TSTP Solution File: SET676+3 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET676+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 : n009.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 15:25:57 EDT 2023
% Result : Theorem 11.48s 2.30s
% Output : Proof 15.47s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : SET676+3 : TPTP v8.1.2. Released v2.2.0.
% 0.11/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.35 % Computer : n009.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 : Sat Aug 26 12:09:20 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.70/0.65 ________ _____
% 0.70/0.65 ___ __ \_________(_)________________________________
% 0.70/0.65 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.70/0.65 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.70/0.65 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.70/0.65
% 0.70/0.65 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.70/0.65 (2023-06-19)
% 0.70/0.65
% 0.70/0.65 (c) Philipp Rümmer, 2009-2023
% 0.70/0.65 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.70/0.65 Amanda Stjerna.
% 0.70/0.65 Free software under BSD-3-Clause.
% 0.70/0.65
% 0.70/0.65 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.70/0.65
% 0.70/0.65 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.70/0.66 Running up to 7 provers in parallel.
% 0.70/0.67 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.70/0.67 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.70/0.67 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.70/0.67 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.70/0.67 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.70/0.67 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.70/0.67 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.85/1.11 Prover 1: Preprocessing ...
% 2.85/1.11 Prover 4: Preprocessing ...
% 2.85/1.15 Prover 0: Preprocessing ...
% 2.85/1.15 Prover 6: Preprocessing ...
% 2.85/1.15 Prover 2: Preprocessing ...
% 2.85/1.15 Prover 3: Preprocessing ...
% 2.85/1.15 Prover 5: Preprocessing ...
% 7.51/1.70 Prover 1: Constructing countermodel ...
% 7.51/1.70 Prover 3: Constructing countermodel ...
% 7.51/1.72 Prover 6: Proving ...
% 7.51/1.72 Prover 5: Proving ...
% 7.51/1.73 Prover 2: Proving ...
% 10.66/2.17 Prover 4: Constructing countermodel ...
% 10.66/2.22 Prover 0: Proving ...
% 11.48/2.29 Prover 3: proved (1621ms)
% 11.48/2.30
% 11.48/2.30 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 11.48/2.30
% 11.48/2.30 Prover 5: stopped
% 12.11/2.31 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 12.11/2.31 Prover 6: stopped
% 12.11/2.31 Prover 2: stopped
% 12.11/2.32 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 12.11/2.32 Prover 0: stopped
% 12.11/2.32 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 12.11/2.32 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 12.11/2.32 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 12.11/2.35 Prover 8: Preprocessing ...
% 12.11/2.35 Prover 7: Preprocessing ...
% 12.11/2.36 Prover 10: Preprocessing ...
% 12.11/2.36 Prover 11: Preprocessing ...
% 12.11/2.38 Prover 13: Preprocessing ...
% 12.76/2.45 Prover 10: Warning: ignoring some quantifiers
% 12.76/2.46 Prover 7: Warning: ignoring some quantifiers
% 12.76/2.47 Prover 10: Constructing countermodel ...
% 12.76/2.48 Prover 7: Constructing countermodel ...
% 13.56/2.50 Prover 8: Warning: ignoring some quantifiers
% 13.72/2.52 Prover 8: Constructing countermodel ...
% 13.72/2.55 Prover 13: Warning: ignoring some quantifiers
% 13.72/2.56 Prover 13: Constructing countermodel ...
% 14.42/2.61 Prover 10: Found proof (size 25)
% 14.42/2.61 Prover 10: proved (293ms)
% 14.42/2.61 Prover 13: stopped
% 14.42/2.61 Prover 1: stopped
% 14.42/2.61 Prover 8: stopped
% 14.42/2.61 Prover 4: stopped
% 14.42/2.61 Prover 7: stopped
% 14.83/2.75 Prover 11: Constructing countermodel ...
