TSTP Solution File: SET658+3 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET658+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n031.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 15:25:53 EDT 2023
% Result : Theorem 14.54s 2.69s
% Output : Proof 17.50s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET658+3 : TPTP v8.1.2. Released v2.2.0.
% 0.13/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.34 % Computer : n031.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
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Sat Aug 26 09:36:08 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.21/0.61 ________ _____
% 0.21/0.61 ___ __ \_________(_)________________________________
% 0.21/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.21/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.21/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.21/0.61
% 0.21/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.21/0.61 (2023-06-19)
% 0.21/0.61
% 0.21/0.61 (c) Philipp Rümmer, 2009-2023
% 0.21/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.21/0.61 Amanda Stjerna.
% 0.21/0.61 Free software under BSD-3-Clause.
% 0.21/0.61
% 0.21/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.21/0.61
% 0.21/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.21/0.63 Running up to 7 provers in parallel.
% 0.21/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.21/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.21/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.21/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.21/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.21/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.21/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.10/1.11 Prover 4: Preprocessing ...
% 3.10/1.12 Prover 1: Preprocessing ...
% 3.10/1.15 Prover 5: Preprocessing ...
% 3.10/1.15 Prover 2: Preprocessing ...
% 3.10/1.15 Prover 6: Preprocessing ...
% 3.10/1.15 Prover 0: Preprocessing ...
% 3.10/1.15 Prover 3: Preprocessing ...
% 7.99/1.82 Prover 5: Proving ...
% 7.99/1.85 Prover 1: Constructing countermodel ...
% 7.99/1.85 Prover 3: Constructing countermodel ...
% 7.99/1.85 Prover 2: Proving ...
% 8.56/1.87 Prover 6: Proving ...
% 10.78/2.22 Prover 4: Constructing countermodel ...
% 11.75/2.36 Prover 0: Proving ...
% 14.54/2.69 Prover 3: proved (2053ms)
% 14.54/2.69
% 14.54/2.69 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 14.54/2.69
% 14.54/2.69 Prover 0: stopped
% 14.54/2.69 Prover 2: stopped
% 14.65/2.70 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 14.65/2.70 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 14.65/2.70 Prover 5: stopped
% 14.71/2.72 Prover 6: stopped
% 14.71/2.72 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 14.71/2.72 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 14.71/2.72 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 14.71/2.75 Prover 7: Preprocessing ...
% 14.71/2.77 Prover 8: Preprocessing ...
% 14.71/2.77 Prover 13: Preprocessing ...
% 14.71/2.79 Prover 10: Preprocessing ...
% 14.71/2.79 Prover 11: Preprocessing ...
% 15.42/2.86 Prover 7: Warning: ignoring some quantifiers
% 15.42/2.87 Prover 7: Constructing countermodel ...
% 15.42/2.88 Prover 10: Warning: ignoring some quantifiers
% 16.02/2.90 Prover 10: Constructing countermodel ...
% 16.02/2.93 Prover 8: Warning: ignoring some quantifiers
% 16.02/2.95 Prover 8: Constructing countermodel ...
% 16.76/2.99 Prover 13: Warning: ignoring some quantifiers
% 16.79/3.00 Prover 13: Constructing countermodel ...
% 16.88/3.02 Prover 10: Found proof (size 16)
% 16.88/3.03 Prover 10: proved (324ms)
% 16.88/3.03 Prover 7: stopped
% 16.88/3.03 Prover 8: stopped
% 16.88/3.03 Prover 4: stopped
% 16.88/3.03 Prover 1: stopped
% 16.88/3.04 Prover 13: stopped
% 16.88/3.15 Prover 11: Constructing countermodel ...
% 16.88/3.16 Prover 11: stopped
% 16.88/3.16
% 16.88/3.16 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 16.88/3.16
% 16.88/3.17 % SZS output start Proof for theBenchmark
% 16.88/3.17 Assumptions after simplification:
% 16.88/3.17 ---------------------------------
% 16.88/3.17
% 16.88/3.17 (p1)
% 17.50/3.21 $i(binary_relation_type) & $i(set_type) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 17.50/3.21 $i] : ! [v3: $i] : ( ~ (range_of(v1) = v2) | ~ (relation_type(v0, v2) =
% 17.50/3.21 v3) | ~ $i(v1) | ~ $i(v0) | ~ ilf_type(v1, binary_relation_type) | ~
% 17.50/3.21 ilf_type(v0, set_type) | ilf_type(v1, v3) | ? [v4: $i] : (domain_of(v1) =
% 17.50/3.21 v4 & $i(v4) & ~ subset(v4, v0)))
% 17.50/3.21
% 17.50/3.21 (p14)
% 17.50/3.21 $i(set_type) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~
% 17.50/3.21 $i(v1) | ~ $i(v0) | ~ member(v2, v0) | ~ subset(v0, v1) | ~ ilf_type(v2,
% 17.50/3.21 set_type) | ~ ilf_type(v1, set_type) | ~ ilf_type(v0, set_type) |
% 17.50/3.21 member(v2, v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~
% 17.50/3.21 ilf_type(v1, set_type) | ~ ilf_type(v0, set_type) | subset(v0, v1) | ?
