TSTP Solution File: SEU096+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SEU096+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 : n008.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 17:42:30 EDT 2023
% Result : Theorem 15.26s 2.85s
% Output : Proof 17.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU096+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.34 % Computer : n008.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Wed Aug 23 18:07:18 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.59 ________ _____
% 0.21/0.59 ___ __ \_________(_)________________________________
% 0.21/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.21/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.21/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.21/0.59
% 0.21/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.21/0.59 (2023-06-19)
% 0.21/0.59
% 0.21/0.59 (c) Philipp Rümmer, 2009-2023
% 0.21/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.21/0.59 Amanda Stjerna.
% 0.21/0.59 Free software under BSD-3-Clause.
% 0.21/0.59
% 0.21/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.21/0.59
% 0.21/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.21/0.61 Running up to 7 provers in parallel.
% 0.21/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.21/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.21/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.21/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.21/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.21/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.21/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.39/1.17 Prover 1: Preprocessing ...
% 3.39/1.17 Prover 4: Preprocessing ...
% 3.39/1.21 Prover 0: Preprocessing ...
% 3.39/1.21 Prover 2: Preprocessing ...
% 3.39/1.21 Prover 6: Preprocessing ...
% 3.39/1.21 Prover 3: Preprocessing ...
% 3.39/1.21 Prover 5: Preprocessing ...
% 6.82/1.67 Prover 2: Proving ...
% 6.82/1.68 Prover 5: Proving ...
% 7.01/1.72 Prover 1: Warning: ignoring some quantifiers
% 7.41/1.76 Prover 1: Constructing countermodel ...
% 7.41/1.79 Prover 3: Warning: ignoring some quantifiers
% 7.96/1.82 Prover 3: Constructing countermodel ...
% 7.96/1.84 Prover 6: Proving ...
% 8.39/1.95 Prover 4: Warning: ignoring some quantifiers
% 9.23/1.99 Prover 4: Constructing countermodel ...
% 9.23/2.02 Prover 0: Proving ...
% 12.43/2.42 Prover 3: gave up
% 12.43/2.43 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 12.95/2.49 Prover 7: Preprocessing ...
% 13.93/2.61 Prover 7: Warning: ignoring some quantifiers
% 13.93/2.62 Prover 7: Constructing countermodel ...
% 15.26/2.85 Prover 2: proved (2233ms)
% 15.26/2.85
% 15.26/2.85 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 15.26/2.85
% 15.26/2.85 Prover 5: stopped
% 15.26/2.85 Prover 6: stopped
% 15.82/2.86 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 15.82/2.86 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 15.82/2.86 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 15.82/2.86 Prover 0: stopped
% 15.82/2.87 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 15.82/2.95 Prover 11: Preprocessing ...
% 15.82/2.95 Prover 8: Preprocessing ...
% 15.82/2.96 Prover 13: Preprocessing ...
% 15.82/2.96 Prover 10: Preprocessing ...
% 15.82/2.96 Prover 7: Found proof (size 14)
% 15.82/2.96 Prover 7: proved (533ms)
% 15.82/2.96 Prover 1: stopped
% 15.82/2.96 Prover 4: stopped
% 15.82/2.98 Prover 10: stopped
% 15.82/3.00 Prover 13: stopped
% 15.82/3.01 Prover 11: stopped
% 16.28/3.04 Prover 8: Warning: ignoring some quantifiers
% 17.03/3.05 Prover 8: Constructing countermodel ...
% 17.03/3.06 Prover 8: stopped
% 17.03/3.06
% 17.03/3.06 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 17.03/3.06
% 17.03/3.06 % SZS output start Proof for theBenchmark
% 17.12/3.07 Assumptions after simplification:
% 17.12/3.07 ---------------------------------
% 17.12/3.07
% 17.12/3.07 (t147_funct_1)
% 17.12/3.09 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_inverse_image(v1, v0)
% 17.12/3.09 = v2) | ~ $i(v1) | ~ $i(v0) | ~ relation(v1) | ~ function(v1) | ?
