TSTP Solution File: SEU247+2 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SEU247+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n010.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 17:43:38 EDT 2023
% Result : Theorem 38.75s 6.50s
% Output : Proof 57.72s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : SEU247+2 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.35 % Computer : n010.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Wed Aug 23 18:55:51 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.63 ________ _____
% 0.21/0.63 ___ __ \_________(_)________________________________
% 0.21/0.63 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.21/0.63 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.21/0.63 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.21/0.63
% 0.21/0.63 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.21/0.63 (2023-06-19)
% 0.21/0.63
% 0.21/0.63 (c) Philipp Rümmer, 2009-2023
% 0.21/0.63 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.21/0.63 Amanda Stjerna.
% 0.21/0.63 Free software under BSD-3-Clause.
% 0.21/0.63
% 0.21/0.63 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.21/0.63
% 0.21/0.63 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.21/0.64 Running up to 7 provers in parallel.
% 0.21/0.66 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.21/0.66 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.21/0.66 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.21/0.66 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.21/0.66 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.21/0.66 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 0.21/0.66 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 6.75/1.75 Prover 4: Preprocessing ...
% 6.75/1.76 Prover 1: Preprocessing ...
% 6.75/1.79 Prover 0: Preprocessing ...
% 6.75/1.79 Prover 6: Preprocessing ...
% 6.75/1.81 Prover 5: Preprocessing ...
% 6.75/1.81 Prover 2: Preprocessing ...
% 7.35/1.84 Prover 3: Preprocessing ...
% 21.52/4.02 Prover 1: Warning: ignoring some quantifiers
% 21.85/4.15 Prover 1: Constructing countermodel ...
% 22.97/4.20 Prover 3: Warning: ignoring some quantifiers
% 23.37/4.26 Prover 3: Constructing countermodel ...
% 23.37/4.29 Prover 6: Proving ...
% 23.37/4.29 Prover 5: Proving ...
% 27.37/4.83 Prover 2: Proving ...
% 30.01/5.21 Prover 4: Warning: ignoring some quantifiers
% 31.15/5.45 Prover 4: Constructing countermodel ...
% 38.04/6.46 Prover 0: Proving ...
% 38.75/6.50 Prover 3: proved (5841ms)
% 38.75/6.50
% 38.75/6.50 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 38.75/6.50
% 38.75/6.51 Prover 5: stopped
% 38.75/6.52 Prover 6: stopped
% 38.90/6.53 Prover 0: stopped
% 38.90/6.55 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 38.90/6.55 Prover 2: stopped
% 38.90/6.55 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 38.90/6.55 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 38.90/6.57 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 38.90/6.57 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 40.79/7.03 Prover 10: Preprocessing ...
% 42.33/7.04 Prover 13: Preprocessing ...
% 42.33/7.05 Prover 7: Preprocessing ...
% 42.43/7.06 Prover 11: Preprocessing ...
% 42.43/7.08 Prover 8: Preprocessing ...
% 45.93/7.67 Prover 10: Warning: ignoring some quantifiers
% 46.76/7.69 Prover 7: Warning: ignoring some quantifiers
% 46.76/7.73 Prover 10: Constructing countermodel ...
% 47.63/7.81 Prover 7: Constructing countermodel ...
% 47.63/7.81 Prover 8: Warning: ignoring some quantifiers
% 47.63/7.84 Prover 13: Warning: ignoring some quantifiers
% 47.63/7.85 Prover 8: Constructing countermodel ...
% 47.97/7.93 Prover 13: Constructing countermodel ...
% 56.32/9.07 Prover 10: Found proof (size 12)
% 56.32/9.07 Prover 10: proved (2535ms)
% 56.32/9.07 Prover 8: stopped
% 56.32/9.07 Prover 13: stopped
% 56.32/9.07 Prover 4: stopped
% 56.32/9.07 Prover 1: stopped
% 56.32/9.07 Prover 7: stopped
% 56.65/9.17 Prover 11: Warning: ignoring some quantifiers
% 56.97/9.26 Prover 11: Constructing countermodel ...
