TSTP Solution File: SET958+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET958+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 : n024.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 15:27:12 EDT 2023
% Result : Theorem 4.36s 1.33s
% Output : Proof 5.84s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET958+1 : TPTP v8.1.2. Released v3.2.0.
% 0.07/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n024.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 16:05:23 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.62 ________ _____
% 0.20/0.62 ___ __ \_________(_)________________________________
% 0.20/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.62
% 0.20/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.62 (2023-06-19)
% 0.20/0.62
% 0.20/0.62 (c) Philipp Rümmer, 2009-2023
% 0.20/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.62 Amanda Stjerna.
% 0.20/0.62 Free software under BSD-3-Clause.
% 0.20/0.62
% 0.20/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.62
% 0.20/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.20/0.63 Running up to 7 provers in parallel.
% 0.20/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.26/0.97 Prover 4: Preprocessing ...
% 2.26/0.97 Prover 1: Preprocessing ...
% 2.38/1.01 Prover 0: Preprocessing ...
% 2.38/1.01 Prover 2: Preprocessing ...
% 2.38/1.01 Prover 5: Preprocessing ...
% 2.38/1.01 Prover 6: Preprocessing ...
% 2.38/1.01 Prover 3: Preprocessing ...
% 3.13/1.17 Prover 3: Warning: ignoring some quantifiers
% 3.66/1.18 Prover 1: Warning: ignoring some quantifiers
% 3.66/1.19 Prover 2: Proving ...
% 3.66/1.19 Prover 6: Proving ...
% 3.66/1.20 Prover 3: Constructing countermodel ...
% 3.66/1.20 Prover 5: Proving ...
% 3.66/1.20 Prover 1: Constructing countermodel ...
% 3.66/1.21 Prover 0: Proving ...
% 3.66/1.21 Prover 4: Constructing countermodel ...
% 4.36/1.32 Prover 0: proved (688ms)
% 4.36/1.32
% 4.36/1.33 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.36/1.33
% 4.36/1.33 Prover 3: stopped
% 4.36/1.33 Prover 2: stopped
% 4.36/1.33 Prover 6: stopped
% 4.36/1.33 Prover 5: stopped
% 4.36/1.33 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 4.36/1.33 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 4.36/1.33 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 4.36/1.33 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 4.36/1.34 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 4.36/1.35 Prover 7: Preprocessing ...
% 4.36/1.35 Prover 8: Preprocessing ...
% 4.92/1.37 Prover 10: Preprocessing ...
% 4.92/1.37 Prover 13: Preprocessing ...
% 4.92/1.37 Prover 11: Preprocessing ...
% 5.27/1.40 Prover 1: Found proof (size 17)
% 5.27/1.40 Prover 7: Warning: ignoring some quantifiers
% 5.27/1.40 Prover 1: proved (766ms)
% 5.27/1.40 Prover 4: stopped
% 5.27/1.40 Prover 11: stopped
% 5.27/1.41 Prover 10: Warning: ignoring some quantifiers
% 5.27/1.41 Prover 7: Constructing countermodel ...
% 5.33/1.41 Prover 10: Constructing countermodel ...
% 5.33/1.41 Prover 7: stopped
% 5.33/1.41 Prover 10: stopped
% 5.33/1.42 Prover 13: Warning: ignoring some quantifiers
% 5.33/1.43 Prover 8: Warning: ignoring some quantifiers
% 5.33/1.43 Prover 13: Constructing countermodel ...
% 5.33/1.43 Prover 8: Constructing countermodel ...
% 5.33/1.43 Prover 13: stopped
% 5.33/1.44 Prover 8: stopped
% 5.33/1.44
% 5.33/1.44 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.33/1.44
% 5.33/1.44 % SZS output start Proof for theBenchmark
% 5.33/1.44 Assumptions after simplification:
% 5.33/1.44 ---------------------------------
% 5.33/1.44
% 5.33/1.44 (d3_tarski)
% 5.33/1.47 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2)
% 5.33/1.47 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & in(v3,
% 5.33/1.47 v1) = v4 & in(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 5.33/1.47 (subset(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ! [v2: $i] : ( ~ (in(v2, v0)
% 5.33/1.47 = 0) | ~ $i(v2) | in(v2, v1) = 0))
% 5.33/1.47
% 5.33/1.47 (t111_zfmisc_1)
% 5.33/1.47 ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) & subset(v0, v1) = v2
% 5.33/1.47 & $i(v1) & $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~
% 5.33/1.47 (ordered_pair(v3, v4) = v5) | ~ (in(v5, v0) = 0) | ~ $i(v4) | ~ $i(v3)
% 5.33/1.47 | in(v5, v1) = 0) & ! [v3: $i] : ( ~ (in(v3, v0) = 0) | ~ $i(v3) | ?