% 17.12/3.09 [v3: $i] : ? [v4: $i] : ((v4 = v0 & relation_image(v1, v2) = v0) |
% 17.12/3.09 (relation_rng(v1) = v3 & $i(v3) & ~ subset(v0, v3))))
% 17.12/3.09
% 17.12/3.09 (t17_finset_1)
% 17.12/3.09 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_image(v1, v0) = v2) |
% 17.12/3.09 ~ $i(v1) | ~ $i(v0) | ~ relation(v1) | ~ function(v1) | ~ finite(v0) |
% 17.12/3.09 finite(v2))
% 17.12/3.09
% 17.12/3.09 (t27_finset_1)
% 17.12/3.09 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 17.12/3.09 (relation_inverse_image(v1, v0) = v3 & relation_rng(v1) = v2 & $i(v3) & $i(v2)
% 17.12/3.09 & $i(v1) & $i(v0) & subset(v0, v2) & relation(v1) & function(v1) &
% 17.12/3.09 finite(v3) & ~ finite(v0))
% 17.12/3.09
% 17.12/3.09 (function-axioms)
% 17.12/3.10 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 17.12/3.10 (relation_inverse_image(v3, v2) = v1) | ~ (relation_inverse_image(v3, v2) =
% 17.12/3.10 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 17.12/3.10 ~ (relation_image(v3, v2) = v1) | ~ (relation_image(v3, v2) = v0)) & !
% 17.12/3.10 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (relation_rng(v2) = v1) |
% 17.12/3.10 ~ (relation_rng(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1
% 17.12/3.10 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0))
% 17.12/3.10
% 17.12/3.10 Further assumptions not needed in the proof:
% 17.12/3.10 --------------------------------------------
% 17.12/3.10 antisymmetry_r2_hidden, cc1_arytm_3, cc1_finset_1, cc1_funct_1, cc1_ordinal1,
% 17.12/3.10 cc1_relat_1, cc2_arytm_3, cc2_finset_1, cc2_funct_1, cc2_ordinal1, cc3_ordinal1,
% 17.12/3.10 cc4_arytm_3, existence_m1_subset_1, fc12_relat_1, fc13_finset_1, fc1_subset_1,
% 17.12/3.10 fc1_xboole_0, fc2_ordinal1, fc4_relat_1, fc6_funct_1, fc6_relat_1, fc8_arytm_3,
% 17.12/3.10 fc8_relat_1, rc1_arytm_3, rc1_finset_1, rc1_funcop_1, rc1_funct_1, rc1_ordinal1,
% 17.12/3.10 rc1_ordinal2, rc1_relat_1, rc1_subset_1, rc1_xboole_0, rc2_arytm_3,
% 17.12/3.10 rc2_finset_1, rc2_funct_1, rc2_ordinal1, rc2_ordinal2, rc2_relat_1,
% 17.12/3.10 rc2_subset_1, rc2_xboole_0, rc3_arytm_3, rc3_finset_1, rc3_funct_1,
% 17.12/3.10 rc3_ordinal1, rc3_relat_1, rc4_funct_1, rc4_ordinal1, rc5_funct_1,
% 17.12/3.10 reflexivity_r1_tarski, t1_subset, t2_subset, t3_subset, t4_subset, t5_subset,
% 17.12/3.10 t6_boole, t7_boole, t8_boole
% 17.12/3.10
% 17.12/3.10 Those formulas are unsatisfiable:
% 17.12/3.10 ---------------------------------
% 17.12/3.10
% 17.12/3.10 Begin of proof
% 17.12/3.10 |
% 17.12/3.10 | ALPHA: (function-axioms) implies:
% 17.12/3.10 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 17.12/3.10 | (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0))
% 17.12/3.10 |
% 17.12/3.10 | DELTA: instantiating (t27_finset_1) with fresh symbols all_79_0, all_79_1,
% 17.12/3.10 | all_79_2, all_79_3 gives:
% 17.12/3.10 | (2) relation_inverse_image(all_79_2, all_79_3) = all_79_0 &
% 17.12/3.10 | relation_rng(all_79_2) = all_79_1 & $i(all_79_0) & $i(all_79_1) &