% 57.23/9.28 Prover 11: stopped
% 57.23/9.28
% 57.23/9.28 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 57.23/9.28
% 57.23/9.29 % SZS output start Proof for theBenchmark
% 57.23/9.31 Assumptions after simplification:
% 57.23/9.31 ---------------------------------
% 57.23/9.31
% 57.23/9.31 (t140_relat_1)
% 57.23/9.35 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 57.23/9.35 (relation_rng_restriction(v0, v3) = v4) | ~ (relation_dom_restriction(v2,
% 57.23/9.35 v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ relation(v2) | ?
% 57.23/9.35 [v5: $i] : (relation_rng_restriction(v0, v2) = v5 &
% 57.23/9.35 relation_dom_restriction(v5, v1) = v4 & $i(v5) & $i(v4)))
% 57.23/9.35
% 57.23/9.35 (t17_wellord1)
% 57.23/9.35 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 57.23/9.35 (relation_rng_restriction(v0, v1) = v2) | ~ (relation_dom_restriction(v2,
% 57.23/9.35 v0) = v3) | ~ $i(v1) | ~ $i(v0) | ~ relation(v1) |
% 57.23/9.35 (relation_restriction(v1, v0) = v3 & $i(v3)))
% 57.23/9.35
% 57.23/9.35 (t18_wellord1)
% 57.23/9.35 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ( ~ (v4
% 57.23/9.35 = v2) & relation_restriction(v1, v0) = v2 & relation_rng_restriction(v0,
% 57.23/9.35 v3) = v4 & relation_dom_restriction(v1, v0) = v3 & $i(v4) & $i(v3) &
% 57.23/9.35 $i(v2) & $i(v1) & $i(v0) & relation(v1))
% 57.23/9.35
% 57.23/9.35 (function-axioms)
% 57.60/9.37 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0
% 57.60/9.37 | ~ (subset_difference(v4, v3, v2) = v1) | ~ (subset_difference(v4, v3,
% 57.60/9.37 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : !
% 57.60/9.37 [v4: $i] : (v1 = v0 | ~ (unordered_triple(v4, v3, v2) = v1) | ~
% 57.60/9.37 (unordered_triple(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 57.60/9.37 $i] : ! [v3: $i] : (v1 = v0 | ~ (meet_of_subsets(v3, v2) = v1) | ~
% 57.60/9.37 (meet_of_subsets(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 57.60/9.37 ! [v3: $i] : (v1 = v0 | ~ (union_of_subsets(v3, v2) = v1) | ~
% 57.60/9.37 (union_of_subsets(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 57.60/9.37 ! [v3: $i] : (v1 = v0 | ~ (complements_of_subsets(v3, v2) = v1) | ~
% 57.60/9.37 (complements_of_subsets(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 57.60/9.37 $i] : ! [v3: $i] : (v1 = v0 | ~ (relation_composition(v3, v2) = v1) | ~
% 57.60/9.37 (relation_composition(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 57.60/9.37 $i] : ! [v3: $i] : (v1 = v0 | ~ (relation_restriction(v3, v2) = v1) | ~
% 57.60/9.37 (relation_restriction(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 57.60/9.37 $i] : ! [v3: $i] : (v1 = v0 | ~ (subset_complement(v3, v2) = v1) | ~
% 57.60/9.37 (subset_complement(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 57.60/9.37 : ! [v3: $i] : (v1 = v0 | ~ (set_difference(v3, v2) = v1) | ~
% 57.60/9.37 (set_difference(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 57.60/9.37 ! [v3: $i] : (v1 = v0 | ~ (cartesian_product2(v3, v2) = v1) | ~
% 57.60/9.37 (cartesian_product2(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 57.60/9.37 : ! [v3: $i] : (v1 = v0 | ~ (fiber(v3, v2) = v1) | ~ (fiber(v3, v2) = v0))
% 57.60/9.37 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 57.60/9.37 (relation_inverse_image(v3, v2) = v1) | ~ (relation_inverse_image(v3, v2) =
% 57.60/9.37 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 57.60/9.37 ~ (relation_rng_restriction(v3, v2) = v1) | ~ (relation_rng_restriction(v3,
% 57.60/9.37 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1
% 57.60/9.37 = v0 | ~ (relation_image(v3, v2) = v1) | ~ (relation_image(v3, v2) = v0))
% 57.60/9.37 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 57.60/9.37 (apply(v3, v2) = v1) | ~ (apply(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i]
% 57.60/9.37 : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (relation_dom_restriction(v3, v2)
% 57.60/9.37 = v1) | ~ (relation_dom_restriction(v3, v2) = v0)) & ! [v0: $i] : !
