TSTP Solution File: SET665+3 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET665+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n029.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 15:25:54 EDT 2023
% Result : Theorem 77.82s 11.43s
% Output : Proof 78.41s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET665+3 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.33 % Computer : n029.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sat Aug 26 10:32:10 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.18/0.63 ________ _____
% 0.18/0.63 ___ __ \_________(_)________________________________
% 0.18/0.63 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.18/0.63 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.18/0.63 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.18/0.63
% 0.18/0.63 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.18/0.63 (2023-06-19)
% 0.18/0.63
% 0.18/0.63 (c) Philipp Rümmer, 2009-2023
% 0.18/0.63 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.18/0.63 Amanda Stjerna.
% 0.18/0.63 Free software under BSD-3-Clause.
% 0.18/0.63
% 0.18/0.63 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.18/0.63
% 0.18/0.63 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.18/0.65 Running up to 7 provers in parallel.
% 0.18/0.67 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.18/0.67 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.18/0.67 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.18/0.67 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.18/0.67 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.18/0.67 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.18/0.67 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.29/1.27 Prover 1: Preprocessing ...
% 3.29/1.27 Prover 4: Preprocessing ...
% 3.82/1.32 Prover 6: Preprocessing ...
% 3.82/1.32 Prover 0: Preprocessing ...
% 3.82/1.32 Prover 3: Preprocessing ...
% 3.82/1.32 Prover 5: Preprocessing ...
% 3.82/1.33 Prover 2: Preprocessing ...
% 11.39/2.43 Prover 3: Constructing countermodel ...
% 11.54/2.45 Prover 1: Constructing countermodel ...
% 11.54/2.50 Prover 5: Proving ...
% 11.54/2.50 Prover 2: Proving ...
% 11.95/2.53 Prover 6: Proving ...
% 16.45/3.22 Prover 4: Constructing countermodel ...
% 17.72/3.42 Prover 0: Proving ...
% 71.15/10.47 Prover 2: stopped
% 71.31/10.52 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 71.31/10.59 Prover 7: Preprocessing ...
% 72.59/10.72 Prover 7: Warning: ignoring some quantifiers
% 72.59/10.72 Prover 7: Constructing countermodel ...
% 77.16/11.32 Prover 7: Found proof (size 62)
% 77.16/11.32 Prover 7: proved (806ms)
% 77.16/11.33 Prover 5: stopped
% 77.16/11.33 Prover 3: stopped
% 77.16/11.33 Prover 1: stopped
% 77.16/11.33 Prover 4: stopped
% 77.16/11.35 Prover 6: stopped
% 77.82/11.42 Prover 0: stopped
% 77.82/11.42
% 77.82/11.43 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 77.82/11.43
% 78.00/11.43 % SZS output start Proof for theBenchmark
% 78.00/11.44 Assumptions after simplification:
% 78.00/11.44 ---------------------------------
% 78.00/11.44
% 78.00/11.44 (p1)
% 78.06/11.46 $i(set_type) & $i(binary_relation_type) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 78.06/11.46 $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (ordered_pair(v2, v3) = v4) | ~
% 78.06/11.46 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ member(v4, v0) | ~
% 78.06/11.46 subset(v0, v1) | ~ ilf_type(v3, set_type) | ~ ilf_type(v2, set_type) | ~
% 78.06/11.46 ilf_type(v1, binary_relation_type) | ~ ilf_type(v0, binary_relation_type) |
% 78.06/11.46 member(v4, v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~
% 78.06/11.46 ilf_type(v1, binary_relation_type) | ~ ilf_type(v0, binary_relation_type) |
% 78.06/11.46 subset(v0, v1) | ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : (ordered_pair(v2,
% 78.06/11.46 v3) = v4 & $i(v4) & $i(v3) & $i(v2) & member(v4, v0) & ilf_type(v3,
% 78.06/11.46 set_type) & ilf_type(v2, set_type) & ~ member(v4, v1)))
% 78.06/11.46
% 78.06/11.46 (p11)
% 78.06/11.46 $i(set_type) & $i(binary_relation_type) & ! [v0: $i] : ( ~ $i(v0) | ~
% 78.06/11.46 relation_like(v0) | ~ ilf_type(v0, set_type) | ilf_type(v0,
% 78.06/11.46 binary_relation_type)) & ! [v0: $i] : ( ~ $i(v0) | ~ ilf_type(v0,
% 78.06/11.46 set_type) | ~ ilf_type(v0, binary_relation_type) | relation_like(v0))
% 78.06/11.46
% 78.06/11.46 (p13)
% 78.06/11.47 $i(set_type) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 78.06/11.47 (relation_type(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ ilf_type(v1,
% 78.06/11.47 set_type) | ~ ilf_type(v0, set_type) | ? [v3: $i] : ? [v4: $i] :
% 78.06/11.47 (subset_type(v3) = v4 & cross_product(v0, v1) = v3 & $i(v4) & $i(v3) & !
