_r2_hidden, cc1_funct_2, cc1_relset_1,
% 17.71/3.31 cc5_funct_2, cc6_funct_2, dt_g1_group_1, dt_k1_funct_1, dt_k1_group_3,
% 17.71/3.31 dt_k1_xboole_0, dt_k1_zfmisc_1, dt_k2_zfmisc_1, dt_l1_group_1, dt_l1_struct_0,
% 17.71/3.31 dt_m1_group_2, dt_m1_relset_1, dt_m1_subset_1, dt_m2_relset_1, dt_u1_group_1,
% 17.71/3.31 dt_u1_struct_0, existence_l1_group_1, existence_l1_struct_0,
% 17.71/3.31 existence_m1_group_2, existence_m1_relset_1, existence_m1_subset_1,
% 17.71/3.31 existence_m2_relset_1, fc1_group_3, fc1_struct_0, fc1_subset_1, fc1_xboole_0,
% 17.71/3.31 fc4_subset_1, free_g1_group_1, rc1_funct_2, rc1_subset_1, rc1_xboole_0,
% 17.71/3.31 rc2_partfun1, rc2_subset_1, rc2_xboole_0, rc3_struct_0, rc5_struct_0,
% 17.71/3.31 redefinition_m2_relset_1, reflexivity_r1_tarski, t1_subset, t2_subset,
% 17.71/3.31 t3_subset, t4_subset, t5_subset, t6_boole, t7_boole, t8_boole
% 17.71/3.31
% 17.71/3.31 Those formulas are unsatisfiable:
% 17.71/3.31 ---------------------------------
% 17.71/3.31
% 17.71/3.31 Begin of proof
% 17.71/3.31 |
% 17.71/3.31 | ALPHA: (dt_k1_latsubgr) implies:
% 17.71/3.31 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (k1_latsubgr(v0) = v1) | ~ $i(v0) | ~
% 17.71/3.31 | l1_group_1(v0) | ~ v4_group_1(v0) | ~ v3_group_1(v0) |
% 17.71/3.31 | v3_struct_0(v0) | ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 17.71/3.31 | (k1_group_3(v0) = v2 & k1_zfmisc_1(v3) = v4 & u1_struct_0(v0) = v3 &
% 17.71/3.31 | $i(v4) & $i(v3) & $i(v2) & m2_relset_1(v1, v2, v4) & v1_funct_2(v1,
% 17.71/3.31 | v2, v4)))
% 17.71/3.31 |
% 17.71/3.31 | ALPHA: (t18_latsubgr) implies:
% 17.71/3.32 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (u1_struct_0(v0) = v1) | ~ $i(v0) | ~
% 17.71/3.32 | l1_group_1(v0) | ~ v4_group_1(v0) | ~ v3_group_1(v0) |
% 17.71/3.32 | v3_struct_0(v0) | ? [v2: $i] : (k1_latsubgr(v0) = v2 & $i(v2) & !
% 17.71/3.32 | [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (k1_funct_1(v2, v3) =
% 17.71/3.32 | v4) | ~ $i(v5) | ~ $i(v3) | ~ r1_rlvect_1(v3, v5) | ~
% 17.71/3.32 | m1_subset_1(v5, v1) | ~ m1_group_2(v3, v0) | ~ v1_group_1(v3) |
% 17.71/3.32 | r2_hidden(v5, v4)) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (
% 17.71/3.32 | ~ (k1_funct_1(v2, v3) = v4) | ~ $i(v5) | ~ $i(v3) | ~
% 17.71/3.32 | r2_hidden(v5, v4) | ~ m1_subset_1(v5, v1) | ~ m1_group_2(v3,
% 17.71/3.32 | v0) | ~ v1_group_1(v3) | r1_rlvect_1(v3, v5))))
% 17.71/3.32 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ (k1_latsubgr(v0) = v1) | ~ $i(v0) | ~
% 17.71/3.32 | l1_group_1(v0) | ~ v4_group_1(v0) | ~ v3_group_1(v0) |
% 17.71/3.32 | v3_struct_0(v0) | ? [v2: $i] : (u1_struct_0(v0) = v2 & $i(v2) & !
