TSTP Solution File: SEU306+2 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SEU306+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 : n024.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 17:43:59 EDT 2023
% Result : Theorem 41.65s 6.23s
% Output : Proof 81.49s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU306+2 : TPTP v8.1.2. Released v3.3.0.
% 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.34 % Computer : n024.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Wed Aug 23 18:45:39 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.21/0.62 ________ _____
% 0.21/0.62 ___ __ \_________(_)________________________________
% 0.21/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.21/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.21/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.21/0.62
% 0.21/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.21/0.62 (2023-06-19)
% 0.21/0.62
% 0.21/0.62 (c) Philipp Rümmer, 2009-2023
% 0.21/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.21/0.62 Amanda Stjerna.
% 0.21/0.62 Free software under BSD-3-Clause.
% 0.21/0.62
% 0.21/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.21/0.62
% 0.21/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.21/0.63 Running up to 7 provers in parallel.
% 0.21/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.21/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.21/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.21/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.21/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.21/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.21/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 13.01/2.44 Prover 4: Preprocessing ...
% 13.01/2.45 Prover 1: Preprocessing ...
% 13.01/2.45 Prover 6: Preprocessing ...
% 13.01/2.45 Prover 2: Preprocessing ...
% 13.01/2.45 Prover 0: Preprocessing ...
% 13.01/2.46 Prover 5: Preprocessing ...
% 13.01/2.48 Prover 3: Preprocessing ...
% 37.40/5.73 Prover 1: Warning: ignoring some quantifiers
% 39.77/5.94 Prover 6: Proving ...
% 39.83/5.95 Prover 1: Constructing countermodel ...
% 39.83/5.99 Prover 3: Warning: ignoring some quantifiers
% 40.30/6.01 Prover 5: Proving ...
% 40.30/6.04 Prover 3: Constructing countermodel ...
% 41.65/6.22 Prover 3: proved (5574ms)
% 41.65/6.22
% 41.65/6.23 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 41.65/6.23
% 41.65/6.23 Prover 6: proved (5577ms)
% 41.65/6.23
% 41.65/6.23 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 41.65/6.23
% 41.65/6.23 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 41.65/6.23 Prover 5: stopped
% 42.04/6.24 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 42.04/6.25 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 45.11/6.69 Prover 10: Preprocessing ...
% 45.82/6.76 Prover 7: Preprocessing ...
% 46.21/6.81 Prover 8: Preprocessing ...
% 51.47/7.48 Prover 2: Proving ...
% 51.47/7.48 Prover 2: stopped
% 51.47/7.50 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 51.47/7.52 Prover 10: Warning: ignoring some quantifiers
% 52.24/7.71 Prover 10: Constructing countermodel ...
% 54.06/7.84 Prover 7: Warning: ignoring some quantifiers
% 55.34/8.01 Prover 7: Constructing countermodel ...
% 55.73/8.05 Prover 11: Preprocessing ...
% 56.76/8.22 Prover 8: Warning: ignoring some quantifiers
% 57.36/8.34 Prover 8: Constructing countermodel ...
% 60.69/8.70 Prover 4: Warning: ignoring some quantifiers
% 63.80/9.10 Prover 4: Constructing countermodel ...
% 75.66/10.63 Prover 10: Found proof (size 13)
% 75.66/10.63 Prover 10: proved (4378ms)
% 75.66/10.63 Prover 4: stopped
% 75.66/10.63 Prover 1: stopped
% 75.66/10.63 Prover 7: stopped
% 75.66/10.63 Prover 8: stopped
% 76.07/10.82 Prover 0: Proving ...
% 76.07/10.82 Prover 0: stopped
% 80.21/11.72 Prover 11: Warning: ignoring some quantifiers
% 80.85/11.91 Prover 11: Constructing countermodel ...
