TSTP Solution File: SET991+1 by Princess---230619
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET991+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 : n016.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 15:27:18 EDT 2023
% Result : Theorem 7.76s 1.87s
% Output : Proof 12.07s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET991+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 : n016.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 16:00:57 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.18/0.61 ________ _____
% 0.18/0.61 ___ __ \_________(_)________________________________
% 0.18/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.18/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.18/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.18/0.61
% 0.18/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.18/0.61 (2023-06-19)
% 0.18/0.61
% 0.18/0.61 (c) Philipp Rümmer, 2009-2023
% 0.18/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.18/0.61 Amanda Stjerna.
% 0.18/0.61 Free software under BSD-3-Clause.
% 0.18/0.61
% 0.18/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.18/0.61
% 0.18/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.18/0.62 Running up to 7 provers in parallel.
% 0.18/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.18/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.18/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.18/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.18/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.18/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.18/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.45/1.07 Prover 4: Preprocessing ...
% 2.45/1.07 Prover 1: Preprocessing ...
% 2.45/1.11 Prover 2: Preprocessing ...
% 2.45/1.11 Prover 6: Preprocessing ...
% 2.45/1.11 Prover 5: Preprocessing ...
% 2.45/1.11 Prover 0: Preprocessing ...
% 2.45/1.12 Prover 3: Preprocessing ...
% 5.62/1.54 Prover 1: Warning: ignoring some quantifiers
% 5.62/1.55 Prover 3: Warning: ignoring some quantifiers
% 5.62/1.57 Prover 6: Proving ...
% 5.62/1.57 Prover 1: Constructing countermodel ...
% 5.62/1.58 Prover 3: Constructing countermodel ...
% 5.62/1.58 Prover 2: Proving ...
% 5.62/1.58 Prover 5: Proving ...
% 6.97/1.69 Prover 4: Warning: ignoring some quantifiers
% 7.08/1.74 Prover 0: Proving ...
% 7.08/1.77 Prover 4: Constructing countermodel ...
% 7.76/1.87 Prover 3: proved (1233ms)
% 7.76/1.87
% 7.76/1.87 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.76/1.87
% 7.76/1.87 Prover 0: stopped
% 7.76/1.87 Prover 6: stopped
% 7.76/1.87 Prover 5: stopped
% 7.76/1.88 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 7.76/1.88 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 7.76/1.88 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 7.76/1.88 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 7.76/1.88 Prover 2: stopped
% 8.37/1.91 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 8.37/1.93 Prover 10: Preprocessing ...
% 8.37/1.95 Prover 8: Preprocessing ...
% 8.37/1.99 Prover 7: Preprocessing ...
% 8.98/1.99 Prover 13: Preprocessing ...
% 8.98/1.99 Prover 11: Preprocessing ...
% 9.00/2.14 Prover 7: Warning: ignoring some quantifiers
% 9.00/2.14 Prover 10: Warning: ignoring some quantifiers
% 9.00/2.15 Prover 10: Constructing countermodel ...
% 9.15/2.16 Prover 7: Constructing countermodel ...
% 10.05/2.19 Prover 8: Warning: ignoring some quantifiers
% 10.05/2.21 Prover 8: Constructing countermodel ...
% 10.05/2.22 Prover 13: Warning: ignoring some quantifiers
% 10.05/2.25 Prover 13: Constructing countermodel ...
% 11.48/2.36 Prover 10: Found proof (size 12)
% 11.48/2.36 Prover 10: proved (482ms)
% 11.48/2.36 Prover 8: stopped
% 11.48/2.36 Prover 1: stopped
% 11.48/2.36 Prover 13: stopped
% 11.48/2.36 Prover 7: stopped
% 11.48/2.36 Prover 4: stopped
% 11.79/2.41 Prover 11: Warning: ignoring some quantifiers
% 11.79/2.42 Prover 11: Constructing countermodel ...