% 78.06/11.47 [v5: $i] : ( ~ $i(v5) | ~ ilf_type(v5, v4) | ilf_type(v5, v2)) & ! [v5:
% 78.06/11.47 $i] : ( ~ $i(v5) | ~ ilf_type(v5, v2) | ilf_type(v5, v4)))) & ! [v0:
% 78.06/11.47 $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (cross_product(v0, v1) = v2) | ~
% 78.06/11.47 $i(v1) | ~ $i(v0) | ~ ilf_type(v1, set_type) | ~ ilf_type(v0, set_type) |
% 78.06/11.47 ? [v3: $i] : ? [v4: $i] : (subset_type(v2) = v3 & relation_type(v0, v1) =
% 78.06/11.47 v4 & $i(v4) & $i(v3) & ! [v5: $i] : ( ~ $i(v5) | ~ ilf_type(v5, v4) |
% 78.06/11.47 ilf_type(v5, v3)) & ! [v5: $i] : ( ~ $i(v5) | ~ ilf_type(v5, v3) |
% 78.06/11.47 ilf_type(v5, v4))))
% 78.06/11.47
% 78.06/11.47 (p2)
% 78.06/11.47 $i(set_type) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4:
% 78.06/11.47 $i] : (v3 = v2 | ~ (identity_relation_of(v0) = v1) | ~ (ordered_pair(v2,
% 78.06/11.47 v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v0) | ~ member(v4, v1) | ~
% 78.06/11.47 ilf_type(v3, set_type) | ~ ilf_type(v2, set_type) | ~ ilf_type(v0,
% 78.06/11.47 set_type)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : !
% 78.06/11.47 [v4: $i] : ( ~ (identity_relation_of(v0) = v1) | ~ (ordered_pair(v2, v3) =
% 78.06/11.47 v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v0) | ~ member(v4, v1) | ~
% 78.06/11.47 ilf_type(v3, set_type) | ~ ilf_type(v2, set_type) | ~ ilf_type(v0,
% 78.06/11.47 set_type) | member(v2, v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 78.06/11.47 [v3: $i] : ( ~ (identity_relation_of(v0) = v1) | ~ (ordered_pair(v2, v2) =
% 78.06/11.47 v3) | ~ $i(v2) | ~ $i(v0) | ~ member(v2, v0) | ~ ilf_type(v2,
% 78.06/11.47 set_type) | ~ ilf_type(v0, set_type) | member(v3, v1))
% 78.06/11.47
% 78.06/11.47 (p20)
% 78.06/11.47 $i(set_type) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 78.06/11.47 (cross_product(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ ilf_type(v1,
% 78.06/11.47 set_type) | ~ ilf_type(v0, set_type) | ? [v3: $i] : (subset_type(v2) =
% 78.06/11.47 v3 & $i(v3) & ! [v4: $i] : ( ~ $i(v4) | ~ ilf_type(v4, v3) |
% 78.06/11.47 relation_like(v4))))
% 78.06/11.47
% 78.06/11.47 (p3)
% 78.06/11.48 $i(set_type) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4:
% 78.06/11.48 $i] : ! [v5: $i] : ( ~ (cross_product(v3, v4) = v5) | ~ (ordered_pair(v0,
% 78.06/11.48 v1) = v2) | ~ $i(v4) | ~ $i(v3) | ~ $i(v1) | ~ $i(v0) | ~
% 78.06/11.48 member(v2, v5) | ~ ilf_type(v4, set_type) | ~ ilf_type(v3, set_type) | ~
% 78.06/11.48 ilf_type(v1, set_type) | ~ ilf_type(v0, set_type) | member(v1, v4)) & !
% 78.06/11.48 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i]
% 78.06/11.48 : ( ~ (cross_product(v3, v4) = v5) | ~ (ordered_pair(v0, v1) = v2) | ~
% 78.06/11.48 $i(v4) | ~ $i(v3) | ~ $i(v1) | ~ $i(v0) | ~ member(v2, v5) | ~
% 78.06/11.48 ilf_type(v4, set_type) | ~ ilf_type(v3, set_type) | ~ ilf_type(v1,
% 78.06/11.48 set_type) | ~ ilf_type(v0, set_type) | member(v0, v3)) & ! [v0: $i] : !
% 78.06/11.48 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~
% 78.06/11.48 (cross_product(v3, v4) = v5) | ~ (ordered_pair(v0, v1) = v2) | ~ $i(v4) |
% 78.06/11.48 ~ $i(v3) | ~ $i(v1) | ~ $i(v0) | ~ member(v1, v4) | ~ member(v0, v3) |
% 78.06/11.48 ~ ilf_type(v4, set_type) | ~ ilf_type(v3, set_type) | ~ ilf_type(v1,
% 78.06/11.48 set_type) | ~ ilf_type(v0, set_type) | member(v2, v5))
% 78.06/11.48
% 78.06/11.48 (p4)
% 78.06/11.48 $i(set_type) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 78.06/11.48 (relation_type(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ ilf_type(v1,
% 78.06/11.48 set_type) | ~ ilf_type(v0, set_type) | ? [v3: $i] : (cross_product(v0,
% 78.06/11.48 v1) = v3 & $i(v3) & ilf_type(v3, v2))) & ! [v0: $i] : ! [v1: $i] : !