% 17.71/3.32 | [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (k1_funct_1(v1, v3) =
% 17.71/3.32 | v4) | ~ $i(v5) | ~ $i(v3) | ~ r1_rlvect_1(v3, v5) | ~
% 17.71/3.32 | m1_subset_1(v5, v2) | ~ m1_group_2(v3, v0) | ~ v1_group_1(v3) |
% 17.71/3.32 | r2_hidden(v5, v4)) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (
% 17.71/3.32 | ~ (k1_funct_1(v1, v3) = v4) | ~ $i(v5) | ~ $i(v3) | ~
% 17.71/3.32 | r2_hidden(v5, v4) | ~ m1_subset_1(v5, v2) | ~ m1_group_2(v3,
% 17.71/3.32 | v0) | ~ v1_group_1(v3) | r1_rlvect_1(v3, v5))))
% 17.71/3.32 |
% 17.71/3.32 | ALPHA: (function-axioms) implies:
% 17.71/3.32 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 17.71/3.32 | (u1_struct_0(v2) = v1) | ~ (u1_struct_0(v2) = v0))
% 17.71/3.32 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 17.71/3.32 | (k1_latsubgr(v2) = v1) | ~ (k1_latsubgr(v2) = v0))
% 17.71/3.32 |
% 17.71/3.32 | DELTA: instantiating (t22_latsubgr) with fresh symbols all_53_0, all_53_1,
% 17.71/3.32 | all_53_2, all_53_3, all_53_4, all_53_5, all_53_6 gives:
% 17.71/3.32 | (6) k1_funct_1(all_53_4, all_53_3) = all_53_2 & k3_group_1(all_53_6,
% 17.71/3.32 | all_53_1) = all_53_0 & k1_latsubgr(all_53_6) = all_53_4 &
% 17.71/3.32 | u1_struct_0(all_53_6) = all_53_5 & $i(all_53_0) & $i(all_53_1) &
% 17.71/3.32 | $i(all_53_2) & $i(all_53_3) & $i(all_53_4) & $i(all_53_5) &
% 17.71/3.32 | $i(all_53_6) & r2_hidden(all_53_1, all_53_2) & m1_subset_1(all_53_1,
% 17.71/3.32 | all_53_5) & m1_group_2(all_53_3, all_53_6) & v1_group_1(all_53_3) &
% 17.71/3.32 | l1_group_1(all_53_6) & v4_group_1(all_53_6) & v3_group_1(all_53_6) & ~
% 17.71/3.32 | r2_hidden(all_53_0, all_53_2) & ~ v3_struct_0(all_53_6)
% 17.71/3.32 |
% 17.71/3.32 | ALPHA: (6) implies:
% 17.71/3.32 | (7) ~ v3_struct_0(all_53_6)
% 17.71/3.32 | (8) ~ r2_hidden(all_53_0, all_53_2)
% 17.71/3.32 | (9) v3_group_1(all_53_6)
% 17.71/3.32 | (10) v4_group_1(all_53_6)
% 17.71/3.32 | (11) l1_group_1(all_53_6)
% 17.71/3.32 | (12) v1_group_1(all_53_3)
% 17.71/3.32 | (13) m1_group_2(all_53_3, all_53_6)
% 17.71/3.32 | (14) m1_subset_1(all_53_1, all_53_5)
% 17.71/3.32 | (15) r2_hidden(all_53_1, all_53_2)
% 17.71/3.32 | (16) $i(all_53_6)
% 17.71/3.32 | (17) $i(all_53_3)
% 17.71/3.32 | (18) $i(all_53_1)
% 17.71/3.32 | (19) $i(all_53_0)
% 17.71/3.32 | (20) u1_struct_0(all_53_6) = all_53_5
% 17.71/3.32 | (21) k1_latsubgr(all_53_6) = all_53_4
% 17.71/3.32 | (22) k3_group_1(all_53_6, all_53_1) = all_53_0
% 17.71/3.32 | (23) k1_funct_1(all_53_4, all_53_3) = all_53_2
% 17.71/3.32 |
% 17.71/3.32 | GROUND_INST: instantiating (2) with all_53_6, all_53_5, simplifying with (7),
% 17.71/3.32 | (9), (10), (11), (16), (20) gives:
% 17.71/3.32 | (24) ? [v0: $i] : (k1_latsubgr(all_53_6) = v0 & $i(v0) & ! [v1: $i] : !