% 14.83/2.76 Prover 11: stopped
% 14.83/2.76
% 14.83/2.76 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 14.83/2.76
% 14.83/2.77 % SZS output start Proof for theBenchmark
% 14.83/2.77 Assumptions after simplification:
% 14.83/2.77 ---------------------------------
% 14.83/2.77
% 14.83/2.77 (p1)
% 15.31/2.79 $i(set_type) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 15.31/2.79 (relation_type(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ ilf_type(v1,
% 15.31/2.79 set_type) | ~ ilf_type(v0, set_type) | ? [v3: $i] : (cross_product(v0,
% 15.31/2.79 v1) = v3 & $i(v3) & ilf_type(v3, v2)))
% 15.31/2.79
% 15.31/2.79 (p3)
% 15.31/2.79 $i(set_type) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 15.31/2.79 (cross_product(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ ilf_type(v1,
% 15.31/2.80 set_type) | ~ ilf_type(v0, set_type) | ilf_type(v2, set_type))
% 15.31/2.80
% 15.31/2.80 (p4)
% 15.31/2.80 $i(set_type) & ! [v0: $i] : ! [v1: $i] : ( ~ (identity_relation_of_type(v0)
% 15.31/2.80 = v1) | ~ $i(v0) | ~ ilf_type(v0, set_type) | ? [v2: $i] :
% 15.31/2.80 (relation_type(v0, v0) = v2 & $i(v2) & ! [v3: $i] : ( ~ $i(v3) | ~
% 15.31/2.80 ilf_type(v3, v2) | ~ ilf_type(v3, set_type) | ilf_type(v3, v1)) & !
% 15.31/2.80 [v3: $i] : ( ~ $i(v3) | ~ ilf_type(v3, v1) | ~ ilf_type(v3, set_type) |
% 15.31/2.80 ilf_type(v3, v2))))
% 15.31/2.80
% 15.31/2.80 (p7)
% 15.31/2.80 $i(set_type) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 15.31/2.80 (relation_type(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ ilf_type(v1,
% 15.31/2.80 set_type) | ~ ilf_type(v0, set_type) | ? [v3: $i] : ? [v4: $i] :
% 15.31/2.80 (subset_type(v3) = v4 & cross_product(v0, v1) = v3 & $i(v4) & $i(v3) & !
% 15.31/2.80 [v5: $i] : ( ~ $i(v5) | ~ ilf_type(v5, v4) | ilf_type(v5, v2)) & ! [v5:
% 15.31/2.80 $i] : ( ~ $i(v5) | ~ ilf_type(v5, v2) | ilf_type(v5, v4))))
% 15.31/2.80
% 15.31/2.80 (prove_relset_1_41)
% 15.31/2.80 $i(set_type) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 15.31/2.80 (identity_relation_of_type(v0) = v2 & cross_product(v0, v0) = v1 & $i(v2) &
% 15.31/2.80 $i(v1) & $i(v0) & ilf_type(v0, set_type) & ~ ilf_type(v1, v2))
% 15.31/2.80
% 15.31/2.80 (function-axioms)
% 15.31/2.80 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 15.31/2.80 (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0)) & ! [v0: $i]
% 15.31/2.80 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (relation_type(v3,
% 15.31/2.80 v2) = v1) | ~ (relation_type(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i]
% 15.31/2.80 : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (cross_product(v3, v2) = v1) | ~
% 15.31/2.80 (cross_product(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 15.31/2.80 (v1 = v0 | ~ (power_set(v2) = v1) | ~ (power_set(v2) = v0)) & ! [v0: $i] :
% 15.31/2.80 ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (member_type(v2) = v1) | ~
% 15.31/2.80 (member_type(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0
% 15.31/2.80 | ~ (subset_type(v2) = v1) | ~ (subset_type(v2) = v0)) & ! [v0: $i] : !