% 80.85/11.91 Prover 11: stopped
% 80.85/11.91
% 80.85/11.91 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 80.85/11.91
% 80.85/11.92 % SZS output start Proof for theBenchmark
% 81.21/11.97 Assumptions after simplification:
% 81.21/11.97 ---------------------------------
% 81.21/11.97
% 81.21/11.97 (d3_pre_topc)
% 81.49/12.05 ! [v0: $i] : ! [v1: $i] : ( ~ (cast_as_carrier_subset(v0) = v1) | ~ $i(v0)
% 81.49/12.05 | ~ one_sorted_str(v0) | (the_carrier(v0) = v1 & $i(v1)))
% 81.49/12.05
% 81.49/12.05 (dt_k2_pre_topc)
% 81.49/12.05 ! [v0: $i] : ! [v1: $i] : ( ~ (cast_as_carrier_subset(v0) = v1) | ~ $i(v0)
% 81.49/12.05 | ~ one_sorted_str(v0) | ? [v2: $i] : ? [v3: $i] : (the_carrier(v0) = v2
% 81.49/12.05 & powerset(v2) = v3 & $i(v3) & $i(v2) & element(v1, v3)))
% 81.49/12.05
% 81.49/12.05 (t12_pre_topc)
% 81.49/12.05 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v2 = v1) &
% 81.49/12.05 cast_as_carrier_subset(v0) = v1 & the_carrier(v0) = v2 & $i(v2) & $i(v1) &
% 81.49/12.05 $i(v0) & one_sorted_str(v0))
% 81.49/12.05
% 81.49/12.05 (function-axioms)
% 81.49/12.09 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 81.49/12.09 $i] : ! [v6: $i] : ! [v7: $i] : (v1 = v0 | ~ (apply_binary_as_element(v7,
% 81.49/12.09 v6, v5, v4, v3, v2) = v1) | ~ (apply_binary_as_element(v7, v6, v5, v4,
% 81.49/12.09 v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] :
% 81.49/12.09 ! [v4: $i] : (v1 = v0 | ~ (apply_binary(v4, v3, v2) = v1) | ~
% 81.49/12.09 (apply_binary(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 81.49/12.09 ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (subset_difference(v4, v3, v2) = v1)
% 81.49/12.09 | ~ (subset_difference(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 81.49/12.09 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~
% 81.49/12.09 (relation_rng_as_subset(v4, v3, v2) = v1) | ~ (relation_rng_as_subset(v4,
% 81.49/12.09 v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] :
% 81.49/12.09 ! [v4: $i] : (v1 = v0 | ~ (meet(v4, v3, v2) = v1) | ~ (meet(v4, v3, v2) =
% 81.49/12.09 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i]
% 81.49/12.09 : (v1 = v0 | ~ (join(v4, v3, v2) = v1) | ~ (join(v4, v3, v2) = v0)) & !
% 81.49/12.09 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 |
% 81.49/12.09 ~ (relation_dom_as_subset(v4, v3, v2) = v1) | ~ (relation_dom_as_subset(v4,
% 81.49/12.09 v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] :
% 81.49/12.09 ! [v4: $i] : (v1 = v0 | ~ (unordered_triple(v4, v3, v2) = v1) | ~
% 81.49/12.09 (unordered_triple(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 81.49/12.09 $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (meet_commut(v4, v3, v2) =
% 81.49/12.09 v1) | ~ (meet_commut(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 81.49/12.09 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (join_commut(v4, v3, v2)
% 81.49/12.09 = v1) | ~ (join_commut(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 81.49/12.09 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (meet_of_subsets(v3, v2) = v1) | ~
% 81.49/12.09 (meet_of_subsets(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 81.49/12.09 ! [v3: $i] : (v1 = v0 | ~ (union_of_subsets(v3, v2) = v1) | ~
% 81.49/12.09 (union_of_subsets(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 81.49/12.09 ! [v3: $i] : (v1 = v0 | ~ (complements_of_subsets(v3, v2) = v1) | ~
% 81.49/12.09 (complements_of_subsets(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 81.49/12.09 $i] : ! [v3: $i] : (v1 = v0 | ~ (relation_composition(v3, v2) = v1) | ~
