TSTP Solution File: SET975+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET975+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 : 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 15:27:15 EDT 2023
% Result : Theorem 5.70s 1.48s
% Output : Proof 7.33s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET975+1 : TPTP v8.1.2. Released v3.2.0.
% 0.03/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n009.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Aug 26 12:17:05 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.61/0.60 ________ _____
% 0.61/0.60 ___ __ \_________(_)________________________________
% 0.61/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.61/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.61/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.61/0.60
% 0.61/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.61/0.60 (2023-06-19)
% 0.61/0.60
% 0.61/0.60 (c) Philipp Rümmer, 2009-2023
% 0.61/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.61/0.60 Amanda Stjerna.
% 0.61/0.60 Free software under BSD-3-Clause.
% 0.61/0.60
% 0.61/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.61/0.60
% 0.61/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.61/0.61 Running up to 7 provers in parallel.
% 0.61/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.61/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.61/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.61/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.61/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.61/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.61/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 1.96/0.99 Prover 1: Preprocessing ...
% 1.96/0.99 Prover 4: Preprocessing ...
% 2.41/1.04 Prover 0: Preprocessing ...
% 2.41/1.04 Prover 5: Preprocessing ...
% 2.41/1.04 Prover 3: Preprocessing ...
% 2.41/1.04 Prover 2: Preprocessing ...
% 2.41/1.04 Prover 6: Preprocessing ...
% 3.98/1.24 Prover 1: Warning: ignoring some quantifiers
% 3.98/1.24 Prover 4: Warning: ignoring some quantifiers
% 3.98/1.25 Prover 3: Warning: ignoring some quantifiers
% 3.98/1.25 Prover 4: Constructing countermodel ...
% 3.98/1.25 Prover 3: Constructing countermodel ...
% 3.98/1.27 Prover 1: Constructing countermodel ...
% 3.98/1.27 Prover 5: Proving ...
% 3.98/1.27 Prover 6: Proving ...
% 3.98/1.28 Prover 0: Proving ...
% 3.98/1.30 Prover 2: Proving ...
% 5.70/1.48 Prover 3: proved (860ms)
% 5.70/1.48
% 5.70/1.48 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.70/1.48
% 5.70/1.48 Prover 2: stopped
% 5.70/1.48 Prover 5: stopped
% 5.70/1.48 Prover 0: stopped
% 5.70/1.48 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 5.70/1.48 Prover 6: stopped
% 5.70/1.49 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 5.70/1.49 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 5.70/1.49 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 5.70/1.49 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 5.98/1.50 Prover 7: Preprocessing ...
% 5.98/1.51 Prover 10: Preprocessing ...
% 5.98/1.51 Prover 13: Preprocessing ...
% 5.98/1.51 Prover 11: Preprocessing ...
% 5.98/1.52 Prover 8: Preprocessing ...
% 6.27/1.56 Prover 7: Warning: ignoring some quantifiers
% 6.27/1.57 Prover 7: Constructing countermodel ...
% 6.27/1.57 Prover 8: Warning: ignoring some quantifiers
% 6.27/1.58 Prover 8: Constructing countermodel ...
% 6.27/1.59 Prover 10: Warning: ignoring some quantifiers
% 6.27/1.61 Prover 10: Constructing countermodel ...
% 6.84/1.63 Prover 11: Warning: ignoring some quantifiers
% 6.84/1.63 Prover 11: Constructing countermodel ...
% 6.84/1.64 Prover 13: Warning: ignoring some quantifiers
% 6.84/1.64 Prover 13: Constructing countermodel ...
