TSTP Solution File: SYN056+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SYN056+1 : TPTP v8.1.2. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n019.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 : Fri Sep 1 03:26:22 EDT 2023
% Result : Theorem 3.87s 1.22s
% Output : Proof 4.88s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SYN056+1 : TPTP v8.1.2. Released v2.0.0.
% 0.12/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.33 % Computer : n019.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sat Aug 26 19:18:58 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.60 ________ _____
% 0.19/0.60 ___ __ \_________(_)________________________________
% 0.19/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.60
% 0.19/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.60 (2023-06-19)
% 0.19/0.60
% 0.19/0.60 (c) Philipp Rümmer, 2009-2023
% 0.19/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.60 Amanda Stjerna.
% 0.19/0.60 Free software under BSD-3-Clause.
% 0.19/0.60
% 0.19/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.60
% 0.19/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.19/0.62 Running up to 7 provers in parallel.
% 0.19/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 1.94/0.95 Prover 4: Preprocessing ...
% 1.94/0.95 Prover 1: Preprocessing ...
% 1.94/0.99 Prover 0: Preprocessing ...
% 1.94/0.99 Prover 2: Preprocessing ...
% 1.94/0.99 Prover 6: Preprocessing ...
% 1.94/0.99 Prover 3: Preprocessing ...
% 1.94/0.99 Prover 5: Preprocessing ...
% 2.85/1.09 Prover 5: Constructing countermodel ...
% 2.85/1.09 Prover 2: Constructing countermodel ...
% 2.85/1.11 Prover 3: Constructing countermodel ...
% 2.85/1.11 Prover 6: Proving ...
% 2.85/1.11 Prover 1: Constructing countermodel ...
% 2.85/1.16 Prover 4: Constructing countermodel ...
% 3.51/1.18 Prover 0: Proving ...
% 3.68/1.22 Prover 2: proved (594ms)
% 3.87/1.22
% 3.87/1.22 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.87/1.22
% 3.87/1.22 Prover 3: gave up
% 3.87/1.22 Prover 5: stopped
% 3.87/1.22 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 3.87/1.22 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 3.87/1.22 Prover 6: stopped
% 3.87/1.23 Prover 0: stopped
% 3.92/1.23 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 3.92/1.23 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 3.92/1.23 Prover 1: gave up
% 3.92/1.25 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 3.92/1.25 Prover 7: Preprocessing ...
% 3.92/1.25 Prover 8: Preprocessing ...
% 3.92/1.25 Prover 10: Preprocessing ...
% 3.92/1.25 Prover 11: Preprocessing ...
% 3.92/1.25 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 3.92/1.25 Prover 13: Preprocessing ...
% 3.92/1.26 Prover 10: Constructing countermodel ...
% 3.92/1.26 Prover 7: Constructing countermodel ...
% 3.92/1.27 Prover 16: Preprocessing ...
% 3.92/1.28 Prover 13: Constructing countermodel ...
% 3.92/1.29 Prover 8: Warning: ignoring some quantifiers
% 3.92/1.29 Prover 8: Constructing countermodel ...
% 3.92/1.30 Prover 16: Constructing countermodel ...
% 3.92/1.34 Prover 10: Found proof (size 24)
% 3.92/1.34 Prover 10: proved (117ms)
% 3.92/1.34 Prover 4: stopped
% 3.92/1.34 Prover 13: stopped
% 3.92/1.34 Prover 16: stopped
% 3.92/1.34 Prover 8: stopped
% 3.92/1.34 Prover 7: stopped
% 3.92/1.38 Prover 11: Constructing countermodel ...
% 3.92/1.38 Prover 11: stopped
% 3.92/1.38
% 3.92/1.38 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.92/1.38
% 3.92/1.39 % SZS output start Proof for theBenchmark
% 3.92/1.39 Assumptions after simplification:
% 3.92/1.39 ---------------------------------
% 3.92/1.39
% 3.92/1.39 (pel26)
% 3.92/1.40 ? [v0: $i] : ($i(v0) & ((big_q(v0) & ~ big_s(v0) & ! [v1: $i] : ( ~ $i(v1)
% 3.92/1.40 | ~ big_p(v1) | big_r(v1))) | (big_p(v0) & ~ big_r(v0) & ! [v1: $i]
% 3.92/1.40 : ( ~ $i(v1) | ~ big_q(v1) | big_s(v1)))))
% 3.92/1.40
% 3.92/1.40 (pel26_1)
% 3.92/1.40 ? [v0: $i] : ? [v1: $i] : ($i(v1) & $i(v0) & ((big_q(v0) & big_p(v1)) | ( !