% 5.33/1.47 [v4: $i] : ? [v5: $i] : (ordered_pair(v4, v5) = v3 & $i(v5) & $i(v4))))
% 5.33/1.47
% 5.33/1.47 (function-axioms)
% 5.33/1.48 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 5.33/1.48 (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0)) & ! [v0:
% 5.33/1.48 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 5.33/1.48 : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0:
% 5.33/1.48 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 5.33/1.48 (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0:
% 5.33/1.48 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 5.33/1.48 : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0:
% 5.33/1.48 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 5.33/1.48 ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 5.33/1.48 [v2: $i] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0))
% 5.33/1.48
% 5.33/1.48 Further assumptions not needed in the proof:
% 5.33/1.48 --------------------------------------------
% 5.33/1.48 antisymmetry_r2_hidden, commutativity_k2_tarski, d5_tarski, fc1_zfmisc_1,
% 5.33/1.48 rc1_xboole_0, rc2_xboole_0, reflexivity_r1_tarski
% 5.33/1.48
% 5.33/1.48 Those formulas are unsatisfiable:
% 5.33/1.48 ---------------------------------
% 5.33/1.48
% 5.33/1.48 Begin of proof
% 5.33/1.48 |
% 5.33/1.48 | ALPHA: (d3_tarski) implies:
% 5.33/1.48 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1)
% 5.33/1.48 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~
% 5.33/1.48 | (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0 & $i(v3)))
% 5.33/1.48 |
% 5.33/1.48 | ALPHA: (function-axioms) implies:
% 5.33/1.49 | (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 5.33/1.49 | ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 5.33/1.49 |
% 5.33/1.49 | DELTA: instantiating (t111_zfmisc_1) with fresh symbols all_14_0, all_14_1,
% 5.33/1.49 | all_14_2 gives:
% 5.33/1.49 | (3) ~ (all_14_0 = 0) & subset(all_14_2, all_14_1) = all_14_0 &
% 5.33/1.49 | $i(all_14_1) & $i(all_14_2) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 5.33/1.49 | ( ~ (ordered_pair(v0, v1) = v2) | ~ (in(v2, all_14_2) = 0) | ~ $i(v1)
% 5.33/1.49 | | ~ $i(v0) | in(v2, all_14_1) = 0) & ! [v0: $i] : ( ~ (in(v0,
% 5.33/1.49 | all_14_2) = 0) | ~ $i(v0) | ? [v1: $i] : ? [v2: $i] :
% 5.33/1.49 | (ordered_pair(v1, v2) = v0 & $i(v2) & $i(v1)))
% 5.33/1.49 |
% 5.33/1.49 | ALPHA: (3) implies:
% 5.33/1.49 | (4) ~ (all_14_0 = 0)
% 5.33/1.49 | (5) $i(all_14_2)
% 5.33/1.49 | (6) $i(all_14_1)
% 5.33/1.49 | (7) subset(all_14_2, all_14_1) = all_14_0
% 5.33/1.49 | (8) ! [v0: $i] : ( ~ (in(v0, all_14_2) = 0) | ~ $i(v0) | ? [v1: $i] : ?