% 81.49/12.09 (relation_composition(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 81.49/12.09 $i] : ! [v3: $i] : (v1 = v0 | ~ (relation_restriction(v3, v2) = v1) | ~
% 81.49/12.09 (relation_restriction(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 81.49/12.09 $i] : ! [v3: $i] : (v1 = v0 | ~ (subset_complement(v3, v2) = v1) | ~
% 81.49/12.09 (subset_complement(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 81.49/12.09 : ! [v3: $i] : (v1 = v0 | ~ (set_difference(v3, v2) = v1) | ~
% 81.49/12.09 (set_difference(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 81.49/12.09 ! [v3: $i] : (v1 = v0 | ~ (fiber(v3, v2) = v1) | ~ (fiber(v3, v2) = v0)) &
% 81.49/12.09 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 81.49/12.09 (relation_inverse_image(v3, v2) = v1) | ~ (relation_inverse_image(v3, v2) =
% 81.49/12.09 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 81.49/12.09 ~ (relation_rng_restriction(v3, v2) = v1) | ~ (relation_rng_restriction(v3,
% 81.49/12.09 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1
% 81.49/12.09 = v0 | ~ (relation_image(v3, v2) = v1) | ~ (relation_image(v3, v2) = v0))
% 81.49/12.09 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 81.49/12.09 (apply(v3, v2) = v1) | ~ (apply(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i]
% 81.49/12.09 : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (relation_dom_restriction(v3, v2)
% 81.49/12.09 = v1) | ~ (relation_dom_restriction(v3, v2) = v0)) & ! [v0: $i] : !
% 81.49/12.09 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (ordered_pair(v3, v2) =
% 81.49/12.09 v1) | ~ (ordered_pair(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 81.49/12.09 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (set_intersection2(v3, v2) = v1) | ~
% 81.49/12.09 (set_intersection2(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 81.49/12.09 : ! [v3: $i] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3,
% 81.49/12.09 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1
% 81.49/12.09 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0))
% 81.49/12.09 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 81.49/12.09 (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) = v0)) &
% 81.49/12.09 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (function_inverse(v2) =
% 81.49/12.09 v1) | ~ (function_inverse(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 81.49/12.09 [v2: $i] : (v1 = v0 | ~ (relation_inverse(v2) = v1) | ~
% 81.49/12.09 (relation_inverse(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1
% 81.49/12.09 = v0 | ~ (union(v2) = v1) | ~ (union(v2) = v0)) & ! [v0: $i] : ! [v1:
% 81.49/12.09 $i] : ! [v2: $i] : (v1 = v0 | ~ (cast_to_subset(v2) = v1) | ~
% 81.49/12.09 (cast_to_subset(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 81.49/12.09 v0 | ~ (cast_as_carrier_subset(v2) = v1) | ~ (cast_as_carrier_subset(v2) =
% 81.49/12.09 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 81.49/12.09 (pair_second(v2) = v1) | ~ (pair_second(v2) = v0)) & ! [v0: $i] : ! [v1:
% 81.49/12.09 $i] : ! [v2: $i] : (v1 = v0 | ~ (the_L_meet(v2) = v1) | ~ (the_L_meet(v2)
% 81.49/12.09 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 81.49/12.09 (inclusion_relation(v2) = v1) | ~ (inclusion_relation(v2) = v0)) & ! [v0:
% 81.49/12.09 $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (set_meet(v2) = v1) | ~
% 81.49/12.09 (set_meet(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 |
% 81.49/12.09 ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0: $i] : ! [v1:
% 81.49/12.09 $i] : ! [v2: $i] : (v1 = v0 | ~ (succ(v2) = v1) | ~ (succ(v2) = v0)) & !
