TSTP Solution File: SET971+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET971+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 : n028.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 15:27:14 EDT 2023
% Result : Theorem 4.10s 1.35s
% Output : Proof 5.89s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET971+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.34 % Computer : n028.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sat Aug 26 11:43:37 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.61 ________ _____
% 0.19/0.61 ___ __ \_________(_)________________________________
% 0.19/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.61
% 0.19/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.61 (2023-06-19)
% 0.19/0.61
% 0.19/0.61 (c) Philipp Rümmer, 2009-2023
% 0.19/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.61 Amanda Stjerna.
% 0.19/0.61 Free software under BSD-3-Clause.
% 0.19/0.61
% 0.19/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.61
% 0.19/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.19/0.63 Running up to 7 provers in parallel.
% 0.19/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.09/0.98 Prover 1: Preprocessing ...
% 2.09/0.98 Prover 4: Preprocessing ...
% 2.09/1.02 Prover 2: Preprocessing ...
% 2.09/1.02 Prover 5: Preprocessing ...
% 2.09/1.02 Prover 6: Preprocessing ...
% 2.09/1.02 Prover 3: Preprocessing ...
% 2.09/1.02 Prover 0: Preprocessing ...
% 3.49/1.17 Prover 1: Warning: ignoring some quantifiers
% 3.49/1.17 Prover 3: Warning: ignoring some quantifiers
% 3.49/1.17 Prover 6: Proving ...
% 3.49/1.17 Prover 5: Proving ...
% 3.49/1.18 Prover 0: Proving ...
% 3.49/1.18 Prover 3: Constructing countermodel ...
% 3.49/1.18 Prover 1: Constructing countermodel ...
% 3.49/1.19 Prover 4: Constructing countermodel ...
% 3.49/1.19 Prover 2: Proving ...
% 4.10/1.35 Prover 3: proved (711ms)
% 4.10/1.35
% 4.10/1.35 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.10/1.35
% 4.10/1.35 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 4.10/1.35 Prover 2: stopped
% 4.10/1.35 Prover 6: stopped
% 4.10/1.36 Prover 5: stopped
% 4.10/1.37 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 4.10/1.37 Prover 7: Preprocessing ...
% 4.10/1.37 Prover 0: stopped
% 4.10/1.38 Prover 8: Preprocessing ...
% 4.10/1.38 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 4.10/1.38 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 4.10/1.38 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 4.10/1.40 Prover 10: Preprocessing ...
% 4.10/1.40 Prover 11: Preprocessing ...
% 4.10/1.41 Prover 13: Preprocessing ...
% 4.10/1.42 Prover 8: Warning: ignoring some quantifiers
% 4.10/1.42 Prover 7: Warning: ignoring some quantifiers
% 4.10/1.42 Prover 7: Constructing countermodel ...
% 4.10/1.42 Prover 8: Constructing countermodel ...
% 4.10/1.43 Prover 10: Warning: ignoring some quantifiers
% 4.10/1.43 Prover 10: Constructing countermodel ...
% 4.10/1.45 Prover 13: Warning: ignoring some quantifiers
% 4.10/1.45 Prover 13: Constructing countermodel ...
% 4.10/1.47 Prover 1: Found proof (size 25)
% 4.10/1.47 Prover 1: proved (834ms)
% 5.46/1.47 Prover 4: Found proof (size 34)
% 5.46/1.47 Prover 4: proved (838ms)
% 5.46/1.47 Prover 13: stopped
% 5.46/1.47 Prover 8: stopped
% 5.46/1.47 Prover 10: stopped
% 5.46/1.47 Prover 7: stopped
% 5.46/1.48 Prover 11: Constructing countermodel ...