% 7.33/1.68 Prover 10: Found proof (size 20)
% 7.33/1.68 Prover 10: proved (193ms)
% 7.33/1.68 Prover 11: stopped
% 7.33/1.68 Prover 7: stopped
% 7.33/1.68 Prover 1: stopped
% 7.33/1.68 Prover 4: stopped
% 7.33/1.68 Prover 13: stopped
% 7.33/1.68 Prover 8: stopped
% 7.33/1.68
% 7.33/1.68 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.33/1.68
% 7.33/1.69 % SZS output start Proof for theBenchmark
% 7.33/1.69 Assumptions after simplification:
% 7.33/1.69 ---------------------------------
% 7.33/1.69
% 7.33/1.69 (d1_tarski)
% 7.33/1.72 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ (singleton(v0) = v1) |
% 7.33/1.72 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ in(v2, v1)) & ? [v0: $i] : ! [v1:
% 7.33/1.72 $i] : ! [v2: $i] : (v2 = v0 | ~ (singleton(v1) = v2) | ~ $i(v1) | ~
% 7.33/1.72 $i(v0) | ? [v3: $i] : ($i(v3) & ( ~ (v3 = v1) | ~ in(v1, v0)) & (v3 = v1 |
% 7.33/1.72 in(v3, v0)))) & ! [v0: $i] : ! [v1: $i] : ( ~ (singleton(v0) = v1) |
% 7.33/1.72 ~ $i(v1) | ~ $i(v0) | in(v0, v1))
% 7.33/1.72
% 7.33/1.72 (l55_zfmisc_1)
% 7.33/1.73 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 7.33/1.73 $i] : ( ~ (cartesian_product2(v2, v3) = v5) | ~ (ordered_pair(v0, v1) = v4)
% 7.33/1.73 | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ in(v4, v5) | in(v1,
% 7.33/1.73 v3)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i]
% 7.33/1.73 : ! [v5: $i] : ( ~ (cartesian_product2(v2, v3) = v5) | ~ (ordered_pair(v0,
% 7.33/1.73 v1) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ in(v4,
% 7.33/1.73 v5) | in(v0, v2)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i]
% 7.33/1.73 : ! [v4: $i] : ! [v5: $i] : ( ~ (cartesian_product2(v2, v3) = v5) | ~
% 7.33/1.73 (ordered_pair(v0, v1) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)
% 7.33/1.73 | ~ in(v1, v3) | ~ in(v0, v2) | in(v4, v5))
% 7.33/1.73
% 7.33/1.73 (t128_zfmisc_1)
% 7.33/1.73 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5:
% 7.33/1.73 $i] : ? [v6: $i] : (cartesian_product2(v5, v3) = v6 & ordered_pair(v0, v1)
% 7.33/1.73 = v4 & singleton(v2) = v5 & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) &
% 7.33/1.73 $i(v1) & $i(v0) & ((v2 = v0 & in(v1, v3) & ~ in(v4, v6)) | (in(v4, v6) & (
% 7.33/1.73 ~ (v2 = v0) | ~ in(v1, v3)))))
% 7.33/1.73
% 7.33/1.73 Further assumptions not needed in the proof:
% 7.33/1.73 --------------------------------------------
% 7.33/1.73 antisymmetry_r2_hidden, commutativity_k2_tarski, d5_tarski, fc1_zfmisc_1,
% 7.33/1.73 rc1_xboole_0, rc2_xboole_0
% 7.33/1.73
% 7.33/1.73 Those formulas are unsatisfiable:
% 7.33/1.73 ---------------------------------
% 7.33/1.73
% 7.33/1.73 Begin of proof
% 7.33/1.74 |
% 7.33/1.74 | ALPHA: (d1_tarski) implies:
% 7.33/1.74 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (singleton(v0) = v1) | ~ $i(v1) | ~
% 7.33/1.74 | $i(v0) | in(v0, v1))
% 7.33/1.74 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ (singleton(v0)
% 7.33/1.74 | = v1) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ in(v2, v1))
% 7.33/1.74 |
% 7.33/1.74 | ALPHA: (l55_zfmisc_1) implies:
% 7.33/1.74 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 7.33/1.74 | ! [v5: $i] : ( ~ (cartesian_product2(v2, v3) = v5) | ~
% 7.33/1.74 | (ordered_pair(v0, v1) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 7.33/1.74 | $i(v0) | ~ in(v1, v3) | ~ in(v0, v2) | in(v4, v5))
% 7.33/1.74 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 7.33/1.74 | ! [v5: $i] : ( ~ (cartesian_product2(v2, v3) = v5) | ~
% 7.33/1.74 | (ordered_pair(v0, v1) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 7.33/1.74 | $i(v0) | ~ in(v4, v5) | in(v0, v2))
% 7.33/1.75 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 7.33/1.75 | ! [v5: $i] : ( ~ (cartesian_product2(v2, v3) = v5) | ~
% 7.33/1.75 | (ordered_pair(v0, v1) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 7.33/1.75 | $i(v0) | ~ in(v4, v5) | in(v1, v3))
% 7.33/1.75 |
% 7.33/1.75 | DELTA: instantiating (t128_zfmisc_1) with fresh symbols all_15_0, all_15_1,
% 7.33/1.75 | all_15_2, all_15_3, all_15_4, all_15_5, all_15_6 gives:
% 7.33/1.75 | (6) cartesian_product2(all_15_1, all_15_3) = all_15_0 &
% 7.33/1.75 | ordered_pair(all_15_6, all_15_5) = all_15_2 & singleton(all_15_4) =
% 7.33/1.75 | all_15_1 & $i(all_15_0) & $i(all_15_1) & $i(all_15_2) & $i(all_15_3) &
% 7.33/1.75 | $i(all_15_4) & $i(all_15_5) & $i(all_15_6) & ((all_15_4 = all_15_6 &
% 7.33/1.75 | in(all_15_5, all_15_3) & ~ in(all_15_2, all_15_0)) | (in(all_15_2,
% 7.33/1.75 | all_15_0) & ( ~ (all_15_4 = all_15_6) | ~ in(all_15_5,
% 7.33/1.75 | all_15_3))))
% 7.33/1.75 |
% 7.33/1.75 | ALPHA: (6) implies:
% 7.33/1.75 | (7) $i(all_15_6)
% 7.33/1.75 | (8) $i(all_15_5)
% 7.33/1.75 | (9) $i(all_15_4)
% 7.33/1.75 | (10) $i(all_15_3)
% 7.33/1.75 | (11) $i(all_15_1)
% 7.33/1.75 | (12) singleton(all_15_4) = all_15_1
% 7.33/1.75 | (13) ordered_pair(all_15_6, all_15_5) = all_15_2
% 7.33/1.75 | (14) cartesian_product2(all_15_1, all_15_3) = all_15_0
% 7.33/1.75 | (15) (all_15_4 = all_15_6 & in(all_15_5, all_15_3) & ~ in(all_15_2,
% 7.33/1.75 | all_15_0)) | (in(all_15_2, all_15_0) & ( ~ (all_15_4 = all_15_6) |
% 7.33/1.75 | ~ in(all_15_5, all_15_3)))
% 7.33/1.75 |
% 7.33/1.75 | GROUND_INST: instantiating (1) with all_15_4, all_15_1, simplifying with (9),
% 7.33/1.75 | (11), (12) gives:
% 7.33/1.75 | (16) in(all_15_4, all_15_1)
% 7.33/1.75 |
% 7.33/1.75 | BETA: splitting (15) gives:
% 7.33/1.75 |
% 7.33/1.75 | Case 1:
% 7.33/1.75 | |
% 7.33/1.75 | | (17) all_15_4 = all_15_6 & in(all_15_5, all_15_3) & ~ in(all_15_2,
% 7.33/1.75 | | all_15_0)
% 7.33/1.76 | |
% 7.33/1.76 | | ALPHA: (17) implies:
% 7.33/1.76 | | (18) all_15_4 = all_15_6
% 7.33/1.76 | | (19) ~ in(all_15_2, all_15_0)
% 7.33/1.76 | | (20) in(all_15_5, all_15_3)
% 7.33/1.76 | |
% 7.33/1.76 | | REDUCE: (16), (18) imply:
% 7.33/1.76 | | (21) in(all_15_6, all_15_1)
% 7.33/1.76 | |
% 7.33/1.76 | | GROUND_INST: instantiating (3) with all_15_6, all_15_5, all_15_1, all_15_3,
% 7.33/1.76 | | all_15_2, all_15_0, simplifying with (7), (8), (10), (11),
% 7.33/1.76 | | (13), (14), (19), (20), (21) gives:
% 7.33/1.76 | | (22) $false
% 7.33/1.76 | |
% 7.33/1.76 | | CLOSE: (22) is inconsistent.