% 78.06/11.48 [v2: $i] : ( ~ (cross_product(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~
% 78.06/11.48 ilf_type(v1, set_type) | ~ ilf_type(v0, set_type) | ? [v3: $i] :
% 78.06/11.48 (relation_type(v0, v1) = v3 & $i(v3) & ilf_type(v2, v3)))
% 78.06/11.48
% 78.06/11.48 (p6)
% 78.06/11.48 $i(set_type) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 78.06/11.48 (cross_product(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ ilf_type(v1,
% 78.06/11.48 set_type) | ~ ilf_type(v0, set_type) | ilf_type(v2, set_type))
% 78.06/11.48
% 78.06/11.48 (p7)
% 78.06/11.48 $i(set_type) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4:
% 78.06/11.48 $i] : (v3 = v2 | ~ (identity_relation_of(v0) = v1) | ~ (ordered_pair(v2,
% 78.06/11.48 v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v0) | ~ member(v4, v1) | ~
% 78.06/11.48 ilf_type(v3, set_type) | ~ ilf_type(v2, set_type) | ~ ilf_type(v0,
% 78.06/11.48 set_type)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : !
% 78.06/11.48 [v4: $i] : ( ~ (identity_relation_of(v0) = v1) | ~ (ordered_pair(v2, v3) =
% 78.06/11.48 v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v0) | ~ member(v4, v1) | ~
% 78.06/11.48 ilf_type(v3, set_type) | ~ ilf_type(v2, set_type) | ~ ilf_type(v0,
% 78.06/11.48 set_type) | member(v2, v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 78.06/11.48 [v3: $i] : ( ~ (identity_relation_of(v0) = v1) | ~ (ordered_pair(v2, v2) =
% 78.06/11.48 v3) | ~ $i(v2) | ~ $i(v0) | ~ member(v2, v0) | ~ ilf_type(v2,
% 78.06/11.48 set_type) | ~ ilf_type(v0, set_type) | member(v3, v1))
% 78.06/11.48
% 78.06/11.48 (p8)
% 78.06/11.48 $i(set_type) & $i(binary_relation_type) & ! [v0: $i] : ! [v1: $i] : ( ~
% 78.06/11.48 (identity_relation_of(v0) = v1) | ~ $i(v0) | ~ ilf_type(v0, set_type) |
% 78.06/11.48 ilf_type(v1, binary_relation_type))
% 78.06/11.48
% 78.06/11.48 (prove_relset_1_28)
% 78.06/11.48 $i(set_type) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (cross_product(v0,
% 78.06/11.48 v0) = v2 & identity_relation_of(v0) = v1 & $i(v2) & $i(v1) & $i(v0) &
% 78.06/11.48 ilf_type(v0, set_type) & ~ subset(v1, v2))
% 78.06/11.48
% 78.06/11.48 (function-axioms)
% 78.06/11.48 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 78.06/11.48 (relation_type(v3, v2) = v1) | ~ (relation_type(v3, v2) = v0)) & ! [v0:
% 78.06/11.48 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 78.06/11.48 (cross_product(v3, v2) = v1) | ~ (cross_product(v3, v2) = v0)) & ! [v0:
% 78.06/11.48 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 78.06/11.48 (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0)) & ! [v0: $i]
% 78.06/11.48 : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (power_set(v2) = v1) | ~
% 78.06/11.48 (power_set(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 |
% 78.06/11.48 ~ (member_type(v2) = v1) | ~ (member_type(v2) = v0)) & ! [v0: $i] : !