% 5.33/1.49 | [v2: $i] : (ordered_pair(v1, v2) = v0 & $i(v2) & $i(v1)))
% 5.33/1.50 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (ordered_pair(v0, v1) =
% 5.33/1.50 | v2) | ~ (in(v2, all_14_2) = 0) | ~ $i(v1) | ~ $i(v0) | in(v2,
% 5.33/1.50 | all_14_1) = 0)
% 5.33/1.50 |
% 5.33/1.50 | GROUND_INST: instantiating (1) with all_14_2, all_14_1, all_14_0, simplifying
% 5.33/1.50 | with (5), (6), (7) gives:
% 5.33/1.50 | (10) all_14_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0,
% 5.33/1.50 | all_14_1) = v1 & in(v0, all_14_2) = 0 & $i(v0))
% 5.33/1.50 |
% 5.33/1.50 | BETA: splitting (10) gives:
% 5.33/1.50 |
% 5.33/1.50 | Case 1:
% 5.33/1.50 | |
% 5.33/1.50 | | (11) all_14_0 = 0
% 5.33/1.50 | |
% 5.33/1.50 | | REDUCE: (4), (11) imply:
% 5.33/1.50 | | (12) $false
% 5.33/1.50 | |
% 5.33/1.50 | | CLOSE: (12) is inconsistent.
% 5.33/1.50 | |
% 5.33/1.50 | Case 2:
% 5.33/1.50 | |
% 5.33/1.50 | | (13) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0, all_14_1) = v1 &
% 5.33/1.50 | | in(v0, all_14_2) = 0 & $i(v0))
% 5.33/1.50 | |
% 5.33/1.50 | | DELTA: instantiating (13) with fresh symbols all_24_0, all_24_1 gives:
% 5.33/1.50 | | (14) ~ (all_24_0 = 0) & in(all_24_1, all_14_1) = all_24_0 & in(all_24_1,
% 5.33/1.50 | | all_14_2) = 0 & $i(all_24_1)
% 5.33/1.50 | |
% 5.33/1.50 | | ALPHA: (14) implies:
% 5.33/1.50 | | (15) ~ (all_24_0 = 0)
% 5.33/1.50 | | (16) $i(all_24_1)
% 5.33/1.50 | | (17) in(all_24_1, all_14_2) = 0
% 5.33/1.50 | | (18) in(all_24_1, all_14_1) = all_24_0
% 5.33/1.50 | |
% 5.33/1.50 | | GROUND_INST: instantiating (8) with all_24_1, simplifying with (16), (17)
% 5.33/1.50 | | gives:
% 5.33/1.50 | | (19) ? [v0: $i] : ? [v1: $i] : (ordered_pair(v0, v1) = all_24_1 &
% 5.33/1.50 | | $i(v1) & $i(v0))
% 5.33/1.50 | |
% 5.33/1.50 | | DELTA: instantiating (19) with fresh symbols all_33_0, all_33_1 gives:
% 5.33/1.50 | | (20) ordered_pair(all_33_1, all_33_0) = all_24_1 & $i(all_33_0) &
% 5.33/1.50 | | $i(all_33_1)
% 5.33/1.50 | |
% 5.33/1.50 | | ALPHA: (20) implies:
% 5.33/1.50 | | (21) $i(all_33_1)
% 5.33/1.50 | | (22) $i(all_33_0)
% 5.33/1.50 | | (23) ordered_pair(all_33_1, all_33_0) = all_24_1
% 5.33/1.50 | |
% 5.33/1.51 | | GROUND_INST: instantiating (9) with all_33_1, all_33_0, all_24_1,
% 5.33/1.51 | | simplifying with (17), (21), (22), (23) gives:
% 5.33/1.51 | | (24) in(all_24_1, all_14_1) = 0
% 5.33/1.51 | |
% 5.33/1.51 | | GROUND_INST: instantiating (2) with all_24_0, 0, all_14_1, all_24_1,
% 5.33/1.51 | | simplifying with (18), (24) gives:
% 5.33/1.51 | | (25) all_24_0 = 0
% 5.33/1.51 | |
% 5.84/1.51 | | REDUCE: (15), (25) imply:
% 5.84/1.51 | | (26) $false
% 5.84/1.51 | |
% 5.84/1.51 | | CLOSE: (26) is inconsistent.
% 5.84/1.51 | |
% 5.84/1.51 | End of split
% 5.84/1.51 |
% 5.84/1.51 End of proof
% 5.84/1.51 % SZS output end Proof for theBenchmark
% 5.84/1.51
% 5.84/1.51 890ms
%------------------------------------------------------------------------------