% 57.60/9.37 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (ordered_pair(v3, v2) =
% 57.60/9.37 v1) | ~ (ordered_pair(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 57.60/9.37 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (set_intersection2(v3, v2) = v1) | ~
% 57.60/9.37 (set_intersection2(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 57.60/9.37 : ! [v3: $i] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3,
% 57.60/9.37 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1
% 57.60/9.37 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0))
% 57.60/9.37 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 57.60/9.37 (function_inverse(v2) = v1) | ~ (function_inverse(v2) = v0)) & ! [v0: $i]
% 57.60/9.37 : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (relation_inverse(v2) = v1) | ~
% 57.60/9.37 (relation_inverse(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1
% 57.60/9.37 = v0 | ~ (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0)) & ! [v0:
% 57.60/9.37 $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (union(v2) = v1) | ~
% 57.60/9.37 (union(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 57.60/9.37 (cast_to_subset(v2) = v1) | ~ (cast_to_subset(v2) = v0)) & ! [v0: $i] : !
% 57.60/9.37 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2)
% 57.60/9.37 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 57.60/9.37 (set_meet(v2) = v1) | ~ (set_meet(v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 57.60/9.37 ! [v2: $i] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) &
% 57.60/9.37 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (succ(v2) = v1) | ~
% 57.60/9.37 (succ(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 57.60/9.37 (relation_field(v2) = v1) | ~ (relation_field(v2) = v0)) & ! [v0: $i] : !
% 57.60/9.37 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~
% 57.60/9.37 (relation_dom(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 57.60/9.37 v0 | ~ (identity_relation(v2) = v1) | ~ (identity_relation(v2) = v0))
% 57.60/9.37
% 57.60/9.37 Further assumptions not needed in the proof:
% 57.60/9.37 --------------------------------------------
% 57.60/9.37 antisymmetry_r2_hidden, antisymmetry_r2_xboole_0, cc1_funct_1, cc1_ordinal1,
% 57.60/9.37 cc1_relat_1, cc2_funct_1, cc2_ordinal1, cc3_ordinal1, commutativity_k2_tarski,
% 57.60/9.37 commutativity_k2_xboole_0, commutativity_k3_xboole_0, connectedness_r1_ordinal1,
% 57.60/9.37 d10_relat_1, d10_xboole_0, d11_relat_1, d12_funct_1, d12_relat_1, d12_relat_2,
% 57.60/9.37 d13_funct_1, d13_relat_1, d14_relat_1, d14_relat_2, d16_relat_2, d1_enumset1,