% 17.50/3.21 [v2: $i] : ($i(v2) & member(v2, v0) & ilf_type(v2, set_type) & ~ member(v2,
% 17.50/3.21 v1)))
% 17.50/3.21
% 17.50/3.21 (p3)
% 17.50/3.21 $i(binary_relation_type) & $i(set_type) & ! [v0: $i] : ! [v1: $i] : ( ~
% 17.50/3.21 (domain_of(v0) = v1) | ~ $i(v0) | ~ ilf_type(v0, binary_relation_type) |
% 17.50/3.21 ilf_type(v1, set_type))
% 17.50/3.21
% 17.50/3.21 (prove_relset_1_20)
% 17.50/3.21 $i(binary_relation_type) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3:
% 17.50/3.21 $i] : (range_of(v0) = v2 & relation_type(v1, v2) = v3 & domain_of(v0) = v1 &
% 17.50/3.21 $i(v3) & $i(v2) & $i(v1) & $i(v0) & ilf_type(v0, binary_relation_type) & ~
% 17.50/3.21 ilf_type(v0, v3))
% 17.50/3.21
% 17.50/3.21 (function-axioms)
% 17.50/3.22 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0
% 17.50/3.22 | ~ (range(v4, v3, v2) = v1) | ~ (range(v4, v3, v2) = v0)) & ! [v0: $i] :
% 17.50/3.22 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~
% 17.50/3.22 (domain(v4, v3, v2) = v1) | ~ (domain(v4, v3, v2) = v0)) & ! [v0: $i] : !
% 17.50/3.22 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (cross_product(v3, v2) =
% 17.50/3.22 v1) | ~ (cross_product(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 17.50/3.22 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~
% 17.50/3.22 (ordered_pair(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 17.50/3.22 [v3: $i] : (v1 = v0 | ~ (relation_type(v3, v2) = v1) | ~ (relation_type(v3,
% 17.50/3.22 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 17.50/3.22 (power_set(v2) = v1) | ~ (power_set(v2) = v0)) & ! [v0: $i] : ! [v1: $i]
% 17.50/3.22 : ! [v2: $i] : (v1 = v0 | ~ (member_type(v2) = v1) | ~ (member_type(v2) =
% 17.50/3.22 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 17.50/3.22 (subset_type(v2) = v1) | ~ (subset_type(v2) = v0)) & ! [v0: $i] : ! [v1:
% 17.50/3.22 $i] : ! [v2: $i] : (v1 = v0 | ~ (range_of(v2) = v1) | ~ (range_of(v2) =
% 17.50/3.22 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 17.50/3.22 (domain_of(v2) = v1) | ~ (domain_of(v2) = v0))
% 17.50/3.22
% 17.50/3.22 Further assumptions not needed in the proof:
% 17.50/3.22 --------------------------------------------
% 17.50/3.22 p10, p11, p12, p13, p15, p16, p17, p18, p19, p2, p20, p21, p22, p23, p24, p25,
% 17.50/3.22 p26, p27, p28, p4, p5, p6, p7, p8, p9
% 17.50/3.22
% 17.50/3.22 Those formulas are unsatisfiable:
% 17.50/3.22 ---------------------------------
% 17.50/3.22
% 17.50/3.22 Begin of proof
% 17.50/3.22 |
% 17.50/3.22 | ALPHA: (p1) implies:
% 17.50/3.22 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 17.50/3.22 | (range_of(v1) = v2) | ~ (relation_type(v0, v2) = v3) | ~ $i(v1) |
% 17.50/3.22 | ~ $i(v0) | ~ ilf_type(v1, binary_relation_type) | ~ ilf_type(v0,
% 17.50/3.22 | set_type) | ilf_type(v1, v3) | ? [v4: $i] : (domain_of(v1) = v4 &
% 17.50/3.22 | $i(v4) & ~ subset(v4, v0)))
% 17.50/3.22 |
% 17.50/3.22 | ALPHA: (p3) implies:
% 17.50/3.22 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (domain_of(v0) = v1) | ~ $i(v0) | ~
% 17.50/3.22 | ilf_type(v0, binary_relation_type) | ilf_type(v1, set_type))
% 17.50/3.22 |
% 17.50/3.22 | ALPHA: (p14) implies:
% 17.50/3.22 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ ilf_type(v1,