% 78.06/11.48 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (subset_type(v2) = v1) | ~
% 78.06/11.48 (subset_type(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0
% 78.06/11.48 | ~ (identity_relation_of(v2) = v1) | ~ (identity_relation_of(v2) = v0))
% 78.06/11.48
% 78.06/11.48 Further assumptions not needed in the proof:
% 78.06/11.48 --------------------------------------------
% 78.06/11.48 p10, p12, p14, p15, p16, p17, p18, p19, p21, p22, p23, p24, p25, p26, p27, p5,
% 78.06/11.48 p9
% 78.06/11.48
% 78.06/11.48 Those formulas are unsatisfiable:
% 78.06/11.48 ---------------------------------
% 78.06/11.48
% 78.06/11.48 Begin of proof
% 78.06/11.48 |
% 78.06/11.49 | ALPHA: (p1) implies:
% 78.06/11.49 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ ilf_type(v1,
% 78.06/11.49 | binary_relation_type) | ~ ilf_type(v0, binary_relation_type) |
% 78.06/11.49 | subset(v0, v1) | ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 78.06/11.49 | (ordered_pair(v2, v3) = v4 & $i(v4) & $i(v3) & $i(v2) & member(v4,
% 78.06/11.49 | v0) & ilf_type(v3, set_type) & ilf_type(v2, set_type) & ~
% 78.06/11.49 | member(v4, v1)))
% 78.06/11.49 |
% 78.06/11.49 | ALPHA: (p3) implies:
% 78.06/11.49 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 78.06/11.49 | ! [v5: $i] : ( ~ (cross_product(v3, v4) = v5) | ~ (ordered_pair(v0,
% 78.06/11.49 | v1) = v2) | ~ $i(v4) | ~ $i(v3) | ~ $i(v1) | ~ $i(v0) | ~
% 78.06/11.49 | member(v1, v4) | ~ member(v0, v3) | ~ ilf_type(v4, set_type) | ~
% 78.06/11.49 | ilf_type(v3, set_type) | ~ ilf_type(v1, set_type) | ~ ilf_type(v0,
% 78.06/11.49 | set_type) | member(v2, v5))
% 78.06/11.49 |
% 78.06/11.49 | ALPHA: (p4) implies:
% 78.06/11.49 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (cross_product(v0, v1) =
% 78.06/11.49 | v2) | ~ $i(v1) | ~ $i(v0) | ~ ilf_type(v1, set_type) | ~
% 78.06/11.49 | ilf_type(v0, set_type) | ? [v3: $i] : (relation_type(v0, v1) = v3 &
% 78.06/11.49 | $i(v3) & ilf_type(v2, v3)))
% 78.06/11.49 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_type(v0, v1) =
% 78.06/11.49 | v2) | ~ $i(v1) | ~ $i(v0) | ~ ilf_type(v1, set_type) | ~
% 78.06/11.49 | ilf_type(v0, set_type) | ? [v3: $i] : (cross_product(v0, v1) = v3 &
% 78.06/11.49 | $i(v3) & ilf_type(v3, v2)))
% 78.06/11.49 |
% 78.06/11.49 | ALPHA: (p6) implies:
% 78.06/11.49 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (cross_product(v0, v1) =
% 78.06/11.49 | v2) | ~ $i(v1) | ~ $i(v0) | ~ ilf_type(v1, set_type) | ~
% 78.06/11.49 | ilf_type(v0, set_type) | ilf_type(v2, set_type))
% 78.06/11.49 |
% 78.06/11.49 | ALPHA: (p7) implies:
% 78.06/11.49 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (
% 78.06/11.49 | ~ (identity_relation_of(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) |
% 78.06/11.49 | ~ $i(v3) | ~ $i(v2) | ~ $i(v0) | ~ member(v4, v1) | ~
% 78.06/11.49 | ilf_type(v3, set_type) | ~ ilf_type(v2, set_type) | ~ ilf_type(v0,
% 78.06/11.49 | set_type) | member(v2, v0))
% 78.06/11.49 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 78.06/11.49 | (v3 = v2 | ~ (identity_relation_of(v0) = v1) | ~ (ordered_pair(v2,
% 78.06/11.49 | v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v0) | ~ member(v4, v1)
% 78.06/11.49 | | ~ ilf_type(v3, set_type) | ~ ilf_type(v2, set_type) | ~
% 78.06/11.49 | ilf_type(v0, set_type))
% 78.06/11.49 |
% 78.06/11.49 | ALPHA: (p8) implies:
% 78.06/11.49 | (8) ! [v0: $i] : ! [v1: $i] : ( ~ (identity_relation_of(v0) = v1) | ~
% 78.06/11.49 | $i(v0) | ~ ilf_type(v0, set_type) | ilf_type(v1,
% 78.06/11.49 | binary_relation_type))
% 78.06/11.49 |
% 78.06/11.49 | ALPHA: (p11) implies:
% 78.06/11.49 | (9) ! [v0: $i] : ( ~ $i(v0) | ~ relation_like(v0) | ~ ilf_type(v0,
% 78.06/11.49 | set_type) | ilf_type(v0, binary_relation_type))
% 78.06/11.49 |
% 78.06/11.49 | ALPHA: (p13) implies:
% 78.06/11.49 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (cross_product(v0, v1) =
% 78.06/11.49 | v2) | ~ $i(v1) | ~ $i(v0) | ~ ilf_type(v1, set_type) | ~
% 78.06/11.49 | ilf_type(v0, set_type) | ? [v3: $i] : ? [v4: $i] :
% 78.06/11.49 | (subset_type(v2) = v3 & relation_type(v0, v1) = v4 & $i(v4) & $i(v3)
% 78.06/11.49 | & ! [v5: $i] : ( ~ $i(v5) | ~ ilf_type(v5, v4) | ilf_type(v5,
% 78.06/11.49 | v3)) & ! [v5: $i] : ( ~ $i(v5) | ~ ilf_type(v5, v3) |
% 78.06/11.49 | ilf_type(v5, v4))))
% 78.06/11.49 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_type(v0, v1) =
% 78.06/11.49 | v2) | ~ $i(v1) | ~ $i(v0) | ~ ilf_type(v1, set_type) | ~
% 78.06/11.49 | ilf_type(v0, set_type) | ? [v3: $i] : ? [v4: $i] :
% 78.06/11.49 | (subset_type(v3) = v4 & cross_product(v0, v1) = v3 & $i(v4) & $i(v3)
% 78.06/11.49 | & ! [v5: $i] : ( ~ $i(v5) | ~ ilf_type(v5, v4) | ilf_type(v5,
% 78.06/11.49 | v2)) & ! [v5: $i] : ( ~ $i(v5) | ~ ilf_type(v5, v2) |
% 78.06/11.49 | ilf_type(v5, v4))))
% 78.06/11.49 |
% 78.06/11.49 | ALPHA: (p20) implies:
% 78.06/11.50 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (cross_product(v0, v1) =
% 78.06/11.50 | v2) | ~ $i(v1) | ~ $i(v0) | ~ ilf_type(v1, set_type) | ~
% 78.06/11.50 | ilf_type(v0, set_type) | ? [v3: $i] : (subset_type(v2) = v3 &
% 78.06/11.50 | $i(v3) & ! [v4: $i] : ( ~ $i(v4) | ~ ilf_type(v4, v3) |
% 78.06/11.50 | relation_like(v4))))
% 78.06/11.50 |
% 78.06/11.50 | ALPHA: (prove_relset_1_28) implies:
% 78.06/11.50 | (13) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (cross_product(v0, v0) = v2
% 78.06/11.50 | & identity_relation_of(v0) = v1 & $i(v2) & $i(v1) & $i(v0) &
% 78.06/11.50 | ilf_type(v0, set_type) & ~ subset(v1, v2))
% 78.06/11.50 |
% 78.06/11.50 | ALPHA: (function-axioms) implies:
% 78.06/11.50 | (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 78.06/11.50 | (subset_type(v2) = v1) | ~ (subset_type(v2) = v0))
% 78.06/11.50 | (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 78.06/11.50 | (cross_product(v3, v2) = v1) | ~ (cross_product(v3, v2) = v0))
% 78.06/11.50 | (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 78.06/11.50 | (relation_type(v3, v2) = v1) | ~ (relation_type(v3, v2) = v0))
% 78.06/11.50 |
% 78.06/11.50 | DELTA: instantiating (13) with fresh symbols all_32_0, all_32_1, all_32_2
% 78.06/11.50 | gives:
% 78.06/11.50 | (17) cross_product(all_32_2, all_32_2) = all_32_0 &
% 78.06/11.50 | identity_relation_of(all_32_2) = all_32_1 & $i(all_32_0) &
% 78.06/11.50 | $i(all_32_1) & $i(all_32_2) & ilf_type(all_32_2, set_type) & ~
% 78.06/11.50 | subset(all_32_1, all_32_0)
% 78.06/11.50 |
% 78.06/11.50 | ALPHA: (17) implies:
% 78.06/11.50 | (18) ~ subset(all_32_1, all_32_0)
% 78.06/11.50 | (19) ilf_type(all_32_2, set_type)
% 78.06/11.50 | (20) $i(all_32_2)
% 78.06/11.50 | (21) $i(all_32_1)
% 78.06/11.50 | (22) $i(all_32_0)
% 78.06/11.50 | (23) identity_relation_of(all_32_2) = all_32_1
% 78.06/11.50 | (24) cross_product(all_32_2, all_32_2) = all_32_0
% 78.06/11.50 |
% 78.06/11.50 | GROUND_INST: instantiating (8) with all_32_2, all_32_1, simplifying with (19),
% 78.06/11.50 | (20), (23) gives:
% 78.06/11.50 | (25) ilf_type(all_32_1, binary_relation_type)
% 78.06/11.50 |
% 78.06/11.50 | GROUND_INST: instantiating (5) with all_32_2, all_32_2, all_32_0, simplifying
% 78.06/11.50 | with (19), (20), (24) gives:
% 78.06/11.50 | (26) ilf_type(all_32_0, set_type)
% 78.06/11.50 |
% 78.06/11.50 | GROUND_INST: instantiating (10) with all_32_2, all_32_2, all_32_0, simplifying
% 78.06/11.50 | with (19), (20), (24) gives:
% 78.06/11.50 | (27) ? [v0: $i] : ? [v1: $i] : (subset_type(all_32_0) = v0 &
% 78.06/11.50 | relation_type(all_32_2, all_32_2) = v1 & $i(v1) & $i(v0) & ! [v2:
% 78.06/11.50 | $i] : ( ~ $i(v2) | ~ ilf_type(v2, v1) | ilf_type(v2, v0)) & !