% 15.31/2.80 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (identity_relation_of_type(v2) = v1) |
% 15.31/2.80 ~ (identity_relation_of_type(v2) = v0))
% 15.31/2.80
% 15.31/2.80 Further assumptions not needed in the proof:
% 15.31/2.80 --------------------------------------------
% 15.31/2.80 p10, p11, p12, p13, p14, p15, p16, p17, p18, p19, p2, p5, p6, p8, p9
% 15.31/2.80
% 15.31/2.80 Those formulas are unsatisfiable:
% 15.31/2.80 ---------------------------------
% 15.31/2.80
% 15.31/2.80 Begin of proof
% 15.31/2.81 |
% 15.31/2.81 | ALPHA: (p1) implies:
% 15.31/2.81 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_type(v0, v1) =
% 15.31/2.81 | v2) | ~ $i(v1) | ~ $i(v0) | ~ ilf_type(v1, set_type) | ~
% 15.31/2.81 | ilf_type(v0, set_type) | ? [v3: $i] : (cross_product(v0, v1) = v3 &
% 15.31/2.81 | $i(v3) & ilf_type(v3, v2)))
% 15.31/2.81 |
% 15.31/2.81 | ALPHA: (p3) implies:
% 15.31/2.81 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (cross_product(v0, v1) =
% 15.31/2.81 | v2) | ~ $i(v1) | ~ $i(v0) | ~ ilf_type(v1, set_type) | ~
% 15.31/2.81 | ilf_type(v0, set_type) | ilf_type(v2, set_type))
% 15.31/2.81 |
% 15.31/2.81 | ALPHA: (p4) implies:
% 15.31/2.81 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ (identity_relation_of_type(v0) = v1) |
% 15.31/2.81 | ~ $i(v0) | ~ ilf_type(v0, set_type) | ? [v2: $i] :
% 15.31/2.81 | (relation_type(v0, v0) = v2 & $i(v2) & ! [v3: $i] : ( ~ $i(v3) | ~
% 15.31/2.81 | ilf_type(v3, v2) | ~ ilf_type(v3, set_type) | ilf_type(v3, v1))
% 15.31/2.81 | & ! [v3: $i] : ( ~ $i(v3) | ~ ilf_type(v3, v1) | ~ ilf_type(v3,
% 15.31/2.81 | set_type) | ilf_type(v3, v2))))
% 15.31/2.81 |
% 15.31/2.81 | ALPHA: (p7) implies:
% 15.31/2.81 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_type(v0, v1) =
% 15.31/2.81 | v2) | ~ $i(v1) | ~ $i(v0) | ~ ilf_type(v1, set_type) | ~
% 15.31/2.81 | ilf_type(v0, set_type) | ? [v3: $i] : ? [v4: $i] : (subset_type(v3)
% 15.31/2.81 | = v4 & cross_product(v0, v1) = v3 & $i(v4) & $i(v3) & ! [v5: $i] :
% 15.31/2.81 | ( ~ $i(v5) | ~ ilf_type(v5, v4) | ilf_type(v5, v2)) & ! [v5: $i]
% 15.31/2.81 | : ( ~ $i(v5) | ~ ilf_type(v5, v2) | ilf_type(v5, v4))))
% 15.31/2.81 |
% 15.31/2.81 | ALPHA: (prove_relset_1_41) implies:
% 15.31/2.81 | (5) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 15.31/2.81 | (identity_relation_of_type(v0) = v2 & cross_product(v0, v0) = v1 &
% 15.31/2.81 | $i(v2) & $i(v1) & $i(v0) & ilf_type(v0, set_type) & ~ ilf_type(v1,
% 15.31/2.81 | v2))
% 15.31/2.81 |
% 15.31/2.81 | ALPHA: (function-axioms) implies:
% 15.31/2.81 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 15.31/2.81 | (cross_product(v3, v2) = v1) | ~ (cross_product(v3, v2) = v0))
% 15.31/2.81 |
% 15.31/2.81 | DELTA: instantiating (5) with fresh symbols all_23_0, all_23_1, all_23_2
% 15.31/2.81 | gives:
% 15.31/2.81 | (7) identity_relation_of_type(all_23_2) = all_23_0 &
% 15.31/2.81 | cross_product(all_23_2, all_23_2) = all_23_1 & $i(all_23_0) &
% 15.31/2.81 | $i(all_23_1) & $i(all_23_2) & ilf_type(all_23_2, set_type) & ~
% 15.31/2.81 | ilf_type(all_23_1, all_23_0)
% 15.31/2.82 |
% 15.31/2.82 | ALPHA: (7) implies:
% 15.43/2.82 | (8) ~ ilf_type(all_23_1, all_23_0)
% 15.43/2.82 | (9) ilf_type(all_23_2, set_type)
% 15.43/2.82 | (10) $i(all_23_2)
% 15.43/2.82 | (11) cross_product(all_23_2, all_23_2) = all_23_1
% 15.43/2.82 | (12) identity_relation_of_type(all_23_2) = all_23_0
% 15.43/2.82 |
% 15.43/2.82 | GROUND_INST: instantiating (2) with all_23_2, all_23_2, all_23_1, simplifying
% 15.43/2.82 | with (9), (10), (11) gives:
% 15.43/2.82 | (13) ilf_type(all_23_1, set_type)
% 15.43/2.82 |
% 15.43/2.82 | GROUND_INST: instantiating (3) with all_23_2, all_23_0, simplifying with (9),
% 15.43/2.82 | (10), (12) gives:
% 15.43/2.82 | (14) ? [v0: $i] : (relation_type(all_23_2, all_23_2) = v0 & $i(v0) & !
% 15.43/2.82 | [v1: $i] : ( ~ $i(v1) | ~ ilf_type(v1, v0) | ~ ilf_type(v1,
% 15.43/2.82 | set_type) | ilf_type(v1, all_23_0)) & ! [v1: $i] : ( ~ $i(v1) |
% 15.43/2.82 | ~ ilf_type(v1, all_23_0) | ~ ilf_type(v1, set_type) |
% 15.43/2.82 | ilf_type(v1, v0)))
% 15.43/2.82 |
% 15.43/2.82 | DELTA: instantiating (14) with fresh symbol all_36_0 gives:
% 15.43/2.82 | (15) relation_type(all_23_2, all_23_2) = all_36_0 & $i(all_36_0) & ! [v0:
% 15.43/2.82 | $i] : ( ~ $i(v0) | ~ ilf_type(v0, all_36_0) | ~ ilf_type(v0,
% 15.43/2.82 | set_type) | ilf_type(v0, all_23_0)) & ! [v0: $i] : ( ~ $i(v0) |
% 15.43/2.82 | ~ ilf_type(v0, all_23_0) | ~ ilf_type(v0, set_type) | ilf_type(v0,
% 15.43/2.82 | all_36_0))
% 15.43/2.82 |
% 15.43/2.82 | ALPHA: (15) implies:
% 15.43/2.82 | (16) relation_type(all_23_2, all_23_2) = all_36_0
% 15.43/2.82 | (17) ! [v0: $i] : ( ~ $i(v0) | ~ ilf_type(v0, all_36_0) | ~ ilf_type(v0,
% 15.43/2.82 | set_type) | ilf_type(v0, all_23_0))
% 15.43/2.82 |
% 15.43/2.82 | GROUND_INST: instantiating (4) with all_23_2, all_23_2, all_36_0, simplifying
% 15.43/2.82 | with (9), (10), (16) gives:
% 15.43/2.82 | (18) ? [v0: $i] : ? [v1: $i] : (subset_type(v0) = v1 &
% 15.43/2.82 | cross_product(all_23_2, all_23_2) = v0 & $i(v1) & $i(v0) & ! [v2:
% 15.43/2.82 | $i] : ( ~ $i(v2) | ~ ilf_type(v2, v1) | ilf_type(v2, all_36_0)) &
% 15.43/2.82 | ! [v2: $i] : ( ~ $i(v2) | ~ ilf_type(v2, all_36_0) | ilf_type(v2,
% 15.43/2.82 | v1)))
% 15.43/2.82 |
% 15.43/2.82 | GROUND_INST: instantiating (1) with all_23_2, all_23_2, all_36_0, simplifying
% 15.43/2.82 | with (9), (10), (16) gives:
% 15.47/2.82 | (19) ? [v0: $i] : (cross_product(all_23_2, all_23_2) = v0 & $i(v0) &
% 15.47/2.82 | ilf_type(v0, all_36_0))
% 15.47/2.82 |
% 15.47/2.82 | DELTA: instantiating (19) with fresh symbol all_48_0 gives:
% 15.47/2.82 | (20) cross_product(all_23_2, all_23_2) = all_48_0 & $i(all_48_0) &
% 15.47/2.82 | ilf_type(all_48_0, all_36_0)
% 15.47/2.82 |
% 15.47/2.82 | ALPHA: (20) implies:
% 15.47/2.82 | (21) ilf_type(all_48_0, all_36_0)
% 15.47/2.82 | (22) $i(all_48_0)
% 15.47/2.82 | (23) cross_product(all_23_2, all_23_2) = all_48_0
% 15.47/2.82 |
% 15.47/2.82 | DELTA: instantiating (18) with fresh symbols all_50_0, all_50_1 gives:
% 15.47/2.83 | (24) subset_type(all_50_1) = all_50_0 & cross_product(all_23_2, all_23_2) =
% 15.47/2.83 | all_50_1 & $i(all_50_0) & $i(all_50_1) & ! [v0: $i] : ( ~ $i(v0) | ~
% 15.47/2.83 | ilf_type(v0, all_50_0) | ilf_type(v0, all_36_0)) & ! [v0: $i] : ( ~
% 15.47/2.83 | $i(v0) | ~ ilf_type(v0, all_36_0) | ilf_type(v0, all_50_0))
% 15.47/2.83 |
% 15.47/2.83 | ALPHA: (24) implies:
% 15.47/2.83 | (25) cross_product(all_23_2, all_23_2) = all_50_1
% 15.47/2.83 |
% 15.47/2.83 | GROUND_INST: instantiating (6) with all_23_1, all_50_1, all_23_2, all_23_2,
% 15.47/2.83 | simplifying with (11), (25) gives:
% 15.47/2.83 | (26) all_50_1 = all_23_1
% 15.47/2.83 |
% 15.47/2.83 | GROUND_INST: instantiating (6) with all_48_0, all_50_1, all_23_2, all_23_2,
% 15.47/2.83 | simplifying with (23), (25) gives:
% 15.47/2.83 | (27) all_50_1 = all_48_0
% 15.47/2.83 |
% 15.47/2.83 | COMBINE_EQS: (26), (27) imply:
% 15.47/2.83 | (28) all_48_0 = all_23_1
% 15.47/2.83 |
% 15.47/2.83 | REDUCE: (22), (28) imply:
% 15.47/2.83 | (29) $i(all_23_1)
% 15.47/2.83 |
% 15.47/2.83 | REDUCE: (21), (28) imply:
% 15.47/2.83 | (30) ilf_type(all_23_1, all_36_0)
% 15.47/2.83 |
% 15.47/2.83 | GROUND_INST: instantiating (17) with all_23_1, simplifying with (8), (13),
% 15.47/2.83 | (29), (30) gives:
% 15.47/2.83 | (31) $false
% 15.47/2.83 |
% 15.47/2.83 | CLOSE: (31) is inconsistent.
% 15.47/2.83 |
% 15.47/2.83 End of proof
% 15.47/2.83 % SZS output end Proof for theBenchmark
% 15.47/2.83
% 15.47/2.83 2178ms
%------------------------------------------------------------------------------