% 17.50/3.22 | set_type) | ~ ilf_type(v0, set_type) | subset(v0, v1) | ? [v2:
% 17.50/3.22 | $i] : ($i(v2) & member(v2, v0) & ilf_type(v2, set_type) & ~
% 17.50/3.22 | member(v2, v1)))
% 17.50/3.22 |
% 17.50/3.22 | ALPHA: (prove_relset_1_20) implies:
% 17.50/3.22 | (4) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (range_of(v0) =
% 17.50/3.22 | v2 & relation_type(v1, v2) = v3 & domain_of(v0) = v1 & $i(v3) &
% 17.50/3.22 | $i(v2) & $i(v1) & $i(v0) & ilf_type(v0, binary_relation_type) & ~
% 17.50/3.22 | ilf_type(v0, v3))
% 17.50/3.22 |
% 17.50/3.22 | ALPHA: (function-axioms) implies:
% 17.50/3.22 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (domain_of(v2)
% 17.50/3.22 | = v1) | ~ (domain_of(v2) = v0))
% 17.50/3.22 |
% 17.50/3.23 | DELTA: instantiating (4) with fresh symbols all_33_0, all_33_1, all_33_2,
% 17.50/3.23 | all_33_3 gives:
% 17.50/3.23 | (6) range_of(all_33_3) = all_33_1 & relation_type(all_33_2, all_33_1) =
% 17.50/3.23 | all_33_0 & domain_of(all_33_3) = all_33_2 & $i(all_33_0) & $i(all_33_1)
% 17.50/3.23 | & $i(all_33_2) & $i(all_33_3) & ilf_type(all_33_3,
% 17.50/3.23 | binary_relation_type) & ~ ilf_type(all_33_3, all_33_0)
% 17.50/3.23 |
% 17.50/3.23 | ALPHA: (6) implies:
% 17.50/3.23 | (7) ~ ilf_type(all_33_3, all_33_0)
% 17.50/3.23 | (8) ilf_type(all_33_3, binary_relation_type)
% 17.50/3.23 | (9) $i(all_33_3)
% 17.50/3.23 | (10) $i(all_33_2)
% 17.50/3.23 | (11) domain_of(all_33_3) = all_33_2
% 17.50/3.23 | (12) relation_type(all_33_2, all_33_1) = all_33_0
% 17.50/3.23 | (13) range_of(all_33_3) = all_33_1
% 17.50/3.23 |
% 17.50/3.23 | GROUND_INST: instantiating (2) with all_33_3, all_33_2, simplifying with (8),
% 17.50/3.23 | (9), (11) gives:
% 17.50/3.23 | (14) ilf_type(all_33_2, set_type)
% 17.50/3.23 |
% 17.50/3.23 | GROUND_INST: instantiating (1) with all_33_2, all_33_3, all_33_1, all_33_0,
% 17.50/3.23 | simplifying with (7), (8), (9), (10), (12), (13), (14) gives:
% 17.50/3.23 | (15) ? [v0: $i] : (domain_of(all_33_3) = v0 & $i(v0) & ~ subset(v0,
% 17.50/3.23 | all_33_2))
% 17.50/3.23 |
% 17.50/3.23 | GROUND_INST: instantiating (3) with all_33_2, all_33_2, simplifying with (10),
% 17.50/3.23 | (14) gives:
% 17.50/3.23 | (16) subset(all_33_2, all_33_2)
% 17.50/3.23 |
% 17.50/3.23 | DELTA: instantiating (15) with fresh symbol all_49_0 gives:
% 17.50/3.23 | (17) domain_of(all_33_3) = all_49_0 & $i(all_49_0) & ~ subset(all_49_0,
% 17.50/3.23 | all_33_2)
% 17.50/3.23 |
% 17.50/3.23 | ALPHA: (17) implies:
% 17.50/3.23 | (18) ~ subset(all_49_0, all_33_2)
% 17.50/3.23 | (19) domain_of(all_33_3) = all_49_0
% 17.50/3.23 |
% 17.50/3.23 | GROUND_INST: instantiating (5) with all_33_2, all_49_0, all_33_3, simplifying
% 17.50/3.23 | with (11), (19) gives:
% 17.50/3.23 | (20) all_49_0 = all_33_2
% 17.50/3.23 |
% 17.50/3.23 | REDUCE: (18), (20) imply:
% 17.50/3.23 | (21) ~ subset(all_33_2, all_33_2)
% 17.50/3.23 |
% 17.50/3.23 | PRED_UNIFY: (16), (21) imply:
% 17.50/3.23 | (22) $false
% 17.50/3.23 |
% 17.50/3.23 | CLOSE: (22) is inconsistent.
% 17.50/3.23 |
% 17.50/3.23 End of proof
% 17.50/3.23 % SZS output end Proof for theBenchmark
% 17.50/3.23
% 17.50/3.23 2620ms
%------------------------------------------------------------------------------