% 17.71/3.32 | [v2: $i] : ! [v3: $i] : ( ~ (k1_funct_1(v0, v1) = v2) | ~ $i(v3) |
% 17.71/3.32 | ~ $i(v1) | ~ r1_rlvect_1(v1, v3) | ~ m1_subset_1(v3, all_53_5)
% 17.71/3.32 | | ~ m1_group_2(v1, all_53_6) | ~ v1_group_1(v1) | r2_hidden(v3,
% 17.71/3.32 | v2)) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 17.71/3.32 | (k1_funct_1(v0, v1) = v2) | ~ $i(v3) | ~ $i(v1) | ~
% 17.71/3.32 | r2_hidden(v3, v2) | ~ m1_subset_1(v3, all_53_5) | ~
% 17.71/3.32 | m1_group_2(v1, all_53_6) | ~ v1_group_1(v1) | r1_rlvect_1(v1,
% 17.71/3.32 | v3)))
% 17.71/3.32 |
% 17.71/3.33 | GROUND_INST: instantiating (1) with all_53_6, all_53_4, simplifying with (7),
% 17.71/3.33 | (9), (10), (11), (16), (21) gives:
% 17.71/3.33 | (25) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (k1_group_3(all_53_6) = v0 &
% 17.71/3.33 | k1_zfmisc_1(v1) = v2 & u1_struct_0(all_53_6) = v1 & $i(v2) & $i(v1)
% 17.71/3.33 | & $i(v0) & m2_relset_1(all_53_4, v0, v2) & v1_funct_2(all_53_4, v0,
% 17.71/3.33 | v2))
% 17.71/3.33 |
% 17.71/3.33 | GROUND_INST: instantiating (3) with all_53_6, all_53_4, simplifying with (7),
% 17.71/3.33 | (9), (10), (11), (16), (21) gives:
% 17.71/3.33 | (26) ? [v0: $i] : (u1_struct_0(all_53_6) = v0 & $i(v0) & ! [v1: $i] : !
% 17.71/3.33 | [v2: $i] : ! [v3: $i] : ( ~ (k1_funct_1(all_53_4, v1) = v2) | ~
% 17.71/3.33 | $i(v3) | ~ $i(v1) | ~ r1_rlvect_1(v1, v3) | ~ m1_subset_1(v3,
% 17.71/3.33 | v0) | ~ m1_group_2(v1, all_53_6) | ~ v1_group_1(v1) |
% 17.71/3.33 | r2_hidden(v3, v2)) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 17.71/3.33 | (k1_funct_1(all_53_4, v1) = v2) | ~ $i(v3) | ~ $i(v1) | ~
% 17.71/3.33 | r2_hidden(v3, v2) | ~ m1_subset_1(v3, v0) | ~ m1_group_2(v1,
% 17.71/3.33 | all_53_6) | ~ v1_group_1(v1) | r1_rlvect_1(v1, v3)))
% 17.71/3.33 |
% 17.71/3.33 | GROUND_INST: instantiating (dt_k3_group_1) with all_53_6, all_53_1, all_53_0,
% 17.71/3.33 | simplifying with (7), (9), (10), (11), (16), (18), (22) gives:
% 17.71/3.33 | (27) ? [v0: $i] : (u1_struct_0(all_53_6) = v0 & $i(v0) & ( ~
% 17.71/3.33 | m1_subset_1(all_53_1, v0) | m1_subset_1(all_53_0, v0)))
% 17.71/3.33 |
% 17.71/3.33 | DELTA: instantiating (27) with fresh symbol all_67_0 gives:
% 17.71/3.33 | (28) u1_struct_0(all_53_6) = all_67_0 & $i(all_67_0) & ( ~
% 17.71/3.33 | m1_subset_1(all_53_1, all_67_0) | m1_subset_1(all_53_0, all_67_0))