% 81.49/12.09 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (pair_first(v2) = v1) |
% 81.49/12.09 ~ (pair_first(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 81.49/12.09 v0 | ~ (the_L_join(v2) = v1) | ~ (the_L_join(v2) = v0)) & ! [v0: $i] : !
% 81.49/12.09 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (relation_rng(v2) = v1) | ~
% 81.49/12.09 (relation_rng(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 81.49/12.09 v0 | ~ (relation_field(v2) = v1) | ~ (relation_field(v2) = v0)) & ! [v0:
% 81.49/12.09 $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~
% 81.49/12.09 (relation_dom(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 81.49/12.09 v0 | ~ (identity_relation(v2) = v1) | ~ (identity_relation(v2) = v0)) & !
% 81.49/12.09 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (the_carrier(v2) = v1) |
% 81.49/12.09 ~ (the_carrier(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 81.49/12.09 v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0))
% 81.49/12.09
% 81.49/12.09 Further assumptions not needed in the proof:
% 81.49/12.09 --------------------------------------------
% 81.49/12.09 antisymmetry_r2_hidden, antisymmetry_r2_xboole_0, cc10_membered, cc11_membered,
% 81.49/12.09 cc12_membered, cc13_membered, cc14_membered, cc15_membered, cc16_membered,
% 81.49/12.09 cc17_membered, cc18_membered, cc19_membered, cc1_arytm_3, cc1_finset_1,
% 81.49/12.09 cc1_finsub_1, cc1_funct_1, cc1_membered, cc1_ordinal1, cc1_relat_1,
% 81.49/12.09 cc1_relset_1, cc20_membered, cc2_arytm_3, cc2_finset_1, cc2_finsub_1,
% 81.49/12.09 cc2_funct_1, cc2_membered, cc2_ordinal1, cc3_arytm_3, cc3_membered,
% 81.49/12.09 cc3_ordinal1, cc4_membered, commutativity_k2_tarski, commutativity_k2_xboole_0,
% 81.49/12.09 commutativity_k3_lattices, commutativity_k3_xboole_0, commutativity_k4_lattices,
% 81.49/12.09 connectedness_r1_ordinal1, d10_relat_1, d10_xboole_0, d11_relat_1, d12_funct_1,
% 81.49/12.09 d12_relat_1, d12_relat_2, d13_funct_1, d13_relat_1, d14_relat_1, d14_relat_2,
% 81.49/12.09 d16_relat_2, d1_enumset1, d1_finset_1, d1_funct_1, d1_funct_2, d1_lattices,
% 81.49/12.09 d1_mcart_1, d1_ordinal1, d1_relat_1, d1_relat_2, d1_relset_1, d1_setfam_1,
% 81.49/12.09 d1_tarski, d1_wellord1, d1_wellord2, d1_xboole_0, d1_zfmisc_1, d2_lattices,
% 81.49/12.09 d2_mcart_1, d2_ordinal1, d2_relat_1, d2_subset_1, d2_tarski, d2_wellord1,
% 81.49/12.09 d2_xboole_0, d2_zfmisc_1, d3_lattices, d3_ordinal1, d3_relat_1, d3_tarski,
% 81.49/12.09 d3_wellord1, d3_xboole_0, d4_funct_1, d4_ordinal1, d4_relat_1, d4_relat_2,