% 78.06/11.50 | [v2: $i] : ( ~ $i(v2) | ~ ilf_type(v2, v0) | ilf_type(v2, v1)))
% 78.06/11.50 |
% 78.06/11.50 | GROUND_INST: instantiating (12) with all_32_2, all_32_2, all_32_0, simplifying
% 78.06/11.50 | with (19), (20), (24) gives:
% 78.06/11.50 | (28) ? [v0: $i] : (subset_type(all_32_0) = v0 & $i(v0) & ! [v1: $i] : ( ~
% 78.06/11.50 | $i(v1) | ~ ilf_type(v1, v0) | relation_like(v1)))
% 78.06/11.50 |
% 78.06/11.50 | GROUND_INST: instantiating (3) with all_32_2, all_32_2, all_32_0, simplifying
% 78.06/11.50 | with (19), (20), (24) gives:
% 78.06/11.50 | (29) ? [v0: $i] : (relation_type(all_32_2, all_32_2) = v0 & $i(v0) &
% 78.06/11.50 | ilf_type(all_32_0, v0))
% 78.06/11.50 |
% 78.06/11.50 | DELTA: instantiating (29) with fresh symbol all_40_0 gives:
% 78.06/11.50 | (30) relation_type(all_32_2, all_32_2) = all_40_0 & $i(all_40_0) &
% 78.06/11.50 | ilf_type(all_32_0, all_40_0)
% 78.06/11.50 |
% 78.06/11.50 | ALPHA: (30) implies:
% 78.06/11.50 | (31) ilf_type(all_32_0, all_40_0)
% 78.06/11.50 | (32) relation_type(all_32_2, all_32_2) = all_40_0
% 78.06/11.50 |
% 78.06/11.50 | DELTA: instantiating (28) with fresh symbol all_42_0 gives:
% 78.06/11.50 | (33) subset_type(all_32_0) = all_42_0 & $i(all_42_0) & ! [v0: $i] : ( ~
% 78.06/11.50 | $i(v0) | ~ ilf_type(v0, all_42_0) | relation_like(v0))
% 78.06/11.50 |
% 78.06/11.50 | ALPHA: (33) implies:
% 78.06/11.51 | (34) subset_type(all_32_0) = all_42_0
% 78.06/11.51 | (35) ! [v0: $i] : ( ~ $i(v0) | ~ ilf_type(v0, all_42_0) |
% 78.06/11.51 | relation_like(v0))
% 78.06/11.51 |
% 78.06/11.51 | DELTA: instantiating (27) with fresh symbols all_45_0, all_45_1 gives:
% 78.06/11.51 | (36) subset_type(all_32_0) = all_45_1 & relation_type(all_32_2, all_32_2) =
% 78.06/11.51 | all_45_0 & $i(all_45_0) & $i(all_45_1) & ! [v0: $i] : ( ~ $i(v0) | ~
% 78.06/11.51 | ilf_type(v0, all_45_0) | ilf_type(v0, all_45_1)) & ! [v0: $i] : ( ~
% 78.06/11.51 | $i(v0) | ~ ilf_type(v0, all_45_1) | ilf_type(v0, all_45_0))
% 78.06/11.51 |
% 78.06/11.51 | ALPHA: (36) implies:
% 78.06/11.51 | (37) relation_type(all_32_2, all_32_2) = all_45_0
% 78.06/11.51 | (38) subset_type(all_32_0) = all_45_1
% 78.06/11.51 | (39) ! [v0: $i] : ( ~ $i(v0) | ~ ilf_type(v0, all_45_0) | ilf_type(v0,
% 78.06/11.51 | all_45_1))
% 78.06/11.51 |
% 78.06/11.51 | GROUND_INST: instantiating (16) with all_40_0, all_45_0, all_32_2, all_32_2,
% 78.06/11.51 | simplifying with (32), (37) gives:
% 78.06/11.51 | (40) all_45_0 = all_40_0
% 78.06/11.51 |
% 78.06/11.51 | GROUND_INST: instantiating (14) with all_42_0, all_45_1, all_32_0, simplifying
% 78.06/11.51 | with (34), (38) gives:
% 78.06/11.51 | (41) all_45_1 = all_42_0
% 78.06/11.51 |
% 78.06/11.51 | GROUND_INST: instantiating (39) with all_32_0, simplifying with (22) gives:
% 78.06/11.51 | (42) ~ ilf_type(all_32_0, all_45_0) | ilf_type(all_32_0, all_45_1)
% 78.06/11.51 |