% 17.71/3.33 |
% 17.71/3.33 | ALPHA: (28) implies:
% 17.71/3.33 | (29) u1_struct_0(all_53_6) = all_67_0
% 17.71/3.33 | (30) ~ m1_subset_1(all_53_1, all_67_0) | m1_subset_1(all_53_0, all_67_0)
% 17.71/3.33 |
% 17.71/3.33 | DELTA: instantiating (25) with fresh symbols all_71_0, all_71_1, all_71_2
% 17.71/3.33 | gives:
% 17.71/3.33 | (31) k1_group_3(all_53_6) = all_71_2 & k1_zfmisc_1(all_71_1) = all_71_0 &
% 17.71/3.33 | u1_struct_0(all_53_6) = all_71_1 & $i(all_71_0) & $i(all_71_1) &
% 17.71/3.33 | $i(all_71_2) & m2_relset_1(all_53_4, all_71_2, all_71_0) &
% 17.71/3.33 | v1_funct_2(all_53_4, all_71_2, all_71_0)
% 17.71/3.33 |
% 17.71/3.33 | ALPHA: (31) implies:
% 17.71/3.33 | (32) u1_struct_0(all_53_6) = all_71_1
% 17.71/3.33 |
% 17.71/3.33 | DELTA: instantiating (26) with fresh symbol all_75_0 gives:
% 17.71/3.33 | (33) u1_struct_0(all_53_6) = all_75_0 & $i(all_75_0) & ! [v0: $i] : !
% 17.71/3.33 | [v1: $i] : ! [v2: $i] : ( ~ (k1_funct_1(all_53_4, v0) = v1) | ~
% 17.71/3.33 | $i(v2) | ~ $i(v0) | ~ r1_rlvect_1(v0, v2) | ~ m1_subset_1(v2,
% 17.71/3.33 | all_75_0) | ~ m1_group_2(v0, all_53_6) | ~ v1_group_1(v0) |
% 17.71/3.33 | r2_hidden(v2, v1)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 17.71/3.33 | (k1_funct_1(all_53_4, v0) = v1) | ~ $i(v2) | ~ $i(v0) | ~
% 17.71/3.33 | r2_hidden(v2, v1) | ~ m1_subset_1(v2, all_75_0) | ~ m1_group_2(v0,
% 17.71/3.33 | all_53_6) | ~ v1_group_1(v0) | r1_rlvect_1(v0, v2))
% 17.71/3.33 |
% 17.71/3.33 | ALPHA: (33) implies:
% 17.71/3.33 | (34) u1_struct_0(all_53_6) = all_75_0
% 17.71/3.33 | (35) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (k1_funct_1(all_53_4,
% 17.71/3.33 | v0) = v1) | ~ $i(v2) | ~ $i(v0) | ~ r2_hidden(v2, v1) | ~
% 17.71/3.33 | m1_subset_1(v2, all_75_0) | ~ m1_group_2(v0, all_53_6) | ~
% 17.71/3.33 | v1_group_1(v0) | r1_rlvect_1(v0, v2))
% 17.71/3.33 |
% 17.71/3.33 | GROUND_INST: instantiating (35) with all_53_3, all_53_2, all_53_1, simplifying
% 17.71/3.33 | with (12), (13), (15), (17), (18), (23) gives:
% 17.71/3.33 | (36) ~ m1_subset_1(all_53_1, all_75_0) | r1_rlvect_1(all_53_3, all_53_1)
% 17.71/3.33 |
% 17.71/3.33 | DELTA: instantiating (24) with fresh symbol all_78_0 gives:
% 17.71/3.33 | (37) k1_latsubgr(all_53_6) = all_78_0 & $i(all_78_0) & ! [v0: $i] : !