% 3.92/1.40 [v2: $i] : ( ~ $i(v2) | ~ big_q(v2)) & ! [v2: $i] : ( ~ $i(v2) | ~
% 3.92/1.40 big_p(v2)))))
% 3.92/1.40
% 3.92/1.40 (pel26_2)
% 3.92/1.40 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ big_s(v1) | ~
% 3.92/1.40 big_q(v1) | ~ big_p(v0) | big_r(v0)) & ! [v0: $i] : ! [v1: $i] : ( ~
% 3.92/1.40 $i(v1) | ~ $i(v0) | ~ big_r(v0) | ~ big_q(v1) | ~ big_p(v0) | big_s(v1))
% 3.92/1.40
% 3.92/1.40 Those formulas are unsatisfiable:
% 3.92/1.40 ---------------------------------
% 3.92/1.40
% 3.92/1.40 Begin of proof
% 3.92/1.40 |
% 3.92/1.40 | ALPHA: (pel26_2) implies:
% 3.92/1.41 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ big_r(v0) | ~
% 3.92/1.41 | big_q(v1) | ~ big_p(v0) | big_s(v1))
% 3.92/1.41 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ big_s(v1) | ~
% 3.92/1.41 | big_q(v1) | ~ big_p(v0) | big_r(v0))
% 3.92/1.41 |
% 3.92/1.41 | DELTA: instantiating (pel26_1) with fresh symbols all_3_0, all_3_1 gives:
% 3.92/1.41 | (3) $i(all_3_0) & $i(all_3_1) & ((big_q(all_3_1) & big_p(all_3_0)) | ( !
% 3.92/1.41 | [v0: $i] : ( ~ $i(v0) | ~ big_q(v0)) & ! [v0: $i] : ( ~ $i(v0) |
% 3.92/1.41 | ~ big_p(v0))))
% 3.92/1.41 |
% 3.92/1.41 | ALPHA: (3) implies:
% 4.88/1.41 | (4) $i(all_3_1)
% 4.88/1.41 | (5) $i(all_3_0)
% 4.88/1.41 | (6) (big_q(all_3_1) & big_p(all_3_0)) | ( ! [v0: $i] : ( ~ $i(v0) | ~
% 4.88/1.41 | big_q(v0)) & ! [v0: $i] : ( ~ $i(v0) | ~ big_p(v0)))
% 4.88/1.41 |
% 4.88/1.41 | DELTA: instantiating (pel26) with fresh symbol all_5_0 gives:
% 4.88/1.41 | (7) $i(all_5_0) & ((big_q(all_5_0) & ~ big_s(all_5_0) & ! [v0: $i] : ( ~
% 4.88/1.41 | $i(v0) | ~ big_p(v0) | big_r(v0))) | (big_p(all_5_0) & ~
% 4.88/1.41 | big_r(all_5_0) & ! [v0: $i] : ( ~ $i(v0) | ~ big_q(v0) |
% 4.88/1.41 | big_s(v0))))
% 4.88/1.41 |
% 4.88/1.41 | ALPHA: (7) implies:
% 4.88/1.41 | (8) $i(all_5_0)
% 4.88/1.41 | (9) (big_q(all_5_0) & ~ big_s(all_5_0) & ! [v0: $i] : ( ~ $i(v0) | ~
% 4.88/1.42 | big_p(v0) | big_r(v0))) | (big_p(all_5_0) & ~ big_r(all_5_0) & !
% 4.88/1.42 | [v0: $i] : ( ~ $i(v0) | ~ big_q(v0) | big_s(v0)))
% 4.88/1.42 |
% 4.88/1.42 | BETA: splitting (6) gives:
% 4.88/1.42 |
% 4.88/1.42 | Case 1:
% 4.88/1.42 | |
% 4.88/1.42 | | (10) big_q(all_3_1) & big_p(all_3_0)
% 4.88/1.42 | |
% 4.88/1.42 | | ALPHA: (10) implies:
% 4.88/1.42 | | (11) big_p(all_3_0)
% 4.88/1.42 | | (12) big_q(all_3_1)
% 4.88/1.42 | |
% 4.88/1.42 | | BETA: splitting (9) gives:
% 4.88/1.42 | |
% 4.88/1.42 | | Case 1:
% 4.88/1.42 | | |
% 4.88/1.42 | | | (13) big_q(all_5_0) & ~ big_s(all_5_0) & ! [v0: $i] : ( ~ $i(v0) | ~
% 4.88/1.42 | | | big_p(v0) | big_r(v0))
% 4.88/1.42 | | |
% 4.88/1.42 | | | ALPHA: (13) implies:
% 4.88/1.42 | | | (14) ~ big_s(all_5_0)
% 4.88/1.42 | | | (15) big_q(all_5_0)
% 4.88/1.42 | | | (16) ! [v0: $i] : ( ~ $i(v0) | ~ big_p(v0) | big_r(v0))
% 4.88/1.42 | | |
% 4.88/1.42 | | | GROUND_INST: instantiating (16) with all_3_0, simplifying with (5), (11)
% 4.88/1.42 | | | gives:
% 4.88/1.42 | | | (17) big_r(all_3_0)
% 4.88/1.42 | | |
% 4.88/1.42 | | | GROUND_INST: instantiating (1) with all_3_0, all_5_0, simplifying with
% 4.88/1.42 | | | (5), (8), (11), (14), (15), (17) gives:
% 4.88/1.42 | | | (18) $false
% 4.88/1.42 | | |
% 4.88/1.42 | | | CLOSE: (18) is inconsistent.