% 5.46/1.49 Prover 11: stopped
% 5.46/1.49
% 5.46/1.49 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.46/1.49
% 5.46/1.50 % SZS output start Proof for theBenchmark
% 5.46/1.50 Assumptions after simplification:
% 5.46/1.50 ---------------------------------
% 5.46/1.50
% 5.46/1.50 (commutativity_k3_xboole_0)
% 5.89/1.53 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_intersection2(v0, v1) = v2)
% 5.89/1.53 | ~ $i(v1) | ~ $i(v0) | (set_intersection2(v1, v0) = v2 & $i(v2)))
% 5.89/1.53
% 5.89/1.53 (t123_zfmisc_1)
% 5.89/1.53 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 5.89/1.53 $i] : ! [v6: $i] : ( ~ (cartesian_product2(v1, v3) = v5) | ~
% 5.89/1.53 (cartesian_product2(v0, v2) = v4) | ~ (set_intersection2(v4, v5) = v6) | ~
% 5.89/1.53 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v7: $i] : ? [v8: $i] :
% 5.89/1.53 (cartesian_product2(v7, v8) = v6 & set_intersection2(v2, v3) = v8 &
% 5.89/1.53 set_intersection2(v0, v1) = v7 & $i(v8) & $i(v7) & $i(v6)))
% 5.89/1.53
% 5.89/1.53 (t124_zfmisc_1)
% 5.89/1.54 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5:
% 5.89/1.54 $i] : ? [v6: $i] : ? [v7: $i] : ( ~ (v7 = v6) & cartesian_product2(v1, v2)
% 5.89/1.54 = v5 & cartesian_product2(v0, v3) = v4 & cartesian_product2(v0, v2) = v7 &
% 5.89/1.54 subset(v2, v3) = 0 & subset(v0, v1) = 0 & set_intersection2(v4, v5) = v6 &
% 5.89/1.54 $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 5.89/1.54
% 5.89/1.54 (t28_xboole_1)
% 5.89/1.54 ! [v0: $i] : ! [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) |
% 5.89/1.54 set_intersection2(v0, v1) = v0)
% 5.89/1.54
% 5.89/1.54 (function-axioms)
% 5.89/1.54 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 5.89/1.54 (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) = v0)) &
% 5.89/1.54 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 5.89/1.54 $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & !
% 5.89/1.54 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 5.89/1.54 (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0)) & !
% 5.89/1.54 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0
% 5.89/1.54 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0))
% 5.89/1.55
% 5.89/1.55 Further assumptions not needed in the proof:
% 5.89/1.55 --------------------------------------------
% 5.89/1.55 idempotence_k3_xboole_0, rc1_xboole_0, rc2_xboole_0, reflexivity_r1_tarski
% 5.89/1.55
% 5.89/1.55 Those formulas are unsatisfiable:
% 5.89/1.55 ---------------------------------
% 5.89/1.55
% 5.89/1.55 Begin of proof
% 5.89/1.55 |
% 5.89/1.55 | ALPHA: (function-axioms) implies:
% 5.89/1.55 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 5.89/1.55 | (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) =
% 5.89/1.55 | v0))
% 5.89/1.55 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 5.89/1.55 | (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) =
% 5.89/1.55 | v0))
% 5.89/1.55 |
% 5.89/1.55 | DELTA: instantiating (t124_zfmisc_1) with fresh symbols all_14_0, all_14_1,
