TSTP Solution File: SET902+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET902+1 : TPTP v8.1.2. Released v3.2.0.
% 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 15:26:57 EDT 2023
% Result : Theorem 7.00s 1.86s
% Output : Proof 8.85s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET902+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.35 % Computer : n029.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sat Aug 26 10:31:55 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.19/0.64 ________ _____
% 0.19/0.64 ___ __ \_________(_)________________________________
% 0.19/0.64 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.64 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.64 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.64
% 0.19/0.64 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.64 (2023-06-19)
% 0.19/0.64
% 0.19/0.64 (c) Philipp Rümmer, 2009-2023
% 0.19/0.64 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.64 Amanda Stjerna.
% 0.19/0.64 Free software under BSD-3-Clause.
% 0.19/0.64
% 0.19/0.64 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.64
% 0.19/0.64 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.19/0.66 Running up to 7 provers in parallel.
% 0.19/0.68 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.68 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.68 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.68 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.68 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.68 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.68 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.13/1.11 Prover 1: Preprocessing ...
% 2.13/1.11 Prover 4: Preprocessing ...
% 2.55/1.16 Prover 6: Preprocessing ...
% 2.55/1.16 Prover 5: Preprocessing ...
% 2.55/1.16 Prover 2: Preprocessing ...
% 2.55/1.16 Prover 3: Preprocessing ...
% 2.55/1.16 Prover 0: Preprocessing ...
% 3.98/1.39 Prover 1: Warning: ignoring some quantifiers
% 3.98/1.45 Prover 3: Warning: ignoring some quantifiers
% 3.98/1.47 Prover 1: Constructing countermodel ...
% 3.98/1.47 Prover 4: Constructing countermodel ...
% 3.98/1.48 Prover 5: Proving ...
% 3.98/1.48 Prover 3: Constructing countermodel ...
% 3.98/1.48 Prover 0: Proving ...
% 3.98/1.48 Prover 6: Proving ...
% 3.98/1.50 Prover 2: Proving ...
% 5.70/1.69 Prover 3: gave up
% 5.70/1.69 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 6.26/1.75 Prover 7: Preprocessing ...
% 6.26/1.82 Prover 7: Warning: ignoring some quantifiers
% 6.26/1.83 Prover 7: Constructing countermodel ...
% 7.00/1.86 Prover 2: proved (1187ms)
% 7.00/1.86
% 7.00/1.86 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.00/1.86
% 7.00/1.88 Prover 1: gave up
% 7.00/1.88 Prover 0: stopped
% 7.00/1.89 Prover 6: stopped
% 7.00/1.89 Prover 5: stopped
% 7.00/1.90 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 7.00/1.90 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 7.00/1.90 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 7.47/1.90 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 7.47/1.90 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 7.47/1.90 Prover 10: Preprocessing ...
% 7.47/1.92 Prover 8: Preprocessing ...
% 7.47/1.93 Prover 11: Preprocessing ...
% 7.47/1.94 Prover 16: Preprocessing ...
% 7.47/1.96 Prover 13: Preprocessing ...
% 7.89/1.97 Prover 10: Warning: ignoring some quantifiers
% 7.89/1.98 Prover 10: Constructing countermodel ...
% 7.89/1.98 Prover 4: Found proof (size 39)
% 7.89/1.98 Prover 4: proved (1305ms)
% 7.89/1.99 Prover 10: stopped
% 7.89/1.99 Prover 7: stopped
% 7.89/1.99 Prover 16: stopped
% 7.89/1.99 Prover 13: stopped
% 7.89/2.00 Prover 8: Warning: ignoring some quantifiers
% 7.89/2.01 Prover 8: Constructing countermodel ...
% 7.89/2.01 Prover 11: Constructing countermodel ...
% 7.89/2.01 Prover 8: stopped
% 7.89/2.02 Prover 11: stopped
% 7.89/2.02
% 7.89/2.02 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.89/2.02
% 7.89/2.03 % SZS output start Proof for theBenchmark
% 7.89/2.03 Assumptions after simplification:
% 7.89/2.03 ---------------------------------
% 7.89/2.03
% 7.89/2.03 (commutativity_k2_xboole_0)
% 8.48/2.08 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_union2(v1, v0) = v2) | ~
% 8.48/2.08 $i(v1) | ~ $i(v0) | (set_union2(v0, v1) = v2 & $i(v2))) & ! [v0: $i] : !