% 4.88/1.42 | | |
% 4.88/1.42 | | Case 2:
% 4.88/1.42 | | |
% 4.88/1.42 | | | (19) big_p(all_5_0) & ~ big_r(all_5_0) & ! [v0: $i] : ( ~ $i(v0) | ~
% 4.88/1.42 | | | big_q(v0) | big_s(v0))
% 4.88/1.42 | | |
% 4.88/1.42 | | | ALPHA: (19) implies:
% 4.88/1.42 | | | (20) ~ big_r(all_5_0)
% 4.88/1.42 | | | (21) big_p(all_5_0)
% 4.88/1.42 | | | (22) ! [v0: $i] : ( ~ $i(v0) | ~ big_q(v0) | big_s(v0))
% 4.88/1.42 | | |
% 4.88/1.42 | | | GROUND_INST: instantiating (22) with all_3_1, simplifying with (4), (12)
% 4.88/1.42 | | | gives:
% 4.88/1.42 | | | (23) big_s(all_3_1)
% 4.88/1.42 | | |
% 4.88/1.43 | | | GROUND_INST: instantiating (2) with all_5_0, all_3_1, simplifying with
% 4.88/1.43 | | | (4), (8), (12), (20), (21), (23) gives:
% 4.88/1.43 | | | (24) $false
% 4.88/1.43 | | |
% 4.88/1.43 | | | CLOSE: (24) is inconsistent.
% 4.88/1.43 | | |
% 4.88/1.43 | | End of split
% 4.88/1.43 | |
% 4.88/1.43 | Case 2:
% 4.88/1.43 | |
% 4.88/1.43 | | (25) ! [v0: $i] : ( ~ $i(v0) | ~ big_q(v0)) & ! [v0: $i] : ( ~ $i(v0)
% 4.88/1.43 | | | ~ big_p(v0))
% 4.88/1.43 | |
% 4.88/1.43 | | ALPHA: (25) implies:
% 4.88/1.43 | | (26) ! [v0: $i] : ( ~ $i(v0) | ~ big_p(v0))
% 4.88/1.43 | | (27) ! [v0: $i] : ( ~ $i(v0) | ~ big_q(v0))
% 4.88/1.43 | |
% 4.88/1.43 | | BETA: splitting (9) gives:
% 4.88/1.43 | |
% 4.88/1.43 | | Case 1:
% 4.88/1.43 | | |
% 4.88/1.43 | | | (28) big_q(all_5_0) & ~ big_s(all_5_0) & ! [v0: $i] : ( ~ $i(v0) | ~
% 4.88/1.43 | | | big_p(v0) | big_r(v0))
% 4.88/1.43 | | |
% 4.88/1.43 | | | ALPHA: (28) implies:
% 4.88/1.43 | | | (29) big_q(all_5_0)
% 4.88/1.43 | | |
% 4.88/1.43 | | | GROUND_INST: instantiating (27) with all_5_0, simplifying with (8), (29)
% 4.88/1.43 | | | gives:
% 4.88/1.43 | | | (30) $false
% 4.88/1.43 | | |
% 4.88/1.43 | | | CLOSE: (30) is inconsistent.
% 4.88/1.43 | | |
% 4.88/1.43 | | Case 2:
% 4.88/1.43 | | |
% 4.88/1.43 | | | (31) big_p(all_5_0) & ~ big_r(all_5_0) & ! [v0: $i] : ( ~ $i(v0) | ~
% 4.88/1.43 | | | big_q(v0) | big_s(v0))
% 4.88/1.43 | | |
% 4.88/1.43 | | | ALPHA: (31) implies:
% 4.88/1.43 | | | (32) big_p(all_5_0)
% 4.88/1.43 | | |
% 4.88/1.43 | | | GROUND_INST: instantiating (26) with all_5_0, simplifying with (8), (32)
% 4.88/1.43 | | | gives:
% 4.88/1.43 | | | (33) $false
% 4.88/1.43 | | |
% 4.88/1.43 | | | CLOSE: (33) is inconsistent.
% 4.88/1.43 | | |
% 4.88/1.43 | | End of split
% 4.88/1.43 | |
% 4.88/1.43 | End of split
% 4.88/1.43 |
% 4.88/1.43 End of proof
% 4.88/1.43 % SZS output end Proof for theBenchmark
% 4.88/1.43
% 4.88/1.43 825ms
%------------------------------------------------------------------------------