% 17.71/3.33 | [v1: $i] : ! [v2: $i] : ( ~ (k1_funct_1(all_78_0, v0) = v1) | ~
% 17.71/3.33 | $i(v2) | ~ $i(v0) | ~ r1_rlvect_1(v0, v2) | ~ m1_subset_1(v2,
% 17.71/3.33 | all_53_5) | ~ m1_group_2(v0, all_53_6) | ~ v1_group_1(v0) |
% 17.71/3.33 | r2_hidden(v2, v1)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 17.71/3.33 | (k1_funct_1(all_78_0, v0) = v1) | ~ $i(v2) | ~ $i(v0) | ~
% 17.71/3.34 | r2_hidden(v2, v1) | ~ m1_subset_1(v2, all_53_5) | ~ m1_group_2(v0,
% 17.71/3.34 | all_53_6) | ~ v1_group_1(v0) | r1_rlvect_1(v0, v2))
% 17.71/3.34 |
% 17.71/3.34 | ALPHA: (37) implies:
% 17.71/3.34 | (38) k1_latsubgr(all_53_6) = all_78_0
% 17.71/3.34 | (39) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (k1_funct_1(all_78_0,
% 17.71/3.34 | v0) = v1) | ~ $i(v2) | ~ $i(v0) | ~ r1_rlvect_1(v0, v2) | ~
% 17.71/3.34 | m1_subset_1(v2, all_53_5) | ~ m1_group_2(v0, all_53_6) | ~
% 17.71/3.34 | v1_group_1(v0) | r2_hidden(v2, v1))
% 17.71/3.34 |
% 17.71/3.34 | GROUND_INST: instantiating (4) with all_67_0, all_71_1, all_53_6, simplifying
% 17.71/3.34 | with (29), (32) gives:
% 17.71/3.34 | (40) all_71_1 = all_67_0
% 17.71/3.34 |
% 17.71/3.34 | GROUND_INST: instantiating (4) with all_53_5, all_75_0, all_53_6, simplifying
% 17.71/3.34 | with (20), (34) gives:
% 17.71/3.34 | (41) all_75_0 = all_53_5
% 17.71/3.34 |
% 17.71/3.34 | GROUND_INST: instantiating (4) with all_71_1, all_75_0, all_53_6, simplifying
% 17.71/3.34 | with (32), (34) gives:
% 17.71/3.34 | (42) all_75_0 = all_71_1
% 17.71/3.34 |
% 17.71/3.34 | GROUND_INST: instantiating (5) with all_53_4, all_78_0, all_53_6, simplifying
% 17.71/3.34 | with (21), (38) gives:
% 17.71/3.34 | (43) all_78_0 = all_53_4
% 17.71/3.34 |
% 17.71/3.34 | COMBINE_EQS: (41), (42) imply:
% 17.71/3.34 | (44) all_71_1 = all_53_5
% 17.71/3.34 |
% 17.71/3.34 | SIMP: (44) implies:
% 17.71/3.34 | (45) all_71_1 = all_53_5
% 17.71/3.34 |
% 17.71/3.34 | COMBINE_EQS: (40), (45) imply:
% 17.71/3.34 | (46) all_67_0 = all_53_5
% 17.71/3.34 |
% 17.71/3.34 | SIMP: (46) implies:
% 17.71/3.34 | (47) all_67_0 = all_53_5
% 17.71/3.34 |
% 17.71/3.34 | BETA: splitting (36) gives:
% 17.71/3.34 |
% 17.71/3.34 | Case 1:
% 17.71/3.34 | |
% 17.71/3.34 | | (48) ~ m1_subset_1(all_53_1, all_75_0)
% 17.71/3.34 | |
% 17.71/3.34 | | REDUCE: (41), (48) imply:
% 17.71/3.34 | | (49) ~ m1_subset_1(all_53_1, all_53_5)
% 17.71/3.34 | |
% 17.71/3.34 | | PRED_UNIFY: (14), (49) imply:
% 17.71/3.34 | | (50) $false
% 17.71/3.34 | |
% 17.71/3.34 | | CLOSE: (50) is inconsistent.