% 81.49/12.09 d4_subset_1, d4_tarski, d4_wellord1, d4_wellord2, d4_xboole_0, d5_funct_1,
% 81.49/12.09 d5_ordinal2, d5_relat_1, d5_subset_1, d5_tarski, d5_wellord1, d6_ordinal1,
% 81.49/12.09 d6_relat_1, d6_relat_2, d6_wellord1, d7_relat_1, d7_wellord1, d7_xboole_0,
% 81.49/12.09 d8_funct_1, d8_lattices, d8_relat_1, d8_relat_2, d8_setfam_1, d8_xboole_0,
% 81.49/12.09 d9_funct_1, d9_relat_2, dt_k10_relat_1, dt_k1_binop_1, dt_k1_enumset1,
% 81.49/12.09 dt_k1_funct_1, dt_k1_lattices, dt_k1_mcart_1, dt_k1_ordinal1, dt_k1_relat_1,
% 81.49/12.09 dt_k1_setfam_1, dt_k1_tarski, dt_k1_wellord1, dt_k1_wellord2, dt_k1_xboole_0,
% 81.49/12.09 dt_k1_zfmisc_1, dt_k2_binop_1, dt_k2_funct_1, dt_k2_lattices, dt_k2_mcart_1,
% 81.49/12.09 dt_k2_relat_1, dt_k2_subset_1, dt_k2_tarski, dt_k2_wellord1, dt_k2_xboole_0,
% 81.49/12.09 dt_k2_zfmisc_1, dt_k3_lattices, dt_k3_relat_1, dt_k3_subset_1, dt_k3_tarski,
% 81.49/12.09 dt_k3_xboole_0, dt_k4_lattices, dt_k4_relat_1, dt_k4_relset_1, dt_k4_tarski,
% 81.49/12.09 dt_k4_xboole_0, dt_k5_ordinal2, dt_k5_relat_1, dt_k5_relset_1, dt_k5_setfam_1,
% 81.49/12.09 dt_k6_relat_1, dt_k6_setfam_1, dt_k6_subset_1, dt_k7_relat_1, dt_k7_setfam_1,
% 81.49/12.09 dt_k8_relat_1, dt_k9_relat_1, dt_l1_lattices, dt_l1_struct_0, dt_l2_lattices,
% 81.49/12.09 dt_l3_lattices, dt_m1_relset_1, dt_m1_subset_1, dt_m2_relset_1, dt_u1_lattices,
% 81.49/12.09 dt_u1_struct_0, dt_u2_lattices, existence_l1_lattices, existence_l1_struct_0,
% 81.49/12.09 existence_l2_lattices, existence_l3_lattices, existence_m1_relset_1,
% 81.49/12.09 existence_m1_subset_1, existence_m2_relset_1, fc10_finset_1, fc10_relat_1,
% 81.49/12.09 fc11_finset_1, fc11_relat_1, fc12_finset_1, fc12_relat_1, fc13_finset_1,
% 81.49/12.09 fc13_relat_1, fc1_finset_1, fc1_finsub_1, fc1_funct_1, fc1_ordinal1,
% 81.49/12.09 fc1_ordinal2, fc1_relat_1, fc1_struct_0, fc1_subset_1, fc1_xboole_0,
% 81.49/12.09 fc1_zfmisc_1, fc2_arytm_3, fc2_funct_1, fc2_ordinal1, fc2_relat_1, fc2_subset_1,
% 81.49/12.09 fc2_xboole_0, fc3_funct_1, fc3_ordinal1, fc3_relat_1, fc3_subset_1,
% 81.49/12.09 fc3_xboole_0, fc4_funct_1, fc4_ordinal1, fc4_relat_1, fc4_subset_1, fc5_funct_1,
% 81.49/12.09 fc5_relat_1, fc6_membered, fc6_relat_1, fc7_relat_1, fc8_relat_1, fc9_finset_1,
% 81.49/12.09 fc9_relat_1, idempotence_k2_xboole_0, idempotence_k3_xboole_0,
% 81.49/12.09 involutiveness_k3_subset_1, involutiveness_k4_relat_1,
% 81.49/12.09 involutiveness_k7_setfam_1, irreflexivity_r2_xboole_0, l1_wellord1, l1_zfmisc_1,
% 81.49/12.09 l23_zfmisc_1, l25_zfmisc_1, l28_zfmisc_1, l29_wellord1, l2_wellord1,