% 78.06/11.51 | GROUND_INST: instantiating (35) with all_32_0, simplifying with (22) gives:
% 78.06/11.51 | (43) ~ ilf_type(all_32_0, all_42_0) | relation_like(all_32_0)
% 78.06/11.51 |
% 78.06/11.51 | GROUND_INST: instantiating (11) with all_32_2, all_32_2, all_40_0, simplifying
% 78.06/11.51 | with (19), (20), (32) gives:
% 78.06/11.51 | (44) ? [v0: $i] : ? [v1: $i] : (subset_type(v0) = v1 &
% 78.06/11.51 | cross_product(all_32_2, all_32_2) = v0 & $i(v1) & $i(v0) & ! [v2:
% 78.06/11.51 | $i] : ( ~ $i(v2) | ~ ilf_type(v2, v1) | ilf_type(v2, all_40_0)) &
% 78.06/11.51 | ! [v2: $i] : ( ~ $i(v2) | ~ ilf_type(v2, all_40_0) | ilf_type(v2,
% 78.06/11.51 | v1)))
% 78.06/11.51 |
% 78.06/11.51 | GROUND_INST: instantiating (4) with all_32_2, all_32_2, all_40_0, simplifying
% 78.06/11.51 | with (19), (20), (32) gives:
% 78.06/11.51 | (45) ? [v0: $i] : (cross_product(all_32_2, all_32_2) = v0 & $i(v0) &
% 78.06/11.51 | ilf_type(v0, all_40_0))
% 78.06/11.51 |
% 78.06/11.51 | DELTA: instantiating (45) with fresh symbol all_62_0 gives:
% 78.06/11.51 | (46) cross_product(all_32_2, all_32_2) = all_62_0 & $i(all_62_0) &
% 78.06/11.51 | ilf_type(all_62_0, all_40_0)
% 78.06/11.51 |
% 78.06/11.51 | ALPHA: (46) implies:
% 78.06/11.51 | (47) $i(all_62_0)
% 78.06/11.51 | (48) cross_product(all_32_2, all_32_2) = all_62_0
% 78.06/11.51 |
% 78.06/11.51 | DELTA: instantiating (44) with fresh symbols all_64_0, all_64_1 gives:
% 78.06/11.51 | (49) subset_type(all_64_1) = all_64_0 & cross_product(all_32_2, all_32_2) =
% 78.06/11.51 | all_64_1 & $i(all_64_0) & $i(all_64_1) & ! [v0: $i] : ( ~ $i(v0) | ~
% 78.06/11.51 | ilf_type(v0, all_64_0) | ilf_type(v0, all_40_0)) & ! [v0: $i] : ( ~
% 78.06/11.51 | $i(v0) | ~ ilf_type(v0, all_40_0) | ilf_type(v0, all_64_0))
% 78.06/11.51 |
% 78.06/11.51 | ALPHA: (49) implies:
% 78.06/11.51 | (50) cross_product(all_32_2, all_32_2) = all_64_1
% 78.06/11.51 |
% 78.06/11.51 | BETA: splitting (42) gives:
% 78.06/11.51 |
% 78.06/11.51 | Case 1:
% 78.06/11.51 | |
% 78.41/11.51 | | (51) ~ ilf_type(all_32_0, all_45_0)
% 78.41/11.51 | |
% 78.41/11.51 | | REDUCE: (40), (51) imply:
% 78.41/11.51 | | (52) ~ ilf_type(all_32_0, all_40_0)
% 78.41/11.51 | |
% 78.41/11.51 | | PRED_UNIFY: (31), (52) imply:
% 78.41/11.51 | | (53) $false
% 78.41/11.51 | |
% 78.41/11.51 | | CLOSE: (53) is inconsistent.
% 78.41/11.51 | |
% 78.41/11.51 | Case 2:
% 78.41/11.51 | |
% 78.41/11.51 | | (54) ilf_type(all_32_0, all_45_1)
% 78.41/11.51 | |
% 78.41/11.51 | | REDUCE: (41), (54) imply:
% 78.41/11.51 | | (55) ilf_type(all_32_0, all_42_0)
% 78.41/11.51 | |
% 78.41/11.51 | | BETA: splitting (43) gives:
% 78.41/11.51 | |
% 78.41/11.51 | | Case 1:
% 78.41/11.51 | | |
% 78.41/11.51 | | | (56) ~ ilf_type(all_32_0, all_42_0)
% 78.41/11.51 | | |
% 78.41/11.51 | | | PRED_UNIFY: (55), (56) imply:
% 78.41/11.51 | | | (57) $false
% 78.41/11.51 | | |
% 78.41/11.51 | | | CLOSE: (57) is inconsistent.