% 11.79/2.43 Prover 11: stopped
% 11.79/2.43
% 11.79/2.43 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 11.79/2.43
% 11.79/2.43 % SZS output start Proof for theBenchmark
% 11.79/2.44 Assumptions after simplification:
% 11.79/2.44 ---------------------------------
% 11.79/2.44
% 11.79/2.44 (d5_funct_1)
% 12.07/2.47 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) | ~
% 12.07/2.47 function(v0) | ~ relation(v0) | ? [v2: $i] : (relation_dom(v0) = v2 &
% 12.07/2.47 $i(v2) & ! [v3: $i] : ! [v4: $i] : ( ~ (apply(v0, v4) = v3) | ~ $i(v4)
% 12.07/2.47 | ~ $i(v3) | ~ $i(v1) | ~ in(v4, v2) | in(v3, v1)) & ! [v3: $i] : (
% 12.07/2.47 ~ $i(v3) | ~ $i(v1) | ~ in(v3, v1) | ? [v4: $i] : (apply(v0, v4) = v3
% 12.07/2.47 & $i(v4) & in(v4, v2))) & ? [v3: $i] : (v3 = v1 | ~ $i(v3) | ? [v4:
% 12.07/2.47 $i] : ? [v5: $i] : ? [v6: $i] : ($i(v5) & $i(v4) & ( ~ in(v4, v3) |
% 12.07/2.47 ! [v7: $i] : ( ~ (apply(v0, v7) = v4) | ~ $i(v7) | ~ in(v7, v2)))
% 12.07/2.47 & (in(v4, v3) | (v6 = v4 & apply(v0, v5) = v4 & in(v5, v2)))))))
% 12.07/2.47
% 12.07/2.47 (t12_funct_1)
% 12.07/2.47 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 12.07/2.47 (apply(v1, v0) = v3 & relation_rng(v1) = v4 & relation_dom(v1) = v2 & $i(v4) &
% 12.07/2.47 $i(v3) & $i(v2) & $i(v1) & $i(v0) & in(v0, v2) & function(v1) & relation(v1)
% 12.07/2.47 & ~ in(v3, v4))
% 12.07/2.47
% 12.07/2.47 (function-axioms)
% 12.07/2.47 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 12.07/2.47 (apply(v3, v2) = v1) | ~ (apply(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i]
% 12.07/2.47 : ! [v2: $i] : (v1 = v0 | ~ (relation_rng(v2) = v1) | ~ (relation_rng(v2) =
% 12.07/2.47 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 12.07/2.47 (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0)) & ! [v0: $i] : !
% 12.07/2.47 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2)
% 12.07/2.47 = v0))
% 12.07/2.47
% 12.07/2.47 Further assumptions not needed in the proof:
% 12.07/2.47 --------------------------------------------
% 12.07/2.47 antisymmetry_r2_hidden, cc1_funct_1, cc1_relat_1, existence_m1_subset_1,
% 12.07/2.47 fc12_relat_1, fc1_subset_1, fc1_xboole_0, fc4_relat_1, fc5_relat_1, fc6_relat_1,
% 12.07/2.47 fc7_relat_1, fc8_relat_1, rc1_funct_1, rc1_relat_1, rc1_subset_1, rc1_xboole_0,
% 12.07/2.47 rc2_relat_1, rc2_subset_1, rc2_xboole_0, rc3_relat_1, reflexivity_r1_tarski,
% 12.07/2.47 t1_subset, t2_subset, t3_subset, t4_subset, t5_subset, t6_boole, t7_boole,
% 12.07/2.47 t8_boole
% 12.07/2.47
% 12.07/2.47 Those formulas are unsatisfiable:
% 12.07/2.47 ---------------------------------
% 12.07/2.47
% 12.07/2.47 Begin of proof
% 12.07/2.48 |
% 12.07/2.48 | ALPHA: (function-axioms) implies:
% 12.07/2.48 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 12.07/2.48 | (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0))
% 12.07/2.48 |
% 12.07/2.48 | DELTA: instantiating (t12_funct_1) with fresh symbols all_37_0, all_37_1,
% 12.07/2.48 | all_37_2, all_37_3, all_37_4 gives:
% 12.07/2.48 | (2) apply(all_37_3, all_37_4) = all_37_1 & relation_rng(all_37_3) =
% 12.07/2.48 | all_37_0 & relation_dom(all_37_3) = all_37_2 & $i(all_37_0) &
% 12.07/2.48 | $i(all_37_1) & $i(all_37_2) & $i(all_37_3) & $i(all_37_4) &
% 12.07/2.48 | in(all_37_4, all_37_2) & function(all_37_3) & relation(all_37_3) & ~
% 12.07/2.48 | in(all_37_1, all_37_0)
% 12.07/2.48 |
% 12.07/2.48 | ALPHA: (2) implies:
% 12.07/2.48 | (3) ~ in(all_37_1, all_37_0)
% 12.07/2.48 | (4) relation(all_37_3)
% 12.07/2.48 | (5) function(all_37_3)
% 12.07/2.48 | (6) in(all_37_4, all_37_2)
% 12.07/2.48 | (7) $i(all_37_4)
% 12.07/2.48 | (8) $i(all_37_3)
% 12.07/2.48 | (9) $i(all_37_1)
% 12.07/2.48 | (10) $i(all_37_0)
% 12.07/2.48 | (11) relation_dom(all_37_3) = all_37_2
% 12.07/2.48 | (12) relation_rng(all_37_3) = all_37_0
% 12.07/2.48 | (13) apply(all_37_3, all_37_4) = all_37_1
% 12.07/2.48 |
% 12.07/2.48 | GROUND_INST: instantiating (d5_funct_1) with all_37_3, all_37_0, simplifying
% 12.07/2.48 | with (4), (5), (8), (12) gives:
% 12.07/2.49 | (14) ? [v0: $i] : (relation_dom(all_37_3) = v0 & $i(v0) & ! [v1: $i] : !