% 81.49/12.09 l2_zfmisc_1, l30_wellord2, l32_xboole_1, l3_subset_1, l3_wellord1, l3_zfmisc_1,
% 81.49/12.09 l4_wellord1, l4_zfmisc_1, l50_zfmisc_1, l55_zfmisc_1, l71_subset_1, l82_funct_1,
% 81.49/12.09 rc1_arytm_3, rc1_finset_1, rc1_funct_1, rc1_funct_2, rc1_membered, rc1_ordinal1,
% 81.49/12.09 rc1_ordinal2, rc1_partfun1, rc1_relat_1, rc1_subset_1, rc1_xboole_0,
% 81.49/12.09 rc2_finset_1, rc2_funct_1, rc2_ordinal1, rc2_partfun1, rc2_relat_1,
% 81.49/12.09 rc2_subset_1, rc2_xboole_0, rc3_finset_1, rc3_funct_1, rc3_ordinal1,
% 81.49/12.09 rc3_relat_1, rc3_struct_0, rc4_funct_1, rc5_struct_0, redefinition_k2_binop_1,
% 81.49/12.09 redefinition_k3_lattices, redefinition_k4_lattices, redefinition_k4_relset_1,
% 81.49/12.09 redefinition_k5_relset_1, redefinition_k5_setfam_1, redefinition_k6_setfam_1,
% 81.49/12.09 redefinition_k6_subset_1, redefinition_m2_relset_1, redefinition_r1_ordinal1,
% 81.49/12.09 redefinition_r2_wellord2, reflexivity_r1_ordinal1, reflexivity_r1_tarski,
% 81.49/12.09 reflexivity_r2_wellord2, s1_funct_1__e10_24__wellord2__1,
% 81.49/12.09 s1_funct_1__e16_22__wellord2__1, s1_ordinal1__e8_6__wellord2,
% 81.49/12.09 s1_ordinal2__e18_27__finset_1, s1_relat_1__e6_21__wellord2,
% 81.49/12.09 s1_tarski__e10_24__wellord2__1, s1_tarski__e10_24__wellord2__2,
% 81.49/12.09 s1_tarski__e16_22__wellord2__1, s1_tarski__e16_22__wellord2__2,
% 81.49/12.09 s1_tarski__e18_27__finset_1__1, s1_tarski__e4_27_3_1__finset_1__1,
% 81.49/12.09 s1_tarski__e6_21__wellord2__1, s1_tarski__e6_22__wellord2__1,
% 81.49/12.09 s1_tarski__e6_27__finset_1__1, s1_tarski__e8_6__wellord2__1,
% 81.49/12.09 s1_xboole_0__e10_24__wellord2__1, s1_xboole_0__e16_22__wellord2__1,
% 81.49/12.09 s1_xboole_0__e18_27__finset_1__1, s1_xboole_0__e4_27_3_1__finset_1,
% 81.49/12.09 s1_xboole_0__e6_21__wellord2__1, s1_xboole_0__e6_22__wellord2,
% 81.49/12.09 s1_xboole_0__e6_27__finset_1, s1_xboole_0__e8_6__wellord2__1,
% 81.49/12.09 s2_funct_1__e10_24__wellord2, s2_funct_1__e16_22__wellord2__1,
% 81.49/12.09 s2_ordinal1__e18_27__finset_1__1, s3_funct_1__e16_22__wellord2,
% 81.49/12.09 symmetry_r1_xboole_0, symmetry_r2_wellord2, t106_zfmisc_1, t10_ordinal1,
% 81.49/12.09 t10_zfmisc_1, t115_relat_1, t116_relat_1, t117_relat_1, t118_relat_1,
% 81.49/12.09 t118_zfmisc_1, t119_relat_1, t119_zfmisc_1, t12_relset_1, t12_xboole_1,
% 81.49/12.09 t136_zfmisc_1, t13_finset_1, t140_relat_1, t143_relat_1, t144_relat_1,
% 81.49/12.09 t145_funct_1, t145_relat_1, t146_funct_1, t146_relat_1, t147_funct_1,
% 81.49/12.09 t14_relset_1, t15_finset_1, t160_relat_1, t166_relat_1, t167_relat_1,