% 17.71/3.34 | |
% 17.71/3.34 | Case 2:
% 17.71/3.34 | |
% 17.71/3.34 | | (51) m1_subset_1(all_53_1, all_75_0)
% 17.71/3.34 | | (52) r1_rlvect_1(all_53_3, all_53_1)
% 17.71/3.34 | |
% 17.71/3.34 | | BETA: splitting (30) gives:
% 17.71/3.34 | |
% 17.71/3.34 | | Case 1:
% 17.71/3.34 | | |
% 17.71/3.34 | | | (53) ~ m1_subset_1(all_53_1, all_67_0)
% 17.71/3.34 | | |
% 17.71/3.34 | | | REDUCE: (47), (53) imply:
% 17.71/3.34 | | | (54) ~ m1_subset_1(all_53_1, all_53_5)
% 17.71/3.34 | | |
% 17.71/3.34 | | | PRED_UNIFY: (14), (54) imply:
% 17.71/3.34 | | | (55) $false
% 17.71/3.34 | | |
% 17.71/3.34 | | | CLOSE: (55) is inconsistent.
% 17.71/3.34 | | |
% 17.71/3.34 | | Case 2:
% 17.71/3.34 | | |
% 17.71/3.34 | | | (56) m1_subset_1(all_53_1, all_67_0)
% 17.71/3.34 | | | (57) m1_subset_1(all_53_0, all_67_0)
% 17.71/3.34 | | |
% 17.71/3.34 | | | REDUCE: (47), (57) imply:
% 17.71/3.34 | | | (58) m1_subset_1(all_53_0, all_53_5)
% 17.71/3.34 | | |
% 17.71/3.34 | | | GROUND_INST: instantiating (t60_group_2) with all_53_6, all_53_5,
% 17.71/3.34 | | | all_53_1, all_53_0, all_53_3, simplifying with (7), (9),
% 17.71/3.34 | | | (10), (11), (13), (14), (16), (17), (18), (20), (22), (52)
% 17.71/3.34 | | | gives:
% 17.71/3.35 | | | (59) r1_rlvect_1(all_53_3, all_53_0)
% 17.71/3.35 | | |
% 17.71/3.35 | | | GROUND_INST: instantiating (39) with all_53_3, all_53_2, all_53_0,
% 17.71/3.35 | | | simplifying with (8), (12), (13), (17), (19), (58), (59)
% 17.71/3.35 | | | gives:
% 17.71/3.35 | | | (60) ~ (k1_funct_1(all_78_0, all_53_3) = all_53_2)
% 17.71/3.35 | | |
% 17.71/3.35 | | | REDUCE: (43), (60) imply:
% 17.71/3.35 | | | (61) ~ (k1_funct_1(all_53_4, all_53_3) = all_53_2)
% 17.71/3.35 | | |
% 17.71/3.35 | | | PRED_UNIFY: (23), (61) imply:
% 17.71/3.35 | | | (62) $false
% 17.71/3.35 | | |
% 17.71/3.35 | | | CLOSE: (62) is inconsistent.
% 17.71/3.35 | | |
% 17.71/3.35 | | End of split
% 17.71/3.35 | |
% 17.71/3.35 | End of split
% 17.71/3.35 |
% 17.71/3.35 End of proof
% 17.71/3.35 % SZS output end Proof for theBenchmark
% 17.71/3.35
% 17.71/3.35 2683ms
%------------------------------------------------------------------------------