% 78.41/11.51 | | |
% 78.41/11.51 | | Case 2:
% 78.41/11.51 | | |
% 78.41/11.51 | | | (58) relation_like(all_32_0)
% 78.41/11.51 | | |
% 78.41/11.51 | | | GROUND_INST: instantiating (15) with all_32_0, all_64_1, all_32_2,
% 78.41/11.51 | | | all_32_2, simplifying with (24), (50) gives:
% 78.41/11.52 | | | (59) all_64_1 = all_32_0
% 78.41/11.52 | | |
% 78.41/11.52 | | | GROUND_INST: instantiating (15) with all_62_0, all_64_1, all_32_2,
% 78.41/11.52 | | | all_32_2, simplifying with (48), (50) gives:
% 78.41/11.52 | | | (60) all_64_1 = all_62_0
% 78.41/11.52 | | |
% 78.41/11.52 | | | COMBINE_EQS: (59), (60) imply:
% 78.41/11.52 | | | (61) all_62_0 = all_32_0
% 78.41/11.52 | | |
% 78.41/11.52 | | | GROUND_INST: instantiating (9) with all_32_0, simplifying with (22), (26),
% 78.41/11.52 | | | (58) gives:
% 78.41/11.52 | | | (62) ilf_type(all_32_0, binary_relation_type)
% 78.41/11.52 | | |
% 78.41/11.52 | | | GROUND_INST: instantiating (1) with all_32_1, all_32_0, simplifying with
% 78.41/11.52 | | | (18), (21), (22), (25), (62) gives:
% 78.41/11.52 | | | (63) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (ordered_pair(v0, v1) =
% 78.41/11.52 | | | v2 & $i(v2) & $i(v1) & $i(v0) & member(v2, all_32_1) &
% 78.41/11.52 | | | ilf_type(v1, set_type) & ilf_type(v0, set_type) & ~ member(v2,
% 78.41/11.52 | | | all_32_0))
% 78.41/11.52 | | |
% 78.41/11.52 | | | DELTA: instantiating (63) with fresh symbols all_118_0, all_118_1,
% 78.41/11.52 | | | all_118_2 gives:
% 78.41/11.52 | | | (64) ordered_pair(all_118_2, all_118_1) = all_118_0 & $i(all_118_0) &
% 78.41/11.52 | | | $i(all_118_1) & $i(all_118_2) & member(all_118_0, all_32_1) &
% 78.41/11.52 | | | ilf_type(all_118_1, set_type) & ilf_type(all_118_2, set_type) & ~
% 78.41/11.52 | | | member(all_118_0, all_32_0)
% 78.41/11.52 | | |
% 78.41/11.52 | | | ALPHA: (64) implies:
% 78.41/11.52 | | | (65) ~ member(all_118_0, all_32_0)
% 78.41/11.52 | | | (66) ilf_type(all_118_2, set_type)
% 78.41/11.52 | | | (67) ilf_type(all_118_1, set_type)
% 78.41/11.52 | | | (68) member(all_118_0, all_32_1)
% 78.41/11.52 | | | (69) $i(all_118_2)
% 78.41/11.52 | | | (70) $i(all_118_1)
% 78.41/11.52 | | | (71) ordered_pair(all_118_2, all_118_1) = all_118_0
% 78.41/11.52 | | |
% 78.41/11.52 | | | GROUND_INST: instantiating (7) with all_32_2, all_32_1, all_118_2,
% 78.41/11.52 | | | all_118_1, all_118_0, simplifying with (19), (20), (23),
% 78.41/11.52 | | | (66), (67), (68), (69), (70), (71) gives:
% 78.41/11.52 | | | (72) all_118_1 = all_118_2
% 78.41/11.52 | | |
% 78.41/11.52 | | | GROUND_INST: instantiating (6) with all_32_2, all_32_1, all_118_2,
% 78.41/11.52 | | | all_118_1, all_118_0, simplifying with (19), (20), (23),
% 78.41/11.52 | | | (66), (67), (68), (69), (70), (71) gives:
% 78.41/11.52 | | | (73) member(all_118_2, all_32_2)
% 78.41/11.52 | | |
% 78.41/11.52 | | | REDUCE: (71), (72) imply:
% 78.41/11.52 | | | (74) ordered_pair(all_118_2, all_118_2) = all_118_0
% 78.41/11.52 | | |
% 78.41/11.52 | | | GROUND_INST: instantiating (2) with all_118_2, all_118_2, all_118_0,
% 78.41/11.52 | | | all_32_2, all_32_2, all_32_0, simplifying with (19), (20),
% 78.41/11.52 | | | (24), (65), (66), (69), (73), (74) gives:
% 78.41/11.52 | | | (75) $false
% 78.41/11.52 | | |
% 78.41/11.52 | | | CLOSE: (75) is inconsistent.
% 78.41/11.52 | | |
% 78.41/11.52 | | End of split
% 78.41/11.52 | |
% 78.41/11.52 | End of split
% 78.41/11.52 |
% 78.41/11.52 End of proof
% 78.41/11.52 % SZS output end Proof for theBenchmark
% 78.41/11.52
% 78.41/11.52 10891ms
%------------------------------------------------------------------------------