% 5.89/1.55 | all_14_2, all_14_3, all_14_4, all_14_5, all_14_6, all_14_7 gives:
% 5.89/1.56 | (3) ~ (all_14_0 = all_14_1) & cartesian_product2(all_14_6, all_14_5) =
% 5.89/1.56 | all_14_2 & cartesian_product2(all_14_7, all_14_4) = all_14_3 &
% 5.89/1.56 | cartesian_product2(all_14_7, all_14_5) = all_14_0 & subset(all_14_5,
% 5.89/1.56 | all_14_4) = 0 & subset(all_14_7, all_14_6) = 0 &
% 5.89/1.56 | set_intersection2(all_14_3, all_14_2) = all_14_1 & $i(all_14_0) &
% 5.89/1.56 | $i(all_14_1) & $i(all_14_2) & $i(all_14_3) & $i(all_14_4) &
% 5.89/1.56 | $i(all_14_5) & $i(all_14_6) & $i(all_14_7)
% 5.89/1.56 |
% 5.89/1.56 | ALPHA: (3) implies:
% 5.89/1.56 | (4) ~ (all_14_0 = all_14_1)
% 5.89/1.56 | (5) $i(all_14_7)
% 5.89/1.56 | (6) $i(all_14_6)
% 5.89/1.56 | (7) $i(all_14_5)
% 5.89/1.56 | (8) $i(all_14_4)
% 5.89/1.56 | (9) $i(all_14_3)
% 5.89/1.56 | (10) $i(all_14_2)
% 5.89/1.56 | (11) set_intersection2(all_14_3, all_14_2) = all_14_1
% 5.89/1.56 | (12) subset(all_14_7, all_14_6) = 0
% 5.89/1.56 | (13) subset(all_14_5, all_14_4) = 0
% 5.89/1.56 | (14) cartesian_product2(all_14_7, all_14_5) = all_14_0
% 5.89/1.56 | (15) cartesian_product2(all_14_7, all_14_4) = all_14_3
% 5.89/1.56 | (16) cartesian_product2(all_14_6, all_14_5) = all_14_2
% 5.89/1.56 |
% 5.89/1.56 | GROUND_INST: instantiating (commutativity_k3_xboole_0) with all_14_3,
% 5.89/1.56 | all_14_2, all_14_1, simplifying with (9), (10), (11) gives:
% 5.89/1.56 | (17) set_intersection2(all_14_2, all_14_3) = all_14_1 & $i(all_14_1)
% 5.89/1.56 |
% 5.89/1.56 | ALPHA: (17) implies:
% 5.89/1.56 | (18) set_intersection2(all_14_2, all_14_3) = all_14_1
% 5.89/1.56 |
% 5.89/1.56 | GROUND_INST: instantiating (t28_xboole_1) with all_14_7, all_14_6, simplifying
% 5.89/1.56 | with (5), (6), (12) gives:
% 5.89/1.56 | (19) set_intersection2(all_14_7, all_14_6) = all_14_7
% 5.89/1.56 |
% 5.89/1.56 | GROUND_INST: instantiating (t28_xboole_1) with all_14_5, all_14_4, simplifying
% 5.89/1.56 | with (7), (8), (13) gives:
% 5.89/1.56 | (20) set_intersection2(all_14_5, all_14_4) = all_14_5
% 5.89/1.56 |
% 5.89/1.57 | GROUND_INST: instantiating (t123_zfmisc_1) with all_14_7, all_14_6, all_14_4,
% 5.89/1.57 | all_14_5, all_14_3, all_14_2, all_14_1, simplifying with (5),
% 5.89/1.57 | (6), (7), (8), (11), (15), (16) gives:
% 5.89/1.57 | (21) ? [v0: $i] : ? [v1: $i] : (cartesian_product2(v0, v1) = all_14_1 &
% 5.89/1.57 | set_intersection2(all_14_4, all_14_5) = v1 &
% 5.89/1.57 | set_intersection2(all_14_7, all_14_6) = v0 & $i(v1) & $i(v0) &
% 5.89/1.57 | $i(all_14_1))
% 5.89/1.57 |
% 5.89/1.57 | DELTA: instantiating (21) with fresh symbols all_22_0, all_22_1 gives:
% 5.89/1.57 | (22) cartesian_product2(all_22_1, all_22_0) = all_14_1 &
% 5.89/1.57 | set_intersection2(all_14_4, all_14_5) = all_22_0 &
% 5.89/1.57 | set_intersection2(all_14_7, all_14_6) = all_22_1 & $i(all_22_0) &
% 5.89/1.57 | $i(all_22_1) & $i(all_14_1)
% 5.89/1.57 |
% 5.89/1.57 | ALPHA: (22) implies:
% 5.89/1.57 | (23) $i(all_22_1)
% 5.89/1.57 | (24) set_intersection2(all_14_7, all_14_6) = all_22_1
% 5.89/1.57 | (25) set_intersection2(all_14_4, all_14_5) = all_22_0
% 5.89/1.57 | (26) cartesian_product2(all_22_1, all_22_0) = all_14_1
% 5.89/1.57 |
% 5.89/1.57 | GROUND_INST: instantiating (1) with all_14_7, all_22_1, all_14_6, all_14_7,
% 5.89/1.57 | simplifying with (19), (24) gives:
% 5.89/1.57 | (27) all_22_1 = all_14_7
% 5.89/1.57 |
% 5.89/1.57 | REDUCE: (26), (27) imply:
% 5.89/1.57 | (28) cartesian_product2(all_14_7, all_22_0) = all_14_1
% 5.89/1.57 |
% 5.89/1.57 | GROUND_INST: instantiating (commutativity_k3_xboole_0) with all_14_4,
% 5.89/1.57 | all_14_5, all_22_0, simplifying with (7), (8), (25) gives:
% 5.89/1.57 | (29) set_intersection2(all_14_5, all_14_4) = all_22_0 & $i(all_22_0)
% 5.89/1.57 |
% 5.89/1.57 | ALPHA: (29) implies:
% 5.89/1.57 | (30) set_intersection2(all_14_5, all_14_4) = all_22_0
% 5.89/1.57 |
% 5.89/1.57 | GROUND_INST: instantiating (t123_zfmisc_1) with all_14_6, all_14_7, all_14_5,
% 5.89/1.57 | all_14_4, all_14_2, all_14_3, all_14_1, simplifying with (5),
% 5.89/1.57 | (6), (7), (8), (15), (16), (18) gives:
% 5.89/1.57 | (31) ? [v0: $i] : ? [v1: $i] : (cartesian_product2(v0, v1) = all_14_1 &
% 5.89/1.57 | set_intersection2(all_14_5, all_14_4) = v1 &
% 5.89/1.57 | set_intersection2(all_14_6, all_14_7) = v0 & $i(v1) & $i(v0) &
% 5.89/1.57 | $i(all_14_1))
% 5.89/1.57 |
% 5.89/1.57 | DELTA: instantiating (31) with fresh symbols all_34_0, all_34_1 gives:
% 5.89/1.58 | (32) cartesian_product2(all_34_1, all_34_0) = all_14_1 &
% 5.89/1.58 | set_intersection2(all_14_5, all_14_4) = all_34_0 &
% 5.89/1.58 | set_intersection2(all_14_6, all_14_7) = all_34_1 & $i(all_34_0) &
% 5.89/1.58 | $i(all_34_1) & $i(all_14_1)
% 5.89/1.58 |
% 5.89/1.58 | ALPHA: (32) implies:
% 5.89/1.58 | (33) set_intersection2(all_14_5, all_14_4) = all_34_0
% 5.89/1.58 |
% 5.89/1.58 | GROUND_INST: instantiating (1) with all_14_5, all_34_0, all_14_4, all_14_5,
% 5.89/1.58 | simplifying with (20), (33) gives:
% 5.89/1.58 | (34) all_34_0 = all_14_5
% 5.89/1.58 |
% 5.89/1.58 | GROUND_INST: instantiating (1) with all_22_0, all_34_0, all_14_4, all_14_5,
% 5.89/1.58 | simplifying with (30), (33) gives:
% 5.89/1.58 | (35) all_34_0 = all_22_0
% 5.89/1.58 |
% 5.89/1.58 | COMBINE_EQS: (34), (35) imply:
% 5.89/1.58 | (36) all_22_0 = all_14_5
% 5.89/1.58 |
% 5.89/1.58 | REDUCE: (28), (36) imply:
% 5.89/1.58 | (37) cartesian_product2(all_14_7, all_14_5) = all_14_1
% 5.89/1.58 |
% 5.89/1.58 | GROUND_INST: instantiating (2) with all_14_0, all_14_1, all_14_5, all_14_7,
% 5.89/1.58 | simplifying with (14), (37) gives:
% 5.89/1.58 | (38) all_14_0 = all_14_1
% 5.89/1.58 |
% 5.89/1.58 | REDUCE: (4), (38) imply:
% 5.89/1.58 | (39) $false
% 5.89/1.58 |
% 5.89/1.58 | CLOSE: (39) is inconsistent.
% 5.89/1.58 |
% 5.89/1.58 End of proof
% 5.89/1.58 % SZS output end Proof for theBenchmark
% 5.89/1.58
% 5.89/1.58 967ms
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