% 17.12/3.10 | $i(all_79_2) & $i(all_79_3) & subset(all_79_3, all_79_1) &
% 17.12/3.10 | relation(all_79_2) & function(all_79_2) & finite(all_79_0) & ~
% 17.12/3.10 | finite(all_79_3)
% 17.12/3.10 |
% 17.12/3.10 | ALPHA: (2) implies:
% 17.12/3.10 | (3) ~ finite(all_79_3)
% 17.12/3.10 | (4) finite(all_79_0)
% 17.12/3.10 | (5) function(all_79_2)
% 17.12/3.10 | (6) relation(all_79_2)
% 17.12/3.10 | (7) subset(all_79_3, all_79_1)
% 17.12/3.10 | (8) $i(all_79_3)
% 17.12/3.10 | (9) $i(all_79_2)
% 17.12/3.10 | (10) $i(all_79_0)
% 17.12/3.10 | (11) relation_rng(all_79_2) = all_79_1
% 17.12/3.10 | (12) relation_inverse_image(all_79_2, all_79_3) = all_79_0
% 17.12/3.10 |
% 17.12/3.10 | GROUND_INST: instantiating (t147_funct_1) with all_79_3, all_79_2, all_79_0,
% 17.12/3.10 | simplifying with (5), (6), (8), (9), (12) gives:
% 17.12/3.10 | (13) ? [v0: $i] : ? [v1: int] : ((v1 = all_79_3 &
% 17.12/3.10 | relation_image(all_79_2, all_79_0) = all_79_3) |
% 17.12/3.10 | (relation_rng(all_79_2) = v0 & $i(v0) & ~ subset(all_79_3, v0)))
% 17.12/3.10 |
% 17.12/3.10 | DELTA: instantiating (13) with fresh symbols all_91_0, all_91_1 gives:
% 17.12/3.10 | (14) (all_91_0 = all_79_3 & relation_image(all_79_2, all_79_0) = all_79_3)
% 17.12/3.10 | | (relation_rng(all_79_2) = all_91_1 & $i(all_91_1) & ~
% 17.12/3.10 | subset(all_79_3, all_91_1))
% 17.12/3.10 |
% 17.12/3.10 | BETA: splitting (14) gives:
% 17.12/3.10 |
% 17.12/3.10 | Case 1:
% 17.12/3.10 | |
% 17.12/3.10 | | (15) all_91_0 = all_79_3 & relation_image(all_79_2, all_79_0) = all_79_3
% 17.12/3.10 | |
% 17.12/3.10 | | ALPHA: (15) implies:
% 17.12/3.11 | | (16) relation_image(all_79_2, all_79_0) = all_79_3
% 17.12/3.11 | |
% 17.12/3.11 | | GROUND_INST: instantiating (t17_finset_1) with all_79_0, all_79_2, all_79_3,
% 17.12/3.11 | | simplifying with (3), (4), (5), (6), (9), (10), (16) gives:
% 17.12/3.11 | | (17) $false
% 17.12/3.11 | |
% 17.12/3.11 | | CLOSE: (17) is inconsistent.
% 17.12/3.11 | |
% 17.12/3.11 | Case 2:
% 17.12/3.11 | |
% 17.12/3.11 | | (18) relation_rng(all_79_2) = all_91_1 & $i(all_91_1) & ~
% 17.12/3.11 | | subset(all_79_3, all_91_1)
% 17.12/3.11 | |
% 17.12/3.11 | | ALPHA: (18) implies:
% 17.12/3.11 | | (19) ~ subset(all_79_3, all_91_1)
% 17.12/3.11 | | (20) relation_rng(all_79_2) = all_91_1
% 17.12/3.11 | |
% 17.12/3.11 | | GROUND_INST: instantiating (1) with all_79_1, all_91_1, all_79_2,
% 17.12/3.11 | | simplifying with (11), (20) gives:
% 17.12/3.11 | | (21) all_91_1 = all_79_1
% 17.12/3.11 | |
% 17.12/3.11 | | PRED_UNIFY: (7), (19) imply:
% 17.12/3.11 | | (22) ~ (all_91_1 = all_79_1)
% 17.12/3.11 | |
% 17.12/3.11 | | REDUCE: (21), (22) imply:
% 17.12/3.11 | | (23) $false
% 17.12/3.11 | |
% 17.12/3.11 | | CLOSE: (23) is inconsistent.
% 17.12/3.11 | |
% 17.12/3.11 | End of split
% 17.12/3.11 |
% 17.12/3.11 End of proof
% 17.12/3.11 % SZS output end Proof for theBenchmark
% 17.12/3.11
% 17.12/3.11 2514ms
%------------------------------------------------------------------------------