% 12.07/2.49 | [v2: $i] : ( ~ (apply(all_37_3, v2) = v1) | ~ $i(v2) | ~ $i(v1) |
% 12.07/2.49 | ~ $i(all_37_0) | ~ in(v2, v0) | in(v1, all_37_0)) & ! [v1: $i] :
% 12.07/2.49 | ( ~ $i(v1) | ~ $i(all_37_0) | ~ in(v1, all_37_0) | ? [v2: $i] :
% 12.07/2.49 | (apply(all_37_3, v2) = v1 & $i(v2) & in(v2, v0))) & ? [v1: any] :
% 12.07/2.49 | (v1 = all_37_0 | ~ $i(v1) | ? [v2: $i] : ? [v3: $i] : ? [v4: $i]
% 12.07/2.49 | : ($i(v3) & $i(v2) & ( ~ in(v2, v1) | ! [v5: $i] : ( ~
% 12.07/2.49 | (apply(all_37_3, v5) = v2) | ~ $i(v5) | ~ in(v5, v0))) &
% 12.07/2.49 | (in(v2, v1) | (v4 = v2 & apply(all_37_3, v3) = v2 & in(v3,
% 12.07/2.49 | v0))))))
% 12.07/2.49 |
% 12.07/2.49 | DELTA: instantiating (14) with fresh symbol all_45_0 gives:
% 12.07/2.49 | (15) relation_dom(all_37_3) = all_45_0 & $i(all_45_0) & ! [v0: $i] : !
% 12.07/2.49 | [v1: $i] : ( ~ (apply(all_37_3, v1) = v0) | ~ $i(v1) | ~ $i(v0) | ~
% 12.07/2.49 | $i(all_37_0) | ~ in(v1, all_45_0) | in(v0, all_37_0)) & ! [v0: $i]
% 12.07/2.49 | : ( ~ $i(v0) | ~ $i(all_37_0) | ~ in(v0, all_37_0) | ? [v1: $i] :
% 12.07/2.49 | (apply(all_37_3, v1) = v0 & $i(v1) & in(v1, all_45_0))) & ? [v0:
% 12.07/2.49 | any] : (v0 = all_37_0 | ~ $i(v0) | ? [v1: $i] : ? [v2: $i] : ?
% 12.07/2.49 | [v3: $i] : ($i(v2) & $i(v1) & ( ~ in(v1, v0) | ! [v4: $i] : ( ~
% 12.07/2.49 | (apply(all_37_3, v4) = v1) | ~ $i(v4) | ~ in(v4, all_45_0)))
% 12.07/2.49 | & (in(v1, v0) | (v3 = v1 & apply(all_37_3, v2) = v1 & in(v2,
% 12.07/2.49 | all_45_0)))))
% 12.07/2.49 |
% 12.07/2.49 | ALPHA: (15) implies:
% 12.07/2.49 | (16) relation_dom(all_37_3) = all_45_0
% 12.07/2.49 | (17) ! [v0: $i] : ! [v1: $i] : ( ~ (apply(all_37_3, v1) = v0) | ~ $i(v1)
% 12.07/2.49 | | ~ $i(v0) | ~ $i(all_37_0) | ~ in(v1, all_45_0) | in(v0,
% 12.07/2.49 | all_37_0))
% 12.07/2.49 |
% 12.07/2.49 | GROUND_INST: instantiating (1) with all_37_2, all_45_0, all_37_3, simplifying
% 12.07/2.49 | with (11), (16) gives:
% 12.07/2.49 | (18) all_45_0 = all_37_2
% 12.07/2.49 |
% 12.07/2.49 | GROUND_INST: instantiating (17) with all_37_1, all_37_4, simplifying with (3),
% 12.07/2.49 | (7), (9), (10), (13) gives:
% 12.07/2.49 | (19) ~ in(all_37_4, all_45_0)
% 12.07/2.49 |
% 12.07/2.49 | REDUCE: (18), (19) imply:
% 12.07/2.49 | (20) ~ in(all_37_4, all_37_2)
% 12.07/2.49 |
% 12.07/2.49 | PRED_UNIFY: (6), (20) imply:
% 12.07/2.49 | (21) $false
% 12.07/2.49 |
% 12.07/2.49 | CLOSE: (21) is inconsistent.
% 12.07/2.49 |
% 12.07/2.49 End of proof
% 12.07/2.49 % SZS output end Proof for theBenchmark
% 12.07/2.49
% 12.07/2.49 1882ms
%------------------------------------------------------------------------------