% 8.48/2.08 [v1: $i] : ! [v2: $i] : ( ~ (set_union2(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0)
% 8.48/2.08 | (set_union2(v1, v0) = v2 & $i(v2)))
% 8.48/2.08
% 8.48/2.08 (idempotence_k2_xboole_0)
% 8.48/2.08 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (set_union2(v0, v0) = v1) | ~
% 8.48/2.08 $i(v0))
% 8.48/2.08
% 8.48/2.08 (l4_zfmisc_1)
% 8.48/2.09 $i(empty_set) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | v0 =
% 8.48/2.09 empty_set | ~ (subset(v0, v2) = 0) | ~ (singleton(v1) = v2) | ~ $i(v1) |
% 8.48/2.09 ~ $i(v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~
% 8.48/2.09 (subset(v0, v0) = v2) | ~ (singleton(v1) = v0) | ~ $i(v1) | ~ $i(v0)) &
% 8.48/2.09 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(empty_set, v1)
% 8.48/2.09 = v2) | ~ (singleton(v0) = v1) | ~ $i(v0))
% 8.48/2.09
% 8.48/2.09 (t43_zfmisc_1)
% 8.48/2.09 $i(empty_set) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 8.48/2.09 (singleton(v0) = v3 & set_union2(v1, v2) = v3 & $i(v3) & $i(v2) & $i(v1) &
% 8.48/2.09 $i(v0) & ( ~ (v3 = v2) | ~ (v1 = empty_set)) & ( ~ (v3 = v1) | ~ (v2 =
% 8.48/2.09 v1)) & ( ~ (v3 = v1) | ~ (v2 = empty_set)))
% 8.48/2.09
% 8.48/2.09 (t7_xboole_1)
% 8.66/2.10 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_union2(v0, v1) = v2) | ~
% 8.66/2.10 $i(v1) | ~ $i(v0) | subset(v0, v2) = 0)
% 8.66/2.10
% 8.66/2.10 Further assumptions not needed in the proof:
% 8.66/2.10 --------------------------------------------
% 8.66/2.10 fc1_xboole_0, fc2_xboole_0, fc3_xboole_0, l1_zfmisc_1, rc1_xboole_0,
% 8.66/2.10 rc2_xboole_0, reflexivity_r1_tarski
% 8.66/2.10
% 8.66/2.10 Those formulas are unsatisfiable:
% 8.66/2.10 ---------------------------------
% 8.66/2.10
% 8.66/2.10 Begin of proof
% 8.66/2.10 |
% 8.66/2.10 | ALPHA: (commutativity_k2_xboole_0) implies:
% 8.66/2.10 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_union2(v1, v0) = v2)
% 8.66/2.10 | | ~ $i(v1) | ~ $i(v0) | (set_union2(v0, v1) = v2 & $i(v2)))
% 8.66/2.10 |
% 8.66/2.10 | ALPHA: (l4_zfmisc_1) implies:
% 8.66/2.10 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | v0 = empty_set |
% 8.66/2.10 | ~ (subset(v0, v2) = 0) | ~ (singleton(v1) = v2) | ~ $i(v1) | ~
% 8.66/2.10 | $i(v0))
% 8.66/2.10 |
% 8.66/2.10 | ALPHA: (t43_zfmisc_1) implies:
% 8.66/2.11 | (3) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (singleton(v0)
% 8.66/2.11 | = v3 & set_union2(v1, v2) = v3 & $i(v3) & $i(v2) & $i(v1) & $i(v0) &
% 8.66/2.11 | ( ~ (v3 = v2) | ~ (v1 = empty_set)) & ( ~ (v3 = v1) | ~ (v2 = v1))
% 8.66/2.11 | & ( ~ (v3 = v1) | ~ (v2 = empty_set)))
% 8.66/2.11 |
% 8.66/2.11 | DELTA: instantiating (3) with fresh symbols all_16_0, all_16_1, all_16_2,
% 8.66/2.11 | all_16_3 gives:
% 8.66/2.11 | (4) singleton(all_16_3) = all_16_0 & set_union2(all_16_2, all_16_1) =
% 8.66/2.11 | all_16_0 & $i(all_16_0) & $i(all_16_1) & $i(all_16_2) & $i(all_16_3) &
% 8.66/2.11 | ( ~ (all_16_0 = all_16_1) | ~ (all_16_2 = empty_set)) & ( ~ (all_16_0
% 8.66/2.11 | = all_16_2) | ~ (all_16_1 = all_16_2)) & ( ~ (all_16_0 = all_16_2)
% 8.66/2.11 | | ~ (all_16_1 = empty_set))