% 81.49/12.09 t16_relset_1, t16_wellord1, t174_relat_1, t178_relat_1, t17_finset_1,
% 81.49/12.09 t17_wellord1, t17_xboole_1, t18_finset_1, t18_wellord1, t19_wellord1,
% 81.49/12.09 t19_xboole_1, t1_boole, t1_subset, t1_xboole_1, t1_zfmisc_1, t20_relat_1,
% 81.49/12.09 t20_wellord1, t21_funct_1, t21_funct_2, t21_ordinal1, t21_relat_1, t21_wellord1,
% 81.49/12.09 t22_funct_1, t22_relset_1, t22_wellord1, t23_funct_1, t23_lattices,
% 81.49/12.09 t23_ordinal1, t23_relset_1, t23_wellord1, t24_ordinal1, t24_wellord1,
% 81.49/12.09 t25_relat_1, t25_wellord1, t25_wellord2, t26_finset_1, t26_lattices,
% 81.49/12.09 t26_wellord2, t26_xboole_1, t28_wellord2, t28_xboole_1, t2_boole, t2_subset,
% 81.49/12.09 t2_tarski, t2_wellord2, t2_xboole_1, t30_relat_1, t31_ordinal1, t31_wellord1,
% 81.49/12.09 t32_ordinal1, t32_wellord1, t33_ordinal1, t33_xboole_1, t33_zfmisc_1,
% 81.49/12.09 t34_funct_1, t35_funct_1, t36_xboole_1, t37_relat_1, t37_xboole_1, t37_zfmisc_1,
% 81.49/12.09 t38_zfmisc_1, t39_wellord1, t39_xboole_1, t39_zfmisc_1, t3_boole, t3_ordinal1,
% 81.49/12.09 t3_subset, t3_wellord2, t3_xboole_0, t3_xboole_1, t40_xboole_1, t41_ordinal1,
% 81.49/12.09 t42_ordinal1, t43_subset_1, t44_relat_1, t45_relat_1, t45_xboole_1, t46_funct_2,
% 81.49/12.09 t46_relat_1, t46_setfam_1, t46_zfmisc_1, t47_relat_1, t47_setfam_1,
% 81.49/12.09 t48_setfam_1, t48_xboole_1, t49_wellord1, t4_boole, t4_subset, t4_wellord2,
% 81.49/12.09 t4_xboole_0, t50_subset_1, t53_wellord1, t54_funct_1, t54_subset_1,
% 81.49/12.09 t54_wellord1, t55_funct_1, t56_relat_1, t57_funct_1, t5_subset, t5_wellord1,
% 81.49/12.09 t5_wellord2, t60_relat_1, t60_xboole_1, t62_funct_1, t63_xboole_1, t64_relat_1,
% 81.49/12.09 t65_relat_1, t65_zfmisc_1, t68_funct_1, t69_enumset1, t6_boole, t6_funct_2,
% 81.49/12.09 t6_wellord2, t6_zfmisc_1, t70_funct_1, t71_relat_1, t72_funct_1, t74_relat_1,
% 81.49/12.09 t7_boole, t7_mcart_1, t7_tarski, t7_wellord2, t7_xboole_1, t83_xboole_1,
% 81.49/12.09 t86_relat_1, t88_relat_1, t8_boole, t8_funct_1, t8_wellord1, t8_xboole_1,
% 81.49/12.09 t8_zfmisc_1, t90_relat_1, t92_zfmisc_1, t94_relat_1, t99_relat_1, t99_zfmisc_1,
% 81.49/12.09 t9_funct_2, t9_tarski, t9_zfmisc_1
% 81.49/12.09
% 81.49/12.09 Those formulas are unsatisfiable:
% 81.49/12.09 ---------------------------------
% 81.49/12.09
% 81.49/12.09 Begin of proof
% 81.49/12.09 |
% 81.49/12.09 | ALPHA: (function-axioms) implies:
% 81.49/12.10 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 81.49/12.10 | (the_carrier(v2) = v1) | ~ (the_carrier(v2) = v0))