% 57.60/9.37 d1_ordinal1, d1_relat_1, d1_relat_2, d1_setfam_1, d1_tarski, d1_xboole_0,
% 57.60/9.37 d1_zfmisc_1, d2_ordinal1, d2_relat_1, d2_subset_1, d2_tarski, d2_wellord1,
% 57.60/9.37 d2_xboole_0, d2_zfmisc_1, d3_ordinal1, d3_relat_1, d3_tarski, d3_wellord1,
% 57.60/9.37 d3_xboole_0, d4_funct_1, d4_ordinal1, d4_relat_1, d4_relat_2, d4_subset_1,
% 57.60/9.37 d4_tarski, d4_wellord1, d4_xboole_0, d5_funct_1, d5_relat_1, d5_subset_1,
% 57.60/9.37 d5_tarski, d5_wellord1, d6_ordinal1, d6_relat_1, d6_relat_2, d6_wellord1,
% 57.60/9.37 d7_relat_1, d7_xboole_0, d8_funct_1, d8_relat_1, d8_relat_2, d8_setfam_1,
% 57.60/9.37 d8_xboole_0, d9_funct_1, d9_relat_2, dt_k10_relat_1, dt_k1_enumset1,
% 57.60/9.37 dt_k1_funct_1, dt_k1_ordinal1, dt_k1_relat_1, dt_k1_setfam_1, dt_k1_tarski,
% 57.60/9.37 dt_k1_wellord1, dt_k1_xboole_0, dt_k1_zfmisc_1, dt_k2_funct_1, dt_k2_relat_1,
% 57.60/9.37 dt_k2_subset_1, dt_k2_tarski, dt_k2_wellord1, dt_k2_xboole_0, dt_k2_zfmisc_1,
% 57.60/9.37 dt_k3_relat_1, dt_k3_subset_1, dt_k3_tarski, dt_k3_xboole_0, dt_k4_relat_1,
% 57.60/9.37 dt_k4_tarski, dt_k4_xboole_0, dt_k5_relat_1, dt_k5_setfam_1, dt_k6_relat_1,
% 57.60/9.37 dt_k6_setfam_1, dt_k6_subset_1, dt_k7_relat_1, dt_k7_setfam_1, dt_k8_relat_1,
% 57.60/9.37 dt_k9_relat_1, dt_m1_subset_1, existence_m1_subset_1, fc10_relat_1,
% 57.60/9.37 fc11_relat_1, fc12_relat_1, fc13_relat_1, fc1_funct_1, fc1_ordinal1,
% 57.60/9.37 fc1_relat_1, fc1_subset_1, fc1_xboole_0, fc1_zfmisc_1, fc2_funct_1,
% 57.60/9.37 fc2_ordinal1, fc2_relat_1, fc2_subset_1, fc2_xboole_0, fc3_funct_1,
% 57.60/9.37 fc3_ordinal1, fc3_relat_1, fc3_subset_1, fc3_xboole_0, fc4_funct_1,
% 57.60/9.37 fc4_ordinal1, fc4_relat_1, fc4_subset_1, fc5_funct_1, fc5_relat_1, fc6_relat_1,
% 57.60/9.37 fc7_relat_1, fc8_relat_1, fc9_relat_1, idempotence_k2_xboole_0,
% 57.60/9.37 idempotence_k3_xboole_0, involutiveness_k3_subset_1, involutiveness_k4_relat_1,
% 57.60/9.37 involutiveness_k7_setfam_1, irreflexivity_r2_xboole_0, l1_wellord1, l1_zfmisc_1,
% 57.60/9.37 l23_zfmisc_1, l25_zfmisc_1, l28_zfmisc_1, l2_wellord1, l2_zfmisc_1,
% 57.60/9.37 l32_xboole_1, l3_subset_1, l3_wellord1, l3_zfmisc_1, l4_wellord1, l4_zfmisc_1,
% 57.60/9.37 l50_zfmisc_1, l55_zfmisc_1, l71_subset_1, l82_funct_1, rc1_funct_1,
% 57.60/9.37 rc1_ordinal1, rc1_relat_1, rc1_subset_1, rc1_xboole_0, rc2_funct_1,
% 57.60/9.37 rc2_ordinal1, rc2_relat_1, rc2_subset_1, rc2_xboole_0, rc3_funct_1,
% 57.60/9.37 rc3_ordinal1, rc3_relat_1, rc4_funct_1, redefinition_k5_setfam_1,
% 57.60/9.37 redefinition_k6_setfam_1, redefinition_k6_subset_1, redefinition_r1_ordinal1,