% 8.66/2.11 |
% 8.66/2.11 | ALPHA: (4) implies:
% 8.66/2.12 | (5) $i(all_16_3)
% 8.66/2.12 | (6) $i(all_16_2)
% 8.66/2.12 | (7) $i(all_16_1)
% 8.66/2.12 | (8) set_union2(all_16_2, all_16_1) = all_16_0
% 8.66/2.12 | (9) singleton(all_16_3) = all_16_0
% 8.66/2.12 | (10) ~ (all_16_0 = all_16_2) | ~ (all_16_1 = empty_set)
% 8.66/2.12 | (11) ~ (all_16_0 = all_16_2) | ~ (all_16_1 = all_16_2)
% 8.66/2.12 | (12) ~ (all_16_0 = all_16_1) | ~ (all_16_2 = empty_set)
% 8.66/2.12 |
% 8.66/2.12 | GROUND_INST: instantiating (1) with all_16_1, all_16_2, all_16_0, simplifying
% 8.66/2.12 | with (6), (7), (8) gives:
% 8.66/2.12 | (13) set_union2(all_16_1, all_16_2) = all_16_0 & $i(all_16_0)
% 8.66/2.12 |
% 8.66/2.12 | ALPHA: (13) implies:
% 8.66/2.12 | (14) set_union2(all_16_1, all_16_2) = all_16_0
% 8.66/2.12 |
% 8.66/2.12 | GROUND_INST: instantiating (t7_xboole_1) with all_16_2, all_16_1, all_16_0,
% 8.66/2.12 | simplifying with (6), (7), (8) gives:
% 8.66/2.12 | (15) subset(all_16_2, all_16_0) = 0
% 8.66/2.12 |
% 8.66/2.13 | GROUND_INST: instantiating (t7_xboole_1) with all_16_1, all_16_2, all_16_0,
% 8.66/2.13 | simplifying with (6), (7), (14) gives:
% 8.66/2.13 | (16) subset(all_16_1, all_16_0) = 0
% 8.66/2.13 |
% 8.66/2.13 | GROUND_INST: instantiating (2) with all_16_2, all_16_3, all_16_0, simplifying
% 8.66/2.13 | with (5), (6), (9), (15) gives:
% 8.66/2.13 | (17) all_16_0 = all_16_2 | all_16_2 = empty_set
% 8.66/2.13 |
% 8.66/2.13 | GROUND_INST: instantiating (2) with all_16_1, all_16_3, all_16_0, simplifying
% 8.66/2.13 | with (5), (7), (9), (16) gives:
% 8.66/2.13 | (18) all_16_0 = all_16_1 | all_16_1 = empty_set
% 8.66/2.13 |
% 8.66/2.13 | BETA: splitting (10) gives:
% 8.66/2.13 |
% 8.66/2.13 | Case 1:
% 8.66/2.13 | |
% 8.66/2.13 | | (19) ~ (all_16_1 = empty_set)
% 8.66/2.13 | |
% 8.66/2.13 | | BETA: splitting (18) gives:
% 8.66/2.13 | |
% 8.66/2.13 | | Case 1:
% 8.66/2.13 | | |
% 8.66/2.13 | | | (20) all_16_1 = empty_set
% 8.66/2.13 | | |
% 8.66/2.13 | | | REDUCE: (19), (20) imply:
% 8.66/2.13 | | | (21) $false
% 8.84/2.13 | | |
% 8.84/2.13 | | | CLOSE: (21) is inconsistent.
% 8.84/2.13 | | |
% 8.84/2.13 | | Case 2:
% 8.84/2.13 | | |
% 8.84/2.13 | | | (22) all_16_0 = all_16_1
% 8.84/2.13 | | |
% 8.84/2.13 | | | BETA: splitting (11) gives:
% 8.84/2.13 | | |
% 8.84/2.13 | | | Case 1:
% 8.84/2.13 | | | |
% 8.84/2.13 | | | | (23) ~ (all_16_0 = all_16_2)
% 8.84/2.13 | | | |
% 8.85/2.13 | | | | REDUCE: (22), (23) imply:
% 8.85/2.13 | | | | (24) ~ (all_16_1 = all_16_2)
% 8.85/2.13 | | | |
% 8.85/2.13 | | | | BETA: splitting (17) gives:
% 8.85/2.13 | | | |
% 8.85/2.13 | | | | Case 1:
% 8.85/2.13 | | | | |
% 8.85/2.14 | | | | | (25) all_16_2 = empty_set
% 8.85/2.14 | | | | |
% 8.85/2.14 | | | | | BETA: splitting (12) gives:
% 8.85/2.14 | | | | |
% 8.85/2.14 | | | | | Case 1:
% 8.85/2.14 | | | | | |
% 8.85/2.14 | | | | | | (26) ~ (all_16_2 = empty_set)
% 8.85/2.14 | | | | | |
% 8.85/2.14 | | | | | | REDUCE: (25), (26) imply:
% 8.85/2.14 | | | | | | (27) $false
% 8.85/2.14 | | | | | |
% 8.85/2.14 | | | | | | CLOSE: (27) is inconsistent.