% 81.49/12.10 |
% 81.49/12.10 | DELTA: instantiating (t12_pre_topc) with fresh symbols all_438_0, all_438_1,
% 81.49/12.10 | all_438_2 gives:
% 81.49/12.10 | (2) ~ (all_438_0 = all_438_1) & cast_as_carrier_subset(all_438_2) =
% 81.49/12.10 | all_438_1 & the_carrier(all_438_2) = all_438_0 & $i(all_438_0) &
% 81.49/12.10 | $i(all_438_1) & $i(all_438_2) & one_sorted_str(all_438_2)
% 81.49/12.10 |
% 81.49/12.10 | ALPHA: (2) implies:
% 81.49/12.10 | (3) ~ (all_438_0 = all_438_1)
% 81.49/12.10 | (4) one_sorted_str(all_438_2)
% 81.49/12.10 | (5) $i(all_438_2)
% 81.49/12.10 | (6) the_carrier(all_438_2) = all_438_0
% 81.49/12.10 | (7) cast_as_carrier_subset(all_438_2) = all_438_1
% 81.49/12.10 |
% 81.49/12.10 | GROUND_INST: instantiating (dt_k2_pre_topc) with all_438_2, all_438_1,
% 81.49/12.10 | simplifying with (4), (5), (7) gives:
% 81.49/12.10 | (8) ? [v0: $i] : ? [v1: $i] : (the_carrier(all_438_2) = v0 & powerset(v0)
% 81.49/12.10 | = v1 & $i(v1) & $i(v0) & element(all_438_1, v1))
% 81.49/12.10 |
% 81.49/12.10 | GROUND_INST: instantiating (d3_pre_topc) with all_438_2, all_438_1,
% 81.49/12.10 | simplifying with (4), (5), (7) gives:
% 81.49/12.10 | (9) the_carrier(all_438_2) = all_438_1 & $i(all_438_1)
% 81.49/12.10 |
% 81.49/12.10 | ALPHA: (9) implies:
% 81.49/12.10 | (10) the_carrier(all_438_2) = all_438_1
% 81.49/12.10 |
% 81.49/12.10 | DELTA: instantiating (8) with fresh symbols all_561_0, all_561_1 gives:
% 81.49/12.10 | (11) the_carrier(all_438_2) = all_561_1 & powerset(all_561_1) = all_561_0 &
% 81.49/12.10 | $i(all_561_0) & $i(all_561_1) & element(all_438_1, all_561_0)
% 81.49/12.10 |
% 81.49/12.10 | ALPHA: (11) implies:
% 81.49/12.10 | (12) the_carrier(all_438_2) = all_561_1
% 81.49/12.10 |
% 81.49/12.10 | GROUND_INST: instantiating (1) with all_438_0, all_561_1, all_438_2,
% 81.49/12.10 | simplifying with (6), (12) gives:
% 81.49/12.10 | (13) all_561_1 = all_438_0
% 81.49/12.10 |
% 81.49/12.10 | GROUND_INST: instantiating (1) with all_438_1, all_561_1, all_438_2,
% 81.49/12.10 | simplifying with (10), (12) gives:
% 81.49/12.10 | (14) all_561_1 = all_438_1
% 81.49/12.10 |
% 81.49/12.10 | COMBINE_EQS: (13), (14) imply:
% 81.49/12.10 | (15) all_438_0 = all_438_1
% 81.49/12.10 |
% 81.49/12.11 | REDUCE: (3), (15) imply:
% 81.49/12.11 | (16) $false
% 81.49/12.11 |
% 81.49/12.11 | CLOSE: (16) is inconsistent.
% 81.49/12.11 |
% 81.49/12.11 End of proof
% 81.49/12.11 % SZS output end Proof for theBenchmark
% 81.49/12.11
% 81.49/12.11 11483ms
%------------------------------------------------------------------------------