% 57.60/9.37 reflexivity_r1_ordinal1, reflexivity_r1_tarski, symmetry_r1_xboole_0,
% 57.60/9.37 t106_zfmisc_1, t10_ordinal1, t10_zfmisc_1, t115_relat_1, t116_relat_1,
% 57.60/9.37 t117_relat_1, t118_relat_1, t118_zfmisc_1, t119_relat_1, t119_zfmisc_1,
% 57.60/9.37 t12_xboole_1, t136_zfmisc_1, t143_relat_1, t144_relat_1, t145_funct_1,
% 57.60/9.37 t145_relat_1, t146_funct_1, t146_relat_1, t147_funct_1, t160_relat_1,
% 57.60/9.37 t166_relat_1, t167_relat_1, t16_wellord1, t174_relat_1, t178_relat_1,
% 57.60/9.37 t17_xboole_1, t19_xboole_1, t1_boole, t1_subset, t1_xboole_1, t1_zfmisc_1,
% 57.60/9.37 t20_relat_1, t21_funct_1, t21_ordinal1, t21_relat_1, t22_funct_1, t23_funct_1,
% 57.60/9.37 t23_ordinal1, t24_ordinal1, t25_relat_1, t26_xboole_1, t28_xboole_1, t2_boole,
% 57.60/9.37 t2_subset, t2_tarski, t2_xboole_1, t30_relat_1, t31_ordinal1, t32_ordinal1,
% 57.60/9.37 t33_ordinal1, t33_xboole_1, t33_zfmisc_1, t34_funct_1, t35_funct_1,
% 57.60/9.37 t36_xboole_1, t37_relat_1, t37_xboole_1, t37_zfmisc_1, t38_zfmisc_1,
% 57.60/9.37 t39_xboole_1, t39_zfmisc_1, t3_boole, t3_ordinal1, t3_subset, t3_xboole_0,
% 57.60/9.37 t3_xboole_1, t40_xboole_1, t41_ordinal1, t42_ordinal1, t43_subset_1,
% 57.60/9.37 t44_relat_1, t45_relat_1, t45_xboole_1, t46_relat_1, t46_setfam_1, t46_zfmisc_1,
% 57.60/9.37 t47_relat_1, t47_setfam_1, t48_setfam_1, t48_xboole_1, t4_boole, t4_subset,
% 57.60/9.37 t4_xboole_0, t50_subset_1, t54_funct_1, t54_subset_1, t55_funct_1, t56_relat_1,
% 57.60/9.37 t57_funct_1, t5_subset, t5_wellord1, t60_relat_1, t60_xboole_1, t62_funct_1,
% 57.60/9.37 t63_xboole_1, t64_relat_1, t65_relat_1, t65_zfmisc_1, t68_funct_1, t69_enumset1,
% 57.60/9.37 t6_boole, t6_zfmisc_1, t70_funct_1, t71_relat_1, t72_funct_1, t74_relat_1,
% 57.60/9.37 t7_boole, t7_tarski, t7_xboole_1, t83_xboole_1, t86_relat_1, t88_relat_1,
% 57.60/9.37 t8_boole, t8_funct_1, t8_wellord1, t8_xboole_1, t8_zfmisc_1, t90_relat_1,
% 57.60/9.37 t92_zfmisc_1, t94_relat_1, t99_relat_1, t99_zfmisc_1, t9_tarski, t9_zfmisc_1
% 57.60/9.37
% 57.60/9.37 Those formulas are unsatisfiable:
% 57.60/9.37 ---------------------------------
% 57.60/9.37
% 57.60/9.37 Begin of proof
% 57.60/9.37 |
% 57.60/9.37 | ALPHA: (function-axioms) implies:
% 57.60/9.37 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 57.60/9.37 | (relation_restriction(v3, v2) = v1) | ~ (relation_restriction(v3,
% 57.60/9.37 | v2) = v0))
% 57.60/9.37 |
% 57.60/9.37 | DELTA: instantiating (t18_wellord1) with fresh symbols all_303_0, all_303_1,
% 57.60/9.37 | all_303_2, all_303_3, all_303_4 gives:
% 57.60/9.37 | (2) ~ (all_303_0 = all_303_2) & relation_restriction(all_303_3, all_303_4)