% 8.85/2.14 | | | | | |
% 8.85/2.14 | | | | | Case 2:
% 8.85/2.14 | | | | | |
% 8.85/2.14 | | | | | | (28) ~ (all_16_0 = all_16_1)
% 8.85/2.14 | | | | | |
% 8.85/2.14 | | | | | | REDUCE: (22), (28) imply:
% 8.85/2.14 | | | | | | (29) $false
% 8.85/2.14 | | | | | |
% 8.85/2.14 | | | | | | CLOSE: (29) is inconsistent.
% 8.85/2.14 | | | | | |
% 8.85/2.14 | | | | | End of split
% 8.85/2.14 | | | | |
% 8.85/2.14 | | | | Case 2:
% 8.85/2.14 | | | | |
% 8.85/2.14 | | | | | (30) all_16_0 = all_16_2
% 8.85/2.14 | | | | |
% 8.85/2.14 | | | | | COMBINE_EQS: (22), (30) imply:
% 8.85/2.14 | | | | | (31) all_16_1 = all_16_2
% 8.85/2.14 | | | | |
% 8.85/2.14 | | | | | REDUCE: (24), (31) imply:
% 8.85/2.14 | | | | | (32) $false
% 8.85/2.14 | | | | |
% 8.85/2.14 | | | | | CLOSE: (32) is inconsistent.
% 8.85/2.14 | | | | |
% 8.85/2.14 | | | | End of split
% 8.85/2.14 | | | |
% 8.85/2.14 | | | Case 2:
% 8.85/2.14 | | | |
% 8.85/2.14 | | | | (33) all_16_0 = all_16_2
% 8.85/2.14 | | | | (34) ~ (all_16_1 = all_16_2)
% 8.85/2.14 | | | |
% 8.85/2.14 | | | | COMBINE_EQS: (22), (33) imply:
% 8.85/2.14 | | | | (35) all_16_1 = all_16_2
% 8.85/2.14 | | | |
% 8.85/2.14 | | | | REDUCE: (34), (35) imply:
% 8.85/2.14 | | | | (36) $false
% 8.85/2.14 | | | |
% 8.85/2.14 | | | | CLOSE: (36) is inconsistent.
% 8.85/2.14 | | | |
% 8.85/2.14 | | | End of split
% 8.85/2.14 | | |
% 8.85/2.14 | | End of split
% 8.85/2.14 | |
% 8.85/2.14 | Case 2:
% 8.85/2.14 | |
% 8.85/2.14 | | (37) all_16_1 = empty_set
% 8.85/2.14 | | (38) ~ (all_16_0 = all_16_2)
% 8.85/2.14 | |
% 8.85/2.14 | | REDUCE: (14), (37) imply:
% 8.85/2.14 | | (39) set_union2(empty_set, all_16_2) = all_16_0
% 8.85/2.14 | |
% 8.85/2.14 | | BETA: splitting (17) gives:
% 8.85/2.14 | |
% 8.85/2.14 | | Case 1:
% 8.85/2.14 | | |
% 8.85/2.14 | | | (40) all_16_2 = empty_set
% 8.85/2.14 | | |
% 8.85/2.14 | | | REDUCE: (38), (40) imply:
% 8.85/2.14 | | | (41) ~ (all_16_0 = empty_set)
% 8.85/2.14 | | |
% 8.85/2.14 | | | REDUCE: (39), (40) imply:
% 8.85/2.14 | | | (42) set_union2(empty_set, empty_set) = all_16_0
% 8.85/2.14 | | |
% 8.85/2.14 | | | REDUCE: (6), (40) imply:
% 8.85/2.14 | | | (43) $i(empty_set)
% 8.85/2.14 | | |
% 8.85/2.15 | | | GROUND_INST: instantiating (idempotence_k2_xboole_0) with empty_set,
% 8.85/2.15 | | | all_16_0, simplifying with (42), (43) gives:
% 8.85/2.15 | | | (44) all_16_0 = empty_set
% 8.85/2.15 | | |
% 8.85/2.15 | | | REDUCE: (41), (44) imply:
% 8.85/2.15 | | | (45) $false
% 8.85/2.15 | | |
% 8.85/2.15 | | | CLOSE: (45) is inconsistent.
% 8.85/2.15 | | |
% 8.85/2.15 | | Case 2:
% 8.85/2.15 | | |
% 8.85/2.15 | | | (46) all_16_0 = all_16_2
% 8.85/2.15 | | |
% 8.85/2.15 | | | REDUCE: (38), (46) imply:
% 8.85/2.15 | | | (47) $false
% 8.85/2.15 | | |
% 8.85/2.15 | | | CLOSE: (47) is inconsistent.
% 8.85/2.15 | | |
% 8.85/2.15 | | End of split
% 8.85/2.15 | |
% 8.85/2.15 | End of split
% 8.85/2.15 |
% 8.85/2.15 End of proof
% 8.85/2.15 % SZS output end Proof for theBenchmark
% 8.85/2.15
% 8.85/2.15 1504ms
%------------------------------------------------------------------------------