% 7.33/1.76 | |
% 7.33/1.76 | Case 2:
% 7.33/1.76 | |
% 7.33/1.76 | | (23) in(all_15_2, all_15_0) & ( ~ (all_15_4 = all_15_6) | ~ in(all_15_5,
% 7.33/1.76 | | all_15_3))
% 7.33/1.76 | |
% 7.33/1.76 | | ALPHA: (23) implies:
% 7.33/1.76 | | (24) in(all_15_2, all_15_0)
% 7.33/1.76 | | (25) ~ (all_15_4 = all_15_6) | ~ in(all_15_5, all_15_3)
% 7.33/1.76 | |
% 7.33/1.76 | | GROUND_INST: instantiating (5) with all_15_6, all_15_5, all_15_1, all_15_3,
% 7.33/1.76 | | all_15_2, all_15_0, simplifying with (7), (8), (10), (11),
% 7.33/1.76 | | (13), (14), (24) gives:
% 7.33/1.76 | | (26) in(all_15_5, all_15_3)
% 7.33/1.76 | |
% 7.33/1.76 | | GROUND_INST: instantiating (4) with all_15_6, all_15_5, all_15_1, all_15_3,
% 7.33/1.76 | | all_15_2, all_15_0, simplifying with (7), (8), (10), (11),
% 7.33/1.76 | | (13), (14), (24) gives:
% 7.33/1.76 | | (27) in(all_15_6, all_15_1)
% 7.33/1.76 | |
% 7.33/1.76 | | BETA: splitting (25) gives:
% 7.33/1.76 | |
% 7.33/1.76 | | Case 1:
% 7.33/1.76 | | |
% 7.33/1.76 | | | (28) ~ in(all_15_5, all_15_3)
% 7.33/1.76 | | |
% 7.33/1.76 | | | PRED_UNIFY: (26), (28) imply:
% 7.33/1.76 | | | (29) $false
% 7.33/1.76 | | |
% 7.33/1.76 | | | CLOSE: (29) is inconsistent.
% 7.33/1.76 | | |
% 7.33/1.76 | | Case 2:
% 7.33/1.76 | | |
% 7.33/1.76 | | | (30) ~ (all_15_4 = all_15_6)
% 7.33/1.76 | | |
% 7.33/1.76 | | | GROUND_INST: instantiating (2) with all_15_4, all_15_1, all_15_6,
% 7.33/1.76 | | | simplifying with (7), (9), (11), (12), (27) gives:
% 7.33/1.76 | | | (31) all_15_4 = all_15_6
% 7.33/1.76 | | |
% 7.33/1.76 | | | REDUCE: (30), (31) imply:
% 7.33/1.76 | | | (32) $false
% 7.33/1.76 | | |
% 7.33/1.76 | | | CLOSE: (32) is inconsistent.
% 7.33/1.76 | | |
% 7.33/1.76 | | End of split
% 7.33/1.76 | |
% 7.33/1.76 | End of split
% 7.33/1.76 |
% 7.33/1.76 End of proof
% 7.33/1.76 % SZS output end Proof for theBenchmark
% 7.33/1.77
% 7.33/1.77 1166ms
%------------------------------------------------------------------------------