% 57.60/9.37 | = all_303_2 & relation_rng_restriction(all_303_4, all_303_1) =
% 57.60/9.37 | all_303_0 & relation_dom_restriction(all_303_3, all_303_4) = all_303_1
% 57.60/9.37 | & $i(all_303_0) & $i(all_303_1) & $i(all_303_2) & $i(all_303_3) &
% 57.60/9.37 | $i(all_303_4) & relation(all_303_3)
% 57.60/9.37 |
% 57.60/9.37 | ALPHA: (2) implies:
% 57.60/9.38 | (3) ~ (all_303_0 = all_303_2)
% 57.60/9.38 | (4) relation(all_303_3)
% 57.60/9.38 | (5) $i(all_303_4)
% 57.60/9.38 | (6) $i(all_303_3)
% 57.60/9.38 | (7) relation_dom_restriction(all_303_3, all_303_4) = all_303_1
% 57.60/9.38 | (8) relation_rng_restriction(all_303_4, all_303_1) = all_303_0
% 57.60/9.38 | (9) relation_restriction(all_303_3, all_303_4) = all_303_2
% 57.60/9.38 |
% 57.60/9.38 | GROUND_INST: instantiating (t140_relat_1) with all_303_4, all_303_4,
% 57.60/9.38 | all_303_3, all_303_1, all_303_0, simplifying with (4), (5), (6),
% 57.60/9.38 | (7), (8) gives:
% 57.60/9.38 | (10) ? [v0: $i] : (relation_rng_restriction(all_303_4, all_303_3) = v0 &
% 57.60/9.38 | relation_dom_restriction(v0, all_303_4) = all_303_0 & $i(v0) &
% 57.60/9.38 | $i(all_303_0))
% 57.60/9.38 |
% 57.60/9.38 | DELTA: instantiating (10) with fresh symbol all_365_0 gives:
% 57.60/9.38 | (11) relation_rng_restriction(all_303_4, all_303_3) = all_365_0 &
% 57.60/9.38 | relation_dom_restriction(all_365_0, all_303_4) = all_303_0 &
% 57.60/9.38 | $i(all_365_0) & $i(all_303_0)
% 57.60/9.38 |
% 57.60/9.38 | ALPHA: (11) implies:
% 57.60/9.38 | (12) relation_dom_restriction(all_365_0, all_303_4) = all_303_0
% 57.60/9.38 | (13) relation_rng_restriction(all_303_4, all_303_3) = all_365_0
% 57.60/9.38 |
% 57.60/9.38 | GROUND_INST: instantiating (t17_wellord1) with all_303_4, all_303_3,
% 57.60/9.38 | all_365_0, all_303_0, simplifying with (4), (5), (6), (12), (13)
% 57.60/9.38 | gives:
% 57.60/9.38 | (14) relation_restriction(all_303_3, all_303_4) = all_303_0 & $i(all_303_0)
% 57.60/9.38 |
% 57.60/9.38 | ALPHA: (14) implies:
% 57.60/9.38 | (15) relation_restriction(all_303_3, all_303_4) = all_303_0
% 57.60/9.38 |
% 57.60/9.38 | GROUND_INST: instantiating (1) with all_303_2, all_303_0, all_303_4,
% 57.60/9.38 | all_303_3, simplifying with (9), (15) gives:
% 57.60/9.38 | (16) all_303_0 = all_303_2
% 57.60/9.38 |
% 57.60/9.38 | REDUCE: (3), (16) imply:
% 57.60/9.38 | (17) $false
% 57.60/9.38 |
% 57.60/9.38 | CLOSE: (17) is inconsistent.
% 57.60/9.38 |
% 57.60/9.38 End of proof
% 57.72/9.38 % SZS output end Proof for theBenchmark
% 57.72/9.38
% 57.72/9.38 8752ms
%------------------------------------------------------------------------------